LMFDB - Embedded newform 20.5.b.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,5,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, 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:	$2.06739926168$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.246034965625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 7x^{6} - 21x^{5} + 49x^{4} - 84x^{3} + 112x^{2} - 192x + 256 $ x^8 - 3x^7 + 7x^6 - 21x^5 + 49x^4 - 84x^3 + 112x^2 - 192*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.4
Root			$-0.641015 + 1.89449i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.5.b.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28203 + 3.78898i) q^{2} +8.14153i q^{3} +(-12.7128 - 9.71518i) q^{4} -11.1803 q^{5} +(-30.8481 - 10.4377i) q^{6} +63.6032i q^{7} +(53.1089 - 35.7134i) q^{8} +14.7155 q^{9} +O(q^{10})$	\(q+(-1.28203 + 3.78898i) q^{2} +8.14153i q^{3} +(-12.7128 - 9.71518i) q^{4} -11.1803 q^{5} +(-30.8481 - 10.4377i) q^{6} +63.6032i q^{7} +(53.1089 - 35.7134i) q^{8} +14.7155 q^{9} +(14.3335 - 42.3621i) q^{10} +33.3808i q^{11} +(79.0964 - 103.502i) q^{12} +274.487 q^{13} +(-240.992 - 81.5412i) q^{14} -91.0251i q^{15} +(67.2304 + 247.014i) q^{16} -284.950 q^{17} +(-18.8657 + 55.7568i) q^{18} +5.17988i q^{19} +(142.133 + 108.619i) q^{20} -517.827 q^{21} +(-126.479 - 42.7952i) q^{22} -584.740i q^{23} +(290.762 + 432.387i) q^{24} +125.000 q^{25} +(-351.900 + 1040.03i) q^{26} +779.271i q^{27} +(617.917 - 808.575i) q^{28} +344.135 q^{29} +(344.892 + 116.697i) q^{30} -1466.69i q^{31} +(-1022.12 - 61.9448i) q^{32} -271.771 q^{33} +(365.314 - 1079.67i) q^{34} -711.105i q^{35} +(-187.075 - 142.964i) q^{36} +1931.76 q^{37} +(-19.6265 - 6.64076i) q^{38} +2234.74i q^{39} +(-593.775 + 399.288i) q^{40} -976.795 q^{41} +(663.870 - 1962.04i) q^{42} +2045.47i q^{43} +(324.300 - 424.363i) q^{44} -164.524 q^{45} +(2215.57 + 749.654i) q^{46} +2561.74i q^{47} +(-2011.07 + 547.358i) q^{48} -1644.37 q^{49} +(-160.254 + 473.623i) q^{50} -2319.93i q^{51} +(-3489.49 - 2666.69i) q^{52} +121.922 q^{53} +(-2952.64 - 999.048i) q^{54} -373.209i q^{55} +(2271.49 + 3377.89i) q^{56} -42.1721 q^{57} +(-441.191 + 1303.92i) q^{58} -3456.33i q^{59} +(-884.325 + 1157.18i) q^{60} +4135.14 q^{61} +(5557.25 + 1880.34i) q^{62} +935.953i q^{63} +(1545.10 - 3793.40i) q^{64} -3068.86 q^{65} +(348.418 - 1029.73i) q^{66} -1694.07i q^{67} +(3622.51 + 2768.34i) q^{68} +4760.68 q^{69} +(2694.37 + 911.659i) q^{70} -7646.84i q^{71} +(781.524 - 525.541i) q^{72} -6008.30 q^{73} +(-2476.58 + 7319.41i) q^{74} +1017.69i q^{75} +(50.3235 - 65.8507i) q^{76} -2123.12 q^{77} +(-8467.40 - 2865.01i) q^{78} +4017.61i q^{79} +(-751.659 - 2761.70i) q^{80} -5152.50 q^{81} +(1252.28 - 3701.06i) q^{82} -3016.13i q^{83} +(6583.03 + 5030.79i) q^{84} +3185.84 q^{85} +(-7750.24 - 2622.35i) q^{86} +2801.79i q^{87} +(1192.14 + 1772.82i) q^{88} +1190.40 q^{89} +(210.925 - 623.380i) q^{90} +17458.2i q^{91} +(-5680.86 + 7433.68i) q^{92} +11941.1 q^{93} +(-9706.41 - 3284.23i) q^{94} -57.9128i q^{95} +(504.325 - 8321.66i) q^{96} -3021.43 q^{97} +(2108.13 - 6230.48i) q^{98} +491.215i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9}+O(q^{10}) $ 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9	$ 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9} - 50 q^{10} - 200 q^{12} + 352 q^{13} - 168 q^{14} - 272 q^{16} - 48 q^{17} + 286 q^{18} - 300 q^{20} + 16 q^{21} + 800 q^{22} + 1552 q^{24} + 1000 q^{25} - 2172 q^{26} + 40 q^{28} + 1200 q^{29} + 1400 q^{30} - 2304 q^{32} - 1120 q^{33} - 2132 q^{34} - 1044 q^{36} - 5728 q^{37} - 3360 q^{38} - 2200 q^{40} + 4896 q^{41} + 12120 q^{42} + 7920 q^{44} - 400 q^{45} + 728 q^{46} + 8640 q^{48} - 5768 q^{49} + 750 q^{50} - 12488 q^{52} + 2592 q^{53} - 17776 q^{54} + 48 q^{56} + 3840 q^{57} - 7428 q^{58} - 9800 q^{60} + 7936 q^{61} + 25680 q^{62} + 18880 q^{64} - 1200 q^{65} - 8080 q^{66} + 2712 q^{68} - 2256 q^{69} + 12000 q^{70} - 36264 q^{72} - 14448 q^{73} - 18492 q^{74} + 12000 q^{76} + 2400 q^{77} - 14480 q^{78} - 13200 q^{80} - 936 q^{81} + 27412 q^{82} + 50464 q^{84} + 11200 q^{85} - 7392 q^{86} + 18080 q^{88} + 23760 q^{89} + 19350 q^{90} - 52680 q^{92} + 11360 q^{93} - 43368 q^{94} + 2688 q^{96} - 4368 q^{97} - 21474 q^{98}+O(q^{100}) $ 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9 - 50 * q^10 - 200 * q^12 + 352 * q^13 - 168 * q^14 - 272 * q^16 - 48 * q^17 + 286 * q^18 - 300 * q^20 + 16 * q^21 + 800 * q^22 + 1552 * q^24 + 1000 * q^25 - 2172 * q^26 + 40 * q^28 + 1200 * q^29 + 1400 * q^30 - 2304 * q^32 - 1120 * q^33 - 2132 * q^34 - 1044 * q^36 - 5728 * q^37 - 3360 * q^38 - 2200 * q^40 + 4896 * q^41 + 12120 * q^42 + 7920 * q^44 - 400 * q^45 + 728 * q^46 + 8640 * q^48 - 5768 * q^49 + 750 * q^50 - 12488 * q^52 + 2592 * q^53 - 17776 * q^54 + 48 * q^56 + 3840 * q^57 - 7428 * q^58 - 9800 * q^60 + 7936 * q^61 + 25680 * q^62 + 18880 * q^64 - 1200 * q^65 - 8080 * q^66 + 2712 * q^68 - 2256 * q^69 + 12000 * q^70 - 36264 * q^72 - 14448 * q^73 - 18492 * q^74 + 12000 * q^76 + 2400 * q^77 - 14480 * q^78 - 13200 * q^80 - 936 * q^81 + 27412 * q^82 + 50464 * q^84 + 11200 * q^85 - 7392 * q^86 + 18080 * q^88 + 23760 * q^89 + 19350 * q^90 - 52680 * q^92 + 11360 * q^93 - 43368 * q^94 + 2688 * q^96 - 4368 * q^97 - 21474 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.28203	+	3.78898i	−0.320508	+	0.947246i
$2$	−1.28203	+	3.78898i	−0.320508	+	0.947246i
$3$			8.14153i			0.904614i	0.891862	+	0.452307i	$0.149399\pi$
$3$			8.14153i			0.904614i	−0.891862	+	0.452307i	$0.850601\pi$
$4$	−12.7128	−	9.71518i	−0.794550	−	0.607199i
$5$	−11.1803			−0.447214
$5$	−11.1803			−0.447214
$6$	−30.8481	−	10.4377i	−0.856892	−	0.289936i
$7$			63.6032i			1.29802i	0.760778	+	0.649012i	$0.224818\pi$
$7$			63.6032i			1.29802i	−0.760778	+	0.649012i	$0.775182\pi$
$8$	53.1089	−	35.7134i	0.829826	−	0.558022i
$9$	14.7155			0.181673
$10$	14.3335	−	42.3621i	0.143335	−	0.423621i
$11$			33.3808i			0.275874i	0.990441	+	0.137937i	$0.0440472\pi$
$11$			33.3808i			0.275874i	−0.990441	+	0.137937i	$0.955953\pi$
$12$	79.0964	−	103.502i	0.549281	−	0.718761i
$13$	274.487			1.62418			0.812091	−	0.583531i	$-0.198329\pi$
$13$	274.487			1.62418			0.812091	+	0.583531i	$0.198329\pi$
$14$	−240.992	−	81.5412i	−1.22955	−	0.416027i
$15$		−	91.0251i		−	0.404556i
$16$	67.2304	+	247.014i	0.262619	+	0.964900i
$17$	−284.950			−0.985986			−0.492993	−	0.870033i	$-0.664097\pi$
$17$	−284.950			−0.985986			−0.492993	+	0.870033i	$0.664097\pi$
$18$	−18.8657	+	55.7568i	−0.0582275	+	0.172089i
$19$			5.17988i			0.0143487i	0.999974	+	0.00717435i	$0.00228368\pi$
$19$			5.17988i			0.0143487i	−0.999974	+	0.00717435i	$0.997716\pi$
$20$	142.133	+	108.619i	0.355333	+	0.271548i
$21$	−517.827			−1.17421
$22$	−126.479	−	42.7952i	−0.261321	−	0.0884198i
$23$		−	584.740i		−	1.10537i	−0.833391	−	0.552684i	$-0.813603\pi$
$23$		−	584.740i		−	1.10537i	0.833391	−	0.552684i	$-0.186397\pi$
$24$	290.762	+	432.387i	0.504795	+	0.750672i
$25$	125.000			0.200000
$26$	−351.900	+	1040.03i	−0.520563	+	1.53850i
$27$			779.271i			1.06896i
$28$	617.917	−	808.575i	0.788159	−	1.03135i
$29$	344.135			0.409197			0.204599	−	0.978846i	$-0.434411\pi$
$29$	344.135			0.409197			0.204599	+	0.978846i	$0.434411\pi$
$30$	344.892	+	116.697i	0.383214	+	0.129663i
$31$		−	1466.69i		−	1.52621i	−0.646275	−	0.763105i	$-0.723674\pi$
$31$		−	1466.69i		−	1.52621i	0.646275	−	0.763105i	$-0.276326\pi$
$32$	−1022.12	−	61.9448i	−0.998169	−	0.0604930i
$33$	−271.771			−0.249560
$34$	365.314	−	1079.67i	0.316016	−	0.933971i
$35$		−	711.105i		−	0.580494i
$36$	−187.075	−	142.964i	−0.144348	−	0.110312i
$37$	1931.76			1.41107			0.705537	−	0.708673i	$-0.250706\pi$
$37$	1931.76			1.41107			0.705537	+	0.708673i	$0.250706\pi$
$38$	−19.6265	−	6.64076i	−0.0135917	−	0.00459886i
$39$			2234.74i			1.46926i
$40$	−593.775	+	399.288i	−0.371109	+	0.249555i
$41$	−976.795			−0.581080			−0.290540	−	0.956863i	$-0.593835\pi$
$41$	−976.795			−0.581080			−0.290540	+	0.956863i	$0.593835\pi$
$42$	663.870	−	1962.04i	0.376344	−	1.11227i
$43$			2045.47i			1.10626i	0.833096	+	0.553128i	$0.186566\pi$
$43$			2045.47i			1.10626i	−0.833096	+	0.553128i	$0.813434\pi$
$44$	324.300	−	424.363i	0.167511	−	0.219196i
$45$	−164.524			−0.0812466
$46$	2215.57	+	749.654i	1.04706	+	0.354279i
$47$			2561.74i			1.15969i	0.814728	+	0.579843i	$0.196886\pi$
$47$			2561.74i			1.15969i	−0.814728	+	0.579843i	$0.803114\pi$
$48$	−2011.07	+	547.358i	−0.872862	+	0.237569i
$49$	−1644.37			−0.684868
$50$	−160.254	+	473.623i	−0.0641015	+	0.189449i
$51$		−	2319.93i		−	0.891937i
$52$	−3489.49	−	2666.69i	−1.29049	−	0.986202i
$53$	121.922			0.0434041			0.0217020	−	0.999764i	$-0.493091\pi$
$53$	121.922			0.0434041			0.0217020	+	0.999764i	$0.493091\pi$
$54$	−2952.64	−	999.048i	−1.01257	−	0.342609i
$55$		−	373.209i		−	0.123375i
$56$	2271.49	+	3377.89i	0.724327	+	1.07713i
$57$	−42.1721			−0.0129800
$58$	−441.191	+	1303.92i	−0.131151	+	0.387611i
$59$		−	3456.33i		−	0.992913i	−0.868061	−	0.496457i	$-0.834634\pi$
$59$		−	3456.33i		−	0.992913i	0.868061	−	0.496457i	$-0.165366\pi$
$60$	−884.325	+	1157.18i	−0.245646	+	0.321440i
$61$	4135.14			1.11130			0.555649	−	0.831417i	$-0.312470\pi$
$61$	4135.14			1.11130			0.555649	+	0.831417i	$0.312470\pi$
$62$	5557.25	+	1880.34i	1.44570	+	0.489162i
$63$			935.953i			0.235816i
$64$	1545.10	−	3793.40i	0.377222	−	0.926123i
$65$	−3068.86			−0.726356
$66$	348.418	−	1029.73i	0.0799858	−	0.236395i
$67$		−	1694.07i		−	0.377383i	−0.982036	−	0.188692i	$-0.939575\pi$
$67$		−	1694.07i		−	0.377383i	0.982036	−	0.188692i	$-0.0604247\pi$
$68$	3622.51	+	2768.34i	0.783415	+	0.598690i
$69$	4760.68			0.999932
$70$	2694.37	+	911.659i	0.549871	+	0.186053i
$71$		−	7646.84i		−	1.51693i	−0.651715	−	0.758464i	$-0.725950\pi$
$71$		−	7646.84i		−	1.51693i	0.651715	−	0.758464i	$-0.274050\pi$
$72$	781.524	−	525.541i	0.150757	−	0.101378i
$73$	−6008.30			−1.12747			−0.563736	−	0.825955i	$-0.690636\pi$
$73$	−6008.30			−1.12747			−0.563736	+	0.825955i	$0.690636\pi$
$74$	−2476.58	+	7319.41i	−0.452260	+	1.33664i
$75$			1017.69i			0.180923i
$76$	50.3235	−	65.8507i	0.00871251	−	0.0114008i
$77$	−2123.12			−0.358092
$78$	−8467.40	−	2865.01i	−1.39175	−	0.470908i
$79$			4017.61i			0.643744i	0.946783	+	0.321872i	$0.104312\pi$
$79$			4017.61i			0.643744i	−0.946783	+	0.321872i	$0.895688\pi$
$80$	−751.659	−	2761.70i	−0.117447	−	0.431516i
$81$	−5152.50			−0.785322
$82$	1252.28	−	3701.06i	0.186240	−	0.550425i
$83$		−	3016.13i		−	0.437818i	−0.975745	−	0.218909i	$-0.929750\pi$
$83$		−	3016.13i		−	0.437818i	0.975745	−	0.218909i	$-0.0702498\pi$
$84$	6583.03	+	5030.79i	0.932970	+	0.712980i
$85$	3185.84			0.440946
$86$	−7750.24	−	2622.35i	−1.04790	−	0.354563i
$87$			2801.79i			0.370166i
$88$	1192.14	+	1772.82i	0.153944	+	0.228928i
$89$	1190.40			0.150284			0.0751421	−	0.997173i	$-0.476059\pi$
$89$	1190.40			0.150284			0.0751421	+	0.997173i	$0.476059\pi$
$90$	210.925	−	623.380i	0.0260401	−	0.0769605i
$91$			17458.2i			2.10823i
$92$	−5680.86	+	7433.68i	−0.671179	+	0.878271i
$93$	11941.1			1.38063
$94$	−9706.41	−	3284.23i	−1.09851	−	0.371688i
$95$		−	57.9128i		−	0.00641693i
$96$	504.325	−	8321.66i	0.0547228	−	0.902958i
$97$	−3021.43			−0.321122			−0.160561	−	0.987026i	$-0.551330\pi$
$97$	−3021.43			−0.321122			−0.160561	+	0.987026i	$0.551330\pi$
$98$	2108.13	−	6230.48i	0.219505	−	0.648738i
$99$			491.215i			0.0501189i
$100$	−1589.10	−	1214.40i	−0.158910	−	0.121440i
$101$	−754.479			−0.0739613			−0.0369806	−	0.999316i	$-0.511774\pi$
$101$	−754.479			−0.0739613			−0.0369806	+	0.999316i	$0.511774\pi$
$102$	8790.17	+	2974.22i	0.844884	+	0.285873i
$103$		−	2192.61i		−	0.206675i	−0.994646	−	0.103337i	$-0.967048\pi$
$103$		−	2192.61i		−	0.206675i	0.994646	−	0.103337i	$-0.0329521\pi$
$104$	14577.7	−	9802.86i	1.34779	−	0.906330i
$105$	5789.49			0.525123
$106$	−156.308	+	461.961i	−0.0139113	+	0.0411143i
$107$		−	13277.7i		−	1.15973i	−0.814713	−	0.579864i	$-0.803106\pi$
$107$		−	13277.7i		−	1.15973i	0.814713	−	0.579864i	$-0.196894\pi$
$108$	7570.76	−	9906.71i	0.649070	−	0.849341i
$109$	−11298.9			−0.951008			−0.475504	−	0.879714i	$-0.657734\pi$
$109$	−11298.9			−0.951008			−0.475504	+	0.879714i	$0.657734\pi$
$110$	1414.08	+	478.465i	0.116866	+	0.0395425i
$111$			15727.5i			1.27648i
$112$	−15710.9	+	4276.07i	−1.25246	+	0.340886i
$113$	−801.291			−0.0627528			−0.0313764	−	0.999508i	$-0.509989\pi$
$113$	−801.291			−0.0627528			−0.0313764	+	0.999508i	$0.509989\pi$
$114$	54.0659	−	159.789i	0.00416020	−	0.0122953i
$115$			6537.59i			0.494336i
$116$	−4374.92	−	3343.33i	−0.325128	−	0.248464i
$117$	4039.21			0.295070
$118$	13096.0	+	4431.12i	0.940533	+	0.318236i
$119$		−	18123.7i		−	1.27983i
$120$	−3250.82	−	4834.24i	−0.225751	−	0.335711i
$121$	13526.7			0.923893
$122$	−5301.37	+	15668.0i	−0.356179	+	1.05267i
$123$		−	7952.60i		−	0.525653i
$124$	−14249.1	+	18645.7i	−0.926713	+	1.21265i
$125$	−1397.54			−0.0894427
$126$	−3546.31	−	1199.92i	−0.223376	−	0.0755808i
$127$		−	12829.5i		−	0.795428i	−0.917510	−	0.397714i	$-0.869804\pi$
$127$		−	12829.5i		−	0.795428i	0.917510	−	0.397714i	$-0.130196\pi$
$128$	12392.3	+	10717.6i	0.756363	+	0.654152i
$129$	−16653.2			−1.00073
$130$	3934.37	−	11627.8i	0.232803	−	0.688038i
$131$			10711.7i			0.624189i	0.950051	+	0.312094i	$0.101031\pi$
$131$			10711.7i			0.624189i	−0.950051	+	0.312094i	$0.898969\pi$
$132$	3454.96	+	2640.30i	0.198288	+	0.151532i
$133$	−329.457			−0.0186250
$134$	6418.82	+	2171.85i	0.357475	+	0.120954i
$135$		−	8712.51i		−	0.478053i
$136$	−15133.4	+	10176.5i	−0.818197	+	0.550202i
$137$	−4859.57			−0.258915			−0.129457	−	0.991585i	$-0.541324\pi$
$137$	−4859.57			−0.258915			−0.129457	+	0.991585i	$0.541324\pi$
$138$	−6103.33	+	18038.1i	−0.320486	+	0.947182i
$139$			4641.90i			0.240252i	0.992759	+	0.120126i	$0.0383298\pi$
$139$			4641.90i			0.240252i	−0.992759	+	0.120126i	$0.961670\pi$
$140$	−6908.52	+	9040.14i	−0.352475	+	0.461232i
$141$	−20856.5			−1.04907
$142$	28973.7	+	9803.47i	1.43690	+	0.486187i
$143$			9162.58i			0.448070i
$144$	989.330	+	3634.94i	0.0477107	+	0.175296i
$145$	−3847.55			−0.182999
$146$	7702.82	−	22765.3i	0.361363	−	1.06799i
$147$		−	13387.7i		−	0.619541i
$148$	−24558.1	−	18767.4i	−1.12117	−	0.856803i
$149$	22750.7			1.02476			0.512380	−	0.858759i	$-0.328764\pi$
$149$	22750.7			1.02476			0.512380	+	0.858759i	$0.328764\pi$
$150$	−3856.02	−	1304.71i	−0.171378	−	0.0579871i
$151$		−	18142.5i		−	0.795688i	−0.917453	−	0.397844i	$-0.869759\pi$
$151$		−	18142.5i		−	0.795688i	0.917453	−	0.397844i	$-0.130241\pi$
$152$	184.991	+	275.097i	0.00800689	+	0.0119069i
$153$	−4193.18			−0.179127
$154$	2721.91	−	8044.49i	0.114771	−	0.339201i
$155$			16398.1i			0.682542i
$156$	21710.9	−	28409.8i	0.892132	−	1.16740i
$157$	−19382.1			−0.786322			−0.393161	−	0.919470i	$-0.628619\pi$
$157$	−19382.1			−0.786322			−0.393161	+	0.919470i	$0.628619\pi$
$158$	−15222.7	−	5150.69i	−0.609784	−	0.206325i
$159$			992.632i			0.0392639i
$160$	11427.7	+	692.564i	0.446395	+	0.0270533i
$161$	37191.3			1.43480
$162$	6605.66	−	19522.7i	0.251702	−	0.743893i
$163$		−	6821.93i		−	0.256763i	−0.991725	−	0.128381i	$-0.959022\pi$
$163$		−	6821.93i		−	0.256763i	0.991725	−	0.128381i	$-0.0409782\pi$
$164$	12417.8	+	9489.74i	0.461697	+	0.352831i
$165$	3038.49			0.111607
$166$	11428.1	+	3866.77i	0.414722	+	0.140324i
$167$			43577.2i			1.56252i	0.624203	+	0.781262i	$0.285424\pi$
$167$			43577.2i			1.56252i	−0.624203	+	0.781262i	$0.714576\pi$
$168$	−27501.2	+	18493.4i	−0.974391	+	0.655236i
$169$	46782.0			1.63797
$170$	−4084.34	+	12071.1i	−0.141327	+	0.417685i
$171$			76.2245i			0.00260677i
$172$	19872.1	−	26003.6i	0.671717	−	0.878975i
$173$	−14633.4			−0.488938			−0.244469	−	0.969657i	$-0.578614\pi$
$173$	−14633.4			−0.488938			−0.244469	+	0.969657i	$0.578614\pi$
$174$	−10615.9	−	3591.97i	−0.350638	−	0.118641i
$175$			7950.40i			0.259605i
$176$	−8245.53	+	2244.20i	−0.266191	+	0.0724498i
$177$	28139.8			0.898204
$178$	−1526.13	+	4510.41i	−0.0481672	+	0.142356i
$179$			2927.65i			0.0913721i	0.998956	+	0.0456860i	$0.0145474\pi$
$179$			2927.65i			0.0913721i	−0.998956	+	0.0456860i	$0.985453\pi$
$180$	2091.56	+	1598.38i	0.0645545	+	0.0493328i
$181$	−8172.78			−0.249467			−0.124733	−	0.992190i	$-0.539808\pi$
$181$	−8172.78			−0.249467			−0.124733	+	0.992190i	$0.539808\pi$
$182$	−66149.0	−	22382.0i	−1.99701	−	0.675703i
$183$			33666.3i			1.00530i
$184$	−20883.1	−	31054.9i	−0.616820	−	0.917264i
$185$	−21597.8			−0.631052
$186$	−15308.8	+	45244.5i	−0.442503	+	1.30780i
$187$		−	9511.85i		−	0.272008i
$188$	24887.8	−	32566.9i	0.704160	−	0.921428i
$189$	−49564.1			−1.38753
$190$	219.431	+	74.2459i	0.00607841	+	0.00205667i
$191$		−	21087.5i		−	0.578041i	−0.957323	−	0.289020i	$-0.906670\pi$
$191$		−	21087.5i		−	0.578041i	0.957323	−	0.289020i	$-0.0933295\pi$
$192$	30884.1	+	12579.5i	0.837784	+	0.341241i
$193$	−41681.9			−1.11901			−0.559504	−	0.828827i	$-0.689008\pi$
$193$	−41681.9			−1.11901			−0.559504	+	0.828827i	$0.689008\pi$
$194$	3873.57	−	11448.2i	0.102922	−	0.304181i
$195$		−	24985.2i		−	0.657072i
$196$	20904.5	+	15975.3i	0.544162	+	0.415851i
$197$	−20183.4			−0.520071			−0.260035	−	0.965599i	$-0.583734\pi$
$197$	−20183.4			−0.520071			−0.260035	+	0.965599i	$0.583734\pi$
$198$	−1861.21	−	629.752i	−0.0474749	−	0.0160635i
$199$			43122.7i			1.08893i	0.838784	+	0.544465i	$0.183267\pi$
$199$			43122.7i			1.08893i	−0.838784	+	0.544465i	$0.816733\pi$
$200$	6638.61	−	4464.18i	0.165965	−	0.111604i
$201$	13792.4			0.341387
$202$	967.265	−	2858.71i	0.0237051	−	0.0700595i
$203$			21888.1i			0.531148i
$204$	−22538.5	+	29492.8i	−0.541583	+	0.708688i
$205$	10920.9			0.259867
$206$	8307.76	+	2810.99i	0.195772	+	0.0662407i
$207$		−	8604.74i		−	0.200816i
$208$	18453.9	+	67802.2i	0.426541	+	1.56717i
$209$	−172.908			−0.00395843
$210$	−7422.30	+	21936.3i	−0.168306	+	0.497421i
$211$		−	78286.9i		−	1.75843i	−0.476429	−	0.879213i	$-0.658069\pi$
$211$		−	78286.9i		−	1.75843i	0.476429	−	0.879213i	$-0.341931\pi$
$212$	−1549.97	−	1184.49i	−0.0344867	−	0.0263549i
$213$	62256.9			1.37224
$214$	50309.1	+	17022.4i	1.09855	+	0.371702i
$215$		−	22869.0i		−	0.494733i
$216$	27830.4	+	41386.2i	0.596502	+	0.887049i
$217$	93286.0			1.98106
$218$	14485.6	−	42811.4i	0.304805	−	0.900838i
$219$		−	48916.7i		−	1.01993i
$220$	−3625.79	+	4744.52i	−0.0749130	+	0.0980274i
$221$	−78215.0			−1.60142
$222$	−59591.2	−	20163.1i	−1.20914	−	0.409121i
$223$		−	80052.1i		−	1.60977i	−0.593432	−	0.804884i	$-0.702228\pi$
$223$		−	80052.1i		−	1.60977i	0.593432	−	0.804884i	$-0.297772\pi$
$224$	3939.89	−	65010.4i	0.0785214	−	1.29565i
$225$	1839.44			0.0363346
$226$	1027.28	−	3036.08i	0.0201127	−	0.0594423i
$227$			96596.3i			1.87460i	0.348522	+	0.937301i	$0.386684\pi$
$227$			96596.3i			1.87460i	−0.348522	+	0.937301i	$0.613316\pi$
$228$	536.126	+	409.710i	0.0103133	+	0.00788146i
$229$	−45904.6			−0.875357			−0.437679	−	0.899131i	$-0.644199\pi$
$229$	−45904.6			−0.875357			−0.437679	+	0.899131i	$0.644199\pi$
$230$	−24770.8	−	8381.39i	−0.468258	−	0.158438i
$231$		−	17285.5i		−	0.323935i
$232$	18276.6	−	12290.2i	0.339563	−	0.228341i
$233$	48534.0			0.893993			0.446997	−	0.894536i	$-0.352494\pi$
$233$	48534.0			0.893993			0.446997	+	0.894536i	$0.352494\pi$
$234$	−5178.39	+	15304.5i	−0.0945721	+	0.279504i
$235$		−	28641.2i		−	0.518627i
$236$	−33578.9	+	43939.6i	−0.602896	+	0.788919i
$237$	−32709.5			−0.582340
$238$	68670.5	+	23235.2i	1.21232	+	0.410196i
$239$			5241.47i			0.0917608i	0.998947	+	0.0458804i	$0.0146093\pi$
$239$			5241.47i			0.0917608i	−0.998947	+	0.0458804i	$0.985391\pi$
$240$	22484.5	−	6119.65i	0.390356	−	0.106244i
$241$	−46204.2			−0.795513			−0.397756	−	0.917491i	$-0.630211\pi$
$241$	−46204.2			−0.795513			−0.397756	+	0.917491i	$0.630211\pi$
$242$	−17341.7	+	51252.5i	−0.296115	+	0.875154i
$243$			21171.7i			0.358545i
$244$	−52569.2	−	40173.6i	−0.882981	−	0.674779i
$245$	18384.6			0.306282
$246$	30132.3	+	10195.5i	0.497923	+	0.168476i
$247$			1421.81i			0.0233049i
$248$	−52380.4	−	77894.1i	−0.851659	−	1.26649i
$249$	24555.9			0.396057
$250$	1791.69	−	5295.27i	0.0286671	−	0.0847243i
$251$			67180.8i			1.06635i	0.846006	+	0.533173i	$0.179000\pi$
$251$			67180.8i			1.06635i	−0.846006	+	0.533173i	$0.821000\pi$
$252$	9092.96	−	11898.6i	0.143187	−	0.187367i
$253$	19519.1			0.304943
$254$	48610.6	+	16447.7i	0.753466	+	0.254941i
$255$			25937.6i			0.398886i
$256$	−56496.1	+	33213.8i	−0.862063	+	0.506802i
$257$	−69998.4			−1.05979			−0.529897	−	0.848062i	$-0.677770\pi$
$257$	−69998.4			−1.05979			−0.529897	+	0.848062i	$0.677770\pi$
$258$	21349.9	−	63098.8i	0.320743	−	0.947942i
$259$			122866.i			1.83161i
$260$	39013.7	+	29814.5i	0.577126	+	0.441043i
$261$	5064.12			0.0743401
$262$	−40586.5	−	13732.7i	−0.591260	−	0.200057i
$263$			1033.64i			0.0149438i	0.999972	+	0.00747188i	$0.00237839\pi$
$263$			1033.64i			0.0149438i	−0.999972	+	0.00747188i	$0.997622\pi$
$264$	−14433.4	+	9705.86i	−0.207091	+	0.139260i
$265$	−1363.13			−0.0194109
$266$	422.374	−	1248.31i	0.00596944	−	0.0176424i
$267$			9691.69i			0.135949i
$268$	−16458.2	+	21536.4i	−0.229147	+	0.299850i
$269$	92501.0			1.27833			0.639163	−	0.769071i	$-0.279281\pi$
$269$	92501.0			1.27833			0.639163	+	0.769071i	$0.279281\pi$
$270$	33011.6	+	11169.7i	0.452833	+	0.153219i
$271$			16540.1i			0.225216i	0.993640	+	0.112608i	$0.0359204\pi$
$271$			16540.1i			0.225216i	−0.993640	+	0.112608i	$0.964080\pi$
$272$	−19157.3	−	70386.7i	−0.258938	−	0.951377i
$273$	−142137.			−1.90713
$274$	6230.12	−	18412.8i	0.0829842	−	0.245256i
$275$			4172.60i			0.0551748i
$276$	−60521.5	−	46250.9i	−0.794496	−	0.607158i
$277$	28924.4			0.376968			0.188484	−	0.982076i	$-0.439643\pi$
$277$	28924.4			0.376968			0.188484	+	0.982076i	$0.439643\pi$
$278$	−17588.1	−	5951.06i	−0.227577	−	0.0770025i
$279$		−	21583.0i		−	0.277271i
$280$	−25396.0	−	37766.0i	−0.323929	−	0.481709i
$281$	141788.			1.79567			0.897837	−	0.440329i	$-0.145138\pi$
$281$	141788.			1.79567			0.897837	+	0.440329i	$0.145138\pi$
$282$	26738.7	−	79025.0i	0.336234	−	0.993725i
$283$		−	3926.64i		−	0.0490284i	−0.999699	−	0.0245142i	$-0.992196\pi$
$283$		−	3926.64i		−	0.0490284i	0.999699	−	0.0245142i	$-0.00780390\pi$
$284$	−74290.4	+	97212.7i	−0.921077	+	1.20528i
$285$	471.499			0.00580485
$286$	−34716.9	−	11746.7i	−0.424433	−	0.143610i
$287$		−	62127.3i		−	0.754256i
$288$	−15041.1	−	911.549i	−0.181340	−	0.0109899i
$289$	−2324.55			−0.0278319
$290$	4932.67	−	14578.3i	0.0586524	−	0.173345i
$291$		−	24599.1i		−	0.290491i
$292$	76382.3	+	58371.7i	0.895833	+	0.684600i
$293$	152172.			1.77255			0.886275	−	0.463160i	$-0.153285\pi$
$293$	152172.			1.77255			0.886275	+	0.463160i	$0.153285\pi$
$294$	50725.6	+	17163.4i	0.586858	+	0.198568i
$295$			38643.0i			0.444044i
$296$	102594.	−	68989.8i	1.17095	−	0.787411i
$297$	−26012.7			−0.294898
$298$	−29167.1	+	86202.0i	−0.328443	+	0.970700i
$299$		−	160503.i		−	1.79532i
$300$	9887.06	−	12937.7i	0.109856	−	0.143752i
$301$	−130098.			−1.43595
$302$	68741.6	+	23259.2i	0.753712	+	0.255024i
$303$		−	6142.61i		−	0.0669064i
$304$	−1279.50	+	348.245i	−0.0138450	+	0.00376824i
$305$	−46232.2			−0.496987
$306$	5375.78	−	15887.9i	0.0574115	−	0.169677i
$307$		−	16244.2i		−	0.172355i	−0.996280	−	0.0861773i	$-0.972535\pi$
$307$		−	16244.2i		−	0.172355i	0.996280	−	0.0861773i	$-0.0274651\pi$
$308$	26990.9	+	20626.5i	0.284522	+	0.217433i
$309$	17851.2			0.186961
$310$	−62132.0	−	21022.8i	−0.646535	−	0.218760i
$311$			76317.7i			0.789050i	0.918885	+	0.394525i	$0.129091\pi$
$311$			76317.7i			0.789050i	−0.918885	+	0.394525i	$0.870909\pi$
$312$	79810.3	+	118685.i	0.819879	+	1.21923i
$313$	−90079.4			−0.919469			−0.459734	−	0.888057i	$-0.652055\pi$
$313$	−90079.4			−0.919469			−0.459734	+	0.888057i	$0.652055\pi$
$314$	24848.4	−	73438.3i	0.252022	−	0.744841i
$315$		−	10464.3i		−	0.105460i
$316$	39031.8	−	51075.0i	0.390881	−	0.511487i
$317$	−63383.9			−0.630755			−0.315377	−	0.948966i	$-0.602131\pi$
$317$	−63383.9			−0.630755			−0.315377	+	0.948966i	$0.602131\pi$
$318$	−3761.07	−	1272.58i	−0.0371926	−	0.0125844i
$319$			11487.5i			0.112887i
$320$	−17274.8	+	42411.5i	−0.168699	+	0.414175i
$321$	108101.			1.04911
$322$	−47680.4	+	140917.i	−0.459863	+	1.35910i
$323$		−	1476.01i		−	0.0141476i
$324$	65502.7	+	50057.5i	0.623978	+	0.476847i
$325$	34310.8			0.324836
$326$	25848.2	+	8745.92i	0.243217	+	0.0822944i
$327$		−	91990.5i		−	0.860295i
$328$	−51876.5	+	34884.7i	−0.482195	+	0.324255i
$329$	−162935.			−1.50530
$330$	−3895.43	+	11512.8i	−0.0357707	+	0.105719i
$331$		−	70436.2i		−	0.642895i	−0.946927	−	0.321448i	$-0.895831\pi$
$331$		−	70436.2i		−	0.642895i	0.946927	−	0.321448i	$-0.104169\pi$
$332$	−29302.3	+	38343.5i	−0.265843	+	0.347869i
$333$	28426.8			0.256354
$334$	−165113.	−	55867.3i	−1.48010	−	0.500801i
$335$			18940.3i			0.168771i
$336$	−34813.8	−	127911.i	−0.308370	−	1.13300i
$337$	23577.5			0.207605			0.103802	−	0.994598i	$-0.466899\pi$
$337$	23577.5			0.207605			0.103802	+	0.994598i	$0.466899\pi$
$338$	−59975.9	+	177256.i	−0.524981	+	1.55156i
$339$		−	6523.73i		−	0.0567671i
$340$	−40500.9	−	30951.0i	−0.350354	−	0.267742i
$341$	48959.2			0.421042
$342$	−288.813	−	97.7221i	−0.00246925	−	0.000835489i
$343$			48124.3i			0.409049i
$344$	73050.6	+	108632.i	0.617315	+	0.918000i
$345$	−53226.0			−0.447183
$346$	18760.5	−	55445.8i	0.156708	−	0.463145i
$347$		−	121680.i		−	1.01056i	−0.862956	−	0.505280i	$-0.831389\pi$
$347$		−	121680.i		−	1.01056i	0.862956	−	0.505280i	$-0.168611\pi$
$348$	27219.9	−	35618.5i	0.224764	−	0.294115i
$349$	−14140.9			−0.116098			−0.0580491	−	0.998314i	$-0.518488\pi$
$349$	−14140.9			−0.116098			−0.0580491	+	0.998314i	$0.518488\pi$
$350$	−30123.9	−	10192.7i	−0.245910	−	0.0832053i
$351$			213899.i			1.73618i
$352$	2067.77	−	34119.3i	0.0166885	−	0.275369i
$353$	−226940.			−1.82122			−0.910608	−	0.413271i	$-0.864386\pi$
$353$	−226940.			−1.82122			−0.910608	+	0.413271i	$0.864386\pi$
$354$	−36076.1	+	106621.i	−0.287881	+	0.850820i
$355$			85494.2i			0.678391i
$356$	−15133.3	−	11565.0i	−0.119408	−	0.0912524i
$357$	147555.			1.15776
$358$	−11092.8	−	3753.34i	−0.0865519	−	0.0292854i
$359$		−	183457.i		−	1.42346i	−0.702452	−	0.711731i	$-0.747911\pi$
$359$		−	183457.i		−	1.42346i	0.702452	−	0.711731i	$-0.252089\pi$
$360$	−8737.70	+	5875.73i	−0.0674205	+	0.0453374i
$361$	130294.			0.999794
$362$	10477.8	−	30966.5i	0.0799560	−	0.236306i
$363$			110128.i			0.835767i
$364$	169610.	−	221943.i	1.28011	−	1.67509i
$365$	67174.8			0.504221
$366$	−127561.	−	43161.3i	−0.952262	−	0.322205i
$367$		−	94098.0i		−	0.698632i	−0.937005	−	0.349316i	$-0.886414\pi$
$367$		−	94098.0i		−	0.698632i	0.937005	−	0.349316i	$-0.113586\pi$
$368$	144439.	−	39312.3i	1.06657	−	0.290291i
$369$	−14374.0			−0.105566
$370$	27689.0	−	81833.5i	0.202257	−	0.597761i
$371$			7754.63i			0.0563395i
$372$	−151804.	−	116010.i	−1.09698	−	0.838318i
$373$	123826.			0.890010			0.445005	−	0.895528i	$-0.353202\pi$
$373$	123826.			0.890010			0.445005	+	0.895528i	$0.353202\pi$
$374$	36040.3	+	12194.5i	0.257659	+	0.0871806i
$375$		−	11378.1i		−	0.0809112i
$376$	91488.7	+	136051.i	0.647130	+	0.962337i
$377$	94460.5			0.664611
$378$	63542.7	−	187798.i	0.444715	−	1.31434i
$379$			282818.i			1.96892i	0.175609	+	0.984460i	$0.443811\pi$
$379$			282818.i			1.96892i	−0.175609	+	0.984460i	$0.556189\pi$
$380$	−562.633	+	736.234i	−0.00389635	+	0.00509857i
$381$	104451.			0.719555
$382$	79900.2	+	27034.8i	0.547547	+	0.185266i
$383$			69105.5i			0.471102i	0.971862	+	0.235551i	$0.0756895\pi$
$383$			69105.5i			0.471102i	−0.971862	+	0.235551i	$0.924311\pi$
$384$	−87257.8	+	100892.i	−0.591755	+	0.684217i
$385$	23737.3			0.160143
$386$	53437.5	−	157932.i	0.358651	−	1.05998i
$387$			30100.1i			0.200977i
$388$	38410.9	+	29353.8i	0.255147	+	0.194985i
$389$	−28018.1			−0.185157			−0.0925783	−	0.995705i	$-0.529511\pi$
$389$	−28018.1			−0.185157			−0.0925783	+	0.995705i	$0.529511\pi$
$390$	94668.4	+	32031.8i	0.622409	+	0.210597i
$391$			166622.i			1.08988i
$392$	−87330.5	+	58726.0i	−0.568321	+	0.382171i
$393$	−87209.6			−0.564650
$394$	25875.8	−	76474.7i	0.166687	−	0.492635i
$395$		−	44918.2i		−	0.287891i
$396$	4772.24	−	6244.72i	0.0304321	−	0.0398219i
$397$	−261226.			−1.65743			−0.828715	−	0.559671i	$-0.810928\pi$
$397$	−261226.			−1.65743			−0.828715	+	0.559671i	$0.810928\pi$
$398$	−163391.	−	55284.6i	−1.03148	−	0.349010i
$399$		−	2682.28i		−	0.0168484i
$400$	8403.80	+	30876.8i	0.0525238	+	0.192980i
$401$	−301385.			−1.87427			−0.937135	−	0.348967i	$-0.886533\pi$
$401$	−301385.			−1.87427			−0.937135	+	0.348967i	$0.886533\pi$
$402$	−17682.2	+	52259.0i	−0.109417	+	0.323377i
$403$		−	402586.i		−	2.47884i
$404$	9591.54	+	7329.90i	0.0587659	+	0.0449092i
$405$	57606.7			0.351207
$406$	−82933.6	−	28061.2i	−0.503128	−	0.170237i
$407$			64483.7i			0.389279i
$408$	−82852.6	−	123209.i	−0.497721	−	0.740152i
$409$	306327.			1.83121			0.915605	−	0.402079i	$-0.131712\pi$
$409$	306327.			1.83121			0.915605	+	0.402079i	$0.131712\pi$
$410$	−14000.9	+	41379.1i	−0.0832892	+	0.246158i
$411$		−	39564.4i		−	0.234218i
$412$	−21301.6	+	27874.2i	−0.125493	+	0.164213i
$413$	219834.			1.28883
$414$	32603.2	+	11031.5i	0.190222	+	0.0643629i
$415$			33721.4i			0.195798i
$416$	−280560.	−	17003.0i	−1.62121	−	0.0982516i
$417$	−37792.2			−0.217335
$418$	221.674	−	655.147i	0.00126871	−	0.00374961i
$419$			13132.1i			0.0748007i	0.999300	+	0.0374003i	$0.0119077\pi$
$419$			13132.1i			0.0748007i	−0.999300	+	0.0374003i	$0.988092\pi$
$420$	−73600.6	−	56245.9i	−0.417237	−	0.318854i
$421$	−189597.			−1.06971			−0.534856	−	0.844943i	$-0.679634\pi$
$421$	−189597.			−1.06971			−0.534856	+	0.844943i	$0.679634\pi$
$422$	296628.	+	100366.i	1.66566	+	0.563589i
$423$			37697.4i			0.210683i
$424$	6475.14	−	4354.25i	0.0360178	−	0.0242204i
$425$	−35618.7			−0.197197
$426$	−79815.3	+	235891.i	−0.439812	+	1.29984i
$427$			263008.i			1.44249i
$428$	−128996.	+	168797.i	−0.704186	+	0.921462i
$429$	−74597.4			−0.405331
$430$	86650.3	+	29318.8i	0.468633	+	0.158566i
$431$		−	312114.i		−	1.68019i	−0.542440	−	0.840095i	$-0.682499\pi$
$431$		−	312114.i		−	1.68019i	0.542440	−	0.840095i	$-0.317501\pi$
$432$	−192491.	+	52390.7i	−1.03144	+	0.280729i
$433$	84490.5			0.450642			0.225321	−	0.974285i	$-0.427657\pi$
$433$	84490.5			0.450642			0.225321	+	0.974285i	$0.427657\pi$
$434$	−119595.	+	353459.i	−0.634944	+	1.87655i
$435$		−	31324.9i		−	0.165543i
$436$	143641.	+	109771.i	0.755623	+	0.577451i
$437$	3028.88			0.0158606
$438$	185345.	+	62712.7i	0.966122	+	0.326894i
$439$		−	89602.9i		−	0.464936i	−0.972604	−	0.232468i	$-0.925320\pi$
$439$		−	89602.9i		−	0.464936i	0.972604	−	0.232468i	$-0.0746801\pi$
$440$	−13328.6	−	19820.7i	−0.0688458	−	0.102380i
$441$	−24197.7			−0.124422
$442$	100274.	−	296355.i	0.513267	−	1.51694i
$443$			81699.7i			0.416306i	0.978096	+	0.208153i	$0.0667452\pi$
$443$			81699.7i			0.416306i	−0.978096	+	0.208153i	$0.933255\pi$
$444$	152795.	−	199940.i	0.775077	−	1.01423i
$445$	−13309.1			−0.0672091
$446$	303316.	+	102629.i	1.52485	+	0.515943i
$447$			185225.i			0.927013i
$448$	241272.	+	98273.5i	1.20213	+	0.489644i
$449$	−153375.			−0.760787			−0.380393	−	0.924825i	$-0.624211\pi$
$449$	−153375.			−0.760787			−0.380393	+	0.924825i	$0.624211\pi$
$450$	−2358.21	+	6969.60i	−0.0116455	+	0.0344178i
$451$		−	32606.2i		−	0.160305i
$452$	10186.6	+	7784.68i	0.0498602	+	0.0381034i
$453$	147708.			0.719791
$454$	−366002.	−	123839.i	−1.77571	−	0.600824i
$455$		−	195189.i		−	0.942828i
$456$	−2239.71	+	1506.11i	−0.0107712	+	0.00724315i
$457$	−107730.			−0.515829			−0.257915	−	0.966168i	$-0.583035\pi$
$457$	−107730.			−0.515829			−0.257915	+	0.966168i	$0.583035\pi$
$458$	58851.1	−	173932.i	0.280559	−	0.829179i
$459$		−	222053.i		−	1.05398i
$460$	63513.9	−	83111.1i	0.300160	−	0.392775i
$461$	−130855.			−0.615729			−0.307865	−	0.951430i	$-0.599614\pi$
$461$	−130855.			−0.615729			−0.307865	+	0.951430i	$0.599614\pi$
$462$	65494.4	+	22160.5i	0.306846	+	0.103824i
$463$		−	265844.i		−	1.24012i	−0.784552	−	0.620062i	$-0.787107\pi$
$463$		−	265844.i		−	1.24012i	0.784552	−	0.620062i	$-0.212893\pi$
$464$	23136.3	+	85006.3i	0.107463	+	0.394834i
$465$	−133505.			−0.617437
$466$	−62222.1	+	183895.i	−0.286532	+	0.846832i
$467$		−	242239.i		−	1.11073i	−0.831605	−	0.555367i	$-0.812578\pi$
$467$		−	242239.i		−	1.11073i	0.831605	−	0.555367i	$-0.187422\pi$
$468$	−51349.7	−	39241.7i	−0.234448	−	0.179166i
$469$	107749.			0.489853
$470$	108521.	+	36718.9i	0.491267	+	0.166224i
$471$		−	157800.i		−	0.711318i
$472$	−123437.	−	183562.i	−0.554068	−	0.823945i
$473$	−68279.3			−0.305187
$474$	41934.5	−	123936.i	0.186644	−	0.551619i
$475$			647.485i			0.00286974i
$476$	−176075.	+	230403.i	−0.777114	+	1.01689i
$477$	1794.14			0.00788534
$478$	−19859.8	−	6719.72i	−0.0869200	−	0.0294100i
$479$			335632.i			1.46282i	0.681935	+	0.731412i	$0.261138\pi$
$479$			335632.i			1.46282i	−0.681935	+	0.731412i	$0.738862\pi$
$480$	−5638.53	+	93039.0i	−0.0244728	+	0.403815i
$481$	530243.			2.29184
$482$	59235.2	−	175067.i	0.254968	−	0.753546i
$483$			302794.i			1.29794i
$484$	−171962.	−	131415.i	−0.734079	−	0.560987i
$485$	33780.7			0.143610
$486$	−80219.2	−	27142.8i	−0.339630	−	0.114916i
$487$		−	17852.3i		−	0.0752725i	−0.999292	−	0.0376363i	$-0.988017\pi$
$487$		−	17852.3i		−	0.0752725i	0.999292	−	0.0376363i	$-0.0119828\pi$
$488$	219612.	−	147680.i	0.922184	−	0.620129i
$489$	55540.9			0.232271
$490$	−23569.6	+	69658.9i	−0.0981657	+	0.290125i
$491$			138734.i			0.575466i	0.957711	+	0.287733i	$0.0929016\pi$
$491$			138734.i			0.575466i	−0.957711	+	0.287733i	$0.907098\pi$
$492$	−77261.0	+	101100.i	−0.319176	+	0.417657i
$493$	−98061.2			−0.403463
$494$	−5387.21	−	1822.80i	−0.0220755	−	0.00746939i
$495$		−	5491.95i		−	0.0224138i
$496$	362293.	−	98606.0i	1.47264	−	0.400811i
$497$	486363.			1.96901
$498$	−31481.4	+	93042.0i	−0.126939	+	0.375163i
$499$			175457.i			0.704644i	0.935879	+	0.352322i	$0.114608\pi$
$499$			175457.i			0.704644i	−0.935879	+	0.352322i	$0.885392\pi$
$500$	17766.7	+	13577.4i	0.0710667	+	0.0543095i
$501$	−354785.			−1.41348
$502$	−254547.	−	86127.9i	−1.01009	−	0.341772i
$503$			244670.i			0.967040i	0.875333	+	0.483520i	$0.160642\pi$
$503$			244670.i			0.967040i	−0.875333	+	0.483520i	$0.839358\pi$
$504$	33426.1	+	49707.4i	0.131590	+	0.195686i
$505$	8435.33			0.0330765
$506$	−25024.1	+	73957.5i	−0.0977365	+	0.288856i
$507$			380877.i			1.48173i
$508$	−124640.	+	163098.i	−0.482983	+	0.632007i
$509$	−173309.			−0.668937			−0.334469	−	0.942407i	$-0.608557\pi$
$509$	−173309.			−0.668937			−0.334469	+	0.942407i	$0.608557\pi$
$510$	−98277.1	−	33252.8i	−0.377843	−	0.127846i
$511$		−	382147.i		−	1.46349i
$512$	−53416.6	−	256644.i	−0.203768	−	0.979019i
$513$	−4036.53			−0.0153382
$514$	89740.0	−	265223.i	0.339672	−	1.00389i
$515$			24514.1i			0.0924277i
$516$	211709.	+	161789.i	0.795134	+	0.607645i
$517$	−85513.1			−0.319927
$518$	−465538.	−	157518.i	−1.73499	−	0.587045i
$519$		−	119139.i		−	0.442301i
$520$	−162983.	+	109599.i	−0.602749	+	0.405323i
$521$	218395.			0.804578			0.402289	−	0.915513i	$-0.368215\pi$
$521$	218395.			0.804578			0.402289	+	0.915513i	$0.368215\pi$
$522$	−6492.35	+	19187.9i	−0.0238266	+	0.0704183i
$523$			137830.i			0.503897i	0.967741	+	0.251949i	$0.0810714\pi$
$523$			137830.i			0.503897i	−0.967741	+	0.251949i	$0.918929\pi$
$524$	104066.	−	136176.i	0.379007	−	0.495949i
$525$	−64728.4			−0.234842
$526$	−3916.46	−	1325.16i	−0.0141554	−	0.00478959i
$527$			417932.i			1.50482i
$528$	−18271.3	−	67131.2i	−0.0655391	−	0.240800i
$529$	−62080.0			−0.221840
$530$	1747.57	−	5164.88i	0.00622134	−	0.0183869i
$531$		−	50861.7i		−	0.180385i
$532$	4188.32	+	3200.73i	0.0147985	+	0.0113091i
$533$	−268117.			−0.943779
$534$	−36721.6	−	12425.0i	−0.128777	−	0.0435728i
$535$			148450.i			0.518646i
$536$	−60501.2	−	89970.4i	−0.210588	−	0.313163i
$537$	−23835.6			−0.0826565
$538$	−118589.	+	350485.i	−0.409713	+	1.21089i
$539$		−	54890.3i		−	0.188937i
$540$	−84643.6	+	110760.i	−0.290273	+	0.379837i
$541$	−311998.			−1.06600			−0.533000	−	0.846115i	$-0.678935\pi$
$541$	−311998.			−1.06600			−0.533000	+	0.846115i	$0.678935\pi$
$542$	−62670.0	−	21204.9i	−0.213335	−	0.0721833i
$543$		−	66538.9i		−	0.225671i
$544$	291254.	+	17651.2i	0.984180	+	0.0596452i
$545$	126326.			0.425304
$546$	182224.	−	538554.i	0.611251	−	1.80652i
$547$		−	275725.i		−	0.921513i	−0.887527	−	0.460757i	$-0.847578\pi$
$547$		−	275725.i		−	0.921513i	0.887527	−	0.460757i	$-0.152422\pi$
$548$	61778.8	+	47211.6i	0.205721	+	0.157213i
$549$	60850.6			0.201893
$550$	−15809.9	−	5349.40i	−0.0522642	−	0.0176840i
$551$			1782.58i			0.00587145i
$552$	252834.	−	170020.i	0.829770	−	0.557985i
$553$	−255533.			−0.835596
$554$	−37082.0	+	109594.i	−0.120821	+	0.357082i
$555$		−	175839.i		−	0.570859i
$556$	45096.9	−	59011.6i	0.145881	−	0.190892i
$557$	301922.			0.973161			0.486580	−	0.873636i	$-0.338244\pi$
$557$	301922.			0.973161			0.486580	+	0.873636i	$0.338244\pi$
$558$	81777.8	+	27670.1i	0.262644	+	0.0888674i
$559$			561454.i			1.79676i
$560$	175653.	−	47807.9i	0.560119	−	0.152449i
$561$	77441.0			0.246062
$562$	−181777.	+	537233.i	−0.575527	+	1.70094i
$563$		−	198587.i		−	0.626518i	−0.949668	−	0.313259i	$-0.898579\pi$
$563$		−	198587.i		−	0.626518i	0.949668	−	0.313259i	$-0.101421\pi$
$564$	265145.	+	202625.i	0.833537	+	0.636993i
$565$	8958.70			0.0280639
$566$	14878.0	+	5034.07i	0.0464420	+	0.0157140i
$567$		−	327715.i		−	1.01937i
$568$	−273095.	−	406115.i	−0.846480	−	1.25879i
$569$	363936.			1.12409			0.562044	−	0.827107i	$-0.310015\pi$
$569$	363936.			1.12409			0.562044	+	0.827107i	$0.310015\pi$
$570$	−604.476	+	1786.50i	−0.00186050	+	0.00549862i
$571$		−	303041.i		−	0.929455i	−0.885454	−	0.464728i	$-0.846152\pi$
$571$		−	303041.i		−	0.929455i	0.885454	−	0.464728i	$-0.153848\pi$
$572$	89016.2	−	116482.i	0.272068	−	0.356014i
$573$	171685.			0.522904
$574$	235399.	+	79649.0i	0.714465	+	0.241745i
$575$		−	73092.5i		−	0.221074i
$576$	22737.0	−	55821.8i	0.0685311	−	0.168251i
$577$	210571.			0.632479			0.316240	−	0.948679i	$-0.397580\pi$
$577$	210571.			0.632479			0.316240	+	0.948679i	$0.397580\pi$
$578$	2980.14	−	8807.68i	0.00892034	−	0.0263637i
$579$		−	339355.i		−	1.01227i
$580$	48913.1	+	37379.6i	0.145402	+	0.111117i
$581$	191836.			0.568299
$582$	93205.5	+	31536.8i	0.275167	+	0.0931046i
$583$			4069.85i			0.0119741i
$584$	−319094.	+	214577.i	−0.935605	+	0.629154i
$585$	−45159.8			−0.131959
$586$	−195089.	+	576576.i	−0.568115	+	1.67904i
$587$		−	468352.i		−	1.35924i	−0.733564	−	0.679620i	$-0.762145\pi$
$587$		−	468352.i		−	1.35924i	0.733564	−	0.679620i	$-0.237855\pi$
$588$	−130064.	+	170195.i	−0.376185	+	0.492256i
$589$	7597.26			0.0218991
$590$	−146418.	−	49541.4i	−0.420619	−	0.142320i
$591$		−	164324.i		−	0.470463i
$592$	129873.	+	477173.i	0.370575	+	1.36155i
$593$	−61460.0			−0.174777			−0.0873883	−	0.996174i	$-0.527852\pi$
$593$	−61460.0			−0.174777			−0.0873883	+	0.996174i	$0.527852\pi$
$594$	33349.0	−	98561.6i	0.0945170	−	0.279341i
$595$			202629.i			0.572359i
$596$	−289225.	−	221027.i	−0.814223	−	0.622233i
$597$	−351085.			−0.985061
$598$	608145.	+	205770.i	1.70061	+	0.575414i
$599$		−	92590.3i		−	0.258055i	−0.991641	−	0.129027i	$-0.958815\pi$
$599$		−	92590.3i		−	0.258055i	0.991641	−	0.129027i	$-0.0411855\pi$
$600$	36345.2	+	54048.4i	0.100959	+	0.150134i
$601$	−58358.7			−0.161568			−0.0807842	−	0.996732i	$-0.525742\pi$
$601$	−58358.7			−0.161568			−0.0807842	+	0.996732i	$0.525742\pi$
$602$	166790.	−	492940.i	0.460232	−	1.36020i
$603$		−	24929.2i		−	0.0685603i
$604$	−176258.	+	230642.i	−0.483141	+	0.632214i
$605$	−151233.			−0.413178
$606$	23274.3	+	7875.01i	0.0633768	+	0.0214440i
$607$			72146.9i			0.195812i	0.995196	+	0.0979062i	$0.0312145\pi$
$607$			72146.9i			0.195812i	−0.995196	+	0.0979062i	$0.968785\pi$
$608$	320.867	−	5294.48i	0.000867995	−	0.0143224i
$609$	−178203.			−0.480484
$610$	59271.1	−	175173.i	0.159288	−	0.470769i
$611$			703165.i			1.88354i
$612$	53307.1	+	40737.5i	0.142325	+	0.108766i
$613$	−481279.			−1.28078			−0.640392	−	0.768048i	$-0.721228\pi$
$613$	−481279.			−1.28078			−0.640392	+	0.768048i	$0.721228\pi$
$614$	61549.2	+	20825.6i	0.163262	+	0.0552409i
$615$			88912.8i			0.235079i
$616$	−112757.	+	75824.1i	−0.297154	+	0.199823i
$617$	−471022.			−1.23729			−0.618644	−	0.785672i	$-0.712318\pi$
$617$	−471022.			−1.23729			−0.618644	+	0.785672i	$0.712318\pi$
$618$	−22885.8	+	67637.9i	−0.0599223	+	0.177098i
$619$		−	668000.i		−	1.74339i	−0.490046	−	0.871697i	$-0.663020\pi$
$619$		−	668000.i		−	1.74339i	0.490046	−	0.871697i	$-0.336980\pi$
$620$	159310.	−	208465.i	0.414438	−	0.542313i
$621$	455671.			1.18159
$622$	−289166.	−	97841.6i	−0.747424	−	0.252896i
$623$			75713.3i			0.195073i
$624$	−552013.	+	150243.i	−1.41769	+	0.385855i
$625$	15625.0			0.0400000
$626$	115485.	−	341309.i	0.294697	−	0.870963i
$627$		−	1407.74i		−	0.00358086i
$628$	246400.	+	188300.i	0.624772	+	0.477454i
$629$	−550455.			−1.39130
$630$	39649.0	+	13415.5i	0.0998966	+	0.0338007i
$631$			483839.i			1.21519i	0.794249	+	0.607593i	$0.207865\pi$
$631$			483839.i			1.21519i	−0.794249	+	0.607593i	$0.792135\pi$
$632$	143483.	+	213371.i	0.359224	+	0.534196i
$633$	637375.			1.59070
$634$	81260.1	−	240161.i	0.202162	−	0.597480i
$635$			143438.i			0.355726i
$636$	9643.60	−	12619.1i	0.0238410	−	0.0311972i
$637$	−451357.			−1.11235
$638$	−43525.9	−	14727.3i	−0.106932	−	0.0361811i
$639$		−	112527.i		−	0.275585i
$640$	−138550.	−	119827.i	−0.338256	−	0.292546i
$641$	−122259.			−0.297553			−0.148777	−	0.988871i	$-0.547534\pi$
$641$	−122259.			−0.297553			−0.148777	+	0.988871i	$0.547534\pi$
$642$	−138589.	+	409593.i	−0.336247	+	0.993762i
$643$		−	39691.4i		−	0.0960008i	−0.998847	−	0.0480004i	$-0.984715\pi$
$643$		−	39691.4i		−	0.0960008i	0.998847	−	0.0480004i	$-0.0152849\pi$
$644$	−472806.	−	361321.i	−1.14002	−	0.871207i
$645$	186189.			0.447542
$646$	5592.56	+	1892.28i	0.0134013	+	0.00453441i
$647$			293173.i			0.700351i	0.936684	+	0.350175i	$0.113878\pi$
$647$			293173.i			0.700351i	−0.936684	+	0.350175i	$0.886122\pi$
$648$	−273643.	+	184013.i	−0.651681	+	0.438227i
$649$	115375.			0.273919
$650$	−43987.5	+	130003.i	−0.104113	+	0.307700i
$651$			759491.i			1.79209i
$652$	−66276.3	+	86725.8i	−0.155906	+	0.204011i
$653$	751251.			1.76181			0.880904	−	0.473294i	$-0.156935\pi$
$653$	751251.			1.76181			0.880904	+	0.473294i	$0.156935\pi$
$654$	348551.	+	117935.i	0.814911	+	0.275731i
$655$		−	119760.i		−	0.279146i
$656$	−65670.3	−	241282.i	−0.152602	−	0.560683i
$657$	−88415.1			−0.204831
$658$	208888.	−	617359.i	0.482460	−	1.42589i
$659$			395047.i			0.909657i	0.890579	+	0.454828i	$0.150299\pi$
$659$			395047.i			0.909657i	−0.890579	+	0.454828i	$0.849701\pi$
$660$	−38627.7	−	29519.5i	−0.0886770	−	0.0677674i
$661$	−7765.79			−0.0177739			−0.00888695	−	0.999961i	$-0.502829\pi$
$661$	−7765.79			−0.0177739			−0.00888695	+	0.999961i	$0.502829\pi$
$662$	266882.	+	90301.4i	0.608980	+	0.206053i
$663$		−	636790.i		−	1.44867i
$664$	−107716.	−	160183.i	−0.244312	−	0.363313i
$665$	3683.44			0.00832933
$666$	−36444.1	+	107709.i	−0.0821634	+	0.242830i
$667$		−	201230.i		−	0.452314i
$668$	423361.	−	553989.i	0.948763	−	1.24150i
$669$	651747.			1.45622
$670$	−71764.6	−	24282.1i	−0.159868	−	0.0540924i
$671$			138034.i			0.306578i
$672$	529284.	+	32076.7i	1.17206	+	0.0710316i
$673$	602808.			1.33091			0.665456	−	0.746437i	$-0.268237\pi$
$673$	602808.			1.33091			0.665456	+	0.746437i	$0.268237\pi$
$674$	−30227.0	+	89334.6i	−0.0665389	+	0.196653i
$675$			97408.8i			0.213792i
$676$	−594730.	−	454496.i	−1.30145	−	0.994572i
$677$	131066.			0.285964			0.142982	−	0.989725i	$-0.454331\pi$
$677$	131066.			0.285964			0.142982	+	0.989725i	$0.454331\pi$
$678$	24718.3	+	8363.62i	0.0537724	+	0.0181943i
$679$		−	192173.i		−	0.416824i
$680$	169196.	−	113777.i	0.365909	−	0.246058i
$681$	−786442.			−1.69579
$682$	−62767.1	+	185505.i	−0.134947	+	0.398830i
$683$			326700.i			0.700338i	0.936687	+	0.350169i	$0.113876\pi$
$683$			326700.i			0.700338i	−0.936687	+	0.350169i	$0.886124\pi$
$684$	740.535	−	969.027i	0.00158283	−	0.00207121i
$685$	54331.7			0.115790
$686$	−182342.	−	61696.7i	−0.387470	−	0.131103i
$687$		−	373734.i		−	0.791861i
$688$	−505260.	+	137518.i	−1.06743	+	0.290524i
$689$	33466.0			0.0704961
$690$	68237.3	−	201672.i	0.143326	−	0.423593i
$691$			223027.i			0.467091i	0.972346	+	0.233545i	$0.0750327\pi$
$691$			223027.i			0.467091i	−0.972346	+	0.233545i	$0.924967\pi$
$692$	186032.	+	142166.i	0.388486	+	0.296883i
$693$	−31242.8			−0.0650555
$694$	461045.	+	155998.i	0.957248	+	0.323892i
$695$		−	51898.0i		−	0.107444i
$696$	100061.	+	148800.i	0.206561	+	0.307173i
$697$	278338.			0.572936
$698$	18129.0	−	53579.5i	0.0372103	−	0.109974i
$699$			395141.i			0.808719i
$700$	77239.6	−	101072.i	0.157632	−	0.206269i
$701$	427680.			0.870327			0.435164	−	0.900351i	$-0.356691\pi$
$701$	427680.			0.870327			0.435164	+	0.900351i	$0.356691\pi$
$702$	−810462.	−	274226.i	−1.64459	−	0.556460i
$703$			10006.3i			0.0202471i
$704$	126627.	+	51576.7i	0.255493	+	0.104066i
$705$	233183.			0.469157
$706$	290944.	−	859872.i	0.583714	−	1.72514i
$707$		−	47987.3i		−	0.0960035i
$708$	−357736.	−	273384.i	−0.713668	−	0.545388i
$709$	−642298.			−1.27775			−0.638873	−	0.769313i	$-0.720599\pi$
$709$	−642298.			−1.27775			−0.638873	+	0.769313i	$0.720599\pi$
$710$	−323936.	−	109606.i	−0.642603	−	0.217429i
$711$			59121.1i			0.116951i
$712$	63220.9	−	42513.3i	0.124710	−	0.0838619i
$713$	−857631.			−1.68702
$714$	−189170.	+	559083.i	−0.371070	+	1.09668i
$715$		−	102441.i		−	0.200383i
$716$	28442.7	−	37218.7i	0.0554810	−	0.0725997i
$717$	−42673.6			−0.0830081
$718$	695117.	+	235198.i	1.34837	+	0.456231i
$719$		−	465657.i		−	0.900759i	−0.892837	−	0.450379i	$-0.851289\pi$
$719$		−	465657.i		−	0.900759i	0.892837	−	0.450379i	$-0.148711\pi$
$720$	−11061.0	−	40639.9i	−0.0213369	−	0.0783948i
$721$	139457.			0.268269
$722$	−167041.	+	493683.i	−0.320442	+	0.947051i
$723$		−	376173.i		−	0.719632i
$724$	103899.	+	79400.1i	0.198214	+	0.151476i
$725$	43016.9			0.0818395
$726$	−417274.	−	141188.i	−0.791677	−	0.267870i
$727$			4334.28i			0.00820064i	0.999992	+	0.00410032i	$0.00130518\pi$
$727$			4334.28i			0.00820064i	−0.999992	+	0.00410032i	$0.998695\pi$
$728$	623494.	+	927187.i	1.17644	+	1.74946i
$729$	−589722.			−1.10967
$730$	−86120.1	+	254524.i	−0.161607	+	0.477621i
$731$		−	582856.i		−	1.09075i
$732$	327075.	−	427993.i	0.610414	−	0.798757i
$733$	−580825.			−1.08103			−0.540515	−	0.841335i	$-0.681770\pi$
$733$	−580825.			−1.08103			−0.540515	+	0.841335i	$0.681770\pi$
$734$	356536.	+	120637.i	0.661776	+	0.223917i
$735$			149679.i			0.277067i
$736$	−36221.6	+	597677.i	−0.0668670	+	1.10334i
$737$	56549.5			0.104110
$738$	18427.9	−	54463.0i	0.0338348	−	0.0999973i
$739$			373926.i			0.684695i	0.939573	+	0.342348i	$0.111222\pi$
$739$			373926.i			0.684695i	−0.939573	+	0.342348i	$0.888778\pi$
$740$	274568.	+	209826.i	0.501402	+	0.383174i
$741$	−11575.7			−0.0210819
$742$	−29382.2	−	9941.67i	−0.0533674	−	0.0180572i
$743$			733317.i			1.32835i	0.747575	+	0.664177i	$0.231218\pi$
$743$			733317.i			1.32835i	−0.747575	+	0.664177i	$0.768782\pi$
$744$	634177.	−	426457.i	1.14568	−	0.770423i
$745$	−254361.			−0.458287
$746$	−158749.	+	469175.i	−0.285255	+	0.843058i
$747$		−	44383.9i		−	0.0795397i
$748$	−92409.4	+	120922.i	−0.165163	+	0.216124i
$749$	844506.			1.50536
$750$	43111.6	+	14587.1i	0.0766428	+	0.0259326i
$751$		−	88381.1i		−	0.156704i	−0.996926	−	0.0783519i	$-0.975034\pi$
$751$		−	88381.1i		−	0.156704i	0.996926	−	0.0783519i	$-0.0249658\pi$
$752$	−632788.	+	172227.i	−1.11898	+	0.304555i
$753$	−546955.			−0.964632
$754$	−121101.	+	357909.i	−0.213013	+	0.629550i
$755$			202839.i			0.355842i
$756$	630098.	+	481524.i	1.10246	+	0.842509i
$757$	1.00702e6			1.75729			0.878647	−	0.477472i	$-0.158447\pi$
$757$	1.00702e6			1.75729			0.878647	+	0.477472i	$0.158447\pi$
$758$	−1.07159e6	−	362581.i	−1.86505	−	0.631054i
$759$			158915.i			0.275856i
$760$	−2068.26	−	3075.68i	−0.00358079	−	0.00532494i
$761$	−64709.6			−0.111738			−0.0558688	−	0.998438i	$-0.517793\pi$
$761$	−64709.6			−0.111738			−0.0558688	+	0.998438i	$0.517793\pi$
$762$	−133910.	+	395764.i	−0.230623	+	0.681596i
$763$		−	718648.i		−	1.23443i
$764$	−204869.	+	268081.i	−0.350986	+	0.459282i
$765$	46881.2			0.0801080
$766$	−261840.	−	88595.3i	−0.446250	−	0.150992i
$767$		−	948717.i		−	1.61267i
$768$	−270411.	−	459965.i	−0.458460	−	0.779834i
$769$	156640.			0.264880			0.132440	−	0.991191i	$-0.457719\pi$
$769$	156640.			0.264880			0.132440	+	0.991191i	$0.457719\pi$
$770$	−30431.9	+	89940.1i	−0.0513272	+	0.151695i
$771$		−	569894.i		−	0.958706i
$772$	529894.	+	404948.i	0.889108	+	0.679461i
$773$	−487717.			−0.816224			−0.408112	−	0.912932i	$-0.633813\pi$
$773$	−487717.			−0.816224			−0.408112	+	0.912932i	$0.633813\pi$
$774$	−114049.	−	38589.2i	−0.190374	−	0.0644145i
$775$		−	183336.i		−	0.305242i
$776$	−160465.	+	107906.i	−0.266475	+	0.179193i
$777$	−1.00032e6			−1.65690
$778$	35920.0	−	106160.i	0.0593441	−	0.175389i
$779$		−	5059.68i		−	0.00833773i
$780$	−242736.	+	317631.i	−0.398974	+	0.522077i
$781$	255257.			0.418481
$782$	−631327.	−	213614.i	−1.03238	−	0.349314i
$783$			268174.i			0.437415i
$784$	−110552.	−	406182.i	−0.179859	−	0.660829i
$785$	216698.			0.351654
$786$	111805.	−	330436.i	0.180975	−	0.534862i
$787$			381516.i			0.615975i	0.951390	+	0.307988i	$0.0996556\pi$
$787$			381516.i			0.615975i	−0.951390	+	0.307988i	$0.900344\pi$
$788$	256588.	+	196086.i	0.413222	+	0.315786i
$789$	−8415.45			−0.0135183
$790$	170194.	+	57586.5i	0.272704	+	0.0922713i
$791$		−	50964.6i		−	0.0814547i
$792$	17543.0	+	26087.9i	0.0279674	+	0.0415899i
$793$	1.13504e6			1.80495
$794$	334899.	−	989781.i	0.531219	−	1.56999i
$795$		−	11098.0i		−	0.0175594i
$796$	418945.	−	548210.i	0.661197	−	0.865208i
$797$	320530.			0.504605			0.252302	−	0.967648i	$-0.418812\pi$
$797$	320530.			0.504605			0.252302	+	0.967648i	$0.418812\pi$
$798$	10163.1	+	3438.77i	0.0159596	+	0.00540004i
$799$		−	729969.i		−	1.14343i
$800$	−127766.	−	7743.10i	−0.199634	−	0.0120986i
$801$	17517.4			0.0273026
$802$	386384.	−	1.14194e6i	0.600718	−	1.77539i
$803$		−	200562.i		−	0.311040i
$804$	−175339.	−	133995.i	−0.271249	−	0.207290i
$805$	−415812.			−0.641660
$806$	1.52539e6	+	516128.i	2.34807	+	0.794488i
$807$			753100.i			1.15639i
$808$	−40069.5	+	26945.0i	−0.0613750	+	0.0412720i
$809$	−916837.			−1.40086			−0.700430	−	0.713721i	$-0.747009\pi$
$809$	−916837.			−1.40086			−0.700430	+	0.713721i	$0.747009\pi$
$810$	−73853.5	+	218271.i	−0.112564	+	0.332679i
$811$		−	420414.i		−	0.639198i	−0.947553	−	0.319599i	$-0.896452\pi$
$811$		−	420414.i		−	0.639198i	0.947553	−	0.319599i	$-0.103548\pi$
$812$	212647.	−	278259.i	0.322513	−	0.422024i
$813$	−134661.			−0.203733
$814$	−244328.	−	82670.1i	−0.368743	−	0.124767i
$815$			76271.5i			0.114828i
$816$	573055.	−	155970.i	0.860630	−	0.234239i
$817$	−10595.3			−0.0158733
$818$	−392720.	+	1.16067e6i	−0.586917	+	1.73461i
$819$			256907.i			0.383008i
$820$	−138835.	−	106099.i	−0.206477	−	0.157791i
$821$	522572.			0.775283			0.387641	−	0.921810i	$-0.373290\pi$
$821$	522572.			0.775283			0.387641	+	0.921810i	$0.373290\pi$
$822$	149909.	+	50722.7i	0.221862	+	0.0750687i
$823$			1.09844e6i			1.62172i	0.585241	+	0.810859i	$0.301000\pi$
$823$			1.09844e6i			1.62172i	−0.585241	+	0.810859i	$0.699000\pi$
$824$	−78305.6	−	116447.i	−0.115329	−	0.171504i
$825$	−33971.3			−0.0499120
$826$	−281834.	+	832947.i	−0.413078	+	1.22084i
$827$			831895.i			1.21635i	0.793804	+	0.608174i	$0.208098\pi$
$827$			831895.i			1.21635i	−0.793804	+	0.608174i	$0.791902\pi$
$828$	−83596.7	+	109390.i	−0.121935	+	0.159558i
$829$	877227.			1.27645			0.638224	−	0.769851i	$-0.279670\pi$
$829$	877227.			1.27645			0.638224	+	0.769851i	$0.279670\pi$
$830$	−127770.	−	43231.8i	−0.185469	−	0.0627548i
$831$			235489.i			0.341011i
$832$	424110.	−	1.04124e6i	0.612678	−	1.50419i
$833$	468562.			0.675270
$834$	48450.7	−	143194.i	0.0696575	−	0.205870i
$835$		−	487208.i		−	0.698782i
$836$	2198.15	+	1679.84i	0.00314517	+	0.00240356i
$837$	1.14295e6			1.63145
$838$	−49757.3	−	16835.7i	−0.0708547	−	0.0239742i
$839$			224242.i			0.318561i	0.987233	+	0.159281i	$0.0509174\pi$
$839$			224242.i			0.318561i	−0.987233	+	0.159281i	$0.949083\pi$
$840$	307473.	−	206762.i	0.435761	−	0.293031i
$841$	−588852.			−0.832557
$842$	243069.	−	718379.i	0.342851	−	1.01328i
$843$			1.15437e6i			1.62439i
$844$	−760572.	+	995246.i	−1.06771	+	1.39716i
$845$	−523039.			−0.732522
$846$	−142835.	−	48329.2i	−0.199569	−	0.0675256i
$847$			860343.i			1.19924i
$848$	8196.87	+	30116.5i	0.0113987	+	0.0418806i
$849$	31968.8			0.0443518
$850$	45664.3	−	134959.i	0.0632032	−	0.186794i
$851$		−	1.12958e6i		−	1.55976i
$852$	−791460.	−	604838.i	−1.09031	−	0.833220i
$853$	−182588.			−0.250943			−0.125471	−	0.992097i	$-0.540044\pi$
$853$	−182588.			−0.250943			−0.125471	+	0.992097i	$0.540044\pi$
$854$	−996533.	−	337184.i	−1.36639	−	0.462329i
$855$		−	852.216i		−	0.00116578i
$856$	−474193.	−	705165.i	−0.647154	−	0.962373i
$857$	−1.26573e6			−1.72337			−0.861687	−	0.507439i	$-0.830592\pi$
$857$	−1.26573e6			−1.72337			−0.861687	+	0.507439i	$0.830592\pi$
$858$	95636.2	−	282649.i	0.129912	−	0.383948i
$859$			390821.i			0.529653i	0.964296	+	0.264826i	$0.0853147\pi$
$859$			390821.i			0.529653i	−0.964296	+	0.264826i	$0.914685\pi$
$860$	−222177.	+	290729.i	−0.300401	+	0.393090i
$861$	505811.			0.682310
$862$	1.18259e6	+	400139.i	1.59155	+	0.538513i
$863$		−	1.15518e6i		−	1.55106i	−0.631309	−	0.775531i	$-0.717482\pi$
$863$		−	1.15518e6i		−	1.55106i	0.631309	−	0.775531i	$-0.282518\pi$
$864$	48271.8	−	796512.i	0.0646645	−	1.06700i
$865$	163607.			0.218660
$866$	−108319.	+	320133.i	−0.144434	+	0.426869i
$867$		−	18925.4i		−	0.0251772i
$868$	−1.18593e6	−	906291.i	−1.57405	−	1.20290i
$869$	−134111.			−0.177592
$870$	118690.	+	40159.5i	0.156810	+	0.0530578i
$871$		−	465001.i		−	0.612940i
$872$	−600073.	+	403523.i	−0.789171	+	0.530683i
$873$	−44461.9			−0.0583391
$874$	−3883.12	+	11476.4i	−0.00508344	+	0.0150239i
$875$		−	88888.2i		−	0.116099i
$876$	−475235.	+	621868.i	−0.619299	+	0.810383i
$877$	−286144.			−0.372036			−0.186018	−	0.982546i	$-0.559558\pi$
$877$	−286144.			−0.372036			−0.186018	+	0.982546i	$0.559558\pi$
$878$	339504.	+	114874.i	0.440409	+	0.149015i
$879$			1.23891e6i			1.60347i
$880$	92187.8	−	25091.0i	0.119044	−	0.0324005i
$881$	−1.13893e6			−1.46739			−0.733696	−	0.679478i	$-0.762206\pi$
$881$	−1.13893e6			−1.46739			−0.733696	+	0.679478i	$0.762206\pi$
$882$	31022.2	−	91684.7i	0.0398782	−	0.117858i
$883$			1.25765e6i			1.61301i	0.591224	+	0.806507i	$0.298645\pi$
$883$			1.25765e6i			1.61301i	−0.591224	+	0.806507i	$0.701355\pi$
$884$	994331.	+	759873.i	1.27241	+	0.972381i
$885$	−314613.			−0.401689
$886$	−309559.	−	104741.i	−0.394344	−	0.133429i
$887$		−	126913.i		−	0.161309i	−0.996742	−	0.0806544i	$-0.974299\pi$
$887$		−	126913.i		−	0.161309i	0.996742	−	0.0806544i	$-0.0257010\pi$
$888$	561683.	+	835269.i	0.712304	+	1.05926i
$889$	815994.			1.03248
$890$	17062.7	−	50427.9i	0.0215410	−	0.0636636i
$891$		−	171994.i		−	0.216650i
$892$	−777721.	+	1.01769e6i	−0.977449	+	1.27904i
$893$	−13269.5			−0.0166400
$894$	−701816.	−	237465.i	−0.878109	−	0.297115i
$895$		−	32732.2i		−	0.0408628i
$896$	−681675.	+	788187.i	−0.849105	+	0.981778i
$897$	1.30674e6			1.62407
$898$	196632.	−	581137.i	0.243838	−	0.720652i
$899$		−	504738.i		−	0.624521i
$900$	−23384.4	−	17870.5i	−0.0288696	−	0.0220623i
$901$	−34741.7			−0.0427958
$902$	123544.	+	41802.1i	0.151848	+	0.0513789i
$903$		−	1.05920e6i		−	1.29898i
$904$	−42555.6	+	28616.8i	−0.0520739	+	0.0350175i
$905$	91374.5			0.111565
$906$	−189366.	+	559661.i	−0.230698	+	0.681819i
$907$			318521.i			0.387190i	0.981082	+	0.193595i	$0.0620147\pi$
$907$			318521.i			0.387190i	−0.981082	+	0.193595i	$0.937985\pi$
$908$	938451.	−	1.22801e6i	1.13826	−	1.48946i
$909$	−11102.5			−0.0134368
$910$	739568.	+	250238.i	0.893090	+	0.302184i
$911$			209882.i			0.252894i	0.991973	+	0.126447i	$0.0403573\pi$
$911$			209882.i			0.252894i	−0.991973	+	0.126447i	$0.959643\pi$
$912$	−2835.25	−	10417.1i	−0.00340880	−	0.0125244i
$913$	100681.			0.120783
$914$	138114.	−	408189.i	0.165327	−	0.488617i
$915$		−	376401.i		−	0.449582i
$916$	583576.	+	445972.i	0.695515	+	0.531516i
$917$	−681299.			−0.810212
$918$	841356.	+	284679.i	0.998376	+	0.337808i
$919$		−	330341.i		−	0.391139i	−0.980690	−	0.195570i	$-0.937344\pi$
$919$		−	330341.i		−	0.391139i	0.980690	−	0.195570i	$-0.0626555\pi$
$920$	233480.	+	347204.i	0.275850	+	0.410213i
$921$	132253.			0.155914
$922$	167761.	−	495809.i	0.197346	−	0.583247i
$923$		−	2.09896e6i		−	2.46377i
$924$	−167932.	+	219747.i	−0.196693	+	0.257382i
$925$	241470.			0.282215
$926$	1.00728e6	+	340820.i	1.17470	+	0.397469i
$927$		−	32265.4i		−	0.0375472i
$928$	−351749.	−	21317.4i	−0.408448	−	0.0247536i
$929$	561048.			0.650083			0.325042	−	0.945700i	$-0.394622\pi$
$929$	561048.			0.650083			0.325042	+	0.945700i	$0.394622\pi$
$930$	171158.	−	505849.i	0.197893	−	0.584865i
$931$		−	8517.62i		−	0.00982696i
$932$	−617003.	−	471517.i	−0.710322	−	0.542832i
$933$	−621343.			−0.713786
$934$	917840.	+	310558.i	1.05214	+	0.355999i
$935$			106346.i			0.121646i
$936$	214518.	−	144254.i	0.244857	−	0.164656i
$937$	−677949.			−0.772179			−0.386090	−	0.922461i	$-0.626174\pi$
$937$	−677949.			−0.772179			−0.386090	+	0.922461i	$0.626174\pi$
$938$	−138137.	+	408258.i	−0.157002	+	0.464011i
$939$		−	733384.i		−	0.831765i
$940$	−278254.	+	364110.i	−0.314910	+	0.412075i
$941$	49257.5			0.0556280			0.0278140	−	0.999613i	$-0.491145\pi$
$941$	49257.5			0.0556280			0.0278140	+	0.999613i	$0.491145\pi$
$942$	597900.	+	202304.i	0.673793	+	0.227983i
$943$			571171.i			0.642307i
$944$	853763.	−	232371.i	0.958062	−	0.260758i
$945$	554144.			0.620524
$946$	87536.1	−	258709.i	0.0978149	−	0.289088i
$947$			928184.i			1.03499i	0.855688	+	0.517493i	$0.173134\pi$
$947$			928184.i			1.03499i	−0.855688	+	0.517493i	$0.826866\pi$
$948$	415829.	+	317778.i	0.462698	+	0.353596i
$949$	−1.64920e6			−1.83122
$950$	−2453.31	−	830.095i	−0.00271835	−	0.000919773i
$951$		−	516042.i		−	0.570590i
$952$	−647260.	−	962531.i	−0.714176	−	1.06204i
$953$	1.38986e6			1.53033			0.765165	−	0.643834i	$-0.222657\pi$
$953$	1.38986e6			1.53033			0.765165	+	0.643834i	$0.222657\pi$
$954$	−2300.15	+	6797.98i	−0.00252731	+	0.00746936i
$955$			235765.i			0.258508i
$956$	50921.8	−	66633.7i	0.0557171	−	0.0729085i
$957$	−93525.8			−0.102119
$958$	−1.27170e6	−	430290.i	−1.38565	−	0.468846i
$959$		−	309084.i		−	0.336078i
$960$	−345294.	−	140643.i	−0.374668	−	0.152607i
$961$	−1.22765e6			−1.32931
$962$	−679788.	+	2.00908e6i	−0.734553	+	2.17094i
$963$		−	195388.i		−	0.210691i
$964$	587384.	+	448882.i	0.632075	+	0.483035i
$965$	466018.			0.500436
$966$	−1.14728e6	−	388192.i	−1.22947	−	0.415999i
$967$		−	1.55110e6i		−	1.65877i	−0.558679	−	0.829384i	$-0.688692\pi$
$967$		−	1.55110e6i		−	1.65877i	0.558679	−	0.829384i	$-0.311308\pi$
$968$	718389.	−	483086.i	0.766671	−	0.515553i
$969$	12016.9			0.0127981
$970$	−43307.8	+	127994.i	−0.0460281	+	0.136034i
$971$			481613.i			0.510810i	0.966834	+	0.255405i	$0.0822089\pi$
$971$			481613.i			0.510810i	−0.966834	+	0.255405i	$0.917791\pi$
$972$	205687.	−	269152.i	0.217708	−	0.284882i
$973$	−295240.			−0.311853
$974$	67642.1	+	22887.2i	0.0713016	+	0.0241254i
$975$			279343.i			0.293852i
$976$	278007.	+	1.02144e6i	0.291848	+	1.07229i
$977$	1.05588e6			1.10618			0.553089	−	0.833122i	$-0.313449\pi$
$977$	1.05588e6			1.10618			0.553089	+	0.833122i	$0.313449\pi$
$978$	−71205.2	+	210444.i	−0.0744447	+	0.220018i
$979$			39736.5i			0.0414595i
$980$	−233720.	−	178610.i	−0.243356	−	0.185974i
$981$	−166269.			−0.172772
$982$	−525661.	−	177861.i	−0.545108	−	0.184441i
$983$		−	844860.i		−	0.874335i	−0.899380	−	0.437167i	$-0.855982\pi$
$983$		−	844860.i		−	0.874335i	0.899380	−	0.437167i	$-0.144018\pi$
$984$	−284015.	−	422354.i	−0.293326	−	0.436200i
$985$	225658.			0.232583
$986$	125717.	−	371552.i	0.129313	−	0.382179i
$987$		−	1.32654e6i		−	1.36172i
$988$	13813.1	−	18075.2i	0.0141507	−	0.0185169i
$989$	1.19607e6			1.22282
$990$	20808.9	+	7040.85i	0.0212314	+	0.00718380i
$991$			1.91051e6i			1.94537i	0.232132	+	0.972684i	$0.425430\pi$
$991$			1.91051e6i			1.94537i	−0.232132	+	0.972684i	$0.574570\pi$
$992$	−90853.6	+	1.49914e6i	−0.0923249	+	1.52341i
$993$	573459.			0.581572
$994$	−623532.	+	1.84282e6i	−0.631083	+	1.86514i
$995$		−	482126.i		−	0.486984i
$996$	−312174.	−	238565.i	−0.314687	−	0.240485i
$997$	−26126.1			−0.0262836			−0.0131418	−	0.999914i	$-0.504183\pi$
$997$	−26126.1			−0.0262836			−0.0131418	+	0.999914i	$0.504183\pi$
$998$	−664804.	−	224941.i	−0.667471	−	0.225844i
$999$			1.50536e6i			1.50838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.5.b.a.11.4	yes	8
3.2	odd	2		180.5.c.a.91.5		8
4.3	odd	2	inner	20.5.b.a.11.3	✓	8
5.2	odd	4		100.5.d.c.99.1		16
5.3	odd	4		100.5.d.c.99.16		16
5.4	even	2		100.5.b.c.51.5		8
8.3	odd	2		320.5.b.d.191.6		8
8.5	even	2		320.5.b.d.191.3		8
12.11	even	2		180.5.c.a.91.6		8
20.3	even	4		100.5.d.c.99.2		16
20.7	even	4		100.5.d.c.99.15		16
20.19	odd	2		100.5.b.c.51.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.b.a.11.3	✓	8	4.3	odd	2	inner
20.5.b.a.11.4	yes	8	1.1	even	1	trivial
100.5.b.c.51.5		8	5.4	even	2
100.5.b.c.51.6		8	20.19	odd	2
100.5.d.c.99.1		16	5.2	odd	4
100.5.d.c.99.2		16	20.3	even	4
100.5.d.c.99.15		16	20.7	even	4
100.5.d.c.99.16		16	5.3	odd	4
180.5.c.a.91.5		8	3.2	odd	2
180.5.c.a.91.6		8	12.11	even	2
320.5.b.d.191.3		8	8.5	even	2
320.5.b.d.191.6		8	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28203 + 3.78898i) q^{2} +8.14153i q^{3} +(-12.7128 - 9.71518i) q^{4} -11.1803 q^{5} +(-30.8481 - 10.4377i) q^{6} +63.6032i q^{7} +(53.1089 - 35.7134i) q^{8} +14.7155 q^{9} +O(q^{10})\)	\(q+(-1.28203 + 3.78898i) q^{2} +8.14153i q^{3} +(-12.7128 - 9.71518i) q^{4} -11.1803 q^{5} +(-30.8481 - 10.4377i) q^{6} +63.6032i q^{7} +(53.1089 - 35.7134i) q^{8} +14.7155 q^{9} +(14.3335 - 42.3621i) q^{10} +33.3808i q^{11} +(79.0964 - 103.502i) q^{12} +274.487 q^{13} +(-240.992 - 81.5412i) q^{14} -91.0251i q^{15} +(67.2304 + 247.014i) q^{16} -284.950 q^{17} +(-18.8657 + 55.7568i) q^{18} +5.17988i q^{19} +(142.133 + 108.619i) q^{20} -517.827 q^{21} +(-126.479 - 42.7952i) q^{22} -584.740i q^{23} +(290.762 + 432.387i) q^{24} +125.000 q^{25} +(-351.900 + 1040.03i) q^{26} +779.271i q^{27} +(617.917 - 808.575i) q^{28} +344.135 q^{29} +(344.892 + 116.697i) q^{30} -1466.69i q^{31} +(-1022.12 - 61.9448i) q^{32} -271.771 q^{33} +(365.314 - 1079.67i) q^{34} -711.105i q^{35} +(-187.075 - 142.964i) q^{36} +1931.76 q^{37} +(-19.6265 - 6.64076i) q^{38} +2234.74i q^{39} +(-593.775 + 399.288i) q^{40} -976.795 q^{41} +(663.870 - 1962.04i) q^{42} +2045.47i q^{43} +(324.300 - 424.363i) q^{44} -164.524 q^{45} +(2215.57 + 749.654i) q^{46} +2561.74i q^{47} +(-2011.07 + 547.358i) q^{48} -1644.37 q^{49} +(-160.254 + 473.623i) q^{50} -2319.93i q^{51} +(-3489.49 - 2666.69i) q^{52} +121.922 q^{53} +(-2952.64 - 999.048i) q^{54} -373.209i q^{55} +(2271.49 + 3377.89i) q^{56} -42.1721 q^{57} +(-441.191 + 1303.92i) q^{58} -3456.33i q^{59} +(-884.325 + 1157.18i) q^{60} +4135.14 q^{61} +(5557.25 + 1880.34i) q^{62} +935.953i q^{63} +(1545.10 - 3793.40i) q^{64} -3068.86 q^{65} +(348.418 - 1029.73i) q^{66} -1694.07i q^{67} +(3622.51 + 2768.34i) q^{68} +4760.68 q^{69} +(2694.37 + 911.659i) q^{70} -7646.84i q^{71} +(781.524 - 525.541i) q^{72} -6008.30 q^{73} +(-2476.58 + 7319.41i) q^{74} +1017.69i q^{75} +(50.3235 - 65.8507i) q^{76} -2123.12 q^{77} +(-8467.40 - 2865.01i) q^{78} +4017.61i q^{79} +(-751.659 - 2761.70i) q^{80} -5152.50 q^{81} +(1252.28 - 3701.06i) q^{82} -3016.13i q^{83} +(6583.03 + 5030.79i) q^{84} +3185.84 q^{85} +(-7750.24 - 2622.35i) q^{86} +2801.79i q^{87} +(1192.14 + 1772.82i) q^{88} +1190.40 q^{89} +(210.925 - 623.380i) q^{90} +17458.2i q^{91} +(-5680.86 + 7433.68i) q^{92} +11941.1 q^{93} +(-9706.41 - 3284.23i) q^{94} -57.9128i q^{95} +(504.325 - 8321.66i) q^{96} -3021.43 q^{97} +(2108.13 - 6230.48i) q^{98} +491.215i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9}+O(q^{10}) \) 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9	\( 8 q + 6 q^{2} - 20 q^{4} + 48 q^{6} + 216 q^{8} - 328 q^{9} - 50 q^{10} - 200 q^{12} + 352 q^{13} - 168 q^{14} - 272 q^{16} - 48 q^{17} + 286 q^{18} - 300 q^{20} + 16 q^{21} + 800 q^{22} + 1552 q^{24} + 1000 q^{25} - 2172 q^{26} + 40 q^{28} + 1200 q^{29} + 1400 q^{30} - 2304 q^{32} - 1120 q^{33} - 2132 q^{34} - 1044 q^{36} - 5728 q^{37} - 3360 q^{38} - 2200 q^{40} + 4896 q^{41} + 12120 q^{42} + 7920 q^{44} - 400 q^{45} + 728 q^{46} + 8640 q^{48} - 5768 q^{49} + 750 q^{50} - 12488 q^{52} + 2592 q^{53} - 17776 q^{54} + 48 q^{56} + 3840 q^{57} - 7428 q^{58} - 9800 q^{60} + 7936 q^{61} + 25680 q^{62} + 18880 q^{64} - 1200 q^{65} - 8080 q^{66} + 2712 q^{68} - 2256 q^{69} + 12000 q^{70} - 36264 q^{72} - 14448 q^{73} - 18492 q^{74} + 12000 q^{76} + 2400 q^{77} - 14480 q^{78} - 13200 q^{80} - 936 q^{81} + 27412 q^{82} + 50464 q^{84} + 11200 q^{85} - 7392 q^{86} + 18080 q^{88} + 23760 q^{89} + 19350 q^{90} - 52680 q^{92} + 11360 q^{93} - 43368 q^{94} + 2688 q^{96} - 4368 q^{97} - 21474 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 - 20 * q^4 + 48 * q^6 + 216 * q^8 - 328 * q^9 - 50 * q^10 - 200 * q^12 + 352 * q^13 - 168 * q^14 - 272 * q^16 - 48 * q^17 + 286 * q^18 - 300 * q^20 + 16 * q^21 + 800 * q^22 + 1552 * q^24 + 1000 * q^25 - 2172 * q^26 + 40 * q^28 + 1200 * q^29 + 1400 * q^30 - 2304 * q^32 - 1120 * q^33 - 2132 * q^34 - 1044 * q^36 - 5728 * q^37 - 3360 * q^38 - 2200 * q^40 + 4896 * q^41 + 12120 * q^42 + 7920 * q^44 - 400 * q^45 + 728 * q^46 + 8640 * q^48 - 5768 * q^49 + 750 * q^50 - 12488 * q^52 + 2592 * q^53 - 17776 * q^54 + 48 * q^56 + 3840 * q^57 - 7428 * q^58 - 9800 * q^60 + 7936 * q^61 + 25680 * q^62 + 18880 * q^64 - 1200 * q^65 - 8080 * q^66 + 2712 * q^68 - 2256 * q^69 + 12000 * q^70 - 36264 * q^72 - 14448 * q^73 - 18492 * q^74 + 12000 * q^76 + 2400 * q^77 - 14480 * q^78 - 13200 * q^80 - 936 * q^81 + 27412 * q^82 + 50464 * q^84 + 11200 * q^85 - 7392 * q^86 + 18080 * q^88 + 23760 * q^89 + 19350 * q^90 - 52680 * q^92 + 11360 * q^93 - 43368 * q^94 + 2688 * q^96 - 4368 * q^97 - 21474 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more