LMFDB - Embedded newform 144.3.w.a.29.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(5,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.w (of order $12$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			29.19
Character	$\chi$	$=$	144.29
Dual form			144.3.w.a.5.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.702398 - 1.87260i) q^{2} +(1.41045 - 2.64776i) q^{3} +(-3.01327 + 2.63062i) q^{4} +(-0.226081 + 0.843746i) q^{5} +(-5.94890 - 0.781440i) q^{6} +(-7.54519 - 4.35622i) q^{7} +(7.04263 + 3.79492i) q^{8} +(-5.02124 - 7.46908i) q^{9} +O(q^{10})$	\(q+(-0.702398 - 1.87260i) q^{2} +(1.41045 - 2.64776i) q^{3} +(-3.01327 + 2.63062i) q^{4} +(-0.226081 + 0.843746i) q^{5} +(-5.94890 - 0.781440i) q^{6} +(-7.54519 - 4.35622i) q^{7} +(7.04263 + 3.79492i) q^{8} +(-5.02124 - 7.46908i) q^{9} +(1.73880 - 0.169286i) q^{10} +(-19.0671 + 5.10901i) q^{11} +(2.71517 + 11.6888i) q^{12} +(4.46433 - 16.6611i) q^{13} +(-2.85773 + 17.1889i) q^{14} +(1.91516 + 1.78867i) q^{15} +(2.15964 - 15.8536i) q^{16} -5.34982i q^{17} +(-10.4597 + 14.6490i) q^{18} +(14.3774 + 14.3774i) q^{19} +(-1.53833 - 3.13717i) q^{20} +(-22.1763 + 13.8336i) q^{21} +(22.9598 + 32.1165i) q^{22} +(4.79666 + 8.30806i) q^{23} +(19.9813 - 13.2946i) q^{24} +(20.9898 + 12.1185i) q^{25} +(-34.3354 + 3.34282i) q^{26} +(-26.8585 + 2.76021i) q^{27} +(34.1953 - 6.72208i) q^{28} +(-6.61082 - 24.6719i) q^{29} +(2.00427 - 4.84269i) q^{30} +(-27.1557 - 47.0351i) q^{31} +(-31.2044 + 7.09138i) q^{32} +(-13.3658 + 57.6911i) q^{33} +(-10.0181 + 3.75770i) q^{34} +(5.38136 - 5.38136i) q^{35} +(34.7787 + 9.29741i) q^{36} +(38.6246 - 38.6246i) q^{37} +(16.8245 - 37.0218i) q^{38} +(-37.8178 - 35.3202i) q^{39} +(-4.79415 + 5.08423i) q^{40} +(10.1568 + 17.5921i) q^{41} +(41.4814 + 31.8108i) q^{42} +(-7.60062 - 28.3659i) q^{43} +(44.0145 - 65.5532i) q^{44} +(7.43721 - 2.54803i) q^{45} +(12.1885 - 14.8178i) q^{46} +(32.8968 + 18.9929i) q^{47} +(-38.9304 - 28.0789i) q^{48} +(13.4532 + 23.3017i) q^{49} +(7.94988 - 47.8176i) q^{50} +(-14.1650 - 7.54568i) q^{51} +(30.3769 + 61.9484i) q^{52} +(-11.0931 - 11.0931i) q^{53} +(24.0342 + 48.3566i) q^{54} -17.2428i q^{55} +(-36.6065 - 59.3126i) q^{56} +(58.3465 - 17.7892i) q^{57} +(-41.5572 + 29.7089i) q^{58} +(4.88246 - 18.2216i) q^{59} +(-10.4762 - 0.351703i) q^{60} +(20.1439 - 5.39753i) q^{61} +(-69.0038 + 83.8892i) q^{62} +(5.34923 + 78.2292i) q^{63} +(35.1972 + 53.4524i) q^{64} +(13.0484 + 7.53352i) q^{65} +(117.421 - 15.4932i) q^{66} +(26.6773 - 99.5610i) q^{67} +(14.0734 + 16.1205i) q^{68} +(28.7632 - 0.982251i) q^{69} +(-13.8570 - 6.29729i) q^{70} -89.4379 q^{71} +(-7.01816 - 71.6571i) q^{72} +46.0108i q^{73} +(-99.4584 - 45.1987i) q^{74} +(61.6920 - 38.4834i) q^{75} +(-81.1445 - 5.50151i) q^{76} +(166.121 + 44.5119i) q^{77} +(-39.5775 + 95.6266i) q^{78} +(3.15641 - 5.46705i) q^{79} +(12.8881 + 5.40638i) q^{80} +(-30.5744 + 75.0080i) q^{81} +(25.8089 - 31.3764i) q^{82} +(5.63889 + 21.0446i) q^{83} +(30.4325 - 100.022i) q^{84} +(4.51389 + 1.20949i) q^{85} +(-47.7793 + 34.1571i) q^{86} +(-74.6495 - 17.2948i) q^{87} +(-153.671 - 36.3772i) q^{88} -68.9602 q^{89} +(-9.99533 - 12.1372i) q^{90} +(-106.264 + 106.264i) q^{91} +(-36.3090 - 12.4162i) q^{92} +(-162.839 + 5.56090i) q^{93} +(12.4596 - 74.9431i) q^{94} +(-15.3813 + 8.88040i) q^{95} +(-25.2361 + 92.6236i) q^{96} +(-51.0238 + 88.3757i) q^{97} +(34.1853 - 41.5596i) q^{98} +(133.900 + 116.760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.702398	−	1.87260i	−0.351199	−	0.936301i
$2$	−0.702398	−	1.87260i	−0.351199	−	0.936301i
$3$	1.41045	−	2.64776i	0.470152	−	0.882586i
$3$	1.41045	−	2.64776i	0.470152	−	0.882586i
$4$	−3.01327	+	2.63062i	−0.753318	+	0.657656i
$5$	−0.226081	+	0.843746i	−0.0452162	+	0.168749i	−0.984842	−	0.173455i	$-0.944507\pi$
$5$	−0.226081	+	0.843746i	−0.0452162	+	0.168749i	0.939626	+	0.342204i	$0.111173\pi$
$6$	−5.94890	−	0.781440i	−0.991483	−	0.130240i
$7$	−7.54519	−	4.35622i	−1.07788	−	0.622317i	−0.147559	−	0.989053i	$-0.547142\pi$
$7$	−7.54519	−	4.35622i	−1.07788	−	0.622317i	−0.930325	+	0.366737i	$0.880475\pi$
$8$	7.04263	+	3.79492i	0.880329	+	0.474365i
$9$	−5.02124	−	7.46908i	−0.557915	−	0.829898i
$10$	1.73880	−	0.169286i	0.173880	−	0.0169286i
$11$	−19.0671	+	5.10901i	−1.73337	+	0.464456i	−0.980956	−	0.194231i	$-0.937779\pi$
$11$	−19.0671	+	5.10901i	−1.73337	+	0.464456i	−0.752417	+	0.658687i	$0.771112\pi$
$12$	2.71517	+	11.6888i	0.226264	+	0.974066i
$13$	4.46433	−	16.6611i	0.343410	−	1.28162i	−0.551049	−	0.834473i	$-0.685772\pi$
$13$	4.46433	−	16.6611i	0.343410	−	1.28162i	0.894459	−	0.447151i	$-0.147561\pi$
$14$	−2.85773	+	17.1889i	−0.204124	+	1.22778i
$15$	1.91516	+	1.78867i	0.127677	+	0.119245i
$16$	2.15964	−	15.8536i	0.134977	−	0.990849i
$17$		−	5.34982i		−	0.314695i	−0.987543	−	0.157348i	$-0.949706\pi$
$17$		−	5.34982i		−	0.314695i	0.987543	−	0.157348i	$-0.0502943\pi$
$18$	−10.4597	+	14.6490i	−0.581095	+	0.813836i
$19$	14.3774	+	14.3774i	0.756704	+	0.756704i	0.975721	−	0.219017i	$-0.0702850\pi$
$19$	14.3774	+	14.3774i	0.756704	+	0.756704i	−0.219017	+	0.975721i	$0.570285\pi$
$20$	−1.53833	−	3.13717i	−0.0769167	−	0.156859i
$21$	−22.1763	+	13.8336i	−1.05602	+	0.658742i
$22$	22.9598	+	32.1165i	1.04363	+	1.45984i
$23$	4.79666	+	8.30806i	0.208550	+	0.361220i	0.951258	−	0.308396i	$-0.0997922\pi$
$23$	4.79666	+	8.30806i	0.208550	+	0.361220i	−0.742708	+	0.669616i	$0.766459\pi$
$24$	19.9813	−	13.2946i	0.832555	−	0.553942i
$25$	20.9898	+	12.1185i	0.839594	+	0.484740i
$26$	−34.3354	+	3.34282i	−1.32059	+	0.128570i
$27$	−26.8585	+	2.76021i	−0.994761	+	0.102230i
$28$	34.1953	−	6.72208i	1.22126	−	0.240074i
$29$	−6.61082	−	24.6719i	−0.227959	−	0.850756i	−0.981197	−	0.193007i	$-0.938176\pi$
$29$	−6.61082	−	24.6719i	−0.227959	−	0.850756i	0.753238	−	0.657748i	$-0.228491\pi$
$30$	2.00427	−	4.84269i	0.0668090	−	0.161423i
$31$	−27.1557	−	47.0351i	−0.875991	−	1.51726i	−0.855704	−	0.517466i	$-0.826875\pi$
$31$	−27.1557	−	47.0351i	−0.875991	−	1.51726i	−0.0202867	−	0.999794i	$-0.506458\pi$
$32$	−31.2044	+	7.09138i	−0.975136	+	0.221606i
$33$	−13.3658	+	57.6911i	−0.405026	+	1.74821i
$34$	−10.0181	+	3.75770i	−0.294650	+	0.110521i
$35$	5.38136	−	5.38136i	0.153753	−	0.153753i
$36$	34.7787	+	9.29741i	0.966075	+	0.258261i
$37$	38.6246	−	38.6246i	1.04391	−	1.04391i	0.0449179	−	0.998991i	$-0.485697\pi$
$37$	38.6246	−	38.6246i	1.04391	−	1.04391i	0.998991	−	0.0449179i	$-0.0143026\pi$
$38$	16.8245	−	37.0218i	0.442749	−	0.974257i
$39$	−37.8178	−	35.3202i	−0.969688	−	0.905646i
$40$	−4.79415	+	5.08423i	−0.119854	+	0.127106i
$41$	10.1568	+	17.5921i	0.247727	+	0.429077i	0.962895	−	0.269877i	$-0.0869829\pi$
$41$	10.1568	+	17.5921i	0.247727	+	0.429077i	−0.715167	+	0.698953i	$0.753650\pi$
$42$	41.4814	+	31.8108i	0.987653	+	0.757400i
$43$	−7.60062	−	28.3659i	−0.176759	−	0.659672i	−0.996245	−	0.0865739i	$-0.972408\pi$
$43$	−7.60062	−	28.3659i	−0.176759	−	0.659672i	0.819487	−	0.573098i	$-0.194259\pi$
$44$	44.0145	−	65.5532i	1.00033	−	1.48985i
$45$	7.43721	−	2.54803i	0.165271	−	0.0566229i
$46$	12.1885	−	14.8178i	0.264968	−	0.322126i
$47$	32.8968	+	18.9929i	0.699931	+	0.404105i	0.807322	−	0.590112i	$-0.200916\pi$
$47$	32.8968	+	18.9929i	0.699931	+	0.404105i	−0.107391	+	0.994217i	$0.534250\pi$
$48$	−38.9304	−	28.0789i	−0.811049	−	0.584978i
$49$	13.4532	+	23.3017i	0.274556	+	0.475545i
$50$	7.94988	−	47.8176i	0.158998	−	0.956352i
$51$	−14.1650	−	7.54568i	−0.277746	−	0.147955i
$52$	30.3769	+	61.9484i	0.584170	+	1.19132i
$53$	−11.0931	−	11.0931i	−0.209303	−	0.209303i	0.594668	−	0.803971i	$-0.297283\pi$
$53$	−11.0931	−	11.0931i	−0.209303	−	0.209303i	−0.803971	+	0.594668i	$0.797283\pi$
$54$	24.0342	+	48.3566i	0.445077	+	0.895492i
$55$		−	17.2428i		−	0.313506i
$56$	−36.6065	−	59.3126i	−0.653687	−	1.05915i
$57$	58.3465	−	17.7892i	1.02362	−	0.312091i
$58$	−41.5572	+	29.7089i	−0.716504	+	0.512223i
$59$	4.88246	−	18.2216i	0.0827536	−	0.308841i	−0.912126	−	0.409911i	$-0.865560\pi$
$59$	4.88246	−	18.2216i	0.0827536	−	0.308841i	0.994879	+	0.101070i	$0.0322266\pi$
$60$	−10.4762	−	0.351703i	−0.174604	−	0.00586172i
$61$	20.1439	−	5.39753i	0.330227	−	0.0884842i	−0.0898960	−	0.995951i	$-0.528653\pi$
$61$	20.1439	−	5.39753i	0.330227	−	0.0884842i	0.420123	+	0.907467i	$0.361987\pi$
$62$	−69.0038	+	83.8892i	−1.11296	+	1.35305i
$63$	5.34923	+	78.2292i	0.0849084	+	1.24173i
$64$	35.1972	+	53.4524i	0.549957	+	0.835193i
$65$	13.0484	+	7.53352i	0.200745	+	0.115900i
$66$	117.421	−	15.4932i	1.77910	−	0.234745i
$67$	26.6773	−	99.5610i	0.398169	−	1.48599i	−0.418147	−	0.908379i	$-0.637320\pi$
$67$	26.6773	−	99.5610i	0.398169	−	1.48599i	0.816316	−	0.577606i	$-0.196013\pi$
$68$	14.0734	+	16.1205i	0.206961	+	0.237066i
$69$	28.7632	−	0.982251i	0.416858	−	0.0142355i
$70$	−13.8570	−	6.29729i	−0.197957	−	0.0899613i
$71$	−89.4379			−1.25969			−0.629845	−	0.776721i	$-0.716881\pi$
$71$	−89.4379			−1.25969			−0.629845	+	0.776721i	$0.716881\pi$
$72$	−7.01816	−	71.6571i	−0.0974744	−	0.995238i
$73$			46.0108i			0.630285i	0.949044	+	0.315142i	$0.102052\pi$
$73$			46.0108i			0.630285i	−0.949044	+	0.315142i	$0.897948\pi$
$74$	−99.4584	−	45.1987i	−1.34403	−	0.610793i
$75$	61.6920	−	38.4834i	0.822560	−	0.513112i
$76$	−81.1445	−	5.50151i	−1.06769	−	0.0723882i
$77$	166.121	+	44.5119i	2.15741	+	0.578077i
$78$	−39.5775	+	95.6266i	−0.507404	+	1.22598i
$79$	3.15641	−	5.46705i	0.0399545	−	0.0692032i	−0.845357	−	0.534202i	$-0.820612\pi$
$79$	3.15641	−	5.46705i	0.0399545	−	0.0692032i	0.885311	+	0.464999i	$0.153945\pi$
$80$	12.8881	+	5.40638i	0.161102	+	0.0675797i
$81$	−30.5744	+	75.0080i	−0.377461	+	0.926025i
$82$	25.8089	−	31.3764i	0.314743	−	0.382639i
$83$	5.63889	+	21.0446i	0.0679385	+	0.253550i	0.991540	−	0.129805i	$-0.0414352\pi$
$83$	5.63889	+	21.0446i	0.0679385	+	0.253550i	−0.923601	+	0.383355i	$0.874769\pi$
$84$	30.4325	−	100.022i	0.362291	−	1.19074i
$85$	4.51389	+	1.20949i	0.0531046	+	0.0142293i
$86$	−47.7793	+	34.1571i	−0.555574	+	0.397175i
$87$	−74.6495	−	17.2948i	−0.858040	−	0.198790i
$88$	−153.671	−	36.3772i	−1.74626	−	0.413377i
$89$	−68.9602			−0.774834			−0.387417	−	0.921905i	$-0.626633\pi$
$89$	−68.9602			−0.774834			−0.387417	+	0.921905i	$0.626633\pi$
$90$	−9.99533	−	12.1372i	−0.111059	−	0.134858i
$91$	−106.264	+	106.264i	−1.16773	+	1.16773i
$92$	−36.3090	−	12.4162i	−0.394663	−	0.134959i
$93$	−162.839	+	5.56090i	−1.75096	+	0.0597946i
$94$	12.4596	−	74.9431i	0.132549	−	0.797267i
$95$	−15.3813	+	8.88040i	−0.161908	+	0.0934779i
$96$	−25.2361	+	92.6236i	−0.262876	+	0.964830i
$97$	−51.0238	+	88.3757i	−0.526018	+	0.911090i	0.473522	+	0.880782i	$0.342982\pi$
$97$	−51.0238	+	88.3757i	−0.526018	+	0.911090i	−0.999541	+	0.0303084i	$0.990351\pi$
$98$	34.1853	−	41.5596i	0.348829	−	0.424078i
$99$	133.900	+	116.760i	1.35253	+	1.17940i
$100$	−95.1273	+	18.7000i	−0.951273	+	0.187000i
$101$	48.9718	−	13.1220i	0.484870	−	0.129920i	−0.00809962	−	0.999967i	$-0.502578\pi$
$101$	48.9718	−	13.1220i	0.484870	−	0.129920i	0.492969	+	0.870047i	$0.335912\pi$
$102$	−4.18056	+	31.8255i	−0.0409859	+	0.312015i
$103$	−24.0189	+	13.8673i	−0.233194	+	0.134634i	−0.612044	−	0.790823i	$-0.709653\pi$
$103$	−24.0189	+	13.8673i	−0.233194	+	0.134634i	0.378851	+	0.925458i	$0.376319\pi$
$104$	94.6681	−	100.396i	0.910270	−	0.965348i
$105$	−6.65837	−	21.8387i	−0.0634131	−	0.207988i
$106$	−12.9811	+	28.5646i	−0.122464	+	0.269477i
$107$	128.607	+	128.607i	1.20194	+	1.20194i	0.973577	+	0.228360i	$0.0733362\pi$
$107$	128.607	+	128.607i	1.20194	+	1.20194i	0.228360	+	0.973577i	$0.426664\pi$
$108$	73.6711	−	78.9720i	0.682139	−	0.731222i
$109$	23.5178	+	23.5178i	0.215759	+	0.215759i	0.806709	−	0.590949i	$-0.201247\pi$
$109$	23.5178	+	23.5178i	0.215759	+	0.215759i	−0.590949	+	0.806709i	$0.701247\pi$
$110$	−32.2890	+	12.1113i	−0.293536	+	0.110103i
$111$	−47.7903	−	156.747i	−0.430544	−	1.41213i
$112$	−85.3565	+	110.210i	−0.762112	+	0.984021i
$113$	12.1264	−	7.00118i	0.107313	−	0.0619573i	−0.445383	−	0.895340i	$-0.646932\pi$
$113$	12.1264	−	7.00118i	0.107313	−	0.0619573i	0.552696	+	0.833383i	$0.313599\pi$
$114$	−74.2945	−	96.7646i	−0.651706	−	0.848812i
$115$	−8.09432	+	2.16887i	−0.0703854	+	0.0188597i
$116$	84.8227	+	56.9526i	0.731230	+	0.490971i
$117$	−146.860	+	50.3149i	−1.25521	+	0.430042i
$118$	−37.5512	+	3.65591i	−0.318231	+	0.0309823i
$119$	−23.3050	+	40.3654i	−0.195840	+	0.339205i
$120$	6.69988	+	19.8648i	0.0558323	+	0.165540i
$121$	232.663	−	134.328i	1.92284	−	1.11015i
$122$	−24.2564	−	33.9302i	−0.198823	−	0.278117i
$123$	60.9055	−	2.07990i	0.495166	−	0.0169097i
$124$	205.559	+	70.2931i	1.65773	+	0.566880i
$125$	−30.4119	+	30.4119i	−0.243296	+	0.243296i
$126$	142.735	−	64.9650i	1.13282	−	0.515596i
$127$	0.611260			0.00481307			0.00240654	−	0.999997i	$-0.499234\pi$
$127$	0.611260			0.00481307			0.00240654	+	0.999997i	$0.499234\pi$
$128$	75.3725	−	103.455i	0.588848	−	0.808244i
$129$	−85.8263	−	19.8842i	−0.665320	−	0.154141i
$130$	4.94208	−	29.7261i	0.0380160	−	0.228662i
$131$	85.3466	+	22.8685i	0.651501	+	0.174569i	0.569407	−	0.822056i	$-0.307173\pi$
$131$	85.3466	+	22.8685i	0.651501	+	0.174569i	0.0820934	+	0.996625i	$0.473839\pi$
$132$	−111.489	−	209.000i	−0.844610	−	1.58333i
$133$	−45.8491	−	171.111i	−0.344730	−	1.28655i
$134$	−205.176	+	19.9755i	−1.53117	+	0.149071i
$135$	3.74329	−	23.2858i	0.0277281	−	0.172487i
$136$	20.3021	−	37.6768i	0.149280	−	0.277035i
$137$	−44.8139	+	77.6199i	−0.327109	+	0.566569i	−0.981937	−	0.189209i	$-0.939408\pi$
$137$	−44.8139	+	77.6199i	−0.327109	+	0.566569i	0.654828	+	0.755778i	$0.272741\pi$
$138$	−22.0426	−	53.1720i	−0.159729	−	0.385305i
$139$	58.1535	+	15.5822i	0.418371	+	0.112102i	0.461862	−	0.886952i	$-0.347181\pi$
$139$	58.1535	+	15.5822i	0.418371	+	0.112102i	−0.0434914	+	0.999054i	$0.513848\pi$
$140$	−2.05918	+	30.3719i	−0.0147084	+	0.216942i
$141$	96.6881	−	60.3139i	0.685731	−	0.427758i
$142$	62.8210	+	167.482i	0.442402	+	1.17945i
$143$			340.487i			2.38103i
$144$	−129.256	+	63.4741i	−0.897609	+	0.440792i
$145$	22.3114			0.153872
$146$	86.1598	−	32.3179i	0.590136	−	0.221355i
$147$	80.6724	−	2.75493i	0.548792	−	0.0187410i
$148$	−14.7797	+	217.993i	−0.0998629	+	1.47293i
$149$	52.6154	−	196.363i	0.353124	−	1.31788i	−0.529706	−	0.848182i	$-0.677698\pi$
$149$	52.6154	−	196.363i	0.353124	−	1.31788i	0.882829	−	0.469694i	$-0.155636\pi$
$150$	−115.396	−	88.4939i	−0.769310	−	0.589959i
$151$	−29.6364	−	17.1106i	−0.196267	−	0.113315i	0.398646	−	0.917105i	$-0.369480\pi$
$151$	−29.6364	−	17.1106i	−0.196267	−	0.113315i	−0.594913	+	0.803790i	$0.702814\pi$
$152$	46.6936	+	155.816i	0.307195	+	1.02510i
$153$	−39.9583	+	26.8627i	−0.261165	+	0.175573i
$154$	−33.3298	−	342.343i	−0.216427	−	2.22301i
$155$	45.8250	−	12.2788i	0.295645	−	0.0792179i
$156$	206.870	+	6.94494i	1.32609	+	0.0445188i
$157$	−33.2153	+	123.961i	−0.211562	+	0.789561i	0.775786	+	0.630996i	$0.217353\pi$
$157$	−33.2153	+	123.961i	−0.211562	+	0.789561i	−0.987349	+	0.158565i	$0.949313\pi$
$158$	−12.4547	−	2.07064i	−0.0788270	−	0.0131053i
$159$	−45.0180	+	13.7255i	−0.283132	+	0.0863237i
$160$	1.07139	−	27.9318i	0.00669618	−	0.174574i
$161$		−	83.5811i		−	0.519137i
$162$	161.936	+	4.56812i	0.999602	+	0.0281982i
$163$	−203.435	−	203.435i	−1.24807	−	1.24807i	−0.956573	−	0.291493i	$-0.905848\pi$
$163$	−203.435	−	203.435i	−1.24807	−	1.24807i	−0.291493	−	0.956573i	$-0.594152\pi$
$164$	−76.8836	−	26.2911i	−0.468802	−	0.160312i
$165$	−45.6548	−	24.3202i	−0.276696	−	0.147395i
$166$	35.4475	−	25.3411i	0.213539	−	0.152657i
$167$	−14.9598	−	25.9112i	−0.0895799	−	0.155157i	0.817754	−	0.575568i	$-0.195219\pi$
$167$	−14.9598	−	25.9112i	−0.0895799	−	0.155157i	−0.907334	+	0.420411i	$0.861886\pi$
$168$	−208.677	+	13.2674i	−1.24213	+	0.0789725i
$169$	−111.304	−	64.2614i	−0.658603	−	0.380245i
$170$	−0.905649	−	9.30226i	−0.00532735	−	0.0547192i
$171$	35.1936	−	179.578i	0.205811	−	1.05016i
$172$	97.5227	+	65.4798i	0.566992	+	0.380697i
$173$	−49.5987	−	185.105i	−0.286698	−	1.06997i	−0.947590	−	0.319490i	$-0.896488\pi$
$173$	−49.5987	−	185.105i	−0.286698	−	1.06997i	0.660892	−	0.750481i	$-0.270178\pi$
$174$	20.0475	+	151.937i	0.115215	+	0.873199i
$175$	−105.582	−	182.873i	−0.603323	−	1.04499i
$176$	39.8181	+	313.315i	0.226239	+	1.78020i
$177$	−41.3599	−	38.6283i	−0.233672	−	0.218239i
$178$	48.4375	+	129.135i	0.272121	+	0.725478i
$179$	184.893	−	184.893i	1.03292	−	1.03292i	0.0334811	−	0.999439i	$-0.489341\pi$
$179$	184.893	−	184.893i	1.03292	−	1.03292i	0.999439	−	0.0334811i	$-0.0106593\pi$
$180$	−15.7075	+	27.2424i	−0.0872636	+	0.151347i
$181$	65.5568	−	65.5568i	0.362192	−	0.362192i	−0.502427	−	0.864619i	$-0.667560\pi$
$181$	65.5568	−	65.5568i	0.362192	−	0.362192i	0.864619	+	0.502427i	$0.167560\pi$
$182$	273.629	+	124.350i	1.50345	+	0.683242i
$183$	14.1207	−	60.9491i	0.0771621	−	0.333055i
$184$	2.25270	+	76.7135i	0.0122430	+	0.416921i
$185$	23.8571	+	41.3217i	0.128957	+	0.223360i
$186$	124.791	+	301.027i	0.670921	+	1.61843i
$187$	27.3323	+	102.006i	0.146162	+	0.545484i
$188$	−149.090	+	29.3080i	−0.793033	+	0.155894i
$189$	214.677	+	96.1753i	1.13586	+	0.508864i
$190$	27.4333	+	22.5655i	0.144386	+	0.118766i
$191$	225.506	+	130.196i	1.18066	+	0.681655i	0.956168	−	0.292820i	$-0.0945937\pi$
$191$	225.506	+	130.196i	1.18066	+	0.681655i	0.224494	+	0.974475i	$0.427927\pi$
$192$	191.173	−	17.8016i	0.995693	−	0.0927165i
$193$	85.0009	+	147.226i	0.440419	+	0.762828i	0.997720	−	0.0674820i	$-0.0214965\pi$
$193$	85.0009	+	147.226i	0.440419	+	0.762828i	−0.557301	+	0.830310i	$0.688163\pi$
$194$	201.332	+	33.4722i	1.03779	+	0.172537i
$195$	38.3512	−	23.9234i	0.196673	−	0.122684i
$196$	−101.836	−	34.8240i	−0.519573	−	0.177673i
$197$	−82.1206	−	82.1206i	−0.416856	−	0.416856i	0.467263	−	0.884119i	$-0.345240\pi$
$197$	−82.1206	−	82.1206i	−0.416856	−	0.416856i	−0.884119	+	0.467263i	$0.845240\pi$
$198$	124.594	−	332.754i	0.629263	−	1.68057i
$199$			284.140i			1.42784i	0.700229	+	0.713918i	$0.253081\pi$
$199$			284.140i			1.42784i	−0.700229	+	0.713918i	$0.746919\pi$
$200$	101.835	+	165.001i	0.509175	+	0.825004i
$201$	−225.986	−	211.061i	−1.12431	−	1.05006i
$202$	−58.9699	−	82.4879i	−0.291930	−	0.408356i
$203$	−57.5963	+	214.952i	−0.283726	+	1.05888i
$204$	62.5330	−	14.5257i	0.306534	−	0.0712042i
$205$	−17.1396	+	4.59253i	−0.0836076	+	0.0224026i
$206$	42.8388	+	35.2375i	0.207956	+	0.171056i
$207$	37.9684	−	77.5433i	0.183422	−	0.374606i
$208$	−254.497	−	106.758i	−1.22354	−	0.513258i
$209$	−347.589	−	200.681i	−1.66311	−	0.960195i
$210$	−36.2184	+	27.8080i	−0.172468	+	0.132419i
$211$	−41.0692	+	153.272i	−0.194641	+	0.726409i	0.797719	+	0.603030i	$0.206040\pi$
$211$	−41.0692	+	153.272i	−0.194641	+	0.726409i	−0.992360	+	0.123380i	$0.960627\pi$
$212$	62.6081	+	4.24476i	0.295321	+	0.0200224i
$213$	−126.148	+	236.810i	−0.592245	+	1.11178i
$214$	150.497	−	331.164i	0.703255	−	1.54749i
$215$	25.6520			0.119311
$216$	−199.629	−	82.4868i	−0.924211	−	0.381883i
$217$			473.185i			2.18057i
$218$	27.5206	−	60.5582i	0.126241	−	0.277790i
$219$	121.825	+	64.8961i	0.556280	+	0.296329i
$220$	45.3594	+	51.9574i	0.206179	+	0.236170i
$221$	−89.1340	−	23.8834i	−0.403321	−	0.108070i
$222$	−259.957	+	199.591i	−1.17098	+	0.899058i
$223$	118.449	−	205.160i	0.531163	−	0.920001i	−0.468176	−	0.883635i	$-0.655089\pi$
$223$	118.449	−	205.160i	0.531163	−	0.920001i	0.999339	−	0.0363657i	$-0.0115781\pi$
$224$	266.334	+	82.4271i	1.18899	+	0.367978i
$225$	−14.8809	−	217.625i	−0.0661375	−	0.967221i
$226$	−21.6280	−	17.7903i	−0.0956990	−	0.0787181i
$227$	−54.5257	−	203.493i	−0.240201	−	0.896444i	−0.975735	−	0.218956i	$-0.929735\pi$
$227$	−54.5257	−	203.493i	−0.240201	−	0.896444i	0.735533	−	0.677489i	$-0.236932\pi$
$228$	−129.017	+	207.091i	−0.565865	+	0.908295i
$229$	−105.249	−	28.2013i	−0.459602	−	0.123150i	0.0215870	−	0.999767i	$-0.493128\pi$
$229$	−105.249	−	28.2013i	−0.459602	−	0.123150i	−0.481189	+	0.876617i	$0.659795\pi$
$230$	9.74686	+	13.6340i	0.0423776	+	0.0592784i
$231$	352.163	−	377.066i	1.52451	−	1.63232i
$232$	47.0703	−	198.843i	0.202889	−	0.857080i
$233$	−253.954			−1.08993			−0.544965	−	0.838459i	$-0.683457\pi$
$233$	−253.954			−1.08993			−0.544965	+	0.838459i	$0.683457\pi$
$234$	197.374	+	239.668i	0.843477	+	1.02422i
$235$	−23.4626	+	23.4626i	−0.0998406	+	0.0998406i
$236$	33.2220	+	67.7506i	0.140771	+	0.287079i
$237$	−10.0235	−	16.0684i	−0.0422931	−	0.0677993i
$238$	91.9577	+	15.2884i	0.386377	+	0.0642368i
$239$	−362.076	+	209.044i	−1.51496	+	0.874663i	−0.515115	+	0.857121i	$0.672251\pi$
$239$	−362.076	+	209.044i	−1.51496	+	0.874663i	−0.999846	+	0.0175416i	$0.994416\pi$
$240$	32.4929	−	26.4992i	0.135387	−	0.110413i
$241$	−64.9733	+	112.537i	−0.269599	+	0.466959i	−0.968758	−	0.248007i	$-0.920224\pi$
$241$	−64.9733	+	112.537i	−0.269599	+	0.466959i	0.699160	+	0.714966i	$0.253558\pi$
$242$	−414.965	−	341.334i	−1.71473	−	1.41047i
$243$	155.479	+	186.749i	0.639833	+	0.768514i
$244$	−46.5001	+	69.2552i	−0.190574	+	0.283833i
$245$	−22.7022	+	6.08304i	−0.0926622	+	0.0248287i
$246$	−46.6747	−	112.591i	−0.189735	−	0.457686i
$247$	303.728	−	175.358i	1.22967	−	0.709950i
$248$	−12.7534	−	434.304i	−0.0514251	−	1.75123i
$249$	63.6745	+	14.7521i	0.255721	+	0.0592453i
$250$	78.3108	+	35.5882i	0.313243	+	0.142353i
$251$	−320.937	−	320.937i	−1.27863	−	1.27863i	−0.941432	−	0.337202i	$-0.890519\pi$
$251$	−320.937	−	320.937i	−1.27863	−	1.27863i	−0.337202	−	0.941432i	$-0.609481\pi$
$252$	−221.910	−	221.654i	−0.880597	−	0.879580i
$253$	−133.904	−	133.904i	−0.529266	−	0.529266i
$254$	−0.429348	−	1.14465i	−0.00169035	−	0.00450648i
$255$	9.56908	−	10.2457i	0.0375258	−	0.0401794i
$256$	−246.672	−	68.4760i	−0.963562	−	0.267484i
$257$	402.208	−	232.215i	1.56501	−	0.903560i	0.568275	−	0.822839i	$-0.307611\pi$
$257$	402.208	−	232.215i	1.56501	−	0.903560i	0.996737	−	0.0807211i	$-0.0257223\pi$
$258$	23.0490	+	174.685i	0.0893373	+	0.677074i
$259$	−459.687	+	123.173i	−1.77485	+	0.475571i
$260$	−59.1364	+	11.6250i	−0.227448	+	0.0447114i
$261$	−151.082	+	173.260i	−0.578858	+	0.663832i
$262$	−17.1236	−	175.883i	−0.0653572	−	0.671309i
$263$	48.1127	−	83.3336i	0.182938	−	0.316858i	−0.759942	−	0.649991i	$-0.774773\pi$
$263$	48.1127	−	83.3336i	0.182938	−	0.316858i	0.942880	+	0.333133i	$0.108106\pi$
$264$	−313.064	+	355.575i	−1.18585	+	1.34687i
$265$	11.8676	−	6.85179i	0.0447836	−	0.0258558i
$266$	−288.218	+	206.045i	−1.08353	+	0.774606i
$267$	−97.2653	+	182.590i	−0.364289	+	0.683857i
$268$	181.522	+	370.182i	0.677319	+	1.38128i
$269$	131.457	−	131.457i	0.488687	−	0.488687i	−0.419205	−	0.907892i	$-0.637691\pi$
$269$	131.457	−	131.457i	0.488687	−	0.488687i	0.907892	+	0.419205i	$0.137691\pi$
$270$	−46.2343	+	9.34622i	−0.171238	+	0.0346156i
$271$	26.3277			0.0971502			0.0485751	−	0.998820i	$-0.484532\pi$
$271$	26.3277			0.0971502			0.0485751	+	0.998820i	$0.484532\pi$
$272$	−84.8138	−	11.5537i	−0.311816	−	0.0424768i
$273$	131.480	+	431.240i	0.481613	+	1.57963i
$274$	176.828	+	29.3985i	0.645359	+	0.107294i
$275$	−462.129	−	123.827i	−1.68047	−	0.450280i
$276$	−84.0874	+	78.6249i	−0.304665	+	0.284873i
$277$	−44.9704	−	167.832i	−0.162348	−	0.605891i	−0.998364	−	0.0571852i	$-0.981787\pi$
$277$	−44.9704	−	167.832i	−0.162348	−	0.605891i	0.836016	−	0.548706i	$-0.184879\pi$
$278$	−11.6677	−	119.843i	−0.0419701	−	0.431091i
$279$	−214.954	+	439.002i	−0.770443	+	1.57349i
$280$	58.3208	−	17.4771i	0.208288	−	0.0624183i
$281$	−38.2172	+	66.1941i	−0.136004	+	0.235566i	−0.925981	−	0.377571i	$-0.876759\pi$
$281$	−38.2172	+	66.1941i	−0.136004	+	0.235566i	0.789976	+	0.613137i	$0.210093\pi$
$282$	−180.857	−	138.694i	−0.641339	−	0.491822i
$283$	−207.635	−	55.6357i	−0.733694	−	0.196593i	−0.127420	−	0.991849i	$-0.540670\pi$
$283$	−207.635	−	55.6357i	−0.733694	−	0.196593i	−0.606274	+	0.795256i	$0.707336\pi$
$284$	269.501	−	235.278i	0.948947	−	0.828442i
$285$	1.81851	+	53.2514i	0.00638075	+	0.186847i
$286$	637.597	−	239.158i	2.22936	−	0.836216i
$287$		−	176.981i		−	0.616660i
$288$	209.651	+	197.460i	0.727953	+	0.685627i
$289$	260.379			0.900967
$290$	−15.6715	−	41.7804i	−0.0540396	−	0.144070i
$291$	162.031	+	259.749i	0.556807	+	0.892607i
$292$	−121.037	−	138.643i	−0.414510	−	0.474805i
$293$	−92.9669	+	346.957i	−0.317293	+	1.18415i	0.604542	+	0.796573i	$0.293356\pi$
$293$	−92.9669	+	346.957i	−0.317293	+	1.18415i	−0.921835	+	0.387581i	$0.873311\pi$
$294$	−61.8230	−	149.132i	−0.210282	−	0.507252i
$295$	14.2706	+	8.23911i	0.0483748	+	0.0279292i
$296$	418.596	−	125.442i	1.41418	−	0.423789i
$297$	498.013	−	189.850i	1.67681	−	0.639225i
$298$	−404.668	+	39.3976i	−1.35794	+	0.132207i
$299$	159.835	−	42.8277i	0.534566	−	0.143237i
$300$	−84.6596	+	278.250i	−0.282199	+	0.927499i
$301$	−66.2199	+	247.136i	−0.220000	+	0.821049i
$302$	−11.2247	+	67.5156i	−0.0371680	+	0.223562i
$303$	34.3288	−	148.173i	0.113296	−	0.489021i
$304$	258.983	−	196.883i	0.851917	−	0.647641i
$305$			18.2166i			0.0597265i
$306$	78.3698	+	55.9576i	0.256110	+	0.182868i
$307$	377.753	+	377.753i	1.23046	+	1.23046i	0.963785	+	0.266679i	$0.0859265\pi$
$307$	377.753	+	377.753i	1.23046	+	1.23046i	0.266679	+	0.963785i	$0.414074\pi$
$308$	−617.662	+	302.875i	−2.00540	+	0.983359i
$309$	2.83973	+	83.1555i	0.00919006	+	0.269112i
$310$	−55.1807	−	77.1874i	−0.178002	−	0.248992i
$311$	−89.5301	−	155.071i	−0.287878	−	0.498619i	0.685425	−	0.728143i	$-0.259616\pi$
$311$	−89.5301	−	155.071i	−0.287878	−	0.498619i	−0.973303	+	0.229524i	$0.926283\pi$
$312$	−132.300	−	392.263i	−0.424038	−	1.25725i
$313$	9.54797	+	5.51252i	0.0305047	+	0.0176119i	0.515175	−	0.857085i	$-0.327727\pi$
$313$	9.54797	+	5.51252i	0.0305047	+	0.0176119i	−0.484670	+	0.874697i	$0.661060\pi$
$314$	255.460	−	24.8711i	0.813567	−	0.0792072i
$315$	−67.2149	−	13.1727i	−0.213381	−	0.0418182i
$316$	4.87065	+	24.7770i	0.0154134	+	0.0784084i
$317$	−46.9548	−	175.238i	−0.148122	−	0.552800i	−0.999597	−	0.0284037i	$-0.990958\pi$
$317$	−46.9548	−	175.238i	−0.148122	−	0.552800i	0.851474	−	0.524397i	$-0.175709\pi$
$318$	57.3229	+	74.6600i	0.180261	+	0.234780i
$319$	252.098	+	436.647i	0.790277	+	1.36880i
$320$	−53.0576	+	17.6129i	−0.165805	+	0.0550404i
$321$	521.915	−	159.126i	1.62590	−	0.495720i
$322$	−156.514	+	58.7072i	−0.486069	+	0.182321i
$323$	76.9164	−	76.9164i	0.238131	−	0.238131i
$324$	−105.189	−	306.449i	−0.324657	−	0.945832i
$325$	295.613	−	295.613i	0.909579	−	0.909579i
$326$	−238.060	+	523.844i	−0.730246	+	1.60688i
$327$	95.4400	−	29.0986i	0.291866	−	0.0889865i
$328$	4.77006	+	162.439i	0.0145429	+	0.495242i
$329$	−165.475	−	286.611i	−0.502963	−	0.871157i
$330$	−13.4742	+	102.576i	−0.0408310	+	0.310836i
$331$	−9.94275	−	37.1068i	−0.0300385	−	0.112105i	0.949279	−	0.314436i	$-0.101815\pi$
$331$	−9.94275	−	37.1068i	−0.0300385	−	0.112105i	−0.979317	+	0.202330i	$0.935149\pi$
$332$	−72.3521	−	48.5794i	−0.217928	−	0.146324i
$333$	−482.434	−	94.5471i	−1.44875	−	0.283925i
$334$	−38.0136	+	46.2138i	−0.113813	+	0.138365i
$335$	77.9729	+	45.0177i	0.232755	+	0.134381i
$336$	171.419	+	381.450i	0.510175	+	1.13527i
$337$	−15.1126	−	26.1759i	−0.0448446	−	0.0776732i	0.842732	−	0.538334i	$-0.180946\pi$
$337$	−15.1126	−	26.1759i	−0.0448446	−	0.0776732i	−0.887576	+	0.460660i	$0.847613\pi$
$338$	−42.1563	+	253.565i	−0.124723	+	0.750192i
$339$	−1.43369	−	41.9826i	−0.00422917	−	0.123842i
$340$	−16.7833	+	8.22981i	−0.0493627	+	0.0242053i
$341$	758.083	+	758.083i	2.22312	+	2.22312i
$342$	−360.998	+	60.2317i	−1.05555	+	0.176116i
$343$			192.488i			0.561190i
$344$	54.1178	−	228.614i	0.157319	−	0.664576i
$345$	−5.67404	+	24.4909i	−0.0164465	+	0.0709881i
$346$	−311.790	+	222.896i	−0.901127	+	0.644208i
$347$	−24.2425	+	90.4741i	−0.0698630	+	0.260732i	−0.992019	−	0.126085i	$-0.959759\pi$
$347$	−24.2425	+	90.4741i	−0.0698630	+	0.260732i	0.922156	+	0.386817i	$0.126426\pi$
$348$	270.435	−	144.261i	0.777113	−	0.414543i
$349$	−185.927	+	49.8190i	−0.532742	+	0.142748i	−0.515154	−	0.857098i	$-0.672265\pi$
$349$	−185.927	+	49.8190i	−0.532742	+	0.142748i	−0.0175877	+	0.999845i	$0.505599\pi$
$350$	−268.287	+	326.161i	−0.766535	+	0.931890i
$351$	−73.9172	+	459.816i	−0.210590	+	1.31002i
$352$	558.747	−	294.636i	1.58735	−	0.837033i
$353$	−349.031	−	201.513i	−0.988757	−	0.570859i	−0.0838546	−	0.996478i	$-0.526723\pi$
$353$	−349.031	−	201.513i	−0.988757	−	0.570859i	−0.904903	+	0.425619i	$0.860056\pi$
$354$	−43.2843	+	104.583i	−0.122272	+	0.295432i
$355$	20.2202	−	75.4629i	0.0569584	−	0.212571i
$356$	207.796	−	181.408i	0.583697	−	0.509574i
$357$	74.0072	+	118.640i	0.207303	+	0.332324i
$358$	−476.099	−	216.362i	−1.32988	−	0.604364i
$359$	366.557			1.02105			0.510526	−	0.859862i	$-0.329451\pi$
$359$	366.557			1.02105			0.510526	+	0.859862i	$0.329451\pi$
$360$	62.0471	+	10.2788i	0.172353	+	0.0285522i
$361$			52.4182i			0.145203i
$362$	−168.809	−	76.7147i	−0.466322	−	0.211919i
$363$	−27.5075	−	805.500i	−0.0757782	−	2.21901i
$364$	40.6618	−	599.741i	0.111708	−	1.64764i
$365$	−38.8214	−	10.4022i	−0.106360	−	0.0284991i
$366$	−124.052	+	16.3681i	−0.338939	+	0.0447217i
$367$	307.579	−	532.742i	0.838089	−	1.45161i	−0.0534010	−	0.998573i	$-0.517006\pi$
$367$	307.579	−	532.742i	0.838089	−	1.45161i	0.891490	−	0.453040i	$-0.149661\pi$
$368$	142.071	−	58.1018i	0.386064	−	0.157885i
$369$	80.3973	−	164.196i	0.217879	−	0.444977i
$370$	60.6218	−	73.6990i	0.163843	−	0.199187i
$371$	35.3754	+	132.023i	0.0953516	+	0.355857i
$372$	476.051	−	445.125i	1.27971	−	1.19657i
$373$	394.402	+	105.680i	1.05738	+	0.283323i	0.745297	−	0.666733i	$-0.232308\pi$
$373$	394.402	+	105.680i	1.05738	+	0.283323i	0.312080	+	0.950056i	$0.398974\pi$
$374$	171.818	−	122.831i	0.459406	−	0.328425i
$375$	37.6288	+	123.418i	0.100343	+	0.329115i
$376$	159.603	+	258.601i	0.424476	+	0.687768i
$377$	−440.574			−1.16863
$378$	29.3094	−	469.558i	0.0775381	−	1.24222i
$379$	262.964	−	262.964i	0.693835	−	0.693835i	−0.269238	−	0.963074i	$-0.586772\pi$
$379$	262.964	−	262.964i	0.693835	−	0.693835i	0.963074	+	0.269238i	$0.0867719\pi$
$380$	22.9871	−	67.2215i	0.0604924	−	0.176899i
$381$	0.862155	−	1.61847i	0.00226287	−	0.00424795i
$382$	85.4103	−	513.733i	0.223587	−	1.34485i
$383$	351.360	−	202.858i	0.917388	−	0.529654i	0.0345873	−	0.999402i	$-0.488988\pi$
$383$	351.360	−	202.858i	0.917388	−	0.529654i	0.882801	+	0.469747i	$0.155655\pi$
$384$	−167.615	−	345.487i	−0.436497	−	0.899706i
$385$	−75.1135	+	130.100i	−0.195100	+	0.337923i
$386$	215.991	−	262.584i	0.559562	−	0.680269i
$387$	−173.703	+	199.201i	−0.448844	+	0.514732i
$388$	−78.7348	−	400.525i	−0.202925	−	1.03228i
$389$	491.809	−	131.780i	1.26429	−	0.338766i	0.436450	−	0.899728i	$-0.356236\pi$
$389$	491.809	−	131.780i	1.26429	−	0.338766i	0.827841	+	0.560963i	$0.189569\pi$
$390$	−71.7368	−	55.0127i	−0.183941	−	0.141058i
$391$	44.4466	−	25.6613i	0.113674	−	0.0656298i
$392$	6.31818	+	215.159i	0.0161178	+	0.548875i
$393$	180.928	−	193.722i	0.460376	−	0.492931i
$394$	−96.0979	+	211.461i	−0.243903	+	0.536702i
$395$	3.89920	+	3.89920i	0.00987139	+	0.00987139i
$396$	−710.630	+	0.410301i	−1.79452	+	0.00103611i
$397$	137.821	+	137.821i	0.347157	+	0.347157i	0.859049	−	0.511893i	$-0.171055\pi$
$397$	137.821	+	137.821i	0.347157	+	0.347157i	−0.511893	+	0.859049i	$0.671055\pi$
$398$	532.080	−	199.579i	1.33688	−	0.501455i
$399$	−517.728	−	119.947i	−1.29757	−	0.300619i
$400$	237.452	−	306.593i	0.593630	−	0.766481i
$401$	−159.923	+	92.3315i	−0.398810	+	0.230253i	−0.685970	−	0.727629i	$-0.740622\pi$
$401$	−159.923	+	92.3315i	−0.398810	+	0.230253i	0.287160	+	0.957883i	$0.407289\pi$
$402$	−236.501	+	571.431i	−0.588312	+	1.42147i
$403$	−904.888	+	242.464i	−2.24538	+	0.601648i
$404$	−113.047	+	168.366i	−0.279818	+	0.416749i
$405$	−56.3754	−	42.7549i	−0.139199	−	0.105568i
$406$	442.976	−	43.1272i	1.09107	−	0.106225i
$407$	−539.126	+	933.793i	−1.32463	+	2.29433i
$408$	−71.1238	−	106.897i	−0.174323	−	0.262001i
$409$	309.169	−	178.499i	0.755913	−	0.436427i	−0.0719132	−	0.997411i	$-0.522910\pi$
$409$	309.169	−	178.499i	0.755913	−	0.436427i	0.827827	+	0.560984i	$0.189577\pi$
$410$	20.6388	+	28.8698i	0.0503385	+	0.0704141i
$411$	142.311	+	228.136i	0.346255	+	0.555074i
$412$	35.8959	−	104.971i	0.0871259	−	0.254784i
$413$	−116.216	+	116.216i	−0.281395	+	0.281395i
$414$	−171.877	−	16.6334i	−0.415161	−	0.0401773i
$415$	−19.0312			−0.0458582
$416$	−21.1563	+	551.558i	−0.0508565	+	1.32586i
$417$	123.281	−	131.998i	0.295637	−	0.316543i
$418$	−131.649	+	791.854i	−0.314950	+	1.89439i
$419$	−370.611	−	99.3049i	−0.884513	−	0.237005i	−0.212160	−	0.977235i	$-0.568050\pi$
$419$	−370.611	−	99.3049i	−0.884513	−	0.237005i	−0.672353	+	0.740230i	$0.734716\pi$
$420$	77.5129	+	48.2903i	0.184555	+	0.114977i
$421$	3.08113	+	11.4989i	0.00731860	+	0.0273134i	0.969489	−	0.245136i	$-0.0788328\pi$
$421$	3.08113	+	11.4989i	0.00731860	+	0.0273134i	−0.962170	+	0.272450i	$0.912166\pi$
$422$	315.865	−	30.7520i	0.748495	−	0.0728719i
$423$	−23.3225	−	341.077i	−0.0551358	−	0.806328i
$424$	−36.0270	−	120.221i	−0.0849695	−	0.283541i
$425$	64.8318	−	112.292i	0.152545	−	0.264216i
$426$	532.057	+	69.8904i	1.24896	+	0.164062i
$427$	−175.502	−	47.0257i	−0.411012	−	0.110130i
$428$	−725.846	−	49.2116i	−1.69590	−	0.114980i
$429$	901.528	+	480.242i	2.10146	+	1.11944i
$430$	−18.0179	−	48.0359i	−0.0419021	−	0.111711i
$431$		−	391.881i		−	0.909236i	−0.890687	−	0.454618i	$-0.849776\pi$
$431$		−	391.881i		−	0.909236i	0.890687	−	0.454618i	$-0.150224\pi$
$432$	−14.2455	+	431.765i	−0.0329756	+	0.999456i
$433$	−417.756			−0.964795			−0.482398	−	0.875952i	$-0.660234\pi$
$433$	−417.756			−0.964795			−0.482398	+	0.875952i	$0.660234\pi$
$434$	886.086	−	332.364i	2.04167	−	0.765815i
$435$	31.4692	−	59.0752i	0.0723430	−	0.135805i
$436$	−132.732	−	8.99907i	−0.304431	−	0.0206401i
$437$	−50.4847	+	188.411i	−0.115526	+	0.431148i
$438$	35.9546	−	273.713i	0.0820882	−	0.624916i
$439$	84.8008	+	48.9598i	0.193168	+	0.111526i	0.593465	−	0.804860i	$-0.297760\pi$
$439$	84.8008	+	48.9598i	0.193168	+	0.111526i	−0.400297	+	0.916386i	$0.631093\pi$
$440$	65.4351	−	121.435i	0.148716	−	0.275988i
$441$	106.490	−	217.487i	0.241475	−	0.493167i
$442$	17.8835	+	183.688i	0.0404604	+	0.415584i
$443$	−452.327	+	121.201i	−1.02105	+	0.273591i	−0.730242	−	0.683189i	$-0.760593\pi$
$443$	−452.327	+	121.201i	−1.02105	+	0.273591i	−0.290813	+	0.956780i	$0.593926\pi$
$444$	556.347	+	346.603i	1.25303	+	0.780637i
$445$	15.5906	−	58.1849i	0.0350350	−	0.130753i
$446$	−467.382	−	77.7042i	−1.04794	−	0.174225i
$447$	−445.711	−	416.275i	−0.997117	−	0.931263i
$448$	−32.7196	−	556.635i	−0.0730348	−	1.24249i
$449$			105.840i			0.235723i	0.993030	+	0.117862i	$0.0376040\pi$
$449$			105.840i			0.235723i	−0.993030	+	0.117862i	$0.962396\pi$
$450$	−397.072	+	180.725i	−0.882382	+	0.401612i
$451$	−283.540	−	283.540i	−0.628691	−	0.628691i
$452$	−18.1227	+	52.9965i	−0.0400944	+	0.117249i
$453$	−87.1054	+	54.3363i	−0.192286	+	0.119948i
$454$	−342.762	+	245.038i	−0.754983	+	0.539731i
$455$	−65.6353	−	113.684i	−0.144253	−	0.249854i
$456$	478.421	+	96.1374i	1.04917	+	0.210828i
$457$	626.181	+	361.526i	1.37020	+	0.791085i	0.990953	−	0.134210i	$-0.0428497\pi$
$457$	626.181	+	361.526i	1.37020	+	0.791085i	0.379247	+	0.925295i	$0.376183\pi$
$458$	21.1167	+	216.898i	0.0461063	+	0.473576i
$459$	14.7666	+	143.688i	0.0321713	+	0.313047i
$460$	18.6849	−	27.8285i	0.0406194	−	0.0604967i
$461$	37.7524	+	140.894i	0.0818925	+	0.305627i	0.994708	−	0.102746i	$-0.0327629\pi$
$461$	37.7524	+	140.894i	0.0818925	+	0.305627i	−0.912815	+	0.408373i	$0.866096\pi$
$462$	−953.452	−	394.610i	−2.06375	−	0.854135i
$463$	−71.0549	−	123.071i	−0.153466	−	0.265811i	0.779033	−	0.626983i	$-0.215710\pi$
$463$	−71.0549	−	123.071i	−0.153466	−	0.265811i	−0.932500	+	0.361171i	$0.882377\pi$
$464$	−405.415	+	51.5227i	−0.873739	+	0.111040i
$465$	32.1229	−	138.652i	0.0690815	−	0.298177i
$466$	178.377	+	475.554i	0.382783	+	1.02050i
$467$	459.423	−	459.423i	0.983775	−	0.983775i	−0.0160956	−	0.999870i	$-0.505124\pi$
$467$	459.423	−	459.423i	0.983775	−	0.983775i	0.999870	+	0.0160956i	$0.00512360\pi$
$468$	310.169	−	537.945i	0.662754	−	1.14946i
$469$	−634.994	+	634.994i	−1.35393	+	1.35393i
$470$	60.4161	+	27.4560i	0.128545	+	0.0584169i
$471$	281.370	+	262.787i	0.597389	+	0.557935i
$472$	103.535	−	109.799i	0.219353	−	0.232626i
$473$	289.843	+	502.024i	0.612777	+	1.06136i
$474$	−23.0493	+	30.0564i	−0.0486272	+	0.0634101i
$475$	127.547	+	476.011i	0.268520	+	1.00213i
$476$	−35.9619	−	182.939i	−0.0755503	−	0.384325i
$477$	−27.1541	+	138.556i	−0.0569268	+	0.290473i
$478$	645.778	+	531.191i	1.35100	+	1.11128i
$479$	309.366	+	178.612i	0.645857	+	0.372886i	0.786867	−	0.617122i	$-0.211702\pi$
$479$	309.366	+	178.612i	0.645857	+	0.372886i	−0.141010	+	0.990008i	$0.545035\pi$
$480$	−72.4454	−	42.2333i	−0.150928	−	0.0879860i
$481$	−471.096	−	815.962i	−0.979409	−	1.69639i
$482$	256.374	+	42.6233i	0.531897	+	0.0884300i
$483$	−221.303	−	117.887i	−0.458183	−	0.244073i
$484$	−347.711	+	1016.82i	−0.718411	+	2.10086i
$485$	−63.0312	−	63.0312i	−0.129961	−	0.129961i
$486$	240.498	−	422.323i	0.494852	−	0.868977i
$487$			67.6264i			0.138863i	0.997587	+	0.0694316i	$0.0221186\pi$
$487$			67.6264i			0.138863i	−0.997587	+	0.0694316i	$0.977881\pi$
$488$	162.349	+	38.4315i	0.332682	+	0.0787530i
$489$	−825.581	+	251.710i	−1.68831	+	0.514745i
$490$	27.3371	+	38.2395i	0.0557900	+	0.0780398i
$491$	212.106	−	791.591i	0.431988	−	1.61220i	−0.316184	−	0.948698i	$-0.602402\pi$
$491$	212.106	−	791.591i	0.431988	−	1.61220i	0.748172	−	0.663505i	$-0.230932\pi$
$492$	−178.053	+	166.487i	−0.361897	+	0.338387i
$493$	−131.990	+	35.3667i	−0.267729	+	0.0717377i
$494$	−541.713	−	445.591i	−1.09659	−	0.902007i
$495$	−128.788	+	86.5804i	−0.260178	+	0.174910i
$496$	−804.321	+	328.936i	−1.62161	+	0.663178i
$497$	674.826	+	389.611i	1.35780	+	0.783925i
$498$	−17.1001	−	129.599i	−0.0343375	−	0.260239i
$499$	−53.4646	+	199.533i	−0.107143	+	0.399865i	−0.998580	−	0.0532816i	$-0.983032\pi$
$499$	−53.4646	+	199.533i	−0.107143	+	0.399865i	0.891436	+	0.453147i	$0.149699\pi$
$500$	11.6371	−	171.642i	0.0232743	−	0.343284i
$501$	−89.7068	+	3.06345i	−0.179055	+	0.00611467i
$502$	−375.562	+	826.413i	−0.748131	+	1.64624i
$503$	−49.7776			−0.0989614			−0.0494807	−	0.998775i	$-0.515757\pi$
$503$	−49.7776			−0.0989614			−0.0494807	+	0.998775i	$0.515757\pi$
$504$	−259.201	+	571.239i	−0.514287	+	1.13341i
$505$			44.2864i			0.0876958i
$506$	−156.695	+	344.804i	−0.309675	+	0.681430i
$507$	−327.138	+	204.068i	−0.645242	+	0.402501i
$508$	−1.84189	+	1.60800i	−0.00362578	+	0.00316535i
$509$	101.934	+	27.3131i	0.200263	+	0.0536602i	0.357556	−	0.933892i	$-0.383610\pi$
$509$	101.934	+	27.3131i	0.200263	+	0.0536602i	−0.157293	+	0.987552i	$0.550277\pi$
$510$	−25.9075	−	10.7225i	−0.0507990	−	0.0210245i
$511$	200.433	−	347.160i	0.392237	−	0.679374i
$512$	45.0337	+	510.016i	0.0879564	+	0.996124i
$513$	−425.840	−	346.471i	−0.830098	−	0.675382i
$514$	−717.356	−	590.068i	−1.39563	−	1.14799i
$515$	−6.27028	−	23.4010i	−0.0121753	−	0.0454389i
$516$	310.926	−	165.860i	0.602570	−	0.321434i
$517$	−724.281	−	194.070i	−1.40093	−	0.375378i
$518$	553.537	+	774.295i	1.06860	+	1.49478i
$519$	−560.070	−	129.757i	−1.07913	−	0.250013i
$520$	63.3062	+	102.574i	0.121743	+	0.197257i
$521$	161.848			0.310649			0.155324	−	0.987864i	$-0.450358\pi$
$521$	161.848			0.310649			0.155324	+	0.987864i	$0.450358\pi$
$522$	430.567	+	161.219i	0.824841	+	0.308848i
$523$	406.971	−	406.971i	0.778147	−	0.778147i	−0.201369	−	0.979516i	$-0.564539\pi$
$523$	406.971	−	406.971i	0.778147	−	0.778147i	0.979516	+	0.201369i	$0.0645389\pi$
$524$	−317.331	+	155.606i	−0.605594	+	0.296957i
$525$	−633.120	+	21.6208i	−1.20594	+	0.0411825i
$526$	−189.845	−	31.5625i	−0.360922	−	0.0600048i
$527$	−251.629	+	145.278i	−0.477475	+	0.275670i
$528$	885.745	+	336.488i	1.67755	+	0.637289i
$529$	218.484	−	378.426i	0.413014	−	0.715360i
$530$	−21.1665	−	17.4107i	−0.0399368	−	0.0328504i
$531$	−160.615	+	55.0274i	−0.302476	+	0.103630i
$532$	588.284	+	394.993i	1.10580	+	0.742468i
$533$	338.448	−	90.6869i	0.634987	−	0.170144i
$534$	410.237	+	53.8883i	0.768234	+	0.100914i
$535$	−137.587	+	79.4361i	−0.257173	+	0.148479i
$536$	565.704	−	599.933i	1.05542	−	1.11928i
$537$	−228.768	−	750.334i	−0.426012	−	1.39727i
$538$	−338.501	−	153.831i	−0.629184	−	0.285932i
$539$	−375.563	−	375.563i	−0.696777	−	0.696777i
$540$	49.9767	+	80.0137i	0.0925494	+	0.148174i
$541$	−500.402	−	500.402i	−0.924957	−	0.924957i	0.0724176	−	0.997374i	$-0.476929\pi$
$541$	−500.402	−	500.402i	−0.924957	−	0.924957i	−0.997374	+	0.0724176i	$0.976929\pi$
$542$	−18.4925	−	49.3013i	−0.0341191	−	0.0909619i
$543$	−81.1135	−	266.043i	−0.149380	−	0.489951i
$544$	37.9376	+	166.938i	0.0697383	+	0.306871i
$545$	−25.1599	+	14.5261i	−0.0461650	+	0.0266534i
$546$	715.190	−	549.112i	1.30987	−	1.00570i
$547$	461.440	−	123.643i	0.843583	−	0.226037i	0.188953	−	0.981986i	$-0.439491\pi$
$547$	461.440	−	123.643i	0.843583	−	0.226037i	0.654631	+	0.755949i	$0.272824\pi$
$548$	−69.1523	−	351.778i	−0.126190	−	0.641932i
$549$	−141.462	−	123.354i	−0.257672	−	0.224688i
$550$	92.7197	+	952.359i	0.168581	+	1.73156i
$551$	259.671	−	449.764i	0.471273	−	0.816268i
$552$	206.296	+	102.236i	0.373725	+	0.185211i
$553$	−47.6313	+	27.5000i	−0.0861326	+	0.0497287i
$554$	−282.695	+	202.096i	−0.510280	+	0.364795i
$555$	143.059	−	4.88541i	0.257764	−	0.00880254i
$556$	−216.223	+	106.027i	−0.388891	+	0.190695i
$557$	−602.645	+	602.645i	−1.08195	+	1.08195i	−0.0856202	+	0.996328i	$0.527287\pi$
$557$	−602.645	+	602.645i	−1.08195	+	1.08195i	−0.996328	+	0.0856202i	$0.972713\pi$
$558$	973.059	+	94.1679i	1.74383	+	0.168760i
$559$	−506.539			−0.906152
$560$	−73.6921	−	96.9357i	−0.131593	−	0.173099i
$561$	308.637	+	71.5049i	0.550155	+	0.127460i
$562$	150.799	+	25.0710i	0.268326	+	0.0446103i
$563$	737.266	+	197.550i	1.30953	+	0.350888i	0.845047	−	0.534693i	$-0.179573\pi$
$563$	737.266	+	197.550i	1.30953	+	0.350888i	0.464485	+	0.885581i	$0.346239\pi$
$564$	−132.684	+	436.092i	−0.235256	+	0.773213i
$565$	3.16567	+	11.8144i	0.00560295	+	0.0209105i
$566$	41.6591	+	427.897i	0.0736027	+	0.756001i
$567$	557.441	−	432.761i	0.983141	−	0.763247i
$568$	−629.878	−	339.409i	−1.10894	−	0.597552i
$569$	−162.828	+	282.027i	−0.286166	+	0.495654i	−0.972891	−	0.231263i	$-0.925714\pi$
$569$	−162.828	+	282.027i	−0.286166	+	0.495654i	0.686725	+	0.726917i	$0.259048\pi$
$570$	98.4413	−	40.8090i	0.172704	−	0.0715948i
$571$	110.932	+	29.7242i	0.194277	+	0.0520564i	0.354645	−	0.935001i	$-0.384602\pi$
$571$	110.932	+	29.7242i	0.194277	+	0.0520564i	−0.160368	+	0.987057i	$0.551268\pi$
$572$	−895.694	−	1025.98i	−1.56590	−	1.79367i
$573$	662.794	−	413.450i	1.15671	−	0.721554i
$574$	−331.416	+	124.311i	−0.577379	+	0.216570i
$575$			232.513i			0.404370i
$576$	222.507	−	531.288i	0.386296	−	0.922375i
$577$	−481.810			−0.835026			−0.417513	−	0.908671i	$-0.637098\pi$
$577$	−481.810			−0.835026			−0.417513	+	0.908671i	$0.637098\pi$
$578$	−182.890	−	487.587i	−0.316419	−	0.843576i
$579$	509.708	−	17.4063i	0.880325	−	0.0300628i
$580$	−67.2304	+	58.6929i	−0.115914	+	0.101195i
$581$	49.1285	−	183.350i	0.0845585	−	0.315577i
$582$	372.595	−	485.866i	0.640198	−	0.834821i
$583$	268.187	+	154.838i	0.460012	+	0.265588i
$584$	−174.607	+	324.037i	−0.298985	+	0.554857i
$585$	−9.25081	−	135.287i	−0.0158134	−	0.231261i
$586$	715.013	−	69.6121i	1.22016	−	0.118792i
$587$	35.1089	−	9.40740i	0.0598107	−	0.0160262i	−0.228790	−	0.973476i	$-0.573477\pi$
$587$	35.1089	−	9.40740i	0.0598107	−	0.0160262i	0.288600	+	0.957450i	$0.406810\pi$
$588$	−235.841	+	220.520i	−0.401090	+	0.375034i
$589$	285.813	−	1066.67i	0.485251	−	1.81098i
$590$	5.40496	−	32.5102i	0.00916095	−	0.0551021i
$591$	−333.263	+	101.608i	−0.563897	+	0.171926i
$592$	−528.923	−	695.754i	−0.893451	−	1.17526i
$593$		−	116.567i		−	0.196572i	−0.995158	−	0.0982861i	$-0.968664\pi$
$593$		−	116.567i		−	0.196572i	0.995158	−	0.0982861i	$-0.0313360\pi$
$594$	−705.316	−	799.229i	−1.18740	−	1.34550i
$595$	−28.7893	−	28.7893i	−0.0483854	−	0.0483854i
$596$	358.014	+	730.108i	0.600694	+	1.22501i
$597$	752.333	+	400.766i	1.26019	+	0.671300i
$598$	−192.467	−	269.226i	−0.321852	−	0.450210i
$599$	−58.7912	−	101.829i	−0.0981490	−	0.169999i	0.812770	−	0.582585i	$-0.197959\pi$
$599$	−58.7912	−	101.829i	−0.0981490	−	0.169999i	−0.910918	+	0.412586i	$0.864626\pi$
$600$	580.515	−	36.9083i	0.967526	−	0.0615139i
$601$	−1027.53	−	593.245i	−1.70970	−	0.987097i	−0.934913	−	0.354876i	$-0.884523\pi$
$601$	−1027.53	−	593.245i	−1.70970	−	0.987097i	−0.774788	−	0.632221i	$-0.782144\pi$
$602$	509.300	−	49.5844i	0.846013	−	0.0823660i
$603$	−877.582	+	300.664i	−1.45536	+	0.498614i
$604$	134.314	−	26.4033i	0.222374	−	0.0437141i
$605$	60.7381	+	226.678i	0.100394	+	0.374674i
$606$	−301.582	+	39.7926i	−0.497660	+	0.0656644i
$607$	326.518	+	565.545i	0.537920	+	0.931705i	0.999016	+	0.0443546i	$0.0141231\pi$
$607$	326.518	+	565.545i	0.537920	+	0.931705i	−0.461096	+	0.887350i	$0.652544\pi$
$608$	−550.593	−	346.682i	−0.905580	−	0.570200i
$609$	487.905	+	455.682i	0.801157	+	0.748246i
$610$	34.1124	−	12.7953i	0.0559220	−	0.0209759i
$611$	463.306	−	463.306i	0.758274	−	0.758274i
$612$	49.7395	−	186.060i	0.0812736	−	0.304019i
$613$	525.240	−	525.240i	0.856835	−	0.856835i	−0.134129	−	0.990964i	$-0.542824\pi$
$613$	525.240	−	525.240i	0.856835	−	0.856835i	0.990964	+	0.134129i	$0.0428238\pi$
$614$	442.047	−	972.713i	0.719947	−	1.58422i
$615$	−12.0147	+	51.8589i	−0.0195360	+	0.0843235i
$616$	1001.01	+	943.896i	1.62501	+	1.53230i
$617$	278.589	+	482.530i	0.451522	+	0.782058i	0.998481	−	0.0551009i	$-0.0175481\pi$
$617$	278.589	+	482.530i	0.451522	+	0.782058i	−0.546959	+	0.837159i	$0.684215\pi$
$618$	153.723	−	63.7260i	0.248742	−	0.103116i
$619$	223.411	+	833.781i	0.360923	+	1.34698i	0.872865	+	0.487962i	$0.162259\pi$
$619$	223.411	+	833.781i	0.360923	+	1.34698i	−0.511943	+	0.859020i	$0.671074\pi$
$620$	−105.783	+	157.548i	−0.170617	+	0.254109i
$621$	−151.763	−	209.902i	−0.244385	−	0.338007i
$622$	−227.500	+	276.575i	−0.365755	+	0.444655i
$623$	520.318	+	300.406i	0.835181	+	0.482192i
$624$	−641.624	+	523.269i	−1.02824	+	0.838572i
$625$	284.178	+	492.211i	0.454685	+	0.787537i
$626$	3.61628	−	21.7515i	0.00577681	−	0.0347469i
$627$	−1021.61	+	637.281i	−1.62937	+	1.01640i
$628$	−226.008	−	460.905i	−0.359886	−	0.733926i
$629$	−206.635	−	206.635i	−0.328513	−	0.328513i
$630$	22.5443	+	135.119i	0.0357847	+	0.214475i
$631$		−	134.339i		−	0.212898i	−0.994318	−	0.106449i	$-0.966052\pi$
$631$		−	134.339i		−	0.212898i	0.994318	−	0.106449i	$-0.0339482\pi$
$632$	42.9764	−	26.5241i	0.0680006	−	0.0419686i
$633$	347.902	+	324.925i	0.549608	+	0.513310i
$634$	−295.169	+	211.014i	−0.465567	+	0.332830i
$635$	−0.138194	+	0.515748i	−0.000217629	+	0.000812202i
$636$	99.5449	−	159.784i	0.156517	−	0.251233i
$637$	448.292	−	120.119i	0.703755	−	0.188570i
$638$	640.593	−	778.780i	1.00406	−	1.22066i
$639$	449.089	+	668.019i	0.702800	+	1.04541i
$640$	70.2496	+	86.9845i	0.109765	+	0.135913i
$641$	−158.586	−	91.5597i	−0.247404	−	0.142839i	0.371171	−	0.928565i	$-0.378956\pi$
$641$	−158.586	−	91.5597i	−0.247404	−	0.142839i	−0.618575	+	0.785726i	$0.712290\pi$
$642$	−664.572	−	865.570i	−1.03516	−	1.34824i
$643$	187.763	−	700.741i	0.292011	−	1.08980i	−0.651552	−	0.758604i	$-0.725882\pi$
$643$	187.763	−	700.741i	0.292011	−	1.08980i	0.943562	−	0.331195i	$-0.107452\pi$
$644$	219.870	+	251.853i	0.341414	+	0.391076i
$645$	36.1809	−	67.9201i	0.0560944	−	0.105303i
$646$	−198.060	−	90.0079i	−0.306594	−	0.139331i
$647$	−358.949			−0.554790			−0.277395	−	0.960756i	$-0.589471\pi$
$647$	−358.949			−0.554790			−0.277395	+	0.960756i	$0.589471\pi$
$648$	−499.973	+	412.227i	−0.771564	+	0.636152i
$649$			372.378i			0.573771i
$650$	−761.204	−	345.927i	−1.17108	−	0.532196i
$651$	1252.88	+	667.405i	1.92454	+	1.02520i
$652$	1148.16	+	77.8443i	1.76099	+	0.119393i
$653$	659.597	+	176.738i	1.01010	+	0.270656i	0.725672	−	0.688041i	$-0.241529\pi$
$653$	659.597	+	176.738i	1.01010	+	0.270656i	0.284430	+	0.958697i	$0.408196\pi$
$654$	−121.527	−	158.282i	−0.185821	−	0.242022i
$655$	−38.5905	+	66.8407i	−0.0589168	+	0.102047i
$656$	300.833	−	123.029i	0.458588	−	0.187545i
$657$	343.658	−	231.031i	0.523072	−	0.351645i
$658$	−420.479	+	511.183i	−0.639025	+	0.776874i
$659$	328.832	+	1227.22i	0.498986	+	1.86224i	0.506452	+	0.862268i	$0.330957\pi$
$659$	328.832	+	1227.22i	0.498986	+	1.86224i	−0.00746639	+	0.999972i	$0.502377\pi$
$660$	201.548	−	46.8172i	0.305376	−	0.0709351i
$661$	−1182.43	−	316.831i	−1.78885	−	0.479321i	−0.796700	−	0.604374i	$-0.793423\pi$
$661$	−1182.43	−	316.831i	−1.78885	−	0.479321i	−0.992150	+	0.125053i	$0.960090\pi$
$662$	−62.5026	+	44.6826i	−0.0944148	+	0.0674964i
$663$	−188.957	+	202.319i	−0.285003	+	0.305156i
$664$	−40.1500	+	169.609i	−0.0604669	+	0.255435i
$665$	154.740			0.232691
$666$	161.811	+	969.816i	0.242960	+	1.45618i
$667$	173.266	−	173.266i	0.259769	−	0.259769i
$668$	113.241	+	38.7239i	0.169522	+	0.0579698i
$669$	−376.147	−	602.994i	−0.562253	−	0.901337i
$670$	29.5322	−	177.633i	0.0440779	−	0.265123i
$671$	−356.509	+	205.831i	−0.531310	+	0.306752i
$672$	593.900	−	588.929i	0.883779	−	0.876382i
$673$	−187.494	+	324.750i	−0.278595	+	0.482540i	−0.971036	−	0.238934i	$-0.923202\pi$
$673$	−187.494	+	324.750i	−0.278595	+	0.482540i	0.692441	+	0.721475i	$0.256535\pi$
$674$	−38.4019	+	46.6858i	−0.0569761	+	0.0692668i
$675$	−597.206	−	267.549i	−0.884750	−	0.396368i
$676$	504.437	−	99.1617i	0.746208	−	0.146689i
$677$	−739.402	+	198.122i	−1.09217	+	0.292647i	−0.759574	−	0.650421i	$-0.774593\pi$
$677$	−739.402	+	198.122i	−1.09217	+	0.292647i	−0.332600	+	0.943068i	$0.607926\pi$
$678$	−77.6097	+	32.1732i	−0.114469	+	0.0474531i
$679$	769.968	−	444.541i	1.13397	−	0.654700i
$680$	27.1997	+	25.6478i	0.0399996	+	0.0377174i
$681$	−615.706	−	142.646i	−0.904120	−	0.209466i
$682$	887.112	−	1952.06i	1.30075	−	2.86226i
$683$	423.146	+	423.146i	0.619540	+	0.619540i	0.945413	−	0.325873i	$-0.105658\pi$
$683$	423.146	+	423.146i	0.619540	+	0.619540i	−0.325873	+	0.945413i	$0.605658\pi$
$684$	366.354	+	633.699i	0.535606	+	0.926461i
$685$	−55.3599	−	55.3599i	−0.0808174	−	0.0808174i
$686$	360.454	−	135.203i	0.525443	−	0.197090i
$687$	−223.119	+	238.897i	−0.324773	+	0.347739i
$688$	−466.115	+	59.2369i	−0.677493	+	0.0861002i
$689$	−234.346	+	135.300i	−0.340124	+	0.196371i
$690$	49.8471	−	6.57714i	0.0722422	−	0.00953208i
$691$	615.162	−	164.832i	0.890248	−	0.238541i	0.215425	−	0.976520i	$-0.430886\pi$
$691$	615.162	−	164.832i	0.890248	−	0.238541i	0.674823	+	0.737979i	$0.264220\pi$
$692$	636.396	+	427.297i	0.919648	+	0.617481i
$693$	−501.669	−	1464.28i	−0.723908	−	2.11295i
$694$	186.450	−	18.1524i	0.268660	−	0.0261561i
$695$	−26.2948	+	45.5440i	−0.0378343	+	0.0655309i
$696$	−460.096	−	405.089i	−0.661058	−	0.582025i
$697$	94.1148	−	54.3372i	0.135028	−	0.0779587i
$698$	223.886	+	313.174i	0.320753	+	0.448674i
$699$	−358.190	+	672.408i	−0.512433	+	0.961957i
$700$	799.215	+	273.300i	1.14174	+	0.390428i
$701$	−154.943	+	154.943i	−0.221032	+	0.221032i	−0.808933	−	0.587901i	$-0.799954\pi$
$701$	−154.943	+	154.943i	−0.221032	+	0.221032i	0.587901	+	0.808933i	$0.299954\pi$
$702$	912.971	−	184.556i	1.30053	−	0.262900i
$703$	1110.64			1.57986
$704$	−944.198	−	839.359i	−1.34119	−	1.19227i
$705$	29.0303	+	95.2160i	0.0411777	+	0.135058i
$706$	−132.195	+	795.139i	−0.187245	+	1.12626i
$707$	−426.664	−	114.324i	−0.603485	−	0.161703i
$708$	226.245	+	7.59541i	0.319555	+	0.0107280i
$709$	156.033	+	582.322i	0.220074	+	0.821328i	0.984318	+	0.176401i	$0.0564456\pi$
$709$	156.033	+	582.322i	0.220074	+	0.821328i	−0.764244	+	0.644927i	$0.776888\pi$
$710$	−155.515	+	15.1406i	−0.219035	+	0.0213247i
$711$	−56.6829	+	3.87592i	−0.0797228	+	0.00545136i
$712$	−485.661	−	261.698i	−0.682108	−	0.367554i
$713$	260.513	−	451.222i	0.365376	−	0.632850i
$714$	170.182	−	221.918i	0.238350	−	0.310810i
$715$	−287.285	−	76.9777i	−0.401797	−	0.107661i
$716$	−70.7492	+	1043.52i	−0.0988118	+	1.45742i
$717$	42.8078	+	1253.54i	0.0597040	+	1.74831i
$718$	−257.469	−	686.416i	−0.358592	−	0.956011i
$719$		−	1115.61i		−	1.55161i	−0.630971	−	0.775806i	$-0.717343\pi$
$719$		−	1115.61i		−	1.55161i	0.630971	−	0.775806i	$-0.282657\pi$
$720$	−24.3337	−	123.409i	−0.0337968	−	0.171402i
$721$	241.636			0.335141
$722$	98.1583	−	36.8184i	0.135953	−	0.0509950i
$723$	206.329	+	330.762i	0.285379	+	0.457485i
$724$	−25.0853	+	369.996i	−0.0346482	+	0.511044i
$725$	160.226	−	597.973i	0.221002	−	0.824790i
$726$	−1489.06	+	617.292i	−2.05104	+	0.850264i
$727$	141.933	+	81.9452i	0.195231	+	0.112717i	0.594429	−	0.804148i	$-0.297378\pi$
$727$	141.933	+	81.9452i	0.195231	+	0.112717i	−0.399198	+	0.916865i	$0.630711\pi$
$728$	−1151.64	+	345.114i	−1.58192	+	0.474057i
$729$	713.762	−	148.271i	0.979098	−	0.203389i
$730$	7.78897	+	80.0035i	0.0106698	+	0.109594i
$731$	−151.752	+	40.6619i	−0.207596	+	0.0556251i
$732$	117.785	+	220.802i	0.160908	+	0.301643i
$733$	−352.346	+	1314.97i	−0.480691	+	1.79396i	0.118036	+	0.993009i	$0.462340\pi$
$733$	−352.346	+	1314.97i	−0.480691	+	1.79396i	−0.598727	+	0.800953i	$0.704327\pi$
$734$	−1213.66	−	201.775i	−1.65348	−	0.274898i
$735$	−15.9140	+	68.6898i	−0.0216518	+	0.0934556i
$736$	−208.592	−	225.233i	−0.283413	−	0.306023i
$737$			2034.63i			2.76070i
$738$	−363.946	−	35.2209i	−0.493151	−	0.0477247i
$739$	591.976	+	591.976i	0.801050	+	0.801050i	0.983260	−	0.182210i	$-0.0583250\pi$
$739$	591.976	+	591.976i	0.801050	+	0.801050i	−0.182210	+	0.983260i	$0.558325\pi$
$740$	−180.590	−	61.7545i	−0.244040	−	0.0834520i
$741$	−35.9094	−	1051.53i	−0.0484608	−	1.41907i
$742$	222.379	−	158.977i	0.299702	−	0.214254i
$743$	305.873	+	529.787i	0.411673	+	0.713038i	0.995073	−	0.0991470i	$-0.0316114\pi$
$743$	305.873	+	529.787i	0.411673	+	0.713038i	−0.583400	+	0.812185i	$0.698278\pi$
$744$	−1167.92	−	578.798i	−1.56978	−	0.777955i
$745$	153.785	+	88.7881i	0.206423	+	0.119179i
$746$	−79.1312	−	812.786i	−0.106074	−	1.08953i
$747$	128.870	−	147.787i	0.172517	−	0.197841i
$748$	−350.698	−	235.470i	−0.468848	−	0.314799i
$749$	−410.125	−	1530.61i	−0.547563	−	2.04353i
$750$	204.683	−	157.152i	0.272910	−	0.209537i
$751$	681.190	+	1179.86i	0.907044	+	1.57105i	0.818150	+	0.575005i	$0.195000\pi$
$751$	681.190	+	1179.86i	0.907044	+	1.57105i	0.0888935	+	0.996041i	$0.471667\pi$
$752$	372.151	−	480.513i	0.494882	−	0.638981i
$753$	−1302.43	+	397.097i	−1.72966	+	0.527353i
$754$	309.458	+	825.020i	0.410422	+	1.09419i
$755$	21.1372	−	21.1372i	0.0279963	−	0.0279963i
$756$	−899.881	+	274.931i	−1.19032	+	0.363666i
$757$	304.498	−	304.498i	0.402243	−	0.402243i	−0.476780	−	0.879023i	$-0.658196\pi$
$757$	304.498	−	304.498i	0.402243	−	0.402243i	0.879023	+	0.476780i	$0.158196\pi$
$758$	−677.131	−	307.721i	−0.893313	−	0.405964i
$759$	−543.412	+	165.680i	−0.715958	+	0.218287i
$760$	−142.025	+	4.17060i	−0.186875	+	0.00548763i
$761$	−429.888	−	744.588i	−0.564899	−	0.978433i	−0.997059	−	0.0766366i	$-0.975582\pi$
$761$	−429.888	−	744.588i	−0.564899	−	0.978433i	0.432160	−	0.901797i	$-0.357751\pi$
$762$	−3.63632	−	0.477663i	−0.00477208	−	0.000626854i
$763$	−74.9975	−	279.894i	−0.0982929	−	0.366834i
$764$	−1022.01	+	200.906i	−1.33771	+	0.262966i
$765$	−13.6315	−	39.7878i	−0.0178190	−	0.0520101i
$766$	−626.666	−	515.470i	−0.818102	−	0.672937i
$767$	−281.795	−	162.694i	−0.367399	−	0.212118i
$768$	−529.227	+	556.545i	−0.689098	+	0.724668i
$769$	−74.5282	−	129.087i	−0.0969158	−	0.167863i	0.813491	−	0.581578i	$-0.197564\pi$
$769$	−74.5282	−	129.087i	−0.0969158	−	0.167863i	−0.910407	+	0.413715i	$0.864231\pi$
$770$	296.386	+	49.2754i	0.384917	+	0.0639940i
$771$	−47.5526	−	1392.48i	−0.0616765	−	1.80607i
$772$	−643.427	−	220.026i	−0.833454	−	0.285008i
$773$	243.686	+	243.686i	0.315247	+	0.315247i	0.846938	−	0.531692i	$-0.178443\pi$
$773$	243.686	+	243.686i	0.315247	+	0.315247i	−0.531692	+	0.846938i	$0.678443\pi$
$774$	495.033	+	185.357i	0.639578	+	0.239480i
$775$		−	1316.34i		−	1.69851i
$776$	−694.720	+	428.767i	−0.895258	+	0.552534i
$777$	−322.236	+	1390.87i	−0.414718	+	1.79005i
$778$	−592.217	−	828.401i	−0.761205	−	1.06478i
$779$	−106.900	+	398.957i	−0.137228	+	0.512141i
$780$	−52.6291	+	172.975i	−0.0674731	+	0.221763i
$781$	1705.32	−	456.940i	2.18351	−	0.585070i
$782$	−79.2725	−	65.2064i	−0.101372	−	0.0833841i
$783$	245.657	+	644.404i	0.313738	+	0.822994i
$784$	398.469	−	162.959i	0.508252	−	0.207856i
$785$	−97.0823	−	56.0505i	−0.123672	−	0.0714019i
$786$	−489.847	−	202.736i	−0.623216	−	0.257934i
$787$	−10.7749	+	40.2123i	−0.0136910	+	0.0510957i	−0.972433	−	0.233181i	$-0.925087\pi$
$787$	−10.7749	+	40.2123i	−0.0136910	+	0.0510957i	0.958742	+	0.284276i	$0.0917533\pi$
$788$	463.481	+	31.4235i	0.588173	+	0.0398775i
$789$	−152.786	−	244.929i	−0.193646	−	0.310429i
$790$	4.56286	−	10.0404i	0.00577577	−	0.0127094i
$791$	−121.995			−0.154228
$792$	499.913	+	1330.44i	0.631204	+	1.67985i
$793$		−	359.716i		−	0.453614i
$794$	161.279	−	354.890i	0.203122	−	0.446964i
$795$	−1.40310	−	41.0868i	−0.00176490	−	0.0516815i
$796$	−747.464	−	856.190i	−0.939025	−	1.07562i
$797$	936.343	+	250.892i	1.17483	+	0.314796i	0.792876	−	0.609383i	$-0.208583\pi$
$797$	936.343	+	250.892i	1.17483	+	0.314796i	0.381959	+	0.924179i	$0.375250\pi$
$798$	139.038	+	1053.75i	0.174233	+	1.32049i
$799$	101.609	−	175.992i	0.127170	−	0.220265i
$800$	−740.911	−	229.303i	−0.926139	−	0.286628i
$801$	346.266	+	515.070i	0.432292	+	0.643033i
$802$	285.230	+	234.618i	0.355648	+	0.292541i
$803$	−235.070	−	877.292i	−0.292739	−	1.09252i
$804$	1236.18	+	41.5005i	1.53754	+	0.0516176i
$805$	70.5212	+	18.8961i	0.0876040	+	0.0234734i
$806$	1089.63	+	1524.19i	1.35190	+	1.89105i
$807$	−162.652	−	533.479i	−0.201551	−	0.661065i
$808$	394.687	+	93.4309i	0.488474	+	0.115632i
$809$	−391.861			−0.484378			−0.242189	−	0.970229i	$-0.577865\pi$
$809$	−391.861			−0.484378			−0.242189	+	0.970229i	$0.577865\pi$
$810$	−40.4649	+	135.600i	−0.0499566	+	0.167407i
$811$	437.026	−	437.026i	0.538873	−	0.538873i	−0.384325	−	0.923198i	$-0.625566\pi$
$811$	437.026	−	437.026i	0.538873	−	0.538873i	0.923198	+	0.384325i	$0.125566\pi$
$812$	−391.905	−	799.225i	−0.482642	−	0.984267i
$813$	37.1340	−	69.7094i	0.0456753	−	0.0857434i
$814$	2127.30	+	353.673i	2.61340	+	0.434488i
$815$	217.640	−	125.654i	0.267043	−	0.154177i
$816$	−150.217	+	208.270i	−0.184090	+	0.255233i
$817$	298.550	−	517.104i	0.365422	−	0.632930i
$818$	−551.416	−	453.573i	−0.674103	−	0.554490i
$819$	1327.27	+	260.117i	1.62059	+	0.317603i
$820$	39.5650	−	58.9263i	0.0482500	−	0.0718613i
$821$	−906.627	+	242.930i	−1.10430	+	0.295895i	−0.764513	−	0.644608i	$-0.777020\pi$
$821$	−906.627	+	242.930i	−1.10430	+	0.295895i	−0.339783	+	0.940504i	$0.610354\pi$
$822$	327.248	−	426.733i	0.398112	−	0.519140i
$823$	−1213.21	+	700.449i	−1.47414	+	0.851092i	−0.999576	−	0.0291311i	$-0.990726\pi$
$823$	−1213.21	+	700.449i	−1.47414	+	0.851092i	−0.474560	+	0.880223i	$0.657393\pi$
$824$	−221.782	+	6.51266i	−0.269153	+	0.00790372i
$825$	−979.676	+	1048.95i	−1.18749	+	1.27146i
$826$	299.257	+	135.997i	0.362297	+	0.164645i
$827$	563.436	+	563.436i	0.681301	+	0.681301i	0.960293	−	0.278992i	$-0.0900003\pi$
$827$	563.436	+	563.436i	0.681301	+	0.681301i	−0.278992	+	0.960293i	$0.590000\pi$
$828$	89.5782	+	333.540i	0.108186	+	0.402826i
$829$	−785.792	−	785.792i	−0.947880	−	0.947880i	0.0508279	−	0.998707i	$-0.483814\pi$
$829$	−785.792	−	785.792i	−0.947880	−	0.947880i	−0.998707	+	0.0508279i	$0.983814\pi$
$830$	13.3675	+	35.6378i	0.0161054	+	0.0429371i
$831$	−507.806	−	117.648i	−0.611079	−	0.141575i
$832$	1047.71	−	347.796i	1.25926	−	0.418024i
$833$	124.660	−	71.9724i	0.149652	−	0.0864015i
$834$	−333.773	−	138.140i	−0.400207	−	0.165636i
$835$	25.2446	−	6.76427i	0.0302331	−	0.00810093i
$836$	1575.30	−	309.670i	1.88433	−	0.370419i
$837$	859.189	+	1188.34i	1.02651	+	1.41976i
$838$	74.3579	+	763.758i	0.0887326	+	0.911406i
$839$	368.686	−	638.583i	0.439435	−	0.761124i	−0.558211	−	0.829699i	$-0.688512\pi$
$839$	368.686	−	638.583i	0.439435	−	0.761124i	0.997646	+	0.0685750i	$0.0218453\pi$
$840$	35.9836	−	179.070i	0.0428376	−	0.213178i
$841$	163.327	−	94.2970i	0.194206	−	0.112125i
$842$	19.3688	−	13.8466i	0.0230033	−	0.0164449i
$843$	121.362	+	194.554i	0.143965	+	0.230787i
$844$	−279.449	−	569.889i	−0.331101	−	0.675224i
$845$	79.3840	−	79.3840i	0.0939455	−	0.0939455i
$846$	−622.319	+	283.245i	−0.735602	+	0.334805i
$847$	−2340.65			−2.76346
$848$	−199.822	+	151.908i	−0.235639	+	0.179136i
$849$	−440.170	+	471.296i	−0.518457	+	0.555119i
$850$	−255.816	−	42.5304i	−0.300960	−	0.0500358i
$851$	506.165	+	135.626i	0.594788	+	0.159373i
$852$	−242.839	−	1045.42i	−0.285022	−	1.22702i
$853$	−141.851	−	529.395i	−0.166297	−	0.620627i	−0.997871	−	0.0652144i	$-0.979227\pi$
$853$	−141.851	−	529.395i	−0.166297	−	0.620627i	0.831575	−	0.555413i	$-0.187440\pi$
$854$	35.2120	+	361.676i	0.0412319	+	0.423509i
$855$	143.562	+	70.2937i	0.167908	+	0.0822148i
$856$	417.679	+	1393.79i	0.487943	+	1.62825i
$857$	−387.117	+	670.506i	−0.451712	+	0.782388i	−0.998493	−	0.0548881i	$-0.982520\pi$
$857$	−387.117	+	670.506i	−0.451712	+	0.782388i	0.546781	+	0.837276i	$0.315853\pi$
$858$	266.070	−	2025.52i	0.310105	−	2.36075i
$859$	−439.785	−	117.840i	−0.511973	−	0.137183i	−0.00642190	−	0.999979i	$-0.502044\pi$
$859$	−439.785	−	117.840i	−0.511973	−	0.137183i	−0.505551	+	0.862797i	$0.668711\pi$
$860$	−77.2963	+	67.4806i	−0.0898795	+	0.0784658i
$861$	−468.604	−	249.624i	−0.544255	−	0.289924i
$862$	−733.836	+	275.256i	−0.851318	+	0.319323i
$863$		−	119.265i		−	0.138199i	−0.997610	−	0.0690993i	$-0.977987\pi$
$863$		−	119.265i		−	0.138199i	0.997610	−	0.0690993i	$-0.0220125\pi$
$864$	818.530	−	276.595i	0.947373	−	0.320133i
$865$	167.395			0.193520
$866$	293.431	+	782.291i	0.338835	+	0.903338i
$867$	367.253	−	689.421i	0.423591	−	0.795180i
$868$	−1244.77	−	1425.83i	−1.43407	−	1.64267i
$869$	−32.2522	+	120.367i	−0.0371142	+	0.138512i
$870$	−132.728	−	17.4350i	−0.152561	−	0.0200402i
$871$	−1539.70	−	888.946i	−1.76774	−	1.02060i
$872$	76.3789	+	254.875i	0.0875905	+	0.292288i
$873$	916.288	−	62.6548i	1.04959	−	0.0717696i
$874$	388.280	−	37.8021i	0.444256	−	0.0432519i
$875$	361.945	−	96.9828i	0.413651	−	0.110838i
$876$	−537.810	+	124.927i	−0.613939	+	0.142611i
$877$	−402.617	+	1502.59i	−0.459085	+	1.71333i	0.216708	+	0.976237i	$0.430468\pi$
$877$	−402.617	+	1502.59i	−0.459085	+	1.71333i	−0.675793	+	0.737092i	$0.736199\pi$
$878$	32.1182	−	193.187i	0.0365811	−	0.220031i
$879$	787.533	+	735.521i	0.895942	+	0.836770i
$880$	−273.361	−	37.2383i	−0.310637	−	0.0423162i
$881$		−	1288.10i		−	1.46209i	−0.682328	−	0.731047i	$-0.739032\pi$
$881$		−	1288.10i		−	1.46209i	0.682328	−	0.731047i	$-0.260968\pi$
$882$	−482.065	−	46.6518i	−0.546558	−	0.0528932i
$883$	392.214	+	392.214i	0.444184	+	0.444184i	0.893415	−	0.449232i	$-0.148302\pi$
$883$	392.214	+	392.214i	0.444184	+	0.444184i	−0.449232	+	0.893415i	$0.648302\pi$
$884$	331.413	−	162.511i	0.374902	−	0.183836i
$885$	41.9432	−	26.1641i	0.0473934	−	0.0295639i
$886$	544.675	+	761.898i	0.614757	+	0.859930i
$887$	−530.663	−	919.136i	−0.598267	−	1.03623i	−0.993077	−	0.117467i	$-0.962523\pi$
$887$	−530.663	−	919.136i	−0.598267	−	1.03623i	0.394809	−	0.918763i	$-0.370811\pi$
$888$	258.272	−	1285.27i	0.290846	−	1.44738i
$889$	−4.61207	−	2.66278i	−0.00518793	−	0.00299526i
$890$	−119.908	+	11.6740i	−0.134728	+	0.0131168i
$891$	199.748	−	1586.39i	0.224184	−	1.78046i
$892$	182.779	+	929.800i	0.204909	+	1.04238i
$893$	199.900	+	746.038i	0.223852	+	0.835429i
$894$	−466.450	+	1127.03i	−0.521756	+	1.26066i
$895$	114.202	+	197.803i	0.127600	+	0.221009i
$896$	−1019.37	+	452.250i	−1.13769	+	0.504743i
$897$	112.043	−	483.612i	0.124909	−	0.539143i
$898$	198.196	−	74.3417i	0.220708	−	0.0827859i
$899$	−980.923	+	980.923i	−1.09113	+	1.09113i
$900$	617.329	+	616.616i	0.685921	+	0.685129i
$901$	−59.3459	+	59.3459i	−0.0658667	+	0.0658667i
$902$	−331.799	+	730.115i	−0.367848	+	0.809440i
$903$	560.956	+	523.908i	0.621213	+	0.580186i
$904$	111.971	−	3.28804i	0.123861	−	0.00363721i
$905$	40.4921	+	70.1344i	0.0447426	+	0.0774965i
$906$	162.933	+	124.948i	0.179838	+	0.137912i
$907$	105.459	+	393.580i	0.116273	+	0.433936i	0.999379	−	0.0352371i	$-0.0112187\pi$
$907$	105.459	+	393.580i	0.116273	+	0.433936i	−0.883106	+	0.469173i	$0.844552\pi$
$908$	699.614	+	469.743i	0.770500	+	0.517338i
$909$	−343.908	−	299.886i	−0.378337	−	0.329908i
$910$	−166.782	+	202.760i	−0.183277	+	0.222813i
$911$	−1308.35	−	755.377i	−1.43617	−	0.829173i	−0.438589	−	0.898688i	$-0.644522\pi$
$911$	−1308.35	−	755.377i	−1.43617	−	0.829173i	−0.997581	+	0.0695142i	$0.977855\pi$
$912$	−156.015	−	963.418i	−0.171069	−	1.05638i
$913$	−215.035	−	372.451i	−0.235525	−	0.407942i
$914$	237.166	−	1426.52i	0.259481	−	1.56075i
$915$	48.2331	+	25.6937i	0.0527138	+	0.0280805i
$916$	391.330	−	191.892i	0.427217	−	0.209489i
$917$	−544.336	−	544.336i	−0.593605	−	0.593605i
$918$	258.699	−	128.579i	0.281807	−	0.140064i
$919$			1211.82i			1.31863i	0.751867	+	0.659315i	$0.229154\pi$
$919$			1211.82i			1.31863i	−0.751867	+	0.659315i	$0.770846\pi$
$920$	−65.2360	−	15.4427i	−0.0709086	−	0.0167856i
$921$	1533.00	−	467.394i	1.66450	−	0.507486i
$922$	237.321	−	169.659i	0.257398	−	0.184012i
$923$	−399.280	+	1490.13i	−0.432590	+	1.61445i
$924$	−69.2450	+	2062.61i	−0.0749405	+	2.23226i
$925$	1278.80	−	342.653i	1.38248	−	0.370435i
$926$	−180.554	+	219.502i	−0.194982	+	0.237043i
$927$	224.181	+	109.768i	0.241835	+	0.118412i
$928$	381.244	+	722.991i	0.410824	+	0.779086i
$929$	67.4263	+	38.9286i	0.0725795	+	0.0419038i	0.535851	−	0.844313i	$-0.319991\pi$
$929$	67.4263	+	38.9286i	0.0725795	+	0.0419038i	−0.463271	+	0.886217i	$0.653324\pi$
$930$	−282.203	+	37.2357i	−0.303445	+	0.0400383i
$931$	−141.595	+	528.440i	−0.152089	+	0.567604i
$932$	765.233	−	668.057i	0.821065	−	0.716799i
$933$	−536.867	+	18.3338i	−0.575421	+	0.0196504i
$934$	−1183.01	−	537.618i	−1.26661	−	0.575608i
$935$	−92.2461			−0.0986589
$936$	−1225.22	−	202.971i	−1.30899	−	0.216849i
$937$			414.817i			0.442708i	0.975194	+	0.221354i	$0.0710476\pi$
$937$			414.817i			0.442708i	−0.975194	+	0.221354i	$0.928952\pi$
$938$	1635.11	+	743.073i	1.74319	+	0.792188i
$939$	28.0628	−	17.5055i	0.0298858	−	0.0186428i
$940$	8.97795	−	132.420i	0.00955101	−	0.140873i
$941$	−1343.14	−	359.893i	−1.42735	−	0.382458i	−0.539266	−	0.842135i	$-0.681298\pi$
$941$	−1343.14	−	359.893i	−1.42735	−	0.382458i	−0.888086	+	0.459678i	$0.847965\pi$
$942$	294.462	−	711.476i	0.312593	−	0.755282i
$943$	−97.4377	+	168.767i	−0.103327	+	0.178968i
$944$	−278.333	−	116.757i	−0.294845	−	0.123683i
$945$	−129.682	+	159.389i	−0.137229	+	0.168666i
$946$	736.505	−	895.382i	0.778546	−	0.946492i
$947$	−164.936	−	615.548i	−0.174166	−	0.649998i	−0.996692	−	0.0812700i	$-0.974102\pi$
$947$	−164.936	−	615.548i	−0.174166	−	0.649998i	0.822526	−	0.568728i	$-0.192564\pi$
$948$	72.4734	+	22.0506i	0.0764488	+	0.0232601i
$949$	766.590	+	205.407i	0.807788	+	0.216446i
$950$	801.791	−	573.194i	0.843990	−	0.603362i
$951$	−530.214	−	122.840i	−0.557534	−	0.129169i
$952$	−317.312	+	195.838i	−0.333311	+	0.205712i
$953$	1255.20			1.31710			0.658552	−	0.752535i	$-0.271169\pi$
$953$	1255.20			1.31710			0.658552	+	0.752535i	$0.271169\pi$
$954$	278.533	−	46.4725i	0.291963	−	0.0487133i
$955$	−160.835	+	160.835i	−0.168414	+	0.168414i
$956$	541.116	−	1582.39i	0.566021	−	1.65522i
$957$	1511.71	−	51.6242i	1.57963	−	0.0539438i
$958$	117.172	−	704.776i	0.122309	−	0.735674i
$959$	676.258	−	390.438i	0.705170	−	0.407130i
$960$	−28.2006	+	165.326i	−0.0293756	+	0.172215i
$961$	−994.365	+	1722.29i	−1.03472	+	1.79219i
$962$	−1197.07	+	1455.31i	−1.24436	+	1.51279i
$963$	314.811	−	1606.34i	0.326906	−	1.66806i
$964$	−100.260	−	510.025i	−0.104004	−	0.529072i
$965$	−143.438	+	38.4342i	−0.148641	+	0.0398282i
$966$	−65.3136	+	497.215i	−0.0676124	+	0.514716i
$967$	0.0694834	−	0.0401162i	7.18546e−5	−	4.14853e-5i	−0.499964	−	0.866046i	$-0.666653\pi$
$967$	0.0694834	−	0.0401162i	7.18546e−5	−	4.14853e-5i	0.500036	+	0.866005i	$0.333320\pi$
$968$	2148.32	−	63.0859i	2.21934	−	0.0651714i
$969$	−95.1689	−	312.143i	−0.0982135	−	0.322129i
$970$	−73.7593	+	162.305i	−0.0760405	+	0.167325i
$971$	−866.649	−	866.649i	−0.892532	−	0.892532i	0.102229	−	0.994761i	$-0.467403\pi$
$971$	−866.649	−	866.649i	−0.892532	−	0.892532i	−0.994761	+	0.102229i	$0.967403\pi$
$972$	−959.768	−	153.718i	−0.987416	−	0.158146i
$973$	−370.900	−	370.900i	−0.381192	−	0.381192i
$974$	126.637	−	47.5007i	0.130018	−	0.0487686i
$975$	−365.763	−	1199.66i	−0.375141	−	1.23042i
$976$	−42.0668	−	331.009i	−0.0431012	−	0.339149i
$977$	76.1641	−	43.9734i	0.0779572	−	0.0450086i	−0.460515	−	0.887652i	$-0.652335\pi$
$977$	76.1641	−	43.9734i	0.0779572	−	0.0450086i	0.538472	+	0.842643i	$0.319002\pi$
$978$	1051.24	+	1369.18i	1.07489	+	1.39998i
$979$	1314.87	−	352.319i	1.34308	−	0.359876i
$980$	52.4058	−	78.0509i	0.0534753	−	0.0796438i
$981$	57.5679	−	293.744i	0.0586828	−	0.299434i
$982$	−1631.32	+	158.822i	−1.66122	+	0.161733i
$983$	−2.53490	+	4.39058i	−0.00257874	+	0.00446651i	−0.867312	−	0.497765i	$-0.834154\pi$
$983$	−2.53490	+	4.39058i	−0.00257874	+	0.00446651i	0.864733	+	0.502232i	$0.167488\pi$
$984$	436.828	+	216.483i	0.443930	+	0.220003i
$985$	87.8549	−	50.7230i	0.0891928	−	0.0514955i
$986$	158.937	+	222.324i	0.161194	+	0.225481i
$987$	−992.270	+	33.8856i	−1.00534	+	0.0343320i
$988$	−453.917	+	1327.40i	−0.459430	+	1.34352i
$989$	199.208	−	199.208i	0.201423	−	0.201423i
$990$	252.591	+	180.355i	0.255143	+	0.182177i
$991$	−1260.68			−1.27213			−0.636065	−	0.771635i	$-0.719439\pi$
$991$	−1260.68			−1.27213			−0.636065	+	0.771635i	$0.719439\pi$
$992$	1180.92	+	1275.13i	1.19044	+	1.28541i
$993$	−112.274	−	26.0115i	−0.113065	−	0.0261949i
$994$	255.590	−	1537.34i	0.257132	−	1.54662i
$995$	−239.742	−	64.2386i	−0.240946	−	0.0645614i
$996$	−230.676	+	123.052i	−0.231602	+	0.123546i
$997$	421.532	+	1573.18i	0.422800	+	1.57791i	0.768681	+	0.639633i	$0.220914\pi$
$997$	421.532	+	1573.18i	0.422800	+	1.57791i	−0.345881	+	0.938279i	$0.612420\pi$
$998$	411.199	−	40.0334i	0.412023	−	0.0401137i
$999$	−930.789	+	1144.01i	−0.931720	+	1.14516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.29.19	yes	184
3.2	odd	2		432.3.x.a.413.28		184
9.4	even	3		432.3.x.a.125.43		184
9.5	odd	6	inner	144.3.w.a.77.4	yes	184
16.5	even	4	inner	144.3.w.a.101.4	yes	184
48.5	odd	4		432.3.x.a.197.43		184
144.5	odd	12	inner	144.3.w.a.5.19	✓	184
144.85	even	12		432.3.x.a.341.28		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.19	✓	184	144.5	odd	12	inner
144.3.w.a.29.19	yes	184	1.1	even	1	trivial
144.3.w.a.77.4	yes	184	9.5	odd	6	inner
144.3.w.a.101.4	yes	184	16.5	even	4	inner
432.3.x.a.125.43		184	9.4	even	3
432.3.x.a.197.43		184	48.5	odd	4
432.3.x.a.341.28		184	144.85	even	12
432.3.x.a.413.28		184	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.702398 - 1.87260i) q^{2} +(1.41045 - 2.64776i) q^{3} +(-3.01327 + 2.63062i) q^{4} +(-0.226081 + 0.843746i) q^{5} +(-5.94890 - 0.781440i) q^{6} +(-7.54519 - 4.35622i) q^{7} +(7.04263 + 3.79492i) q^{8} +(-5.02124 - 7.46908i) q^{9} +O(q^{10})\)	\(q+(-0.702398 - 1.87260i) q^{2} +(1.41045 - 2.64776i) q^{3} +(-3.01327 + 2.63062i) q^{4} +(-0.226081 + 0.843746i) q^{5} +(-5.94890 - 0.781440i) q^{6} +(-7.54519 - 4.35622i) q^{7} +(7.04263 + 3.79492i) q^{8} +(-5.02124 - 7.46908i) q^{9} +(1.73880 - 0.169286i) q^{10} +(-19.0671 + 5.10901i) q^{11} +(2.71517 + 11.6888i) q^{12} +(4.46433 - 16.6611i) q^{13} +(-2.85773 + 17.1889i) q^{14} +(1.91516 + 1.78867i) q^{15} +(2.15964 - 15.8536i) q^{16} -5.34982i q^{17} +(-10.4597 + 14.6490i) q^{18} +(14.3774 + 14.3774i) q^{19} +(-1.53833 - 3.13717i) q^{20} +(-22.1763 + 13.8336i) q^{21} +(22.9598 + 32.1165i) q^{22} +(4.79666 + 8.30806i) q^{23} +(19.9813 - 13.2946i) q^{24} +(20.9898 + 12.1185i) q^{25} +(-34.3354 + 3.34282i) q^{26} +(-26.8585 + 2.76021i) q^{27} +(34.1953 - 6.72208i) q^{28} +(-6.61082 - 24.6719i) q^{29} +(2.00427 - 4.84269i) q^{30} +(-27.1557 - 47.0351i) q^{31} +(-31.2044 + 7.09138i) q^{32} +(-13.3658 + 57.6911i) q^{33} +(-10.0181 + 3.75770i) q^{34} +(5.38136 - 5.38136i) q^{35} +(34.7787 + 9.29741i) q^{36} +(38.6246 - 38.6246i) q^{37} +(16.8245 - 37.0218i) q^{38} +(-37.8178 - 35.3202i) q^{39} +(-4.79415 + 5.08423i) q^{40} +(10.1568 + 17.5921i) q^{41} +(41.4814 + 31.8108i) q^{42} +(-7.60062 - 28.3659i) q^{43} +(44.0145 - 65.5532i) q^{44} +(7.43721 - 2.54803i) q^{45} +(12.1885 - 14.8178i) q^{46} +(32.8968 + 18.9929i) q^{47} +(-38.9304 - 28.0789i) q^{48} +(13.4532 + 23.3017i) q^{49} +(7.94988 - 47.8176i) q^{50} +(-14.1650 - 7.54568i) q^{51} +(30.3769 + 61.9484i) q^{52} +(-11.0931 - 11.0931i) q^{53} +(24.0342 + 48.3566i) q^{54} -17.2428i q^{55} +(-36.6065 - 59.3126i) q^{56} +(58.3465 - 17.7892i) q^{57} +(-41.5572 + 29.7089i) q^{58} +(4.88246 - 18.2216i) q^{59} +(-10.4762 - 0.351703i) q^{60} +(20.1439 - 5.39753i) q^{61} +(-69.0038 + 83.8892i) q^{62} +(5.34923 + 78.2292i) q^{63} +(35.1972 + 53.4524i) q^{64} +(13.0484 + 7.53352i) q^{65} +(117.421 - 15.4932i) q^{66} +(26.6773 - 99.5610i) q^{67} +(14.0734 + 16.1205i) q^{68} +(28.7632 - 0.982251i) q^{69} +(-13.8570 - 6.29729i) q^{70} -89.4379 q^{71} +(-7.01816 - 71.6571i) q^{72} +46.0108i q^{73} +(-99.4584 - 45.1987i) q^{74} +(61.6920 - 38.4834i) q^{75} +(-81.1445 - 5.50151i) q^{76} +(166.121 + 44.5119i) q^{77} +(-39.5775 + 95.6266i) q^{78} +(3.15641 - 5.46705i) q^{79} +(12.8881 + 5.40638i) q^{80} +(-30.5744 + 75.0080i) q^{81} +(25.8089 - 31.3764i) q^{82} +(5.63889 + 21.0446i) q^{83} +(30.4325 - 100.022i) q^{84} +(4.51389 + 1.20949i) q^{85} +(-47.7793 + 34.1571i) q^{86} +(-74.6495 - 17.2948i) q^{87} +(-153.671 - 36.3772i) q^{88} -68.9602 q^{89} +(-9.99533 - 12.1372i) q^{90} +(-106.264 + 106.264i) q^{91} +(-36.3090 - 12.4162i) q^{92} +(-162.839 + 5.56090i) q^{93} +(12.4596 - 74.9431i) q^{94} +(-15.3813 + 8.88040i) q^{95} +(-25.2361 + 92.6236i) q^{96} +(-51.0238 + 88.3757i) q^{97} +(34.1853 - 41.5596i) q^{98} +(133.900 + 116.760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more