LMFDB - Embedded newform 87.6.g.b.25.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,6,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, degree $6$, 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:	$13.9533923237$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			25.11
Character	$\chi$	$=$	87.25
Dual form			87.6.g.b.7.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73808 - 7.61502i) q^{2} +(8.10872 - 3.90495i) q^{3} +(-26.1367 - 12.5868i) q^{4} +(-21.6674 + 94.9309i) q^{5} +(-15.6427 - 68.5352i) q^{6} +(-141.588 + 68.1854i) q^{7} +(14.5636 - 18.2622i) q^{8} +(50.5027 - 63.3284i) q^{9} +O(q^{10})$	\(q+(1.73808 - 7.61502i) q^{2} +(8.10872 - 3.90495i) q^{3} +(-26.1367 - 12.5868i) q^{4} +(-21.6674 + 94.9309i) q^{5} +(-15.6427 - 68.5352i) q^{6} +(-141.588 + 68.1854i) q^{7} +(14.5636 - 18.2622i) q^{8} +(50.5027 - 63.3284i) q^{9} +(685.241 + 329.995i) q^{10} +(331.912 + 416.204i) q^{11} -261.086 q^{12} +(307.139 + 385.140i) q^{13} +(273.141 + 1196.71i) q^{14} +(195.006 + 854.378i) q^{15} +(-692.543 - 868.421i) q^{16} -1203.18 q^{17} +(-394.469 - 494.649i) q^{18} +(2063.29 + 993.628i) q^{19} +(1761.18 - 2208.46i) q^{20} +(-881.840 + 1105.79i) q^{21} +(3746.30 - 1804.12i) q^{22} +(736.439 + 3226.55i) q^{23} +(46.7792 - 204.953i) q^{24} +(-5726.87 - 2757.91i) q^{25} +(3466.69 - 1669.47i) q^{26} +(162.218 - 710.722i) q^{27} +4558.88 q^{28} +(-1866.67 - 4126.34i) q^{29} +6845.04 q^{30} +(4.20140 - 18.4075i) q^{31} +(-7143.30 + 3440.03i) q^{32} +(4316.64 + 2078.78i) q^{33} +(-2091.23 + 9162.26i) q^{34} +(-3405.05 - 14918.5i) q^{35} +(-2117.07 + 1019.53i) q^{36} +(-8494.42 + 10651.7i) q^{37} +(11152.7 - 13985.0i) q^{38} +(3994.46 + 1923.63i) q^{39} +(1418.09 + 1778.23i) q^{40} +17474.0 q^{41} +(6887.93 + 8637.19i) q^{42} +(1404.76 + 6154.66i) q^{43} +(-3436.41 - 15055.9i) q^{44} +(4917.56 + 6166.42i) q^{45} +25850.2 q^{46} +(-15657.2 - 19633.5i) q^{47} +(-9006.78 - 4337.44i) q^{48} +(4919.04 - 6168.27i) q^{49} +(-30955.3 + 38816.8i) q^{50} +(-9756.26 + 4698.37i) q^{51} +(-3179.93 - 13932.2i) q^{52} +(2863.49 - 12545.8i) q^{53} +(-5130.22 - 2470.58i) q^{54} +(-46702.3 + 22490.6i) q^{55} +(-816.823 + 3578.74i) q^{56} +20610.7 q^{57} +(-34666.6 + 7042.87i) q^{58} +26440.8 q^{59} +(5657.04 - 24785.1i) q^{60} +(-18667.3 + 8989.71i) q^{61} +(-132.871 - 63.9875i) q^{62} +(-2832.53 + 12410.1i) q^{63} +(5871.01 + 25722.6i) q^{64} +(-43216.6 + 20812.0i) q^{65} +(23332.7 - 29258.2i) q^{66} +(-403.824 + 506.379i) q^{67} +(31447.2 + 15144.2i) q^{68} +(18571.1 + 23287.4i) q^{69} -119523. q^{70} +(-7621.56 - 9557.14i) q^{71} +(-421.013 - 1844.58i) q^{72} +(9924.60 + 43482.5i) q^{73} +(66348.7 + 83198.7i) q^{74} -57207.1 q^{75} +(-41421.0 - 51940.3i) q^{76} +(-75373.9 - 36298.2i) q^{77} +(21591.2 - 27074.5i) q^{78} +(11114.4 - 13937.0i) q^{79} +(97445.5 - 46927.3i) q^{80} +(-1459.96 - 6396.50i) q^{81} +(30371.2 - 133065. i) q^{82} +(51113.3 + 24614.9i) q^{83} +(36966.7 - 17802.2i) q^{84} +(26069.8 - 114219. i) q^{85} +49309.5 q^{86} +(-31249.5 - 26170.0i) q^{87} +12434.6 q^{88} +(7047.73 - 30878.1i) q^{89} +(55504.5 - 26729.6i) q^{90} +(-69748.3 - 33589.0i) q^{91} +(21363.7 - 93600.6i) q^{92} +(-37.8126 - 165.668i) q^{93} +(-176723. + 85105.5i) q^{94} +(-139032. + 174341. i) q^{95} +(-44489.9 + 55788.5i) q^{96} +(156332. + 75285.4i) q^{97} +(-38421.9 - 48179.5i) q^{98} +43120.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 10 q^{2} + 117 q^{3} - 202 q^{4} + 49 q^{5} - 90 q^{6} - 60 q^{7} + 273 q^{8} - 1053 q^{9}+O(q^{10}) $ 78 * q + 10 * q^2 + 117 * q^3 - 202 * q^4 + 49 * q^5 - 90 * q^6 - 60 * q^7 + 273 * q^8 - 1053 * q^9	\( 78 q + 10 q^{2} + 117 q^{3} - 202 q^{4} + 49 q^{5} - 90 q^{6} - 60 q^{7} + 273 q^{8} - 1053 q^{9} + 288 q^{10} + 460 q^{11} - 12294 q^{12} + 1883 q^{13} - 4565 q^{14} - 441 q^{15} - 7794 q^{16} - 9592 q^{17} + 810 q^{18} + 2538 q^{19} - 116 q^{20} + 540 q^{21} + 2812 q^{22} - 8224 q^{23} - 8064 q^{24} + 11226 q^{25} - 12824 q^{26} + 9477 q^{27} + 58598 q^{28} + 9286 q^{29} + 10008 q^{30} - 7224 q^{31} - 31647 q^{32} - 360 q^{33} - 3153 q^{34} + 27153 q^{35} - 16362 q^{36} + 17228 q^{37} - 25396 q^{38} + 11340 q^{39} - 32434 q^{40} + 57300 q^{41} + 5049 q^{42} + 33473 q^{43} + 33742 q^{44} - 6804 q^{45} - 28276 q^{46} + 87241 q^{47} - 30402 q^{48} - 72481 q^{49} - 155243 q^{50} + 2475 q^{51} - 198520 q^{52} + 161593 q^{53} - 2187 q^{54} - 123661 q^{55} - 253890 q^{56} + 31590 q^{57} + 301566 q^{58} + 64628 q^{59} + 49302 q^{60} + 87396 q^{61} - 128679 q^{62} - 15633 q^{63} + 42865 q^{64} - 136204 q^{65} + 207 q^{66} + 23066 q^{67} - 28244 q^{68} - 135144 q^{69} + 121526 q^{70} - 276862 q^{71} + 72576 q^{72} + 30459 q^{73} + 481517 q^{74} - 538758 q^{75} + 441053 q^{76} + 70464 q^{77} + 123795 q^{78} - 86879 q^{79} + 281480 q^{80} - 85293 q^{81} + 597939 q^{82} + 262084 q^{83} - 66285 q^{84} + 98649 q^{85} + 53476 q^{86} - 276039 q^{87} + 1616024 q^{88} + 37596 q^{89} + 23328 q^{90} + 87713 q^{91} - 190625 q^{92} + 65016 q^{93} - 377368 q^{94} - 169368 q^{95} - 535626 q^{96} + 683983 q^{97} - 29629 q^{98} - 133974 q^{99}+O(q^{100}) \) 78 * q + 10 * q^2 + 117 * q^3 - 202 * q^4 + 49 * q^5 - 90 * q^6 - 60 * q^7 + 273 * q^8 - 1053 * q^9 + 288 * q^10 + 460 * q^11 - 12294 * q^12 + 1883 * q^13 - 4565 * q^14 - 441 * q^15 - 7794 * q^16 - 9592 * q^17 + 810 * q^18 + 2538 * q^19 - 116 * q^20 + 540 * q^21 + 2812 * q^22 - 8224 * q^23 - 8064 * q^24 + 11226 * q^25 - 12824 * q^26 + 9477 * q^27 + 58598 * q^28 + 9286 * q^29 + 10008 * q^30 - 7224 * q^31 - 31647 * q^32 - 360 * q^33 - 3153 * q^34 + 27153 * q^35 - 16362 * q^36 + 17228 * q^37 - 25396 * q^38 + 11340 * q^39 - 32434 * q^40 + 57300 * q^41 + 5049 * q^42 + 33473 * q^43 + 33742 * q^44 - 6804 * q^45 - 28276 * q^46 + 87241 * q^47 - 30402 * q^48 - 72481 * q^49 - 155243 * q^50 + 2475 * q^51 - 198520 * q^52 + 161593 * q^53 - 2187 * q^54 - 123661 * q^55 - 253890 * q^56 + 31590 * q^57 + 301566 * q^58 + 64628 * q^59 + 49302 * q^60 + 87396 * q^61 - 128679 * q^62 - 15633 * q^63 + 42865 * q^64 - 136204 * q^65 + 207 * q^66 + 23066 * q^67 - 28244 * q^68 - 135144 * q^69 + 121526 * q^70 - 276862 * q^71 + 72576 * q^72 + 30459 * q^73 + 481517 * q^74 - 538758 * q^75 + 441053 * q^76 + 70464 * q^77 + 123795 * q^78 - 86879 * q^79 + 281480 * q^80 - 85293 * q^81 + 597939 * q^82 + 262084 * q^83 - 66285 * q^84 + 98649 * q^85 + 53476 * q^86 - 276039 * q^87 + 1616024 * q^88 + 37596 * q^89 + 23328 * q^90 + 87713 * q^91 - 190625 * q^92 + 65016 * q^93 - 377368 * q^94 - 169368 * q^95 - 535626 * q^96 + 683983 * q^97 - 29629 * q^98 - 133974 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	1.73808	−	7.61502i	0.307252	−	1.34616i	−0.551674	−	0.834060i	$-0.686011\pi$
$2$	1.73808	−	7.61502i	0.307252	−	1.34616i	0.858926	−	0.512099i	$-0.171132\pi$
$3$	8.10872	−	3.90495i	0.520175	−	0.250503i
$3$	8.10872	−	3.90495i	0.520175	−	0.250503i
$4$	−26.1367	−	12.5868i	−0.816771	−	0.393336i
$5$	−21.6674	+	94.9309i	−0.387597	+	1.69818i	0.285299	+	0.958438i	$0.407907\pi$
$5$	−21.6674	+	94.9309i	−0.387597	+	1.69818i	−0.672897	+	0.739737i	$0.734950\pi$
$6$	−15.6427	−	68.5352i	−0.177392	−	0.777205i
$7$	−141.588	+	68.1854i	−1.09215	+	0.525952i	−0.891182	−	0.453646i	$-0.850123\pi$
$7$	−141.588	+	68.1854i	−1.09215	+	0.525952i	−0.200969	+	0.979598i	$0.564409\pi$
$8$	14.5636	−	18.2622i	0.0804533	−	0.100885i
$9$	50.5027	−	63.3284i	0.207830	−	0.260610i
$10$	685.241	+	329.995i	2.16692	+	1.04354i
$11$	331.912	+	416.204i	0.827068	+	1.03711i	0.998650	+	0.0519406i	$0.0165407\pi$
$11$	331.912	+	416.204i	0.827068	+	1.03711i	−0.171582	+	0.985170i	$0.554888\pi$
$12$	−261.086			−0.523395
$13$	307.139	+	385.140i	0.504054	+	0.632064i	0.967138	−	0.254251i	$-0.0818288\pi$
$13$	307.139	+	385.140i	0.504054	+	0.632064i	−0.463084	+	0.886314i	$0.653257\pi$
$14$	273.141	+	1196.71i	0.372450	+	1.63181i
$15$	195.006	+	854.378i	0.223779	+	0.980442i
$16$	−692.543	−	868.421i	−0.676311	−	0.848068i
$17$	−1203.18			−1.00974			−0.504869	−	0.863196i	$-0.668459\pi$
$17$	−1203.18			−1.00974			−0.504869	+	0.863196i	$0.668459\pi$
$18$	−394.469	−	494.649i	−0.286967	−	0.359845i
$19$	2063.29	+	993.628i	1.31122	+	0.631451i	0.953222	−	0.302270i	$-0.0977446\pi$
$19$	2063.29	+	993.628i	1.31122	+	0.631451i	0.358000	+	0.933722i	$0.383459\pi$
$20$	1761.18	−	2208.46i	0.984532	−	1.23456i
$21$	−881.840	+	1105.79i	−0.436357	+	0.547174i
$22$	3746.30	−	1804.12i	1.65023	−	0.794711i
$23$	736.439	+	3226.55i	0.290280	+	1.27180i	0.884137	+	0.467228i	$0.154747\pi$
$23$	736.439	+	3226.55i	0.290280	+	1.27180i	−0.593857	+	0.804571i	$0.702395\pi$
$24$	46.7792	−	204.953i	0.0165777	−	0.0726317i
$25$	−5726.87	−	2757.91i	−1.83260	−	0.882533i
$26$	3466.69	−	1669.47i	1.00573	−	0.484334i
$27$	162.218	−	710.722i	0.0428242	−	0.187625i
$28$	4558.88			1.09891
$29$	−1866.67	−	4126.34i	−0.412167	−	0.911108i
$29$	−1866.67	−	4126.34i	−0.412167	−	0.911108i
$30$	6845.04			1.38859
$31$	4.20140	−	18.4075i	0.000785217	−	0.00344026i	−0.974534	−	0.224241i	$-0.928010\pi$
$31$	4.20140	−	18.4075i	0.000785217	−	0.00344026i	0.975319	+	0.220800i	$0.0708670\pi$
$32$	−7143.30	+	3440.03i	−1.23317	+	0.593865i
$33$	4316.64	+	2078.78i	0.690019	+	0.332296i
$34$	−2091.23	+	9162.26i	−0.310244	+	1.35927i
$35$	−3405.05	−	14918.5i	−0.469844	−	2.05852i
$36$	−2117.07	+	1019.53i	−0.272257	+	0.131112i
$37$	−8494.42	+	10651.7i	−1.02007	+	1.27913i	−0.0603463	+	0.998178i	$0.519220\pi$
$37$	−8494.42	+	10651.7i	−1.02007	+	1.27913i	−0.959723	+	0.280949i	$0.909351\pi$
$38$	11152.7	−	13985.0i	1.25291	−	1.57110i
$39$	3994.46	+	1923.63i	0.420530	+	0.202516i
$40$	1418.09	+	1778.23i	0.140137	+	0.175727i
$41$	17474.0			1.62343			0.811714	−	0.584055i	$-0.198535\pi$
$41$	17474.0			1.62343			0.811714	+	0.584055i	$0.198535\pi$
$42$	6887.93	+	8637.19i	0.602511	+	0.755526i
$43$	1404.76	+	6154.66i	0.115859	+	0.507613i	0.999241	+	0.0389586i	$0.0124040\pi$
$43$	1404.76	+	6154.66i	0.115859	+	0.507613i	−0.883381	+	0.468655i	$0.844739\pi$
$44$	−3436.41	−	15055.9i	−0.267592	−	1.17240i
$45$	4917.56	+	6166.42i	0.362008	+	0.453944i
$46$	25850.2			1.80123
$47$	−15657.2	−	19633.5i	−1.03388	−	1.29644i	−0.954054	−	0.299636i	$-0.903135\pi$
$47$	−15657.2	−	19633.5i	−1.03388	−	1.29644i	−0.0798261	−	0.996809i	$-0.525437\pi$
$48$	−9006.78	−	4337.44i	−0.564243	−	0.271725i
$49$	4919.04	−	6168.27i	0.292678	−	0.367006i
$50$	−30955.3	+	38816.8i	−1.75110	+	2.19581i
$51$	−9756.26	+	4698.37i	−0.525240	+	0.252942i
$52$	−3179.93	−	13932.2i	−0.163083	−	0.714514i
$53$	2863.49	−	12545.8i	0.140025	−	0.613489i	−0.855402	−	0.517965i	$-0.826690\pi$
$53$	2863.49	−	12545.8i	0.140025	−	0.613489i	0.995427	−	0.0955248i	$-0.0304529\pi$
$54$	−5130.22	−	2470.58i	−0.239415	−	0.115296i
$55$	−46702.3	+	22490.6i	−2.08176	+	1.00252i
$56$	−816.823	+	3578.74i	−0.0348063	+	0.152496i
$57$	20610.7			0.840245
$58$	−34666.6	+	7042.87i	−1.35314	+	0.274903i
$59$	26440.8			0.988883			0.494441	−	0.869211i	$-0.335373\pi$
$59$	26440.8			0.988883			0.494441	+	0.869211i	$0.335373\pi$
$60$	5657.04	−	24785.1i	0.202867	−	0.888817i
$61$	−18667.3	+	8989.71i	−0.642329	+	0.309329i	−0.726546	−	0.687118i	$-0.758875\pi$
$61$	−18667.3	+	8989.71i	−0.642329	+	0.309329i	0.0842169	+	0.996447i	$0.473161\pi$
$62$	−132.871	−	63.9875i	−0.00438988	−	0.00211405i
$63$	−2832.53	+	12410.1i	−0.0899130	+	0.393935i
$64$	5871.01	+	25722.6i	0.179169	+	0.784990i
$65$	−43216.6	+	20812.0i	−1.26872	+	0.610986i
$66$	23332.7	−	29258.2i	0.659332	−	0.826777i
$67$	−403.824	+	506.379i	−0.0109902	+	0.0137812i	−0.787296	−	0.616575i	$-0.788520\pi$
$67$	−403.824	+	506.379i	−0.0109902	+	0.0137812i	0.776306	+	0.630356i	$0.217091\pi$
$68$	31447.2	+	15144.2i	0.824725	+	0.397167i
$69$	18571.1	+	23287.4i	0.469586	+	0.588842i
$70$	−119523.			−2.91546
$71$	−7621.56	−	9557.14i	−0.179431	−	0.225000i	0.683980	−	0.729501i	$-0.260248\pi$
$71$	−7621.56	−	9557.14i	−0.179431	−	0.225000i	−0.863411	+	0.504501i	$0.831676\pi$
$72$	−421.013	−	1844.58i	−0.00957115	−	0.0419339i
$73$	9924.60	+	43482.5i	0.217975	+	0.955009i	0.958972	+	0.283501i	$0.0914959\pi$
$73$	9924.60	+	43482.5i	0.217975	+	0.955009i	−0.740997	+	0.671508i	$0.765647\pi$
$74$	66348.7	+	83198.7i	1.40849	+	1.76619i
$75$	−57207.1			−1.17435
$76$	−41421.0	−	51940.3i	−0.822596	−	1.03150i
$77$	−75373.9	−	36298.2i	−1.44875	−	0.697683i
$78$	21591.2	−	27074.5i	0.401828	−	0.503876i
$79$	11114.4	−	13937.0i	0.200364	−	0.251248i	−0.671491	−	0.741013i	$-0.734346\pi$
$79$	11114.4	−	13937.0i	0.200364	−	0.251248i	0.871855	+	0.489764i	$0.162917\pi$
$80$	97445.5	−	46927.3i	1.70230	−	0.819786i
$81$	−1459.96	−	6396.50i	−0.0247245	−	0.108325i
$82$	30371.2	−	133065.i	0.498802	−	2.18539i
$83$	51113.3	+	24614.9i	0.814402	+	0.392195i	0.794242	−	0.607602i	$-0.207868\pi$
$83$	51113.3	+	24614.9i	0.814402	+	0.392195i	0.0201597	+	0.999797i	$0.493583\pi$
$84$	36966.7	−	17802.2i	0.571627	−	0.275281i
$85$	26069.8	−	114219.i	0.391372	−	1.71471i
$86$	49309.5			0.718926
$87$	−31249.5	−	26170.0i	−0.442634	−	0.370686i
$88$	12434.6			0.171169
$89$	7047.73	−	30878.1i	0.0943136	−	0.413215i	−0.905627	−	0.424074i	$-0.860600\pi$
$89$	7047.73	−	30878.1i	0.0943136	−	0.413215i	0.999941	+	0.0108594i	$0.00345672\pi$
$90$	55504.5	−	26729.6i	0.722308	−	0.347845i
$91$	−69748.3	−	33589.0i	−0.882938	−	0.425201i
$92$	21363.7	−	93600.6i	0.263152	−	1.15295i
$93$	−37.8126	−	165.668i	−0.000453345	−	0.00198624i
$94$	−176723.	+	85105.5i	−2.06288	+	0.993432i
$95$	−139032.	+	174341.i	−1.58054	+	1.98194i
$96$	−44489.9	+	55788.5i	−0.492701	+	0.617827i
$97$	156332.	+	75285.4i	1.68701	+	0.812422i	0.995978	+	0.0895997i	$0.0285588\pi$
$97$	156332.	+	75285.4i	1.68701	+	0.812422i	0.691034	+	0.722822i	$0.257156\pi$
$98$	−38421.9	−	48179.5i	−0.404123	−	0.506754i
$99$	43120.0			0.442171
$100$	114968.	+	144165.i	1.14968	+	1.44165i
$101$	−24563.1	−	107618.i	−0.239596	−	1.04974i	−0.941379	−	0.337350i	$-0.890469\pi$
$101$	−24563.1	−	107618.i	−0.239596	−	1.04974i	0.701783	−	0.712391i	$-0.252388\pi$
$102$	18821.0	+	82460.3i	0.179120	+	0.784774i
$103$	31432.2	+	39414.7i	0.291932	+	0.366071i	0.906070	−	0.423128i	$-0.139068\pi$
$103$	31432.2	+	39414.7i	0.291932	+	0.366071i	−0.614138	+	0.789198i	$0.710496\pi$
$104$	11506.6			0.104319
$105$	−85866.7	−	107673.i	−0.760066	−	0.953093i
$106$	−90559.2	−	43611.0i	−0.782831	−	0.376992i
$107$	19402.8	−	24330.3i	0.163834	−	0.205441i	−0.693137	−	0.720806i	$-0.743772\pi$
$107$	19402.8	−	24330.3i	0.163834	−	0.205441i	0.856971	+	0.515364i	$0.172343\pi$
$108$	−13185.5	+	16534.1i	−0.108777	+	0.136402i
$109$	98209.9	−	47295.4i	0.791752	−	0.381287i	0.00611936	−	0.999981i	$-0.498052\pi$
$109$	98209.9	−	47295.4i	0.791752	−	0.381287i	0.785632	+	0.618694i	$0.212338\pi$
$110$	90094.5	+	394730.i	0.709932	+	3.11041i
$111$	−27284.6	+	119542.i	−0.210189	+	0.920899i
$112$	157270.	+	75737.1i	1.18468	+	0.570510i
$113$	116067.	−	55894.8i	0.855089	−	0.411789i	0.0456252	−	0.998959i	$-0.485472\pi$
$113$	116067.	−	55894.8i	0.855089	−	0.411789i	0.809464	+	0.587169i	$0.199758\pi$
$114$	35823.1	−	156951.i	0.258167	−	1.13110i
$115$	−322256.			−2.27225
$116$	−3148.56	+	131344.i	−0.0217254	+	0.906287i
$117$	39901.7			0.269480
$118$	45956.2	−	201347.i	0.303836	−	1.33119i
$119$	170357.	−	82039.4i	1.10279	−	0.531074i
$120$	18442.8	+	8881.58i	0.116916	+	0.0563037i
$121$	−27223.4	+	119273.i	−0.169036	+	0.740594i
$122$	36011.5	+	157777.i	0.219049	+	0.959718i
$123$	141692.	−	68235.2i	0.844466	−	0.406674i
$124$	−341.502	+	428.230i	−0.00199452	+	0.00250105i
$125$	196177.	−	245998.i	1.12298	−	1.40817i
$126$	89580.1	+	43139.5i	0.502673	+	0.242074i
$127$	−12703.7	−	15929.9i	−0.0698909	−	0.0876405i	0.745657	−	0.666330i	$-0.232136\pi$
$127$	−12703.7	−	15929.9i	−0.0698909	−	0.0876405i	−0.815548	+	0.578689i	$0.803564\pi$
$128$	−47628.7			−0.256947
$129$	35424.5	+	44420.9i	0.187426	+	0.235025i
$130$	83370.2	+	365269.i	0.432666	+	1.89563i
$131$	−61113.5	−	267756.i	−0.311142	−	1.36320i	−0.852639	−	0.522501i	$-0.824999\pi$
$131$	−61113.5	−	267756.i	−0.311142	−	1.36320i	0.541497	−	0.840703i	$-0.317858\pi$
$132$	−86657.5	−	108665.i	−0.432884	−	0.542819i
$133$	−359889.			−1.76417
$134$	3154.21	+	3955.25i	0.0151750	+	0.0190288i
$135$	63954.7	+	30798.9i	0.302021	+	0.145446i
$136$	−17522.7	+	21972.7i	−0.0812368	+	0.101868i
$137$	50725.3	−	63607.5i	0.230900	−	0.289539i	−0.652861	−	0.757477i	$-0.726432\pi$
$137$	50725.3	−	63607.5i	0.230900	−	0.289539i	0.883761	+	0.467938i	$0.155003\pi$
$138$	209612.	−	100944.i	0.936956	−	0.451214i
$139$	−32032.7	−	140344.i	−0.140623	−	0.616109i	−0.995291	−	0.0969342i	$-0.969096\pi$
$139$	−32032.7	−	140344.i	−0.140623	−	0.616109i	0.854668	−	0.519175i	$-0.173761\pi$
$140$	−98778.9	+	432779.i	−0.425936	+	1.86615i
$141$	−203628.	−	98062.1i	−0.862561	−	0.415388i
$142$	−86024.7	+	41427.3i	−0.358016	+	0.172411i
$143$	−58354.0	+	255665.i	−0.238633	+	1.04552i
$144$	−89970.9			−0.361573
$145$	432163.	−	87798.2i	1.70698	−	0.346789i
$146$	348370.			1.35257
$147$	15800.2	−	69225.4i	0.0603074	−	0.264224i
$148$	356086.	−	171482.i	1.33629	−	0.643523i
$149$	−138783.	−	66834.5i	−0.512119	−	0.246624i	0.159932	−	0.987128i	$-0.448872\pi$
$149$	−138783.	−	66834.5i	−0.512119	−	0.246624i	−0.672052	+	0.740504i	$0.734587\pi$
$150$	−99430.5	+	435633.i	−0.360821	+	1.58086i
$151$	28401.3	+	124434.i	0.101367	+	0.444117i	0.999985	+	0.00538626i	$0.00171451\pi$
$151$	28401.3	+	124434.i	0.101367	+	0.444117i	−0.898619	+	0.438730i	$0.855428\pi$
$152$	48194.7	−	23209.4i	0.169196	−	0.0814806i
$153$	−60763.9	+	76195.5i	−0.209854	+	0.263148i
$154$	−407417.	+	510885.i	−1.38432	+	1.73589i
$155$	1656.41	+	797.685i	0.00553782	+	0.00266687i
$156$	−80189.7	−	100555.i	−0.263820	−	0.330819i
$157$	−61715.7			−0.199823			−0.0999117	−	0.994996i	$-0.531856\pi$
$157$	−61715.7			−0.199823			−0.0999117	+	0.994996i	$0.531856\pi$
$158$	−86813.2	−	108860.i	−0.276658	−	0.346918i
$159$	−25771.4	−	112912.i	−0.0808434	−	0.354198i
$160$	−171789.	−	752656.i	−0.530512	−	2.32432i
$161$	−324275.	−	406627.i	−0.985935	−	1.23632i
$162$	−51247.0			−0.153420
$163$	−86671.9	−	108683.i	−0.255511	−	0.320400i	0.637487	−	0.770461i	$-0.279974\pi$
$163$	−86671.9	−	108683.i	−0.255511	−	0.320400i	−0.892998	+	0.450060i	$0.851402\pi$
$164$	−456713.	−	219941.i	−1.32597	−	0.638553i
$165$	−290871.	+	364741.i	−0.831746	+	1.04298i
$166$	276282.	−	346446.i	0.778184	−	0.975811i
$167$	−175503.	+	84518.0i	−0.486961	+	0.234508i	−0.661220	−	0.750192i	$-0.729961\pi$
$167$	−175503.	+	84518.0i	−0.486961	+	0.234508i	0.174259	+	0.984700i	$0.444247\pi$
$168$	7351.41	+	32208.6i	0.0200954	+	0.0880439i
$169$	28621.8	−	125400.i	0.0770869	−	0.337740i
$170$	−824470.	−	397044.i	−2.18803	−	1.05370i
$171$	167126.	−	80483.9i	0.437074	−	0.210484i
$172$	40751.5	−	178544.i	0.105032	−	0.460176i
$173$	−86898.8			−0.220749			−0.110374	−	0.993890i	$-0.535205\pi$
$173$	−86898.8			−0.220749			−0.110374	+	0.993890i	$0.535205\pi$
$174$	−253600.	+	192480.i	−0.635003	+	0.481962i
$175$	998908.			2.46564
$176$	131578.	−	576479.i	0.320184	−	1.40282i
$177$	214401.	−	103250.i	0.514392	−	0.247718i
$178$	−222888.	−	107337.i	−0.527275	−	0.253922i
$179$	26322.7	−	115327.i	0.0614042	−	0.269029i	−0.934901	−	0.354907i	$-0.884512\pi$
$179$	26322.7	−	115327.i	0.0614042	−	0.269029i	0.996306	+	0.0858780i	$0.0273695\pi$
$180$	−50913.3	−	223066.i	−0.117125	−	0.513159i
$181$	26784.1	−	12898.5i	0.0607688	−	0.0292647i	−0.403253	−	0.915089i	$-0.632120\pi$
$181$	26784.1	−	12898.5i	0.0607688	−	0.0292647i	0.464021	+	0.885824i	$0.346406\pi$
$182$	−377009.	+	472755.i	−0.843672	+	1.05793i
$183$	−116264.	+	145790.i	−0.256635	+	0.321810i
$184$	69649.0	+	33541.2i	0.151660	+	0.0730355i
$185$	−827121.	−	1.03718e6i	−1.77680	−	2.22804i
$186$	−1327.29			−0.00281308
$187$	−399350.	−	500769.i	−0.835122	−	1.04721i
$188$	162105.	+	710229.i	0.334505	+	1.46556i
$189$	25492.7	+	111691.i	0.0519113	+	0.227438i
$190$	1.08596e6	+	1.36175e6i	2.18238	+	2.73661i
$191$	−484062.			−0.960102			−0.480051	−	0.877240i	$-0.659382\pi$
$191$	−484062.			−0.960102			−0.480051	+	0.877240i	$0.659382\pi$
$192$	148052.	+	185651.i	0.289842	+	0.363450i
$193$	857335.	+	412871.i	1.65675	+	0.797849i	0.999004	+	0.0446095i	$0.0142044\pi$
$193$	857335.	+	412871.i	1.65675	+	0.797849i	0.657746	+	0.753240i	$0.271510\pi$
$194$	845018.	−	1.05962e6i	1.61199	−	2.02137i
$195$	−269161.	+	337518.i	−0.506905	+	0.635638i
$196$	−206206.	+	99303.5i	−0.383408	+	0.184639i
$197$	165825.	+	726526.i	0.304428	+	1.33379i	0.863367	+	0.504576i	$0.168351\pi$
$197$	165825.	+	726526.i	0.304428	+	1.33379i	−0.558939	+	0.829209i	$0.688792\pi$
$198$	74946.0	−	328360.i	0.135858	−	0.595233i
$199$	−103814.	−	49994.1i	−0.185833	−	0.0894924i	0.338654	−	0.940911i	$-0.390028\pi$
$199$	−103814.	−	49994.1i	−0.185833	−	0.0894924i	−0.524487	+	0.851419i	$0.675743\pi$
$200$	−133769.	+	64419.9i	−0.236473	+	0.113879i
$201$	−1297.11	+	5682.99i	−0.00226457	+	0.00992172i
$202$	−862207.			−1.48673
$203$	545655.	+	456962.i	0.929348	+	0.778287i
$204$	314133.			0.528492
$205$	−378616.	+	1.65882e6i	−0.629237	+	2.75687i
$206$	354775.	−	170851.i	0.582486	−	0.280510i
$207$	241524.	+	116312.i	0.391773	+	0.188668i
$208$	121757.	−	533453.i	0.195135	−	0.854944i
$209$	271278.	+	1.18855e6i	0.429585	+	1.88214i
$210$	−969179.	+	466732.i	−1.51655	+	0.730330i
$211$	−293539.	+	368086.i	−0.453900	+	0.569172i	−0.955147	−	0.296132i	$-0.904303\pi$
$211$	−293539.	+	368086.i	−0.453900	+	0.569172i	0.501247	+	0.865304i	$0.332875\pi$
$212$	−232752.	+	291862.i	−0.355676	+	0.446004i
$213$	−99121.3	−	47734.3i	−0.149699	−	0.0720911i
$214$	−151552.	−	190041.i	−0.226219	−	0.283669i
$215$	−614705.			−0.906923
$216$	−10616.9	−	13313.1i	−0.0154832	−	0.0194154i
$217$	660.255	+	2892.77i	0.000951837	+	0.00417027i
$218$	−189459.	−	830074.i	−0.270006	−	1.18297i
$219$	250273.	+	313832.i	0.352617	+	0.442168i
$220$	1.50373e6			2.09465
$221$	−369544.	−	463394.i	−0.508963	−	0.638219i
$222$	862890.	+	415546.i	1.17510	+	0.565896i
$223$	485129.	−	608332.i	0.653273	−	0.819179i	−0.339319	−	0.940671i	$-0.610197\pi$
$223$	485129.	−	608332.i	0.653273	−	0.819179i	0.992592	+	0.121492i	$0.0387680\pi$
$224$	776849.	−	974138.i	1.03447	−	1.29718i
$225$	−463876.	+	223391.i	−0.610866	+	0.294178i
$226$	−223907.	−	981000.i	−0.291606	−	1.27761i
$227$	−159384.	+	698306.i	−0.205296	+	0.899459i	0.762354	+	0.647160i	$0.224044\pi$
$227$	−159384.	+	698306.i	−0.205296	+	0.899459i	−0.967649	+	0.252298i	$0.918814\pi$
$228$	−538695.	−	259422.i	−0.686288	−	0.330499i
$229$	−98065.3	+	47225.7i	−0.123574	+	0.0595100i	−0.494649	−	0.869093i	$-0.664703\pi$
$229$	−98065.3	+	47225.7i	−0.123574	+	0.0595100i	0.371075	+	0.928603i	$0.378989\pi$
$230$	−560106.	+	2.45398e6i	−0.698153	+	3.05881i
$231$	−752929.			−0.928376
$232$	−102541.	−	26004.8i	−0.125078	−	0.0317200i
$233$	124238.			0.149922			0.0749611	−	0.997186i	$-0.476117\pi$
$233$	124238.			0.149922			0.0749611	+	0.997186i	$0.476117\pi$
$234$	69352.3	−	303852.i	0.0827982	−	0.362763i
$235$	2.20308e6	−	1.06095e6i	2.60232	−	1.25321i
$236$	−691075.	−	332804.i	−0.807691	−	0.388963i
$237$	35700.2	−	156413.i	0.0412857	−	0.180885i
$238$	−328639.	−	1.43986e6i	−0.376077	−	1.64770i
$239$	1.36304e6	−	656404.i	1.54352	−	0.743322i	0.547879	−	0.836557i	$-0.315435\pi$
$239$	1.36304e6	−	656404.i	1.54352	−	0.743322i	0.995644	+	0.0932359i	$0.0297211\pi$
$240$	606910.	−	761041.i	0.680136	−	0.852864i
$241$	−344783.	+	432344.i	−0.382387	+	0.479498i	−0.935358	−	0.353702i	$-0.884923\pi$
$241$	−344783.	+	432344.i	−0.382387	+	0.479498i	0.552971	+	0.833200i	$0.313494\pi$
$242$	860953.	+	414613.i	0.945020	+	0.455098i
$243$	−36816.4	−	46166.4i	−0.0399969	−	0.0501545i
$244$	601053.			0.646306
$245$	478977.	+	600618.i	0.509800	+	0.639269i
$246$	−273341.	−	1.19759e6i	−0.287983	−	1.26174i
$247$	251031.	+	1.09984e6i	0.261809	+	1.14706i
$248$	−274.974	−	344.807i	−0.000283898	−	0.000355997i
$249$	510583.			0.521877
$250$	−1.53231e6	−	1.92145e6i	−1.55059	−	1.94438i
$251$	−4314.62	−	2077.81i	−0.00432273	−	0.00208172i	0.431721	−	0.902007i	$-0.357906\pi$
$251$	−4314.62	−	2077.81i	−0.00432273	−	0.00208172i	−0.436044	+	0.899925i	$0.643621\pi$
$252$	230236.	−	288707.i	0.228387	−	0.286388i
$253$	−1.09847e6	+	1.37744e6i	−1.07892	+	1.35292i
$254$	−143387.	+	69051.5i	−0.139452	+	0.0671566i
$255$	−234628.	−	1.02797e6i	−0.225959	−	0.989990i
$256$	−270655.	+	1.18582e6i	−0.258116	+	1.13088i
$257$	1.81268e6	+	872942.i	1.71194	+	0.824428i	0.991377	+	0.131041i	$0.0418320\pi$
$257$	1.81268e6	+	872942.i	1.71194	+	0.824428i	0.720566	+	0.693387i	$0.243882\pi$
$258$	399837.	−	192551.i	0.373967	−	0.180093i
$259$	476424.	−	2.08735e6i	0.441310	−	1.93351i
$260$	1.39149e6			1.27658
$261$	−355586.	−	90177.7i	−0.323105	−	0.0819404i
$262$	−2.14519e6			−1.93069
$263$	−175091.	+	767123.i	−0.156090	+	0.683873i	0.834952	+	0.550322i	$0.185495\pi$
$263$	−175091.	+	767123.i	−0.156090	+	0.683873i	−0.991042	+	0.133551i	$0.957362\pi$
$264$	100829.	−	48556.7i	0.0890380	−	0.0428784i
$265$	1.12894e6	+	543666.i	0.987539	+	0.475574i
$266$	−625515.	+	2.74056e6i	−0.542043	+	2.37485i
$267$	−63429.6	−	277903.i	−0.0544520	−	0.238570i
$268$	16928.3	−	8152.23i	0.0143971	−	0.00693329i
$269$	1.21388e6	−	1.52216e6i	1.02281	−	1.28257i	0.0641750	−	0.997939i	$-0.479558\pi$
$269$	1.21388e6	−	1.52216e6i	1.02281	−	1.28257i	0.958638	−	0.284628i	$-0.0918701\pi$
$270$	345693.	−	433485.i	0.288590	−	0.361880i
$271$	−505208.	−	243295.i	−0.417875	−	0.201238i	0.213118	−	0.977026i	$-0.431638\pi$
$271$	−505208.	−	243295.i	−0.417875	−	0.201238i	−0.630993	+	0.775788i	$0.717352\pi$
$272$	833255.	+	1.04487e6i	0.682897	+	0.856326i
$273$	−696733.			−0.565796
$274$	−396208.	−	496829.i	−0.318821	−	0.399789i
$275$	−752960.	−	3.29893e6i	−0.600399	−	2.63052i
$276$	−192274.	−	842406.i	−0.151931	−	0.665654i
$277$	982328.	+	1.23180e6i	0.769232	+	0.964586i	0.999964	−	0.00843105i	$-0.00268372\pi$
$277$	982328.	+	1.23180e6i	0.769232	+	0.964586i	−0.230733	+	0.973017i	$0.574112\pi$
$278$	−1.12440e6			−0.872588
$279$	−953.537	−	1195.70i	−0.000733377	−	0.000919625i
$280$	−322034.	−	155084.i	−0.245475	−	0.118214i
$281$	557395.	−	698951.i	0.421112	−	0.528057i	−0.525344	−	0.850890i	$-0.676064\pi$
$281$	557395.	−	698951.i	0.421112	−	0.528057i	0.946456	+	0.322832i	$0.104635\pi$
$282$	−1.10067e6	+	1.38019e6i	−0.824201	+	1.03352i
$283$	596758.	−	287383.i	0.442927	−	0.213302i	−0.199108	−	0.979977i	$-0.563805\pi$
$283$	596758.	−	287383.i	0.442927	−	0.213302i	0.642035	+	0.766675i	$0.278090\pi$
$284$	78908.9	+	345723.i	0.0580538	+	0.254350i
$285$	−446579.	+	1.95659e6i	−0.325677	+	1.42688i
$286$	1.84548e6	+	888734.i	1.33411	+	0.642476i
$287$	−2.47412e6	+	1.19147e6i	−1.77303	+	0.853846i
$288$	−142904.	+	626104.i	−0.101523	+	0.444801i
$289$	27788.6			0.0195714
$290$	82547.9	−	3.44353e6i	0.0576383	−	2.40441i
$291$	1.56164e6			1.08105
$292$	287908.	−	1.26141e6i	0.197604	−	0.865761i
$293$	−84628.7	+	40755.0i	−0.0575902	+	0.0277340i	−0.462457	−	0.886642i	$-0.653032\pi$
$293$	−84628.7	+	40755.0i	−0.0575902	+	0.0277340i	0.404867	+	0.914376i	$0.367318\pi$
$294$	−499691.	−	240639.i	−0.337158	−	0.162367i
$295$	−572902.	+	2.51005e6i	−0.383288	+	1.67930i
$296$	70813.3	+	310253.i	0.0469770	+	0.205820i
$297$	349648.	−	168382.i	0.230006	−	0.110765i
$298$	−750162.	+	940674.i	−0.489344	+	0.613618i
$299$	−1.01649e6	+	1.27463e6i	−0.657541	+	0.824531i
$300$	1.49520e6	+	720052.i	0.959173	+	0.461914i
$301$	−618556.	−	775645.i	−0.393516	−	0.493454i
$302$	996932.			0.628997
$303$	−619419.	−	776727.i	−0.387595	−	0.486029i
$304$	−566029.	−	2.47993e6i	−0.351281	−	1.53906i
$305$	−448929.	−	1.96689e6i	−0.276330	−	1.21068i
$306$	474618.	+	595152.i	0.289762	+	0.363349i
$307$	−1.81539e6			−1.09932			−0.549661	−	0.835388i	$-0.685243\pi$
$307$	−1.81539e6			−1.09932			−0.549661	+	0.835388i	$0.685243\pi$
$308$	1.51315e6	+	1.89743e6i	0.908876	+	1.13969i
$309$	408787.	+	196861.i	0.243557	+	0.117291i
$310$	8953.37	−	11227.2i	0.00529154	−	0.00663538i
$311$	−266045.	+	333610.i	−0.155975	+	0.195586i	−0.853679	−	0.520800i	$-0.825634\pi$
$311$	−266045.	+	333610.i	−0.155975	+	0.195586i	0.697704	+	0.716386i	$0.254205\pi$
$312$	93303.5	−	44932.6i	0.0542639	−	0.0261321i
$313$	602092.	+	2.63794e6i	0.347378	+	1.52196i	0.783109	+	0.621884i	$0.213633\pi$
$313$	602092.	+	2.63794e6i	0.347378	+	1.52196i	−0.435732	+	0.900077i	$0.643510\pi$
$314$	−107267.	+	469966.i	−0.0613961	+	0.268994i
$315$	−1.11673e6	−	537788.i	−0.634120	−	0.305376i
$316$	−465916.	+	224374.i	−0.262476	+	0.126402i
$317$	−497555.	+	2.17993e6i	−0.278095	+	1.21841i	0.622104	+	0.782934i	$0.286278\pi$
$317$	−497555.	+	2.17993e6i	−0.278095	+	1.21841i	−0.900199	+	0.435478i	$0.856579\pi$
$318$	−904619.			−0.501646
$319$	1.09783e6	−	2.14650e6i	0.604029	−	1.18101i
$320$	−2.56907e6			−1.40250
$321$	62322.9	−	273055.i	0.0337587	−	0.147906i
$322$	−3.66009e6	+	1.76261e6i	−1.96722	+	0.947362i
$323$	−2.48251e6	−	1.19551e6i	−1.32399	−	0.637600i
$324$	−42352.7	+	185559.i	−0.0224140	+	0.0982021i
$325$	−696762.	−	3.05271e6i	−0.365911	−	1.60316i
$326$	−978267.	+	471109.i	−0.509816	+	0.245514i
$327$	611670.	−	767010.i	0.316335	−	0.396672i
$328$	254485.	−	319114.i	0.130610	−	0.163780i
$329$	3.55560e6	+	1.71229e6i	1.81102	+	0.872141i
$330$	2.27195e6	+	2.84894e6i	1.14846	+	1.44012i
$331$	−1.09969e6			−0.551697			−0.275848	−	0.961201i	$-0.588959\pi$
$331$	−1.09969e6			−0.551697			−0.275848	+	0.961201i	$0.588959\pi$
$332$	−1.02611e6	−	1.28670e6i	−0.510915	−	0.640667i
$333$	245562.	+	1.07588e6i	0.121353	+	0.531681i
$334$	338568.	+	1.48336e6i	0.166065	+	0.727580i
$335$	−39321.2	−	49307.2i	−0.0191432	−	0.0240048i
$336$	1.57101e6			0.759153
$337$	1.65900e6	+	2.08032e6i	0.795742	+	0.997829i	0.999822	+	0.0188747i	$0.00600836\pi$
$337$	1.65900e6	+	2.08032e6i	0.795742	+	0.997829i	−0.204080	+	0.978954i	$0.565420\pi$
$338$	−905180.	−	435912.i	−0.430966	−	0.207542i
$339$	722886.	−	906470.i	0.341641	−	0.428405i
$340$	−2.11902e6	+	2.65717e6i	−0.994120	+	1.24659i
$341$	9055.80	−	4361.04i	0.00421736	−	0.00203097i
$342$	−322408.	−	1.41256e6i	−0.149053	−	0.653043i
$343$	311839.	−	1.36626e6i	0.143118	−	0.627043i
$344$	132856.	+	63980.0i	0.0605320	+	0.0291507i
$345$	−2.61308e6	+	1.25839e6i	−1.18197	+	0.569205i
$346$	−151037.	+	661737.i	−0.0678255	+	0.297163i
$347$	449760.			0.200520			0.100260	−	0.994961i	$-0.468033\pi$
$347$	449760.			0.200520			0.100260	+	0.994961i	$0.468033\pi$
$348$	487362.	+	1.07733e6i	0.215727	+	0.476870i
$349$	525185.			0.230807			0.115404	−	0.993319i	$-0.463184\pi$
$349$	525185.			0.230807			0.115404	+	0.993319i	$0.463184\pi$
$350$	1.73618e6	−	7.60671e6i	0.757574	−	3.31915i
$351$	323551.	−	155814.i	0.140177	−	0.0675055i
$352$	−3.80270e6	−	1.83129e6i	−1.63582	−	0.787770i
$353$	993570.	−	4.35311e6i	0.424386	−	1.85936i	−0.0813723	−	0.996684i	$-0.525930\pi$
$353$	993570.	−	4.35311e6i	0.424386	−	1.85936i	0.505759	−	0.862675i	$-0.331213\pi$
$354$	−413606.	−	1.81213e6i	−0.175420	−	0.768565i
$355$	1.07241e6	−	516444.i	0.451636	−	0.217496i
$356$	−572860.	+	718343.i	−0.239565	+	0.300405i
$357$	1.06101e6	−	1.33047e6i	0.440606	−	0.552502i
$358$	−832470.	−	400896.i	−0.343290	−	0.165320i
$359$	2.37868e6	+	2.98278e6i	0.974094	+	1.22147i	0.975166	+	0.221475i	$0.0710872\pi$
$359$	2.37868e6	+	2.98278e6i	0.974094	+	1.22147i	−0.00107236	+	0.999999i	$0.500341\pi$
$360$	184230.			0.0749209
$361$	1.72605e6	+	2.16439e6i	0.697083	+	0.874114i
$362$	−51669.8	−	226380.i	−0.0207236	−	0.0907961i
$363$	245010.	+	1.07346e6i	0.0975928	+	0.427582i
$364$	1.40021e6	+	1.75581e6i	0.553911	+	0.694583i
$365$	−4.34287e6			−1.70626
$366$	908119.	+	1.13875e6i	0.354356	+	0.444349i
$367$	−465040.	−	223951.i	−0.180229	−	0.0867938i	0.341593	−	0.939848i	$-0.389033\pi$
$367$	−465040.	−	223951.i	−0.180229	−	0.0867938i	−0.521823	+	0.853054i	$0.674748\pi$
$368$	2.29199e6	−	2.87406e6i	0.882252	−	1.10631i
$369$	882485.	−	1.10660e6i	0.337397	−	0.423083i
$370$	−9.33573e6	+	4.49585e6i	−3.54522	+	1.70729i
$371$	450000.	+	1.97158e6i	0.169738	+	0.743669i
$372$	−1096.93	+	4805.95i	−0.000410979	+	0.00180062i
$373$	455561.	+	219387.i	0.169541	+	0.0816466i	0.516729	−	0.856149i	$-0.327149\pi$
$373$	455561.	+	219387.i	0.169541	+	0.0816466i	−0.347188	+	0.937795i	$0.612864\pi$
$374$	−4.50747e6	+	2.17069e6i	−1.66630	+	0.802450i
$375$	630132.	−	2.76079e6i	0.231395	−	1.01381i
$376$	−586577.			−0.213971
$377$	1.01589e6	−	1.98629e6i	0.368124	−	0.719764i
$378$	894838.			0.322118
$379$	157999.	−	692241.i	0.0565012	−	0.247548i	−0.938788	−	0.344494i	$-0.888050\pi$
$379$	157999.	−	692241.i	0.0565012	−	0.247548i	0.995290	+	0.0969464i	$0.0309076\pi$
$380$	5.82822e6	−	2.80672e6i	2.07051	−	0.997104i
$381$	−165216.	−	79564.0i	−0.0583097	−	0.0280805i
$382$	−841338.	+	3.68614e6i	−0.294993	+	1.29245i
$383$	367909.	+	1.61192e6i	0.128157	+	0.561494i	0.997709	+	0.0676521i	$0.0215508\pi$
$383$	367909.	+	1.61192e6i	0.128157	+	0.561494i	−0.869552	+	0.493842i	$0.835592\pi$
$384$	−386208.	+	185988.i	−0.133657	+	0.0643660i
$385$	5.07897e6	−	6.36883e6i	1.74632	−	2.18982i
$386$	4.63414e6	−	5.81102e6i	1.58307	−	1.98511i
$387$	460709.	+	221866.i	0.156368	+	0.0753031i
$388$	−3.13839e6	−	3.93542e6i	−1.05835	−	1.32713i
$389$	−3.29823e6			−1.10511			−0.552556	−	0.833476i	$-0.686347\pi$
$389$	−3.29823e6			−1.10511			−0.552556	+	0.833476i	$0.686347\pi$
$390$	2.10238e6	+	2.63630e6i	0.699923	+	0.877675i
$391$	−886069.	−	3.88212e6i	−0.293107	−	1.28418i
$392$	−41007.3	−	179665.i	−0.0134786	−	0.0590537i
$393$	−1.54113e6	−	1.93251e6i	−0.503335	−	0.631162i
$394$	5.82073e6			1.88902
$395$	1.08224e6	+	1.35708e6i	0.349003	+	0.437636i
$396$	−1.12701e6	−	542741.i	−0.361153	−	0.173922i
$397$	1.36064e6	−	1.70619e6i	0.433277	−	0.543313i	−0.516480	−	0.856299i	$-0.672758\pi$
$397$	1.36064e6	−	1.70619e6i	0.433277	−	0.543313i	0.949758	+	0.312986i	$0.101329\pi$
$398$	−561143.	+	703651.i	−0.177568	+	0.222664i
$399$	−2.91824e6	+	1.40535e6i	−0.917674	+	0.441928i
$400$	1.57107e6	+	6.88331e6i	0.490959	+	2.15103i
$401$	88516.1	−	387814.i	0.0274892	−	0.120438i	−0.959322	−	0.282315i	$-0.908898\pi$
$401$	88516.1	−	387814.i	0.0274892	−	0.120438i	0.986811	+	0.161877i	$0.0517548\pi$
$402$	41021.7	+	19755.0i	0.0126604	+	0.00609694i
$403$	8379.90	−	4035.55i	0.00257026	−	0.00123777i
$404$	−712565.	+	3.12195e6i	−0.217206	+	0.951640i
$405$	638859.			0.193539
$406$	4.42817e6	−	3.36094e6i	1.33324	−	1.01192i
$407$	−7.25267e6			−2.17026
$408$	−56283.9	+	246596.i	−0.0167392	+	0.0733390i
$409$	−1.97758e6	+	952350.i	−0.584554	+	0.281506i	−0.702696	−	0.711490i	$-0.748021\pi$
$409$	−1.97758e6	+	952350.i	−0.584554	+	0.281506i	0.118142	+	0.992997i	$0.462306\pi$
$410$	1.19739e7	+	5.76634e6i	3.51785	+	1.69411i
$411$	162933.	−	713856.i	0.0475778	−	0.208452i
$412$	−325429.	−	1.42580e6i	−0.0944525	−	0.413823i
$413$	−3.74371e6	+	1.80288e6i	−1.08001	+	0.520105i
$414$	1.30551e6	−	1.63705e6i	0.374350	−	0.469420i
$415$	−3.44420e6	+	4.31889e6i	−0.981676	+	1.23098i
$416$	−3.51888e6	−	1.69461e6i	−0.996946	−	0.480104i
$417$	−807782.	−	1.01293e6i	−0.227486	−	0.285258i
$418$	9.52232e6			2.66564
$419$	−3.22893e6	−	4.04895e6i	−0.898512	−	1.12670i	−0.991380	−	0.131020i	$-0.958175\pi$
$419$	−3.22893e6	−	4.04895e6i	−0.898512	−	1.12670i	0.0928678	−	0.995678i	$-0.470397\pi$
$420$	889010.	+	3.89501e6i	0.245914	+	1.07742i
$421$	118763.	+	520335.i	0.0326570	+	0.143080i	0.988628	−	0.150381i	$-0.0480501\pi$
$421$	118763.	+	520335.i	0.0326570	+	0.143080i	−0.955971	+	0.293461i	$0.905193\pi$
$422$	2.29279e6	+	2.87507e6i	0.626735	+	0.785900i
$423$	−2.03409e6			−0.552738
$424$	−187410.	−	235005.i	−0.0506265	−	0.0634837i
$425$	6.89046e6	+	3.31827e6i	1.85044	+	0.891127i
$426$	−535779.	+	671845.i	−0.143041	+	0.179368i
$427$	2.03011e6	−	2.54568e6i	0.538827	−	0.675668i
$428$	−813364.	+	391695.i	−0.214623	+	0.103357i
$429$	525186.	+	2.30099e6i	0.137775	+	0.603631i
$430$	−1.06841e6	+	4.68099e6i	−0.278654	+	1.22086i
$431$	2.23835e6	+	1.07793e6i	0.580410	+	0.279511i	0.700965	−	0.713196i	$-0.252753\pi$
$431$	2.23835e6	+	1.07793e6i	0.580410	+	0.279511i	−0.120555	+	0.992707i	$0.538467\pi$
$432$	−729549.	+	351332.i	−0.188081	+	0.0905751i
$433$	217671.	−	953678.i	0.0557931	−	0.244446i	−0.939340	−	0.342988i	$-0.888561\pi$
$433$	217671.	−	953678.i	0.0557931	−	0.244446i	0.995133	+	0.0985426i	$0.0314181\pi$
$434$	23176.1			0.00590630
$435$	3.16144e6	−	2.39951e6i	0.801054	−	0.607993i
$436$	−3.16218e6			−0.796654
$437$	−1.68650e6	+	7.38905e6i	−0.422458	+	1.85091i
$438$	2.82484e6	−	1.36037e6i	0.703571	−	0.338822i
$439$	−3.57015e6	−	1.71929e6i	−0.884149	−	0.425784i	−0.0640105	−	0.997949i	$-0.520389\pi$
$439$	−3.57015e6	−	1.71929e6i	−0.884149	−	0.425784i	−0.820138	+	0.572166i	$0.806103\pi$
$440$	−269426.	+	1.18043e6i	−0.0663448	+	0.290676i
$441$	−142202.	−	623029.i	−0.0348185	−	0.152550i
$442$	−4.17105e6	+	2.00867e6i	−1.01552	+	0.489050i
$443$	4.16726e6	−	5.22557e6i	1.00888	−	1.26510i	0.0449406	−	0.998990i	$-0.485690\pi$
$443$	4.16726e6	−	5.22557e6i	1.00888	−	1.26510i	0.963943	−	0.266110i	$-0.0857384\pi$
$444$	2.21777e6	−	2.78100e6i	0.533900	−	0.669489i
$445$	2.77858e6	+	1.33809e6i	0.665155	+	0.320322i
$446$	−3.78927e6	−	4.75160e6i	−0.902025	−	1.13110i
$447$	−1.38634e6			−0.328171
$448$	−2.58517e6	−	3.24170e6i	−0.608547	−	0.763094i
$449$	1.57919e6	+	6.91886e6i	0.369673	+	1.61964i	0.727676	+	0.685921i	$0.240601\pi$
$449$	1.57919e6	+	6.91886e6i	0.369673	+	1.61964i	−0.358003	+	0.933720i	$0.616542\pi$
$450$	894874.	+	3.92070e6i	0.208320	+	0.912709i
$451$	5.79984e6	+	7.27277e6i	1.34269	+	1.68367i
$452$	−3.73713e6			−0.860384
$453$	716207.	+	898095.i	0.163981	+	0.205626i
$454$	5.04060e6	+	2.42742e6i	1.14774	+	0.552721i
$455$	4.69990e6	−	5.89348e6i	1.06429	−	1.33458i
$456$	300166.	−	376396.i	0.0676005	−	0.0847683i
$457$	−5.04389e6	+	2.42901e6i	−1.12973	+	0.544049i	−0.902885	−	0.429881i	$-0.858555\pi$
$457$	−5.04389e6	+	2.42901e6i	−1.12973	+	0.544049i	−0.226845	+	0.973931i	$0.572841\pi$
$458$	189180.	+	828851.i	0.0421416	+	0.184635i
$459$	−195177.	+	855128.i	−0.0432412	+	0.189452i
$460$	8.42269e6	+	4.05615e6i	1.85591	+	0.893758i
$461$	6.82267e6	−	3.28563e6i	1.49521	−	0.720055i	0.505458	−	0.862851i	$-0.331323\pi$
$461$	6.82267e6	−	3.28563e6i	1.49521	−	0.720055i	0.989752	+	0.142796i	$0.0456092\pi$
$462$	−1.30865e6	+	5.73357e6i	−0.285245	+	1.24974i
$463$	−2.40534e6			−0.521463			−0.260731	−	0.965411i	$-0.583964\pi$
$463$	−2.40534e6			−0.521463			−0.260731	+	0.965411i	$0.583964\pi$
$464$	−2.29065e6	+	4.47873e6i	−0.493928	+	0.965739i
$465$	16546.3			0.00354869
$466$	215936.	−	946079.i	0.0460639	−	0.201819i
$467$	−2.49217e6	+	1.20016e6i	−0.528792	+	0.254653i	−0.679177	−	0.733975i	$-0.737663\pi$
$467$	−2.49217e6	+	1.20016e6i	−0.528792	+	0.254653i	0.150385	+	0.988628i	$0.451949\pi$
$468$	−1.04290e6	−	502233.i	−0.220103	−	0.105996i
$469$	22649.1	−	99232.2i	0.00475465	−	0.0208315i
$470$	−4.25001e6	−	1.86205e7i	−0.887453	−	3.88819i
$471$	−500435.	+	240997.i	−0.103943	+	0.0500563i
$472$	385073.	−	482867.i	0.0795589	−	0.0997637i
$473$	−2.09534e6	+	2.62747e6i	−0.430628	+	0.539990i
$474$	−1.12904e6	−	543716.i	−0.230814	−	0.111154i
$475$	−9.07585e6	−	1.13808e7i	−1.84567	−	2.31439i
$476$	−5.48516e6			−1.10961
$477$	−649888.	−	814934.i	−0.130780	−	0.163993i
$478$	−2.62947e6	−	1.15205e7i	−0.526378	−	2.30621i
$479$	−1.10437e6	−	4.83858e6i	−0.219926	−	0.963561i	−0.957532	−	0.288328i	$-0.906901\pi$
$479$	−1.10437e6	−	4.83858e6i	−0.219926	−	0.963561i	0.737605	−	0.675232i	$-0.235957\pi$
$480$	−4.33208e6	−	5.43225e6i	−0.858209	−	1.07616i
$481$	−6.71136e6			−1.32266
$482$	2.69305e6	+	3.37698e6i	0.527992	+	0.662080i
$483$	−4.21731e6	−	2.03095e6i	−0.822561	−	0.396124i
$484$	2.21279e6	−	2.77476e6i	0.429366	−	0.538408i
$485$	−1.05342e7	+	1.32095e7i	−2.03352	+	2.54995i
$486$	−415548.	+	200117.i	−0.0798051	+	0.0384321i
$487$	279834.	+	1.22603e6i	0.0534660	+	0.234250i	0.994600	−	0.103784i	$-0.0330952\pi$
$487$	279834.	+	1.22603e6i	0.0534660	+	0.234250i	−0.941134	+	0.338034i	$0.890238\pi$
$488$	−107692.	+	471828.i	−0.0204707	+	0.0896880i
$489$	−1.12720e6	−	542831.i	−0.213171	−	0.102658i
$490$	5.40623e6	−	2.60350e6i	1.01719	−	0.489855i
$491$	−1.00089e6	+	4.38517e6i	−0.187362	+	0.820886i	0.790639	+	0.612283i	$0.209749\pi$
$491$	−1.00089e6	+	4.38517e6i	−0.187362	+	0.820886i	−0.978000	+	0.208603i	$0.933108\pi$
$492$	−4.56222e6			−0.849695
$493$	2.24595e6	+	4.96473e6i	0.416181	+	0.919981i
$494$	8.81161e6			1.62457
$495$	−934296.	+	4.09342e6i	−0.171384	+	0.750884i
$496$	−18895.1	+	9099.42i	−0.00344863	+	0.00166077i
$497$	1.73078e6	+	833501.i	0.314305	+	0.151361i
$498$	887434.	−	3.88810e6i	0.160348	−	0.702530i
$499$	1.30816e6	+	5.73144e6i	0.235186	+	1.03042i	0.945267	+	0.326297i	$0.105801\pi$
$499$	1.30816e6	+	5.73144e6i	0.235186	+	1.03042i	−0.710082	+	0.704119i	$0.751342\pi$
$500$	−8.22372e6	+	3.96034e6i	−1.47110	+	0.708447i
$501$	−1.09307e6	+	1.37066e6i	−0.194560	+	0.243970i
$502$	−23321.8	+	29244.6i	−0.00413049	+	0.00517948i
$503$	−37414.3	−	18017.8i	−0.00659353	−	0.00317527i	0.430584	−	0.902550i	$-0.358308\pi$
$503$	−37414.3	−	18017.8i	−0.00659353	−	0.00317527i	−0.437178	+	0.899375i	$0.644022\pi$
$504$	185384.	+	232464.i	0.0325084	+	0.0407642i
$505$	1.07485e7			1.87551
$506$	8.58000e6	+	1.07590e7i	1.48974	+	1.86808i
$507$	−257596.	−	1.12860e6i	−0.0445061	−	0.194994i
$508$	131526.	+	576254.i	0.0226127	+	0.0990728i
$509$	−3.86127e6	−	4.84188e6i	−0.660596	−	0.828361i	0.332812	−	0.942993i	$-0.392002\pi$
$509$	−3.86127e6	−	4.84188e6i	−0.660596	−	0.828361i	−0.993408	+	0.114632i	$0.963431\pi$
$510$	−8.23583e6			−1.40211
$511$	−4.37008e6	−	5.47991e6i	−0.740350	−	0.928369i
$512$	7.18641e6	+	3.46079e6i	1.21154	+	0.583446i
$513$	1.04090e6	−	1.30524e6i	0.174628	−	0.218977i
$514$	9.79807e6	−	1.22864e7i	1.63581	−	2.05124i
$515$	−4.42272e6	+	2.12987e6i	−0.734804	+	0.353863i
$516$	−366763.	−	1.60689e6i	−0.0606403	−	0.265683i
$517$	2.97475e6	−	1.30332e7i	0.489467	−	2.14450i
$518$	−1.50671e7	−	7.25596e6i	−2.46721	−	1.18815i
$519$	−704638.	+	339336.i	−0.114828	+	0.0552982i
$520$	−249317.	+	1.09233e6i	−0.0404336	+	0.177151i
$521$	−1.96691e6			−0.317462			−0.158731	−	0.987322i	$-0.550740\pi$
$521$	−1.96691e6			−0.317462			−0.158731	+	0.987322i	$0.550740\pi$
$522$	−1.30474e6	+	2.55106e6i	−0.209579	+	0.409774i
$523$	4.22718e6			0.675766			0.337883	−	0.941188i	$-0.390289\pi$
$523$	4.22718e6			0.675766			0.337883	+	0.941188i	$0.390289\pi$
$524$	−1.77287e6	+	7.76747e6i	−0.282065	+	1.23581i
$525$	8.09986e6	−	3.90069e6i	1.28256	−	0.617651i
$526$	5.53734e6	+	2.66664e6i	0.872643	+	0.420243i
$527$	−5055.05	+	22147.6i	−0.000792864	+	0.00347376i
$528$	−1.18420e6	−	5.18831e6i	−0.184858	−	0.809918i
$529$	−4.06933e6	+	1.95968e6i	−0.632242	+	0.304472i
$530$	6.10221e6	−	7.65193e6i	0.943621	−	1.18326i
$531$	1.33533e6	−	1.67445e6i	0.205519	−	0.257713i
$532$	9.40630e6	+	4.52983e6i	1.44092	+	0.693910i
$533$	5.36696e6	+	6.72995e6i	0.818296	+	1.02611i
$534$	−2.22648e6			−0.337883
$535$	1.88929e6	+	2.36910e6i	0.285374	+	0.357848i
$536$	3366.45	+	14749.4i	0.000506128	+	0.00221749i
$537$	−236904.	−	1.03795e6i	−0.0354517	−	0.155324i
$538$	−9.48147e6	−	1.18894e7i	−1.41228	−	1.77094i
$539$	4.19995e6			0.622690
$540$	−1.28390e6	−	1.60996e6i	−0.189473	−	0.237592i
$541$	−2.61666e6	−	1.26012e6i	−0.384374	−	0.185105i	0.231711	−	0.972785i	$-0.425568\pi$
$541$	−2.61666e6	−	1.26012e6i	−0.384374	−	0.185105i	−0.616085	+	0.787680i	$0.711282\pi$
$542$	−2.73079e6	+	3.42430e6i	−0.399292	+	0.500696i
$543$	166817.	−	209181.i	0.0242795	−	0.0304455i
$544$	8.59469e6	−	4.13898e6i	1.24518	−	0.599648i
$545$	2.36184e6	+	1.03479e7i	0.340612	+	1.49232i
$546$	−1.21098e6	+	5.30564e6i	−0.173842	+	0.761651i
$547$	−3.69202e6	−	1.77799e6i	−0.527590	−	0.254074i	0.151075	−	0.988522i	$-0.451727\pi$
$547$	−3.69202e6	−	1.77799e6i	−0.527590	−	0.254074i	−0.678664	+	0.734449i	$0.737441\pi$
$548$	−2.12640e6	+	1.02402e6i	−0.302478	+	0.145666i
$549$	−373446.	+	1.63617e6i	−0.0528807	+	0.231685i
$550$	−2.64302e7			−3.72557
$551$	248555.	−	1.03686e7i	0.0348774	−	1.45493i
$552$	695741.			0.0971851
$553$	−623371.	+	2.73117e6i	−0.0866829	+	0.379783i
$554$	1.10876e7	−	5.33949e6i	1.53483	−	0.739137i
$555$	−1.07570e7	−	5.18031e6i	−1.48238	−	0.713876i
$556$	−929253.	+	4.07132e6i	−0.127481	+	0.558533i
$557$	−1.87182e6	−	8.20098e6i	−0.255638	−	1.12002i	−0.925861	−	0.377864i	$-0.876659\pi$
$557$	−1.87182e6	−	8.20098e6i	−0.255638	−	1.12002i	0.670223	−	0.742160i	$-0.266199\pi$
$558$	−10762.6	+	5182.99i	−0.00146329	+	0.000704685i
$559$	−1.93895e6	+	2.43137e6i	−0.262445	+	0.329095i
$560$	−1.05974e7	+	1.32887e7i	−1.42800	+	1.79066i
$561$	−5.19370e6	−	2.50115e6i	−0.696739	−	0.335532i
$562$	−4.35374e6	−	5.45941e6i	−0.581462	−	0.729130i
$563$	−1.16953e7			−1.55504			−0.777519	−	0.628859i	$-0.783522\pi$
$563$	−1.16953e7			−1.55504			−0.777519	+	0.628859i	$0.783522\pi$
$564$	4.08788e6	+	5.12604e6i	0.541128	+	0.678553i
$565$	2.79128e6	+	1.22294e7i	0.367860	+	1.61170i
$566$	−1.15122e6	−	5.04382e6i	−0.151049	−	0.661787i
$567$	642861.	+	806123.i	0.0839769	+	0.105304i
$568$	−285532.			−0.0371350
$569$	−6.46528e6	−	8.10721e6i	−0.837157	−	1.04976i	−0.998027	−	0.0627859i	$-0.980001\pi$
$569$	−6.46528e6	−	8.10721e6i	−0.837157	−	1.04976i	0.160870	−	0.986976i	$-0.448570\pi$
$570$	1.41233e7	+	6.80143e6i	1.82075	+	0.876825i
$571$	875602.	−	1.09797e6i	0.112387	−	0.140929i	−0.722456	−	0.691417i	$-0.756987\pi$
$571$	875602.	−	1.09797e6i	0.112387	−	0.140929i	0.834843	+	0.550488i	$0.185558\pi$
$572$	4.74318e6	−	5.94776e6i	0.606149	−	0.760087i
$573$	−3.92512e6	+	1.89024e6i	−0.499421	+	0.240508i
$574$	4.77288e6	+	2.09113e7i	0.604645	+	2.64912i
$575$	4.68106e6	−	2.05090e7i	0.590438	−	2.58688i
$576$	1.92547e6	+	927257.i	0.241813	+	0.116451i
$577$	−4.72623e6	+	2.27603e6i	−0.590984	+	0.284603i	−0.705376	−	0.708833i	$-0.749222\pi$
$577$	−4.72623e6	+	2.27603e6i	−0.590984	+	0.284603i	0.114393	+	0.993436i	$0.463508\pi$
$578$	48298.7	−	211611.i	0.00601335	−	0.0263462i
$579$	8.56413e6			1.06166
$580$	−1.24004e7	−	3.14478e6i	−1.53061	−	0.388168i
$581$	−8.91542e6			−1.09573
$582$	2.71425e6	−	1.18919e7i	0.332156	−	1.45527i
$583$	6.17202e6	−	2.97229e6i	0.752066	−	0.362176i
$584$	938623.	+	452017.i	0.113883	+	0.0548432i
$585$	−864563.	+	3.78790e6i	−0.104450	+	0.457624i
$586$	163259.	+	715285.i	0.0196396	+	0.0860468i
$587$	9.99280e6	−	4.81228e6i	1.19699	−	0.576442i	0.274177	−	0.961679i	$-0.411595\pi$
$587$	9.99280e6	−	4.81228e6i	1.19699	−	0.576442i	0.922818	+	0.385237i	$0.125880\pi$
$588$	−1.28429e6	+	1.61045e6i	−0.153186	+	0.192089i
$589$	26959.0	−	33805.5i	0.00320195	−	0.00401512i
$590$	1.81183e7	+	8.72533e6i	2.14283	+	1.03193i
$591$	4.18168e6	+	5.24366e6i	0.492473	+	0.617541i
$592$	1.51329e7			1.77467
$593$	574743.	+	720705.i	0.0671177	+	0.0841629i	0.814257	−	0.580505i	$-0.197145\pi$
$593$	574743.	+	720705.i	0.0671177	+	0.0841629i	−0.747139	+	0.664667i	$0.768573\pi$
$594$	−674514.	−	2.95524e6i	−0.0784377	−	0.343658i
$595$	4.09689e6	+	1.79497e7i	0.474419	+	2.07857i
$596$	2.78610e6	+	3.49366e6i	0.321278	+	0.402870i
$597$	−1.03702e6			−0.119084
$598$	7.93962e6	+	9.95597e6i	0.907918	+	1.13849i
$599$	1.00735e7	+	4.85115e6i	1.14713	+	0.552430i	0.908171	−	0.418599i	$-0.137479\pi$
$599$	1.00735e7	+	4.85115e6i	1.14713	+	0.552430i	0.238961	+	0.971029i	$0.423193\pi$
$600$	−833141.	+	1.04473e6i	−0.0944801	+	0.118474i
$601$	2.98918e6	−	3.74832e6i	0.337572	−	0.423302i	−0.583852	−	0.811860i	$-0.698455\pi$
$601$	2.98918e6	−	3.74832e6i	0.337572	−	0.423302i	0.921424	+	0.388558i	$0.127027\pi$
$602$	−6.98165e6	+	3.36219e6i	−0.785176	+	0.378121i
$603$	11674.0	+	51147.0i	0.00130745	+	0.00572831i
$604$	823907.	−	3.60977e6i	0.0918937	−	0.402613i
$605$	−1.07329e7	−	5.16868e6i	−1.19214	−	0.574104i
$606$	−6.99140e6	+	3.36688e6i	−0.773361	+	0.372431i
$607$	797210.	−	3.49281e6i	0.0878215	−	0.384771i	−0.911847	−	0.410531i	$-0.865343\pi$
$607$	797210.	−	3.49281e6i	0.0878215	−	0.384771i	0.999668	+	0.0257597i	$0.00820048\pi$
$608$	−1.81568e7			−1.99196
$609$	6.20898e6	+	1.57462e6i	0.678386	+	0.172041i
$610$	−1.57582e7			−1.71467
$611$	2.75272e6	−	1.20605e7i	0.298304	−	1.30696i
$612$	2.54722e6	−	1.22668e6i	0.274908	−	0.132389i
$613$	688387.	+	331510.i	0.0739915	+	0.0356324i	0.470514	−	0.882393i	$-0.344069\pi$
$613$	688387.	+	331510.i	0.0739915	+	0.0356324i	−0.396522	+	0.918025i	$0.629783\pi$
$614$	−3.15530e6	+	1.38243e7i	−0.337769	+	1.47986i
$615$	3.40754e6	+	1.49294e7i	0.363290	+	1.59168i
$616$	−1.76060e6	+	847860.i	−0.186943	+	0.0900269i
$617$	−8.96171e6	+	1.12376e7i	−0.947715	+	1.18840i	0.0342646	+	0.999413i	$0.489091\pi$
$617$	−8.96171e6	+	1.12376e7i	−0.947715	+	1.18840i	−0.981980	+	0.188985i	$0.939480\pi$
$618$	2.20961e6	−	2.77076e6i	0.232726	−	0.291829i
$619$	−7.25993e6	−	3.49620e6i	−0.761563	−	0.366750i	0.0124471	−	0.999923i	$-0.496038\pi$
$619$	−7.25993e6	−	3.49620e6i	−0.761563	−	0.366750i	−0.774010	+	0.633173i	$0.781752\pi$
$620$	−33252.8	−	41697.7i	−0.00347415	−	0.00435645i
$621$	2.41264e6			0.251052
$622$	2.07804e6	+	2.60578e6i	0.215366	+	0.270061i
$623$	1.10756e6	+	4.85254e6i	0.114327	+	0.500897i
$624$	−1.09581e6	−	4.80107e6i	−0.112661	−	0.493602i
$625$	6.71742e6	+	8.42338e6i	0.687864	+	0.862554i
$626$	2.11344e7			2.15553
$627$	6.84094e6	+	8.57827e6i	0.694940	+	0.871427i
$628$	1.61304e6	+	776800.i	0.163210	+	0.0785978i
$629$	1.02203e7	−	1.28159e7i	1.03000	−	1.29158i
$630$	−6.03623e6	+	7.56920e6i	−0.605919	+	0.759799i
$631$	4.66271e6	−	2.24544e6i	0.466192	−	0.224506i	−0.186016	−	0.982547i	$-0.559557\pi$
$631$	4.66271e6	−	2.24544e6i	0.466192	−	0.224506i	0.652207	+	0.758041i	$0.273843\pi$
$632$	−92654.8	−	405947.i	−0.00922731	−	0.0404275i
$633$	−942866.	+	4.13097e6i	−0.0935278	+	0.409772i
$634$	1.57354e7	+	7.57778e6i	1.55473	+	0.748719i
$635$	1.78750e6	−	860814.i	0.175918	−	0.0847178i
$636$	−747615.	+	3.27552e6i	−0.0732884	+	0.321098i
$637$	3.88648e6			0.379497
$638$	−1.44375e7	−	1.20908e7i	−1.40424	−	1.17599i
$639$	−990147.			−0.0959285
$640$	1.03199e6	−	4.52143e6i	0.0995921	−	0.436341i
$641$	7.17225e6	−	3.45397e6i	0.689462	−	0.332027i	−0.0561362	−	0.998423i	$-0.517878\pi$
$641$	7.17225e6	−	3.45397e6i	0.689462	−	0.332027i	0.745598	+	0.666396i	$0.232164\pi$
$642$	−1.97099e6	−	949181.i	−0.188733	−	0.0908890i
$643$	4.24353e6	−	1.85921e7i	0.404762	−	1.77338i	−0.202915	−	0.979196i	$-0.565041\pi$
$643$	4.24353e6	−	1.85921e7i	0.404762	−	1.77338i	0.607677	−	0.794184i	$-0.292101\pi$
$644$	3.35734e6	+	1.47095e7i	0.318992	+	1.39760i
$645$	−4.98447e6	+	2.40039e6i	−0.471758	+	0.227187i
$646$	−1.34187e7	+	1.68265e7i	−1.26511	+	1.58640i
$647$	8.72348e6	−	1.09389e7i	0.819274	−	1.02734i	−0.179774	−	0.983708i	$-0.557537\pi$
$647$	8.72348e6	−	1.09389e7i	0.819274	−	1.02734i	0.999048	−	0.0436291i	$-0.0138920\pi$
$648$	−138076.	−	66494.1i	−0.0129176	−	0.00622079i
$649$	8.77602e6	+	1.10048e7i	0.817873	+	1.02558i
$650$	−2.44575e7			−2.27054
$651$	16650.0	+	20878.4i	0.00153979	+	0.00193083i
$652$	897347.	+	3.93153e6i	0.0826687	+	0.362195i
$653$	993296.	+	4.35191e6i	0.0911582	+	0.399390i	0.999836	−	0.0181078i	$-0.00576422\pi$
$653$	993296.	+	4.35191e6i	0.0911582	+	0.399390i	−0.908678	+	0.417498i	$0.862907\pi$
$654$	−4.77767e6	−	5.99101e6i	−0.436789	−	0.547716i
$655$	2.67425e7			2.43556
$656$	−1.21015e7	−	1.51748e7i	−1.09794	−	1.37678i
$657$	3.25489e6	+	1.56747e6i	0.294187	+	0.141673i
$658$	1.92190e7	−	2.40999e7i	1.73048	−	2.16995i
$659$	−1.03428e7	+	1.29695e7i	−0.927739	+	1.16335i	0.0585438	+	0.998285i	$0.481354\pi$
$659$	−1.03428e7	+	1.29695e7i	−0.927739	+	1.16335i	−0.986283	+	0.165063i	$0.947217\pi$
$660$	1.21933e7	−	5.87199e6i	1.08959	−	0.524717i
$661$	−780081.	−	3.41776e6i	−0.0694442	−	0.304255i	0.928264	−	0.371923i	$-0.121301\pi$
$661$	−780081.	−	3.41776e6i	−0.0694442	−	0.304255i	−0.997708	+	0.0676678i	$0.978444\pi$
$662$	−1.91135e6	+	8.37417e6i	−0.169510	+	0.742671i
$663$	−4.80606e6	−	2.31448e6i	−0.424625	−	0.204489i
$664$	1.19391e6	−	574959.i	0.105088	−	0.0506077i
$665$	7.79784e6	−	3.41646e7i	0.683786	−	2.99586i
$666$	8.61962e6			0.753014
$667$	1.19391e7	−	9.06171e6i	1.03910	−	0.788671i
$668$	5.65088e6			0.489976
$669$	1.55826e6	−	6.82720e6i	0.134610	−	0.589763i
$670$	−443819.	+	213732.i	−0.0381961	+	0.0183943i
$671$	−9.93746e6	−	4.78563e6i	−0.852058	−	0.410329i
$672$	2.49529e6	−	1.09326e7i	0.213156	−	0.933897i
$673$	−2.75844e6	−	1.20855e7i	−0.234761	−	1.02856i	−0.945633	−	0.325235i	$-0.894557\pi$
$673$	−2.75844e6	−	1.20855e7i	−0.234761	−	1.02856i	0.710872	−	0.703321i	$-0.248300\pi$
$674$	1.87252e7	−	9.01758e6i	1.58773	−	0.764610i
$675$	−2.88911e6	+	3.62283e6i	−0.244065	+	0.306047i
$676$	−2.32646e6	+	2.91729e6i	−0.195808	+	0.245535i
$677$	1.12668e7	+	5.42578e6i	0.944772	+	0.454978i	0.841850	−	0.539711i	$-0.181466\pi$
$677$	1.12668e7	+	5.42578e6i	0.944772	+	0.454978i	0.102922	+	0.994689i	$0.467181\pi$
$678$	−5.64636e6	−	7.08031e6i	−0.471731	−	0.591532i
$679$	−2.72681e7			−2.26977
$680$	−1.70622e6	−	2.13953e6i	−0.141502	−	0.177438i
$681$	1.43445e6	+	6.28476e6i	0.118527	+	0.519303i
$682$	−17469.7	−	76539.9i	−0.00143822	−	0.00630126i
$683$	974570.	+	1.22207e6i	0.0799395	+	0.100241i	0.820193	−	0.572087i	$-0.193866\pi$
$683$	974570.	+	1.22207e6i	0.0799395	+	0.100241i	−0.740254	+	0.672328i	$0.765295\pi$
$684$	−5.38116e6			−0.439780
$685$	4.93923e6	+	6.19360e6i	0.402192	+	0.504333i
$686$	−9.86208e6	−	4.74933e6i	−0.800126	−	0.385320i
$687$	−610769.	+	765881.i	−0.0493725	+	0.0619112i
$688$	4.37198e6	−	5.48229e6i	0.352133	−	0.441561i
$689$	5.71137e6	−	2.75045e6i	0.458344	−	0.220727i
$690$	5.04095e6	+	2.20859e7i	0.403079	+	1.76600i
$691$	−4.72364e6	+	2.06956e7i	−0.376341	+	1.64886i	0.332215	+	0.943204i	$0.392204\pi$
$691$	−4.72364e6	+	2.06956e7i	−0.376341	+	1.64886i	−0.708556	+	0.705654i	$0.750653\pi$
$692$	2.27125e6	+	1.09377e6i	0.180301	+	0.0868286i
$693$	−6.10529e6	+	2.94015e6i	−0.482918	+	0.232561i
$694$	781719.	−	3.42493e6i	0.0616101	−	0.269932i
$695$	1.40171e7			1.10077
$696$	−933027.	+	189554.i	−0.0730081	+	0.0148323i
$697$	−2.10244e7			−1.63924
$698$	912814.	−	3.99930e6i	0.0709159	−	0.310703i
$699$	1.00741e6	−	485145.i	0.0779858	−	0.0375560i
$700$	−2.61081e7	−	1.25730e7i	−2.01387	−	0.969827i
$701$	269263.	−	1.17972e6i	0.0206957	−	0.0906740i	−0.963525	−	0.267617i	$-0.913764\pi$
$701$	269263.	−	1.17972e6i	0.0206957	−	0.0906740i	0.984221	+	0.176943i	$0.0566209\pi$
$702$	−624170.	−	2.73467e6i	−0.0478036	−	0.209441i
$703$	−2.81103e7	+	1.35372e7i	−2.14524	+	1.03309i
$704$	−8.75719e6	+	1.09812e7i	−0.665937	+	0.835058i
$705$	1.37212e7	−	1.72058e7i	1.03973	−	1.30378i
$706$	−3.14222e7	−	1.51321e7i	−2.37260	−	1.14258i
$707$	1.08158e7	+	1.35626e7i	0.813789	+	1.02046i
$708$	−6.90332e6			−0.517577
$709$	4.24536e6	+	5.32352e6i	0.317175	+	0.397725i	0.914705	−	0.404121i	$-0.132423\pi$
$709$	4.24536e6	+	5.32352e6i	0.317175	+	0.397725i	−0.597530	+	0.801846i	$0.703851\pi$
$710$	−2.06880e6	−	9.06402e6i	−0.154019	−	0.674800i
$711$	−321302.	−	1.40772e6i	−0.0238363	−	0.104434i
$712$	−461261.	−	578404.i	−0.0340994	−	0.0427593i
$713$	62486.9			0.00460325
$714$	−8.28743e6	−	1.03921e7i	−0.608379	−	0.762883i
$715$	−2.30062e7	−	1.10792e7i	−1.68298	−	0.810481i
$716$	−2.13959e6	+	2.68296e6i	−0.155972	+	0.195583i
$717$	8.48926e6	−	1.06452e7i	0.616697	−	0.773314i
$718$	2.68483e7	−	1.29294e7i	1.94359	−	0.935984i
$719$	3.18846e6	+	1.39696e7i	0.230017	+	1.00777i	0.949625	+	0.313389i	$0.101464\pi$
$719$	3.18846e6	+	1.39696e7i	0.230017	+	1.00777i	−0.719608	+	0.694380i	$0.755679\pi$
$720$	1.94943e6	−	8.54102e6i	0.140145	−	0.614014i
$721$	−7.13793e6	−	3.43745e6i	−0.511369	−	0.246262i
$722$	1.94819e7	−	9.38199e6i	1.39088	−	0.669811i
$723$	−1.10746e6	+	4.85212e6i	−0.0787923	+	0.345212i
$724$	−862398.			−0.0611451
$725$	−689889.	+	2.87791e7i	−0.0487455	+	2.03345i
$726$	8.60027e6			0.605579
$727$	−2.08003e6	+	9.11320e6i	−0.145960	+	0.639492i	0.848023	+	0.529959i	$0.177793\pi$
$727$	−2.08003e6	+	9.11320e6i	−0.145960	+	0.639492i	−0.993983	+	0.109533i	$0.965065\pi$
$728$	−1.62920e6	+	784579.i	−0.113932	+	0.0548666i
$729$	−478812.	−	230584.i	−0.0333692	−	0.0160698i
$730$	−7.54826e6	+	3.30711e7i	−0.524251	+	2.29690i
$731$	−1.69018e6	−	7.40518e6i	−0.116988	−	0.512557i
$732$	4.87377e6	−	2.34708e6i	0.336192	−	0.161901i
$733$	−1.20909e7	+	1.51615e7i	−0.831186	+	1.04227i	0.167224	+	0.985919i	$0.446520\pi$
$733$	−1.20909e7	+	1.51615e7i	−0.831186	+	1.04227i	−0.998411	+	0.0563558i	$0.982052\pi$
$734$	−2.51367e6	+	3.15204e6i	−0.172214	+	0.215949i
$735$	6.22928e6	+	2.99986e6i	0.425324	+	0.204825i
$736$	−1.63600e7	−	2.05148e7i	−1.11324	−	1.39596i
$737$	−344791.			−0.0233823
$738$	−6.89296e6	−	8.64350e6i	−0.465870	−	0.584183i
$739$	−3.99108e6	−	1.74861e7i	−0.268831	−	1.17783i	−0.911375	−	0.411577i	$-0.864978\pi$
$739$	−3.99108e6	−	1.74861e7i	−0.268831	−	1.17783i	0.642544	−	0.766249i	$-0.277879\pi$
$740$	8.56349e6	+	3.75191e7i	0.574873	+	2.51868i
$741$	6.33036e6	+	7.93802e6i	0.423529	+	0.531088i
$742$	1.57958e7			1.05325
$743$	−1.62927e6	−	2.04304e6i	−0.108273	−	0.135771i	0.724742	−	0.689020i	$-0.241959\pi$
$743$	−1.62927e6	−	2.04304e6i	−0.108273	−	0.135771i	−0.833015	+	0.553250i	$0.813388\pi$
$744$	−3576.14	−	1722.18i	−0.000236855	−	0.000114063i
$745$	9.35172e6	−	1.17267e7i	0.617306	−	0.774078i
$746$	2.46244e6	−	3.08780e6i	0.162001	−	0.203143i
$747$	4.14018e6	−	1.99380e6i	0.271467	−	0.130732i
$748$	4.13463e6	+	1.81150e7i	0.270198	+	1.18381i
$749$	−1.08824e6	+	4.76787e6i	−0.0708792	+	0.310542i
$750$	−1.99283e7	−	9.59694e6i	−1.29365	−	0.622988i
$751$	−1.30297e7	+	6.27478e6i	−0.843015	+	0.405975i	−0.804980	−	0.593302i	$-0.797824\pi$
$751$	−1.30297e7	+	6.27478e6i	−0.843015	+	0.405975i	−0.0380349	+	0.999276i	$0.512110\pi$
$752$	−6.20688e6	+	2.71941e7i	−0.400248	+	1.75360i
$753$	−43099.8			−0.00277005
$754$	−1.33600e7	−	1.11884e7i	−0.855810	−	0.716702i
$755$	−1.24280e7			−0.793477
$756$	739532.	−	3.24010e6i	0.0470600	−	0.206184i
$757$	8.06793e6	−	3.88531e6i	0.511708	−	0.246426i	−0.160167	−	0.987090i	$-0.551203\pi$
$757$	8.06793e6	−	3.88531e6i	0.511708	−	0.246426i	0.671875	+	0.740664i	$0.265489\pi$
$758$	−4.99681e6	−	2.40634e6i	−0.315879	−	0.152119i
$759$	−3.52836e6	+	1.54587e7i	−0.222315	+	0.974024i
$760$	1.15903e6	+	5.07805e6i	0.0727883	+	0.318906i
$761$	−928249.	+	447021.i	−0.0581036	+	0.0279812i	−0.462710	−	0.886510i	$-0.653123\pi$
$761$	−928249.	+	447021.i	−0.0581036	+	0.0279812i	0.404606	+	0.914491i	$0.367409\pi$
$762$	−893041.	+	1.11984e6i	−0.0557165	+	0.0698663i
$763$	−1.06805e7	+	1.33930e7i	−0.664173	+	0.832847i
$764$	1.26518e7	+	6.09277e6i	0.784184	+	0.377643i
$765$	−5.91671e6	−	7.41932e6i	−0.365533	−	0.458364i
$766$	1.29142e7			0.795237
$767$	8.12101e6	+	1.01834e7i	0.498450	+	0.625037i
$768$	2.43589e6	+	1.06723e7i	0.149024	+	0.652915i
$769$	718875.	+	3.14960e6i	0.0438367	+	0.192061i	0.992105	−	0.125408i	$-0.0400241\pi$
$769$	718875.	+	3.14960e6i	0.0438367	+	0.192061i	−0.948269	+	0.317469i	$0.897167\pi$
$770$	−3.96711e7	−	4.97460e7i	−2.41128	−	3.02365i
$771$	1.81073e7			1.09703
$772$	−1.72112e7	−	2.15821e7i	−1.03936	−	1.30332i
$773$	2.54395e7	+	1.22510e7i	1.53130	+	0.737436i	0.994347	−	0.106176i	$-0.0338607\pi$
$773$	2.54395e7	+	1.22510e7i	1.53130	+	0.737436i	0.536954	+	0.843612i	$0.319575\pi$
$774$	2.49026e6	−	3.12269e6i	0.149414	−	0.187360i
$775$	−74827.3	+	93830.5i	−0.00447513	+	0.00561164i
$776$	3.65163e6	−	1.75853e6i	0.217687	−	0.104833i
$777$	−4.28781e6	−	1.87861e7i	−0.254791	−	1.11631i
$778$	−5.73258e6	+	2.51161e7i	−0.339548	+	1.48766i
$779$	3.60540e7	+	1.73627e7i	2.12868	+	1.02512i
$780$	1.12832e7	−	5.43372e6i	0.664045	−	0.319787i
$781$	1.44804e6	−	6.34426e6i	0.0849477	−	0.372180i
$782$	−3.11025e7			−1.81877
$783$	−3.23549e6	+	657322.i	−0.188597	+	0.0383154i
$784$	−8.76330e6			−0.509187
$785$	1.33722e6	−	5.85872e6i	0.0774510	−	0.339335i
$786$	−1.73947e7	+	8.37686e6i	−1.00429	+	0.483643i
$787$	−1.53100e7	−	7.37291e6i	−0.881127	−	0.424328i	−0.0620911	−	0.998070i	$-0.519777\pi$
$787$	−1.53100e7	−	7.37291e6i	−0.881127	−	0.424328i	−0.819036	+	0.573742i	$0.805491\pi$
$788$	4.81050e6	−	2.10762e7i	0.275978	−	1.20914i
$789$	1.57582e6	+	6.90410e6i	0.0901183	+	0.394834i
$790$	1.22152e7	−	5.88254e6i	0.696359	−	0.335349i
$791$	−1.26225e7	+	1.58281e7i	−0.717305	+	0.899472i
$792$	627982.	−	787465.i	0.0355741	−	0.0446086i
$793$	−9.19577e6	−	4.42845e6i	−0.519284	−	0.250074i
$794$	−1.06277e7	−	1.33268e7i	−0.598260	−	0.750194i
$795$	1.12772e7			0.632825
$796$	2.08408e6	+	2.61336e6i	0.116582	+	0.146190i
$797$	−2.23020e6	−	9.77113e6i	−0.124365	−	0.544877i	−0.998271	−	0.0587827i	$-0.981278\pi$
$797$	−2.23020e6	−	9.77113e6i	−0.124365	−	0.544877i	0.873906	−	0.486095i	$-0.161579\pi$
$798$	5.62964e6	+	2.46651e7i	0.312949	+	1.37112i
$799$	1.88385e7	+	2.36227e7i	1.04395	+	1.30907i
$800$	5.03961e7			2.78402
$801$	−1.59953e6	−	2.00575e6i	−0.0880869	−	0.110458i
$802$	−2.79937e6	−	1.34810e6i	−0.153682	−	0.0740096i
$803$	−1.48035e7	+	1.85630e7i	−0.810170	+	1.01592i
$804$	105433.	−	132208.i	0.00575221	−	0.00721304i
$805$	4.56277e7	−	2.19731e7i	2.48164	−	1.19509i
$806$	−16165.9	−	70827.3i	−0.000876519	−	0.00384028i
$807$	3.89907e6	−	1.70829e7i	0.210755	−	0.923376i
$808$	−2.32307e6	−	1.11873e6i	−0.125180	−	0.0602833i
$809$	−2.14295e7	+	1.03199e7i	−1.15117	+	0.554376i	−0.909386	−	0.415953i	$-0.863448\pi$
$809$	−2.14295e7	+	1.03199e7i	−1.15117	+	0.554376i	−0.241788	+	0.970329i	$0.577734\pi$
$810$	1.11039e6	−	4.86493e6i	0.0594651	−	0.260534i
$811$	−1.86487e7			−0.995629			−0.497814	−	0.867284i	$-0.665864\pi$
$811$	−1.86487e7			−0.995629			−0.497814	+	0.867284i	$0.665864\pi$
$812$	−8.50995e6	−	1.88115e7i	−0.452936	−	1.00123i
$813$	−5.04664e6			−0.267779
$814$	−1.26057e7	+	5.52293e7i	−0.666817	+	2.92152i
$815$	1.21953e7	−	5.87296e6i	0.643131	−	0.309716i
$816$	1.08368e7	+	5.21872e6i	0.569738	+	0.274371i
$817$	−3.21701e6	+	1.40947e7i	−0.168616	+	0.738754i
$818$	3.81499e6	+	1.67145e7i	0.199347	+	0.873396i
$819$	−5.64961e6	+	2.72071e6i	−0.294313	+	0.141734i
$820$	3.07750e7	−	3.85906e7i	1.59832	−	2.00423i
$821$	1.39830e7	−	1.75341e7i	0.724005	−	0.907873i	−0.274553	−	0.961572i	$-0.588530\pi$
$821$	1.39830e7	−	1.75341e7i	0.724005	−	0.907873i	0.998557	+	0.0536991i	$0.0171012\pi$
$822$	−5.15284e6	−	2.48148e6i	−0.265991	−	0.128095i
$823$	−1.91783e7	−	2.40488e7i	−0.986983	−	1.23764i	−0.971324	−	0.237760i	$-0.923587\pi$
$823$	−1.91783e7	−	2.40488e7i	−0.986983	−	1.23764i	−0.0156587	−	0.999877i	$-0.504985\pi$
$824$	1.17756e6			0.0604180
$825$	−1.89877e7	−	2.38098e7i	−0.971266	−	1.21793i
$826$	7.22208e6	+	3.16420e7i	0.368309	+	1.61367i
$827$	−4.89627e6	−	2.14519e7i	−0.248944	−	1.09069i	−0.932606	−	0.360896i	$-0.882471\pi$
$827$	−4.89627e6	−	2.14519e7i	−0.248944	−	1.09069i	0.683662	−	0.729798i	$-0.260386\pi$
$828$	−4.84865e6	−	6.08001e6i	−0.245779	−	0.308197i
$829$	9.65473e6			0.487926			0.243963	−	0.969785i	$-0.421552\pi$
$829$	9.65473e6			0.487926			0.243963	+	0.969785i	$0.421552\pi$
$830$	2.69022e7	+	3.37342e7i	1.35548	+	1.69971i
$831$	1.27755e7	+	6.15238e6i	0.641766	+	0.309058i
$832$	−8.10358e6	+	1.01616e7i	−0.405853	+	0.508924i
$833$	−5.91849e6	+	7.42155e6i	−0.295528	+	0.370580i
$834$	−9.11745e6	+	4.39073e6i	−0.453898	+	0.218586i
$835$	−4.22067e6	−	1.84920e7i	−0.209491	−	0.917840i
$836$	7.86965e6	−	3.44792e7i	0.389439	−	1.70625i
$837$	−12401.1	−	5972.06i	−0.000611853	−	0.000294653i
$838$	−3.64450e7	+	1.75510e7i	−1.79278	+	0.863360i
$839$	−3.95223e6	+	1.73158e7i	−0.193837	+	0.849256i	0.780678	+	0.624934i	$0.214874\pi$
$839$	−3.95223e6	+	1.73158e7i	−0.193837	+	0.849256i	−0.974515	+	0.224322i	$0.927983\pi$
$840$	−3.21688e6			−0.157303
$841$	−1.35422e7	+	1.54051e7i	−0.660236	+	0.751058i
$842$	4.16879e6			0.202642
$843$	1.79039e6	−	7.84420e6i	0.0867717	−	0.380172i
$844$	1.23052e7	−	5.92585e6i	0.594608	−	0.286348i
$845$	1.12842e7	+	5.43419e6i	0.543662	+	0.261814i
$846$	−3.53541e6	+	1.54897e7i	−0.169830	+	0.744073i
$847$	−4.27819e6	−	1.87440e7i	−0.204904	−	0.897745i
$848$	−1.28781e7	+	6.20176e6i	−0.614981	+	0.296159i
$849$	3.71672e6	−	4.66062e6i	0.176966	−	0.221909i
$850$	3.72449e7	−	4.67036e7i	1.76815	−	2.21719i
$851$	−4.06237e7	−	1.95634e7i	−1.92290	−	0.926018i
$852$	1.98988e6	+	2.49523e6i	0.0939135	+	0.117764i
$853$	−3.83552e7			−1.80489			−0.902446	−	0.430803i	$-0.858230\pi$
$853$	−3.83552e7			−1.80489			−0.902446	+	0.430803i	$0.858230\pi$
$854$	−1.58569e7	−	1.98839e7i	−0.744001	−	0.932948i
$855$	4.01922e6	+	1.76093e7i	0.188030	+	0.823811i
$856$	−161750.	−	708674.i	−0.00754502	−	0.0330569i
$857$	−1.69733e7	−	2.12838e7i	−0.789429	−	0.989913i	−0.999924	−	0.0123181i	$-0.996079\pi$
$857$	−1.69733e7	−	2.12838e7i	−0.789429	−	0.989913i	0.210495	−	0.977595i	$-0.432492\pi$
$858$	1.84349e7			0.854915
$859$	2.36885e7	+	2.97045e7i	1.09536	+	1.37353i	0.921326	+	0.388792i	$0.127107\pi$
$859$	2.36885e7	+	2.97045e7i	1.09536	+	1.37353i	0.174030	+	0.984740i	$0.444321\pi$
$860$	1.60663e7	+	7.73714e6i	0.740749	+	0.356726i
$861$	−1.54093e7	+	1.93226e7i	−0.708394	+	0.888298i
$862$	1.20989e7	−	1.51716e7i	0.554598	−	0.695444i
$863$	1.10967e7	−	5.34387e6i	0.507184	−	0.244247i	−0.162751	−	0.986667i	$-0.552037\pi$
$863$	1.10967e7	−	5.34387e6i	0.507184	−	0.244247i	0.669934	+	0.742420i	$0.266322\pi$
$864$	1.28614e6	+	5.63494e6i	0.0586143	+	0.256806i
$865$	1.88287e6	−	8.24938e6i	0.0855617	−	0.374870i
$866$	−6.88396e6	−	3.31514e6i	−0.311920	−	0.150213i
$867$	225330.	−	108513.i	0.0101805	−	0.00490269i
$868$	19153.7	−	83917.8i	0.000862886	−	0.00378055i
$869$	9.48967e6			0.426287
$870$	−1.27775e7	−	2.82450e7i	−0.572330	−	1.26515i
$871$	−319057.			−0.0142503
$872$	566573.	−	2.48232e6i	0.0252327	−	0.110552i
$873$	1.26629e7	−	6.09812e6i	0.562337	−	0.270807i
$874$	5.33365e7	+	2.56855e7i	2.36182	+	1.13739i
$875$	−1.10029e7	+	4.82068e7i	−0.485833	+	2.12857i
$876$	−2.59117e6	−	1.13527e7i	−0.114087	−	0.499847i
$877$	2.11949e6	−	1.02069e6i	0.0930536	−	0.0448122i	−0.386778	−	0.922173i	$-0.626412\pi$
$877$	2.11949e6	−	1.02069e6i	0.0930536	−	0.0448122i	0.479832	+	0.877361i	$0.340698\pi$
$878$	−1.92977e7	+	2.41985e7i	−0.844829	+	1.05938i
$879$	−527084.	+	660942.i	−0.0230095	+	0.0288530i
$880$	5.18747e7	+	2.49815e7i	2.25813	+	1.08746i
$881$	−1.45842e7	−	1.82881e7i	−0.633059	−	0.793831i	0.357057	−	0.934083i	$-0.383780\pi$
$881$	−1.45842e7	−	1.82881e7i	−0.633059	−	0.793831i	−0.990116	+	0.140252i	$0.955209\pi$
$882$	−4.99154e6			−0.216054
$883$	−1.48123e7	−	1.85740e7i	−0.639324	−	0.801687i	0.351594	−	0.936152i	$-0.385640\pi$
$883$	−1.48123e7	−	1.85740e7i	−0.639324	−	0.801687i	−0.990918	+	0.134466i	$0.957068\pi$
$884$	3.82603e6	+	1.67629e7i	0.164671	+	0.721472i
$885$	5.15612e6	+	2.25904e7i	0.221292	+	0.969542i
$886$	−3.25499e7	−	4.08162e7i	−1.39304	−	1.74682i
$887$	−2.79224e7			−1.19164			−0.595819	−	0.803119i	$-0.703172\pi$
$887$	−2.79224e7			−1.19164			−0.595819	+	0.803119i	$0.703172\pi$
$888$	1.78573e6	+	2.23923e6i	0.0759947	+	0.0952944i
$889$	2.88488e6	+	1.38929e6i	0.122426	+	0.0589573i
$890$	1.50190e7	−	1.88333e7i	0.635575	−	0.796985i
$891$	2.17767e6	−	2.73072e6i	0.0918964	−	0.115234i
$892$	−2.03366e7	+	9.79359e6i	−0.855788	+	0.412126i
$893$	−1.27970e7	−	5.60671e7i	−0.537005	−	2.35277i
$894$	−2.40957e6	+	1.05570e7i	−0.100831	+	0.441771i
$895$	1.03778e7	+	4.99768e6i	0.433059	+	0.208550i
$896$	6.74367e6	−	3.24758e6i	0.280625	−	0.135142i
$897$	−3.26501e6	+	1.43050e7i	−0.135489	+	0.593616i
$898$	5.54321e7			2.29388
$899$	−83798.4	+	17024.5i	−0.00345809	+	0.000702546i
$900$	1.49360e7			0.614648
$901$	−3.44529e6	+	1.50948e7i	−0.141389	+	0.619464i
$902$	6.54629e7	−	3.15253e7i	2.67904	−	1.29016i
$903$	−8.04455e6	−	3.87405e6i	−0.328309	−	0.158105i
$904$	669589.	−	2.93366e6i	0.0272513	−	0.119396i
$905$	644130.	+	2.82212e6i	0.0261428	+	0.114539i
$906$	8.08384e6	−	3.89297e6i	0.327188	−	0.157565i
$907$	2.56447e7	−	3.21575e7i	1.03509	−	1.29797i	0.0815635	−	0.996668i	$-0.474009\pi$
$907$	2.56447e7	−	3.21575e7i	1.03509	−	1.29797i	0.953530	−	0.301298i	$-0.0974199\pi$
$908$	1.29552e7	−	1.62453e7i	0.521469	−	0.653902i
$909$	−8.05578e6	−	3.87946e6i	−0.323369	−	0.155726i
$910$	−3.67102e7	−	4.60332e7i	−1.46955	−	1.84275i
$911$	4.40603e7			1.75894			0.879470	−	0.475954i	$-0.157897\pi$
$911$	4.40603e7			1.75894			0.879470	+	0.475954i	$0.157897\pi$
$912$	−1.42738e7	−	1.78988e7i	−0.568267	−	0.712584i
$913$	6.72030e6	+	2.94436e7i	0.266816	+	1.16900i
$914$	9.73028e6	+	4.26311e7i	0.385265	+	1.68796i
$915$	−1.13208e7	−	1.41959e7i	−0.447019	−	0.560544i
$916$	3.15752e6			0.124339
$917$	2.69100e7	+	3.37441e7i	1.05679	+	1.32518i
$918$	6.17259e6	+	2.97256e6i	0.241747	+	0.116419i
$919$	−3.20961e6	+	4.02473e6i	−0.125361	+	0.157198i	−0.840551	−	0.541732i	$-0.817769\pi$
$919$	−3.20961e6	+	4.02473e6i	−0.125361	+	0.157198i	0.715190	+	0.698930i	$0.246340\pi$
$920$	−4.69320e6	+	5.88509e6i	−0.182810	+	0.229236i
$921$	−1.47205e7	+	7.08902e6i	−0.571839	+	0.275383i
$922$	−1.31618e7	−	5.76655e7i	−0.509903	−	2.23403i
$923$	1.33996e6	−	5.87075e6i	0.0517711	−	0.226824i
$924$	1.96791e7	+	9.47694e6i	0.758271	+	0.365164i
$925$	7.80228e7	−	3.75738e7i	2.99825	−	1.44388i
$926$	−4.18066e6	+	1.83167e7i	−0.160220	+	0.701971i
$927$	4.08347e6			0.156074
$928$	2.75290e7	+	2.30543e7i	1.04935	+	0.878782i
$929$	−1.05055e7			−0.399374			−0.199687	−	0.979860i	$-0.563992\pi$
$929$	−1.05055e7			−0.399374			−0.199687	+	0.979860i	$0.563992\pi$
$930$	28758.8	−	126000.i	0.00109034	−	0.00477710i
$931$	1.62784e7	−	7.83925e6i	0.615512	−	0.296415i
$932$	−3.24718e6	−	1.56376e6i	−0.122452	−	0.0589699i
$933$	−854553.	+	3.74404e6i	−0.0321392	+	0.140811i
$934$	4.80769e6	+	2.10639e7i	0.180331	+	0.790080i
$935$	5.61913e7	−	2.70603e7i	2.10204	−	1.01229i
$936$	581112.	−	728691.i	0.0216805	−	0.0271865i
$937$	−1.07136e7	+	1.34345e7i	−0.398647	+	0.499887i	−0.940126	−	0.340827i	$-0.889293\pi$
$937$	−1.07136e7	+	1.34345e7i	−0.398647	+	0.499887i	0.541479	+	0.840714i	$0.317864\pi$
$938$	−716290.	−	344947.i	−0.0265816	−	0.0128010i
$939$	1.51832e7	+	1.90391e7i	0.561953	+	0.704666i
$940$	−7.09351e7			−2.61843
$941$	−8.58641e6	−	1.07670e7i	−0.316110	−	0.396389i	0.598238	−	0.801318i	$-0.295868\pi$
$941$	−8.58641e6	−	1.07670e7i	−0.316110	−	0.396389i	−0.914348	+	0.404929i	$0.867296\pi$
$942$	965401.	+	4.22970e6i	0.0354471	+	0.155304i
$943$	1.28685e7	+	5.63808e7i	0.471249	+	2.06468i
$944$	−1.83114e7	−	2.29618e7i	−0.668792	−	0.838639i
$945$	−1.11553e7			−0.406351
$946$	1.63664e7	+	2.05228e7i	0.594601	+	0.745606i
$947$	−1.34894e7	−	6.49616e6i	−0.488786	−	0.235387i	0.173223	−	0.984883i	$-0.444582\pi$
$947$	−1.34894e7	−	6.49616e6i	−0.488786	−	0.235387i	−0.662009	+	0.749496i	$0.730296\pi$
$948$	−2.90182e6	+	3.63876e6i	−0.104870	+	0.131502i
$949$	−1.36986e7	+	1.71776e7i	−0.493755	+	0.619150i
$950$	−1.02439e8	+	4.93321e7i	−3.68262	+	1.77346i
$951$	4.47799e6	+	1.96194e7i	0.160558	+	0.703451i
$952$	982787.	−	4.30587e6i	0.0351453	−	0.153981i
$953$	−1.92802e7	−	9.28485e6i	−0.687668	−	0.331164i	0.0572118	−	0.998362i	$-0.481779\pi$
$953$	−1.92802e7	−	9.28485e6i	−0.687668	−	0.331164i	−0.744880	+	0.667199i	$0.767493\pi$
$954$	−7.33530e6	+	3.53249e6i	−0.260944	+	0.125664i
$955$	1.04883e7	−	4.59524e7i	0.372133	−	1.63042i
$956$	−4.38873e7			−1.55308
$957$	520006.	−	2.16923e7i	0.0183539	−	0.765643i
$958$	−3.87654e7			−1.36468
$959$	−2.84501e6	+	1.24648e7i	−0.0998936	+	0.437662i
$960$	−2.08319e7	+	1.00321e7i	−0.729543	+	0.351329i
$961$	2.57937e7	+	1.24216e7i	0.900958	+	0.433878i
$962$	−1.16649e7	+	5.11072e7i	−0.406390	+	1.78051i
$963$	−560906.	−	2.45749e6i	−0.0194906	−	0.0853938i
$964$	1.44533e7	−	6.96034e6i	0.500927	−	0.241234i
$965$	−5.77703e7	+	7.24417e7i	−1.99704	+	2.50421i
$966$	−2.27958e7	+	2.85850e7i	−0.785980	+	0.985587i
$967$	−4.68531e7	−	2.25633e7i	−1.61128	−	0.775954i	−0.611402	−	0.791320i	$-0.709394\pi$
$967$	−4.68531e7	−	2.25633e7i	−1.61128	−	0.775954i	−0.999882	+	0.0153662i	$0.995109\pi$
$968$	1.78172e6	+	2.23421e6i	0.0611155	+	0.0766364i
$969$	−2.47984e7			−0.848427
$970$	8.22812e7	+	1.03177e8i	2.80783	+	3.52091i
$971$	6.63422e6	+	2.90664e7i	0.225809	+	0.989335i	0.953017	+	0.302918i	$0.0979607\pi$
$971$	6.63422e6	+	2.90664e7i	0.225809	+	0.989335i	−0.727207	+	0.686418i	$0.759182\pi$
$972$	381175.	+	1.67004e6i	0.0129407	+	0.0566970i
$973$	1.41049e7	+	1.76870e7i	0.477625	+	0.598923i
$974$	9.82263e6			0.331765
$975$	−1.75705e7	−	2.20328e7i	−0.591935	−	0.742263i
$976$	2.07348e7	+	9.98534e6i	0.696746	+	0.335535i
$977$	5.12962e6	−	6.43234e6i	0.171929	−	0.215592i	−0.688400	−	0.725331i	$-0.741687\pi$
$977$	5.12962e6	−	6.43234e6i	0.171929	−	0.215592i	0.860329	+	0.509739i	$0.170258\pi$
$978$	−6.09284e6	+	7.64018e6i	−0.203691	+	0.255421i
$979$	1.51908e7	−	7.31552e6i	0.506553	−	0.243943i
$980$	−4.95903e6	−	2.17269e7i	−0.164942	−	0.722659i
$981$	1.96472e6	−	8.60801e6i	0.0651822	−	0.285582i
$982$	3.16536e7	+	1.52436e7i	1.04748	+	0.504438i
$983$	6.81380e6	−	3.28135e6i	0.224908	−	0.108310i	−0.318037	−	0.948078i	$-0.603023\pi$
$983$	6.81380e6	−	3.28135e6i	0.224908	−	0.108310i	0.542945	+	0.839768i	$0.317309\pi$
$984$	817421.	−	3.58135e6i	0.0269127	−	0.117912i
$985$	−7.25628e7			−2.38300
$986$	4.17102e7	−	8.47385e6i	1.36631	−	0.277580i
$987$	3.55178e7			1.16052
$988$	7.28229e6	−	3.19058e7i	0.237343	−	1.03987i
$989$	−1.88238e7	+	9.06506e6i	−0.611951	+	0.294700i
$990$	2.95476e7	+	1.42294e7i	0.958151	+	0.461421i
$991$	−1.92035e6	+	8.41362e6i	−0.0621151	+	0.272144i	−0.996443	−	0.0842709i	$-0.973144\pi$
$991$	−1.92035e6	+	8.41362e6i	−0.0621151	+	0.272144i	0.934328	+	0.356415i	$0.116001\pi$
$992$	33310.7	+	145944.i	0.00107474	+	0.00470875i
$993$	−8.91708e6	+	4.29424e6i	−0.286979	+	0.138202i
$994$	9.35537e6	−	1.17313e7i	0.300327	−	0.376599i
$995$	6.99535e6	−	8.77190e6i	0.224002	−	0.280890i
$996$	−1.33450e7	−	6.42659e6i	−0.426254	−	0.205273i
$997$	2.51175e6	+	3.14963e6i	0.0800274	+	0.100351i	0.820233	−	0.572029i	$-0.193844\pi$
$997$	2.51175e6	+	3.14963e6i	0.0800274	+	0.100351i	−0.740206	+	0.672380i	$0.765272\pi$
$998$	4.59188e7			1.45936
$999$	6.19243e6	+	7.76507e6i	0.196312	+	0.246168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.6.g.b.25.11	yes	78
29.7	even	7	inner	87.6.g.b.7.11	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.6.g.b.7.11	✓	78	29.7	even	7	inner
87.6.g.b.25.11	yes	78	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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73808 - 7.61502i) q^{2} +(8.10872 - 3.90495i) q^{3} +(-26.1367 - 12.5868i) q^{4} +(-21.6674 + 94.9309i) q^{5} +(-15.6427 - 68.5352i) q^{6} +(-141.588 + 68.1854i) q^{7} +(14.5636 - 18.2622i) q^{8} +(50.5027 - 63.3284i) q^{9} +O(q^{10})\)	\(q+(1.73808 - 7.61502i) q^{2} +(8.10872 - 3.90495i) q^{3} +(-26.1367 - 12.5868i) q^{4} +(-21.6674 + 94.9309i) q^{5} +(-15.6427 - 68.5352i) q^{6} +(-141.588 + 68.1854i) q^{7} +(14.5636 - 18.2622i) q^{8} +(50.5027 - 63.3284i) q^{9} +(685.241 + 329.995i) q^{10} +(331.912 + 416.204i) q^{11} -261.086 q^{12} +(307.139 + 385.140i) q^{13} +(273.141 + 1196.71i) q^{14} +(195.006 + 854.378i) q^{15} +(-692.543 - 868.421i) q^{16} -1203.18 q^{17} +(-394.469 - 494.649i) q^{18} +(2063.29 + 993.628i) q^{19} +(1761.18 - 2208.46i) q^{20} +(-881.840 + 1105.79i) q^{21} +(3746.30 - 1804.12i) q^{22} +(736.439 + 3226.55i) q^{23} +(46.7792 - 204.953i) q^{24} +(-5726.87 - 2757.91i) q^{25} +(3466.69 - 1669.47i) q^{26} +(162.218 - 710.722i) q^{27} +4558.88 q^{28} +(-1866.67 - 4126.34i) q^{29} +6845.04 q^{30} +(4.20140 - 18.4075i) q^{31} +(-7143.30 + 3440.03i) q^{32} +(4316.64 + 2078.78i) q^{33} +(-2091.23 + 9162.26i) q^{34} +(-3405.05 - 14918.5i) q^{35} +(-2117.07 + 1019.53i) q^{36} +(-8494.42 + 10651.7i) q^{37} +(11152.7 - 13985.0i) q^{38} +(3994.46 + 1923.63i) q^{39} +(1418.09 + 1778.23i) q^{40} +17474.0 q^{41} +(6887.93 + 8637.19i) q^{42} +(1404.76 + 6154.66i) q^{43} +(-3436.41 - 15055.9i) q^{44} +(4917.56 + 6166.42i) q^{45} +25850.2 q^{46} +(-15657.2 - 19633.5i) q^{47} +(-9006.78 - 4337.44i) q^{48} +(4919.04 - 6168.27i) q^{49} +(-30955.3 + 38816.8i) q^{50} +(-9756.26 + 4698.37i) q^{51} +(-3179.93 - 13932.2i) q^{52} +(2863.49 - 12545.8i) q^{53} +(-5130.22 - 2470.58i) q^{54} +(-46702.3 + 22490.6i) q^{55} +(-816.823 + 3578.74i) q^{56} +20610.7 q^{57} +(-34666.6 + 7042.87i) q^{58} +26440.8 q^{59} +(5657.04 - 24785.1i) q^{60} +(-18667.3 + 8989.71i) q^{61} +(-132.871 - 63.9875i) q^{62} +(-2832.53 + 12410.1i) q^{63} +(5871.01 + 25722.6i) q^{64} +(-43216.6 + 20812.0i) q^{65} +(23332.7 - 29258.2i) q^{66} +(-403.824 + 506.379i) q^{67} +(31447.2 + 15144.2i) q^{68} +(18571.1 + 23287.4i) q^{69} -119523. q^{70} +(-7621.56 - 9557.14i) q^{71} +(-421.013 - 1844.58i) q^{72} +(9924.60 + 43482.5i) q^{73} +(66348.7 + 83198.7i) q^{74} -57207.1 q^{75} +(-41421.0 - 51940.3i) q^{76} +(-75373.9 - 36298.2i) q^{77} +(21591.2 - 27074.5i) q^{78} +(11114.4 - 13937.0i) q^{79} +(97445.5 - 46927.3i) q^{80} +(-1459.96 - 6396.50i) q^{81} +(30371.2 - 133065. i) q^{82} +(51113.3 + 24614.9i) q^{83} +(36966.7 - 17802.2i) q^{84} +(26069.8 - 114219. i) q^{85} +49309.5 q^{86} +(-31249.5 - 26170.0i) q^{87} +12434.6 q^{88} +(7047.73 - 30878.1i) q^{89} +(55504.5 - 26729.6i) q^{90} +(-69748.3 - 33589.0i) q^{91} +(21363.7 - 93600.6i) q^{92} +(-37.8126 - 165.668i) q^{93} +(-176723. + 85105.5i) q^{94} +(-139032. + 174341. i) q^{95} +(-44489.9 + 55788.5i) q^{96} +(156332. + 75285.4i) q^{97} +(-38421.9 - 48179.5i) q^{98} +43120.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 10 q^{2} + 117 q^{3} - 202 q^{4} + 49 q^{5} - 90 q^{6} - 60 q^{7} + 273 q^{8} - 1053 q^{9}+O(q^{10}) \) 78 * q + 10 * q^2 + 117 * q^3 - 202 * q^4 + 49 * q^5 - 90 * q^6 - 60 * q^7 + 273 * q^8 - 1053 * q^9	\( 78 q + 10 q^{2} + 117 q^{3} - 202 q^{4} + 49 q^{5} - 90 q^{6} - 60 q^{7} + 273 q^{8} - 1053 q^{9} + 288 q^{10} + 460 q^{11} - 12294 q^{12} + 1883 q^{13} - 4565 q^{14} - 441 q^{15} - 7794 q^{16} - 9592 q^{17} + 810 q^{18} + 2538 q^{19} - 116 q^{20} + 540 q^{21} + 2812 q^{22} - 8224 q^{23} - 8064 q^{24} + 11226 q^{25} - 12824 q^{26} + 9477 q^{27} + 58598 q^{28} + 9286 q^{29} + 10008 q^{30} - 7224 q^{31} - 31647 q^{32} - 360 q^{33} - 3153 q^{34} + 27153 q^{35} - 16362 q^{36} + 17228 q^{37} - 25396 q^{38} + 11340 q^{39} - 32434 q^{40} + 57300 q^{41} + 5049 q^{42} + 33473 q^{43} + 33742 q^{44} - 6804 q^{45} - 28276 q^{46} + 87241 q^{47} - 30402 q^{48} - 72481 q^{49} - 155243 q^{50} + 2475 q^{51} - 198520 q^{52} + 161593 q^{53} - 2187 q^{54} - 123661 q^{55} - 253890 q^{56} + 31590 q^{57} + 301566 q^{58} + 64628 q^{59} + 49302 q^{60} + 87396 q^{61} - 128679 q^{62} - 15633 q^{63} + 42865 q^{64} - 136204 q^{65} + 207 q^{66} + 23066 q^{67} - 28244 q^{68} - 135144 q^{69} + 121526 q^{70} - 276862 q^{71} + 72576 q^{72} + 30459 q^{73} + 481517 q^{74} - 538758 q^{75} + 441053 q^{76} + 70464 q^{77} + 123795 q^{78} - 86879 q^{79} + 281480 q^{80} - 85293 q^{81} + 597939 q^{82} + 262084 q^{83} - 66285 q^{84} + 98649 q^{85} + 53476 q^{86} - 276039 q^{87} + 1616024 q^{88} + 37596 q^{89} + 23328 q^{90} + 87713 q^{91} - 190625 q^{92} + 65016 q^{93} - 377368 q^{94} - 169368 q^{95} - 535626 q^{96} + 683983 q^{97} - 29629 q^{98} - 133974 q^{99}+O(q^{100}) \) 78 * q + 10 * q^2 + 117 * q^3 - 202 * q^4 + 49 * q^5 - 90 * q^6 - 60 * q^7 + 273 * q^8 - 1053 * q^9 + 288 * q^10 + 460 * q^11 - 12294 * q^12 + 1883 * q^13 - 4565 * q^14 - 441 * q^15 - 7794 * q^16 - 9592 * q^17 + 810 * q^18 + 2538 * q^19 - 116 * q^20 + 540 * q^21 + 2812 * q^22 - 8224 * q^23 - 8064 * q^24 + 11226 * q^25 - 12824 * q^26 + 9477 * q^27 + 58598 * q^28 + 9286 * q^29 + 10008 * q^30 - 7224 * q^31 - 31647 * q^32 - 360 * q^33 - 3153 * q^34 + 27153 * q^35 - 16362 * q^36 + 17228 * q^37 - 25396 * q^38 + 11340 * q^39 - 32434 * q^40 + 57300 * q^41 + 5049 * q^42 + 33473 * q^43 + 33742 * q^44 - 6804 * q^45 - 28276 * q^46 + 87241 * q^47 - 30402 * q^48 - 72481 * q^49 - 155243 * q^50 + 2475 * q^51 - 198520 * q^52 + 161593 * q^53 - 2187 * q^54 - 123661 * q^55 - 253890 * q^56 + 31590 * q^57 + 301566 * q^58 + 64628 * q^59 + 49302 * q^60 + 87396 * q^61 - 128679 * q^62 - 15633 * q^63 + 42865 * q^64 - 136204 * q^65 + 207 * q^66 + 23066 * q^67 - 28244 * q^68 - 135144 * q^69 + 121526 * q^70 - 276862 * q^71 + 72576 * q^72 + 30459 * q^73 + 481517 * q^74 - 538758 * q^75 + 441053 * q^76 + 70464 * q^77 + 123795 * q^78 - 86879 * q^79 + 281480 * q^80 - 85293 * q^81 + 597939 * q^82 + 262084 * q^83 - 66285 * q^84 + 98649 * q^85 + 53476 * q^86 - 276039 * q^87 + 1616024 * q^88 + 37596 * q^89 + 23328 * q^90 + 87713 * q^91 - 190625 * q^92 + 65016 * q^93 - 377368 * q^94 - 169368 * q^95 - 535626 * q^96 + 683983 * q^97 - 29629 * q^98 - 133974 * q^99

Introduction

L-functions

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