LMFDB - Embedded newform 25.5.f.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,5,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

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

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

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, 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:	$2.58424907710$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			2.1
Character	$\chi$	$=$	25.2
Dual form			25.5.f.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.04610 - 1.11599i) q^{2} +(-6.53588 - 12.8274i) q^{3} +(33.1852 + 10.7825i) q^{4} +(-24.8595 + 2.64690i) q^{5} +(31.7372 + 97.6770i) q^{6} +(31.4475 + 31.4475i) q^{7} +(-120.091 - 61.1893i) q^{8} +(-74.2134 + 102.146i) q^{9} +O(q^{10})$	\(q+(-7.04610 - 1.11599i) q^{2} +(-6.53588 - 12.8274i) q^{3} +(33.1852 + 10.7825i) q^{4} +(-24.8595 + 2.64690i) q^{5} +(31.7372 + 97.6770i) q^{6} +(31.4475 + 31.4475i) q^{7} +(-120.091 - 61.1893i) q^{8} +(-74.2134 + 102.146i) q^{9} +(178.116 + 9.09265i) q^{10} +(48.2953 - 35.0886i) q^{11} +(-78.5828 - 496.152i) q^{12} +(-71.7290 + 11.3608i) q^{13} +(-186.487 - 256.678i) q^{14} +(196.431 + 301.582i) q^{15} +(326.221 + 237.014i) q^{16} +(-165.824 + 325.448i) q^{17} +(636.909 - 636.909i) q^{18} +(-417.464 + 135.642i) q^{19} +(-853.507 - 180.210i) q^{20} +(197.852 - 608.926i) q^{21} +(-379.452 + 193.341i) q^{22} +(-32.2472 + 203.601i) q^{23} +1940.38i q^{24} +(610.988 - 131.601i) q^{25} +518.088 q^{26} +(643.555 + 101.929i) q^{27} +(704.508 + 1382.68i) q^{28} +(-548.364 - 178.174i) q^{29} +(-1047.51 - 2344.19i) q^{30} +(232.198 + 714.633i) q^{31} +(-509.208 - 509.208i) q^{32} +(-765.747 - 390.168i) q^{33} +(1531.61 - 2108.08i) q^{34} +(-865.008 - 698.530i) q^{35} +(-3564.18 + 2589.53i) q^{36} +(-276.397 - 1745.10i) q^{37} +(3092.87 - 489.863i) q^{38} +(614.540 + 845.842i) q^{39} +(3147.36 + 1203.27i) q^{40} +(-121.921 - 88.5807i) q^{41} +(-2073.64 + 4069.75i) q^{42} +(-2369.75 + 2369.75i) q^{43} +(1981.03 - 643.677i) q^{44} +(1574.54 - 2735.73i) q^{45} +(454.433 - 1398.60i) q^{46} +(-644.052 + 328.161i) q^{47} +(908.122 - 5733.66i) q^{48} -423.107i q^{49} +(-4451.95 + 245.418i) q^{50} +5258.45 q^{51} +(-2502.84 - 396.410i) q^{52} +(-258.680 - 507.687i) q^{53} +(-4420.80 - 1436.40i) q^{54} +(-1107.72 + 1000.12i) q^{55} +(-1852.31 - 5700.81i) q^{56} +(4468.43 + 4468.43i) q^{57} +(3664.99 + 1867.40i) q^{58} +(-1277.03 + 1757.68i) q^{59} +(3266.79 + 12126.1i) q^{60} +(-2002.27 + 1454.73i) q^{61} +(-838.567 - 5294.51i) q^{62} +(-5546.06 + 878.410i) q^{63} +(-772.560 - 1063.34i) q^{64} +(1753.07 - 472.282i) q^{65} +(4960.11 + 3603.73i) q^{66} +(2517.04 - 4939.97i) q^{67} +(-9012.05 + 9012.05i) q^{68} +(2822.42 - 917.061i) q^{69} +(5315.38 + 5887.26i) q^{70} +(744.451 - 2291.19i) q^{71} +(15162.6 - 7725.73i) q^{72} +(378.921 - 2392.41i) q^{73} +12604.6i q^{74} +(-5681.44 - 6977.24i) q^{75} -15316.2 q^{76} +(2622.22 + 415.318i) q^{77} +(-3386.16 - 6645.71i) q^{78} +(-10891.8 - 3538.95i) q^{79} +(-8737.04 - 5028.56i) q^{80} +(261.609 + 805.149i) q^{81} +(760.212 + 760.212i) q^{82} +(2427.32 + 1236.78i) q^{83} +(13131.5 - 18074.0i) q^{84} +(3260.87 - 8529.39i) q^{85} +(19342.1 - 14052.8i) q^{86} +(1298.53 + 8198.60i) q^{87} +(-7946.88 + 1258.66i) q^{88} +(2630.29 + 3620.28i) q^{89} +(-14147.4 + 17519.1i) q^{90} +(-2612.96 - 1898.43i) q^{91} +(-3265.45 + 6408.82i) q^{92} +(7649.25 - 7649.25i) q^{93} +(4904.28 - 1593.50i) q^{94} +(10018.9 - 4476.99i) q^{95} +(-3203.68 + 9859.92i) q^{96} +(-10337.2 + 5267.09i) q^{97} +(-472.185 + 2981.26i) q^{98} +7537.22i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) $ 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−7.04610	−	1.11599i	−1.76153	−	0.278998i	−0.809969	−	0.586473i	$-0.800516\pi$
$2$	−7.04610	−	1.11599i	−1.76153	−	0.278998i	−0.951556	+	0.307475i	$0.900516\pi$
$3$	−6.53588	−	12.8274i	−0.726208	−	1.42526i	−0.897939	−	0.440120i	$-0.854936\pi$
$3$	−6.53588	−	12.8274i	−0.726208	−	1.42526i	0.171730	−	0.985144i	$-0.445064\pi$
$4$	33.1852	+	10.7825i	2.07407	+	0.673907i
$5$	−24.8595	+	2.64690i	−0.994379	+	0.105876i
$5$	−24.8595	+	2.64690i	−0.994379	+	0.105876i
$6$	31.7372	+	97.6770i	0.881588	+	2.71325i
$7$	31.4475	+	31.4475i	0.641786	+	0.641786i	0.950994	−	0.309208i	$-0.100064\pi$
$7$	31.4475	+	31.4475i	0.641786	+	0.641786i	−0.309208	+	0.950994i	$0.600064\pi$
$8$	−120.091	−	61.1893i	−1.87642	−	0.956084i
$9$	−74.2134	+	102.146i	−0.916215	+	1.26106i
$10$	178.116	+	9.09265i	1.78116	+	0.0909265i
$11$	48.2953	−	35.0886i	0.399135	−	0.289988i	−0.370054	−	0.929010i	$-0.620661\pi$
$11$	48.2953	−	35.0886i	0.399135	−	0.289988i	0.769189	+	0.639022i	$0.220661\pi$
$12$	−78.5828	−	496.152i	−0.545714	−	3.44550i
$13$	−71.7290	+	11.3608i	−0.424432	+	0.0672234i	−0.364997	−	0.931009i	$-0.618930\pi$
$13$	−71.7290	+	11.3608i	−0.424432	+	0.0672234i	−0.0594350	+	0.998232i	$0.518930\pi$
$14$	−186.487	−	256.678i	−0.951465	−	1.30958i
$15$	196.431	+	301.582i	0.873028	+	1.34037i
$16$	326.221	+	237.014i	1.27430	+	0.925834i
$17$	−165.824	+	325.448i	−0.573785	+	1.12612i	0.403656	+	0.914911i	$0.367739\pi$
$17$	−165.824	+	325.448i	−0.573785	+	1.12612i	−0.977441	+	0.211206i	$0.932261\pi$
$18$	636.909	−	636.909i	1.96577	−	1.96577i
$19$	−417.464	+	135.642i	−1.15641	+	0.375741i	−0.823554	−	0.567237i	$-0.808012\pi$
$19$	−417.464	+	135.642i	−1.15641	+	0.375741i	−0.332856	+	0.942978i	$0.608012\pi$
$20$	−853.507	−	180.210i	−2.13377	−	0.450525i
$21$	197.852	−	608.926i	0.448644	−	1.38079i
$22$	−379.452	+	193.341i	−0.783992	+	0.399464i
$23$	−32.2472	+	203.601i	−0.0609587	+	0.384878i	0.938280	+	0.345876i	$0.112418\pi$
$23$	−32.2472	+	203.601i	−0.0609587	+	0.384878i	−0.999239	+	0.0390026i	$0.987582\pi$
$24$			1940.38i			3.36871i
$25$	610.988	−	131.601i	0.977580	−	0.210562i
$26$	518.088			0.766402
$27$	643.555	+	101.929i	0.882791	+	0.139820i
$28$	704.508	+	1382.68i	0.898607	+	1.76362i
$29$	−548.364	−	178.174i	−0.652038	−	0.211860i	−0.0357255	−	0.999362i	$-0.511374\pi$
$29$	−548.364	−	178.174i	−0.652038	−	0.211860i	−0.616313	+	0.787502i	$0.711374\pi$
$30$	−1047.51	−	2344.19i	−1.16390	−	2.60466i
$31$	232.198	+	714.633i	0.241621	+	0.743635i	0.996174	+	0.0873946i	$0.0278541\pi$
$31$	232.198	+	714.633i	0.241621	+	0.743635i	−0.754552	+	0.656240i	$0.772146\pi$
$32$	−509.208	−	509.208i	−0.497273	−	0.497273i
$33$	−765.747	−	390.168i	−0.703165	−	0.358281i
$34$	1531.61	−	2108.08i	1.32492	−	1.82360i
$35$	−865.008	−	698.530i	−0.706129	−	0.570229i
$36$	−3564.18	+	2589.53i	−2.75014	+	1.99809i
$37$	−276.397	−	1745.10i	−0.201897	−	1.27473i	−0.855465	−	0.517860i	$-0.826729\pi$
$37$	−276.397	−	1745.10i	−0.201897	−	1.27473i	0.653568	−	0.756868i	$-0.273271\pi$
$38$	3092.87	−	489.863i	2.14188	−	0.339240i
$39$	614.540	+	845.842i	0.404037	+	0.556109i
$40$	3147.36	+	1203.27i	1.96710	+	0.752042i
$41$	−121.921	−	88.5807i	−0.0725288	−	0.0526953i	0.550930	−	0.834551i	$-0.314273\pi$
$41$	−121.921	−	88.5807i	−0.0725288	−	0.0526953i	−0.623459	+	0.781856i	$0.714273\pi$
$42$	−2073.64	+	4069.75i	−1.17553	+	2.30712i
$43$	−2369.75	+	2369.75i	−1.28164	+	1.28164i	−0.341900	+	0.939736i	$0.611070\pi$
$43$	−2369.75	+	2369.75i	−1.28164	+	1.28164i	−0.939736	+	0.341900i	$0.888930\pi$
$44$	1981.03	−	643.677i	1.02326	−	0.332478i
$45$	1574.54	−	2735.73i	0.777549	−	1.35098i
$46$	454.433	−	1398.60i	0.214761	−	0.660965i
$47$	−644.052	+	328.161i	−0.291558	+	0.148556i	−0.593652	−	0.804722i	$-0.702314\pi$
$47$	−644.052	+	328.161i	−0.291558	+	0.148556i	0.302094	+	0.953278i	$0.402314\pi$
$48$	908.122	−	5733.66i	0.394150	−	2.48857i
$49$		−	423.107i		−	0.176221i
$50$	−4451.95	+	245.418i	−1.78078	+	0.0981673i
$51$	5258.45			2.02170
$52$	−2502.84	−	396.410i	−0.925605	−	0.146601i
$53$	−258.680	−	507.687i	−0.0920896	−	0.180736i	0.840367	−	0.542017i	$-0.182339\pi$
$53$	−258.680	−	507.687i	−0.0920896	−	0.180736i	−0.932457	+	0.361281i	$0.882339\pi$
$54$	−4420.80	−	1436.40i	−1.51605	−	0.492594i
$55$	−1107.72	+	1000.12i	−0.366189	+	0.330617i
$56$	−1852.31	−	5700.81i	−0.590659	−	1.81786i
$57$	4468.43	+	4468.43i	1.37532	+	1.37532i
$58$	3664.99	+	1867.40i	1.08947	+	0.555114i
$59$	−1277.03	+	1757.68i	−0.366856	+	0.504934i	−0.952043	−	0.305964i	$-0.901021\pi$
$59$	−1277.03	+	1757.68i	−0.366856	+	0.504934i	0.585187	+	0.810898i	$0.301021\pi$
$60$	3266.79	+	12126.1i	0.907443	+	3.36836i
$61$	−2002.27	+	1454.73i	−0.538100	+	0.390952i	−0.823379	−	0.567492i	$-0.807914\pi$
$61$	−2002.27	+	1454.73i	−0.538100	+	0.390952i	0.285279	+	0.958445i	$0.407914\pi$
$62$	−838.567	−	5294.51i	−0.218150	−	1.37734i
$63$	−5546.06	+	878.410i	−1.39735	+	0.221318i
$64$	−772.560	−	1063.34i	−0.188613	−	0.259604i
$65$	1753.07	−	472.282i	0.414929	−	0.111783i
$66$	4960.11	+	3603.73i	1.13868	+	0.827302i
$67$	2517.04	−	4939.97i	0.560713	−	1.10046i	−0.420456	−	0.907313i	$-0.638130\pi$
$67$	2517.04	−	4939.97i	0.560713	−	1.10046i	0.981169	−	0.193149i	$-0.0618700\pi$
$68$	−9012.05	+	9012.05i	−1.94897	+	1.94897i
$69$	2822.42	−	917.061i	0.592822	−	0.192619i
$70$	5315.38	+	5887.26i	1.08477	+	1.20148i
$71$	744.451	−	2291.19i	0.147679	−	0.454510i	−0.849667	−	0.527320i	$-0.823197\pi$
$71$	744.451	−	2291.19i	0.147679	−	0.454510i	0.997346	+	0.0728103i	$0.0231968\pi$
$72$	15162.6	−	7725.73i	2.92488	−	1.49030i
$73$	378.921	−	2392.41i	0.0711054	−	0.448942i	−0.926290	−	0.376812i	$-0.877020\pi$
$73$	378.921	−	2392.41i	0.0711054	−	0.448942i	0.997395	−	0.0721301i	$-0.0229797\pi$
$74$			12604.6i			2.30179i
$75$	−5681.44	−	6977.24i	−1.01003	−	1.24040i
$76$	−15316.2			−2.65170
$77$	2622.22	+	415.318i	0.442270	+	0.0700487i
$78$	−3386.16	−	6645.71i	−0.556568	−	1.09233i
$79$	−10891.8	−	3538.95i	−1.74520	−	0.567049i	−0.749695	−	0.661783i	$-0.769800\pi$
$79$	−10891.8	−	3538.95i	−1.74520	−	0.567049i	−0.995503	+	0.0947339i	$0.969800\pi$
$80$	−8737.04	−	5028.56i	−1.36516	−	0.785712i
$81$	261.609	+	805.149i	0.0398733	+	0.122717i
$82$	760.212	+	760.212i	0.113059	+	0.113059i
$83$	2427.32	+	1236.78i	0.352347	+	0.179530i	0.621201	−	0.783651i	$-0.286645\pi$
$83$	2427.32	+	1236.78i	0.352347	+	0.179530i	−0.268854	+	0.963181i	$0.586645\pi$
$84$	13131.5	−	18074.0i	1.86104	−	2.56151i
$85$	3260.87	−	8529.39i	0.451331	−	1.18054i
$86$	19342.1	−	14052.8i	2.61521	−	1.90006i
$87$	1298.53	+	8198.60i	0.171559	+	1.08318i
$88$	−7946.88	+	1258.66i	−1.02620	+	0.162534i
$89$	2630.29	+	3620.28i	0.332065	+	0.457048i	0.942103	−	0.335324i	$-0.108846\pi$
$89$	2630.29	+	3620.28i	0.332065	+	0.457048i	−0.610038	+	0.792372i	$0.708846\pi$
$90$	−14147.4	+	17519.1i	−1.74659	+	2.16285i
$91$	−2612.96	−	1898.43i	−0.315537	−	0.229251i
$92$	−3265.45	+	6408.82i	−0.385805	+	0.757185i
$93$	7649.25	−	7649.25i	0.884408	−	0.884408i
$94$	4904.28	−	1593.50i	0.555034	−	0.180342i
$95$	10018.9	−	4476.99i	1.11013	−	0.496065i
$96$	−3203.68	+	9859.92i	−0.347622	+	1.06987i
$97$	−10337.2	+	5267.09i	−1.09865	+	0.559792i	−0.906770	−	0.421625i	$-0.861460\pi$
$97$	−10337.2	+	5267.09i	−1.09865	+	0.559792i	−0.191884	+	0.981418i	$0.561460\pi$
$98$	−472.185	+	2981.26i	−0.0491654	+	0.310418i
$99$			7537.22i			0.769025i
$100$	21694.7	+	2220.77i	2.16947	+	0.222077i
$101$	−10555.7			−1.03477			−0.517385	−	0.855753i	$-0.673094\pi$
$101$	−10555.7			−1.03477			−0.517385	+	0.855753i	$0.673094\pi$
$102$	−37051.6	−	5868.39i	−3.56128	−	0.564051i
$103$	2389.79	+	4690.22i	0.225260	+	0.442098i	0.975781	−	0.218748i	$-0.0701973\pi$
$103$	2389.79	+	4690.22i	0.225260	+	0.442098i	−0.750521	+	0.660847i	$0.770197\pi$
$104$	9309.15	+	3024.73i	0.860683	+	0.279653i
$105$	−3306.73	+	15661.3i	−0.299930	+	1.42053i
$106$	1256.11	+	3865.90i	0.111793	+	0.344064i
$107$	11597.9	+	11597.9i	1.01301	+	1.01301i	0.999914	+	0.0130953i	$0.00416847\pi$
$107$	11597.9	+	11597.9i	1.01301	+	1.01301i	0.0130953	+	0.999914i	$0.495832\pi$
$108$	20257.4	+	10321.7i	1.73675	+	0.884917i
$109$	9477.04	−	13044.0i	0.797664	−	1.09789i	−0.195447	−	0.980714i	$-0.562616\pi$
$109$	9477.04	−	13044.0i	0.797664	−	1.09789i	0.993111	−	0.117176i	$-0.0373841\pi$
$110$	8921.23	−	5810.72i	0.737292	−	0.480225i
$111$	−20578.6	+	14951.2i	−1.67020	+	1.21347i
$112$	2805.36	+	17712.3i	0.223641	+	1.41202i
$113$	−132.731	+	21.0225i	−0.0103948	+	0.00164637i	−0.161630	−	0.986851i	$-0.551675\pi$
$113$	−132.731	+	21.0225i	−0.0103948	+	0.00164637i	0.151235	+	0.988498i	$0.451675\pi$
$114$	−26498.3	−	36471.7i	−2.03896	−	2.80638i
$115$	262.737	−	5146.76i	0.0198667	−	0.389169i
$116$	−16276.4	−	11825.5i	−1.20960	−	0.878827i
$117$	4162.79	−	8169.94i	0.304098	−	0.596825i
$118$	10959.6	−	10959.6i	0.787102	−	0.787102i
$119$	−15449.3	+	5019.78i	−1.09097	+	0.354479i
$120$	−5135.99	−	48236.8i	−0.356666	−	3.34978i
$121$	−3423.09	+	10535.2i	−0.233802	+	0.719567i
$122$	15731.7	−	8015.68i	1.05695	−	0.538544i
$123$	−339.399	+	2142.88i	−0.0224336	+	0.141640i
$124$			26218.9i			1.70518i
$125$	−14840.5	+	4888.77i	−0.949792	+	0.312881i
$126$	40058.4			2.52321
$127$	8336.72	+	1320.41i	0.516878	+	0.0818654i	0.409423	−	0.912345i	$-0.365730\pi$
$127$	8336.72	+	1320.41i	0.516878	+	0.0818654i	0.107455	+	0.994210i	$0.465730\pi$
$128$	9487.76	+	18620.8i	0.579087	+	1.13652i
$129$	45886.0	+	14909.3i	2.75741	+	0.895935i
$130$	−12879.4	+	1371.33i	−0.762095	+	0.0811437i
$131$	1550.46	+	4771.82i	0.0903478	+	0.278062i	0.986013	−	0.166666i	$-0.0533003\pi$
$131$	1550.46	+	4771.82i	0.0903478	+	0.278062i	−0.895666	+	0.444728i	$0.853300\pi$
$132$	−21204.5	−	21204.5i	−1.21697	−	1.21697i
$133$	−17393.8	−	8862.60i	−0.983313	−	0.501023i
$134$	−23248.3	+	31998.5i	−1.29474	+	1.78205i
$135$	−16268.2	−	830.476i	−0.892633	−	0.0455679i
$136$	39827.9	−	28936.7i	2.15332	−	1.56448i
$137$	−5356.83	−	33821.7i	−0.285408	−	1.80200i	−0.547339	−	0.836911i	$-0.684359\pi$
$137$	−5356.83	−	33821.7i	−0.285408	−	1.80200i	0.261931	−	0.965087i	$-0.415641\pi$
$138$	−20910.5	+	3311.90i	−1.09801	+	0.173908i
$139$	19144.3	+	26349.9i	0.990857	+	1.36380i	0.930770	+	0.365604i	$0.119138\pi$
$139$	19144.3	+	26349.9i	0.990857	+	1.36380i	0.0600864	+	0.998193i	$0.480862\pi$
$140$	−21173.5	−	32507.8i	−1.08028	−	1.65856i
$141$	8418.89	+	6116.68i	0.423464	+	0.307665i
$142$	−7802.42	+	15313.1i	−0.386948	+	0.759429i
$143$	−3065.54	+	3065.54i	−0.149911	+	0.149911i
$144$	−48420.0	+	15732.6i	−2.33507	+	0.758710i
$145$	14103.7	+	2977.85i	0.670804	+	0.141634i
$146$	−5339.83	+	16434.3i	−0.250508	+	0.770984i
$147$	−5427.36	+	2765.38i	−0.251162	+	0.127973i
$148$	9644.31	−	60891.8i	0.440299	−	2.77994i
$149$		−	22699.4i		−	1.02245i	−0.859446	−	0.511226i	$-0.829192\pi$
$149$		−	22699.4i		−	1.02245i	0.859446	−	0.511226i	$-0.170808\pi$
$150$	32245.5	+	55502.8i	1.43313	+	2.46679i
$151$	−6340.56			−0.278082			−0.139041	−	0.990287i	$-0.544402\pi$
$151$	−6340.56			−0.278082			−0.139041	+	0.990287i	$0.544402\pi$
$152$	58433.5	+	9254.96i	2.52915	+	0.400578i
$153$	−20936.8	−	41090.8i	−0.894392	−	1.75534i
$154$	−18012.9	−	5852.75i	−0.759526	−	0.246785i
$155$	−7663.89	−	17150.8i	−0.318997	−	0.713873i
$156$	11273.3	+	34695.7i	0.463236	+	1.42570i
$157$	−25494.6	−	25494.6i	−1.03430	−	1.03430i	−0.999390	−	0.0349133i	$-0.988884\pi$
$157$	−25494.6	−	25494.6i	−1.03430	−	1.03430i	−0.0349133	−	0.999390i	$-0.511116\pi$
$158$	72795.1	+	37091.0i	2.91600	+	1.48578i
$159$	−4821.60	+	6636.37i	−0.190720	+	0.262504i
$160$	14006.5	+	11310.8i	0.547128	+	0.441829i
$161$	−7416.82	+	5388.64i	−0.286132	+	0.207887i
$162$	−944.781	−	5965.11i	−0.0359999	−	0.227294i
$163$	9982.90	−	1581.14i	0.375735	−	0.0595106i	0.0342890	−	0.999412i	$-0.489083\pi$
$163$	9982.90	−	1581.14i	0.375735	−	0.0595106i	0.341446	+	0.939901i	$0.389083\pi$
$164$	−3090.84	−	4254.18i	−0.114918	−	0.158172i
$165$	20068.8	+	7672.51i	0.737147	+	0.281818i
$166$	−15722.9	−	11423.3i	−0.570579	−	0.414550i
$167$	18906.9	−	37107.0i	0.677936	−	1.33052i	−0.253754	−	0.967269i	$-0.581665\pi$
$167$	18906.9	−	37107.0i	0.677936	−	1.33052i	0.931690	−	0.363255i	$-0.118335\pi$
$168$	−61020.0	+	61020.0i	−2.16199	+	2.16199i
$169$	−22147.1	+	7196.04i	−0.775433	+	0.251954i
$170$	−32495.1	+	56459.8i	−1.12440	+	1.95363i
$171$	17126.1	−	52708.8i	0.585688	−	1.80256i
$172$	−104192.	+	53088.6i	−3.52191	+	1.79450i
$173$	−1644.71	+	10384.3i	−0.0549537	+	0.346964i	0.944857	+	0.327484i	$0.106201\pi$
$173$	−1644.71	+	10384.3i	−0.0549537	+	0.346964i	−0.999810	+	0.0194794i	$0.993799\pi$
$174$		−	59217.3i		−	1.95592i
$175$	23352.6	+	15075.5i	0.762533	+	0.492262i
$176$	24071.4			0.777100
$177$	30892.9	+	4892.95i	0.986078	+	0.156179i
$178$	−14493.1	−	28444.2i	−0.457425	−	0.897747i
$179$	−16714.5	−	5430.87i	−0.521660	−	0.169498i	0.0363386	−	0.999340i	$-0.488431\pi$
$179$	−16714.5	−	5430.87i	−0.521660	−	0.169498i	−0.557998	+	0.829842i	$0.688431\pi$
$180$	81749.3	−	73808.3i	2.52313	−	2.27803i
$181$	−103.656	−	319.019i	−0.00316400	−	0.00973778i	0.949462	−	0.313882i	$-0.101630\pi$
$181$	−103.656	−	319.019i	−0.00316400	−	0.00973778i	−0.952626	+	0.304144i	$0.901630\pi$
$182$	16292.6	+	16292.6i	0.491866	+	0.491866i
$183$	31747.0	+	16175.9i	0.947983	+	0.483022i
$184$	16330.8	−	22477.4i	0.482360	−	0.663911i
$185$	11490.2	+	42650.7i	0.335725	+	1.24619i
$186$	−62433.9	+	45360.9i	−1.80466	+	1.31116i
$187$	3410.99	+	21536.1i	0.0975433	+	0.615864i
$188$	−24911.4	+	3945.58i	−0.704827	+	0.111634i
$189$	17032.8	+	23443.6i	0.476828	+	0.656298i
$190$	−75590.5	+	20364.3i	−2.09392	+	0.564107i
$191$	30173.8	+	21922.5i	0.827110	+	0.600930i	0.918740	−	0.394863i	$-0.129208\pi$
$191$	30173.8	+	21922.5i	0.827110	+	0.600930i	−0.0916305	+	0.995793i	$0.529208\pi$
$192$	−8590.48	+	16859.8i	−0.233032	+	0.457350i
$193$	22387.3	−	22387.3i	0.601018	−	0.601018i	−0.339565	−	0.940583i	$-0.610280\pi$
$193$	22387.3	−	22387.3i	0.601018	−	0.601018i	0.940583	+	0.339565i	$0.110280\pi$
$194$	78715.3	−	25576.1i	2.09149	−	0.679566i
$195$	−17516.0	−	19400.6i	−0.460645	−	0.510206i
$196$	4562.16	−	14040.9i	0.118757	−	0.365496i
$197$	−20525.8	+	10458.4i	−0.528893	+	0.269485i	−0.697981	−	0.716116i	$-0.745918\pi$
$197$	−20525.8	+	10458.4i	−0.528893	+	0.269485i	0.169088	+	0.985601i	$0.445918\pi$
$198$	8411.48	−	53108.0i	0.214557	−	1.35466i
$199$		−	15173.4i		−	0.383156i	−0.981477	−	0.191578i	$-0.938639\pi$
$199$		−	15173.4i		−	0.383156i	0.981477	−	0.191578i	$-0.0613605\pi$
$200$	−81426.6	−	21581.8i	−2.03567	−	0.539546i
$201$	−79818.0			−1.97564
$202$	74376.4	+	11780.1i	1.82277	+	0.288699i
$203$	−11641.5	−	22847.8i	−0.282500	−	0.554438i
$204$	174503.	+	56699.3i	4.19316	+	1.36244i
$205$	3265.36	+	1879.36i	0.0777003	+	0.0447200i
$206$	−11604.4	−	35714.8i	−0.273457	−	0.841615i
$207$	−18403.8	−	18403.8i	−0.429504	−	0.429504i
$208$	−26092.2	−	13294.6i	−0.603092	−	0.307291i
$209$	−15402.1	+	21199.1i	−0.352603	+	0.485317i
$210$	40777.5	−	106661.i	0.924659	−	2.41861i
$211$	9994.42	−	7261.37i	0.224488	−	0.163100i	−0.469857	−	0.882743i	$-0.655694\pi$
$211$	9994.42	−	7261.37i	0.224488	−	0.163100i	0.694344	+	0.719643i	$0.255694\pi$
$212$	−3110.18	−	19636.9i	−0.0692013	−	0.436920i
$213$	−34255.5	+	5425.54i	−0.755043	+	0.119587i
$214$	−68777.1	−	94663.5i	−1.50181	−	2.06707i
$215$	52638.2	−	65183.1i	1.13874	−	1.41013i
$216$	−71048.0	−	51619.4i	−1.52281	−	1.10638i
$217$	−15171.4	+	29775.5i	−0.322185	+	0.632324i
$218$	−81333.2	+	81333.2i	−1.71141	+	1.71141i
$219$	−33165.0	+	10775.9i	−0.691498	+	0.224681i
$220$	−47543.7	+	21245.1i	−0.982308	+	0.438948i
$221$	8197.05	−	25227.9i	0.167831	−	0.516532i
$222$	161684.	−	82382.2i	3.28066	−	1.67158i
$223$	−12749.4	+	80496.8i	−0.256378	+	1.61871i	0.437915	+	0.899016i	$0.355717\pi$
$223$	−12749.4	+	80496.8i	−0.256378	+	1.61871i	−0.694293	+	0.719692i	$0.744283\pi$
$224$		−	32026.7i		−	0.638286i
$225$	−31900.9	+	72176.5i	−0.630142	+	1.42571i
$226$	958.696			0.0187700
$227$	−56116.9	−	8888.05i	−1.08904	−	0.172486i	−0.414004	−	0.910275i	$-0.635870\pi$
$227$	−56116.9	−	8888.05i	−1.08904	−	0.172486i	−0.675032	+	0.737789i	$0.735870\pi$
$228$	100105.	+	196467.i	1.92568	+	3.77937i
$229$	6667.98	+	2166.56i	0.127152	+	0.0413142i	0.371902	−	0.928272i	$-0.378706\pi$
$229$	6667.98	+	2166.56i	0.127152	+	0.0413142i	−0.244750	+	0.969586i	$0.578706\pi$
$230$	−7595.01	+	35971.4i	−0.143573	+	0.679988i
$231$	−11811.0	−	36350.7i	−0.221342	−	0.681221i
$232$	54951.1	+	54951.1i	1.02094	+	1.02094i
$233$	9697.85	+	4941.30i	0.178634	+	0.0910185i	0.541021	−	0.841009i	$-0.318038\pi$
$233$	9697.85	+	4941.30i	0.178634	+	0.0910185i	−0.362387	+	0.932028i	$0.618038\pi$
$234$	−38449.1	+	52920.6i	−0.702189	+	0.966480i
$235$	15142.2	−	9862.66i	0.274191	−	0.178590i
$236$	−61330.5	+	44559.2i	−1.10117	+	0.800043i
$237$	25791.8	+	162843.i	0.459183	+	2.89916i
$238$	114459.	−	18128.6i	2.02068	−	0.320044i
$239$	−19663.3	−	27064.1i	−0.344239	−	0.473804i	0.601435	−	0.798922i	$-0.294596\pi$
$239$	−19663.3	−	27064.1i	−0.344239	−	0.473804i	−0.945673	+	0.325118i	$0.894596\pi$
$240$	−7399.00	+	144939.i	−0.128455	+	2.51631i
$241$	82897.2	+	60228.3i	1.42727	+	1.03697i	0.990517	+	0.137389i	$0.0438711\pi$
$241$	82897.2	+	60228.3i	1.42727	+	1.03697i	0.436752	+	0.899582i	$0.356129\pi$
$242$	35876.6	−	70411.8i	0.612605	−	1.20231i
$243$	45937.6	−	45937.6i	0.777957	−	0.777957i
$244$	−82131.4	+	26686.1i	−1.37952	+	0.448235i
$245$	1119.92	+	10518.2i	0.0186576	+	0.175231i
$246$	4782.87	−	14720.2i	0.0790349	−	0.243244i
$247$	28403.3	−	14472.2i	0.465559	−	0.237214i
$248$	15843.0	−	100029.i	0.257593	−	1.62638i
$249$		−	39219.6i		−	0.632563i
$250$	110024.	−	17884.8i	1.76038	−	0.286158i
$251$	50063.2			0.794641			0.397320	−	0.917680i	$-0.369940\pi$
$251$	50063.2			0.794641			0.397320	+	0.917680i	$0.369940\pi$
$252$	−193519.	−	30650.3i	−3.04735	−	0.482652i
$253$	5586.67	+	10964.5i	0.0872795	+	0.171296i
$254$	−57267.8	−	18607.4i	−0.887653	−	0.288416i
$255$	−130722.	+	13918.6i	−2.01034	+	0.214050i
$256$	−39572.5	−	121792.i	−0.603829	−	1.85839i
$257$	−45888.7	−	45888.7i	−0.694768	−	0.694768i	0.268509	−	0.963277i	$-0.413469\pi$
$257$	−45888.7	−	45888.7i	−0.694768	−	0.694768i	−0.963277	+	0.268509i	$0.913469\pi$
$258$	−306679.	−	156261.i	−4.60727	−	2.34752i
$259$	46187.1	−	63571.1i	0.688528	−	0.947677i
$260$	63268.5	+	3229.79i	0.935924	+	0.0477779i
$261$	58895.7	−	42790.2i	0.864575	−	0.628151i
$262$	−5599.37	−	35353.0i	−0.0815711	−	0.515020i
$263$	−53875.6	+	8533.06i	−0.778898	+	0.123365i	−0.533209	−	0.845983i	$-0.679014\pi$
$263$	−53875.6	+	8533.06i	−0.778898	+	0.123365i	−0.245689	+	0.969349i	$0.579014\pi$
$264$	68085.1	+	93711.1i	0.976887	+	1.34457i
$265$	7774.44	+	11936.1i	0.110708	+	0.169970i
$266$	112668.	+	81858.1i	1.59235	+	1.15691i
$267$	29247.5	−	57401.4i	0.410266	−	0.805193i
$268$	136794.	−	136794.i	1.90457	−	1.90457i
$269$	13667.9	−	4440.96i	0.188885	−	0.0613723i	−0.213047	−	0.977042i	$-0.568339\pi$
$269$	13667.9	−	4440.96i	0.188885	−	0.0613723i	0.401932	+	0.915670i	$0.368339\pi$
$270$	113701.	+	24006.8i	1.55968	+	0.329312i
$271$	−28143.9	+	86618.0i	−0.383218	+	1.17942i	0.554547	+	0.832152i	$0.312892\pi$
$271$	−28143.9	+	86618.0i	−0.383218	+	1.17942i	−0.937765	+	0.347271i	$0.887108\pi$
$272$	−131231.	+	66865.5i	−1.77377	+	0.903783i
$273$	−7273.87	+	45925.4i	−0.0975978	+	0.616208i
$274$			244289.i			3.25389i
$275$	24890.1	−	27794.4i	0.329126	−	0.367530i
$276$	103551.			1.35936
$277$	70821.9	+	11217.1i	0.923014	+	0.146191i	0.599814	−	0.800140i	$-0.295241\pi$
$277$	70821.9	+	11217.1i	0.923014	+	0.146191i	0.323200	+	0.946331i	$0.395241\pi$
$278$	−105487.	−	207029.i	−1.36492	−	2.67881i
$279$	−90229.1	−	29317.2i	−1.15915	−	0.376629i
$280$	61136.9	+	136816.i	0.779807	+	1.74511i
$281$	−23770.6	−	73158.5i	−0.301043	−	0.926514i	−0.981124	−	0.193378i	$-0.938056\pi$
$281$	−23770.6	−	73158.5i	−0.301043	−	0.926514i	0.680082	−	0.733136i	$-0.261944\pi$
$282$	−52494.2	−	52494.2i	−0.660105	−	0.660105i
$283$	73193.2	+	37293.8i	0.913898	+	0.465654i	0.846691	−	0.532085i	$-0.178591\pi$
$283$	73193.2	+	37293.8i	0.913898	+	0.465654i	0.0672067	+	0.997739i	$0.478591\pi$
$284$	49409.5	−	68006.3i	0.612595	−	0.843165i
$285$	−122910.	−	99255.4i	−1.51321	−	1.22198i
$286$	25021.2	−	18179.0i	0.305898	−	0.222248i
$287$	−1048.47	−	6619.76i	−0.0127289	−	0.0803671i
$288$	89803.6	−	14223.5i	1.08270	−	0.171483i
$289$	−29326.3	−	40364.2i	−0.351125	−	0.483282i
$290$	−96052.5	−	36721.8i	−1.14212	−	0.436645i
$291$	135126.	+	98174.7i	1.59570	+	1.15935i
$292$	38370.8	−	75306.9i	0.450023	−	0.883220i
$293$	−70253.2	+	70253.2i	−0.818334	+	0.818334i	−0.985867	−	0.167532i	$-0.946420\pi$
$293$	−70253.2	+	70253.2i	−0.818334	+	0.818334i	0.167532	+	0.985867i	$0.446420\pi$
$294$	41327.9	−	13428.2i	0.478132	−	0.155355i
$295$	27093.8	−	47075.1i	0.311334	−	0.540937i
$296$	−73588.9	+	226483.i	−0.839903	+	2.58495i
$297$	34657.2	−	17658.7i	0.392899	−	0.200192i
$298$	−25332.4	+	159943.i	−0.285262	+	1.80107i
$299$		−	14970.4i		−	0.167452i
$300$	−113307.	−	292801.i	−1.25897	−	3.25335i
$301$	−149045.			−1.64507
$302$	44676.2	+	7076.01i	0.489849	+	0.0775845i
$303$	68990.6	+	135402.i	0.751458	+	1.47482i
$304$	−168335.	−	54695.3i	−1.82149	−	0.591838i
$305$	45924.8	−	41463.7i	0.493683	−	0.445727i
$306$	101666.	+	312896.i	1.08576	+	3.34162i
$307$	68607.0	+	68607.0i	0.727933	+	0.727933i	0.970208	−	0.242274i	$-0.0778934\pi$
$307$	68607.0	+	68607.0i	0.727933	+	0.727933i	−0.242274	+	0.970208i	$0.577893\pi$
$308$	82540.6	+	42056.5i	0.870094	+	0.443335i
$309$	44543.9	−	61309.4i	0.466521	−	0.642111i
$310$	34860.4	+	129399.i	0.362751	+	1.34650i
$311$	−18746.2	+	13619.9i	−0.193817	+	0.140816i	−0.680462	−	0.732784i	$-0.738221\pi$
$311$	−18746.2	+	13619.9i	−0.193817	+	0.140816i	0.486645	+	0.873600i	$0.338221\pi$
$312$	−22044.1	−	139181.i	−0.226456	−	1.42979i
$313$	−104123.	+	16491.5i	−1.06282	+	0.168334i	−0.663271	−	0.748379i	$-0.730832\pi$
$313$	−104123.	+	16491.5i	−1.06282	+	0.168334i	−0.399547	+	0.916713i	$0.630832\pi$
$314$	151185.	+	208089.i	1.53338	+	2.11052i
$315$	135547.	−	36516.7i	1.36606	−	0.368019i
$316$	−323287.	−	234882.i	−3.23753	−	2.35220i
$317$	−52905.5	+	103833.i	−0.526481	+	1.03328i	0.462692	+	0.886519i	$0.346884\pi$
$317$	−52905.5	+	103833.i	−0.526481	+	1.03328i	−0.989173	+	0.146757i	$0.953116\pi$
$318$	41379.6	−	41379.6i	0.409197	−	0.409197i
$319$	−32735.3	+	10636.3i	−0.321688	+	0.104523i
$320$	22020.0	+	24389.1i	0.215039	+	0.238175i
$321$	72968.5	−	224574.i	0.708150	−	2.17946i
$322$	58273.4	−	29691.8i	0.562029	−	0.286368i
$323$	25081.1	−	158356.i	0.240404	−	1.51785i
$324$			29539.8i			0.281396i
$325$	−42330.4	+	16380.9i	−0.400761	+	0.155085i
$326$	−72105.1			−0.678470
$327$	−229262.	−	36311.5i	−2.14405	−	0.339585i
$328$	9221.39	+	18098.0i	0.0857134	+	0.168222i
$329$	−30573.7	−	9934.00i	−0.282459	−	0.0917767i
$330$	−132844.	−	76457.9i	−1.21988	−	0.702093i
$331$	912.842	+	2809.44i	0.00833182	+	0.0256427i	0.955136	−	0.296168i	$-0.0957087\pi$
$331$	912.842	+	2809.44i	0.00833182	+	0.0256427i	−0.946804	+	0.321810i	$0.895709\pi$
$332$	67215.4	+	67215.4i	0.609807	+	0.609807i
$333$	198767.	+	101277.i	1.79249	+	0.913320i
$334$	−174631.	+	240359.i	−1.56541	+	2.15461i
$335$	−49496.7	+	129468.i	−0.441049	+	1.15364i
$336$	208867.	−	151751.i	1.85009	−	1.34417i
$337$	−5612.01	−	35432.8i	−0.0494150	−	0.311994i	−0.999999	−	0.00152596i	$-0.999514\pi$
$337$	−5612.01	−	35432.8i	−0.0494150	−	0.311994i	0.950584	−	0.310468i	$-0.100486\pi$
$338$	164082.	−	25988.0i	1.43624	−	0.227478i
$339$	1137.18	+	1565.19i	0.00989528	+	0.0136197i
$340$	200181.	−	247889.i	1.73167	−	2.14437i
$341$	36289.6	+	26365.9i	0.312085	+	0.226743i
$342$	−179495.	+	352279.i	−1.53462	+	3.01185i
$343$	88811.2	−	88811.2i	0.754882	−	0.754882i
$344$	429588.	−	139582.i	3.63024	−	1.17954i
$345$	−67736.6	+	30268.4i	−0.569096	+	0.254303i
$346$	23177.6	−	71333.2i	0.193605	−	0.595854i
$347$	−85436.0	+	43531.8i	−0.709548	+	0.361533i	−0.771224	−	0.636563i	$-0.780355\pi$
$347$	−85436.0	+	43531.8i	−0.709548	+	0.361533i	0.0616762	+	0.998096i	$0.480355\pi$
$348$	−45309.6	+	286073.i	−0.374138	+	2.36221i
$349$		−	118442.i		−	0.972420i	−0.873842	−	0.486210i	$-0.838379\pi$
$349$		−	118442.i		−	0.972420i	0.873842	−	0.486210i	$-0.161621\pi$
$350$	−147720.	−	132285.i	−1.20588	−	1.07988i
$351$	−47319.5			−0.384084
$352$	−42459.8	−	6724.97i	−0.342683	−	0.0542756i
$353$	−97140.7	−	190649.i	−0.779564	−	1.52998i	−0.846600	−	0.532230i	$-0.821354\pi$
$353$	−97140.7	−	190649.i	−0.779564	−	1.52998i	0.0670363	−	0.997751i	$-0.478646\pi$
$354$	−212214.	−	68952.4i	−1.69343	−	0.550228i
$355$	−12442.1	+	58928.2i	−0.0987274	+	0.467591i
$356$	48250.8	+	148501.i	0.380719	+	1.17173i
$357$	165365.	+	165365.i	1.29750	+	1.29750i
$358$	111711.	+	56919.7i	0.871627	+	0.444116i
$359$	−73632.6	+	101347.i	−0.571323	+	0.786358i	−0.992711	−	0.120522i	$-0.961543\pi$
$359$	−73632.6	+	101347.i	−0.571323	+	0.786358i	0.421388	+	0.906881i	$0.361543\pi$
$360$	−356485.	+	232192.i	−2.75066	+	1.79160i
$361$	50445.6	−	36650.9i	0.387087	−	0.281235i
$362$	374.345	+	2363.52i	0.00285664	+	0.0180361i
$363$	157512.	−	24947.4i	1.19536	−	0.189327i
$364$	−66241.9	−	91174.1i	−0.499954	−	0.688127i
$365$	−3087.29	+	60477.1i	−0.0231735	+	0.453947i
$366$	−205640.	−	149407.i	−1.53513	−	1.11534i
$367$	−33820.7	+	66376.9i	−0.251102	+	0.492816i	−0.981808	−	0.189876i	$-0.939191\pi$
$367$	−33820.7	+	66376.9i	−0.251102	+	0.492816i	0.730706	+	0.682693i	$0.239191\pi$
$368$	−58775.8	+	58775.8i	−0.434013	+	0.434013i
$369$	18096.3	−	5879.85i	0.132904	−	0.0431831i
$370$	−33363.2	−	313344.i	−0.243705	−	2.28886i
$371$	7830.68	−	24100.3i	0.0568920	−	0.175096i
$372$	336320.	−	171363.i	2.43034	−	1.23832i
$373$	−23865.8	+	150683.i	−0.171537	+	1.08304i	0.740235	+	0.672348i	$0.234714\pi$
$373$	−23865.8	+	150683.i	−0.171537	+	1.08304i	−0.911772	+	0.410696i	$0.865286\pi$
$374$		−	155552.i		−	1.11207i
$375$	159706.	+	158412.i	1.13569	+	1.12649i
$376$	97424.8			0.689118
$377$	41357.8	+	6550.43i	0.290988	+	0.0460879i
$378$	−93851.8	−	184194.i	−0.656839	−	1.28912i
$379$	19434.4	+	6314.64i	0.135299	+	0.0439612i	0.375884	−	0.926667i	$-0.377339\pi$
$379$	19434.4	+	6314.64i	0.135299	+	0.0439612i	−0.240585	+	0.970628i	$0.577339\pi$
$380$	380753.	−	40540.5i	2.63679	−	0.280751i
$381$	−37550.4	−	115568.i	−0.258681	−	0.796139i
$382$	−188142.	−	188142.i	−1.28932	−	1.28932i
$383$	−138126.	−	70378.9i	−0.941627	−	0.479783i	−0.0853795	−	0.996349i	$-0.527210\pi$
$383$	−138126.	−	70378.9i	−0.941627	−	0.479783i	−0.856248	+	0.516566i	$0.827210\pi$
$384$	176845.	−	243406.i	1.19931	−	1.65070i
$385$	−66286.3	−	3383.84i	−0.447200	−	0.0228291i
$386$	−182727.	+	132759.i	−1.22639	+	0.891025i
$387$	−66193.1	−	417927.i	−0.441968	−	2.79048i
$388$	−399836.	+	63327.8i	−2.65594	+	0.420659i
$389$	53386.5	+	73480.2i	0.352803	+	0.485592i	0.948126	−	0.317895i	$-0.102976\pi$
$389$	53386.5	+	73480.2i	0.352803	+	0.485592i	−0.595323	+	0.803487i	$0.702976\pi$
$390$	101769.	+	156246.i	0.669091	+	1.02726i
$391$	−60914.0	−	44256.6i	−0.398441	−	0.289484i
$392$	−25889.7	+	50811.3i	−0.168482	+	0.330665i
$393$	51076.3	−	51076.3i	0.330700	−	0.330700i
$394$	156299.	−	50784.5i	1.00684	−	0.327144i
$395$	280131.	+	59147.1i	1.79543	+	0.379087i
$396$	−81270.2	+	250124.i	−0.518252	+	1.59502i
$397$	−114565.	+	58374.0i	−0.726896	+	0.370372i	−0.777952	−	0.628324i	$-0.783741\pi$
$397$	−114565.	+	58374.0i	−0.726896	+	0.370372i	0.0510557	+	0.998696i	$0.483741\pi$
$398$	−16933.4	+	106913.i	−0.106900	+	0.674939i
$399$			281042.i			1.76533i
$400$	230509.	+	101881.i	1.44068	+	0.636758i
$401$	234027.			1.45538			0.727692	−	0.685904i	$-0.240593\pi$
$401$	234027.			1.45538			0.727692	+	0.685904i	$0.240593\pi$
$402$	562405.	+	89076.3i	3.48015	+	0.551201i
$403$	−24774.1	−	48621.9i	−0.152541	−	0.299379i
$404$	−350292.	−	113817.i	−2.14619	−	0.697339i
$405$	−8634.61	−	19323.1i	−0.0526420	−	0.117806i
$406$	56529.5	+	173980.i	0.342944	+	1.05547i
$407$	−74581.9	−	74581.9i	−0.450240	−	0.450240i
$408$	−631492.	−	321761.i	−3.79356	−	1.93292i
$409$	40911.3	−	56309.5i	0.244566	−	0.336616i	−0.669033	−	0.743233i	$-0.733291\pi$
$409$	40911.3	−	56309.5i	0.244566	−	0.336616i	0.913599	+	0.406617i	$0.133291\pi$
$410$	−20910.7	−	16886.3i	−0.124394	−	0.100454i
$411$	−398832.	+	289769.i	−2.36106	+	1.71541i
$412$	28733.1	+	181414.i	0.169273	+	1.06875i
$413$	−95433.8	+	15115.2i	−0.559503	+	0.0886165i
$414$	109137.	+	150214.i	0.636751	+	0.876412i
$415$	−63615.5	−	24320.8i	−0.369374	−	0.141215i
$416$	42309.9	+	30740.0i	0.244487	+	0.177630i
$417$	212875.	−	417792.i	1.22420	−	2.40263i
$418$	132183.	−	132183.i	0.756522	−	0.756522i
$419$	180861.	−	58765.3i	1.03019	−	0.334729i	0.255324	−	0.966856i	$-0.417818\pi$
$419$	180861.	−	58765.3i	1.03019	−	0.334729i	0.774865	+	0.632127i	$0.217818\pi$
$420$	−278603.	+	484068.i	−1.57938	+	2.74415i
$421$	27560.4	−	84822.1i	0.155497	−	0.478569i	−0.842714	−	0.538361i	$-0.819044\pi$
$421$	27560.4	−	84822.1i	0.155497	−	0.478569i	0.998211	+	0.0597918i	$0.0190437\pi$
$422$	−78525.3	+	40010.7i	−0.440945	+	0.224673i
$423$	14277.0	−	90141.3i	0.0797913	−	0.503782i
$424$			76797.1i			0.427182i
$425$	−58487.1	+	220667.i	−0.323804	+	1.22169i
$426$	247423.			1.36339
$427$	−108714.	−	17218.6i	−0.596253	−	0.0944372i
$428$	259825.	+	509935.i	1.41838	+	2.78373i
$429$	59358.8	+	19286.9i	0.322531	+	0.104797i
$430$	−443638.	+	400543.i	−2.39934	+	2.16627i
$431$	31161.2	+	95904.3i	0.167749	+	0.516278i	0.999228	−	0.0392775i	$-0.0125056\pi$
$431$	31161.2	+	95904.3i	0.167749	+	0.516278i	−0.831479	+	0.555556i	$0.812506\pi$
$432$	185783.	+	185783.i	0.995491	+	0.995491i
$433$	−221351.	−	112784.i	−1.18061	−	0.601551i	−0.250244	−	0.968183i	$-0.580511\pi$
$433$	−221351.	−	112784.i	−1.18061	−	0.601551i	−0.930366	+	0.366632i	$0.880511\pi$
$434$	140128.	−	192870.i	0.743954	−	1.02396i
$435$	−53981.7	−	200376.i	−0.285278	−	1.05893i
$436$	455145.	−	330682.i	2.39429	−	1.73955i
$437$	−14154.8	−	89370.0i	−0.0741210	−	0.467982i
$438$	245709.	−	38916.6i	1.28078	−	0.202855i
$439$	−90615.8	−	124722.i	−0.470191	−	0.647163i	0.506392	−	0.862304i	$-0.330979\pi$
$439$	−90615.8	−	124722.i	−0.470191	−	0.647163i	−0.976583	+	0.215141i	$0.930979\pi$
$440$	194224.	−	52324.3i	1.00322	−	0.270270i
$441$	43218.7	+	31400.2i	0.222226	+	0.161457i
$442$	−85911.4	+	168611.i	−0.439750	+	0.863059i
$443$	−125513.	+	125513.i	−0.639559	+	0.639559i	−0.950447	−	0.310888i	$-0.899374\pi$
$443$	−125513.	+	125513.i	−0.639559	+	0.639559i	0.310888	+	0.950447i	$0.399374\pi$
$444$	−844116.	+	274270.i	−4.28190	+	1.39127i
$445$	−74970.1	−	83036.1i	−0.378589	−	0.419322i
$446$	179668.	−	552960.i	0.903234	−	2.77987i
$447$	−291174.	+	148361.i	−1.45726	+	0.742513i
$448$	9144.23	−	57734.4i	0.0455608	−	0.287659i
$449$			323701.i			1.60565i	0.596214	+	0.802825i	$0.296671\pi$
$449$			323701.i			1.60565i	−0.596214	+	0.802825i	$0.703329\pi$
$450$	305326.	−	472962.i	1.50778	−	2.33561i
$451$	−8996.39			−0.0442298
$452$	−4631.37	−	733.537i	−0.0226690	−	0.00359042i
$453$	41441.1	+	81332.7i	0.201946	+	0.396341i
$454$	385486.	+	125252.i	1.87024	+	0.607678i
$455$	69981.9	+	40277.7i	0.338036	+	0.194555i
$456$	−263197.	−	810038.i	−1.26576	−	3.89561i
$457$	216002.	+	216002.i	1.03425	+	1.03425i	0.999392	+	0.0348595i	$0.0110984\pi$
$457$	216002.	+	216002.i	1.03425	+	1.03425i	0.0348595	+	0.999392i	$0.488902\pi$
$458$	−44565.4	−	22707.2i	−0.212455	−	0.108251i
$459$	−139889.	+	192541.i	−0.663987	+	0.913899i
$460$	64214.0	−	167963.i	0.303469	−	0.793777i
$461$	166727.	−	121134.i	0.784521	−	0.569988i	−0.121811	−	0.992553i	$-0.538870\pi$
$461$	166727.	−	121134.i	0.784521	−	0.569988i	0.906332	+	0.422565i	$0.138870\pi$
$462$	42654.7	+	269311.i	0.199840	+	1.26174i
$463$	231467.	−	36660.7i	1.07976	−	0.171017i	0.408883	−	0.912587i	$-0.365918\pi$
$463$	231467.	−	36660.7i	1.07976	−	0.171017i	0.670876	+	0.741570i	$0.265918\pi$
$464$	−136658.	−	188094.i	−0.634746	−	0.873653i
$465$	−169909.	+	210403.i	−0.785799	+	0.973075i
$466$	−62817.6	−	45639.6i	−0.289274	−	0.210170i
$467$	107429.	−	210842.i	0.492593	−	0.966769i	−0.502190	−	0.864757i	$-0.667472\pi$
$467$	107429.	−	210842.i	0.492593	−	0.966769i	0.994783	−	0.102011i	$-0.0325278\pi$
$468$	226236.	−	226236.i	1.03293	−	1.03293i
$469$	234505.	−	76195.2i	1.06612	−	0.346403i
$470$	−117700.	+	52594.7i	−0.532821	+	0.238093i
$471$	−160399.	+	493658.i	−0.723036	+	2.22528i
$472$	260910.	−	132940.i	1.17113	−	0.596723i
$473$	−31296.6	+	197599.i	−0.139886	+	0.883205i
$474$		−	1.17619e6i		−	5.23506i
$475$	−237215.	+	137815.i	−1.05137	+	0.610813i
$476$	−566813.			−2.50165
$477$	71055.7	+	11254.1i	0.312293	+	0.0494624i
$478$	108346.	+	212641.i	0.474195	+	0.930659i
$479$	135568.	+	44048.6i	0.590860	+	0.191982i	0.589160	−	0.808016i	$-0.299459\pi$
$479$	135568.	+	44048.6i	0.590860	+	0.191982i	0.00170023	+	0.999999i	$0.499459\pi$
$480$	53543.6	−	253592.i	0.232394	−	1.10066i
$481$	39651.3	+	122034.i	0.171383	+	0.527463i
$482$	−516888.	−	516888.i	−2.22486	−	2.22486i
$483$	117598.	+	59918.9i	0.504085	+	0.256844i
$484$	−227192.	+	312703.i	−0.969844	+	1.33488i
$485$	243037.	−	158299.i	1.03321	−	0.672967i
$486$	−374947.	+	272415.i	−1.58744	+	1.15334i
$487$	6440.53	+	40663.9i	0.0271559	+	0.171456i	0.997539	−	0.0701163i	$-0.0223371\pi$
$487$	6440.53	+	40663.9i	0.0271559	+	0.171456i	−0.970383	+	0.241572i	$0.922337\pi$
$488$	329468.	−	52182.7i	1.38348	−	0.219122i
$489$	−85528.9	−	117720.i	−0.357680	−	0.492305i
$490$	3847.17	−	75362.3i	0.0160232	−	0.313879i
$491$	55293.6	+	40173.2i	0.229357	+	0.166638i	0.696529	−	0.717529i	$-0.254727\pi$
$491$	55293.6	+	40173.2i	0.229357	+	0.166638i	−0.467172	+	0.884167i	$0.654727\pi$
$492$	−34368.6	+	67452.3i	−0.141982	+	0.278655i
$493$	148918.	−	148918.i	0.612709	−	0.612709i
$494$	−216283.	+	70274.6i	−0.886276	+	0.287968i
$495$	−19950.3	−	187371.i	−0.0814214	−	0.764703i
$496$	−93629.7	+	288163.i	−0.380584	+	1.17132i
$497$	95463.2	−	48640.9i	0.386477	−	0.196920i
$498$	−43768.7	+	276345.i	−0.176484	+	1.11428i
$499$		−	46319.6i		−	0.186022i	−0.995665	−	0.0930109i	$-0.970351\pi$
$499$		−	46319.6i		−	0.186022i	0.995665	−	0.0930109i	$-0.0296491\pi$
$500$	−545198.	+	2216.60i	−2.18079	+	0.00886639i
$501$	−599559.			−2.38867
$502$	−352750.	−	55870.1i	−1.39978	−	0.221703i
$503$	−38597.8	−	75752.4i	−0.152555	−	0.299406i	0.802063	−	0.597240i	$-0.203736\pi$
$503$	−38597.8	−	75752.4i	−0.152555	−	0.299406i	−0.954618	+	0.297834i	$0.903736\pi$
$504$	719781.	+	233871.i	2.83360	+	0.920694i
$505$	262409.	−	27939.9i	1.02895	−	0.109557i
$506$	−27128.0	−	83491.4i	−0.105954	−	0.326092i
$507$	237057.	+	237057.i	0.922227	+	0.922227i
$508$	262418.	+	133709.i	1.01687	+	0.518123i
$509$	−40166.2	+	55284.0i	−0.155033	+	0.213385i	−0.879468	−	0.475959i	$-0.842101\pi$
$509$	−40166.2	+	55284.0i	−0.155033	+	0.213385i	0.724434	+	0.689344i	$0.242101\pi$
$510$	936616.	+	47813.2i	3.60098	+	0.183826i
$511$	87151.5	−	63319.3i	0.333759	−	0.242490i
$512$	90605.2	+	572059.i	0.345631	+	2.18223i
$513$	−282487.	+	44741.5i	−1.07340	+	0.170011i
$514$	272125.	+	374548.i	1.03001	+	1.41769i
$515$	−71823.5	−	110271.i	−0.270802	−	0.415764i
$516$	1.36198e6	+	989533.i	5.11529	+	3.71647i
$517$	−19590.0	+	38447.5i	−0.0732915	+	0.143843i
$518$	−396384.	+	396384.i	−1.47726	+	1.47726i
$519$	143953.	−	46773.1i	0.534423	−	0.173645i
$520$	−239427.	−	50552.7i	−0.885454	−	0.186955i
$521$	82832.5	−	254932.i	0.305158	−	0.939181i	−0.674460	−	0.738312i	$-0.735623\pi$
$521$	82832.5	−	254932.i	0.305158	−	0.939181i	0.979618	−	0.200869i	$-0.0643766\pi$
$522$	−462739.	+	235777.i	−1.69822	+	0.865288i
$523$	−3764.83	+	23770.2i	−0.0137639	+	0.0869019i	−0.993614	−	0.112832i	$-0.964008\pi$
$523$	−3764.83	+	23770.2i	−0.0137639	+	0.0869019i	0.979850	+	0.199734i	$0.0640078\pi$
$524$			175072.i			0.637607i
$525$	40749.7	−	398084.i	0.147845	−	1.44430i
$526$	389136.			1.40647
$527$	−271080.	−	42934.8i	−0.976059	−	0.154592i
$528$	−157328.	−	308773.i	−0.564336	−	1.10757i
$529$	225731.	+	73344.5i	0.806641	+	0.262094i
$530$	−41458.9	−	92779.5i	−0.147593	−	0.330294i
$531$	−84767.0	−	260886.i	−0.300634	−	0.925256i
$532$	−481656.	−	481656.i	−1.70182	−	1.70182i
$533$	9751.60	+	4968.69i	0.0343259	+	0.0174899i
$534$	−270140.	+	371816.i	−0.947341	+	1.30390i
$535$	−319018.	−	257620.i	−1.11457	−	0.900062i
$536$	−604547.	+	439229.i	−2.10427	+	1.52884i
$537$	39580.1	+	249899.i	0.137255	+	0.866594i
$538$	−101261.	+	16038.2i	−0.349848	+	0.0554104i
$539$	−14846.2	−	20434.1i	−0.0511022	−	0.0703361i
$540$	−530910.	−	202972.i	−1.82068	−	0.696063i
$541$	−423927.	−	308001.i	−1.44843	−	1.05234i	−0.986196	−	0.165585i	$-0.947049\pi$
$541$	−423927.	−	308001.i	−1.44843	−	1.05234i	−0.462232	−	0.886759i	$-0.652951\pi$
$542$	294970.	−	578911.i	1.00410	−	1.97067i
$543$	−3414.70	+	3414.70i	−0.0115812	+	0.0115812i
$544$	250160.	−	81281.8i	0.845316	−	0.274660i
$545$	−201068.	+	349353.i	−0.676940	+	1.17617i
$546$	102505.	−	315477.i	0.343842	−	1.05824i
$547$	185511.	−	94522.3i	0.620003	−	0.315907i	−0.115625	−	0.993293i	$-0.536887\pi$
$547$	185511.	−	94522.3i	0.620003	−	0.315907i	0.735628	+	0.677386i	$0.236887\pi$
$548$	186916.	−	1.18014e6i	0.622422	−	3.92982i
$549$		−	312484.i		−	1.03677i
$550$	−206397.	+	168065.i	−0.682304	+	0.555587i
$551$	253090.			0.833628
$552$	−395062.	−	62571.6i	−1.29654	−	0.205352i
$553$	−231228.	−	453811.i	−0.756119	−	1.48397i
$554$	−486500.	−	158074.i	−1.58512	−	0.515038i
$555$	471999.	−	426149.i	1.53234	−	1.38349i
$556$	351190.	+	1.08085e6i	1.13604	+	3.49636i
$557$	413755.	+	413755.i	1.33362	+	1.33362i	0.902104	+	0.431519i	$0.142022\pi$
$557$	413755.	+	413755.i	1.33362	+	1.33362i	0.431519	+	0.902104i	$0.357978\pi$
$558$	603045.	+	307267.i	1.93679	+	0.986841i
$559$	143057.	−	196901.i	0.457811	−	0.630123i
$560$	−116623.	−	432894.i	−0.371883	−	1.38040i
$561$	253959.	−	184512.i	0.806932	−	0.586271i
$562$	85845.9	+	542010.i	0.271799	+	1.71607i
$563$	315415.	−	49956.8i	0.995096	−	0.157608i	0.362412	−	0.932018i	$-0.381953\pi$
$563$	315415.	−	49956.8i	0.995096	−	0.157608i	0.632684	+	0.774410i	$0.281953\pi$
$564$	213429.	+	293760.i	0.670959	+	0.923495i
$565$	3243.98	−	873.934i	0.0101620	−	0.00273767i
$566$	−474107.	−	344459.i	−1.47994	−	1.07524i
$567$	−17093.0	+	33546.9i	−0.0531682	+	0.104348i
$568$	−229598.	+	229598.i	−0.711658	+	0.711658i
$569$	−417182.	+	135550.i	−1.28855	+	0.418675i	−0.871583	−	0.490248i	$-0.836906\pi$
$569$	−417182.	+	135550.i	−1.28855	+	0.418675i	−0.416965	+	0.908923i	$0.636906\pi$
$570$	755270.	+	836530.i	2.32462	+	2.57473i
$571$	−155926.	+	479890.i	−0.478240	+	1.47187i	0.363298	+	0.931673i	$0.381651\pi$
$571$	−155926.	+	479890.i	−0.478240	+	1.47187i	−0.841538	+	0.540198i	$0.818349\pi$
$572$	−134785.	+	68676.3i	−0.411954	+	0.209901i
$573$	83996.6	−	530334.i	0.255831	−	1.61525i
$574$			47813.5i			0.145120i
$575$	7091.48	+	128641.i	0.0214487	+	0.389085i
$576$	165950.			0.500187
$577$	45188.4	+	7157.14i	0.135730	+	0.0214975i	0.223930	−	0.974605i	$-0.428111\pi$
$577$	45188.4	+	7157.14i	0.135730	+	0.0214975i	−0.0881998	+	0.996103i	$0.528111\pi$
$578$	161590.	+	317138.i	0.483681	+	0.949277i
$579$	−433491.	−	140850.i	−1.29307	−	0.420145i
$580$	435924.	+	250894.i	1.29585	+	0.745819i
$581$	37439.5	+	115227.i	0.110912	+	0.341351i
$582$	−842548.	−	842548.i	−2.48742	−	2.48742i
$583$	−30307.1	−	15442.2i	−0.0891675	−	0.0454331i
$584$	−191895.	+	264121.i	−0.562650	+	0.774421i
$585$	−81859.8	+	214119.i	−0.239199	+	0.625668i
$586$	573413.	−	416609.i	1.66983	−	1.21320i
$587$	10807.1	+	68233.5i	0.0313642	+	0.198026i	0.998395	−	0.0566336i	$-0.0180367\pi$
$587$	10807.1	+	68233.5i	0.0313642	+	0.198026i	−0.967031	+	0.254659i	$0.918037\pi$
$588$	−209926.	+	33249.0i	−0.607171	+	0.0961664i
$589$	−193869.	−	266838.i	−0.558827	−	0.769160i
$590$	−243441.	+	301459.i	−0.699342	+	0.866013i
$591$	268308.	+	194938.i	0.768174	+	0.558111i
$592$	323446.	−	634799.i	0.922909	−	1.81131i
$593$	−109954.	+	109954.i	−0.312680	+	0.312680i	−0.845947	−	0.533267i	$-0.820964\pi$
$593$	−109954.	+	109954.i	−0.312680	+	0.312680i	0.533267	+	0.845947i	$0.320964\pi$
$594$	−263905.	+	85748.0i	−0.747954	+	0.243025i
$595$	370774.	−	165682.i	1.04731	−	0.467995i
$596$	244757.	−	753285.i	0.689038	−	2.12064i
$597$	−194635.	+	99171.3i	−0.546099	+	0.278251i
$598$	−16706.9	+	105483.i	−0.0467189	+	0.294971i
$599$			50977.3i			0.142077i	0.997474	+	0.0710384i	$0.0226313\pi$
$599$			50977.3i			0.142077i	−0.997474	+	0.0710384i	$0.977369\pi$
$600$	255356.	+	1.18555e6i	0.709323	+	3.29319i
$601$	−204481.			−0.566114			−0.283057	−	0.959103i	$-0.591349\pi$
$601$	−204481.			−0.566114			−0.283057	+	0.959103i	$0.591349\pi$
$602$	1.05019e6	+	166333.i	2.89784	+	0.458972i
$603$	317800.	+	623718.i	0.874016	+	1.71535i
$604$	−210412.	−	68367.2i	−0.576763	−	0.187402i
$605$	57210.6	−	270960.i	0.156302	−	0.740277i
$606$	−335008.	−	1.03105e6i	−0.912241	−	2.80759i
$607$	−126240.	−	126240.i	−0.342626	−	0.342626i	0.514728	−	0.857354i	$-0.327893\pi$
$607$	−126240.	−	126240.i	−0.342626	−	0.342626i	−0.857354	+	0.514728i	$0.827893\pi$
$608$	281646.	+	143506.i	0.761898	+	0.388206i
$609$	−216990.	+	298661.i	−0.585066	+	0.805275i
$610$	−369864.	+	240906.i	−0.993992	+	0.647423i
$611$	42469.0	−	30855.6i	0.113760	−	0.0826516i
$612$	−251730.	−	1.58936e6i	−0.672097	−	4.24345i
$613$	−260697.	+	41290.4i	−0.693770	+	0.109882i	−0.493354	−	0.869828i	$-0.664229\pi$
$613$	−260697.	+	41290.4i	−0.693770	+	0.109882i	−0.200416	+	0.979711i	$0.564229\pi$
$614$	−406847.	−	559977.i	−1.07918	−	1.48537i
$615$	2765.28	−	54169.2i	0.00731121	−	0.143220i
$616$	−289491.	−	210328.i	−0.762911	−	0.554288i
$617$	3785.15	−	7428.77i	0.00994289	−	0.0195140i	−0.885982	−	0.463720i	$-0.846514\pi$
$617$	3785.15	−	7428.77i	0.00994289	−	0.0195140i	0.895925	+	0.444206i	$0.146514\pi$
$618$	−382282.	+	382282.i	−1.00094	+	1.00094i
$619$	−437905.	+	142284.i	−1.14287	+	0.371342i	−0.818455	−	0.574571i	$-0.805169\pi$
$619$	−437905.	+	142284.i	−1.14287	+	0.371342i	−0.324419	+	0.945913i	$0.605169\pi$
$620$	−69398.9	−	651788.i	−0.180538	−	1.69560i
$621$	−41505.6	+	127741.i	−0.107628	+	0.331244i
$622$	147287.	−	75046.5i	0.380701	−	0.193977i
$623$	−31132.8	+	196565.i	−0.0802125	+	0.506442i
$624$			421586.i			1.08272i
$625$	355987.	−	160814.i	0.911327	−	0.411683i
$626$	752067.			1.91915
$627$	372595.	+	59013.3i	0.947768	+	0.150112i
$628$	−571146.	−	1.12094e6i	−1.44820	−	2.84225i
$629$	613773.	+	199427.i	1.55134	+	0.504060i
$630$	−995832.	+	106031.i	−2.50902	+	0.267147i
$631$	−68000.4	−	209284.i	−0.170786	−	0.525626i	0.828630	−	0.559797i	$-0.189121\pi$
$631$	−68000.4	−	209284.i	−0.170786	−	0.525626i	−0.999416	+	0.0341711i	$0.989121\pi$
$632$	1.09146e6	+	1.09146e6i	2.73258	+	2.73258i
$633$	−158467.	−	80742.8i	−0.395485	−	0.201510i
$634$	488654.	−	672575.i	1.21569	−	1.67326i
$635$	−210742.	−	10758.1i	−0.522640	−	0.0266802i
$636$	−231562.	+	168240.i	−0.572472	+	0.415925i
$637$	4806.82	+	30349.0i	0.0118462	+	0.0747939i
$638$	242526.	−	38412.4i	0.595823	−	0.0943691i
$639$	178787.	+	246079.i	0.437859	+	0.602661i
$640$	−285148.	−	437790.i	−0.696163	−	1.06882i
$641$	383210.	+	278418.i	0.932654	+	0.677613i	0.946641	−	0.322289i	$-0.104452\pi$
$641$	383210.	+	278418.i	0.932654	+	0.677613i	−0.0139871	+	0.999902i	$0.504452\pi$
$642$	−764766.	+	1.50094e6i	−1.85549	+	3.64161i
$643$	−442593.	+	442593.i	−1.07049	+	1.07049i	−0.0731710	+	0.997319i	$0.523312\pi$
$643$	−442593.	+	442593.i	−1.07049	+	1.07049i	−0.997319	+	0.0731710i	$0.976688\pi$
$644$	−304232.	+	98850.9i	−0.733555	+	0.238347i
$645$	−1.18017e6	−	249181.i	−2.83677	−	0.598956i
$646$	−353447.	+	1.08780e6i	−0.846954	+	2.60666i
$647$	465014.	−	236937.i	1.11086	−	0.566010i	0.200441	−	0.979706i	$-0.435762\pi$
$647$	465014.	−	236937.i	1.11086	−	0.566010i	0.910415	+	0.413696i	$0.135762\pi$
$648$	17849.7	−	112699.i	0.0425090	−	0.268391i
$649$			129697.i			0.307921i
$650$	316545.	−	68181.1i	0.749220	−	0.161375i
$651$	481100.			1.13520
$652$	348333.	+	55170.5i	0.819407	+	0.129781i
$653$	105165.	+	206399.i	0.246630	+	0.484040i	0.980823	−	0.194902i	$-0.0624389\pi$
$653$	105165.	+	206399.i	0.246630	+	0.484040i	−0.734192	+	0.678942i	$0.762439\pi$
$654$	1.57488e6	+	511708.i	3.68206	+	1.19637i
$655$	−51174.1	−	114521.i	−0.119280	−	0.266933i
$656$	−18778.4	−	57793.8i	−0.0436365	−	0.134299i
$657$	216254.	+	216254.i	0.500995	+	0.500995i
$658$	204339.	+	104116.i	0.471954	+	0.240473i
$659$	−334721.	+	460704.i	−0.770748	+	1.06084i	0.225495	+	0.974244i	$0.427600\pi$
$659$	−334721.	+	460704.i	−0.770748	+	1.06084i	−0.996243	+	0.0865995i	$0.972400\pi$
$660$	583258.	+	471006.i	1.33898	+	1.08128i
$661$	−141775.	+	103006.i	−0.324487	+	0.235754i	−0.738088	−	0.674705i	$-0.764271\pi$
$661$	−141775.	+	103006.i	−0.324487	+	0.235754i	0.413601	+	0.910458i	$0.364271\pi$
$662$	−3296.66	−	20814.3i	−0.00752244	−	0.0474948i
$663$	−377183.	+	59739.9i	−0.858075	+	0.135906i
$664$	−215821.	−	297052.i	−0.489505	−	0.673746i
$665$	455860.	+	174280.i	1.03083	+	0.394098i
$666$	−1.28751e6	−	935432.i	−2.90270	−	2.10894i
$667$	53959.5	−	105902.i	0.121288	−	0.238040i
$668$	1.02754e6	−	1.02754e6i	2.30274	−	2.30274i
$669$	1.11589e6	−	362575.i	2.49327	−	0.810113i
$670$	493244.	−	857003.i	1.09878	−	1.90912i
$671$	−45655.7	+	140514.i	−0.101403	+	0.312086i
$672$	−410818.	+	209322.i	−0.909727	+	0.463529i
$673$	−82391.4	+	520199.i	−0.181908	+	1.14852i	0.712634	+	0.701536i	$0.247502\pi$
$673$	−82391.4	+	520199.i	−0.181908	+	1.14852i	−0.894541	+	0.446985i	$0.852498\pi$
$674$			255926.i			0.563372i
$675$	406618.	−	22415.2i	0.892440	−	0.0491967i
$676$	−812549.			−1.77810
$677$	−776957.	−	123058.i	−1.69520	−	0.268493i	−0.767288	−	0.641303i	$-0.778394\pi$
$677$	−776957.	−	123058.i	−1.69520	−	0.268493i	−0.927908	+	0.372810i	$0.878394\pi$
$678$	−6265.92	−	12297.6i	−0.0136309	−	0.0267522i
$679$	−490717.	−	159444.i	−1.06437	−	0.345834i
$680$	−913508.	+	824771.i	−1.97558	+	1.78367i
$681$	252763.	+	777924.i	0.545028	+	1.67742i
$682$	−226276.	−	226276.i	−0.486485	−	0.486485i
$683$	−676026.	−	344452.i	−1.44918	−	0.738393i	−0.460389	−	0.887717i	$-0.652290\pi$
$683$	−676026.	−	344452.i	−1.44918	−	0.738393i	−0.988788	+	0.149324i	$0.952290\pi$
$684$	1.13667e6	−	1.56449e6i	2.42952	−	3.34395i
$685$	222691.	+	826611.i	0.474593	+	1.76165i
$686$	−724885.	+	526660.i	−1.54036	+	1.11913i
$687$	−15789.8	−	99693.1i	−0.0334552	−	0.211228i
$688$	−1.33472e6	+	211399.i	−2.81977	+	0.446608i
$689$	24322.5	+	33477.1i	0.0512354	+	0.0705195i
$690$	511058.	−	137680.i	1.07343	−	0.289184i
$691$	−319675.	−	232258.i	−0.669503	−	0.486423i	0.200356	−	0.979723i	$-0.435790\pi$
$691$	−319675.	−	232258.i	−0.669503	−	0.486423i	−0.869859	+	0.493301i	$0.835790\pi$
$692$	−166549.	+	326870.i	−0.347800	+	0.682595i
$693$	−237027.	+	237027.i	−0.493550	+	0.493550i
$694$	650572.	−	211384.i	1.35075	−	0.438887i
$695$	−545664.	−	604372.i	−1.12968	−	1.25122i
$696$	345725.	−	1.06403e6i	0.713695	−	2.19653i
$697$	49045.8	−	24990.1i	0.100957	−	0.0514402i
$698$	−132180.	+	834552.i	−0.271303	+	1.71294i
$699$		−	156694.i		−	0.320699i
$700$	612408.	+	752083.i	1.24981	+	1.53486i
$701$	−380888.			−0.775106			−0.387553	−	0.921848i	$-0.626680\pi$
$701$	−380888.			−0.775106			−0.387553	+	0.921848i	$0.626680\pi$
$702$	333418.	+	52808.2i	0.676573	+	0.107159i
$703$	352096.	+	691026.i	0.712443	+	1.39825i
$704$	−74622.1	−	24246.2i	−0.150564	−	0.0489213i
$705$	−225480.	−	129774.i	−0.453658	−	0.261101i
$706$	471700.	+	1.45174e6i	0.946360	+	2.91260i
$707$	−331950.	−	331950.i	−0.664101	−	0.664101i
$708$	972427.	+	495476.i	1.93995	+	0.988453i
$709$	461493.	−	635191.i	0.918063	−	1.26361i	−0.0462739	−	0.998929i	$-0.514735\pi$
$709$	461493.	−	635191.i	0.918063	−	1.26361i	0.964337	−	0.264677i	$-0.0852653\pi$
$710$	153432.	−	401328.i	0.304368	−	0.796129i
$711$	1.16981e6	−	849914.i	2.31406	−	1.68126i
$712$	−94350.9	−	595708.i	−0.186117	−	1.17510i
$713$	−152987.	+	24230.8i	−0.300938	+	0.0476638i
$714$	−980633.	−	1.34973e6i	−1.92358	−	2.64758i
$715$	68093.6	−	84321.9i	0.133197	−	0.164941i
$716$	−496115.	−	360449.i	−0.967735	−	0.703101i
$717$	−218646.	+	429116.i	−0.425307	+	0.834711i
$718$	631925.	−	631925.i	1.22579	−	1.22579i
$719$	−564082.	+	183281.i	−1.09115	+	0.354536i	−0.798691	−	0.601741i	$-0.794474\pi$
$719$	−564082.	+	183281.i	−1.09115	+	0.354536i	−0.292460	+	0.956278i	$0.594474\pi$
$720$	1.16205e6	−	519267.i	2.24161	−	1.00167i
$721$	−72343.0	+	222649.i	−0.139164	+	0.428302i
$722$	−396347.	+	201949.i	−0.760328	+	0.387406i
$723$	230766.	−	1.45700e6i	0.441464	−	2.78729i
$724$		−	11704.4i		−	0.0223291i
$725$	−358492.	−	36696.9i	−0.682029	−	0.0698157i
$726$	−1.13768e6			−2.15848
$727$	876576.	+	138836.i	1.65852	+	0.262684i	0.914237	−	0.405180i	$-0.132791\pi$
$727$	876576.	+	138836.i	1.65852	+	0.262684i	0.744283	+	0.667864i	$0.232791\pi$
$728$	197629.	+	387870.i	0.372897	+	0.731852i
$729$	−824284.	−	267826.i	−1.55104	−	0.503962i
$730$	89245.3	−	422682.i	0.167471	−	0.793174i
$731$	−378268.	−	1.16419e6i	−0.707889	−	2.17866i
$732$	879113.	+	879113.i	1.64068	+	1.64068i
$733$	585182.	+	298165.i	1.08914	+	0.554944i	0.903897	−	0.427750i	$-0.140693\pi$
$733$	585182.	+	298165.i	1.08914	+	0.554944i	0.185241	+	0.982693i	$0.440693\pi$
$734$	312381.	−	429955.i	0.579818	−	0.798051i
$735$	127602.	−	83111.6i	0.236201	−	0.153846i
$736$	120096.	−	87254.5i	0.221703	−	0.161077i
$737$	−51775.4	−	326897.i	−0.0953210	−	0.601833i
$738$	−134070.	+	21234.7i	−0.246162	+	0.0389882i
$739$	224227.	+	308622.i	0.410581	+	0.565117i	0.963360	−	0.268211i	$-0.0864326\pi$
$739$	224227.	+	308622.i	0.410581	+	0.565117i	−0.552779	+	0.833328i	$0.686433\pi$
$740$	−78577.9	+	1.53927e6i	−0.143495	+	2.81093i
$741$	−371281.	−	269751.i	−0.676185	−	0.491277i
$742$	−82071.5	+	161074.i	−0.149068	+	0.292563i
$743$	589663.	−	589663.i	1.06814	−	1.06814i	0.0706337	−	0.997502i	$-0.477498\pi$
$743$	589663.	−	589663.i	1.06814	−	1.06814i	0.997502	−	0.0706337i	$-0.0225021\pi$
$744$	−1.38666e6	+	450552.i	−2.50509	+	0.813953i
$745$	60083.2	+	564296.i	0.108253	+	1.01670i
$746$	336322.	−	1.03509e6i	0.604335	−	1.85995i
$747$	−306472.	+	156155.i	−0.549223	+	0.279843i
$748$	−119020.	+	751460.i	−0.212723	+	1.34308i
$749$			729453.i			1.30027i
$750$	−948516.	−	1.29442e6i	−1.68625	−	2.30119i
$751$	249077.			0.441624			0.220812	−	0.975316i	$-0.429129\pi$
$751$	249077.			0.441624			0.220812	+	0.975316i	$0.429129\pi$
$752$	−287882.	−	45596.1i	−0.509072	−	0.0806291i
$753$	−327207.	−	642179.i	−0.577075	−	1.13257i
$754$	−284101.	−	92309.9i	−0.499723	−	0.162370i
$755$	157623.	−	16782.8i	0.276519	−	0.0294423i
$756$	312455.	+	961637.i	0.546693	+	1.68255i
$757$	−575601.	−	575601.i	−1.00445	−	1.00445i	−0.999990	−	0.00446313i	$-0.998579\pi$
$757$	−575601.	−	575601.i	−1.00445	−	1.00445i	−0.00446313	−	0.999990i	$-0.501421\pi$
$758$	−129890.	−	66182.3i	−0.226067	−	0.115187i
$759$	104132.	−	143325.i	0.180758	−	0.248793i
$760$	−1.47712e6	−	75405.6i	−2.55735	−	0.130550i
$761$	681202.	−	494922.i	1.17627	−	0.854610i	0.184523	−	0.982828i	$-0.440926\pi$
$761$	681202.	−	494922.i	1.17627	−	0.854610i	0.991746	+	0.128218i	$0.0409259\pi$
$762$	135611.	+	856212.i	0.233552	+	1.47459i
$763$	708232.	−	112173.i	1.21654	−	0.192681i
$764$	764942.	+	1.05285e6i	1.31052	+	1.80377i
$765$	629242.	+	966079.i	1.07521	+	1.65078i
$766$	894710.	+	650045.i	1.52484	+	1.10786i
$767$	71631.2	−	140584.i	0.121762	−	0.238971i
$768$	−1.30363e6	+	1.30363e6i	−2.21020	+	2.21020i
$769$	137047.	−	44529.4i	0.231749	−	0.0752999i	−0.190840	−	0.981621i	$-0.561121\pi$
$769$	137047.	−	44529.4i	0.231749	−	0.0752999i	0.422589	+	0.906321i	$0.361121\pi$
$770$	463283.	+	97817.9i	0.781385	+	0.164982i
$771$	−288709.	+	888555.i	−0.485682	+	1.49477i
$772$	984319.	−	501536.i	1.65159	−	0.841525i
$773$	−34716.5	+	219191.i	−0.0581001	+	0.366830i	0.941459	+	0.337128i	$0.109456\pi$
$773$	−34716.5	+	219191.i	−0.0581001	+	0.366830i	−0.999559	+	0.0297013i	$0.990544\pi$
$774$			3.01862e6i			5.03880i
$775$	235917.	+	406074.i	0.392786	+	0.676086i
$776$	1.56370e6			2.59675
$777$	−1.11732e6	−	176967.i	−1.85071	−	0.293123i
$778$	−294163.	−	577328.i	−0.485992	−	0.953814i
$779$	62912.9	+	20441.6i	0.103673	+	0.0336853i
$780$	−372085.	−	832678.i	−0.611580	−	1.36864i
$781$	−44441.0	−	136775.i	−0.0728587	−	0.224236i
$782$	379816.	+	379816.i	0.621098	+	0.621098i
$783$	−334741.	−	170559.i	−0.545991	−	0.278196i
$784$	100282.	−	138027.i	0.163152	−	0.224559i
$785$	701263.	+	566300.i	1.13800	+	0.918982i
$786$	−416890.	+	302888.i	−0.674802	+	0.490272i
$787$	95303.0	+	601720.i	0.153871	+	0.971504i	0.936920	+	0.349544i	$0.113664\pi$
$787$	95303.0	+	601720.i	0.153871	+	0.971504i	−0.783049	+	0.621960i	$0.786336\pi$
$788$	−793921.	+	125745.i	−1.27857	+	0.202506i
$789$	461581.	+	635312.i	0.741471	+	1.02055i
$790$	−1.90783e6	−	729381.i	−3.05692	−	1.16869i
$791$	−4835.16	−	3512.95i	−0.00772784	−	0.00561460i
$792$	461197.	−	905151.i	0.735252	−	1.44301i
$793$	127094.	−	127094.i	0.202105	−	0.202105i
$794$	872384.	−	283455.i	1.38378	−	0.449617i
$795$	102297.	−	177739.i	0.161855	−	0.281221i
$796$	163607.	−	503531.i	0.258212	−	0.794694i
$797$	−13346.1	+	6800.17i	−0.0210105	+	0.0107054i	−0.464464	−	0.885592i	$-0.653753\pi$
$797$	−13346.1	+	6800.17i	−0.0210105	+	0.0107054i	0.443454	+	0.896297i	$0.353753\pi$
$798$	313641.	−	1.98025e6i	0.492523	−	3.10967i
$799$		−	264022.i		−	0.413568i
$800$	−378132.	−	244107.i	−0.590832	−	0.381418i
$801$	−564999.			−0.880609
$802$	−1.64898e6	−	261173.i	−2.56370	−	0.406049i
$803$	−65646.3	−	128838.i	−0.101807	−	0.199808i
$804$	−2.64877e6	−	860639.i	−4.09763	−	1.33140i
$805$	170115.	−	153590.i	0.262513	−	0.237013i
$806$	120299.	+	370243.i	0.185179	+	0.569923i
$807$	−146297.	−	146297.i	−0.224641	−	0.224641i
$808$	1.26764e6	+	645895.i	1.94166	+	0.989326i
$809$	35355.8	−	48663.1i	0.0540212	−	0.0743537i	−0.781152	−	0.624341i	$-0.785368\pi$
$809$	35355.8	−	48663.1i	0.0540212	−	0.0743537i	0.835173	+	0.549987i	$0.185368\pi$
$810$	39275.8	+	145789.i	0.0598626	+	0.222205i
$811$	−78506.8	+	57038.5i	−0.119362	+	0.0867215i	−0.645865	−	0.763452i	$-0.723503\pi$
$811$	−78506.8	+	57038.5i	−0.119362	+	0.0867215i	0.526503	+	0.850173i	$0.323503\pi$
$812$	−139970.	−	883734.i	−0.212286	−	1.34032i
$813$	1.29503e6	−	205112.i	1.95929	−	0.310320i
$814$	442279.	+	608744.i	0.667494	+	0.918726i
$815$	−243985.	+	65730.0i	−0.367322	+	0.0989575i
$816$	1.71542e6	+	1.24632e6i	2.57626	+	1.87176i
$817$	667846.	−	1.31072e6i	1.00053	−	1.96366i
$818$	−351106.	+	351106.i	−0.524725	+	0.524725i
$819$	387834.	−	126015.i	0.578200	−	0.187869i
$820$	88097.2	+	97575.6i	0.131019	+	0.145115i
$821$	−297955.	+	917012.i	−0.442043	+	1.36047i	0.443651	+	0.896200i	$0.353683\pi$
$821$	−297955.	+	917012.i	−0.442043	+	1.36047i	−0.885694	+	0.464269i	$0.846317\pi$
$822$	3.13359e6	−	1.59664e6i	4.63766	−	2.36300i
$823$	−128380.	+	810561.i	−0.189539	+	1.19670i	0.691045	+	0.722812i	$0.257151\pi$
$823$	−128380.	+	810561.i	−0.189539	+	1.19670i	−0.880584	+	0.473890i	$0.842849\pi$
$824$		−	709482.i		−	1.04493i
$825$	−519209.	−	137614.i	−0.762841	−	0.202188i
$826$	689305.			1.01030
$827$	−37975.2	−	6014.68i	−0.0555250	−	0.00879430i	0.128610	−	0.991695i	$-0.458948\pi$
$827$	−37975.2	−	6014.68i	−0.0555250	−	0.00879430i	−0.184135	+	0.982901i	$0.558948\pi$
$828$	−412294.	−	809173.i	−0.601377	−	1.18027i
$829$	−299268.	−	97237.9i	−0.435462	−	0.141490i	0.0830788	−	0.996543i	$-0.473525\pi$
$829$	−299268.	−	97237.9i	−0.435462	−	0.141490i	−0.518541	+	0.855053i	$0.673525\pi$
$830$	421099.	+	242361.i	0.611263	+	0.351809i
$831$	−318997.	−	981773.i	−0.461940	−	1.42170i
$832$	67495.2	+	67495.2i	0.0975049	+	0.0975049i
$833$	137699.	+	70161.4i	0.198446	+	0.101113i
$834$	−1.96619e6	+	2.70623e6i	−2.82680	+	3.89075i
$835$	−371798.	+	972505.i	−0.533255	+	1.39482i
$836$	−739700.	+	537424.i	−1.05838	+	0.768961i
$837$	76590.4	+	483573.i	0.109326	+	0.690257i
$838$	−1.33995e6	+	212227.i	−1.90809	+	0.302212i
$839$	−798531.	−	1.09908e6i	−1.13440	−	1.56137i	−0.779421	−	0.626500i	$-0.784487\pi$
$839$	−798531.	−	1.09908e6i	−1.13440	−	1.56137i	−0.354983	−	0.934873i	$-0.615513\pi$
$840$	1.35541e6	−	1.67844e6i	1.92094	−	2.37874i
$841$	−303245.	−	220321.i	−0.428748	−	0.311504i
$842$	−288854.	+	566908.i	−0.407431	+	0.799628i
$843$	−783070.	+	783070.i	−1.10191	+	1.10191i
$844$	409963.	−	133205.i	0.575519	−	0.186997i
$845$	531519.	−	237511.i	0.744399	−	0.332637i
$846$	−201194.	+	619212.i	−0.281109	+	0.865164i
$847$	−438953.	+	223658.i	−0.611859	+	0.311758i
$848$	35942.0	−	226929.i	0.0499817	−	0.315572i
$849$		−	1.18262e6i		−	1.64071i
$850$	658369.	−	1.48957e6i	0.911237	−	2.06169i
$851$	364217.			0.502922
$852$	−1.19528e6	−	189313.i	−1.64661	−	0.260797i
$853$	−214080.	−	420156.i	−0.294224	−	0.577447i	0.695818	−	0.718218i	$-0.255042\pi$
$853$	−214080.	−	420156.i	−0.294224	−	0.577447i	−0.990042	+	0.140771i	$0.955042\pi$
$854$	746795.	+	242648.i	1.02397	+	0.332707i
$855$	−286231.	+	1.35564e6i	−0.391548	+	1.85444i
$856$	−683136.	−	2.10248e6i	−0.932309	−	2.86935i
$857$	−188214.	−	188214.i	−0.256265	−	0.256265i	0.567268	−	0.823533i	$-0.308000\pi$
$857$	−188214.	−	188214.i	−0.256265	−	0.256265i	−0.823533	+	0.567268i	$0.808000\pi$
$858$	−396724.	−	202141.i	−0.538908	−	0.274587i
$859$	−175260.	+	241225.i	−0.237518	+	0.326916i	−0.911091	−	0.412205i	$-0.864759\pi$
$859$	−175260.	+	241225.i	−0.237518	+	0.326916i	0.673573	+	0.739121i	$0.264759\pi$
$860$	2.44965e6	−	1.59554e6i	3.31212	−	2.15730i
$861$	−78061.5	+	56715.0i	−0.105300	+	0.0765053i
$862$	−112536.	−	710527.i	−0.151453	−	0.956238i
$863$	1.10633e6	−	175225.i	1.48546	−	0.235274i	0.639613	−	0.768697i	$-0.279095\pi$
$863$	1.10633e6	−	175225.i	1.48546	−	0.235274i	0.845849	+	0.533423i	$0.179095\pi$
$864$	−275800.	−	379606.i	−0.369459	−	0.508517i
$865$	13400.4	−	262501.i	0.0179096	−	0.350832i
$866$	1.43380e6	+	1.04172e6i	1.91184	+	1.38904i
$867$	−326094.	+	639996.i	−0.433815	+	0.851410i
$868$	−824519.	+	824519.i	−1.09436	+	1.09436i
$869$	−650199.	+	211262.i	−0.861007	+	0.279758i
$870$	156742.	+	1.47211e6i	0.207085	+	1.94492i
$871$	−124423.	+	382935.i	−0.164008	+	0.504764i
$872$	−1.93626e6	+	986575.i	−2.54643	+	1.29747i
$873$	229150.	−	1.44680e6i	0.300671	−	1.89836i
$874$			645507.i			0.845041i
$875$	−620437.	−	312957.i	−0.810366	−	0.408761i
$876$	−1.21678e6			−1.58563
$877$	−126321.	−	20007.3i	−0.164239	−	0.0260129i	0.0737732	−	0.997275i	$-0.476496\pi$
$877$	−126321.	−	20007.3i	−0.164239	−	0.0260129i	−0.238012	+	0.971262i	$0.576496\pi$
$878$	499299.	+	979929.i	0.647697	+	1.27118i
$879$	1.36033e6	+	441998.i	1.76062	+	0.572062i
$880$	−598404.	+	63714.8i	−0.772732	+	0.0822763i
$881$	111912.	+	344429.i	0.144186	+	0.443759i	0.996905	−	0.0786101i	$-0.0250482\pi$
$881$	111912.	+	344429.i	0.144186	+	0.443759i	−0.852719	+	0.522369i	$0.825048\pi$
$882$	−269481.	−	269481.i	−0.346410	−	0.346410i
$883$	132263.	+	67391.3i	0.169636	+	0.0864336i	0.536747	−	0.843743i	$-0.319653\pi$
$883$	132263.	+	67391.3i	0.169636	+	0.0864336i	−0.367111	+	0.930177i	$0.619653\pi$
$884$	544041.	−	748808.i	0.696189	−	0.958222i
$885$	−780931.	−	39865.7i	−0.997072	−	0.0508994i
$886$	1.02445e6	−	744304.i	1.30503	−	0.948163i
$887$	−83502.4	−	527214.i	−0.106133	−	0.670099i	−0.982190	−	0.187891i	$-0.939835\pi$
$887$	−83502.4	−	527214.i	−0.106133	−	0.670099i	0.876057	−	0.482208i	$-0.160165\pi$
$888$	3.38616e6	−	536314.i	4.29419	−	0.680132i
$889$	220646.	+	303693.i	0.279185	+	0.384265i
$890$	435579.	+	668747.i	0.549904	+	0.844271i
$891$	40886.0	+	29705.4i	0.0515014	+	0.0374180i
$892$	−1.29105e6	+	2.53383e6i	−1.62261	+	3.18455i
$893$	224356.	−	224356.i	0.281342	−	0.281342i
$894$	2.21721e6	−	720416.i	2.77417	−	0.901381i
$895$	429889.	+	90767.0i	0.536674	+	0.113314i
$896$	−287211.	+	883944.i	−0.357754	+	1.10105i
$897$	−192031.	+	97844.7i	−0.238664	+	0.121605i
$898$	361248.	−	2.28083e6i	0.447974	−	2.82839i
$899$		−	433251.i		−	0.536068i
$900$	−1.83688e6	+	2.05122e6i	−2.26776	+	2.53237i
$901$	208121.			0.256370
$902$	63389.4	+	10039.9i	0.0779119	+	0.0123400i
$903$	974141.	+	1.91186e6i	1.19467	+	2.34466i
$904$	17226.1	+	5597.10i	0.0210790	+	0.00684899i
$905$	3421.24	+	7656.29i	0.00417721	+	0.00934806i
$906$	−201231.	−	619326.i	−0.245154	−	0.754507i
$907$	686984.	+	686984.i	0.835088	+	0.835088i	0.988208	−	0.153120i	$-0.0489321\pi$
$907$	686984.	+	686984.i	0.835088	+	0.835088i	−0.153120	+	0.988208i	$0.548932\pi$
$908$	−1.76641e6	−	900033.i	−2.14250	−	1.09166i
$909$	783373.	−	1.07822e6i	0.948071	−	1.30491i
$910$	−448150.	−	361900.i	−0.541179	−	0.437025i
$911$	−1.09950e6	+	798835.i	−1.32483	+	0.962543i	−0.324968	+	0.945725i	$0.605354\pi$
$911$	−1.09950e6	+	798835.i	−1.32483	+	0.962543i	−0.999859	+	0.0168180i	$0.994646\pi$
$912$	398618.	+	2.51678e6i	0.479256	+	3.02590i
$913$	160625.	−	25440.5i	0.192695	−	0.0305200i
$914$	−1.28092e6	−	1.76303e6i	−1.53331	−	2.11041i
$915$	−832030.	−	318093.i	−0.993795	−	0.379938i
$916$	197917.	+	143795.i	0.235881	+	0.171377i
$917$	−101304.	+	198820.i	−0.120472	+	0.236440i
$918$	1.20055e6	−	1.20055e6i	1.42461	−	1.42461i
$919$	−220172.	+	71538.3i	−0.260694	+	0.0847047i	−0.436448	−	0.899729i	$-0.643764\pi$
$919$	−220172.	+	71538.3i	−0.260694	+	0.0847047i	0.175754	+	0.984434i	$0.443764\pi$
$920$	−346479.	+	602002.i	−0.409356	+	0.711250i
$921$	431641.	−	1.32845e6i	0.508866	−	1.56613i
$922$	−1.30996e6	+	667459.i	−1.54098	+	0.785168i
$923$	−27369.1	+	172802.i	−0.0321261	+	0.202836i
$924$		−	1.33366e6i		−	1.56207i
$925$	−398533.	−	1.02986e6i	−0.465780	−	1.20364i
$926$	−1.67185e6			−1.94974
$927$	−656442.	−	103970.i	−0.763900	−	0.120990i
$928$	188504.	+	369959.i	0.218889	+	0.429594i
$929$	874076.	+	284004.i	1.01279	+	0.329074i	0.767963	−	0.640494i	$-0.221270\pi$
$929$	874076.	+	284004.i	1.01279	+	0.329074i	0.244822	+	0.969568i	$0.421270\pi$
$930$	1.43201e6	−	1.29290e6i	1.65569	−	1.49486i
$931$	57391.3	+	176632.i	0.0662135	+	0.203784i
$932$	268545.	+	268545.i	0.309162	+	0.309162i
$933$	297230.	+	151446.i	0.341452	+	0.173978i
$934$	−992254.	+	1.36572e6i	−1.13744	+	1.56555i
$935$	−141800.	−	526349.i	−0.162200	−	0.602075i
$936$	−999827.	+	726417.i	−1.14123	+	0.829152i
$937$	3088.68	+	19501.1i	0.00351798	+	0.0222116i	0.989385	−	0.145319i	$-0.0464208\pi$
$937$	3088.68	+	19501.1i	0.00351798	+	0.0222116i	−0.985867	+	0.167530i	$0.946421\pi$
$938$	−1.73738e6	+	275173.i	−1.97464	+	0.312752i
$939$	892079.	+	1.22784e6i	1.01175	+	1.39255i
$940$	608841.	−	164023.i	0.689046	−	0.185630i
$941$	−428046.	−	310994.i	−0.483405	−	0.351214i	0.319237	−	0.947675i	$-0.396573\pi$
$941$	−428046.	−	310994.i	−0.483405	−	0.351214i	−0.802642	+	0.596460i	$0.796573\pi$
$942$	1.68111e6	−	3.29936e6i	1.89449	−	3.71815i
$943$	21966.7	−	21966.7i	0.0247025	−	0.0247025i
$944$	−833186.	+	270719.i	−0.934971	+	0.303790i
$945$	−485479.	−	537712.i	−0.543634	−	0.602124i
$946$	441037.	−	1.35737e6i	0.492825	−	1.51676i
$947$	−716628.	+	365140.i	−0.799086	+	0.407155i	−0.805331	−	0.592826i	$-0.798012\pi$
$947$	−716628.	+	365140.i	−0.799086	+	0.407155i	0.00624447	+	0.999981i	$0.498012\pi$
$948$	−899953.	+	5.68208e6i	−1.00139	+	6.32253i
$949$			175910.i			0.195325i
$950$	1.82524e6	−	706326.i	2.02243	−	0.782633i
$951$	1.67769e6			1.85503
$952$	2.16247e6	+	342502.i	2.38604	+	0.377911i
$953$	77730.5	+	152555.i	0.0855866	+	0.167973i	0.929833	−	0.367983i	$-0.119951\pi$
$953$	77730.5	+	152555.i	0.0855866	+	0.167973i	−0.844246	+	0.535956i	$0.819951\pi$
$954$	−488106.	−	158595.i	−0.536312	−	0.174258i
$955$	−808132.	−	465116.i	−0.886085	−	0.509982i
$956$	−360709.	−	1.11015e6i	−0.394676	−	1.21469i
$957$	350390.	+	350390.i	0.382585	+	0.382585i
$958$	−906065.	−	461663.i	−0.987252	−	0.503030i
$959$	895149.	−	1.23207e6i	0.973326	−	1.33967i
$960$	168929.	−	441863.i	0.183299	−	0.479452i
$961$	290360.	−	210959.i	0.314406	−	0.228429i
$962$	−143198.	−	904116.i	−0.154734	−	0.976954i
$963$	−2.04541e6	+	323961.i	−2.20560	+	0.349333i
$964$	2.10155e6	+	2.89253e6i	2.26144	+	3.11260i
$965$	−497280.	+	615794.i	−0.534006	+	0.661273i
$966$	−761735.	−	553433.i	−0.816300	−	0.593076i
$967$	588224.	−	1.15445e6i	0.629057	−	1.23459i	−0.327996	−	0.944679i	$-0.606373\pi$
$967$	588224.	−	1.15445e6i	0.629057	−	1.23459i	0.957053	−	0.289914i	$-0.0936268\pi$
$968$	1.05572e6	−	1.05572e6i	1.12668	−	1.12668i
$969$	−2.19521e6	+	713268.i	−2.33792	+	0.759636i
$970$	−1.88912e6	+	844161.i	−2.00778	+	0.897185i
$971$	−133428.	+	410648.i	−0.141517	+	0.435544i	−0.996547	−	0.0830350i	$-0.973539\pi$
$971$	−133428.	+	410648.i	−0.141517	+	0.435544i	0.855030	+	0.518579i	$0.173539\pi$
$972$	2.01977e6	−	1.02912e6i	2.13781	−	1.08927i
$973$	−226598.	+	1.43068e6i	−0.239348	+	1.51118i
$974$		−	293710.i		−	0.309600i
$975$	486791.	+	435925.i	0.512074	+	0.458567i
$976$	−997975.			−1.04766
$977$	1.10208e6	+	174552.i	1.15458	+	0.182867i	0.704221	−	0.709981i	$-0.251296\pi$
$977$	1.10208e6	+	174552.i	1.15458	+	0.182867i	0.450358	+	0.892848i	$0.351296\pi$
$978$	471270.	+	924919.i	0.492711	+	0.966999i
$979$	254061.	+	82549.5i	0.265077	+	0.0861289i
$980$	−76248.1	+	361125.i	−0.0793920	+	0.376015i
$981$	629072.	+	1.93608e6i	0.653675	+	2.01181i
$982$	−344771.	−	344771.i	−0.357526	−	0.357526i
$983$	−830942.	−	423386.i	−0.859931	−	0.438157i	−0.0323326	−	0.999477i	$-0.510294\pi$
$983$	−830942.	−	423386.i	−0.859931	−	0.438157i	−0.827599	+	0.561320i	$0.810294\pi$
$984$	171880.	−	236573.i	0.177515	−	0.244329i
$985$	482579.	−	314321.i	0.497389	−	0.323967i
$986$	−1.21549e6	+	883102.i	−1.25025	+	0.908358i
$987$	72398.8	+	457108.i	0.0743185	+	0.469228i
$988$	1.09861e6	−	174003.i	1.12546	−	0.178256i
$989$	−406064.	−	558899.i	−0.415147	−	0.571401i
$990$	−68533.3	+	1.34250e6i	−0.0699248	+	1.36976i
$991$	−1.01894e6	−	740300.i	−1.03753	−	0.753808i	−0.0677262	−	0.997704i	$-0.521574\pi$
$991$	−1.01894e6	−	740300.i	−1.03753	−	0.753808i	−0.969801	+	0.243896i	$0.921574\pi$
$992$	245660.	−	482134.i	0.249638	−	0.489942i
$993$	30071.5	−	30071.5i	0.0304970	−	0.0304970i
$994$	−726926.	+	236193.i	−0.735729	+	0.239053i
$995$	40162.5	+	377202.i	0.0405671	+	0.381003i
$996$	422886.	−	1.30151e6i	0.426289	−	1.31198i
$997$	−370263.	+	188659.i	−0.372495	+	0.189796i	−0.630209	−	0.776426i	$-0.717031\pi$
$997$	−370263.	+	188659.i	−0.372495	+	0.189796i	0.257714	+	0.966221i	$0.417031\pi$
$998$	−51692.3	+	326373.i	−0.0518997	+	0.327682i
$999$		−	1.15124e6i		−	1.15355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.2.1	✓	72
5.2	odd	4		125.5.f.a.93.9		72
5.3	odd	4		125.5.f.b.93.1		72
5.4	even	2		125.5.f.c.32.9		72
25.9	even	10		125.5.f.a.82.9		72
25.12	odd	20		125.5.f.c.43.9		72
25.13	odd	20	inner	25.5.f.a.13.1	yes	72
25.16	even	5		125.5.f.b.82.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.2.1	✓	72	1.1	even	1	trivial
25.5.f.a.13.1	yes	72	25.13	odd	20	inner
125.5.f.a.82.9		72	25.9	even	10
125.5.f.a.93.9		72	5.2	odd	4
125.5.f.b.82.1		72	25.16	even	5
125.5.f.b.93.1		72	5.3	odd	4
125.5.f.c.32.9		72	5.4	even	2
125.5.f.c.43.9		72	25.12	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.04610 - 1.11599i) q^{2} +(-6.53588 - 12.8274i) q^{3} +(33.1852 + 10.7825i) q^{4} +(-24.8595 + 2.64690i) q^{5} +(31.7372 + 97.6770i) q^{6} +(31.4475 + 31.4475i) q^{7} +(-120.091 - 61.1893i) q^{8} +(-74.2134 + 102.146i) q^{9} +O(q^{10})\)	\(q+(-7.04610 - 1.11599i) q^{2} +(-6.53588 - 12.8274i) q^{3} +(33.1852 + 10.7825i) q^{4} +(-24.8595 + 2.64690i) q^{5} +(31.7372 + 97.6770i) q^{6} +(31.4475 + 31.4475i) q^{7} +(-120.091 - 61.1893i) q^{8} +(-74.2134 + 102.146i) q^{9} +(178.116 + 9.09265i) q^{10} +(48.2953 - 35.0886i) q^{11} +(-78.5828 - 496.152i) q^{12} +(-71.7290 + 11.3608i) q^{13} +(-186.487 - 256.678i) q^{14} +(196.431 + 301.582i) q^{15} +(326.221 + 237.014i) q^{16} +(-165.824 + 325.448i) q^{17} +(636.909 - 636.909i) q^{18} +(-417.464 + 135.642i) q^{19} +(-853.507 - 180.210i) q^{20} +(197.852 - 608.926i) q^{21} +(-379.452 + 193.341i) q^{22} +(-32.2472 + 203.601i) q^{23} +1940.38i q^{24} +(610.988 - 131.601i) q^{25} +518.088 q^{26} +(643.555 + 101.929i) q^{27} +(704.508 + 1382.68i) q^{28} +(-548.364 - 178.174i) q^{29} +(-1047.51 - 2344.19i) q^{30} +(232.198 + 714.633i) q^{31} +(-509.208 - 509.208i) q^{32} +(-765.747 - 390.168i) q^{33} +(1531.61 - 2108.08i) q^{34} +(-865.008 - 698.530i) q^{35} +(-3564.18 + 2589.53i) q^{36} +(-276.397 - 1745.10i) q^{37} +(3092.87 - 489.863i) q^{38} +(614.540 + 845.842i) q^{39} +(3147.36 + 1203.27i) q^{40} +(-121.921 - 88.5807i) q^{41} +(-2073.64 + 4069.75i) q^{42} +(-2369.75 + 2369.75i) q^{43} +(1981.03 - 643.677i) q^{44} +(1574.54 - 2735.73i) q^{45} +(454.433 - 1398.60i) q^{46} +(-644.052 + 328.161i) q^{47} +(908.122 - 5733.66i) q^{48} -423.107i q^{49} +(-4451.95 + 245.418i) q^{50} +5258.45 q^{51} +(-2502.84 - 396.410i) q^{52} +(-258.680 - 507.687i) q^{53} +(-4420.80 - 1436.40i) q^{54} +(-1107.72 + 1000.12i) q^{55} +(-1852.31 - 5700.81i) q^{56} +(4468.43 + 4468.43i) q^{57} +(3664.99 + 1867.40i) q^{58} +(-1277.03 + 1757.68i) q^{59} +(3266.79 + 12126.1i) q^{60} +(-2002.27 + 1454.73i) q^{61} +(-838.567 - 5294.51i) q^{62} +(-5546.06 + 878.410i) q^{63} +(-772.560 - 1063.34i) q^{64} +(1753.07 - 472.282i) q^{65} +(4960.11 + 3603.73i) q^{66} +(2517.04 - 4939.97i) q^{67} +(-9012.05 + 9012.05i) q^{68} +(2822.42 - 917.061i) q^{69} +(5315.38 + 5887.26i) q^{70} +(744.451 - 2291.19i) q^{71} +(15162.6 - 7725.73i) q^{72} +(378.921 - 2392.41i) q^{73} +12604.6i q^{74} +(-5681.44 - 6977.24i) q^{75} -15316.2 q^{76} +(2622.22 + 415.318i) q^{77} +(-3386.16 - 6645.71i) q^{78} +(-10891.8 - 3538.95i) q^{79} +(-8737.04 - 5028.56i) q^{80} +(261.609 + 805.149i) q^{81} +(760.212 + 760.212i) q^{82} +(2427.32 + 1236.78i) q^{83} +(13131.5 - 18074.0i) q^{84} +(3260.87 - 8529.39i) q^{85} +(19342.1 - 14052.8i) q^{86} +(1298.53 + 8198.60i) q^{87} +(-7946.88 + 1258.66i) q^{88} +(2630.29 + 3620.28i) q^{89} +(-14147.4 + 17519.1i) q^{90} +(-2612.96 - 1898.43i) q^{91} +(-3265.45 + 6408.82i) q^{92} +(7649.25 - 7649.25i) q^{93} +(4904.28 - 1593.50i) q^{94} +(10018.9 - 4476.99i) q^{95} +(-3203.68 + 9859.92i) q^{96} +(-10337.2 + 5267.09i) q^{97} +(-472.185 + 2981.26i) q^{98} +7537.22i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Introduction

L-functions

Modular forms

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Database

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