LMFDB - Embedded newform 405.4.e.q.271.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,4,Mod(136,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.136"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-5,0,-17,-15,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.84779568.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 13x^{4} - 4x^{3} + 152x^{2} - 96x + 64 $ x^6 - x^5 + 13x^4 - 4x^3 + 152x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.3
Root			$1.83685 + 3.18152i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.q.136.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.29244 + 2.23857i) q^{2} +(0.659207 - 1.14178i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(11.4468 + 19.8264i) q^{7} +24.0869 q^{8} -12.9244 q^{10} +(-5.54140 - 9.59799i) q^{11} +(5.81841 - 10.0778i) q^{13} +(-29.5885 + 51.2487i) q^{14} +(25.8572 + 44.7861i) q^{16} +10.0643 q^{17} +117.865 q^{19} +(3.29603 + 5.70890i) q^{20} +(14.3238 - 24.8096i) q^{22} +(-86.2204 + 149.338i) q^{23} +(-12.5000 - 21.6506i) q^{25} +30.0798 q^{26} +30.1831 q^{28} +(-89.1603 - 154.430i) q^{29} +(-70.2642 + 121.701i) q^{31} +(29.5100 - 51.1128i) q^{32} +(13.0075 + 22.5296i) q^{34} -114.468 q^{35} +250.074 q^{37} +(152.333 + 263.848i) q^{38} +(-60.2174 + 104.300i) q^{40} +(-180.784 + 313.128i) q^{41} +(180.354 + 312.382i) q^{43} -14.6117 q^{44} -445.738 q^{46} +(300.060 + 519.720i) q^{47} +(-90.5568 + 156.849i) q^{49} +(32.3110 - 55.9642i) q^{50} +(-7.67107 - 13.2867i) q^{52} +201.312 q^{53} +55.4140 q^{55} +(275.718 + 477.557i) q^{56} +(230.468 - 399.183i) q^{58} +(-207.886 + 360.069i) q^{59} +(27.3135 + 47.3083i) q^{61} -363.248 q^{62} +566.275 q^{64} +(29.0921 + 50.3889i) q^{65} +(265.539 - 459.928i) q^{67} +(6.63444 - 11.4912i) q^{68} +(-147.942 - 256.244i) q^{70} -933.534 q^{71} -560.199 q^{73} +(323.205 + 559.807i) q^{74} +(77.6972 - 134.575i) q^{76} +(126.862 - 219.732i) q^{77} +(-405.391 - 702.157i) q^{79} -258.572 q^{80} -934.611 q^{82} +(-269.105 - 466.104i) q^{83} +(-25.1607 + 43.5796i) q^{85} +(-466.192 + 807.468i) q^{86} +(-133.475 - 231.186i) q^{88} +686.173 q^{89} +266.408 q^{91} +(113.674 + 196.889i) q^{92} +(-775.619 + 1343.41i) q^{94} +(-294.662 + 510.369i) q^{95} +(-357.327 - 618.909i) q^{97} -468.156 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8} + 50 q^{10} - 5 q^{11} - 7 q^{13} - 60 q^{14} - 161 q^{16} + 310 q^{17} - 100 q^{19} - 85 q^{20} + 229 q^{22} - 285 q^{23} - 75 q^{25} + 370 q^{26}+ \cdots - 610 q^{98}+O(q^{100}) $ 6 * q - 5 * q^2 - 17 * q^4 - 15 * q^5 + 4 * q^7 + 150 * q^8 + 50 * q^10 - 5 * q^11 - 7 * q^13 - 60 * q^14 - 161 * q^16 + 310 * q^17 - 100 * q^19 - 85 * q^20 + 229 * q^22 - 285 * q^23 - 75 * q^25 + 370 * q^26 - 668 * q^28 - 115 * q^29 + 115 * q^31 - 775 * q^32 - 413 * q^34 - 40 * q^35 - 768 * q^37 + 1150 * q^38 - 375 * q^40 - 580 * q^41 + 797 * q^43 - 2830 * q^44 - 570 * q^46 + 145 * q^47 - 577 * q^49 - 125 * q^50 - 825 * q^52 - 800 * q^53 + 50 * q^55 + 2190 * q^56 + 59 * q^58 - 380 * q^59 + 152 * q^61 - 2010 * q^62 + 5874 * q^64 - 35 * q^65 - 2 * q^67 - 475 * q^68 - 300 * q^70 + 80 * q^71 - 1960 * q^73 + 2720 * q^74 + 3276 * q^76 - 1950 * q^77 - 1013 * q^79 + 1610 * q^80 + 8 * q^82 - 270 * q^83 - 775 * q^85 + 1555 * q^86 + 5193 * q^88 + 2040 * q^89 - 1264 * q^91 + 1215 * q^92 - 3833 * q^94 + 250 * q^95 - 720 * q^97 - 610 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.29244	+	2.23857i	0.456946	+	0.791454i	0.998798	−	0.0490204i	$-0.0156099\pi$
$2$	1.29244	+	2.23857i	0.456946	+	0.791454i	−0.541852	+	0.840474i	$0.682277\pi$
$3$		0			0
$3$		0			0
$4$	0.659207	−	1.14178i	0.0824008	−	0.142722i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	11.4468	+	19.8264i	0.618067	+	1.07052i	0.989838	+	0.142199i	$0.0454174\pi$
$7$	11.4468	+	19.8264i	0.618067	+	1.07052i	−0.371771	+	0.928324i	$0.621249\pi$
$8$	24.0869			1.06450
$9$		0			0
$10$	−12.9244			−0.408705
$11$	−5.54140	−	9.59799i	−0.151891	−	0.263082i	0.780032	−	0.625740i	$-0.215203\pi$
$11$	−5.54140	−	9.59799i	−0.151891	−	0.263082i	−0.931922	+	0.362658i	$0.881869\pi$
$12$		0			0
$13$	5.81841	−	10.0778i	0.124134	−	0.215006i	−0.797260	−	0.603636i	$-0.793718\pi$
$13$	5.81841	−	10.0778i	0.124134	−	0.215006i	0.921394	+	0.388630i	$0.127052\pi$
$14$	−29.5885	+	51.2487i	−0.564847	+	0.978343i
$15$		0			0
$16$	25.8572	+	44.7861i	0.404019	+	0.699782i
$17$	10.0643			0.143585			0.0717926	−	0.997420i	$-0.477128\pi$
$17$	10.0643			0.143585			0.0717926	+	0.997420i	$0.477128\pi$
$18$		0			0
$19$	117.865			1.42316			0.711579	−	0.702606i	$-0.247980\pi$
$19$	117.865			1.42316			0.711579	+	0.702606i	$0.247980\pi$
$20$	3.29603	+	5.70890i	0.0368508	+	0.0638274i
$21$		0			0
$22$	14.3238	−	24.8096i	0.138812	−	0.240429i
$23$	−86.2204	+	149.338i	−0.781661	+	1.35388i	0.149313	+	0.988790i	$0.452294\pi$
$23$	−86.2204	+	149.338i	−0.781661	+	1.35388i	−0.930974	+	0.365086i	$0.881039\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	30.0798			0.226889
$27$		0			0
$28$	30.1831			0.203717
$29$	−89.1603	−	154.430i	−0.570919	−	0.988860i	−0.996472	−	0.0839270i	$-0.973254\pi$
$29$	−89.1603	−	154.430i	−0.570919	−	0.988860i	0.425553	−	0.904933i	$-0.360080\pi$
$30$		0			0
$31$	−70.2642	+	121.701i	−0.407091	+	0.705102i	−0.994562	−	0.104143i	$-0.966790\pi$
$31$	−70.2642	+	121.701i	−0.407091	+	0.705102i	0.587471	+	0.809245i	$0.300123\pi$
$32$	29.5100	−	51.1128i	0.163021	−	0.282361i
$33$		0			0
$34$	13.0075	+	22.5296i	0.0656107	+	0.113641i
$35$	−114.468			−0.552816
$36$		0			0
$37$	250.074			1.11113			0.555566	−	0.831473i	$-0.312502\pi$
$37$	250.074			1.11113			0.555566	+	0.831473i	$0.312502\pi$
$38$	152.333	+	263.848i	0.650307	+	1.12636i
$39$		0			0
$40$	−60.2174	+	104.300i	−0.238030	+	0.412280i
$41$	−180.784	+	313.128i	−0.688629	+	1.19274i	0.283652	+	0.958927i	$0.408454\pi$
$41$	−180.784	+	313.128i	−0.688629	+	1.19274i	−0.972281	+	0.233813i	$0.924880\pi$
$42$		0			0
$43$	180.354	+	312.382i	0.639620	+	1.10786i	0.985516	+	0.169582i	$0.0542418\pi$
$43$	180.354	+	312.382i	0.639620	+	1.10786i	−0.345896	+	0.938273i	$0.612425\pi$
$44$	−14.6117			−0.0500636
$45$		0			0
$46$	−445.738			−1.42871
$47$	300.060	+	519.720i	0.931241	+	1.61296i	0.781204	+	0.624276i	$0.214606\pi$
$47$	300.060	+	519.720i	0.931241	+	1.61296i	0.150037	+	0.988680i	$0.452061\pi$
$48$		0			0
$49$	−90.5568	+	156.849i	−0.264014	+	0.457286i
$50$	32.3110	−	55.9642i	0.0913892	−	0.158291i
$51$		0			0
$52$	−7.67107	−	13.2867i	−0.0204574	−	0.0354333i
$53$	201.312			0.521742			0.260871	−	0.965374i	$-0.415990\pi$
$53$	201.312			0.521742			0.260871	+	0.965374i	$0.415990\pi$
$54$		0			0
$55$	55.4140			0.135855
$56$	275.718	+	477.557i	0.657934	+	1.13958i
$57$		0			0
$58$	230.468	−	399.183i	0.521758	−	0.903712i
$59$	−207.886	+	360.069i	−0.458719	+	0.794525i	−0.998894	−	0.0470283i	$-0.985025\pi$
$59$	−207.886	+	360.069i	−0.458719	+	0.794525i	0.540174	+	0.841553i	$0.318358\pi$
$60$		0			0
$61$	27.3135	+	47.3083i	0.0573301	+	0.0992986i	0.893266	−	0.449528i	$-0.148408\pi$
$61$	27.3135	+	47.3083i	0.0573301	+	0.0992986i	−0.835936	+	0.548827i	$0.815075\pi$
$62$	−363.248			−0.744074
$63$		0			0
$64$	566.275			1.10601
$65$	29.0921	+	50.3889i	0.0555143	+	0.0961535i
$66$		0			0
$67$	265.539	−	459.928i	0.484191	−	0.838643i	−0.515644	−	0.856803i	$-0.672447\pi$
$67$	265.539	−	459.928i	0.484191	−	0.838643i	0.999835	+	0.0181595i	$0.00578066\pi$
$68$	6.63444	−	11.4912i	0.0118315	−	0.0204928i
$69$		0			0
$70$	−147.942	−	256.244i	−0.252607	−	0.437528i
$71$	−933.534			−1.56042			−0.780212	−	0.625515i	$-0.784889\pi$
$71$	−933.534			−1.56042			−0.780212	+	0.625515i	$0.784889\pi$
$72$		0			0
$73$	−560.199			−0.898169			−0.449085	−	0.893489i	$-0.648250\pi$
$73$	−560.199			−0.898169			−0.449085	+	0.893489i	$0.648250\pi$
$74$	323.205	+	559.807i	0.507727	+	0.879409i
$75$		0			0
$76$	77.6972	−	134.575i	0.117269	−	0.203117i
$77$	126.862	−	219.732i	0.187757	−	0.325205i
$78$		0			0
$79$	−405.391	−	702.157i	−0.577342	−	0.999985i	−0.995783	−	0.0917413i	$-0.970757\pi$
$79$	−405.391	−	702.157i	−0.577342	−	0.999985i	0.418441	−	0.908244i	$-0.362577\pi$
$80$	−258.572			−0.361366
$81$		0			0
$82$	−934.611			−1.25867
$83$	−269.105	−	466.104i	−0.355881	−	0.616404i	0.631387	−	0.775468i	$-0.282486\pi$
$83$	−269.105	−	466.104i	−0.355881	−	0.616404i	−0.987268	+	0.159064i	$0.949152\pi$
$84$		0			0
$85$	−25.1607	+	43.5796i	−0.0321066	+	0.0556103i
$86$	−466.192	+	807.468i	−0.584544	+	1.01246i
$87$		0			0
$88$	−133.475	−	231.186i	−0.161688	−	0.280052i
$89$	686.173			0.817238			0.408619	−	0.912705i	$-0.366010\pi$
$89$	686.173			0.817238			0.408619	+	0.912705i	$0.366010\pi$
$90$		0			0
$91$	266.408			0.306892
$92$	113.674	+	196.889i	0.128819	+	0.223121i
$93$		0			0
$94$	−775.619	+	1343.41i	−0.851053	+	1.47407i
$95$	−294.662	+	510.369i	−0.318228	+	0.551187i
$96$		0			0
$97$	−357.327	−	618.909i	−0.374032	−	0.647842i	0.616150	−	0.787629i	$-0.288692\pi$
$97$	−357.327	−	618.909i	−0.374032	−	0.647842i	−0.990182	+	0.139787i	$0.955358\pi$
$98$	−468.156			−0.482560
$99$		0			0
$100$	−32.9603			−0.0329603
$101$	−486.953	−	843.428i	−0.479739	−	0.830933i	0.519991	−	0.854172i	$-0.325935\pi$
$101$	−486.953	−	843.428i	−0.479739	−	0.830933i	−0.999730	+	0.0232390i	$0.992602\pi$
$102$		0			0
$103$	379.614	−	657.511i	0.363151	−	0.628995i	−0.625327	−	0.780363i	$-0.715034\pi$
$103$	379.614	−	657.511i	0.363151	−	0.628995i	0.988478	+	0.151368i	$0.0483677\pi$
$104$	140.148	−	242.743i	0.132141	−	0.228874i
$105$		0			0
$106$	260.183	+	450.650i	0.238408	+	0.412934i
$107$	1832.06			1.65525			0.827625	−	0.561282i	$-0.189692\pi$
$107$	1832.06			1.65525			0.827625	+	0.561282i	$0.189692\pi$
$108$		0			0
$109$	1370.91			1.20467			0.602335	−	0.798244i	$-0.294237\pi$
$109$	1370.91			1.20467			0.602335	+	0.798244i	$0.294237\pi$
$110$	71.6192	+	124.048i	0.0620784	+	0.107523i
$111$		0			0
$112$	−591.963	+	1025.31i	−0.499422	+	0.865025i
$113$	−291.783	+	505.384i	−0.242909	+	0.420730i	−0.961542	−	0.274659i	$-0.911435\pi$
$113$	−291.783	+	505.384i	−0.242909	+	0.420730i	0.718633	+	0.695390i	$0.244768\pi$
$114$		0			0
$115$	−431.102	−	746.691i	−0.349569	−	0.605472i
$116$	−235.100			−0.188177
$117$		0			0
$118$	−1074.72			−0.838439
$119$	115.204	+	199.538i	0.0887453	+	0.153711i
$120$		0			0
$121$	604.086	−	1046.31i	0.453859	−	0.786106i
$122$	−70.6020	+	122.286i	−0.0523935	+	0.0907482i
$123$		0			0
$124$	92.6372	+	160.452i	0.0670892	+	0.116202i
$125$	125.000			0.0894427
$126$		0			0
$127$	−2432.76			−1.69978			−0.849891	−	0.526958i	$-0.823333\pi$
$127$	−2432.76			−1.69978			−0.849891	+	0.526958i	$0.823333\pi$
$128$	495.796	+	858.744i	0.342364	+	0.592992i
$129$		0			0
$130$	−75.1994	+	130.249i	−0.0507340	+	0.0878739i
$131$	−250.537	+	433.942i	−0.167095	+	0.289418i	−0.937397	−	0.348262i	$-0.886772\pi$
$131$	−250.537	+	433.942i	−0.167095	+	0.289418i	0.770302	+	0.637679i	$0.220105\pi$
$132$		0			0
$133$	1349.17	+	2336.83i	0.879608	+	1.52353i
$134$	1372.77			0.884996
$135$		0			0
$136$	242.418			0.152847
$137$	−1261.53	−	2185.04i	−0.786716	−	1.36263i	−0.927969	−	0.372658i	$-0.878447\pi$
$137$	−1261.53	−	2185.04i	−0.786716	−	1.36263i	0.141253	−	0.989973i	$-0.454887\pi$
$138$		0			0
$139$	319.421	−	553.253i	0.194913	−	0.337599i	−0.751959	−	0.659210i	$-0.770891\pi$
$139$	319.421	−	553.253i	0.194913	−	0.337599i	0.946872	+	0.321611i	$0.104224\pi$
$140$	−75.4578	+	130.697i	−0.0455525	+	0.0788992i
$141$		0			0
$142$	−1206.54	−	2089.78i	−0.713029	−	1.23500i
$143$	−128.969			−0.0754189
$144$		0			0
$145$	891.603			0.510645
$146$	−724.023	−	1254.04i	−0.410415	−	0.710859i
$147$		0			0
$148$	164.850	−	285.529i	0.0915581	−	0.158583i
$149$	1337.07	−	2315.87i	0.735146	−	1.27331i	−0.219513	−	0.975610i	$-0.570447\pi$
$149$	1337.07	−	2315.87i	0.735146	−	1.27331i	0.954659	−	0.297701i	$-0.0962198\pi$
$150$		0			0
$151$	518.339	+	897.790i	0.279350	+	0.483848i	0.971223	−	0.238171i	$-0.0765477\pi$
$151$	518.339	+	897.790i	0.279350	+	0.483848i	−0.691873	+	0.722019i	$0.743214\pi$
$152$	2839.00			1.51496
$153$		0			0
$154$	655.847			0.343179
$155$	−351.321	−	608.506i	−0.182057	−	0.315331i
$156$		0			0
$157$	190.929	−	330.699i	0.0970560	−	0.168106i	−0.813409	−	0.581692i	$-0.802391\pi$
$157$	190.929	−	330.699i	0.0970560	−	0.168106i	0.910465	+	0.413586i	$0.135724\pi$
$158$	1047.88	−	1814.99i	0.527628	−	0.913878i
$159$		0			0
$160$	147.550	+	255.564i	0.0729054	+	0.126276i
$161$	−3947.78			−1.93248
$162$		0			0
$163$	2421.17			1.16344			0.581719	−	0.813390i	$-0.302380\pi$
$163$	2421.17			1.16344			0.581719	+	0.813390i	$0.302380\pi$
$164$	238.349	+	412.832i	0.113487	+	0.196566i
$165$		0			0
$166$	695.603	−	1204.82i	0.325237	−	0.563326i
$167$	1767.88	−	3062.06i	0.819178	−	1.41886i	−0.0871109	−	0.996199i	$-0.527763\pi$
$167$	1767.88	−	3062.06i	0.819178	−	1.41886i	0.906289	−	0.422659i	$-0.138903\pi$
$168$		0			0
$169$	1030.79	+	1785.38i	0.469182	+	0.812646i
$170$	−130.075			−0.0586840
$171$		0			0
$172$	475.561			0.210821
$173$	−1571.94	−	2722.68i	−0.690824	−	1.19654i	−0.971568	−	0.236759i	$-0.923915\pi$
$173$	−1571.94	−	2722.68i	−0.690824	−	1.19654i	0.280745	−	0.959783i	$-0.409419\pi$
$174$		0			0
$175$	286.169	−	495.659i	0.123613	−	0.214105i
$176$	286.571	−	496.355i	0.122733	−	0.212581i
$177$		0			0
$178$	886.836	+	1536.05i	0.373434	+	0.646806i
$179$	−3299.06			−1.37756			−0.688780	−	0.724970i	$-0.741853\pi$
$179$	−3299.06			−1.37756			−0.688780	+	0.724970i	$0.741853\pi$
$180$		0			0
$181$	1875.10			0.770026			0.385013	−	0.922911i	$-0.374197\pi$
$181$	1875.10			0.770026			0.385013	+	0.922911i	$0.374197\pi$
$182$	344.316	+	596.373i	0.140233	+	0.242891i
$183$		0			0
$184$	−2076.79	+	3597.10i	−0.832080	+	1.44121i
$185$	−625.184	+	1082.85i	−0.248456	+	0.430339i
$186$		0			0
$187$	−55.7703	−	96.5969i	−0.0218092	−	0.0377747i
$188$	791.207			0.306940
$189$		0			0
$190$	−1523.33			−0.581652
$191$	680.810	+	1179.20i	0.257915	+	0.446721i	0.965683	−	0.259723i	$-0.0836313\pi$
$191$	680.810	+	1179.20i	0.257915	+	0.446721i	−0.707768	+	0.706445i	$0.750298\pi$
$192$		0			0
$193$	−1117.10	+	1934.88i	−0.416636	+	0.721634i	−0.995599	−	0.0937198i	$-0.970124\pi$
$193$	−1117.10	+	1934.88i	−0.416636	+	0.721634i	0.578963	+	0.815354i	$0.303458\pi$
$194$	923.647	−	1599.80i	0.341825	−	0.592058i
$195$		0			0
$196$	119.391	+	206.792i	0.0435099	+	0.0753614i
$197$	−346.625			−0.125360			−0.0626801	−	0.998034i	$-0.519965\pi$
$197$	−346.625			−0.125360			−0.0626801	+	0.998034i	$0.519965\pi$
$198$		0			0
$199$	4198.77			1.49569			0.747846	−	0.663872i	$-0.231088\pi$
$199$	4198.77			1.49569			0.747846	+	0.663872i	$0.231088\pi$
$200$	−301.087	−	521.498i	−0.106450	−	0.184377i
$201$		0			0
$202$	1258.71	−	2180.16i	0.438430	−	0.759383i
$203$	2041.19	−	3535.45i	0.705732	−	1.22236i
$204$		0			0
$205$	−903.922	−	1565.64i	−0.307964	−	0.533410i
$206$	1962.51			0.663761
$207$		0			0
$208$	601.792			0.200610
$209$	−653.136	−	1131.26i	−0.216164	−	0.374408i
$210$		0			0
$211$	−2364.23	+	4094.96i	−0.771375	+	1.33606i	0.165434	+	0.986221i	$0.447098\pi$
$211$	−2364.23	+	4094.96i	−0.771375	+	1.33606i	−0.936809	+	0.349841i	$0.886236\pi$
$212$	132.706	−	229.854i	0.0429919	−	0.0744642i
$213$		0			0
$214$	2367.82	+	4101.19i	0.756360	+	1.31005i
$215$	−1803.54			−0.572094
$216$		0			0
$217$	−3217.19			−1.00644
$218$	1771.81	+	3068.87i	0.550469	+	0.953440i
$219$		0			0
$220$	36.5293	−	63.2706i	0.0111946	−	0.0193896i
$221$	58.5582	−	101.426i	0.0178238	−	0.0308716i
$222$		0			0
$223$	−1215.08	−	2104.58i	−0.364878	−	0.631987i	0.623879	−	0.781521i	$-0.285556\pi$
$223$	−1215.08	−	2104.58i	−0.364878	−	0.631987i	−0.988757	+	0.149534i	$0.952223\pi$
$224$	1351.18			0.403032
$225$		0			0
$226$	−1508.45			−0.443985
$227$	292.343	+	506.354i	0.0854780	+	0.148052i	0.905595	−	0.424144i	$-0.139425\pi$
$227$	292.343	+	506.354i	0.0854780	+	0.148052i	−0.820117	+	0.572196i	$0.806092\pi$
$228$		0			0
$229$	2365.89	−	4097.84i	0.682717	−	1.18250i	−0.291431	−	0.956592i	$-0.594132\pi$
$229$	2365.89	−	4097.84i	0.682717	−	1.18250i	0.974148	−	0.225909i	$-0.0725351\pi$
$230$	1114.35	−	1930.10i	0.319469	−	0.553336i
$231$		0			0
$232$	−2147.60	−	3719.75i	−0.607745	−	1.05264i
$233$	1228.45			0.345401			0.172701	−	0.984974i	$-0.444751\pi$
$233$	1228.45			0.345401			0.172701	+	0.984974i	$0.444751\pi$
$234$		0			0
$235$	−3000.60			−0.832927
$236$	274.079	+	474.719i	0.0755977	+	0.130939i
$237$		0			0
$238$	−297.787	+	515.782i	−0.0811036	+	0.140476i
$239$	60.2727	−	104.395i	0.0163126	−	0.0282543i	−0.857754	−	0.514061i	$-0.828141\pi$
$239$	60.2727	−	104.395i	0.0163126	−	0.0282543i	0.874066	+	0.485806i	$0.161474\pi$
$240$		0			0
$241$	−866.278	−	1500.44i	−0.231543	−	0.401044i	0.726719	−	0.686935i	$-0.241044\pi$
$241$	−866.278	−	1500.44i	−0.231543	−	0.401044i	−0.958262	+	0.285890i	$0.907711\pi$
$242$	3122.97			0.829555
$243$		0			0
$244$	72.0209			0.0188962
$245$	−452.784	−	784.245i	−0.118071	−	0.204504i
$246$		0			0
$247$	685.786	−	1187.82i	0.176662	−	0.305987i
$248$	−1692.45	+	2931.41i	−0.433349	+	0.750583i
$249$		0			0
$250$	161.555	+	279.821i	0.0408705	+	0.0707898i
$251$	−3287.82			−0.826793			−0.413397	−	0.910551i	$-0.635658\pi$
$251$	−3287.82			−0.826793			−0.413397	+	0.910551i	$0.635658\pi$
$252$		0			0
$253$	1911.13			0.474908
$254$	−3144.19	−	5445.90i	−0.776709	−	1.34530i
$255$		0			0
$256$	983.530	−	1703.52i	0.240120	−	0.415900i
$257$	744.912	−	1290.22i	0.180803	−	0.313160i	−0.761351	−	0.648339i	$-0.775464\pi$
$257$	744.912	−	1290.22i	0.180803	−	0.313160i	0.942154	+	0.335180i	$0.108797\pi$
$258$		0			0
$259$	2862.53	+	4958.05i	0.686754	+	1.18949i
$260$	76.7107			0.0182977
$261$		0			0
$262$	−1295.21			−0.305414
$263$	−355.072	−	615.003i	−0.0832497	−	0.144193i	0.821394	−	0.570361i	$-0.193197\pi$
$263$	−355.072	−	615.003i	−0.0832497	−	0.144193i	−0.904644	+	0.426168i	$0.859863\pi$
$264$		0			0
$265$	−503.280	+	871.706i	−0.116665	+	0.202070i
$266$	−3487.44	+	6040.42i	−0.803866	+	1.39234i
$267$		0			0
$268$	−350.091	−	606.375i	−0.0797955	−	0.138210i
$269$	3667.61			0.831294			0.415647	−	0.909526i	$-0.363555\pi$
$269$	3667.61			0.831294			0.415647	+	0.909526i	$0.363555\pi$
$270$		0			0
$271$	−1990.45			−0.446166			−0.223083	−	0.974799i	$-0.571612\pi$
$271$	−1990.45			−0.446166			−0.223083	+	0.974799i	$0.571612\pi$
$272$	260.235	+	450.740i	0.0580112	+	0.100478i
$273$		0			0
$274$	3260.91	−	5648.06i	0.718973	−	1.24530i
$275$	−138.535	+	239.950i	−0.0303781	+	0.0526164i
$276$		0			0
$277$	−4157.34	−	7200.73i	−0.901770	−	1.56191i	−0.825195	−	0.564848i	$-0.808935\pi$
$277$	−4157.34	−	7200.73i	−0.901770	−	1.56191i	−0.0765757	−	0.997064i	$-0.524399\pi$
$278$	1651.33			0.356259
$279$		0			0
$280$	−2757.18			−0.588474
$281$	−2882.56	−	4992.75i	−0.611955	−	1.05994i	−0.990911	−	0.134522i	$-0.957050\pi$
$281$	−2882.56	−	4992.75i	−0.611955	−	1.05994i	0.378955	−	0.925415i	$-0.376283\pi$
$282$		0			0
$283$	−228.780	+	396.259i	−0.0480551	+	0.0832338i	−0.889052	−	0.457805i	$-0.848636\pi$
$283$	−228.780	+	396.259i	−0.0480551	+	0.0832338i	0.840997	+	0.541039i	$0.181969\pi$
$284$	−615.392	+	1065.89i	−0.128580	+	0.222707i
$285$		0			0
$286$	−166.684	−	288.705i	−0.0344624	−	0.0596906i
$287$	−8277.59			−1.70248
$288$		0			0
$289$	−4811.71			−0.979383
$290$	1152.34	+	1995.91i	0.233337	+	0.404152i
$291$		0			0
$292$	−369.287	+	639.624i	−0.0740099	+	0.128189i
$293$	−2651.41	+	4592.38i	−0.528659	+	0.915664i	0.470783	+	0.882249i	$0.343972\pi$
$293$	−2651.41	+	4592.38i	−0.528659	+	0.915664i	−0.999442	+	0.0334147i	$0.989362\pi$
$294$		0			0
$295$	−1039.43	−	1800.34i	−0.205145	−	0.355322i
$296$	6023.51			1.18280
$297$		0			0
$298$	6912.30			1.34369
$299$	1003.33	+	1737.82i	0.194061	+	0.336123i
$300$		0			0
$301$	−4128.93	+	7151.52i	−0.790657	+	1.36946i
$302$	−1339.84	+	2320.68i	−0.255296	+	0.442185i
$303$		0			0
$304$	3047.66	+	5278.70i	0.574984	+	0.995901i
$305$	−273.135			−0.0512776
$306$		0			0
$307$	−6583.54			−1.22392			−0.611959	−	0.790890i	$-0.709618\pi$
$307$	−6583.54			−1.22392			−0.611959	+	0.790890i	$0.709618\pi$
$308$	−167.257	−	289.697i	−0.0309427	−	0.0535943i
$309$		0			0
$310$	908.121	−	1572.91i	0.166380	−	0.288179i
$311$	4064.02	−	7039.10i	0.740996	−	1.28344i	−0.211047	−	0.977476i	$-0.567687\pi$
$311$	4064.02	−	7039.10i	0.740996	−	1.28344i	0.952042	−	0.305966i	$-0.0989794\pi$
$312$		0			0
$313$	2603.82	+	4509.94i	0.470212	+	0.814431i	0.999420	−	0.0340613i	$-0.0108441\pi$
$313$	2603.82	+	4509.94i	0.470212	+	0.814431i	−0.529208	+	0.848492i	$0.677511\pi$
$314$	987.056			0.177397
$315$		0			0
$316$	−1068.94			−0.190294
$317$	1631.17	+	2825.27i	0.289008	+	0.500577i	0.973573	−	0.228375i	$-0.0733412\pi$
$317$	1631.17	+	2825.27i	0.289008	+	0.500577i	−0.684565	+	0.728952i	$0.740008\pi$
$318$		0			0
$319$	−988.146	+	1711.52i	−0.173434	+	0.300397i
$320$	−1415.69	+	2452.04i	−0.247311	+	0.428354i
$321$		0			0
$322$	−5102.26	−	8837.37i	−0.883037	−	1.52946i
$323$	1186.22			0.204345
$324$		0			0
$325$	−290.921			−0.0496535
$326$	3129.21	+	5419.95i	0.531628	+	0.920807i
$327$		0			0
$328$	−4354.55	+	7542.30i	−0.733048	+	1.26968i
$329$	−6869.44	+	11898.2i	−1.15114	+	1.99383i
$330$		0			0
$331$	−5180.23	−	8972.43i	−0.860216	−	1.48994i	−0.871720	−	0.490004i	$-0.836995\pi$
$331$	−5180.23	−	8972.43i	−0.860216	−	1.48994i	0.0115047	−	0.999934i	$-0.496338\pi$
$332$	−709.583			−0.117299
$333$		0			0
$334$	9139.51			1.49728
$335$	1327.70	+	2299.64i	0.216537	+	0.375053i
$336$		0			0
$337$	1867.63	−	3234.83i	0.301888	−	0.522886i	−0.674675	−	0.738115i	$-0.735716\pi$
$337$	1867.63	−	3234.83i	0.301888	−	0.522886i	0.976564	+	0.215229i	$0.0690497\pi$
$338$	−2664.47	+	4615.00i	−0.428781	+	0.742671i
$339$		0			0
$340$	33.1722	+	57.4560i	0.00529122	+	0.00916467i
$341$	1557.45			0.247333
$342$		0			0
$343$	3706.15			0.583421
$344$	4344.17	+	7524.32i	0.680878	+	1.17931i
$345$		0			0
$346$	4063.28	−	7037.80i	0.631338	−	1.09351i
$347$	−98.5050	+	170.616i	−0.0152393	+	0.0263952i	−0.873544	−	0.486744i	$-0.838184\pi$
$347$	−98.5050	+	170.616i	−0.0152393	+	0.0263952i	0.858305	+	0.513140i	$0.171518\pi$
$348$		0			0
$349$	3667.10	+	6351.60i	0.562451	+	0.974193i	0.997282	+	0.0736811i	$0.0234747\pi$
$349$	3667.10	+	6351.60i	0.562451	+	0.974193i	−0.434831	+	0.900512i	$0.643192\pi$
$350$	1479.42			0.225939
$351$		0			0
$352$	−654.107			−0.0990456
$353$	−2308.14	−	3997.82i	−0.348017	−	0.602783i	0.637880	−	0.770136i	$-0.279812\pi$
$353$	−2308.14	−	3997.82i	−0.348017	−	0.602783i	−0.985897	+	0.167352i	$0.946478\pi$
$354$		0			0
$355$	2333.84	−	4042.32i	0.348921	−	0.604350i
$356$	452.330	−	783.458i	0.0673411	−	0.116638i
$357$		0			0
$358$	−4263.83	−	7385.17i	−0.629470	−	1.09027i
$359$	−1153.79			−0.169623			−0.0848115	−	0.996397i	$-0.527029\pi$
$359$	−1153.79			−0.169623			−0.0848115	+	0.996397i	$0.527029\pi$
$360$		0			0
$361$	7033.09			1.02538
$362$	2423.44	+	4197.53i	0.351860	+	0.609440i
$363$		0			0
$364$	175.618	−	304.179i	0.0252881	−	0.0438003i
$365$	1400.50	−	2425.73i	0.200837	−	0.347859i
$366$		0			0
$367$	1724.52	+	2986.96i	0.245285	+	0.424845i	0.962212	−	0.272303i	$-0.0877853\pi$
$367$	1724.52	+	2986.96i	0.245285	+	0.424845i	−0.716927	+	0.697148i	$0.754452\pi$
$368$	−8917.69			−1.26322
$369$		0			0
$370$	−3232.05			−0.454125
$371$	2304.37	+	3991.28i	0.322471	+	0.558537i
$372$		0			0
$373$	−181.440	+	314.263i	−0.0251866	+	0.0436245i	−0.878344	−	0.478029i	$-0.841351\pi$
$373$	−181.440	+	314.263i	−0.0251866	+	0.0436245i	0.853157	+	0.521654i	$0.174685\pi$
$374$	144.159	−	249.691i	0.0199313	−	0.0345220i
$375$		0			0
$376$	7227.54	+	12518.5i	0.991308	+	1.71700i
$377$	−2075.09			−0.283481
$378$		0			0
$379$	−7719.79			−1.04628			−0.523139	−	0.852248i	$-0.675239\pi$
$379$	−7719.79			−1.04628			−0.523139	+	0.852248i	$0.675239\pi$
$380$	388.486	+	672.877i	0.0524445	+	0.0908365i
$381$		0			0
$382$	−1759.81	+	3048.08i	−0.235706	+	0.408255i
$383$	2836.83	−	4913.53i	0.378473	−	0.655534i	−0.612367	−	0.790573i	$-0.709783\pi$
$383$	2836.83	−	4913.53i	0.378473	−	0.655534i	0.990840	+	0.135039i	$0.0431160\pi$
$384$		0			0
$385$	634.311	+	1098.66i	0.0839675	+	0.145436i
$386$	−5775.13			−0.761520
$387$		0			0
$388$	−942.210			−0.123282
$389$	4090.23	+	7084.48i	0.533117	+	0.923386i	0.999252	+	0.0386726i	$0.0123129\pi$
$389$	4090.23	+	7084.48i	0.533117	+	0.923386i	−0.466135	+	0.884714i	$0.654354\pi$
$390$		0			0
$391$	−867.747	+	1502.98i	−0.112235	+	0.194397i
$392$	−2181.24	+	3778.01i	−0.281044	+	0.486782i
$393$		0			0
$394$	−447.991	−	775.943i	−0.0572829	−	0.0992169i
$395$	4053.91			0.516390
$396$		0			0
$397$	−12940.5			−1.63594			−0.817968	−	0.575263i	$-0.804900\pi$
$397$	−12940.5			−1.63594			−0.817968	+	0.575263i	$0.804900\pi$
$398$	5426.65	+	9399.23i	0.683450	+	1.18377i
$399$		0			0
$400$	646.431	−	1119.65i	0.0808039	−	0.139956i
$401$	−3290.65	+	5699.56i	−0.409793	+	0.709782i	−0.994866	−	0.101198i	$-0.967732\pi$
$401$	−3290.65	+	5699.56i	−0.409793	+	0.709782i	0.585073	+	0.810980i	$0.301066\pi$
$402$		0			0
$403$	817.652	+	1416.21i	0.101067	+	0.175054i
$404$	−1284.01			−0.158124
$405$		0			0
$406$	10552.5			1.28993
$407$	−1385.76	−	2400.20i	−0.168770	−	0.292319i
$408$		0			0
$409$	−2460.92	+	4262.44i	−0.297518	+	0.515316i	−0.975567	−	0.219700i	$-0.929492\pi$
$409$	−2460.92	+	4262.44i	−0.297518	+	0.515316i	0.678050	+	0.735016i	$0.262825\pi$
$410$	2336.53	−	4046.98i	0.281446	−	0.487479i
$411$		0			0
$412$	−500.488	−	866.871i	−0.0598478	−	0.103659i
$413$	−9518.48			−1.13408
$414$		0			0
$415$	2691.05			0.318310
$416$	−343.403	−	594.791i	−0.0404729	−	0.0701011i
$417$		0			0
$418$	1688.28	−	2924.18i	0.197551	−	0.342168i
$419$	1957.14	−	3389.87i	0.228193	−	0.395241i	−0.729080	−	0.684429i	$-0.760052\pi$
$419$	1957.14	−	3389.87i	0.228193	−	0.395241i	0.957273	+	0.289187i	$0.0933851\pi$
$420$		0			0
$421$	2629.38	+	4554.22i	0.304390	+	0.527219i	0.977125	−	0.212664i	$-0.0682140\pi$
$421$	2629.38	+	4554.22i	0.304390	+	0.527219i	−0.672735	+	0.739883i	$0.734881\pi$
$422$	−12222.5			−1.40991
$423$		0			0
$424$	4848.99			0.555395
$425$	−125.804	−	217.898i	−0.0143585	−	0.0248697i
$426$		0			0
$427$	−625.302	+	1083.05i	−0.0708677	+	0.122746i
$428$	1207.70	−	2091.81i	0.136394	−	0.236241i
$429$		0			0
$430$	−2330.96	−	4037.34i	−0.261416	−	0.452786i
$431$	14350.1			1.60376			0.801881	−	0.597484i	$-0.203833\pi$
$431$	14350.1			1.60376			0.801881	+	0.597484i	$0.203833\pi$
$432$		0			0
$433$	863.149			0.0957974			0.0478987	−	0.998852i	$-0.484748\pi$
$433$	863.149			0.0957974			0.0478987	+	0.998852i	$0.484748\pi$
$434$	−4158.02	−	7201.90i	−0.459888	−	0.796549i
$435$		0			0
$436$	903.710	−	1565.27i	0.0992658	−	0.171933i
$437$	−10162.3	+	17601.7i	−1.11243	+	1.92678i
$438$		0			0
$439$	8071.03	+	13979.4i	0.877470	+	1.51982i	0.854108	+	0.520095i	$0.174104\pi$
$439$	8071.03	+	13979.4i	0.877470	+	1.51982i	0.0233618	+	0.999727i	$0.492563\pi$
$440$	1334.75			0.144618
$441$		0			0
$442$	302.731			0.0325780
$443$	−2942.05	−	5095.77i	−0.315532	−	0.546518i	0.664018	−	0.747716i	$-0.268850\pi$
$443$	−2942.05	−	5095.77i	−0.315532	−	0.546518i	−0.979551	+	0.201198i	$0.935516\pi$
$444$		0			0
$445$	−1715.43	+	2971.22i	−0.182740	+	0.316515i
$446$	3140.83	−	5440.08i	0.333459	−	0.577568i
$447$		0			0
$448$	6482.02	+	11227.2i	0.683586	+	1.18401i
$449$	−16858.4			−1.77193			−0.885965	−	0.463753i	$-0.846503\pi$
$449$	−16858.4			−1.77193			−0.885965	+	0.463753i	$0.846503\pi$
$450$		0			0
$451$	4007.20			0.418385
$452$	384.691	+	666.305i	0.0400317	+	0.0693370i
$453$		0			0
$454$	−755.672	+	1308.86i	−0.0781177	+	0.135304i
$455$	−666.020	+	1153.58i	−0.0686231	+	0.118859i
$456$		0			0
$457$	−3811.52	−	6601.74i	−0.390143	−	0.675747i	0.602325	−	0.798251i	$-0.294241\pi$
$457$	−3811.52	−	6601.74i	−0.390143	−	0.675747i	−0.992468	+	0.122504i	$0.960908\pi$
$458$	12231.1			1.24786
$459$		0			0
$460$	−1136.74			−0.115219
$461$	2039.70	+	3532.86i	0.206070	+	0.356923i	0.950473	−	0.310807i	$-0.100599\pi$
$461$	2039.70	+	3532.86i	0.206070	+	0.356923i	−0.744403	+	0.667730i	$0.767266\pi$
$462$		0			0
$463$	2749.61	−	4762.46i	0.275994	−	0.478035i	−0.694392	−	0.719597i	$-0.744326\pi$
$463$	2749.61	−	4762.46i	0.275994	−	0.478035i	0.970385	+	0.241562i	$0.0776597\pi$
$464$	4610.88	−	7986.27i	0.461325	−	0.799038i
$465$		0			0
$466$	1587.70	+	2749.97i	0.157830	+	0.273369i
$467$	6422.51			0.636399			0.318199	−	0.948024i	$-0.396922\pi$
$467$	6422.51			0.636399			0.318199	+	0.948024i	$0.396922\pi$
$468$		0			0
$469$	12158.3			1.19705
$470$	−3878.10	−	6717.06i	−0.380603	−	0.659223i
$471$		0			0
$472$	−5007.33	+	8672.96i	−0.488308	+	0.845774i
$473$	1998.82	−	3462.07i	0.194305	−	0.336545i
$474$		0			0
$475$	−1473.31	−	2551.85i	−0.142316	−	0.246498i
$476$	303.772			0.0292507
$477$		0			0
$478$	311.595			0.0298160
$479$	−99.3800	−	172.131i	−0.00947973	−	0.0164194i	0.861247	−	0.508187i	$-0.169684\pi$
$479$	−99.3800	−	172.131i	−0.00947973	−	0.0164194i	−0.870726	+	0.491768i	$0.836351\pi$
$480$		0			0
$481$	1455.03	−	2520.19i	0.137929	−	0.238900i
$482$	2239.22	−	3878.45i	0.211605	−	0.366511i
$483$		0			0
$484$	−796.434	−	1379.46i	−0.0747966	−	0.129552i
$485$	3573.27			0.334544
$486$		0			0
$487$	−1308.73			−0.121774			−0.0608871	−	0.998145i	$-0.519393\pi$
$487$	−1308.73			−0.121774			−0.0608871	+	0.998145i	$0.519393\pi$
$488$	657.899	+	1139.51i	0.0610280	+	0.105704i
$489$		0			0
$490$	1170.39	−	2027.18i	0.107904	−	0.186895i
$491$	6237.41	−	10803.5i	0.573300	−	0.992984i	−0.422924	−	0.906165i	$-0.638996\pi$
$491$	6237.41	−	10803.5i	0.573300	−	0.992984i	0.996224	−	0.0868193i	$-0.0276703\pi$
$492$		0			0
$493$	−897.335	−	1554.23i	−0.0819755	−	0.141986i
$494$	3545.34			0.322900
$495$		0			0
$496$	−7267.35			−0.657890
$497$	−10685.9	−	18508.6i	−0.964447	−	1.67047i
$498$		0			0
$499$	−1573.41	+	2725.23i	−0.141153	+	0.244485i	−0.927931	−	0.372751i	$-0.878414\pi$
$499$	−1573.41	+	2725.23i	−0.141153	+	0.244485i	0.786778	+	0.617236i	$0.211748\pi$
$500$	82.4008	−	142.722i	0.00737015	−	0.0127655i
$501$		0			0
$502$	−4249.30	−	7360.00i	−0.377800	−	0.654369i
$503$	5419.35			0.480391			0.240196	−	0.970725i	$-0.422788\pi$
$503$	5419.35			0.480391			0.240196	+	0.970725i	$0.422788\pi$
$504$		0			0
$505$	4869.53			0.429092
$506$	2470.02	+	4278.19i	0.217007	+	0.375867i
$507$		0			0
$508$	−1603.69	+	2777.67i	−0.140063	+	0.242597i
$509$	−8597.28	+	14890.9i	−0.748660	+	1.29672i	0.199805	+	0.979836i	$0.435969\pi$
$509$	−8597.28	+	14890.9i	−0.748660	+	1.29672i	−0.948465	+	0.316881i	$0.897364\pi$
$510$		0			0
$511$	−6412.47	−	11106.7i	−0.555129	−	0.961511i
$512$	13017.3			1.12361
$513$		0			0
$514$	3851.01			0.330468
$515$	1898.07	+	3287.56i	0.162406	+	0.281295i
$516$		0			0
$517$	3325.51	−	5759.96i	0.282893	−	0.489986i
$518$	−7399.30	+	12816.0i	−0.627619	+	1.08707i
$519$		0			0
$520$	700.739	+	1213.72i	0.0590951	+	0.102356i
$521$	19829.5			1.66746			0.833730	−	0.552172i	$-0.186201\pi$
$521$	19829.5			1.66746			0.833730	+	0.552172i	$0.186201\pi$
$522$		0			0
$523$	5392.82			0.450882			0.225441	−	0.974257i	$-0.427618\pi$
$523$	5392.82			0.450882			0.225441	+	0.974257i	$0.427618\pi$
$524$	330.311	+	572.115i	0.0275376	+	0.0476965i
$525$		0			0
$526$	917.817	−	1589.71i	0.0760812	−	0.131777i
$527$	−707.159	+	1224.83i	−0.0584522	+	0.101242i
$528$		0			0
$529$	−8784.42	−	15215.1i	−0.721987	−	1.25052i
$530$	−2601.83			−0.213238
$531$		0			0
$532$	3557.53			0.289922
$533$	2103.76	+	3643.81i	0.170964	+	0.296118i
$534$		0			0
$535$	−4580.14	+	7933.04i	−0.370125	+	0.641075i
$536$	6396.03	−	11078.3i	0.515423	−	0.892738i
$537$		0			0
$538$	4740.16	+	8210.20i	0.379856	+	0.657931i
$539$	2007.25			0.160405
$540$		0			0
$541$	−11475.8			−0.911984			−0.455992	−	0.889984i	$-0.650715\pi$
$541$	−11475.8			−0.911984			−0.455992	+	0.889984i	$0.650715\pi$
$542$	−2572.53	−	4455.75i	−0.203874	−	0.353120i
$543$		0			0
$544$	296.997	−	514.414i	0.0234074	−	0.0405429i
$545$	−3427.27	+	5936.20i	−0.269372	+	0.466567i
$546$		0			0
$547$	3964.55	+	6866.79i	0.309893	+	0.536751i	0.978339	−	0.207010i	$-0.0663733\pi$
$547$	3964.55	+	6866.79i	0.309893	+	0.536751i	−0.668445	+	0.743761i	$0.733040\pi$
$548$	−3326.44			−0.259304
$549$		0			0
$550$	−716.192			−0.0555246
$551$	−10508.8	−	18201.9i	−0.812508	−	1.40731i
$552$		0			0
$553$	9280.82	−	16074.8i	0.713672	−	1.23612i
$554$	10746.2	−	18613.0i	0.824121	−	1.42742i
$555$		0			0
$556$	−421.128	−	729.416i	−0.0321220	−	0.0556369i
$557$	−9519.36			−0.724144			−0.362072	−	0.932150i	$-0.617931\pi$
$557$	−9519.36			−0.724144			−0.362072	+	0.932150i	$0.617931\pi$
$558$		0			0
$559$	4197.49			0.317594
$560$	−2959.82	−	5126.55i	−0.223348	−	0.386851i
$561$		0			0
$562$	7451.07	−	12905.6i	0.559261	−	0.968668i
$563$	5961.14	−	10325.0i	0.446238	−	0.772907i	−0.551899	−	0.833911i	$-0.686097\pi$
$563$	5961.14	−	10325.0i	0.446238	−	0.772907i	0.998138	+	0.0610035i	$0.0194301\pi$
$564$		0			0
$565$	−1458.92	−	2526.92i	−0.108632	−	0.188156i
$566$	−1182.74			−0.0878343
$567$		0			0
$568$	−22486.0			−1.66108
$569$	−8795.72	−	15234.6i	−0.648042	−	1.12244i	−0.983590	−	0.180418i	$-0.942255\pi$
$569$	−8795.72	−	15234.6i	−0.648042	−	1.12244i	0.335548	−	0.942023i	$-0.391078\pi$
$570$		0			0
$571$	−4125.37	+	7145.34i	−0.302349	+	0.523684i	−0.976668	−	0.214757i	$-0.931104\pi$
$571$	−4125.37	+	7145.34i	−0.302349	+	0.523684i	0.674319	+	0.738440i	$0.264437\pi$
$572$	−85.0170	+	147.254i	−0.00621458	+	0.0107640i
$573$		0			0
$574$	−10698.3	−	18530.0i	−0.777939	−	1.34743i
$575$	4311.02			0.312664
$576$		0			0
$577$	−15922.4			−1.14880			−0.574401	−	0.818574i	$-0.694765\pi$
$577$	−15922.4			−1.14880			−0.574401	+	0.818574i	$0.694765\pi$
$578$	−6218.84	−	10771.3i	−0.447525	−	0.775136i
$579$		0			0
$580$	587.750	−	1018.01i	0.0420776	−	0.0728805i
$581$	6160.76	−	10670.8i	0.439917	−	0.761958i
$582$		0			0
$583$	−1115.55	−	1932.19i	−0.0792476	−	0.137261i
$584$	−13493.5			−0.956103
$585$		0			0
$586$	−13707.1			−0.966274
$587$	4794.83	+	8304.88i	0.337144	+	0.583951i	0.983894	−	0.178751i	$-0.0572057\pi$
$587$	4794.83	+	8304.88i	0.337144	+	0.583951i	−0.646750	+	0.762702i	$0.723872\pi$
$588$		0			0
$589$	−8281.67	+	14344.3i	−0.579355	+	1.00347i
$590$	2686.80	−	4653.67i	0.187481	−	0.324726i
$591$		0			0
$592$	6466.21	+	11199.8i	0.448919	+	0.777550i
$593$	5311.77			0.367838			0.183919	−	0.982941i	$-0.441122\pi$
$593$	5311.77			0.367838			0.183919	+	0.982941i	$0.441122\pi$
$594$		0			0
$595$	−1152.04			−0.0793762
$596$	−1762.81	−	3053.27i	−0.121153	−	0.209844i
$597$		0			0
$598$	−2593.49	+	4492.06i	−0.177351	+	0.307180i
$599$	3173.02	−	5495.83i	0.216437	−	0.374881i	−0.737279	−	0.675589i	$-0.763890\pi$
$599$	3173.02	−	5495.83i	0.216437	−	0.374881i	0.953716	+	0.300708i	$0.0972229\pi$
$600$		0			0
$601$	4906.67	+	8498.60i	0.333023	+	0.576814i	0.983103	−	0.183053i	$-0.0585978\pi$
$601$	4906.67	+	8498.60i	0.333023	+	0.576814i	−0.650080	+	0.759866i	$0.725265\pi$
$602$	−21345.6			−1.44515
$603$		0			0
$604$	1366.77			0.0920746
$605$	3020.43	+	5231.54i	0.202972	+	0.351557i
$606$		0			0
$607$	2085.48	−	3612.15i	0.139451	−	0.241537i	−0.787838	−	0.615883i	$-0.788800\pi$
$607$	2085.48	−	3612.15i	0.139451	−	0.241537i	0.927289	+	0.374346i	$0.122133\pi$
$608$	3478.19	−	6024.40i	0.232005	−	0.401845i
$609$		0			0
$610$	−353.010	−	611.431i	−0.0234311	−	0.0405838i
$611$	6983.50			0.462393
$612$		0			0
$613$	−3157.32			−0.208031			−0.104016	−	0.994576i	$-0.533169\pi$
$613$	−3157.32			−0.208031			−0.104016	+	0.994576i	$0.533169\pi$
$614$	−8508.82	−	14737.7i	−0.559264	−	0.968674i
$615$		0			0
$616$	3055.72	−	5292.67i	0.199868	−	0.346181i
$617$	1481.47	−	2565.99i	0.0966643	−	0.167428i	−0.813638	−	0.581372i	$-0.802516\pi$
$617$	1481.47	−	2565.99i	0.0966643	−	0.167428i	0.910302	+	0.413945i	$0.135849\pi$
$618$		0			0
$619$	−2347.86	−	4066.62i	−0.152453	−	0.264057i	0.779676	−	0.626184i	$-0.215384\pi$
$619$	−2347.86	−	4066.62i	−0.152453	−	0.264057i	−0.932129	+	0.362127i	$0.882051\pi$
$620$	−926.372			−0.0600064
$621$		0			0
$622$	21010.0			1.35438
$623$	7854.46	+	13604.3i	0.505108	+	0.874873i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−6730.54	+	11657.6i	−0.429723	+	0.744302i
$627$		0			0
$628$	−251.723	−	435.998i	−0.0159950	−	0.0277041i
$629$	2516.81			0.159542
$630$		0			0
$631$	−17397.6			−1.09760			−0.548800	−	0.835954i	$-0.684915\pi$
$631$	−17397.6			−1.09760			−0.548800	+	0.835954i	$0.684915\pi$
$632$	−9764.62	−	16912.8i	−0.614582	−	1.06449i
$633$		0			0
$634$	−4216.37	+	7302.97i	−0.264122	+	0.457473i
$635$	6081.90	−	10534.2i	0.380083	−	0.658323i
$636$		0			0
$637$	1053.79	+	1825.22i	0.0655460	+	0.113529i
$638$	−5108.47			−0.317000
$639$		0			0
$640$	−4957.96			−0.306220
$641$	3451.73	+	5978.57i	0.212691	+	0.368392i	0.952556	−	0.304364i	$-0.0984438\pi$
$641$	3451.73	+	5978.57i	0.212691	+	0.368392i	−0.739865	+	0.672756i	$0.765110\pi$
$642$		0			0
$643$	6066.04	−	10506.7i	0.372039	−	0.644391i	−0.617840	−	0.786304i	$-0.711992\pi$
$643$	6066.04	−	10506.7i	0.372039	−	0.644391i	0.989879	+	0.141913i	$0.0453253\pi$
$644$	−2602.40	+	4507.49i	−0.159238	+	0.275808i
$645$		0			0
$646$	1533.12	+	2655.44i	0.0933744	+	0.161729i
$647$	16784.3			1.01988			0.509939	−	0.860211i	$-0.329668\pi$
$647$	16784.3			1.01988			0.509939	+	0.860211i	$0.329668\pi$
$648$		0			0
$649$	4607.92			0.278700
$650$	−375.997	−	651.246i	−0.0226889	−	0.0392984i
$651$		0			0
$652$	1596.05	−	2764.44i	0.0958682	−	0.166049i
$653$	7855.76	−	13606.6i	0.470781	−	0.815416i	−0.528661	−	0.848833i	$-0.677306\pi$
$653$	7855.76	−	13606.6i	0.470781	−	0.815416i	0.999441	+	0.0334172i	$0.0106390\pi$
$654$		0			0
$655$	−1252.68	−	2169.71i	−0.0747273	−	0.129431i
$656$	−18698.4			−1.11288
$657$		0			0
$658$	−35513.3			−2.10403
$659$	10113.5	+	17517.1i	0.597825	+	1.03546i	0.993141	+	0.116919i	$0.0373017\pi$
$659$	10113.5	+	17517.1i	0.597825	+	1.03546i	−0.395316	+	0.918545i	$0.629365\pi$
$660$		0			0
$661$	−7493.41	+	12979.0i	−0.440938	+	0.763727i	−0.997759	−	0.0669056i	$-0.978687\pi$
$661$	−7493.41	+	12979.0i	−0.440938	+	0.763727i	0.556822	+	0.830632i	$0.312021\pi$
$662$	13390.3	−	23192.6i	0.786144	−	1.36164i
$663$		0			0
$664$	−6481.92	−	11227.0i	−0.378836	−	0.656164i
$665$	−13491.7			−0.786745
$666$		0			0
$667$	30749.7			1.78506
$668$	−2330.80	−	4037.06i	−0.135002	−	0.233830i
$669$		0			0
$670$	−3431.93	+	5944.28i	−0.197891	+	0.342758i
$671$	302.710	−	524.309i	0.0174158	−	0.0301650i
$672$		0			0
$673$	−3416.87	−	5918.20i	−0.195707	−	0.338974i	0.751425	−	0.659818i	$-0.229367\pi$
$673$	−3416.87	−	5918.20i	−0.195707	−	0.338974i	−0.947132	+	0.320844i	$0.896033\pi$
$674$	9655.19			0.551787
$675$		0			0
$676$	2718.02			0.154644
$677$	15219.6	+	26361.2i	0.864015	+	1.49652i	0.868022	+	0.496525i	$0.165391\pi$
$677$	15219.6	+	26361.2i	0.864015	+	1.49652i	−0.00400745	+	0.999992i	$0.501276\pi$
$678$		0			0
$679$	8180.48	−	14169.0i	0.462354	−	0.800820i
$680$	−606.045	+	1049.70i	−0.0341776	+	0.0591973i
$681$		0			0
$682$	2012.91	+	3486.46i	0.113018	+	0.195753i
$683$	−9675.88			−0.542075			−0.271038	−	0.962569i	$-0.587367\pi$
$683$	−9675.88			−0.542075			−0.271038	+	0.962569i	$0.587367\pi$
$684$		0			0
$685$	12615.3			0.703660
$686$	4789.97	+	8296.47i	0.266592	+	0.461751i
$687$		0			0
$688$	−9326.90	+	16154.7i	−0.516838	+	0.895190i
$689$	1171.32	−	2028.78i	0.0647657	−	0.112177i
$690$		0			0
$691$	−6705.28	−	11613.9i	−0.369147	−	0.639382i	0.620285	−	0.784376i	$-0.287017\pi$
$691$	−6705.28	−	11613.9i	−0.369147	−	0.639382i	−0.989432	+	0.144994i	$0.953684\pi$
$692$	−4144.94			−0.227698
$693$		0			0
$694$	−509.247			−0.0278541
$695$	1597.10	+	2766.26i	0.0871678	+	0.150979i
$696$		0			0
$697$	−1819.47	+	3151.41i	−0.0988769	+	0.171260i
$698$	−9479.00	+	16418.1i	−0.514019	+	0.890307i
$699$		0			0
$700$	−377.289	−	653.484i	−0.0203717	−	0.0352848i
$701$	−12796.5			−0.689466			−0.344733	−	0.938701i	$-0.612031\pi$
$701$	−12796.5			−0.689466			−0.344733	+	0.938701i	$0.612031\pi$
$702$		0			0
$703$	29474.9			1.58132
$704$	−3137.96	−	5435.11i	−0.167992	−	0.290971i
$705$		0			0
$706$	5966.26	−	10333.9i	0.318050	−	0.550879i
$707$	11148.1	−	19309.0i	0.593022	−	1.02714i
$708$		0			0
$709$	−2424.66	−	4199.64i	−0.128435	−	0.222455i	0.794636	−	0.607087i	$-0.207662\pi$
$709$	−2424.66	−	4199.64i	−0.128435	−	0.222455i	−0.923070	+	0.384631i	$0.874329\pi$
$710$	12065.4			0.637753
$711$		0			0
$712$	16527.8			0.869952
$713$	−12116.4	−	20986.2i	−0.636414	−	1.10230i
$714$		0			0
$715$	322.422	−	558.451i	0.0168642	−	0.0292096i
$716$	−2174.76	+	3766.80i	−0.113512	+	0.196609i
$717$		0			0
$718$	−1491.20	−	2582.83i	−0.0775085	−	0.134249i
$719$	33988.7			1.76296			0.881479	−	0.472224i	$-0.156549\pi$
$719$	33988.7			1.76296			0.881479	+	0.472224i	$0.156549\pi$
$720$		0			0
$721$	17381.4			0.897806
$722$	9089.83	+	15744.1i	0.468544	+	0.811542i
$723$		0			0
$724$	1236.07	−	2140.94i	0.0634508	−	0.109900i
$725$	−2229.01	+	3860.75i	−0.114184	+	0.197772i
$726$		0			0
$727$	8156.13	+	14126.8i	0.416085	+	0.720681i	0.995542	−	0.0943224i	$-0.0300685\pi$
$727$	8156.13	+	14126.8i	0.416085	+	0.720681i	−0.579456	+	0.815003i	$0.696735\pi$
$728$	6416.96			0.326687
$729$		0			0
$730$	7240.23			0.367086
$731$	1815.13	+	3143.90i	0.0918400	+	0.159072i
$732$		0			0
$733$	18915.9	−	32763.3i	0.953172	−	1.65094i	0.214673	−	0.976686i	$-0.431131\pi$
$733$	18915.9	−	32763.3i	0.953172	−	1.65094i	0.738498	−	0.674256i	$-0.235535\pi$
$734$	−4457.68	+	7720.93i	−0.224164	+	0.388263i
$735$		0			0
$736$	5088.73	+	8813.94i	0.254855	+	0.441421i
$737$	−5885.84			−0.294176
$738$		0			0
$739$	−16860.9			−0.839295			−0.419647	−	0.907687i	$-0.637846\pi$
$739$	−16860.9			−0.839295			−0.419647	+	0.907687i	$0.637846\pi$
$740$	824.251	+	1427.64i	0.0409460	+	0.0709206i
$741$		0			0
$742$	−5956.51	+	10317.0i	−0.294704	+	0.510442i
$743$	−203.039	+	351.673i	−0.0100253	+	0.0173643i	−0.870995	−	0.491293i	$-0.836525\pi$
$743$	−203.039	+	351.673i	−0.0100253	+	0.0173643i	0.860969	+	0.508657i	$0.169858\pi$
$744$		0			0
$745$	6685.33	+	11579.3i	0.328767	+	0.569442i
$746$	−937.999			−0.0460357
$747$		0			0
$748$	−147.056			−0.00718839
$749$	20971.1	+	36323.1i	1.02306	+	1.77198i
$750$		0			0
$751$	7553.15	−	13082.4i	0.367002	−	0.635666i	−0.622093	−	0.782943i	$-0.713718\pi$
$751$	7553.15	−	13082.4i	0.367002	−	0.635666i	0.989095	+	0.147277i	$0.0470509\pi$
$752$	−15517.5	+	26877.0i	−0.752479	+	1.30333i
$753$		0			0
$754$	−2681.92	−	4645.22i	−0.129535	−	0.224362i
$755$	−5183.39			−0.249858
$756$		0			0
$757$	−14265.4			−0.684919			−0.342460	−	0.939533i	$-0.611260\pi$
$757$	−14265.4			−0.684919			−0.342460	+	0.939533i	$0.611260\pi$
$758$	−9977.36	−	17281.3i	−0.478092	−	0.828080i
$759$		0			0
$760$	−7097.50	+	12293.2i	−0.338755	+	0.586740i
$761$	−11500.6	+	19919.7i	−0.547828	+	0.948867i	0.450595	+	0.892729i	$0.351212\pi$
$761$	−11500.6	+	19919.7i	−0.547828	+	0.948867i	−0.998423	+	0.0561380i	$0.982121\pi$
$762$		0			0
$763$	15692.4	+	27180.1i	0.744567	+	1.28963i
$764$	1795.18			0.0850095
$765$		0			0
$766$	14665.7			0.691767
$767$	2419.13	+	4190.06i	0.113885	+	0.197255i
$768$		0			0
$769$	−6147.31	+	10647.5i	−0.288267	+	0.499294i	−0.973396	−	0.229128i	$-0.926413\pi$
$769$	−6147.31	+	10647.5i	−0.288267	+	0.499294i	0.685129	+	0.728422i	$0.259746\pi$
$770$	−1639.62	+	2839.90i	−0.0767372	+	0.132913i
$771$		0			0
$772$	1472.80	+	2550.96i	0.0686622	+	0.118926i
$773$	5938.46			0.276315			0.138158	−	0.990410i	$-0.455882\pi$
$773$	5938.46			0.276315			0.138158	+	0.990410i	$0.455882\pi$
$774$		0			0
$775$	3513.21			0.162836
$776$	−8606.93	−	14907.6i	−0.398158	−	0.689630i
$777$		0			0
$778$	−10572.7	+	18312.5i	−0.487212	+	0.843875i
$779$	−21308.1	+	36906.7i	−0.980029	+	1.69746i
$780$		0			0
$781$	5173.09	+	8960.05i	0.237014	+	0.410520i
$782$	−4486.04			−0.205141
$783$		0			0
$784$	−9366.19			−0.426667
$785$	954.645	+	1653.49i	0.0434048	+	0.0751793i
$786$		0			0
$787$	−16212.5	+	28080.9i	−0.734325	+	1.27189i	0.220694	+	0.975343i	$0.429168\pi$
$787$	−16212.5	+	28080.9i	−0.734325	+	1.27189i	−0.955019	+	0.296545i	$0.904166\pi$
$788$	−228.497	+	395.769i	−0.0103298	+	0.0178917i
$789$		0			0
$790$	5239.42	+	9074.95i	0.235962	+	0.408699i
$791$	−13359.9			−0.600535
$792$		0			0
$793$	635.685			0.0284664
$794$	−16724.8	−	28968.3i	−0.747535	−	1.29477i
$795$		0			0
$796$	2767.85	−	4794.06i	0.123246	−	0.213469i
$797$	10495.2	−	18178.2i	0.466449	−	0.807913i	−0.532817	−	0.846231i	$-0.678867\pi$
$797$	10495.2	−	18178.2i	0.466449	−	0.807913i	0.999266	+	0.0383177i	$0.0121999\pi$
$798$		0			0
$799$	3019.89	+	5230.61i	0.133712	+	0.231597i
$800$	−1475.50			−0.0652085
$801$		0			0
$802$	−17011.8			−0.749013
$803$	3104.29	+	5376.79i	0.136423	+	0.236292i
$804$		0			0
$805$	9869.45	−	17094.4i	0.432115	−	0.748445i
$806$	−2113.53	+	3660.74i	−0.0923646	+	0.159980i
$807$		0			0
$808$	−11729.2	−	20315.6i	−0.510684	−	0.884531i
$809$	−4943.95			−0.214858			−0.107429	−	0.994213i	$-0.534262\pi$
$809$	−4943.95			−0.214858			−0.107429	+	0.994213i	$0.534262\pi$
$810$		0			0
$811$	−19844.5			−0.859230			−0.429615	−	0.903012i	$-0.641351\pi$
$811$	−19844.5			−0.859230			−0.429615	+	0.903012i	$0.641351\pi$
$812$	−2691.14	−	4661.18i	−0.116306	−	0.201448i
$813$		0			0
$814$	3582.02	−	6204.23i	0.154238	−	0.267148i
$815$	−6052.91	+	10484.0i	−0.260153	+	0.450597i
$816$		0			0
$817$	21257.3	+	36818.8i	0.910282	+	1.57665i
$818$	−12722.4			−0.543798
$819$		0			0
$820$	−2383.49			−0.101506
$821$	−6304.12	−	10919.1i	−0.267985	−	0.464163i	0.700357	−	0.713793i	$-0.253024\pi$
$821$	−6304.12	−	10919.1i	−0.267985	−	0.464163i	−0.968341	+	0.249630i	$0.919691\pi$
$822$		0			0
$823$	−12421.7	+	21515.0i	−0.526116	+	0.911260i	0.473421	+	0.880836i	$0.343019\pi$
$823$	−12421.7	+	21515.0i	−0.526116	+	0.911260i	−0.999537	+	0.0304237i	$0.990314\pi$
$824$	9143.75	−	15837.4i	0.386575	−	0.669567i
$825$		0			0
$826$	−12302.0	−	21307.8i	−0.518212	−	0.897569i
$827$	33361.1			1.40276			0.701379	−	0.712789i	$-0.252568\pi$
$827$	33361.1			1.40276			0.701379	+	0.712789i	$0.252568\pi$
$828$		0			0
$829$	−5049.62			−0.211557			−0.105778	−	0.994390i	$-0.533733\pi$
$829$	−5049.62			−0.211557			−0.105778	+	0.994390i	$0.533733\pi$
$830$	3478.02	+	6024.10i	0.145450	+	0.251927i
$831$		0			0
$832$	3294.82	−	5706.80i	0.137293	−	0.237798i
$833$	−911.389	+	1578.57i	−0.0379085	+	0.0656594i
$834$		0			0
$835$	8839.40	+	15310.3i	0.366347	+	0.634532i
$836$	−1722.21			−0.0712485
$837$		0			0
$838$	10117.9			0.417087
$839$	8732.33	+	15124.8i	0.359325	+	0.622369i	0.987848	−	0.155422i	$-0.0496737\pi$
$839$	8732.33	+	15124.8i	0.359325	+	0.622369i	−0.628523	+	0.777791i	$0.716340\pi$
$840$		0			0
$841$	−3704.61	+	6416.57i	−0.151897	+	0.263093i
$842$	−6796.63	+	11772.1i	−0.278180	+	0.481821i
$843$		0			0
$844$	3117.03	+	5398.85i	0.127124	+	0.220185i
$845$	−10307.9			−0.419649
$846$		0			0
$847$	27659.3			1.12206
$848$	5205.37	+	9015.96i	0.210794	+	0.365105i
$849$		0			0
$850$	325.187	−	563.240i	0.0131221	−	0.0227282i
$851$	−21561.5	+	37345.5i	−0.868528	+	1.50433i
$852$		0			0
$853$	−1373.24	−	2378.51i	−0.0551216	−	0.0954734i	0.837148	−	0.546977i	$-0.184221\pi$
$853$	−1373.24	−	2378.51i	−0.0551216	−	0.0954734i	−0.892270	+	0.451503i	$0.850888\pi$
$854$	−3232.66			−0.129531
$855$		0			0
$856$	44128.7			1.76202
$857$	−7828.41	−	13559.2i	−0.312034	−	0.540459i	0.666768	−	0.745265i	$-0.267677\pi$
$857$	−7828.41	−	13559.2i	−0.312034	−	0.540459i	−0.978803	+	0.204806i	$0.934344\pi$
$858$		0			0
$859$	17253.7	−	29884.2i	0.685317	−	1.18700i	−0.288021	−	0.957624i	$-0.592997\pi$
$859$	17253.7	−	29884.2i	0.685317	−	1.18700i	0.973337	−	0.229379i	$-0.0736695\pi$
$860$	−1188.90	+	2059.24i	−0.0471410	+	0.0816506i
$861$		0			0
$862$	18546.7	+	32123.8i	0.732833	+	1.26930i
$863$	26576.7			1.04830			0.524150	−	0.851626i	$-0.324383\pi$
$863$	26576.7			1.04830			0.524150	+	0.851626i	$0.324383\pi$
$864$		0			0
$865$	15719.4			0.617892
$866$	1115.57	+	1932.22i	0.0437742	+	0.0758192i
$867$		0			0
$868$	−2120.79	+	3673.32i	−0.0829313	+	0.143641i
$869$	−4492.86	+	7781.87i	−0.175385	+	0.303777i
$870$		0			0
$871$	−3090.04	−	5352.10i	−0.120209	−	0.208208i
$872$	33020.9			1.28237
$873$		0			0
$874$	−52536.8			−2.03328
$875$	1430.85	+	2478.30i	0.0552816	+	0.0957505i
$876$		0			0
$877$	6699.73	−	11604.3i	0.257963	−	0.446806i	−0.707733	−	0.706480i	$-0.750282\pi$
$877$	6699.73	−	11604.3i	0.257963	−	0.446806i	0.965696	+	0.259674i	$0.0836153\pi$
$878$	−20862.6	+	36135.1i	−0.801913	+	1.38895i
$879$		0			0
$880$	1432.85	+	2481.78i	0.0548881	+	0.0950689i
$881$	−44435.4			−1.69928			−0.849641	−	0.527362i	$-0.823181\pi$
$881$	−44435.4			−1.69928			−0.849641	+	0.527362i	$0.823181\pi$
$882$		0			0
$883$	−11162.1			−0.425408			−0.212704	−	0.977117i	$-0.568227\pi$
$883$	−11162.1			−0.425408			−0.212704	+	0.977117i	$0.568227\pi$
$884$	−77.2039	−	133.721i	−0.00293738	−	0.00508770i
$885$		0			0
$886$	7604.83	−	13171.9i	0.288362	−	0.499458i
$887$	−5795.60	+	10038.3i	−0.219388	+	0.379991i	−0.954621	−	0.297823i	$-0.903739\pi$
$887$	−5795.60	+	10038.3i	−0.219388	+	0.379991i	0.735233	+	0.677814i	$0.237073\pi$
$888$		0			0
$889$	−27847.2	−	48232.8i	−1.05058	−	1.81966i
$890$	−8868.36			−0.334009
$891$		0			0
$892$	−3203.96			−0.120265
$893$	35366.5	+	61256.6i	1.32530	+	2.29549i
$894$		0			0
$895$	8247.65	−	14285.3i	0.308032	−	0.533527i
$896$	−11350.5	+	19659.7i	−0.423208	+	0.733017i
$897$		0			0
$898$	−21788.4	−	37738.7i	−0.809676	−	1.40240i
$899$	25059.1			0.929663
$900$		0			0
$901$	2026.06			0.0749144
$902$	5179.06	+	8970.39i	0.191179	+	0.331132i
$903$		0			0
$904$	−7028.17	+	12173.2i	−0.258577	+	0.447868i
$905$	−4687.74	+	8119.40i	−0.172183	+	0.298230i
$906$		0			0
$907$	−4326.19	−	7493.19i	−0.158378	−	0.274319i	0.775906	−	0.630849i	$-0.217293\pi$
$907$	−4326.19	−	7493.19i	−0.158378	−	0.274319i	−0.934284	+	0.356530i	$0.883960\pi$
$908$	770.859			0.0281738
$909$		0			0
$910$	−3443.16			−0.125428
$911$	18356.2	+	31793.9i	0.667583	+	1.15629i	0.978578	+	0.205876i	$0.0660043\pi$
$911$	18356.2	+	31793.9i	0.667583	+	1.15629i	−0.310995	+	0.950411i	$0.600662\pi$
$912$		0			0
$913$	−2982.44	+	5165.74i	−0.108110	+	0.187252i
$914$	9852.30	−	17064.7i	0.356548	−	0.617560i
$915$		0			0
$916$	−3119.22	−	5402.64i	−0.112513	−	0.194878i
$917$	−11471.3			−0.413104
$918$		0			0
$919$	−42003.3			−1.50768			−0.753841	−	0.657057i	$-0.771801\pi$
$919$	−42003.3			−1.50768			−0.753841	+	0.657057i	$0.771801\pi$
$920$	−10383.9	−	17985.5i	−0.372118	−	0.644526i
$921$		0			0
$922$	−5272.36	+	9132.00i	−0.188325	+	0.326189i
$923$	−5431.69	+	9407.96i	−0.193701	+	0.335500i
$924$		0			0
$925$	−3125.92	−	5414.25i	−0.111113	−	0.192454i
$926$	14214.8			0.504457
$927$		0			0
$928$	−10524.5			−0.372288
$929$	6556.30	+	11355.8i	0.231545	+	0.401048i	0.958263	−	0.285888i	$-0.0922887\pi$
$929$	6556.30	+	11355.8i	0.231545	+	0.401048i	−0.726718	+	0.686936i	$0.758955\pi$
$930$		0			0
$931$	−10673.4	+	18487.0i	−0.375734	+	0.650790i
$932$	809.803	−	1402.62i	0.0284614	−	0.0492965i
$933$		0			0
$934$	8300.69	+	14377.2i	0.290800	+	0.503680i
$935$	557.703			0.0195068
$936$		0			0
$937$	49863.5			1.73849			0.869247	−	0.494378i	$-0.164604\pi$
$937$	49863.5			1.73849			0.869247	+	0.494378i	$0.164604\pi$
$938$	15713.8	+	27217.1i	0.546987	+	0.947410i
$939$		0			0
$940$	−1978.02	+	3426.03i	−0.0686339	+	0.118877i
$941$	4676.14	−	8099.31i	0.161996	−	0.280584i	−0.773589	−	0.633688i	$-0.781540\pi$
$941$	4676.14	−	8099.31i	0.161996	−	0.280584i	0.935584	+	0.353104i	$0.114874\pi$
$942$		0			0
$943$	−31174.6	−	53996.0i	−1.07655	−	1.86464i
$944$	−21501.4			−0.741326
$945$		0			0
$946$	10333.4			0.355147
$947$	2005.69	+	3473.96i	0.0688239	+	0.119207i	0.898384	−	0.439211i	$-0.144742\pi$
$947$	2005.69	+	3473.96i	0.0688239	+	0.119207i	−0.829560	+	0.558418i	$0.811409\pi$
$948$		0			0
$949$	−3259.47	+	5645.57i	−0.111493	+	0.193112i
$950$	3808.32	−	6596.21i	0.130061	−	0.225273i
$951$		0			0
$952$	2774.90	+	4806.27i	0.0944696	+	0.163626i
$953$	−39128.6			−1.33001			−0.665005	−	0.746839i	$-0.731571\pi$
$953$	−39128.6			−1.33001			−0.665005	+	0.746839i	$0.731571\pi$
$954$		0			0
$955$	−6808.10			−0.230686
$956$	−79.4643	−	137.636i	−0.00268835	−	0.00465636i
$957$		0			0
$958$	256.885	−	444.938i	0.00866345	−	0.0150055i
$959$	28880.9	−	50023.3i	0.972486	−	1.68440i
$960$		0			0
$961$	5021.39	+	8697.31i	0.168554	+	0.291944i
$962$	7522.15			0.252104
$963$		0			0
$964$	−2284.22			−0.0763174
$965$	−5585.50	−	9674.38i	−0.186325	−	0.322725i
$966$		0			0
$967$	−8817.49	+	15272.3i	−0.293228	+	0.507885i	−0.974571	−	0.224079i	$-0.928063\pi$
$967$	−8817.49	+	15272.3i	−0.293228	+	0.507885i	0.681343	+	0.731964i	$0.261396\pi$
$968$	14550.6	−	25202.3i	0.483134	−	0.836812i
$969$		0			0
$970$	4618.24	+	7999.02i	0.152869	+	0.264776i
$971$	26827.3			0.886642			0.443321	−	0.896363i	$-0.353800\pi$
$971$	26827.3			0.886642			0.443321	+	0.896363i	$0.353800\pi$
$972$		0			0
$973$	14625.3			0.481877
$974$	−1691.45	−	2929.67i	−0.0556442	−	0.0963787i
$975$		0			0
$976$	−1412.50	+	2446.53i	−0.0463249	+	0.0802371i
$977$	−4171.82	+	7225.80i	−0.136610	+	0.236616i	−0.926211	−	0.377004i	$-0.876954\pi$
$977$	−4171.82	+	7225.80i	−0.136610	+	0.236616i	0.789601	+	0.613620i	$0.210287\pi$
$978$		0			0
$979$	−3802.36	−	6585.88i	−0.124131	−	0.215001i
$980$	−1193.91			−0.0389165
$981$		0			0
$982$	32245.8			1.04787
$983$	−18445.0	−	31947.7i	−0.598479	−	1.03660i	−0.993046	−	0.117729i	$-0.962439\pi$
$983$	−18445.0	−	31947.7i	−0.598479	−	1.03660i	0.394567	−	0.918867i	$-0.370895\pi$
$984$		0			0
$985$	866.561	−	1500.93i	0.0280314	−	0.0485518i
$986$	2319.50	−	4017.49i	0.0749167	−	0.129760i
$987$		0			0
$988$	−904.149	−	1566.03i	−0.0291142	−	0.0504272i
$989$	−62200.7			−1.99987
$990$		0			0
$991$	−24259.3			−0.777619			−0.388810	−	0.921318i	$-0.627114\pi$
$991$	−24259.3			−0.777619			−0.388810	+	0.921318i	$0.627114\pi$
$992$	4146.99	+	7182.80i	0.132729	+	0.229893i
$993$		0			0
$994$	27621.8	−	47842.4i	0.881400	−	1.52663i
$995$	−10496.9	+	18181.2i	−0.334447	+	0.579279i
$996$		0			0
$997$	−15850.1	−	27453.2i	−0.503488	−	0.872067i	−0.999992	−	0.00403269i	$-0.998716\pi$
$997$	−15850.1	−	27453.2i	−0.503488	−	0.872067i	0.496504	−	0.868035i	$-0.334617\pi$
$998$	−8134.15			−0.257998
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.q.271.3		6
3.2	odd	2		405.4.e.v.271.1		6
9.2	odd	6		405.4.e.v.136.1		6
9.4	even	3		135.4.a.h.1.1	yes	3
9.5	odd	6		135.4.a.e.1.3	✓	3
9.7	even	3	inner	405.4.e.q.136.3		6
36.23	even	6		2160.4.a.bi.1.3		3
36.31	odd	6		2160.4.a.bq.1.3		3
45.4	even	6		675.4.a.p.1.3		3
45.13	odd	12		675.4.b.n.649.5		6
45.14	odd	6		675.4.a.s.1.1		3
45.22	odd	12		675.4.b.n.649.2		6
45.23	even	12		675.4.b.m.649.2		6
45.32	even	12		675.4.b.m.649.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.a.e.1.3	✓	3	9.5	odd	6
135.4.a.h.1.1	yes	3	9.4	even	3
405.4.e.q.136.3		6	9.7	even	3	inner
405.4.e.q.271.3		6	1.1	even	1	trivial
405.4.e.v.136.1		6	9.2	odd	6
405.4.e.v.271.1		6	3.2	odd	2
675.4.a.p.1.3		3	45.4	even	6
675.4.a.s.1.1		3	45.14	odd	6
675.4.b.m.649.2		6	45.23	even	12
675.4.b.m.649.5		6	45.32	even	12
675.4.b.n.649.2		6	45.22	odd	12
675.4.b.n.649.5		6	45.13	odd	12
2160.4.a.bi.1.3		3	36.23	even	6
2160.4.a.bq.1.3		3	36.31	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.29244 + 2.23857i) q^{2} +(0.659207 - 1.14178i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(11.4468 + 19.8264i) q^{7} +24.0869 q^{8} -12.9244 q^{10} +(-5.54140 - 9.59799i) q^{11} +(5.81841 - 10.0778i) q^{13} +(-29.5885 + 51.2487i) q^{14} +(25.8572 + 44.7861i) q^{16} +10.0643 q^{17} +117.865 q^{19} +(3.29603 + 5.70890i) q^{20} +(14.3238 - 24.8096i) q^{22} +(-86.2204 + 149.338i) q^{23} +(-12.5000 - 21.6506i) q^{25} +30.0798 q^{26} +30.1831 q^{28} +(-89.1603 - 154.430i) q^{29} +(-70.2642 + 121.701i) q^{31} +(29.5100 - 51.1128i) q^{32} +(13.0075 + 22.5296i) q^{34} -114.468 q^{35} +250.074 q^{37} +(152.333 + 263.848i) q^{38} +(-60.2174 + 104.300i) q^{40} +(-180.784 + 313.128i) q^{41} +(180.354 + 312.382i) q^{43} -14.6117 q^{44} -445.738 q^{46} +(300.060 + 519.720i) q^{47} +(-90.5568 + 156.849i) q^{49} +(32.3110 - 55.9642i) q^{50} +(-7.67107 - 13.2867i) q^{52} +201.312 q^{53} +55.4140 q^{55} +(275.718 + 477.557i) q^{56} +(230.468 - 399.183i) q^{58} +(-207.886 + 360.069i) q^{59} +(27.3135 + 47.3083i) q^{61} -363.248 q^{62} +566.275 q^{64} +(29.0921 + 50.3889i) q^{65} +(265.539 - 459.928i) q^{67} +(6.63444 - 11.4912i) q^{68} +(-147.942 - 256.244i) q^{70} -933.534 q^{71} -560.199 q^{73} +(323.205 + 559.807i) q^{74} +(77.6972 - 134.575i) q^{76} +(126.862 - 219.732i) q^{77} +(-405.391 - 702.157i) q^{79} -258.572 q^{80} -934.611 q^{82} +(-269.105 - 466.104i) q^{83} +(-25.1607 + 43.5796i) q^{85} +(-466.192 + 807.468i) q^{86} +(-133.475 - 231.186i) q^{88} +686.173 q^{89} +266.408 q^{91} +(113.674 + 196.889i) q^{92} +(-775.619 + 1343.41i) q^{94} +(-294.662 + 510.369i) q^{95} +(-357.327 - 618.909i) q^{97} -468.156 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} - 17 q^{4} - 15 q^{5} + 4 q^{7} + 150 q^{8} + 50 q^{10} - 5 q^{11} - 7 q^{13} - 60 q^{14} - 161 q^{16} + 310 q^{17} - 100 q^{19} - 85 q^{20} + 229 q^{22} - 285 q^{23} - 75 q^{25} + 370 q^{26}+ \cdots - 610 q^{98}+O(q^{100}) \) 6 * q - 5 * q^2 - 17 * q^4 - 15 * q^5 + 4 * q^7 + 150 * q^8 + 50 * q^10 - 5 * q^11 - 7 * q^13 - 60 * q^14 - 161 * q^16 + 310 * q^17 - 100 * q^19 - 85 * q^20 + 229 * q^22 - 285 * q^23 - 75 * q^25 + 370 * q^26 - 668 * q^28 - 115 * q^29 + 115 * q^31 - 775 * q^32 - 413 * q^34 - 40 * q^35 - 768 * q^37 + 1150 * q^38 - 375 * q^40 - 580 * q^41 + 797 * q^43 - 2830 * q^44 - 570 * q^46 + 145 * q^47 - 577 * q^49 - 125 * q^50 - 825 * q^52 - 800 * q^53 + 50 * q^55 + 2190 * q^56 + 59 * q^58 - 380 * q^59 + 152 * q^61 - 2010 * q^62 + 5874 * q^64 - 35 * q^65 - 2 * q^67 - 475 * q^68 - 300 * q^70 + 80 * q^71 - 1960 * q^73 + 2720 * q^74 + 3276 * q^76 - 1950 * q^77 - 1013 * q^79 + 1610 * q^80 + 8 * q^82 - 270 * q^83 - 775 * q^85 + 1555 * q^86 + 5193 * q^88 + 2040 * q^89 - 1264 * q^91 + 1215 * q^92 - 3833 * q^94 + 250 * q^95 - 720 * q^97 - 610 * q^98

Introduction

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