LMFDB - Embedded newform 144.3.w.a.5.4

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			5.4
Character	$\chi$	$=$	144.5
Dual form			144.3.w.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88582 - 0.666085i) q^{2} +(2.99994 + 0.0192045i) q^{3} +(3.11266 + 2.51224i) q^{4} +(-0.345472 - 1.28932i) q^{5} +(-5.64456 - 2.03443i) q^{6} +(4.11923 - 2.37824i) q^{7} +(-4.19657 - 6.81093i) q^{8} +(8.99926 + 0.115225i) q^{9} +O(q^{10})$	\(q+(-1.88582 - 0.666085i) q^{2} +(2.99994 + 0.0192045i) q^{3} +(3.11266 + 2.51224i) q^{4} +(-0.345472 - 1.28932i) q^{5} +(-5.64456 - 2.03443i) q^{6} +(4.11923 - 2.37824i) q^{7} +(-4.19657 - 6.81093i) q^{8} +(8.99926 + 0.115225i) q^{9} +(-0.207297 + 2.66154i) q^{10} +(0.498663 + 0.133616i) q^{11} +(9.28955 + 7.59633i) q^{12} +(3.10316 + 11.5812i) q^{13} +(-9.35225 + 1.74118i) q^{14} +(-1.01163 - 3.87452i) q^{15} +(3.37733 + 15.6395i) q^{16} -12.5043i q^{17} +(-16.8943 - 6.21157i) q^{18} +(14.2044 - 14.2044i) q^{19} +(2.16374 - 4.88113i) q^{20} +(12.4031 - 7.05546i) q^{21} +(-0.851390 - 0.584128i) q^{22} +(0.183103 - 0.317144i) q^{23} +(-12.4586 - 20.5130i) q^{24} +(20.1076 - 11.6092i) q^{25} +(1.86202 - 23.9070i) q^{26} +(26.9950 + 0.518494i) q^{27} +(18.7965 + 2.94583i) q^{28} +(-0.734316 + 2.74050i) q^{29} +(-0.672991 + 7.98049i) q^{30} +(-14.3899 + 24.9240i) q^{31} +(4.04818 - 31.7429i) q^{32} +(1.49339 + 0.410417i) q^{33} +(-8.32891 + 23.5809i) q^{34} +(-4.48939 - 4.48939i) q^{35} +(27.7222 + 22.9669i) q^{36} +(-38.8945 - 38.8945i) q^{37} +(-36.2484 + 17.3257i) q^{38} +(9.08688 + 34.8023i) q^{39} +(-7.33167 + 7.76371i) q^{40} +(7.97394 - 13.8113i) q^{41} +(-28.0896 + 5.04383i) q^{42} +(-16.5064 + 61.6026i) q^{43} +(1.21649 + 1.66866i) q^{44} +(-2.96043 - 11.6427i) q^{45} +(-0.556545 + 0.476116i) q^{46} +(-67.2078 + 38.8024i) q^{47} +(9.83143 + 46.9824i) q^{48} +(-13.1880 + 22.8422i) q^{49} +(-45.6521 + 8.49942i) q^{50} +(0.240139 - 37.5121i) q^{51} +(-19.4355 + 43.8441i) q^{52} +(-10.3029 + 10.3029i) q^{53} +(-50.5625 - 18.9588i) q^{54} -0.689097i q^{55} +(-33.4847 - 18.0754i) q^{56} +(42.8852 - 42.3397i) q^{57} +(3.21020 - 4.67899i) q^{58} +(26.3048 + 98.1709i) q^{59} +(6.58482 - 14.6015i) q^{60} +(-36.2654 - 9.71727i) q^{61} +(43.7383 - 37.4174i) q^{62} +(37.3441 - 20.9278i) q^{63} +(-28.7776 + 57.1651i) q^{64} +(13.8598 - 8.00193i) q^{65} +(-2.54290 - 1.76870i) q^{66} +(-1.31178 - 4.89562i) q^{67} +(31.4137 - 38.9216i) q^{68} +(0.555389 - 0.947896i) q^{69} +(5.47589 + 11.4565i) q^{70} -77.3554 q^{71} +(-36.9812 - 61.7769i) q^{72} -105.834i q^{73} +(47.4412 + 99.2553i) q^{74} +(60.5446 - 34.4406i) q^{75} +(79.8986 - 8.52870i) q^{76} +(2.37188 - 0.635543i) q^{77} +(6.04506 - 71.6837i) q^{78} +(-17.3463 - 30.0446i) q^{79} +(18.9975 - 9.75747i) q^{80} +(80.9734 + 2.07388i) q^{81} +(-24.2369 + 20.7343i) q^{82} +(-17.2099 + 64.2283i) q^{83} +(56.3317 + 9.19829i) q^{84} +(-16.1220 + 4.31988i) q^{85} +(72.1607 - 105.177i) q^{86} +(-2.25553 + 8.20724i) q^{87} +(-1.18262 - 3.95709i) q^{88} -43.9825 q^{89} +(-2.17219 + 23.9280i) q^{90} +(40.3254 + 40.3254i) q^{91} +(1.36668 - 0.527164i) q^{92} +(-43.6475 + 74.4942i) q^{93} +(152.588 - 28.4084i) q^{94} +(-23.2213 - 13.4068i) q^{95} +(12.7539 - 95.1490i) q^{96} +(-88.1367 - 152.657i) q^{97} +(40.0850 - 34.2921i) q^{98} +(4.47220 + 1.25991i) 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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.88582	−	0.666085i	−0.942912	−	0.333042i
$2$	−1.88582	−	0.666085i	−0.942912	−	0.333042i
$3$	2.99994	+	0.0192045i	0.999980	+	0.00640151i
$3$	2.99994	+	0.0192045i	0.999980	+	0.00640151i
$4$	3.11266	+	2.51224i	0.778165	+	0.628059i
$5$	−0.345472	−	1.28932i	−0.0690944	−	0.257864i	0.922735	−	0.385435i	$-0.125949\pi$
$5$	−0.345472	−	1.28932i	−0.0690944	−	0.257864i	−0.991829	+	0.127571i	$0.959282\pi$
$6$	−5.64456	−	2.03443i	−0.940761	−	0.339072i
$7$	4.11923	−	2.37824i	0.588462	−	0.339748i	−0.176027	−	0.984385i	$-0.556325\pi$
$7$	4.11923	−	2.37824i	0.588462	−	0.339748i	0.764489	+	0.644637i	$0.222991\pi$
$8$	−4.19657	−	6.81093i	−0.524571	−	0.851367i
$9$	8.99926	+	0.115225i	0.999918	+	0.0128028i
$10$	−0.207297	+	2.66154i	−0.0207297	+	0.266154i
$11$	0.498663	+	0.133616i	0.0453330	+	0.0121469i	0.281414	−	0.959586i	$-0.409196\pi$
$11$	0.498663	+	0.133616i	0.0453330	+	0.0121469i	−0.236081	+	0.971733i	$0.575863\pi$
$12$	9.28955	+	7.59633i	0.774129	+	0.633028i
$13$	3.10316	+	11.5812i	0.238705	+	0.890858i	0.976444	+	0.215772i	$0.0692268\pi$
$13$	3.10316	+	11.5812i	0.238705	+	0.890858i	−0.737739	+	0.675086i	$0.764107\pi$
$14$	−9.35225	+	1.74118i	−0.668018	+	0.124370i
$15$	−1.01163	−	3.87452i	−0.0674423	−	0.258301i
$16$	3.37733	+	15.6395i	0.211083	+	0.977468i
$17$		−	12.5043i		−	0.735546i	−0.929916	−	0.367773i	$-0.880120\pi$
$17$		−	12.5043i		−	0.735546i	0.929916	−	0.367773i	$-0.119880\pi$
$18$	−16.8943	−	6.21157i	−0.938571	−	0.345087i
$19$	14.2044	−	14.2044i	0.747602	−	0.747602i	−0.226426	−	0.974028i	$-0.572704\pi$
$19$	14.2044	−	14.2044i	0.747602	−	0.747602i	0.974028	+	0.226426i	$0.0727042\pi$
$20$	2.16374	−	4.88113i	0.108187	−	0.244056i
$21$	12.4031	−	7.05546i	0.590624	−	0.335974i
$22$	−0.851390	−	0.584128i	−0.0386996	−	0.0265513i
$23$	0.183103	−	0.317144i	0.00796101	−	0.0137889i	−0.862017	−	0.506879i	$-0.830799\pi$
$23$	0.183103	−	0.317144i	0.00796101	−	0.0137889i	0.869978	+	0.493090i	$0.164133\pi$
$24$	−12.4586	−	20.5130i	−0.519110	−	0.854707i
$25$	20.1076	−	11.6092i	0.804306	−	0.464366i
$26$	1.86202	−	23.9070i	0.0716160	−	0.919499i
$27$	26.9950	+	0.518494i	0.999816	+	0.0192035i
$28$	18.7965	+	2.94583i	0.671303	+	0.105208i
$29$	−0.734316	+	2.74050i	−0.0253212	+	0.0945001i	−0.977430	−	0.211259i	$-0.932244\pi$
$29$	−0.734316	+	2.74050i	−0.0253212	+	0.0945001i	0.952109	+	0.305759i	$0.0989103\pi$
$30$	−0.672991	+	7.98049i	−0.0224330	+	0.266016i
$31$	−14.3899	+	24.9240i	−0.464190	+	0.804001i	−0.999165	−	0.0408672i	$-0.986988\pi$
$31$	−14.3899	+	24.9240i	−0.464190	+	0.804001i	0.534974	+	0.844868i	$0.320321\pi$
$32$	4.04818	−	31.7429i	0.126506	−	0.991966i
$33$	1.49339	+	0.410417i	0.0452543	+	0.0124369i
$34$	−8.32891	+	23.5809i	−0.244968	+	0.693555i
$35$	−4.48939	−	4.48939i	−0.128268	−	0.128268i
$36$	27.7222	+	22.9669i	0.770061	+	0.637970i
$37$	−38.8945	−	38.8945i	−1.05120	−	1.05120i	−0.998616	−	0.0525876i	$-0.983253\pi$
$37$	−38.8945	−	38.8945i	−1.05120	−	1.05120i	−0.0525876	−	0.998616i	$-0.516747\pi$
$38$	−36.2484	+	17.3257i	−0.953906	+	0.455940i
$39$	9.08688	+	34.8023i	0.232997	+	0.892368i
$40$	−7.33167	+	7.76371i	−0.183292	+	0.194093i
$41$	7.97394	−	13.8113i	0.194486	−	0.336860i	−0.752246	−	0.658883i	$-0.771029\pi$
$41$	7.97394	−	13.8113i	0.194486	−	0.336860i	0.946732	+	0.322022i	$0.104363\pi$
$42$	−28.0896	+	5.04383i	−0.668801	+	0.120091i
$43$	−16.5064	+	61.6026i	−0.383869	+	1.43262i	0.456072	+	0.889943i	$0.349256\pi$
$43$	−16.5064	+	61.6026i	−0.383869	+	1.43262i	−0.839942	+	0.542677i	$0.817411\pi$
$44$	1.21649	+	1.66866i	0.0276476	+	0.0379241i
$45$	−2.96043	−	11.6427i	−0.0657874	−	0.258727i
$46$	−0.556545	+	0.476116i	−0.0120988	+	0.0103503i
$47$	−67.2078	+	38.8024i	−1.42995	+	0.825583i	−0.997116	−	0.0758893i	$-0.975820\pi$
$47$	−67.2078	+	38.8024i	−1.42995	+	0.825583i	−0.432836	+	0.901473i	$0.642487\pi$
$48$	9.83143	+	46.9824i	0.204821	+	0.978799i
$49$	−13.1880	+	22.8422i	−0.269142	+	0.466168i
$50$	−45.6521	+	8.49942i	−0.913043	+	0.169988i
$51$	0.240139	−	37.5121i	0.00470860	−	0.735531i
$52$	−19.4355	+	43.8441i	−0.373760	+	0.843155i
$53$	−10.3029	+	10.3029i	−0.194394	+	0.194394i	−0.797592	−	0.603198i	$-0.793893\pi$
$53$	−10.3029	+	10.3029i	−0.194394	+	0.194394i	0.603198	+	0.797592i	$0.293893\pi$
$54$	−50.5625	−	18.9588i	−0.936342	−	0.351088i
$55$		−	0.689097i		−	0.0125290i
$56$	−33.4847	−	18.0754i	−0.597940	−	0.322774i
$57$	42.8852	−	42.3397i	0.752373	−	0.742801i
$58$	3.21020	−	4.67899i	0.0553482	−	0.0806723i
$59$	26.3048	+	98.1709i	0.445844	+	1.66391i	0.713698	+	0.700453i	$0.247019\pi$
$59$	26.3048	+	98.1709i	0.445844	+	1.66391i	−0.267854	+	0.963459i	$0.586315\pi$
$60$	6.58482	−	14.6015i	0.109747	−	0.243359i
$61$	−36.2654	−	9.71727i	−0.594514	−	0.159300i	−0.0509986	−	0.998699i	$-0.516240\pi$
$61$	−36.2654	−	9.71727i	−0.594514	−	0.159300i	−0.543515	+	0.839399i	$0.682907\pi$
$62$	43.7383	−	37.4174i	0.705457	−	0.603507i
$63$	37.3441	−	20.9278i	0.592763	−	0.332187i
$64$	−28.7776	+	57.1651i	−0.449650	+	0.893205i
$65$	13.8598	−	8.00193i	0.213227	−	0.123107i
$66$	−2.54290	−	1.76870i	−0.0385288	−	0.0267985i
$67$	−1.31178	−	4.89562i	−0.0195788	−	0.0730690i	0.955445	−	0.295168i	$-0.0953757\pi$
$67$	−1.31178	−	4.89562i	−0.0195788	−	0.0730690i	−0.975024	+	0.222099i	$0.928709\pi$
$68$	31.4137	−	38.9216i	0.461967	−	0.572377i
$69$	0.555389	−	0.947896i	0.00804912	−	0.0137376i
$70$	5.47589	+	11.4565i	0.0782269	+	0.163665i
$71$	−77.3554			−1.08951			−0.544756	−	0.838594i	$-0.683378\pi$
$71$	−77.3554			−1.08951			−0.544756	+	0.838594i	$0.683378\pi$
$72$	−36.9812	−	61.7769i	−0.513628	−	0.858013i
$73$		−	105.834i		−	1.44978i	−0.688867	−	0.724888i	$-0.741891\pi$
$73$		−	105.834i		−	1.44978i	0.688867	−	0.724888i	$-0.258109\pi$
$74$	47.4412	+	99.2553i	0.641097	+	1.34129i
$75$	60.5446	−	34.4406i	0.807262	−	0.459208i
$76$	79.8986	−	8.52870i	1.05130	−	0.112220i
$77$	2.37188	−	0.635543i	0.0308036	−	0.00825380i
$78$	6.04506	−	71.6837i	0.0775007	−	0.919022i
$79$	−17.3463	−	30.0446i	−0.219573	−	0.380312i	0.735104	−	0.677954i	$-0.237133\pi$
$79$	−17.3463	−	30.0446i	−0.219573	−	0.380312i	−0.954678	+	0.297642i	$0.903800\pi$
$80$	18.9975	−	9.75747i	0.237469	−	0.121968i
$81$	80.9734	+	2.07388i	0.999672	+	0.0256034i
$82$	−24.2369	+	20.7343i	−0.295572	+	0.252857i
$83$	−17.2099	+	64.2283i	−0.207349	+	0.773835i	0.781372	+	0.624065i	$0.214520\pi$
$83$	−17.2099	+	64.2283i	−0.207349	+	0.773835i	−0.988721	+	0.149770i	$0.952147\pi$
$84$	56.3317	+	9.19829i	0.670615	+	0.109503i
$85$	−16.1220	+	4.31988i	−0.189671	+	0.0508222i
$86$	72.1607	−	105.177i	0.839078	−	1.22299i
$87$	−2.25553	+	8.20724i	−0.0259257	+	0.0943361i
$88$	−1.18262	−	3.95709i	−0.0134389	−	0.0449669i
$89$	−43.9825			−0.494186			−0.247093	−	0.968992i	$-0.579475\pi$
$89$	−43.9825			−0.494186			−0.247093	+	0.968992i	$0.579475\pi$
$90$	−2.17219	+	23.9280i	−0.0241355	+	0.265867i
$91$	40.3254	+	40.3254i	0.443136	+	0.443136i
$92$	1.36668	−	0.527164i	0.0148552	−	0.00573004i
$93$	−43.6475	+	74.4942i	−0.469328	+	0.801013i
$94$	152.588	−	28.4084i	1.62327	−	0.302218i
$95$	−23.2213	−	13.4068i	−0.244435	−	0.141125i
$96$	12.7539	−	95.1490i	0.132853	−	0.991136i
$97$	−88.1367	−	152.657i	−0.908626	−	1.57379i	−0.815974	−	0.578088i	$-0.803799\pi$
$97$	−88.1367	−	152.657i	−0.908626	−	1.57379i	−0.0926520	−	0.995699i	$-0.529534\pi$
$98$	40.0850	−	34.2921i	0.409031	−	0.349919i
$99$	4.47220	+	1.25991i	0.0451737	+	0.0127263i
$100$	91.7532	+	14.3798i	0.917532	+	0.143798i
$101$	149.801	+	40.1390i	1.48317	+	0.397415i	0.907426	−	0.420212i	$-0.138044\pi$
$101$	149.801	+	40.1390i	1.48317	+	0.397415i	0.575748	+	0.817627i	$0.304711\pi$
$102$	−25.4391	+	70.5812i	−0.249403	+	0.691973i
$103$	−18.1132	−	10.4577i	−0.175856	−	0.101531i	0.409488	−	0.912315i	$-0.365707\pi$
$103$	−18.1132	−	10.4577i	−0.175856	−	0.101531i	−0.585344	+	0.810785i	$0.699041\pi$
$104$	65.8558	−	69.7365i	0.633229	−	0.670543i
$105$	−13.3817	−	13.5541i	−0.127445	−	0.129087i
$106$	26.2920	−	12.5668i	0.248037	−	0.118555i
$107$	−62.3967	+	62.3967i	−0.583147	+	0.583147i	−0.935767	−	0.352620i	$-0.885291\pi$
$107$	−62.3967	+	62.3967i	−0.583147	+	0.583147i	0.352620	+	0.935767i	$0.385291\pi$
$108$	82.7238	+	69.4318i	0.765961	+	0.642887i
$109$	−74.0433	+	74.0433i	−0.679297	+	0.679297i	−0.959841	−	0.280544i	$-0.909485\pi$
$109$	−74.0433	+	74.0433i	−0.679297	+	0.679297i	0.280544	+	0.959841i	$0.409485\pi$
$110$	−0.458997	+	1.29951i	−0.00417270	+	0.0118138i
$111$	−115.934	−	117.428i	−1.04445	−	1.05791i
$112$	51.1064	+	56.3906i	0.456308	+	0.503487i
$113$	48.3384	+	27.9082i	0.427773	+	0.246975i	0.698398	−	0.715710i	$-0.253897\pi$
$113$	48.3384	+	27.9082i	0.427773	+	0.246975i	−0.270624	+	0.962685i	$0.587230\pi$
$114$	−109.076	+	51.2799i	−0.956805	+	0.449824i
$115$	−0.472157	−	0.126514i	−0.00410572	−	0.00110012i
$116$	−9.17047	+	6.68549i	−0.0790558	+	0.0576335i
$117$	26.5917	+	104.579i	0.227280	+	0.893841i
$118$	15.7839	−	202.654i	0.133762	−	1.71741i
$119$	−29.7382	−	51.5080i	−0.249901	−	0.432841i
$120$	−22.1437	+	23.1498i	−0.184531	+	0.192915i
$121$	−104.558	−	60.3667i	−0.864118	−	0.498899i
$122$	61.9175	+	42.4809i	0.507521	+	0.348204i
$123$	24.1866	−	41.2798i	0.196639	−	0.335608i
$124$	−107.406	+	41.4293i	−0.866177	+	0.334107i
$125$	−45.5107	−	45.5107i	−0.364086	−	0.364086i
$126$	−84.3640	+	14.5917i	−0.669556	+	0.115808i
$127$	58.5207			0.460793			0.230397	−	0.973097i	$-0.425998\pi$
$127$	58.5207			0.460793			0.230397	+	0.973097i	$0.425998\pi$
$128$	92.3463	−	88.6349i	0.721456	−	0.692461i
$129$	−50.7012	+	184.487i	−0.393032	+	1.43013i
$130$	−31.4670	+	5.85846i	−0.242054	+	0.0450651i
$131$	66.2847	−	17.7609i	0.505990	−	0.135580i	0.00321127	−	0.999995i	$-0.498978\pi$
$131$	66.2847	−	17.7609i	0.505990	−	0.135580i	0.502778	+	0.864415i	$0.332311\pi$
$132$	3.61736	+	5.02924i	0.0274042	+	0.0381003i
$133$	24.7298	−	92.2929i	0.185939	−	0.693932i
$134$	−0.787118	+	10.1060i	−0.00587401	+	0.0754182i
$135$	−8.65753	−	34.9843i	−0.0641298	−	0.259143i
$136$	−85.1658	+	52.4751i	−0.626219	+	0.385846i
$137$	15.9170	+	27.5691i	0.116183	+	0.201234i	0.918252	−	0.395997i	$-0.129601\pi$
$137$	15.9170	+	27.5691i	0.116183	+	0.201234i	−0.802069	+	0.597231i	$0.796268\pi$
$138$	−1.67875	+	1.41763i	−0.0121648	+	0.0102727i
$139$	−129.995	+	34.8322i	−0.935219	+	0.250591i	−0.694079	−	0.719899i	$-0.744188\pi$
$139$	−129.995	+	34.8322i	−0.935219	+	0.250591i	−0.241140	+	0.970490i	$0.577521\pi$
$140$	−2.69554	−	25.2524i	−0.0192539	−	0.180374i
$141$	−202.364	+	115.114i	−1.43521	+	0.816413i
$142$	145.879	+	51.5253i	1.02731	+	0.362854i
$143$			6.18972i			0.0432848i
$144$	28.5914	+	141.133i	0.198551	+	0.980090i
$145$	3.78707			0.0261177
$146$	−70.4942	+	199.584i	−0.482837	+	1.36701i
$147$	−40.0017	+	68.2720i	−0.272121	+	0.464435i
$148$	−23.3532	−	218.778i	−0.157792	−	1.47823i
$149$	60.1577	+	224.511i	0.403743	+	1.50679i	0.806363	+	0.591421i	$0.201433\pi$
$149$	60.1577	+	224.511i	0.403743	+	1.50679i	−0.402620	+	0.915367i	$0.631900\pi$
$150$	−137.117	+	24.6210i	−0.914112	+	0.164140i
$151$	160.396	−	92.6049i	1.06223	−	0.613277i	0.136180	−	0.990684i	$-0.456517\pi$
$151$	160.396	−	92.6049i	1.06223	−	0.613277i	0.926048	+	0.377407i	$0.123184\pi$
$152$	−156.355	−	37.1356i	−1.02865	−	0.244313i
$153$	1.44080	−	112.529i	0.00941701	−	0.735486i
$154$	−4.89627	−	0.381350i	−0.0317940	−	0.00247630i
$155$	37.1064	+	9.94262i	0.239396	+	0.0641459i
$156$	−59.1473	+	131.156i	−0.379150	+	0.840745i
$157$	61.5122	+	229.567i	0.391797	+	1.46221i	0.827167	+	0.561956i	$0.189951\pi$
$157$	61.5122	+	229.567i	0.391797	+	1.46221i	−0.435370	+	0.900252i	$0.643382\pi$
$158$	12.6997	+	68.2130i	0.0803781	+	0.431728i
$159$	−31.1058	+	30.7101i	−0.195634	+	0.193145i
$160$	−42.3253	+	5.74689i	−0.264533	+	0.0359181i
$161$		−	1.74185i		−	0.0108190i
$162$	−151.320	−	57.8462i	−0.934076	−	0.357075i
$163$	178.466	−	178.466i	1.09488	−	1.09488i	0.0998824	−	0.994999i	$-0.468153\pi$
$163$	178.466	−	178.466i	1.09488	−	1.09488i	0.994999	−	0.0998824i	$-0.0318467\pi$
$164$	59.5174	−	22.9574i	0.362911	−	0.139984i
$165$	0.0132338	−	2.06725i	8.02047e−5	−	0.0125288i
$166$	75.2364	−	109.660i	0.453231	−	0.660603i
$167$	153.816	−	266.417i	0.921055	−	1.59531i	0.123268	−	0.992373i	$-0.460662\pi$
$167$	153.816	−	266.417i	0.921055	−	1.59531i	0.797786	−	0.602940i	$-0.206004\pi$
$168$	−100.105	−	54.8680i	−0.595862	−	0.326595i
$169$	21.8648	−	12.6237i	0.129378	−	0.0746963i
$170$	33.2807	+	2.59210i	0.195769	+	0.0152476i
$171$	129.466	−	126.193i	0.757112	−	0.737970i
$172$	−206.139	+	150.280i	−1.19848	+	0.873722i
$173$	68.2518	−	254.719i	0.394519	−	1.47236i	−0.428079	−	0.903741i	$-0.640809\pi$
$173$	68.2518	−	254.719i	0.394519	−	1.47236i	0.822598	−	0.568624i	$-0.192524\pi$
$174$	9.72026	−	13.9750i	0.0558635	−	0.0803163i
$175$	55.2187	−	95.6416i	0.315535	−	0.546523i
$176$	−0.405543	+	8.25010i	−0.00230422	+	0.0468756i
$177$	77.0275	+	295.012i	0.435183	+	1.66673i
$178$	82.9433	+	29.2961i	0.465974	+	0.164585i
$179$	−31.7185	−	31.7185i	−0.177198	−	0.177198i	0.612935	−	0.790133i	$-0.289989\pi$
$179$	−31.7185	−	31.7185i	−0.177198	−	0.177198i	−0.790133	+	0.612935i	$0.789989\pi$
$180$	20.0345	−	43.6772i	0.111303	−	0.242651i
$181$	72.1636	+	72.1636i	0.398694	+	0.398694i	0.877772	−	0.479078i	$-0.159029\pi$
$181$	72.1636	+	72.1636i	0.398694	+	0.398694i	−0.479078	+	0.877772i	$0.659029\pi$
$182$	−49.1864	−	102.907i	−0.270255	−	0.565421i
$183$	−108.607	−	29.8477i	−0.593482	−	0.163102i
$184$	−2.92845	+	0.0838130i	−0.0159155	+	0.000455505i
$185$	−36.7105	+	63.5845i	−0.198435	+	0.343700i
$186$	131.931	−	111.410i	0.709306	−	0.598979i
$187$	1.67078	−	6.23542i	0.00893463	−	0.0333445i
$188$	−306.676	−	48.0630i	−1.63125	−	0.255654i
$189$	112.432	−	62.0648i	0.594877	−	0.328385i
$190$	34.8612	+	40.7503i	0.183480	+	0.214475i
$191$	−288.137	+	166.356i	−1.50857	+	0.870975i	−0.508622	+	0.860990i	$0.669845\pi$
$191$	−288.137	+	166.356i	−1.50857	+	0.870975i	−0.999950	+	0.00998486i	$0.996822\pi$
$192$	−87.4289	+	170.939i	−0.455359	+	0.890308i
$193$	107.093	−	185.490i	0.554884	−	0.961087i	−0.443029	−	0.896507i	$-0.646096\pi$
$193$	107.093	−	185.490i	0.554884	−	0.961087i	0.997913	−	0.0645796i	$-0.0205706\pi$
$194$	64.5276	+	346.591i	0.332617	+	1.78655i
$195$	41.7321	−	23.7391i	0.214011	−	0.121739i
$196$	−98.4347	+	37.9688i	−0.502218	+	0.193718i
$197$	81.2066	−	81.2066i	0.412216	−	0.412216i	−0.470294	−	0.882510i	$-0.655852\pi$
$197$	81.2066	−	81.2066i	0.412216	−	0.412216i	0.882510	+	0.470294i	$0.155852\pi$
$198$	−7.59458	−	5.35483i	−0.0383565	−	0.0270446i
$199$			268.462i			1.34905i	0.738251	+	0.674527i	$0.235652\pi$
$199$			268.462i			1.34905i	−0.738251	+	0.674527i	$0.764348\pi$
$200$	−163.452	−	88.2332i	−0.817261	−	0.441166i
$201$	−3.84124	−	14.7118i	−0.0191106	−	0.0731928i
$202$	−255.762	−	175.475i	−1.26615	−	0.868688i
$203$	3.49276	+	13.0351i	0.0172057	+	0.0642126i
$204$	94.9867	−	116.159i	0.465621	−	0.569408i
$205$	−20.5619	−	5.50955i	−0.100302	−	0.0268759i
$206$	27.1926	+	31.7862i	0.132003	+	0.154302i
$207$	1.68434	−	2.83297i	0.00813689	−	0.0136858i
$208$	−170.643	+	87.6452i	−0.820399	+	0.421371i
$209$	8.98117	−	5.18528i	0.0429721	−	0.0248100i
$210$	16.2073	+	34.4740i	0.0771776	+	0.164162i
$211$	28.7402	+	107.260i	0.136209	+	0.508340i	0.999990	+	0.00447219i	$0.00142355\pi$
$211$	28.7402	+	107.260i	0.136209	+	0.508340i	−0.863781	+	0.503868i	$0.831910\pi$
$212$	−57.9526	+	6.18609i	−0.273361	+	0.0291797i
$213$	−232.061	−	1.48557i	−1.08949	−	0.00697452i
$214$	159.231	−	76.1077i	0.744069	−	0.355644i
$215$	85.1280			0.395944
$216$	−109.755	−	186.037i	−0.508125	−	0.861283i
$217$			136.890i			0.630832i
$218$	188.952	−	90.3135i	0.866751	−	0.414282i
$219$	2.03249	−	317.495i	0.00928075	−	1.44975i
$220$	1.73117	−	2.14492i	0.00786897	−	0.00974966i
$221$	144.814	−	38.8028i	0.655267	−	0.175578i
$222$	140.414	+	298.671i	0.632498	+	1.34536i
$223$	11.3197	+	19.6063i	0.0507611	+	0.0879208i	0.890289	−	0.455395i	$-0.150502\pi$
$223$	11.3197	+	19.6063i	0.0507611	+	0.0879208i	−0.839528	+	0.543316i	$0.817169\pi$
$224$	−58.8168	−	140.384i	−0.262575	−	0.626714i
$225$	182.292	−	102.157i	0.810185	−	0.454031i
$226$	−72.5684	−	84.8274i	−0.321099	−	0.375342i
$227$	−73.8987	+	275.794i	−0.325545	+	1.21495i	0.588218	+	0.808703i	$0.299830\pi$
$227$	−73.8987	+	275.794i	−0.325545	+	1.21495i	−0.913763	+	0.406248i	$0.866837\pi$
$228$	239.855	−	24.0512i	1.05199	−	0.105488i
$229$	−296.629	+	79.4816i	−1.29533	+	0.347081i	−0.839681	−	0.543080i	$-0.817258\pi$
$229$	−296.629	+	79.4816i	−1.29533	+	0.347081i	−0.455645	+	0.890162i	$0.650591\pi$
$230$	0.806136	+	0.553080i	0.00350494	+	0.00240470i
$231$	7.12770	−	1.86104i	0.0308558	−	0.00805645i
$232$	21.7470	−	6.49934i	0.0937371	−	0.0280144i
$233$	266.138			1.14222			0.571111	−	0.820873i	$-0.306512\pi$
$233$	266.138			1.14222			0.571111	+	0.820873i	$0.306512\pi$
$234$	19.5115	−	214.931i	0.0833823	−	0.918507i
$235$	73.2471	+	73.2471i	0.311690	+	0.311690i
$236$	−164.751	+	371.657i	−0.698095	+	1.57482i
$237$	−51.4608	−	90.4652i	−0.217134	−	0.381710i
$238$	21.7722	+	116.943i	0.0914800	+	0.491358i
$239$	−158.381	−	91.4411i	−0.662680	−	0.382599i	0.130617	−	0.991433i	$-0.458304\pi$
$239$	−158.381	−	91.4411i	−0.662680	−	0.382599i	−0.793298	+	0.608834i	$0.791637\pi$
$240$	57.1788	−	28.9070i	0.238245	−	0.120446i
$241$	−35.6354	−	61.7224i	−0.147865	−	0.256110i	0.782573	−	0.622559i	$-0.213907\pi$
$241$	−35.6354	−	61.7224i	−0.147865	−	0.256110i	−0.930438	+	0.366449i	$0.880573\pi$
$242$	156.969	+	183.486i	0.648633	+	0.758205i
$243$	242.876	+	7.77656i	0.999488	+	0.0320023i
$244$	−88.4697	−	121.354i	−0.362581	−	0.497351i
$245$	34.0070	+	9.11215i	0.138804	+	0.0371924i
$246$	−73.1075	+	61.7362i	−0.297185	+	0.250960i
$247$	208.582	+	120.425i	0.844463	+	0.487551i
$248$	230.144	−	6.58678i	0.928001	−	0.0265596i
$249$	−52.8622	+	192.351i	−0.212298	+	0.772492i
$250$	55.5112	+	116.139i	0.222045	+	0.464557i
$251$	207.026	−	207.026i	0.824804	−	0.824804i	−0.161989	−	0.986793i	$-0.551791\pi$
$251$	207.026	−	207.026i	0.824804	−	0.824804i	0.986793	+	0.161989i	$0.0517909\pi$
$252$	168.815	+	28.6761i	0.669901	+	0.113794i
$253$	0.133682	−	0.133682i	0.000528389	−	0.000528389i
$254$	−110.360	−	38.9798i	−0.434487	−	0.153464i
$255$	−48.4480	+	12.6498i	−0.189992	+	0.0496069i
$256$	−233.187	+	105.639i	−0.910888	+	0.412654i
$257$	−368.501	−	212.754i	−1.43386	−	0.827837i	−0.436444	−	0.899732i	$-0.643762\pi$
$257$	−368.501	−	212.754i	−1.43386	−	0.827837i	−0.997412	+	0.0718947i	$0.977095\pi$
$258$	218.498	−	314.139i	0.846890	−	1.21759i
$259$	−252.716	−	67.7151i	−0.975738	−	0.261448i
$260$	63.2435	+	9.91168i	0.243244	+	0.0381218i
$261$	−6.92407	+	24.5779i	−0.0265290	+	0.0941682i
$262$	−136.831	−	10.6572i	−0.522257	−	0.0406765i
$263$	−77.4543	−	134.155i	−0.294503	−	0.510094i	0.680366	−	0.732872i	$-0.261821\pi$
$263$	−77.4543	−	134.155i	−0.294503	−	0.510094i	−0.974869	+	0.222778i	$0.928487\pi$
$264$	−3.47180	−	11.8937i	−0.0131507	−	0.0450520i
$265$	16.8430	+	9.72433i	0.0635586	+	0.0366956i
$266$	−108.111	+	157.576i	−0.406432	+	0.592391i
$267$	−131.945	−	0.844664i	−0.494176	−	0.00316353i
$268$	8.21584	−	18.5339i	0.0306561	−	0.0691564i
$269$	134.839	+	134.839i	0.501262	+	0.501262i	0.911830	−	0.410568i	$-0.134670\pi$
$269$	134.839	+	134.839i	0.501262	+	0.501262i	−0.410568	+	0.911830i	$0.634670\pi$
$270$	−6.97597	+	71.7410i	−0.0258369	+	0.265707i
$271$	354.956			1.30980			0.654901	−	0.755715i	$-0.272710\pi$
$271$	354.956			1.30980			0.654901	+	0.755715i	$0.272710\pi$
$272$	195.561	−	42.2311i	0.718973	−	0.155261i
$273$	120.199	+	121.748i	0.440290	+	0.445964i
$274$	−11.6533	−	62.5925i	−0.0425304	−	0.228440i
$275$	11.5781	−	3.10234i	0.0421022	−	0.0112812i
$276$	4.11008	−	1.55521i	0.0148916	−	0.00563483i
$277$	35.7381	−	133.377i	0.129019	−	0.481504i	−0.870932	−	0.491403i	$-0.836484\pi$
$277$	35.7381	−	133.377i	0.129019	−	0.481504i	0.999951	+	0.00989889i	$0.00315097\pi$
$278$	268.350	+	20.9007i	0.965286	+	0.0751822i
$279$	−132.370	+	222.640i	−0.474446	+	0.797992i
$280$	−11.7369	+	49.4170i	−0.0419175	+	0.176489i
$281$	90.7711	+	157.220i	0.323029	+	0.559503i	0.981111	−	0.193443i	$-0.0619655\pi$
$281$	90.7711	+	157.220i	0.323029	+	0.559503i	−0.658083	+	0.752946i	$0.728632\pi$
$282$	458.299	−	82.2932i	1.62517	−	0.291820i
$283$	−281.851	+	75.5217i	−0.995940	+	0.266861i	−0.719744	−	0.694240i	$-0.755741\pi$
$283$	−281.851	+	75.5217i	−0.995940	+	0.266861i	−0.276196	+	0.961101i	$0.589074\pi$
$284$	−240.781	−	194.335i	−0.847821	−	0.684278i
$285$	−69.4050	−	40.6656i	−0.243526	−	0.142686i
$286$	4.12288	−	11.6727i	0.0144157	−	0.0408137i
$287$		−	75.8558i		−	0.264306i
$288$	40.0882	−	285.196i	0.139195	−	0.990265i
$289$	132.643			0.458972
$290$	−7.14175	−	2.52251i	−0.0246267	−	0.00869832i
$291$	−261.473	−	459.655i	−0.898533	−	1.57957i
$292$	265.879	−	329.424i	0.910546	−	1.12817i
$293$	−112.829	−	421.084i	−0.385082	−	1.43715i	−0.838037	−	0.545613i	$-0.816297\pi$
$293$	−112.829	−	421.084i	−0.385082	−	1.43715i	0.452955	−	0.891533i	$-0.350370\pi$
$294$	120.911	−	102.104i	0.411262	−	0.347294i
$295$	117.486	−	67.8306i	0.398258	−	0.229934i
$296$	−101.685	+	428.132i	−0.343529	+	1.44639i
$297$	13.3921	+	3.86553i	0.0450914	+	0.0130152i
$298$	36.0969	−	463.459i	0.121131	−	1.55523i
$299$	4.24109	+	1.13640i	0.0141843	+	0.00380066i
$300$	274.978	+	44.9006i	0.916593	+	0.149669i
$301$	78.5122	+	293.012i	0.260838	+	0.973461i
$302$	−364.162	+	67.7989i	−1.20583	+	0.224500i
$303$	448.622	+	123.291i	1.48060	+	0.406902i
$304$	270.123	+	174.177i	0.888564	+	0.572951i
$305$			50.1147i			0.164310i
$306$	−77.6712	+	211.251i	−0.253827	+	0.690362i
$307$	21.1902	−	21.1902i	0.0690236	−	0.0690236i	−0.671752	−	0.740776i	$-0.734458\pi$
$307$	21.1902	−	21.1902i	0.0690236	−	0.0690236i	0.740776	+	0.671752i	$0.234458\pi$
$308$	8.97949	+	3.98049i	0.0291542	+	0.0129237i
$309$	−54.1377	−	31.7202i	−0.175203	−	0.102654i
$310$	−63.3534	−	43.4660i	−0.204366	−	0.140213i
$311$	78.1884	−	135.426i	0.251410	−	0.435454i	−0.712505	−	0.701667i	$-0.752439\pi$
$311$	78.1884	−	135.426i	0.251410	−	0.435454i	0.963914	+	0.266213i	$0.0857725\pi$
$312$	198.903	−	207.941i	0.637509	−	0.666476i
$313$	−336.842	+	194.476i	−1.07617	+	0.621328i	−0.929861	−	0.367910i	$-0.880073\pi$
$313$	−336.842	+	194.476i	−1.07617	+	0.621328i	−0.146311	+	0.989239i	$0.546740\pi$
$314$	36.9097	−	473.895i	0.117547	−	1.50922i
$315$	−39.8839	−	40.9185i	−0.126616	−	0.129900i
$316$	21.4861	−	137.097i	0.0679941	−	0.433850i
$317$	151.141	−	564.067i	0.476786	−	1.77939i	−0.137713	−	0.990472i	$-0.543975\pi$
$317$	151.141	−	564.067i	0.476786	−	1.77939i	0.614499	−	0.788918i	$-0.289358\pi$
$318$	79.1156	−	37.1947i	0.248791	−	0.116964i
$319$	−0.732352	+	1.26847i	−0.00229577	+	0.00397640i
$320$	83.6460	+	17.3546i	0.261394	+	0.0542332i
$321$	−188.385	+	185.988i	−0.586868	+	0.579402i
$322$	−1.16022	+	3.28483i	−0.00360317	+	0.0102013i
$323$	−177.616	−	177.616i	−0.549896	−	0.549896i
$324$	246.833	+	209.880i	0.761830	+	0.647777i
$325$	196.845	+	196.845i	0.605676	+	0.605676i
$326$	−455.428	+	217.682i	−1.39702	+	0.667735i
$327$	−223.547	+	220.703i	−0.683631	+	0.674934i
$328$	−127.531	+	3.64996i	−0.388813	+	0.0111279i
$329$	−184.563	+	319.672i	−0.560981	+	0.971648i
$330$	−1.40192	+	3.88965i	−0.00424824	+	0.0117868i
$331$	−129.310	+	482.590i	−0.390663	+	1.45797i	0.438380	+	0.898790i	$0.355553\pi$
$331$	−129.310	+	482.590i	−0.390663	+	1.45797i	−0.829043	+	0.559185i	$0.811114\pi$
$332$	−214.925	+	156.686i	−0.647366	+	0.471945i
$333$	−345.541	−	354.504i	−1.03766	−	1.06458i
$334$	−467.527	+	399.962i	−1.39978	+	1.19749i
$335$	−5.85884	+	3.38260i	−0.0174891	+	0.0100973i
$336$	152.233	+	170.150i	0.453075	+	0.506398i
$337$	80.2544	−	139.005i	0.238144	−	0.412477i	−0.722038	−	0.691853i	$-0.756794\pi$
$337$	80.2544	−	139.005i	0.238144	−	0.412477i	0.960182	+	0.279377i	$0.0901278\pi$
$338$	−49.6417	+	9.24218i	−0.146869	+	0.0273437i
$339$	144.476	+	84.6511i	0.426183	+	0.249708i
$340$	−61.0350	−	27.0560i	−0.179515	−	0.0795765i
$341$	−10.5060	+	10.5060i	−0.0308093	+	0.0308093i
$342$	−328.206	+	151.742i	−0.959665	+	0.443690i
$343$			358.524i			1.04526i
$344$	488.842	−	146.096i	1.42105	−	0.424697i
$345$	−1.41401	−	0.388602i	−0.00409859	−	0.00112638i
$346$	−298.375	+	434.894i	−0.862357	+	1.25692i
$347$	−3.09336	−	11.5446i	−0.00891458	−	0.0332697i	0.961325	−	0.275415i	$-0.0888154\pi$
$347$	−3.09336	−	11.5446i	−0.00891458	−	0.0332697i	−0.970240	+	0.242146i	$0.922149\pi$
$348$	−27.6392	+	19.8799i	−0.0794231	+	0.0571262i
$349$	272.152	+	72.9229i	0.779805	+	0.208948i	0.626699	−	0.779262i	$-0.284406\pi$
$349$	272.152	+	72.9229i	0.779805	+	0.208948i	0.153106	+	0.988210i	$0.451072\pi$
$350$	−167.838	+	143.583i	−0.479537	+	0.410237i
$351$	77.7651	+	314.242i	0.221553	+	0.895277i
$352$	6.26005	−	15.2881i	0.0177842	−	0.0434321i
$353$	−137.580	+	79.4318i	−0.389745	+	0.225019i	−0.682050	−	0.731306i	$-0.738911\pi$
$353$	−137.580	+	79.4318i	−0.389745	+	0.225019i	0.292305	+	0.956325i	$0.405578\pi$
$354$	51.2426	−	607.647i	0.144753	−	1.71652i
$355$	26.7241	+	99.7358i	0.0752793	+	0.280946i
$356$	−136.903	−	110.495i	−0.384558	−	0.310378i
$357$	−88.2235	−	155.092i	−0.247125	−	0.434432i
$358$	38.6882	+	80.9426i	0.108068	+	0.226097i
$359$	−472.757			−1.31687			−0.658436	−	0.752636i	$-0.728782\pi$
$359$	−472.757			−1.31687			−0.658436	+	0.752636i	$0.728782\pi$
$360$	−66.8742	+	69.0229i	−0.185762	+	0.191730i
$361$		−	42.5324i		−	0.117818i
$362$	−88.0207	−	184.155i	−0.243151	−	0.508715i
$363$	−312.509	−	183.105i	−0.860906	−	0.504420i
$364$	24.2124	+	226.826i	0.0665175	+	0.623149i
$365$	−136.453	+	36.5626i	−0.373845	+	0.100172i
$366$	184.933	+	128.629i	0.505281	+	0.351446i
$367$	21.5137	+	37.2629i	0.0586206	+	0.101534i	0.893846	−	0.448373i	$-0.147996\pi$
$367$	21.5137	+	37.2629i	0.0586206	+	0.101534i	−0.835226	+	0.549907i	$0.814663\pi$
$368$	5.57837	+	1.79254i	0.0151586	+	0.00487104i
$369$	73.3510	−	123.372i	0.198783	−	0.334343i
$370$	111.582	−	95.4568i	0.301574	−	0.257991i
$371$	−17.9372	+	66.9425i	−0.0483482	+	0.180438i
$372$	−323.007	+	122.223i	−0.868298	+	0.328555i
$373$	−230.327	+	61.7159i	−0.617499	+	0.165458i	−0.553990	−	0.832523i	$-0.686896\pi$
$373$	−230.327	+	61.7159i	−0.617499	+	0.165458i	−0.0635083	+	0.997981i	$0.520229\pi$
$374$	−7.30411	+	10.6460i	−0.0195297	+	0.0284653i
$375$	−135.655	−	137.403i	−0.361748	−	0.366409i
$376$	546.323	+	294.911i	1.45299	+	0.784337i
$377$	−34.0169			−0.0902305
$378$	−253.367	+	42.1542i	−0.670283	+	0.111519i
$379$	−244.733	−	244.733i	−0.645734	−	0.645734i	0.306225	−	0.951959i	$-0.400934\pi$
$379$	−244.733	−	244.733i	−0.645734	−	0.645734i	−0.951959	+	0.306225i	$0.900934\pi$
$380$	−38.5990	−	100.068i	−0.101576	−	0.263338i
$381$	175.559	+	1.12386i	0.460784	+	0.00294977i
$382$	654.184	−	121.794i	1.71252	−	0.318834i
$383$	401.068	+	231.557i	1.04718	+	0.604587i	0.921857	−	0.387530i	$-0.126671\pi$
$383$	401.068	+	231.557i	1.04718	+	0.604587i	0.125318	+	0.992117i	$0.460005\pi$
$384$	278.736	−	264.126i	0.725874	−	0.687828i
$385$	−1.63884	−	2.83855i	−0.00425672	−	0.00737285i
$386$	−325.510	+	278.468i	−0.843289	+	0.721420i
$387$	−155.643	+	552.476i	−0.402179	+	1.42759i
$388$	109.172	−	696.591i	0.281370	−	1.79534i
$389$	−79.0028	−	21.1687i	−0.203092	−	0.0544184i	0.155839	−	0.987783i	$-0.450192\pi$
$389$	−79.0028	−	21.1687i	−0.203092	−	0.0544184i	−0.358931	+	0.933364i	$0.616859\pi$
$390$	−94.5116	+	16.9707i	−0.242337	+	0.0435147i
$391$	−3.96566	−	2.28957i	−0.0101424	−	0.00585569i
$392$	210.921	−	6.03661i	0.538064	−	0.0153995i
$393$	199.191	−	52.0087i	0.506847	−	0.132338i
$394$	−207.232	+	99.0508i	−0.525969	+	0.251398i
$395$	−32.7445	+	32.7445i	−0.0828974	+	0.0828974i
$396$	10.7553	+	15.1569i	0.0271598	+	0.0382750i
$397$	171.035	−	171.035i	0.430818	−	0.430818i	−0.458088	−	0.888907i	$-0.651466\pi$
$397$	171.035	−	171.035i	0.430818	−	0.430818i	0.888907	+	0.458088i	$0.151466\pi$
$398$	178.818	−	506.271i	0.449292	−	1.27204i
$399$	75.9604	−	276.398i	0.190377	−	0.692727i
$400$	249.471	+	275.265i	0.623678	+	0.688163i
$401$	−605.450	−	349.557i	−1.50985	−	0.871712i	−0.999934	−	0.0114882i	$-0.996343\pi$
$401$	−605.450	−	349.557i	−1.50985	−	0.871712i	−0.509916	−	0.860224i	$-0.670324\pi$
$402$	−2.55539	+	30.3024i	−0.00635668	+	0.0753790i
$403$	−333.303	−	89.3083i	−0.827055	−	0.221609i
$404$	365.440	+	501.274i	0.904555	+	1.24078i
$405$	−25.3002	−	105.117i	−0.0624696	−	0.259549i
$406$	2.09579	−	26.9085i	0.00516204	−	0.0662770i
$407$	−14.1983	−	24.5922i	−0.0348853	−	0.0604231i
$408$	−256.500	+	155.786i	−0.628677	+	0.381830i
$409$	134.809	+	77.8320i	0.329606	+	0.190298i	0.655666	−	0.755051i	$-0.272388\pi$
$409$	134.809	+	77.8320i	0.329606	+	0.190298i	−0.326060	+	0.945349i	$0.605721\pi$
$410$	35.1063	+	24.0860i	0.0856252	+	0.0587464i
$411$	47.2206	+	83.0113i	0.114892	+	0.201974i
$412$	−30.1081	−	78.0558i	−0.0730780	−	0.189456i
$413$	341.829	+	341.829i	0.827674	+	0.827674i
$414$	−5.06336	+	4.22056i	−0.0122303	+	0.0101946i
$415$	88.7564			0.213871
$416$	380.182	−	51.6207i	0.913898	−	0.124088i
$417$	−390.647	+	101.998i	−0.936804	+	0.244599i
$418$	−20.3907	+	3.79630i	−0.0487817	+	0.00908207i
$419$	−223.063	+	59.7696i	−0.532371	+	0.142648i	−0.514983	−	0.857201i	$-0.672202\pi$
$419$	−223.063	+	59.7696i	−0.532371	+	0.142648i	−0.0173878	+	0.999849i	$0.505535\pi$
$420$	−7.60150	−	75.8073i	−0.0180988	−	0.180494i
$421$	67.1350	−	250.551i	0.159466	−	0.595134i	−0.839216	−	0.543798i	$-0.816986\pi$
$421$	67.1350	−	250.551i	0.159466	−	0.595134i	0.998681	−	0.0513354i	$-0.0163477\pi$
$422$	17.2452	−	221.416i	0.0408655	−	0.524683i
$423$	−609.291	+	341.449i	−1.44040	+	0.807208i
$424$	113.409	+	26.9354i	0.267474	+	0.0635270i
$425$	−145.164	−	251.432i	−0.341563	−	0.591604i
$426$	436.637	+	157.374i	1.02497	+	0.369423i
$427$	−172.495	+	46.2200i	−0.403970	+	0.108244i
$428$	−350.975	+	37.4645i	−0.820036	+	0.0875340i
$429$	−0.118871	+	18.5688i	−0.000277088	+	0.0432839i
$430$	−160.536	−	56.7025i	−0.373341	−	0.131866i
$431$		−	250.950i		−	0.582251i	−0.956685	−	0.291126i	$-0.905970\pi$
$431$		−	250.950i		−	0.582251i	0.956685	−	0.291126i	$-0.0940298\pi$
$432$	83.0621	+	423.939i	0.192273	+	0.981341i
$433$	−44.7243			−0.103289			−0.0516447	−	0.998666i	$-0.516446\pi$
$433$	−44.7243			−0.103289			−0.0516447	+	0.998666i	$0.516446\pi$
$434$	91.1807	−	258.151i	0.210094	−	0.594819i
$435$	11.3610	+	0.0727289i	0.0261172	+	0.000167193i
$436$	−416.486	+	44.4574i	−0.955244	+	0.101967i
$437$	−1.90398	−	7.10574i	−0.00435692	−	0.0162603i
$438$	−215.311	+	597.385i	−0.491578	+	1.36389i
$439$	207.408	−	119.747i	0.472455	−	0.272772i	−0.244812	−	0.969571i	$-0.578726\pi$
$439$	207.408	−	119.747i	0.472455	−	0.272772i	0.717267	+	0.696798i	$0.245393\pi$
$440$	−4.69339	+	2.89184i	−0.0106668	+	0.00657237i
$441$	−121.314	+	204.043i	−0.275088	+	0.462684i
$442$	−298.940	−	23.2832i	−0.676334	−	0.0526769i
$443$	605.761	+	162.313i	1.36741	+	0.366395i	0.866531	−	0.499124i	$-0.166345\pi$
$443$	605.761	+	162.313i	1.36741	+	0.366395i	0.500876	+	0.865519i	$0.333011\pi$
$444$	−65.8568	−	656.769i	−0.148326	−	1.47921i
$445$	15.1947	+	56.7076i	0.0341455	+	0.127433i
$446$	−8.28752	−	44.5140i	−0.0185819	−	0.0998072i
$447$	176.158	+	674.676i	0.394089	+	1.50934i
$448$	17.4106	+	303.916i	0.0388629	+	0.678385i
$449$			348.909i			0.777081i	0.921432	+	0.388540i	$0.127021\pi$
$449$			348.909i			0.777081i	−0.921432	+	0.388540i	$0.872979\pi$
$450$	−411.815	+	71.2282i	−0.915144	+	0.158285i
$451$	5.82172	−	5.82172i	0.0129085	−	0.0129085i
$452$	80.3491	+	208.306i	0.177763	+	0.460854i
$453$	482.958	−	274.729i	1.06613	−	0.606465i
$454$	323.062	−	470.876i	0.711590	−	1.03717i
$455$	38.0610	−	65.9236i	0.0836506	−	0.144887i
$456$	−468.344	−	114.407i	−1.02707	−	0.250893i
$457$	67.1955	−	38.7953i	0.147036	−	0.0848913i	−0.424677	−	0.905345i	$-0.639612\pi$
$457$	67.1955	−	38.7953i	0.147036	−	0.0848913i	0.571713	+	0.820454i	$0.306279\pi$
$458$	612.332	+	47.6921i	1.33697	+	0.104131i
$459$	6.48339	−	337.553i	0.0141250	−	0.735410i
$460$	−1.15183	−	1.57997i	−0.00250398	−	0.00343471i
$461$	82.4112	−	307.563i	0.178766	−	0.667165i	−0.817113	−	0.576477i	$-0.804427\pi$
$461$	82.4112	−	307.563i	0.178766	−	0.667165i	0.995879	−	0.0906873i	$-0.0289064\pi$
$462$	−14.6812	−	1.23806i	−0.0317775	−	0.00267978i
$463$	209.514	−	362.889i	0.452514	−	0.783776i	−0.546028	−	0.837767i	$-0.683861\pi$
$463$	209.514	−	362.889i	0.452514	−	0.783776i	0.998541	+	0.0539905i	$0.0171941\pi$
$464$	−45.3401	−	2.22874i	−0.0977158	−	0.00480333i
$465$	111.126	+	30.5399i	0.238980	+	0.0656771i
$466$	−501.889	−	177.270i	−1.07702	−	0.380409i
$467$	245.316	+	245.316i	0.525302	+	0.525302i	0.919168	−	0.393866i	$-0.128863\pi$
$467$	245.316	+	245.316i	0.525302	+	0.525302i	−0.393866	+	0.919168i	$0.628863\pi$
$468$	−179.957	+	392.325i	−0.384524	+	0.838301i
$469$	−17.0465	−	17.0465i	−0.0363464	−	0.0363464i
$470$	−89.3424	−	186.920i	−0.190090	−	0.397702i
$471$	180.124	+	689.867i	0.382429	+	1.46469i
$472$	558.245	−	591.141i	1.18272	−	1.25242i
$473$	−16.4622	+	28.5134i	−0.0348039	+	0.0602821i
$474$	36.7884	+	204.879i	0.0776128	+	0.432233i
$475$	120.716	−	450.519i	0.254140	−	0.948462i
$476$	36.8355	−	235.036i	0.0773855	−	0.493774i
$477$	−93.9053	+	91.5310i	−0.196866	+	0.191889i
$478$	237.770	+	277.937i	0.497428	+	0.581458i
$479$	448.069	−	258.693i	0.935425	−	0.540068i	0.0469019	−	0.998899i	$-0.485065\pi$
$479$	448.069	−	258.693i	0.935425	−	0.540068i	0.888523	+	0.458831i	$0.151732\pi$
$480$	−127.084	+	16.4275i	−0.264758	+	0.0342239i
$481$	329.748	−	571.140i	0.685546	−	1.18740i
$482$	26.0898	+	140.134i	0.0541282	+	0.290734i
$483$	0.0334515	−	5.22545i	6.92577e−5	−	0.0108187i
$484$	−173.799	−	450.576i	−0.359089	−	0.930943i
$485$	−166.375	+	166.375i	−0.343042	+	0.343042i
$486$	−452.841	−	176.441i	−0.931771	−	0.363047i
$487$			3.16024i			0.00648920i	0.999995	+	0.00324460i	$0.00103279\pi$
$487$			3.16024i			0.00648920i	−0.999995	+	0.00324460i	$0.998967\pi$
$488$	86.0063	+	287.780i	0.176242	+	0.589713i
$489$	538.814	−	531.959i	1.10187	−	1.08785i
$490$	−58.0617	−	39.8354i	−0.118493	−	0.0812968i
$491$	220.209	+	821.830i	0.448490	+	1.67379i	0.706553	+	0.707660i	$0.250249\pi$
$491$	220.209	+	821.830i	0.448490	+	1.67379i	−0.258063	+	0.966128i	$0.583084\pi$
$492$	178.989	−	67.7277i	0.363799	−	0.137658i
$493$	34.2680	+	9.18209i	0.0695092	+	0.0186249i
$494$	−313.136	−	366.034i	−0.633879	−	0.740960i
$495$	0.0794010	−	6.20136i	0.000160406	−	0.0125280i
$496$	−438.399	−	140.874i	−0.883868	−	0.284020i
$497$	−318.645	+	183.970i	−0.641136	+	0.370160i
$498$	227.811	−	327.528i	0.457451	−	0.657688i
$499$	52.3985	+	195.554i	0.105007	+	0.391891i	0.998346	−	0.0574921i	$-0.0183104\pi$
$499$	52.3985	+	195.554i	0.105007	+	0.391891i	−0.893339	+	0.449383i	$0.851644\pi$
$500$	−27.3258	−	255.993i	−0.0546515	−	0.511987i
$501$	466.555	−	796.282i	0.931248	−	1.58938i
$502$	−528.311	+	252.517i	−1.05241	+	0.503023i
$503$	606.713			1.20619			0.603094	−	0.797670i	$-0.293934\pi$
$503$	606.713			1.20619			0.603094	+	0.797670i	$0.293934\pi$
$504$	−299.255	−	166.523i	−0.593759	−	0.330403i
$505$		−	207.008i		−	0.409916i
$506$	−0.341145	+	0.163058i	−0.000674200	+	0.000322248i
$507$	65.8356	−	37.4503i	0.129853	−	0.0738666i
$508$	182.155	+	147.018i	0.358573	+	0.289405i
$509$	429.811	−	115.167i	0.844422	−	0.226262i	0.189427	−	0.981895i	$-0.439337\pi$
$509$	429.811	−	115.167i	0.844422	−	0.226262i	0.654996	+	0.755633i	$0.272670\pi$
$510$	99.7903	+	8.41527i	0.195667	+	0.0165005i
$511$	−251.698	−	435.953i	−0.492559	−	0.853138i
$512$	510.115	−	43.8947i	0.996318	−	0.0857319i
$513$	390.814	−	376.084i	0.761821	−	0.733108i
$514$	553.215	+	646.670i	1.07629	+	1.25811i
$515$	−7.22566	+	26.9665i	−0.0140304	+	0.0523622i
$516$	−621.291	+	446.873i	−1.20405	+	0.866032i
$517$	−38.6986	+	10.3693i	−0.0748523	+	0.0200566i
$518$	431.474	+	296.029i	0.832962	+	0.571485i
$519$	209.643	−	762.831i	0.403936	−	1.46981i
$520$	−112.664	−	60.8172i	−0.216662	−	0.116956i
$521$	142.377			0.273277			0.136638	−	0.990621i	$-0.456370\pi$
$521$	142.377			0.273277			0.136638	+	0.990621i	$0.456370\pi$
$522$	29.4286	−	41.7376i	0.0563765	−	0.0799570i
$523$	−669.282	−	669.282i	−1.27970	−	1.27970i	−0.940836	−	0.338863i	$-0.889958\pi$
$523$	−669.282	−	669.282i	−1.27970	−	1.27970i	−0.338863	−	0.940836i	$-0.610042\pi$
$524$	250.941	+	111.239i	0.478896	+	0.212288i
$525$	167.489	−	285.858i	0.319027	−	0.544492i
$526$	56.7067	+	304.584i	0.107807	+	0.579056i
$527$	311.657	+	179.935i	0.591380	+	0.341433i
$528$	−1.37504	+	24.7420i	−0.00260425	+	0.0468598i
$529$	264.433	+	458.011i	0.499873	+	0.865806i
$530$	−25.2858	−	29.5573i	−0.0477090	−	0.0557684i
$531$	225.412	+	886.496i	0.424505	+	1.66948i
$532$	308.837	−	225.150i	0.580521	−	0.423213i
$533$	184.695	+	49.4888i	0.346519	+	0.0928496i
$534$	248.262	+	89.4794i	0.464911	+	0.167564i
$535$	102.006	+	58.8930i	0.190665	+	0.110080i
$536$	−27.8388	+	29.4792i	−0.0519380	+	0.0549986i
$537$	−94.5443	−	95.7625i	−0.176060	−	0.178329i
$538$	−164.469	−	344.098i	−0.305704	−	0.639587i
$539$	−9.62843	+	9.62843i	−0.0178635	+	0.0178635i
$540$	60.9410	−	130.644i	0.112854	−	0.241934i
$541$	356.554	−	356.554i	0.659065	−	0.659065i	−0.296094	−	0.955159i	$-0.595684\pi$
$541$	356.554	−	356.554i	0.659065	−	0.659065i	0.955159	+	0.296094i	$0.0956840\pi$
$542$	−669.385	−	236.431i	−1.23503	−	0.436220i
$543$	215.100	+	217.872i	0.396133	+	0.401238i
$544$	−396.922	−	50.6196i	−0.729637	−	0.0930508i
$545$	121.045	+	69.8856i	0.222102	+	0.128231i
$546$	−145.580	−	309.658i	−0.266630	−	0.567140i
$547$	−233.723	−	62.6259i	−0.427282	−	0.114490i	0.0387682	−	0.999248i	$-0.487657\pi$
$547$	−233.723	−	62.6259i	−0.427282	−	0.114490i	−0.466050	+	0.884758i	$0.654323\pi$
$548$	−19.7158	+	125.801i	−0.0359777	+	0.229563i
$549$	−325.242	−	91.6269i	−0.592426	−	0.166898i
$550$	−23.9007	−	1.86153i	−0.0434558	−	0.00338459i
$551$	28.4968	+	49.3579i	0.0517183	+	0.0895787i
$552$	−8.78679	+	0.195194i	−0.0159181	+	0.000353613i
$553$	−142.907	−	82.5072i	−0.258421	−	0.149199i
$554$	−156.236	+	227.720i	−0.282014	+	0.411047i
$555$	−111.350	+	190.045i	−0.200631	+	0.342423i
$556$	−492.138	−	218.159i	−0.885141	−	0.392372i
$557$	145.377	+	145.377i	0.261001	+	0.261001i	0.825461	−	0.564460i	$-0.190915\pi$
$557$	145.377	+	145.377i	0.261001	+	0.261001i	−0.564460	+	0.825461i	$0.690915\pi$
$558$	397.924	−	331.690i	0.713126	−	0.594426i
$559$	−764.651			−1.36789
$560$	55.0496	−	85.3739i	0.0983029	−	0.152453i
$561$	5.13197	−	18.6738i	0.00914790	−	0.0332866i
$562$	−66.4563	−	356.951i	−0.118250	−	0.635144i
$563$	437.783	−	117.304i	0.777589	−	0.208354i	0.151868	−	0.988401i	$-0.451471\pi$
$563$	437.783	−	117.304i	0.777589	−	0.208354i	0.625722	+	0.780046i	$0.284805\pi$
$564$	−919.086	−	150.076i	−1.62958	−	0.266092i
$565$	19.2830	−	71.9651i	0.0341292	−	0.127372i
$566$	581.825	+	45.3160i	1.02796	+	0.0800636i
$567$	338.481	−	184.031i	0.596967	−	0.324570i
$568$	324.627	+	526.862i	0.571527	+	0.927575i
$569$	0.131748	+	0.228194i	0.000231543	+	0.000401044i	0.866141	−	0.499799i	$-0.166593\pi$
$569$	0.131748	+	0.228194i	0.000231543	+	0.000401044i	−0.865910	+	0.500201i	$0.833260\pi$
$570$	103.799	+	122.918i	0.182103	+	0.215645i
$571$	291.980	−	78.2357i	0.511348	−	0.137015i	0.00608627	−	0.999981i	$-0.498063\pi$
$571$	291.980	−	78.2357i	0.511348	−	0.137015i	0.505262	+	0.862966i	$0.331396\pi$
$572$	−15.5500	+	19.2665i	−0.0271854	+	0.0336827i
$573$	−867.589	+	493.525i	−1.51412	+	0.861300i
$574$	−50.5264	+	143.051i	−0.0880250	+	0.249217i
$575$		−	8.50269i		−	0.0147873i
$576$	−265.564	+	511.128i	−0.461049	+	0.887375i
$577$	−574.805			−0.996195			−0.498098	−	0.867121i	$-0.665968\pi$
$577$	−574.805			−0.996195			−0.498098	+	0.867121i	$0.665968\pi$
$578$	−250.141	−	88.3514i	−0.432770	−	0.152857i
$579$	324.833	−	554.401i	0.561025	−	0.957515i
$580$	11.7879	+	9.51402i	0.0203239	+	0.0164035i
$581$	81.8587	+	305.501i	0.140893	+	0.525819i
$582$	186.923	+	1040.99i	0.321173	+	1.78865i
$583$	−6.51428	+	3.76102i	−0.0111737	+	0.00645115i
$584$	−720.826	+	444.138i	−1.23429	+	0.760511i
$585$	125.650	−	70.4145i	0.214786	−	0.120367i
$586$	−67.7019	+	869.244i	−0.115532	+	1.48335i
$587$	−422.452	−	113.196i	−0.719680	−	0.192838i	−0.119651	−	0.992816i	$-0.538178\pi$
$587$	−422.452	−	113.196i	−0.719680	−	0.192838i	−0.600029	+	0.799978i	$0.704844\pi$
$588$	−296.027	+	112.014i	−0.503448	+	0.190499i
$589$	149.632	+	558.433i	0.254043	+	0.948103i
$590$	−266.739	+	49.6609i	−0.452100	+	0.0841710i
$591$	245.174	−	242.055i	0.414846	−	0.409569i
$592$	476.931	−	739.650i	0.805627	−	1.24941i
$593$			1051.17i			1.77264i	0.463074	+	0.886320i	$0.346746\pi$
$593$			1051.17i			1.77264i	−0.463074	+	0.886320i	$0.653254\pi$
$594$	−22.6804	−	16.2100i	−0.0381825	−	0.0272896i
$595$	−56.1366	+	56.1366i	−0.0943473	+	0.0943473i
$596$	−376.776	+	849.959i	−0.632174	+	1.42611i
$597$	−5.15568	+	805.368i	−0.00863597	+	1.34903i
$598$	−7.24102	−	4.96797i	−0.0121087	−	0.00830765i
$599$	−97.2793	+	168.493i	−0.162403	+	0.281290i	−0.935730	−	0.352717i	$-0.885258\pi$
$599$	−97.2793	+	168.493i	−0.162403	+	0.281290i	0.773327	+	0.634007i	$0.218591\pi$
$600$	−488.652	−	267.833i	−0.814420	−	0.446389i
$601$	−318.748	+	184.030i	−0.530364	+	0.306206i	−0.741164	−	0.671323i	$-0.765726\pi$
$601$	−318.748	+	184.030i	−0.530364	+	0.306206i	0.210801	+	0.977529i	$0.432393\pi$
$602$	47.1104	−	604.864i	0.0782565	−	1.00476i
$603$	−11.2409	−	44.2081i	−0.0186417	−	0.0733137i
$604$	731.905	+	114.706i	1.21176	+	0.189911i
$605$	−41.7101	+	155.664i	−0.0689423	+	0.257296i
$606$	−763.899	−	531.326i	−1.26056	−	0.876775i
$607$	−237.973	+	412.181i	−0.392048	+	0.679046i	−0.992719	−	0.120449i	$-0.961566\pi$
$607$	−237.973	+	412.181i	−0.392048	+	0.679046i	0.600672	+	0.799496i	$0.294900\pi$
$608$	−393.388	−	508.392i	−0.647020	−	0.836172i
$609$	10.2277	+	39.1717i	0.0167943	+	0.0643214i
$610$	33.3806	−	94.5075i	0.0547224	−	0.154930i
$611$	−657.933	−	657.933i	−1.07681	−	1.07681i
$612$	287.185	−	346.646i	0.469257	−	0.566415i
$613$	297.181	+	297.181i	0.484797	+	0.484797i	0.906660	−	0.421863i	$-0.138624\pi$
$613$	297.181	+	297.181i	0.484797	+	0.484797i	−0.421863	+	0.906660i	$0.638624\pi$
$614$	−54.0756	+	25.8466i	−0.0880709	+	0.0420954i
$615$	−61.5787	−	16.9232i	−0.100128	−	0.0275174i
$616$	−14.2824	−	13.4876i	−0.0231857	−	0.0218955i
$617$	−444.267	+	769.492i	−0.720043	+	1.24715i	0.240939	+	0.970540i	$0.422545\pi$
$617$	−444.267	+	769.492i	−0.720043	+	1.24715i	−0.960982	+	0.276611i	$0.910789\pi$
$618$	80.9657	+	95.8790i	0.131013	+	0.155144i
$619$	87.0089	−	324.722i	0.140564	−	0.524591i	−0.859349	−	0.511389i	$-0.829131\pi$
$619$	87.0089	−	324.722i	0.140564	−	0.524591i	0.999913	−	0.0132015i	$-0.00420229\pi$
$620$	90.5213	+	124.168i	0.146002	+	0.200271i
$621$	5.10731	−	8.46637i	0.00822434	−	0.0136335i
$622$	−237.655	+	203.310i	−0.382082	+	0.326865i
$623$	−181.174	+	104.601i	−0.290809	+	0.167899i
$624$	−513.601	+	259.653i	−0.823079	+	0.416111i
$625$	247.274	−	428.290i	0.395638	−	0.685265i
$626$	764.762	−	142.382i	1.22166	−	0.227447i
$627$	27.0425	−	15.3830i	0.0431301	−	0.0245344i
$628$	−385.259	+	869.097i	−0.613470	+	1.38391i
$629$	−486.348	+	486.348i	−0.773209	+	0.773209i
$630$	47.9589	+	103.731i	0.0761252	+	0.164653i
$631$		−	629.666i		−	0.997886i	−0.866635	−	0.498943i	$-0.833722\pi$
$631$		−	629.666i		−	0.997886i	0.866635	−	0.498943i	$-0.166278\pi$
$632$	−131.837	+	244.229i	−0.208603	+	0.386438i
$633$	84.1589	+	322.325i	0.132952	+	0.509202i
$634$	−660.742	+	963.057i	−1.04218	+	1.51902i
$635$	−20.2173	−	75.4519i	−0.0318382	−	0.118822i
$636$	−173.973	+	17.4449i	−0.273542	+	0.0274292i
$637$	−305.463	−	81.8487i	−0.479534	−	0.128491i
$638$	2.22600	−	1.90430i	0.00348902	−	0.00298480i
$639$	−696.141	−	8.91326i	−1.08942	−	0.0139488i
$640$	−146.182	−	88.4431i	−0.228409	−	0.138192i
$641$	446.270	−	257.654i	0.696208	−	0.401956i	−0.109725	−	0.993962i	$-0.534997\pi$
$641$	446.270	−	257.654i	0.696208	−	0.401956i	0.805934	+	0.592006i	$0.201664\pi$
$642$	479.144	−	225.261i	0.746330	−	0.350873i
$643$	−131.105	−	489.292i	−0.203896	−	0.760951i	−0.989783	−	0.142581i	$-0.954460\pi$
$643$	−131.105	−	489.292i	−0.203896	−	0.760951i	0.785887	−	0.618370i	$-0.212207\pi$
$644$	4.37595	−	5.42180i	0.00679495	−	0.00841895i
$645$	255.379	+	1.63484i	0.395936	+	0.00253464i
$646$	216.646	+	453.261i	0.335365	+	0.701642i
$647$	−607.192			−0.938474			−0.469237	−	0.883072i	$-0.655471\pi$
$647$	−607.192			−0.938474			−0.469237	+	0.883072i	$0.655471\pi$
$648$	−325.686	−	560.208i	−0.502601	−	0.864518i
$649$			52.4689i			0.0808458i
$650$	−240.099	−	502.329i	−0.369383	−	0.772814i
$651$	−2.62892	+	410.663i	−0.00403827	+	0.630819i
$652$	1003.85	−	107.155i	1.53965	−	0.164348i
$653$	−1191.22	+	319.186i	−1.82423	+	0.488800i	−0.997295	−	0.0735044i	$-0.976582\pi$
$653$	−1191.22	+	319.186i	−1.82423	+	0.488800i	−0.826930	+	0.562304i	$0.809915\pi$
$654$	568.578	−	267.306i	0.869386	−	0.408725i
$655$	−45.7990	−	79.3262i	−0.0699222	−	0.121109i
$656$	242.932	+	78.0632i	0.370323	+	0.118999i
$657$	12.1947	−	952.425i	0.0185611	−	1.44966i
$658$	560.982	−	479.911i	0.852556	−	0.729348i
$659$	29.9766	−	111.874i	0.0454880	−	0.169763i	−0.939445	−	0.342700i	$-0.888659\pi$
$659$	29.9766	−	111.874i	0.0454880	−	0.169763i	0.984933	+	0.172936i	$0.0553254\pi$
$660$	5.23461	−	6.40140i	0.00793122	−	0.00969908i
$661$	−609.368	+	163.280i	−0.921889	+	0.247019i	−0.688392	−	0.725338i	$-0.741683\pi$
$661$	−609.368	+	163.280i	−0.921889	+	0.247019i	−0.233496	+	0.972358i	$0.575017\pi$
$662$	565.301	−	823.948i	0.853928	−	1.24463i
$663$	435.178	−	113.625i	0.656377	−	0.171380i
$664$	509.678	−	152.323i	0.767587	−	0.229402i
$665$	−127.539			−0.191787
$666$	415.499	+	898.691i	0.623872	+	1.34939i
$667$	0.734679	+	0.734679i	0.00110147	+	0.00110147i
$668$	1148.08	−	442.845i	1.71868	−	0.662941i
$669$	33.5820	+	59.0352i	0.0501972	+	0.0882440i
$670$	13.3018	−	2.47651i	0.0198535	−	0.00369628i
$671$	−16.7858	−	9.69128i	−0.0250161	−	0.0144430i
$672$	−173.751	−	422.273i	−0.258558	−	0.628382i
$673$	461.108	+	798.662i	0.685153	+	1.18672i	0.973389	+	0.229160i	$0.0735979\pi$
$673$	461.108	+	798.662i	0.685153	+	1.18672i	−0.288236	+	0.957559i	$0.593069\pi$
$674$	−243.934	+	208.682i	−0.361921	+	0.309617i
$675$	548.825	−	302.964i	0.813075	−	0.448835i
$676$	99.7715	+	15.6364i	0.147591	+	0.0231308i
$677$	−707.727	−	189.635i	−1.04539	−	0.280111i	−0.305043	−	0.952339i	$-0.598671\pi$
$677$	−707.727	−	189.635i	−1.04539	−	0.280111i	−0.740344	+	0.672228i	$0.765337\pi$
$678$	−216.072	−	255.870i	−0.318690	−	0.377390i
$679$	−726.111	−	419.221i	−1.06938	−	0.617409i
$680$	97.0796	+	91.6773i	0.142764	+	0.134820i
$681$	−226.988	+	825.945i	−0.333316	+	1.21284i
$682$	26.8103	−	12.8145i	0.0393112	−	0.0187896i
$683$	142.145	−	142.145i	0.208119	−	0.208119i	−0.595349	−	0.803467i	$-0.702986\pi$
$683$	142.145	−	142.145i	0.208119	−	0.208119i	0.803467	+	0.595349i	$0.202986\pi$
$684$	720.011	−	67.5457i	1.05265	−	0.0987510i
$685$	30.0465	−	30.0465i	0.0438635	−	0.0438635i
$686$	238.807	−	676.113i	0.348116	−	0.985587i
$687$	−891.397	+	232.743i	−1.29752	+	0.338782i
$688$	−1019.18	−	50.0990i	−1.48137	−	0.0728183i
$689$	−151.290	−	87.3476i	−0.219580	−	0.126774i
$690$	2.40774	+	1.67469i	0.00348948	+	0.00242708i
$691$	364.993	+	97.7997i	0.528210	+	0.141534i	0.513062	−	0.858352i	$-0.328511\pi$
$691$	364.993	+	97.7997i	0.528210	+	0.141534i	0.0151487	+	0.999885i	$0.495178\pi$
$692$	852.360	−	621.390i	1.23173	−	0.897962i
$693$	21.4184	−	5.44612i	0.0309068	−	0.00785876i
$694$	−1.85614	+	23.8315i	−0.00267455	+	0.0343393i
$695$	89.8196	+	155.572i	0.129237	+	0.223845i
$696$	65.3645	−	19.0800i	0.0939145	−	0.0274137i
$697$	−172.700	−	99.7084i	−0.247776	−	0.143054i
$698$	−464.658	−	318.796i	−0.665699	−	0.456728i
$699$	798.397	+	5.11105i	1.14220	+	0.00731195i
$700$	412.151	−	158.977i	0.588788	−	0.227111i
$701$	−287.537	−	287.537i	−0.410181	−	0.410181i	0.471621	−	0.881802i	$-0.343669\pi$
$701$	−287.537	−	287.537i	−0.410181	−	0.410181i	−0.881802	+	0.471621i	$0.843669\pi$
$702$	62.6608	−	644.404i	0.0892604	−	0.917954i
$703$	−1104.95			−1.57176
$704$	−21.9885	+	24.6609i	−0.0312337	+	0.0350298i
$705$	218.330	+	221.144i	0.309688	+	0.313679i
$706$	312.360	−	58.1545i	0.442436	−	0.0823717i
$707$	712.523	−	190.920i	1.00781	−	0.270043i
$708$	−501.379	+	1111.78i	−0.708162	+	1.57031i
$709$	−269.191	+	1004.64i	−0.379678	+	1.41698i	0.466711	+	0.884410i	$0.345439\pi$
$709$	−269.191	+	1004.64i	−0.379678	+	1.41698i	−0.846389	+	0.532566i	$0.821228\pi$
$710$	16.0355	−	205.885i	0.0225852	−	0.289979i
$711$	−152.642	−	272.378i	−0.214686	−	0.383092i
$712$	184.576	+	299.562i	0.259236	+	0.420733i
$713$	5.26967	+	9.12734i	0.00739085	+	0.0128013i
$714$	63.0695	+	351.241i	0.0883327	+	0.491934i
$715$	7.98053	−	2.13838i	0.0111616	−	0.00299074i
$716$	−19.0445	−	178.413i	−0.0265985	−	0.249180i
$717$	−473.376	−	277.359i	−0.660218	−	0.386833i
$718$	891.537	+	314.896i	1.24169	+	0.438575i
$719$		−	1070.30i		−	1.48859i	−0.667850	−	0.744296i	$-0.732785\pi$
$719$		−	1070.30i		−	1.48859i	0.667850	−	0.744296i	$-0.267215\pi$
$720$	172.088	−	85.6210i	0.239011	−	0.118918i
$721$	−99.4833			−0.137980
$722$	−28.3302	+	80.2086i	−0.0392385	+	0.111092i
$723$	−105.719	−	185.848i	−0.146222	−	0.257051i
$724$	43.3288	+	405.913i	0.0598464	+	0.560653i
$725$	17.0496	+	63.6299i	0.0235166	+	0.0877653i
$726$	467.374	+	553.460i	0.643766	+	0.762342i
$727$	941.649	−	543.662i	1.29525	−	0.747815i	0.315673	−	0.948868i	$-0.397770\pi$
$727$	941.649	−	543.662i	1.29525	−	0.747815i	0.979580	+	0.201053i	$0.0644363\pi$
$728$	105.425	−	443.882i	0.144815	−	0.609728i
$729$	728.462	+	27.9935i	0.999262	+	0.0383999i
$730$	281.681	+	21.9390i	0.385864	+	0.0300534i
$731$	770.297	+	206.400i	1.05376	+	0.282354i
$732$	−263.073	−	365.753i	−0.359389	−	0.499662i
$733$	−134.218	−	500.908i	−0.183108	−	0.683367i	−0.995028	−	0.0995985i	$-0.968244\pi$
$733$	−134.218	−	500.908i	−0.183108	−	0.683367i	0.811920	−	0.583769i	$-0.198423\pi$
$734$	−15.7509	−	84.6012i	−0.0214590	−	0.115261i
$735$	101.844	+	27.9890i	0.138563	+	0.0380802i
$736$	−9.32584	−	7.09609i	−0.0126710	−	0.00964142i
$737$		−	2.61654i		−	0.00355026i
$738$	−220.504	+	183.801i	−0.298785	+	0.249052i
$739$	278.867	−	278.867i	0.377357	−	0.377357i	−0.492791	−	0.870148i	$-0.664023\pi$
$739$	278.867	−	278.867i	0.377357	−	0.377357i	0.870148	+	0.492791i	$0.164023\pi$
$740$	−274.007	+	105.691i	−0.370279	+	0.142826i
$741$	623.422	+	365.274i	0.841325	+	0.492947i
$742$	78.4158	−	114.294i	0.105682	−	0.154035i
$743$	−120.359	+	208.467i	−0.161990	+	0.280575i	−0.935582	−	0.353109i	$-0.885125\pi$
$743$	−120.359	+	208.467i	−0.161990	+	0.280575i	0.773592	+	0.633684i	$0.218458\pi$
$744$	690.545	−	15.3401i	0.928152	−	0.0206184i
$745$	268.684	−	155.125i	0.360650	−	0.208221i
$746$	475.464	+	37.0320i	0.637352	+	0.0496407i
$747$	−162.277	+	576.025i	−0.217239	+	0.771117i
$748$	20.8654	−	15.2114i	0.0278949	−	0.0203361i
$749$	−108.632	+	405.421i	−0.145036	+	0.541283i
$750$	164.300	+	349.477i	0.219066	+	0.465969i
$751$	249.258	−	431.728i	0.331902	−	0.574871i	−0.650983	−	0.759092i	$-0.725643\pi$
$751$	249.258	−	431.728i	0.331902	−	0.574871i	0.982885	+	0.184222i	$0.0589764\pi$
$752$	−833.833	−	920.047i	−1.10882	−	1.22347i
$753$	625.040	−	617.089i	0.830067	−	0.819507i
$754$	64.1499	+	22.6581i	0.0850794	+	0.0300506i
$755$	−174.810	−	174.810i	−0.231536	−	0.231536i
$756$	505.884	+	89.2686i	0.669159	+	0.118080i
$757$	476.124	+	476.124i	0.628962	+	0.628962i	0.947807	−	0.318845i	$-0.103295\pi$
$757$	476.124	+	476.124i	0.628962	+	0.628962i	−0.318845	+	0.947807i	$0.603295\pi$
$758$	298.510	+	624.536i	0.393813	+	0.823927i
$759$	0.403606	−	0.398472i	0.000531761	−	0.000524996i
$760$	6.13679	+	214.422i	0.00807473	+	0.282134i
$761$	700.315	−	1212.98i	0.920257	−	1.59393i	0.121239	−	0.992623i	$-0.461313\pi$
$761$	700.315	−	1212.98i	0.920257	−	1.59393i	0.799017	−	0.601308i	$-0.205354\pi$
$762$	−330.324	−	119.056i	−0.433496	−	0.156242i
$763$	−128.909	+	481.094i	−0.168950	+	0.630530i
$764$	−1314.80	−	206.059i	−1.72094	−	0.269710i
$765$	−145.584	+	37.0181i	−0.190306	+	0.0483897i
$766$	−602.107	−	703.821i	−0.786041	−	0.918826i
$767$	−1055.30	+	609.280i	−1.37588	+	0.794367i
$768$	−701.576	+	312.433i	−0.913511	+	0.406814i
$769$	−55.9685	+	96.9402i	−0.0727808	+	0.126060i	−0.900119	−	0.435644i	$-0.856521\pi$
$769$	−55.9685	+	96.9402i	−0.0727808	+	0.126060i	0.827338	+	0.561704i	$0.189854\pi$
$770$	1.19984	+	6.44461i	0.00155824	+	0.00836962i
$771$	−1101.39	−	645.326i	−1.42853	−	0.836999i
$772$	799.337	−	308.325i	1.03541	−	0.399385i
$773$	152.282	−	152.282i	0.197001	−	0.197001i	−0.601712	−	0.798713i	$-0.705515\pi$
$773$	152.282	−	152.282i	0.197001	−	0.197001i	0.798713	+	0.601712i	$0.205515\pi$
$774$	661.512	−	938.201i	0.854667	−	1.21215i
$775$			668.218i			0.862217i
$776$	−669.867	+	1240.93i	−0.863231	+	1.59914i
$777$	−756.832	−	207.994i	−0.974044	−	0.267689i
$778$	134.885	+	92.5431i	0.173374	+	0.118950i
$779$	−82.9160	−	309.447i	−0.106439	−	0.397236i
$780$	189.536	+	30.9490i	0.242995	+	0.0396782i
$781$	−38.5742	−	10.3359i	−0.0493908	−	0.0132342i
$782$	5.95348	+	6.95920i	0.00761315	+	0.00889923i
$783$	−21.2438	+	73.5992i	−0.0271313	+	0.0939965i
$784$	−401.781	−	129.107i	−0.512475	−	0.164678i
$785$	274.734	−	158.618i	0.349980	−	0.202061i
$786$	−410.281	−	34.5989i	−0.521986	−	0.0440189i
$787$	218.805	+	816.590i	0.278024	+	1.03760i	0.953788	+	0.300481i	$0.0971472\pi$
$787$	218.805	+	816.590i	0.278024	+	1.03760i	−0.675764	+	0.737118i	$0.736186\pi$
$788$	456.779	−	48.7584i	0.579668	−	0.0618762i
$789$	−229.782	−	403.944i	−0.291232	−	0.511969i
$790$	83.5609	−	39.9397i	0.105773	−	0.0505566i
$791$	265.489			0.335637
$792$	−10.1868	−	35.7471i	−0.0128621	−	0.0451353i
$793$		−	450.149i		−	0.567653i
$794$	−436.465	+	208.618i	−0.549705	+	0.262743i
$795$	50.3413	+	29.4959i	0.0633224	+	0.0371017i
$796$	−674.439	+	835.630i	−0.847285	+	1.04979i
$797$	−631.135	+	169.112i	−0.791889	+	0.212186i	−0.632020	−	0.774952i	$-0.717774\pi$
$797$	−631.135	+	169.112i	−0.791889	+	0.212186i	−0.159869	+	0.987138i	$0.551107\pi$
$798$	−327.353	+	470.642i	−0.410216	+	0.589777i
$799$	485.196	+	840.385i	0.607255	+	1.05180i
$800$	−287.109	−	685.271i	−0.358886	−	0.856589i
$801$	−395.810	−	5.06788i	−0.494145	−	0.00632694i
$802$	908.937	+	1062.48i	1.13334	+	1.32479i
$803$	14.1411	−	52.7753i	0.0176103	−	0.0657227i
$804$	25.0030	−	55.4428i	0.0310982	−	0.0689587i
$805$	−2.24581	+	0.601762i	−0.00278982	+	0.000747530i
$806$	569.064	+	390.428i	0.706035	+	0.484402i
$807$	401.921	+	407.100i	0.498043	+	0.504461i
$808$	−355.265	−	1188.73i	−0.439684	−	1.47120i
$809$	−645.098			−0.797402			−0.398701	−	0.917081i	$-0.630539\pi$
$809$	−645.098			−0.797402			−0.398701	+	0.917081i	$0.630539\pi$
$810$	−22.3052	+	215.084i	−0.0275373	+	0.265536i
$811$	98.6565	+	98.6565i	0.121648	+	0.121648i	0.765310	−	0.643662i	$-0.222586\pi$
$811$	98.6565	+	98.6565i	0.121648	+	0.121648i	−0.643662	+	0.765310i	$0.722586\pi$
$812$	−21.8756	+	49.3486i	−0.0269404	+	0.0607742i
$813$	1064.85	+	6.81677i	1.30977	+	0.00838471i
$814$	10.3950	+	55.8338i	0.0127703	+	0.0685919i
$815$	−291.754	−	168.444i	−0.357981	−	0.206680i
$816$	587.481	−	122.935i	0.719952	−	0.150656i
$817$	640.567	+	1109.50i	0.784048	+	1.35801i
$818$	−202.383	−	236.572i	−0.247412	−	0.289207i
$819$	358.252	+	367.545i	0.437426	+	0.448773i
$820$	−50.1610	−	68.8058i	−0.0611720	−	0.0839095i
$821$	388.752	+	104.166i	0.473511	+	0.126877i	0.487679	−	0.873023i	$-0.337844\pi$
$821$	388.752	+	104.166i	0.473511	+	0.126877i	−0.0141687	+	0.999900i	$0.504510\pi$
$822$	−33.7573	−	187.998i	−0.0410672	−	0.228707i
$823$	−648.909	−	374.648i	−0.788467	−	0.455222i	0.0509554	−	0.998701i	$-0.483773\pi$
$823$	−648.909	−	374.648i	−0.788467	−	0.455222i	−0.839423	+	0.543479i	$0.817107\pi$
$824$	4.78685	+	167.254i	0.00580928	+	0.202978i
$825$	34.7932	−	9.08449i	0.0421735	−	0.0110115i
$826$	−416.943	−	872.317i	−0.504773	−	1.05607i
$827$	−59.9029	+	59.9029i	−0.0724340	+	0.0724340i	−0.742396	−	0.669962i	$-0.766311\pi$
$827$	−59.9029	+	59.9029i	−0.0724340	+	0.0724340i	0.669962	+	0.742396i	$0.266311\pi$
$828$	12.3599	−	4.58661i	0.0149274	−	0.00553938i
$829$	−465.462	+	465.462i	−0.561474	+	0.561474i	−0.929726	−	0.368252i	$-0.879956\pi$
$829$	−465.462	+	465.462i	−0.561474	+	0.561474i	0.368252	+	0.929726i	$0.379956\pi$
$830$	−167.379	−	59.1193i	−0.201661	−	0.0712281i
$831$	109.774	−	399.435i	0.132098	−	0.480668i
$832$	−751.339	−	155.886i	−0.903052	−	0.187363i
$833$	285.625	+	164.906i	0.342888	+	0.197966i
$834$	804.631	+	67.8542i	0.964785	+	0.0813600i
$835$	−396.636	−	106.278i	−0.475014	−	0.127280i
$836$	40.9820	+	6.42280i	0.0490215	+	0.00768278i
$837$	−401.379	+	665.364i	−0.479544	+	0.794939i
$838$	460.470	+	35.8641i	0.549486	+	0.0427973i
$839$	77.2086	+	133.729i	0.0920245	+	0.159391i	0.908363	−	0.418183i	$-0.137333\pi$
$839$	77.2086	+	133.729i	0.0920245	+	0.159391i	−0.816338	+	0.577574i	$0.804000\pi$
$840$	−36.1590	+	148.023i	−0.0430465	+	0.176217i
$841$	721.356	+	416.475i	0.857736	+	0.495214i
$842$	−293.493	+	427.778i	−0.348567	+	0.508050i
$843$	269.288	+	473.394i	0.319441	+	0.561559i
$844$	−180.004	+	406.066i	−0.213274	+	0.481120i
$845$	−23.8297	−	23.8297i	−0.0282008	−	0.0282008i
$846$	1376.45	−	238.073i	1.62701	−	0.281410i
$847$	−574.266			−0.678000
$848$	−195.928	−	126.335i	−0.231047	−	0.148980i
$849$	−846.986	+	221.148i	−0.997628	+	0.260480i
$850$	106.279	+	570.847i	0.125034	+	0.671585i
$851$	−19.4569	+	5.21346i	−0.0228636	+	0.00612627i
$852$	−718.597	−	587.617i	−0.843423	−	0.689692i
$853$	323.958	−	1209.03i	0.379786	−	1.41738i	−0.466438	−	0.884554i	$-0.654463\pi$
$853$	323.958	−	1209.03i	0.379786	−	1.41738i	0.846224	−	0.532828i	$-0.178871\pi$
$854$	356.082	+	27.7338i	0.416958	+	0.0324752i
$855$	−207.430	−	123.327i	−0.242608	−	0.144242i
$856$	686.832	+	163.128i	0.802374	+	0.190570i
$857$	−544.941	−	943.866i	−0.635871	−	1.10136i	−0.986330	−	0.164782i	$-0.947308\pi$
$857$	−544.941	−	943.866i	−0.635871	−	1.10136i	0.350459	−	0.936578i	$-0.386025\pi$
$858$	12.5926	−	34.9383i	0.0146766	−	0.0407206i
$859$	1376.03	−	368.706i	1.60190	−	0.429227i	0.656282	−	0.754515i	$-0.272128\pi$
$859$	1376.03	−	368.706i	1.60190	−	0.429227i	0.945615	+	0.325288i	$0.105461\pi$
$860$	264.975	+	213.862i	0.308110	+	0.248676i
$861$	1.45677	−	227.563i	0.00169196	−	0.264300i
$862$	−167.154	+	473.248i	−0.193914	+	0.549012i
$863$			636.743i			0.737825i	0.929464	+	0.368912i	$0.120270\pi$
$863$			636.743i			0.737825i	−0.929464	+	0.368912i	$0.879730\pi$
$864$	125.739	−	854.802i	0.145532	−	0.989354i
$865$	−351.994			−0.406929
$866$	84.3422	+	29.7902i	0.0973929	+	0.0343998i
$867$	397.921	+	2.54734i	0.458963	+	0.00293811i
$868$	−343.901	+	426.094i	−0.396200	+	0.490891i
$869$	−4.63549	−	17.2999i	−0.00533428	−	0.0199078i
$870$	−21.3764	−	7.70453i	−0.0245705	−	0.00885579i
$871$	52.6263	−	30.3838i	0.0604205	−	0.0348838i
$872$	815.032	+	193.576i	0.934670	+	0.221991i
$873$	−775.576	−	1383.96i	−0.888403	−	1.58529i
$874$	−1.14246	+	14.6684i	−0.00130716	+	0.0167830i
$875$	−295.705	−	79.2338i	−0.337948	−	0.0905529i
$876$	803.948	−	983.147i	0.917749	−	1.12231i
$877$	−38.3652	−	143.181i	−0.0437460	−	0.163262i	0.940597	−	0.339524i	$-0.110266\pi$
$877$	−38.3652	−	143.181i	−0.0437460	−	0.163262i	−0.984343	+	0.176262i	$0.943599\pi$
$878$	−470.896	+	87.6705i	−0.536328	+	0.0998525i
$879$	−330.394	−	1265.39i	−0.375875	−	1.43958i
$880$	10.7771	−	2.32731i	0.0122467	−	0.00264467i
$881$		−	1227.45i		−	1.39325i	−0.717436	−	0.696624i	$-0.754685\pi$
$881$		−	1227.45i		−	1.39325i	0.717436	−	0.696624i	$-0.245315\pi$
$882$	364.687	−	303.985i	0.413477	−	0.344654i
$883$	297.625	−	297.625i	0.337061	−	0.337061i	−0.518199	−	0.855260i	$-0.673397\pi$
$883$	297.625	−	297.625i	0.337061	−	0.337061i	0.855260	+	0.518199i	$0.173397\pi$
$884$	548.239	+	243.027i	0.620180	+	0.274918i
$885$	353.754	−	201.231i	0.399722	−	0.227380i
$886$	−1034.24	−	709.582i	−1.16732	−	0.800883i
$887$	400.875	−	694.336i	0.451945	−	0.782792i	−0.546562	−	0.837419i	$-0.684064\pi$
$887$	400.875	−	694.336i	0.451945	−	0.782792i	0.998507	+	0.0546272i	$0.0173970\pi$
$888$	−313.269	+	1282.42i	−0.352781	+	1.44416i
$889$	241.060	−	139.176i	0.271159	−	0.156554i
$890$	9.11744	−	117.061i	0.0102443	−	0.131530i
$891$	40.1013	+	11.8535i	0.0450071	+	0.0133036i
$892$	−14.0213	+	89.4657i	−0.0157189	+	0.100298i
$893$	−403.482	+	1505.82i	−0.451828	+	1.68624i
$894$	117.189	−	1389.66i	0.131084	−	1.55442i
$895$	−29.9374	+	51.8531i	−0.0334496	+	0.0579364i
$896$	169.601	−	584.730i	0.189287	−	0.652600i
$897$	12.7012	+	3.49057i	0.0141596	+	0.00389138i
$898$	232.403	−	657.981i	0.258801	−	0.732718i
$899$	−57.7377	−	57.7377i	−0.0642243	−	0.0642243i
$900$	824.054	+	139.980i	0.915616	+	0.155533i
$901$	128.830	+	128.830i	0.142985	+	0.142985i
$902$	−14.8565	+	7.10098i	−0.0164706	+	0.00787248i
$903$	229.905	+	880.525i	0.254601	+	0.975110i
$904$	−12.7746	−	446.348i	−0.0141312	−	0.493748i
$905$	68.1114	−	117.972i	0.0752613	−	0.130356i
$906$	−1093.77	+	196.399i	−1.20725	+	0.216776i
$907$	−424.872	+	1585.65i	−0.468437	+	1.74823i	0.176799	+	0.984247i	$0.443426\pi$
$907$	−424.872	+	1585.65i	−0.468437	+	1.74823i	−0.645236	+	0.763984i	$0.723241\pi$
$908$	−922.881	+	672.802i	−1.01639	+	0.740971i
$909$	1343.47	+	378.482i	1.47796	+	0.416372i
$910$	−115.687	+	98.9685i	−0.127129	+	0.108757i
$911$	745.454	−	430.388i	0.818281	−	0.472435i	−0.0315420	−	0.999502i	$-0.510042\pi$
$911$	745.454	−	430.388i	0.818281	−	0.472435i	0.849823	+	0.527067i	$0.176708\pi$
$912$	807.008	+	527.708i	0.884878	+	0.578628i
$913$	−17.1639	+	29.7288i	−0.0187995	+	0.0325616i
$914$	−152.560	+	28.4033i	−0.166914	+	0.0310758i
$915$	−0.962429	+	150.341i	−0.00105183	+	0.164307i
$916$	−1122.98	−	497.804i	−1.22597	−	0.543454i
$917$	230.802	−	230.802i	0.251693	−	0.251693i
$918$	−237.066	+	632.248i	−0.258242	+	0.688723i
$919$			1495.51i			1.62733i	0.581336	+	0.813663i	$0.302530\pi$
$919$			1495.51i			1.62733i	−0.581336	+	0.813663i	$0.697470\pi$
$920$	1.11976	+	3.74676i	0.00121713	+	0.00407256i
$921$	63.9764	−	63.1625i	0.0694640	−	0.0685803i
$922$	−360.276	+	525.116i	−0.390755	+	0.569541i
$923$	−240.046	−	895.864i	−0.260072	−	0.970601i
$924$	26.8615	+	12.1137i	0.0290709	+	0.0131100i
$925$	−1233.61	−	330.545i	−1.33363	−	0.357346i
$926$	−636.821	+	544.790i	−0.687711	+	0.588326i
$927$	−161.800	−	96.1983i	−0.174542	−	0.103774i
$928$	84.0189	+	34.4034i	0.0905376	+	0.0370726i
$929$	252.170	−	145.591i	0.271443	−	0.156718i	−0.358100	−	0.933683i	$-0.616575\pi$
$929$	252.170	−	145.591i	0.271443	−	0.156718i	0.629543	+	0.776966i	$0.283242\pi$
$930$	−189.222	−	131.612i	−0.203464	−	0.141518i
$931$	137.133	+	511.788i	0.147297	+	0.549719i
$932$	828.397	+	668.602i	0.888838	+	0.717384i
$933$	237.161	−	404.769i	0.254192	−	0.433836i
$934$	−299.222	−	626.024i	−0.320366	−	0.670262i
$935$	−8.61666			−0.00921568
$936$	600.689	−	619.989i	0.641762	−	0.662381i
$937$		−	581.132i		−	0.620205i	−0.950703	−	0.310102i	$-0.899637\pi$
$937$		−	581.132i		−	0.620205i	0.950703	−	0.310102i	$-0.100363\pi$
$938$	20.7923	+	43.5011i	0.0221666	+	0.0463764i
$939$	−1014.24	+	576.947i	−1.08013	+	0.614427i
$940$	43.9794	+	412.008i	0.0467866	+	0.438306i
$941$	804.751	−	215.632i	0.855208	−	0.229152i	0.195527	−	0.980698i	$-0.437358\pi$
$941$	804.751	−	215.632i	0.855208	−	0.229152i	0.659681	+	0.751546i	$0.270691\pi$
$942$	119.828	−	1420.95i	0.127206	−	1.50843i
$943$	−2.92011	−	5.05778i	−0.00309662	−	0.00536350i
$944$	−1446.50	+	742.949i	−1.53231	+	0.787022i
$945$	−118.863	−	123.519i	−0.125781	−	0.130708i
$946$	50.0372	−	42.8060i	0.0528935	−	0.0452495i
$947$	−298.003	+	1112.16i	−0.314681	+	1.17441i	0.609605	+	0.792706i	$0.291328\pi$
$947$	−298.003	+	1112.16i	−0.314681	+	1.17441i	−0.924286	+	0.381701i	$0.875338\pi$
$948$	67.0900	−	410.869i	0.0707700	−	0.433406i
$949$	1225.68	−	328.419i	1.29154	−	0.346068i
$950$	−527.734	+	769.193i	−0.555509	+	0.809677i
$951$	464.247	−	1689.26i	0.488167	−	1.77630i
$952$	−226.020	+	418.702i	−0.237415	+	0.439813i
$953$	1723.97			1.80899			0.904497	−	0.426480i	$-0.140247\pi$
$953$	1723.97			1.80899			0.904497	+	0.426480i	$0.140247\pi$
$954$	238.056	−	110.062i	0.249535	−	0.115369i
$955$	314.030	+	314.030i	0.328827	+	0.328827i
$956$	−263.264	−	682.515i	−0.275380	−	0.713928i
$957$	−2.22137	+	3.79127i	−0.00232118	+	0.00396162i
$958$	−1017.29	+	189.397i	−1.06189	+	0.197700i
$959$	131.132	+	75.7090i	0.136738	+	0.0789457i
$960$	250.599	+	53.6692i	0.261041	+	0.0559054i
$961$	66.3617	+	114.942i	0.0690548	+	0.119606i
$962$	−1002.27	+	857.429i	−1.04186	+	0.891298i
$963$	−568.714	+	554.335i	−0.590565	+	0.575633i
$964$	44.1402	−	281.646i	0.0457886	−	0.292164i
$965$	−276.153	−	73.9950i	−0.286169	−	0.0766788i
$966$	−3.54368	+	9.83200i	−0.00366840	+	0.0101781i
$967$	−1449.77	−	837.027i	−1.49925	−	0.865592i	−0.499249	−	0.866459i	$-0.666391\pi$
$967$	−1449.77	−	837.027i	−1.49925	−	0.865592i	−1.00000		0.000866967i	$0.999724\pi$
$968$	27.6320	+	965.473i	0.0285455	+	0.997389i
$969$	−529.427	−	536.249i	−0.546364	−	0.553405i
$970$	424.575	−	202.934i	0.437706	−	0.209211i
$971$	−160.003	+	160.003i	−0.164782	+	0.164782i	−0.784681	−	0.619899i	$-0.787173\pi$
$971$	−160.003	+	160.003i	−0.164782	+	0.164782i	0.619899	+	0.784681i	$0.287173\pi$
$972$	736.453	+	634.367i	0.757668	+	0.652641i
$973$	−452.642	+	452.642i	−0.465202	+	0.465202i
$974$	2.10499	−	5.95966i	0.00216118	−	0.00611875i
$975$	586.741	+	594.302i	0.601786	+	0.609540i
$976$	29.4932	−	599.990i	0.0302184	−	0.614744i
$977$	541.867	+	312.847i	0.554624	+	0.320212i	0.750985	−	0.660319i	$-0.229579\pi$
$977$	541.867	+	312.847i	0.554624	+	0.320212i	−0.196361	+	0.980532i	$0.562912\pi$
$978$	−1370.44	+	644.285i	−1.40126	+	0.658778i
$979$	−21.9325	−	5.87678i	−0.0224029	−	0.00600284i
$980$	82.9604	+	113.797i	0.0846535	+	0.116119i
$981$	−674.867	+	657.804i	−0.687938	+	0.670544i
$982$	132.134	−	1696.50i	0.134556	−	1.72760i
$983$	551.974	+	956.047i	0.561520	+	0.972581i	0.997364	+	0.0725589i	$0.0231165\pi$
$983$	551.974	+	956.047i	0.561520	+	0.972581i	−0.435844	+	0.900022i	$0.643550\pi$
$984$	−382.655	+	8.50049i	−0.388877	+	0.00863871i
$985$	−132.756	−	76.6466i	−0.134778	−	0.0778138i
$986$	−58.5074	−	40.1412i	−0.0593382	−	0.0407112i
$987$	−559.816	+	955.453i	−0.567190	+	0.968037i
$988$	346.710	+	898.851i	0.350921	+	0.909769i
$989$	16.5145	+	16.5145i	0.0166982	+	0.0166982i
$990$	−4.28037	+	11.6418i	−0.00432360	+	0.0117594i
$991$	791.937			0.799129			0.399564	−	0.916705i	$-0.369161\pi$
$991$	791.937			0.799129			0.399564	+	0.916705i	$0.369161\pi$
$992$	732.908	+	557.674i	0.738819	+	0.562172i
$993$	−397.188	+	1445.26i	−0.399988	+	1.45544i
$994$	723.447	−	134.690i	0.727814	−	0.135503i
$995$	346.133	−	92.7460i	0.347872	−	0.0932121i
$996$	−647.772	+	465.920i	−0.650374	+	0.467791i
$997$	153.202	−	571.758i	0.153663	−	0.573478i	−0.845553	−	0.533891i	$-0.820729\pi$
$997$	153.202	−	571.758i	0.153663	−	0.573478i	0.999216	−	0.0395867i	$-0.0126041\pi$
$998$	31.4411	−	403.682i	0.0315041	−	0.404491i
$999$	−1029.79	−	1070.13i	−1.03082	−	1.07120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.5.4	✓	184
3.2	odd	2		432.3.x.a.341.43		184
9.2	odd	6	inner	144.3.w.a.101.21	yes	184
9.7	even	3		432.3.x.a.197.26		184
16.13	even	4	inner	144.3.w.a.77.21	yes	184
48.29	odd	4		432.3.x.a.125.26		184
144.29	odd	12	inner	144.3.w.a.29.4	yes	184
144.61	even	12		432.3.x.a.413.43		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.4	✓	184	1.1	even	1	trivial
144.3.w.a.29.4	yes	184	144.29	odd	12	inner
144.3.w.a.77.21	yes	184	16.13	even	4	inner
144.3.w.a.101.21	yes	184	9.2	odd	6	inner
432.3.x.a.125.26		184	48.29	odd	4
432.3.x.a.197.26		184	9.7	even	3
432.3.x.a.341.43		184	3.2	odd	2
432.3.x.a.413.43		184	144.61	even	12

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)

\(f(q)\)	\(=\)	\(q+(-1.88582 - 0.666085i) q^{2} +(2.99994 + 0.0192045i) q^{3} +(3.11266 + 2.51224i) q^{4} +(-0.345472 - 1.28932i) q^{5} +(-5.64456 - 2.03443i) q^{6} +(4.11923 - 2.37824i) q^{7} +(-4.19657 - 6.81093i) q^{8} +(8.99926 + 0.115225i) q^{9} +O(q^{10})\)	\(q+(-1.88582 - 0.666085i) q^{2} +(2.99994 + 0.0192045i) q^{3} +(3.11266 + 2.51224i) q^{4} +(-0.345472 - 1.28932i) q^{5} +(-5.64456 - 2.03443i) q^{6} +(4.11923 - 2.37824i) q^{7} +(-4.19657 - 6.81093i) q^{8} +(8.99926 + 0.115225i) q^{9} +(-0.207297 + 2.66154i) q^{10} +(0.498663 + 0.133616i) q^{11} +(9.28955 + 7.59633i) q^{12} +(3.10316 + 11.5812i) q^{13} +(-9.35225 + 1.74118i) q^{14} +(-1.01163 - 3.87452i) q^{15} +(3.37733 + 15.6395i) q^{16} -12.5043i q^{17} +(-16.8943 - 6.21157i) q^{18} +(14.2044 - 14.2044i) q^{19} +(2.16374 - 4.88113i) q^{20} +(12.4031 - 7.05546i) q^{21} +(-0.851390 - 0.584128i) q^{22} +(0.183103 - 0.317144i) q^{23} +(-12.4586 - 20.5130i) q^{24} +(20.1076 - 11.6092i) q^{25} +(1.86202 - 23.9070i) q^{26} +(26.9950 + 0.518494i) q^{27} +(18.7965 + 2.94583i) q^{28} +(-0.734316 + 2.74050i) q^{29} +(-0.672991 + 7.98049i) q^{30} +(-14.3899 + 24.9240i) q^{31} +(4.04818 - 31.7429i) q^{32} +(1.49339 + 0.410417i) q^{33} +(-8.32891 + 23.5809i) q^{34} +(-4.48939 - 4.48939i) q^{35} +(27.7222 + 22.9669i) q^{36} +(-38.8945 - 38.8945i) q^{37} +(-36.2484 + 17.3257i) q^{38} +(9.08688 + 34.8023i) q^{39} +(-7.33167 + 7.76371i) q^{40} +(7.97394 - 13.8113i) q^{41} +(-28.0896 + 5.04383i) q^{42} +(-16.5064 + 61.6026i) q^{43} +(1.21649 + 1.66866i) q^{44} +(-2.96043 - 11.6427i) q^{45} +(-0.556545 + 0.476116i) q^{46} +(-67.2078 + 38.8024i) q^{47} +(9.83143 + 46.9824i) q^{48} +(-13.1880 + 22.8422i) q^{49} +(-45.6521 + 8.49942i) q^{50} +(0.240139 - 37.5121i) q^{51} +(-19.4355 + 43.8441i) q^{52} +(-10.3029 + 10.3029i) q^{53} +(-50.5625 - 18.9588i) q^{54} -0.689097i q^{55} +(-33.4847 - 18.0754i) q^{56} +(42.8852 - 42.3397i) q^{57} +(3.21020 - 4.67899i) q^{58} +(26.3048 + 98.1709i) q^{59} +(6.58482 - 14.6015i) q^{60} +(-36.2654 - 9.71727i) q^{61} +(43.7383 - 37.4174i) q^{62} +(37.3441 - 20.9278i) q^{63} +(-28.7776 + 57.1651i) q^{64} +(13.8598 - 8.00193i) q^{65} +(-2.54290 - 1.76870i) q^{66} +(-1.31178 - 4.89562i) q^{67} +(31.4137 - 38.9216i) q^{68} +(0.555389 - 0.947896i) q^{69} +(5.47589 + 11.4565i) q^{70} -77.3554 q^{71} +(-36.9812 - 61.7769i) q^{72} -105.834i q^{73} +(47.4412 + 99.2553i) q^{74} +(60.5446 - 34.4406i) q^{75} +(79.8986 - 8.52870i) q^{76} +(2.37188 - 0.635543i) q^{77} +(6.04506 - 71.6837i) q^{78} +(-17.3463 - 30.0446i) q^{79} +(18.9975 - 9.75747i) q^{80} +(80.9734 + 2.07388i) q^{81} +(-24.2369 + 20.7343i) q^{82} +(-17.2099 + 64.2283i) q^{83} +(56.3317 + 9.19829i) q^{84} +(-16.1220 + 4.31988i) q^{85} +(72.1607 - 105.177i) q^{86} +(-2.25553 + 8.20724i) q^{87} +(-1.18262 - 3.95709i) q^{88} -43.9825 q^{89} +(-2.17219 + 23.9280i) q^{90} +(40.3254 + 40.3254i) q^{91} +(1.36668 - 0.527164i) q^{92} +(-43.6475 + 74.4942i) q^{93} +(152.588 - 28.4084i) q^{94} +(-23.2213 - 13.4068i) q^{95} +(12.7539 - 95.1490i) q^{96} +(-88.1367 - 152.657i) q^{97} +(40.0850 - 34.2921i) q^{98} +(4.47220 + 1.25991i) 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

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