LMFDB - Embedded newform 50.6.e.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,6,Mod(9,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("50.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.e (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.01919099065$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	50.19
Dual form			50.6.e.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.80423 + 1.23607i) q^{2} +(-14.7520 - 20.3044i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-53.1272 - 17.3924i) q^{5} +(81.2178 + 59.0082i) q^{6} -248.570i q^{7} +(-37.6183 + 51.7771i) q^{8} +(-119.557 + 367.957i) q^{9} +O(q^{10})$	\(q+(-3.80423 + 1.23607i) q^{2} +(-14.7520 - 20.3044i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-53.1272 - 17.3924i) q^{5} +(81.2178 + 59.0082i) q^{6} -248.570i q^{7} +(-37.6183 + 51.7771i) q^{8} +(-119.557 + 367.957i) q^{9} +(223.606 + 0.495932i) q^{10} +(87.4160 + 269.039i) q^{11} +(-381.909 - 124.090i) q^{12} +(88.2041 + 28.6592i) q^{13} +(307.249 + 945.615i) q^{14} +(430.591 + 1335.29i) q^{15} +(79.1084 - 243.470i) q^{16} +(-833.600 + 1147.35i) q^{17} -1547.57i q^{18} +(-1400.55 - 1017.56i) q^{19} +(-851.262 + 274.506i) q^{20} +(-5047.07 + 3666.91i) q^{21} +(-665.100 - 915.432i) q^{22} +(3750.91 - 1218.75i) q^{23} +1606.25 q^{24} +(2520.01 + 1848.03i) q^{25} -370.973 q^{26} +(3434.63 - 1115.98i) q^{27} +(-2337.69 - 3217.55i) q^{28} +(2948.87 - 2142.48i) q^{29} +(-3288.58 - 4547.52i) q^{30} +(1445.18 + 1049.99i) q^{31} +1024.00i q^{32} +(4173.12 - 5743.80i) q^{33} +(1753.00 - 5395.17i) q^{34} +(-4323.23 + 13205.8i) q^{35} +(1912.91 + 5887.32i) q^{36} +(-7398.79 - 2404.01i) q^{37} +(6585.76 + 2139.84i) q^{38} +(-719.280 - 2213.72i) q^{39} +(2899.08 - 2096.50i) q^{40} +(935.981 - 2880.65i) q^{41} +(14667.6 - 20188.3i) q^{42} +6093.41i q^{43} +(3661.73 + 2660.40i) q^{44} +(12751.4 - 17469.2i) q^{45} +(-12762.9 + 9272.77i) q^{46} +(-10927.3 - 15040.1i) q^{47} +(-6110.54 + 1985.44i) q^{48} -44979.9 q^{49} +(-11871.0 - 3915.41i) q^{50} +35593.6 q^{51} +(1411.27 - 458.548i) q^{52} +(-5015.92 - 6903.82i) q^{53} +(-11686.7 + 8490.88i) q^{54} +(35.0728 - 15813.7i) q^{55} +(12870.2 + 9350.76i) q^{56} +43448.3i q^{57} +(-8569.93 + 11795.5i) q^{58} +(-13353.8 + 41098.7i) q^{59} +(18131.5 + 13234.9i) q^{60} +(4190.06 + 12895.7i) q^{61} +(-6795.65 - 2208.04i) q^{62} +(91463.0 + 29718.1i) q^{63} +(-1265.73 - 3895.53i) q^{64} +(-4187.58 - 3056.67i) q^{65} +(-8775.75 + 27009.0i) q^{66} +(-9121.93 + 12555.3i) q^{67} +22691.3i q^{68} +(-80079.6 - 58181.2i) q^{69} +(123.274 - 55581.7i) q^{70} +(-20250.7 + 14713.0i) q^{71} +(-14554.3 - 20032.2i) q^{72} +(-11629.5 + 3778.66i) q^{73} +31118.2 q^{74} +(347.896 - 78429.5i) q^{75} -27698.7 q^{76} +(66874.9 - 21729.0i) q^{77} +(5472.61 + 7532.40i) q^{78} +(48013.6 - 34883.9i) q^{79} +(-8437.36 + 11559.0i) q^{80} +(2732.55 + 1985.32i) q^{81} +12115.6i q^{82} +(-59634.6 + 82080.0i) q^{83} +(-30844.9 + 94931.0i) q^{84} +(64242.1 - 46457.3i) q^{85} +(-7531.87 - 23180.7i) q^{86} +(-87003.8 - 28269.3i) q^{87} +(-17218.5 - 5594.62i) q^{88} +(6194.99 + 19066.2i) q^{89} +(-26916.1 + 82218.3i) q^{90} +(7123.82 - 21924.9i) q^{91} +(37091.1 - 51051.5i) q^{92} -44833.0i q^{93} +(60160.6 + 43709.2i) q^{94} +(56709.3 + 78418.8i) q^{95} +(20791.8 - 15106.1i) q^{96} +(-79997.2 - 110107. i) q^{97} +(171114. - 55598.2i) q^{98} -109446. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9}+O(q^{10}) $ 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9	\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9} + 80 q^{10} + 716 q^{11} - 160 q^{12} - 784 q^{14} - 940 q^{15} - 3072 q^{16} + 1910 q^{17} - 5990 q^{19} - 640 q^{20} - 4344 q^{21} + 4720 q^{22} + 12410 q^{23} + 4608 q^{24} + 23660 q^{25} - 15248 q^{26} + 27600 q^{27} - 3040 q^{28} - 17170 q^{29} - 14720 q^{30} - 18834 q^{31} - 56930 q^{33} + 11696 q^{34} + 28450 q^{35} - 10976 q^{36} + 3540 q^{37} + 13432 q^{39} - 1280 q^{40} + 37146 q^{41} - 43560 q^{42} + 1184 q^{44} + 75240 q^{45} + 28672 q^{46} - 17830 q^{47} - 2560 q^{48} - 54656 q^{49} + 8800 q^{50} - 85984 q^{51} + 22350 q^{53} + 16080 q^{54} - 64730 q^{55} + 12544 q^{56} + 18000 q^{59} + 78720 q^{60} + 67086 q^{61} - 159600 q^{62} + 132820 q^{63} + 49152 q^{64} - 195820 q^{65} - 52256 q^{66} - 90790 q^{67} - 212608 q^{69} + 180080 q^{70} - 122874 q^{71} + 121200 q^{73} + 281456 q^{74} + 672810 q^{75} - 102400 q^{76} + 434040 q^{77} + 170720 q^{78} + 113600 q^{79} - 28160 q^{80} + 115878 q^{81} - 582750 q^{83} - 174816 q^{84} + 107770 q^{85} - 26888 q^{86} - 911580 q^{87} - 56960 q^{88} - 357730 q^{89} - 282920 q^{90} - 216324 q^{91} + 451040 q^{92} + 79136 q^{94} + 135000 q^{95} + 18432 q^{96} - 123520 q^{97} - 206240 q^{98} + 235252 q^{99}+O(q^{100}) \) 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9 + 80 * q^10 + 716 * q^11 - 160 * q^12 - 784 * q^14 - 940 * q^15 - 3072 * q^16 + 1910 * q^17 - 5990 * q^19 - 640 * q^20 - 4344 * q^21 + 4720 * q^22 + 12410 * q^23 + 4608 * q^24 + 23660 * q^25 - 15248 * q^26 + 27600 * q^27 - 3040 * q^28 - 17170 * q^29 - 14720 * q^30 - 18834 * q^31 - 56930 * q^33 + 11696 * q^34 + 28450 * q^35 - 10976 * q^36 + 3540 * q^37 + 13432 * q^39 - 1280 * q^40 + 37146 * q^41 - 43560 * q^42 + 1184 * q^44 + 75240 * q^45 + 28672 * q^46 - 17830 * q^47 - 2560 * q^48 - 54656 * q^49 + 8800 * q^50 - 85984 * q^51 + 22350 * q^53 + 16080 * q^54 - 64730 * q^55 + 12544 * q^56 + 18000 * q^59 + 78720 * q^60 + 67086 * q^61 - 159600 * q^62 + 132820 * q^63 + 49152 * q^64 - 195820 * q^65 - 52256 * q^66 - 90790 * q^67 - 212608 * q^69 + 180080 * q^70 - 122874 * q^71 + 121200 * q^73 + 281456 * q^74 + 672810 * q^75 - 102400 * q^76 + 434040 * q^77 + 170720 * q^78 + 113600 * q^79 - 28160 * q^80 + 115878 * q^81 - 582750 * q^83 - 174816 * q^84 + 107770 * q^85 - 26888 * q^86 - 911580 * q^87 - 56960 * q^88 - 357730 * q^89 - 282920 * q^90 - 216324 * q^91 + 451040 * q^92 + 79136 * q^94 + 135000 * q^95 + 18432 * q^96 - 123520 * q^97 - 206240 * q^98 + 235252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−3.80423	+	1.23607i	−0.672499	+	0.218508i
$2$	−3.80423	+	1.23607i	−0.672499	+	0.218508i
$3$	−14.7520	−	20.3044i	−0.946344	−	1.30253i	−0.953132	−	0.302554i	$-0.902161\pi$
$3$	−14.7520	−	20.3044i	−0.946344	−	1.30253i	0.00678823	−	0.999977i	$-0.497839\pi$
$4$	12.9443	−	9.40456i	0.404508	−	0.293893i
$5$	−53.1272	−	17.3924i	−0.950369	−	0.311126i
$5$	−53.1272	−	17.3924i	−0.950369	−	0.311126i
$6$	81.2178	+	59.0082i	0.921028	+	0.669166i
$7$		−	248.570i		−	1.91736i	−0.284492	−	0.958679i	$-0.591825\pi$
$7$		−	248.570i		−	1.91736i	0.284492	−	0.958679i	$-0.408175\pi$
$8$	−37.6183	+	51.7771i	−0.207813	+	0.286031i
$9$	−119.557	+	367.957i	−0.492003	+	1.51423i
$10$	223.606	+	0.495932i	0.707105	+	0.00156827i
$11$	87.4160	+	269.039i	0.217826	+	0.670399i	0.998941	+	0.0460117i	$0.0146511\pi$
$11$	87.4160	+	269.039i	0.217826	+	0.670399i	−0.781115	+	0.624387i	$0.785349\pi$
$12$	−381.909	−	124.090i	−0.765608	−	0.248761i
$13$	88.2041	+	28.6592i	0.144754	+	0.0470334i	0.380498	−	0.924782i	$-0.375753\pi$
$13$	88.2041	+	28.6592i	0.144754	+	0.0470334i	−0.235744	+	0.971815i	$0.575753\pi$
$14$	307.249	+	945.615i	0.418958	+	1.28942i
$15$	430.591	+	1335.29i	0.494125	+	1.53232i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−833.600	+	1147.35i	−0.699577	+	0.962885i	0.300382	+	0.953819i	$0.402886\pi$
$17$	−833.600	+	1147.35i	−0.699577	+	0.962885i	−0.999959	+	0.00906590i	$0.997114\pi$
$18$		−	1547.57i		−	1.12582i
$19$	−1400.55	−	1017.56i	−0.890048	−	0.646657i	0.0458429	−	0.998949i	$-0.485403\pi$
$19$	−1400.55	−	1017.56i	−0.890048	−	0.646657i	−0.935890	+	0.352291i	$0.885403\pi$
$20$	−851.262	+	274.506i	−0.475870	+	0.153453i
$21$	−5047.07	+	3666.91i	−2.49742	+	1.81448i
$22$	−665.100	−	915.432i	−0.292975	−	0.403245i
$23$	3750.91	−	1218.75i	1.47849	−	0.480389i	0.544826	−	0.838549i	$-0.316596\pi$
$23$	3750.91	−	1218.75i	1.47849	−	0.480389i	0.933660	+	0.358160i	$0.116596\pi$
$24$	1606.25			0.569227
$25$	2520.01	+	1848.03i	0.806402	+	0.591368i
$26$	−370.973			−0.107624
$27$	3434.63	−	1115.98i	0.906716	−	0.294610i
$28$	−2337.69	−	3217.55i	−0.563497	−	0.775587i
$29$	2948.87	−	2142.48i	0.651120	−	0.473066i	−0.212532	−	0.977154i	$-0.568171\pi$
$29$	2948.87	−	2142.48i	0.651120	−	0.473066i	0.863653	+	0.504088i	$0.168171\pi$
$30$	−3288.58	−	4547.52i	−0.667122	−	0.922510i
$31$	1445.18	+	1049.99i	0.270096	+	0.196236i	0.714586	−	0.699548i	$-0.246615\pi$
$31$	1445.18	+	1049.99i	0.270096	+	0.196236i	−0.444490	+	0.895784i	$0.646615\pi$
$32$			1024.00i			0.176777i
$33$	4173.12	−	5743.80i	0.667077	−	0.918152i
$34$	1753.00	−	5395.17i	0.260066	−	0.800402i
$35$	−4323.23	+	13205.8i	−0.596539	+	1.82220i
$36$	1912.91	+	5887.32i	0.246001	+	0.757114i
$37$	−7398.79	−	2404.01i	−0.888498	−	0.288690i	−0.171017	−	0.985268i	$-0.554705\pi$
$37$	−7398.79	−	2404.01i	−0.888498	−	0.288690i	−0.717481	+	0.696578i	$0.754705\pi$
$38$	6585.76	+	2139.84i	0.739855	+	0.240394i
$39$	−719.280	−	2213.72i	−0.0757246	−	0.233056i
$40$	2899.08	−	2096.50i	0.286491	−	0.207179i
$41$	935.981	−	2880.65i	0.0869576	−	0.267628i	−0.898117	−	0.439757i	$-0.855065\pi$
$41$	935.981	−	2880.65i	0.0869576	−	0.267628i	0.985074	+	0.172129i	$0.0550646\pi$
$42$	14667.6	−	20188.3i	1.28303	−	1.76594i
$43$			6093.41i			0.502561i	0.967914	+	0.251281i	$0.0808517\pi$
$43$			6093.41i			0.502561i	−0.967914	+	0.251281i	$0.919148\pi$
$44$	3661.73	+	2660.40i	0.285138	+	0.207165i
$45$	12751.4	−	17469.2i	0.938699	−	1.28600i
$46$	−12762.9	+	9272.77i	−0.889311	+	0.646122i
$47$	−10927.3	−	15040.1i	−0.721553	−	0.993133i	−0.999471	−	0.0325279i	$-0.989644\pi$
$47$	−10927.3	−	15040.1i	−0.721553	−	0.993133i	0.277918	−	0.960605i	$-0.410356\pi$
$48$	−6110.54	+	1985.44i	−0.382804	+	0.124381i
$49$	−44979.9			−2.67626
$50$	−11871.0	−	3915.41i	−0.671523	−	0.221489i
$51$	35593.6			1.91623
$52$	1411.27	−	458.548i	0.0723770	−	0.0235167i
$53$	−5015.92	−	6903.82i	−0.245279	−	0.337598i	0.668572	−	0.743648i	$-0.266906\pi$
$53$	−5015.92	−	6903.82i	−0.245279	−	0.337598i	−0.913851	+	0.406050i	$0.866906\pi$
$54$	−11686.7	+	8490.88i	−0.545390	+	0.396249i
$55$	35.0728	−	15813.7i	0.00156338	−	0.704897i
$56$	12870.2	+	9350.76i	0.548423	+	0.398453i
$57$			43448.3i			1.77127i
$58$	−8569.93	+	11795.5i	−0.334509	+	0.460411i
$59$	−13353.8	+	41098.7i	−0.499429	+	1.53708i	0.310510	+	0.950570i	$0.399500\pi$
$59$	−13353.8	+	41098.7i	−0.499429	+	1.53708i	−0.809939	+	0.586514i	$0.800500\pi$
$60$	18131.5	+	13234.9i	0.650214	+	0.474615i
$61$	4190.06	+	12895.7i	0.144177	+	0.443731i	0.996904	−	0.0786252i	$-0.0250530\pi$
$61$	4190.06	+	12895.7i	0.144177	+	0.443731i	−0.852727	+	0.522356i	$0.825053\pi$
$62$	−6795.65	−	2208.04i	−0.224518	−	0.0729504i
$63$	91463.0	+	29718.1i	2.90332	+	0.943345i
$64$	−1265.73	−	3895.53i	−0.0386271	−	0.118882i
$65$	−4187.58	−	3056.67i	−0.122936	−	0.0897357i
$66$	−8775.75	+	27009.0i	−0.247984	+	0.763218i
$67$	−9121.93	+	12555.3i	−0.248256	+	0.341695i	−0.914900	−	0.403682i	$-0.867730\pi$
$67$	−9121.93	+	12555.3i	−0.248256	+	0.341695i	0.666644	+	0.745377i	$0.267730\pi$
$68$			22691.3i			0.595096i
$69$	−80079.6	−	58181.2i	−2.02488	−	1.47116i
$70$	123.274	−	55581.7i	0.00300694	−	1.35577i
$71$	−20250.7	+	14713.0i	−0.476754	+	0.346382i	−0.800068	−	0.599910i	$-0.795203\pi$
$71$	−20250.7	+	14713.0i	−0.476754	+	0.346382i	0.323313	+	0.946292i	$0.395203\pi$
$72$	−14554.3	−	20032.2i	−0.330871	−	0.455405i
$73$	−11629.5	+	3778.66i	−0.255420	+	0.0829909i	−0.433928	−	0.900948i	$-0.642873\pi$
$73$	−11629.5	+	3778.66i	−0.255420	+	0.0829909i	0.178508	+	0.983938i	$0.442873\pi$
$74$	31118.2			0.660595
$75$	347.896	−	78429.5i	0.00714162	−	1.61000i
$76$	−27698.7			−0.550080
$77$	66874.9	−	21729.0i	1.28539	−	0.417650i
$78$	5472.61	+	7532.40i	0.101849	+	0.140184i
$79$	48013.6	−	34883.9i	0.865559	−	0.628865i	−0.0638327	−	0.997961i	$-0.520332\pi$
$79$	48013.6	−	34883.9i	0.865559	−	0.628865i	0.929392	+	0.369095i	$0.120332\pi$
$80$	−8437.36	+	11559.0i	−0.147395	+	0.201928i
$81$	2732.55	+	1985.32i	0.0462761	+	0.0336215i
$82$			12115.6i			0.198980i
$83$	−59634.6	+	82080.0i	−0.950174	+	1.30780i	0.00127564	+	0.999999i	$0.499594\pi$
$83$	−59634.6	+	82080.0i	−0.950174	+	1.30780i	−0.951450	+	0.307804i	$0.900406\pi$
$84$	−30844.9	+	94931.0i	−0.476964	+	1.46794i
$85$	64242.1	−	46457.3i	0.964434	−	0.697440i
$86$	−7531.87	−	23180.7i	−0.109814	−	0.337972i
$87$	−87003.8	−	28269.3i	−1.23237	−	0.400420i
$88$	−17218.5	−	5594.62i	−0.237022	−	0.0770130i
$89$	6194.99	+	19066.2i	0.0829021	+	0.255146i	0.983912	−	0.178651i	$-0.0571733\pi$
$89$	6194.99	+	19066.2i	0.0829021	+	0.255146i	−0.901010	+	0.433797i	$0.857173\pi$
$90$	−26916.1	+	82218.3i	−0.350272	+	1.06995i
$91$	7123.82	−	21924.9i	0.0901798	−	0.277545i
$92$	37091.1	−	51051.5i	0.456877	−	0.628838i
$93$		−	44833.0i		−	0.537515i
$94$	60160.6	+	43709.2i	0.702251	+	0.510215i
$95$	56709.3	+	78418.8i	0.644682	+	0.891480i
$96$	20791.8	−	15106.1i	0.230257	−	0.167292i
$97$	−79997.2	−	110107.i	−0.863267	−	1.18819i	−0.980781	−	0.195114i	$-0.937492\pi$
$97$	−79997.2	−	110107.i	−0.863267	−	1.18819i	0.117513	−	0.993071i	$-0.462508\pi$
$98$	171114.	−	55598.2i	1.79978	−	0.584784i
$99$	−109446.			−1.12231
$100$	49999.5	+	221.787i	0.499995	+	0.00221787i
$101$	−113713.			−1.10920			−0.554598	−	0.832118i	$-0.687128\pi$
$101$	−113713.			−1.10920			−0.554598	+	0.832118i	$0.687128\pi$
$102$	−135406.	+	43996.2i	−1.28866	+	0.418711i
$103$	−34436.6	−	47398.0i	−0.319836	−	0.440217i	0.618581	−	0.785721i	$-0.287708\pi$
$103$	−34436.6	−	47398.0i	−0.319836	−	0.440217i	−0.938417	+	0.345504i	$0.887708\pi$
$104$	−4801.98	+	3488.84i	−0.0435348	+	0.0316299i
$105$	331913.	−	107032.i	2.93800	−	0.947415i
$106$	27615.3	+	20063.7i	0.238718	+	0.173439i
$107$		−	132165.i		−	1.11598i	−0.829848	−	0.557989i	$-0.811573\pi$
$107$		−	132165.i		−	1.11598i	0.829848	−	0.557989i	$-0.188427\pi$
$108$	33963.5	−	46746.8i	0.280191	−	0.385649i
$109$	−16808.0	+	51729.7i	−0.135503	+	0.417036i	−0.995668	−	0.0929804i	$-0.970361\pi$
$109$	−16808.0	+	51729.7i	−0.135503	+	0.417036i	0.860165	+	0.510016i	$0.170361\pi$
$110$	19413.3	+	60202.1i	0.152974	+	0.474384i
$111$	60335.1	+	185692.i	0.464796	+	1.43050i
$112$	−60519.4	−	19663.9i	−0.455879	−	0.148124i
$113$	133590.	+	43406.1i	0.984188	+	0.319782i	0.756530	−	0.653959i	$-0.226893\pi$
$113$	133590.	+	43406.1i	0.984188	+	0.319782i	0.227658	+	0.973741i	$0.426893\pi$
$114$	−53705.1	−	165287.i	−0.387038	−	1.19118i
$115$	−220473.	−	488.982i	−1.55457	−	0.00344785i
$116$	18021.9	−	55465.7i	0.124353	−	0.382719i
$117$	−21090.8	+	29028.9i	−0.142439	+	0.196050i
$118$		−	172855.i		−	1.14282i
$119$	285197.	+	207208.i	1.84619	+	1.34134i
$120$	−85335.7	−	27936.6i	−0.540975	−	0.177101i
$121$	65552.7	−	47626.8i	0.407031	−	0.295725i
$122$	−31879.9	−	43878.9i	−0.193918	−	0.266905i
$123$	−72297.7	+	23491.0i	−0.430885	+	0.140003i
$124$	28581.5			0.166928
$125$	−101739.	−	142010.i	−0.582389	−	0.812910i
$126$	−384680.			−2.15860
$127$	−124806.	+	40552.1i	−0.686637	+	0.223102i	−0.631499	−	0.775377i	$-0.717560\pi$
$127$	−124806.	+	40552.1i	−0.686637	+	0.223102i	−0.0551385	+	0.998479i	$0.517560\pi$
$128$	9630.27	+	13254.9i	0.0519534	+	0.0715077i
$129$	123723.	−	89890.2i	0.654602	−	0.475596i
$130$	19708.8	+	6452.13i	0.102282	+	0.0334846i
$131$	210091.	+	152640.i	1.06962	+	0.777125i	0.975844	−	0.218468i	$-0.0701059\pi$
$131$	210091.	+	152640.i	1.06962	+	0.777125i	0.0937771	+	0.995593i	$0.470106\pi$
$132$		−	113596.i		−	0.567449i
$133$	−252933.	+	348133.i	−1.23987	+	1.70654i
$134$	19182.7	−	59038.4i	0.0922887	−	0.284035i
$135$	−201882.	−	447.751i	−0.953375	−	0.00211447i
$136$	−28048.0	−	86322.8i	−0.130033	−	0.400201i
$137$	58679.3	+	19066.1i	0.267106	+	0.0867880i	0.439508	−	0.898239i	$-0.355153\pi$
$137$	58679.3	+	19066.1i	0.267106	+	0.0867880i	−0.172402	+	0.985027i	$0.555153\pi$
$138$	376557.	+	122351.i	1.68319	+	0.546901i
$139$	−100713.	−	309962.i	−0.442128	−	1.36073i	−0.885603	−	0.464442i	$-0.846255\pi$
$139$	−100713.	−	309962.i	−0.442128	−	1.36073i	0.443476	−	0.896286i	$-0.353745\pi$
$140$	68233.8	+	211598.i	0.294225	+	0.912412i
$141$	−144182.	+	443746.i	−0.610749	+	1.87969i
$142$	58852.0	−	81002.9i	0.244929	−	0.337116i
$143$			26235.6i			0.107288i
$144$	80128.8	+	58217.0i	0.322020	+	0.233961i
$145$	−193928.	+	62536.0i	−0.765987	+	0.247008i
$146$	39570.6	−	28749.7i	0.153635	−	0.111622i
$147$	663545.	+	913291.i	2.53266	+	3.48591i
$148$	−118381.	+	38464.2i	−0.444249	+	0.144345i
$149$	−254419.			−0.938823			−0.469411	−	0.882980i	$-0.655534\pi$
$149$	−254419.			−0.938823			−0.469411	+	0.882980i	$0.655534\pi$
$150$	95620.7	+	298793.i	0.346995	+	1.08428i
$151$	408763.			1.45891			0.729455	−	0.684028i	$-0.239774\pi$
$151$	408763.			1.45891			0.729455	+	0.684028i	$0.239774\pi$
$152$	105372.	−	34237.5i	0.369928	−	0.120197i
$153$	−322514.	−	443903.i	−1.11383	−	1.53306i
$154$	−227549.	+	165324.i	−0.773165	+	0.561738i
$155$	−58516.6	−	80918.1i	−0.195637	−	0.270530i
$156$	−30129.6	−	21890.4i	−0.0991247	−	0.0720183i
$157$		−	26353.3i		−	0.0853269i	−0.999090	−	0.0426635i	$-0.986416\pi$
$157$		−	26353.3i		−	0.0853269i	0.999090	−	0.0426635i	$-0.0135843\pi$
$158$	−139536.	+	192054.i	−0.444675	+	0.612043i
$159$	−66183.2	+	203691.i	−0.207613	+	0.638968i
$160$	17809.9	−	54402.3i	0.0549997	−	0.168003i
$161$	−302943.	−	932363.i	−0.921078	−	2.83479i
$162$	−12849.2	−	4174.97i	−0.0384672	−	0.0124987i
$163$	−109653.	−	35628.5i	−0.323261	−	0.105034i	0.142891	−	0.989738i	$-0.454360\pi$
$163$	−109653.	−	35628.5i	−0.323261	−	0.105034i	−0.466152	+	0.884705i	$0.654360\pi$
$164$	−14975.7	−	46090.5i	−0.0434788	−	0.133814i
$165$	−321605.	+	232572.i	−0.919630	+	0.665039i
$166$	125407.	−	385963.i	0.353225	−	1.08712i
$167$	−183788.	+	252962.i	−0.509947	+	0.701882i	−0.983910	−	0.178663i	$-0.942823\pi$
$167$	−183788.	+	252962.i	−0.509947	+	0.701882i	0.473964	+	0.880544i	$0.342823\pi$
$168$		−	399265.i		−	1.09141i
$169$	−293424.	−	213185.i	−0.790275	−	0.574169i
$170$	−186967.	+	256142.i	−0.496184	+	0.679764i
$171$	541862.	−	393686.i	1.41709	−	1.02958i
$172$	57305.8	+	78874.7i	0.147699	+	0.203290i
$173$	−403731.	+	131180.i	−1.02560	+	0.333237i	−0.773049	−	0.634347i	$-0.781269\pi$
$173$	−403731.	+	131180.i	−1.02560	+	0.333237i	−0.252550	+	0.967584i	$0.581269\pi$
$174$	365925.			0.916260
$175$	459363.	−	626397.i	1.13386	−	1.54616i
$176$	72418.3			0.176225
$177$	1.03148e6	−	335148.i	2.47473	−	0.804089i
$178$	−47134.3	−	64874.8i	−0.111503	−	0.153471i
$179$	−2841.46	+	2064.44i	−0.00662841	+	0.00481582i	−0.591095	−	0.806602i	$-0.701304\pi$
$179$	−2841.46	+	2064.44i	−0.00662841	+	0.00481582i	0.584466	+	0.811418i	$0.301304\pi$
$180$	767.491	−	346047.i	0.00176560	−	0.796075i
$181$	122391.	+	88922.3i	0.277686	+	0.201750i	0.717907	−	0.696139i	$-0.245100\pi$
$181$	122391.	+	88922.3i	0.277686	+	0.201750i	−0.440222	+	0.897889i	$0.645100\pi$
$182$			92212.6i			0.206354i
$183$	200028.	−	275315.i	0.441533	−	0.607718i
$184$	−77999.7	+	240058.i	−0.169843	+	0.522724i
$185$	351266.	+	256402.i	0.754582	+	0.550797i
$186$	55416.7	+	170555.i	0.117451	+	0.361478i
$187$	−381552.	−	123974.i	−0.797902	−	0.259254i
$188$	−282892.	−	91917.2i	−0.583749	−	0.189671i
$189$	−277399.	−	853746.i	−0.564872	−	1.73850i
$190$	−312666.	−	228226.i	−0.628343	−	0.458651i
$191$	−27631.9	+	85042.4i	−0.0548060	+	0.168675i	−0.974713	−	0.223462i	$-0.928264\pi$
$191$	−27631.9	+	85042.4i	−0.0548060	+	0.168675i	0.919907	+	0.392137i	$0.128264\pi$
$192$	−60424.4	+	83167.0i	−0.118293	+	0.162816i
$193$			657779.i			1.27112i	0.772051	+	0.635560i	$0.219231\pi$
$193$			657779.i			1.27112i	−0.772051	+	0.635560i	$0.780769\pi$
$194$	440427.	+	319989.i	0.840174	+	0.610422i
$195$	−288.588	+	130119.i	−0.000543490	+	0.245049i
$196$	−582232.	+	423016.i	−1.08257	+	0.786532i
$197$	−103741.	−	142788.i	−0.190452	−	0.262135i	0.703103	−	0.711088i	$-0.251797\pi$
$197$	−103741.	−	142788.i	−0.190452	−	0.262135i	−0.893556	+	0.448953i	$0.851797\pi$
$198$	416357.	−	135283.i	0.754750	−	0.245233i
$199$	660873.			1.18300			0.591501	−	0.806305i	$-0.298536\pi$
$199$	660873.			1.18300			0.591501	+	0.806305i	$0.298536\pi$
$200$	−190484.	+	60959.1i	−0.336731	+	0.107761i
$201$	389495.			0.680004
$202$	432592.	−	140558.i	0.745933	−	0.242368i
$203$	−532556.	−	733000.i	−0.907037	−	1.24843i
$204$	460734.	−	334743.i	0.775130	−	0.563165i
$205$	−99827.7	+	136762.i	−0.165908	+	0.227291i
$206$	189592.	+	137747.i	0.311280	+	0.226158i
$207$			1.52589e6i			2.47512i
$208$	13955.4	−	19207.9i	0.0223657	−	0.0307838i
$209$	151332.	−	465752.i	0.239643	−	0.737545i
$210$	−1.13037e6	+	817441.i	−1.76878	+	1.27911i
$211$	−194768.	−	599434.i	−0.301170	−	0.926905i	−0.981079	−	0.193609i	$-0.937981\pi$
$211$	−194768.	−	599434.i	−0.301170	−	0.926905i	0.679909	−	0.733297i	$-0.262019\pi$
$212$	−129855.	−	42192.4i	−0.198435	−	0.0644755i
$213$	597479.	+	194133.i	0.902347	+	0.293190i
$214$	163365.	+	502784.i	0.243850	+	0.750494i
$215$	105979.	−	323726.i	0.156360	−	0.477619i
$216$	−71422.7	+	219817.i	−0.104160	+	0.320572i
$217$	260995.	−	359228.i	0.376255	−	0.517870i
$218$		−	217567.i		−	0.310064i
$219$	248283.	+	180388.i	0.349813	+	0.254154i
$220$	−148267.	−	205026.i	−0.206532	−	0.285596i
$221$	−106409.	+	77310.8i	−0.146554	+	0.106478i
$222$	−459057.	−	631838.i	−0.625150	−	0.860445i
$223$	86631.2	−	28148.2i	0.116657	−	0.0379043i	−0.250107	−	0.968218i	$-0.580466\pi$
$223$	86631.2	−	28148.2i	0.116657	−	0.0379043i	0.366764	+	0.930314i	$0.380466\pi$
$224$	254535.			0.338944
$225$	−981278.	+	706311.i	−1.29222	+	0.930122i
$226$	−561860.			−0.731740
$227$	−770204.	+	250254.i	−0.992067	+	0.322342i	−0.759691	−	0.650284i	$-0.774650\pi$
$227$	−770204.	+	250254.i	−0.992067	+	0.322342i	−0.232376	+	0.972626i	$0.574650\pi$
$228$	408613.	+	562407.i	0.520565	+	0.716496i
$229$	−586482.	+	426104.i	−0.739037	+	0.536942i	−0.892409	−	0.451227i	$-0.850987\pi$
$229$	−586482.	+	426104.i	−0.739037	+	0.536942i	0.153372	+	0.988168i	$0.450987\pi$
$230$	839332.	−	270659.i	1.04620	−	0.337367i
$231$	−1.42774e6	−	1.03731e6i	−1.76043	−	1.27902i
$232$			233281.i			0.284550i
$233$	−235099.	+	323585.i	−0.283701	+	0.390480i	−0.926955	−	0.375172i	$-0.877584\pi$
$233$	−235099.	+	323585.i	−0.283701	+	0.390480i	0.643255	+	0.765652i	$0.277584\pi$
$234$	44352.3	−	136502.i	0.0529513	−	0.162967i
$235$	318953.	+	989094.i	0.376753	+	1.16834i
$236$	213660.	+	657578.i	0.249714	+	0.768542i
$237$	−1.41660e6	−	460281.i	−1.63823	−	0.532294i
$238$	−1.34108e6	−	435742.i	−1.53466	−	0.498640i
$239$	−39034.9	−	120137.i	−0.0442037	−	0.136045i	0.926519	−	0.376248i	$-0.122786\pi$
$239$	−39034.9	−	120137.i	−0.0442037	−	0.136045i	−0.970723	+	0.240203i	$0.922786\pi$
$240$	359168.	+	796.591i	0.402503	+	0.000892704i
$241$	18494.7	−	56920.7i	0.0205118	−	0.0631288i	−0.940277	−	0.340411i	$-0.889434\pi$
$241$	18494.7	−	56920.7i	0.0205118	−	0.0631288i	0.960788	+	0.277282i	$0.0894337\pi$
$242$	−190507.	+	262211.i	−0.209109	+	0.287814i
$243$		−	962338.i		−	1.04547i
$244$	175516.	+	127520.i	0.188730	+	0.137121i
$245$	2.38966e6	+	782310.i	2.54343	+	0.832652i
$246$	246000.	−	178730.i	0.259178	−	0.188304i
$247$	−94371.4	−	129891.i	−0.0984234	−	0.135468i
$248$	−108730.	+	35328.6i	−0.112259	+	0.0364752i
$249$	2.54632e6			2.60265
$250$	562572.	+	414480.i	0.569283	+	0.419424i
$251$	−126865.			−0.127104			−0.0635518	−	0.997979i	$-0.520243\pi$
$251$	−126865.			−0.127104			−0.0635518	+	0.997979i	$0.520243\pi$
$252$	1.46341e6	−	475490.i	1.45166	−	0.471672i
$253$	655779.	+	902603.i	0.644105	+	0.886534i
$254$	424667.	−	308538.i	0.413013	−	0.300072i
$255$	−1.89099e6	−	619061.i	−1.82112	−	0.596187i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$			572838.i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$257$			572838.i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$258$	−359561.	+	494893.i	−0.336297	+	0.462873i
$259$	−597565.	+	1.83911e6i	−0.553523	+	1.70357i
$260$	−82951.9	−	183.977i	−0.0761014	−	0.000168784i
$261$	435785.	+	1.34121e6i	0.395978	+	1.21869i
$262$	−987909.	−	320991.i	−0.889127	−	0.288895i
$263$	−908507.	−	295192.i	−0.809914	−	0.263157i	−0.125353	−	0.992112i	$-0.540006\pi$
$263$	−908507.	−	295192.i	−0.809914	−	0.263157i	−0.684561	+	0.728955i	$0.740006\pi$
$264$	140412.	+	432144.i	0.123992	+	0.381609i
$265$	146408.	+	454020.i	0.128070	+	0.397155i
$266$	531900.	−	1.63702e6i	0.460920	−	1.41857i
$267$	295740.	−	407051.i	0.253882	−	0.349439i
$268$			248306.i			0.211179i
$269$	−1.24886e6	−	907351.i	−1.05229	−	0.764530i	−0.0796398	−	0.996824i	$-0.525377\pi$
$269$	−1.24886e6	−	907351.i	−1.05229	−	0.764530i	−0.972646	+	0.232293i	$0.925377\pi$
$270$	768559.	−	247837.i	0.641605	−	0.206898i
$271$	1.61785e6	−	1.17544e6i	1.33818	−	0.972248i	0.338675	−	0.940903i	$-0.390021\pi$
$271$	1.61785e6	−	1.17544e6i	1.33818	−	0.972248i	0.999509	−	0.0313444i	$-0.00997885\pi$
$272$	213402.	+	293722.i	0.174894	+	0.240721i
$273$	−550263.	+	178791.i	−0.446852	+	0.145191i
$274$	−246796.			−0.198592
$275$	−276902.	+	839526.i	−0.220797	+	0.669426i
$276$	−1.58374e6			−1.25144
$277$	420232.	−	136542.i	0.329071	−	0.106922i	−0.139822	−	0.990177i	$-0.544653\pi$
$277$	420232.	−	136542.i	0.329071	−	0.106922i	0.468893	+	0.883255i	$0.344653\pi$
$278$	766268.	+	1.05468e6i	0.594660	+	0.818480i
$279$	−559131.	+	406232.i	−0.430034	+	0.312438i
$280$	−521126.	−	720624.i	−0.397235	−	0.549305i
$281$	149999.	+	108981.i	0.113324	+	0.0823349i	0.643004	−	0.765863i	$-0.277688\pi$
$281$	149999.	+	108981.i	0.113324	+	0.0823349i	−0.529680	+	0.848198i	$0.677688\pi$
$282$		−	1.86633e6i		−	1.39754i
$283$	1.12999e6	−	1.55530e6i	0.838707	−	1.15438i	−0.147532	−	0.989057i	$-0.547133\pi$
$283$	1.12999e6	−	1.55530e6i	0.838707	−	1.15438i	0.986239	−	0.165324i	$-0.0528669\pi$
$284$	−123761.	+	380898.i	−0.0910520	+	0.280229i
$285$	755673.	−	2.30829e6i	0.551089	−	1.68336i
$286$	−32429.0	−	99806.1i	−0.0234433	−	0.0721510i
$287$	−716043.	−	232657.i	−0.513138	−	0.166729i
$288$	−376788.	−	122426.i	−0.267680	−	0.0869746i
$289$	−182768.	−	562501.i	−0.128723	−	0.396167i
$290$	660449.	−	477610.i	0.461152	−	0.333487i
$291$	−1.05553e6	+	3.24860e6i	−0.730700	+	2.24886i
$292$	−114999.	+	158282.i	−0.0789290	+	0.108636i
$293$			1.40925e6i			0.959001i	0.877542	+	0.479500i	$0.159182\pi$
$293$			1.40925e6i			0.959001i	−0.877542	+	0.479500i	$0.840818\pi$
$294$	−3.65317e6	−	2.65418e6i	−2.46491	−	1.79086i
$295$	1.42425e6	−	1.95120e6i	0.952868	−	1.30541i
$296$	402802.	−	292653.i	0.267216	−	0.194144i
$297$	600484.	+	826495.i	0.395012	+	0.543687i
$298$	967867.	−	314479.i	0.631357	−	0.205140i
$299$	365774.			0.236611
$300$	−733092.	−	1.01848e6i	−0.470279	−	0.653358i
$301$	1.51464e6			0.963590
$302$	−1.55503e6	+	505258.i	−0.981115	+	0.318784i
$303$	1.67751e6	+	2.30889e6i	1.04968	+	1.44476i
$304$	−358540.	+	260494.i	−0.222512	+	0.161664i
$305$	1681.13	−	757988.i	0.00103479	−	0.466566i
$306$	1.77561e6	+	1.29006e6i	1.08404	+	0.787599i
$307$		−	1.72286e6i		−	1.04329i	−0.853163	−	0.521645i	$-0.825319\pi$
$307$		−	1.72286e6i		−	1.04329i	0.853163	−	0.521645i	$-0.174681\pi$
$308$	661295.	−	910195.i	0.397208	−	0.546711i
$309$	−454379.	+	1.39843e6i	−0.270721	+	0.833193i
$310$	322631.	+	235500.i	0.190678	+	0.139183i
$311$	−297608.	−	915944.i	−0.174479	−	0.536992i	0.825130	−	0.564943i	$-0.191102\pi$
$311$	−297608.	−	915944.i	−0.174479	−	0.536992i	−0.999609	+	0.0279508i	$0.991102\pi$
$312$	141678.	+	46033.9i	0.0823978	+	0.0267727i
$313$	−822127.	−	267125.i	−0.474327	−	0.154118i	0.0620911	−	0.998070i	$-0.480223\pi$
$313$	−822127.	−	267125.i	−0.474327	−	0.154118i	−0.536418	+	0.843952i	$0.680223\pi$
$314$	32574.5	+	100254.i	0.0186446	+	0.0573822i
$315$	−4.34231e6	−	3.16961e6i	−2.46572	−	1.79982i
$316$	293433.	−	903094.i	0.165307	−	0.508763i
$317$	259896.	−	357716.i	0.145262	−	0.199936i	−0.730186	−	0.683249i	$-0.760567\pi$
$317$	259896.	−	357716.i	0.145262	−	0.199936i	0.875448	+	0.483313i	$0.160567\pi$
$318$		−	856694.i		−	0.475070i
$319$	834189.	+	606074.i	0.458974	+	0.333464i
$320$	−507.834	+	228973.i	−0.000277234	+	0.125000i
$321$	−2.68353e6	+	1.94970e6i	−1.45360	+	1.05610i
$322$	2.30493e6	+	3.17246e6i	1.23885	+	1.70513i
$323$	2.33499e6	−	758684.i	1.24531	−	0.404627i
$324$	54042.0			0.0286002
$325$	169312.	+	235225.i	0.0889158	+	0.123531i
$326$	461185.			0.240343
$327$	1.29829e6	−	421841.i	0.671435	−	0.218162i
$328$	113942.	+	156828.i	0.0584789	+	0.0804892i
$329$	−3.73852e6	+	2.71620e6i	−1.90419	+	1.38348i
$330$	935984.	−	1.28228e6i	0.473133	−	0.648184i
$331$	−580905.	−	422052.i	−0.291431	−	0.211737i	0.432457	−	0.901654i	$-0.357647\pi$
$331$	−580905.	−	422052.i	−0.291431	−	0.211737i	−0.723888	+	0.689918i	$0.757647\pi$
$332$			1.62330e6i			0.808267i
$333$	1.76915e6	−	2.43502e6i	0.874286	−	1.20335i
$334$	386491.	−	1.18950e6i	0.189572	−	0.583442i
$335$	702989.	−	508373.i	0.342245	−	0.247497i
$336$	493519.	+	1.51890e6i	0.238482	+	0.733972i
$337$	2.76683e6	+	898998.i	1.32711	+	0.431205i	0.884932	−	0.465720i	$-0.154205\pi$
$337$	2.76683e6	+	898998.i	1.32711	+	0.431205i	0.442182	+	0.896926i	$0.354205\pi$
$338$	1.37976e6	+	448312.i	0.656920	+	0.213446i
$339$	−1.08939e6	−	3.35280e6i	−0.514855	−	1.58456i
$340$	394657.	−	1.20552e6i	0.185149	−	0.565560i
$341$	−156155.	+	480595.i	−0.0727226	+	0.223817i
$342$	−1.57474e6	+	2.16745e6i	−0.728022	+	1.00204i
$343$			7.00292e6i			3.21399i
$344$	−315499.	−	229223.i	−0.143748	−	0.104439i
$345$	3.24249e6	+	4.48379e6i	1.46667	+	2.02814i
$346$	1.37374e6	−	998079.i	0.616898	−	0.448203i
$347$	−2.21980e6	−	3.05529e6i	−0.989669	−	1.36216i	−0.931454	−	0.363859i	$-0.881459\pi$
$347$	−2.21980e6	−	3.05529e6i	−0.989669	−	1.36216i	−0.0582155	−	0.998304i	$-0.518541\pi$
$348$	−1.39206e6	+	452308.i	−0.616184	+	0.200210i
$349$	−434817.			−0.191092			−0.0955460	−	0.995425i	$-0.530460\pi$
$349$	−434817.			−0.191092			−0.0955460	+	0.995425i	$0.530460\pi$
$350$	−973251.	+	2.95076e6i	−0.424673	+	1.28755i
$351$	334932.			0.145107
$352$	−275496.	+	89514.0i	−0.118511	+	0.0385065i
$353$	−1.86648e6	−	2.56899e6i	−0.797236	−	1.09730i	−0.993169	−	0.116684i	$-0.962773\pi$
$353$	−1.86648e6	−	2.56899e6i	−0.797236	−	1.09730i	0.195933	−	0.980617i	$-0.437227\pi$
$354$	−3.50972e6	+	2.54996e6i	−1.48855	+	1.08150i
$355$	1.33176e6	−	429452.i	0.560861	−	0.180860i
$356$	259499.	+	188537.i	0.108520	+	0.0788446i
$357$		−	8.84750e6i		−	3.67409i
$358$	8257.77	−	11365.8i	0.00340530	−	0.00468699i
$359$	503376.	−	1.54923e6i	0.206137	−	0.634425i	−0.793528	−	0.608534i	$-0.791758\pi$
$359$	503376.	−	1.54923e6i	0.206137	−	0.634425i	0.999665	−	0.0258905i	$-0.00824211\pi$
$360$	424818.	+	1.31739e6i	0.172761	+	0.535745i
$361$	160951.	+	495356.i	0.0650018	+	0.200055i
$362$	−575517.	−	186997.i	−0.230827	−	0.0750003i
$363$	−1.93407e6	−	628418.i	−0.770382	−	0.250312i
$364$	−113981.	−	350798.i	−0.0450899	−	0.138772i
$365$	683564.	+	1516.06i	0.268563	+	0.000595642i
$366$	−420643.	+	1.29461e6i	−0.164139	+	0.505168i
$367$	−1.46510e6	+	2.01654e6i	−0.567810	+	0.781523i	−0.992293	−	0.123913i	$-0.960456\pi$
$367$	−1.46510e6	+	2.01654e6i	−0.567810	+	0.781523i	0.424483	+	0.905436i	$0.360456\pi$
$368$		−	1.00965e6i		−	0.388643i
$369$	948055.	+	688803.i	0.362466	+	0.263347i
$370$	−1.65322e6	−	541222.i	−0.627809	−	0.205528i
$371$	−1.71608e6	+	1.24681e6i	−0.647296	+	0.470288i
$372$	−421635.	−	580331.i	−0.157972	−	0.217429i
$373$	−3.02937e6	+	984303.i	−1.12741	+	0.366317i	−0.812590	−	0.582836i	$-0.801943\pi$
$373$	−3.02937e6	+	984303.i	−1.12741	+	0.366317i	−0.314817	+	0.949153i	$0.601943\pi$
$374$	1.60475e6			0.593237
$375$	−1.38256e6	+	4.16069e6i	−0.507700	+	1.52787i
$376$	1.18980e6			0.434015
$377$	321505.	−	104463.i	0.116502	−	0.0378538i
$378$	2.11058e6	+	2.90496e6i	0.759751	+	1.04571i
$379$	1.32769e6	−	964625.i	0.474788	−	0.344954i	−0.324516	−	0.945880i	$-0.605202\pi$
$379$	1.32769e6	−	964625.i	0.474788	−	0.344954i	0.799304	+	0.600927i	$0.205202\pi$
$380$	1.47156e6	+	481748.i	0.522779	+	0.171144i
$381$	2.66454e6	+	1.93590e6i	0.940393	+	0.683235i
$382$		−	357675.i		−	0.125410i
$383$	2.56247e6	−	3.52693e6i	0.892610	−	1.22857i	−0.0801564	−	0.996782i	$-0.525542\pi$
$383$	2.56247e6	−	3.52693e6i	0.892610	−	1.22857i	0.972766	−	0.231789i	$-0.0744580\pi$
$384$	127068.	−	391075.i	0.0439752	−	0.135342i
$385$	−3.93080e6	−	8718.04i	−1.35154	−	0.00299755i
$386$	−813059.	−	2.50234e6i	−0.277750	−	0.854827i
$387$	−2.24211e6	−	728507.i	−0.760993	−	0.247261i
$388$	−2.07101e6	−	672912.i	−0.698398	−	0.226923i
$389$	686955.	+	2.11423e6i	0.230173	+	0.708399i	0.997725	+	0.0674128i	$0.0214744\pi$
$389$	686955.	+	2.11423e6i	0.230173	+	0.708399i	−0.767552	+	0.640986i	$0.778526\pi$
$390$	−159738.	−	495358.i	−0.0531797	−	0.164914i
$391$	−1.72843e6	+	5.31956e6i	−0.571755	+	1.75968i
$392$	1.69206e6	−	2.32893e6i	0.556162	−	0.765492i
$393$		−	6.51755e6i		−	2.12864i
$394$	571151.	+	414966.i	0.185358	+	0.134670i
$395$	−3.15755e6	+	1.01821e6i	−1.01826	+	0.328357i
$396$	−1.41670e6	+	1.02929e6i	−0.453983	+	0.329838i
$397$	1.06333e6	+	1.46355e6i	0.338605	+	0.466050i	0.944033	−	0.329850i	$-0.106998\pi$
$397$	1.06333e6	+	1.46355e6i	0.338605	+	0.466050i	−0.605428	+	0.795900i	$0.706998\pi$
$398$	−2.51411e6	+	816884.i	−0.795566	+	0.258495i
$399$	1.07999e7			3.39617
$400$	649293.	−	467353.i	0.202904	−	0.146048i
$401$	−3.77532e6			−1.17245			−0.586223	−	0.810150i	$-0.699386\pi$
$401$	−3.77532e6			−1.17245			−0.586223	+	0.810150i	$0.699386\pi$
$402$	−1.48173e6	+	481442.i	−0.457302	+	0.148586i
$403$	97379.1	+	134031.i	0.0298678	+	0.0411095i
$404$	−1.47194e6	+	1.06943e6i	−0.448679	+	0.325985i
$405$	−110644.	−	153000.i	−0.0335188	−	0.0463505i
$406$	2.93200e6	+	2.13022e6i	0.882773	+	0.641372i
$407$		−	2.20071e6i		−	0.658532i
$408$	−1.33897e6	+	1.84294e6i	−0.398218	+	0.548100i
$409$	−1.71622e6	+	5.28199e6i	−0.507301	+	1.56131i	0.289567	+	0.957158i	$0.406489\pi$
$409$	−1.71622e6	+	5.28199e6i	−0.507301	+	1.56131i	−0.796868	+	0.604154i	$0.793511\pi$
$410$	210720.	−	643668.i	0.0619079	−	0.189105i
$411$	−478514.	−	1.47272e6i	−0.139730	−	0.430045i
$412$	−891514.	−	289671.i	−0.258753	−	0.0840739i
$413$	1.02159e7	+	3.31934e6i	2.94714	+	0.957583i
$414$	−1.88610e6	−	5.80481e6i	−0.540833	−	1.66451i
$415$	4.59580e6	−	3.32349e6i	1.30991	−	0.947271i
$416$	−29347.1	+	90321.0i	−0.00831441	+	0.0255891i
$417$	−4.80789e6	+	6.61749e6i	−1.35399	+	1.86360i
$418$			1.95888e6i			0.548362i
$419$	−2.54079e6	−	1.84599e6i	−0.707024	−	0.513683i	0.175188	−	0.984535i	$-0.443947\pi$
$419$	−2.54079e6	−	1.84599e6i	−0.707024	−	0.513683i	−0.882212	+	0.470852i	$0.843947\pi$
$420$	3.28979e6	−	4.50695e6i	0.910007	−	1.24669i
$421$	−1.14505e6	+	831926.i	−0.314861	+	0.228760i	−0.733979	−	0.679172i	$-0.762339\pi$
$421$	−1.14505e6	+	831926.i	−0.314861	+	0.228760i	0.419119	+	0.907931i	$0.362339\pi$
$422$	1.48188e6	+	2.03964e6i	0.405073	+	0.557534i
$423$	6.84056e6	−	2.22263e6i	1.85884	−	0.603972i
$424$	546150.			0.147536
$425$	−4.22101e6	+	1.35082e6i	−1.13356	+	0.362765i
$426$	−2.51291e6			−0.670892
$427$	3.20548e6	−	1.04152e6i	0.850791	−	0.276439i
$428$	−1.24295e6	−	1.71078e6i	−0.327978	−	0.451423i
$429$	532699.	−	387029.i	0.139746	−	0.101531i
$430$	−3021.92	+	1.36252e6i	−0.000788154	+	0.355364i
$431$	−3.91287e6	−	2.84287e6i	−1.01462	−	0.737163i	−0.0494452	−	0.998777i	$-0.515745\pi$
$431$	−3.91287e6	−	2.84287e6i	−1.01462	−	0.737163i	−0.965173	+	0.261614i	$0.915745\pi$
$432$		−	924515.i		−	0.238344i
$433$	710822.	−	978363.i	0.182197	−	0.250773i	−0.708143	−	0.706069i	$-0.750467\pi$
$433$	710822.	−	978363.i	0.182197	−	0.250773i	0.890340	+	0.455296i	$0.150467\pi$
$434$	−548852.	+	1.68919e6i	−0.139872	+	0.430482i
$435$	4.13060e6	+	3.01508e6i	1.04662	+	0.763968i
$436$	268928.	+	827674.i	0.0677516	+	0.208518i
$437$	−6.49346e6	−	2.10985e6i	−1.62657	−	0.528505i
$438$	−1.16749e6	−	379342.i	−0.290783	−	0.0944813i
$439$	−2.15282e6	−	6.62570e6i	−0.533146	−	1.64086i	−0.747621	−	0.664126i	$-0.768804\pi$
$439$	−2.15282e6	−	6.62570e6i	−0.533146	−	1.64086i	0.214474	−	0.976730i	$-0.431196\pi$
$440$	817466.	+	596698.i	0.201297	+	0.146934i
$441$	5.37764e6	−	1.65507e7i	1.31673	−	4.05247i
$442$	309243.	−	425637.i	0.0752912	−	0.103629i
$443$		−	100654.i		−	0.0243680i	−0.999926	−	0.0121840i	$-0.996122\pi$
$443$		−	100654.i		−	0.0243680i	0.999926	−	0.0121840i	$-0.00387839\pi$
$444$	2.52735e6	+	1.83623e6i	0.608426	+	0.442048i
$445$	2485.54	−	1.12068e6i	0.000595004	−	0.268276i
$446$	−294772.	+	214164.i	−0.0701695	+	0.0509811i
$447$	3.75320e6	+	5.16583e6i	0.888449	+	1.22285i
$448$	−968310.	+	314623.i	−0.227939	+	0.0740620i
$449$	896856.			0.209946			0.104973	−	0.994475i	$-0.466524\pi$
$449$	896856.			0.209946			0.104973	+	0.994475i	$0.466524\pi$
$450$	2.85995e6	−	3.89989e6i	0.665776	−	0.907865i
$451$	856827.			0.198359
$452$	2.13744e6	−	694497.i	0.492094	−	0.159891i
$453$	−6.03008e6	−	8.29970e6i	−1.38063	−	1.90028i
$454$	2.62070e6	−	1.90405e6i	0.596729	−	0.433549i
$455$	−759796.	+	1.04091e6i	−0.172055	+	0.235713i
$456$	−2.24963e6	−	1.63445e6i	−0.506639	−	0.368095i
$457$		−	1.82311e6i		−	0.408340i	−0.978935	−	0.204170i	$-0.934550\pi$
$457$		−	1.82311e6i		−	0.408340i	0.978935	−	0.204170i	$-0.0654496\pi$
$458$	1.70442e6	−	2.34593e6i	0.379675	−	0.522578i
$459$	−1.58269e6	+	4.87102e6i	−0.350642	+	1.07916i
$460$	−2.85846e6	+	2.06712e6i	−0.629850	+	0.455482i
$461$	−258554.	−	795747.i	−0.0566629	−	0.174390i	0.918720	−	0.394911i	$-0.129224\pi$
$461$	−258554.	−	795747.i	−0.0566629	−	0.174390i	−0.975382	+	0.220520i	$0.929224\pi$
$462$	6.71361e6	+	2.18139e6i	1.46336	+	0.475475i
$463$	−6.25020e6	−	2.03081e6i	−1.35501	−	0.440269i	−0.460634	−	0.887590i	$-0.652378\pi$
$463$	−6.25020e6	−	2.03081e6i	−1.35501	−	0.440269i	−0.894373	+	0.447321i	$0.852378\pi$
$464$	−288351.	−	887452.i	−0.0621764	−	0.191359i
$465$	−779756.	+	2.38185e6i	−0.167235	+	0.510838i
$466$	494395.	−	1.52159e6i	0.105465	−	0.324588i
$467$	−3.03168e6	+	4.17275e6i	−0.643266	+	0.885380i	−0.998785	−	0.0492893i	$-0.984304\pi$
$467$	−3.03168e6	+	4.17275e6i	−0.643266	+	0.885380i	0.355518	+	0.934669i	$0.384304\pi$
$468$			574108.i			0.121165i
$469$	3.12086e6	+	2.26743e6i	0.655151	+	0.475995i
$470$	−2.43595e6	−	3.36849e6i	−0.508656	−	0.703381i
$471$	−535089.	+	388765.i	−0.111141	+	0.0807486i
$472$	−1.62562e6	−	2.23748e6i	−0.335865	−	0.462279i
$473$	−1.63936e6	+	532661.i	−0.336916	+	0.109471i
$474$	5.95800e6			1.21802
$475$	−1.64891e6	−	5.15249e6i	−0.335323	−	1.04781i
$476$	5.64036e6			1.14101
$477$	3.14000e6	−	1.02025e6i	0.631879	−	0.205310i
$478$	296996.	+	408779.i	0.0594539	+	0.0818312i
$479$	−1.20338e6	+	874308.i	−0.239643	+	0.174111i	−0.701124	−	0.713039i	$-0.747318\pi$
$479$	−1.20338e6	+	874308.i	−0.239643	+	0.174111i	0.461481	+	0.887150i	$0.347318\pi$
$480$	−1.36734e6	+	440925.i	−0.270878	+	0.0873498i
$481$	−583706.	−	424087.i	−0.115035	−	0.0835781i
$482$			239400.i			0.0469360i
$483$	−1.44621e7	+	1.99054e7i	−2.82074	+	3.88242i
$484$	400622.	−	1.23299e6i	0.0777360	−	0.239247i
$485$	2.33500e6	+	7.24101e6i	0.450747	+	1.39780i
$486$	1.18952e6	+	3.66095e6i	0.228444	+	0.703078i
$487$	2.56799e6	+	834391.i	0.490649	+	0.159422i	0.543884	−	0.839160i	$-0.316953\pi$
$487$	2.56799e6	+	834391.i	0.490649	+	0.159422i	−0.0532346	+	0.998582i	$0.516953\pi$
$488$	−825324.	−	268164.i	−0.156883	−	0.0509743i
$489$	894193.	+	2.75204e6i	0.169106	+	0.520455i
$490$	−1.00578e7	−	22307.0i	−1.89240	−	0.00419711i
$491$	1.45447e6	−	4.47640e6i	0.272271	−	0.837964i	−0.717658	−	0.696396i	$-0.754786\pi$
$491$	1.45447e6	−	4.47640e6i	0.272271	−	0.837964i	0.989929	−	0.141568i	$-0.0452143\pi$
$492$	−714919.	+	984002.i	−0.133151	+	0.183267i
$493$			5.16937e6i			0.957900i
$494$	519565.	+	377486.i	0.0957904	+	0.0695958i
$495$	5.81456e6	+	1.90353e6i	1.06661	+	0.349178i
$496$	369966.	−	268796.i	0.0675240	−	0.0490590i
$497$	3.65721e6	+	5.03371e6i	0.664138	+	0.914108i
$498$	−9.68678e6	+	3.14743e6i	−1.75028	+	0.568699i
$499$	−8.02906e6			−1.44349			−0.721744	−	0.692160i	$-0.756659\pi$
$499$	−8.02906e6			−1.44349			−0.721744	+	0.692160i	$0.756659\pi$
$500$	−2.65248e6	−	881397.i	−0.474490	−	0.157669i
$501$	7.84749e6			1.39681
$502$	482623.	−	156814.i	0.0854769	−	0.0277731i
$503$	4.85617e6	+	6.68395e6i	0.855804	+	1.17791i	0.982554	+	0.185979i	$0.0595455\pi$
$503$	4.85617e6	+	6.68395e6i	0.855804	+	1.17791i	−0.126750	+	0.991935i	$0.540455\pi$
$504$	−4.97940e6	+	3.61775e6i	−0.873174	+	0.634398i
$505$	6.04128e6	+	1.97775e6i	1.05415	+	0.345099i
$506$	−3.61041e6	−	2.62312e6i	−0.626874	−	0.455451i
$507$			9.10272e6i			1.57272i
$508$	−1.23415e6	+	1.69867e6i	−0.212183	+	0.292044i
$509$	608531.	−	1.87287e6i	0.104109	−	0.320415i	−0.885411	−	0.464808i	$-0.846123\pi$
$509$	608531.	−	1.87287e6i	0.104109	−	0.320415i	0.989520	+	0.144394i	$0.0461232\pi$
$510$	7.95896e6	+	17652.0i	1.35497	+	0.00300517i
$511$	939259.	+	2.89074e6i	0.159123	+	0.489731i
$512$	249314.	+	81007.0i	0.0420312	+	0.0136568i
$513$	−5.94593e6	−	1.93195e6i	−0.997532	−	0.324118i
$514$	−708066.	−	2.17920e6i	−0.118213	−	0.363823i
$515$	1.00516e6	+	3.11706e6i	0.167000	+	0.517878i
$516$	756129.	−	2.32713e6i	0.125018	−	0.384765i
$517$	3.09116e6	−	4.25462e6i	0.508622	−	0.700058i
$518$		−	7.73504e6i		−	1.26660i
$519$	8.61941e6	+	6.26236e6i	1.40462	+	1.02052i
$520$	315795.	−	101834.i	0.0512150	−	0.0165153i
$521$	6.72234e6	−	4.88407e6i	1.08499	−	0.788293i	0.106445	−	0.994319i	$-0.466053\pi$
$521$	6.72234e6	−	4.88407e6i	1.08499	−	0.788293i	0.978547	+	0.206026i	$0.0660531\pi$
$522$	−3.31565e6	−	4.56360e6i	−0.532589	−	0.733046i
$523$	7.02766e6	−	2.28343e6i	1.12346	−	0.365033i	0.312371	−	0.949960i	$-0.398877\pi$
$523$	7.02766e6	−	2.28343e6i	1.12346	−	0.365033i	0.811086	+	0.584927i	$0.198877\pi$
$524$	4.15500e6			0.661062
$525$	−1.94952e7	−	86476.4i	−3.08695	−	0.0136930i
$526$	3.82104e6			0.602168
$527$	−2.40941e6	+	782863.i	−0.377906	+	0.122789i
$528$	−1.06832e6	−	1.47041e6i	−0.166769	−	0.229538i
$529$	7.37689e6	−	5.35963e6i	1.14613	−	0.832713i
$530$	−1.11817e6	−	1.54623e6i	−0.172909	−	0.239102i
$531$	−1.35260e7	−	9.82723e6i	−2.08178	−	1.51250i
$532$			6.88506e6i			1.05470i
$533$	165115.	−	227261.i	0.0251749	−	0.0346503i
$534$	−621919.	+	1.91407e6i	−0.0943802	+	0.290472i
$535$	−2.29867e6	+	7.02154e6i	−0.347210	+	1.06059i
$536$	−306924.	−	944614.i	−0.0461443	−	0.142018i
$537$	83834.7	+	27239.6i	0.0125455	+	0.00407628i
$538$	5.87250e6	+	1.90809e6i	0.874716	+	0.284213i
$539$	−3.93196e6	−	1.21013e7i	−0.582958	−	1.79416i
$540$	−2.61743e6	+	1.89282e6i	−0.386270	+	0.279335i
$541$	−533203.	+	1.64103e6i	−0.0783248	+	0.241059i	−0.982551	−	0.185996i	$-0.940449\pi$
$541$	−533203.	+	1.64103e6i	−0.0783248	+	0.241059i	0.904226	+	0.427055i	$0.140449\pi$
$542$	−4.70176e6	+	6.47141e6i	−0.687483	+	0.946239i
$543$		−	3.79687e6i		−	0.552619i
$544$	−1.17489e6	−	853606.i	−0.170216	−	0.123669i
$545$	1.79267e6	−	2.45592e6i	0.258528	−	0.354179i
$546$	1.87233e6	−	1.36032e6i	0.268782	−	0.195281i
$547$	2.90415e6	+	3.99722e6i	0.415003	+	0.571202i	0.964430	−	0.264339i	$-0.0851539\pi$
$547$	2.90415e6	+	3.99722e6i	0.415003	+	0.571202i	−0.549427	+	0.835542i	$0.685154\pi$
$548$	938870.	−	305057.i	0.133553	−	0.0433940i
$549$	−5.24602e6			−0.742846
$550$	15685.0	−	3.53602e6i	0.00221094	−	0.498434i
$551$	−6.31013e6			−0.885440
$552$	6.02491e6	−	1.95761e6i	0.841594	−	0.273451i
$553$	−8.67109e6	−	1.19347e7i	−1.20576	−	1.65959i
$554$	−1.42988e6	+	1.03887e6i	−0.197937	+	0.143809i
$555$	24207.5	−	1.09147e7i	0.00333594	−	1.50411i
$556$	−4.21871e6	−	3.06507e6i	−0.578753	−	0.420488i
$557$			949638.i			0.129694i	0.997895	+	0.0648470i	$0.0206559\pi$
$557$			949638.i			0.129694i	−0.997895	+	0.0648470i	$0.979344\pi$
$558$	1.62493e6	−	2.23652e6i	0.220927	−	0.304080i
$559$	−174632.	+	537463.i	−0.0236372	+	0.0727477i
$560$	2.87322e6	+	2.09727e6i	0.387168	+	0.282608i
$561$	3.11145e6	+	9.57607e6i	0.417404	+	1.28464i
$562$	−705338.	−	229178.i	−0.0942013	−	0.0306078i
$563$	1.37803e7	+	4.47749e6i	1.83226	+	0.595338i	0.999105	+	0.0423003i	$0.0134686\pi$
$563$	1.37803e7	+	4.47749e6i	1.83226	+	0.595338i	0.833156	+	0.553038i	$0.186531\pi$
$564$	2.30691e6	+	7.09993e6i	0.305374	+	0.939845i
$565$	−6.34233e6	−	4.62950e6i	−0.835849	−	0.610117i
$566$	−2.37629e6	+	7.31348e6i	−0.311788	+	0.959584i
$567$	493490.	−	679230.i	0.0644645	−	0.0887277i
$568$		−	1.60200e6i		−	0.208349i
$569$	−1.02512e7	−	7.44796e6i	−1.32738	−	0.964399i	−0.999808	−	0.0195732i	$-0.993769\pi$
$569$	−1.02512e7	−	7.44796e6i	−1.32738	−	0.964399i	−0.327573	−	0.944826i	$-0.606231\pi$
$570$	−21547.4	+	9.71532e6i	−0.00277785	+	1.25248i
$571$	−7.71763e6	+	5.60719e6i	−0.990590	+	0.719705i	−0.960050	−	0.279828i	$-0.909723\pi$
$571$	−7.71763e6	+	5.60719e6i	−0.990590	+	0.719705i	−0.0305395	+	0.999534i	$0.509723\pi$
$572$	246734.	+	339601.i	0.0315311	+	0.0433989i
$573$	2.13437e6	−	693497.i	0.271570	−	0.0882385i
$574$	3.01157e6			0.381516
$575$	1.17046e7	+	3.86054e6i	1.47634	+	0.486943i
$576$	1.58472e6			0.199019
$577$	5.41915e6	−	1.76079e6i	0.677628	−	0.220175i	0.0500716	−	0.998746i	$-0.484055\pi$
$577$	5.41915e6	−	1.76079e6i	0.677628	−	0.220175i	0.627557	+	0.778571i	$0.284055\pi$
$578$	1.39058e6	+	1.91397e6i	0.173131	+	0.238295i
$579$	1.33558e7	−	9.70358e6i	1.65567	−	1.20292i
$580$	−1.92214e6	+	2.63330e6i	−0.237255	+	0.325035i
$581$	2.04026e7	+	1.48234e7i	2.50752	+	1.82182i
$582$		−	1.36631e7i		−	1.67202i
$583$	1.41892e6	−	1.95298e6i	0.172897	−	0.237972i
$584$	241834.	−	744289.i	0.0293417	−	0.0903045i
$585$	1.62538e6	−	1.17541e6i	0.196365	−	0.142003i
$586$	−1.74193e6	−	5.36111e6i	−0.209549	−	0.644927i
$587$	8.56316e6	+	2.78234e6i	1.02574	+	0.333284i	0.773106	−	0.634277i	$-0.218702\pi$
$587$	8.56316e6	+	2.78234e6i	1.02574	+	0.333284i	0.252638	+	0.967561i	$0.418702\pi$
$588$	1.71782e7	+	5.58154e6i	2.04897	+	0.665749i
$589$	−955623.	−	2.94110e6i	−0.113501	−	0.349319i
$590$	−3.00637e6	+	9.18329e6i	−0.355559	+	1.08610i
$591$	−1.36883e6	+	4.21282e6i	−0.161206	+	0.496140i
$592$	−1.17061e6	+	1.61121e6i	−0.137280	+	0.188950i
$593$		−	1.36694e7i		−	1.59630i	−0.602459	−	0.798150i	$-0.705812\pi$
$593$		−	1.36694e7i		−	1.59630i	0.602459	−	0.798150i	$-0.294188\pi$
$594$	−3.30598e6	−	2.40194e6i	−0.384445	−	0.279316i
$595$	−1.15479e7	−	1.59686e7i	−1.33724	−	1.84916i
$596$	−3.29327e6	+	2.39270e6i	−0.379762	+	0.275913i
$597$	−9.74922e6	−	1.34187e7i	−1.11953	−	1.54090i
$598$	−1.39149e6	+	452122.i	−0.159121	+	0.0517014i
$599$	2.30869e6			0.262904			0.131452	−	0.991323i	$-0.458036\pi$
$599$	2.30869e6			0.262904			0.131452	+	0.991323i	$0.458036\pi$
$600$	4.04776e6	+	2.96839e6i	0.459026	+	0.336623i
$601$	−6.54511e6			−0.739146			−0.369573	−	0.929202i	$-0.620496\pi$
$601$	−6.54511e6			−0.739146			−0.369573	+	0.929202i	$0.620496\pi$
$602$	−5.76202e6	+	1.87219e6i	−0.648013	+	0.210552i
$603$	−3.52921e6	−	4.85755e6i	−0.395262	−	0.544031i
$604$	5.29113e6	−	3.84423e6i	0.590142	−	0.428763i
$605$	−4.31098e6	+	1.39016e6i	−0.478837	+	0.154410i
$606$	−9.23555e6	−	6.71002e6i	−1.02160	−	0.742237i
$607$		−	1.64517e7i		−	1.81233i	−0.422921	−	0.906167i	$-0.638995\pi$
$607$		−	1.64517e7i		−	1.81233i	0.422921	−	0.906167i	$-0.361005\pi$
$608$	1.04198e6	−	1.43416e6i	0.114314	−	0.157340i
$609$	−7.02688e6	+	2.16265e7i	−0.767749	+	2.36289i
$610$	930529.	+	2.88564e6i	0.101252	+	0.313991i
$611$	−532794.	−	1.63977e6i	−0.0577372	−	0.177697i
$612$	−8.34943e6	−	2.71289e6i	−0.901110	−	0.292789i
$613$	−1.67940e7	−	5.45670e6i	−1.80511	−	0.586514i	−0.805127	−	0.593103i	$-0.797903\pi$
$613$	−1.67940e7	−	5.45670e6i	−1.80511	−	0.586514i	−0.999978	+	0.00658862i	$0.997903\pi$
$614$	2.12958e6	+	6.55416e6i	0.227967	+	0.701611i
$615$	4.24954e6	+	9424.98i	0.453059	+	0.00100483i
$616$	−1.39065e6	+	4.27999e6i	−0.147661	+	0.454455i
$617$	−2.15541e6	+	2.96667e6i	−0.227939	+	0.313731i	−0.907633	−	0.419765i	$-0.862112\pi$
$617$	−2.15541e6	+	2.96667e6i	−0.227939	+	0.313731i	0.679694	+	0.733496i	$0.262112\pi$
$618$		−	5.88160e6i		−	0.619476i
$619$	1.35390e7	+	9.83666e6i	1.42023	+	1.03186i	0.991733	+	0.128320i	$0.0409585\pi$
$619$	1.35390e7	+	9.83666e6i	1.42023	+	1.03186i	0.428502	+	0.903541i	$0.359041\pi$
$620$	−1.51845e6	−	497102.i	−0.158644	−	0.0519357i
$621$	1.15229e7	−	8.37189e6i	1.19904	−	0.871153i
$622$	2.26434e6	+	3.11659e6i	0.234674	+	0.323001i
$623$	4.73928e6	−	1.53989e6i	0.489207	−	0.158953i
$624$	−595876.			−0.0612624
$625$	2.93523e6	+	9.31407e6i	0.300568	+	0.953761i
$626$	3.45774e6			0.352661
$627$	−1.16893e7	+	3.79808e6i	−1.18746	+	0.385829i
$628$	−247841.	−	341124.i	−0.0250769	−	0.0345155i
$629$	8.92588e6	−	6.48503e6i	0.899548	−	0.653560i
$630$	2.04370e7	+	6.69052e6i	2.05147	+	0.671597i
$631$	8.10923e6	+	5.89170e6i	0.810785	+	0.589070i	0.914058	−	0.405583i	$-0.132931\pi$
$631$	8.10923e6	+	5.89170e6i	0.810785	+	0.589070i	−0.103273	+	0.994653i	$0.532931\pi$
$632$			3.79828e6i			0.378263i
$633$	−9.29795e6	+	1.27975e7i	−0.922313	+	1.26945i
$634$	−546542.	+	1.68208e6i	−0.0540008	+	0.166198i
$635$	7.33592e6	+	16270.2i	0.721972	+	0.00160125i
$636$	1.05893e6	+	3.25906e6i	0.103807	+	0.319484i
$637$	−3.96741e6	−	1.28909e6i	−0.387399	−	0.125874i
$638$	−3.92259e6	−	1.27453e6i	−0.381524	−	0.123965i
$639$	−2.99265e6	−	9.21044e6i	−0.289937	−	0.892336i
$640$	−281094.	−	871692.i	−0.0271270	−	0.0841227i
$641$	−960096.	+	2.95487e6i	−0.0922932	+	0.284049i	−0.986539	−	0.163527i	$-0.947713\pi$
$641$	−960096.	+	2.95487e6i	−0.0922932	+	0.284049i	0.894246	+	0.447577i	$0.147713\pi$
$642$	7.79880e6	−	1.07341e7i	0.746775	−	1.02785i
$643$		−	284792.i		−	0.0271644i	−0.999908	−	0.0135822i	$-0.995677\pi$
$643$		−	284792.i		−	0.0271644i	0.999908	−	0.0135822i	$-0.00432348\pi$
$644$	−1.26898e7	−	9.21971e6i	−1.20571	−	0.875997i
$645$	−8.13649e6	+	2.62377e6i	−0.770083	+	0.248328i
$646$	−7.94504e6	+	5.77241e6i	−0.749057	+	0.544222i
$647$	7.92224e6	+	1.09040e7i	0.744025	+	1.02406i	0.998377	+	0.0569509i	$0.0181378\pi$
$647$	7.92224e6	+	1.09040e7i	0.744025	+	1.02406i	−0.254352	+	0.967112i	$0.581862\pi$
$648$	−205588.	+	66799.6i	−0.0192336	+	0.00624937i
$649$	−1.22245e7			−1.13925
$650$	−934854.	−	685568.i	−0.0867882	−	0.0636454i
$651$	−1.11441e7			−1.03061
$652$	−1.75445e6	+	570057.i	−0.161630	+	0.0525169i
$653$	1.30961e6	+	1.80252e6i	0.120188	+	0.165424i	0.864872	−	0.501993i	$-0.167400\pi$
$653$	1.30961e6	+	1.80252e6i	0.120188	+	0.165424i	−0.744684	+	0.667417i	$0.767400\pi$
$654$	−4.41758e6	+	3.20956e6i	−0.403869	+	0.293428i
$655$	−8.50678e6	−	1.17634e7i	−0.774751	−	1.07134i
$656$	−627310.	−	455768.i	−0.0569145	−	0.0413508i
$657$		−	4.73093e6i		−	0.427595i
$658$	1.08648e7	−	1.49541e7i	0.978265	−	1.34647i
$659$	−1.41640e6	+	4.35922e6i	−0.127049	+	0.391017i	−0.994269	−	0.106909i	$-0.965905\pi$
$659$	−1.41640e6	+	4.35922e6i	−0.127049	+	0.391017i	0.867220	+	0.497926i	$0.165905\pi$
$660$	−1.97571e6	+	6.03503e6i	−0.176548	+	0.539286i
$661$	−3.20740e6	−	9.87137e6i	−0.285529	−	0.878767i	−0.986240	−	0.165322i	$-0.947134\pi$
$661$	−3.20740e6	−	9.87137e6i	−0.285529	−	0.878767i	0.700711	−	0.713445i	$-0.252866\pi$
$662$	2.73158e6	+	887544.i	0.242253	+	0.0787127i
$663$	3.13951e6	+	1.02009e6i	0.277381	+	0.0901267i
$664$	−2.00651e6	−	6.17541e6i	−0.176613	−	0.543558i
$665$	1.94925e7	−	1.40962e7i	1.70928	−	1.23609i
$666$	−3.72039e6	+	1.14502e7i	−0.325014	+	1.00029i
$667$	8.44983e6	−	1.16302e7i	0.735416	−	1.01221i
$668$			5.00285e6i			0.433787i
$669$	−1.84952e6	−	1.34376e6i	−0.159769	−	0.116079i
$670$	−2.04595e6	+	2.80291e6i	−0.176079	+	0.241225i
$671$	−3.10316e6	+	2.25458e6i	−0.266071	+	0.193312i
$672$	−3.75492e6	−	5.16820e6i	−0.320758	−	0.441485i
$673$	7.01700e6	−	2.27996e6i	0.597192	−	0.194039i	0.00520417	−	0.999986i	$-0.498343\pi$
$673$	7.01700e6	−	2.27996e6i	0.597192	−	0.194039i	0.591988	+	0.805947i	$0.298343\pi$
$674$	−1.16369e7			−0.986704
$675$	1.07177e7	+	3.53501e6i	0.905400	+	0.298629i
$676$	−5.80307e6			−0.488417
$677$	−6.43432e6	+	2.09064e6i	−0.539549	+	0.175310i	−0.566099	−	0.824337i	$-0.691548\pi$
$677$	−6.43432e6	+	2.09064e6i	−0.539549	+	0.175310i	0.0265497	+	0.999647i	$0.491548\pi$
$678$	8.28858e6	+	1.14083e7i	0.692478	+	0.953114i
$679$	−2.73692e7	+	1.98849e7i	−2.27818	+	1.65519i
$680$	−11253.3	+	5.07391e6i	−0.000933273	+	0.420795i
$681$	1.64434e7	+	1.19468e7i	1.35870	+	0.987152i
$682$		−	2.02131e6i		−	0.166407i
$683$	−6.21987e6	+	8.56092e6i	−0.510187	+	0.702213i	−0.983951	−	0.178439i	$-0.942895\pi$
$683$	−6.21987e6	+	8.56092e6i	−0.510187	+	0.702213i	0.473764	+	0.880652i	$0.342895\pi$
$684$	3.31156e6	−	1.01919e7i	0.270641	−	0.832946i
$685$	−2.78587e6	−	2.03351e6i	−0.226847	−	0.165584i
$686$	−8.65609e6	−	2.66407e7i	−0.702281	−	2.16140i
$687$	1.73036e7	+	5.62229e6i	1.39877	+	0.454487i
$688$	1.48356e6	+	482039.i	0.119491	+	0.0388250i
$689$	−244566.	−	752698.i	−0.0196268	−	0.0604050i
$690$	−1.78774e7	−	1.30494e7i	−1.42949	−	1.04344i
$691$	−341046.	+	1.04963e6i	−0.0271717	+	0.0836260i	−0.963723	−	0.266905i	$-0.913999\pi$
$691$	−341046.	+	1.04963e6i	−0.0271717	+	0.0836260i	0.936551	+	0.350531i	$0.113999\pi$
$692$	−3.99232e6	+	5.49495e6i	−0.316927	+	0.436213i
$693$			2.72049e7i			2.15186i
$694$	1.22212e7	+	8.87920e6i	0.963195	+	0.699802i
$695$	−40407.7	+	1.82191e7i	−0.00317324	+	1.43075i
$696$	4.73663e6	−	3.44136e6i	0.370635	−	0.269282i
$697$	2.52489e6	+	3.47521e6i	0.196861	+	0.270956i
$698$	1.65414e6	−	537463.i	0.128509	−	0.0417551i
$699$	1.00384e7			0.777091
$700$	55129.5	−	1.24284e7i	0.00425245	−	0.958669i
$701$	2.31858e6			0.178208			0.0891041	−	0.996022i	$-0.471600\pi$
$701$	2.31858e6			0.178208			0.0891041	+	0.996022i	$0.471600\pi$
$702$	−1.27416e6	+	413999.i	−0.0975843	+	0.0317071i
$703$	7.91612e6	+	1.08956e7i	0.604122	+	0.831502i
$704$	937402.	−	681063.i	0.0712844	−	0.0517911i
$705$	1.53778e7	−	2.10673e7i	1.16526	−	1.59638i
$706$	1.02760e7	+	7.46593e6i	0.775909	+	0.563731i
$707$			2.82657e7i			2.12672i
$708$	1.01998e7	−	1.40389e7i	0.764734	−	1.05257i
$709$	3.27281e6	−	1.00727e7i	0.244515	−	0.752540i	−0.751201	−	0.660074i	$-0.770525\pi$
$709$	3.27281e6	−	1.00727e7i	0.244515	−	0.752540i	0.995716	−	0.0924663i	$-0.0294751\pi$
$710$	−4.53548e6	+	3.27988e6i	−0.337659	+	0.244181i
$711$	7.09546e6	+	2.18376e7i	0.526388	+	1.62006i
$712$	−1.22024e6	−	396479.i	−0.0902079	−	0.0293103i
$713$	6.70041e6	+	2.17710e6i	0.493603	+	0.160381i
$714$	1.09361e7	+	3.36579e7i	0.802819	+	2.47082i
$715$	456301.	−	1.39382e6i	0.0333800	−	0.101963i
$716$	−17365.5	+	53445.4i	−0.00126591	+	0.00389608i
$717$	−1.86347e6	+	2.56485e6i	−0.135371	+	0.186322i
$718$			6.51583e6i			0.471692i
$719$	−1.72187e7	−	1.25101e7i	−1.24216	−	0.902484i	−0.244422	−	0.969669i	$-0.578598\pi$
$719$	−1.72187e7	−	1.25101e7i	−1.24216	−	0.902484i	−0.997741	+	0.0671852i	$0.978598\pi$
$720$	−3.24449e6	−	4.48655e6i	−0.233246	−	0.322538i
$721$	−1.17817e7	+	8.55990e6i	−0.844053	+	0.613240i
$722$	−1.22459e6	−	1.68550e6i	−0.0874273	−	0.120333i
$723$	−1.42858e6	+	464173.i	−0.101638	+	0.0330243i
$724$	2.42054e6			0.171619
$725$	1.13905e7	+	50526.0i	0.804821	+	0.00357001i
$726$	8.13442e6			0.572776
$727$	−2.37479e7	+	7.71616e6i	−1.66644	+	0.541459i	−0.982206	−	0.187806i	$-0.939862\pi$
$727$	−2.37479e7	+	7.71616e6i	−1.66644	+	0.541459i	−0.684232	+	0.729264i	$0.739862\pi$
$728$	867220.	+	1.19363e6i	0.0606458	+	0.0834718i
$729$	−1.88757e7	+	1.37140e7i	−1.31548	+	0.955754i
$730$	−2.60230e6	+	839164.i	−0.180739	+	0.0582827i
$731$	−6.99128e6	−	5.07946e6i	−0.483909	−	0.351580i
$732$		−	5.44492e6i		−	0.375590i
$733$	−9.41017e6	+	1.29520e7i	−0.646901	+	0.890383i	−0.998960	−	0.0455952i	$-0.985482\pi$
$733$	−9.41017e6	+	1.29520e7i	−0.646901	+	0.890383i	0.352059	+	0.935978i	$0.385482\pi$
$734$	3.08100e6	−	9.48234e6i	0.211082	−	0.649644i
$735$	−1.93679e7	−	6.00613e7i	−1.32241	−	4.10087i
$736$	1.24800e6	+	3.84093e6i	0.0849216	+	0.261362i
$737$	−4.17525e6	−	1.35662e6i	−0.283148	−	0.0920005i
$738$	−4.45802e6	−	1.44850e6i	−0.301302	−	0.0978988i
$739$	−3.73460e6	−	1.14939e7i	−0.251555	−	0.774206i	−0.994489	−	0.104842i	$-0.966566\pi$
$739$	−3.73460e6	−	1.14939e7i	−0.251555	−	0.774206i	0.742934	−	0.669365i	$-0.233434\pi$
$740$	6.95822e6	+	15432.5i	0.467110	+	0.00103599i
$741$	−1.24520e6	+	3.83232e6i	−0.0833091	+	0.256399i
$742$	4.98722e6	−	6.86432e6i	0.332544	−	0.457707i
$743$			1.27611e7i			0.848037i	0.905654	+	0.424018i	$0.139381\pi$
$743$			1.27611e7i			0.848037i	−0.905654	+	0.424018i	$0.860619\pi$
$744$	2.32132e6	+	1.68654e6i	0.153746	+	0.111703i
$745$	1.35166e7	+	4.42497e6i	0.892228	+	0.292092i
$746$	1.03078e7	−	7.48902e6i	0.678136	−	0.492695i
$747$	−2.30722e7	−	3.17562e7i	−1.51282	−	2.08222i
$748$	−6.10483e6	+	1.98358e6i	−0.398951	+	0.129627i
$749$	−3.28521e7			−2.13973
$750$	116687.	−	1.75371e7i	0.00757480	−	1.13843i
$751$	2.04227e7			1.32134			0.660668	−	0.750678i	$-0.270273\pi$
$751$	2.04227e7			1.32134			0.660668	+	0.750678i	$0.270273\pi$
$752$	−4.52627e6	+	1.47067e6i	−0.291874	+	0.0948357i
$753$	1.87152e6	+	2.57592e6i	0.120284	+	0.165556i
$754$	−1.09395e6	+	794803.i	−0.0700761	+	0.0509133i
$755$	−2.17164e7	−	7.10938e6i	−1.38650	−	0.453904i
$756$	−1.16198e7	−	8.44230e6i	−0.739427	−	0.537225i
$757$		−	1.14011e7i		−	0.723115i	−0.932350	−	0.361557i	$-0.882245\pi$
$757$		−	1.14011e7i		−	0.723115i	0.932350	−	0.361557i	$-0.117755\pi$
$758$	−3.85850e6	+	5.31077e6i	−0.243919	+	0.335726i
$759$	8.65277e6	−	2.66305e7i	0.545193	−	1.67793i
$760$	−6.19360e6	−	13736.7i	−0.388964	−	0.000862676i
$761$	−3.46110e6	−	1.06522e7i	−0.216647	−	0.666770i	−0.999033	−	0.0439760i	$-0.985997\pi$
$761$	−3.46110e6	−	1.06522e7i	−0.216647	−	0.666770i	0.782386	−	0.622794i	$-0.214003\pi$
$762$	−1.25294e7	−	4.07105e6i	−0.781705	−	0.253991i
$763$	1.28584e7	+	4.17795e6i	0.799606	+	0.259808i
$764$	442111.	+	1.36068e6i	0.0274030	+	0.0843377i
$765$	9.41373e6	+	2.91926e7i	0.581579	+	1.80352i
$766$	−5.38868e6	+	1.65846e7i	−0.331826	+	1.02126i
$767$	−2.35571e6	+	3.24236e6i	−0.144589	+	0.199009i
$768$			1.64480e6i			0.100626i
$769$	7.91304e6	+	5.74916e6i	0.482533	+	0.350581i	0.802306	−	0.596913i	$-0.203606\pi$
$769$	7.91304e6	+	5.74916e6i	0.482533	+	0.350581i	−0.319772	+	0.947494i	$0.603606\pi$
$770$	1.49644e7	−	4.82557e6i	0.909563	−	0.293306i
$771$	1.16312e7	−	8.45053e6i	0.704672	−	0.511974i
$772$	6.18612e6	+	8.51447e6i	0.373573	+	0.514179i
$773$	1.98389e7	−	6.44604e6i	1.19418	−	0.388011i	0.356561	−	0.934272i	$-0.383949\pi$
$773$	1.98389e7	−	6.44604e6i	1.19418	−	0.388011i	0.837615	+	0.546261i	$0.183949\pi$
$774$	9.43000e6			0.565795
$775$	1.70146e6	+	5.31670e6i	0.101758	+	0.317971i
$776$	8.71036e6			0.519256
$777$	4.61575e7	−	1.49975e7i	2.74277	−	0.891181i
$778$	−5.22666e6	−	7.19388e6i	−0.309582	−	0.426103i
$779$	−4.24211e6	+	3.08207e6i	−0.250460	+	0.181970i
$780$	1.21997e6	+	1.68701e6i	0.0717983	+	0.0992842i
$781$	−5.72861e6	−	4.16208e6i	−0.336064	−	0.244164i
$782$		−	2.23733e7i		−	1.30832i
$783$	7.73733e6	−	1.06495e7i	0.451011	−	0.620763i
$784$	−3.55828e6	+	1.09513e7i	−0.206752	+	0.636318i
$785$	−458349.	+	1.40008e6i	−0.0265474	+	0.0810920i
$786$	8.05613e6	+	2.47942e7i	0.465125	+	1.43151i
$787$	−3.23111e7	−	1.04985e7i	−1.85958	−	0.604214i	−0.994773	−	0.102106i	$-0.967442\pi$
$787$	−3.23111e7	−	1.04985e7i	−1.85958	−	0.604214i	−0.864805	−	0.502107i	$-0.832558\pi$
$788$	−2.68571e6	−	872641.i	−0.154079	−	0.0500634i
$789$	7.40863e6	+	2.28014e7i	0.423687	+	1.30398i
$790$	1.07534e7	−	7.77645e6i	0.613027	−	0.443316i
$791$	1.07894e7	−	3.32064e7i	0.613137	−	1.88704i
$792$	4.11717e6	−	5.66679e6i	0.233231	−	0.321014i
$793$			1.25754e6i			0.0710130i
$794$	−5.85422e6	−	4.25334e6i	−0.329547	−	0.239430i
$795$	7.05882e6	−	9.67045e6i	0.396108	−	0.542661i
$796$	8.55452e6	−	6.21522e6i	0.478534	−	0.347675i
$797$	1.18975e7	+	1.63755e7i	0.663452	+	0.913163i	0.999590	−	0.0286495i	$-0.00912065\pi$
$797$	1.18975e7	+	1.63755e7i	0.663452	+	0.913163i	−0.336137	+	0.941813i	$0.609121\pi$
$798$	−4.10854e7	+	1.33495e7i	−2.28392	+	0.742089i
$799$	2.63653e7			1.46105
$800$	−1.89238e6	+	2.58049e6i	−0.104540	+	0.142553i
$801$	−7.75621e6			−0.427138
$802$	1.43622e7	−	4.66655e6i	0.788468	−	0.256189i
$803$	−2.03321e6	−	2.79847e6i	−0.111274	−	0.153155i
$804$	5.04172e6	−	3.66303e6i	0.275067	−	0.199848i
$805$	−121546.	+	5.48028e7i	−0.00661076	+	2.98066i
$806$	−536123.	−	389516.i	−0.0290688	−	0.0211197i
$807$			3.87427e7i			2.09414i
$808$	4.27770e6	−	5.88775e6i	0.230506	−	0.317264i
$809$	−1.25661e6	+	3.86745e6i	−0.0675040	+	0.207756i	−0.979119	−	0.203290i	$-0.934836\pi$
$809$	−1.25661e6	+	3.86745e6i	−0.0675040	+	0.207756i	0.911615	+	0.411046i	$0.134836\pi$
$810$	610032.	+	445285.i	0.0326693	+	0.0238465i
$811$	−1.07011e6	−	3.29345e6i	−0.0571315	−	0.175833i	0.918419	−	0.395610i	$-0.129467\pi$
$811$	−1.07011e6	−	3.29345e6i	−0.0571315	−	0.175833i	−0.975550	+	0.219778i	$0.929467\pi$
$812$	−1.37871e7	−	4.47970e6i	−0.733809	−	0.238429i
$813$	−4.77333e7	−	1.55095e7i	−2.53277	−	0.822945i
$814$	2.72023e6	+	8.37200e6i	0.143895	+	0.442862i
$815$	5.20591e6	+	3.79999e6i	0.274538	+	0.200396i
$816$	2.81575e6	−	8.66600e6i	0.148037	−	0.455610i
$817$	6.20038e6	−	8.53409e6i	0.324985	−	0.447304i
$818$		−	2.22153e7i		−	1.16083i
$819$	7.21571e6	+	5.24252e6i	0.375898	+	0.273106i
$820$	−6008.51	+	2.70912e6i	−0.000312056	+	0.140700i
$821$	8.35234e6	−	6.06833e6i	0.432465	−	0.314204i	−0.350169	−	0.936687i	$-0.613876\pi$
$821$	8.35234e6	−	6.06833e6i	0.432465	−	0.314204i	0.782634	+	0.622483i	$0.213876\pi$
$822$	3.64075e6	+	5.01107e6i	0.187937	+	0.258673i
$823$	−4.19104e6	+	1.36175e6i	−0.215686	+	0.0700806i	−0.414867	−	0.909882i	$-0.636172\pi$
$823$	−4.19104e6	+	1.36175e6i	−0.215686	+	0.0700806i	0.199181	+	0.979963i	$0.436172\pi$
$824$	3.74957e6			0.192382
$825$	2.11310e7	−	6.76239e6i	1.08090	−	0.345912i
$826$	−4.29664e7			−2.19119
$827$	−8.10793e6	+	2.63443e6i	−0.412236	+	0.133944i	−0.507791	−	0.861481i	$-0.669538\pi$
$827$	−8.10793e6	+	2.63443e6i	−0.412236	+	0.133944i	0.0955544	+	0.995424i	$0.469538\pi$
$828$	1.43503e7	+	1.97515e7i	0.727419	+	1.00121i
$829$	2.65153e7	−	1.92645e7i	1.34002	−	0.973579i	0.340573	−	0.940218i	$-0.389379\pi$
$829$	2.65153e7	−	1.92645e7i	1.34002	−	0.973579i	0.999443	−	0.0333603i	$-0.0106209\pi$
$830$	−1.33754e7	+	1.83240e7i	−0.673924	+	0.923264i
$831$	−8.97168e6	−	6.51831e6i	−0.450683	−	0.327441i
$832$		−	379876.i		−	0.0190254i
$833$	3.74952e7	−	5.16077e7i	1.87225	−	2.57693i
$834$	1.01106e7	−	3.11173e7i	0.503342	−	1.54913i
$835$	1.41637e7	−	1.02426e7i	0.703011	−	0.508389i
$836$	−2.42131e6	−	7.45203e6i	−0.119821	−	0.368773i
$837$	6.13543e6	+	1.99352e6i	0.302713	+	0.0983575i
$838$	1.19475e7	+	3.88198e6i	0.587716	+	0.190961i
$839$	2.34675e6	+	7.22256e6i	0.115097	+	0.354231i	0.991967	−	0.126496i	$-0.0403730\pi$
$839$	2.34675e6	+	7.22256e6i	0.115097	+	0.354231i	−0.876871	+	0.480726i	$0.840373\pi$
$840$	−6.94420e6	+	2.12119e7i	−0.339566	+	1.03724i
$841$	−2.23267e6	+	6.87145e6i	−0.108851	+	0.335010i
$842$	3.32771e6	−	4.58019e6i	0.161758	−	0.222640i
$843$		−	4.65334e6i		−	0.225526i
$844$	−8.15855e6	−	5.92753e6i	−0.394236	−	0.286430i
$845$	1.18810e7	+	1.64293e7i	0.572415	+	0.791547i
$846$	−2.32757e7	+	1.69108e7i	−1.11809	+	0.812341i
$847$	−1.18386e7	−	1.62944e7i	−0.567011	−	0.780423i
$848$	−2.07768e6	+	675079.i	−0.0992176	+	0.0322377i
$849$	−4.82493e7			−2.29732
$850$	1.43880e7	−	1.03563e7i	0.683050	−	0.491650i
$851$	−3.06821e7			−1.45232
$852$	9.55966e6	−	3.10612e6i	0.451174	−	0.146595i
$853$	3.54610e6	+	4.88078e6i	0.166870	+	0.229677i	0.884260	−	0.466995i	$-0.154663\pi$
$853$	3.54610e6	+	4.88078e6i	0.166870	+	0.229677i	−0.717390	+	0.696672i	$0.754663\pi$
$854$	−1.09070e7	+	7.92438e6i	−0.511752	+	0.371809i
$855$	−3.56348e7	+	1.14911e7i	−1.66709	+	0.537585i
$856$	6.84310e6	+	4.97180e6i	0.319204	+	0.231915i
$857$			1.63536e7i			0.760610i	0.924861	+	0.380305i	$0.124181\pi$
$857$			1.63536e7i			0.760610i	−0.924861	+	0.380305i	$0.875819\pi$
$858$	−1.54811e6	+	2.13080e6i	−0.0717934	+	0.0988152i
$859$	2.40629e6	−	7.40579e6i	0.111266	−	0.342443i	−0.879884	−	0.475189i	$-0.842380\pi$
$859$	2.40629e6	−	7.40579e6i	0.111266	−	0.342443i	0.991150	+	0.132746i	$0.0423796\pi$
$860$	−1.67268e6	−	5.18709e6i	−0.0771198	−	0.239154i
$861$	5.83914e6	+	1.79710e7i	0.268436	+	0.826161i
$862$	1.83994e7	+	5.97834e6i	0.843405	+	0.274039i
$863$	−3.26899e7	−	1.06216e7i	−1.49413	−	0.485471i	−0.555827	−	0.831298i	$-0.687598\pi$
$863$	−3.26899e7	−	1.06216e7i	−1.49413	−	0.485471i	−0.938298	+	0.345827i	$0.887598\pi$
$864$	1.14276e6	+	3.51707e6i	0.0520801	+	0.160286i
$865$	2.37307e7	+	52631.8i	1.07838	+	0.00239171i
$866$	−1.49481e6	+	4.60054e6i	−0.0677314	+	0.208456i
$867$	−8.72507e6	+	1.20090e7i	−0.394204	+	0.542576i
$868$		−	7.10449e6i		−	0.320061i
$869$	1.35823e7	+	9.86811e6i	0.610131	+	0.443286i
$870$	−1.94406e7	−	6.36433e6i	−0.870785	−	0.285072i
$871$	−1.16442e6	+	845997.i	−0.0520071	+	0.0377854i
$872$	−2.04612e6	−	2.81625e6i	−0.0911257	−	0.125424i
$873$	5.00788e7	−	1.62716e7i	2.22391	−	0.722593i
$874$	2.73105e7			1.20935
$875$	−3.52993e7	+	2.52893e7i	−1.55864	+	1.11665i
$876$	4.91031e6			0.216196
$877$	−7.63607e6	+	2.48111e6i	−0.335252	+	0.108930i	−0.471805	−	0.881703i	$-0.656397\pi$
$877$	−7.63607e6	+	2.48111e6i	−0.335252	+	0.108930i	0.136553	+	0.990633i	$0.456397\pi$
$878$	1.63796e7	+	2.25446e7i	0.717080	+	0.986976i
$879$	2.86140e7	−	2.07893e7i	1.24913	−	0.907545i
$880$	−3.84739e6	−	1.25953e6i	−0.167478	−	0.0548280i
$881$	−3.22525e7	−	2.34328e7i	−1.39999	−	1.01715i	−0.994685	−	0.102966i	$-0.967167\pi$
$881$	−3.22525e7	−	2.34328e7i	−1.39999	−	1.01715i	−0.405301	−	0.914183i	$-0.632833\pi$
$882$			6.96096e7i			3.01299i
$883$	8.42727e6	−	1.15991e7i	0.363735	−	0.500638i	−0.587450	−	0.809261i	$-0.699868\pi$
$883$	8.42727e6	−	1.15991e7i	0.363735	−	0.500638i	0.951185	+	0.308622i	$0.0998679\pi$
$884$	−650315.	+	2.00146e6i	−0.0279894	+	0.0861424i
$885$	−6.06288e7	−	134467.i	−2.60208	−	0.00577110i
$886$	124415.	+	382909.i	0.00532461	+	0.0163875i
$887$	−1.76388e7	−	5.73119e6i	−0.752765	−	0.244588i	−0.0925946	−	0.995704i	$-0.529516\pi$
$887$	−1.76388e7	−	5.73119e6i	−0.752765	−	0.244588i	−0.660171	+	0.751116i	$0.729516\pi$
$888$	−1.18843e7	−	3.86145e6i	−0.505757	−	0.164330i
$889$	1.00800e7	+	3.10231e7i	0.427766	+	1.31653i
$890$	1.37578e6	+	4.26640e6i	0.0582203	+	0.180545i
$891$	−295258.	+	908712.i	−0.0124597	+	0.0383470i
$892$	856656.	−	1.17909e6i	0.0360491	−	0.0496173i
$893$			3.21835e7i			1.35053i
$894$	−2.06633e7	−	1.50128e7i	−0.864682	−	0.628228i
$895$	186865.	−	60258.2i	0.00779776	−	0.00251454i
$896$	3.29477e6	−	2.39379e6i	0.137106	−	0.0996132i
$897$	−5.39592e6	−	7.42684e6i	−0.223915	−	0.308193i
$898$	−3.41184e6	+	1.10858e6i	−0.141188	+	0.0458748i
$899$	6.51123e6			0.268698
$900$	−6.05938e6	+	1.83712e7i	−0.249357	+	0.756015i
$901$	1.21024e7			0.496660
$902$	−3.25956e6	+	1.05910e6i	−0.133396	+	0.0433430i
$903$	−2.23440e7	−	3.07539e7i	−0.911887	−	1.25511i
$904$	−7.27287e6	+	5.28405e6i	−0.295995	+	0.215053i
$905$	−4.95572e6	−	6.85288e6i	−0.201134	−	0.278132i
$906$	3.31988e7	+	2.41203e7i	1.34370	+	0.976254i
$907$			4.50526e7i			1.81845i	0.416302	+	0.909226i	$0.363326\pi$
$907$			4.50526e7i			1.81845i	−0.416302	+	0.909226i	$0.636674\pi$
$908$	−7.61620e6	+	1.04828e7i	−0.306566	+	0.421951i
$909$	1.35952e7	−	4.18417e7i	0.545727	−	1.67958i
$910$	1.60380e6	−	4.89900e6i	0.0642019	−	0.196112i
$911$	−4.05671e6	−	1.24853e7i	−0.161949	−	0.498427i	0.836850	−	0.547433i	$-0.184395\pi$
$911$	−4.05671e6	−	1.24853e7i	−0.161949	−	0.498427i	−0.998799	+	0.0490054i	$0.984395\pi$
$912$	1.05784e7	+	3.43713e6i	0.421146	+	0.136838i
$913$	−2.72957e7	−	8.86892e6i	−1.08372	−	0.352122i
$914$	2.25349e6	+	6.93552e6i	0.0892257	+	0.274608i
$915$	−1.54153e7	+	1.11477e7i	−0.608695	+	0.440184i
$916$	−3.58426e6	+	1.10312e7i	−0.141143	+	0.434395i
$917$	3.79418e7	−	5.22223e7i	1.49003	−	2.05085i
$918$		−	2.04868e7i		−	0.802355i
$919$	3.51410e7	+	2.55315e7i	1.37254	+	0.997211i	0.997534	+	0.0701895i	$0.0223604\pi$
$919$	3.51410e7	+	2.55315e7i	1.37254	+	0.997211i	0.375009	+	0.927021i	$0.377640\pi$
$920$	8.31911e6	−	1.13970e7i	0.324047	−	0.443938i
$921$	−3.49818e7	+	2.54158e7i	−1.35892	+	0.987311i
$922$	1.96719e6	+	2.70761e6i	0.0762114	+	0.104896i
$923$	−2.20786e6	+	717377.i	−0.0853036	+	0.0277168i
$924$	−2.82364e7			−1.08800
$925$	−1.42023e7	−	1.97313e7i	−0.545764	−	0.758230i
$926$	2.62874e7			1.00744
$927$	2.15576e7	−	7.00448e6i	0.823949	−	0.267717i
$928$	2.19390e6	+	3.01965e6i	0.0836271	+	0.115103i
$929$	−1.63615e6	+	1.18873e6i	−0.0621991	+	0.0451903i	−0.618450	−	0.785824i	$-0.712239\pi$
$929$	−1.63615e6	+	1.18873e6i	−0.0621991	+	0.0451903i	0.556251	+	0.831014i	$0.312239\pi$
$930$	22234.1	−	1.00249e7i	0.000842971	−	0.380080i
$931$	6.29963e7	+	4.57695e7i	2.38200	+	1.73062i
$932$			6.39958e6i			0.241330i
$933$	−1.42074e7	+	1.95548e7i	−0.534331	+	0.735444i
$934$	6.37539e6	−	1.96214e7i	0.239133	−	0.735976i
$935$	1.81146e7	+	1.32225e7i	0.677641	+	0.494635i
$936$	−709637.	−	2.18404e6i	−0.0264756	−	0.0814836i
$937$	1.09683e7	+	3.56382e6i	0.408123	+	0.132607i	0.505881	−	0.862603i	$-0.331167\pi$
$937$	1.09683e7	+	3.56382e6i	0.408123	+	0.132607i	−0.0977587	+	0.995210i	$0.531167\pi$
$938$	−1.46751e7	−	4.76824e6i	−0.544597	−	0.176950i
$939$	6.70422e6	+	2.06335e7i	0.248133	+	0.763675i
$940$	1.34306e7	+	9.80349e6i	0.495765	+	0.361877i
$941$	1.72863e6	−	5.32019e6i	0.0636399	−	0.195863i	−0.914181	−	0.405306i	$-0.867165\pi$
$941$	1.72863e6	−	5.32019e6i	0.0636399	−	0.195863i	0.977821	+	0.209443i	$0.0671650\pi$
$942$	1.55506e6	−	2.14036e6i	0.0570979	−	0.0785885i
$943$		−	1.19458e7i		−	0.437458i
$944$	8.94991e6	+	6.50249e6i	0.326880	+	0.237493i
$945$	−111297.	+	5.01818e7i	−0.00405420	+	1.82796i
$946$	5.57810e6	−	4.05273e6i	0.202656	−	0.147238i
$947$	−7.81069e6	−	1.07505e7i	−0.283018	−	0.389541i	0.643712	−	0.765267i	$-0.277393\pi$
$947$	−7.81069e6	−	1.07505e7i	−0.283018	−	0.389541i	−0.926731	+	0.375726i	$0.877393\pi$
$948$	−2.26656e7	+	7.36449e6i	−0.819117	+	0.266147i
$949$	−1.13406e6			−0.0408763
$950$	1.26417e7	+	1.75631e7i	0.454460	+	0.631381i
$951$	−1.10972e7			−0.397890
$952$	−2.14572e7	+	6.97187e6i	−0.767328	+	0.249320i
$953$	1.75831e6	+	2.42010e6i	0.0627137	+	0.0863180i	0.839222	−	0.543789i	$-0.183011\pi$
$953$	1.75831e6	+	2.42010e6i	0.0627137	+	0.0863180i	−0.776508	+	0.630107i	$0.783011\pi$
$954$	−1.06842e7	+	7.76251e6i	−0.380076	+	0.276141i
$955$	2.94710e6	−	4.03748e6i	0.104565	−	0.143252i
$956$	−1.63512e6	−	1.18798e6i	−0.0578634	−	0.0420402i
$957$		−	2.58786e7i		−	0.913399i
$958$	3.49723e6	−	4.81353e6i	0.123115	−	0.169453i
$959$	4.73925e6	−	1.45859e7i	0.166404	−	0.512138i
$960$	4.65666e6	−	3.36751e6i	0.163078	−	0.117932i
$961$	−7.86082e6	−	2.41931e7i	−0.274574	−	0.845051i
$962$	2.74475e6	+	891824.i	0.0956237	+	0.0310700i
$963$	4.86310e7	+	1.58012e7i	1.68985	+	0.549064i
$964$	−295914.	−	910731.i	−0.0102559	−	0.0315644i
$965$	1.14404e7	−	3.49460e7i	0.395478	−	1.20803i
$966$	3.04127e7	−	9.36006e7i	1.04860	−	3.22727i
$967$	2.28444e7	−	3.14426e7i	0.785622	−	1.08132i	−0.209018	−	0.977912i	$-0.567027\pi$
$967$	2.28444e7	−	3.14426e7i	0.785622	−	1.08132i	0.994639	−	0.103404i	$-0.0329734\pi$
$968$			5.18577e6i			0.177879i
$969$	−4.98505e7	−	3.62185e7i	−1.70553	−	1.23914i
$970$	−1.78333e7	−	2.46602e7i	−0.608557	−	0.841526i
$971$	3.01686e7	−	2.19188e7i	1.02685	−	0.746050i	0.0591740	−	0.998248i	$-0.481153\pi$
$971$	3.01686e7	−	2.19188e7i	1.02685	−	0.746050i	0.967676	+	0.252198i	$0.0811533\pi$
$972$	−9.05037e6	−	1.24568e7i	−0.307256	−	0.422902i
$973$	−7.70472e7	+	2.50341e7i	−2.60900	+	0.847716i
$974$	−1.08006e7			−0.364796
$975$	2.27841e6	−	6.90783e6i	0.0767576	−	0.232718i
$976$	3.47119e6			0.116642
$977$	−2.24792e7	+	7.30394e6i	−0.753434	+	0.244805i	−0.660458	−	0.750863i	$-0.729638\pi$
$977$	−2.24792e7	+	7.30394e6i	−0.753434	+	0.244805i	−0.0929756	+	0.995668i	$0.529638\pi$
$978$	−6.80343e6	−	9.36412e6i	−0.227447	−	0.313054i
$979$	−4.58801e6	+	3.33338e6i	−0.152992	+	0.111155i
$980$	3.82896e7	−	1.23472e7i	1.27355	−	0.410681i
$981$	−1.70248e7	−	1.23692e7i	−0.564819	−	0.410365i
$982$			1.88271e7i			0.623023i
$983$	7.40694e6	−	1.01948e7i	0.244486	−	0.336507i	−0.669084	−	0.743186i	$-0.733314\pi$
$983$	7.40694e6	−	1.01948e7i	0.244486	−	0.336507i	0.913571	+	0.406680i	$0.133314\pi$
$984$	1.50342e6	−	4.62705e6i	0.0494986	−	0.152341i
$985$	3.02806e6	+	9.39024e6i	0.0994431	+	0.308380i
$986$	−6.38969e6	−	1.96654e7i	−0.209309	−	0.644186i
$987$	1.10302e8	+	3.58392e7i	3.60404	+	1.17102i
$988$	−2.44314e6	−	793824.i	−0.0796262	−	0.0258721i
$989$	7.42631e6	+	2.28558e7i	0.241425	+	0.743030i
$990$	−2.44728e7	−	54277.8i	−0.793589	−	0.00176009i
$991$	−3.84414e6	+	1.18310e7i	−0.124341	+	0.382683i	−0.993780	−	0.111357i	$-0.964480\pi$
$991$	−3.84414e6	+	1.18310e7i	−0.124341	+	0.382683i	0.869439	+	0.494040i	$0.164480\pi$
$992$	−1.07519e6	+	1.47987e6i	−0.0346900	+	0.0477467i
$993$			1.80211e7i			0.579973i
$994$	−2.01349e7	−	1.46288e7i	−0.646372	−	0.469617i
$995$	−3.51103e7	−	1.14942e7i	−1.12429	−	0.368062i
$996$	3.29603e7	−	2.39470e7i	1.05279	−	0.764898i
$997$	1.01540e7	+	1.39758e7i	0.323519	+	0.445286i	0.939538	−	0.342446i	$-0.111255\pi$
$997$	1.01540e7	+	1.39758e7i	0.323519	+	0.445286i	−0.616018	+	0.787732i	$0.711255\pi$
$998$	3.05444e7	−	9.92446e6i	0.970744	−	0.315414i
$999$	−2.80950e7			−0.890666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.e.a.19.1	✓	48
25.4	even	10	inner	50.6.e.a.29.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.e.a.19.1	✓	48	1.1	even	1	trivial
50.6.e.a.29.1	yes	48	25.4	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.80423 + 1.23607i) q^{2} +(-14.7520 - 20.3044i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-53.1272 - 17.3924i) q^{5} +(81.2178 + 59.0082i) q^{6} -248.570i q^{7} +(-37.6183 + 51.7771i) q^{8} +(-119.557 + 367.957i) q^{9} +O(q^{10})\)	\(q+(-3.80423 + 1.23607i) q^{2} +(-14.7520 - 20.3044i) q^{3} +(12.9443 - 9.40456i) q^{4} +(-53.1272 - 17.3924i) q^{5} +(81.2178 + 59.0082i) q^{6} -248.570i q^{7} +(-37.6183 + 51.7771i) q^{8} +(-119.557 + 367.957i) q^{9} +(223.606 + 0.495932i) q^{10} +(87.4160 + 269.039i) q^{11} +(-381.909 - 124.090i) q^{12} +(88.2041 + 28.6592i) q^{13} +(307.249 + 945.615i) q^{14} +(430.591 + 1335.29i) q^{15} +(79.1084 - 243.470i) q^{16} +(-833.600 + 1147.35i) q^{17} -1547.57i q^{18} +(-1400.55 - 1017.56i) q^{19} +(-851.262 + 274.506i) q^{20} +(-5047.07 + 3666.91i) q^{21} +(-665.100 - 915.432i) q^{22} +(3750.91 - 1218.75i) q^{23} +1606.25 q^{24} +(2520.01 + 1848.03i) q^{25} -370.973 q^{26} +(3434.63 - 1115.98i) q^{27} +(-2337.69 - 3217.55i) q^{28} +(2948.87 - 2142.48i) q^{29} +(-3288.58 - 4547.52i) q^{30} +(1445.18 + 1049.99i) q^{31} +1024.00i q^{32} +(4173.12 - 5743.80i) q^{33} +(1753.00 - 5395.17i) q^{34} +(-4323.23 + 13205.8i) q^{35} +(1912.91 + 5887.32i) q^{36} +(-7398.79 - 2404.01i) q^{37} +(6585.76 + 2139.84i) q^{38} +(-719.280 - 2213.72i) q^{39} +(2899.08 - 2096.50i) q^{40} +(935.981 - 2880.65i) q^{41} +(14667.6 - 20188.3i) q^{42} +6093.41i q^{43} +(3661.73 + 2660.40i) q^{44} +(12751.4 - 17469.2i) q^{45} +(-12762.9 + 9272.77i) q^{46} +(-10927.3 - 15040.1i) q^{47} +(-6110.54 + 1985.44i) q^{48} -44979.9 q^{49} +(-11871.0 - 3915.41i) q^{50} +35593.6 q^{51} +(1411.27 - 458.548i) q^{52} +(-5015.92 - 6903.82i) q^{53} +(-11686.7 + 8490.88i) q^{54} +(35.0728 - 15813.7i) q^{55} +(12870.2 + 9350.76i) q^{56} +43448.3i q^{57} +(-8569.93 + 11795.5i) q^{58} +(-13353.8 + 41098.7i) q^{59} +(18131.5 + 13234.9i) q^{60} +(4190.06 + 12895.7i) q^{61} +(-6795.65 - 2208.04i) q^{62} +(91463.0 + 29718.1i) q^{63} +(-1265.73 - 3895.53i) q^{64} +(-4187.58 - 3056.67i) q^{65} +(-8775.75 + 27009.0i) q^{66} +(-9121.93 + 12555.3i) q^{67} +22691.3i q^{68} +(-80079.6 - 58181.2i) q^{69} +(123.274 - 55581.7i) q^{70} +(-20250.7 + 14713.0i) q^{71} +(-14554.3 - 20032.2i) q^{72} +(-11629.5 + 3778.66i) q^{73} +31118.2 q^{74} +(347.896 - 78429.5i) q^{75} -27698.7 q^{76} +(66874.9 - 21729.0i) q^{77} +(5472.61 + 7532.40i) q^{78} +(48013.6 - 34883.9i) q^{79} +(-8437.36 + 11559.0i) q^{80} +(2732.55 + 1985.32i) q^{81} +12115.6i q^{82} +(-59634.6 + 82080.0i) q^{83} +(-30844.9 + 94931.0i) q^{84} +(64242.1 - 46457.3i) q^{85} +(-7531.87 - 23180.7i) q^{86} +(-87003.8 - 28269.3i) q^{87} +(-17218.5 - 5594.62i) q^{88} +(6194.99 + 19066.2i) q^{89} +(-26916.1 + 82218.3i) q^{90} +(7123.82 - 21924.9i) q^{91} +(37091.1 - 51051.5i) q^{92} -44833.0i q^{93} +(60160.6 + 43709.2i) q^{94} +(56709.3 + 78418.8i) q^{95} +(20791.8 - 15106.1i) q^{96} +(-79997.2 - 110107. i) q^{97} +(171114. - 55598.2i) q^{98} -109446. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9}+O(q^{10}) \) 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9	\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9} + 80 q^{10} + 716 q^{11} - 160 q^{12} - 784 q^{14} - 940 q^{15} - 3072 q^{16} + 1910 q^{17} - 5990 q^{19} - 640 q^{20} - 4344 q^{21} + 4720 q^{22} + 12410 q^{23} + 4608 q^{24} + 23660 q^{25} - 15248 q^{26} + 27600 q^{27} - 3040 q^{28} - 17170 q^{29} - 14720 q^{30} - 18834 q^{31} - 56930 q^{33} + 11696 q^{34} + 28450 q^{35} - 10976 q^{36} + 3540 q^{37} + 13432 q^{39} - 1280 q^{40} + 37146 q^{41} - 43560 q^{42} + 1184 q^{44} + 75240 q^{45} + 28672 q^{46} - 17830 q^{47} - 2560 q^{48} - 54656 q^{49} + 8800 q^{50} - 85984 q^{51} + 22350 q^{53} + 16080 q^{54} - 64730 q^{55} + 12544 q^{56} + 18000 q^{59} + 78720 q^{60} + 67086 q^{61} - 159600 q^{62} + 132820 q^{63} + 49152 q^{64} - 195820 q^{65} - 52256 q^{66} - 90790 q^{67} - 212608 q^{69} + 180080 q^{70} - 122874 q^{71} + 121200 q^{73} + 281456 q^{74} + 672810 q^{75} - 102400 q^{76} + 434040 q^{77} + 170720 q^{78} + 113600 q^{79} - 28160 q^{80} + 115878 q^{81} - 582750 q^{83} - 174816 q^{84} + 107770 q^{85} - 26888 q^{86} - 911580 q^{87} - 56960 q^{88} - 357730 q^{89} - 282920 q^{90} - 216324 q^{91} + 451040 q^{92} + 79136 q^{94} + 135000 q^{95} + 18432 q^{96} - 123520 q^{97} - 206240 q^{98} + 235252 q^{99}+O(q^{100}) \) 48 * q + 192 * q^4 + 180 * q^5 + 72 * q^6 + 686 * q^9 + 80 * q^10 + 716 * q^11 - 160 * q^12 - 784 * q^14 - 940 * q^15 - 3072 * q^16 + 1910 * q^17 - 5990 * q^19 - 640 * q^20 - 4344 * q^21 + 4720 * q^22 + 12410 * q^23 + 4608 * q^24 + 23660 * q^25 - 15248 * q^26 + 27600 * q^27 - 3040 * q^28 - 17170 * q^29 - 14720 * q^30 - 18834 * q^31 - 56930 * q^33 + 11696 * q^34 + 28450 * q^35 - 10976 * q^36 + 3540 * q^37 + 13432 * q^39 - 1280 * q^40 + 37146 * q^41 - 43560 * q^42 + 1184 * q^44 + 75240 * q^45 + 28672 * q^46 - 17830 * q^47 - 2560 * q^48 - 54656 * q^49 + 8800 * q^50 - 85984 * q^51 + 22350 * q^53 + 16080 * q^54 - 64730 * q^55 + 12544 * q^56 + 18000 * q^59 + 78720 * q^60 + 67086 * q^61 - 159600 * q^62 + 132820 * q^63 + 49152 * q^64 - 195820 * q^65 - 52256 * q^66 - 90790 * q^67 - 212608 * q^69 + 180080 * q^70 - 122874 * q^71 + 121200 * q^73 + 281456 * q^74 + 672810 * q^75 - 102400 * q^76 + 434040 * q^77 + 170720 * q^78 + 113600 * q^79 - 28160 * q^80 + 115878 * q^81 - 582750 * q^83 - 174816 * q^84 + 107770 * q^85 - 26888 * q^86 - 911580 * q^87 - 56960 * q^88 - 357730 * q^89 - 282920 * q^90 - 216324 * q^91 + 451040 * q^92 + 79136 * q^94 + 135000 * q^95 + 18432 * q^96 - 123520 * q^97 - 206240 * q^98 + 235252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more