LMFDB - Embedded newform 37.3.d.a.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,3,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, degree $2$, 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:	$1.00817697813$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} + 8 x^{9} + 42 x^{8} - 268 x^{7} + 884 x^{6} + 704 x^{5} + 761 x^{4} + \cdots + 16 $ x^12 - 6x^11 + 18x^10 + 8x^9 + 42x^8 - 268x^7 + 884x^6 + 704x^5 + 761x^4 - 2054x^3 + 3042x^2 + 312*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.3
Root			$-0.0496173 - 0.0496173i$ of defining polynomial
Character	$\chi$	$=$	37.31
Dual form			37.3.d.a.6.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04962 - 1.04962i) q^{2} +0.377912i q^{3} -1.79661i q^{4} +(5.26886 - 5.26886i) q^{5} +(0.396663 - 0.396663i) q^{6} -5.54265 q^{7} +(-6.08422 + 6.08422i) q^{8} +8.85718 q^{9} +O(q^{10})$	\(q+(-1.04962 - 1.04962i) q^{2} +0.377912i q^{3} -1.79661i q^{4} +(5.26886 - 5.26886i) q^{5} +(0.396663 - 0.396663i) q^{6} -5.54265 q^{7} +(-6.08422 + 6.08422i) q^{8} +8.85718 q^{9} -11.0606 q^{10} +18.1924i q^{11} +0.678959 q^{12} +(7.75987 - 7.75987i) q^{13} +(5.81766 + 5.81766i) q^{14} +(1.99117 + 1.99117i) q^{15} +5.58578 q^{16} +(-18.1161 + 18.1161i) q^{17} +(-9.29665 - 9.29665i) q^{18} +(2.37917 - 2.37917i) q^{19} +(-9.46607 - 9.46607i) q^{20} -2.09463i q^{21} +(19.0950 - 19.0950i) q^{22} +(16.3967 - 16.3967i) q^{23} +(-2.29930 - 2.29930i) q^{24} -30.5218i q^{25} -16.2898 q^{26} +6.74844i q^{27} +9.95796i q^{28} +(20.1686 + 20.1686i) q^{29} -4.17992i q^{30} +(-10.4372 - 10.4372i) q^{31} +(18.4739 + 18.4739i) q^{32} -6.87512 q^{33} +38.0300 q^{34} +(-29.2034 + 29.2034i) q^{35} -15.9129i q^{36} +(-32.1547 - 18.3051i) q^{37} -4.99444 q^{38} +(2.93255 + 2.93255i) q^{39} +64.1138i q^{40} -2.51067i q^{41} +(-2.19856 + 2.19856i) q^{42} +(-19.0228 + 19.0228i) q^{43} +32.6846 q^{44} +(46.6673 - 46.6673i) q^{45} -34.4206 q^{46} -33.0588 q^{47} +2.11093i q^{48} -18.2791 q^{49} +(-32.0362 + 32.0362i) q^{50} +(-6.84630 - 6.84630i) q^{51} +(-13.9414 - 13.9414i) q^{52} -39.9577 q^{53} +(7.08328 - 7.08328i) q^{54} +(95.8532 + 95.8532i) q^{55} +(33.7227 - 33.7227i) q^{56} +(0.899117 + 0.899117i) q^{57} -42.3387i q^{58} +(46.2148 - 46.2148i) q^{59} +(3.57734 - 3.57734i) q^{60} +(3.22864 + 3.22864i) q^{61} +21.9101i q^{62} -49.0922 q^{63} -61.1243i q^{64} -81.7713i q^{65} +(7.21625 + 7.21625i) q^{66} +44.2028i q^{67} +(32.5476 + 32.5476i) q^{68} +(6.19652 + 6.19652i) q^{69} +61.3049 q^{70} -92.4046 q^{71} +(-53.8890 + 53.8890i) q^{72} -87.3712i q^{73} +(14.5368 + 52.9635i) q^{74} +11.5346 q^{75} +(-4.27443 - 4.27443i) q^{76} -100.834i q^{77} -6.15610i q^{78} +(39.7257 - 39.7257i) q^{79} +(29.4307 - 29.4307i) q^{80} +77.1643 q^{81} +(-2.63525 + 2.63525i) q^{82} -112.357 q^{83} -3.76323 q^{84} +190.903i q^{85} +39.9334 q^{86} +(-7.62196 + 7.62196i) q^{87} +(-110.686 - 110.686i) q^{88} +(113.101 + 113.101i) q^{89} -97.9655 q^{90} +(-43.0102 + 43.0102i) q^{91} +(-29.4585 - 29.4585i) q^{92} +(3.94434 - 3.94434i) q^{93} +(34.6991 + 34.6991i) q^{94} -25.0710i q^{95} +(-6.98153 + 6.98153i) q^{96} +(-6.42063 + 6.42063i) q^{97} +(19.1860 + 19.1860i) q^{98} +161.133i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9	$ 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9} - 16 q^{10} + 64 q^{12} + 14 q^{13} - 70 q^{14} - 2 q^{15} - 96 q^{16} + 2 q^{17} + 132 q^{18} + 14 q^{19} - 24 q^{20} + 22 q^{22} + 56 q^{23} - 84 q^{24} - 48 q^{26} + 60 q^{29} + 72 q^{31} + 208 q^{32} + 56 q^{33} + 112 q^{34} - 154 q^{35} - 66 q^{37} - 336 q^{38} - 46 q^{39} + 90 q^{42} + 70 q^{43} + 80 q^{44} + 232 q^{45} - 424 q^{46} - 384 q^{47} + 144 q^{49} - 34 q^{50} - 126 q^{51} + 328 q^{52} - 56 q^{53} - 194 q^{54} + 70 q^{55} + 16 q^{56} - 94 q^{57} + 184 q^{59} + 276 q^{60} + 132 q^{61} - 400 q^{63} + 614 q^{66} + 116 q^{68} + 368 q^{69} + 556 q^{70} + 68 q^{71} - 692 q^{72} - 382 q^{74} + 116 q^{75} + 12 q^{76} - 2 q^{79} + 4 q^{80} - 76 q^{81} + 374 q^{82} + 108 q^{83} - 1436 q^{84} + 140 q^{86} - 420 q^{87} - 788 q^{88} + 278 q^{89} - 664 q^{90} - 450 q^{91} + 652 q^{92} + 584 q^{93} + 118 q^{94} + 1584 q^{96} - 244 q^{97} + 416 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9 - 16 * q^10 + 64 * q^12 + 14 * q^13 - 70 * q^14 - 2 * q^15 - 96 * q^16 + 2 * q^17 + 132 * q^18 + 14 * q^19 - 24 * q^20 + 22 * q^22 + 56 * q^23 - 84 * q^24 - 48 * q^26 + 60 * q^29 + 72 * q^31 + 208 * q^32 + 56 * q^33 + 112 * q^34 - 154 * q^35 - 66 * q^37 - 336 * q^38 - 46 * q^39 + 90 * q^42 + 70 * q^43 + 80 * q^44 + 232 * q^45 - 424 * q^46 - 384 * q^47 + 144 * q^49 - 34 * q^50 - 126 * q^51 + 328 * q^52 - 56 * q^53 - 194 * q^54 + 70 * q^55 + 16 * q^56 - 94 * q^57 + 184 * q^59 + 276 * q^60 + 132 * q^61 - 400 * q^63 + 614 * q^66 + 116 * q^68 + 368 * q^69 + 556 * q^70 + 68 * q^71 - 692 * q^72 - 382 * q^74 + 116 * q^75 + 12 * q^76 - 2 * q^79 + 4 * q^80 - 76 * q^81 + 374 * q^82 + 108 * q^83 - 1436 * q^84 + 140 * q^86 - 420 * q^87 - 788 * q^88 + 278 * q^89 - 664 * q^90 - 450 * q^91 + 652 * q^92 + 584 * q^93 + 118 * q^94 + 1584 * q^96 - 244 * q^97 + 416 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.04962	−	1.04962i	−0.524809	−	0.524809i	0.394211	−	0.919020i	$-0.371018\pi$
$2$	−1.04962	−	1.04962i	−0.524809	−	0.524809i	−0.919020	+	0.394211i	$0.871018\pi$
$3$			0.377912i			0.125971i	0.998014	+	0.0629853i	$0.0200621\pi$
$3$			0.377912i			0.125971i	−0.998014	+	0.0629853i	$0.979938\pi$
$4$		−	1.79661i		−	0.449152i
$5$	5.26886	−	5.26886i	1.05377	−	1.05377i	0.0553026	−	0.998470i	$-0.482388\pi$
$5$	5.26886	−	5.26886i	1.05377	−	1.05377i	0.998470	−	0.0553026i	$-0.0176123\pi$
$6$	0.396663	−	0.396663i	0.0661105	−	0.0661105i
$7$	−5.54265			−0.791807			−0.395903	−	0.918292i	$-0.629568\pi$
$7$	−5.54265			−0.791807			−0.395903	+	0.918292i	$0.629568\pi$
$8$	−6.08422	+	6.08422i	−0.760527	+	0.760527i
$9$	8.85718			0.984131
$10$	−11.0606			−1.10606
$11$			18.1924i			1.65385i	0.562310	+	0.826927i	$0.309913\pi$
$11$			18.1924i			1.65385i	−0.562310	+	0.826927i	$0.690087\pi$
$12$	0.678959			0.0565799
$13$	7.75987	−	7.75987i	0.596913	−	0.596913i	−0.342577	−	0.939490i	$-0.611300\pi$
$13$	7.75987	−	7.75987i	0.596913	−	0.596913i	0.939490	+	0.342577i	$0.111300\pi$
$14$	5.81766	+	5.81766i	0.415547	+	0.415547i
$15$	1.99117	+	1.99117i	0.132744	+	0.132744i
$16$	5.58578			0.349111
$17$	−18.1161	+	18.1161i	−1.06565	+	1.06565i	−0.0679669	+	0.997688i	$0.521651\pi$
$17$	−18.1161	+	18.1161i	−1.06565	+	1.06565i	−0.997688	+	0.0679669i	$0.978349\pi$
$18$	−9.29665	−	9.29665i	−0.516481	−	0.516481i
$19$	2.37917	−	2.37917i	0.125219	−	0.125219i	−0.641720	−	0.766939i	$-0.721779\pi$
$19$	2.37917	−	2.37917i	0.125219	−	0.125219i	0.766939	+	0.641720i	$0.221779\pi$
$20$	−9.46607	−	9.46607i	−0.473304	−	0.473304i
$21$		−	2.09463i		−	0.0997444i
$22$	19.0950	−	19.0950i	0.867957	−	0.867957i
$23$	16.3967	−	16.3967i	0.712901	−	0.712901i	−0.254240	−	0.967141i	$-0.581825\pi$
$23$	16.3967	−	16.3967i	0.712901	−	0.712901i	0.967141	+	0.254240i	$0.0818254\pi$
$24$	−2.29930	−	2.29930i	−0.0958041	−	0.0958041i
$25$		−	30.5218i		−	1.22087i
$26$	−16.2898			−0.626530
$27$			6.74844i			0.249942i
$28$			9.95796i			0.355641i
$29$	20.1686	+	20.1686i	0.695469	+	0.695469i	0.963430	−	0.267960i	$-0.0863497\pi$
$29$	20.1686	+	20.1686i	0.695469	+	0.695469i	−0.267960	+	0.963430i	$0.586350\pi$
$30$		−	4.17992i		−	0.139331i
$31$	−10.4372	−	10.4372i	−0.336684	−	0.336684i	0.518434	−	0.855118i	$-0.326515\pi$
$31$	−10.4372	−	10.4372i	−0.336684	−	0.336684i	−0.855118	+	0.518434i	$0.826515\pi$
$32$	18.4739	+	18.4739i	0.577311	+	0.577311i
$33$	−6.87512			−0.208337
$34$	38.0300			1.11853
$35$	−29.2034	+	29.2034i	−0.834384	+	0.834384i
$36$		−	15.9129i		−	0.442024i
$37$	−32.1547	−	18.3051i	−0.869045	−	0.494732i
$37$	−32.1547	−	18.3051i	−0.869045	−	0.494732i
$38$	−4.99444			−0.131433
$39$	2.93255	+	2.93255i	0.0751935	+	0.0751935i
$40$			64.1138i			1.60285i
$41$		−	2.51067i		−	0.0612359i	−0.999531	−	0.0306180i	$-0.990252\pi$
$41$		−	2.51067i		−	0.0612359i	0.999531	−	0.0306180i	$-0.00974753\pi$
$42$	−2.19856	+	2.19856i	−0.0523467	+	0.0523467i
$43$	−19.0228	+	19.0228i	−0.442391	+	0.442391i	−0.892815	−	0.450424i	$-0.851273\pi$
$43$	−19.0228	+	19.0228i	−0.442391	+	0.442391i	0.450424	+	0.892815i	$0.351273\pi$
$44$	32.6846			0.742831
$45$	46.6673	−	46.6673i	1.03705	−	1.03705i
$46$	−34.4206			−0.748273
$47$	−33.0588			−0.703378			−0.351689	−	0.936117i	$-0.614393\pi$
$47$	−33.0588			−0.703378			−0.351689	+	0.936117i	$0.614393\pi$
$48$			2.11093i			0.0439777i
$49$	−18.2791			−0.373042
$50$	−32.0362	+	32.0362i	−0.640724	+	0.640724i
$51$	−6.84630	−	6.84630i	−0.134241	−	0.134241i
$52$	−13.9414	−	13.9414i	−0.268104	−	0.268104i
$53$	−39.9577			−0.753918			−0.376959	−	0.926230i	$-0.623030\pi$
$53$	−39.9577			−0.753918			−0.376959	+	0.926230i	$0.623030\pi$
$54$	7.08328	−	7.08328i	0.131172	−	0.131172i
$55$	95.8532	+	95.8532i	1.74278	+	1.74278i
$56$	33.7227	−	33.7227i	0.602191	−	0.602191i
$57$	0.899117	+	0.899117i	0.0157740	+	0.0157740i
$58$		−	42.3387i		−	0.729977i
$59$	46.2148	−	46.2148i	0.783303	−	0.783303i	−0.197084	−	0.980387i	$-0.563147\pi$
$59$	46.2148	−	46.2148i	0.783303	−	0.783303i	0.980387	+	0.197084i	$0.0631472\pi$
$60$	3.57734	−	3.57734i	0.0596224	−	0.0596224i
$61$	3.22864	+	3.22864i	0.0529286	+	0.0529286i	0.733076	−	0.680147i	$-0.238084\pi$
$61$	3.22864	+	3.22864i	0.0529286	+	0.0529286i	−0.680147	+	0.733076i	$0.738084\pi$
$62$			21.9101i			0.353389i
$63$	−49.0922			−0.779242
$64$		−	61.1243i		−	0.955066i
$65$		−	81.7713i		−	1.25802i
$66$	7.21625	+	7.21625i	0.109337	+	0.109337i
$67$			44.2028i			0.659743i	0.944026	+	0.329872i	$0.107005\pi$
$67$			44.2028i			0.659743i	−0.944026	+	0.329872i	$0.892995\pi$
$68$	32.5476	+	32.5476i	0.478641	+	0.478641i
$69$	6.19652	+	6.19652i	0.0898046	+	0.0898046i
$70$	61.3049			0.875784
$71$	−92.4046			−1.30147			−0.650736	−	0.759304i	$-0.725540\pi$
$71$	−92.4046			−1.30147			−0.650736	+	0.759304i	$0.725540\pi$
$72$	−53.8890	+	53.8890i	−0.748459	+	0.748459i
$73$		−	87.3712i		−	1.19687i	−0.801173	−	0.598433i	$-0.795790\pi$
$73$		−	87.3712i		−	1.19687i	0.801173	−	0.598433i	$-0.204210\pi$
$74$	14.5368	+	52.9635i	0.196443	+	0.715722i
$75$	11.5346			0.153794
$76$	−4.27443	−	4.27443i	−0.0562425	−	0.0562425i
$77$		−	100.834i		−	1.30953i
$78$		−	6.15610i		−	0.0789244i
$79$	39.7257	−	39.7257i	0.502857	−	0.502857i	−0.409467	−	0.912325i	$-0.634285\pi$
$79$	39.7257	−	39.7257i	0.502857	−	0.502857i	0.912325	+	0.409467i	$0.134285\pi$
$80$	29.4307	−	29.4307i	0.367883	−	0.367883i
$81$	77.1643			0.952646
$82$	−2.63525	+	2.63525i	−0.0321372	+	0.0321372i
$83$	−112.357			−1.35370			−0.676849	−	0.736122i	$-0.736655\pi$
$83$	−112.357			−1.35370			−0.676849	+	0.736122i	$0.736655\pi$
$84$	−3.76323			−0.0448004
$85$			190.903i			2.24591i
$86$	39.9334			0.464342
$87$	−7.62196	+	7.62196i	−0.0876087	+	0.0876087i
$88$	−110.686	−	110.686i	−1.25780	−	1.25780i
$89$	113.101	+	113.101i	1.27080	+	1.27080i	0.945671	+	0.325124i	$0.105406\pi$
$89$	113.101	+	113.101i	1.27080	+	1.27080i	0.325124	+	0.945671i	$0.394594\pi$
$90$	−97.9655			−1.08851
$91$	−43.0102	+	43.0102i	−0.472639	+	0.472639i
$92$	−29.4585	−	29.4585i	−0.320201	−	0.320201i
$93$	3.94434	−	3.94434i	0.0424123	−	0.0424123i
$94$	34.6991	+	34.6991i	0.369139	+	0.369139i
$95$		−	25.0710i		−	0.263906i
$96$	−6.98153	+	6.98153i	−0.0727242	+	0.0727242i
$97$	−6.42063	+	6.42063i	−0.0661921	+	0.0661921i	−0.739428	−	0.673236i	$-0.764904\pi$
$97$	−6.42063	+	6.42063i	−0.0661921	+	0.0661921i	0.673236	+	0.739428i	$0.264904\pi$
$98$	19.1860	+	19.1860i	0.195776	+	0.195776i
$99$			161.133i			1.62761i
$100$	−54.8357			−0.548357
$101$		−	72.9137i		−	0.721918i	−0.932582	−	0.360959i	$-0.882449\pi$
$101$		−	72.9137i		−	0.721918i	0.932582	−	0.360959i	$-0.117551\pi$
$102$			14.3720i			0.140902i
$103$	59.4600	+	59.4600i	0.577282	+	0.577282i	0.934153	−	0.356872i	$-0.116157\pi$
$103$	59.4600	+	59.4600i	0.577282	+	0.577282i	−0.356872	+	0.934153i	$0.616157\pi$
$104$			94.4255i			0.907937i
$105$	−11.0363	−	11.0363i	−0.105108	−	0.105108i
$106$	41.9402	+	41.9402i	0.395663	+	0.395663i
$107$	64.2881			0.600824			0.300412	−	0.953810i	$-0.402876\pi$
$107$	64.2881			0.600824			0.300412	+	0.953810i	$0.402876\pi$
$108$	12.1243			0.112262
$109$	−25.6002	+	25.6002i	−0.234864	+	0.234864i	−0.814720	−	0.579855i	$-0.803109\pi$
$109$	−25.6002	+	25.6002i	−0.234864	+	0.234864i	0.579855	+	0.814720i	$0.303109\pi$
$110$		−	201.218i		−	1.82926i
$111$	6.91772	−	12.1516i	0.0623218	−	0.109474i
$112$	−30.9600			−0.276428
$113$	55.8577	+	55.8577i	0.494316	+	0.494316i	0.909663	−	0.415347i	$-0.136340\pi$
$113$	55.8577	+	55.8577i	0.494316	+	0.494316i	−0.415347	+	0.909663i	$0.636340\pi$
$114$		−	1.88746i		−	0.0165566i
$115$		−	172.784i		−	1.50247i
$116$	36.2351	−	36.2351i	0.312371	−	0.312371i
$117$	68.7306	−	68.7306i	0.587441	−	0.587441i
$118$	−97.0158			−0.822168
$119$	100.411	−	100.411i	0.843792	−	0.843792i
$120$	−24.2294			−0.201911
$121$	−209.963			−1.73523
$122$		−	6.77768i		−	0.0555547i
$123$	0.948814			0.00771393
$124$	−18.7515	+	18.7515i	−0.151222	+	0.151222i
$125$	−29.0936	−	29.0936i	−0.232749	−	0.232749i
$126$	51.5281	+	51.5281i	0.408953	+	0.408953i
$127$	132.802			1.04568			0.522841	−	0.852430i	$-0.324872\pi$
$127$	132.802			1.04568			0.522841	+	0.852430i	$0.324872\pi$
$128$	9.73872	−	9.73872i	0.0760838	−	0.0760838i
$129$	−7.18896	−	7.18896i	−0.0557283	−	0.0557283i
$130$	−85.8286	+	85.8286i	−0.660220	+	0.660220i
$131$	−90.8033	−	90.8033i	−0.693155	−	0.693155i	0.269770	−	0.962925i	$-0.413052\pi$
$131$	−90.8033	−	90.8033i	−0.693155	−	0.693155i	−0.962925	+	0.269770i	$0.913052\pi$
$132$			12.3519i			0.0935749i
$133$	−13.1869	+	13.1869i	−0.0991496	+	0.0991496i
$134$	46.3960	−	46.3960i	0.346239	−	0.346239i
$135$	35.5566	+	35.5566i	0.263382	+	0.263382i
$136$		−	220.445i		−	1.62092i
$137$	15.1210			0.110372			0.0551860	−	0.998476i	$-0.482425\pi$
$137$	15.1210			0.110372			0.0551860	+	0.998476i	$0.482425\pi$
$138$		−	13.0079i		−	0.0942605i
$139$		−	218.618i		−	1.57279i	−0.617724	−	0.786395i	$-0.711945\pi$
$139$		−	218.618i		−	1.57279i	0.617724	−	0.786395i	$-0.288055\pi$
$140$	52.4671	+	52.4671i	0.374765	+	0.374765i
$141$		−	12.4933i		−	0.0886050i
$142$	96.9894	+	96.9894i	0.683024	+	0.683024i
$143$	141.170	+	141.170i	0.987206	+	0.987206i
$144$	49.4742			0.343571
$145$	212.531			1.46573
$146$	−91.7063	+	91.7063i	−0.628126	+	0.628126i
$147$		−	6.90788i		−	0.0469924i
$148$	−32.8871	+	57.7693i	−0.222210	+	0.390333i
$149$	−224.519			−1.50684			−0.753421	−	0.657539i	$-0.771598\pi$
$149$	−224.519			−1.50684			−0.753421	+	0.657539i	$0.771598\pi$
$150$	−12.1069	−	12.1069i	−0.0807124	−	0.0807124i
$151$			220.465i			1.46004i	0.683428	+	0.730018i	$0.260488\pi$
$151$			220.465i			1.46004i	−0.683428	+	0.730018i	$0.739512\pi$
$152$			28.9508i			0.190466i
$153$	−160.458	+	160.458i	−1.04874	+	1.04874i
$154$	−105.837	+	105.837i	−0.687254	+	0.687254i
$155$	−109.984			−0.709576
$156$	5.26863	−	5.26863i	0.0337733	−	0.0337733i
$157$	82.7157			0.526851			0.263426	−	0.964680i	$-0.415148\pi$
$157$	82.7157			0.526851			0.263426	+	0.964680i	$0.415148\pi$
$158$	−83.3936			−0.527808
$159$		−	15.1005i		−	0.0949716i
$160$	194.673			1.21671
$161$	−90.8812	+	90.8812i	−0.564480	+	0.564480i
$162$	−80.9930	−	80.9930i	−0.499957	−	0.499957i
$163$	−139.231	−	139.231i	−0.854180	−	0.854180i	0.136465	−	0.990645i	$-0.456426\pi$
$163$	−139.231	−	139.231i	−0.854180	−	0.854180i	−0.990645	+	0.136465i	$0.956426\pi$
$164$	−4.51069			−0.0275042
$165$	−36.2241	+	36.2241i	−0.219540	+	0.219540i
$166$	117.932	+	117.932i	0.710433	+	0.710433i
$167$	75.9417	−	75.9417i	0.454741	−	0.454741i	−0.442184	−	0.896924i	$-0.645796\pi$
$167$	75.9417	−	75.9417i	0.454741	−	0.454741i	0.896924	+	0.442184i	$0.145796\pi$
$168$	12.7442	+	12.7442i	0.0758583	+	0.0758583i
$169$			48.5690i			0.287390i
$170$	200.375	−	200.375i	1.17868	−	1.17868i
$171$	21.0727	−	21.0727i	0.123232	−	0.123232i
$172$	34.1766	+	34.1766i	0.198701	+	0.198701i
$173$			79.1788i			0.457681i	0.973464	+	0.228841i	$0.0734935\pi$
$173$			79.1788i			0.457681i	−0.973464	+	0.228841i	$0.926507\pi$
$174$	16.0003			0.0919557
$175$			169.171i			0.966694i
$176$			101.619i			0.577378i
$177$	17.4651	+	17.4651i	0.0986731	+	0.0986731i
$178$		−	237.425i		−	1.33385i
$179$	−122.752	−	122.752i	−0.685767	−	0.685767i	0.275527	−	0.961293i	$-0.411148\pi$
$179$	−122.752	−	122.752i	−0.685767	−	0.685767i	−0.961293	+	0.275527i	$0.911148\pi$
$180$	−83.8427	−	83.8427i	−0.465793	−	0.465793i
$181$	136.182			0.752387			0.376193	−	0.926541i	$-0.377233\pi$
$181$	136.182			0.752387			0.376193	+	0.926541i	$0.377233\pi$
$182$	90.2885			0.496091
$183$	−1.22014	+	1.22014i	−0.00666745	+	0.00666745i
$184$			199.523i			1.08436i
$185$	−265.866	+	72.9715i	−1.43711	+	0.394441i
$186$	−8.28010			−0.0445167
$187$	−329.576	−	329.576i	−1.76244	−	1.76244i
$188$			59.3936i			0.315924i
$189$		−	37.4042i		−	0.197906i
$190$	−26.3150	+	26.3150i	−0.138500	+	0.138500i
$191$	124.156	−	124.156i	0.650033	−	0.650033i	−0.302968	−	0.953001i	$-0.597977\pi$
$191$	124.156	−	124.156i	0.650033	−	0.650033i	0.953001	+	0.302968i	$0.0979774\pi$
$192$	23.0996			0.120310
$193$	66.0477	−	66.0477i	0.342216	−	0.342216i	−0.514984	−	0.857200i	$-0.672202\pi$
$193$	66.0477	−	66.0477i	0.342216	−	0.342216i	0.857200	+	0.514984i	$0.172202\pi$
$194$	13.4784			0.0694763
$195$	30.9024			0.158474
$196$			32.8403i			0.167553i
$197$	59.3236			0.301135			0.150568	−	0.988600i	$-0.451890\pi$
$197$	59.3236			0.301135			0.150568	+	0.988600i	$0.451890\pi$
$198$	169.128	−	169.128i	0.854183	−	0.854183i
$199$	24.4969	+	24.4969i	0.123100	+	0.123100i	0.765973	−	0.642873i	$-0.222258\pi$
$199$	24.4969	+	24.4969i	0.123100	+	0.123100i	−0.642873	+	0.765973i	$0.722258\pi$
$200$	185.701	+	185.701i	0.928506	+	0.928506i
$201$	−16.7048			−0.0831083
$202$	−76.5315	+	76.5315i	−0.378869	+	0.378869i
$203$	−111.787	−	111.787i	−0.550677	−	0.550677i
$204$	−12.3001	+	12.3001i	−0.0602947	+	0.0602947i
$205$	−13.2284	−	13.2284i	−0.0645287	−	0.0645287i
$206$		−	124.821i		−	0.605925i
$207$	145.229	−	145.229i	0.701588	−	0.701588i
$208$	43.3449	−	43.3449i	0.208389	−	0.208389i
$209$	43.2828	+	43.2828i	0.207095	+	0.207095i
$210$			23.1678i			0.110323i
$211$	33.2939			0.157791			0.0788955	−	0.996883i	$-0.474861\pi$
$211$	33.2939			0.157791			0.0788955	+	0.996883i	$0.474861\pi$
$212$			71.7882i			0.338624i
$213$		−	34.9208i		−	0.163947i
$214$	−67.4779	−	67.4779i	−0.315317	−	0.315317i
$215$			200.457i			0.932360i
$216$	−41.0590	−	41.0590i	−0.190088	−	0.190088i
$217$	57.8497	+	57.8497i	0.266588	+	0.266588i
$218$	53.7409			0.246518
$219$	33.0186			0.150770
$220$	172.210	−	172.210i	0.782775	−	0.782775i
$221$			281.157i			1.27221i
$222$	−20.0155	+	5.49362i	−0.0901600	+	0.0247460i
$223$	356.943			1.60064			0.800320	−	0.599574i	$-0.204663\pi$
$223$	356.943			1.60064			0.800320	+	0.599574i	$0.204663\pi$
$224$	−102.395	−	102.395i	−0.457119	−	0.457119i
$225$		−	270.337i		−	1.20150i
$226$		−	117.258i		−	0.518843i
$227$	−126.548	+	126.548i	−0.557479	+	0.557479i	−0.928589	−	0.371110i	$-0.878977\pi$
$227$	−126.548	+	126.548i	−0.557479	+	0.557479i	0.371110	+	0.928589i	$0.378977\pi$
$228$	1.61536	−	1.61536i	0.00708491	−	0.00708491i
$229$	−235.918			−1.03021			−0.515104	−	0.857128i	$-0.672247\pi$
$229$	−235.918			−1.03021			−0.515104	+	0.857128i	$0.672247\pi$
$230$	−181.357	+	181.357i	−0.788510	+	0.788510i
$231$	38.1064			0.164963
$232$	−245.421			−1.05785
$233$			33.5791i			0.144116i	0.997400	+	0.0720582i	$0.0229567\pi$
$233$			33.5791i			0.144116i	−0.997400	+	0.0720582i	$0.977043\pi$
$234$	−144.282			−0.616588
$235$	−174.182	+	174.182i	−0.741200	+	0.741200i
$236$	−83.0299	−	83.0299i	−0.351822	−	0.351822i
$237$	15.0128	+	15.0128i	0.0633453	+	0.0633453i
$238$	−210.787			−0.885659
$239$	−5.37141	+	5.37141i	−0.0224745	+	0.0224745i	−0.718255	−	0.695780i	$-0.755059\pi$
$239$	−5.37141	+	5.37141i	−0.0224745	+	0.0224745i	0.695780	+	0.718255i	$0.255059\pi$
$240$	11.1222	+	11.1222i	0.0463425	+	0.0463425i
$241$	264.741	−	264.741i	1.09851	−	1.09851i	0.103924	−	0.994585i	$-0.466860\pi$
$241$	264.741	−	264.741i	1.09851	−	1.09851i	0.994585	−	0.103924i	$-0.0331400\pi$
$242$	220.381	+	220.381i	0.910664	+	0.910664i
$243$			89.8973i			0.369948i
$244$	5.80060	−	5.80060i	0.0237730	−	0.0237730i
$245$	−96.3099	+	96.3099i	−0.393102	+	0.393102i
$246$	−0.995891	−	0.995891i	−0.00404834	−	0.00404834i
$247$		−	36.9241i		−	0.149490i
$248$	127.004			0.512115
$249$		−	42.4610i		−	0.170526i
$250$			61.0742i			0.244297i
$251$	−60.1852	−	60.1852i	−0.239782	−	0.239782i	0.576978	−	0.816760i	$-0.304232\pi$
$251$	−60.1852	−	60.1852i	−0.239782	−	0.239782i	−0.816760	+	0.576978i	$0.804232\pi$
$252$			88.1994i			0.349998i
$253$	298.296	+	298.296i	1.17903	+	1.17903i
$254$	−139.391	−	139.391i	−0.548783	−	0.548783i
$255$	−72.1444			−0.282919
$256$	−264.941			−1.03493
$257$	103.677	−	103.677i	0.403412	−	0.403412i	−0.476021	−	0.879434i	$-0.657922\pi$
$257$	103.677	−	103.677i	0.403412	−	0.403412i	0.879434	+	0.476021i	$0.157922\pi$
$258$			15.0913i			0.0584934i
$259$	178.222	+	101.459i	0.688116	+	0.391732i
$260$	−146.911			−0.565042
$261$	178.637	+	178.637i	0.684433	+	0.684433i
$262$			190.617i			0.727547i
$263$		−	232.453i		−	0.883851i	−0.897052	−	0.441926i	$-0.854296\pi$
$263$		−	232.453i		−	0.883851i	0.897052	−	0.441926i	$-0.145704\pi$
$264$	41.8297	−	41.8297i	0.158446	−	0.158446i
$265$	−210.531	+	210.531i	−0.794458	+	0.794458i
$266$	27.6824			0.104069
$267$	−42.7421	+	42.7421i	−0.160083	+	0.160083i
$268$	79.4150			0.296325
$269$	183.875			0.683550			0.341775	−	0.939782i	$-0.388972\pi$
$269$	183.875			0.683550			0.341775	+	0.939782i	$0.388972\pi$
$270$		−	74.6417i		−	0.276451i
$271$	10.9050			0.0402398			0.0201199	−	0.999798i	$-0.493595\pi$
$271$	10.9050			0.0402398			0.0201199	+	0.999798i	$0.493595\pi$
$272$	−101.193	+	101.193i	−0.372032	+	0.372032i
$273$	−16.2541	−	16.2541i	−0.0595387	−	0.0595387i
$274$	−15.8712	−	15.8712i	−0.0579242	−	0.0579242i
$275$	555.264			2.01914
$276$	11.1327	−	11.1327i	0.0403359	−	0.0403359i
$277$	−210.314	−	210.314i	−0.759256	−	0.759256i	0.216931	−	0.976187i	$-0.430395\pi$
$277$	−210.314	−	210.314i	−0.759256	−	0.759256i	−0.976187	+	0.216931i	$0.930395\pi$
$278$	−229.465	+	229.465i	−0.825414	+	0.825414i
$279$	−92.4442	−	92.4442i	−0.331341	−	0.331341i
$280$		−	355.360i		−	1.26914i
$281$	−353.860	+	353.860i	−1.25929	+	1.25929i	−0.307856	+	0.951433i	$0.599611\pi$
$281$	−353.860	+	353.860i	−1.25929	+	1.25929i	−0.951433	+	0.307856i	$0.900389\pi$
$282$	−13.1132	+	13.1132i	−0.0465007	+	0.0465007i
$283$	305.613	+	305.613i	1.07991	+	1.07991i	0.996517	+	0.0833885i	$0.0265742\pi$
$283$	305.613	+	305.613i	1.07991	+	1.07991i	0.0833885	+	0.996517i	$0.473426\pi$
$284$			166.015i			0.584559i
$285$	9.47464			0.0332444
$286$		−	296.350i		−	1.03619i
$287$			13.9158i			0.0484870i
$288$	163.627	+	163.627i	0.568150	+	0.568150i
$289$		−	367.388i		−	1.27124i
$290$	−223.076	−	223.076i	−0.769229	−	0.769229i
$291$	−2.42643	−	2.42643i	−0.00833826	−	0.00833826i
$292$	−156.972			−0.537574
$293$	−81.8505			−0.279353			−0.139677	−	0.990197i	$-0.544606\pi$
$293$	−81.8505			−0.279353			−0.139677	+	0.990197i	$0.544606\pi$
$294$	−7.25063	+	7.25063i	−0.0246620	+	0.0246620i
$295$		−	486.999i		−	1.65084i
$296$	307.008	−	84.2639i	1.03719	−	0.284675i
$297$	−122.770			−0.413368
$298$	235.659	+	235.659i	0.790804	+	0.790804i
$299$		−	254.473i		−	0.851079i
$300$		−	20.7231i		−	0.0690769i
$301$	105.437	−	105.437i	0.350288	−	0.350288i
$302$	231.404	−	231.404i	0.766239	−	0.766239i
$303$	27.5550			0.0909405
$304$	13.2895	−	13.2895i	0.0437155	−	0.0437155i
$305$	34.0225			0.111549
$306$	336.839			1.10078
$307$		−	441.470i		−	1.43801i	−0.695003	−	0.719007i	$-0.744597\pi$
$307$		−	441.470i		−	1.43801i	0.695003	−	0.719007i	$-0.255403\pi$
$308$	−181.159			−0.588179
$309$	−22.4706	+	22.4706i	−0.0727205	+	0.0727205i
$310$	115.441	+	115.441i	0.372392	+	0.372392i
$311$	−26.4826	−	26.4826i	−0.0851531	−	0.0851531i	0.663247	−	0.748400i	$-0.269178\pi$
$311$	−26.4826	−	26.4826i	−0.0851531	−	0.0851531i	−0.748400	+	0.663247i	$0.769178\pi$
$312$	−35.6845			−0.114373
$313$	301.149	−	301.149i	0.962137	−	0.962137i	−0.0371719	−	0.999309i	$-0.511835\pi$
$313$	301.149	−	301.149i	0.962137	−	0.962137i	0.999309	+	0.0371719i	$0.0118349\pi$
$314$	−86.8198	−	86.8198i	−0.276496	−	0.276496i
$315$	−258.660	+	258.660i	−0.821143	+	0.821143i
$316$	−71.3715	−	71.3715i	−0.225859	−	0.225859i
$317$			374.514i			1.18143i	0.806880	+	0.590716i	$0.201155\pi$
$317$			374.514i			1.18143i	−0.806880	+	0.590716i	$0.798845\pi$
$318$	−15.8497	+	15.8497i	−0.0498419	+	0.0498419i
$319$	−366.915	+	366.915i	−1.15020	+	1.15020i
$320$	−322.055	−	322.055i	−1.00642	−	1.00642i
$321$			24.2953i			0.0756861i
$322$	190.781			0.592488
$323$			86.2027i			0.266881i
$324$		−	138.634i		−	0.427883i
$325$	−236.845	−	236.845i	−0.728754	−	0.728754i
$326$			292.279i			0.896562i
$327$	−9.67463	−	9.67463i	−0.0295860	−	0.0295860i
$328$	15.2755	+	15.2755i	0.0465716	+	0.0465716i
$329$	183.233			0.556939
$330$	76.0428			0.230433
$331$	−284.416	+	284.416i	−0.859261	+	0.859261i	−0.991251	−	0.131990i	$-0.957863\pi$
$331$	−284.416	+	284.416i	−0.859261	+	0.859261i	0.131990	+	0.991251i	$0.457863\pi$
$332$			201.861i			0.608016i
$333$	−284.800	−	162.132i	−0.855255	−	0.486882i
$334$	−159.419			−0.477304
$335$	232.898	+	232.898i	0.695219	+	0.695219i
$336$		−	11.7001i		−	0.0348219i
$337$			408.598i			1.21246i	0.795290	+	0.606229i	$0.207319\pi$
$337$			408.598i			1.21246i	−0.795290	+	0.606229i	$0.792681\pi$
$338$	50.9788	−	50.9788i	0.150825	−	0.150825i
$339$	−21.1093	+	21.1093i	−0.0622693	+	0.0622693i
$340$	342.977			1.00876
$341$	189.878	−	189.878i	0.556826	−	0.556826i
$342$	−44.2366			−0.129347
$343$	372.904			1.08718
$344$		−	231.478i		−	0.672902i
$345$	65.2972			0.189267
$346$	83.1075	−	83.1075i	0.240195	−	0.240195i
$347$	169.743	+	169.743i	0.489173	+	0.489173i	0.908045	−	0.418872i	$-0.137574\pi$
$347$	169.743	+	169.743i	0.489173	+	0.489173i	−0.418872	+	0.908045i	$0.637574\pi$
$348$	13.6937	+	13.6937i	0.0393496	+	0.0393496i
$349$	−70.7682			−0.202774			−0.101387	−	0.994847i	$-0.532328\pi$
$349$	−70.7682			−0.202774			−0.101387	+	0.994847i	$0.532328\pi$
$350$	177.565	−	177.565i	0.507330	−	0.507330i
$351$	52.3670	+	52.3670i	0.149194	+	0.149194i
$352$	−336.085	+	336.085i	−0.954788	+	0.954788i
$353$	35.6639	+	35.6639i	0.101031	+	0.101031i	0.755816	−	0.654785i	$-0.227241\pi$
$353$	35.6639	+	35.6639i	0.101031	+	0.101031i	−0.654785	+	0.755816i	$0.727241\pi$
$354$		−	36.6634i		−	0.103569i
$355$	−486.867	+	486.867i	−1.37146	+	1.37146i
$356$	203.198	−	203.198i	0.570780	−	0.570780i
$357$	37.9466	+	37.9466i	0.106293	+	0.106293i
$358$			257.686i			0.719793i
$359$	−623.797			−1.73760			−0.868798	−	0.495168i	$-0.835107\pi$
$359$	−623.797			−1.73760			−0.868798	+	0.495168i	$0.835107\pi$
$360$			567.868i			1.57741i
$361$			349.679i			0.968640i
$362$	−142.939	−	142.939i	−0.394859	−	0.394859i
$363$		−	79.3475i		−	0.218588i
$364$	77.2724	+	77.2724i	0.212287	+	0.212287i
$365$	−460.347	−	460.347i	−1.26122	−	1.26122i
$366$	2.56137			0.00699827
$367$	−189.927			−0.517512			−0.258756	−	0.965943i	$-0.583313\pi$
$367$	−189.927			−0.517512			−0.258756	+	0.965943i	$0.583313\pi$
$368$	91.5884	−	91.5884i	0.248882	−	0.248882i
$369$		−	22.2375i		−	0.0602642i
$370$	355.649	+	202.465i	0.961214	+	0.547202i
$371$	221.471			0.596957
$372$	−7.08643	−	7.08643i	−0.0190496	−	0.0190496i
$373$		−	149.878i		−	0.401817i	−0.979610	−	0.200909i	$-0.935611\pi$
$373$		−	149.878i		−	0.401817i	0.979610	−	0.200909i	$-0.0643894\pi$
$374$			691.857i			1.84988i
$375$	10.9948	−	10.9948i	0.0293195	−	0.0293195i
$376$	201.137	−	201.137i	0.534938	−	0.534938i
$377$	313.011			0.830269
$378$	−39.2601	+	39.2601i	−0.103863	+	0.103863i
$379$	−226.618			−0.597937			−0.298968	−	0.954263i	$-0.596643\pi$
$379$	−226.618			−0.597937			−0.298968	+	0.954263i	$0.596643\pi$
$380$	−45.0428			−0.118534
$381$			50.1873i			0.131725i
$382$	−260.633			−0.682286
$383$	427.831	−	427.831i	1.11705	−	1.11705i	0.124879	−	0.992172i	$-0.460146\pi$
$383$	427.831	−	427.831i	1.11705	−	1.11705i	0.992172	−	0.124879i	$-0.0398543\pi$
$384$	3.68038	+	3.68038i	0.00958432	+	0.00958432i
$385$	−531.280	−	531.280i	−1.37995	−	1.37995i
$386$	−138.650			−0.359196
$387$	−168.489	+	168.489i	−0.435371	+	0.435371i
$388$	11.5353	+	11.5353i	0.0297303	+	0.0297303i
$389$	539.254	−	539.254i	1.38626	−	1.38626i	0.553223	−	0.833033i	$-0.313398\pi$
$389$	539.254	−	539.254i	1.38626	−	1.38626i	0.833033	−	0.553223i	$-0.186602\pi$
$390$	−32.4357	−	32.4357i	−0.0831683	−	0.0831683i
$391$			594.090i			1.51941i
$392$	111.214	−	111.214i	0.283709	−	0.283709i
$393$	34.3157	−	34.3157i	0.0873172	−	0.0873172i
$394$	−62.2671	−	62.2671i	−0.158038	−	0.158038i
$395$		−	418.619i		−	1.05979i
$396$	289.493			0.731043
$397$		−	249.597i		−	0.628707i	−0.949306	−	0.314354i	$-0.898212\pi$
$397$		−	249.597i		−	0.628707i	0.949306	−	0.314354i	$-0.101788\pi$
$398$		−	51.4248i		−	0.129208i
$399$	−4.98349	−	4.98349i	−0.0124899	−	0.0124899i
$400$		−	170.488i		−	0.426220i
$401$	−252.449	−	252.449i	−0.629550	−	0.629550i	0.318405	−	0.947955i	$-0.396853\pi$
$401$	−252.449	−	252.449i	−0.629550	−	0.629550i	−0.947955	+	0.318405i	$0.896853\pi$
$402$	17.5336	+	17.5336i	0.0436159	+	0.0436159i
$403$	−161.983			−0.401942
$404$	−130.997			−0.324251
$405$	406.568	−	406.568i	1.00387	−	1.00387i
$406$			234.668i			0.578000i
$407$	333.013	−	584.970i	0.818215	−	1.43727i
$408$	83.3088			0.204188
$409$	27.2406	+	27.2406i	0.0666030	+	0.0666030i	0.739624	−	0.673021i	$-0.235004\pi$
$409$	27.2406	+	27.2406i	0.0666030	+	0.0666030i	−0.673021	+	0.739624i	$0.735004\pi$
$410$			27.7695i			0.0677305i
$411$			5.71439i			0.0139036i
$412$	106.826	−	106.826i	0.259287	−	0.259287i
$413$	−256.153	+	256.153i	−0.620224	+	0.620224i
$414$	−304.869			−0.736399
$415$	−591.993	+	591.993i	−1.42649	+	1.42649i
$416$	286.711			0.689209
$417$	82.6183			0.198125
$418$		−	90.8607i		−	0.217370i
$419$	221.675			0.529058			0.264529	−	0.964378i	$-0.414783\pi$
$419$	221.675			0.529058			0.264529	+	0.964378i	$0.414783\pi$
$420$	−19.8279	+	19.8279i	−0.0472094	+	0.0472094i
$421$	138.621	+	138.621i	0.329266	+	0.329266i	0.852307	−	0.523041i	$-0.175203\pi$
$421$	138.621	+	138.621i	0.329266	+	0.329266i	−0.523041	+	0.852307i	$0.675203\pi$
$422$	−34.9458	−	34.9458i	−0.0828101	−	0.0828101i
$423$	−292.808			−0.692217
$424$	243.111	−	243.111i	0.573375	−	0.573375i
$425$	552.937	+	552.937i	1.30103	+	1.30103i
$426$	−36.6535	+	36.6535i	−0.0860410	+	0.0860410i
$427$	−17.8952	−	17.8952i	−0.0419092	−	0.0419092i
$428$		−	115.500i		−	0.269861i
$429$	−53.3500	+	53.3500i	−0.124359	+	0.124359i
$430$	210.403	−	210.403i	0.489310	−	0.489310i
$431$	−525.402	−	525.402i	−1.21903	−	1.21903i	−0.967972	−	0.251058i	$-0.919221\pi$
$431$	−525.402	−	525.402i	−1.21903	−	1.21903i	−0.251058	−	0.967972i	$-0.580779\pi$
$432$			37.6953i			0.0872576i
$433$	229.718			0.530527			0.265263	−	0.964176i	$-0.414541\pi$
$433$	229.718			0.530527			0.265263	+	0.964176i	$0.414541\pi$
$434$		−	121.440i		−	0.279816i
$435$			80.3181i			0.184639i
$436$	45.9935	+	45.9935i	0.105490	+	0.105490i
$437$		−	78.0212i		−	0.178538i
$438$	−34.6569	−	34.6569i	−0.0791254	−	0.0791254i
$439$	420.037	+	420.037i	0.956803	+	0.956803i	0.999105	−	0.0423019i	$-0.0134691\pi$
$439$	420.037	+	420.037i	0.956803	+	0.956803i	−0.0423019	+	0.999105i	$0.513469\pi$
$440$	−1166.38			−2.65087
$441$	−161.901			−0.367123
$442$	295.108	−	295.108i	0.667665	−	0.667665i
$443$			637.682i			1.43946i	0.694252	+	0.719732i	$0.255735\pi$
$443$			637.682i			1.43946i	−0.694252	+	0.719732i	$0.744265\pi$
$444$	−21.8317	−	12.4284i	−0.0491705	−	0.0279919i
$445$	1191.82			2.67826
$446$	−374.653	−	374.653i	−0.840029	−	0.840029i
$447$		−	84.8486i		−	0.189818i
$448$			338.790i			0.756228i
$449$	208.249	−	208.249i	0.463807	−	0.463807i	−0.436094	−	0.899901i	$-0.643639\pi$
$449$	208.249	−	208.249i	0.463807	−	0.463807i	0.899901	+	0.436094i	$0.143639\pi$
$450$	−283.750	+	283.750i	−0.630557	+	0.630557i
$451$	45.6752			0.101275
$452$	100.354	−	100.354i	0.222023	−	0.222023i
$453$	−83.3165			−0.183922
$454$	265.653			0.585139
$455$			453.229i			0.996109i
$456$	−10.9408			−0.0239931
$457$	167.982	−	167.982i	0.367576	−	0.367576i	−0.499017	−	0.866592i	$-0.666305\pi$
$457$	167.982	−	167.982i	0.367576	−	0.367576i	0.866592	+	0.499017i	$0.166305\pi$
$458$	247.623	+	247.623i	0.540662	+	0.540662i
$459$	−122.256	−	122.256i	−0.266352	−	0.266352i
$460$	−310.425			−0.674837
$461$	−579.698	+	579.698i	−1.25748	+	1.25748i	−0.305186	+	0.952293i	$0.598719\pi$
$461$	−579.698	+	579.698i	−1.25748	+	1.25748i	−0.952293	+	0.305186i	$0.901281\pi$
$462$	−39.9971	−	39.9971i	−0.0865738	−	0.0865738i
$463$	235.818	−	235.818i	0.509325	−	0.509325i	−0.404994	−	0.914319i	$-0.632726\pi$
$463$	235.818	−	235.818i	0.509325	−	0.509325i	0.914319	+	0.404994i	$0.132726\pi$
$464$	112.657	+	112.657i	0.242796	+	0.242796i
$465$		−	41.5644i		−	0.0893858i
$466$	35.2452	−	35.2452i	0.0756335	−	0.0756335i
$467$	−172.057	+	172.057i	−0.368430	+	0.368430i	−0.866905	−	0.498474i	$-0.833894\pi$
$467$	−172.057	+	172.057i	−0.368430	+	0.368430i	0.498474	+	0.866905i	$0.333894\pi$
$468$	−123.482	−	123.482i	−0.263850	−	0.263850i
$469$		−	245.000i		−	0.522389i
$470$	365.649			0.777977
$471$			31.2592i			0.0663678i
$472$			562.363i			1.19145i
$473$	−346.071	−	346.071i	−0.731651	−	0.731651i
$474$		−	31.5155i		−	0.0664883i
$475$	−72.6165	−	72.6165i	−0.152877	−	0.152877i
$476$	−180.400	−	180.400i	−0.378991	−	0.378991i
$477$	−353.912			−0.741954
$478$	11.2759			0.0235897
$479$	56.2384	−	56.2384i	0.117408	−	0.117408i	−0.645962	−	0.763370i	$-0.723543\pi$
$479$	56.2384	−	56.2384i	0.117408	−	0.117408i	0.763370	+	0.645962i	$0.223543\pi$
$480$			73.5694i			0.153270i
$481$	−391.561	+	107.471i	−0.814056	+	0.223432i
$482$	−555.753			−1.15301
$483$	−34.3451	−	34.3451i	−0.0711079	−	0.0711079i
$484$			377.221i			0.779382i
$485$			67.6588i			0.139503i
$486$	94.3578	−	94.3578i	0.194152	−	0.194152i
$487$	−152.415	+	152.415i	−0.312967	+	0.312967i	−0.846058	−	0.533091i	$-0.821030\pi$
$487$	−152.415	+	152.415i	−0.312967	+	0.312967i	0.533091	+	0.846058i	$0.321030\pi$
$488$	−39.2875			−0.0805072
$489$	52.6172	−	52.6172i	0.107602	−	0.107602i
$490$	202.177			0.412606
$491$	487.992			0.993874			0.496937	−	0.867786i	$-0.334458\pi$
$491$	487.992			0.993874			0.496937	+	0.867786i	$0.334458\pi$
$492$		−	1.70465i		−	0.00346473i
$493$	−730.754			−1.48226
$494$	−38.7561	+	38.7561i	−0.0784537	+	0.0784537i
$495$	848.989	+	848.989i	1.71513	+	1.71513i
$496$	−58.2998	−	58.2998i	−0.117540	−	0.117540i
$497$	512.166			1.03051
$498$	−44.5678	+	44.5678i	−0.0894937	+	0.0894937i
$499$	−588.787	−	588.787i	−1.17993	−	1.17993i	−0.979760	−	0.200174i	$-0.935849\pi$
$499$	−588.787	−	588.787i	−1.17993	−	1.17993i	−0.200174	−	0.979760i	$-0.564151\pi$
$500$	−52.2697	+	52.2697i	−0.104539	+	0.104539i
$501$	28.6993	+	28.6993i	0.0572840	+	0.0572840i
$502$			126.343i			0.251679i
$503$	−90.4426	+	90.4426i	−0.179806	+	0.179806i	−0.791271	−	0.611465i	$-0.790580\pi$
$503$	−90.4426	+	90.4426i	−0.179806	+	0.179806i	0.611465	+	0.791271i	$0.290580\pi$
$504$	298.688	−	298.688i	0.592635	−	0.592635i
$505$	−384.172	−	384.172i	−0.760737	−	0.760737i
$506$		−	626.192i		−	1.23753i
$507$	−18.3548			−0.0362027
$508$		−	238.592i		−	0.469670i
$509$			925.458i			1.81819i	0.416590	+	0.909094i	$0.363225\pi$
$509$			925.458i			1.81819i	−0.416590	+	0.909094i	$0.636775\pi$
$510$	75.7240	+	75.7240i	0.148478	+	0.148478i
$511$			484.268i			0.947686i
$512$	239.132	+	239.132i	0.467054	+	0.467054i
$513$	16.0557	+	16.0557i	0.0312976	+	0.0312976i
$514$	−217.642			−0.423428
$515$	626.573			1.21665
$516$	−12.9157	+	12.9157i	−0.0250305	+	0.0250305i
$517$		−	601.418i		−	1.16328i
$518$	−80.5721	−	293.558i	−0.155545	−	0.566714i
$519$	−29.9226			−0.0576544
$520$	497.515	+	497.515i	0.956759	+	0.956759i
$521$			87.8448i			0.168608i	0.996440	+	0.0843040i	$0.0268667\pi$
$521$			87.8448i			0.168608i	−0.996440	+	0.0843040i	$0.973133\pi$
$522$		−	375.001i		−	0.718393i
$523$	17.6675	−	17.6675i	0.0337811	−	0.0337811i	−0.690014	−	0.723796i	$-0.742396\pi$
$523$	17.6675	−	17.6675i	0.0337811	−	0.0337811i	0.723796	+	0.690014i	$0.242396\pi$
$524$	−163.138	+	163.138i	−0.311332	+	0.311332i
$525$	−63.9319			−0.121775
$526$	−243.987	+	243.987i	−0.463853	+	0.463853i
$527$	378.163			0.717577
$528$	−38.4029			−0.0727327
$529$		−	8.70501i		−	0.0164556i
$530$	441.955			0.833877
$531$	409.333	−	409.333i	0.770873	−	0.770873i
$532$	23.6917	+	23.6917i	0.0445332	+	0.0445332i
$533$	−19.4825	−	19.4825i	−0.0365525	−	0.0365525i
$534$	89.7258			0.168026
$535$	338.725	−	338.725i	0.633131	−	0.633131i
$536$	−268.939	−	268.939i	−0.501753	−	0.501753i
$537$	46.3895	−	46.3895i	0.0863865	−	0.0863865i
$538$	−192.998	−	192.998i	−0.358733	−	0.358733i
$539$		−	332.540i		−	0.616957i
$540$	63.8813	−	63.8813i	0.118299	−	0.118299i
$541$	89.2845	−	89.2845i	0.165036	−	0.165036i	−0.619757	−	0.784793i	$-0.712769\pi$
$541$	89.2845	−	89.2845i	0.165036	−	0.165036i	0.784793	+	0.619757i	$0.212769\pi$
$542$	−11.4461	−	11.4461i	−0.0211182	−	0.0211182i
$543$			51.4648i			0.0947786i
$544$	−669.353			−1.23043
$545$			269.768i			0.494987i
$546$			34.1211i			0.0624929i
$547$	−75.5441	−	75.5441i	−0.138106	−	0.138106i	0.634674	−	0.772780i	$-0.281134\pi$
$547$	−75.5441	−	75.5441i	−0.138106	−	0.138106i	−0.772780	+	0.634674i	$0.781134\pi$
$548$		−	27.1664i		−	0.0495738i
$549$	28.5967	+	28.5967i	0.0520887	+	0.0520887i
$550$	−582.815	−	582.815i	−1.05966	−	1.05966i
$551$	95.9691			0.174173
$552$	−75.4019			−0.136598
$553$	−220.186	+	220.186i	−0.398166	+	0.398166i
$554$			441.498i			0.796928i
$555$	−27.5768	−	100.474i	−0.0496880	−	0.181034i
$556$	−392.770			−0.706422
$557$	−154.792	−	154.792i	−0.277902	−	0.277902i	0.554369	−	0.832271i	$-0.312960\pi$
$557$	−154.792	−	154.792i	−0.277902	−	0.277902i	−0.832271	+	0.554369i	$0.812960\pi$
$558$			194.062i			0.347781i
$559$			295.229i			0.528138i
$560$	−163.124	+	163.124i	−0.291292	+	0.291292i
$561$	124.551	−	124.551i	0.222015	−	0.222015i
$562$	742.835			1.32177
$563$	−65.2182	+	65.2182i	−0.115840	+	0.115840i	−0.762651	−	0.646810i	$-0.776103\pi$
$563$	−65.2182	+	65.2182i	−0.115840	+	0.115840i	0.646810	+	0.762651i	$0.276103\pi$
$564$	−22.4456			−0.0397971
$565$	588.613			1.04179
$566$		−	641.554i		−	1.13349i
$567$	−427.695			−0.754311
$568$	562.210	−	562.210i	0.989806	−	0.989806i
$569$	511.812	+	511.812i	0.899494	+	0.899494i	0.995391	−	0.0958970i	$-0.0305719\pi$
$569$	511.812	+	511.812i	0.899494	+	0.899494i	−0.0958970	+	0.995391i	$0.530572\pi$
$570$	−9.94475	−	9.94475i	−0.0174469	−	0.0174469i
$571$	124.918			0.218771			0.109386	−	0.993999i	$-0.465112\pi$
$571$	124.918			0.218771			0.109386	+	0.993999i	$0.465112\pi$
$572$	253.628	−	253.628i	0.443405	−	0.443405i
$573$	46.9202	+	46.9202i	0.0818851	+	0.0818851i
$574$	14.6062	−	14.6062i	0.0254464	−	0.0254464i
$575$	−500.457	−	500.457i	−0.870361	−	0.870361i
$576$		−	541.389i		−	0.939911i
$577$	−86.4511	+	86.4511i	−0.149829	+	0.149829i	−0.778041	−	0.628213i	$-0.783787\pi$
$577$	−86.4511	+	86.4511i	−0.149829	+	0.149829i	0.628213	+	0.778041i	$0.283787\pi$
$578$	−385.617	+	385.617i	−0.667157	+	0.667157i
$579$	24.9602	+	24.9602i	0.0431092	+	0.0431092i
$580$		−	381.835i		−	0.658336i
$581$	622.755			1.07187
$582$			5.09365i			0.00875198i
$583$		−	726.925i		−	1.24687i
$584$	531.586	+	531.586i	0.910249	+	0.910249i
$585$		−	724.263i		−	1.23806i
$586$	85.9117	+	85.9117i	0.146607	+	0.146607i
$587$	500.633	+	500.633i	0.852867	+	0.852867i	0.990485	−	0.137619i	$-0.0439449\pi$
$587$	500.633	+	500.633i	0.852867	+	0.852867i	−0.137619	+	0.990485i	$0.543945\pi$
$588$	−12.4107			−0.0211067
$589$	−49.6637			−0.0843187
$590$	−511.163	+	511.163i	−0.866378	+	0.866378i
$591$			22.4191i			0.0379342i
$592$	−179.609	−	102.248i	−0.303393	−	0.172716i
$593$	−719.626			−1.21354			−0.606768	−	0.794879i	$-0.707534\pi$
$593$	−719.626			−1.21354			−0.606768	+	0.794879i	$0.707534\pi$
$594$	128.862	+	128.862i	0.216939	+	0.216939i
$595$		−	1058.11i		−	1.77833i
$596$			403.373i			0.676801i
$597$	−9.25768	+	9.25768i	−0.0155070	+	0.0155070i
$598$	−267.099	+	267.099i	−0.446654	+	0.446654i
$599$	−259.577			−0.433351			−0.216676	−	0.976244i	$-0.569521\pi$
$599$	−259.577			−0.433351			−0.216676	+	0.976244i	$0.569521\pi$
$600$	−70.1787	+	70.1787i	−0.116965	+	0.116965i
$601$	−292.942			−0.487424			−0.243712	−	0.969848i	$-0.578365\pi$
$601$	−292.942			−0.487424			−0.243712	+	0.969848i	$0.578365\pi$
$602$	−221.337			−0.367669
$603$			391.512i			0.649274i
$604$	396.090			0.655777
$605$	−1106.27	+	1106.27i	−1.82854	+	1.82854i
$606$	−28.9222	−	28.9222i	−0.0477263	−	0.0477263i
$607$	−315.803	−	315.803i	−0.520268	−	0.520268i	0.397384	−	0.917652i	$-0.369918\pi$
$607$	−315.803	−	315.803i	−0.520268	−	0.520268i	−0.917652	+	0.397384i	$0.869918\pi$
$608$	87.9053			0.144581
$609$	42.2458	−	42.2458i	0.0693692	−	0.0693692i
$610$	−35.7106	−	35.7106i	−0.0585420	−	0.0585420i
$611$	−256.532	+	256.532i	−0.419855	+	0.419855i
$612$	288.280	+	288.280i	0.471045	+	0.471045i
$613$			405.498i			0.661498i	0.943719	+	0.330749i	$0.107301\pi$
$613$			405.498i			0.661498i	−0.943719	+	0.330749i	$0.892699\pi$
$614$	−463.375	+	463.375i	−0.754682	+	0.754682i
$615$	4.99917	−	4.99917i	0.00812873	−	0.00812873i
$616$	613.496	+	613.496i	0.995935	+	0.995935i
$617$			327.089i			0.530128i	0.964231	+	0.265064i	$0.0853931\pi$
$617$			327.089i			0.530128i	−0.964231	+	0.265064i	$0.914607\pi$
$618$	47.1712			0.0763287
$619$			525.496i			0.848943i	0.905441	+	0.424472i	$0.139540\pi$
$619$			525.496i			0.848943i	−0.905441	+	0.424472i	$0.860460\pi$
$620$			197.599i			0.318707i
$621$	110.652	+	110.652i	0.178184	+	0.178184i
$622$			55.5932i			0.0893782i
$623$	−626.878	−	626.878i	−1.00622	−	1.00622i
$624$	16.3805	+	16.3805i	0.0262509	+	0.0262509i
$625$	456.465			0.730344
$626$	−632.182			−1.00988
$627$	−16.3571	+	16.3571i	−0.0260878	+	0.0260878i
$628$		−	148.608i		−	0.236636i
$629$	914.136	−	250.901i	1.45332	−	0.398888i
$630$	542.988			0.861886
$631$	517.188	+	517.188i	0.819632	+	0.819632i	0.986055	−	0.166422i	$-0.0532215\pi$
$631$	517.188	+	517.188i	0.819632	+	0.819632i	−0.166422	+	0.986055i	$0.553221\pi$
$632$			483.400i			0.764874i
$633$			12.5822i			0.0198770i
$634$	393.096	−	393.096i	0.620026	−	0.620026i
$635$	699.713	−	699.713i	1.10191	−	1.10191i
$636$	−27.1296			−0.0426566
$637$	−141.843	+	141.843i	−0.222674	+	0.222674i
$638$	770.241			1.20727
$639$	−818.444			−1.28082
$640$		−	102.624i		−	0.160350i
$641$	−1064.31			−1.66039			−0.830196	−	0.557472i	$-0.811772\pi$
$641$	−1064.31			−1.66039			−0.830196	+	0.557472i	$0.811772\pi$
$642$	25.5007	−	25.5007i	0.0397207	−	0.0397207i
$643$	−607.938	−	607.938i	−0.945470	−	0.945470i	0.0531178	−	0.998588i	$-0.483084\pi$
$643$	−607.938	−	607.938i	−0.945470	−	0.945470i	−0.998588	+	0.0531178i	$0.983084\pi$
$644$	163.278	+	163.278i	0.253537	+	0.253537i
$645$	−75.7552			−0.117450
$646$	90.4798	−	90.4798i	0.140062	−	0.140062i
$647$	506.664	+	506.664i	0.783097	+	0.783097i	0.980352	−	0.197255i	$-0.0632028\pi$
$647$	506.664	+	506.664i	0.783097	+	0.783097i	−0.197255	+	0.980352i	$0.563203\pi$
$648$	−469.485	+	469.485i	−0.724513	+	0.724513i
$649$	840.758	+	840.758i	1.29547	+	1.29547i
$650$			497.193i			0.764913i
$651$	−21.8621	+	21.8621i	−0.0335823	+	0.0335823i
$652$	−250.144	+	250.144i	−0.383657	+	0.383657i
$653$	124.218	+	124.218i	0.190226	+	0.190226i	0.795794	−	0.605568i	$-0.207054\pi$
$653$	124.218	+	124.218i	0.190226	+	0.190226i	−0.605568	+	0.795794i	$0.707054\pi$
$654$			20.3093i			0.0310540i
$655$	−956.860			−1.46085
$656$		−	14.0241i		−	0.0213781i
$657$		−	773.863i		−	1.17787i
$658$	−192.325	−	192.325i	−0.292287	−	0.292287i
$659$		−	454.252i		−	0.689305i	−0.938730	−	0.344653i	$-0.887997\pi$
$659$		−	454.252i		−	0.689305i	0.938730	−	0.344653i	$-0.112003\pi$
$660$	65.0804	+	65.0804i	0.0986067	+	0.0986067i
$661$	−389.416	−	389.416i	−0.589132	−	0.589132i	0.348265	−	0.937396i	$-0.386771\pi$
$661$	−389.416	−	389.416i	−0.589132	−	0.589132i	−0.937396	+	0.348265i	$0.886771\pi$
$662$	597.055			0.901896
$663$	−106.253			−0.160261
$664$	683.604	−	683.604i	1.02952	−	1.02952i
$665$			138.960i			0.208962i
$666$	128.755	+	469.107i	0.193325	+	0.704365i
$667$	661.398			0.991602
$668$	−136.437	−	136.437i	−0.204247	−	0.204247i
$669$			134.893i			0.201634i
$670$		−	488.908i		−	0.729714i
$671$	−58.7367	+	58.7367i	−0.0875361	+	0.0875361i
$672$	38.6961	−	38.6961i	0.0575835	−	0.0575835i
$673$	−25.6563			−0.0381222			−0.0190611	−	0.999818i	$-0.506068\pi$
$673$	−25.6563			−0.0381222			−0.0190611	+	0.999818i	$0.506068\pi$
$674$	428.872	−	428.872i	0.636309	−	0.636309i
$675$	205.975			0.305148
$676$	87.2593			0.129082
$677$		−	37.6324i		−	0.0555870i	−0.999614	−	0.0277935i	$-0.991152\pi$
$677$		−	37.6324i		−	0.0555870i	0.999614	−	0.0277935i	$-0.00884809\pi$
$678$	44.3134			0.0653590
$679$	35.5873	−	35.5873i	0.0524113	−	0.0524113i
$680$	−1161.49	−	1161.49i	−1.70808	−	1.70808i
$681$	−47.8239	−	47.8239i	−0.0702260	−	0.0702260i
$682$	−398.598			−0.584454
$683$	−136.128	+	136.128i	−0.199308	+	0.199308i	−0.799703	−	0.600395i	$-0.795010\pi$
$683$	−136.128	+	136.128i	−0.199308	+	0.199308i	0.600395	+	0.799703i	$0.295010\pi$
$684$	−37.8594	−	37.8594i	−0.0553500	−	0.0553500i
$685$	79.6702	−	79.6702i	0.116307	−	0.116307i
$686$	−391.407	−	391.407i	−0.570564	−	0.570564i
$687$		−	89.1561i		−	0.129776i
$688$	−106.257	+	106.257i	−0.154444	+	0.154444i
$689$	−310.066	+	310.066i	−0.450023	+	0.450023i
$690$	−68.5371	−	68.5371i	−0.0993291	−	0.0993291i
$691$			1141.32i			1.65170i	0.563890	+	0.825850i	$0.309304\pi$
$691$			1141.32i			1.65170i	−0.563890	+	0.825850i	$0.690696\pi$
$692$	142.253			0.205568
$693$		−	893.105i		−	1.28875i
$694$		−	356.331i		−	0.513445i
$695$	−1151.87	−	1151.87i	−1.65736	−	1.65736i
$696$		−	92.7474i		−	0.133258i
$697$	45.4837	+	45.4837i	0.0652564	+	0.0652564i
$698$	74.2795	+	74.2795i	0.106418	+	0.106418i
$699$	−12.6899			−0.0181544
$700$	303.935			0.434192
$701$	30.7153	−	30.7153i	0.0438163	−	0.0438163i	−0.684859	−	0.728675i	$-0.740136\pi$
$701$	30.7153	−	30.7153i	0.0438163	−	0.0438163i	0.728675	+	0.684859i	$0.240136\pi$
$702$		−	109.931i		−	0.156596i
$703$	−120.052	+	32.9505i	−0.170771	+	0.0468713i
$704$	1112.00			1.57954
$705$	−65.8255	−	65.8255i	−0.0933695	−	0.0933695i
$706$		−	74.8669i		−	0.106044i
$707$			404.135i			0.571619i
$708$	31.3780	−	31.3780i	0.0443192	−	0.0443192i
$709$	180.362	−	180.362i	0.254390	−	0.254390i	−0.568378	−	0.822768i	$-0.692429\pi$
$709$	180.362	−	180.362i	0.254390	−	0.254390i	0.822768	+	0.568378i	$0.192429\pi$
$710$	1022.05			1.43950
$711$	351.858	−	351.858i	0.494878	−	0.494878i
$712$	−1376.26			−1.93295
$713$	−342.272			−0.480044
$714$		−	79.6589i		−	0.111567i
$715$	1487.62			2.08058
$716$	−220.538	+	220.538i	−0.308013	+	0.308013i
$717$	−2.02992	−	2.02992i	−0.00283113	−	0.00283113i
$718$	654.748	+	654.748i	0.911905	+	0.911905i
$719$	−171.807			−0.238952			−0.119476	−	0.992837i	$-0.538122\pi$
$719$	−171.807			−0.238952			−0.119476	+	0.992837i	$0.538122\pi$
$720$	260.673	−	260.673i	0.362046	−	0.362046i
$721$	−329.566	−	329.566i	−0.457095	−	0.457095i
$722$	367.029	−	367.029i	0.508351	−	0.508351i
$723$	100.049	+	100.049i	0.138380	+	0.138380i
$724$		−	244.665i		−	0.337936i
$725$	615.582	−	615.582i	0.849079	−	0.849079i
$726$	−83.2845	+	83.2845i	−0.114717	+	0.114717i
$727$	304.684	+	304.684i	0.419098	+	0.419098i	0.884893	−	0.465795i	$-0.154232\pi$
$727$	304.684	+	304.684i	0.419098	+	0.419098i	−0.465795	+	0.884893i	$0.654232\pi$
$728$		−	523.367i		−	0.718910i
$729$	660.506			0.906043
$730$			966.376i			1.32380i
$731$		−	689.240i		−	0.942873i
$732$	2.19212	+	2.19212i	0.00299469	+	0.00299469i
$733$			641.352i			0.874968i	0.899226	+	0.437484i	$0.144130\pi$
$733$			641.352i			0.874968i	−0.899226	+	0.437484i	$0.855870\pi$
$734$	199.351	+	199.351i	0.271595	+	0.271595i
$735$	−36.3967	−	36.3967i	−0.0495193	−	0.0495193i
$736$	605.824			0.823131
$737$	−804.154			−1.09112
$738$	−23.3409	+	23.3409i	−0.0316272	+	0.0316272i
$739$			6.01293i			0.00813658i	0.999992	+	0.00406829i	$0.00129498\pi$
$739$			6.01293i			0.00813658i	−0.999992	+	0.00406829i	$0.998705\pi$
$740$	131.101	+	477.656i	0.177164	+	0.645481i
$741$	13.9541			0.0188314
$742$	−232.460	−	232.460i	−0.313288	−	0.313288i
$743$		−	529.715i		−	0.712941i	−0.934307	−	0.356471i	$-0.883980\pi$
$743$		−	529.715i		−	0.712941i	0.934307	−	0.356471i	$-0.116020\pi$
$744$			47.9965i			0.0645114i
$745$	−1182.96	+	1182.96i	−1.58787	+	1.58787i
$746$	−157.314	+	157.314i	−0.210877	+	0.210877i
$747$	−995.166			−1.33222
$748$	−592.118	+	592.118i	−0.791601	+	0.791601i
$749$	−356.326			−0.475736
$750$	−23.0807			−0.0307742
$751$		−	696.245i		−	0.927091i	−0.886073	−	0.463545i	$-0.846577\pi$
$751$		−	696.245i		−	0.927091i	0.886073	−	0.463545i	$-0.153423\pi$
$752$	−184.659			−0.245557
$753$	22.7447	−	22.7447i	0.0302054	−	0.0302054i
$754$	−328.542	−	328.542i	−0.435732	−	0.435732i
$755$	1161.60	+	1161.60i	1.53854	+	1.53854i
$756$	−67.2007			−0.0888898
$757$	−503.637	+	503.637i	−0.665306	+	0.665306i	−0.956626	−	0.291320i	$-0.905906\pi$
$757$	−503.637	+	503.637i	−0.665306	+	0.665306i	0.291320	+	0.956626i	$0.405906\pi$
$758$	237.862	+	237.862i	0.313802	+	0.313802i
$759$	−112.729	+	112.729i	−0.148524	+	0.148524i
$760$	152.538	+	152.538i	0.200707	+	0.200707i
$761$			246.317i			0.323676i	0.986817	+	0.161838i	$0.0517422\pi$
$761$			246.317i			0.323676i	−0.986817	+	0.161838i	$0.948258\pi$
$762$	52.6774	−	52.6774i	0.0691305	−	0.0691305i
$763$	141.893	−	141.893i	0.185967	−	0.185967i
$764$	−223.060	−	223.060i	−0.291964	−	0.291964i
$765$			1690.86i			2.21027i
$766$	−898.117			−1.17248
$767$		−	717.242i		−	0.935127i
$768$		−	100.124i		−	0.130370i
$769$	810.146	+	810.146i	1.05351	+	1.05351i	0.998485	+	0.0550210i	$0.0175226\pi$
$769$	810.146	+	810.146i	1.05351	+	1.05351i	0.0550210	+	0.998485i	$0.482477\pi$
$770$			1115.28i			1.44842i
$771$	39.1808	+	39.1808i	0.0508181	+	0.0508181i
$772$	−118.662	−	118.662i	−0.153707	−	0.153707i
$773$	294.190			0.380582			0.190291	−	0.981728i	$-0.439057\pi$
$773$	294.190			0.380582			0.190291	+	0.981728i	$0.439057\pi$
$774$	353.697			0.456973
$775$	−318.562	+	318.562i	−0.411048	+	0.411048i
$776$		−	78.1290i		−	0.100682i
$777$	−38.3424	+	67.3522i	−0.0493468	+	0.0866824i
$778$	−1132.02			−1.45504
$779$	−5.97332	−	5.97332i	−0.00766793	−	0.00766793i
$780$		−	55.5194i		−	0.0711787i
$781$		−	1681.06i		−	2.15245i
$782$	623.567	−	623.567i	0.797401	−	0.797401i
$783$	−136.107	+	136.107i	−0.173827	+	0.173827i
$784$	−102.103			−0.130233
$785$	435.817	−	435.817i	0.555181	−	0.555181i
$786$	−72.0366			−0.0916496
$787$	887.447			1.12763			0.563816	−	0.825900i	$-0.309333\pi$
$787$	887.447			1.12763			0.563816	+	0.825900i	$0.309333\pi$
$788$		−	106.581i		−	0.135255i
$789$	87.8467			0.111339
$790$	−439.389	+	439.389i	−0.556189	+	0.556189i
$791$	−309.600	−	309.600i	−0.391403	−	0.391403i
$792$	−980.370	−	980.370i	−1.23784	−	1.23784i
$793$	50.1077			0.0631875
$794$	−261.981	+	261.981i	−0.329951	+	0.329951i
$795$	−79.5623	−	79.5623i	−0.100078	−	0.100078i
$796$	44.0113	−	44.0113i	0.0552906	−	0.0552906i
$797$	−522.357	−	522.357i	−0.655404	−	0.655404i	0.298885	−	0.954289i	$-0.403385\pi$
$797$	−522.357	−	522.357i	−0.655404	−	0.655404i	−0.954289	+	0.298885i	$0.903385\pi$
$798$			10.4615i			0.0131097i
$799$	598.897	−	598.897i	0.749558	−	0.749558i
$800$	563.858	−	563.858i	0.704823	−	0.704823i
$801$	1001.75	+	1001.75i	1.25063	+	1.25063i
$802$			529.951i			0.660786i
$803$	1589.49			1.97944
$804$			30.0119i			0.0373282i
$805$			957.681i			1.18967i
$806$	170.020	+	170.020i	0.210943	+	0.210943i
$807$			69.4885i			0.0861072i
$808$	443.623	+	443.623i	0.549038	+	0.549038i
$809$	180.910	+	180.910i	0.223622	+	0.223622i	0.810022	−	0.586400i	$-0.199455\pi$
$809$	180.910	+	180.910i	0.223622	+	0.223622i	−0.586400	+	0.810022i	$0.699455\pi$
$810$	−853.482			−1.05368
$811$	914.793			1.12798			0.563991	−	0.825781i	$-0.309265\pi$
$811$	914.793			1.12798			0.563991	+	0.825781i	$0.309265\pi$
$812$	−200.838	+	200.838i	−0.247338	+	0.247338i
$813$			4.12112i			0.00506903i
$814$	−963.532	+	264.458i	−1.18370	+	0.324888i
$815$	−1467.18			−1.80022
$816$	−38.2419	−	38.2419i	−0.0468651	−	0.0468651i
$817$			90.5171i			0.110792i
$818$		−	57.1845i		−	0.0699077i
$819$	−380.949	+	380.949i	−0.465139	+	0.465139i
$820$	−23.7662	+	23.7662i	−0.0289832	+	0.0289832i
$821$	−1307.60			−1.59270			−0.796348	−	0.604839i	$-0.793237\pi$
$821$	−1307.60			−1.59270			−0.796348	+	0.604839i	$0.793237\pi$
$822$	5.99792	−	5.99792i	0.00729675	−	0.00729675i
$823$	71.3330			0.0866743			0.0433372	−	0.999061i	$-0.486201\pi$
$823$	71.3330			0.0866743			0.0433372	+	0.999061i	$0.486201\pi$
$824$	−723.535			−0.878077
$825$			209.841i			0.254353i
$826$	537.724			0.650998
$827$	−423.902	+	423.902i	−0.512578	+	0.512578i	−0.915316	−	0.402737i	$-0.868059\pi$
$827$	−423.902	+	423.902i	−0.512578	+	0.512578i	0.402737	+	0.915316i	$0.368059\pi$
$828$	−260.919	−	260.919i	−0.315120	−	0.315120i
$829$	139.431	+	139.431i	0.168191	+	0.168191i	0.786184	−	0.617993i	$-0.212054\pi$
$829$	139.431	+	139.431i	0.168191	+	0.168191i	−0.617993	+	0.786184i	$0.712054\pi$
$830$	1242.73			1.49727
$831$	79.4802	−	79.4802i	0.0956440	−	0.0956440i
$832$	−474.316	−	474.316i	−0.570091	−	0.570091i
$833$	331.146	−	331.146i	0.397534	−	0.397534i
$834$	−86.7176	−	86.7176i	−0.103978	−	0.103978i
$835$		−	800.252i		−	0.958386i
$836$	77.7621	−	77.7621i	0.0930169	−	0.0930169i
$837$	70.4348	−	70.4348i	0.0841515	−	0.0841515i
$838$	−232.674	−	232.674i	−0.277654	−	0.277654i
$839$		−	946.465i		−	1.12809i	−0.825745	−	0.564043i	$-0.809245\pi$
$839$		−	946.465i		−	1.12809i	0.825745	−	0.564043i	$-0.190755\pi$
$840$	134.295			0.159875
$841$		−	27.4541i		−	0.0326446i
$842$		−	290.998i		−	0.345604i
$843$	−133.728	−	133.728i	−0.158633	−	0.158633i
$844$		−	59.8160i		−	0.0708721i
$845$	255.903	+	255.903i	0.302844	+	0.302844i
$846$	307.336	+	307.336i	0.363281	+	0.363281i
$847$	1163.75			1.37397
$848$	−223.194			−0.263201
$849$	−115.495	+	115.495i	−0.136036	+	0.136036i
$850$		−	1160.74i		−	1.36558i
$851$	−827.375	+	227.088i	−0.972238	+	0.266848i
$852$	−62.7389			−0.0736372
$853$	−718.017	−	718.017i	−0.841755	−	0.841755i	0.147332	−	0.989087i	$-0.452931\pi$
$853$	−718.017	−	718.017i	−0.841755	−	0.841755i	−0.989087	+	0.147332i	$0.952931\pi$
$854$			37.5663i			0.0439886i
$855$		−	222.059i		−	0.259718i
$856$	−391.143	+	391.143i	−0.456943	+	0.456943i
$857$	241.022	−	241.022i	0.281239	−	0.281239i	−0.552364	−	0.833603i	$-0.686274\pi$
$857$	241.022	−	241.022i	0.281239	−	0.281239i	0.833603	+	0.552364i	$0.186274\pi$
$858$	111.994			0.130529
$859$	944.215	−	944.215i	1.09920	−	1.09920i	0.104698	−	0.994504i	$-0.466612\pi$
$859$	944.215	−	944.215i	1.09920	−	1.09920i	0.994504	−	0.104698i	$-0.0333877\pi$
$860$	360.143			0.418771
$861$	−5.25894			−0.00610794
$862$			1102.94i			1.27952i
$863$	1108.91			1.28495			0.642473	−	0.766309i	$-0.277909\pi$
$863$	1108.91			1.28495			0.642473	+	0.766309i	$0.277909\pi$
$864$	−124.670	+	124.670i	−0.144294	+	0.144294i
$865$	417.182	+	417.182i	0.482292	+	0.482292i
$866$	−241.116	−	241.116i	−0.278425	−	0.278425i
$867$	138.840			0.160139
$868$	103.933	−	103.933i	0.119739	−	0.119739i
$869$	722.706	+	722.706i	0.831652	+	0.831652i
$870$	84.3033	−	84.3033i	0.0969003	−	0.0969003i
$871$	343.008	+	343.008i	0.393809	+	0.393809i
$872$		−	311.515i		−	0.357242i
$873$	−56.8687	+	56.8687i	−0.0651417	+	0.0651417i
$874$	−81.8924	+	81.8924i	−0.0936984	+	0.0936984i
$875$	161.255	+	161.255i	0.184292	+	0.184292i
$876$		−	59.3215i		−	0.0677186i
$877$	−696.297			−0.793954			−0.396977	−	0.917829i	$-0.629941\pi$
$877$	−696.297			−0.793954			−0.396977	+	0.917829i	$0.629941\pi$
$878$		−	881.755i		−	1.00428i
$879$		−	30.9323i		−	0.0351903i
$880$	535.414	+	535.414i	0.608425	+	0.608425i
$881$		−	310.219i		−	0.352121i	−0.984379	−	0.176061i	$-0.943664\pi$
$881$		−	310.219i		−	0.352121i	0.984379	−	0.176061i	$-0.0563355\pi$
$882$	169.934	+	169.934i	0.192669	+	0.192669i
$883$	534.700	+	534.700i	0.605549	+	0.605549i	0.941780	−	0.336231i	$-0.109152\pi$
$883$	534.700	+	534.700i	0.605549	+	0.605549i	−0.336231	+	0.941780i	$0.609152\pi$
$884$	505.129			0.571413
$885$	184.043			0.207958
$886$	669.322	−	669.322i	0.755443	−	0.755443i
$887$			474.335i			0.534764i	0.963591	+	0.267382i	$0.0861585\pi$
$887$			474.335i			0.534764i	−0.963591	+	0.267382i	$0.913841\pi$
$888$	31.8443	+	116.022i	0.0358607	+	0.130656i
$889$	−736.072			−0.827977
$890$	−1250.96	−	1250.96i	−1.40557	−	1.40557i
$891$			1403.80i			1.57554i
$892$		−	641.285i		−	0.718930i
$893$	−78.6524	+	78.6524i	−0.0880766	+	0.0880766i
$894$	−89.0585	+	89.0585i	−0.0996181	+	0.0996181i
$895$	−1293.53			−1.44528
$896$	−53.9783	+	53.9783i	−0.0602436	+	0.0602436i
$897$	96.1683			0.107211
$898$	−437.164			−0.486820
$899$		−	421.008i		−	0.468307i
$900$	−485.690			−0.539655
$901$	723.878	−	723.878i	0.803416	−	0.803416i
$902$	−47.9414	−	47.9414i	−0.0531501	−	0.0531501i
$903$	39.8458	+	39.8458i	0.0441261	+	0.0441261i
$904$	−679.701			−0.751882
$905$	717.524	−	717.524i	0.792844	−	0.792844i
$906$	87.4504	+	87.4504i	0.0965236	+	0.0965236i
$907$	−729.638	+	729.638i	−0.804452	+	0.804452i	−0.983788	−	0.179336i	$-0.942605\pi$
$907$	−729.638	+	729.638i	−0.804452	+	0.804452i	0.179336	+	0.983788i	$0.442605\pi$
$908$	227.356	+	227.356i	0.250393	+	0.250393i
$909$		−	645.810i		−	0.710462i
$910$	475.717	−	475.717i	0.522766	−	0.522766i
$911$	199.232	−	199.232i	0.218696	−	0.218696i	−0.589253	−	0.807949i	$-0.700578\pi$
$911$	199.232	−	199.232i	0.218696	−	0.218696i	0.807949	+	0.589253i	$0.200578\pi$
$912$	5.02226	+	5.02226i	0.00550687	+	0.00550687i
$913$		−	2044.04i		−	2.23882i
$914$	−352.634			−0.385814
$915$			12.8575i			0.0140519i
$916$			423.851i			0.462720i
$917$	503.291	+	503.291i	0.548845	+	0.548845i
$918$			256.643i			0.279568i
$919$	−77.9734	−	77.9734i	−0.0848459	−	0.0848459i	0.663410	−	0.748256i	$-0.269109\pi$
$919$	−77.9734	−	77.9734i	−0.0848459	−	0.0848459i	−0.748256	+	0.663410i	$0.769109\pi$
$920$	1051.26	+	1051.26i	1.14267	+	1.14267i
$921$	166.837			0.181148
$922$	1216.92			1.31987
$923$	−717.047	+	717.047i	−0.776866	+	0.776866i
$924$		−	68.4622i		−	0.0740932i
$925$	−558.704	+	981.419i	−0.604005	+	1.06099i
$926$	−495.037			−0.534597
$927$	526.648	+	526.648i	0.568121	+	0.568121i
$928$			745.188i			0.803004i
$929$		−	1756.58i		−	1.89083i	−0.325870	−	0.945415i	$-0.605657\pi$
$929$		−	1756.58i		−	1.89083i	0.325870	−	0.945415i	$-0.394343\pi$
$930$	−43.6267	+	43.6267i	−0.0469104	+	0.0469104i
$931$	−43.4890	+	43.4890i	−0.0467122	+	0.0467122i
$932$	60.3285			0.0647301
$933$	10.0081	−	10.0081i	0.0107268	−	0.0107268i
$934$	361.188			0.386711
$935$	−3472.98			−3.71441
$936$			836.343i			0.893529i
$937$	−1070.63			−1.14261			−0.571306	−	0.820737i	$-0.693563\pi$
$937$	−1070.63			−1.14261			−0.571306	+	0.820737i	$0.693563\pi$
$938$	−257.157	+	257.157i	−0.274154	+	0.274154i
$939$	113.808	+	113.808i	0.121201	+	0.121201i
$940$	312.937	+	312.937i	0.332911	+	0.332911i
$941$	1074.54			1.14191			0.570957	−	0.820980i	$-0.306572\pi$
$941$	1074.54			1.14191			0.570957	+	0.820980i	$0.306572\pi$
$942$	32.8102	−	32.8102i	0.0348304	−	0.0348304i
$943$	−41.1668	−	41.1668i	−0.0436552	−	0.0436552i
$944$	258.146	−	258.146i	0.273459	−	0.273459i
$945$	−197.078	−	197.078i	−0.208548	−	0.208548i
$946$			726.484i			0.767953i
$947$	−129.643	+	129.643i	−0.136899	+	0.136899i	−0.772236	−	0.635336i	$-0.780861\pi$
$947$	−129.643	+	129.643i	−0.136899	+	0.136899i	0.635336	+	0.772236i	$0.280861\pi$
$948$	26.9722	−	26.9722i	0.0284516	−	0.0284516i
$949$	−677.989	−	677.989i	−0.714425	−	0.714425i
$950$			152.439i			0.160462i
$951$	−141.533			−0.148826
$952$			1221.85i			1.28345i
$953$			502.255i			0.527025i	0.964656	+	0.263512i	$0.0848810\pi$
$953$			502.255i			0.527025i	−0.964656	+	0.263512i	$0.915119\pi$
$954$	371.472	+	371.472i	0.389384	+	0.389384i
$955$		−	1308.32i		−	1.36997i
$956$	9.65032	+	9.65032i	0.0100945	+	0.0100945i
$957$	−138.662	−	138.662i	−0.144892	−	0.144892i
$958$	−118.058			−0.123233
$959$	−83.8101			−0.0873932
$960$	121.709	−	121.709i	0.126780	−	0.126780i
$961$		−	743.130i		−	0.773288i
$962$	523.793	+	298.186i	0.544483	+	0.309965i
$963$	569.412			0.591289
$964$	−475.635	−	475.635i	−0.493398	−	0.493398i
$965$		−	695.992i		−	0.721236i
$966$			72.0984i			0.0746361i
$967$	−85.0575	+	85.0575i	−0.0879602	+	0.0879602i	−0.749718	−	0.661758i	$-0.769811\pi$
$967$	−85.0575	+	85.0575i	−0.0879602	+	0.0879602i	0.661758	+	0.749718i	$0.269811\pi$
$968$	1277.46	−	1277.46i	1.31969	−	1.31969i
$969$	−32.5770			−0.0336192
$970$	71.0159	−	71.0159i	0.0732122	−	0.0732122i
$971$	−496.661			−0.511494			−0.255747	−	0.966744i	$-0.582321\pi$
$971$	−496.661			−0.511494			−0.255747	+	0.966744i	$0.582321\pi$
$972$	161.510			0.166163
$973$			1211.72i			1.24535i
$974$	319.955			0.328496
$975$	89.5066	−	89.5066i	0.0918016	−	0.0918016i
$976$	18.0345	+	18.0345i	0.0184779	+	0.0184779i
$977$	1186.94	+	1186.94i	1.21488	+	1.21488i	0.969402	+	0.245479i	$0.0789451\pi$
$977$	1186.94	+	1186.94i	1.21488	+	1.21488i	0.245479	+	0.969402i	$0.421055\pi$
$978$	−110.456			−0.112941
$979$	−2057.57	+	2057.57i	−2.10171	+	2.10171i
$980$	173.031	+	173.031i	0.176562	+	0.176562i
$981$	−226.746	+	226.746i	−0.231137	+	0.231137i
$982$	−512.205	−	512.205i	−0.521594	−	0.521594i
$983$			1471.76i			1.49721i	0.663017	+	0.748605i	$0.269276\pi$
$983$			1471.76i			1.49721i	−0.663017	+	0.748605i	$0.730724\pi$
$984$	−5.77279	+	5.77279i	−0.00586666	+	0.00586666i
$985$	312.568	−	312.568i	0.317328	−	0.317328i
$986$	767.012	+	767.012i	0.777903	+	0.777903i
$987$			69.2460i			0.0701580i
$988$	−66.3381			−0.0671438
$989$			623.824i			0.630763i
$990$		−	1782.23i		−	1.80023i
$991$	672.226	+	672.226i	0.678331	+	0.678331i	0.959622	−	0.281291i	$-0.0907628\pi$
$991$	672.226	+	672.226i	0.678331	+	0.678331i	−0.281291	+	0.959622i	$0.590763\pi$
$992$		−	385.633i		−	0.388743i
$993$	−107.484	−	107.484i	−0.108242	−	0.108242i
$994$	−537.578	−	537.578i	−0.540823	−	0.540823i
$995$	258.142			0.259439
$996$	−76.2858			−0.0765922
$997$	−584.483	+	584.483i	−0.586242	+	0.586242i	−0.936611	−	0.350370i	$-0.886056\pi$
$997$	−584.483	+	584.483i	−0.586242	+	0.586242i	0.350370	+	0.936611i	$0.386056\pi$
$998$			1236.00i			1.23848i
$999$	123.531	−	216.994i	0.123655	−	0.217211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.3.d.a.31.3	yes	12
3.2	odd	2		333.3.i.a.253.4		12
4.3	odd	2		592.3.k.e.401.3		12
37.6	odd	4	inner	37.3.d.a.6.3	✓	12
111.80	even	4		333.3.i.a.154.4		12
148.43	even	4		592.3.k.e.561.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.3.d.a.6.3	✓	12	37.6	odd	4	inner
37.3.d.a.31.3	yes	12	1.1	even	1	trivial
333.3.i.a.154.4		12	111.80	even	4
333.3.i.a.253.4		12	3.2	odd	2
592.3.k.e.401.3		12	4.3	odd	2
592.3.k.e.561.4		12	148.43	even	4

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04962 - 1.04962i) q^{2} +0.377912i q^{3} -1.79661i q^{4} +(5.26886 - 5.26886i) q^{5} +(0.396663 - 0.396663i) q^{6} -5.54265 q^{7} +(-6.08422 + 6.08422i) q^{8} +8.85718 q^{9} +O(q^{10})\)	\(q+(-1.04962 - 1.04962i) q^{2} +0.377912i q^{3} -1.79661i q^{4} +(5.26886 - 5.26886i) q^{5} +(0.396663 - 0.396663i) q^{6} -5.54265 q^{7} +(-6.08422 + 6.08422i) q^{8} +8.85718 q^{9} -11.0606 q^{10} +18.1924i q^{11} +0.678959 q^{12} +(7.75987 - 7.75987i) q^{13} +(5.81766 + 5.81766i) q^{14} +(1.99117 + 1.99117i) q^{15} +5.58578 q^{16} +(-18.1161 + 18.1161i) q^{17} +(-9.29665 - 9.29665i) q^{18} +(2.37917 - 2.37917i) q^{19} +(-9.46607 - 9.46607i) q^{20} -2.09463i q^{21} +(19.0950 - 19.0950i) q^{22} +(16.3967 - 16.3967i) q^{23} +(-2.29930 - 2.29930i) q^{24} -30.5218i q^{25} -16.2898 q^{26} +6.74844i q^{27} +9.95796i q^{28} +(20.1686 + 20.1686i) q^{29} -4.17992i q^{30} +(-10.4372 - 10.4372i) q^{31} +(18.4739 + 18.4739i) q^{32} -6.87512 q^{33} +38.0300 q^{34} +(-29.2034 + 29.2034i) q^{35} -15.9129i q^{36} +(-32.1547 - 18.3051i) q^{37} -4.99444 q^{38} +(2.93255 + 2.93255i) q^{39} +64.1138i q^{40} -2.51067i q^{41} +(-2.19856 + 2.19856i) q^{42} +(-19.0228 + 19.0228i) q^{43} +32.6846 q^{44} +(46.6673 - 46.6673i) q^{45} -34.4206 q^{46} -33.0588 q^{47} +2.11093i q^{48} -18.2791 q^{49} +(-32.0362 + 32.0362i) q^{50} +(-6.84630 - 6.84630i) q^{51} +(-13.9414 - 13.9414i) q^{52} -39.9577 q^{53} +(7.08328 - 7.08328i) q^{54} +(95.8532 + 95.8532i) q^{55} +(33.7227 - 33.7227i) q^{56} +(0.899117 + 0.899117i) q^{57} -42.3387i q^{58} +(46.2148 - 46.2148i) q^{59} +(3.57734 - 3.57734i) q^{60} +(3.22864 + 3.22864i) q^{61} +21.9101i q^{62} -49.0922 q^{63} -61.1243i q^{64} -81.7713i q^{65} +(7.21625 + 7.21625i) q^{66} +44.2028i q^{67} +(32.5476 + 32.5476i) q^{68} +(6.19652 + 6.19652i) q^{69} +61.3049 q^{70} -92.4046 q^{71} +(-53.8890 + 53.8890i) q^{72} -87.3712i q^{73} +(14.5368 + 52.9635i) q^{74} +11.5346 q^{75} +(-4.27443 - 4.27443i) q^{76} -100.834i q^{77} -6.15610i q^{78} +(39.7257 - 39.7257i) q^{79} +(29.4307 - 29.4307i) q^{80} +77.1643 q^{81} +(-2.63525 + 2.63525i) q^{82} -112.357 q^{83} -3.76323 q^{84} +190.903i q^{85} +39.9334 q^{86} +(-7.62196 + 7.62196i) q^{87} +(-110.686 - 110.686i) q^{88} +(113.101 + 113.101i) q^{89} -97.9655 q^{90} +(-43.0102 + 43.0102i) q^{91} +(-29.4585 - 29.4585i) q^{92} +(3.94434 - 3.94434i) q^{93} +(34.6991 + 34.6991i) q^{94} -25.0710i q^{95} +(-6.98153 + 6.98153i) q^{96} +(-6.42063 + 6.42063i) q^{97} +(19.1860 + 19.1860i) q^{98} +161.133i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9	\( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9} - 16 q^{10} + 64 q^{12} + 14 q^{13} - 70 q^{14} - 2 q^{15} - 96 q^{16} + 2 q^{17} + 132 q^{18} + 14 q^{19} - 24 q^{20} + 22 q^{22} + 56 q^{23} - 84 q^{24} - 48 q^{26} + 60 q^{29} + 72 q^{31} + 208 q^{32} + 56 q^{33} + 112 q^{34} - 154 q^{35} - 66 q^{37} - 336 q^{38} - 46 q^{39} + 90 q^{42} + 70 q^{43} + 80 q^{44} + 232 q^{45} - 424 q^{46} - 384 q^{47} + 144 q^{49} - 34 q^{50} - 126 q^{51} + 328 q^{52} - 56 q^{53} - 194 q^{54} + 70 q^{55} + 16 q^{56} - 94 q^{57} + 184 q^{59} + 276 q^{60} + 132 q^{61} - 400 q^{63} + 614 q^{66} + 116 q^{68} + 368 q^{69} + 556 q^{70} + 68 q^{71} - 692 q^{72} - 382 q^{74} + 116 q^{75} + 12 q^{76} - 2 q^{79} + 4 q^{80} - 76 q^{81} + 374 q^{82} + 108 q^{83} - 1436 q^{84} + 140 q^{86} - 420 q^{87} - 788 q^{88} + 278 q^{89} - 664 q^{90} - 450 q^{91} + 652 q^{92} + 584 q^{93} + 118 q^{94} + 1584 q^{96} - 244 q^{97} + 416 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^5 + 6 * q^6 - 4 * q^7 + 36 * q^8 - 60 * q^9 - 16 * q^10 + 64 * q^12 + 14 * q^13 - 70 * q^14 - 2 * q^15 - 96 * q^16 + 2 * q^17 + 132 * q^18 + 14 * q^19 - 24 * q^20 + 22 * q^22 + 56 * q^23 - 84 * q^24 - 48 * q^26 + 60 * q^29 + 72 * q^31 + 208 * q^32 + 56 * q^33 + 112 * q^34 - 154 * q^35 - 66 * q^37 - 336 * q^38 - 46 * q^39 + 90 * q^42 + 70 * q^43 + 80 * q^44 + 232 * q^45 - 424 * q^46 - 384 * q^47 + 144 * q^49 - 34 * q^50 - 126 * q^51 + 328 * q^52 - 56 * q^53 - 194 * q^54 + 70 * q^55 + 16 * q^56 - 94 * q^57 + 184 * q^59 + 276 * q^60 + 132 * q^61 - 400 * q^63 + 614 * q^66 + 116 * q^68 + 368 * q^69 + 556 * q^70 + 68 * q^71 - 692 * q^72 - 382 * q^74 + 116 * q^75 + 12 * q^76 - 2 * q^79 + 4 * q^80 - 76 * q^81 + 374 * q^82 + 108 * q^83 - 1436 * q^84 + 140 * q^86 - 420 * q^87 - 788 * q^88 + 278 * q^89 - 664 * q^90 - 450 * q^91 + 652 * q^92 + 584 * q^93 + 118 * q^94 + 1584 * q^96 - 244 * q^97 + 416 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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