LMFDB - Embedded newform 150.6.g.a.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 67300 x^{18} - 605415 x^{17} + 1505002471 x^{16} - 12026298320 x^{15} + \cdots + 45\!\cdots\!05 $ x^20 - 10x^19 + 67300x^18 - 605415x^17 + 1505002471x^16 - 12026298320x^15 + 15161344295580x^14 - 105918997871590x^13 + 72521519492275041x^12 - 433752716999522710x^11 + 150954604904063839080x^10 - 750799480917962811625x^9 + 100084099910299358028076x^8 - 395836369710607771806480x^7 + 22144208384329171616972475x^6 - 65050346450081546072582845x^5 + 865137734840778899106150416x^4 - 1622318535480468844324766865x^3 + 11299132807307021058314145735x^2 - 10498749516125580450644510315*x + 45940690246932155189634577205
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Root			$0.500000 + 3.30996i$ of defining polynomial
Character	$\chi$	$=$	150.91
Dual form			150.6.g.a.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23607 + 2.35114i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-38.1312 - 40.8780i) q^{5} +(11.1246 - 34.2380i) q^{6} -22.2017 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})$	\(q+(3.23607 + 2.35114i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-38.1312 - 40.8780i) q^{5} +(11.1246 - 34.2380i) q^{6} -22.2017 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(-27.2854 - 221.936i) q^{10} +(132.319 + 96.1350i) q^{11} +(116.498 - 84.6411i) q^{12} +(37.6553 - 27.3582i) q^{13} +(-71.8462 - 52.1993i) q^{14} +(-243.847 + 440.073i) q^{15} +(-207.108 + 150.473i) q^{16} +(-396.729 + 1221.01i) q^{17} -324.000 q^{18} +(-382.612 + 1177.56i) q^{19} +(433.505 - 782.351i) q^{20} +(61.7463 + 190.036i) q^{21} +(202.165 + 622.199i) q^{22} +(1059.62 + 769.861i) q^{23} +576.000 q^{24} +(-217.019 + 3117.46i) q^{25} +186.178 q^{26} +(589.773 + 428.495i) q^{27} +(-109.771 - 337.841i) q^{28} +(355.346 + 1093.64i) q^{29} +(-1823.78 + 850.787i) q^{30} +(-1742.50 + 5362.85i) q^{31} -1024.00 q^{32} +(454.871 - 1399.95i) q^{33} +(-4154.60 + 3018.49i) q^{34} +(846.578 + 907.560i) q^{35} +(-1048.49 - 761.770i) q^{36} +(-6827.54 + 4960.50i) q^{37} +(-4006.77 + 2911.09i) q^{38} +(-338.898 - 246.224i) q^{39} +(3242.27 - 1512.51i) q^{40} +(1636.46 - 1188.95i) q^{41} +(-246.985 + 760.142i) q^{42} +6633.78 q^{43} +(-808.659 + 2488.80i) q^{44} +(4444.98 + 863.299i) q^{45} +(1618.96 + 4982.64i) q^{46} +(853.898 + 2628.03i) q^{47} +(1863.98 + 1354.26i) q^{48} -16314.1 q^{49} +(-8031.86 + 9578.06i) q^{50} +11554.6 q^{51} +(602.485 + 437.731i) q^{52} +(762.303 + 2346.13i) q^{53} +(901.094 + 2773.28i) q^{54} +(-1115.66 - 9074.66i) q^{55} +(439.085 - 1351.36i) q^{56} +11143.4 q^{57} +(-1421.38 + 4374.57i) q^{58} +(-25790.3 + 18737.8i) q^{59} +(-7902.19 - 1534.75i) q^{60} +(14408.7 + 10468.5i) q^{61} +(-18247.7 + 13257.7i) q^{62} +(1454.89 - 1057.04i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-2554.19 - 496.072i) q^{65} +(4763.47 - 3460.86i) q^{66} +(7869.06 - 24218.5i) q^{67} -20541.5 q^{68} +(3642.66 - 11210.9i) q^{69} +(605.781 + 4927.35i) q^{70} +(7933.96 + 24418.2i) q^{71} +(-1601.94 - 4930.28i) q^{72} +(-66181.4 - 48083.6i) q^{73} -33757.2 q^{74} +(27287.4 - 6812.55i) q^{75} -19810.6 q^{76} +(-2937.70 - 2134.36i) q^{77} +(-517.790 - 1593.59i) q^{78} +(-8291.07 - 25517.3i) q^{79} +(14048.3 + 2728.45i) q^{80} +(2027.46 - 6239.88i) q^{81} +8091.08 q^{82} +(1803.17 - 5549.59i) q^{83} +(-2586.46 + 1879.18i) q^{84} +(65040.0 - 30341.0i) q^{85} +(21467.4 + 15597.0i) q^{86} +(8372.77 - 6083.18i) q^{87} +(-8468.39 + 6152.64i) q^{88} +(21501.9 + 15622.0i) q^{89} +(12354.5 + 13244.5i) q^{90} +(-836.012 + 607.398i) q^{91} +(-6475.84 + 19930.6i) q^{92} +50749.5 q^{93} +(-3415.59 + 10512.1i) q^{94} +(62725.8 - 29261.4i) q^{95} +(2847.90 + 8764.94i) q^{96} +(27437.3 + 84443.2i) q^{97} +(-52793.5 - 38356.7i) q^{98} -13247.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9} + 220 q^{10} + 380 q^{11} + 720 q^{12} - 230 q^{13} - 920 q^{14} - 630 q^{15} - 1280 q^{16} + 2870 q^{17} - 6480 q^{18} + 1560 q^{19} + 1120 q^{20} + 2880 q^{21} - 720 q^{22} + 760 q^{23} + 11520 q^{24} + 1725 q^{25} + 7320 q^{26} + 3645 q^{27} - 5120 q^{28} + 12000 q^{29} + 5220 q^{30} - 1710 q^{31} - 20480 q^{32} - 1620 q^{33} + 20620 q^{34} - 22440 q^{35} - 6480 q^{36} - 5595 q^{37} - 5240 q^{38} + 2070 q^{39} - 9280 q^{40} - 2820 q^{41} - 11520 q^{42} + 66020 q^{43} + 2880 q^{44} - 8505 q^{45} + 21960 q^{46} - 19630 q^{47} + 11520 q^{48} - 61780 q^{49} + 100 q^{50} - 41130 q^{51} - 3680 q^{52} + 62735 q^{53} - 14580 q^{54} + 66590 q^{55} + 20480 q^{56} + 51660 q^{57} - 48000 q^{58} + 105100 q^{59} + 15120 q^{60} + 34790 q^{61} - 28560 q^{62} + 18630 q^{63} - 20480 q^{64} - 44345 q^{65} + 13680 q^{66} - 19470 q^{67} + 73120 q^{68} + 49410 q^{69} - 81240 q^{70} - 111720 q^{71} + 25920 q^{72} - 198830 q^{73} - 104120 q^{74} + 60975 q^{75} - 91840 q^{76} + 144740 q^{77} + 41220 q^{78} + 71210 q^{79} - 26880 q^{80} - 32805 q^{81} + 166680 q^{82} - 288690 q^{83} - 33120 q^{84} + 338735 q^{85} + 39920 q^{86} + 108225 q^{87} - 24320 q^{88} + 114225 q^{89} + 17820 q^{90} - 155800 q^{91} - 87840 q^{92} + 97740 q^{93} + 78520 q^{94} - 416900 q^{95} - 46080 q^{96} - 446970 q^{97} - 123380 q^{98} - 90720 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9 + 220 * q^10 + 380 * q^11 + 720 * q^12 - 230 * q^13 - 920 * q^14 - 630 * q^15 - 1280 * q^16 + 2870 * q^17 - 6480 * q^18 + 1560 * q^19 + 1120 * q^20 + 2880 * q^21 - 720 * q^22 + 760 * q^23 + 11520 * q^24 + 1725 * q^25 + 7320 * q^26 + 3645 * q^27 - 5120 * q^28 + 12000 * q^29 + 5220 * q^30 - 1710 * q^31 - 20480 * q^32 - 1620 * q^33 + 20620 * q^34 - 22440 * q^35 - 6480 * q^36 - 5595 * q^37 - 5240 * q^38 + 2070 * q^39 - 9280 * q^40 - 2820 * q^41 - 11520 * q^42 + 66020 * q^43 + 2880 * q^44 - 8505 * q^45 + 21960 * q^46 - 19630 * q^47 + 11520 * q^48 - 61780 * q^49 + 100 * q^50 - 41130 * q^51 - 3680 * q^52 + 62735 * q^53 - 14580 * q^54 + 66590 * q^55 + 20480 * q^56 + 51660 * q^57 - 48000 * q^58 + 105100 * q^59 + 15120 * q^60 + 34790 * q^61 - 28560 * q^62 + 18630 * q^63 - 20480 * q^64 - 44345 * q^65 + 13680 * q^66 - 19470 * q^67 + 73120 * q^68 + 49410 * q^69 - 81240 * q^70 - 111720 * q^71 + 25920 * q^72 - 198830 * q^73 - 104120 * q^74 + 60975 * q^75 - 91840 * q^76 + 144740 * q^77 + 41220 * q^78 + 71210 * q^79 - 26880 * q^80 - 32805 * q^81 + 166680 * q^82 - 288690 * q^83 - 33120 * q^84 + 338735 * q^85 + 39920 * q^86 + 108225 * q^87 - 24320 * q^88 + 114225 * q^89 + 17820 * q^90 - 155800 * q^91 - 87840 * q^92 + 97740 * q^93 + 78520 * q^94 - 416900 * q^95 - 46080 * q^96 - 446970 * q^97 - 123380 * q^98 - 90720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$2$	3.23607	+	2.35114i	0.572061	+	0.415627i
$3$	−2.78115	−	8.55951i	−0.178411	−	0.549093i
$3$	−2.78115	−	8.55951i	−0.178411	−	0.549093i
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	−38.1312	−	40.8780i	−0.682112	−	0.731248i
$5$	−38.1312	−	40.8780i	−0.682112	−	0.731248i
$6$	11.1246	−	34.2380i	0.126156	−	0.388267i
$7$	−22.2017			−0.171254			−0.0856270	−	0.996327i	$-0.527289\pi$
$7$	−22.2017			−0.171254			−0.0856270	+	0.996327i	$0.527289\pi$
$8$	−19.7771	+	60.8676i	−0.109254	+	0.336249i
$9$	−65.5304	+	47.6106i	−0.269672	+	0.195928i
$10$	−27.2854	−	221.936i	−0.0862839	−	0.701823i
$11$	132.319	+	96.1350i	0.329715	+	0.239552i	0.740310	−	0.672266i	$-0.234679\pi$
$11$	132.319	+	96.1350i	0.329715	+	0.239552i	−0.410595	+	0.911818i	$0.634679\pi$
$12$	116.498	−	84.6411i	0.233543	−	0.169679i
$13$	37.6553	−	27.3582i	0.0617971	−	0.0448982i	−0.556458	−	0.830876i	$-0.687840\pi$
$13$	37.6553	−	27.3582i	0.0617971	−	0.0448982i	0.618255	+	0.785978i	$0.287840\pi$
$14$	−71.8462	−	52.1993i	−0.0979679	−	0.0711778i
$15$	−243.847	+	440.073i	−0.279826	+	0.505005i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−396.729	+	1221.01i	−0.332944	+	1.02470i	0.634782	+	0.772691i	$0.281090\pi$
$17$	−396.729	+	1221.01i	−0.332944	+	1.02470i	−0.967726	+	0.252005i	$0.918910\pi$
$18$	−324.000			−0.235702
$19$	−382.612	+	1177.56i	−0.243150	+	0.748340i	0.752785	+	0.658267i	$0.228710\pi$
$19$	−382.612	+	1177.56i	−0.243150	+	0.748340i	−0.995935	+	0.0900734i	$0.971290\pi$
$20$	433.505	−	782.351i	0.242337	−	0.437348i
$21$	61.7463	+	190.036i	0.0305536	+	0.0940344i
$22$	202.165	+	622.199i	0.0890530	+	0.274077i
$23$	1059.62	+	769.861i	0.417668	+	0.303454i	0.776699	−	0.629872i	$-0.216893\pi$
$23$	1059.62	+	769.861i	0.417668	+	0.303454i	−0.359031	+	0.933326i	$0.616893\pi$
$24$	576.000			0.204124
$25$	−217.019	+	3117.46i	−0.0694460	+	0.997586i
$26$	186.178			0.0540126
$27$	589.773	+	428.495i	0.155695	+	0.113119i
$28$	−109.771	−	337.841i	−0.0264602	−	0.0814362i
$29$	355.346	+	1093.64i	0.0784615	+	0.241480i	0.982592	−	0.185777i	$-0.0594801\pi$
$29$	355.346	+	1093.64i	0.0784615	+	0.241480i	−0.904130	+	0.427256i	$0.859480\pi$
$30$	−1823.78	+	850.787i	−0.369972	+	0.172591i
$31$	−1742.50	+	5362.85i	−0.325662	+	1.00229i	0.645478	+	0.763779i	$0.276658\pi$
$31$	−1742.50	+	5362.85i	−0.325662	+	1.00229i	−0.971141	+	0.238507i	$0.923342\pi$
$32$	−1024.00			−0.176777
$33$	454.871	−	1399.95i	0.0727115	−	0.223783i
$34$	−4154.60	+	3018.49i	−0.616356	+	0.447809i
$35$	846.578	+	907.560i	0.116815	+	0.125229i
$36$	−1048.49	−	761.770i	−0.134836	−	0.0979642i
$37$	−6827.54	+	4960.50i	−0.819898	+	0.595691i	−0.916683	−	0.399614i	$-0.869144\pi$
$37$	−6827.54	+	4960.50i	−0.819898	+	0.595691i	0.0967850	+	0.995305i	$0.469144\pi$
$38$	−4006.77	+	2911.09i	−0.450127	+	0.327037i
$39$	−338.898	−	246.224i	−0.0356786	−	0.0259220i
$40$	3242.27	−	1512.51i	0.320405	−	0.149468i
$41$	1636.46	−	1188.95i	0.152035	−	0.110460i	−0.509167	−	0.860668i	$-0.670046\pi$
$41$	1636.46	−	1188.95i	0.152035	−	0.110460i	0.661202	+	0.750208i	$0.270046\pi$
$42$	−246.985	+	760.142i	−0.0216047	+	0.0664923i
$43$	6633.78			0.547129			0.273565	−	0.961854i	$-0.411797\pi$
$43$	6633.78			0.547129			0.273565	+	0.961854i	$0.411797\pi$
$44$	−808.659	+	2488.80i	−0.0629700	+	0.193802i
$45$	4444.98	+	863.299i	0.327219	+	0.0635521i
$46$	1618.96	+	4982.64i	0.112808	+	0.347188i
$47$	853.898	+	2628.03i	0.0563847	+	0.173534i	0.975283	−	0.220961i	$-0.0709194\pi$
$47$	853.898	+	2628.03i	0.0563847	+	0.173534i	−0.918898	+	0.394495i	$0.870919\pi$
$48$	1863.98	+	1354.26i	0.116772	+	0.0848395i
$49$	−16314.1			−0.970672
$50$	−8031.86	+	9578.06i	−0.454351	+	0.541817i
$51$	11554.6			0.622054
$52$	602.485	+	437.731i	0.0308985	+	0.0224491i
$53$	762.303	+	2346.13i	0.0372767	+	0.114726i	0.967963	−	0.251091i	$-0.0807895\pi$
$53$	762.303	+	2346.13i	0.0372767	+	0.114726i	−0.930687	+	0.365817i	$0.880789\pi$
$54$	901.094	+	2773.28i	0.0420519	+	0.129422i
$55$	−1115.66	−	9074.66i	−0.0497308	−	0.404505i
$56$	439.085	−	1351.36i	0.0187102	−	0.0575841i
$57$	11143.4			0.454289
$58$	−1421.38	+	4374.57i	−0.0554807	+	0.170752i
$59$	−25790.3	+	18737.8i	−0.964555	+	0.700791i	−0.954204	−	0.299156i	$-0.903295\pi$
$59$	−25790.3	+	18737.8i	−0.964555	+	0.700791i	−0.0103512	+	0.999946i	$0.503295\pi$
$60$	−7902.19	−	1534.75i	−0.283380	−	0.0550377i
$61$	14408.7	+	10468.5i	0.495792	+	0.360214i	0.807407	−	0.589994i	$-0.200870\pi$
$61$	14408.7	+	10468.5i	0.495792	+	0.360214i	−0.311615	+	0.950208i	$0.600870\pi$
$62$	−18247.7	+	13257.7i	−0.602876	+	0.438015i
$63$	1454.89	−	1057.04i	0.0461825	−	0.0335535i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−2554.19	−	496.072i	−0.0749843	−	0.0145634i
$66$	4763.47	−	3460.86i	0.134606	−	0.0977967i
$67$	7869.06	−	24218.5i	0.214159	−	0.659113i	−0.785054	−	0.619428i	$-0.787365\pi$
$67$	7869.06	−	24218.5i	0.214159	−	0.659113i	0.999212	−	0.0396848i	$-0.0126354\pi$
$68$	−20541.5			−0.538715
$69$	3642.66	−	11210.9i	0.0921076	−	0.283478i
$70$	605.781	+	4927.35i	0.0147765	+	0.120190i
$71$	7933.96	+	24418.2i	0.186786	+	0.574868i	0.999975	−	0.00713230i	$-0.00227030\pi$
$71$	7933.96	+	24418.2i	0.186786	+	0.574868i	−0.813189	+	0.582000i	$0.802270\pi$
$72$	−1601.94	−	4930.28i	−0.0364180	−	0.112083i
$73$	−66181.4	−	48083.6i	−1.45355	−	1.05606i	−0.984986	−	0.172632i	$-0.944773\pi$
$73$	−66181.4	−	48083.6i	−1.45355	−	1.05606i	−0.468560	−	0.883432i	$-0.655227\pi$
$74$	−33757.2			−0.716618
$75$	27287.4	−	6812.55i	0.560157	−	0.139848i
$76$	−19810.6			−0.393426
$77$	−2937.70	−	2134.36i	−0.0564651	−	0.0410243i
$78$	−517.790	−	1593.59i	−0.00963645	−	0.0296579i
$79$	−8291.07	−	25517.3i	−0.149466	−	0.460009i	0.848092	−	0.529849i	$-0.177751\pi$
$79$	−8291.07	−	25517.3i	−0.149466	−	0.460009i	−0.997558	+	0.0698395i	$0.977751\pi$
$80$	14048.3	+	2728.45i	0.245414	+	0.0476641i
$81$	2027.46	−	6239.88i	0.0343352	−	0.105673i
$82$	8091.08			0.132884
$83$	1803.17	−	5549.59i	0.0287304	−	0.0884231i	−0.935663	−	0.352894i	$-0.885197\pi$
$83$	1803.17	−	5549.59i	0.0287304	−	0.0884231i	0.964394	+	0.264471i	$0.0851975\pi$
$84$	−2586.46	+	1879.18i	−0.0399952	+	0.0290582i
$85$	65040.0	−	30341.0i	0.976412	−	0.455493i
$86$	21467.4	+	15597.0i	0.312992	+	0.227402i
$87$	8372.77	−	6083.18i	0.118596	−	0.0861653i
$88$	−8468.39	+	6152.64i	−0.116572	+	0.0846945i
$89$	21501.9	+	15622.0i	0.287741	+	0.209056i	0.722287	−	0.691594i	$-0.243091\pi$
$89$	21501.9	+	15622.0i	0.287741	+	0.209056i	−0.434546	+	0.900650i	$0.643091\pi$
$90$	12354.5	+	13244.5i	0.160775	+	0.172357i
$91$	−836.012	+	607.398i	−0.0105830	+	0.00768900i
$92$	−6475.84	+	19930.6i	−0.0797676	+	0.245499i
$93$	50749.5			0.608450
$94$	−3415.59	+	10512.1i	−0.0398700	+	0.122707i
$95$	62725.8	−	29261.4i	0.713078	−	0.332649i
$96$	2847.90	+	8764.94i	0.0315389	+	0.0970668i
$97$	27437.3	+	84443.2i	0.296082	+	0.911245i	0.982856	+	0.184375i	$0.0590260\pi$
$97$	27437.3	+	84443.2i	0.296082	+	0.911245i	−0.686774	+	0.726871i	$0.740974\pi$
$98$	−52793.5	−	38356.7i	−0.555284	−	0.403437i
$99$	−13247.9			−0.135850
$100$	−48511.0	+	12111.2i	−0.485110	+	0.121112i
$101$	90889.7			0.886566			0.443283	−	0.896382i	$-0.353814\pi$
$101$	90889.7			0.886566			0.443283	+	0.896382i	$0.353814\pi$
$102$	37391.4	+	27166.4i	0.355853	+	0.258543i
$103$	−15733.1	−	48421.5i	−0.146124	−	0.449723i	0.851030	−	0.525117i	$-0.175979\pi$
$103$	−15733.1	−	48421.5i	−0.146124	−	0.449723i	−0.997154	+	0.0753939i	$0.975979\pi$
$104$	920.515	+	2833.06i	0.00834541	+	0.0256845i
$105$	5413.81	−	9770.35i	0.0479214	−	0.0864843i
$106$	−3049.21	+	9384.51i	−0.0263586	+	0.0811235i
$107$	89217.2			0.753337			0.376668	−	0.926348i	$-0.377070\pi$
$107$	89217.2			0.753337			0.376668	+	0.926348i	$0.377070\pi$
$108$	−3604.37	+	11093.1i	−0.0297352	+	0.0915155i
$109$	−23174.9	+	16837.5i	−0.186832	+	0.135741i	−0.677270	−	0.735735i	$-0.736837\pi$
$109$	−23174.9	+	16837.5i	−0.186832	+	0.135741i	0.490438	+	0.871476i	$0.336837\pi$
$110$	17725.5	−	31989.3i	0.139674	−	0.252071i
$111$	61447.9	+	44644.5i	0.473369	+	0.343922i
$112$	4598.16	−	3340.76i	0.0346369	−	0.0251652i
$113$	59357.6	−	43125.8i	0.437300	−	0.317717i	−0.347261	−	0.937769i	$-0.612888\pi$
$113$	59357.6	−	43125.8i	0.437300	−	0.317717i	0.784561	+	0.620051i	$0.212888\pi$
$114$	36060.9	+	26199.8i	0.259881	+	0.188815i
$115$	−8934.35	−	72671.0i	−0.0629968	−	0.512408i
$116$	−14884.9	+	10814.5i	−0.102707	+	0.0746213i
$117$	−1165.03	+	3585.59i	−0.00786813	+	0.0242156i
$118$	−127515.			−0.843052
$119$	8808.05	−	27108.4i	0.0570180	−	0.175483i
$120$	−21963.6	−	23545.7i	−0.139236	−	0.149265i
$121$	−41501.2	−	127728.i	−0.257690	−	0.793089i
$122$	22014.5	+	67753.6i	0.133909	+	0.412129i
$123$	−14728.1	−	10700.6i	−0.0877777	−	0.0637742i
$124$	−90221.4			−0.526933
$125$	135710.	−	110001.i	0.776852	−	0.629683i
$126$	7193.35			0.0403650
$127$	50499.0	+	36689.7i	0.277827	+	0.201853i	0.717969	−	0.696075i	$-0.245072\pi$
$127$	50499.0	+	36689.7i	0.277827	+	0.201853i	−0.440142	+	0.897928i	$0.645072\pi$
$128$	−5062.93	−	15582.1i	−0.0273135	−	0.0840623i
$129$	−18449.6	−	56781.9i	−0.0976139	−	0.300425i
$130$	−7099.20	−	7610.59i	−0.0368427	−	0.0394966i
$131$	30501.5	−	93873.9i	0.155290	−	0.477932i	−0.842900	−	0.538069i	$-0.819154\pi$
$131$	30501.5	−	93873.9i	0.155290	−	0.477932i	0.998190	+	0.0601371i	$0.0191538\pi$
$132$	23551.9			0.117650
$133$	8494.64	−	26143.8i	0.0416405	−	0.128156i
$134$	82405.8	−	59871.3i	0.396457	−	0.288043i
$135$	−4972.76	−	40447.8i	−0.0234835	−	0.191012i
$136$	−66473.6	−	48295.9i	−0.308178	−	0.223904i
$137$	79924.9	−	58068.9i	0.363815	−	0.264327i	−0.390826	−	0.920464i	$-0.627811\pi$
$137$	79924.9	−	58068.9i	0.363815	−	0.264327i	0.754642	+	0.656137i	$0.227811\pi$
$138$	38146.4	−	27715.0i	0.170512	−	0.123884i
$139$	−358150.	−	260211.i	−1.57227	−	1.14232i	−0.924938	−	0.380119i	$-0.875883\pi$
$139$	−358150.	−	260211.i	−1.57227	−	1.14232i	−0.647336	−	0.762205i	$-0.724117\pi$
$140$	−9624.55	+	17369.5i	−0.0415012	+	0.0748976i
$141$	20119.8	−	14617.9i	0.0852268	−	0.0619209i
$142$	−31735.8	+	97672.9i	−0.132078	+	0.406493i
$143$	7612.58			0.0311309
$144$	6407.78	−	19721.1i	0.0257514	−	0.0792547i
$145$	31156.1	−	56227.8i	0.123062	−	0.222091i
$146$	−101116.	−	311204.i	−0.392590	−	1.20827i
$147$	45372.0	+	139641.i	0.173179	+	0.532989i
$148$	−109241.	−	79368.0i	−0.409949	−	0.297846i
$149$	104164.			0.384372			0.192186	−	0.981359i	$-0.438442\pi$
$149$	104164.			0.384372			0.192186	+	0.981359i	$0.438442\pi$
$150$	104321.	+	42110.8i	0.378569	+	0.152815i
$151$	−439470.			−1.56851			−0.784253	−	0.620441i	$-0.786954\pi$
$151$	−439470.			−1.56851			−0.784253	+	0.620441i	$0.786954\pi$
$152$	−64108.3	−	46577.4i	−0.225064	−	0.163518i
$153$	−32135.0	−	98901.4i	−0.110981	−	0.341566i
$154$	−4488.40	−	13813.9i	−0.0152507	−	0.0469368i
$155$	285666.	−	133262.i	0.955057	−	0.445531i
$156$	2071.16	−	6374.37i	0.00681400	−	0.0209713i
$157$	33093.3			0.107150			0.0535749	−	0.998564i	$-0.482938\pi$
$157$	33093.3			0.107150			0.0535749	+	0.998564i	$0.482938\pi$
$158$	33164.3	−	102069.i	0.105688	−	0.325276i
$159$	17961.6	−	13049.9i	0.0563446	−	0.0409368i
$160$	39046.4	+	41859.1i	0.120582	+	0.129268i
$161$	−23525.4	−	17092.2i	−0.0715274	−	0.0519677i
$162$	21231.8	−	15425.8i	0.0635624	−	0.0461808i
$163$	−129326.	+	93960.6i	−0.381255	+	0.276998i	−0.761863	−	0.647739i	$-0.775715\pi$
$163$	−129326.	+	93960.6i	−0.381255	+	0.276998i	0.380608	+	0.924737i	$0.375715\pi$
$164$	26183.3	+	19023.3i	0.0760177	+	0.0552301i
$165$	−74571.8	+	34787.5i	−0.213238	+	0.0994750i
$166$	18883.1	−	13719.3i	0.0531866	−	0.0386423i
$167$	−161478.	+	496977.i	−0.448044	+	1.37894i	0.431066	+	0.902320i	$0.358138\pi$
$167$	−161478.	+	496977.i	−0.448044	+	1.37894i	−0.879110	+	0.476618i	$0.841862\pi$
$168$	−12788.2			−0.0349571
$169$	−114066.	+	351060.i	−0.307214	+	0.945507i
$170$	281810.	+	54732.8i	0.747883	+	0.145253i
$171$	−30991.6	−	95382.4i	−0.0810502	−	0.249447i
$172$	32799.2	+	100946.i	0.0845361	+	0.260175i
$173$	−111261.	−	80836.1i	−0.282637	−	0.205348i	0.437430	−	0.899253i	$-0.355889\pi$
$173$	−111261.	−	80836.1i	−0.282637	−	0.205348i	−0.720067	+	0.693905i	$0.755889\pi$
$174$	41397.3			0.103657
$175$	4818.18	−	69212.8i	0.0118929	−	0.170841i
$176$	−41870.0			−0.101888
$177$	232113.	+	168640.i	0.556886	+	0.404602i
$178$	32852.0	+	101108.i	0.0777162	+	0.239186i
$179$	158354.	+	487364.i	0.369400	+	1.13690i	0.947180	+	0.320703i	$0.103919\pi$
$179$	158354.	+	487364.i	0.369400	+	1.13690i	−0.577780	+	0.816193i	$0.696081\pi$
$180$	8840.45	+	71907.2i	0.0203373	+	0.165421i
$181$	−214012.	+	658662.i	−0.485559	+	1.49440i	0.345611	+	0.938378i	$0.387672\pi$
$181$	−214012.	+	658662.i	−0.485559	+	1.49440i	−0.831170	+	0.556019i	$0.812328\pi$
$182$	−4133.47			−0.00924988
$183$	49532.6	−	152446.i	0.109336	−	0.336502i
$184$	−67815.8	+	49271.1i	−0.147668	+	0.107287i
$185$	463118.	+	89946.2i	0.994860	+	0.193221i
$186$	164229.	+	119319.i	0.348070	+	0.252888i
$187$	−169876.	+	123422.i	−0.355245	+	0.258101i
$188$	−35768.5	+	25987.4i	−0.0738085	+	0.0536250i
$189$	−13094.0	−	9513.32i	−0.0266635	−	0.0193721i
$190$	271782.	+	52785.3i	0.546182	+	0.106079i
$191$	−400907.	+	291276.i	−0.795170	+	0.577725i	−0.909493	−	0.415719i	$-0.863530\pi$
$191$	−400907.	+	291276.i	−0.795170	+	0.577725i	0.114323	+	0.993444i	$0.463530\pi$
$192$	−11391.6	+	35059.7i	−0.0223014	+	0.0686366i
$193$	421685.			0.814882			0.407441	−	0.913231i	$-0.366421\pi$
$193$	421685.			0.814882			0.407441	+	0.913231i	$0.366421\pi$
$194$	−109749.	+	337773.i	−0.209361	+	0.644348i
$195$	2857.46	+	23242.3i	0.00538139	+	0.0437716i
$196$	−80661.3	−	248250.i	−0.149977	−	0.461582i
$197$	263037.	+	809544.i	0.482893	+	1.48619i	0.835009	+	0.550236i	$0.185462\pi$
$197$	263037.	+	809544.i	0.482893	+	1.48619i	−0.352116	+	0.935956i	$0.614538\pi$
$198$	−42871.2	−	31147.8i	−0.0777146	−	0.0564630i
$199$	−762597.			−1.36509			−0.682547	−	0.730842i	$-0.739128\pi$
$199$	−762597.			−1.36509			−0.682547	+	0.730842i	$0.739128\pi$
$200$	−185460.	−	74863.6i	−0.327850	−	0.132341i
$201$	−229183.			−0.400122
$202$	294125.	+	213694.i	0.507170	+	0.368481i
$203$	−7889.28	−	24280.7i	−0.0134369	−	0.0413544i
$204$	57128.9	+	175825.i	0.0961127	+	0.295804i
$205$	−111002.	−	21558.7i	−0.184479	−	0.0358293i
$206$	62932.5	−	193686.i	0.103325	−	0.318003i
$207$	−106091.			−0.172089
$208$	−3682.06	+	11332.2i	−0.00590110	+	0.0181617i
$209$	−163832.	+	119031.i	−0.259437	+	0.188492i
$210$	40490.9	−	18888.9i	0.0633592	−	0.0295569i
$211$	−678172.	−	492721.i	−1.04866	−	0.761895i	−0.0767014	−	0.997054i	$-0.524439\pi$
$211$	−678172.	−	492721.i	−1.04866	−	0.761895i	−0.971957	+	0.235159i	$0.924439\pi$
$212$	−31931.7	+	23199.8i	−0.0487959	+	0.0354523i
$213$	186942.	−	135822.i	0.282331	−	0.205126i
$214$	288713.	+	209762.i	0.430955	+	0.313107i
$215$	−252954.	−	271176.i	−0.373204	−	0.400087i
$216$	−37745.5	+	27423.7i	−0.0550466	+	0.0399937i
$217$	38686.4	−	119064.i	0.0557710	−	0.171646i
$218$	−114583.			−0.163297
$219$	−227512.	+	700208.i	−0.320548	+	0.986545i
$220$	132572.	−	61844.5i	0.184670	−	0.0861479i
$221$	18465.6	+	56831.1i	0.0254321	+	0.0782719i
$222$	93884.0	+	288945.i	0.127852	+	0.393489i
$223$	−200012.	−	145317.i	−0.269336	−	0.195684i	0.444917	−	0.895572i	$-0.353233\pi$
$223$	−200012.	−	145317.i	−0.269336	−	0.195684i	−0.714253	+	0.699888i	$0.753233\pi$
$224$	22734.5			0.0302737
$225$	−134203.	−	214620.i	−0.176728	−	0.282628i
$226$	293480.			0.382215
$227$	−57746.2	−	41955.1i	−0.0743804	−	0.0540406i	0.549974	−	0.835182i	$-0.314638\pi$
$227$	−57746.2	−	41955.1i	−0.0743804	−	0.0540406i	−0.624354	+	0.781141i	$0.714638\pi$
$228$	55096.2	+	169569.i	0.0701915	+	0.216027i
$229$	−3471.31	−	10683.6i	−0.00437426	−	0.0134626i	0.948846	−	0.315741i	$-0.102253\pi$
$229$	−3471.31	−	10683.6i	−0.00437426	−	0.0134626i	−0.953220	+	0.302278i	$0.902253\pi$
$230$	141948.	−	256174.i	0.176933	−	0.319312i
$231$	−10098.9	+	31081.2i	−0.0124521	+	0.0383237i
$232$	−73595.1			−0.0897696
$233$	223652.	−	688329.i	0.269887	−	0.830628i	−0.720640	−	0.693310i	$-0.756152\pi$
$233$	223652.	−	688329.i	0.269887	−	0.830628i	0.990527	−	0.137318i	$-0.0438483\pi$
$234$	−12200.3	+	8864.05i	−0.0145657	+	0.0105826i
$235$	74868.3	−	135116.i	0.0884358	−	0.159601i
$236$	−412646.	−	299805.i	−0.482278	−	0.350395i
$237$	−195357.	+	141935.i	−0.225921	+	0.164141i
$238$	92239.1	−	67015.6i	0.105553	−	0.0766891i
$239$	378813.	+	275223.i	0.428973	+	0.311667i	0.781238	−	0.624233i	$-0.214589\pi$
$239$	378813.	+	275223.i	0.428973	+	0.311667i	−0.352265	+	0.935900i	$0.614589\pi$
$240$	−15716.4	−	127835.i	−0.0176126	−	0.143259i
$241$	−958350.	+	696282.i	−1.06287	+	0.772223i	−0.974618	−	0.223875i	$-0.928129\pi$
$241$	−958350.	+	696282.i	−1.06287	+	0.772223i	−0.0882558	+	0.996098i	$0.528129\pi$
$242$	166005.	−	510911.i	0.182214	−	0.560798i
$243$	−59049.0			−0.0641500
$244$	−88058.0	+	271015.i	−0.0946878	+	0.291419i
$245$	622076.	+	666887.i	0.662107	+	0.709802i
$246$	−22502.5	−	69255.7i	−0.0237079	−	0.0729655i
$247$	17808.5	+	54809.0i	0.0185731	+	0.0571623i
$248$	−291962.	−	212123.i	−0.301438	−	0.219007i
$249$	−52516.7			−0.0536783
$250$	697796.	−	36896.7i	0.706120	−	0.0373368i
$251$	−792280.			−0.793770			−0.396885	−	0.917868i	$-0.629909\pi$
$251$	−792280.			−0.793770			−0.396885	+	0.917868i	$0.629909\pi$
$252$	23278.2	+	16912.6i	0.0230912	+	0.0167768i
$253$	66197.1	+	203734.i	0.0650186	+	0.200107i
$254$	77155.7	+	237461.i	0.0750384	+	0.230944i
$255$	−440590.	−	472328.i	−0.424311	−	0.454876i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	−277417.			−0.261999			−0.131000	−	0.991382i	$-0.541819\pi$
$257$	−277417.			−0.261999			−0.131000	+	0.991382i	$0.541819\pi$
$258$	73798.2	−	227128.i	0.0690235	−	0.212432i
$259$	151583.	−	110131.i	0.140411	−	0.102015i
$260$	−5079.94	−	41319.6i	−0.00466042	−	0.0379073i
$261$	−75355.0	−	54748.6i	−0.0684716	−	0.0497475i
$262$	319415.	−	232069.i	0.287477	−	0.208864i
$263$	1.19913e6	−	871221.i	1.06900	−	0.776674i	0.0932683	−	0.995641i	$-0.470269\pi$
$263$	1.19913e6	−	871221.i	1.06900	−	0.776674i	0.975732	+	0.218967i	$0.0702686\pi$
$264$	76215.5	+	55373.8i	0.0673028	+	0.0488984i
$265$	66837.4	−	120622.i	0.0584662	−	0.105514i
$266$	88957.1	−	64631.1i	0.0770862	−	0.0560064i
$267$	73916.9	−	227493.i	0.0634550	−	0.195294i
$268$	407437.			0.346516
$269$	−361135.	+	1.11146e6i	−0.304291	+	0.936512i	0.675649	+	0.737223i	$0.263863\pi$
$269$	−361135.	+	1.11146e6i	−0.304291	+	0.936512i	−0.979941	+	0.199289i	$0.936137\pi$
$270$	79006.3	−	142583.i	0.0659557	−	0.119031i
$271$	−416329.	−	1.28133e6i	−0.344361	−	1.05983i	−0.961925	−	0.273313i	$-0.911881\pi$
$271$	−416329.	−	1.28133e6i	−0.344361	−	1.05983i	0.617565	−	0.786520i	$-0.288119\pi$
$272$	−101563.	−	312577.i	−0.0832360	−	0.256174i
$273$	7524.11	+	5466.58i	0.00611010	+	0.00443925i
$274$	395171.			0.317986
$275$	−328412.	+	391634.i	−0.261871	+	0.312283i
$276$	188606.			0.149033
$277$	1.20830e6	+	877885.i	0.946187	+	0.687445i	0.949902	−	0.312548i	$-0.101182\pi$
$277$	1.20830e6	+	877885.i	0.946187	+	0.687445i	−0.00371487	+	0.999993i	$0.501182\pi$
$278$	−547205.	−	1.68412e6i	−0.424657	−	1.30696i
$279$	−141142.	−	434391.i	−0.108554	−	0.334095i
$280$	−71983.9	+	33580.3i	−0.0548707	+	0.0255970i
$281$	−334423.	+	1.02925e6i	−0.252656	+	0.777596i	0.741626	+	0.670814i	$0.234055\pi$
$281$	−334423.	+	1.02925e6i	−0.252656	+	0.777596i	−0.994282	+	0.106783i	$0.965945\pi$
$282$	99477.8			0.0744909
$283$	607897.	−	1.87091e6i	0.451195	−	1.38863i	−0.424351	−	0.905498i	$-0.639498\pi$
$283$	607897.	−	1.87091e6i	0.451195	−	1.38863i	0.875545	−	0.483136i	$-0.160502\pi$
$284$	−332342.	+	241461.i	−0.244506	+	0.177644i
$285$	−424913.	−	455521.i	−0.309876	−	0.332198i
$286$	24634.8	+	17898.2i	0.0178088	+	0.0129388i
$287$	−36332.1	+	26396.8i	−0.0260367	+	0.0189168i
$288$	67103.1	−	48753.3i	0.0476718	−	0.0346356i
$289$	−184772.	−	134245.i	−0.130134	−	0.0945482i
$290$	233023.	−	108704.i	0.162706	−	0.0759019i
$291$	646485.	−	469699.i	0.447534	−	0.325153i
$292$	404465.	−	1.24481e6i	0.277603	−	0.854373i
$293$	1.13004e6			0.768997			0.384499	−	0.923126i	$-0.374374\pi$
$293$	1.13004e6			0.768997			0.384499	+	0.923126i	$0.374374\pi$
$294$	−181488.	+	558562.i	−0.122456	+	0.376880i
$295$	1.74938e6	+	339763.i	1.17039	+	0.227311i
$296$	−166905.	−	513680.i	−0.110723	−	0.340772i
$297$	36844.5	+	113396.i	0.0242372	+	0.0745943i
$298$	337082.	+	244904.i	0.219884	+	0.159755i
$299$	60962.4			0.0394352
$300$	238582.	+	381547.i	0.153051	+	0.244763i
$301$	−147281.			−0.0936982
$302$	−1.42215e6	−	1.03325e6i	−0.897282	−	0.651914i
$303$	−252778.	−	777971.i	−0.158173	−	0.486807i
$304$	−97948.8	−	301455.i	−0.0607876	−	0.187085i
$305$	−121489.	−	988175.i	−0.0747801	−	0.608253i
$306$	128540.	−	395606.i	0.0784757	−	0.241523i
$307$	1.94751e6			1.17933			0.589664	−	0.807649i	$-0.299260\pi$
$307$	1.94751e6			1.17933			0.589664	+	0.807649i	$0.299260\pi$
$308$	17953.6	−	55255.5i	0.0107839	−	0.0331893i
$309$	−370708.	+	269335.i	−0.220870	+	0.160471i
$310$	1.23775e6	+	240395.i	0.731526	+	0.142076i
$311$	−1.40769e6	−	1.02274e6i	−0.825286	−	0.599605i	0.0929356	−	0.995672i	$-0.470375\pi$
$311$	−1.40769e6	−	1.02274e6i	−0.825286	−	0.599605i	−0.918222	+	0.396067i	$0.870375\pi$
$312$	21689.5	−	15758.3i	0.0126143	−	0.00916481i
$313$	18989.3	−	13796.5i	0.0109559	−	0.00795991i	−0.582294	−	0.812978i	$-0.697845\pi$
$313$	18989.3	−	13796.5i	0.0109559	−	0.00795991i	0.593250	+	0.805018i	$0.297845\pi$
$314$	107092.	+	77807.1i	0.0612963	+	0.0445343i
$315$	−98686.1	−	19166.7i	−0.0560376	−	0.0108836i
$316$	347301.	−	252329.i	0.195654	−	0.142151i
$317$	164797.	−	507193.i	0.0921087	−	0.283482i	−0.894381	−	0.447307i	$-0.852383\pi$
$317$	164797.	−	507193.i	0.0921087	−	0.283482i	0.986489	+	0.163825i	$0.0523833\pi$
$318$	88807.1			0.0492470
$319$	−58118.5	+	178870.i	−0.0319770	+	0.0984151i
$320$	27940.2	+	227262.i	0.0152530	+	0.124066i
$321$	−248127.	−	763655.i	−0.134404	−	0.413652i
$322$	−35943.6	−	110623.i	−0.0193189	−	0.0594574i
$323$	−1.28601e6	−	934344.i	−0.685866	−	0.498311i
$324$	104976.			0.0555556
$325$	77116.0	+	123326.i	0.0404983	+	0.0647659i
$326$	−639421.			−0.333229
$327$	208574.	+	151538.i	0.107868	+	0.0783703i
$328$	40004.5	+	123121.i	0.0205317	+	0.0631900i
$329$	−18958.0	−	58346.7i	−0.00965611	−	0.0297185i
$330$	−323110.	−	62754.0i	−0.163330	−	0.0317217i
$331$	−49102.4	+	151122.i	−0.0246339	+	0.0758153i	−0.962618	−	0.270864i	$-0.912691\pi$
$331$	−49102.4	+	151122.i	−0.0246339	+	0.0758153i	0.937984	+	0.346679i	$0.112691\pi$
$332$	93363.0			0.0464868
$333$	211239.	−	650127.i	0.104391	−	0.321283i
$334$	−1.69101e6	+	1.22859e6i	−0.829433	+	0.602618i
$335$	−1.29006e6	+	601809.i	−0.628055	+	0.292986i
$336$	−41383.4	−	30066.8i	−0.0199976	−	0.0145291i
$337$	2.61339e6	−	1.89874e6i	1.25351	−	0.910730i	0.255092	−	0.966917i	$-0.417894\pi$
$337$	2.61339e6	−	1.89874e6i	1.25351	−	0.910730i	0.998420	+	0.0561863i	$0.0178941\pi$
$338$	−1.19452e6	+	867869.i	−0.568724	+	0.413202i
$339$	−534218.	−	388132.i	−0.252476	−	0.183434i
$340$	783271.	+	839693.i	0.367464	+	0.393934i
$341$	−746122.	+	542090.i	−0.347475	+	0.252456i
$342$	123966.	−	381529.i	0.0573111	−	0.176385i
$343$	735344.			0.337486
$344$	−131197.	+	403783.i	−0.0597761	+	0.183972i
$345$	−597180.	+	278583.i	−0.270120	+	0.126010i
$346$	−169992.	−	523182.i	−0.0763377	−	0.234943i
$347$	1.03028e6	+	3.17089e6i	0.459339	+	1.41370i	0.865964	+	0.500106i	$0.166706\pi$
$347$	1.03028e6	+	3.17089e6i	0.459339	+	1.41370i	−0.406625	+	0.913595i	$0.633294\pi$
$348$	133964.	+	97330.8i	0.0592982	+	0.0430826i
$349$	−153929.			−0.0676482			−0.0338241	−	0.999428i	$-0.510769\pi$
$349$	−153929.			−0.0676482			−0.0338241	+	0.999428i	$0.510769\pi$
$350$	178321.	−	212649.i	0.0778094	−	0.0927883i
$351$	33931.0			0.0147004
$352$	−135494.	−	98442.3i	−0.0582860	−	0.0423472i
$353$	−461002.	−	1.41882e6i	−0.196909	−	0.606024i	−0.999949	−	0.0100988i	$-0.996785\pi$
$353$	−461002.	−	1.41882e6i	−0.196909	−	0.606024i	0.803040	−	0.595925i	$-0.203215\pi$
$354$	354637.	+	1.09146e6i	0.150410	+	0.462914i
$355$	695636.	−	1.25542e6i	0.292962	−	0.528711i
$356$	−131408.	+	404432.i	−0.0549536	+	0.169130i
$357$	−256531.			−0.106529
$358$	−633416.	+	1.94945e6i	−0.261205	+	0.803907i
$359$	1.64493e6	−	1.19511e6i	0.673614	−	0.489409i	−0.197619	−	0.980279i	$-0.563321\pi$
$359$	1.64493e6	−	1.19511e6i	0.673614	−	0.489409i	0.871233	+	0.490870i	$0.163321\pi$
$360$	−140456.	+	253482.i	−0.0571193	+	0.103084i
$361$	762951.	+	554316.i	0.308126	+	0.223867i
$362$	−2.24116e6	+	1.62830e6i	−0.898881	+	0.653075i
$363$	−977865.	+	710461.i	−0.389504	+	0.282992i
$364$	−13376.2	−	9718.37i	−0.00529150	−	0.00384450i
$365$	558018.	+	4.53885e6i	0.219238	+	1.78326i
$366$	518712.	−	376866.i	0.202406	−	0.147057i
$367$	609722.	−	1.87653e6i	0.236302	−	0.727261i	−0.760645	−	0.649169i	$-0.775117\pi$
$367$	609722.	−	1.87653e6i	0.236302	−	0.727261i	0.996946	−	0.0780928i	$-0.0248830\pi$
$368$	−335300.			−0.129067
$369$	−50630.7	+	155825.i	−0.0193575	+	0.0595761i
$370$	1.28720e6	+	1.37993e6i	0.488814	+	0.524025i
$371$	−16924.4	−	52088.0i	−0.00638379	−	0.0196473i
$372$	250919.	+	772251.i	0.0940106	+	0.289335i
$373$	2.62769e6	+	1.90913e6i	0.977917	+	0.710498i	0.957242	−	0.289288i	$-0.0934184\pi$
$373$	2.62769e6	+	1.90913e6i	0.977917	+	0.710498i	0.0206751	+	0.999786i	$0.493418\pi$
$374$	−839913.			−0.310495
$375$	−1.31899e6	−	855685.i	−0.484353	−	0.314221i
$376$	−176849.			−0.0645110
$377$	43300.8	+	31459.8i	0.0156907	+	0.0114000i
$378$	−20005.8	−	61571.5i	−0.00720156	−	0.0221641i
$379$	−181592.	−	558884.i	−0.0649381	−	0.199859i	0.913323	−	0.407236i	$-0.133507\pi$
$379$	−181592.	−	558884.i	−0.0649381	−	0.199859i	−0.978261	+	0.207377i	$0.933507\pi$
$380$	755401.	+	809816.i	0.268360	+	0.287692i
$381$	173600.	−	534287.i	0.0612686	−	0.188565i
$382$	−1.98219e6			−0.695004
$383$	1.09673e6	−	3.37539e6i	0.382035	−	1.17578i	−0.556574	−	0.830798i	$-0.687884\pi$
$383$	1.09673e6	−	3.37539e6i	0.382035	−	1.17578i	0.938609	−	0.344984i	$-0.112116\pi$
$384$	−119294.	+	86672.5i	−0.0412850	+	0.0299953i
$385$	24769.6	+	201473.i	0.00851661	+	0.0692731i
$386$	1.36460e6	+	991441.i	0.466163	+	0.338687i
$387$	−434714.	+	315838.i	−0.147546	+	0.107198i
$388$	−1.14931e6	+	835020.i	−0.387576	+	0.281590i
$389$	−374021.	−	271742.i	−0.125320	−	0.0910506i	0.523359	−	0.852112i	$-0.324679\pi$
$389$	−374021.	−	271742.i	−0.125320	−	0.0910506i	−0.648680	+	0.761061i	$0.724679\pi$
$390$	−45398.9	+	81931.9i	−0.0151142	+	0.0272767i
$391$	−1.36039e6	+	988379.i	−0.450008	+	0.326950i
$392$	322645.	−	992999.i	0.106050	−	0.326388i
$393$	−888343.			−0.290135
$394$	−1.05215e6	+	3.23818e6i	−0.341457	+	1.05090i
$395$	−726946.	+	1.31193e6i	−0.234428	+	0.423075i
$396$	−65501.4	−	201592.i	−0.0209900	−	0.0646006i
$397$	1.35038e6	+	4.15604e6i	0.430011	+	1.32344i	0.898114	+	0.439763i	$0.144938\pi$
$397$	1.35038e6	+	4.15604e6i	0.430011	+	1.32344i	−0.468103	+	0.883674i	$0.655062\pi$
$398$	−2.46782e6	−	1.79297e6i	−0.780917	−	0.567370i
$399$	−247403.			−0.0777988
$400$	−424147.	−	678306.i	−0.132546	−	0.211971i
$401$	3.36689e6			1.04560			0.522802	−	0.852454i	$-0.324887\pi$
$401$	3.36689e6			1.04560			0.522802	+	0.852454i	$0.324887\pi$
$402$	−741653.	−	538842.i	−0.228895	−	0.166302i
$403$	81103.7	+	249611.i	0.0248758	+	0.0765600i
$404$	449383.	+	1.38306e6i	0.136982	+	0.421587i
$405$	−332383.	+	155056.i	−0.100694	+	0.0469733i
$406$	31557.1	−	97122.9i	0.00950129	−	0.0292420i
$407$	−1.38029e6			−0.413032
$408$	−228516.	+	703299.i	−0.0679619	+	0.209165i
$409$	3.69241e6	−	2.68269e6i	1.09144	−	0.792981i	0.111802	−	0.993731i	$-0.464338\pi$
$409$	3.69241e6	−	2.68269e6i	1.09144	−	0.792981i	0.979643	+	0.200750i	$0.0643379\pi$
$410$	−308523.	−	330747.i	−0.0906417	−	0.0971710i
$411$	−719324.	−	522620.i	−0.210049	−	0.152609i
$412$	659037.	−	478819.i	0.191279	−	0.138972i
$413$	572589.	−	416011.i	0.165184	−	0.120013i
$414$	−343318.	−	249435.i	−0.0984454	−	0.0715247i
$415$	−295613.	+	137903.i	−0.0842566	+	0.0393054i
$416$	−38559.1	+	28014.8i	−0.0109243	+	0.00793696i
$417$	−1.23121e6	+	3.78928e6i	−0.346731	+	1.06713i
$418$	−810027.			−0.226756
$419$	1.00532e6	−	3.09406e6i	0.279749	−	0.860980i	−0.708174	−	0.706038i	$-0.750481\pi$
$419$	1.00532e6	−	3.09406e6i	0.279749	−	0.860980i	0.987923	−	0.154942i	$-0.0495192\pi$
$420$	175442.	+	34074.1i	0.0485300	+	0.00942543i
$421$	−122906.	−	378266.i	−0.0337962	−	0.104014i	0.932735	−	0.360562i	$-0.117415\pi$
$421$	−122906.	−	378266.i	−0.0337962	−	0.104014i	−0.966532	+	0.256548i	$0.917415\pi$
$422$	−1.03616e6	−	3.18896e6i	−0.283233	−	0.871701i
$423$	−181078.	−	131561.i	−0.0492057	−	0.0357500i
$424$	−157879.			−0.0426492
$425$	−3.72033e6	−	1.50177e6i	−0.999101	−	0.403301i
$426$	924294.			0.246766
$427$	−319897.	−	232419.i	−0.0849064	−	0.0616881i
$428$	441114.	+	1.35761e6i	0.116397	+	0.358233i
$429$	−21171.7	−	65159.9i	−0.00555410	−	0.0170937i
$430$	−181005.	−	1.47227e6i	−0.0472084	−	0.383988i
$431$	−2.02236e6	+	6.22419e6i	−0.524403	+	1.61395i	0.241090	+	0.970503i	$0.422495\pi$
$431$	−2.02236e6	+	6.22419e6i	−0.524403	+	1.61395i	−0.765493	+	0.643444i	$0.777505\pi$
$432$	−186624.			−0.0481125
$433$	−1.95421e6	+	6.01445e6i	−0.500902	+	1.54162i	0.306651	+	0.951822i	$0.400791\pi$
$433$	−1.95421e6	+	6.01445e6i	−0.500902	+	1.54162i	−0.807553	+	0.589795i	$0.799209\pi$
$434$	405129.	−	294343.i	0.103245	−	0.0750118i
$435$	−567932.	−	110303.i	−0.143904	−	0.0279489i
$436$	−370798.	−	269401.i	−0.0934160	−	0.0678707i
$437$	−1.31198e6	+	953211.i	−0.328643	+	0.238773i
$438$	−2.38253e6	+	1.73101e6i	−0.593408	+	0.431136i
$439$	−5.84092e6	−	4.24367e6i	−1.44650	−	1.05095i	−0.986632	−	0.162961i	$-0.947895\pi$
$439$	−5.84092e6	−	4.24367e6i	−1.44650	−	1.05095i	−0.459871	−	0.887985i	$-0.652105\pi$
$440$	574418.	+	111563.i	0.141448	+	0.0274718i
$441$	1.06907e6	−	776723.i	0.261763	−	0.190182i
$442$	−73862.2	+	227325.i	−0.0179832	+	0.0553466i
$443$	3.99240e6			0.966552			0.483276	−	0.875468i	$-0.339447\pi$
$443$	3.99240e6			0.966552			0.483276	+	0.875468i	$0.339447\pi$
$444$	−375536.	+	1.15578e6i	−0.0904054	+	0.278239i
$445$	−181296.	−	1.47464e6i	−0.0433999	−	0.353010i
$446$	−305591.	−	940513.i	−0.0727451	−	0.223886i
$447$	−289696.	−	891592.i	−0.0685762	−	0.211056i
$448$	73570.5	+	53452.1i	0.0173184	+	0.0125826i
$449$	6.48422e6			1.51789			0.758947	−	0.651152i	$-0.225714\pi$
$449$	6.48422e6			1.51789			0.758947	+	0.651152i	$0.225714\pi$
$450$	70314.1	−	1.01006e6i	0.0163686	−	0.235133i
$451$	330834.			0.0765893
$452$	949721.	+	690013.i	0.218650	+	0.158859i
$453$	1.22223e6	+	3.76164e6i	0.279839	+	0.861256i
$454$	−88228.3	−	271539.i	−0.0200895	−	0.0618290i
$455$	56707.4	+	11013.6i	0.0128414	+	0.00249403i
$456$	−220385.	+	678275.i	−0.0496329	+	0.152754i
$457$	4.58375e6			1.02667			0.513334	−	0.858189i	$-0.328410\pi$
$457$	4.58375e6			1.02667			0.513334	+	0.858189i	$0.328410\pi$
$458$	13885.2	−	42734.4i	0.00309307	−	0.00951949i
$459$	−757175.	+	550120.i	−0.167751	+	0.121878i
$460$	1.06165e6	−	495258.i	0.233931	−	0.109128i
$461$	3.33324e6	+	2.42174e6i	0.730489	+	0.530732i	0.889718	−	0.456510i	$-0.150901\pi$
$461$	3.33324e6	+	2.42174e6i	0.730489	+	0.530732i	−0.159229	+	0.987242i	$0.550901\pi$
$462$	−105757.	+	76837.0i	−0.0230518	+	0.0167481i
$463$	−4.20908e6	+	3.05808e6i	−0.912505	+	0.662973i	−0.941647	−	0.336602i	$-0.890722\pi$
$463$	−4.20908e6	+	3.05808e6i	−0.912505	+	0.662973i	0.0291424	+	0.999575i	$0.490722\pi$
$464$	−238159.	−	173033.i	−0.0513537	−	0.0373107i
$465$	−1.93514e6	−	2.07454e6i	−0.415031	−	0.444927i
$466$	2.34211e6	−	1.70164e6i	0.499624	−	0.362998i
$467$	−360861.	+	1.11061e6i	−0.0765680	+	0.235652i	−0.982014	−	0.188810i	$-0.939537\pi$
$467$	−360861.	+	1.11061e6i	−0.0765680	+	0.235652i	0.905446	+	0.424462i	$0.139537\pi$
$468$	−60321.7			−0.0127309
$469$	−174706.	+	537691.i	−0.0366756	+	0.112876i
$470$	559955.	−	261217.i	0.116925	−	0.0545453i
$471$	−92037.6	−	283263.i	−0.0191167	−	0.0588352i
$472$	−630466.	−	1.94038e6i	−0.130259	−	0.400895i
$473$	877772.	+	637739.i	0.180397	+	0.131066i
$474$	−965896.			−0.197462
$475$	−3.58796e6	−	1.44833e6i	−0.729648	−	0.294533i
$476$	456055.			0.0922571
$477$	−161654.	−	117449.i	−0.0325306	−	0.0236348i
$478$	578774.	+	1.78128e6i	0.115862	+	0.356585i
$479$	−1.70607e6	−	5.25075e6i	−0.339749	−	1.04564i	−0.964335	−	0.264685i	$-0.914732\pi$
$479$	−1.70607e6	−	5.25075e6i	−0.339749	−	1.04564i	0.624586	−	0.780956i	$-0.285268\pi$
$480$	249699.	−	450634.i	0.0494668	−	0.0892732i
$481$	−121383.	+	373578.i	−0.0239219	+	0.0736239i
$482$	−4.73834e6			−0.928986
$483$	−80873.2	+	248902.i	−0.0157738	+	0.0485468i
$484$	1.73843e6	−	1.26304e6i	0.337321	−	0.245078i
$485$	2.40565e6	−	4.34150e6i	0.464385	−	0.838081i
$486$	−191087.	−	138833.i	−0.0366978	−	0.0266625i
$487$	−4.13096e6	+	3.00132e6i	−0.789275	+	0.573442i	−0.907748	−	0.419515i	$-0.862200\pi$
$487$	−4.13096e6	+	3.00132e6i	−0.789275	+	0.573442i	0.118473	+	0.992957i	$0.462200\pi$
$488$	−922155.	+	669985.i	−0.175289	+	0.127355i
$489$	1.16393e6	+	845645.i	0.220118	+	0.159925i
$490$	445136.	+	3.62068e6i	0.0837533	+	0.681240i
$491$	−2.03484e6	+	1.47839e6i	−0.380913	+	0.276749i	−0.761722	−	0.647904i	$-0.775646\pi$
$491$	−2.03484e6	+	1.47839e6i	−0.380913	+	0.276749i	0.380809	+	0.924654i	$0.375646\pi$
$492$	90010.2	−	277023.i	0.0167640	−	0.0515944i
$493$	−1.47632e6			−0.273567
$494$	−71234.1	+	219236.i	−0.0131332	+	0.0404198i
$495$	505160.	+	541549.i	0.0926650	+	0.0993401i
$496$	−446079.	−	1.37289e6i	−0.0814156	−	0.250571i
$497$	−176147.	−	542126.i	−0.0319878	−	0.0984485i
$498$	−169948.	−	123474.i	−0.0307073	−	0.0223102i
$499$	1.02714e6			0.184662			0.0923309	−	0.995728i	$-0.470568\pi$
$499$	1.02714e6			0.184662			0.0923309	+	0.995728i	$0.470568\pi$
$500$	2.34487e6	+	1.52122e6i	0.419462	+	0.272124i
$501$	4.70297e6			0.837101
$502$	−2.56387e6	−	1.86276e6i	−0.454085	−	0.329912i
$503$	−1.58684e6	−	4.88379e6i	−0.279649	−	0.860670i	−0.987952	−	0.154762i	$-0.950539\pi$
$503$	−1.58684e6	−	4.88379e6i	−0.279649	−	0.860670i	0.708303	−	0.705908i	$-0.249461\pi$
$504$	35565.9	+	109460.i	0.00623673	+	0.0191947i
$505$	−3.46573e6	−	3.71539e6i	−0.604737	−	0.648299i
$506$	−264788.	+	814935.i	−0.0459751	+	0.141497i
$507$	3.32214e6			0.573982
$508$	−308623.	+	949843.i	−0.0530602	+	0.163302i
$509$	8.60778e6	−	6.25392e6i	1.47264	−	1.06994i	0.492803	−	0.870141i	$-0.335972\pi$
$509$	8.60778e6	−	6.25392e6i	1.47264	−	1.06994i	0.979838	−	0.199795i	$-0.0640275\pi$
$510$	−315271.	−	2.56437e6i	−0.0536733	−	0.436572i
$511$	1.46934e6	+	1.06754e6i	0.248926	+	0.180855i
$512$	212079.	−	154084.i	0.0357538	−	0.0259767i
$513$	−730234.	+	530546.i	−0.122509	+	0.0890081i
$514$	−897739.	−	652246.i	−0.149880	−	0.108894i
$515$	−1.37945e6	+	2.48951e6i	−0.229186	+	0.413615i
$516$	772825.	−	561490.i	0.127778	−	0.0928364i
$517$	−139659.	+	429826.i	−0.0229796	+	0.0707240i
$518$	749467.			0.122724
$519$	−382483.	+	1.17716e6i	−0.0623294	+	0.191830i
$520$	80709.2	−	145657.i	0.0130892	−	0.0236223i
$521$	2.36213e6	+	7.26988e6i	0.381249	+	1.17336i	0.939165	+	0.343466i	$0.111601\pi$
$521$	2.36213e6	+	7.26988e6i	0.381249	+	1.17336i	−0.557916	+	0.829897i	$0.688399\pi$
$522$	−115132.	−	354340.i	−0.0184936	−	0.0569173i
$523$	6.24661e6	+	4.53843e6i	0.998598	+	0.725524i	0.961787	−	0.273799i	$-0.0882802\pi$
$523$	6.24661e6	+	4.53843e6i	0.998598	+	0.725524i	0.0368105	+	0.999322i	$0.488280\pi$
$524$	1.57928e6			0.251264
$525$	−605828.	+	151250.i	−0.0959292	+	0.0239495i
$526$	5.92884e6			0.934341
$527$	−5.85677e6	−	4.25519e6i	−0.918611	−	0.667410i
$528$	116447.	+	358387.i	0.0181779	+	0.0559457i
$529$	−1.45883e6	−	4.48980e6i	−0.226654	−	0.697570i
$530$	499890.	−	233197.i	0.0773009	−	0.0360607i
$531$	797934.	−	2.45579e6i	0.122809	−	0.377968i
$532$	439828.			0.0673758
$533$	29093.6	−	89541.0i	0.00443588	−	0.0136522i
$534$	774068.	−	562393.i	0.117470	−	0.0853468i
$535$	−3.40196e6	−	3.64702e6i	−0.513860	−	0.550876i
$536$	1.31849e6	+	957942.i	0.198228	+	0.144021i
$537$	3.73119e6	−	2.71087e6i	0.558356	−	0.405669i
$538$	−3.78186e6	+	2.74768e6i	−0.563313	+	0.409271i
$539$	−2.15866e6	−	1.56836e6i	−0.320045	−	0.232527i
$540$	590904.	−	275655.i	0.0872032	−	0.0406800i
$541$	−4.05618e6	+	2.94699e6i	−0.595833	+	0.432898i	−0.844397	−	0.535717i	$-0.820041\pi$
$541$	−4.05618e6	+	2.94699e6i	−0.595833	+	0.432898i	0.248564	+	0.968615i	$0.420041\pi$
$542$	1.66532e6	−	5.12532e6i	0.243500	−	0.749415i
$543$	6.23302e6			0.907191
$544$	406250.	−	1.25031e6i	0.0588568	−	0.181142i
$545$	1.57197e6	+	305306.i	0.226701	+	0.0440296i
$546$	11495.8	+	35380.5i	0.00165028	+	0.00507904i
$547$	−931842.	−	2.86792e6i	−0.133160	−	0.409825i	0.862139	−	0.506671i	$-0.169124\pi$
$547$	−931842.	−	2.86792e6i	−0.133160	−	0.409825i	−0.995299	+	0.0968469i	$0.969124\pi$
$548$	1.27880e6	+	929102.i	0.181908	+	0.132164i
$549$	−1.44262e6			−0.204277
$550$	−1.98355e6	+	495211.i	−0.279600	+	0.0698045i
$551$	−1.42379e6			−0.199787
$552$	610343.	+	443440.i	0.0852562	+	0.0619422i
$553$	184076.	+	566527.i	0.0255967	+	0.0787785i
$554$	1.84613e6	+	5.68179e6i	0.255556	+	0.786522i
$555$	−518106.	−	4.21421e6i	−0.0713981	−	0.580743i
$556$	2.18882e6	−	6.73649e6i	0.300278	−	0.924159i
$557$	−4.49167e6			−0.613437			−0.306719	−	0.951800i	$-0.599231\pi$
$557$	−4.49167e6			−0.613437			−0.306719	+	0.951800i	$0.599231\pi$
$558$	564569.	−	1.73756e6i	0.0767594	−	0.236241i
$559$	249797.	−	181488.i	0.0338110	−	0.0245651i
$560$	−311897.	−	60576.2i	−0.0420282	−	0.00816267i
$561$	1.52888e6	+	1.11080e6i	0.205101	+	0.149014i
$562$	−3.50212e6	+	2.54444e6i	−0.467725	+	0.339822i
$563$	−3.79688e6	+	2.75859e6i	−0.504842	+	0.366789i	−0.810864	−	0.585235i	$-0.801002\pi$
$563$	−3.79688e6	+	2.75859e6i	−0.504842	+	0.366789i	0.306021	+	0.952025i	$0.401002\pi$
$564$	321917.	+	233886.i	0.0426134	+	0.0309604i
$565$	−4.02627e6	−	781978.i	−0.530618	−	0.103056i
$566$	6.36598e6	−	4.62515e6i	0.835265	−	0.606855i
$567$	−45013.1	+	138536.i	−0.00588005	+	0.0180969i
$568$	−1.64319e6			−0.213706
$569$	1.08443e6	−	3.33752e6i	0.140417	−	0.432159i	−0.855976	−	0.517015i	$-0.827043\pi$
$569$	1.08443e6	−	3.33752e6i	0.140417	−	0.432159i	0.996393	+	0.0848562i	$0.0270431\pi$
$570$	−304053.	−	2.47313e6i	−0.0391978	−	0.318830i
$571$	−164873.	−	507425.i	−0.0211621	−	0.0651301i	0.939918	−	0.341401i	$-0.110901\pi$
$571$	−164873.	−	507425.i	−0.0211621	−	0.0651301i	−0.961080	+	0.276271i	$0.910901\pi$
$572$	37638.7	+	115840.i	0.00480999	+	0.0148036i
$573$	3.60816e6	+	2.62148e6i	0.459092	+	0.333550i
$574$	−179636.			−0.0227569
$575$	−2.62996e6	+	3.13625e6i	−0.331727	+	0.395586i
$576$	331776.			0.0416667
$577$	−7.11838e6	−	5.17180e6i	−0.890106	−	0.646700i	0.0457999	−	0.998951i	$-0.485416\pi$
$577$	−7.11838e6	−	5.17180e6i	−0.890106	−	0.646700i	−0.935906	+	0.352251i	$0.885416\pi$
$578$	−282307.	−	868851.i	−0.0351481	−	0.108175i
$579$	−1.17277e6	−	3.60942e6i	−0.145384	−	0.447446i
$580$	1.00966e6	+	196094.i	0.124625	+	0.0242044i
$581$	−40033.5	+	123210.i	−0.00492020	+	0.0151428i
$582$	3.19640e6			0.391159
$583$	−124678.	+	383720.i	−0.0151921	+	0.0467566i
$584$	4.23561e6	−	3.07735e6i	0.513906	−	0.373375i
$585$	190995.	−	89098.8i	0.0230746	−	0.0107642i
$586$	3.65689e6	+	2.65688e6i	0.439914	+	0.319616i
$587$	−9.75381e6	+	7.08656e6i	−1.16837	+	0.848868i	−0.990812	−	0.135244i	$-0.956818\pi$
$587$	−9.75381e6	+	7.08656e6i	−1.16837	+	0.848868i	−0.177554	+	0.984111i	$0.556818\pi$
$588$	−1.90057e6	+	1.38084e6i	−0.226694	+	0.164703i
$589$	−5.64838e6	−	4.10379e6i	−0.670866	−	0.487412i
$590$	4.86228e6	+	5.21254e6i	0.575056	+	0.616480i
$591$	6.19776e6	−	4.50293e6i	0.729904	−	0.530306i
$592$	667620.	−	2.05472e6i	0.0782933	−	0.240962i
$593$	8.68777e6			1.01455			0.507273	−	0.861785i	$-0.330654\pi$
$593$	8.68777e6			1.01455			0.507273	+	0.861785i	$0.330654\pi$
$594$	−147378.	+	453583.i	−0.0171383	+	0.0527461i
$595$	−1.44400e6	+	673621.i	−0.167215	+	0.0780051i
$596$	515015.	+	1.58505e6i	0.0593887	+	0.182780i
$597$	2.12090e6	+	6.52746e6i	0.243548	+	0.749563i
$598$	197279.	+	143331.i	0.0225594	+	0.0163903i
$599$	6.42676e6			0.731855			0.365927	−	0.930643i	$-0.380752\pi$
$599$	6.42676e6			0.731855			0.365927	+	0.930643i	$0.380752\pi$
$600$	−125003.	+	1.79565e6i	−0.0141756	+	0.203631i
$601$	1.41550e7			1.59854			0.799269	−	0.600974i	$-0.205220\pi$
$601$	1.41550e7			1.59854			0.799269	+	0.600974i	$0.205220\pi$
$602$	−476612.	−	346279.i	−0.0536011	−	0.0389435i
$603$	637394.	+	1.96170e6i	0.0713862	+	0.219704i
$604$	−2.17286e6	−	6.68737e6i	−0.242348	−	0.745869i
$605$	−3.63876e6	+	6.56690e6i	−0.404171	+	0.729411i
$606$	1.01111e6	−	3.11188e6i	0.111845	−	0.344224i
$607$	8.23542e6			0.907223			0.453612	−	0.891199i	$-0.350135\pi$
$607$	8.23542e6			0.907223			0.453612	+	0.891199i	$0.350135\pi$
$608$	391795.	−	1.20582e6i	0.0429833	−	0.132289i
$609$	−185890.	+	135057.i	−0.0203101	+	0.0147562i
$610$	1.93019e6	−	3.48344e6i	0.210027	−	0.379039i
$611$	104052.	+	75598.1i	0.0112758	+	0.00819234i
$612$	1.34609e6	−	977991.i	0.145277	−	0.105550i
$613$	−6.81905e6	+	4.95433e6i	−0.732947	+	0.532517i	−0.890494	−	0.454994i	$-0.849641\pi$
$613$	−6.81905e6	+	4.95433e6i	−0.732947	+	0.532517i	0.157548	+	0.987511i	$0.449641\pi$
$614$	6.30228e6	+	4.57888e6i	0.674648	+	0.490160i
$615$	124182.	+	1.01008e6i	0.0132395	+	0.107688i
$616$	188012.	−	136599.i	0.0199634	−	0.0145043i
$617$	2.42531e6	−	7.46434e6i	0.256481	−	0.789366i	−0.737054	−	0.675834i	$-0.763784\pi$
$617$	2.42531e6	−	7.46434e6i	0.256481	−	0.789366i	0.993534	−	0.113532i	$-0.0362164\pi$
$618$	−1.83288e6			−0.193047
$619$	−1.45842e6	+	4.48856e6i	−0.152988	+	0.470848i	−0.997951	−	0.0639757i	$-0.979622\pi$
$619$	−1.45842e6	+	4.48856e6i	−0.152988	+	0.470848i	0.844964	+	0.534824i	$0.179622\pi$
$620$	3.44025e6	+	3.68807e6i	0.359427	+	0.385318i
$621$	295055.	+	908087.i	0.0307025	+	0.0944927i
$622$	−2.15075e6	−	6.61933e6i	−0.222902	−	0.686022i
$623$	−477378.	−	346836.i	−0.0492768	−	0.0358017i
$624$	107239.			0.0110253
$625$	−9.67143e6	−	1.35309e6i	−0.990355	−	0.138557i
$626$	93888.1			0.00957579
$627$	1.47448e6	+	1.07127e6i	0.149786	+	0.108826i
$628$	163622.	+	503578.i	0.0165556	+	0.0509528i
$629$	−3.34812e6	−	1.03044e7i	−0.337422	−	1.03848i
$630$	−274291.	−	294050.i	−0.0275334	−	0.0295168i
$631$	−547548.	+	1.68518e6i	−0.0547455	+	0.168489i	−0.974691	−	0.223558i	$-0.928233\pi$
$631$	−547548.	+	1.68518e6i	−0.0547455	+	0.168489i	0.919945	+	0.392047i	$0.128233\pi$
$632$	1.71715e6			0.171008
$633$	−2.33135e6	+	7.17516e6i	−0.231259	+	0.711741i
$634$	1.72578e6	−	1.25385e6i	0.170514	−	0.123886i
$635$	−425790.	−	3.46332e6i	−0.0419045	−	0.340846i
$636$	287386.	+	208798.i	0.0281723	+	0.0204684i
$637$	−614312.	+	446324.i	−0.0599847	+	0.0435814i
$638$	−608625.	+	442192.i	−0.0591968	+	0.0430090i
$639$	−1.68248e6	−	1.22239e6i	−0.163004	−	0.118429i
$640$	−443909.	+	801128.i	−0.0428395	+	0.0773129i
$641$	−1.13128e7	+	8.21920e6i	−1.08749	+	0.790104i	−0.978973	−	0.203991i	$-0.934609\pi$
$641$	−1.13128e7	+	8.21920e6i	−1.08749	+	0.790104i	−0.108512	+	0.994095i	$0.534609\pi$
$642$	992507.	−	3.05462e6i	0.0950377	−	0.292496i
$643$	5.76504e6			0.549889			0.274945	−	0.961460i	$-0.411340\pi$
$643$	5.76504e6			0.549889			0.274945	+	0.961460i	$0.411340\pi$
$644$	143775.	−	442492.i	0.0136605	−	0.0420428i
$645$	−1.61763e6	+	2.91935e6i	−0.153101	+	0.276303i
$646$	−1.96485e6	−	6.04720e6i	−0.185246	−	0.570129i
$647$	−2.85927e6	−	8.79994e6i	−0.268531	−	0.826454i	−0.990859	−	0.134903i	$-0.956928\pi$
$647$	−2.85927e6	−	8.79994e6i	−0.268531	−	0.826454i	0.722328	−	0.691551i	$-0.243072\pi$
$648$	339709.	+	246813.i	0.0317812	+	0.0230904i
$649$	−5.21390e6			−0.485904
$650$	−40404.1	+	580402.i	−0.00375096	+	0.0538822i
$651$	−1.12673e6			−0.104199
$652$	−2.06921e6	−	1.50337e6i	−0.190628	−	0.138499i
$653$	−2.80935e6	−	8.64629e6i	−0.257824	−	0.793500i	−0.993260	−	0.115906i	$-0.963023\pi$
$653$	−2.80935e6	−	8.64629e6i	−0.257824	−	0.793500i	0.735436	−	0.677594i	$-0.236977\pi$
$654$	318673.	+	980774.i	0.0291340	+	0.0896653i
$655$	−5.00043e6	+	2.33269e6i	−0.455412	+	0.212448i
$656$	−160018.	+	492485.i	−0.0145181	+	0.0446821i
$657$	6.62618e6			0.598894
$658$	75831.9	−	233387.i	0.00682790	−	0.0210141i
$659$	7.42985e6	−	5.39810e6i	0.666448	−	0.484203i	−0.202386	−	0.979306i	$-0.564870\pi$
$659$	7.42985e6	−	5.39810e6i	0.666448	−	0.484203i	0.868834	+	0.495103i	$0.164870\pi$
$660$	−898062.	−	962753.i	−0.0802503	−	0.0860310i
$661$	1.83025e6	+	1.32975e6i	0.162932	+	0.118377i	0.666264	−	0.745716i	$-0.267893\pi$
$661$	1.83025e6	+	1.32975e6i	0.162932	+	0.118377i	−0.503332	+	0.864093i	$0.667893\pi$
$662$	−514207.	+	373594.i	−0.0456030	+	0.0331325i
$663$	435091.	−	316112.i	0.0384411	−	0.0279291i
$664$	302129.	+	219510.i	0.0265933	+	0.0193212i
$665$	−1.39262e6	+	649652.i	−0.122118	+	0.0569675i
$666$	2.21212e6	−	1.60720e6i	0.193252	−	0.140406i
$667$	−465420.	+	1.43242e6i	−0.0405070	+	0.124668i
$668$	−8.36084e6			−0.724951
$669$	−687580.	+	2.11615e6i	−0.0593961	+	0.182802i
$670$	−5.58966e6	−	1.08562e6i	−0.481059	−	0.0934306i
$671$	900143.	+	2.77036e6i	0.0771801	+	0.237536i
$672$	−63228.2	−	194596.i	−0.00540117	−	0.0166231i
$673$	2.15654e6	+	1.56682e6i	0.183535	+	0.133346i	0.675759	−	0.737122i	$-0.263816\pi$
$673$	2.15654e6	+	1.56682e6i	0.183535	+	0.133346i	−0.492224	+	0.870469i	$0.663816\pi$
$674$	1.29213e7			1.09561
$675$	−1.46381e6	+	1.74560e6i	−0.123659	+	0.147464i
$676$	−5.90603e6			−0.497083
$677$	−1.49549e7	−	1.08654e7i	−1.25404	−	0.911116i	−0.255594	−	0.966784i	$-0.582271\pi$
$677$	−1.49549e7	−	1.08654e7i	−1.25404	−	0.911116i	−0.998449	+	0.0556688i	$0.982271\pi$
$678$	−816212.	−	2.51204e6i	−0.0681913	−	0.209871i
$679$	−609154.	−	1.87478e6i	−0.0507052	−	0.156055i
$680$	560481.	+	4.55889e6i	0.0464824	+	0.378082i
$681$	−198514.	+	610963.i	−0.0164030	+	0.0504832i
$682$	−3.68903e6			−0.303705
$683$	928751.	−	2.85840e6i	0.0761811	−	0.234461i	−0.905713	−	0.423891i	$-0.860664\pi$
$683$	928751.	−	2.85840e6i	0.0761811	−	0.234461i	0.981894	+	0.189430i	$0.0606639\pi$
$684$	1.29819e6	−	943193.i	0.106096	−	0.0770833i
$685$	−5.42137e6	−	1.05293e6i	−0.441451	−	0.0857382i
$686$	2.37962e6	+	1.72890e6i	0.193063	+	0.140268i
$687$	−81792.1	+	59425.4i	−0.00661179	+	0.00480375i
$688$	−1.37391e6	+	998205.i	−0.110659	+	0.0803986i
$689$	92890.5	+	67488.9i	0.00745458	+	0.00541607i
$690$	−2.58750e6	−	502542.i	−0.206899	−	0.0401836i
$691$	−3.65352e6	+	2.65444e6i	−0.291082	+	0.211484i	−0.723737	−	0.690076i	$-0.757577\pi$
$691$	−3.65352e6	+	2.65444e6i	−0.291082	+	0.211484i	0.432654	+	0.901560i	$0.357577\pi$
$692$	679969.	−	2.09273e6i	0.0539789	−	0.166130i
$693$	294126.			0.0232649
$694$	−4.12114e6	+	1.26836e7i	−0.324802	+	0.999637i
$695$	3.01979e6	+	2.45626e7i	0.237146	+	1.92891i
$696$	204679.	+	629938.i	0.0160159	+	0.0492918i
$697$	802491.	+	2.46981e6i	0.0625689	+	0.192567i
$698$	−498124.	−	361908.i	−0.0386989	−	0.0281164i
$699$	−6.51377e6			−0.504243
$700$	1.07703e6	−	268889.i	0.0830771	−	0.0207409i
$701$	−6.30234e6			−0.484403			−0.242202	−	0.970226i	$-0.577870\pi$
$701$	−6.30234e6			−0.484403			−0.242202	+	0.970226i	$0.577870\pi$
$702$	109803.	+	79776.5i	0.00840952	+	0.00610987i
$703$	−3.22898e6	−	9.93779e6i	−0.246421	−	0.758406i
$704$	−207017.	−	637132.i	−0.0157425	−	0.0484504i
$705$	−1.36474e6	−	265059.i	−0.103414	−	0.0200849i
$706$	1.84401e6	−	5.67527e6i	0.139236	−	0.428524i
$707$	−2.01790e6			−0.151828
$708$	−1.41855e6	+	4.36585e6i	−0.106356	+	0.327330i
$709$	4.81952e6	−	3.50159e6i	0.360071	−	0.261607i	−0.393011	−	0.919534i	$-0.628566\pi$
$709$	4.81952e6	−	3.50159e6i	0.360071	−	0.261607i	0.753082	+	0.657927i	$0.228566\pi$
$710$	5.20280e6	−	2.42709e6i	0.387339	−	0.180692i
$711$	1.75821e6	+	1.27741e6i	0.130436	+	0.0947671i
$712$	−1.37612e6	+	999811.i	−0.101732	+	0.0739125i
$713$	−5.97504e6	+	4.34112e6i	−0.440166	+	0.319800i
$714$	−830152.	−	603141.i	−0.0609413	−	0.0442765i
$715$	−290277.	−	311187.i	−0.0212348	−	0.0227644i
$716$	−6.63322e6	+	4.81932e6i	−0.483551	+	0.351320i
$717$	1.30224e6	−	4.00789e6i	0.0946006	−	0.291151i
$718$	8.13297e6			0.588760
$719$	−4.46291e6	+	1.37354e7i	−0.321956	+	0.990878i	0.650840	+	0.759215i	$0.274417\pi$
$719$	−4.46291e6	+	1.37354e7i	−0.321956	+	0.990878i	−0.972796	+	0.231663i	$0.925583\pi$
$720$	−1.05050e6	+	490053.i	−0.0755202	+	0.0352299i
$721$	349302.	+	1.07504e6i	0.0250243	+	0.0770170i
$722$	1.16568e6	+	3.58761e6i	0.0832220	+	0.256131i
$723$	8.62515e6	+	6.26654e6i	0.613650	+	0.445843i
$724$	−1.10809e7			−0.785651
$725$	−3.48650e6	+	870435.i	−0.246345	+	0.0615023i
$726$	−4.83483e6			−0.340439
$727$	9.87025e6	+	7.17116e6i	0.692616	+	0.503215i	0.877519	−	0.479542i	$-0.159197\pi$
$727$	9.87025e6	+	7.17116e6i	0.692616	+	0.503215i	−0.184903	+	0.982757i	$0.559197\pi$
$728$	−20437.0	−	62898.6i	−0.00142919	−	0.00439858i
$729$	164224.	+	505430.i	0.0114451	+	0.0352243i
$730$	−8.86569e6	+	1.60000e7i	−0.615752	+	1.11125i
$731$	−2.63181e6	+	8.09988e6i	−0.182164	+	0.560642i
$732$	2.56465e6			0.176909
$733$	−2.92525e6	+	9.00301e6i	−0.201096	+	0.618910i	0.798755	+	0.601656i	$0.205492\pi$
$733$	−2.92525e6	+	9.00301e6i	−0.201096	+	0.618910i	−0.999851	+	0.0172538i	$0.994508\pi$
$734$	6.38509e6	−	4.63904e6i	0.437448	−	0.317825i
$735$	3.97813e6	−	7.17938e6i	0.271620	−	0.490195i
$736$	−1.08505e6	−	788337.i	−0.0738340	−	0.0536436i
$737$	3.36947e6	−	2.44806e6i	0.228503	−	0.166017i
$738$	−530212.	+	385221.i	−0.0358351	+	0.0260357i
$739$	2.09714e7	+	1.52366e7i	1.41259	+	1.02631i	0.992939	+	0.118624i	$0.0378484\pi$
$739$	2.09714e7	+	1.52366e7i	1.41259	+	1.02631i	0.419653	+	0.907684i	$0.362152\pi$
$740$	921078.	+	7.49194e6i	0.0618325	+	0.502938i
$741$	419610.	−	304864.i	0.0280737	−	0.0203968i
$742$	67697.6	−	208352.i	0.00451402	−	0.0138927i
$743$	2.40848e6			0.160055			0.0800277	−	0.996793i	$-0.474499\pi$
$743$	2.40848e6			0.160055			0.0800277	+	0.996793i	$0.474499\pi$
$744$	−1.00368e6	+	3.08900e6i	−0.0664755	+	0.204591i
$745$	−3.97190e6	−	4.25801e6i	−0.262185	−	0.281071i
$746$	4.01475e6	+	1.23561e7i	0.264126	+	0.812898i
$747$	146057.	+	449517.i	0.00957681	+	0.0294744i
$748$	−2.71802e6	−	1.97475e6i	−0.177622	−	0.129050i
$749$	−1.98077e6			−0.129012
$750$	−2.25650e6	−	5.87018e6i	−0.146481	−	0.381064i
$751$	6.06385e6			0.392327			0.196164	−	0.980571i	$-0.437152\pi$
$751$	6.06385e6			0.392327			0.196164	+	0.980571i	$0.437152\pi$
$752$	−572297.	−	415798.i	−0.0369043	−	0.0268125i
$753$	2.20345e6	+	6.78153e6i	0.141617	+	0.435853i
$754$	66157.7	+	203612.i	0.00423791	+	0.0130430i
$755$	1.67575e7	+	1.79646e7i	1.06990	+	1.14697i
$756$	80023.2	−	246286.i	0.00509227	−	0.0156724i
$757$	1.52305e7			0.965992			0.482996	−	0.875623i	$-0.339549\pi$
$757$	1.52305e7			0.965992			0.482996	+	0.875623i	$0.339549\pi$
$758$	726369.	−	2.23554e6i	0.0459182	−	0.141322i
$759$	1.55976e6	−	1.13323e6i	0.0982771	−	0.0714025i
$760$	540538.	+	4.39667e6i	0.0339463	+	0.276115i
$761$	−1.44685e7	−	1.05120e7i	−0.905651	−	0.657994i	0.0342600	−	0.999413i	$-0.489093\pi$
$761$	−1.44685e7	−	1.05120e7i	−0.905651	−	0.657994i	−0.939911	+	0.341419i	$0.889093\pi$
$762$	1.81797e6	−	1.32083e6i	0.113422	−	0.0824061i
$763$	514522.	−	373822.i	0.0319957	−	0.0232463i
$764$	−6.41451e6	−	4.66041e6i	−0.397585	−	0.288862i
$765$	−2.81754e6	+	5.08485e6i	−0.174067	+	0.314141i
$766$	1.14851e7	−	8.34442e6i	0.707234	−	0.513836i
$767$	−458512.	+	1.41115e6i	−0.0281425	+	0.0866136i
$768$	−589824.			−0.0360844
$769$	−7.61991e6	+	2.34517e7i	−0.464659	+	1.43007i	0.394753	+	0.918787i	$0.370830\pi$
$769$	−7.61991e6	+	2.34517e7i	−0.464659	+	1.43007i	−0.859411	+	0.511285i	$0.829170\pi$
$770$	−393535.	+	710217.i	−0.0239197	+	0.0431682i
$771$	771538.	+	2.37455e6i	0.0467435	+	0.143862i
$772$	2.08493e6	+	6.41674e6i	0.125906	+	0.387500i
$773$	5.12841e6	+	3.72601e6i	0.308698	+	0.224283i	0.731338	−	0.682015i	$-0.238896\pi$
$773$	5.12841e6	+	3.72601e6i	0.308698	+	0.224283i	−0.422639	+	0.906298i	$0.638896\pi$
$774$	−2.14935e6			−0.128960
$775$	−1.63403e7	−	6.59599e6i	−0.977250	−	0.394481i
$776$	−5.68249e6			−0.338754
$777$	−1.36425e6	−	991183.i	−0.0810663	−	0.0588981i
$778$	−571453.	−	1.75875e6i	−0.0338479	−	0.104173i
$779$	773937.	+	2.38193e6i	0.0456943	+	0.140633i
$780$	−339547.	+	158398.i	−0.0199831	+	0.00932208i
$781$	−1.29764e6	+	3.99371e6i	−0.0761247	+	0.234288i
$782$	−6.72612e6			−0.393322
$783$	−259047.	+	797266.i	−0.0150999	+	0.0464728i
$784$	3.37878e6	−	2.45483e6i	0.196323	−	0.142637i
$785$	−1.26189e6	−	1.35279e6i	−0.0730882	−	0.0783530i
$786$	−2.87474e6	−	2.08862e6i	−0.165975	−	0.120588i
$787$	1.31013e7	−	9.51868e6i	0.754013	−	0.547822i	−0.143055	−	0.989715i	$-0.545693\pi$
$787$	1.31013e7	−	9.51868e6i	0.754013	−	0.547822i	0.897068	+	0.441892i	$0.145693\pi$
$788$	−1.10182e7	+	8.00521e6i	−0.632115	+	0.459259i
$789$	−1.07922e7	−	7.84099e6i	−0.617188	−	0.448413i
$790$	−5.43697e6	+	2.53633e6i	−0.309948	+	0.144590i
$791$	−1.31784e6	+	957465.i	−0.0748895	+	0.0544104i
$792$	262005.	−	806370.i	0.0148422	−	0.0456795i
$793$	828963.			0.0468114
$794$	−5.40151e6	+	1.66241e7i	−0.304063	+	0.935811i
$795$	−1.21835e6	−	236627.i	−0.0683683	−	0.0132784i
$796$	−3.77049e6	−	1.16044e7i	−0.210919	−	0.649141i
$797$	−5.74640e6	−	1.76856e7i	−0.320442	−	0.986220i	−0.973456	−	0.228874i	$-0.926496\pi$
$797$	−5.74640e6	−	1.76856e7i	−0.320442	−	0.986220i	0.653014	−	0.757346i	$-0.273504\pi$
$798$	−800614.	−	581680.i	−0.0445057	−	0.0323353i
$799$	−3.54760e6			−0.196593
$800$	222227.	−	3.19227e6i	0.0122764	−	0.176350i
$801$	−2.15280e6			−0.118556
$802$	1.08955e7	+	7.91603e6i	0.598150	+	0.434582i
$803$	−4.13451e6	−	1.27247e7i	−0.226274	−	0.696400i
$804$	−1.13314e6	−	3.48746e6i	−0.0618223	−	0.190269i
$805$	198358.	+	1.61342e6i	0.0107885	+	0.0877521i
$806$	−324415.	+	998446.i	−0.0175899	+	0.0541361i
$807$	1.05179e7			0.568521
$808$	−1.79753e6	+	5.53224e6i	−0.0968609	+	0.298107i
$809$	2.16283e7	−	1.57139e7i	1.16185	−	0.844136i	0.171843	−	0.985124i	$-0.445028\pi$
$809$	2.16283e7	−	1.57139e7i	1.16185	−	0.844136i	0.990011	+	0.140988i	$0.0450279\pi$
$810$	−1.44017e6	−	279709.i	−0.0771262	−	0.0149794i
$811$	−6.06847e6	−	4.40900e6i	−0.323987	−	0.235390i	0.413888	−	0.910328i	$-0.364170\pi$
$811$	−6.06847e6	−	4.40900e6i	−0.323987	−	0.235390i	−0.737875	+	0.674938i	$0.764170\pi$
$812$	330471.	−	240101.i	0.0175891	−	0.0127792i
$813$	−9.80967e6	+	7.12714e6i	−0.520509	+	0.378172i
$814$	−4.46671e6	−	3.24525e6i	−0.236280	−	0.171667i
$815$	8.77226e6	+	1.70374e6i	0.462613	+	0.0898481i
$816$	−2.39305e6	+	1.73865e6i	−0.125813	+	0.0914086i
$817$	−2.53817e6	+	7.81168e6i	−0.133035	+	0.409439i
$818$	1.82563e7			0.953957
$819$	25865.6	−	79606.1i	0.00134745	−	0.00414702i
$820$	−220768.	−	1.79570e6i	−0.0114657	−	0.0932609i
$821$	4.38367e6	+	1.34916e7i	0.226976	+	0.698561i	0.998085	+	0.0618575i	$0.0197024\pi$
$821$	4.38367e6	+	1.34916e7i	0.226976	+	0.698561i	−0.771109	+	0.636703i	$0.780298\pi$
$822$	−1.09903e6	−	3.38247e6i	−0.0567322	−	0.174604i
$823$	8.76295e6	+	6.36666e6i	0.450973	+	0.327651i	0.789980	−	0.613133i	$-0.210091\pi$
$823$	8.76295e6	+	6.36666e6i	0.450973	+	0.327651i	−0.339007	+	0.940784i	$0.610091\pi$
$824$	3.25846e6			0.167184
$825$	4.26556e6	+	1.72185e6i	0.218193	+	0.0880768i
$826$	2.83104e6			0.144376
$827$	−1.93635e7	−	1.40684e7i	−0.984511	−	0.715289i	−0.0257990	−	0.999667i	$-0.508213\pi$
$827$	−1.93635e7	−	1.40684e7i	−0.984511	−	0.715289i	−0.958712	+	0.284378i	$0.908213\pi$
$828$	−524543.	−	1.61438e6i	−0.0265892	−	0.0818331i
$829$	8.51027e6	+	2.61919e7i	0.430088	+	1.32367i	0.898038	+	0.439919i	$0.144993\pi$
$829$	8.51027e6	+	2.61919e7i	0.430088	+	1.32367i	−0.467950	+	0.883755i	$0.655007\pi$
$830$	−1.28085e6	−	248766.i	−0.0645363	−	0.0125342i
$831$	4.15378e6	−	1.27840e7i	0.208661	−	0.642192i
$832$	−190646.			−0.00954817
$833$	6.47227e6	−	1.99196e7i	0.323180	−	0.994644i
$834$	−1.28934e7	+	9.36761e6i	−0.641878	+	0.466352i
$835$	2.64727e7	−	1.23495e7i	1.31396	−	0.612959i
$836$	−2.62130e6	−	1.90449e6i	−0.129718	−	0.0942460i
$837$	−3.32564e6	+	2.41622e6i	−0.164082	+	0.119213i
$838$	1.05278e7	−	7.64893e6i	0.517881	−	0.376262i
$839$	1.45928e7	+	1.06023e7i	0.715705	+	0.519990i	0.885009	−	0.465574i	$-0.154152\pi$
$839$	1.45928e7	+	1.06023e7i	0.715705	+	0.519990i	−0.169304	+	0.985564i	$0.554152\pi$
$840$	487629.	+	522755.i	0.0238447	+	0.0255623i
$841$	1.55241e7	−	1.12789e7i	0.756861	−	0.549892i
$842$	491624.	−	1.51306e6i	0.0238975	−	0.0735490i
$843$	9.73994e6			0.472049
$844$	4.14462e6	−	1.27558e7i	0.200276	−	0.616386i
$845$	1.87001e7	−	8.72356e6i	0.900954	−	0.420293i
$846$	−276663.	−	851481.i	−0.0132900	−	0.0409024i
$847$	921398.	+	2.83577e6i	0.0441305	+	0.135820i
$848$	−510908.	−	371196.i	−0.0243979	−	0.0177261i
$849$	−1.77048e7			−0.842987
$850$	−8.50839e6	−	1.36068e7i	−0.403924	−	0.645966i
$851$	−1.10535e7			−0.523210
$852$	2.99108e6	+	2.17315e6i	0.141166	+	0.102563i
$853$	−1.23050e7	−	3.78710e7i	−0.579042	−	1.78211i	−0.621984	−	0.783030i	$-0.713673\pi$
$853$	−1.23050e7	−	3.78710e7i	−0.579042	−	1.78211i	0.0429427	−	0.999078i	$-0.486327\pi$
$854$	−488759.	−	1.50425e6i	−0.0229324	−	0.0705788i
$855$	−2.71729e6	+	4.90392e6i	−0.127122	+	0.229418i
$856$	−1.76446e6	+	5.43044e6i	−0.0823051	+	0.253309i
$857$	−1.86855e7			−0.869066			−0.434533	−	0.900656i	$-0.643087\pi$
$857$	−1.86855e7			−0.869066			−0.434533	+	0.900656i	$0.643087\pi$
$858$	84687.0	−	260640.i	0.00392734	−	0.0120871i
$859$	1.01770e7	−	7.39399e6i	0.470582	−	0.341898i	−0.327086	−	0.944995i	$-0.606067\pi$
$859$	1.01770e7	−	7.39399e6i	0.470582	−	0.341898i	0.797668	+	0.603097i	$0.206067\pi$
$860$	2.87578e6	−	5.18995e6i	0.132590	−	0.239286i
$861$	326989.	+	237571.i	0.0150323	+	0.0109216i
$862$	−2.11784e7	+	1.53870e7i	−0.970791	+	0.705321i
$863$	2.56820e7	−	1.86591e7i	1.17382	−	0.852830i	0.182359	−	0.983232i	$-0.441627\pi$
$863$	2.56820e7	−	1.86591e7i	1.17382	−	0.852830i	0.991461	+	0.130402i	$0.0416267\pi$
$864$	−603928.	−	438779.i	−0.0275233	−	0.0199969i
$865$	938115.	+	7.63052e6i	0.0426301	+	0.346748i
$866$	−2.04648e7	+	1.48685e7i	−0.927284	+	0.673711i
$867$	−635191.	+	1.95492e6i	−0.0286983	+	0.0883243i
$868$	2.00307e6			0.0902394
$869$	1.35604e6	−	4.17347e6i	0.0609150	−	0.187477i
$870$	−1.57853e6	−	1.69224e6i	−0.0707057	−	0.0757989i
$871$	−366262.	−	1.12724e6i	−0.0163586	−	0.0503466i
$872$	−566529.	−	1.74360e6i	−0.0252308	−	0.0776524i
$873$	−5.81837e6	−	4.22729e6i	−0.258384	−	0.187727i
$874$	−6.48680e6			−0.287244
$875$	−3.01300e6	+	2.44221e6i	−0.133039	+	0.107836i
$876$	−1.17799e7			−0.518658
$877$	1.16336e7	+	8.45234e6i	0.510760	+	0.371089i	0.813112	−	0.582108i	$-0.197772\pi$
$877$	1.16336e7	+	8.45234e6i	0.510760	+	0.371089i	−0.302352	+	0.953196i	$0.597772\pi$
$878$	−8.92412e6	−	2.74656e7i	−0.390687	−	1.20241i
$879$	−3.14281e6	−	9.67259e6i	−0.137198	−	0.422251i
$880$	1.59655e6	+	1.71156e6i	0.0694988	+	0.0745051i
$881$	1.27775e7	−	3.93250e7i	0.554632	−	1.70698i	−0.142283	−	0.989826i	$-0.545444\pi$
$881$	1.27775e7	−	3.93250e7i	0.554632	−	1.70698i	0.696914	−	0.717154i	$-0.254556\pi$
$882$	5.28576e6			0.228790
$883$	4.20263e6	−	1.29344e7i	0.181393	−	0.558269i	−0.818475	−	0.574542i	$-0.805180\pi$
$883$	4.20263e6	−	1.29344e7i	0.181393	−	0.558269i	0.999868	+	0.0162729i	$0.00518006\pi$
$884$	−773495.	+	561977.i	−0.0332910	+	0.0241873i
$885$	−1.95709e6	−	1.59188e7i	−0.0839950	−	0.683205i
$886$	1.29197e7	+	9.38671e6i	0.552927	+	0.401725i
$887$	−9.13887e6	+	6.63977e6i	−0.390017	+	0.283364i	−0.765462	−	0.643481i	$-0.777490\pi$
$887$	−9.13887e6	+	6.63977e6i	−0.390017	+	0.283364i	0.375446	+	0.926844i	$0.377490\pi$
$888$	−3.93266e6	+	2.85725e6i	−0.167361	+	0.121595i
$889$	−1.12116e6	−	814574.i	−0.0475790	−	0.0345681i
$890$	2.88040e6	−	5.19829e6i	0.121893	−	0.219981i
$891$	868142.	−	630742.i	0.0366350	−	0.0266169i
$892$	1.22236e6	−	3.76205e6i	0.0514385	−	0.158312i
$893$	−3.42137e6			−0.143573
$894$	1.15878e6	−	3.56637e6i	0.0484907	−	0.149239i
$895$	1.38842e7	−	2.50570e7i	0.579380	−	1.04561i
$896$	112406.	+	345949.i	0.00467755	+	0.0143960i
$897$	−169546.	−	521808.i	−0.00703568	−	0.0216536i
$898$	2.09834e7	+	1.52453e7i	0.868329	+	0.630878i
$899$	−6.48423e6			−0.267584
$900$	2.60232e6	−	3.10329e6i	0.107092	−	0.127707i
$901$	−3.16706e6			−0.129970
$902$	1.07060e6	+	777837.i	0.0438138	+	0.0318326i
$903$	409612.	+	1.26065e6i	0.0167168	+	0.0514490i
$904$	1.45104e6	+	4.46586e6i	0.0590554	+	0.181754i
$905$	3.50853e7	−	1.63672e7i	1.42398	−	0.664282i
$906$	−4.88893e6	+	1.50466e7i	−0.197876	+	0.609000i
$907$	7.43281e6			0.300009			0.150005	−	0.988685i	$-0.452071\pi$
$907$	7.43281e6			0.300009			0.150005	+	0.988685i	$0.452071\pi$
$908$	352913.	−	1.08616e6i	0.0142054	−	0.0437197i
$909$	−5.95603e6	+	4.32731e6i	−0.239082	+	0.173703i
$910$	157614.	+	168968.i	0.00630946	+	0.00676396i
$911$	−3.19778e7	−	2.32333e7i	−1.27659	−	0.927500i	−0.277150	−	0.960827i	$-0.589390\pi$
$911$	−3.19778e7	−	2.32333e7i	−1.27659	−	0.927500i	−0.999445	+	0.0333261i	$0.989390\pi$
$912$	−2.30790e6	+	1.67679e6i	−0.0918819	+	0.0667561i
$913$	772103.	−	560966.i	0.0306548	−	0.0222720i
$914$	1.48333e7	+	1.07770e7i	0.587317	+	0.426711i
$915$	−8.12041e6	+	3.78815e6i	−0.320646	+	0.149580i
$916$	145408.	−	105645.i	0.00572598	−	0.00416017i
$917$	−677184.	+	2.08416e6i	−0.0265940	+	0.0818479i
$918$	−3.74368e6			−0.146620
$919$	−7.76589e6	+	2.39010e7i	−0.303321	+	0.933526i	0.676977	+	0.736004i	$0.263290\pi$
$919$	−7.76589e6	+	2.39010e7i	−0.303321	+	0.933526i	−0.980298	+	0.197522i	$0.936710\pi$
$920$	4.60000e6	+	893407.i	0.179180	+	0.0348001i
$921$	−5.41633e6	−	1.66698e7i	−0.210405	−	0.647560i
$922$	5.09273e6	+	1.56738e7i	0.197298	+	0.607222i
$923$	966794.	+	702417.i	0.0373534	+	0.0271388i
$924$	−522891.			−0.0201480
$925$	−1.39824e7	−	2.23611e7i	−0.537314	−	0.859287i
$926$	−2.08109e7			−0.797558
$927$	3.33638e6	+	2.42402e6i	0.127519	+	0.0926481i
$928$	−363874.	−	1.11989e6i	−0.0138702	−	0.0426880i
$929$	−1.13110e7	−	3.48118e7i	−0.429995	−	1.32339i	−0.898130	−	0.439731i	$-0.855074\pi$
$929$	−1.13110e7	−	3.48118e7i	−0.429995	−	1.32339i	0.468135	−	0.883657i	$-0.344926\pi$
$930$	−1.38472e6	−	1.12631e7i	−0.0524994	−	0.427024i
$931$	6.24197e6	−	1.92108e7i	0.236019	−	0.726393i
$932$	1.15800e7			0.436687
$933$	−4.83919e6	+	1.48935e7i	−0.181999	+	0.560135i
$934$	−3.77898e6	+	2.74559e6i	−0.141745	+	0.102984i
$935$	1.15228e7	+	2.23795e6i	0.431052	+	0.0837185i
$936$	−195205.	−	141825.i	−0.00728286	−	0.00529130i
$937$	7.33287e6	−	5.32764e6i	0.272851	−	0.198238i	−0.442942	−	0.896550i	$-0.646065\pi$
$937$	7.33287e6	−	5.32764e6i	0.272851	−	0.198238i	0.715793	+	0.698312i	$0.246065\pi$
$938$	−1.82955e6	+	1.32925e6i	−0.0678949	+	0.0493285i
$939$	−170903.	−	124169.i	−0.00632538	−	0.00459566i
$940$	2.42621e6	+	471215.i	0.0895589	+	0.0173940i
$941$	−1.44538e6	+	1.05013e6i	−0.0532117	+	0.0386605i	−0.614073	−	0.789249i	$-0.710470\pi$
$941$	−1.44538e6	+	1.05013e6i	−0.0532117	+	0.0386605i	0.560861	+	0.827910i	$0.310470\pi$
$942$	368150.	−	1.13305e6i	0.0135176	−	0.0416028i
$943$	2.64936e6			0.0970199
$944$	2.52187e6	−	7.76150e6i	0.0921068	−	0.283476i
$945$	110404.	+	898010.i	0.00402164	+	0.0327116i
$946$	1.34112e6	+	4.12753e6i	0.0487235	+	0.149956i
$947$	1.05801e7	+	3.25620e7i	0.383365	+	1.17988i	0.937659	+	0.347556i	$0.112988\pi$
$947$	1.05801e7	+	3.25620e7i	0.383365	+	1.17988i	−0.554294	+	0.832321i	$0.687012\pi$
$948$	−3.12571e6	−	2.27096e6i	−0.112961	−	0.0820707i
$949$	−3.80756e6			−0.137240
$950$	−8.20565e6	−	1.31227e7i	−0.294988	−	0.471752i
$951$	−4.79965e6			−0.172091
$952$	1.47583e6	+	1.07225e6i	0.0527767	+	0.0383446i
$953$	−1.31680e7	−	4.05269e7i	−0.469664	−	1.44548i	−0.853021	−	0.521876i	$-0.825232\pi$
$953$	−1.31680e7	−	4.05269e7i	−0.469664	−	1.44548i	0.383358	−	0.923600i	$-0.374768\pi$
$954$	−246986.	−	760145.i	−0.00878621	−	0.0270412i
$955$	2.71938e7	+	5.28156e6i	0.964855	+	0.187393i
$956$	−2.31510e6	+	7.12513e6i	−0.0819265	+	0.252144i
$957$	1.69268e6			0.0597441
$958$	6.82429e6	−	2.10030e7i	0.240239	−	0.739380i
$959$	−1.77447e6	+	1.28923e6i	−0.0623048	+	0.0452671i
$960$	1.86755e6	−	871206.i	0.0654024	−	0.0305100i
$961$	−2.56241e6	−	1.86170e6i	−0.0895036	−	0.0650282i
$962$	−1.27114e6	+	923537.i	−0.0442849	+	0.0321748i
$963$	−5.84644e6	+	4.24768e6i	−0.203154	+	0.147600i
$964$	−1.53336e7	−	1.11405e7i	−0.531437	−	0.386111i
$965$	−1.60794e7	−	1.72376e7i	−0.555841	−	0.595881i
$966$	−846915.	+	615320.i	−0.0292009	+	0.0212157i
$967$	−2.95585e6	+	9.09717e6i	−0.101652	+	0.312853i	−0.988930	−	0.148382i	$-0.952593\pi$
$967$	−2.95585e6	+	9.09717e6i	−0.101652	+	0.312853i	0.887278	+	0.461235i	$0.152593\pi$
$968$	8.59526e6			0.294829
$969$	−4.42092e6	+	1.36062e7i	−0.151253	+	0.465508i
$970$	1.79923e7	−	8.39337e6i	0.613986	−	0.286423i
$971$	8.15375e6	+	2.50947e7i	0.277530	+	0.854149i	0.988539	+	0.150966i	$0.0482384\pi$
$971$	8.15375e6	+	2.50947e7i	0.277530	+	0.854149i	−0.711009	+	0.703183i	$0.751762\pi$
$972$	−291954.	−	898543.i	−0.00991172	−	0.0305052i
$973$	7.95154e6	+	5.77713e6i	0.269258	+	0.195628i
$974$	−2.04246e7			−0.689852
$975$	841139.	−	1.00306e6i	0.0283371	−	0.0337922i
$976$	−4.55938e6			−0.153208
$977$	3.12770e7	+	2.27241e7i	1.04831	+	0.761640i	0.971890	−	0.235436i	$-0.0756517\pi$
$977$	3.12770e7	+	2.27241e7i	1.04831	+	0.761640i	0.0764179	+	0.997076i	$0.475652\pi$
$978$	1.77833e6	+	5.47313e6i	0.0594518	+	0.182974i
$979$	1.34327e6	+	4.13417e6i	0.0447927	+	0.137858i
$980$	−7.07224e6	+	1.27633e7i	−0.235230	+	0.424521i
$981$	717013.	−	2.20674e6i	0.0237878	−	0.0732114i
$982$	−1.00608e7			−0.332930
$983$	−7.96438e6	+	2.45118e7i	−0.262886	+	0.809081i	0.729286	+	0.684209i	$0.239852\pi$
$983$	−7.96438e6	+	2.45118e7i	−0.262886	+	0.809081i	−0.992173	+	0.124873i	$0.960148\pi$
$984$	942599.	−	684838.i	0.0310341	−	0.0225476i
$985$	2.30626e7	−	4.16213e7i	0.757387	−	1.36686i
$986$	−4.77747e6	−	3.47104e6i	−0.156497	−	0.113702i
$987$	−446694.	+	324542.i	−0.0145954	+	0.0106042i
$988$	−745973.	+	541981.i	−0.0243126	+	0.0176641i
$989$	7.02930e6	+	5.10709e6i	0.228519	+	0.166029i
$990$	361474.	+	2.94019e6i	0.0117217	+	0.0953427i
$991$	−1.72875e6	+	1.25601e6i	−0.0559176	+	0.0406265i	−0.615393	−	0.788220i	$-0.711003\pi$
$991$	−1.72875e6	+	1.25601e6i	−0.0559176	+	0.0406265i	0.559475	+	0.828847i	$0.311003\pi$
$992$	1.78432e6	−	5.49156e6i	0.0575695	−	0.177181i
$993$	1.43009e6			0.0460246
$994$	704589.	−	2.16850e6i	0.0226188	−	0.0696136i
$995$	2.90788e7	+	3.11734e7i	0.931147	+	0.998222i
$996$	−259657.	−	799141.i	−0.00829376	−	0.0255256i
$997$	1.03563e7	+	3.18734e7i	0.329964	+	1.01553i	0.969150	+	0.246473i	$0.0792717\pi$
$997$	1.03563e7	+	3.18734e7i	0.329964	+	1.01553i	−0.639185	+	0.769053i	$0.720728\pi$
$998$	3.32388e6	+	2.41494e6i	0.105638	+	0.0767504i
$999$	−6.15225e6			−0.195039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.a.91.2	yes	20
25.11	even	5	inner	150.6.g.a.61.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.a.61.2	✓	20	25.11	even	5	inner
150.6.g.a.91.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 + 2.35114i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-38.1312 - 40.8780i) q^{5} +(11.1246 - 34.2380i) q^{6} -22.2017 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\)	\(q+(3.23607 + 2.35114i) q^{2} +(-2.78115 - 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-38.1312 - 40.8780i) q^{5} +(11.1246 - 34.2380i) q^{6} -22.2017 q^{7} +(-19.7771 + 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(-27.2854 - 221.936i) q^{10} +(132.319 + 96.1350i) q^{11} +(116.498 - 84.6411i) q^{12} +(37.6553 - 27.3582i) q^{13} +(-71.8462 - 52.1993i) q^{14} +(-243.847 + 440.073i) q^{15} +(-207.108 + 150.473i) q^{16} +(-396.729 + 1221.01i) q^{17} -324.000 q^{18} +(-382.612 + 1177.56i) q^{19} +(433.505 - 782.351i) q^{20} +(61.7463 + 190.036i) q^{21} +(202.165 + 622.199i) q^{22} +(1059.62 + 769.861i) q^{23} +576.000 q^{24} +(-217.019 + 3117.46i) q^{25} +186.178 q^{26} +(589.773 + 428.495i) q^{27} +(-109.771 - 337.841i) q^{28} +(355.346 + 1093.64i) q^{29} +(-1823.78 + 850.787i) q^{30} +(-1742.50 + 5362.85i) q^{31} -1024.00 q^{32} +(454.871 - 1399.95i) q^{33} +(-4154.60 + 3018.49i) q^{34} +(846.578 + 907.560i) q^{35} +(-1048.49 - 761.770i) q^{36} +(-6827.54 + 4960.50i) q^{37} +(-4006.77 + 2911.09i) q^{38} +(-338.898 - 246.224i) q^{39} +(3242.27 - 1512.51i) q^{40} +(1636.46 - 1188.95i) q^{41} +(-246.985 + 760.142i) q^{42} +6633.78 q^{43} +(-808.659 + 2488.80i) q^{44} +(4444.98 + 863.299i) q^{45} +(1618.96 + 4982.64i) q^{46} +(853.898 + 2628.03i) q^{47} +(1863.98 + 1354.26i) q^{48} -16314.1 q^{49} +(-8031.86 + 9578.06i) q^{50} +11554.6 q^{51} +(602.485 + 437.731i) q^{52} +(762.303 + 2346.13i) q^{53} +(901.094 + 2773.28i) q^{54} +(-1115.66 - 9074.66i) q^{55} +(439.085 - 1351.36i) q^{56} +11143.4 q^{57} +(-1421.38 + 4374.57i) q^{58} +(-25790.3 + 18737.8i) q^{59} +(-7902.19 - 1534.75i) q^{60} +(14408.7 + 10468.5i) q^{61} +(-18247.7 + 13257.7i) q^{62} +(1454.89 - 1057.04i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-2554.19 - 496.072i) q^{65} +(4763.47 - 3460.86i) q^{66} +(7869.06 - 24218.5i) q^{67} -20541.5 q^{68} +(3642.66 - 11210.9i) q^{69} +(605.781 + 4927.35i) q^{70} +(7933.96 + 24418.2i) q^{71} +(-1601.94 - 4930.28i) q^{72} +(-66181.4 - 48083.6i) q^{73} -33757.2 q^{74} +(27287.4 - 6812.55i) q^{75} -19810.6 q^{76} +(-2937.70 - 2134.36i) q^{77} +(-517.790 - 1593.59i) q^{78} +(-8291.07 - 25517.3i) q^{79} +(14048.3 + 2728.45i) q^{80} +(2027.46 - 6239.88i) q^{81} +8091.08 q^{82} +(1803.17 - 5549.59i) q^{83} +(-2586.46 + 1879.18i) q^{84} +(65040.0 - 30341.0i) q^{85} +(21467.4 + 15597.0i) q^{86} +(8372.77 - 6083.18i) q^{87} +(-8468.39 + 6152.64i) q^{88} +(21501.9 + 15622.0i) q^{89} +(12354.5 + 13244.5i) q^{90} +(-836.012 + 607.398i) q^{91} +(-6475.84 + 19930.6i) q^{92} +50749.5 q^{93} +(-3415.59 + 10512.1i) q^{94} +(62725.8 - 29261.4i) q^{95} +(2847.90 + 8764.94i) q^{96} +(27437.3 + 84443.2i) q^{97} +(-52793.5 - 38356.7i) q^{98} -13247.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9	\( 20 q + 20 q^{2} + 45 q^{3} - 80 q^{4} - 55 q^{5} - 180 q^{6} + 180 q^{7} + 320 q^{8} - 405 q^{9} + 220 q^{10} + 380 q^{11} + 720 q^{12} - 230 q^{13} - 920 q^{14} - 630 q^{15} - 1280 q^{16} + 2870 q^{17} - 6480 q^{18} + 1560 q^{19} + 1120 q^{20} + 2880 q^{21} - 720 q^{22} + 760 q^{23} + 11520 q^{24} + 1725 q^{25} + 7320 q^{26} + 3645 q^{27} - 5120 q^{28} + 12000 q^{29} + 5220 q^{30} - 1710 q^{31} - 20480 q^{32} - 1620 q^{33} + 20620 q^{34} - 22440 q^{35} - 6480 q^{36} - 5595 q^{37} - 5240 q^{38} + 2070 q^{39} - 9280 q^{40} - 2820 q^{41} - 11520 q^{42} + 66020 q^{43} + 2880 q^{44} - 8505 q^{45} + 21960 q^{46} - 19630 q^{47} + 11520 q^{48} - 61780 q^{49} + 100 q^{50} - 41130 q^{51} - 3680 q^{52} + 62735 q^{53} - 14580 q^{54} + 66590 q^{55} + 20480 q^{56} + 51660 q^{57} - 48000 q^{58} + 105100 q^{59} + 15120 q^{60} + 34790 q^{61} - 28560 q^{62} + 18630 q^{63} - 20480 q^{64} - 44345 q^{65} + 13680 q^{66} - 19470 q^{67} + 73120 q^{68} + 49410 q^{69} - 81240 q^{70} - 111720 q^{71} + 25920 q^{72} - 198830 q^{73} - 104120 q^{74} + 60975 q^{75} - 91840 q^{76} + 144740 q^{77} + 41220 q^{78} + 71210 q^{79} - 26880 q^{80} - 32805 q^{81} + 166680 q^{82} - 288690 q^{83} - 33120 q^{84} + 338735 q^{85} + 39920 q^{86} + 108225 q^{87} - 24320 q^{88} + 114225 q^{89} + 17820 q^{90} - 155800 q^{91} - 87840 q^{92} + 97740 q^{93} + 78520 q^{94} - 416900 q^{95} - 46080 q^{96} - 446970 q^{97} - 123380 q^{98} - 90720 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 + 45 * q^3 - 80 * q^4 - 55 * q^5 - 180 * q^6 + 180 * q^7 + 320 * q^8 - 405 * q^9 + 220 * q^10 + 380 * q^11 + 720 * q^12 - 230 * q^13 - 920 * q^14 - 630 * q^15 - 1280 * q^16 + 2870 * q^17 - 6480 * q^18 + 1560 * q^19 + 1120 * q^20 + 2880 * q^21 - 720 * q^22 + 760 * q^23 + 11520 * q^24 + 1725 * q^25 + 7320 * q^26 + 3645 * q^27 - 5120 * q^28 + 12000 * q^29 + 5220 * q^30 - 1710 * q^31 - 20480 * q^32 - 1620 * q^33 + 20620 * q^34 - 22440 * q^35 - 6480 * q^36 - 5595 * q^37 - 5240 * q^38 + 2070 * q^39 - 9280 * q^40 - 2820 * q^41 - 11520 * q^42 + 66020 * q^43 + 2880 * q^44 - 8505 * q^45 + 21960 * q^46 - 19630 * q^47 + 11520 * q^48 - 61780 * q^49 + 100 * q^50 - 41130 * q^51 - 3680 * q^52 + 62735 * q^53 - 14580 * q^54 + 66590 * q^55 + 20480 * q^56 + 51660 * q^57 - 48000 * q^58 + 105100 * q^59 + 15120 * q^60 + 34790 * q^61 - 28560 * q^62 + 18630 * q^63 - 20480 * q^64 - 44345 * q^65 + 13680 * q^66 - 19470 * q^67 + 73120 * q^68 + 49410 * q^69 - 81240 * q^70 - 111720 * q^71 + 25920 * q^72 - 198830 * q^73 - 104120 * q^74 + 60975 * q^75 - 91840 * q^76 + 144740 * q^77 + 41220 * q^78 + 71210 * q^79 - 26880 * q^80 - 32805 * q^81 + 166680 * q^82 - 288690 * q^83 - 33120 * q^84 + 338735 * q^85 + 39920 * q^86 + 108225 * q^87 - 24320 * q^88 + 114225 * q^89 + 17820 * q^90 - 155800 * q^91 - 87840 * q^92 + 97740 * q^93 + 78520 * q^94 - 416900 * q^95 - 46080 * q^96 - 446970 * q^97 - 123380 * q^98 - 90720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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