LMFDB - Embedded newform 150.6.g.d.31.3

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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	150.31
Dual form			150.6.g.d.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-30.6277 - 46.7648i) q^{5} +(29.1246 + 21.1603i) q^{6} -78.0347 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})$	\(q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-30.6277 - 46.7648i) q^{5} +(29.1246 + 21.1603i) q^{6} -78.0347 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(140.046 - 174.319i) q^{10} +(120.944 + 372.226i) q^{11} +(-44.4984 + 136.952i) q^{12} +(-103.126 + 317.389i) q^{13} +(-96.4561 - 296.861i) q^{14} +(-470.394 - 178.479i) q^{15} +(79.1084 - 243.470i) q^{16} +(705.326 + 512.450i) q^{17} +324.000 q^{18} +(2251.90 + 1636.10i) q^{19} +(836.256 + 317.295i) q^{20} +(-568.182 + 412.809i) q^{21} +(-1266.54 + 920.194i) q^{22} +(817.413 + 2515.74i) q^{23} -576.000 q^{24} +(-1248.88 + 2864.60i) q^{25} -1334.89 q^{26} +(-225.273 - 693.320i) q^{27} +(1010.10 - 733.882i) q^{28} +(4800.50 - 3487.77i) q^{29} +(97.5341 - 2010.10i) q^{30} +(593.563 + 431.249i) q^{31} +1024.00 q^{32} +(2849.71 + 2070.44i) q^{33} +(-1077.64 + 3316.64i) q^{34} +(2390.02 + 3649.27i) q^{35} +(400.486 + 1232.57i) q^{36} +(-679.704 + 2091.91i) q^{37} +(-3440.59 + 10589.0i) q^{38} +(928.134 + 2856.50i) q^{39} +(-173.394 + 3573.50i) q^{40} +(735.494 - 2263.62i) q^{41} +(-2272.73 - 1651.23i) q^{42} +5240.89 q^{43} +(-5066.15 - 3680.77i) q^{44} +(-4369.17 + 1188.89i) q^{45} +(-8560.06 + 6219.25i) q^{46} +(5606.90 - 4073.65i) q^{47} +(-711.975 - 2191.23i) q^{48} -10717.6 q^{49} +(-12441.3 - 1210.20i) q^{50} +7846.48 q^{51} +(-1650.02 - 5078.23i) q^{52} +(-27438.2 + 19935.0i) q^{53} +(2359.09 - 1713.98i) q^{54} +(13702.8 - 17056.3i) q^{55} +(4040.41 + 2935.53i) q^{56} +25051.5 q^{57} +(19202.0 + 13951.1i) q^{58} +(-15544.9 + 47842.2i) q^{59} +(7767.42 - 2113.57i) q^{60} +(-3760.99 - 11575.1i) q^{61} +(-906.884 + 2791.10i) q^{62} +(-1953.24 + 6011.44i) q^{63} +(1265.73 + 3895.53i) q^{64} +(18001.1 - 4898.25i) q^{65} +(-4353.97 + 13400.1i) q^{66} +(-3564.38 - 2589.68i) q^{67} -13949.3 q^{68} +(19260.1 + 13993.3i) q^{69} +(-10928.4 + 13602.9i) q^{70} +(-47014.5 + 34158.0i) q^{71} +(-4193.94 + 3047.08i) q^{72} +(-7406.86 - 22796.0i) q^{73} -8798.27 q^{74} +(6060.59 + 27464.2i) q^{75} -44535.9 q^{76} +(-9437.79 - 29046.5i) q^{77} +(-9719.55 + 7061.66i) q^{78} +(13450.5 - 9772.33i) q^{79} +(-13808.7 + 3757.46i) q^{80} +(-5307.96 - 3856.46i) q^{81} +9520.43 q^{82} +(51093.0 + 37121.2i) q^{83} +(3472.42 - 10687.0i) q^{84} +(2362.04 - 48679.6i) q^{85} +(6478.10 + 19937.5i) q^{86} +(16502.6 - 50789.9i) q^{87} +(7740.39 - 23822.5i) q^{88} +(9492.50 + 29214.9i) q^{89} +(-9923.38 - 15151.8i) q^{90} +(8047.40 - 24767.4i) q^{91} +(-34240.2 - 24877.0i) q^{92} +6603.16 q^{93} +(22427.6 + 16294.6i) q^{94} +(7541.27 - 155419. i) q^{95} +(7455.90 - 5417.03i) q^{96} +(54812.6 - 39823.7i) q^{97} +(-13247.7 - 40772.1i) q^{98} +31701.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9}+O(q^{10}) $ 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9	\( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9} + 44 q^{10} - 135 q^{11} + 1008 q^{12} + 616 q^{13} - 48 q^{14} + 531 q^{15} - 1792 q^{16} - 3372 q^{17} + 9072 q^{18} + 488 q^{19} - 944 q^{20} - 387 q^{21} - 1920 q^{22} - 620 q^{23} - 16128 q^{24} + 6659 q^{25} - 1616 q^{26} + 5103 q^{27} + 688 q^{28} + 5682 q^{29} + 2844 q^{30} + 3339 q^{31} + 28672 q^{32} + 4320 q^{33} + 14032 q^{34} - 23984 q^{35} - 9072 q^{36} + 4506 q^{37} - 1528 q^{38} - 5544 q^{39} - 5056 q^{40} + 44962 q^{41} - 1548 q^{42} + 38028 q^{43} - 7680 q^{44} + 9396 q^{45} + 7480 q^{46} - 58300 q^{47} + 16128 q^{48} + 114402 q^{49} + 7476 q^{50} + 2448 q^{51} + 9856 q^{52} - 138 q^{53} + 20412 q^{54} + 96850 q^{55} + 2752 q^{56} + 1908 q^{57} + 22728 q^{58} + 40245 q^{59} - 16704 q^{60} + 79380 q^{61} - 54504 q^{62} - 972 q^{63} - 28672 q^{64} + 3532 q^{65} + 4860 q^{66} - 34352 q^{67} - 4352 q^{68} - 16830 q^{69} - 69476 q^{70} + 115860 q^{71} - 36288 q^{72} - 121214 q^{73} - 37856 q^{74} + 21969 q^{75} - 3392 q^{76} + 195005 q^{77} + 14904 q^{78} + 36224 q^{79} + 29696 q^{80} - 45927 q^{81} + 34608 q^{82} + 85051 q^{83} + 1728 q^{84} + 137496 q^{85} - 18568 q^{86} + 127062 q^{87} - 8640 q^{88} - 53826 q^{89} + 3564 q^{90} - 408104 q^{91} + 29920 q^{92} - 185166 q^{93} - 233200 q^{94} - 482004 q^{95} + 64512 q^{96} - 244169 q^{97} - 395952 q^{98} + 99630 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9 + 44 * q^10 - 135 * q^11 + 1008 * q^12 + 616 * q^13 - 48 * q^14 + 531 * q^15 - 1792 * q^16 - 3372 * q^17 + 9072 * q^18 + 488 * q^19 - 944 * q^20 - 387 * q^21 - 1920 * q^22 - 620 * q^23 - 16128 * q^24 + 6659 * q^25 - 1616 * q^26 + 5103 * q^27 + 688 * q^28 + 5682 * q^29 + 2844 * q^30 + 3339 * q^31 + 28672 * q^32 + 4320 * q^33 + 14032 * q^34 - 23984 * q^35 - 9072 * q^36 + 4506 * q^37 - 1528 * q^38 - 5544 * q^39 - 5056 * q^40 + 44962 * q^41 - 1548 * q^42 + 38028 * q^43 - 7680 * q^44 + 9396 * q^45 + 7480 * q^46 - 58300 * q^47 + 16128 * q^48 + 114402 * q^49 + 7476 * q^50 + 2448 * q^51 + 9856 * q^52 - 138 * q^53 + 20412 * q^54 + 96850 * q^55 + 2752 * q^56 + 1908 * q^57 + 22728 * q^58 + 40245 * q^59 - 16704 * q^60 + 79380 * q^61 - 54504 * q^62 - 972 * q^63 - 28672 * q^64 + 3532 * q^65 + 4860 * q^66 - 34352 * q^67 - 4352 * q^68 - 16830 * q^69 - 69476 * q^70 + 115860 * q^71 - 36288 * q^72 - 121214 * q^73 - 37856 * q^74 + 21969 * q^75 - 3392 * q^76 + 195005 * q^77 + 14904 * q^78 + 36224 * q^79 + 29696 * q^80 - 45927 * q^81 + 34608 * q^82 + 85051 * q^83 + 1728 * q^84 + 137496 * q^85 - 18568 * q^86 + 127062 * q^87 - 8640 * q^88 - 53826 * q^89 + 3564 * q^90 - 408104 * q^91 + 29920 * q^92 - 185166 * q^93 - 233200 * q^94 - 482004 * q^95 + 64512 * q^96 - 244169 * q^97 - 395952 * q^98 + 99630 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$3$	7.28115	−	5.29007i	0.467086	−	0.339358i
$3$	7.28115	−	5.29007i	0.467086	−	0.339358i
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	−30.6277	−	46.7648i	−0.547885	−	0.836553i
$5$	−30.6277	−	46.7648i	−0.547885	−	0.836553i
$6$	29.1246	+	21.1603i	0.330280	+	0.239962i
$7$	−78.0347			−0.601925			−0.300963	−	0.953636i	$-0.597308\pi$
$7$	−78.0347			−0.601925			−0.300963	+	0.953636i	$0.597308\pi$
$8$	−51.7771	−	37.6183i	−0.286031	−	0.207813i
$9$	25.0304	−	77.0356i	0.103006	−	0.317019i
$10$	140.046	−	174.319i	0.442864	−	0.551246i
$11$	120.944	+	372.226i	0.301371	+	0.927524i	0.981007	+	0.193974i	$0.0621378\pi$
$11$	120.944	+	372.226i	0.301371	+	0.927524i	−0.679636	+	0.733550i	$0.737862\pi$
$12$	−44.4984	+	136.952i	−0.0892055	+	0.274546i
$13$	−103.126	+	317.389i	−0.169243	+	0.520875i	−0.999324	−	0.0367672i	$-0.988294\pi$
$13$	−103.126	+	317.389i	−0.169243	+	0.520875i	0.830081	+	0.557643i	$0.188294\pi$
$14$	−96.4561	−	296.861i	−0.131525	−	0.404794i
$15$	−470.394	−	178.479i	−0.539801	−	0.204813i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	705.326	+	512.450i	0.591927	+	0.430060i	0.843004	−	0.537907i	$-0.180785\pi$
$17$	705.326	+	512.450i	0.591927	+	0.430060i	−0.251078	+	0.967967i	$0.580785\pi$
$18$	324.000			0.235702
$19$	2251.90	+	1636.10i	1.43108	+	1.03974i	0.989814	+	0.142365i	$0.0454708\pi$
$19$	2251.90	+	1636.10i	1.43108	+	1.03974i	0.441267	+	0.897376i	$0.354529\pi$
$20$	836.256	+	317.295i	0.467481	+	0.177373i
$21$	−568.182	+	412.809i	−0.281151	+	0.204268i
$22$	−1266.54	+	920.194i	−0.557907	+	0.405343i
$23$	817.413	+	2515.74i	0.322197	+	0.991621i	0.972690	+	0.232109i	$0.0745625\pi$
$23$	817.413	+	2515.74i	0.322197	+	0.991621i	−0.650493	+	0.759513i	$0.725438\pi$
$24$	−576.000			−0.204124
$25$	−1248.88	+	2864.60i	−0.399643	+	0.916671i
$26$	−1334.89			−0.387269
$27$	−225.273	−	693.320i	−0.0594703	−	0.183031i
$28$	1010.10	−	733.882i	0.243484	−	0.176901i
$29$	4800.50	−	3487.77i	1.05996	−	0.770109i	0.0858827	−	0.996305i	$-0.472629\pi$
$29$	4800.50	−	3487.77i	1.05996	−	0.770109i	0.974082	+	0.226196i	$0.0726290\pi$
$30$	97.5341	−	2010.10i	0.0197858	−	0.407769i
$31$	593.563	+	431.249i	0.110934	+	0.0805979i	0.641869	−	0.766814i	$-0.278159\pi$
$31$	593.563	+	431.249i	0.110934	+	0.0805979i	−0.530935	+	0.847412i	$0.678159\pi$
$32$	1024.00			0.176777
$33$	2849.71	+	2070.44i	0.455529	+	0.330961i
$34$	−1077.64	+	3316.64i	−0.159874	+	0.492041i
$35$	2390.02	+	3649.27i	0.329786	+	0.503542i
$36$	400.486	+	1232.57i	0.0515028	+	0.158509i
$37$	−679.704	+	2091.91i	−0.0816235	+	0.251211i	−0.983537	−	0.180704i	$-0.942162\pi$
$37$	−679.704	+	2091.91i	−0.0816235	+	0.251211i	0.901914	+	0.431916i	$0.142162\pi$
$38$	−3440.59	+	10589.0i	−0.386522	+	1.18959i
$39$	928.134	+	2856.50i	0.0977123	+	0.300728i
$40$	−173.394	+	3573.50i	−0.0171350	+	0.353138i
$41$	735.494	−	2263.62i	0.0683312	−	0.210302i	−0.911060	−	0.412273i	$-0.864735\pi$
$41$	735.494	−	2263.62i	0.0683312	−	0.210302i	0.979391	+	0.201971i	$0.0647348\pi$
$42$	−2272.73	−	1651.23i	−0.198804	−	0.144439i
$43$	5240.89			0.432249			0.216125	−	0.976366i	$-0.430658\pi$
$43$	5240.89			0.432249			0.216125	+	0.976366i	$0.430658\pi$
$44$	−5066.15	−	3680.77i	−0.394500	−	0.286621i
$45$	−4369.17	+	1188.89i	−0.321638	+	0.0875203i
$46$	−8560.06	+	6219.25i	−0.596461	+	0.433354i
$47$	5606.90	−	4073.65i	0.370236	−	0.268992i	−0.387073	−	0.922049i	$-0.626514\pi$
$47$	5606.90	−	4073.65i	0.370236	−	0.268992i	0.757309	+	0.653057i	$0.226514\pi$
$48$	−711.975	−	2191.23i	−0.0446028	−	0.137273i
$49$	−10717.6			−0.637686
$50$	−12441.3	−	1210.20i	−0.703785	−	0.0684595i
$51$	7846.48			0.422425
$52$	−1650.02	−	5078.23i	−0.0846213	−	0.260438i
$53$	−27438.2	+	19935.0i	−1.34173	+	0.974826i	−0.342354	+	0.939571i	$0.611224\pi$
$53$	−27438.2	+	19935.0i	−1.34173	+	0.974826i	−0.999378	+	0.0352550i	$0.988776\pi$
$54$	2359.09	−	1713.98i	0.110093	−	0.0799874i
$55$	13702.8	−	17056.3i	0.610807	−	0.760290i
$56$	4040.41	+	2935.53i	0.172169	+	0.125088i
$57$	25051.5			1.02128
$58$	19202.0	+	13951.1i	0.749508	+	0.544549i
$59$	−15544.9	+	47842.2i	−0.581376	+	1.78929i	0.0319856	+	0.999488i	$0.489817\pi$
$59$	−15544.9	+	47842.2i	−0.581376	+	1.78929i	−0.613361	+	0.789802i	$0.710183\pi$
$60$	7767.42	−	2113.57i	0.278547	−	0.0757948i
$61$	−3760.99	−	11575.1i	−0.129413	−	0.398291i	0.865266	−	0.501312i	$-0.167149\pi$
$61$	−3760.99	−	11575.1i	−0.129413	−	0.398291i	−0.994679	+	0.103021i	$0.967149\pi$
$62$	−906.884	+	2791.10i	−0.0299621	+	0.0922139i
$63$	−1953.24	+	6011.44i	−0.0620017	+	0.190822i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	18001.1	−	4898.25i	0.528466	−	0.143800i
$66$	−4353.97	+	13400.1i	−0.123034	+	0.378660i
$67$	−3564.38	−	2589.68i	−0.0970058	−	0.0704788i	0.538225	−	0.842801i	$-0.319095\pi$
$67$	−3564.38	−	2589.68i	−0.0970058	−	0.0704788i	−0.635231	+	0.772322i	$0.719095\pi$
$68$	−13949.3			−0.365831
$69$	19260.1	+	13993.3i	0.487008	+	0.353832i
$70$	−10928.4	+	13602.9i	−0.266571	+	0.331809i
$71$	−47014.5	+	34158.0i	−1.10684	+	0.804168i	−0.982163	−	0.188029i	$-0.939790\pi$
$71$	−47014.5	+	34158.0i	−1.10684	+	0.804168i	−0.124679	+	0.992197i	$0.539790\pi$
$72$	−4193.94	+	3047.08i	−0.0953436	+	0.0692712i
$73$	−7406.86	−	22796.0i	−0.162677	−	0.500669i	0.836180	−	0.548455i	$-0.184784\pi$
$73$	−7406.86	−	22796.0i	−0.162677	−	0.500669i	−0.998858	+	0.0477854i	$0.984784\pi$
$74$	−8798.27			−0.186775
$75$	6060.59	+	27464.2i	0.124412	+	0.563786i
$76$	−44535.9			−0.884457
$77$	−9437.79	−	29046.5i	−0.181403	−	0.558300i
$78$	−9719.55	+	7061.66i	−0.180888	+	0.131423i
$79$	13450.5	−	9772.33i	0.242476	−	0.176169i	−0.459909	−	0.887966i	$-0.652118\pi$
$79$	13450.5	−	9772.33i	0.242476	−	0.176169i	0.702386	+	0.711796i	$0.252118\pi$
$80$	−13808.7	+	3757.46i	−0.241229	+	0.0656402i
$81$	−5307.96	−	3856.46i	−0.0898908	−	0.0653095i
$82$	9520.43			0.156359
$83$	51093.0	+	37121.2i	0.814078	+	0.591462i	0.915010	−	0.403431i	$-0.132183\pi$
$83$	51093.0	+	37121.2i	0.814078	+	0.591462i	−0.100932	+	0.994893i	$0.532183\pi$
$84$	3472.42	−	10687.0i	0.0536950	−	0.165256i
$85$	2362.04	−	48679.6i	0.0354600	−	0.730802i
$86$	6478.10	+	19937.5i	0.0944499	+	0.290687i
$87$	16502.6	−	50789.9i	0.233752	−	0.719415i
$88$	7740.39	−	23822.5i	0.106551	−	0.327929i
$89$	9492.50	+	29214.9i	0.127030	+	0.390957i	0.994265	−	0.106940i	$-0.0341054\pi$
$89$	9492.50	+	29214.9i	0.127030	+	0.390957i	−0.867236	+	0.497898i	$0.834105\pi$
$90$	−9923.38	−	15151.8i	−0.129138	−	0.197178i
$91$	8047.40	−	24767.4i	0.101871	−	0.313528i
$92$	−34240.2	−	24877.0i	−0.421762	−	0.306428i
$93$	6603.16			0.0791671
$94$	22427.6	+	16294.6i	0.261796	+	0.190206i
$95$	7541.27	−	155419.i	0.0857306	−	1.76683i
$96$	7455.90	−	5417.03i	0.0825700	−	0.0599906i
$97$	54812.6	−	39823.7i	0.591495	−	0.429746i	−0.251355	−	0.967895i	$-0.580876\pi$
$97$	54812.6	−	39823.7i	0.591495	−	0.429746i	0.842850	+	0.538149i	$0.180876\pi$
$98$	−13247.7	−	40772.1i	−0.139340	−	0.428843i
$99$	31701.9			0.325085
$100$	−10774.4	−	48825.3i	−0.107744	−	0.488253i
$101$	117286.			1.14405			0.572024	−	0.820237i	$-0.306158\pi$
$101$	117286.			1.14405			0.572024	+	0.820237i	$0.306158\pi$
$102$	9698.79	+	29849.8i	0.0923032	+	0.284080i
$103$	−52632.4	+	38239.7i	−0.488832	+	0.355158i	−0.804735	−	0.593634i	$-0.797693\pi$
$103$	−52632.4	+	38239.7i	−0.488832	+	0.355158i	0.315903	+	0.948792i	$0.397693\pi$
$104$	17279.2	−	12554.1i	0.156654	−	0.113815i
$105$	36707.0	+	13927.5i	0.324920	+	0.123282i
$106$	−109753.	−	79740.1i	−0.948748	−	0.689306i
$107$	76342.8			0.644627			0.322313	−	0.946633i	$-0.395539\pi$
$107$	76342.8			0.644627			0.322313	+	0.946633i	$0.395539\pi$
$108$	9436.37	+	6855.93i	0.0778477	+	0.0565597i
$109$	64681.9	−	199071.i	0.521455	−	1.60487i	−0.249767	−	0.968306i	$-0.580354\pi$
$109$	64681.9	−	199071.i	0.521455	−	1.60487i	0.771221	−	0.636567i	$-0.219646\pi$
$110$	81823.8	+	31045.9i	0.644760	+	0.244637i
$111$	6117.33	+	18827.2i	0.0471253	+	0.145037i
$112$	−6173.19	+	18999.1i	−0.0465013	+	0.143116i
$113$	−26380.6	+	81191.1i	−0.194352	+	0.598153i	0.805632	+	0.592416i	$0.201826\pi$
$113$	−26380.6	+	81191.1i	−0.194352	+	0.598153i	−0.999984	+	0.00573645i	$0.998174\pi$
$114$	30965.3	+	95301.4i	0.223158	+	0.686811i
$115$	92612.4	−	115277.i	0.653017	−	0.812830i
$116$	−29338.0	+	90293.2i	−0.202435	+	0.623031i
$117$	21869.0	+	15888.7i	0.147694	+	0.107306i
$118$	−201217.			−1.33033
$119$	−55039.9	−	39988.8i	−0.356295	−	0.258864i
$120$	17641.6	+	26936.5i	0.111837	+	0.170761i
$121$	6368.06	−	4626.67i	0.0395406	−	0.0287280i
$122$	39385.5	−	28615.3i	0.239573	−	0.174060i
$123$	−6619.44	−	20372.6i	−0.0394511	−	0.121418i
$124$	−11739.0			−0.0685607
$125$	172213.	−	29332.3i	0.985803	−	0.167908i
$126$	−25283.2			−0.141875
$127$	−87222.7	−	268444.i	−0.479866	−	1.47688i	−0.839281	−	0.543698i	$-0.817024\pi$
$127$	−87222.7	−	268444.i	−0.479866	−	1.47688i	0.359415	−	0.933178i	$-0.382976\pi$
$128$	−13254.9	+	9630.27i	−0.0715077	+	0.0519534i
$129$	38159.7	−	27724.7i	0.201898	−	0.146687i
$130$	40884.7	+	62425.9i	0.212179	+	0.323971i
$131$	−63434.2	−	46087.7i	−0.322957	−	0.234642i	0.414479	−	0.910059i	$-0.363964\pi$
$131$	−63434.2	−	46087.7i	−0.322957	−	0.234642i	−0.737436	+	0.675417i	$0.763964\pi$
$132$	−56359.0			−0.281532
$133$	−175726.	−	127672.i	−0.861404	−	0.625846i
$134$	5445.89	−	16760.7i	0.0262004	−	0.0806364i
$135$	−25523.3	+	31769.7i	−0.120532	+	0.150030i
$136$	−17242.3	−	53066.3i	−0.0799369	−	0.246021i
$137$	−66449.5	+	204510.i	−0.302475	+	0.930923i	0.678132	+	0.734940i	$0.262790\pi$
$137$	−66449.5	+	204510.i	−0.302475	+	0.930923i	−0.980607	+	0.195983i	$0.937210\pi$
$138$	−29426.9	+	90566.6i	−0.131536	+	0.404828i
$139$	104871.	+	322758.i	0.460380	+	1.41690i	0.864701	+	0.502287i	$0.167508\pi$
$139$	104871.	+	322758.i	0.460380	+	1.41690i	−0.404321	+	0.914617i	$0.632492\pi$
$140$	−65256.9	−	24760.0i	−0.281389	−	0.106766i
$141$	19274.8	−	59321.8i	0.0816474	−	0.251285i
$142$	−188058.	−	136632.i	−0.782656	−	0.568633i
$143$	−130613.			−0.534129
$144$	−16775.8	−	12188.3i	−0.0674181	−	0.0489821i
$145$	−310133.	−	117672.i	−1.22498	−	0.464785i
$146$	77565.6	−	56354.7i	0.301153	−	0.218800i
$147$	−78036.4	+	56696.8i	−0.297854	+	0.216404i
$148$	−10875.3	−	33470.6i	−0.0408117	−	0.125606i
$149$	355192.			1.31068			0.655342	−	0.755332i	$-0.272525\pi$
$149$	355192.			1.31068			0.655342	+	0.755332i	$0.272525\pi$
$150$	−96988.9	+	57003.5i	−0.351961	+	0.206859i
$151$	−61457.5			−0.219348			−0.109674	−	0.993968i	$-0.534981\pi$
$151$	−61457.5			−0.219348			−0.109674	+	0.993968i	$0.534981\pi$
$152$	−55049.4	−	169425.i	−0.193261	−	0.594796i
$153$	57131.4	−	41508.4i	0.197309	−	0.143353i
$154$	98833.8	−	71807.0i	0.335818	−	0.243986i
$155$	1987.76	−	40966.0i	0.00664560	−	0.136960i
$156$	−38878.2	−	28246.7i	−0.127907	−	0.0929299i
$157$	−460291.			−1.49033			−0.745167	−	0.666878i	$-0.767630\pi$
$157$	−460291.			−1.49033			−0.745167	+	0.666878i	$0.767630\pi$
$158$	53801.8	+	39089.3i	0.171457	+	0.124571i
$159$	−94324.2	+	290300.i	−0.295890	+	0.910655i
$160$	−31362.8	−	47887.1i	−0.0968534	−	0.147883i
$161$	−63786.5	−	196315.i	−0.193939	−	0.596882i
$162$	8109.84	−	24959.5i	0.0242787	−	0.0747221i
$163$	−54142.3	+	166633.i	−0.159613	+	0.491238i	−0.998599	−	0.0529148i	$-0.983149\pi$
$163$	−54142.3	+	166633.i	−0.159613	+	0.491238i	0.838986	+	0.544153i	$0.183149\pi$
$164$	11767.9	+	36217.9i	0.0341656	+	0.105151i
$165$	9543.27	−	196679.i	0.0272890	−	0.562403i
$166$	−78063.1	+	240253.i	−0.219875	+	0.676705i
$167$	56446.3	+	41010.6i	0.156619	+	0.113790i	0.663335	−	0.748323i	$-0.269141\pi$
$167$	56446.3	+	41010.6i	0.156619	+	0.113790i	−0.506716	+	0.862113i	$0.669141\pi$
$168$	44948.0			0.122867
$169$	210281.	+	152778.i	0.566349	+	0.411477i
$170$	188108.	−	51185.6i	0.499211	−	0.135839i
$171$	182404.	−	132524.i	0.477027	−	0.346580i
$172$	−67839.6	+	49288.3i	−0.174848	+	0.127035i
$173$	211824.	+	651927.i	0.538096	+	1.65609i	0.736863	+	0.676042i	$0.236306\pi$
$173$	211824.	+	651927.i	0.538096	+	1.65609i	−0.198767	+	0.980047i	$0.563694\pi$
$174$	213615.			0.534882
$175$	97456.3	−	223538.i	0.240555	−	0.551767i
$176$	100194.			0.243814
$177$	139904.	+	430580.i	0.335657	+	1.03305i
$178$	−99406.7	+	72223.2i	−0.235161	+	0.170855i
$179$	36472.4	−	26498.7i	0.0850808	−	0.0618148i	−0.544432	−	0.838805i	$-0.683255\pi$
$179$	36472.4	−	26498.7i	0.0850808	−	0.0618148i	0.629512	+	0.776990i	$0.283255\pi$
$180$	45374.8	−	56479.4i	0.104384	−	0.129930i
$181$	32305.3	+	23471.1i	0.0732954	+	0.0532522i	0.623830	−	0.781560i	$-0.285576\pi$
$181$	32305.3	+	23471.1i	0.0732954	+	0.0532522i	−0.550534	+	0.834813i	$0.685576\pi$
$182$	104168.			0.233107
$183$	−88617.5	−	64384.4i	−0.195610	−	0.142119i
$184$	52314.4	−	161007.i	0.113914	−	0.350591i
$185$	118646.	−	32284.4i	0.254872	−	0.0693526i
$186$	8161.96	+	25119.9i	0.0172986	+	0.0532397i
$187$	−105442.	+	324518.i	−0.220501	+	0.678634i
$188$	−34266.3	+	105461.i	−0.0707087	+	0.217619i
$189$	17579.1	+	54103.0i	0.0357967	+	0.110171i
$190$	600572.	−	163420.i	1.20693	−	0.328414i
$191$	45144.6	−	138941.i	0.0895411	−	0.275579i	−0.896252	−	0.443546i	$-0.853720\pi$
$191$	45144.6	−	138941.i	0.0895411	−	0.275579i	0.985793	+	0.167967i	$0.0537202\pi$
$192$	29823.6	+	21668.1i	0.0583858	+	0.0424197i
$193$	−197403.			−0.381469			−0.190735	−	0.981642i	$-0.561087\pi$
$193$	−197403.			−0.381469			−0.190735	+	0.981642i	$0.561087\pi$
$194$	219250.	+	159295.i	0.418250	+	0.303876i
$195$	105157.	−	130892.i	0.198040	−	0.246506i
$196$	138731.	−	100794.i	0.257950	−	0.187411i
$197$	−831543.	+	604151.i	−1.52658	+	1.10912i	−0.568476	+	0.822700i	$0.692467\pi$
$197$	−831543.	+	604151.i	−1.52658	+	1.10912i	−0.958103	+	0.286424i	$0.907533\pi$
$198$	39185.7	+	120601.i	0.0710338	+	0.218619i
$199$	736664.			1.31867			0.659336	−	0.751848i	$-0.270837\pi$
$199$	736664.			1.31867			0.659336	+	0.751848i	$0.270837\pi$
$200$	172425.	−	101340.i	0.304807	−	0.179145i
$201$	−39652.4			−0.0692276
$202$	144974.	+	446184.i	0.249984	+	0.769370i
$203$	−374605.	+	272167.i	−0.638019	+	0.463548i
$204$	−101567.	+	73792.7i	−0.170874	+	0.124148i
$205$	−128384.	+	34934.3i	−0.213367	+	0.0580586i
$206$	−210530.	−	152959.i	−0.345657	−	0.251134i
$207$	214261.			0.347551
$208$	69116.8	+	50216.3i	0.110771	+	0.0804797i
$209$	−336646.	+	1.03609e6i	−0.533099	+	1.64071i
$210$	−7611.04	+	156857.i	−0.0119096	+	0.245446i
$211$	−276389.	−	850639.i	−0.427381	−	1.31534i	−0.900696	−	0.434450i	$-0.856943\pi$
$211$	−276389.	−	850639.i	−0.427381	−	1.31534i	0.473315	−	0.880893i	$-0.343057\pi$
$212$	167687.	−	516089.i	0.256248	−	0.788651i
$213$	−161621.	+	497420.i	−0.244090	+	0.751232i
$214$	94364.8	+	290425.i	0.140856	+	0.433511i
$215$	−160517.	−	245089.i	−0.236823	−	0.361600i
$216$	−14417.5	+	44372.5i	−0.0210259	+	0.0647112i
$217$	−46318.5	−	33652.4i	−0.0667737	−	0.0485139i
$218$	837260.			1.19322
$219$	−174523.	−	126798.i	−0.245890	−	0.178650i
$220$	−16965.8	+	349651.i	−0.0236329	+	0.487055i
$221$	−235384.	+	171016.i	−0.324187	+	0.235536i
$222$	−64061.5	+	46543.4i	−0.0872398	+	0.0633835i
$223$	−233239.	−	717835.i	−0.314079	−	0.966634i	−0.976132	−	0.217178i	$-0.930315\pi$
$223$	−233239.	−	717835.i	−0.314079	−	0.966634i	0.662054	−	0.749457i	$-0.269685\pi$
$224$	−79907.5			−0.106406
$225$	189416.	+	167910.i	0.249436	+	0.221117i
$226$	−341477.			−0.444724
$227$	−193539.	−	595652.i	−0.249290	−	0.767235i	−0.994901	−	0.100854i	$-0.967843\pi$
$227$	−193539.	−	595652.i	−0.249290	−	0.767235i	0.745612	−	0.666381i	$-0.232157\pi$
$228$	−324273.	+	235598.i	−0.413118	+	0.300147i
$229$	−347626.	+	252565.i	−0.438050	+	0.318262i	−0.784860	−	0.619673i	$-0.787265\pi$
$229$	−347626.	+	252565.i	−0.438050	+	0.318262i	0.346809	+	0.937936i	$0.387265\pi$
$230$	553017.	+	209828.i	0.689316	+	0.261543i
$231$	−222376.	−	161566.i	−0.274194	−	0.199214i
$232$	−379759.			−0.463221
$233$	907248.	+	659154.i	1.09480	+	0.795422i	0.980204	−	0.197990i	$-0.0634414\pi$
$233$	907248.	+	659154.i	1.09480	+	0.795422i	0.114600	+	0.993412i	$0.463441\pi$
$234$	−33412.8	+	102834.i	−0.0398909	+	0.122772i
$235$	−362230.	−	137439.i	−0.427873	−	0.162345i
$236$	−248718.	−	765475.i	−0.290688	−	0.894645i
$237$	46238.6	−	142308.i	0.0534729	−	0.164573i
$238$	84093.5	−	258813.i	0.0962321	−	0.296172i
$239$	416087.	+	1.28058e6i	0.471182	+	1.45015i	0.851038	+	0.525104i	$0.175974\pi$
$239$	416087.	+	1.28058e6i	0.471182	+	1.45015i	−0.379856	+	0.925046i	$0.624026\pi$
$240$	−80666.3	+	100408.i	−0.0903991	+	0.112523i
$241$	16669.4	−	51303.1i	0.0184875	−	0.0568985i	−0.941387	−	0.337328i	$-0.890477\pi$
$241$	16669.4	−	51303.1i	0.0184875	−	0.0568985i	0.959875	+	0.280429i	$0.0904769\pi$
$242$	25472.2	+	18506.7i	0.0279594	+	0.0203137i
$243$	−59049.0			−0.0641500
$244$	157542.	+	114461.i	0.169403	+	0.123079i
$245$	328256.	+	501206.i	0.349379	+	0.533459i
$246$	69319.7	−	50363.7i	0.0730330	−	0.0530616i
$247$	−751509.	+	546003.i	−0.783776	+	0.569446i
$248$	−14510.1	−	44657.6i	−0.0149811	−	0.0461070i
$249$	568389.			0.580962
$250$	324453.	+	618879.i	0.328324	+	0.626262i
$251$	1.41632e6			1.41898			0.709492	−	0.704713i	$-0.248924\pi$
$251$	1.41632e6			1.41898			0.709492	+	0.704713i	$0.248924\pi$
$252$	−31251.8	−	96183.1i	−0.0310008	−	0.0954108i
$253$	−837562.	+	608525.i	−0.822651	+	0.597691i
$254$	913408.	−	663630.i	0.888342	−	0.645419i
$255$	−240320.	−	366939.i	−0.231440	−	0.353381i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−1.97990e6			−1.86987			−0.934933	−	0.354824i	$-0.884541\pi$
$257$	−1.97990e6			−1.86987			−0.934933	+	0.354824i	$0.884541\pi$
$258$	152639.	+	110899.i	0.142763	+	0.103724i
$259$	53040.4	−	163242.i	0.0491312	−	0.151210i
$260$	−186946.	+	232697.i	−0.171507	+	0.213480i
$261$	−148524.	−	457109.i	−0.134957	−	0.415354i
$262$	96918.9	−	298286.i	0.0872278	−	0.268460i
$263$	212289.	−	653359.i	0.189251	−	0.582455i	−0.810744	−	0.585400i	$-0.800937\pi$
$263$	212289.	−	653359.i	0.189251	−	0.582455i	0.999996	+	0.00294497i	$0.000937414\pi$
$264$	−69663.5	−	214402.i	−0.0615171	−	0.189330i
$265$	1.77263e6	+	672576.i	1.55061	+	0.588338i
$266$	268485.	−	826313.i	0.232657	−	0.716045i
$267$	223665.	+	162502.i	0.192008	+	0.139502i
$268$	70493.1			0.0599529
$269$	−1.11032e6	−	806697.i	−0.935553	−	0.679719i	0.0117930	−	0.999930i	$-0.496246\pi$
$269$	−1.11032e6	−	806697.i	−0.935553	−	0.679719i	−0.947346	+	0.320211i	$0.896246\pi$
$270$	−152408.	−	57827.1i	−0.127232	−	0.0482749i
$271$	1.11806e6	−	812318.i	0.924787	−	0.671897i	−0.0199239	−	0.999801i	$-0.506342\pi$
$271$	1.11806e6	−	812318.i	0.924787	−	0.671897i	0.944711	+	0.327904i	$0.106342\pi$
$272$	180564.	−	131187.i	0.147982	−	0.107515i
$273$	−72426.6	−	222906.i	−0.0588155	−	0.181015i
$274$	−860140.			−0.692138
$275$	−1.21732e6	−	118413.i	−0.970675	−	0.0944207i
$276$	−380909.			−0.300988
$277$	−259907.	−	799911.i	−0.203525	−	0.626386i	−0.999771	−	0.0214124i	$-0.993184\pi$
$277$	−259907.	−	799911.i	−0.203525	−	0.626386i	0.796246	−	0.604974i	$-0.206816\pi$
$278$	−1.09822e6	+	797903.i	−0.852269	+	0.619210i
$279$	48078.6	−	34931.2i	0.0369778	−	0.0268660i
$280$	13530.7	−	278857.i	0.0103140	−	0.212563i
$281$	−1.27657e6	−	927480.i	−0.964445	−	0.700710i	−0.0102663	−	0.999947i	$-0.503268\pi$
$281$	−1.27657e6	−	927480.i	−0.964445	−	0.700710i	−0.954179	+	0.299237i	$0.903268\pi$
$282$	249498.			0.186829
$283$	938377.	+	681771.i	0.696484	+	0.506026i	0.878785	−	0.477217i	$-0.158355\pi$
$283$	938377.	+	681771.i	0.696484	+	0.506026i	−0.182301	+	0.983243i	$0.558355\pi$
$284$	287327.	−	884301.i	0.211388	−	0.650586i
$285$	−767269.	−	1.17153e6i	−0.559546	−	0.854357i
$286$	−161447.	−	496881.i	−0.116712	−	0.359201i
$287$	−57394.0	+	176641.i	−0.0411303	+	0.126586i
$288$	25631.1	−	78884.4i	0.0182090	−	0.0560415i
$289$	−203879.	−	627476.i	−0.143591	−	0.441929i
$290$	64304.7	−	1.32527e6i	0.0449001	−	0.925354i
$291$	188429.	−	579925.i	0.130441	−	0.401457i
$292$	310262.	+	225419.i	0.212947	+	0.154715i
$293$	−418323.			−0.284671			−0.142335	−	0.989818i	$-0.545461\pi$
$293$	−418323.			−0.284671			−0.142335	+	0.989818i	$0.545461\pi$
$294$	−312146.	−	226787.i	−0.210615	−	0.153021i
$295$	2.71343e6	−	738345.i	1.81536	−	0.493974i
$296$	113887.	−	82743.9i	0.0755519	−	0.0548917i
$297$	230827.	−	167705.i	0.151843	−	0.110320i
$298$	439042.	+	1.35123e6i	0.286395	+	0.881433i
$299$	−882765.			−0.571041
$300$	−336739.	−	298508.i	−0.216018	−	0.191493i
$301$	−408971.			−0.260182
$302$	−75965.7	−	233798.i	−0.0479292	−	0.147511i
$303$	853980.	−	620453.i	0.534369	−	0.388242i
$304$	576485.	−	418841.i	0.357770	−	0.259935i
$305$	−426117.	+	530401.i	−0.262289	+	0.326479i
$306$	228526.	+	166034.i	0.139518	+	0.101366i
$307$	−2.20471e6			−1.33507			−0.667536	−	0.744577i	$-0.732651\pi$
$307$	−2.20471e6			−1.33507			−0.667536	+	0.744577i	$0.732651\pi$
$308$	395335.	+	287228.i	0.237459	+	0.172524i
$309$	−180934.	+	556858.i	−0.107801	+	0.331778i
$310$	158301.	−	43074.9i	0.0935577	−	0.0254578i
$311$	−788924.	−	2.42806e6i	−0.462524	−	1.42350i	−0.862070	−	0.506790i	$-0.830832\pi$
$311$	−788924.	−	2.42806e6i	−0.462524	−	1.42350i	0.399546	−	0.916713i	$-0.369168\pi$
$312$	59400.6	−	182816.i	0.0345465	−	0.106323i
$313$	255218.	−	785479.i	0.147248	−	0.453183i	−0.850045	−	0.526710i	$-0.823425\pi$
$313$	255218.	−	785479.i	0.147248	−	0.453183i	0.997293	+	0.0735267i	$0.0234254\pi$
$314$	−568951.	−	1.75105e6i	−0.325650	−	1.00225i
$315$	340947.	−	92774.3i	0.193602	−	0.0526806i
$316$	−82201.9	+	252991.i	−0.0463089	+	0.142524i
$317$	−990858.	−	719900.i	−0.553813	−	0.402369i	0.275376	−	0.961336i	$-0.411198\pi$
$317$	−990858.	−	719900.i	−0.553813	−	0.402369i	−0.829189	+	0.558968i	$0.811198\pi$
$318$	−1.22096e6			−0.677069
$319$	1.87883e6	+	1.36505e6i	1.03374	+	0.751054i
$320$	143407.	−	178503.i	0.0782880	−	0.0974474i
$321$	555863.	−	403858.i	0.301096	−	0.218759i
$322$	667981.	−	485317.i	0.359025	−	0.260847i
$323$	749904.	+	2.30797e6i	0.399944	+	1.23090i
$324$	104976.			0.0555556
$325$	−780400.	−	691797.i	−0.409835	−	0.363304i
$326$	−700833.			−0.365234
$327$	−582137.	−	1.79163e6i	−0.301062	−	0.926574i
$328$	−123235.	+	89535.5i	−0.0632484	+	0.0459527i
$329$	−437533.	+	317886.i	−0.222854	+	0.161913i
$330$	760006.	−	206804.i	0.384178	−	0.104538i
$331$	−373673.	−	271489.i	−0.187466	−	0.136202i	0.490094	−	0.871670i	$-0.336962\pi$
$331$	−373673.	−	271489.i	−0.187466	−	0.136202i	−0.677560	+	0.735468i	$0.736962\pi$
$332$	−1.01047e6			−0.503128
$333$	144138.	+	104723.i	0.0712310	+	0.0517524i
$334$	−86242.2	+	265426.i	−0.0423013	+	0.130190i
$335$	−11936.6	+	246003.i	−0.00581124	+	0.119765i
$336$	55558.7	+	170992.i	0.0268475	+	0.0826282i
$337$	−685943.	+	2.11111e6i	−0.329013	+	1.01260i	0.640584	+	0.767888i	$0.278693\pi$
$337$	−685943.	+	2.11111e6i	−0.329013	+	1.01260i	−0.969597	+	0.244709i	$0.921307\pi$
$338$	−321281.	+	988802.i	−0.152966	+	0.470780i
$339$	237425.	+	730720.i	0.112209	+	0.345344i
$340$	427235.	+	652336.i	0.200433	+	0.306037i
$341$	−88734.5	+	273097.i	−0.0413244	+	0.127183i
$342$	729614.	+	530096.i	0.337309	+	0.245069i
$343$	2.14787e6			0.985764
$344$	−271358.	−	197153.i	−0.123637	−	0.0898272i
$345$	64499.4	−	1.32928e6i	0.0291748	−	0.601268i
$346$	−2.21825e6	+	1.61165e6i	−0.996139	+	0.723738i
$347$	77417.2	−	56246.9i	0.0345155	−	0.0250769i	−0.570394	−	0.821371i	$-0.693209\pi$
$347$	77417.2	−	56246.9i	0.0345155	−	0.0250769i	0.604909	+	0.796294i	$0.293209\pi$
$348$	264042.	+	812639.i	0.116876	+	0.359707i
$349$	2.90872e6			1.27832			0.639158	−	0.769076i	$-0.279283\pi$
$349$	2.90872e6			1.27832			0.639158	+	0.769076i	$0.279283\pi$
$350$	970851.	+	94437.8i	0.423626	+	0.0412075i
$351$	243284.			0.105401
$352$	123846.	+	381160.i	0.0532753	+	0.163965i
$353$	280732.	−	203964.i	0.119910	−	0.0871198i	−0.526214	−	0.850352i	$-0.676389\pi$
$353$	280732.	−	203964.i	0.119910	−	0.0871198i	0.646124	+	0.763232i	$0.276389\pi$
$354$	−1.46509e6	+	1.06445e6i	−0.621379	+	0.451458i
$355$	3.03734e6	+	1.15244e6i	1.27915	+	0.485341i
$356$	−397627.	−	288893.i	−0.166284	−	0.120813i
$357$	−612298.			−0.254268
$358$	145889.	+	105995.i	0.0601612	+	0.0437097i
$359$	728845.	−	2.24316e6i	0.298469	−	0.918593i	−0.683565	−	0.729890i	$-0.739571\pi$
$359$	728845.	−	2.24316e6i	0.298469	−	0.918593i	0.982034	−	0.188704i	$-0.0604286\pi$
$360$	270947.	+	102804.i	0.110186	+	0.0418073i
$361$	1.62906e6	+	5.01373e6i	0.657914	+	2.02485i
$362$	−49358.0	+	151908.i	−0.0197964	+	0.0609271i
$363$	21891.4	−	67374.9i	0.00871982	−	0.0268369i
$364$	128758.	+	396278.i	0.0509357	+	0.156764i
$365$	−839192.	+	1.04457e6i	−0.329708	+	0.410398i
$366$	135395.	−	416704.i	0.0528325	−	0.162602i
$367$	−279415.	−	203007.i	−0.108289	−	0.0786766i	0.532323	−	0.846541i	$-0.321319\pi$
$367$	−279415.	−	203007.i	−0.108289	−	0.0786766i	−0.640612	+	0.767865i	$0.721319\pi$
$368$	677172.			0.260663
$369$	−155969.	−	113318.i	−0.0596312	−	0.0433246i
$370$	269471.	+	411449.i	0.102331	+	0.156247i
$371$	2.14113e6	−	1.55562e6i	0.807623	−	0.586772i
$372$	−85473.1	+	62099.8i	−0.0320237	+	0.0232666i
$373$	−653018.	−	2.00978e6i	−0.243026	−	0.747958i	−0.995955	−	0.0898555i	$-0.971359\pi$
$373$	−653018.	−	2.00978e6i	−0.243026	−	0.747958i	0.752929	−	0.658102i	$-0.228641\pi$
$374$	−1.36488e6			−0.504561
$375$	1.09874e6	−	1.12459e6i	0.403474	−	0.412967i
$376$	−443553.			−0.161799
$377$	611923.	+	1.88331e6i	0.221740	+	0.682445i
$378$	−184091.	+	133750.i	−0.0662679	+	0.0481464i
$379$	3.76520e6	−	2.73557e6i	1.34645	−	0.978251i	0.347267	−	0.937766i	$-0.387110\pi$
$379$	3.76520e6	−	2.73557e6i	1.34645	−	0.978251i	0.999180	−	0.0404853i	$-0.0128904\pi$
$380$	1.36403e6	+	2.08271e6i	0.484581	+	0.739895i
$381$	−2.05517e6	−	1.49317e6i	−0.725329	−	0.526982i
$382$	584364.			0.204892
$383$	−1.94667e6	−	1.41434e6i	−0.678101	−	0.492669i	0.194626	−	0.980877i	$-0.437651\pi$
$383$	−1.94667e6	−	1.41434e6i	−0.678101	−	0.492669i	−0.872727	+	0.488208i	$0.837651\pi$
$384$	−45566.4	+	140239.i	−0.0157695	+	0.0485334i
$385$	−1.06930e6	+	1.33099e6i	−0.367660	+	0.457637i
$386$	−244003.	−	750964.i	−0.0833541	−	0.256538i
$387$	131182.	−	403735.i	0.0445241	−	0.137031i
$388$	−334985.	+	1.03098e6i	−0.112965	+	0.347672i
$389$	542232.	+	1.66882e6i	0.181682	+	0.559159i	0.999875	−	0.0157836i	$-0.00502429\pi$
$389$	542232.	+	1.66882e6i	0.181682	+	0.559159i	−0.818194	+	0.574943i	$0.805024\pi$
$390$	627925.	+	238250.i	0.209048	+	0.0793178i
$391$	−712646.	+	2.19330e6i	−0.235739	+	0.725531i
$392$	554926.	+	403177.i	0.182398	+	0.132520i
$393$	−705681.			−0.230477
$394$	−3.32617e6	−	2.41661e6i	−1.07945	−	0.784269i
$395$	−868958.	−	329703.i	−0.280224	−	0.106324i
$396$	−410358.	+	298143.i	−0.131500	+	0.0955402i
$397$	−244905.	+	177934.i	−0.0779868	+	0.0566607i	−0.626096	−	0.779746i	$-0.715348\pi$
$397$	−244905.	+	177934.i	−0.0779868	+	0.0566607i	0.548109	+	0.836407i	$0.315348\pi$
$398$	910567.	+	2.80244e6i	0.288140	+	0.886805i
$399$	−1.95488e6			−0.614736
$400$	598647.	+	530680.i	0.187077	+	0.165838i
$401$	4.76687e6			1.48038			0.740188	−	0.672400i	$-0.234736\pi$
$401$	4.76687e6			1.48038			0.740188	+	0.672400i	$0.234736\pi$
$402$	−49013.1	−	150847.i	−0.0151268	−	0.0465555i
$403$	−198086.	+	143918.i	−0.0607562	+	0.0441419i
$404$	−1.51819e6	+	1.10303e6i	−0.462777	+	0.336227i
$405$	−17775.6	+	366340.i	−0.00538501	+	0.110981i
$406$	−1.49842e6	−	1.08867e6i	−0.451148	−	0.327778i
$407$	−860870.			−0.257603
$408$	−406268.	−	295171.i	−0.120827	−	0.0877856i
$409$	−1.77305e6	+	5.45687e6i	−0.524097	+	1.61300i	0.241997	+	0.970277i	$0.422197\pi$
$409$	−1.77305e6	+	5.45687e6i	−0.524097	+	1.61300i	−0.766094	+	0.642728i	$0.777803\pi$
$410$	−291589.	−	445221.i	−0.0856666	−	0.130802i
$411$	598045.	+	1.84059e6i	0.174634	+	0.537469i
$412$	321660.	−	989969.i	0.0933587	−	0.287328i
$413$	1.21304e6	−	3.73335e6i	0.349945	−	1.07702i
$414$	264842.	+	815099.i	0.0759426	+	0.233727i
$415$	171103.	−	3.52629e6i	0.0487683	−	1.00507i
$416$	−105601.	+	325007.i	−0.0299182	+	0.0920786i
$417$	2.47099e6	+	1.79528e6i	0.695875	+	0.505583i
$418$	−4.35764e6			−1.21986
$419$	−2.46394e6	−	1.79016e6i	−0.685638	−	0.498145i	0.189586	−	0.981864i	$-0.439286\pi$
$419$	−2.46394e6	−	1.79016e6i	−0.685638	−	0.498145i	−0.875223	+	0.483719i	$0.839286\pi$
$420$	−606128.	+	164932.i	−0.167664	+	0.0456228i
$421$	−1.92118e6	+	1.39582e6i	−0.528277	+	0.383816i	−0.819713	−	0.572774i	$-0.805867\pi$
$421$	−1.92118e6	+	1.39582e6i	−0.528277	+	0.383816i	0.291436	+	0.956590i	$0.405867\pi$
$422$	2.89439e6	−	2.10289e6i	0.791180	−	0.574826i
$423$	−173473.	−	533896.i	−0.0471391	−	0.145079i
$424$	2.17059e6			0.586359
$425$	−2.34883e6	+	1.38048e6i	−0.630783	+	0.370731i
$426$	−2.09207e6			−0.558538
$427$	293487.	+	903261.i	0.0778968	+	0.239742i
$428$	−988202.	+	717970.i	−0.260757	+	0.189451i
$429$	−951013.	+	690952.i	−0.249484	+	0.181261i
$430$	733965.	−	913588.i	0.191427	−	0.238276i
$431$	2.60750e6	+	1.89446e6i	0.676132	+	0.491239i	0.872072	−	0.489377i	$-0.162776\pi$
$431$	2.60750e6	+	1.89446e6i	0.676132	+	0.491239i	−0.195940	+	0.980616i	$0.562776\pi$
$432$	−186624.			−0.0481125
$433$	−4.35991e6	−	3.16766e6i	−1.11753	−	0.811931i	−0.133695	−	0.991023i	$-0.542684\pi$
$433$	−4.35991e6	−	3.16766e6i	−1.11753	−	0.811931i	−0.983832	+	0.179092i	$0.942684\pi$
$434$	70768.4	−	217803.i	0.0180349	−	0.0555059i
$435$	−2.88062e6	+	783838.i	−0.729898	+	0.198611i
$436$	1.03491e6	+	3.18513e6i	0.260727	+	0.802437i
$437$	−2.27526e6	+	7.00255e6i	−0.569939	+	1.75409i
$438$	266647.	−	820655.i	0.0664127	−	0.204397i
$439$	1.76169e6	+	5.42194e6i	0.436284	+	1.34274i	0.891765	+	0.452499i	$0.149467\pi$
$439$	1.76169e6	+	5.42194e6i	0.436284	+	1.34274i	−0.455481	+	0.890245i	$0.650533\pi$
$440$	−1.35112e6	+	367651.i	−0.332708	+	0.0905323i
$441$	−268265.	+	825636.i	−0.0656853	+	0.202159i
$442$	−941534.	−	684065.i	−0.229235	−	0.166549i
$443$	4.80140e6			1.16241			0.581204	−	0.813758i	$-0.302582\pi$
$443$	4.80140e6			1.16241			0.581204	+	0.813758i	$0.302582\pi$
$444$	−256246.	−	186174.i	−0.0616879	−	0.0448189i
$445$	1.07549e6	−	1.33870e6i	0.257459	−	0.320467i
$446$	2.44251e6	−	1.77458e6i	0.581431	−	0.422435i
$447$	2.58621e6	−	1.87899e6i	0.612202	−	0.444791i
$448$	−98771.1	−	303986.i	−0.0232506	−	0.0715581i
$449$	5.33912e6			1.24984			0.624920	−	0.780689i	$-0.285132\pi$
$449$	5.33912e6			1.24984			0.624920	+	0.780689i	$0.285132\pi$
$450$	−404639.	+	928129.i	−0.0941968	+	0.216061i
$451$	931531.			0.215653
$452$	−422089.	−	1.29906e6i	−0.0971758	−	0.299076i
$453$	−447482.	+	325114.i	−0.102454	+	0.0744373i
$454$	2.02677e6	−	1.47253e6i	0.461492	−	0.335294i
$455$	−1.40471e6	+	382233.i	−0.318097	+	0.0865565i
$456$	−1.29709e6	−	942392.i	−0.292118	−	0.212236i
$457$	2.44745e6			0.548180			0.274090	−	0.961704i	$-0.411623\pi$
$457$	2.44745e6			0.548180			0.274090	+	0.961704i	$0.411623\pi$
$458$	−1.39051e6	−	1.01026e6i	−0.309748	−	0.225045i
$459$	196400.	−	604458.i	0.0435122	−	0.133917i
$460$	−114666.	+	2.36316e6i	−0.0252661	+	0.520713i
$461$	1.66371e6	+	5.12036e6i	0.364606	+	1.12214i	0.950227	+	0.311558i	$0.100851\pi$
$461$	1.66371e6	+	5.12036e6i	0.364606	+	1.12214i	−0.585621	+	0.810585i	$0.699149\pi$
$462$	339761.	−	1.04568e6i	0.0740573	−	0.227925i
$463$	1.62951e6	−	5.01510e6i	0.353267	−	1.08724i	−0.603740	−	0.797181i	$-0.706324\pi$
$463$	1.62951e6	−	5.01510e6i	0.353267	−	1.08724i	0.957007	−	0.290064i	$-0.0936765\pi$
$464$	−469409.	−	1.44469e6i	−0.101218	−	0.311516i
$465$	−202240.	−	308795.i	−0.0433745	−	0.0662275i
$466$	−1.38615e6	+	4.26614e6i	−0.295696	+	0.910060i
$467$	−665137.	−	483250.i	−0.141130	−	0.102537i	0.514980	−	0.857202i	$-0.327799\pi$
$467$	−665137.	−	483250.i	−0.141130	−	0.102537i	−0.656110	+	0.754665i	$0.727799\pi$
$468$	−432505.			−0.0912801
$469$	278145.	+	202085.i	0.0583902	+	0.0424230i
$470$	75106.8	−	1.54789e6i	0.0156832	−	0.323218i
$471$	−3.35145e6	+	2.43497e6i	−0.696115	+	0.505757i
$472$	2.60461e6	−	1.89236e6i	0.538130	−	0.390974i
$473$	633853.	+	1.95080e6i	0.130267	+	0.400921i
$474$	598525.			0.122359
$475$	−7.49912e6	+	4.40747e6i	−1.52502	+	0.896305i
$476$	1.08853e6			0.220203
$477$	848917.	+	2.61270e6i	0.170832	+	0.525767i
$478$	−4.35732e6	+	3.16578e6i	−0.872267	+	0.633739i
$479$	−360586.	+	261981.i	−0.0718076	+	0.0521713i	−0.623110	−	0.782134i	$-0.714131\pi$
$479$	−360586.	+	261981.i	−0.0718076	+	0.0521713i	0.551302	+	0.834306i	$0.314131\pi$
$480$	−481683.	−	182762.i	−0.0954242	−	0.0362062i
$481$	−593855.	−	431461.i	−0.117036	−	0.0850313i
$482$	215773.			0.0423038
$483$	−1.50296e6	−	1.09196e6i	−0.293143	−	0.212981i
$484$	−38918.1	+	119778.i	−0.00755159	+	0.0232414i
$485$	−3.54113e6	−	1.34359e6i	−0.683577	−	0.259365i
$486$	−72988.6	−	224636.i	−0.0140173	−	0.0431408i
$487$	2.52651e6	−	7.77581e6i	0.482724	−	1.48567i	−0.352525	−	0.935802i	$-0.614677\pi$
$487$	2.52651e6	−	7.77581e6i	0.482724	−	1.48567i	0.835250	−	0.549871i	$-0.185323\pi$
$488$	−240703.	+	740808.i	−0.0457543	+	0.140817i
$489$	487281.	+	1.49970e6i	0.0921526	+	0.283616i
$490$	−1.50095e6	+	1.86828e6i	−0.282408	+	0.351522i
$491$	2.33124e6	−	7.17482e6i	0.436399	−	1.34310i	−0.455248	−	0.890365i	$-0.650449\pi$
$491$	2.33124e6	−	7.17482e6i	0.436399	−	1.34310i	0.891646	−	0.452732i	$-0.149551\pi$
$492$	277279.	+	201455.i	0.0516421	+	0.0375202i
$493$	5.17322e6			0.958614
$494$	−3.00604e6	−	2.18401e6i	−0.554213	−	0.402659i
$495$	−970958.	−	1.48253e6i	−0.178110	−	0.271951i
$496$	151952.	−	110400.i	0.0277334	−	0.0201495i
$497$	3.66876e6	−	2.66551e6i	0.666236	−	0.484049i
$498$	702568.	+	2.16228e6i	0.126945	+	0.390696i
$499$	−7.45209e6			−1.33976			−0.669880	−	0.742470i	$-0.733654\pi$
$499$	−7.45209e6			−1.33976			−0.669880	+	0.742470i	$0.733654\pi$
$500$	−1.95331e6	+	1.99927e6i	−0.349419	+	0.357640i
$501$	627943.			0.111770
$502$	1.75067e6	+	5.38801e6i	0.310059	+	0.954265i
$503$	−65245.7	+	47403.8i	−0.0114983	+	0.00835397i	−0.593520	−	0.804820i	$-0.702262\pi$
$503$	−65245.7	+	47403.8i	−0.0114983	+	0.00835397i	0.582021	+	0.813174i	$0.302262\pi$
$504$	327273.	−	237778.i	0.0573897	−	0.0416960i
$505$	−3.59222e6	−	5.48487e6i	−0.626807	−	0.957057i
$506$	−3.35025e6	−	2.43410e6i	−0.581702	−	0.422632i
$507$	2.33930e6			0.404172
$508$	3.65363e6	+	2.65452e6i	0.628153	+	0.456380i
$509$	710399.	−	2.18638e6i	0.121537	−	0.374052i	−0.871717	−	0.490009i	$-0.836993\pi$
$509$	710399.	−	2.18638e6i	0.121537	−	0.374052i	0.993254	+	0.115957i	$0.0369935\pi$
$510$	1.09887e6	−	1.36779e6i	0.187077	−	0.232860i
$511$	577992.	+	1.77888e6i	0.0979195	+	0.301365i
$512$	81007.0	−	249314.i	0.0136568	−	0.0420312i
$513$	627048.	−	1.92985e6i	0.105198	−	0.323766i
$514$	−2.44729e6	−	7.53199e6i	−0.408581	−	1.25748i
$515$	3.40028e6	+	1.29015e6i	0.564932	+	0.214349i
$516$	−233212.	+	717752.i	−0.0385590	+	0.118672i
$517$	2.19444e6	+	1.59435e6i	0.361075	+	0.262336i
$518$	686570.			0.112424
$519$	4.99106e6	+	3.62622e6i	0.813344	+	0.590929i
$520$	−1.11631e6	−	423555.i	−0.181041	−	0.0686912i
$521$	−2.10744e6	+	1.53115e6i	−0.340143	+	0.247128i	−0.744722	−	0.667375i	$-0.767418\pi$
$521$	−2.10744e6	+	1.53115e6i	−0.340143	+	0.247128i	0.404579	+	0.914503i	$0.367418\pi$
$522$	1.55536e6	−	1.13004e6i	0.249836	−	0.181516i
$523$	−3.74450e6	−	1.15244e7i	−0.598603	−	1.84231i	−0.535903	−	0.844279i	$-0.680029\pi$
$523$	−3.74450e6	−	1.15244e7i	−0.598603	−	1.84231i	−0.0627002	−	0.998032i	$-0.519971\pi$
$524$	1.25454e6			0.199599
$525$	−472936.	−	2.14316e6i	−0.0748866	−	0.339357i
$526$	2.74793e6			0.433053
$527$	197662.	+	608343.i	0.0310026	+	0.0954161i
$528$	729526.	−	530032.i	0.113882	−	0.0827403i
$529$	−453661.	+	329604.i	−0.0704843	+	0.0512099i
$530$	−367546.	+	7.57482e6i	−0.0568359	+	1.17134i
$531$	3.29646e6	+	2.39502e6i	0.507354	+	0.368614i
$532$	3.47535e6			0.532377
$533$	642599.	+	466876.i	0.0979766	+	0.0711841i
$534$	−341730.	+	1.05174e6i	−0.0518597	+	0.159608i
$535$	−2.33821e6	−	3.57015e6i	−0.353182	−	0.539265i
$536$	87134.3	+	268172.i	0.0131002	+	0.0403182i
$537$	125381.	−	385883.i	0.0187627	−	0.0577457i
$538$	1.69642e6	−	5.22105e6i	0.252684	−	0.777682i
$539$	−1.29622e6	−	3.98937e6i	−0.192180	−	0.591469i
$540$	31601.1	−	651271.i	0.00466356	−	0.0961120i
$541$	−944626.	+	2.90726e6i	−0.138761	+	0.427062i	−0.996156	−	0.0875967i	$-0.972081\pi$
$541$	−944626.	+	2.90726e6i	−0.138761	+	0.427062i	0.857395	+	0.514659i	$0.172081\pi$
$542$	4.47224e6	+	3.24927e6i	0.653923	+	0.475103i
$543$	359384.			0.0523069
$544$	722254.	+	524748.i	0.104639	+	0.0760246i
$545$	−1.12905e7	+	3.07224e6i	−1.62826	+	0.443062i
$546$	758462.	−	551055.i	0.108881	−	0.0791067i
$547$	−3.14735e6	+	2.28668e6i	−0.449755	+	0.326766i	−0.789499	−	0.613752i	$-0.789660\pi$
$547$	−3.14735e6	+	2.28668e6i	−0.449755	+	0.326766i	0.339744	+	0.940518i	$0.389660\pi$
$548$	−1.06319e6	−	3.27217e6i	−0.151238	−	0.465462i
$549$	−985835.			−0.139596
$550$	−1.05422e6	−	4.77734e6i	−0.148602	−	0.673409i
$551$	1.65165e7			2.31761
$552$	−470830.	−	1.44906e6i	−0.0657682	−	0.202414i
$553$	−1.04960e6	+	762580.i	−0.145953	+	0.106041i
$554$	2.72178e6	−	1.97749e6i	0.376772	−	0.273741i
$555$	693090.	−	862710.i	0.0955118	−	0.118886i
$556$	−4.39288e6	−	3.19161e6i	−0.602646	−	0.437848i
$557$	−8.79718e6			−1.20145			−0.600725	−	0.799456i	$-0.705121\pi$
$557$	−8.79718e6			−1.20145			−0.600725	+	0.799456i	$0.705121\pi$
$558$	192314.	+	139725.i	0.0261473	+	0.0189971i
$559$	−540473.	+	1.66340e6i	−0.0731550	+	0.225148i
$560$	1.07756e6	−	293212.i	0.145202	−	0.0395105i
$561$	948982.	+	2.92067e6i	0.127307	+	0.391809i
$562$	1.95042e6	−	6.00277e6i	0.260488	−	0.801699i
$563$	−736326.	+	2.26618e6i	−0.0979037	+	0.301317i	−0.988000	−	0.154457i	$-0.950637\pi$
$563$	−736326.	+	2.26618e6i	−0.0979037	+	0.301317i	0.890096	+	0.455773i	$0.150637\pi$
$564$	308397.	+	949148.i	0.0408237	+	0.125642i
$565$	4.60486e6	−	1.25302e6i	0.606869	−	0.165134i
$566$	−1.43371e6	+	4.41251e6i	−0.188114	+	0.578955i
$567$	414205.	+	300937.i	0.0541075	+	0.0393114i
$568$	3.71924e6			0.483708
$569$	−7.07810e6	−	5.14254e6i	−0.916507	−	0.665882i	0.0261448	−	0.999658i	$-0.491677\pi$
$569$	−7.07810e6	−	5.14254e6i	−0.916507	−	0.665882i	−0.942652	+	0.333777i	$0.891677\pi$
$570$	3.50835e6	−	4.36695e6i	0.452289	−	0.562978i
$571$	1.65507e6	−	1.20248e6i	0.212434	−	0.154343i	−0.476480	−	0.879185i	$-0.658088\pi$
$571$	1.65507e6	−	1.20248e6i	0.212434	−	0.154343i	0.688914	+	0.724843i	$0.258088\pi$
$572$	1.69069e6	−	1.22836e6i	0.216060	−	0.156977i
$573$	−406301.	−	1.25047e6i	−0.0516966	−	0.159106i
$574$	−742924.			−0.0941162
$575$	−8.22743e6	−	800309.i	−1.03775	−	0.100946i
$576$	331776.			0.0416667
$577$	701100.	+	2.15776e6i	0.0876678	+	0.269814i	0.985274	−	0.170985i	$-0.0546951\pi$
$577$	701100.	+	2.15776e6i	0.0876678	+	0.269814i	−0.897606	+	0.440799i	$0.854695\pi$
$578$	2.13505e6	−	1.55121e6i	0.265821	−	0.193130i
$579$	−1.43732e6	+	1.04427e6i	−0.178179	+	0.129455i
$580$	5.12110e6	−	1.39349e6i	0.632110	−	0.172002i
$581$	−3.98702e6	−	2.89674e6i	−0.490014	−	0.356016i
$582$	2.43908e6			0.298482
$583$	−1.07388e7	−	7.80220e6i	−1.30853	−	0.950705i
$584$	−474039.	+	1.45894e6i	−0.0575151	+	0.177013i
$585$	73236.1	−	1.50933e6i	0.00884780	−	0.182346i
$586$	−517076.	−	1.59140e6i	−0.0622029	−	0.191441i
$587$	3.78020e6	−	1.16343e7i	0.452814	−	1.39362i	−0.420868	−	0.907122i	$-0.638275\pi$
$587$	3.78020e6	−	1.16343e7i	0.452814	−	1.39362i	0.873682	−	0.486497i	$-0.161725\pi$
$588$	476916.	−	1.46780e6i	0.0568851	−	0.175074i
$589$	631077.	+	1.94226e6i	0.0749539	+	0.230684i
$590$	6.16282e6	+	9.40986e6i	0.728869	+	1.11289i
$591$	−2.85859e6	+	8.79784e6i	−0.336654	+	1.03611i
$592$	455549.	+	330975.i	0.0534233	+	0.0388143i
$593$	1.41409e7			1.65135			0.825675	−	0.564146i	$-0.190794\pi$
$593$	1.41409e7			1.65135			0.825675	+	0.564146i	$0.190794\pi$
$594$	923306.	+	670821.i	0.107369	+	0.0780083i
$595$	−184321.	+	3.79869e6i	−0.0213443	+	0.439888i
$596$	−4.59771e6	+	3.34043e6i	−0.530183	+	0.385200i
$597$	5.36376e6	−	3.89700e6i	0.615933	−	0.447502i
$598$	−1.09116e6	−	3.35824e6i	−0.124777	−	0.384024i
$599$	432118.			0.0492080			0.0246040	−	0.999697i	$-0.492168\pi$
$599$	432118.			0.0492080			0.0246040	+	0.999697i	$0.492168\pi$
$600$	719358.	−	1.65001e6i	0.0815768	−	0.187115i
$601$	2.17670e6			0.245817			0.122908	−	0.992418i	$-0.460778\pi$
$601$	2.17670e6			0.245817			0.122908	+	0.992418i	$0.460778\pi$
$602$	−505516.	−	1.55582e6i	−0.0568518	−	0.174972i
$603$	−288715.	+	209764.i	−0.0323353	+	0.0234929i
$604$	795523.	−	577981.i	0.0887279	−	0.0644646i
$605$	−411404.	−	156096.i	−0.0456962	−	0.0173382i
$606$	3.41592e6	+	2.48181e6i	0.377856	+	0.274528i
$607$	−1.78166e6			−0.196270			−0.0981349	−	0.995173i	$-0.531288\pi$
$607$	−1.78166e6			−0.196270			−0.0981349	+	0.995173i	$0.531288\pi$
$608$	2.30594e6	+	1.67536e6i	0.252982	+	0.183802i
$609$	−1.28778e6	+	3.96337e6i	−0.140701	+	0.433034i
$610$	−2.54448e6	−	965435.i	−0.276869	−	0.105051i
$611$	714716.	+	2.19967e6i	0.0774516	+	0.238372i
$612$	−349156.	+	1.07459e6i	−0.0376826	+	0.115975i
$613$	2.92856e6	−	9.01317e6i	0.314777	−	0.968783i	−0.661070	−	0.750324i	$-0.729897\pi$
$613$	2.92856e6	−	9.01317e6i	0.314777	−	0.968783i	0.975846	−	0.218458i	$-0.0701027\pi$
$614$	−2.72517e6	−	8.38721e6i	−0.291724	−	0.897835i
$615$	−749979.	+	933522.i	−0.0799579	+	0.0995260i
$616$	−604019.	+	1.85898e6i	−0.0641355	+	0.197389i
$617$	1.49452e6	+	1.08583e6i	0.158048	+	0.114829i	0.663998	−	0.747734i	$-0.268858\pi$
$617$	1.49452e6	+	1.08583e6i	0.158048	+	0.114829i	−0.505950	+	0.862563i	$0.668858\pi$
$618$	−2.34206e6			−0.246676
$619$	−1.27303e6	−	924909.i	−0.133540	−	0.0970225i	0.519010	−	0.854768i	$-0.326301\pi$
$619$	−1.27303e6	−	924909.i	−0.133540	−	0.0970225i	−0.652550	+	0.757746i	$0.726301\pi$
$620$	359537.	+	548969.i	0.0375634	+	0.0573547i
$621$	1.56007e6	−	1.13346e6i	0.162336	−	0.117944i
$622$	8.26172e6	−	6.00249e6i	0.856238	−	0.622094i
$623$	−740744.	−	2.27978e6i	−0.0764624	−	0.235327i
$624$	768897.			0.0790509
$625$	−6.64620e6	−	7.15510e6i	−0.680571	−	0.732682i
$626$	3.30361e6			0.336940
$627$	3.02981e6	+	9.32481e6i	0.307785	+	0.947264i
$628$	5.95814e6	−	4.32884e6i	0.602853	−	0.437998i
$629$	−1.55141e6	+	1.12717e6i	−0.156351	+	0.113596i
$630$	774368.	+	1.18236e6i	0.0777313	+	0.118686i
$631$	−4.87716e6	−	3.54346e6i	−0.487634	−	0.354287i	0.316640	−	0.948546i	$-0.397445\pi$
$631$	−4.87716e6	−	3.54346e6i	−0.487634	−	0.354287i	−0.804274	+	0.594259i	$0.797445\pi$
$632$	−1.06404e6			−0.105966
$633$	−6.51237e6	−	4.73151e6i	−0.645996	−	0.469343i
$634$	1.51390e6	−	4.65929e6i	0.149580	−	0.460359i
$635$	−9.88228e6	+	1.23008e7i	−0.972574	+	1.21059i
$636$	−1.50919e6	−	4.64480e6i	−0.147945	−	0.455328i
$637$	1.10526e6	−	3.40165e6i	0.107924	−	0.332155i
$638$	−2.87059e6	+	8.83478e6i	−0.279203	+	0.859298i
$639$	1.45459e6	+	4.47678e6i	0.140925	+	0.433724i
$640$	856326.	+	324910.i	0.0826398	+	0.0313555i
$641$	−1.60199e6	+	4.93043e6i	−0.153998	+	0.473957i	−0.998058	−	0.0622915i	$-0.980159\pi$
$641$	−1.60199e6	+	4.93043e6i	−0.153998	+	0.473957i	0.844060	+	0.536249i	$0.180159\pi$
$642$	2.22345e6	+	1.61543e6i	0.212907	+	0.154686i
$643$	−1.65767e7			−1.58114			−0.790570	−	0.612371i	$-0.790216\pi$
$643$	−1.65767e7			−1.58114			−0.790570	+	0.612371i	$0.790216\pi$
$644$	2.67192e6	+	1.94127e6i	0.253869	+	0.184447i
$645$	−2.46528e6	−	935387.i	−0.233328	−	0.0885304i
$646$	−7.85309e6	+	5.70561e6i	−0.740388	+	0.537923i
$647$	−1.20624e7	+	8.76383e6i	−1.13285	+	0.823063i	−0.986107	−	0.166111i	$-0.946879\pi$
$647$	−1.20624e7	+	8.76383e6i	−1.13285	+	0.823063i	−0.146743	+	0.989175i	$0.546879\pi$
$648$	129757.	+	399352.i	0.0121393	+	0.0373610i
$649$	−1.96882e7			−1.83482
$650$	1.66713e6	−	3.82392e6i	0.154769	−	0.354998i
$651$	−515275.			−0.0476526
$652$	−866277.	−	2.66613e6i	−0.0798065	−	0.245619i
$653$	1.33537e7	−	9.70202e6i	1.22551	−	0.890388i	0.228968	−	0.973434i	$-0.426465\pi$
$653$	1.33537e7	−	9.70202e6i	1.22551	−	0.890388i	0.996546	+	0.0830465i	$0.0264650\pi$
$654$	6.09622e6	−	4.42916e6i	0.557335	−	0.404928i
$655$	−212432.	+	4.37805e6i	−0.0193471	+	0.398728i
$656$	−492940.	−	358142.i	−0.0447234	−	0.0324934i
$657$	−1.94150e6			−0.175478
$658$	−1.75013e6	−	1.27154e6i	−0.157582	−	0.114490i
$659$	1.80865e6	−	5.56645e6i	0.162234	−	0.499304i	−0.836588	−	0.547832i	$-0.815453\pi$
$659$	1.80865e6	−	5.56645e6i	0.162234	−	0.499304i	0.998822	+	0.0485283i	$0.0154531\pi$
$660$	1.72615e6	+	2.63561e6i	0.154247	+	0.235517i
$661$	−1.55163e6	−	4.77544e6i	−0.138129	−	0.425118i	0.857934	−	0.513759i	$-0.171748\pi$
$661$	−1.55163e6	−	4.77544e6i	−0.138129	−	0.425118i	−0.996064	+	0.0886412i	$0.971748\pi$
$662$	570922.	−	1.75712e6i	0.0506328	−	0.155832i
$663$	−809177.	+	2.49039e6i	−0.0714923	+	0.220031i
$664$	−1.24901e6	−	3.84406e6i	−0.109937	−	0.338353i
$665$	−588481.	+	1.21281e7i	−0.0516034	+	1.06350i
$666$	−220224.	+	677780.i	−0.0192388	+	0.0592111i
$667$	1.26983e7	+	9.22585e6i	1.10517	+	0.802956i
$668$	−1.11634e6			−0.0967958
$669$	−5.49564e6	−	3.99282e6i	−0.474737	−	0.344916i
$670$	−950607.	+	258667.i	−0.0818115	+	0.0222615i
$671$	3.85370e6	−	2.79987e6i	0.330424	−	0.240067i
$672$	−581819.	+	422716.i	−0.0497009	+	0.0361098i
$673$	5.83974e6	+	1.79729e7i	0.496999	+	1.52961i	0.813818	+	0.581120i	$0.197385\pi$
$673$	5.83974e6	+	1.79729e7i	0.496999	+	1.52961i	−0.316818	+	0.948486i	$0.602615\pi$
$674$	−8.87903e6			−0.752862
$675$	2.26742e6	+	220560.i	0.191546	+	0.0186323i
$676$	−4.15875e6			−0.350023
$677$	2.75763e6	+	8.48710e6i	0.231240	+	0.711685i	0.997598	+	0.0692705i	$0.0220672\pi$
$677$	2.75763e6	+	8.48710e6i	0.231240	+	0.711685i	−0.766357	+	0.642414i	$0.777933\pi$
$678$	−2.48635e6	+	1.80644e6i	−0.207725	+	0.150921i
$679$	−4.27728e6	+	3.10763e6i	−0.356036	+	0.258675i
$680$	−1.95354e6	+	2.43163e6i	−0.162013	+	0.201663i
$681$	−4.56023e6	−	3.31320e6i	−0.376807	−	0.273766i
$682$	−1.14860e6			−0.0945603
$683$	4.75817e6	+	3.45702e6i	0.390291	+	0.283563i	0.765575	−	0.643347i	$-0.222455\pi$
$683$	4.75817e6	+	3.45702e6i	0.390291	+	0.283563i	−0.375284	+	0.926910i	$0.622455\pi$
$684$	−1.11475e6	+	3.43085e6i	−0.0911041	+	0.280389i
$685$	1.15991e7	−	3.15620e6i	0.944489	−	0.257003i
$686$	2.65492e6	+	8.17099e6i	0.215397	+	0.662925i
$687$	−1.19503e6	+	3.67793e6i	−0.0966025	+	0.297312i
$688$	414598.	−	1.27600e6i	0.0333931	−	0.102773i
$689$	−3.49757e6	−	1.07644e7i	−0.280684	−	0.863858i
$690$	5.13660e6	−	1.39771e6i	0.410727	−	0.111762i
$691$	−4.14401e6	+	1.27540e7i	−0.330161	+	1.01613i	0.638896	+	0.769293i	$0.279391\pi$
$691$	−4.14401e6	+	1.27540e7i	−0.330161	+	1.01613i	−0.969057	+	0.246838i	$0.920609\pi$
$692$	−8.87300e6	−	6.44661e6i	−0.704377	−	0.511760i
$693$	−2.47385e6			−0.195677
$694$	309669.	+	224987.i	0.0244061	+	0.0177321i
$695$	1.18818e7	−	1.47896e7i	0.933081	−	1.16143i
$696$	−2.76509e6	+	2.00895e6i	−0.216364	+	0.157198i
$697$	1.67875e6	−	1.21969e6i	0.130890	−	0.0950968i
$698$	3.59537e6	+	1.10654e7i	0.279322	+	0.859665i
$699$	1.00928e7			0.781300
$700$	840775.	+	3.81007e6i	0.0648537	+	0.293892i
$701$	6.79235e6			0.522065			0.261033	−	0.965330i	$-0.415937\pi$
$701$	6.79235e6			0.522065			0.261033	+	0.965330i	$0.415937\pi$
$702$	300715.	+	925507.i	0.0230310	+	0.0708822i
$703$	−4.95319e6	+	3.59871e6i	−0.378005	+	0.274636i
$704$	−1.29693e6	+	942278.i	−0.0986249	+	0.0716552i
$705$	−3.36451e6	+	915509.i	−0.254947	+	0.0693729i
$706$	1.12293e6	+	815856.i	0.0847892	+	0.0616030i
$707$	−9.15240e6			−0.688631
$708$	−5.86037e6	−	4.25781e6i	−0.439381	−	0.319229i
$709$	3.65048e6	−	1.12350e7i	0.272731	−	0.839379i	−0.717080	−	0.696991i	$-0.754522\pi$
$709$	3.65048e6	−	1.12350e7i	0.272731	−	0.839379i	0.989811	−	0.142388i	$-0.0454781\pi$
$710$	−629779.	+	1.29792e7i	−0.0468859	+	0.966279i
$711$	−416147.	−	1.28077e6i	−0.0308726	−	0.0950160i
$712$	607520.	−	1.86975e6i	0.0449118	−	0.138224i
$713$	−599723.	+	1.84576e6i	−0.0441801	+	0.135972i
$714$	−756841.	−	2.32932e6i	−0.0555596	−	0.170995i
$715$	4.00038e6	+	6.10809e6i	0.292642	+	0.446828i
$716$	−222899.	+	686013.i	−0.0162490	+	0.0500092i
$717$	9.80396e6	+	7.12299e6i	0.712203	+	0.517446i
$718$	9.43437e6			0.682971
$719$	−1.78791e7	−	1.29899e7i	−1.28980	−	0.937097i	−0.290001	−	0.957026i	$-0.593656\pi$
$719$	−1.78791e7	−	1.29899e7i	−1.28980	−	0.937097i	−0.999801	+	0.0199297i	$0.993656\pi$
$720$	−56179.7	+	1.15782e6i	−0.00403876	+	0.0832354i
$721$	4.10715e6	−	2.98402e6i	0.294240	−	0.213778i
$722$	−1.70597e7	+	1.23946e7i	−1.21795	+	0.884893i
$723$	−150025.	−	461728.i	−0.0106737	−	0.0328504i
$724$	−638904.			−0.0452991
$725$	3.99577e6	+	1.81073e7i	0.282329	+	1.27941i
$726$	283369.			0.0199531
$727$	4.08804e6	+	1.25817e7i	0.286866	+	0.882882i	0.985833	+	0.167728i	$0.0536432\pi$
$727$	4.08804e6	+	1.25817e7i	0.286866	+	0.882882i	−0.698968	+	0.715153i	$0.746357\pi$
$728$	−1.34838e6	+	979653.i	−0.0942937	+	0.0685084i
$729$	−429945.	+	312373.i	−0.0299636	+	0.0217698i
$730$	−5.01107e6	−	1.90132e6i	−0.348036	−	0.132053i
$731$	3.69654e6	+	2.68569e6i	0.255860	+	0.185893i
$732$	1.75260e6			0.120894
$733$	1.10550e6	+	803192.i	0.0759974	+	0.0552153i	0.625135	−	0.780516i	$-0.285044\pi$
$733$	1.10550e6	+	803192.i	0.0759974	+	0.0552153i	−0.549138	+	0.835732i	$0.685044\pi$
$734$	426908.	−	1.31389e6i	0.0292479	−	0.0900156i
$735$	5.04149e6	+	1.91286e6i	0.344224	+	0.130607i
$736$	837031.	+	2.57612e6i	0.0569570	+	0.175295i
$737$	532856.	−	1.63996e6i	0.0361361	−	0.111215i
$738$	238300.	−	733412.i	0.0161058	−	0.0495686i
$739$	5.64981e6	+	1.73883e7i	0.380559	+	1.17124i	0.939651	+	0.342135i	$0.111150\pi$
$739$	5.64981e6	+	1.73883e7i	0.380559	+	1.17124i	−0.559091	+	0.829106i	$0.688850\pi$
$740$	−1.23216e6	+	1.53371e6i	−0.0827157	+	0.102959i
$741$	−2.58346e6	+	7.95107e6i	−0.172845	+	0.531961i
$742$	8.56452e6	+	6.22249e6i	0.571075	+	0.414911i
$743$	2.14819e7			1.42758			0.713790	−	0.700360i	$-0.246977\pi$
$743$	2.14819e7			1.42758			0.713790	+	0.700360i	$0.246977\pi$
$744$	−341892.	−	248399.i	−0.0226442	−	0.0164520i
$745$	−1.08787e7	−	1.66105e7i	−0.718105	−	1.09646i
$746$	6.83849e6	−	4.96846e6i	0.449897	−	0.326869i
$747$	4.13853e6	−	3.00682e6i	0.271359	−	0.197154i
$748$	−1.68708e6	−	5.19229e6i	−0.110251	−	0.339317i
$749$	−5.95738e6			−0.388017
$750$	5.63631e6	+	2.78977e6i	0.365882	+	0.181099i
$751$	2.94885e7			1.90788			0.953942	−	0.299990i	$-0.0969833\pi$
$751$	2.94885e7			1.90788			0.953942	+	0.299990i	$0.0969833\pi$
$752$	−548261.	−	1.68737e6i	−0.0353544	−	0.108810i
$753$	1.03125e7	−	7.49244e6i	0.662788	−	0.481544i
$754$	−6.40814e6	+	4.65579e6i	−0.410491	+	0.298239i
$755$	1.88230e6	+	2.87405e6i	0.120177	+	0.183496i
$756$	−736364.	−	535000.i	−0.0468585	−	0.0340447i
$757$	−1.36656e7			−0.866739			−0.433369	−	0.901216i	$-0.642675\pi$
$757$	−1.36656e7			−0.866739			−0.433369	+	0.901216i	$0.642675\pi$
$758$	1.50608e7	+	1.09423e7i	0.952082	+	0.691728i
$759$	−2.87928e6	+	8.86152e6i	−0.181418	+	0.558347i
$760$	−6.23707e6	+	7.76347e6i	−0.391694	+	0.487553i
$761$	2.38006e6	+	7.32507e6i	0.148979	+	0.458511i	0.997501	−	0.0706491i	$-0.0225070\pi$
$761$	2.38006e6	+	7.32507e6i	0.148979	+	0.458511i	−0.848522	+	0.529160i	$0.822507\pi$
$762$	3.14002e6	−	9.66398e6i	0.195905	−	0.602932i
$763$	−5.04743e6	+	1.55344e7i	−0.313877	+	0.966013i
$764$	722314.	+	2.22305e6i	0.0447706	+	0.137790i
$765$	−3.69094e6	−	1.40043e6i	−0.228025	−	0.0865182i
$766$	2.97424e6	−	9.15377e6i	0.183149	−	0.563674i
$767$	−1.35815e7	−	9.86755e6i	−0.833604	−	0.605649i
$768$	−589824.			−0.0360844
$769$	1.60260e7	+	1.16436e7i	0.977258	+	0.710020i	0.957094	−	0.289777i	$-0.0935812\pi$
$769$	1.60260e7	+	1.16436e7i	0.977258	+	0.710020i	0.0201640	+	0.999797i	$0.493581\pi$
$770$	−6.38509e6	−	2.42266e6i	−0.388097	−	0.147253i
$771$	−1.44160e7	+	1.04738e7i	−0.873389	+	0.634554i
$772$	2.55523e6	−	1.85649e6i	0.154308	−	0.112111i
$773$	2.01930e6	+	6.21477e6i	0.121549	+	0.374090i	0.993257	−	0.115937i	$-0.0369869\pi$
$773$	2.01930e6	+	6.21477e6i	0.121549	+	0.374090i	−0.871707	+	0.490027i	$0.836987\pi$
$774$	1.69805e6			0.101882
$775$	−1.97665e6	+	1.16174e6i	−0.118216	+	0.0694791i
$776$	−4.33613e6			−0.258493
$777$	−477364.	−	1.46917e6i	−0.0283659	−	0.0873013i
$778$	−5.67833e6	+	4.12555e6i	−0.336335	+	0.244362i
$779$	5.35975e6	−	3.89409e6i	0.316447	−	0.229912i
$780$	−130197.	+	2.68326e6i	−0.00766242	+	0.157916i
$781$	−1.84006e7	−	1.33688e7i	−1.07946	−	0.784270i
$782$	−9.22468e6			−0.539429
$783$	−3.49956e6	−	2.54258e6i	−0.203990	−	0.148208i
$784$	−847851.	+	2.60942e6i	−0.0492640	+	0.151619i
$785$	1.40977e7	+	2.15254e7i	0.816533	+	1.24674i
$786$	−872270.	−	2.68457e6i	−0.0503610	−	0.154995i
$787$	8.38932e6	−	2.58197e7i	0.482825	−	1.48598i	−0.352281	−	0.935894i	$-0.614594\pi$
$787$	8.38932e6	−	2.58197e7i	0.482825	−	1.48598i	0.835106	−	0.550088i	$-0.185406\pi$
$788$	5.08194e6	−	1.56406e7i	0.291551	−	0.897300i
$789$	−1.91060e6	−	5.88023e6i	−0.109264	−	0.336281i
$790$	180175.	−	3.71325e6i	0.0102713	−	0.211683i
$791$	2.05860e6	−	6.33572e6i	0.116985	−	0.360043i
$792$	−1.64143e6	−	1.19257e6i	−0.0929844	−	0.0675571i
$793$	4.06167e6			0.229362
$794$	−979620.	−	711735.i	−0.0551450	−	0.0400652i
$795$	1.64647e7	−	4.48018e6i	0.923926	−	0.251407i
$796$	−9.53558e6	+	6.92800e6i	−0.533414	+	0.387548i
$797$	5.38741e6	−	3.91418e6i	0.300424	−	0.218271i	−0.427353	−	0.904085i	$-0.640554\pi$
$797$	5.38741e6	−	3.91418e6i	0.300424	−	0.218271i	0.727777	+	0.685814i	$0.240554\pi$
$798$	−2.41637e6	−	7.43681e6i	−0.134325	−	0.413409i
$799$	6.04224e6			0.334835
$800$	−1.27886e6	+	2.93335e6i	−0.0706476	+	0.162046i
$801$	2.48819e6			0.137026
$802$	5.89217e6	+	1.81342e7i	0.323474	+	0.995551i
$803$	7.58944e6	−	5.51405e6i	0.415356	−	0.301774i
$804$	513271.	−	372913.i	0.0280031	−	0.0203455i
$805$	−7.22697e6	+	8.99563e6i	−0.393067	+	0.489263i
$806$	−792342.	−	575670.i	−0.0429611	−	0.0312131i
$807$	−1.23519e7			−0.667652
$808$	−6.07275e6	−	4.41211e6i	−0.327233	−	0.237749i
$809$	3.11448e6	−	9.58540e6i	0.167307	−	0.514919i	−0.831892	−	0.554938i	$-0.812742\pi$
$809$	3.11448e6	−	9.58540e6i	0.167307	−	0.514919i	0.999199	+	0.0400193i	$0.0127419\pi$
$810$	−1.41561e6	+	385199.i	−0.0758109	+	0.0206287i
$811$	503407.	+	1.54933e6i	0.0268762	+	0.0827163i	0.963595	−	0.267367i	$-0.0861534\pi$
$811$	503407.	+	1.54933e6i	0.0268762	+	0.0827163i	−0.936719	+	0.350083i	$0.886153\pi$
$812$	2.28938e6	−	7.04600e6i	0.121851	−	0.375018i
$813$	3.84355e6	−	1.18292e7i	0.203942	−	0.627668i
$814$	−1.06409e6	−	3.27494e6i	−0.0562884	−	0.173238i
$815$	9.45081e6	−	2.57164e6i	0.498396	−	0.135617i
$816$	620722.	−	1.91039e6i	0.0326341	−	0.100437i
$817$	1.18019e7	+	8.57461e6i	0.618584	+	0.449427i
$818$	−2.29508e7			−1.19926
$819$	−1.70654e6	−	1.23987e6i	−0.0889009	−	0.0645903i
$820$	1.33330e6	−	1.65959e6i	0.0692456	−	0.0861921i
$821$	3.01127e7	−	2.18782e7i	1.55917	−	1.13280i	0.622476	−	0.782639i	$-0.286127\pi$
$821$	3.01127e7	−	2.18782e7i	1.55917	−	1.13280i	0.936689	−	0.350161i	$-0.113873\pi$
$822$	−6.26281e6	+	4.55020e6i	−0.323288	+	0.234883i
$823$	8.66407e6	+	2.66653e7i	0.445885	+	1.37229i	0.881511	+	0.472164i	$0.156527\pi$
$823$	8.66407e6	+	2.66653e7i	0.445885	+	1.37229i	−0.435626	+	0.900128i	$0.643473\pi$
$824$	4.16366e6			0.213628
$825$	−9.48992e6	+	5.57753e6i	−0.485431	+	0.285304i
$826$	1.57019e7			0.800759
$827$	−1.59037e6	−	4.89465e6i	−0.0808601	−	0.248862i	0.902451	−	0.430792i	$-0.141766\pi$
$827$	−1.59037e6	−	4.89465e6i	−0.0808601	−	0.248862i	−0.983312	+	0.181930i	$0.941766\pi$
$828$	−2.77346e6	+	2.01504e6i	−0.140587	+	0.102143i
$829$	−4.78500e6	+	3.47651e6i	−0.241822	+	0.175694i	−0.702095	−	0.712084i	$-0.747752\pi$
$829$	−4.78500e6	+	3.47651e6i	−0.241822	+	0.175694i	0.460273	+	0.887778i	$0.347752\pi$
$830$	1.36263e7	−	3.70782e6i	0.686566	−	0.186820i
$831$	−6.12400e6	−	4.44935e6i	−0.307633	−	0.223508i
$832$	−1.36693e6			−0.0684601
$833$	−7.55940e6	−	5.49223e6i	−0.377463	−	0.274243i
$834$	−3.77534e6	+	1.16193e7i	−0.187949	+	0.578449i
$835$	189030.	−	3.89576e6i	0.00938243	−	0.193364i
$836$	−5.38634e6	−	1.65774e7i	−0.266549	−	0.820355i
$837$	165280.	−	508678.i	0.00815466	−	0.0250974i
$838$	3.76456e6	−	1.15861e7i	0.185184	−	0.569939i
$839$	−1.00614e7	−	3.09659e7i	−0.493464	−	1.51873i	−0.819337	−	0.573312i	$-0.805658\pi$
$839$	−1.00614e7	−	3.09659e7i	−0.493464	−	1.51873i	0.325874	−	0.945413i	$-0.394342\pi$
$840$	−1.37665e6	−	2.10198e6i	−0.0673173	−	0.102785i
$841$	4.54198e6	−	1.39788e7i	0.221439	−	0.681520i
$842$	−7.68471e6	−	5.58327e6i	−0.373548	−	0.271399i
$843$	−1.42013e7			−0.688271
$844$	1.15775e7	+	8.41158e6i	0.559449	+	0.406463i
$845$	704202.	−	1.45130e7i	0.0339278	−	0.699223i
$846$	1.81664e6	−	1.31986e6i	0.0872654	−	0.0634020i
$847$	−496929.	+	361040.i	−0.0238005	+	0.0172921i
$848$	2.68300e6	+	8.25742e6i	0.128124	+	0.394325i
$849$	1.04391e7			0.497042
$850$	−8.15499e6	−	7.22912e6i	−0.387147	−	0.343193i
$851$	−5.81830e6			−0.275405
$852$	−2.58594e6	−	7.95871e6i	−0.122045	−	0.375616i
$853$	6.42222e6	−	4.66601e6i	0.302212	−	0.219570i	−0.426335	−	0.904565i	$-0.640196\pi$
$853$	6.42222e6	−	4.66601e6i	0.302212	−	0.219570i	0.728548	+	0.684995i	$0.240196\pi$
$854$	−3.07344e6	+	2.23298e6i	−0.144205	+	0.104771i
$855$	−1.17841e7	−	4.47115e6i	−0.551289	−	0.209172i
$856$	−3.95281e6	−	2.87188e6i	−0.184383	−	0.133962i
$857$	−2.86619e7			−1.33307			−0.666536	−	0.745473i	$-0.732224\pi$
$857$	−2.86619e7			−1.33307			−0.666536	+	0.745473i	$0.732224\pi$
$858$	−3.80405e6	−	2.76381e6i	−0.176412	−	0.128171i
$859$	−3.83621e6	+	1.18066e7i	−0.177386	+	0.545938i	−0.999734	−	0.0230463i	$-0.992663\pi$
$859$	−3.83621e6	+	1.18066e7i	−0.177386	+	0.545938i	0.822348	+	0.568984i	$0.192663\pi$
$860$	4.38273e6	+	1.66291e6i	0.202068	+	0.0766695i
$861$	516546.	+	1.58977e6i	0.0237466	+	0.0730845i
$862$	−3.98391e6	+	1.22612e7i	−0.182617	+	0.562038i
$863$	−5.13149e6	+	1.57931e7i	−0.234540	+	0.721839i	0.762642	+	0.646820i	$0.223902\pi$
$863$	−5.13149e6	+	1.57931e7i	−0.234540	+	0.721839i	−0.997182	+	0.0750187i	$0.976098\pi$
$864$	−230680.	−	709960.i	−0.0105130	−	0.0323556i
$865$	2.39995e7	−	2.98729e7i	1.09059	−	1.35749i
$866$	6.66135e6	−	2.05015e7i	0.301834	−	0.928949i
$867$	−4.80387e6	−	3.49021e6i	−0.217042	−	0.157690i
$868$	916045.			0.0412684
$869$	5.26426e6	+	3.82471e6i	0.236477	+	0.171810i
$870$	−6.54253e6	−	9.98964e6i	−0.293054	−	0.447457i
$871$	1.18952e6	−	864234.i	0.0531282	−	0.0385999i
$872$	−1.08377e7	+	7.87407e6i	−0.482666	+	0.350678i
$873$	−1.69586e6	−	5.21932e6i	−0.0753103	−	0.231781i
$874$	−2.94516e7			−1.30416
$875$	−1.34386e7	+	2.28894e6i	−0.593379	+	0.101068i
$876$	3.45155e6			0.151969
$877$	19418.4	+	59763.6i	0.000852539	+	0.00262384i	0.951482	−	0.307705i	$-0.0995609\pi$
$877$	19418.4	+	59763.6i	0.000852539	+	0.00262384i	−0.950629	+	0.310329i	$0.899561\pi$
$878$	−1.84487e7	+	1.34038e7i	−0.807662	+	0.586801i
$879$	−3.04588e6	+	2.21296e6i	−0.132966	+	0.0966053i
$880$	−3.06871e6	−	4.68553e6i	−0.133582	−	0.203964i
$881$	−2.06724e7	−	1.50194e7i	−0.897328	−	0.651947i	0.0404500	−	0.999182i	$-0.487121\pi$
$881$	−2.06724e7	−	1.50194e7i	−0.897328	−	0.651947i	−0.937778	+	0.347234i	$0.887121\pi$
$882$	−3.47250e6			−0.150304
$883$	605042.	+	439589.i	0.0261146	+	0.0189734i	0.600766	−	0.799425i	$-0.294862\pi$
$883$	605042.	+	439589.i	0.0261146	+	0.0189734i	−0.574651	+	0.818398i	$0.694862\pi$
$884$	1.43854e6	−	4.42736e6i	0.0619142	−	0.190552i
$885$	1.58510e7	−	1.97302e7i	0.680297	−	0.846787i
$886$	5.93486e6	+	1.82656e7i	0.253996	+	0.781718i
$887$	2.96889e6	−	9.13730e6i	0.126702	−	0.389950i	−0.867505	−	0.497429i	$-0.834278\pi$
$887$	2.96889e6	−	9.13730e6i	0.126702	−	0.389950i	0.994207	+	0.107478i	$0.0342777\pi$
$888$	391509.	−	1.20494e6i	0.0166613	−	0.0512783i
$889$	6.80639e6	+	2.09479e7i	0.288843	+	0.888969i
$890$	6.42210e6	+	2.43670e6i	0.271771	+	0.103116i
$891$	793511.	−	2.44218e6i	0.0334856	−	0.103058i
$892$	9.77003e6	+	7.09834e6i	0.411134	+	0.298706i
$893$	1.92910e7			0.809519
$894$	1.03448e7	+	7.51597e6i	0.432892	+	0.314515i
$895$	−2.35627e6	−	894025.i	−0.0983259	−	0.0373072i
$896$	1.03434e6	−	751495.i	0.0430423	−	0.0312720i
$897$	−6.42754e6	+	4.66988e6i	−0.266725	+	0.193787i
$898$	6.59952e6	+	2.03112e7i	0.273100	+	0.840515i
$899$	4.35349e6			0.179655
$900$	−4.03097e6	−	392106.i	−0.165884	−	0.0161360i
$901$	−2.95686e7			−1.21344
$902$	1.15144e6	+	3.54375e6i	0.0471219	+	0.145026i
$903$	−2.97778e6	+	2.16349e6i	−0.121527	+	0.0882947i
$904$	4.42018e6	−	3.21145e6i	0.179895	−	0.130701i
$905$	108186.	−	2.22962e6i	0.00439085	−	0.0904917i
$906$	−1.78993e6	−	1.30046e6i	−0.0724461	−	0.0526351i
$907$	−9.55528e6			−0.385678			−0.192839	−	0.981230i	$-0.561770\pi$
$907$	−9.55528e6			−0.385678			−0.192839	+	0.981230i	$0.561770\pi$
$908$	8.10707e6	+	5.89013e6i	0.326324	+	0.237089i
$909$	2.93572e6	−	9.03522e6i	0.117843	−	0.362685i
$910$	−3.19042e6	−	4.87138e6i	−0.127716	−	0.195006i
$911$	−2.42894e6	−	7.47551e6i	−0.0969664	−	0.298432i	0.890795	−	0.454406i	$-0.150148\pi$
$911$	−2.42894e6	−	7.47551e6i	−0.0969664	−	0.298432i	−0.987761	+	0.155974i	$0.950148\pi$
$912$	1.98178e6	−	6.09929e6i	0.0788984	−	0.242824i
$913$	−7.63812e6	+	2.35077e7i	−0.303256	+	0.933326i
$914$	3.02521e6	+	9.31064e6i	0.119782	+	0.368650i
$915$	−296767.	+	6.11612e6i	−0.0117183	+	0.241503i
$916$	2.12450e6	−	6.53855e6i	0.0836602	−	0.257480i
$917$	4.95007e6	+	3.59643e6i	0.194396	+	0.141237i
$918$	2.54226e6			0.0995665
$919$	3.91181e7	+	2.84209e7i	1.52788	+	1.11007i	0.957404	+	0.288752i	$0.0932403\pi$
$919$	3.91181e7	+	2.84209e7i	1.52788	+	1.11007i	0.570474	+	0.821316i	$0.306760\pi$
$920$	−9.13173e6	+	2.48481e6i	−0.355700	+	0.0967886i
$921$	−1.60528e7	+	1.16631e7i	−0.623594	+	0.453068i
$922$	−1.74226e7	+	1.26582e7i	−0.674970	+	0.490395i
$923$	−5.99297e6	−	1.84445e7i	−0.231546	−	0.712627i
$924$	4.39795e6			0.169461
$925$	−5.14361e6	−	4.55963e6i	−0.197658	−	0.175217i
$926$	2.10928e7			0.808362
$927$	1.62841e6	+	5.01172e6i	0.0622391	+	0.191552i
$928$	4.91571e6	−	3.57147e6i	0.187377	−	0.136137i
$929$	2.03897e7	−	1.48140e7i	0.775126	−	0.563162i	−0.128386	−	0.991724i	$-0.540980\pi$
$929$	2.03897e7	−	1.48140e7i	0.775126	−	0.563162i	0.903512	+	0.428562i	$0.140980\pi$
$930$	924745.	−	1.15106e6i	0.0350602	−	0.0436405i
$931$	−2.41349e7	−	1.75350e7i	−0.912581	−	0.663029i
$932$	−1.79427e7			−0.676626
$933$	−1.85889e7	−	1.35056e7i	−0.699116	−	0.507937i
$934$	1.01624e6	−	3.12766e6i	0.0381179	−	0.117315i
$935$	1.84055e7	−	5.00827e6i	0.688523	−	0.187352i
$936$	−534605.	−	1.64535e6i	−0.0199454	−	0.0613858i
$937$	4.35427e6	−	1.34011e7i	0.162019	−	0.498643i	−0.836785	−	0.547531i	$-0.815568\pi$
$937$	4.35427e6	−	1.34011e7i	0.162019	−	0.498643i	0.998804	+	0.0488880i	$0.0155677\pi$
$938$	−424968.	+	1.30792e6i	−0.0157707	+	0.0485371i
$939$	−2.29696e6	−	7.06931e6i	−0.0850138	−	0.261645i
$940$	5.98135e6	−	1.62757e6i	0.220790	−	0.0600787i
$941$	1.22531e7	−	3.77113e7i	0.451100	−	1.38834i	−0.424553	−	0.905403i	$-0.639569\pi$
$941$	1.22531e7	−	3.77113e7i	0.451100	−	1.38834i	0.875653	−	0.482941i	$-0.160431\pi$
$942$	−1.34058e7	−	9.73989e6i	−0.492227	−	0.357624i
$943$	6.29587e6			0.230556
$944$	1.04184e7	+	7.56943e6i	0.380515	+	0.276461i
$945$	1.99170e6	−	2.47914e6i	0.0725513	−	0.0903069i
$946$	−6.63779e6	+	4.82264e6i	−0.241155	+	0.175209i
$947$	1.97089e7	−	1.43194e7i	0.714147	−	0.518858i	−0.170362	−	0.985382i	$-0.554494\pi$
$947$	1.97089e7	−	1.43194e7i	0.714147	−	0.518858i	0.884509	+	0.466523i	$0.154494\pi$
$948$	739817.	+	2.27692e6i	0.0267364	+	0.0822863i
$949$	7.99903e6			0.288318
$950$	−2.60364e7	−	2.30804e7i	−0.935993	−	0.829725i
$951$	−1.10229e7			−0.395225
$952$	1.34550e6	+	4.14101e6i	0.0481160	+	0.148086i
$953$	−2.32671e7	+	1.69046e7i	−0.829871	+	0.602937i	−0.919523	−	0.393037i	$-0.871425\pi$
$953$	−2.32671e7	+	1.69046e7i	−0.829871	+	0.602937i	0.0896518	+	0.995973i	$0.471425\pi$
$954$	−8.88998e6	+	6.45895e6i	−0.316249	+	0.229769i
$955$	−7.88021e6	+	2.14426e6i	−0.279595	+	0.0760799i
$956$	−1.74293e7	−	1.26631e7i	−0.616786	−	0.448121i
$957$	2.09012e7			0.737721
$958$	−1.44235e6	−	1.04793e6i	−0.0507757	−	0.0368907i
$959$	5.18536e6	−	1.59589e7i	0.182068	−	0.560346i
$960$	99874.9	−	2.05834e6i	0.00349767	−	0.0720840i
$961$	−8.68055e6	−	2.67160e7i	−0.303207	−	0.933174i
$962$	907330.	−	2.79248e6i	0.0316102	−	0.0972863i
$963$	1.91089e6	−	5.88111e6i	0.0664002	−	0.204359i
$964$	266710.	+	820850.i	0.00924373	+	0.0284493i
$965$	6.04599e6	+	9.23148e6i	0.209001	+	0.319119i
$966$	2.29631e6	−	7.06733e6i	0.0791751	−	0.243676i
$967$	−1.42241e7	−	1.03344e7i	−0.489168	−	0.355401i	0.315696	−	0.948860i	$-0.397762\pi$
$967$	−1.42241e7	−	1.03344e7i	−0.489168	−	0.355401i	−0.804864	+	0.593459i	$0.797762\pi$
$968$	−503767.			−0.0172799
$969$	1.76695e7	+	1.28376e7i	0.604524	+	0.439213i
$970$	734238.	−	1.51320e7i	0.0250558	−	0.516378i
$971$	−2.99974e7	+	2.17944e7i	−1.02102	+	0.741817i	−0.966493	−	0.256695i	$-0.917367\pi$
$971$	−2.99974e7	+	2.17944e7i	−1.02102	+	0.741817i	−0.0545315	+	0.998512i	$0.517367\pi$
$972$	764346.	−	555330.i	0.0259492	−	0.0188532i
$973$	−8.18354e6	−	2.51863e7i	−0.277114	−	0.852870i
$974$	3.27039e7			1.10459
$975$	−9.34186e6	−	908713.i	−0.314718	−	0.0306137i
$976$	−3.11573e6			−0.104697
$977$	1.30545e7	+	4.01776e7i	0.437546	+	1.34663i	0.890455	+	0.455072i	$0.150387\pi$
$977$	1.30545e7	+	4.01776e7i	0.437546	+	1.34663i	−0.452908	+	0.891557i	$0.649613\pi$
$978$	−5.10287e6	+	3.70745e6i	−0.170596	+	0.123945i
$979$	−9.72650e6	+	7.06671e6i	−0.324339	+	0.235646i
$980$	−8.96265e6	−	3.40064e6i	−0.298106	−	0.113109i
$981$	−1.37165e7	−	9.96562e6i	−0.455062	−	0.330622i
$982$	3.01762e7			0.998587
$983$	2.61005e7	+	1.89631e7i	0.861520	+	0.625931i	0.928298	−	0.371837i	$-0.121272\pi$
$983$	2.61005e7	+	1.89631e7i	0.861520	+	0.625931i	−0.0667783	+	0.997768i	$0.521272\pi$
$984$	−423644.	+	1.30384e6i	−0.0139481	+	0.0429277i
$985$	5.37213e7	+	2.03831e7i	1.76423	+	0.669391i
$986$	6.39445e6	+	1.96801e7i	0.209465	+	0.644667i
$987$	−1.50410e6	+	4.62915e6i	−0.0491456	+	0.151255i
$988$	4.59281e6	−	1.41352e7i	0.149688	−	0.460692i
$989$	4.28397e6	+	1.31847e7i	0.139269	+	0.428627i
$990$	4.43972e6	−	5.52625e6i	0.143969	−	0.179202i
$991$	1.23015e7	−	3.78601e7i	0.397900	−	1.22461i	−0.528780	−	0.848759i	$-0.677350\pi$
$991$	1.23015e7	−	3.78601e7i	0.397900	−	1.22461i	0.926680	−	0.375851i	$-0.122650\pi$
$992$	607809.	+	441599.i	0.0196105	+	0.0142478i
$993$	−4.15697e6			−0.133784
$994$	1.46750e7	+	1.06620e7i	0.471100	+	0.342274i
$995$	−2.25623e7	−	3.44499e7i	−0.722481	−	1.10314i
$996$	−7.35738e6	+	5.34545e6i	−0.235004	+	0.170740i
$997$	1.72354e7	−	1.25223e7i	0.549140	−	0.398974i	−0.278328	−	0.960486i	$-0.589780\pi$
$997$	1.72354e7	−	1.25223e7i	0.549140	−	0.398974i	0.827468	+	0.561512i	$0.189780\pi$
$998$	−9.21129e6	−	2.83494e7i	−0.292748	−	0.900986i
$999$	1.60348e6			0.0508336

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.d.31.3	✓	28
25.21	even	5	inner	150.6.g.d.121.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.d.31.3	✓	28	1.1	even	1	trivial
150.6.g.d.121.3	yes	28	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-30.6277 - 46.7648i) q^{5} +(29.1246 + 21.1603i) q^{6} -78.0347 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\)	\(q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-30.6277 - 46.7648i) q^{5} +(29.1246 + 21.1603i) q^{6} -78.0347 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(140.046 - 174.319i) q^{10} +(120.944 + 372.226i) q^{11} +(-44.4984 + 136.952i) q^{12} +(-103.126 + 317.389i) q^{13} +(-96.4561 - 296.861i) q^{14} +(-470.394 - 178.479i) q^{15} +(79.1084 - 243.470i) q^{16} +(705.326 + 512.450i) q^{17} +324.000 q^{18} +(2251.90 + 1636.10i) q^{19} +(836.256 + 317.295i) q^{20} +(-568.182 + 412.809i) q^{21} +(-1266.54 + 920.194i) q^{22} +(817.413 + 2515.74i) q^{23} -576.000 q^{24} +(-1248.88 + 2864.60i) q^{25} -1334.89 q^{26} +(-225.273 - 693.320i) q^{27} +(1010.10 - 733.882i) q^{28} +(4800.50 - 3487.77i) q^{29} +(97.5341 - 2010.10i) q^{30} +(593.563 + 431.249i) q^{31} +1024.00 q^{32} +(2849.71 + 2070.44i) q^{33} +(-1077.64 + 3316.64i) q^{34} +(2390.02 + 3649.27i) q^{35} +(400.486 + 1232.57i) q^{36} +(-679.704 + 2091.91i) q^{37} +(-3440.59 + 10589.0i) q^{38} +(928.134 + 2856.50i) q^{39} +(-173.394 + 3573.50i) q^{40} +(735.494 - 2263.62i) q^{41} +(-2272.73 - 1651.23i) q^{42} +5240.89 q^{43} +(-5066.15 - 3680.77i) q^{44} +(-4369.17 + 1188.89i) q^{45} +(-8560.06 + 6219.25i) q^{46} +(5606.90 - 4073.65i) q^{47} +(-711.975 - 2191.23i) q^{48} -10717.6 q^{49} +(-12441.3 - 1210.20i) q^{50} +7846.48 q^{51} +(-1650.02 - 5078.23i) q^{52} +(-27438.2 + 19935.0i) q^{53} +(2359.09 - 1713.98i) q^{54} +(13702.8 - 17056.3i) q^{55} +(4040.41 + 2935.53i) q^{56} +25051.5 q^{57} +(19202.0 + 13951.1i) q^{58} +(-15544.9 + 47842.2i) q^{59} +(7767.42 - 2113.57i) q^{60} +(-3760.99 - 11575.1i) q^{61} +(-906.884 + 2791.10i) q^{62} +(-1953.24 + 6011.44i) q^{63} +(1265.73 + 3895.53i) q^{64} +(18001.1 - 4898.25i) q^{65} +(-4353.97 + 13400.1i) q^{66} +(-3564.38 - 2589.68i) q^{67} -13949.3 q^{68} +(19260.1 + 13993.3i) q^{69} +(-10928.4 + 13602.9i) q^{70} +(-47014.5 + 34158.0i) q^{71} +(-4193.94 + 3047.08i) q^{72} +(-7406.86 - 22796.0i) q^{73} -8798.27 q^{74} +(6060.59 + 27464.2i) q^{75} -44535.9 q^{76} +(-9437.79 - 29046.5i) q^{77} +(-9719.55 + 7061.66i) q^{78} +(13450.5 - 9772.33i) q^{79} +(-13808.7 + 3757.46i) q^{80} +(-5307.96 - 3856.46i) q^{81} +9520.43 q^{82} +(51093.0 + 37121.2i) q^{83} +(3472.42 - 10687.0i) q^{84} +(2362.04 - 48679.6i) q^{85} +(6478.10 + 19937.5i) q^{86} +(16502.6 - 50789.9i) q^{87} +(7740.39 - 23822.5i) q^{88} +(9492.50 + 29214.9i) q^{89} +(-9923.38 - 15151.8i) q^{90} +(8047.40 - 24767.4i) q^{91} +(-34240.2 - 24877.0i) q^{92} +6603.16 q^{93} +(22427.6 + 16294.6i) q^{94} +(7541.27 - 155419. i) q^{95} +(7455.90 - 5417.03i) q^{96} +(54812.6 - 39823.7i) q^{97} +(-13247.7 - 40772.1i) q^{98} +31701.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9}+O(q^{10}) \) 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9	\( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9} + 44 q^{10} - 135 q^{11} + 1008 q^{12} + 616 q^{13} - 48 q^{14} + 531 q^{15} - 1792 q^{16} - 3372 q^{17} + 9072 q^{18} + 488 q^{19} - 944 q^{20} - 387 q^{21} - 1920 q^{22} - 620 q^{23} - 16128 q^{24} + 6659 q^{25} - 1616 q^{26} + 5103 q^{27} + 688 q^{28} + 5682 q^{29} + 2844 q^{30} + 3339 q^{31} + 28672 q^{32} + 4320 q^{33} + 14032 q^{34} - 23984 q^{35} - 9072 q^{36} + 4506 q^{37} - 1528 q^{38} - 5544 q^{39} - 5056 q^{40} + 44962 q^{41} - 1548 q^{42} + 38028 q^{43} - 7680 q^{44} + 9396 q^{45} + 7480 q^{46} - 58300 q^{47} + 16128 q^{48} + 114402 q^{49} + 7476 q^{50} + 2448 q^{51} + 9856 q^{52} - 138 q^{53} + 20412 q^{54} + 96850 q^{55} + 2752 q^{56} + 1908 q^{57} + 22728 q^{58} + 40245 q^{59} - 16704 q^{60} + 79380 q^{61} - 54504 q^{62} - 972 q^{63} - 28672 q^{64} + 3532 q^{65} + 4860 q^{66} - 34352 q^{67} - 4352 q^{68} - 16830 q^{69} - 69476 q^{70} + 115860 q^{71} - 36288 q^{72} - 121214 q^{73} - 37856 q^{74} + 21969 q^{75} - 3392 q^{76} + 195005 q^{77} + 14904 q^{78} + 36224 q^{79} + 29696 q^{80} - 45927 q^{81} + 34608 q^{82} + 85051 q^{83} + 1728 q^{84} + 137496 q^{85} - 18568 q^{86} + 127062 q^{87} - 8640 q^{88} - 53826 q^{89} + 3564 q^{90} - 408104 q^{91} + 29920 q^{92} - 185166 q^{93} - 233200 q^{94} - 482004 q^{95} + 64512 q^{96} - 244169 q^{97} - 395952 q^{98} + 99630 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9 + 44 * q^10 - 135 * q^11 + 1008 * q^12 + 616 * q^13 - 48 * q^14 + 531 * q^15 - 1792 * q^16 - 3372 * q^17 + 9072 * q^18 + 488 * q^19 - 944 * q^20 - 387 * q^21 - 1920 * q^22 - 620 * q^23 - 16128 * q^24 + 6659 * q^25 - 1616 * q^26 + 5103 * q^27 + 688 * q^28 + 5682 * q^29 + 2844 * q^30 + 3339 * q^31 + 28672 * q^32 + 4320 * q^33 + 14032 * q^34 - 23984 * q^35 - 9072 * q^36 + 4506 * q^37 - 1528 * q^38 - 5544 * q^39 - 5056 * q^40 + 44962 * q^41 - 1548 * q^42 + 38028 * q^43 - 7680 * q^44 + 9396 * q^45 + 7480 * q^46 - 58300 * q^47 + 16128 * q^48 + 114402 * q^49 + 7476 * q^50 + 2448 * q^51 + 9856 * q^52 - 138 * q^53 + 20412 * q^54 + 96850 * q^55 + 2752 * q^56 + 1908 * q^57 + 22728 * q^58 + 40245 * q^59 - 16704 * q^60 + 79380 * q^61 - 54504 * q^62 - 972 * q^63 - 28672 * q^64 + 3532 * q^65 + 4860 * q^66 - 34352 * q^67 - 4352 * q^68 - 16830 * q^69 - 69476 * q^70 + 115860 * q^71 - 36288 * q^72 - 121214 * q^73 - 37856 * q^74 + 21969 * q^75 - 3392 * q^76 + 195005 * q^77 + 14904 * q^78 + 36224 * q^79 + 29696 * q^80 - 45927 * q^81 + 34608 * q^82 + 85051 * q^83 + 1728 * q^84 + 137496 * q^85 - 18568 * q^86 + 127062 * q^87 - 8640 * q^88 - 53826 * q^89 + 3564 * q^90 - 408104 * q^91 + 29920 * q^92 - 185166 * q^93 - 233200 * q^94 - 482004 * q^95 + 64512 * q^96 - 244169 * q^97 - 395952 * q^98 + 99630 * q^99

Introduction

L-functions

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