LMFDB - Embedded newform 49.4.c.e.30.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,4,Mod(18,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not 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:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.5922408960000.19
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 54x^{6} + 176x^{5} + 1307x^{4} - 2912x^{3} - 15314x^{2} + 16800x + 86044 $ x^8 - 4x^7 - 54x^6 + 176x^5 + 1307x^4 - 2912x^3 - 15314x^2 + 16800*x + 86044
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			30.4
Root			$-4.23824 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	49.30
Dual form			49.4.c.e.18.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76556 - 3.05805i) q^{2} +(3.91110 + 6.77422i) q^{3} +(-2.23444 - 3.87016i) q^{4} +(1.03865 - 1.79899i) q^{5} +27.6212 q^{6} +12.4689 q^{8} +(-17.0934 + 29.6066i) q^{9} +O(q^{10})$	\(q+(1.76556 - 3.05805i) q^{2} +(3.91110 + 6.77422i) q^{3} +(-2.23444 - 3.87016i) q^{4} +(1.03865 - 1.79899i) q^{5} +27.6212 q^{6} +12.4689 q^{8} +(-17.0934 + 29.6066i) q^{9} +(-3.66760 - 6.35247i) q^{10} +(-24.5934 - 42.5970i) q^{11} +(17.4782 - 30.2731i) q^{12} -44.8559 q^{13} +16.2490 q^{15} +(39.8901 - 69.0916i) q^{16} +(-13.2589 - 22.9652i) q^{17} +(60.3590 + 104.545i) q^{18} +(-38.8675 + 67.3205i) q^{19} -9.28317 q^{20} -173.685 q^{22} +(-27.8755 + 48.2818i) q^{23} +(48.7670 + 84.4669i) q^{24} +(60.3424 + 104.516i) q^{25} +(-79.1960 + 137.171i) q^{26} -56.2164 q^{27} +121.436 q^{29} +(28.6887 - 49.6903i) q^{30} +(-152.776 - 264.616i) q^{31} +(-90.9815 - 157.585i) q^{32} +(192.374 - 333.202i) q^{33} -93.6380 q^{34} +152.776 q^{36} +(-38.5934 + 66.8457i) q^{37} +(137.246 + 237.717i) q^{38} +(-175.436 - 303.864i) q^{39} +(12.9508 - 22.4314i) q^{40} +248.720 q^{41} -147.179 q^{43} +(-109.905 + 190.360i) q^{44} +(35.5080 + 61.5017i) q^{45} +(98.4319 + 170.489i) q^{46} +(-134.925 + 233.698i) q^{47} +624.056 q^{48} +426.154 q^{50} +(103.714 - 179.638i) q^{51} +(100.228 + 173.599i) q^{52} +(70.5603 + 122.214i) q^{53} +(-99.2536 + 171.912i) q^{54} -102.176 q^{55} -608.058 q^{57} +(214.403 - 371.356i) q^{58} +(212.417 + 367.917i) q^{59} +(-36.3074 - 62.8863i) q^{60} +(293.998 - 509.220i) q^{61} -1078.95 q^{62} -4.29373 q^{64} +(-46.5895 + 80.6954i) q^{65} +(-679.299 - 1176.58i) q^{66} +(89.8171 + 155.568i) q^{67} +(-59.2525 + 102.628i) q^{68} -436.095 q^{69} +674.872 q^{71} +(-213.135 + 369.161i) q^{72} +(-118.744 - 205.671i) q^{73} +(136.278 + 236.041i) q^{74} +(-472.010 + 817.546i) q^{75} +347.388 q^{76} -1238.97 q^{78} +(-247.926 + 429.421i) q^{79} +(-82.8636 - 143.524i) q^{80} +(241.654 + 418.556i) q^{81} +(439.131 - 760.598i) q^{82} -24.4406 q^{83} -55.0855 q^{85} +(-259.854 + 450.080i) q^{86} +(474.947 + 822.633i) q^{87} +(-306.652 - 531.136i) q^{88} +(-536.144 + 928.628i) q^{89} +250.767 q^{90} +249.144 q^{92} +(1195.05 - 2069.88i) q^{93} +(476.439 + 825.216i) q^{94} +(80.7393 + 139.845i) q^{95} +(711.675 - 1232.66i) q^{96} +1667.43 q^{97} +1681.54 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 34 q^{4} + 132 q^{8} - 40 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 34 * q^4 + 132 * q^8 - 40 * q^9	$ 8 q - 2 q^{2} - 34 q^{4} + 132 q^{8} - 40 q^{9} - 100 q^{11} - 128 q^{15} + 174 q^{16} + 370 q^{18} - 680 q^{22} - 352 q^{23} + 128 q^{25} + 520 q^{29} + 552 q^{30} + 30 q^{32} - 100 q^{36} - 212 q^{37} - 952 q^{39} + 1080 q^{43} - 460 q^{44} - 696 q^{46} + 2732 q^{50} - 428 q^{51} - 16 q^{53} - 3768 q^{57} + 780 q^{58} + 1064 q^{60} - 3356 q^{64} + 756 q^{65} + 1944 q^{67} + 4496 q^{71} - 270 q^{72} + 284 q^{74} - 2688 q^{78} + 1048 q^{79} + 1256 q^{81} - 6568 q^{85} - 4820 q^{86} - 1260 q^{88} + 7024 q^{92} + 5368 q^{93} - 2192 q^{95} + 6680 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 34 * q^4 + 132 * q^8 - 40 * q^9 - 100 * q^11 - 128 * q^15 + 174 * q^16 + 370 * q^18 - 680 * q^22 - 352 * q^23 + 128 * q^25 + 520 * q^29 + 552 * q^30 + 30 * q^32 - 100 * q^36 - 212 * q^37 - 952 * q^39 + 1080 * q^43 - 460 * q^44 - 696 * q^46 + 2732 * q^50 - 428 * q^51 - 16 * q^53 - 3768 * q^57 + 780 * q^58 + 1064 * q^60 - 3356 * q^64 + 756 * q^65 + 1944 * q^67 + 4496 * q^71 - 270 * q^72 + 284 * q^74 - 2688 * q^78 + 1048 * q^79 + 1256 * q^81 - 6568 * q^85 - 4820 * q^86 - 1260 * q^88 + 7024 * q^92 + 5368 * q^93 - 2192 * q^95 + 6680 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.76556	−	3.05805i	0.624221	−	1.08118i	−0.364470	−	0.931215i	$-0.618750\pi$
$2$	1.76556	−	3.05805i	0.624221	−	1.08118i	0.988691	−	0.149968i	$-0.0479170\pi$
$3$	3.91110	+	6.77422i	0.752691	+	1.30370i	0.946514	+	0.322663i	$0.104578\pi$
$3$	3.91110	+	6.77422i	0.752691	+	1.30370i	−0.193823	+	0.981037i	$0.562089\pi$
$4$	−2.23444	−	3.87016i	−0.279304	−	0.483769i
$5$	1.03865	−	1.79899i	0.0928996	−	0.160907i	−0.815830	−	0.578291i	$-0.803720\pi$
$5$	1.03865	−	1.79899i	0.0928996	−	0.160907i	0.908730	+	0.417384i	$0.137053\pi$
$6$	27.6212			1.87938
$7$		0			0
$7$		0			0
$8$	12.4689			0.551051
$9$	−17.0934	+	29.6066i	−0.633088	+	1.09654i
$10$	−3.66760	−	6.35247i	−0.115980	−	0.200883i
$11$	−24.5934	−	42.5970i	−0.674108	−	1.16759i	−0.976729	−	0.214478i	$-0.931195\pi$
$11$	−24.5934	−	42.5970i	−0.674108	−	1.16759i	0.302621	−	0.953111i	$-0.402138\pi$
$12$	17.4782	−	30.2731i	0.420460	−	0.728258i
$13$	−44.8559			−0.956983			−0.478492	−	0.878092i	$-0.658816\pi$
$13$	−44.8559			−0.956983			−0.478492	+	0.878092i	$0.658816\pi$
$14$		0			0
$15$	16.2490			0.279699
$16$	39.8901	−	69.0916i	0.623282	−	1.07956i
$17$	−13.2589	−	22.9652i	−0.189163	−	0.327639i	0.755809	−	0.654793i	$-0.227244\pi$
$17$	−13.2589	−	22.9652i	−0.189163	−	0.327639i	−0.944971	+	0.327153i	$0.893911\pi$
$18$	60.3590	+	104.545i	0.790375	+	1.36897i
$19$	−38.8675	+	67.3205i	−0.469306	+	0.812862i	−0.999384	−	0.0350869i	$-0.988829\pi$
$19$	−38.8675	+	67.3205i	−0.469306	+	0.812862i	0.530078	+	0.847949i	$0.322163\pi$
$20$	−9.28317			−0.103789
$21$		0			0
$22$	−173.685			−1.68317
$23$	−27.8755	+	48.2818i	−0.252715	+	0.437715i	−0.964272	−	0.264913i	$-0.914657\pi$
$23$	−27.8755	+	48.2818i	−0.252715	+	0.437715i	0.711558	+	0.702628i	$0.247990\pi$
$24$	48.7670	+	84.4669i	0.414772	+	0.718406i
$25$	60.3424	+	104.516i	0.482739	+	0.836129i
$26$	−79.1960	+	137.171i	−0.597369	+	1.03467i
$27$	−56.2164			−0.400698
$28$		0			0
$29$	121.436			0.777588			0.388794	−	0.921325i	$-0.372892\pi$
$29$	121.436			0.777588			0.388794	+	0.921325i	$0.372892\pi$
$30$	28.6887	−	49.6903i	0.174594	−	0.302406i
$31$	−152.776	−	264.616i	−0.885143	−	1.53311i	−0.845549	−	0.533897i	$-0.820727\pi$
$31$	−152.776	−	264.616i	−0.885143	−	1.53311i	−0.0395940	−	0.999216i	$-0.512606\pi$
$32$	−90.9815	−	157.585i	−0.502607	−	0.870540i
$33$	192.374	−	333.202i	1.01479	−	1.75767i
$34$	−93.6380			−0.472317
$35$		0			0
$36$	152.776			0.707298
$37$	−38.5934	+	66.8457i	−0.171479	+	0.297010i	−0.938937	−	0.344089i	$-0.888188\pi$
$37$	−38.5934	+	66.8457i	−0.171479	+	0.297010i	0.767458	+	0.641099i	$0.221521\pi$
$38$	137.246	+	237.717i	0.585902	+	1.01481i
$39$	−175.436	−	303.864i	−0.720313	−	1.24762i
$40$	12.9508	−	22.4314i	0.0511924	−	0.0886679i
$41$	248.720			0.947403			0.473702	−	0.880685i	$-0.342917\pi$
$41$	248.720			0.947403			0.473702	+	0.880685i	$0.342917\pi$
$42$		0			0
$43$	−147.179			−0.521967			−0.260984	−	0.965343i	$-0.584047\pi$
$43$	−147.179			−0.521967			−0.260984	+	0.965343i	$0.584047\pi$
$44$	−109.905	+	190.360i	−0.376563	+	0.652226i
$45$	35.5080	+	61.5017i	0.117627	+	0.203736i
$46$	98.4319	+	170.489i	0.315500	+	0.546462i
$47$	−134.925	+	233.698i	−0.418742	+	0.725283i	−0.995813	−	0.0914112i	$-0.970862\pi$
$47$	−134.925	+	233.698i	−0.418742	+	0.725283i	0.577071	+	0.816694i	$0.304196\pi$
$48$	624.056			1.87656
$49$		0			0
$50$	426.154			1.20534
$51$	103.714	−	179.638i	0.284762	−	0.493222i
$52$	100.228	+	173.599i	0.267290	+	0.462959i
$53$	70.5603	+	122.214i	0.182872	+	0.316743i	0.942857	−	0.333197i	$-0.108127\pi$
$53$	70.5603	+	122.214i	0.182872	+	0.316743i	−0.759986	+	0.649940i	$0.774794\pi$
$54$	−99.2536	+	171.912i	−0.250124	+	0.433228i
$55$	−102.176			−0.250497
$56$		0			0
$57$	−608.058			−1.41297
$58$	214.403	−	371.356i	0.485387	−	0.840715i
$59$	212.417	+	367.917i	0.468717	+	0.811842i	0.999361	−	0.0357532i	$-0.0113830\pi$
$59$	212.417	+	367.917i	0.468717	+	0.811842i	−0.530643	+	0.847595i	$0.678050\pi$
$60$	−36.3074	−	62.8863i	−0.0781211	−	0.135310i
$61$	293.998	−	509.220i	0.617092	−	1.06883i	−0.372922	−	0.927863i	$-0.621644\pi$
$61$	293.998	−	509.220i	0.617092	−	1.06883i	0.990014	−	0.140972i	$-0.0450227\pi$
$62$	−1078.95			−2.21010
$63$		0			0
$64$	−4.29373			−0.00838618
$65$	−46.5895	+	80.6954i	−0.0889033	+	0.153985i
$66$	−679.299	−	1176.58i	−1.26691	−	2.19435i
$67$	89.8171	+	155.568i	0.163775	+	0.283666i	0.936219	−	0.351416i	$-0.114300\pi$
$67$	89.8171	+	155.568i	0.163775	+	0.283666i	−0.772445	+	0.635082i	$0.780966\pi$
$68$	−59.2525	+	102.628i	−0.105668	+	0.183022i
$69$	−436.095			−0.760865
$70$		0			0
$71$	674.872			1.12806			0.564032	−	0.825753i	$-0.309250\pi$
$71$	674.872			1.12806			0.564032	+	0.825753i	$0.309250\pi$
$72$	−213.135	+	369.161i	−0.348864	+	0.604251i
$73$	−118.744	−	205.671i	−0.190383	−	0.329754i	0.754994	−	0.655732i	$-0.227640\pi$
$73$	−118.744	−	205.671i	−0.190383	−	0.329754i	−0.945377	+	0.325978i	$0.894306\pi$
$74$	136.278	+	236.041i	0.214081	+	0.370800i
$75$	−472.010	+	817.546i	−0.726707	+	1.25869i
$76$	347.388			0.524317
$77$		0			0
$78$	−1238.97			−1.79854
$79$	−247.926	+	429.421i	−0.353087	+	0.611564i	−0.986789	−	0.162013i	$-0.948201\pi$
$79$	−247.926	+	429.421i	−0.353087	+	0.611564i	0.633702	+	0.773578i	$0.281535\pi$
$80$	−82.8636	−	143.524i	−0.115805	−	0.200581i
$81$	241.654	+	418.556i	0.331487	+	0.574152i
$82$	439.131	−	760.598i	0.591389	−	1.02432i
$83$	−24.4406			−0.0323217			−0.0161609	−	0.999869i	$-0.505144\pi$
$83$	−24.4406			−0.0323217			−0.0161609	+	0.999869i	$0.505144\pi$
$84$		0			0
$85$	−55.0855			−0.0702925
$86$	−259.854	+	450.080i	−0.325823	+	0.564342i
$87$	474.947	+	822.633i	0.585284	+	1.01374i
$88$	−306.652	−	531.136i	−0.371468	−	0.643402i
$89$	−536.144	+	928.628i	−0.638552	+	1.10600i	0.347199	+	0.937792i	$0.387133\pi$
$89$	−536.144	+	928.628i	−0.638552	+	1.10600i	−0.985751	+	0.168213i	$0.946200\pi$
$90$	250.767			0.293702
$91$		0			0
$92$	249.144			0.282337
$93$	1195.05	−	2069.88i	1.33248	−	2.30792i
$94$	476.439	+	825.216i	0.522776	+	0.905474i
$95$	80.7393	+	139.845i	0.0871966	+	0.151029i
$96$	711.675	−	1232.66i	0.756615	−	1.31050i
$97$	1667.43			1.74538			0.872690	−	0.488275i	$-0.162374\pi$
$97$	1667.43			1.74538			0.872690	+	0.488275i	$0.162374\pi$
$98$		0			0
$99$	1681.54			1.70708
$100$	269.662	−	467.069i	0.269662	−	0.467069i
$101$	38.5593	+	66.7867i	0.0379881	+	0.0657973i	0.884394	−	0.466740i	$-0.154572\pi$
$101$	38.5593	+	66.7867i	0.0379881	+	0.0657973i	−0.846406	+	0.532538i	$0.821238\pi$
$102$	−366.228	−	634.325i	−0.355509	−	0.615760i
$103$	−82.3463	+	142.628i	−0.0787749	+	0.136442i	−0.902722	−	0.430225i	$-0.858434\pi$
$103$	−82.3463	+	142.628i	−0.0787749	+	0.136442i	0.823947	+	0.566667i	$0.191768\pi$
$104$	−559.302			−0.527347
$105$		0			0
$106$	498.315			0.456610
$107$	−511.311	+	885.617i	−0.461966	+	0.800148i	−0.999059	−	0.0433749i	$-0.986189\pi$
$107$	−511.311	+	885.617i	−0.461966	+	0.800148i	0.537093	+	0.843523i	$0.319522\pi$
$108$	125.612	+	217.566i	0.111917	+	0.193845i
$109$	−681.259	−	1179.97i	−0.598649	−	1.03689i	−0.993021	−	0.117940i	$-0.962371\pi$
$109$	−681.259	−	1179.97i	−0.598649	−	1.03689i	0.394372	−	0.918951i	$-0.370962\pi$
$110$	−180.398	+	312.458i	−0.156366	+	0.270833i
$111$	−603.770			−0.516282
$112$		0			0
$113$	−1538.41			−1.28072			−0.640360	−	0.768075i	$-0.721215\pi$
$113$	−1538.41			−1.28072			−0.640360	+	0.768075i	$0.721215\pi$
$114$	−1073.57	+	1859.47i	−0.882006	+	1.52768i
$115$	57.9057	+	100.296i	0.0469542	+	0.0813270i
$116$	−271.340	−	469.975i	−0.217184	−	0.376174i
$117$	766.739	−	1328.03i	0.605855	−	1.04937i
$118$	1500.14			1.17033
$119$		0			0
$120$	202.607			0.154128
$121$	−544.169	+	942.529i	−0.408842	+	0.708136i
$122$	−1038.15	−	1798.12i	−0.770404	−	1.33438i
$123$	972.769	+	1684.88i	0.713102	+	1.23513i
$124$	−682.738	+	1182.54i	−0.494449	+	0.856411i
$125$	510.360			0.365184
$126$		0			0
$127$	−170.358			−0.119030			−0.0595151	−	0.998227i	$-0.518955\pi$
$127$	−170.358			−0.119030			−0.0595151	+	0.998227i	$0.518955\pi$
$128$	720.271	−	1247.55i	0.497372	−	0.861473i
$129$	−575.632	−	997.023i	−0.392880	−	0.680488i
$130$	164.514	+	284.946i	0.110991	+	0.192242i
$131$	375.968	−	651.195i	0.250751	−	0.434314i	−0.712981	−	0.701183i	$-0.752656\pi$
$131$	375.968	−	651.195i	0.250751	−	0.434314i	0.963733	+	0.266869i	$0.0859890\pi$
$132$	−1719.39			−1.13374
$133$		0			0
$134$	634.312			0.408927
$135$	−58.3891	+	101.133i	−0.0372247	+	0.0644750i
$136$	−165.324	−	286.350i	−0.104238	−	0.180546i
$137$	−259.311	−	449.140i	−0.161711	−	0.280092i	0.773771	−	0.633465i	$-0.218368\pi$
$137$	−259.311	−	449.140i	−0.161711	−	0.280092i	−0.935483	+	0.353373i	$0.885035\pi$
$138$	−769.954	+	1333.60i	−0.474948	+	0.822634i
$139$	−2975.72			−1.81581			−0.907905	−	0.419177i	$-0.862319\pi$
$139$	−2975.72			−1.81581			−0.907905	+	0.419177i	$0.862319\pi$
$140$		0			0
$141$	−2110.83			−1.26073
$142$	1191.53	−	2063.79i	0.704161	−	1.21964i
$143$	1103.16	+	1910.73i	0.645110	+	1.11736i
$144$	1363.71	+	2362.02i	0.789186	+	1.36691i
$145$	126.129	−	218.462i	0.0722376	−	0.125119i
$146$	−838.604			−0.475365
$147$		0			0
$148$	344.938			0.191579
$149$	1358.97	−	2353.80i	0.747188	−	1.29417i	−0.201977	−	0.979390i	$-0.564737\pi$
$149$	1358.97	−	2353.80i	0.747188	−	1.29417i	0.949165	−	0.314778i	$-0.101930\pi$
$150$	1666.73	+	2886.86i	0.907252	+	1.57141i
$151$	−353.825	−	612.843i	−0.190688	−	0.330281i	0.754791	−	0.655966i	$-0.227738\pi$
$151$	−353.825	−	612.843i	−0.190688	−	0.330281i	−0.945478	+	0.325685i	$0.894405\pi$
$152$	−484.634	+	839.410i	−0.258612	+	0.447929i
$153$	906.561			0.479027
$154$		0			0
$155$	−634.724			−0.328918
$156$	−784.000	+	1357.93i	−0.402373	+	0.696931i
$157$	−1558.96	−	2700.19i	−0.792473	−	1.37260i	−0.924431	−	0.381349i	$-0.875460\pi$
$157$	−1558.96	−	2700.19i	−0.792473	−	1.37260i	0.131958	−	0.991255i	$-0.457874\pi$
$158$	875.459	+	1516.34i	0.440809	+	0.763503i
$159$	−551.937	+	955.983i	−0.275292	+	0.476820i
$160$	−377.991			−0.186768
$161$		0			0
$162$	1706.62			0.827684
$163$	−904.387	+	1566.44i	−0.434583	+	0.752720i	−0.997262	−	0.0739557i	$-0.976438\pi$
$163$	−904.387	+	1566.44i	−0.434583	+	0.752720i	0.562678	+	0.826676i	$0.309771\pi$
$164$	−555.749	−	962.585i	−0.264614	−	0.458325i
$165$	−399.619	−	692.160i	−0.188547	−	0.326573i
$166$	−43.1514	+	74.7404i	−0.0201759	+	0.0349457i
$167$	3147.38			1.45839			0.729197	−	0.684303i	$-0.239894\pi$
$167$	3147.38			1.45839			0.729197	+	0.684303i	$0.239894\pi$
$168$		0			0
$169$	−184.949			−0.0841827
$170$	−97.2570	+	168.454i	−0.0438781	+	0.0759991i
$171$	−1328.75	−	2301.47i	−0.594224	−	1.02923i
$172$	328.862	+	569.606i	0.145788	+	0.252512i
$173$	1642.18	−	2844.34i	0.721691	−	1.25001i	−0.238631	−	0.971110i	$-0.576699\pi$
$173$	1642.18	−	2844.34i	0.721691	−	1.25001i	0.960322	−	0.278895i	$-0.0899681\pi$
$174$	3354.20			1.46139
$175$		0			0
$176$	−3924.13			−1.68064
$177$	−1661.57	+	2877.92i	−0.705599	+	1.22213i
$178$	1893.19	+	3279.11i	0.797196	+	1.38078i
$179$	−1399.41	−	2423.85i	−0.584341	−	1.01211i	−0.994957	−	0.100300i	$-0.968020\pi$
$179$	−1399.41	−	2423.85i	−0.584341	−	1.01211i	0.410616	−	0.911808i	$-0.365314\pi$
$180$	158.681	−	274.843i	0.0657076	−	0.113809i
$181$	−3723.04			−1.52890			−0.764451	−	0.644682i	$-0.776990\pi$
$181$	−3723.04			−1.52890			−0.764451	+	0.644682i	$0.776990\pi$
$182$		0			0
$183$	4599.42			1.85792
$184$	−347.576	+	602.019i	−0.139259	+	0.241203i
$185$	80.1699	+	138.858i	0.0318606	+	0.0551842i
$186$	−4219.86	−	7309.02i	−1.66352	−	2.88131i
$187$	−652.164	+	1129.58i	−0.255032	+	0.441728i
$188$	1205.93			0.467826
$189$		0			0
$190$	570.202			0.217720
$191$	−479.825	+	831.081i	−0.181774	+	0.314842i	−0.942485	−	0.334249i	$-0.891517\pi$
$191$	−479.825	+	831.081i	−0.181774	+	0.314842i	0.760710	+	0.649091i	$0.224851\pi$
$192$	−16.7932	−	29.0867i	−0.00631221	−	0.0109331i
$193$	1895.12	+	3282.45i	0.706808	+	1.22423i	0.966035	+	0.258411i	$0.0831988\pi$
$193$	1895.12	+	3282.45i	0.706808	+	1.22423i	−0.259227	+	0.965816i	$0.583468\pi$
$194$	2943.95	−	5099.08i	1.08950	−	1.88707i
$195$	−728.865			−0.267667
$196$		0			0
$197$	5117.99			1.85097			0.925487	−	0.378779i	$-0.123656\pi$
$197$	5117.99			1.85097			0.925487	+	0.378779i	$0.123656\pi$
$198$	2968.86	−	5142.22i	1.06560	−	1.84566i
$199$	−432.427	−	748.986i	−0.154040	−	0.266805i	0.778669	−	0.627435i	$-0.215895\pi$
$199$	−432.427	−	748.986i	−0.154040	−	0.266805i	−0.932709	+	0.360630i	$0.882562\pi$
$200$	752.402	+	1303.20i	0.266014	+	0.460750i
$201$	−702.567	+	1216.88i	−0.246544	+	0.427026i
$202$	272.316			0.0948519
$203$		0			0
$204$	−926.969			−0.318141
$205$	258.333	−	447.445i	0.0880134	−	0.152444i
$206$	290.775	+	503.637i	0.0983460	+	0.170340i
$207$	−952.973	−	1650.60i	−0.319982	−	0.554224i
$208$	−1789.30	+	3099.17i	−0.596471	+	1.03312i
$209$	3823.53			1.26545
$210$		0			0
$211$	−1344.61			−0.438707			−0.219353	−	0.975645i	$-0.570395\pi$
$211$	−1344.61			−0.438707			−0.219353	+	0.975645i	$0.570395\pi$
$212$	315.325	−	546.159i	0.102154	−	0.176936i
$213$	2639.49	+	4571.73i	0.849084	+	1.47066i
$214$	1805.51	+	3127.23i	0.576738	+	0.998939i
$215$	−152.867	+	264.774i	−0.0484905	+	0.0839881i
$216$	−700.955			−0.220805
$217$		0			0
$218$	−4811.23			−1.49476
$219$	928.842	−	1608.80i	0.286600	−	0.496405i
$220$	228.305	+	395.435i	0.0699650	+	0.121183i
$221$	594.741	+	1030.12i	0.181026	+	0.313545i
$222$	−1066.00	+	1846.36i	−0.322274	+	0.558196i
$223$	−864.916			−0.259727			−0.129863	−	0.991532i	$-0.541454\pi$
$223$	−864.916			−0.259727			−0.129863	+	0.991532i	$0.541454\pi$
$224$		0			0
$225$	−4125.83			−1.22247
$226$	−2716.16	+	4704.53i	−0.799452	+	1.38469i
$227$	−857.672	−	1485.53i	−0.250774	−	0.434353i	0.712965	−	0.701200i	$-0.247352\pi$
$227$	−857.672	−	1485.53i	−0.250774	−	0.434353i	−0.963739	+	0.266846i	$0.914018\pi$
$228$	1358.67	+	2353.28i	0.394649	+	0.683552i
$229$	−522.729	+	905.394i	−0.150842	+	0.261267i	−0.931537	−	0.363646i	$-0.881532\pi$
$229$	−522.729	+	905.394i	−0.150842	+	0.261267i	0.780695	+	0.624912i	$0.214865\pi$
$230$	408.945			0.117239
$231$		0			0
$232$	1514.17			0.428491
$233$	−724.335	+	1254.58i	−0.203660	+	0.352749i	−0.949705	−	0.313146i	$-0.898617\pi$
$233$	−724.335	+	1254.58i	−0.203660	+	0.352749i	0.746045	+	0.665895i	$0.231950\pi$
$234$	−2707.45	−	4689.45i	−0.756375	−	1.31008i
$235$	280.280	+	485.459i	0.0778019	+	0.134757i
$236$	949.263	−	1644.17i	0.261830	−	0.453502i
$237$	−3878.65			−1.06306
$238$		0			0
$239$	−3153.12			−0.853383			−0.426691	−	0.904397i	$-0.640321\pi$
$239$	−3153.12			−0.853383			−0.426691	+	0.904397i	$0.640321\pi$
$240$	648.175	−	1122.67i	0.174331	−	0.301951i
$241$	−190.506	−	329.966i	−0.0509194	−	0.0881950i	0.839442	−	0.543449i	$-0.182882\pi$
$241$	−190.506	−	329.966i	−0.0509194	−	0.0881950i	−0.890362	+	0.455254i	$0.849549\pi$
$242$	1921.53	+	3328.19i	0.510416	+	0.884067i
$243$	−2649.18	+	4588.52i	−0.699363	+	1.21133i
$244$	−2627.68			−0.689426
$245$		0			0
$246$	6869.94			1.78053
$247$	1743.44	−	3019.72i	0.449118	−	0.777895i
$248$	−1904.95	−	3299.47i	−0.487759	−	0.844824i
$249$	−95.5895	−	165.566i	−0.0243283	−	0.0421378i
$250$	901.074	−	1560.71i	0.227956	−	0.394831i
$251$	−3776.23			−0.949617			−0.474808	−	0.880089i	$-0.657483\pi$
$251$	−3776.23			−0.949617			−0.474808	+	0.880089i	$0.657483\pi$
$252$		0			0
$253$	2742.21			0.681428
$254$	−300.778	+	520.963i	−0.0743012	+	0.128693i
$255$	−215.445	−	373.161i	−0.0529086	−	0.0916403i
$256$	−2560.55	−	4435.00i	−0.625133	−	1.08276i
$257$	2129.21	−	3687.90i	0.516795	−	0.895116i	−0.483014	−	0.875612i	$-0.660458\pi$
$257$	2129.21	−	3687.90i	0.516795	−	0.895116i	0.999810	−	0.0195034i	$-0.00620851\pi$
$258$	−4065.26			−0.980977
$259$		0			0
$260$	416.405			0.0993244
$261$	−2075.75	+	3595.30i	−0.492282	+	0.852658i
$262$	−1327.59	−	2299.45i	−0.313049	−	0.542216i
$263$	−2099.41	−	3636.29i	−0.492226	−	0.852560i	0.507734	−	0.861514i	$-0.330483\pi$
$263$	−2099.41	−	3636.29i	−0.492226	−	0.852560i	−0.999960	+	0.00895400i	$0.997150\pi$
$264$	2398.69	−	4154.65i	0.559202	−	0.968565i
$265$	293.150			0.0679548
$266$		0			0
$267$	−8387.65			−1.92253
$268$	401.381	−	695.212i	0.0914860	−	0.158458i
$269$	1870.29	+	3239.44i	0.423917	+	0.734247i	0.996319	−	0.0857271i	$-0.0273213\pi$
$269$	1870.29	+	3239.44i	0.423917	+	0.734247i	−0.572401	+	0.819974i	$0.693988\pi$
$270$	206.179	+	357.113i	0.0464729	+	0.0804933i
$271$	2178.15	−	3772.66i	0.488240	−	0.845656i	−0.511669	−	0.859183i	$-0.670972\pi$
$271$	2178.15	−	3772.66i	0.488240	−	0.845656i	0.999909	+	0.0135265i	$0.00430574\pi$
$272$	−2115.60			−0.471607
$273$		0			0
$274$	−1831.32			−0.403775
$275$	2968.05	−	5140.81i	0.650837	−	1.12728i
$276$	974.426	+	1687.76i	0.212513	+	0.368083i
$277$	672.152	+	1164.20i	0.145797	+	0.252527i	0.929670	−	0.368394i	$-0.120092\pi$
$277$	672.152	+	1164.20i	0.145797	+	0.252527i	−0.783873	+	0.620921i	$0.786759\pi$
$278$	−5253.83	+	9099.90i	−1.13347	+	1.96322i
$279$	10445.9			2.24150
$280$		0			0
$281$	4205.54			0.892817			0.446408	−	0.894829i	$-0.352703\pi$
$281$	4205.54			0.892817			0.446408	+	0.894829i	$0.352703\pi$
$282$	−3726.80	+	6455.00i	−0.786977	+	1.36308i
$283$	2376.02	+	4115.38i	0.499079	+	0.864431i	0.999999	−	0.00106280i	$-0.000338299\pi$
$283$	2376.02	+	4115.38i	0.499079	+	0.864431i	−0.500920	+	0.865494i	$0.667005\pi$
$284$	−1507.96	−	2611.86i	−0.315073	−	0.545723i
$285$	−631.559	+	1093.89i	−0.131264	+	0.227356i
$286$	7790.79			1.61077
$287$		0			0
$288$	6220.73			1.27278
$289$	2104.90	−	3645.80i	0.428435	−	0.742071i
$290$	−445.378	−	771.418i	−0.0901845	−	0.156204i
$291$	6521.48	+	11295.5i	1.31373	+	2.27545i
$292$	−530.654	+	919.119i	−0.106350	+	0.184203i
$293$	4961.17			0.989196			0.494598	−	0.869122i	$-0.335315\pi$
$293$	4961.17			0.989196			0.494598	+	0.869122i	$0.335315\pi$
$294$		0			0
$295$	882.506			0.174174
$296$	−481.216	+	833.490i	−0.0944936	+	0.163668i
$297$	1382.55	+	2394.65i	0.270114	+	0.467850i
$298$	−4798.69	−	8311.58i	−0.932822	−	1.61569i
$299$	1250.38	−	2165.72i	0.241844	−	0.418886i
$300$	4218.71			0.811890
$301$		0			0
$302$	−2498.80			−0.476126
$303$	−301.619	+	522.419i	−0.0571866	+	0.0990501i
$304$	3100.85	+	5370.84i	0.585020	+	1.01329i
$305$	−610.722	−	1057.80i	−0.114655	−	0.198589i
$306$	1600.59	−	2772.31i	0.299019	−	0.517915i
$307$	4234.00			0.787124			0.393562	−	0.919298i	$-0.371243\pi$
$307$	4234.00			0.787124			0.393562	+	0.919298i	$0.371243\pi$
$308$		0			0
$309$	−1288.26			−0.237173
$310$	−1120.65	+	1941.02i	−0.205317	+	0.355620i
$311$	−342.350	−	592.968i	−0.0624209	−	0.108116i	0.833126	−	0.553083i	$-0.186549\pi$
$311$	−342.350	−	592.968i	−0.0624209	−	0.108116i	−0.895547	+	0.444967i	$0.853215\pi$
$312$	−2187.49	−	3788.84i	−0.396930	−	0.687502i
$313$	−2972.04	+	5147.72i	−0.536707	+	0.929604i	0.462371	+	0.886686i	$0.346999\pi$
$313$	−2972.04	+	5147.72i	−0.536707	+	0.929604i	−0.999079	+	0.0429180i	$0.986335\pi$
$314$	−11009.8			−1.97872
$315$		0			0
$316$	2215.90			0.394475
$317$	1411.95	−	2445.56i	0.250166	−	0.433301i	−0.713405	−	0.700752i	$-0.752848\pi$
$317$	1411.95	−	2445.56i	0.250166	−	0.433301i	0.963571	+	0.267451i	$0.0861813\pi$
$318$	1948.96	+	3375.70i	0.343686	+	0.595282i
$319$	−2986.52	−	5172.80i	−0.524178	−	0.907904i
$320$	−4.45967	+	7.72438i	−0.000779073	+	0.00134939i
$321$	−7999.16			−1.39087
$322$		0			0
$323$	2061.37			0.355101
$324$	1079.92	−	1870.48i	0.185171	−	0.320726i
$325$	−2706.71	−	4688.16i	−0.461974	−	0.800162i
$326$	3193.51	+	5531.32i	0.542552	+	0.939728i
$327$	5328.94	−	9230.00i	0.901196	−	1.56092i
$328$	3101.26			0.522068
$329$		0			0
$330$	−2822.21			−0.470780
$331$	1406.48	−	2436.10i	0.233557	−	0.404533i	−0.725295	−	0.688438i	$-0.758297\pi$
$331$	1406.48	−	2436.10i	0.233557	−	0.404533i	0.958852	+	0.283905i	$0.0916301\pi$
$332$	54.6109	+	94.5888i	0.00902760	+	0.0156363i
$333$	−1319.38	−	2285.24i	−0.217122	−	0.376067i
$334$	5556.91	−	9624.85i	0.910361	−	1.57679i
$335$	373.154			0.0608584
$336$		0			0
$337$	4260.10			0.688612			0.344306	−	0.938857i	$-0.388114\pi$
$337$	4260.10			0.688612			0.344306	+	0.938857i	$0.388114\pi$
$338$	−326.540	+	565.584i	−0.0525486	+	0.0910169i
$339$	−6016.87	−	10421.5i	−0.963986	−	1.66967i
$340$	123.085	+	213.190i	0.0196330	+	0.0340054i
$341$	−7514.58	+	13015.6i	−1.19336	+	2.06697i
$342$	−9384.00			−1.48371
$343$		0			0
$344$	−1835.16			−0.287631
$345$	−452.950	+	784.532i	−0.0706840	+	0.122428i
$346$	−5798.74	−	10043.7i	−0.900990	−	1.56056i
$347$	−18.0292	−	31.2275i	−0.00278922	−	0.00483106i	0.864627	−	0.502414i	$-0.167555\pi$
$347$	−18.0292	−	31.2275i	−0.00278922	−	0.00483106i	−0.867417	+	0.497583i	$0.834221\pi$
$348$	2122.48	−	3676.24i	0.326945	−	0.566285i
$349$	242.692			0.0372236			0.0186118	−	0.999827i	$-0.494075\pi$
$349$	242.692			0.0372236			0.0186118	+	0.999827i	$0.494075\pi$
$350$		0			0
$351$	2521.63			0.383461
$352$	−4475.09	+	7751.08i	−0.677622	+	1.17368i
$353$	−54.9949	−	95.2539i	−0.00829201	−	0.0143622i	0.861850	−	0.507164i	$-0.169306\pi$
$353$	−54.9949	−	95.2539i	−0.00829201	−	0.0143622i	−0.870142	+	0.492802i	$0.835973\pi$
$354$	5867.20	+	10162.3i	0.880899	+	1.52576i
$355$	700.955	−	1214.09i	0.104797	−	0.181513i
$356$	4791.92			0.713402
$357$		0			0
$358$	−9883.01			−1.45903
$359$	−6202.23	+	10742.6i	−0.911814	+	1.57931i	−0.100314	+	0.994956i	$0.531985\pi$
$359$	−6202.23	+	10742.6i	−0.911814	+	1.57931i	−0.811500	+	0.584352i	$0.801349\pi$
$360$	442.745	+	766.857i	0.0648187	+	0.112269i
$361$	408.136	+	706.913i	0.0595038	+	0.103064i
$362$	−6573.26	+	11385.2i	−0.954373	+	1.65302i
$363$	−8513.20			−1.23093
$364$		0			0
$365$	−493.335			−0.0707461
$366$	8120.58	−	14065.3i	1.15975	−	2.00875i
$367$	6929.81	+	12002.8i	0.985649	+	1.70719i	0.639015	+	0.769194i	$0.279342\pi$
$367$	6929.81	+	12002.8i	0.985649	+	1.70719i	0.346634	+	0.938001i	$0.387325\pi$
$368$	2223.91	+	3851.93i	0.315025	+	0.545640i
$369$	−4251.47	+	7363.76i	−0.599790	+	1.03887i
$370$	566.181			0.0795523
$371$		0			0
$372$	−10681.0			−1.48867
$373$	−2449.03	+	4241.85i	−0.339963	+	0.588832i	−0.984425	−	0.175803i	$-0.943748\pi$
$373$	−2449.03	+	4241.85i	−0.339963	+	0.588832i	0.644463	+	0.764636i	$0.277081\pi$
$374$	2302.88	+	3988.70i	0.318393	+	0.551472i
$375$	1996.07	+	3457.30i	0.274871	+	0.476091i
$376$	−1682.37	+	2913.94i	−0.230748	+	0.399668i
$377$	−5447.11			−0.744139
$378$		0			0
$379$	−9806.25			−1.32906			−0.664530	−	0.747262i	$-0.731368\pi$
$379$	−9806.25			−1.32906			−0.664530	+	0.747262i	$0.731368\pi$
$380$	360.814	−	624.948i	0.0487088	−	0.0843662i
$381$	−666.287	−	1154.04i	−0.0895930	−	0.155180i
$382$	1694.32	+	2934.65i	0.226935	+	0.393063i
$383$	5364.84	−	9292.18i	0.715746	−	1.23971i	−0.246926	−	0.969034i	$-0.579420\pi$
$383$	5364.84	−	9292.18i	0.715746	−	1.23971i	0.962671	−	0.270673i	$-0.0872463\pi$
$384$	11268.2			1.49747
$385$		0			0
$386$	13383.8			1.76482
$387$	2515.79	−	4357.47i	0.330451	−	0.572359i
$388$	−3725.76	−	6453.21i	−0.487492	−	0.844361i
$389$	−2632.03	−	4558.80i	−0.343057	−	0.594191i	0.641942	−	0.766753i	$-0.278129\pi$
$389$	−2632.03	−	4558.80i	−0.343057	−	0.594191i	−0.984999	+	0.172562i	$0.944796\pi$
$390$	−1286.86	+	2228.90i	−0.167084	+	0.289397i
$391$	1478.40			0.191217
$392$		0			0
$393$	5881.79			0.754954
$394$	9036.15	−	15651.1i	1.15542	−	2.00124i
$395$	515.016	+	892.034i	0.0656032	+	0.113628i
$396$	−3757.29	−	6507.81i	−0.476795	−	0.825833i
$397$	607.450	−	1052.13i	0.0767935	−	0.133010i	−0.825071	−	0.565029i	$-0.808865\pi$
$397$	607.450	−	1052.13i	0.0767935	−	0.133010i	0.901865	+	0.432018i	$0.142198\pi$
$398$	−3053.91			−0.384620
$399$		0			0
$400$	9628.26			1.20353
$401$	−1147.73	+	1987.92i	−0.142929	+	0.247561i	−0.928599	−	0.371086i	$-0.878986\pi$
$401$	−1147.73	+	1987.92i	−0.142929	+	0.247561i	0.785669	+	0.618647i	$0.212319\pi$
$402$	2480.86	+	4296.97i	0.307796	+	0.533117i
$403$	6852.92	+	11869.6i	0.847067	+	1.46716i
$404$	172.317	−	298.461i	0.0212205	−	0.0367550i
$405$	1003.97			0.123180
$406$		0			0
$407$	3796.57			0.462381
$408$	1293.20	−	2239.88i	0.156919	−	0.271791i
$409$	2323.27	+	4024.03i	0.280876	+	0.486492i	0.971601	−	0.236626i	$-0.0760416\pi$
$409$	2323.27	+	4024.03i	0.280876	+	0.486492i	−0.690724	+	0.723118i	$0.742708\pi$
$410$	−912.206	−	1579.99i	−0.109880	−	0.190317i
$411$	2028.38	−	3513.26i	0.243437	−	0.421646i
$412$	735.990			0.0880087
$413$		0			0
$414$	−6730.14			−0.798957
$415$	−25.3852	+	43.9684i	−0.00300267	+	0.00520078i
$416$	4081.06	+	7068.60i	0.480986	+	0.833093i
$417$	−11638.3	−	20158.2i	−1.36674	−	2.36727i
$418$	6750.69	−	11692.5i	0.789922	−	1.36818i
$419$	−7541.24			−0.879269			−0.439634	−	0.898177i	$-0.644892\pi$
$419$	−7541.24			−0.879269			−0.439634	+	0.898177i	$0.644892\pi$
$420$		0			0
$421$	−6243.63			−0.722794			−0.361397	−	0.932412i	$-0.617700\pi$
$421$	−6243.63			−0.722794			−0.361397	+	0.932412i	$0.617700\pi$
$422$	−2374.00	+	4111.90i	−0.273850	+	0.474322i
$423$	−4612.66	−	7989.36i	−0.530202	−	0.918336i
$424$	879.808	+	1523.87i	0.100772	+	0.174542i
$425$	1600.15	−	2771.55i	0.182632	−	0.316329i
$426$	18640.8			2.12006
$427$		0			0
$428$	4569.97			0.516116
$429$	−8629.12	+	14946.1i	−0.971137	+	1.68206i
$430$	539.794	+	934.951i	0.0605376	+	0.104854i
$431$	−5732.90	−	9929.68i	−0.640706	−	1.10974i	−0.985275	−	0.170974i	$-0.945309\pi$
$431$	−5732.90	−	9929.68i	−0.640706	−	1.10974i	0.344570	−	0.938761i	$-0.388025\pi$
$432$	−2242.48	+	3884.08i	−0.249748	+	0.432576i
$433$	−5156.40			−0.572289			−0.286144	−	0.958187i	$-0.592374\pi$
$433$	−5156.40			−0.572289			−0.286144	+	0.958187i	$0.592374\pi$
$434$		0			0
$435$	1973.21			0.217491
$436$	−3044.46	+	5273.16i	−0.334411	+	0.579216i
$437$	−2166.90	−	3753.18i	−0.237201	−	0.410844i
$438$	−3279.86	−	5680.89i	−0.357803	−	0.619734i
$439$	−2532.12	+	4385.77i	−0.275289	+	0.476814i	−0.970208	−	0.242274i	$-0.922107\pi$
$439$	−2532.12	+	4385.77i	−0.275289	+	0.476814i	0.694919	+	0.719088i	$0.255440\pi$
$440$	−1274.01			−0.138037
$441$		0			0
$442$	4200.22			0.452000
$443$	−6351.82	+	11001.7i	−0.681228	+	1.17992i	0.293378	+	0.955996i	$0.405220\pi$
$443$	−6351.82	+	11001.7i	−0.681228	+	1.17992i	−0.974606	+	0.223925i	$0.928113\pi$
$444$	1349.09	+	2336.68i	0.144200	+	0.249762i
$445$	1113.73	+	1929.04i	0.118642	+	0.205495i
$446$	−1527.06	+	2644.95i	−0.162127	+	0.280812i
$447$	21260.2			2.24961
$448$		0			0
$449$	13942.2			1.46542			0.732709	−	0.680542i	$-0.238256\pi$
$449$	13942.2			1.46542			0.732709	+	0.680542i	$0.238256\pi$
$450$	−7284.41	+	12617.0i	−0.763090	+	1.32171i
$451$	−6116.87	−	10594.7i	−0.638652	−	1.10618i
$452$	3437.48	+	5953.88i	0.357711	+	0.619573i
$453$	2767.69	−	4793.78i	0.287058	−	0.497199i
$454$	−6057.10			−0.626154
$455$		0			0
$456$	−7581.80			−0.778619
$457$	7607.01	−	13175.7i	0.778646	−	1.34865i	−0.154077	−	0.988059i	$-0.549240\pi$
$457$	7607.01	−	13175.7i	0.778646	−	1.34865i	0.932722	−	0.360595i	$-0.117426\pi$
$458$	1845.82	+	3197.06i	0.188318	+	0.326177i
$459$	745.369	+	1291.02i	0.0757971	+	0.131284i
$460$	258.773	−	448.208i	0.0262290	−	0.0454300i
$461$	11430.2			1.15479			0.577394	−	0.816465i	$-0.304070\pi$
$461$	11430.2			1.15479			0.577394	+	0.816465i	$0.304070\pi$
$462$		0			0
$463$	−9347.88			−0.938300			−0.469150	−	0.883119i	$-0.655440\pi$
$463$	−9347.88			−0.938300			−0.469150	+	0.883119i	$0.655440\pi$
$464$	4844.08	−	8390.20i	0.484657	−	0.839451i
$465$	−2482.47	−	4299.76i	−0.247574	−	0.428810i
$466$	2557.72	+	4430.10i	0.254258	+	0.440387i
$467$	1815.42	−	3144.40i	0.179888	−	0.311575i	−0.761954	−	0.647631i	$-0.775760\pi$
$467$	1815.42	−	3144.40i	0.179888	−	0.311575i	0.941842	+	0.336056i	$0.109093\pi$
$468$	−6852.92			−0.676872
$469$		0			0
$470$	1979.41			0.194262
$471$	12194.5	−	21121.4i	1.19298	−	2.06629i
$472$	2648.60	+	4587.51i	0.258287	+	0.447367i
$473$	3619.63	+	6269.38i	0.351862	+	0.609443i
$474$	−6848.01	+	11861.1i	−0.663586	+	1.14936i
$475$	−9381.43			−0.906210
$476$		0			0
$477$	−4824.46			−0.463096
$478$	−5567.04	+	9642.39i	−0.532700	+	0.922663i
$479$	3260.62	+	5647.57i	0.311027	+	0.538714i	0.978585	−	0.205844i	$-0.0659939\pi$
$479$	3260.62	+	5647.57i	0.311027	+	0.538714i	−0.667558	+	0.744557i	$0.732661\pi$
$480$	−1478.36	−	2560.60i	−0.140578	−	0.243489i
$481$	1731.14	−	2998.42i	0.164102	−	0.284234i
$482$	−1345.40			−0.127140
$483$		0			0
$484$	4863.65			0.456766
$485$	1731.87	−	2999.69i	0.162145	−	0.280843i
$486$	9354.61	+	16202.7i	0.873115	+	1.51228i
$487$	1833.14	+	3175.10i	0.170570	+	0.295436i	0.938619	−	0.344955i	$-0.112106\pi$
$487$	1833.14	+	3175.10i	0.170570	+	0.295436i	−0.768049	+	0.640391i	$0.778772\pi$
$488$	3665.83	−	6349.40i	0.340049	−	0.588983i
$489$	−14148.6			−1.30843
$490$		0			0
$491$	−12470.7			−1.14623			−0.573113	−	0.819476i	$-0.694264\pi$
$491$	−12470.7			−1.14623			−0.573113	+	0.819476i	$0.694264\pi$
$492$	4347.18	−	7529.53i	0.398345	−	0.689954i
$493$	−1610.11	−	2788.79i	−0.147091	−	0.254768i
$494$	−6156.30	−	10663.0i	−0.560698	−	0.971158i
$495$	1746.53	−	3025.07i	0.158587	−	0.274681i
$496$	−24377.0			−2.20678
$497$		0			0
$498$	−675.078			−0.0607449
$499$	1151.97	−	1995.26i	0.103345	−	0.178998i	−0.809716	−	0.586822i	$-0.800379\pi$
$499$	1151.97	−	1995.26i	0.103345	−	0.178998i	0.913061	+	0.407824i	$0.133712\pi$
$500$	−1140.37	−	1975.17i	−0.101998	−	0.176665i
$501$	12309.7	+	21321.1i	1.09772	+	1.90131i
$502$	−6667.18	+	11547.9i	−0.592771	+	1.02671i
$503$	10520.4			0.932570			0.466285	−	0.884635i	$-0.345592\pi$
$503$	10520.4			0.932570			0.466285	+	0.884635i	$0.345592\pi$
$504$		0			0
$505$	160.198			0.0141163
$506$	4841.55	−	8385.81i	0.425362	−	0.736748i
$507$	−723.355	−	1252.89i	−0.0633636	−	0.109749i
$508$	380.654	+	659.312i	0.0332457	+	0.0575832i
$509$	−4831.11	+	8367.73i	−0.420698	+	0.728670i	−0.996008	−	0.0892655i	$-0.971548\pi$
$509$	−4831.11	+	8367.73i	−0.420698	+	0.728670i	0.575310	+	0.817935i	$0.304881\pi$
$510$	−1521.53			−0.132107
$511$		0			0
$512$	−6558.89			−0.566142
$513$	2184.99	−	3784.51i	0.188050	−	0.325712i
$514$	−7518.51	−	13022.4i	−0.645189	−	1.11750i
$515$	171.058	+	296.281i	0.0146363	+	0.0253508i
$516$	−2572.42	+	4455.57i	−0.219466	+	0.380127i
$517$	13273.1			1.12911
$518$		0			0
$519$	25690.9			2.17284
$520$	−580.919	+	1006.18i	−0.0489903	+	0.0848537i
$521$	4303.90	+	7454.58i	0.361914	+	0.626854i	0.988276	−	0.152679i	$-0.0487899\pi$
$521$	4303.90	+	7454.58i	0.361914	+	0.626854i	−0.626361	+	0.779533i	$0.715457\pi$
$522$	7329.74	+	12695.5i	0.614586	+	1.06449i
$523$	−5241.36	+	9078.30i	−0.438219	+	0.759018i	−0.997552	−	0.0699250i	$-0.977724\pi$
$523$	−5241.36	+	9078.30i	−0.438219	+	0.759018i	0.559333	+	0.828943i	$0.311057\pi$
$524$	−3360.30			−0.280144
$525$		0			0
$526$	−14826.6			−1.22903
$527$	−4051.30	+	7017.06i	−0.334872	+	0.580015i
$528$	−15347.7	−	26582.9i	−1.26500	−	2.19105i
$529$	4529.41	+	7845.18i	0.372270	+	0.644791i
$530$	517.574	−	896.465i	0.0424189	−	0.0734716i
$531$	−14523.7			−1.18696
$532$		0			0
$533$	−11156.6			−0.906649
$534$	−14808.9	+	25649.8i	−1.20008	+	2.07861i
$535$	1062.15	+	1839.69i	0.0858328	+	0.148667i
$536$	1119.92	+	1939.75i	0.0902483	+	0.156315i
$537$	10946.5	−	18959.9i	0.879656	−	1.52361i
$538$	13208.5			1.05847
$539$		0			0
$540$	521.866			0.0415881
$541$	−10361.3	+	17946.3i	−0.823416	+	1.42620i	0.0797082	+	0.996818i	$0.474601\pi$
$541$	−10361.3	+	17946.3i	−0.823416	+	1.42620i	−0.903124	+	0.429380i	$0.858732\pi$
$542$	−7691.32	−	13321.8i	−0.609540	−	1.05575i
$543$	−14561.2	−	25220.7i	−1.15079	−	1.99323i
$544$	−2412.64	+	4178.81i	−0.190149	+	0.329347i
$545$	−2830.35			−0.222457
$546$		0			0
$547$	−4175.09			−0.326351			−0.163176	−	0.986597i	$-0.552174\pi$
$547$	−4175.09			−0.326351			−0.163176	+	0.986597i	$0.552174\pi$
$548$	−1158.83	+	2007.15i	−0.0903334	+	0.156462i
$549$	10050.9	+	17408.6i	0.781348	+	1.35333i
$550$	−10480.6	−	18152.9i	−0.812532	−	1.40735i
$551$	−4719.91	+	8175.12i	−0.364927	+	0.632072i
$552$	−5437.61			−0.419276
$553$		0			0
$554$	4746.91			0.364038
$555$	−627.105	+	1086.18i	−0.0479624	+	0.0830733i
$556$	6649.06	+	11516.5i	0.507164	+	0.878433i
$557$	5080.87	+	8800.33i	0.386505	+	0.669447i	0.991977	−	0.126420i	$-0.0403488\pi$
$557$	5080.87	+	8800.33i	0.386505	+	0.669447i	−0.605472	+	0.795867i	$0.707015\pi$
$558$	18442.8	−	31943.9i	1.39919	−	2.42347i
$559$	6601.85			0.499514
$560$		0			0
$561$	−10202.7			−0.767841
$562$	7425.15	−	12860.7i	0.557315	−	0.965298i
$563$	−8552.22	−	14812.9i	−0.640201	−	1.10886i	−0.985388	−	0.170326i	$-0.945518\pi$
$563$	−8552.22	−	14812.9i	−0.640201	−	1.10886i	0.345187	−	0.938534i	$-0.387816\pi$
$564$	4716.50	+	8169.22i	0.352129	+	0.609905i
$565$	−1597.87	+	2767.59i	−0.118978	+	0.206076i
$566$	16780.0			1.24614
$567$		0			0
$568$	8414.89			0.621621
$569$	9128.79	−	15811.5i	0.672581	−	1.16495i	−0.304588	−	0.952484i	$-0.598519\pi$
$569$	9128.79	−	15811.5i	0.672581	−	1.16495i	0.977170	−	0.212461i	$-0.0681479\pi$
$570$	2230.12	+	3862.68i	0.163876	+	0.283841i
$571$	−6815.25	−	11804.4i	−0.499491	−	0.865143i	0.500509	−	0.865731i	$-0.333146\pi$
$571$	−6815.25	−	11804.4i	−0.499491	−	0.865143i	−1.00000		0.000587868i	$0.999813\pi$
$572$	4929.87	−	8538.79i	0.360364	−	0.624169i
$573$	−7506.57			−0.547280
$574$		0			0
$575$	−6728.30			−0.487981
$576$	73.3943	−	127.123i	0.00530920	−	0.00919580i
$577$	2221.04	+	3846.96i	0.160248	+	0.277558i	0.934958	−	0.354759i	$-0.115437\pi$
$577$	2221.04	+	3846.96i	0.160248	+	0.277558i	−0.774709	+	0.632317i	$0.782104\pi$
$578$	−7432.68	−	12873.8i	−0.534877	−	0.926433i
$579$	−14824.0	+	25676.0i	−1.06402	+	1.84293i
$580$	−1127.31			−0.0807052
$581$		0			0
$582$	46056.4			3.28024
$583$	3470.63	−	6011.32i	0.246551	−	0.427038i
$584$	−1480.61	−	2564.49i	−0.104911	−	0.181711i
$585$	−1592.75	−	2758.72i	−0.112567	−	0.194972i
$586$	8759.26	−	15171.5i	0.617477	−	1.06950i
$587$	−3103.38			−0.218211			−0.109106	−	0.994030i	$-0.534799\pi$
$587$	−3103.38			−0.218211			−0.109106	+	0.994030i	$0.534799\pi$
$588$		0			0
$589$	23752.1			1.66161
$590$	1558.12	−	2698.74i	0.108723	−	0.188314i
$591$	20017.0	+	34670.4i	1.39321	+	2.41311i
$592$	3078.99	+	5332.96i	0.213759	+	0.370242i
$593$	2968.86	−	5142.21i	0.205592	−	0.356096i	−0.744729	−	0.667367i	$-0.767421\pi$
$593$	2968.86	−	5142.21i	0.205592	−	0.356096i	0.950321	+	0.311271i	$0.100755\pi$
$594$	9763.93			0.674443
$595$		0			0
$596$	−12146.1			−0.834772
$597$	3382.53	−	5858.72i	0.231889	−	0.401644i
$598$	−4415.25	−	7647.44i	−0.301928	−	0.522955i
$599$	1300.16	+	2251.95i	0.0886866	+	0.153610i	0.906956	−	0.421225i	$-0.138400\pi$
$599$	1300.16	+	2251.95i	0.0886866	+	0.153610i	−0.818270	+	0.574835i	$0.805066\pi$
$600$	−5885.44	+	10193.9i	−0.400453	+	0.693605i
$601$	13881.4			0.942156			0.471078	−	0.882092i	$-0.343865\pi$
$601$	13881.4			0.942156			0.471078	+	0.882092i	$0.343865\pi$
$602$		0			0
$603$	−6141.11			−0.414735
$604$	−1581.20	+	2738.71i	−0.106520	+	0.184498i
$605$	1130.40	+	1957.91i	0.0759626	+	0.131571i
$606$	1065.05	+	1844.73i	0.0713942	+	0.123658i
$607$	−6142.28	+	10638.7i	−0.410721	+	0.711389i	−0.994969	−	0.100186i	$-0.968056\pi$
$607$	−6142.28	+	10638.7i	−0.410721	+	0.711389i	0.584248	+	0.811575i	$0.301390\pi$
$608$	14144.9			0.943505
$609$		0			0
$610$	−4313.07			−0.286281
$611$	6052.20	−	10482.7i	0.400729	−	0.694084i
$612$	−2025.65	−	3508.53i	−0.133794	−	0.231738i
$613$	−11031.0	−	19106.2i	−0.726815	−	1.25888i	−0.958223	−	0.286023i	$-0.907666\pi$
$613$	−11031.0	−	19106.2i	−0.726815	−	1.25888i	0.231408	−	0.972857i	$-0.425667\pi$
$614$	7475.40	−	12947.8i	0.491340	−	0.851025i
$615$	4041.46			0.264988
$616$		0			0
$617$	−12182.2			−0.794871			−0.397436	−	0.917630i	$-0.630100\pi$
$617$	−12182.2			−0.794871			−0.397436	+	0.917630i	$0.630100\pi$
$618$	−2274.50	+	3939.55i	−0.148048	+	0.256427i
$619$	11624.3	+	20133.9i	0.754799	+	1.30735i	0.945474	+	0.325698i	$0.105599\pi$
$619$	11624.3	+	20133.9i	0.754799	+	1.30735i	−0.190675	+	0.981653i	$0.561068\pi$
$620$	1418.25	+	2456.48i	0.0918682	+	0.159120i
$621$	1567.06	−	2714.22i	0.101262	−	0.175391i
$622$	−2417.76			−0.155858
$623$		0			0
$624$	−27992.6			−1.79583
$625$	−7012.72	+	12146.4i	−0.448814	+	0.777368i
$626$	10494.6	+	18177.3i	0.670048	+	1.16056i
$627$	14954.2	+	25901.5i	0.952494	+	1.64977i
$628$	−6966.78	+	12066.8i	−0.442683	+	0.766749i
$629$	2046.83			0.129749
$630$		0			0
$631$	19184.4			1.21033			0.605165	−	0.796100i	$-0.293107\pi$
$631$	19184.4			1.21033			0.605165	+	0.796100i	$0.293107\pi$
$632$	−3091.36	+	5354.39i	−0.194569	+	0.337004i
$633$	−5258.92	−	9108.72i	−0.330211	−	0.571942i
$634$	−4985.76	−	8635.59i	−0.312318	−	0.540951i
$635$	−176.942	+	306.473i	−0.0110579	+	0.0191528i
$636$	4933.07			0.307561
$637$		0			0
$638$	−21091.6			−1.30881
$639$	−11535.8	+	19980.7i	−0.714164	+	1.23697i
$640$	−1496.22	−	2591.53i	−0.0924113	−	0.160061i
$641$	9716.68	+	16829.8i	0.598730	+	1.03703i	0.993009	+	0.118040i	$0.0376611\pi$
$641$	9716.68	+	16829.8i	0.598730	+	1.03703i	−0.394279	+	0.918991i	$0.629006\pi$
$642$	−14123.0	+	24461.8i	−0.868211	+	1.50379i
$643$	−5777.47			−0.354341			−0.177170	−	0.984180i	$-0.556694\pi$
$643$	−5777.47			−0.354341			−0.177170	+	0.984180i	$0.556694\pi$
$644$		0			0
$645$	−2391.52			−0.145994
$646$	3639.48	−	6303.76i	0.221661	−	0.383929i
$647$	−14615.7	−	25315.2i	−0.888106	−	1.53824i	−0.842112	−	0.539302i	$-0.818688\pi$
$647$	−14615.7	−	25315.2i	−0.888106	−	1.53824i	−0.0459932	−	0.998942i	$-0.514645\pi$
$648$	3013.15	+	5218.93i	0.182666	+	0.316387i
$649$	10448.1	−	18096.6i	0.631932	−	1.09454i
$650$	−19115.5			−1.15349
$651$		0			0
$652$	8083.18			0.485524
$653$	3546.63	−	6142.95i	0.212543	−	0.368135i	−0.739967	−	0.672643i	$-0.765159\pi$
$653$	3546.63	−	6142.95i	0.212543	−	0.368135i	0.952510	+	0.304508i	$0.0984922\pi$
$654$	−18817.2	−	32592.3i	−1.12509	−	1.94872i
$655$	−780.997	−	1352.73i	−0.0465894	−	0.0806952i
$656$	9921.46	−	17184.5i	0.590500	−	1.02278i
$657$	8118.98			0.482118
$658$		0			0
$659$	19014.2			1.12396			0.561980	−	0.827151i	$-0.310040\pi$
$659$	19014.2			1.12396			0.561980	+	0.827151i	$0.310040\pi$
$660$	−1785.84	+	3093.17i	−0.105324	+	0.182427i
$661$	−10529.2	−	18237.1i	−0.619573	−	1.07313i	−0.989564	−	0.144097i	$-0.953972\pi$
$661$	−10529.2	−	18237.1i	−0.619573	−	1.07313i	0.369990	−	0.929036i	$-0.379361\pi$
$662$	−4966.48	−	8602.19i	−0.291583	−	0.505036i
$663$	−4652.18	+	8057.82i	−0.272513	+	0.472006i
$664$	−304.746			−0.0178109
$665$		0			0
$666$	−9317.83			−0.542130
$667$	−3385.08	+	5863.13i	−0.196508	+	0.340362i
$668$	−7032.63	−	12180.9i	−0.407336	−	0.705527i
$669$	−3382.77	−	5859.13i	−0.195494	−	0.338605i
$670$	658.827	−	1141.12i	0.0379891	−	0.0657991i
$671$	−28921.6			−1.66395
$672$		0			0
$673$	9634.87			0.551853			0.275926	−	0.961179i	$-0.411015\pi$
$673$	9634.87			0.551853			0.275926	+	0.961179i	$0.411015\pi$
$674$	7521.48	−	13027.6i	0.429846	−	0.744516i
$675$	−3392.23	−	5875.52i	−0.193433	−	0.335035i
$676$	413.257	+	715.783i	0.0235126	+	0.0407250i
$677$	4185.66	−	7249.77i	0.237619	−	0.411568i	−0.722412	−	0.691463i	$-0.756966\pi$
$677$	4185.66	−	7249.77i	0.237619	−	0.411568i	0.960030	+	0.279895i	$0.0902998\pi$
$678$	−42492.7			−2.40696
$679$		0			0
$680$	−686.854			−0.0387348
$681$	6708.88	−	11620.1i	0.377511	−	0.653868i
$682$	26534.9	+	45959.9i	1.48985	+	2.58049i
$683$	6034.42	+	10451.9i	0.338069	+	0.585552i	0.984069	−	0.177785i	$-0.0568931\pi$
$683$	6034.42	+	10451.9i	0.338069	+	0.585552i	−0.646001	+	0.763337i	$0.723560\pi$
$684$	−5938.03	+	10285.0i	−0.331939	+	0.574935i
$685$	−1077.33			−0.0600917
$686$		0			0
$687$	−8177.78			−0.454151
$688$	−5870.98	+	10168.8i	−0.325333	+	0.563493i
$689$	−3165.05	−	5482.02i	−0.175005	−	0.303118i
$690$	1599.42	+	2770.28i	0.0882449	+	0.152845i
$691$	1490.64	−	2581.87i	0.0820648	−	0.142140i	−0.822072	−	0.569384i	$-0.807182\pi$
$691$	1490.64	−	2581.87i	0.0820648	−	0.142140i	0.904137	+	0.427243i	$0.140515\pi$
$692$	−14677.4			−0.806286
$693$		0			0
$694$	−127.327			−0.00696435
$695$	−3090.73	+	5353.30i	−0.168688	+	0.292176i
$696$	5922.06	+	10257.3i	0.322522	+	0.558624i
$697$	−3297.76	−	5711.89i	−0.179213	−	0.310407i
$698$	428.489	−	742.165i	0.0232357	−	0.0402455i
$699$	−11331.8			−0.613172
$700$		0			0
$701$	−28978.0			−1.56132			−0.780660	−	0.624956i	$-0.785117\pi$
$701$	−28978.0			−1.56132			−0.780660	+	0.624956i	$0.785117\pi$
$702$	4452.11	−	7711.28i	0.239365	−	0.414592i
$703$	−3000.06	−	5196.25i	−0.160952	−	0.278777i
$704$	105.597	+	182.900i	0.00565319	+	0.00979161i
$705$	−2192.41	+	3797.36i	−0.117122	+	0.202861i
$706$	−388.388			−0.0207042
$707$		0			0
$708$	14850.7			0.788307
$709$	8186.22	−	14178.9i	0.433625	−	0.751060i	−0.563558	−	0.826077i	$-0.690568\pi$
$709$	8186.22	−	14178.9i	0.433625	−	0.751060i	0.997182	+	0.0750169i	$0.0239011\pi$
$710$	−2475.16	−	4287.10i	−0.130833	−	0.226609i
$711$	−8475.79	−	14680.5i	−0.447070	−	0.774349i
$712$	−6685.11	+	11578.9i	−0.351875	+	0.609465i
$713$	17034.9			0.894755
$714$		0			0
$715$	4583.18			0.239722
$716$	−6253.79	+	10831.9i	−0.326418	+	0.565373i
$717$	−12332.2	−	21359.9i	−0.642334	−	1.11255i
$718$	21900.9	+	37933.4i	1.13835	+	1.97168i
$719$	11505.3	−	19927.7i	0.596765	−	1.03363i	−0.396530	−	0.918022i	$-0.629786\pi$
$719$	11505.3	−	19927.7i	0.596765	−	1.03363i	0.993295	−	0.115605i	$-0.0368808\pi$
$720$	5665.68			0.293260
$721$		0			0
$722$	2882.36			0.148574
$723$	1490.18	−	2581.06i	0.0766532	−	0.132767i
$724$	8318.89	+	14408.7i	0.427029	+	0.739636i
$725$	7327.73	+	12692.0i	0.375372	+	0.650164i
$726$	−15030.6	+	26033.8i	−0.768372	+	1.33086i
$727$	24636.8			1.25685			0.628423	−	0.777872i	$-0.283701\pi$
$727$	24636.8			1.25685			0.628423	+	0.777872i	$0.283701\pi$
$728$		0			0
$729$	−28395.6			−1.44264
$730$	−871.015	+	1508.64i	−0.0441612	+	0.0764895i
$731$	1951.44	+	3379.99i	0.0987367	+	0.171017i
$732$	−10277.1	−	17800.5i	−0.518925	−	0.898805i
$733$	3452.38	−	5979.70i	0.173965	−	0.301317i	−0.765837	−	0.643034i	$-0.777675\pi$
$733$	3452.38	−	5979.70i	0.173965	−	0.301317i	0.939803	+	0.341718i	$0.111009\pi$
$734$	48940.1			2.46105
$735$		0			0
$736$	10144.6			0.508065
$737$	4417.81	−	7651.88i	0.220804	−	0.382443i
$738$	15012.5	+	26002.4i	0.748804	+	1.29697i
$739$	4617.44	+	7997.65i	0.229845	+	0.398103i	0.957762	−	0.287562i	$-0.0928448\pi$
$739$	4617.44	+	7997.65i	0.229845	+	0.398103i	−0.727917	+	0.685665i	$0.759511\pi$
$740$	358.269	−	620.540i	0.0177976	−	0.0308264i
$741$	27275.0			1.35219
$742$		0			0
$743$	20216.9			0.998232			0.499116	−	0.866535i	$-0.333658\pi$
$743$	20216.9			0.998232			0.499116	+	0.866535i	$0.333658\pi$
$744$	14900.9	−	25809.1i	0.734265	−	1.27178i
$745$	−2822.98	−	4889.55i	−0.138827	−	0.240455i
$746$	8647.84	+	14978.5i	0.424424	+	0.735123i
$747$	417.772	−	723.603i	0.0204625	−	0.0354421i
$748$	5828.88			0.284926
$749$		0			0
$750$	14096.8			0.686321
$751$	−12027.5	+	20832.2i	−0.584405	+	1.01222i	0.410544	+	0.911841i	$0.365339\pi$
$751$	−12027.5	+	20832.2i	−0.584405	+	1.01222i	−0.994949	+	0.100378i	$0.967995\pi$
$752$	10764.4	+	18644.4i	0.521989	+	0.904112i
$753$	−14769.2	−	25581.0i	−0.714768	−	1.23801i
$754$	−9617.23	+	16657.5i	−0.464508	+	0.804551i
$755$	−1470.00			−0.0708593
$756$		0			0
$757$	−30328.2			−1.45614			−0.728069	−	0.685504i	$-0.759582\pi$
$757$	−30328.2			−1.45614			−0.728069	+	0.685504i	$0.759582\pi$
$758$	−17313.6	+	29988.0i	−0.829627	+	1.43696i
$759$	10725.1	+	18576.3i	0.512905	+	0.888377i
$760$	1006.73	+	1743.70i	0.0480498	+	0.0832248i
$761$	−16917.1	+	29301.2i	−0.805839	+	1.39575i	0.109884	+	0.993944i	$0.464952\pi$
$761$	−16917.1	+	29301.2i	−0.805839	+	1.39575i	−0.915723	+	0.401810i	$0.868381\pi$
$762$	−4705.49			−0.223703
$763$		0			0
$764$	4288.55			0.203082
$765$	941.598	−	1630.90i	0.0445014	−	0.0770786i
$766$	−18943.9	−	32811.9i	−0.893567	−	1.54770i
$767$	−9528.14	−	16503.2i	−0.448555	−	0.776919i
$768$	20029.1	−	34691.4i	0.941065	−	1.62997i
$769$	−31738.1			−1.48830			−0.744151	−	0.668011i	$-0.767146\pi$
$769$	−31738.1			−1.48830			−0.744151	+	0.668011i	$0.767146\pi$
$770$		0			0
$771$	33310.2			1.55595
$772$	8469.06	−	14668.8i	0.394829	−	0.683864i
$773$	13747.1	+	23810.7i	0.639650	+	1.10791i	0.985510	+	0.169619i	$0.0542538\pi$
$773$	13747.1	+	23810.7i	0.639650	+	1.10791i	−0.345860	+	0.938286i	$0.612413\pi$
$774$	−8883.57	−	15386.8i	−0.412550	−	0.714557i
$775$	18437.8	−	31935.2i	0.854587	−	1.48019i
$776$	20791.0			0.961794
$777$		0			0
$778$	−18588.0			−0.856573
$779$	−9667.12	+	16743.9i	−0.444622	+	0.770108i
$780$	1628.60	+	2820.82i	0.0747606	+	0.129489i
$781$	−16597.4	−	28747.5i	−0.760436	−	1.31711i
$782$	2610.21	−	4521.01i	0.119362	−	0.206740i
$783$	−6826.68			−0.311578
$784$		0			0
$785$	−6476.84			−0.294482
$786$	10384.7	−	17986.8i	0.471258	−	0.816243i
$787$	−234.178	−	405.608i	−0.0106068	−	0.0183715i	0.860673	−	0.509158i	$-0.170043\pi$
$787$	−234.178	−	405.608i	−0.0106068	−	0.0183715i	−0.871280	+	0.490786i	$0.836710\pi$
$788$	−11435.8	−	19807.4i	−0.516985	−	0.895445i
$789$	16422.0	−	28443.8i	0.740988	−	1.28343i
$790$	3637.18			0.163804
$791$		0			0
$792$	20966.9			0.940688
$793$	−13187.6	+	22841.5i	−0.590547	+	1.02286i
$794$	−2144.98	−	3715.22i	−0.0958723	−	0.166056i
$795$	1146.54	+	1985.86i	0.0511490	+	0.0885927i
$796$	−1932.46	+	3347.12i	−0.0860481	+	0.149040i
$797$	−37723.8			−1.67659			−0.838297	−	0.545214i	$-0.816449\pi$
$797$	−37723.8			−1.67659			−0.838297	+	0.545214i	$0.816449\pi$
$798$		0			0
$799$	7155.87			0.316841
$800$	10980.1	−	19018.1i	0.485256	−	0.840488i
$801$	−18329.0	−	31746.8i	−0.808520	−	1.40040i
$802$	4052.77	+	7019.60i	0.178439	+	0.309066i
$803$	−5840.66	+	10116.3i	−0.256678	+	0.444579i
$804$	6279.36			0.275443
$805$		0			0
$806$	48397.1			2.11503
$807$	−14629.8	+	25339.6i	−0.638158	+	1.10532i
$808$	480.791	+	832.755i	0.0209334	+	0.0362577i
$809$	3898.57	+	6752.51i	0.169427	+	0.293456i	0.938218	−	0.346043i	$-0.112475\pi$
$809$	3898.57	+	6752.51i	0.169427	+	0.293456i	−0.768792	+	0.639499i	$0.779142\pi$
$810$	1772.58	−	3070.20i	0.0768915	−	0.133180i
$811$	−16925.9			−0.732860			−0.366430	−	0.930446i	$-0.619420\pi$
$811$	−16925.9			−0.732860			−0.366430	+	0.930446i	$0.619420\pi$
$812$		0			0
$813$	34075.8			1.46998
$814$	6703.09	−	11610.1i	0.288628	−	0.499918i
$815$	1878.68	+	3253.97i	0.0807452	+	0.139855i
$816$	−8274.32	−	14331.5i	−0.354975	−	0.614834i
$817$	5720.48	−	9908.16i	0.244962	−	0.424287i
$818$	16407.5			0.701316
$819$		0			0
$820$	−2308.91			−0.0983301
$821$	15004.7	−	25988.8i	0.637840	−	1.10477i	−0.348066	−	0.937470i	$-0.613162\pi$
$821$	15004.7	−	25988.8i	0.637840	−	1.10477i	0.985906	−	0.167301i	$-0.0535051\pi$
$822$	−7162.49	−	12405.8i	−0.303918	−	0.526401i
$823$	11692.8	+	20252.5i	0.495243	+	0.857786i	0.999985	−	0.00548398i	$-0.00174562\pi$
$823$	11692.8	+	20252.5i	0.495243	+	0.857786i	−0.504742	+	0.863270i	$0.668412\pi$
$824$	−1026.76	+	1778.41i	−0.0434090	+	0.0751867i
$825$	46433.3			1.95952
$826$		0			0
$827$	−37325.9			−1.56947			−0.784734	−	0.619833i	$-0.787200\pi$
$827$	−37325.9			−1.56947			−0.784734	+	0.619833i	$0.787200\pi$
$828$	−4258.71	+	7376.31i	−0.178745	+	0.309595i
$829$	−12335.7	−	21366.0i	−0.516809	−	0.895140i	−0.999809	−	0.0195199i	$-0.993786\pi$
$829$	−12335.7	−	21366.0i	−0.516809	−	0.895140i	0.483000	−	0.875620i	$-0.339547\pi$
$830$	89.6383	+	155.258i	0.00374866	+	0.00649288i
$831$	−5257.70	+	9106.61i	−0.219480	+	0.380150i
$832$	192.599			0.00802544
$833$		0			0
$834$	−82193.0			−3.41260
$835$	3269.03	−	5662.12i	0.135484	−	0.234666i
$836$	−8543.44	−	14797.7i	−0.353446	−	0.612187i
$837$	8588.53	+	14875.8i	0.354675	+	0.614315i
$838$	−13314.5	+	23061.5i	−0.548858	+	0.950650i
$839$	−14147.4			−0.582147			−0.291074	−	0.956701i	$-0.594013\pi$
$839$	−14147.4			−0.582147			−0.291074	+	0.956701i	$0.594013\pi$
$840$		0			0
$841$	−9642.35			−0.395356
$842$	−11023.5	+	19093.3i	−0.451183	+	0.781472i
$843$	16448.3	+	28489.3i	0.672015	+	1.16396i
$844$	3004.46	+	5203.87i	0.122533	+	0.212233i
$845$	−192.097	+	332.723i	−0.00782054	+	0.0135456i
$846$	−32575.8			−1.32385
$847$		0			0
$848$	11258.6			0.455923
$849$	−18585.7	+	32191.3i	−0.751305	+	1.30130i
$850$	−5650.35	−	9786.69i	−0.228006	−	0.394918i
$851$	−2151.62	−	3726.71i	−0.0866704	−	0.150118i
$852$	11795.5	−	20430.5i	0.474306	−	0.821522i
$853$	−27963.6			−1.12246			−0.561229	−	0.827661i	$-0.689671\pi$
$853$	−27963.6			−1.12246			−0.561229	+	0.827661i	$0.689671\pi$
$854$		0			0
$855$	−5520.44			−0.220813
$856$	−6375.47	+	11042.6i	−0.254567	+	0.440923i
$857$	16927.9	+	29320.0i	0.674734	+	1.16867i	0.976547	+	0.215306i	$0.0690748\pi$
$857$	16927.9	+	29320.0i	0.674734	+	1.16867i	−0.301813	+	0.953367i	$0.597592\pi$
$858$	30470.5	+	52776.5i	1.21241	+	2.09995i
$859$	−12141.3	+	21029.4i	−0.482255	+	0.835291i	−0.999793	−	0.0203699i	$-0.993516\pi$
$859$	−12141.3	+	21029.4i	−0.482255	+	0.835291i	0.517537	+	0.855661i	$0.326849\pi$
$860$	1366.29			0.0541745
$861$		0			0
$862$	−40487.2			−1.59977
$863$	9833.49	−	17032.1i	0.387875	−	0.671819i	−0.604289	−	0.796765i	$-0.706543\pi$
$863$	9833.49	−	17032.1i	0.387875	−	0.671819i	0.992163	+	0.124947i	$0.0398760\pi$
$864$	5114.65	+	8858.83i	0.201393	+	0.348824i
$865$	−3411.29	−	5908.53i	−0.134090	−	0.232250i
$866$	−9103.96	+	15768.5i	−0.357235	+	0.618749i
$867$	32929.9			1.28992
$868$		0			0
$869$	24389.4			0.952075
$870$	3483.84	−	6034.18i	0.135762	−	0.235147i
$871$	−4028.83	−	6978.13i	−0.156730	−	0.271464i
$872$	−8494.53	−	14713.0i	−0.329887	−	0.571380i
$873$	−28502.0	+	49366.9i	−1.10498	+	1.91388i
$874$	−15303.2			−0.592264
$875$		0			0
$876$	−8301.75			−0.320194
$877$	18030.5	−	31229.8i	0.694238	−	1.20246i	−0.276199	−	0.961101i	$-0.589075\pi$
$877$	18030.5	−	31229.8i	0.694238	−	1.20246i	0.970437	−	0.241355i	$-0.0775919\pi$
$878$	8941.26	+	15486.7i	0.343682	+	0.595275i
$879$	19403.6	+	33608.1i	0.744560	+	1.28962i
$880$	−4075.79	+	7059.48i	−0.156131	+	0.270426i
$881$	15889.7			0.607646			0.303823	−	0.952728i	$-0.401737\pi$
$881$	15889.7			0.607646			0.303823	+	0.952728i	$0.401737\pi$
$882$		0			0
$883$	14861.3			0.566390			0.283195	−	0.959062i	$-0.408606\pi$
$883$	14861.3			0.566390			0.283195	+	0.959062i	$0.408606\pi$
$884$	2657.82	−	4603.48i	0.101122	−	0.175149i
$885$	3451.57	+	5978.29i	0.131100	+	0.227071i
$886$	22429.1	+	38848.3i	0.850474	+	1.47306i
$887$	−19094.9	+	33073.4i	−0.722824	+	1.25197i	0.237039	+	0.971500i	$0.423823\pi$
$887$	−19094.9	+	33073.4i	−0.722824	+	1.25197i	−0.959863	+	0.280468i	$0.909510\pi$
$888$	−7528.33			−0.284498
$889$		0			0
$890$	7865.45			0.296237
$891$	11886.2	−	20587.4i	0.446915	−	0.774080i
$892$	1932.60	+	3347.36i	0.0725428	+	0.125648i
$893$	−10488.4	−	18166.5i	−0.393036	−	0.680759i
$894$	37536.3	−	65014.8i	1.40425	−	2.43224i
$895$	−5813.99			−0.217140
$896$		0			0
$897$	19561.4			0.728135
$898$	24615.8	−	42635.9i	0.914745	−	1.58438i
$899$	−18552.5	−	32133.9i	−0.688277	−	1.19213i
$900$	9218.89	+	15967.6i	0.341440	+	0.591392i
$901$	1871.11	−	3240.86i	0.0691850	−	0.119832i
$902$	−43198.9			−1.59464
$903$		0			0
$904$	−19182.2			−0.705742
$905$	−3866.93	+	6697.72i	−0.142034	+	0.246011i
$906$	−9773.06	−	16927.4i	−0.358376	−	0.620725i
$907$	−8432.75	−	14606.0i	−0.308715	−	0.534711i	0.669366	−	0.742933i	$-0.266566\pi$
$907$	−8432.75	−	14606.0i	−0.308715	−	0.534711i	−0.978082	+	0.208222i	$0.933232\pi$
$908$	−3832.83	+	6638.65i	−0.140085	+	0.242634i
$909$	−2636.44			−0.0961993
$910$		0			0
$911$	26754.1			0.973000			0.486500	−	0.873681i	$-0.338273\pi$
$911$	26754.1			0.973000			0.486500	+	0.873681i	$0.338273\pi$
$912$	−24255.5	+	42011.8i	−0.880680	+	1.52538i
$913$	601.077	+	1041.10i	0.0217883	+	0.0377385i
$914$	−26861.3	−	46525.2i	−0.972095	−	1.68372i
$915$	4777.19	−	8274.33i	0.172600	−	0.298952i
$916$	4672.02			0.168524
$917$		0			0
$918$	5263.99			0.189257
$919$	20763.8	−	35963.9i	0.745303	−	1.29090i	−0.204750	−	0.978814i	$-0.565638\pi$
$919$	20763.8	−	35963.9i	0.745303	−	1.29090i	0.950053	−	0.312088i	$-0.101028\pi$
$920$	722.018	+	1250.57i	0.0258742	+	0.0448154i
$921$	16559.6	+	28682.1i	0.592461	+	1.02617i
$922$	20180.8	−	34954.1i	0.720844	−	1.24854i
$923$	−30272.0			−1.07954
$924$		0			0
$925$	−9315.27			−0.331118
$926$	−16504.3	+	28586.2i	−0.585707	+	1.01447i
$927$	−2815.15	−	4875.99i	−0.0997430	−	0.172760i
$928$	−11048.4	−	19136.4i	−0.390821	−	0.676922i
$929$	2292.34	−	3970.45i	0.0809572	−	0.140222i	−0.822704	−	0.568470i	$-0.807536\pi$
$929$	2292.34	−	3970.45i	0.0809572	−	0.140222i	0.903661	+	0.428248i	$0.140869\pi$
$930$	−17531.8			−0.618163
$931$		0			0
$932$	6473.92			0.227532
$933$	2677.93	−	4638.31i	0.0939673	−	0.162756i
$934$	−6410.48	−	11103.3i	−0.224580	−	0.388983i
$935$	1354.74	+	2346.48i	0.0473847	+	0.0820727i
$936$	9560.37	−	16559.0i	0.333857	−	0.578258i
$937$	6928.18			0.241552			0.120776	−	0.992680i	$-0.461462\pi$
$937$	6928.18			0.241552			0.120776	+	0.992680i	$0.461462\pi$
$938$		0			0
$939$	−46495.7			−1.61590
$940$	1252.54	−	2169.45i	0.0434609	−	0.0752764i
$941$	10472.5	+	18138.9i	0.362798	+	0.628384i	0.988420	−	0.151742i	$-0.0484882\pi$
$941$	10472.5	+	18138.9i	0.362798	+	0.628384i	−0.625622	+	0.780126i	$0.715155\pi$
$942$	−43060.3	−	74582.5i	−1.48936	−	2.57965i
$943$	−6933.19	+	12008.6i	−0.239423	+	0.414693i
$944$	33893.3			1.16857
$945$		0			0
$946$	25562.8			0.878559
$947$	−14639.5	+	25356.3i	−0.502342	+	0.870082i	0.497654	+	0.867376i	$0.334195\pi$
$947$	−14639.5	+	25356.3i	−0.502342	+	0.870082i	−0.999996	+	0.00270685i	$0.999138\pi$
$948$	8666.60	+	15011.0i	0.296918	+	0.514277i
$949$	5326.39	+	9225.57i	0.182194	+	0.315569i
$950$	−16563.5	+	28688.9i	−0.565676	+	0.979779i
$951$	22089.0			0.753192
$952$		0			0
$953$	2136.81			0.0726316			0.0363158	−	0.999340i	$-0.488438\pi$
$953$	2136.81			0.0726316			0.0363158	+	0.999340i	$0.488438\pi$
$954$	−8517.89	+	14753.4i	−0.289074	+	0.500692i
$955$	996.739	+	1726.40i	0.0337735	+	0.0584975i
$956$	7045.45	+	12203.1i	0.238354	+	0.412840i
$957$	23361.1	−	40462.7i	0.789089	−	1.36674i
$958$	23027.4			0.776597
$959$		0			0
$960$	−69.7689			−0.00234561
$961$	−31785.7	+	55054.5i	−1.06696	+	1.84802i
$962$	−6112.88	−	10587.8i	−0.204872	−	0.354849i
$963$	−17480.1	−	30276.4i	−0.584930	−	1.01313i
$964$	−851.348	+	1474.58i	−0.0284440	+	0.0492665i
$965$	7873.47			0.262649
$966$		0			0
$967$	−3921.32			−0.130405			−0.0652023	−	0.997872i	$-0.520769\pi$
$967$	−3921.32			−0.130405			−0.0652023	+	0.997872i	$0.520769\pi$
$968$	−6785.18	+	11752.3i	−0.225293	+	0.390219i
$969$	8062.21	+	13964.2i	0.267281	+	0.462945i
$970$	−6115.47	−	10592.3i	−0.202429	−	0.350617i
$971$	23904.5	−	41403.9i	0.790045	−	1.36840i	−0.135894	−	0.990723i	$-0.543391\pi$
$971$	23904.5	−	41403.9i	0.790045	−	1.36840i	0.925939	−	0.377674i	$-0.123276\pi$
$972$	23677.7			0.781341
$973$		0			0
$974$	12946.1			0.425894
$975$	21172.4	−	36671.7i	0.695447	−	1.20455i
$976$	−23455.2	−	40625.6i	−0.769245	−	1.33237i
$977$	25664.6	+	44452.3i	0.840411	+	1.45563i	0.889547	+	0.456843i	$0.151020\pi$
$977$	25664.6	+	44452.3i	0.840411	+	1.45563i	−0.0491363	+	0.998792i	$0.515647\pi$
$978$	−24980.2	+	43267.1i	−0.816749	+	1.41465i
$979$	52742.4			1.72181
$980$		0			0
$981$	46580.1			1.51599
$982$	−22017.9	+	38136.1i	−0.715499	+	1.23928i
$983$	−8163.16	−	14139.0i	−0.264867	−	0.458763i	0.702662	−	0.711524i	$-0.251995\pi$
$983$	−8163.16	−	14139.0i	−0.264867	−	0.458763i	−0.967529	+	0.252761i	$0.918661\pi$
$984$	12129.3	+	21008.6i	0.392956	+	0.680620i
$985$	5315.80	−	9207.23i	0.171955	−	0.297834i
$986$	−11371.0			−0.367268
$987$		0			0
$988$	−15582.4			−0.501763
$989$	4102.69	−	7106.06i	0.131909	−	0.228473i
$990$	−6167.21	−	10681.9i	−0.197987	−	0.342923i
$991$	−16885.0	−	29245.7i	−0.541242	−	0.937458i	−0.998833	−	0.0482954i	$-0.984621\pi$
$991$	−16885.0	−	29245.7i	−0.541242	−	0.937458i	0.457592	−	0.889163i	$-0.348712\pi$
$992$	−27799.7	+	48150.4i	−0.889758	+	1.54111i
$993$	22003.6			0.703185
$994$		0			0
$995$	−1796.56			−0.0572410
$996$	−427.177	+	739.893i	−0.0135900	+	0.0235385i
$997$	25347.7	+	43903.5i	0.805185	+	1.39462i	0.916166	+	0.400799i	$0.131267\pi$
$997$	25347.7	+	43903.5i	0.805185	+	1.39462i	−0.110981	+	0.993823i	$0.535399\pi$
$998$	−4067.74	−	7045.53i	−0.129020	−	0.223469i
$999$	2169.58	−	3757.82i	0.0687112	−	0.119011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.c.e.30.4		8
3.2	odd	2		441.4.e.y.226.1		8
7.2	even	3		49.4.a.e.1.1	✓	4
7.3	odd	6	inner	49.4.c.e.18.3		8
7.4	even	3	inner	49.4.c.e.18.4		8
7.5	odd	6		49.4.a.e.1.2	yes	4
7.6	odd	2	inner	49.4.c.e.30.3		8
21.2	odd	6		441.4.a.u.1.4		4
21.5	even	6		441.4.a.u.1.3		4
21.11	odd	6		441.4.e.y.361.1		8
21.17	even	6		441.4.e.y.361.2		8
21.20	even	2		441.4.e.y.226.2		8
28.19	even	6		784.4.a.bf.1.1		4
28.23	odd	6		784.4.a.bf.1.4		4
35.9	even	6		1225.4.a.bb.1.4		4
35.19	odd	6		1225.4.a.bb.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.a.e.1.1	✓	4	7.2	even	3
49.4.a.e.1.2	yes	4	7.5	odd	6
49.4.c.e.18.3		8	7.3	odd	6	inner
49.4.c.e.18.4		8	7.4	even	3	inner
49.4.c.e.30.3		8	7.6	odd	2	inner
49.4.c.e.30.4		8	1.1	even	1	trivial
441.4.a.u.1.3		4	21.5	even	6
441.4.a.u.1.4		4	21.2	odd	6
441.4.e.y.226.1		8	3.2	odd	2
441.4.e.y.226.2		8	21.20	even	2
441.4.e.y.361.1		8	21.11	odd	6
441.4.e.y.361.2		8	21.17	even	6
784.4.a.bf.1.1		4	28.19	even	6
784.4.a.bf.1.4		4	28.23	odd	6
1225.4.a.bb.1.3		4	35.19	odd	6
1225.4.a.bb.1.4		4	35.9	even	6

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.76556 - 3.05805i) q^{2} +(3.91110 + 6.77422i) q^{3} +(-2.23444 - 3.87016i) q^{4} +(1.03865 - 1.79899i) q^{5} +27.6212 q^{6} +12.4689 q^{8} +(-17.0934 + 29.6066i) q^{9} +O(q^{10})\)	\(q+(1.76556 - 3.05805i) q^{2} +(3.91110 + 6.77422i) q^{3} +(-2.23444 - 3.87016i) q^{4} +(1.03865 - 1.79899i) q^{5} +27.6212 q^{6} +12.4689 q^{8} +(-17.0934 + 29.6066i) q^{9} +(-3.66760 - 6.35247i) q^{10} +(-24.5934 - 42.5970i) q^{11} +(17.4782 - 30.2731i) q^{12} -44.8559 q^{13} +16.2490 q^{15} +(39.8901 - 69.0916i) q^{16} +(-13.2589 - 22.9652i) q^{17} +(60.3590 + 104.545i) q^{18} +(-38.8675 + 67.3205i) q^{19} -9.28317 q^{20} -173.685 q^{22} +(-27.8755 + 48.2818i) q^{23} +(48.7670 + 84.4669i) q^{24} +(60.3424 + 104.516i) q^{25} +(-79.1960 + 137.171i) q^{26} -56.2164 q^{27} +121.436 q^{29} +(28.6887 - 49.6903i) q^{30} +(-152.776 - 264.616i) q^{31} +(-90.9815 - 157.585i) q^{32} +(192.374 - 333.202i) q^{33} -93.6380 q^{34} +152.776 q^{36} +(-38.5934 + 66.8457i) q^{37} +(137.246 + 237.717i) q^{38} +(-175.436 - 303.864i) q^{39} +(12.9508 - 22.4314i) q^{40} +248.720 q^{41} -147.179 q^{43} +(-109.905 + 190.360i) q^{44} +(35.5080 + 61.5017i) q^{45} +(98.4319 + 170.489i) q^{46} +(-134.925 + 233.698i) q^{47} +624.056 q^{48} +426.154 q^{50} +(103.714 - 179.638i) q^{51} +(100.228 + 173.599i) q^{52} +(70.5603 + 122.214i) q^{53} +(-99.2536 + 171.912i) q^{54} -102.176 q^{55} -608.058 q^{57} +(214.403 - 371.356i) q^{58} +(212.417 + 367.917i) q^{59} +(-36.3074 - 62.8863i) q^{60} +(293.998 - 509.220i) q^{61} -1078.95 q^{62} -4.29373 q^{64} +(-46.5895 + 80.6954i) q^{65} +(-679.299 - 1176.58i) q^{66} +(89.8171 + 155.568i) q^{67} +(-59.2525 + 102.628i) q^{68} -436.095 q^{69} +674.872 q^{71} +(-213.135 + 369.161i) q^{72} +(-118.744 - 205.671i) q^{73} +(136.278 + 236.041i) q^{74} +(-472.010 + 817.546i) q^{75} +347.388 q^{76} -1238.97 q^{78} +(-247.926 + 429.421i) q^{79} +(-82.8636 - 143.524i) q^{80} +(241.654 + 418.556i) q^{81} +(439.131 - 760.598i) q^{82} -24.4406 q^{83} -55.0855 q^{85} +(-259.854 + 450.080i) q^{86} +(474.947 + 822.633i) q^{87} +(-306.652 - 531.136i) q^{88} +(-536.144 + 928.628i) q^{89} +250.767 q^{90} +249.144 q^{92} +(1195.05 - 2069.88i) q^{93} +(476.439 + 825.216i) q^{94} +(80.7393 + 139.845i) q^{95} +(711.675 - 1232.66i) q^{96} +1667.43 q^{97} +1681.54 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 34 q^{4} + 132 q^{8} - 40 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 34 * q^4 + 132 * q^8 - 40 * q^9	\( 8 q - 2 q^{2} - 34 q^{4} + 132 q^{8} - 40 q^{9} - 100 q^{11} - 128 q^{15} + 174 q^{16} + 370 q^{18} - 680 q^{22} - 352 q^{23} + 128 q^{25} + 520 q^{29} + 552 q^{30} + 30 q^{32} - 100 q^{36} - 212 q^{37} - 952 q^{39} + 1080 q^{43} - 460 q^{44} - 696 q^{46} + 2732 q^{50} - 428 q^{51} - 16 q^{53} - 3768 q^{57} + 780 q^{58} + 1064 q^{60} - 3356 q^{64} + 756 q^{65} + 1944 q^{67} + 4496 q^{71} - 270 q^{72} + 284 q^{74} - 2688 q^{78} + 1048 q^{79} + 1256 q^{81} - 6568 q^{85} - 4820 q^{86} - 1260 q^{88} + 7024 q^{92} + 5368 q^{93} - 2192 q^{95} + 6680 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 34 * q^4 + 132 * q^8 - 40 * q^9 - 100 * q^11 - 128 * q^15 + 174 * q^16 + 370 * q^18 - 680 * q^22 - 352 * q^23 + 128 * q^25 + 520 * q^29 + 552 * q^30 + 30 * q^32 - 100 * q^36 - 212 * q^37 - 952 * q^39 + 1080 * q^43 - 460 * q^44 - 696 * q^46 + 2732 * q^50 - 428 * q^51 - 16 * q^53 - 3768 * q^57 + 780 * q^58 + 1064 * q^60 - 3356 * q^64 + 756 * q^65 + 1944 * q^67 + 4496 * q^71 - 270 * q^72 + 284 * q^74 - 2688 * q^78 + 1048 * q^79 + 1256 * q^81 - 6568 * q^85 - 4820 * q^86 - 1260 * q^88 + 7024 * q^92 + 5368 * q^93 - 2192 * q^95 + 6680 * q^99

Introduction

L-functions

Modular forms

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