LMFDB - Embedded newform 333.3.i.a.154.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(154,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("333.154");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.i (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:	$9.07359280320$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			154.4
Root			$-0.0496173 + 0.0496173i$ of defining polynomial
Character	$\chi$	$=$	333.154
Dual form			333.3.i.a.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04962 - 1.04962i) q^{2} +1.79661i q^{4} +(-5.26886 - 5.26886i) q^{5} -5.54265 q^{7} +(6.08422 + 6.08422i) q^{8} +O(q^{10})$	\(q+(1.04962 - 1.04962i) q^{2} +1.79661i q^{4} +(-5.26886 - 5.26886i) q^{5} -5.54265 q^{7} +(6.08422 + 6.08422i) q^{8} -11.0606 q^{10} +18.1924i q^{11} +(7.75987 + 7.75987i) q^{13} +(-5.81766 + 5.81766i) q^{14} +5.58578 q^{16} +(18.1161 + 18.1161i) q^{17} +(2.37917 + 2.37917i) q^{19} +(9.46607 - 9.46607i) q^{20} +(19.0950 + 19.0950i) q^{22} +(-16.3967 - 16.3967i) q^{23} +30.5218i q^{25} +16.2898 q^{26} -9.95796i q^{28} +(-20.1686 + 20.1686i) q^{29} +(-10.4372 + 10.4372i) q^{31} +(-18.4739 + 18.4739i) q^{32} +38.0300 q^{34} +(29.2034 + 29.2034i) q^{35} +(-32.1547 + 18.3051i) q^{37} +4.99444 q^{38} -64.1138i q^{40} -2.51067i q^{41} +(-19.0228 - 19.0228i) q^{43} -32.6846 q^{44} -34.4206 q^{46} +33.0588 q^{47} -18.2791 q^{49} +(32.0362 + 32.0362i) q^{50} +(-13.9414 + 13.9414i) q^{52} +39.9577 q^{53} +(95.8532 - 95.8532i) q^{55} +(-33.7227 - 33.7227i) q^{56} +42.3387i q^{58} +(-46.2148 - 46.2148i) q^{59} +(3.22864 - 3.22864i) q^{61} +21.9101i q^{62} +61.1243i q^{64} -81.7713i q^{65} -44.2028i q^{67} +(-32.5476 + 32.5476i) q^{68} +61.3049 q^{70} +92.4046 q^{71} +87.3712i q^{73} +(-14.5368 + 52.9635i) q^{74} +(-4.27443 + 4.27443i) q^{76} -100.834i q^{77} +(39.7257 + 39.7257i) q^{79} +(-29.4307 - 29.4307i) q^{80} +(-2.63525 - 2.63525i) q^{82} +112.357 q^{83} -190.903i q^{85} -39.9334 q^{86} +(-110.686 + 110.686i) q^{88} +(-113.101 + 113.101i) q^{89} +(-43.0102 - 43.0102i) q^{91} +(29.4585 - 29.4585i) q^{92} +(34.6991 - 34.6991i) q^{94} -25.0710i q^{95} +(-6.42063 - 6.42063i) q^{97} +(-19.1860 + 19.1860i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 36 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 36 * q^8	$ 12 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 36 q^{8} - 16 q^{10} + 14 q^{13} + 70 q^{14} - 96 q^{16} - 2 q^{17} + 14 q^{19} + 24 q^{20} + 22 q^{22} - 56 q^{23} + 48 q^{26} - 60 q^{29} + 72 q^{31} - 208 q^{32} + 112 q^{34} + 154 q^{35} - 66 q^{37} + 336 q^{38} + 70 q^{43} - 80 q^{44} - 424 q^{46} + 384 q^{47} + 144 q^{49} + 34 q^{50} + 328 q^{52} + 56 q^{53} + 70 q^{55} - 16 q^{56} - 184 q^{59} + 132 q^{61} - 116 q^{68} + 556 q^{70} - 68 q^{71} + 382 q^{74} + 12 q^{76} - 2 q^{79} - 4 q^{80} + 374 q^{82} - 108 q^{83} - 140 q^{86} - 788 q^{88} - 278 q^{89} - 450 q^{91} - 652 q^{92} + 118 q^{94} - 244 q^{97} - 416 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 36 * q^8 - 16 * q^10 + 14 * q^13 + 70 * q^14 - 96 * q^16 - 2 * q^17 + 14 * q^19 + 24 * q^20 + 22 * q^22 - 56 * q^23 + 48 * q^26 - 60 * q^29 + 72 * q^31 - 208 * q^32 + 112 * q^34 + 154 * q^35 - 66 * q^37 + 336 * q^38 + 70 * q^43 - 80 * q^44 - 424 * q^46 + 384 * q^47 + 144 * q^49 + 34 * q^50 + 328 * q^52 + 56 * q^53 + 70 * q^55 - 16 * q^56 - 184 * q^59 + 132 * q^61 - 116 * q^68 + 556 * q^70 - 68 * q^71 + 382 * q^74 + 12 * q^76 - 2 * q^79 - 4 * q^80 + 374 * q^82 - 108 * q^83 - 140 * q^86 - 788 * q^88 - 278 * q^89 - 450 * q^91 - 652 * q^92 + 118 * q^94 - 244 * q^97 - 416 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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	$-0.628982\pi$
$2$	1.04962	−	1.04962i	0.524809	−	0.524809i	0.919020	+	0.394211i	$0.128982\pi$
$3$		0			0
$3$		0			0
$4$			1.79661i			0.449152i
$5$	−5.26886	−	5.26886i	−1.05377	−	1.05377i	−0.998470	−	0.0553026i	$-0.982388\pi$
$5$	−5.26886	−	5.26886i	−1.05377	−	1.05377i	−0.0553026	−	0.998470i	$-0.517612\pi$
$6$		0			0
$7$	−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
$9$		0			0
$10$	−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			0
$13$	7.75987	+	7.75987i	0.596913	+	0.596913i	0.939490	−	0.342577i	$-0.111300\pi$
$13$	7.75987	+	7.75987i	0.596913	+	0.596913i	−0.342577	+	0.939490i	$0.611300\pi$
$14$	−5.81766	+	5.81766i	−0.415547	+	0.415547i
$15$		0			0
$16$	5.58578			0.349111
$17$	18.1161	+	18.1161i	1.06565	+	1.06565i	0.997688	+	0.0679669i	$0.0216512\pi$
$17$	18.1161	+	18.1161i	1.06565	+	1.06565i	0.0679669	+	0.997688i	$0.478349\pi$
$18$		0			0
$19$	2.37917	+	2.37917i	0.125219	+	0.125219i	0.766939	−	0.641720i	$-0.221779\pi$
$19$	2.37917	+	2.37917i	0.125219	+	0.125219i	−0.641720	+	0.766939i	$0.721779\pi$
$20$	9.46607	−	9.46607i	0.473304	−	0.473304i
$21$		0			0
$22$	19.0950	+	19.0950i	0.867957	+	0.867957i
$23$	−16.3967	−	16.3967i	−0.712901	−	0.712901i	0.254240	−	0.967141i	$-0.418175\pi$
$23$	−16.3967	−	16.3967i	−0.712901	−	0.712901i	−0.967141	+	0.254240i	$0.918175\pi$
$24$		0			0
$25$			30.5218i			1.22087i
$26$	16.2898			0.626530
$27$		0			0
$28$		−	9.95796i		−	0.355641i
$29$	−20.1686	+	20.1686i	−0.695469	+	0.695469i	−0.963430	−	0.267960i	$-0.913650\pi$
$29$	−20.1686	+	20.1686i	−0.695469	+	0.695469i	0.267960	+	0.963430i	$0.413650\pi$
$30$		0			0
$31$	−10.4372	+	10.4372i	−0.336684	+	0.336684i	−0.855118	−	0.518434i	$-0.826515\pi$
$31$	−10.4372	+	10.4372i	−0.336684	+	0.336684i	0.518434	+	0.855118i	$0.326515\pi$
$32$	−18.4739	+	18.4739i	−0.577311	+	0.577311i
$33$		0			0
$34$	38.0300			1.11853
$35$	29.2034	+	29.2034i	0.834384	+	0.834384i
$36$		0			0
$37$	−32.1547	+	18.3051i	−0.869045	+	0.494732i
$37$	−32.1547	+	18.3051i	−0.869045	+	0.494732i
$38$	4.99444			0.131433
$39$		0			0
$40$		−	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	$-0.00974753\pi$
$42$		0			0
$43$	−19.0228	−	19.0228i	−0.442391	−	0.442391i	0.450424	−	0.892815i	$-0.351273\pi$
$43$	−19.0228	−	19.0228i	−0.442391	−	0.442391i	−0.892815	+	0.450424i	$0.851273\pi$
$44$	−32.6846			−0.742831
$45$		0			0
$46$	−34.4206			−0.748273
$47$	33.0588			0.703378			0.351689	−	0.936117i	$-0.385607\pi$
$47$	33.0588			0.703378			0.351689	+	0.936117i	$0.385607\pi$
$48$		0			0
$49$	−18.2791			−0.373042
$50$	32.0362	+	32.0362i	0.640724	+	0.640724i
$51$		0			0
$52$	−13.9414	+	13.9414i	−0.268104	+	0.268104i
$53$	39.9577			0.753918			0.376959	−	0.926230i	$-0.376970\pi$
$53$	39.9577			0.753918			0.376959	+	0.926230i	$0.376970\pi$
$54$		0			0
$55$	95.8532	−	95.8532i	1.74278	−	1.74278i
$56$	−33.7227	−	33.7227i	−0.602191	−	0.602191i
$57$		0			0
$58$			42.3387i			0.729977i
$59$	−46.2148	−	46.2148i	−0.783303	−	0.783303i	0.197084	−	0.980387i	$-0.436853\pi$
$59$	−46.2148	−	46.2148i	−0.783303	−	0.783303i	−0.980387	+	0.197084i	$0.936853\pi$
$60$		0			0
$61$	3.22864	−	3.22864i	0.0529286	−	0.0529286i	−0.680147	−	0.733076i	$-0.738084\pi$
$61$	3.22864	−	3.22864i	0.0529286	−	0.0529286i	0.733076	+	0.680147i	$0.238084\pi$
$62$			21.9101i			0.353389i
$63$		0			0
$64$			61.1243i			0.955066i
$65$		−	81.7713i		−	1.25802i
$66$		0			0
$67$		−	44.2028i		−	0.659743i	−0.944026	−	0.329872i	$-0.892995\pi$
$67$		−	44.2028i		−	0.659743i	0.944026	−	0.329872i	$-0.107005\pi$
$68$	−32.5476	+	32.5476i	−0.478641	+	0.478641i
$69$		0			0
$70$	61.3049			0.875784
$71$	92.4046			1.30147			0.650736	−	0.759304i	$-0.274460\pi$
$71$	92.4046			1.30147			0.650736	+	0.759304i	$0.274460\pi$
$72$		0			0
$73$			87.3712i			1.19687i	0.801173	+	0.598433i	$0.204210\pi$
$73$			87.3712i			1.19687i	−0.801173	+	0.598433i	$0.795790\pi$
$74$	−14.5368	+	52.9635i	−0.196443	+	0.715722i
$75$		0			0
$76$	−4.27443	+	4.27443i	−0.0562425	+	0.0562425i
$77$		−	100.834i		−	1.30953i
$78$		0			0
$79$	39.7257	+	39.7257i	0.502857	+	0.502857i	0.912325	−	0.409467i	$-0.134285\pi$
$79$	39.7257	+	39.7257i	0.502857	+	0.502857i	−0.409467	+	0.912325i	$0.634285\pi$
$80$	−29.4307	−	29.4307i	−0.367883	−	0.367883i
$81$		0			0
$82$	−2.63525	−	2.63525i	−0.0321372	−	0.0321372i
$83$	112.357			1.35370			0.676849	−	0.736122i	$-0.263345\pi$
$83$	112.357			1.35370			0.676849	+	0.736122i	$0.263345\pi$
$84$		0			0
$85$		−	190.903i		−	2.24591i
$86$	−39.9334			−0.464342
$87$		0			0
$88$	−110.686	+	110.686i	−1.25780	+	1.25780i
$89$	−113.101	+	113.101i	−1.27080	+	1.27080i	−0.325124	+	0.945671i	$0.605406\pi$
$89$	−113.101	+	113.101i	−1.27080	+	1.27080i	−0.945671	+	0.325124i	$0.894594\pi$
$90$		0			0
$91$	−43.0102	−	43.0102i	−0.472639	−	0.472639i
$92$	29.4585	−	29.4585i	0.320201	−	0.320201i
$93$		0			0
$94$	34.6991	−	34.6991i	0.369139	−	0.369139i
$95$		−	25.0710i		−	0.263906i
$96$		0			0
$97$	−6.42063	−	6.42063i	−0.0661921	−	0.0661921i	0.673236	−	0.739428i	$-0.264904\pi$
$97$	−6.42063	−	6.42063i	−0.0661921	−	0.0661921i	−0.739428	+	0.673236i	$0.764904\pi$
$98$	−19.1860	+	19.1860i	−0.195776	+	0.195776i
$99$		0			0
$100$	−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	$-0.117551\pi$
$102$		0			0
$103$	59.4600	−	59.4600i	0.577282	−	0.577282i	−0.356872	−	0.934153i	$-0.616157\pi$
$103$	59.4600	−	59.4600i	0.577282	−	0.577282i	0.934153	+	0.356872i	$0.116157\pi$
$104$			94.4255i			0.907937i
$105$		0			0
$106$	41.9402	−	41.9402i	0.395663	−	0.395663i
$107$	−64.2881			−0.600824			−0.300412	−	0.953810i	$-0.597124\pi$
$107$	−64.2881			−0.600824			−0.300412	+	0.953810i	$0.597124\pi$
$108$		0			0
$109$	−25.6002	−	25.6002i	−0.234864	−	0.234864i	0.579855	−	0.814720i	$-0.303109\pi$
$109$	−25.6002	−	25.6002i	−0.234864	−	0.234864i	−0.814720	+	0.579855i	$0.803109\pi$
$110$		−	201.218i		−	1.82926i
$111$		0			0
$112$	−30.9600			−0.276428
$113$	−55.8577	+	55.8577i	−0.494316	+	0.494316i	−0.909663	−	0.415347i	$-0.863660\pi$
$113$	−55.8577	+	55.8577i	−0.494316	+	0.494316i	0.415347	+	0.909663i	$0.363660\pi$
$114$		0			0
$115$			172.784i			1.50247i
$116$	−36.2351	−	36.2351i	−0.312371	−	0.312371i
$117$		0			0
$118$	−97.0158			−0.822168
$119$	−100.411	−	100.411i	−0.843792	−	0.843792i
$120$		0			0
$121$	−209.963			−1.73523
$122$		−	6.77768i		−	0.0555547i
$123$		0			0
$124$	−18.7515	−	18.7515i	−0.151222	−	0.151222i
$125$	29.0936	−	29.0936i	0.232749	−	0.232749i
$126$		0			0
$127$	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
$129$		0			0
$130$	−85.8286	−	85.8286i	−0.660220	−	0.660220i
$131$	90.8033	−	90.8033i	0.693155	−	0.693155i	−0.269770	−	0.962925i	$-0.586948\pi$
$131$	90.8033	−	90.8033i	0.693155	−	0.693155i	0.962925	+	0.269770i	$0.0869476\pi$
$132$		0			0
$133$	−13.1869	−	13.1869i	−0.0991496	−	0.0991496i
$134$	−46.3960	−	46.3960i	−0.346239	−	0.346239i
$135$		0			0
$136$			220.445i			1.62092i
$137$	−15.1210			−0.110372			−0.0551860	−	0.998476i	$-0.517575\pi$
$137$	−15.1210			−0.110372			−0.0551860	+	0.998476i	$0.517575\pi$
$138$		0			0
$139$			218.618i			1.57279i	0.617724	+	0.786395i	$0.288055\pi$
$139$			218.618i			1.57279i	−0.617724	+	0.786395i	$0.711945\pi$
$140$	−52.4671	+	52.4671i	−0.374765	+	0.374765i
$141$		0			0
$142$	96.9894	−	96.9894i	0.683024	−	0.683024i
$143$	−141.170	+	141.170i	−0.987206	+	0.987206i
$144$		0			0
$145$	212.531			1.46573
$146$	91.7063	+	91.7063i	0.628126	+	0.628126i
$147$		0			0
$148$	−32.8871	−	57.7693i	−0.222210	−	0.390333i
$149$	224.519			1.50684			0.753421	−	0.657539i	$-0.228402\pi$
$149$	224.519			1.50684			0.753421	+	0.657539i	$0.228402\pi$
$150$		0			0
$151$		−	220.465i		−	1.46004i	−0.683428	−	0.730018i	$-0.739512\pi$
$151$		−	220.465i		−	1.46004i	0.683428	−	0.730018i	$-0.260488\pi$
$152$			28.9508i			0.190466i
$153$		0			0
$154$	−105.837	−	105.837i	−0.687254	−	0.687254i
$155$	109.984			0.709576
$156$		0			0
$157$	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
$159$		0			0
$160$	194.673			1.21671
$161$	90.8812	+	90.8812i	0.564480	+	0.564480i
$162$		0			0
$163$	−139.231	+	139.231i	−0.854180	+	0.854180i	−0.990645	−	0.136465i	$-0.956426\pi$
$163$	−139.231	+	139.231i	−0.854180	+	0.854180i	0.136465	+	0.990645i	$0.456426\pi$
$164$	4.51069			0.0275042
$165$		0			0
$166$	117.932	−	117.932i	0.710433	−	0.710433i
$167$	−75.9417	−	75.9417i	−0.454741	−	0.454741i	0.442184	−	0.896924i	$-0.354204\pi$
$167$	−75.9417	−	75.9417i	−0.454741	−	0.454741i	−0.896924	+	0.442184i	$0.854204\pi$
$168$		0			0
$169$		−	48.5690i		−	0.287390i
$170$	−200.375	−	200.375i	−1.17868	−	1.17868i
$171$		0			0
$172$	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	$0.926507\pi$
$174$		0			0
$175$		−	169.171i		−	0.966694i
$176$			101.619i			0.577378i
$177$		0			0
$178$			237.425i			1.33385i
$179$	122.752	−	122.752i	0.685767	−	0.685767i	−0.275527	−	0.961293i	$-0.588852\pi$
$179$	122.752	−	122.752i	0.685767	−	0.685767i	0.961293	+	0.275527i	$0.0888522\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$		−	199.523i		−	1.08436i
$185$	265.866	+	72.9715i	1.43711	+	0.394441i
$186$		0			0
$187$	−329.576	+	329.576i	−1.76244	+	1.76244i
$188$			59.3936i			0.315924i
$189$		0			0
$190$	−26.3150	−	26.3150i	−0.138500	−	0.138500i
$191$	−124.156	−	124.156i	−0.650033	−	0.650033i	0.302968	−	0.953001i	$-0.402023\pi$
$191$	−124.156	−	124.156i	−0.650033	−	0.650033i	−0.953001	+	0.302968i	$0.902023\pi$
$192$		0			0
$193$	66.0477	+	66.0477i	0.342216	+	0.342216i	0.857200	−	0.514984i	$-0.172202\pi$
$193$	66.0477	+	66.0477i	0.342216	+	0.342216i	−0.514984	+	0.857200i	$0.672202\pi$
$194$	−13.4784			−0.0694763
$195$		0			0
$196$		−	32.8403i		−	0.167553i
$197$	−59.3236			−0.301135			−0.150568	−	0.988600i	$-0.548110\pi$
$197$	−59.3236			−0.301135			−0.150568	+	0.988600i	$0.548110\pi$
$198$		0			0
$199$	24.4969	−	24.4969i	0.123100	−	0.123100i	−0.642873	−	0.765973i	$-0.722258\pi$
$199$	24.4969	−	24.4969i	0.123100	−	0.123100i	0.765973	+	0.642873i	$0.222258\pi$
$200$	−185.701	+	185.701i	−0.928506	+	0.928506i
$201$		0			0
$202$	−76.5315	−	76.5315i	−0.378869	−	0.378869i
$203$	111.787	−	111.787i	0.550677	−	0.550677i
$204$		0			0
$205$	−13.2284	+	13.2284i	−0.0645287	+	0.0645287i
$206$		−	124.821i		−	0.605925i
$207$		0			0
$208$	43.3449	+	43.3449i	0.208389	+	0.208389i
$209$	−43.2828	+	43.2828i	−0.207095	+	0.207095i
$210$		0			0
$211$	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
$213$		0			0
$214$	−67.4779	+	67.4779i	−0.315317	+	0.315317i
$215$			200.457i			0.932360i
$216$		0			0
$217$	57.8497	−	57.8497i	0.266588	−	0.266588i
$218$	−53.7409			−0.246518
$219$		0			0
$220$	172.210	+	172.210i	0.782775	+	0.782775i
$221$			281.157i			1.27221i
$222$		0			0
$223$	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
$225$		0			0
$226$			117.258i			0.518843i
$227$	126.548	+	126.548i	0.557479	+	0.557479i	0.928589	−	0.371110i	$-0.121023\pi$
$227$	126.548	+	126.548i	0.557479	+	0.557479i	−0.371110	+	0.928589i	$0.621023\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$	−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	$0.977043\pi$
$234$		0			0
$235$	−174.182	−	174.182i	−0.741200	−	0.741200i
$236$	83.0299	−	83.0299i	0.351822	−	0.351822i
$237$		0			0
$238$	−210.787			−0.885659
$239$	5.37141	+	5.37141i	0.0224745	+	0.0224745i	0.718255	−	0.695780i	$-0.244941\pi$
$239$	5.37141	+	5.37141i	0.0224745	+	0.0224745i	−0.695780	+	0.718255i	$0.744941\pi$
$240$		0			0
$241$	264.741	+	264.741i	1.09851	+	1.09851i	0.994585	+	0.103924i	$0.0331400\pi$
$241$	264.741	+	264.741i	1.09851	+	1.09851i	0.103924	+	0.994585i	$0.466860\pi$
$242$	−220.381	+	220.381i	−0.910664	+	0.910664i
$243$		0			0
$244$	5.80060	+	5.80060i	0.0237730	+	0.0237730i
$245$	96.3099	+	96.3099i	0.393102	+	0.393102i
$246$		0			0
$247$			36.9241i			0.149490i
$248$	−127.004			−0.512115
$249$		0			0
$250$		−	61.0742i		−	0.244297i
$251$	60.1852	−	60.1852i	0.239782	−	0.239782i	−0.576978	−	0.816760i	$-0.695768\pi$
$251$	60.1852	−	60.1852i	0.239782	−	0.239782i	0.816760	+	0.576978i	$0.195768\pi$
$252$		0			0
$253$	298.296	−	298.296i	1.17903	−	1.17903i
$254$	139.391	−	139.391i	0.548783	−	0.548783i
$255$		0			0
$256$	−264.941			−1.03493
$257$	−103.677	−	103.677i	−0.403412	−	0.403412i	0.476021	−	0.879434i	$-0.342078\pi$
$257$	−103.677	−	103.677i	−0.403412	−	0.403412i	−0.879434	+	0.476021i	$0.842078\pi$
$258$		0			0
$259$	178.222	−	101.459i	0.688116	−	0.391732i
$260$	146.911			0.565042
$261$		0			0
$262$		−	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	$-0.145704\pi$
$264$		0			0
$265$	−210.531	−	210.531i	−0.794458	−	0.794458i
$266$	−27.6824			−0.104069
$267$		0			0
$268$	79.4150			0.296325
$269$	−183.875			−0.683550			−0.341775	−	0.939782i	$-0.611028\pi$
$269$	−183.875			−0.683550			−0.341775	+	0.939782i	$0.611028\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$	−15.8712	+	15.8712i	−0.0579242	+	0.0579242i
$275$	−555.264			−2.01914
$276$		0			0
$277$	−210.314	+	210.314i	−0.759256	+	0.759256i	−0.976187	−	0.216931i	$-0.930395\pi$
$277$	−210.314	+	210.314i	−0.759256	+	0.759256i	0.216931	+	0.976187i	$0.430395\pi$
$278$	229.465	+	229.465i	0.825414	+	0.825414i
$279$		0			0
$280$			355.360i			1.26914i
$281$	353.860	+	353.860i	1.25929	+	1.25929i	0.951433	+	0.307856i	$0.0996114\pi$
$281$	353.860	+	353.860i	1.25929	+	1.25929i	0.307856	+	0.951433i	$0.400389\pi$
$282$		0			0
$283$	305.613	−	305.613i	1.07991	−	1.07991i	0.0833885	−	0.996517i	$-0.473426\pi$
$283$	305.613	−	305.613i	1.07991	−	1.07991i	0.996517	−	0.0833885i	$-0.0265742\pi$
$284$			166.015i			0.584559i
$285$		0			0
$286$			296.350i			1.03619i
$287$			13.9158i			0.0484870i
$288$		0			0
$289$			367.388i			1.27124i
$290$	223.076	−	223.076i	0.769229	−	0.769229i
$291$		0			0
$292$	−156.972			−0.537574
$293$	81.8505			0.279353			0.139677	−	0.990197i	$-0.455394\pi$
$293$	81.8505			0.279353			0.139677	+	0.990197i	$0.455394\pi$
$294$		0			0
$295$			486.999i			1.65084i
$296$	−307.008	−	84.2639i	−1.03719	−	0.284675i
$297$		0			0
$298$	235.659	−	235.659i	0.790804	−	0.790804i
$299$		−	254.473i		−	0.851079i
$300$		0			0
$301$	105.437	+	105.437i	0.350288	+	0.350288i
$302$	−231.404	−	231.404i	−0.766239	−	0.766239i
$303$		0			0
$304$	13.2895	+	13.2895i	0.0437155	+	0.0437155i
$305$	−34.0225			−0.111549
$306$		0			0
$307$			441.470i			1.43801i	0.695003	+	0.719007i	$0.255403\pi$
$307$			441.470i			1.43801i	−0.695003	+	0.719007i	$0.744597\pi$
$308$	181.159			0.588179
$309$		0			0
$310$	115.441	−	115.441i	0.372392	−	0.372392i
$311$	26.4826	−	26.4826i	0.0851531	−	0.0851531i	−0.663247	−	0.748400i	$-0.730822\pi$
$311$	26.4826	−	26.4826i	0.0851531	−	0.0851531i	0.748400	+	0.663247i	$0.230822\pi$
$312$		0			0
$313$	301.149	+	301.149i	0.962137	+	0.962137i	0.999309	−	0.0371719i	$-0.0118349\pi$
$313$	301.149	+	301.149i	0.962137	+	0.962137i	−0.0371719	+	0.999309i	$0.511835\pi$
$314$	86.8198	−	86.8198i	0.276496	−	0.276496i
$315$		0			0
$316$	−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	$0.798845\pi$
$318$		0			0
$319$	−366.915	−	366.915i	−1.15020	−	1.15020i
$320$	322.055	−	322.055i	1.00642	−	1.00642i
$321$		0			0
$322$	190.781			0.592488
$323$			86.2027i			0.266881i
$324$		0			0
$325$	−236.845	+	236.845i	−0.728754	+	0.728754i
$326$			292.279i			0.896562i
$327$		0			0
$328$	15.2755	−	15.2755i	0.0465716	−	0.0465716i
$329$	−183.233			−0.556939
$330$		0			0
$331$	−284.416	−	284.416i	−0.859261	−	0.859261i	0.131990	−	0.991251i	$-0.457863\pi$
$331$	−284.416	−	284.416i	−0.859261	−	0.859261i	−0.991251	+	0.131990i	$0.957863\pi$
$332$			201.861i			0.608016i
$333$		0			0
$334$	−159.419			−0.477304
$335$	−232.898	+	232.898i	−0.695219	+	0.695219i
$336$		0			0
$337$		−	408.598i		−	1.21246i	−0.795290	−	0.606229i	$-0.792681\pi$
$337$		−	408.598i		−	1.21246i	0.795290	−	0.606229i	$-0.207319\pi$
$338$	−50.9788	−	50.9788i	−0.150825	−	0.150825i
$339$		0			0
$340$	342.977			1.00876
$341$	−189.878	−	189.878i	−0.556826	−	0.556826i
$342$		0			0
$343$	372.904			1.08718
$344$		−	231.478i		−	0.672902i
$345$		0			0
$346$	83.1075	+	83.1075i	0.240195	+	0.240195i
$347$	−169.743	+	169.743i	−0.489173	+	0.489173i	−0.908045	−	0.418872i	$-0.862426\pi$
$347$	−169.743	+	169.743i	−0.489173	+	0.489173i	0.418872	+	0.908045i	$0.362426\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$	−336.085	−	336.085i	−0.954788	−	0.954788i
$353$	−35.6639	+	35.6639i	−0.101031	+	0.101031i	−0.755816	−	0.654785i	$-0.772759\pi$
$353$	−35.6639	+	35.6639i	−0.101031	+	0.101031i	0.654785	+	0.755816i	$0.272759\pi$
$354$		0			0
$355$	−486.867	−	486.867i	−1.37146	−	1.37146i
$356$	−203.198	−	203.198i	−0.570780	−	0.570780i
$357$		0			0
$358$		−	257.686i		−	0.719793i
$359$	623.797			1.73760			0.868798	−	0.495168i	$-0.164893\pi$
$359$	623.797			1.73760			0.868798	+	0.495168i	$0.164893\pi$
$360$		0			0
$361$		−	349.679i		−	0.968640i
$362$	142.939	−	142.939i	0.394859	−	0.394859i
$363$		0			0
$364$	77.2724	−	77.2724i	0.212287	−	0.212287i
$365$	460.347	−	460.347i	1.26122	−	1.26122i
$366$		0			0
$367$	−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
$369$		0			0
$370$	355.649	−	202.465i	0.961214	−	0.547202i
$371$	−221.471			−0.596957
$372$		0			0
$373$			149.878i			0.401817i	0.979610	+	0.200909i	$0.0643894\pi$
$373$			149.878i			0.401817i	−0.979610	+	0.200909i	$0.935611\pi$
$374$			691.857i			1.84988i
$375$		0			0
$376$	201.137	+	201.137i	0.534938	+	0.534938i
$377$	−313.011			−0.830269
$378$		0			0
$379$	−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
$381$		0			0
$382$	−260.633			−0.682286
$383$	−427.831	−	427.831i	−1.11705	−	1.11705i	−0.992172	−	0.124879i	$-0.960146\pi$
$383$	−427.831	−	427.831i	−1.11705	−	1.11705i	−0.124879	−	0.992172i	$-0.539854\pi$
$384$		0			0
$385$	−531.280	+	531.280i	−1.37995	+	1.37995i
$386$	138.650			0.359196
$387$		0			0
$388$	11.5353	−	11.5353i	0.0297303	−	0.0297303i
$389$	−539.254	−	539.254i	−1.38626	−	1.38626i	−0.833033	−	0.553223i	$-0.813398\pi$
$389$	−539.254	−	539.254i	−1.38626	−	1.38626i	−0.553223	−	0.833033i	$-0.686602\pi$
$390$		0			0
$391$		−	594.090i		−	1.51941i
$392$	−111.214	−	111.214i	−0.283709	−	0.283709i
$393$		0			0
$394$	−62.2671	+	62.2671i	−0.158038	+	0.158038i
$395$		−	418.619i		−	1.05979i
$396$		0			0
$397$			249.597i			0.628707i	0.949306	+	0.314354i	$0.101788\pi$
$397$			249.597i			0.628707i	−0.949306	+	0.314354i	$0.898212\pi$
$398$		−	51.4248i		−	0.129208i
$399$		0			0
$400$			170.488i			0.426220i
$401$	252.449	−	252.449i	0.629550	−	0.629550i	−0.318405	−	0.947955i	$-0.603147\pi$
$401$	252.449	−	252.449i	0.629550	−	0.629550i	0.947955	+	0.318405i	$0.103147\pi$
$402$		0			0
$403$	−161.983			−0.401942
$404$	130.997			0.324251
$405$		0			0
$406$		−	234.668i		−	0.578000i
$407$	−333.013	−	584.970i	−0.818215	−	1.43727i
$408$		0			0
$409$	27.2406	−	27.2406i	0.0666030	−	0.0666030i	−0.673021	−	0.739624i	$-0.735004\pi$
$409$	27.2406	−	27.2406i	0.0666030	−	0.0666030i	0.739624	+	0.673021i	$0.235004\pi$
$410$			27.7695i			0.0677305i
$411$		0			0
$412$	106.826	+	106.826i	0.259287	+	0.259287i
$413$	256.153	+	256.153i	0.620224	+	0.620224i
$414$		0			0
$415$	−591.993	−	591.993i	−1.42649	−	1.42649i
$416$	−286.711			−0.689209
$417$		0			0
$418$			90.8607i			0.217370i
$419$	−221.675			−0.529058			−0.264529	−	0.964378i	$-0.585217\pi$
$419$	−221.675			−0.529058			−0.264529	+	0.964378i	$0.585217\pi$
$420$		0			0
$421$	138.621	−	138.621i	0.329266	−	0.329266i	−0.523041	−	0.852307i	$-0.675203\pi$
$421$	138.621	−	138.621i	0.329266	−	0.329266i	0.852307	+	0.523041i	$0.175203\pi$
$422$	34.9458	−	34.9458i	0.0828101	−	0.0828101i
$423$		0			0
$424$	243.111	+	243.111i	0.573375	+	0.573375i
$425$	−552.937	+	552.937i	−1.30103	+	1.30103i
$426$		0			0
$427$	−17.8952	+	17.8952i	−0.0419092	+	0.0419092i
$428$		−	115.500i		−	0.269861i
$429$		0			0
$430$	210.403	+	210.403i	0.489310	+	0.489310i
$431$	525.402	−	525.402i	1.21903	−	1.21903i	0.251058	−	0.967972i	$-0.419221\pi$
$431$	525.402	−	525.402i	1.21903	−	1.21903i	0.967972	−	0.251058i	$-0.0807787\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	45.9935	−	45.9935i	0.105490	−	0.105490i
$437$		−	78.0212i		−	0.178538i
$438$		0			0
$439$	420.037	−	420.037i	0.956803	−	0.956803i	−0.0423019	−	0.999105i	$-0.513469\pi$
$439$	420.037	−	420.037i	0.956803	−	0.956803i	0.999105	+	0.0423019i	$0.0134691\pi$
$440$	1166.38			2.65087
$441$		0			0
$442$	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	$0.744265\pi$
$444$		0			0
$445$	1191.82			2.67826
$446$	374.653	−	374.653i	0.840029	−	0.840029i
$447$		0			0
$448$		−	338.790i		−	0.756228i
$449$	−208.249	−	208.249i	−0.463807	−	0.463807i	0.436094	−	0.899901i	$-0.356361\pi$
$449$	−208.249	−	208.249i	−0.463807	−	0.463807i	−0.899901	+	0.436094i	$0.856361\pi$
$450$		0			0
$451$	45.6752			0.101275
$452$	−100.354	−	100.354i	−0.222023	−	0.222023i
$453$		0			0
$454$	265.653			0.585139
$455$			453.229i			0.996109i
$456$		0			0
$457$	167.982	+	167.982i	0.367576	+	0.367576i	0.866592	−	0.499017i	$-0.166305\pi$
$457$	167.982	+	167.982i	0.367576	+	0.367576i	−0.499017	+	0.866592i	$0.666305\pi$
$458$	−247.623	+	247.623i	−0.540662	+	0.540662i
$459$		0			0
$460$	−310.425			−0.674837
$461$	579.698	+	579.698i	1.25748	+	1.25748i	0.952293	+	0.305186i	$0.0987186\pi$
$461$	579.698	+	579.698i	1.25748	+	1.25748i	0.305186	+	0.952293i	$0.401281\pi$
$462$		0			0
$463$	235.818	+	235.818i	0.509325	+	0.509325i	0.914319	−	0.404994i	$-0.132726\pi$
$463$	235.818	+	235.818i	0.509325	+	0.509325i	−0.404994	+	0.914319i	$0.632726\pi$
$464$	−112.657	+	112.657i	−0.242796	+	0.242796i
$465$		0			0
$466$	35.2452	+	35.2452i	0.0756335	+	0.0756335i
$467$	172.057	+	172.057i	0.368430	+	0.368430i	0.866905	−	0.498474i	$-0.166106\pi$
$467$	172.057	+	172.057i	0.368430	+	0.368430i	−0.498474	+	0.866905i	$0.666106\pi$
$468$		0			0
$469$			245.000i			0.522389i
$470$	−365.649			−0.777977
$471$		0			0
$472$		−	562.363i		−	1.19145i
$473$	346.071	−	346.071i	0.731651	−	0.731651i
$474$		0			0
$475$	−72.6165	+	72.6165i	−0.152877	+	0.152877i
$476$	180.400	−	180.400i	0.378991	−	0.378991i
$477$		0			0
$478$	11.2759			0.0235897
$479$	−56.2384	−	56.2384i	−0.117408	−	0.117408i	0.645962	−	0.763370i	$-0.276457\pi$
$479$	−56.2384	−	56.2384i	−0.117408	−	0.117408i	−0.763370	+	0.645962i	$0.776457\pi$
$480$		0			0
$481$	−391.561	−	107.471i	−0.814056	−	0.223432i
$482$	555.753			1.15301
$483$		0			0
$484$		−	377.221i		−	0.779382i
$485$			67.6588i			0.139503i
$486$		0			0
$487$	−152.415	−	152.415i	−0.312967	−	0.312967i	0.533091	−	0.846058i	$-0.321030\pi$
$487$	−152.415	−	152.415i	−0.312967	−	0.312967i	−0.846058	+	0.533091i	$0.821030\pi$
$488$	39.2875			0.0805072
$489$		0			0
$490$	202.177			0.412606
$491$	−487.992			−0.993874			−0.496937	−	0.867786i	$-0.665542\pi$
$491$	−487.992			−0.993874			−0.496937	+	0.867786i	$0.665542\pi$
$492$		0			0
$493$	−730.754			−1.48226
$494$	38.7561	+	38.7561i	0.0784537	+	0.0784537i
$495$		0			0
$496$	−58.2998	+	58.2998i	−0.117540	+	0.117540i
$497$	−512.166			−1.03051
$498$		0			0
$499$	−588.787	+	588.787i	−1.17993	+	1.17993i	−0.200174	+	0.979760i	$0.564151\pi$
$499$	−588.787	+	588.787i	−1.17993	+	1.17993i	−0.979760	+	0.200174i	$0.935849\pi$
$500$	52.2697	+	52.2697i	0.104539	+	0.104539i
$501$		0			0
$502$		−	126.343i		−	0.251679i
$503$	90.4426	+	90.4426i	0.179806	+	0.179806i	0.791271	−	0.611465i	$-0.209420\pi$
$503$	90.4426	+	90.4426i	0.179806	+	0.179806i	−0.611465	+	0.791271i	$0.709420\pi$
$504$		0			0
$505$	−384.172	+	384.172i	−0.760737	+	0.760737i
$506$		−	626.192i		−	1.23753i
$507$		0			0
$508$			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	$0.636775\pi$
$510$		0			0
$511$		−	484.268i		−	0.947686i
$512$	−239.132	+	239.132i	−0.467054	+	0.467054i
$513$		0			0
$514$	−217.642			−0.423428
$515$	−626.573			−1.21665
$516$		0			0
$517$			601.418i			1.16328i
$518$	80.5721	−	293.558i	0.155545	−	0.566714i
$519$		0			0
$520$	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	$0.973133\pi$
$522$		0			0
$523$	17.6675	+	17.6675i	0.0337811	+	0.0337811i	0.723796	−	0.690014i	$-0.242396\pi$
$523$	17.6675	+	17.6675i	0.0337811	+	0.0337811i	−0.690014	+	0.723796i	$0.742396\pi$
$524$	163.138	+	163.138i	0.311332	+	0.311332i
$525$		0			0
$526$	−243.987	−	243.987i	−0.463853	−	0.463853i
$527$	−378.163			−0.717577
$528$		0			0
$529$			8.70501i			0.0164556i
$530$	−441.955			−0.833877
$531$		0			0
$532$	23.6917	−	23.6917i	0.0445332	−	0.0445332i
$533$	19.4825	−	19.4825i	0.0365525	−	0.0365525i
$534$		0			0
$535$	338.725	+	338.725i	0.633131	+	0.633131i
$536$	268.939	−	268.939i	0.501753	−	0.501753i
$537$		0			0
$538$	−192.998	+	192.998i	−0.358733	+	0.358733i
$539$		−	332.540i		−	0.616957i
$540$		0			0
$541$	89.2845	+	89.2845i	0.165036	+	0.165036i	0.784793	−	0.619757i	$-0.212769\pi$
$541$	89.2845	+	89.2845i	0.165036	+	0.165036i	−0.619757	+	0.784793i	$0.712769\pi$
$542$	11.4461	−	11.4461i	0.0211182	−	0.0211182i
$543$		0			0
$544$	−669.353			−1.23043
$545$			269.768i			0.494987i
$546$		0			0
$547$	−75.5441	+	75.5441i	−0.138106	+	0.138106i	−0.772780	−	0.634674i	$-0.781134\pi$
$547$	−75.5441	+	75.5441i	−0.138106	+	0.138106i	0.634674	+	0.772780i	$0.281134\pi$
$548$		−	27.1664i		−	0.0495738i
$549$		0			0
$550$	−582.815	+	582.815i	−1.05966	+	1.05966i
$551$	−95.9691			−0.174173
$552$		0			0
$553$	−220.186	−	220.186i	−0.398166	−	0.398166i
$554$			441.498i			0.796928i
$555$		0			0
$556$	−392.770			−0.706422
$557$	154.792	−	154.792i	0.277902	−	0.277902i	−0.554369	−	0.832271i	$-0.687040\pi$
$557$	154.792	−	154.792i	0.277902	−	0.277902i	0.832271	+	0.554369i	$0.187040\pi$
$558$		0			0
$559$		−	295.229i		−	0.528138i
$560$	163.124	+	163.124i	0.291292	+	0.291292i
$561$		0			0
$562$	742.835			1.32177
$563$	65.2182	+	65.2182i	0.115840	+	0.115840i	0.762651	−	0.646810i	$-0.223897\pi$
$563$	65.2182	+	65.2182i	0.115840	+	0.115840i	−0.646810	+	0.762651i	$0.723897\pi$
$564$		0			0
$565$	588.613			1.04179
$566$		−	641.554i		−	1.13349i
$567$		0			0
$568$	562.210	+	562.210i	0.989806	+	0.989806i
$569$	−511.812	+	511.812i	−0.899494	+	0.899494i	−0.995391	−	0.0958970i	$-0.969428\pi$
$569$	−511.812	+	511.812i	−0.899494	+	0.899494i	0.0958970	+	0.995391i	$0.469428\pi$
$570$		0			0
$571$	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
$573$		0			0
$574$	14.6062	+	14.6062i	0.0254464	+	0.0254464i
$575$	500.457	−	500.457i	0.870361	−	0.870361i
$576$		0			0
$577$	−86.4511	−	86.4511i	−0.149829	−	0.149829i	0.628213	−	0.778041i	$-0.283787\pi$
$577$	−86.4511	−	86.4511i	−0.149829	−	0.149829i	−0.778041	+	0.628213i	$0.783787\pi$
$578$	385.617	+	385.617i	0.667157	+	0.667157i
$579$		0			0
$580$			381.835i			0.658336i
$581$	−622.755			−1.07187
$582$		0			0
$583$			726.925i			1.24687i
$584$	−531.586	+	531.586i	−0.910249	+	0.910249i
$585$		0			0
$586$	85.9117	−	85.9117i	0.146607	−	0.146607i
$587$	−500.633	+	500.633i	−0.852867	+	0.852867i	−0.990485	−	0.137619i	$-0.956055\pi$
$587$	−500.633	+	500.633i	−0.852867	+	0.852867i	0.137619	+	0.990485i	$0.456055\pi$
$588$		0			0
$589$	−49.6637			−0.0843187
$590$	511.163	+	511.163i	0.866378	+	0.866378i
$591$		0			0
$592$	−179.609	+	102.248i	−0.303393	+	0.172716i
$593$	719.626			1.21354			0.606768	−	0.794879i	$-0.292466\pi$
$593$	719.626			1.21354			0.606768	+	0.794879i	$0.292466\pi$
$594$		0			0
$595$			1058.11i			1.77833i
$596$			403.373i			0.676801i
$597$		0			0
$598$	−267.099	−	267.099i	−0.446654	−	0.446654i
$599$	259.577			0.433351			0.216676	−	0.976244i	$-0.430479\pi$
$599$	259.577			0.433351			0.216676	+	0.976244i	$0.430479\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	396.090			0.655777
$605$	1106.27	+	1106.27i	1.82854	+	1.82854i
$606$		0			0
$607$	−315.803	+	315.803i	−0.520268	+	0.520268i	−0.917652	−	0.397384i	$-0.869918\pi$
$607$	−315.803	+	315.803i	−0.520268	+	0.520268i	0.397384	+	0.917652i	$0.369918\pi$
$608$	−87.9053			−0.144581
$609$		0			0
$610$	−35.7106	+	35.7106i	−0.0585420	+	0.0585420i
$611$	256.532	+	256.532i	0.419855	+	0.419855i
$612$		0			0
$613$		−	405.498i		−	0.661498i	−0.943719	−	0.330749i	$-0.892699\pi$
$613$		−	405.498i		−	0.661498i	0.943719	−	0.330749i	$-0.107301\pi$
$614$	463.375	+	463.375i	0.754682	+	0.754682i
$615$		0			0
$616$	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	$0.914607\pi$
$618$		0			0
$619$		−	525.496i		−	0.848943i	−0.905441	−	0.424472i	$-0.860460\pi$
$619$		−	525.496i		−	0.848943i	0.905441	−	0.424472i	$-0.139540\pi$
$620$			197.599i			0.318707i
$621$		0			0
$622$		−	55.5932i		−	0.0893782i
$623$	626.878	−	626.878i	1.00622	−	1.00622i
$624$		0			0
$625$	456.465			0.730344
$626$	632.182			1.00988
$627$		0			0
$628$			148.608i			0.236636i
$629$	−914.136	−	250.901i	−1.45332	−	0.398888i
$630$		0			0
$631$	517.188	−	517.188i	0.819632	−	0.819632i	−0.166422	−	0.986055i	$-0.553221\pi$
$631$	517.188	−	517.188i	0.819632	−	0.819632i	0.986055	+	0.166422i	$0.0532215\pi$
$632$			483.400i			0.764874i
$633$		0			0
$634$	393.096	+	393.096i	0.620026	+	0.620026i
$635$	−699.713	−	699.713i	−1.10191	−	1.10191i
$636$		0			0
$637$	−141.843	−	141.843i	−0.222674	−	0.222674i
$638$	−770.241			−1.20727
$639$		0			0
$640$			102.624i			0.160350i
$641$	1064.31			1.66039			0.830196	−	0.557472i	$-0.188228\pi$
$641$	1064.31			1.66039			0.830196	+	0.557472i	$0.188228\pi$
$642$		0			0
$643$	−607.938	+	607.938i	−0.945470	+	0.945470i	−0.998588	−	0.0531178i	$-0.983084\pi$
$643$	−607.938	+	607.938i	−0.945470	+	0.945470i	0.0531178	+	0.998588i	$0.483084\pi$
$644$	−163.278	+	163.278i	−0.253537	+	0.253537i
$645$		0			0
$646$	90.4798	+	90.4798i	0.140062	+	0.140062i
$647$	−506.664	+	506.664i	−0.783097	+	0.783097i	−0.980352	−	0.197255i	$-0.936797\pi$
$647$	−506.664	+	506.664i	−0.783097	+	0.783097i	0.197255	+	0.980352i	$0.436797\pi$
$648$		0			0
$649$	840.758	−	840.758i	1.29547	−	1.29547i
$650$			497.193i			0.764913i
$651$		0			0
$652$	−250.144	−	250.144i	−0.383657	−	0.383657i
$653$	−124.218	+	124.218i	−0.190226	+	0.190226i	−0.795794	−	0.605568i	$-0.792946\pi$
$653$	−124.218	+	124.218i	−0.190226	+	0.190226i	0.605568	+	0.795794i	$0.292946\pi$
$654$		0			0
$655$	−956.860			−1.46085
$656$		−	14.0241i		−	0.0213781i
$657$		0			0
$658$	−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	$-0.112003\pi$
$660$		0			0
$661$	−389.416	+	389.416i	−0.589132	+	0.589132i	−0.937396	−	0.348265i	$-0.886771\pi$
$661$	−389.416	+	389.416i	−0.589132	+	0.589132i	0.348265	+	0.937396i	$0.386771\pi$
$662$	−597.055			−0.901896
$663$		0			0
$664$	683.604	+	683.604i	1.02952	+	1.02952i
$665$			138.960i			0.208962i
$666$		0			0
$667$	661.398			0.991602
$668$	136.437	−	136.437i	0.204247	−	0.204247i
$669$		0			0
$670$			488.908i			0.729714i
$671$	58.7367	+	58.7367i	0.0875361	+	0.0875361i
$672$		0			0
$673$	−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
$675$		0			0
$676$	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	$-0.00884809\pi$
$678$		0			0
$679$	35.5873	+	35.5873i	0.0524113	+	0.0524113i
$680$	1161.49	−	1161.49i	1.70808	−	1.70808i
$681$		0			0
$682$	−398.598			−0.584454
$683$	136.128	+	136.128i	0.199308	+	0.199308i	0.799703	−	0.600395i	$-0.204990\pi$
$683$	136.128	+	136.128i	0.199308	+	0.199308i	−0.600395	+	0.799703i	$0.704990\pi$
$684$		0			0
$685$	79.6702	+	79.6702i	0.116307	+	0.116307i
$686$	391.407	−	391.407i	0.570564	−	0.570564i
$687$		0			0
$688$	−106.257	−	106.257i	−0.154444	−	0.154444i
$689$	310.066	+	310.066i	0.450023	+	0.450023i
$690$		0			0
$691$		−	1141.32i		−	1.65170i	−0.563890	−	0.825850i	$-0.690696\pi$
$691$		−	1141.32i		−	1.65170i	0.563890	−	0.825850i	$-0.309304\pi$
$692$	−142.253			−0.205568
$693$		0			0
$694$			356.331i			0.513445i
$695$	1151.87	−	1151.87i	1.65736	−	1.65736i
$696$		0			0
$697$	45.4837	−	45.4837i	0.0652564	−	0.0652564i
$698$	−74.2795	+	74.2795i	−0.106418	+	0.106418i
$699$		0			0
$700$	303.935			0.434192
$701$	−30.7153	−	30.7153i	−0.0438163	−	0.0438163i	0.684859	−	0.728675i	$-0.259864\pi$
$701$	−30.7153	−	30.7153i	−0.0438163	−	0.0438163i	−0.728675	+	0.684859i	$0.759864\pi$
$702$		0			0
$703$	−120.052	−	32.9505i	−0.170771	−	0.0468713i
$704$	−1112.00			−1.57954
$705$		0			0
$706$			74.8669i			0.106044i
$707$			404.135i			0.571619i
$708$		0			0
$709$	180.362	+	180.362i	0.254390	+	0.254390i	0.822768	−	0.568378i	$-0.192429\pi$
$709$	180.362	+	180.362i	0.254390	+	0.254390i	−0.568378	+	0.822768i	$0.692429\pi$
$710$	−1022.05			−1.43950
$711$		0			0
$712$	−1376.26			−1.93295
$713$	342.272			0.480044
$714$		0			0
$715$	1487.62			2.08058
$716$	220.538	+	220.538i	0.308013	+	0.308013i
$717$		0			0
$718$	654.748	−	654.748i	0.911905	−	0.911905i
$719$	171.807			0.238952			0.119476	−	0.992837i	$-0.461878\pi$
$719$	171.807			0.238952			0.119476	+	0.992837i	$0.461878\pi$
$720$		0			0
$721$	−329.566	+	329.566i	−0.457095	+	0.457095i
$722$	−367.029	−	367.029i	−0.508351	−	0.508351i
$723$		0			0
$724$			244.665i			0.337936i
$725$	−615.582	−	615.582i	−0.849079	−	0.849079i
$726$		0			0
$727$	304.684	−	304.684i	0.419098	−	0.419098i	−0.465795	−	0.884893i	$-0.654232\pi$
$727$	304.684	−	304.684i	0.419098	−	0.419098i	0.884893	+	0.465795i	$0.154232\pi$
$728$		−	523.367i		−	0.718910i
$729$		0			0
$730$		−	966.376i		−	1.32380i
$731$		−	689.240i		−	0.942873i
$732$		0			0
$733$		−	641.352i		−	0.874968i	−0.899226	−	0.437484i	$-0.855870\pi$
$733$		−	641.352i		−	0.874968i	0.899226	−	0.437484i	$-0.144130\pi$
$734$	−199.351	+	199.351i	−0.271595	+	0.271595i
$735$		0			0
$736$	605.824			0.823131
$737$	804.154			1.09112
$738$		0			0
$739$		−	6.01293i		−	0.00813658i	−0.999992	−	0.00406829i	$-0.998705\pi$
$739$		−	6.01293i		−	0.00813658i	0.999992	−	0.00406829i	$-0.00129498\pi$
$740$	−131.101	+	477.656i	−0.177164	+	0.645481i
$741$		0			0
$742$	−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	$-0.116020\pi$
$744$		0			0
$745$	−1182.96	−	1182.96i	−1.58787	−	1.58787i
$746$	157.314	+	157.314i	0.210877	+	0.210877i
$747$		0			0
$748$	−592.118	−	592.118i	−0.791601	−	0.791601i
$749$	356.326			0.475736
$750$		0			0
$751$			696.245i			0.927091i	0.886073	+	0.463545i	$0.153423\pi$
$751$			696.245i			0.927091i	−0.886073	+	0.463545i	$0.846577\pi$
$752$	184.659			0.245557
$753$		0			0
$754$	−328.542	+	328.542i	−0.435732	+	0.435732i
$755$	−1161.60	+	1161.60i	−1.53854	+	1.53854i
$756$		0			0
$757$	−503.637	−	503.637i	−0.665306	−	0.665306i	0.291320	−	0.956626i	$-0.405906\pi$
$757$	−503.637	−	503.637i	−0.665306	−	0.665306i	−0.956626	+	0.291320i	$0.905906\pi$
$758$	−237.862	+	237.862i	−0.313802	+	0.313802i
$759$		0			0
$760$	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	$0.948258\pi$
$762$		0			0
$763$	141.893	+	141.893i	0.185967	+	0.185967i
$764$	223.060	−	223.060i	0.291964	−	0.291964i
$765$		0			0
$766$	−898.117			−1.17248
$767$		−	717.242i		−	0.935127i
$768$		0			0
$769$	810.146	−	810.146i	1.05351	−	1.05351i	0.0550210	−	0.998485i	$-0.482477\pi$
$769$	810.146	−	810.146i	1.05351	−	1.05351i	0.998485	−	0.0550210i	$-0.0175226\pi$
$770$			1115.28i			1.44842i
$771$		0			0
$772$	−118.662	+	118.662i	−0.153707	+	0.153707i
$773$	−294.190			−0.380582			−0.190291	−	0.981728i	$-0.560943\pi$
$773$	−294.190			−0.380582			−0.190291	+	0.981728i	$0.560943\pi$
$774$		0			0
$775$	−318.562	−	318.562i	−0.411048	−	0.411048i
$776$		−	78.1290i		−	0.100682i
$777$		0			0
$778$	−1132.02			−1.45504
$779$	5.97332	−	5.97332i	0.00766793	−	0.00766793i
$780$		0			0
$781$			1681.06i			2.15245i
$782$	−623.567	−	623.567i	−0.797401	−	0.797401i
$783$		0			0
$784$	−102.103			−0.130233
$785$	−435.817	−	435.817i	−0.555181	−	0.555181i
$786$		0			0
$787$	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
$789$		0			0
$790$	−439.389	−	439.389i	−0.556189	−	0.556189i
$791$	309.600	−	309.600i	0.391403	−	0.391403i
$792$		0			0
$793$	50.1077			0.0631875
$794$	261.981	+	261.981i	0.329951	+	0.329951i
$795$		0			0
$796$	44.0113	+	44.0113i	0.0552906	+	0.0552906i
$797$	522.357	−	522.357i	0.655404	−	0.655404i	−0.298885	−	0.954289i	$-0.596615\pi$
$797$	522.357	−	522.357i	0.655404	−	0.655404i	0.954289	+	0.298885i	$0.0966149\pi$
$798$		0			0
$799$	598.897	+	598.897i	0.749558	+	0.749558i
$800$	−563.858	−	563.858i	−0.704823	−	0.704823i
$801$		0			0
$802$		−	529.951i		−	0.660786i
$803$	−1589.49			−1.97944
$804$		0			0
$805$		−	957.681i		−	1.18967i
$806$	−170.020	+	170.020i	−0.210943	+	0.210943i
$807$		0			0
$808$	443.623	−	443.623i	0.549038	−	0.549038i
$809$	−180.910	+	180.910i	−0.223622	+	0.223622i	−0.810022	−	0.586400i	$-0.800545\pi$
$809$	−180.910	+	180.910i	−0.223622	+	0.223622i	0.586400	+	0.810022i	$0.300545\pi$
$810$		0			0
$811$	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
$813$		0			0
$814$	−963.532	−	264.458i	−1.18370	−	0.324888i
$815$	1467.18			1.80022
$816$		0			0
$817$		−	90.5171i		−	0.110792i
$818$		−	57.1845i		−	0.0699077i
$819$		0			0
$820$	−23.7662	−	23.7662i	−0.0289832	−	0.0289832i
$821$	1307.60			1.59270			0.796348	−	0.604839i	$-0.206763\pi$
$821$	1307.60			1.59270			0.796348	+	0.604839i	$0.206763\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	537.724			0.650998
$827$	423.902	+	423.902i	0.512578	+	0.512578i	0.915316	−	0.402737i	$-0.131941\pi$
$827$	423.902	+	423.902i	0.512578	+	0.512578i	−0.402737	+	0.915316i	$0.631941\pi$
$828$		0			0
$829$	139.431	−	139.431i	0.168191	−	0.168191i	−0.617993	−	0.786184i	$-0.712054\pi$
$829$	139.431	−	139.431i	0.168191	−	0.168191i	0.786184	+	0.617993i	$0.212054\pi$
$830$	−1242.73			−1.49727
$831$		0			0
$832$	−474.316	+	474.316i	−0.570091	+	0.570091i
$833$	−331.146	−	331.146i	−0.397534	−	0.397534i
$834$		0			0
$835$			800.252i			0.958386i
$836$	−77.7621	−	77.7621i	−0.0930169	−	0.0930169i
$837$		0			0
$838$	−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	$-0.190755\pi$
$840$		0			0
$841$			27.4541i			0.0326446i
$842$		−	290.998i		−	0.345604i
$843$		0			0
$844$			59.8160i			0.0708721i
$845$	−255.903	+	255.903i	−0.302844	+	0.302844i
$846$		0			0
$847$	1163.75			1.37397
$848$	223.194			0.263201
$849$		0			0
$850$			1160.74i			1.36558i
$851$	827.375	+	227.088i	0.972238	+	0.266848i
$852$		0			0
$853$	−718.017	+	718.017i	−0.841755	+	0.841755i	−0.989087	−	0.147332i	$-0.952931\pi$
$853$	−718.017	+	718.017i	−0.841755	+	0.841755i	0.147332	+	0.989087i	$0.452931\pi$
$854$			37.5663i			0.0439886i
$855$		0			0
$856$	−391.143	−	391.143i	−0.456943	−	0.456943i
$857$	−241.022	−	241.022i	−0.281239	−	0.281239i	0.552364	−	0.833603i	$-0.313726\pi$
$857$	−241.022	−	241.022i	−0.281239	−	0.281239i	−0.833603	+	0.552364i	$0.813726\pi$
$858$		0			0
$859$	944.215	+	944.215i	1.09920	+	1.09920i	0.994504	+	0.104698i	$0.0333877\pi$
$859$	944.215	+	944.215i	1.09920	+	1.09920i	0.104698	+	0.994504i	$0.466612\pi$
$860$	−360.143			−0.418771
$861$		0			0
$862$		−	1102.94i		−	1.27952i
$863$	−1108.91			−1.28495			−0.642473	−	0.766309i	$-0.722091\pi$
$863$	−1108.91			−1.28495			−0.642473	+	0.766309i	$0.722091\pi$
$864$		0			0
$865$	417.182	−	417.182i	0.482292	−	0.482292i
$866$	241.116	−	241.116i	0.278425	−	0.278425i
$867$		0			0
$868$	103.933	+	103.933i	0.119739	+	0.119739i
$869$	−722.706	+	722.706i	−0.831652	+	0.831652i
$870$		0			0
$871$	343.008	−	343.008i	0.393809	−	0.393809i
$872$		−	311.515i		−	0.357242i
$873$		0			0
$874$	−81.8924	−	81.8924i	−0.0936984	−	0.0936984i
$875$	−161.255	+	161.255i	−0.184292	+	0.184292i
$876$		0			0
$877$	−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
$879$		0			0
$880$	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	$-0.0563355\pi$
$882$		0			0
$883$	534.700	−	534.700i	0.605549	−	0.605549i	−0.336231	−	0.941780i	$-0.609152\pi$
$883$	534.700	−	534.700i	0.605549	−	0.605549i	0.941780	+	0.336231i	$0.109152\pi$
$884$	−505.129			−0.571413
$885$		0			0
$886$	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	$0.913841\pi$
$888$		0			0
$889$	−736.072			−0.827977
$890$	1250.96	−	1250.96i	1.40557	−	1.40557i
$891$		0			0
$892$			641.285i			0.718930i
$893$	78.6524	+	78.6524i	0.0880766	+	0.0880766i
$894$		0			0
$895$	−1293.53			−1.44528
$896$	53.9783	+	53.9783i	0.0602436	+	0.0602436i
$897$		0			0
$898$	−437.164			−0.486820
$899$		−	421.008i		−	0.468307i
$900$		0			0
$901$	723.878	+	723.878i	0.803416	+	0.803416i
$902$	47.9414	−	47.9414i	0.0531501	−	0.0531501i
$903$		0			0
$904$	−679.701			−0.751882
$905$	−717.524	−	717.524i	−0.792844	−	0.792844i
$906$		0			0
$907$	−729.638	−	729.638i	−0.804452	−	0.804452i	0.179336	−	0.983788i	$-0.442605\pi$
$907$	−729.638	−	729.638i	−0.804452	−	0.804452i	−0.983788	+	0.179336i	$0.942605\pi$
$908$	−227.356	+	227.356i	−0.250393	+	0.250393i
$909$		0			0
$910$	475.717	+	475.717i	0.522766	+	0.522766i
$911$	−199.232	−	199.232i	−0.218696	−	0.218696i	0.589253	−	0.807949i	$-0.299422\pi$
$911$	−199.232	−	199.232i	−0.218696	−	0.218696i	−0.807949	+	0.589253i	$0.799422\pi$
$912$		0			0
$913$			2044.04i			2.23882i
$914$	352.634			0.385814
$915$		0			0
$916$		−	423.851i		−	0.462720i
$917$	−503.291	+	503.291i	−0.548845	+	0.548845i
$918$		0			0
$919$	−77.9734	+	77.9734i	−0.0848459	+	0.0848459i	−0.748256	−	0.663410i	$-0.769109\pi$
$919$	−77.9734	+	77.9734i	−0.0848459	+	0.0848459i	0.663410	+	0.748256i	$0.269109\pi$
$920$	−1051.26	+	1051.26i	−1.14267	+	1.14267i
$921$		0			0
$922$	1216.92			1.31987
$923$	717.047	+	717.047i	0.776866	+	0.776866i
$924$		0			0
$925$	−558.704	−	981.419i	−0.604005	−	1.06099i
$926$	495.037			0.534597
$927$		0			0
$928$		−	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	$-0.394343\pi$
$930$		0			0
$931$	−43.4890	−	43.4890i	−0.0467122	−	0.0467122i
$932$	−60.3285			−0.0647301
$933$		0			0
$934$	361.188			0.386711
$935$	3472.98			3.71441
$936$		0			0
$937$	−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
$939$		0			0
$940$	312.937	−	312.937i	0.332911	−	0.332911i
$941$	−1074.54			−1.14191			−0.570957	−	0.820980i	$-0.693428\pi$
$941$	−1074.54			−1.14191			−0.570957	+	0.820980i	$0.693428\pi$
$942$		0			0
$943$	−41.1668	+	41.1668i	−0.0436552	+	0.0436552i
$944$	−258.146	−	258.146i	−0.273459	−	0.273459i
$945$		0			0
$946$		−	726.484i		−	0.767953i
$947$	129.643	+	129.643i	0.136899	+	0.136899i	0.772236	−	0.635336i	$-0.219139\pi$
$947$	129.643	+	129.643i	0.136899	+	0.136899i	−0.635336	+	0.772236i	$0.719139\pi$
$948$		0			0
$949$	−677.989	+	677.989i	−0.714425	+	0.714425i
$950$			152.439i			0.160462i
$951$		0			0
$952$		−	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	$0.915119\pi$
$954$		0			0
$955$			1308.32i			1.36997i
$956$	−9.65032	+	9.65032i	−0.0100945	+	0.0100945i
$957$		0			0
$958$	−118.058			−0.123233
$959$	83.8101			0.0873932
$960$		0			0
$961$			743.130i			0.773288i
$962$	−523.793	+	298.186i	−0.544483	+	0.309965i
$963$		0			0
$964$	−475.635	+	475.635i	−0.493398	+	0.493398i
$965$		−	695.992i		−	0.721236i
$966$		0			0
$967$	−85.0575	−	85.0575i	−0.0879602	−	0.0879602i	0.661758	−	0.749718i	$-0.269811\pi$
$967$	−85.0575	−	85.0575i	−0.0879602	−	0.0879602i	−0.749718	+	0.661758i	$0.769811\pi$
$968$	−1277.46	−	1277.46i	−1.31969	−	1.31969i
$969$		0			0
$970$	71.0159	+	71.0159i	0.0732122	+	0.0732122i
$971$	496.661			0.511494			0.255747	−	0.966744i	$-0.417679\pi$
$971$	496.661			0.511494			0.255747	+	0.966744i	$0.417679\pi$
$972$		0			0
$973$		−	1211.72i		−	1.24535i
$974$	−319.955			−0.328496
$975$		0			0
$976$	18.0345	−	18.0345i	0.0184779	−	0.0184779i
$977$	−1186.94	+	1186.94i	−1.21488	+	1.21488i	−0.245479	+	0.969402i	$0.578945\pi$
$977$	−1186.94	+	1186.94i	−1.21488	+	1.21488i	−0.969402	+	0.245479i	$0.921055\pi$
$978$		0			0
$979$	−2057.57	−	2057.57i	−2.10171	−	2.10171i
$980$	−173.031	+	173.031i	−0.176562	+	0.176562i
$981$		0			0
$982$	−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	$0.730724\pi$
$984$		0			0
$985$	312.568	+	312.568i	0.317328	+	0.317328i
$986$	−767.012	+	767.012i	−0.777903	+	0.777903i
$987$		0			0
$988$	−66.3381			−0.0671438
$989$			623.824i			0.630763i
$990$		0			0
$991$	672.226	−	672.226i	0.678331	−	0.678331i	−0.281291	−	0.959622i	$-0.590763\pi$
$991$	672.226	−	672.226i	0.678331	−	0.678331i	0.959622	+	0.281291i	$0.0907628\pi$
$992$		−	385.633i		−	0.388743i
$993$		0			0
$994$	−537.578	+	537.578i	−0.540823	+	0.540823i
$995$	−258.142			−0.259439
$996$		0			0
$997$	−584.483	−	584.483i	−0.586242	−	0.586242i	0.350370	−	0.936611i	$-0.386056\pi$
$997$	−584.483	−	584.483i	−0.586242	−	0.586242i	−0.936611	+	0.350370i	$0.886056\pi$
$998$			1236.00i			1.23848i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.3.d.a.6.3	✓	12	3.2	odd	2
37.3.d.a.31.3	yes	12	111.68	even	4
333.3.i.a.154.4		12	1.1	even	1	trivial
333.3.i.a.253.4		12	37.31	odd	4	inner
592.3.k.e.401.3		12	444.179	odd	4
592.3.k.e.561.4		12	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04962 - 1.04962i) q^{2} +1.79661i q^{4} +(-5.26886 - 5.26886i) q^{5} -5.54265 q^{7} +(6.08422 + 6.08422i) q^{8} +O(q^{10})\)	\(q+(1.04962 - 1.04962i) q^{2} +1.79661i q^{4} +(-5.26886 - 5.26886i) q^{5} -5.54265 q^{7} +(6.08422 + 6.08422i) q^{8} -11.0606 q^{10} +18.1924i q^{11} +(7.75987 + 7.75987i) q^{13} +(-5.81766 + 5.81766i) q^{14} +5.58578 q^{16} +(18.1161 + 18.1161i) q^{17} +(2.37917 + 2.37917i) q^{19} +(9.46607 - 9.46607i) q^{20} +(19.0950 + 19.0950i) q^{22} +(-16.3967 - 16.3967i) q^{23} +30.5218i q^{25} +16.2898 q^{26} -9.95796i q^{28} +(-20.1686 + 20.1686i) q^{29} +(-10.4372 + 10.4372i) q^{31} +(-18.4739 + 18.4739i) q^{32} +38.0300 q^{34} +(29.2034 + 29.2034i) q^{35} +(-32.1547 + 18.3051i) q^{37} +4.99444 q^{38} -64.1138i q^{40} -2.51067i q^{41} +(-19.0228 - 19.0228i) q^{43} -32.6846 q^{44} -34.4206 q^{46} +33.0588 q^{47} -18.2791 q^{49} +(32.0362 + 32.0362i) q^{50} +(-13.9414 + 13.9414i) q^{52} +39.9577 q^{53} +(95.8532 - 95.8532i) q^{55} +(-33.7227 - 33.7227i) q^{56} +42.3387i q^{58} +(-46.2148 - 46.2148i) q^{59} +(3.22864 - 3.22864i) q^{61} +21.9101i q^{62} +61.1243i q^{64} -81.7713i q^{65} -44.2028i q^{67} +(-32.5476 + 32.5476i) q^{68} +61.3049 q^{70} +92.4046 q^{71} +87.3712i q^{73} +(-14.5368 + 52.9635i) q^{74} +(-4.27443 + 4.27443i) q^{76} -100.834i q^{77} +(39.7257 + 39.7257i) q^{79} +(-29.4307 - 29.4307i) q^{80} +(-2.63525 - 2.63525i) q^{82} +112.357 q^{83} -190.903i q^{85} -39.9334 q^{86} +(-110.686 + 110.686i) q^{88} +(-113.101 + 113.101i) q^{89} +(-43.0102 - 43.0102i) q^{91} +(29.4585 - 29.4585i) q^{92} +(34.6991 - 34.6991i) q^{94} -25.0710i q^{95} +(-6.42063 - 6.42063i) q^{97} +(-19.1860 + 19.1860i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 36 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 36 * q^8	\( 12 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 36 q^{8} - 16 q^{10} + 14 q^{13} + 70 q^{14} - 96 q^{16} - 2 q^{17} + 14 q^{19} + 24 q^{20} + 22 q^{22} - 56 q^{23} + 48 q^{26} - 60 q^{29} + 72 q^{31} - 208 q^{32} + 112 q^{34} + 154 q^{35} - 66 q^{37} + 336 q^{38} + 70 q^{43} - 80 q^{44} - 424 q^{46} + 384 q^{47} + 144 q^{49} + 34 q^{50} + 328 q^{52} + 56 q^{53} + 70 q^{55} - 16 q^{56} - 184 q^{59} + 132 q^{61} - 116 q^{68} + 556 q^{70} - 68 q^{71} + 382 q^{74} + 12 q^{76} - 2 q^{79} - 4 q^{80} + 374 q^{82} - 108 q^{83} - 140 q^{86} - 788 q^{88} - 278 q^{89} - 450 q^{91} - 652 q^{92} + 118 q^{94} - 244 q^{97} - 416 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^5 - 4 * q^7 - 36 * q^8 - 16 * q^10 + 14 * q^13 + 70 * q^14 - 96 * q^16 - 2 * q^17 + 14 * q^19 + 24 * q^20 + 22 * q^22 - 56 * q^23 + 48 * q^26 - 60 * q^29 + 72 * q^31 - 208 * q^32 + 112 * q^34 + 154 * q^35 - 66 * q^37 + 336 * q^38 + 70 * q^43 - 80 * q^44 - 424 * q^46 + 384 * q^47 + 144 * q^49 + 34 * q^50 + 328 * q^52 + 56 * q^53 + 70 * q^55 - 16 * q^56 - 184 * q^59 + 132 * q^61 - 116 * q^68 + 556 * q^70 - 68 * q^71 + 382 * q^74 + 12 * q^76 - 2 * q^79 - 4 * q^80 + 374 * q^82 - 108 * q^83 - 140 * q^86 - 788 * q^88 - 278 * q^89 - 450 * q^91 - 652 * q^92 + 118 * q^94 - 244 * q^97 - 416 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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