LMFDB - Embedded newform 49.5.d.c.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,5,Mod(19,49)]

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([5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("49.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	49.d (of order $6$, 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:	$5.06512819111$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} - 140 x^{14} + 1120 x^{13} + 8358 x^{12} - 65072 x^{11} - 277636 x^{10} + \cdots + 4890937156 $ x^16 - 8x^15 - 140x^14 + 1120x^13 + 8358x^12 - 65072x^11 - 277636x^10 + 2012320x^9 + 5569235x^8 - 35114128x^7 - 67281340x^6 + 333960872x^5 + 452600898x^4 - 1507177456x^3 - 1556646896x^2 + 2372409872*x + 4890937156
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$-1.11701 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	49.19
Dual form			49.5.d.c.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.858610 + 1.48716i) q^{2} +(13.9722 - 8.06687i) q^{3} +(6.52558 + 11.3026i) q^{4} +(6.78727 + 3.91863i) q^{5} +27.7052i q^{6} -49.8872 q^{8} +(89.6489 - 155.277i) q^{9} +O(q^{10})$	\(q+(-0.858610 + 1.48716i) q^{2} +(13.9722 - 8.06687i) q^{3} +(6.52558 + 11.3026i) q^{4} +(6.78727 + 3.91863i) q^{5} +27.7052i q^{6} -49.8872 q^{8} +(89.6489 - 155.277i) q^{9} +(-11.6552 + 6.72915i) q^{10} +(-15.2563 - 26.4247i) q^{11} +(182.354 + 105.282i) q^{12} +162.301i q^{13} +126.444 q^{15} +(-61.5756 + 106.652i) q^{16} +(299.315 - 172.810i) q^{17} +(153.947 + 266.644i) q^{18} +(-228.537 - 131.946i) q^{19} +102.285i q^{20} +52.3969 q^{22} +(-106.589 + 184.618i) q^{23} +(-697.036 + 402.434i) q^{24} +(-281.789 - 488.072i) q^{25} +(-241.367 - 139.353i) q^{26} -1585.91i q^{27} -1011.68 q^{29} +(-108.566 + 188.043i) q^{30} +(-237.120 + 136.901i) q^{31} +(-504.837 - 874.403i) q^{32} +(-426.329 - 246.141i) q^{33} +593.504i q^{34} +2340.04 q^{36} +(-773.001 + 1338.88i) q^{37} +(392.448 - 226.580i) q^{38} +(1309.26 + 2267.71i) q^{39} +(-338.598 - 195.490i) q^{40} +531.628i q^{41} -1470.93 q^{43} +(199.112 - 344.873i) q^{44} +(1216.94 - 702.602i) q^{45} +(-183.038 - 317.030i) q^{46} +(2064.25 + 1191.79i) q^{47} +1986.89i q^{48} +967.786 q^{50} +(2788.07 - 4829.07i) q^{51} +(-1834.43 + 1059.11i) q^{52} +(-1603.31 - 2777.02i) q^{53} +(2358.50 + 1361.68i) q^{54} -239.135i q^{55} -4257.56 q^{57} +(868.637 - 1504.52i) q^{58} +(2700.71 - 1559.25i) q^{59} +(825.123 + 1429.15i) q^{60} +(-3416.15 - 1972.32i) q^{61} -470.179i q^{62} -236.587 q^{64} +(-635.998 + 1101.58i) q^{65} +(732.101 - 422.679i) q^{66} +(3459.63 + 5992.26i) q^{67} +(3906.41 + 2255.36i) q^{68} +3439.38i q^{69} +8580.05 q^{71} +(-4472.34 + 7746.32i) q^{72} +(311.150 - 179.642i) q^{73} +(-1327.41 - 2299.15i) q^{74} +(-7874.44 - 4546.31i) q^{75} -3444.09i q^{76} -4496.58 q^{78} +(-1043.58 + 1807.53i) q^{79} +(-835.859 + 482.584i) q^{80} +(-5531.80 - 9581.36i) q^{81} +(-790.613 - 456.461i) q^{82} -10594.2i q^{83} +2708.71 q^{85} +(1262.95 - 2187.50i) q^{86} +(-14135.4 + 8161.08i) q^{87} +(761.095 + 1318.25i) q^{88} +(9033.60 + 5215.55i) q^{89} +2413.04i q^{90} -2782.23 q^{92} +(-2208.73 + 3825.63i) q^{93} +(-3544.76 + 2046.57i) q^{94} +(-1034.09 - 1791.10i) q^{95} +(-14107.4 - 8144.91i) q^{96} +1403.85i q^{97} -5470.85 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{2} - 52 q^{4} - 744 q^{8} + 352 q^{9}+O(q^{10}) $ 16 * q + 12 * q^2 - 52 * q^4 - 744 * q^8 + 352 * q^9	$ 16 q + 12 q^{2} - 52 q^{4} - 744 q^{8} + 352 q^{9} - 120 q^{11} - 1264 q^{15} + 300 q^{16} - 340 q^{18} + 3904 q^{22} - 1752 q^{23} + 2192 q^{25} + 2496 q^{29} - 456 q^{30} - 3156 q^{32} + 9880 q^{36} - 2368 q^{37} + 7672 q^{39} - 17104 q^{43} - 264 q^{44} - 7208 q^{46} - 11112 q^{50} + 11976 q^{51} - 5496 q^{53} - 18400 q^{57} + 17496 q^{58} - 2856 q^{60} + 7960 q^{64} - 30240 q^{65} + 7440 q^{67} + 19968 q^{71} + 1508 q^{72} + 1080 q^{74} + 44912 q^{78} + 14096 q^{79} - 3432 q^{81} + 23824 q^{85} - 44496 q^{86} + 44464 q^{88} - 64464 q^{92} - 9584 q^{93} - 22488 q^{95} + 60288 q^{99}+O(q^{100}) $ 16 * q + 12 * q^2 - 52 * q^4 - 744 * q^8 + 352 * q^9 - 120 * q^11 - 1264 * q^15 + 300 * q^16 - 340 * q^18 + 3904 * q^22 - 1752 * q^23 + 2192 * q^25 + 2496 * q^29 - 456 * q^30 - 3156 * q^32 + 9880 * q^36 - 2368 * q^37 + 7672 * q^39 - 17104 * q^43 - 264 * q^44 - 7208 * q^46 - 11112 * q^50 + 11976 * q^51 - 5496 * q^53 - 18400 * q^57 + 17496 * q^58 - 2856 * q^60 + 7960 * q^64 - 30240 * q^65 + 7440 * q^67 + 19968 * q^71 + 1508 * q^72 + 1080 * q^74 + 44912 * q^78 + 14096 * q^79 - 3432 * q^81 + 23824 * q^85 - 44496 * q^86 + 44464 * q^88 - 64464 * q^92 - 9584 * q^93 - 22488 * q^95 + 60288 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.858610	+	1.48716i	−0.214653	+	0.371789i	−0.953165	−	0.302451i	$-0.902195\pi$
$2$	−0.858610	+	1.48716i	−0.214653	+	0.371789i	0.738513	+	0.674240i	$0.235529\pi$
$3$	13.9722	−	8.06687i	1.55247	−	0.896319i	0.554531	−	0.832163i	$-0.312898\pi$
$3$	13.9722	−	8.06687i	1.55247	−	0.896319i	0.997940	−	0.0641563i	$-0.0204356\pi$
$4$	6.52558	+	11.3026i	0.407849	+	0.706414i
$5$	6.78727	+	3.91863i	0.271491	+	0.156745i	0.629565	−	0.776948i	$-0.283233\pi$
$5$	6.78727	+	3.91863i	0.271491	+	0.156745i	−0.358074	+	0.933693i	$0.616567\pi$
$6$			27.7052i			0.769589i
$7$		0			0
$7$		0			0
$8$	−49.8872			−0.779488
$9$	89.6489	−	155.277i	1.10678	−	1.91699i
$10$	−11.6552	+	6.72915i	−0.116552	+	0.0672915i
$11$	−15.2563	−	26.4247i	−0.126085	−	0.218386i	0.796071	−	0.605203i	$-0.206908\pi$
$11$	−15.2563	−	26.4247i	−0.126085	−	0.218386i	−0.922157	+	0.386817i	$0.873575\pi$
$12$	182.354	+	105.282i	1.26635	+	0.731125i
$13$			162.301i			0.960361i	0.877170	+	0.480181i	$0.159429\pi$
$13$			162.301i			0.960361i	−0.877170	+	0.480181i	$0.840571\pi$
$14$		0			0
$15$	126.444			0.561975
$16$	−61.5756	+	106.652i	−0.240530	+	0.416609i
$17$	299.315	−	172.810i	1.03569	−	0.597957i	0.117082	−	0.993122i	$-0.462646\pi$
$17$	299.315	−	172.810i	1.03569	−	0.597957i	0.918610	+	0.395165i	$0.129313\pi$
$18$	153.947	+	266.644i	0.475145	+	0.822975i
$19$	−228.537	−	131.946i	−0.633066	−	0.365501i	0.148872	−	0.988856i	$-0.452436\pi$
$19$	−228.537	−	131.946i	−0.633066	−	0.365501i	−0.781939	+	0.623355i	$0.785769\pi$
$20$			102.285i			0.255713i
$21$		0			0
$22$	52.3969			0.108258
$23$	−106.589	+	184.618i	−0.201492	+	0.348995i	−0.949009	−	0.315248i	$-0.897912\pi$
$23$	−106.589	+	184.618i	−0.201492	+	0.348995i	0.747517	+	0.664243i	$0.231246\pi$
$24$	−697.036	+	402.434i	−1.21013	+	0.698670i
$25$	−281.789	−	488.072i	−0.450862	−	0.780916i
$26$	−241.367	−	139.353i	−0.357052	−	0.206144i
$27$		−	1585.91i		−	2.17546i
$28$		0			0
$29$	−1011.68			−1.20295			−0.601474	−	0.798893i	$-0.705419\pi$
$29$	−1011.68			−1.20295			−0.601474	+	0.798893i	$0.705419\pi$
$30$	−108.566	+	188.043i	−0.120629	+	0.208936i
$31$	−237.120	+	136.901i	−0.246743	+	0.142457i	−0.618272	−	0.785964i	$-0.712167\pi$
$31$	−237.120	+	136.901i	−0.246743	+	0.142457i	0.371529	+	0.928421i	$0.378834\pi$
$32$	−504.837	−	874.403i	−0.493005	−	0.853909i
$33$	−426.329	−	246.141i	−0.391487	−	0.226025i
$34$			593.504i			0.513412i
$35$		0			0
$36$	2340.04			1.80559
$37$	−773.001	+	1338.88i	−0.564646	+	0.977996i	0.432436	+	0.901664i	$0.357654\pi$
$37$	−773.001	+	1338.88i	−0.564646	+	0.977996i	−0.997083	+	0.0763314i	$0.975679\pi$
$38$	392.448	−	226.580i	0.271779	−	0.156911i
$39$	1309.26	+	2267.71i	0.860791	+	1.49093i
$40$	−338.598	−	195.490i	−0.211624	−	0.122181i
$41$			531.628i			0.316257i	0.987419	+	0.158128i	$0.0505460\pi$
$41$			531.628i			0.316257i	−0.987419	+	0.158128i	$0.949454\pi$
$42$		0			0
$43$	−1470.93			−0.795526			−0.397763	−	0.917488i	$-0.630213\pi$
$43$	−1470.93			−0.795526			−0.397763	+	0.917488i	$0.630213\pi$
$44$	199.112	−	344.873i	0.102847	−	0.178137i
$45$	1216.94	−	702.602i	0.600959	−	0.346964i
$46$	−183.038	−	317.030i	−0.0865017	−	0.149825i
$47$	2064.25	+	1191.79i	0.934471	+	0.539517i	0.888223	−	0.459413i	$-0.151940\pi$
$47$	2064.25	+	1191.79i	0.934471	+	0.539517i	0.0462479	+	0.998930i	$0.485274\pi$
$48$			1986.89i			0.862365i
$49$		0			0
$50$	967.786			0.387115
$51$	2788.07	−	4829.07i	1.07192	−	1.85662i
$52$	−1834.43	+	1059.11i	−0.678413	+	0.391682i
$53$	−1603.31	−	2777.02i	−0.570777	−	0.988614i	−0.996486	−	0.0837543i	$-0.973309\pi$
$53$	−1603.31	−	2777.02i	−0.570777	−	0.988614i	0.425710	−	0.904860i	$-0.360024\pi$
$54$	2358.50	+	1361.68i	0.808814	+	0.466969i
$55$		−	239.135i		−	0.0790530i
$56$		0			0
$57$	−4257.56			−1.31042
$58$	868.637	−	1504.52i	0.258216	−	0.447243i
$59$	2700.71	−	1559.25i	0.775842	−	0.447932i	−0.0591128	−	0.998251i	$-0.518827\pi$
$59$	2700.71	−	1559.25i	0.775842	−	0.447932i	0.834955	+	0.550319i	$0.185494\pi$
$60$	825.123	+	1429.15i	0.229201	+	0.396987i
$61$	−3416.15	−	1972.32i	−0.918074	−	0.530050i	−0.0350540	−	0.999385i	$-0.511160\pi$
$61$	−3416.15	−	1972.32i	−0.918074	−	0.530050i	−0.883020	+	0.469335i	$0.844494\pi$
$62$		−	470.179i		−	0.122315i
$63$		0			0
$64$	−236.587			−0.0577605
$65$	−635.998	+	1101.58i	−0.150532	+	0.260729i
$66$	732.101	−	422.679i	0.168067	−	0.0970337i
$67$	3459.63	+	5992.26i	0.770692	+	1.33488i	0.937184	+	0.348834i	$0.113422\pi$
$67$	3459.63	+	5992.26i	0.770692	+	1.33488i	−0.166493	+	0.986043i	$0.553244\pi$
$68$	3906.41	+	2255.36i	0.844811	+	0.487752i
$69$			3439.38i			0.722406i
$70$		0			0
$71$	8580.05			1.70205			0.851027	−	0.525122i	$-0.175980\pi$
$71$	8580.05			1.70205			0.851027	+	0.525122i	$0.175980\pi$
$72$	−4472.34	+	7746.32i	−0.862719	+	1.49427i
$73$	311.150	−	179.642i	0.0583880	−	0.0337104i	−0.470522	−	0.882388i	$-0.655934\pi$
$73$	311.150	−	179.642i	0.0583880	−	0.0337104i	0.528910	+	0.848678i	$0.322601\pi$
$74$	−1327.41	−	2299.15i	−0.242405	−	0.419859i
$75$	−7874.44	−	4546.31i	−1.39990	−	0.808233i
$76$		−	3444.09i		−	0.596276i
$77$		0			0
$78$	−4496.58			−0.739083
$79$	−1043.58	+	1807.53i	−0.167214	+	0.289623i	−0.937439	−	0.348149i	$-0.886810\pi$
$79$	−1043.58	+	1807.53i	−0.167214	+	0.289623i	0.770225	+	0.637772i	$0.220144\pi$
$80$	−835.859	+	482.584i	−0.130603	+	0.0754037i
$81$	−5531.80	−	9581.36i	−0.843134	−	1.46035i
$82$	−790.613	−	456.461i	−0.117581	−	0.0678853i
$83$		−	10594.2i		−	1.53784i	−0.639344	−	0.768921i	$-0.720794\pi$
$83$		−	10594.2i		−	1.53784i	0.639344	−	0.768921i	$-0.279206\pi$
$84$		0			0
$85$	2708.71			0.374908
$86$	1262.95	−	2187.50i	0.170762	−	0.295768i
$87$	−14135.4	+	8161.08i	−1.86754	+	1.07822i
$88$	761.095	+	1318.25i	0.0982818	+	0.170229i
$89$	9033.60	+	5215.55i	1.14046	+	0.658446i	0.946545	−	0.322572i	$-0.104547\pi$
$89$	9033.60	+	5215.55i	1.14046	+	0.658446i	0.193917	+	0.981018i	$0.437881\pi$
$90$			2413.04i			0.297907i
$91$		0			0
$92$	−2782.23			−0.328714
$93$	−2208.73	+	3825.63i	−0.255374	+	0.442320i
$94$	−3544.76	+	2046.57i	−0.401173	+	0.231617i
$95$	−1034.09	−	1791.10i	−0.114581	−	0.198460i
$96$	−14107.4	−	8144.91i	−1.53075	−	0.883779i
$97$			1403.85i			0.149203i	0.997213	+	0.0746016i	$0.0237685\pi$
$97$			1403.85i			0.149203i	−0.997213	+	0.0746016i	$0.976231\pi$
$98$		0			0
$99$	−5470.85			−0.558193
$100$	3677.67	−	6369.91i	0.367767	−	0.636991i
$101$	12169.0	−	7025.77i	1.19292	−	0.688734i	0.233954	−	0.972248i	$-0.424833\pi$
$101$	12169.0	−	7025.77i	1.19292	−	0.688734i	0.958968	+	0.283514i	$0.0915002\pi$
$102$	4787.72	+	8292.58i	0.460181	+	0.797057i
$103$	1514.35	+	874.310i	0.142742	+	0.0824121i	0.569670	−	0.821873i	$-0.307071\pi$
$103$	1514.35	+	874.310i	0.142742	+	0.0824121i	−0.426928	+	0.904286i	$0.640404\pi$
$104$		−	8096.75i		−	0.748590i
$105$		0			0
$106$	5506.48			0.490075
$107$	−4231.69	+	7329.49i	−0.369612	+	0.640186i	−0.989505	−	0.144500i	$-0.953843\pi$
$107$	−4231.69	+	7329.49i	−0.369612	+	0.640186i	0.619893	+	0.784686i	$0.287176\pi$
$108$	17925.0	−	10349.0i	1.53678	−	0.887260i
$109$	5476.26	+	9485.16i	0.460926	+	0.798347i	0.999007	−	0.0445458i	$-0.0141841\pi$
$109$	5476.26	+	9485.16i	0.460926	+	0.798347i	−0.538081	+	0.842893i	$0.680851\pi$
$110$	355.631	+	205.324i	0.0293910	+	0.0169689i
$111$			24942.8i			2.02441i
$112$		0			0
$113$	5884.58			0.460849			0.230424	−	0.973090i	$-0.425989\pi$
$113$	5884.58			0.460849			0.230424	+	0.973090i	$0.425989\pi$
$114$	3655.59	−	6331.66i	0.281285	−	0.487201i
$115$	−1446.90	+	835.369i	−0.109407	+	0.0631659i
$116$	−6601.79	−	11434.6i	−0.490620	−	0.849779i
$117$	25201.5	+	14550.1i	1.84101	+	1.06291i
$118$			5355.16i			0.384599i
$119$		0			0
$120$	−6307.96			−0.438053
$121$	6854.99	−	11873.2i	0.468205	−	0.810955i
$122$	5866.29	−	3386.90i	0.394134	−	0.227553i
$123$	4288.57	+	7428.03i	0.283467	+	0.490979i
$124$	−3094.69	−	1786.72i	−0.201267	−	0.116202i
$125$		−	9315.19i		−	0.596172i
$126$		0			0
$127$	−8451.12			−0.523971			−0.261985	−	0.965072i	$-0.584377\pi$
$127$	−8451.12			−0.523971			−0.261985	+	0.965072i	$0.584377\pi$
$128$	8280.52	−	14342.3i	0.505403	−	0.875384i
$129$	−20552.1	+	11865.8i	−1.23503	+	0.713045i
$130$	−1092.15	−	1891.66i	−0.0646242	−	0.111932i
$131$	693.743	+	400.533i	0.0404255	+	0.0233397i	0.520077	−	0.854120i	$-0.325903\pi$
$131$	693.743	+	400.533i	0.0404255	+	0.0233397i	−0.479651	+	0.877459i	$0.659237\pi$
$132$		−	6424.86i		−	0.368736i
$133$		0			0
$134$	−11881.9			−0.661723
$135$	6214.61	−	10764.0i	0.340994	−	0.590618i
$136$	−14932.0	+	8620.99i	−0.807309	+	0.466100i
$137$	−11404.4	−	19753.1i	−0.607621	−	1.05243i	−0.991631	−	0.129102i	$-0.958790\pi$
$137$	−11404.4	−	19753.1i	−0.607621	−	1.05243i	0.384010	−	0.923329i	$-0.374543\pi$
$138$	−5114.89	−	2953.08i	−0.268583	−	0.155066i
$139$			32895.2i			1.70256i	0.524709	+	0.851281i	$0.324174\pi$
$139$			32895.2i			1.70256i	−0.524709	+	0.851281i	$0.675826\pi$
$140$		0			0
$141$	38456.2			1.93432
$142$	−7366.92	+	12759.9i	−0.365350	+	0.632805i
$143$	4288.76	−	2476.11i	0.209729	−	0.121087i
$144$	11040.4	+	19122.5i	0.532425	+	0.922187i
$145$	−6866.53	−	3964.39i	−0.326589	−	0.188556i
$146$			616.971i			0.0289440i
$147$		0			0
$148$	−20177.1			−0.921161
$149$	−14980.9	+	25947.7i	−0.674786	+	1.16876i	0.301745	+	0.953389i	$0.402431\pi$
$149$	−14980.9	+	25947.7i	−0.674786	+	1.16876i	−0.976531	+	0.215375i	$0.930902\pi$
$150$	13522.1	−	7807.01i	0.600984	−	0.346978i
$151$	2258.81	+	3912.37i	0.0990662	+	0.171588i	0.911298	−	0.411747i	$-0.135081\pi$
$151$	2258.81	+	3912.37i	0.0990662	+	0.171588i	−0.812232	+	0.583334i	$0.801748\pi$
$152$	11401.1	+	6582.41i	0.493467	+	0.284904i
$153$		−	61968.8i		−	2.64722i
$154$		0			0
$155$	−2145.86			−0.0893178
$156$	−17087.4	+	29596.2i	−0.702144	+	1.21615i
$157$	27466.2	−	15857.6i	1.11429	−	0.643337i	0.174354	−	0.984683i	$-0.444216\pi$
$157$	27466.2	−	15857.6i	1.11429	−	0.643337i	0.939938	+	0.341346i	$0.110883\pi$
$158$	−1792.06	−	3103.94i	−0.0717857	−	0.124336i
$159$	−44803.7	−	25867.4i	−1.77223	−	1.02320i
$160$		−	7913.07i		−	0.309104i
$161$		0			0
$162$	18998.6			0.723923
$163$	−6752.59	+	11695.8i	−0.254153	+	0.440206i	−0.964665	−	0.263479i	$-0.915130\pi$
$163$	−6752.59	+	11695.8i	−0.254153	+	0.440206i	0.710512	+	0.703685i	$0.248463\pi$
$164$	−6008.79	+	3469.18i	−0.223408	+	0.128985i
$165$	−1929.07	−	3341.25i	−0.0708567	−	0.122727i
$166$	15755.2	+	9096.28i	0.571753	+	0.330102i
$167$			24965.3i			0.895168i	0.894242	+	0.447584i	$0.147715\pi$
$167$			24965.3i			0.895168i	−0.894242	+	0.447584i	$0.852285\pi$
$168$		0			0
$169$	2219.36			0.0777060
$170$	−2325.72	+	4028.27i	−0.0804748	+	0.139387i
$171$	−40976.2	+	23657.6i	−1.40133	+	0.809056i
$172$	−9598.65	−	16625.4i	−0.324454	−	0.561971i
$173$	−22021.5	−	12714.1i	−0.735791	−	0.424809i	0.0847461	−	0.996403i	$-0.472992\pi$
$173$	−22021.5	−	12714.1i	−0.735791	−	0.424809i	−0.820537	+	0.571594i	$0.806325\pi$
$174$		−	28028.8i		−	0.925775i
$175$		0			0
$176$	3757.66			0.121309
$177$	25156.6	−	43572.5i	0.802981	−	1.39080i
$178$	−15512.7	+	8956.25i	−0.489606	+	0.282674i
$179$	1806.29	+	3128.58i	0.0563742	+	0.0976429i	0.892835	−	0.450383i	$-0.148713\pi$
$179$	1806.29	+	3128.58i	0.0563742	+	0.0976429i	−0.836461	+	0.548026i	$0.815379\pi$
$180$	15882.5	+	9169.77i	0.490201	+	0.283018i
$181$		−	15458.2i		−	0.471847i	−0.971772	−	0.235923i	$-0.924189\pi$
$181$		−	15458.2i		−	0.471847i	0.971772	−	0.235923i	$-0.0758114\pi$
$182$		0			0
$183$	−63641.8			−1.90038
$184$	5317.45	−	9210.10i	0.157061	−	0.272037i
$185$	−10493.1	+	6058.21i	−0.306592	+	0.177011i
$186$	−3792.87	−	6569.45i	−0.109633	−	0.189890i
$187$	−9132.88	−	5272.87i	−0.261171	−	0.150787i
$188$			31108.5i			0.880165i
$189$		0			0
$190$	3551.53			0.0983804
$191$	−6687.81	+	11583.6i	−0.183323	+	0.317525i	−0.943010	−	0.332764i	$-0.892019\pi$
$191$	−6687.81	+	11583.6i	−0.183323	+	0.317525i	0.759687	+	0.650289i	$0.225352\pi$
$192$	−3305.65	+	1908.52i	−0.0896715	+	0.0517719i
$193$	−6881.78	−	11919.6i	−0.184751	−	0.319998i	0.758742	−	0.651392i	$-0.225814\pi$
$193$	−6881.78	−	11919.6i	−0.184751	−	0.319998i	−0.943492	+	0.331394i	$0.892481\pi$
$194$	−2087.75	−	1205.36i	−0.0554721	−	0.0320269i
$195$			20522.1i			0.539699i
$196$		0			0
$197$	25150.4			0.648057			0.324028	−	0.946047i	$-0.394963\pi$
$197$	25150.4			0.648057			0.324028	+	0.946047i	$0.394963\pi$
$198$	4697.32	−	8136.00i	0.119817	−	0.207530i
$199$	37057.7	−	21395.3i	0.935778	−	0.540271i	0.0471434	−	0.998888i	$-0.484988\pi$
$199$	37057.7	−	21395.3i	0.935778	−	0.540271i	0.888634	+	0.458617i	$0.151655\pi$
$200$	14057.7	+	24348.6i	0.351441	+	0.608714i
$201$	96677.7	+	55816.9i	2.39295	+	1.38157i
$202$			24129.6i			0.591354i
$203$		0			0
$204$	72775.0			1.74873
$205$	−2083.25	+	3608.30i	−0.0495717	+	0.0858608i
$206$	−2600.47	+	1501.38i	−0.0612798	+	0.0353799i
$207$	19111.3	+	33101.7i	0.446014	+	0.772519i
$208$	−17309.7	−	9993.78i	−0.400096	−	0.230995i
$209$			8052.02i			0.184337i
$210$		0			0
$211$	−3516.62			−0.0789879			−0.0394940	−	0.999220i	$-0.512575\pi$
$211$	−3516.62			−0.0789879			−0.0394940	+	0.999220i	$0.512575\pi$
$212$	20925.1	−	36243.3i	0.465581	−	0.806410i
$213$	119883.	−	69214.2i	2.64239	−	1.52558i
$214$	−7266.74	−	12586.4i	−0.158676	−	0.274835i
$215$	−9983.57	−	5764.02i	−0.215978	−	0.124695i
$216$			79116.8i			1.69575i
$217$		0			0
$218$	−18807.9			−0.395756
$219$	2898.31	−	5020.01i	0.0604305	−	0.104669i
$220$	2702.86	−	1560.50i	0.0558442	−	0.0322416i
$221$	28047.2	+	48579.1i	0.574255	+	0.994639i
$222$	−37093.8	−	21416.1i	−0.752655	−	0.434545i
$223$		−	67281.8i		−	1.35297i	−0.736457	−	0.676485i	$-0.763503\pi$
$223$		−	67281.8i		−	1.35297i	0.736457	−	0.676485i	$-0.236497\pi$
$224$		0			0
$225$	−101048.			−1.99601
$226$	−5052.56	+	8751.29i	−0.0989224	+	0.171339i
$227$	−64372.8	+	37165.7i	−1.24925	+	0.721257i	−0.970961	−	0.239239i	$-0.923102\pi$
$227$	−64372.8	+	37165.7i	−1.24925	+	0.721257i	−0.278293	+	0.960496i	$0.589769\pi$
$228$	−27783.1	−	48121.7i	−0.534454	−	0.925701i
$229$	24218.4	+	13982.5i	0.461822	+	0.266633i	0.712810	−	0.701357i	$-0.247422\pi$
$229$	24218.4	+	13982.5i	0.461822	+	0.266633i	−0.250988	+	0.967990i	$0.580755\pi$
$230$		−	2869.03i		−	0.0542349i
$231$		0			0
$232$	50469.8			0.937683
$233$	19940.4	−	34537.8i	0.367301	−	0.636184i	−0.621842	−	0.783143i	$-0.713615\pi$
$233$	19940.4	−	34537.8i	0.367301	−	0.636184i	0.989143	+	0.146959i	$0.0469486\pi$
$234$	−43276.6	+	24985.8i	−0.790354	+	0.456311i
$235$	9340.39	+	16178.0i	0.169133	+	0.292948i
$236$	35247.3	+	20350.1i	0.632852	+	0.365377i
$237$			33673.7i			0.599508i
$238$		0			0
$239$	−29726.5			−0.520413			−0.260206	−	0.965553i	$-0.583791\pi$
$239$	−29726.5			−0.520413			−0.260206	+	0.965553i	$0.583791\pi$
$240$	−7785.88	+	13485.5i	−0.135172	+	0.234124i
$241$	−54411.1	+	31414.3i	−0.936814	+	0.540870i	−0.888960	−	0.457985i	$-0.848571\pi$
$241$	−54411.1	+	31414.3i	−0.936814	+	0.540870i	−0.0478537	+	0.998854i	$0.515238\pi$
$242$	11771.5	+	20388.9i	0.201003	+	0.348147i
$243$	−43334.5	−	25019.2i	−0.733874	−	0.423702i
$244$		−	51482.0i		−	0.864721i
$245$		0			0
$246$	−14728.9			−0.243388
$247$	21415.0	−	37091.8i	0.351013	−	0.607972i
$248$	11829.2	−	6829.62i	0.192333	−	0.111043i
$249$	−85462.0	−	148025.i	−1.37840	−	2.38745i
$250$	13853.1	+	7998.11i	0.221650	+	0.127970i
$251$		−	62181.9i		−	0.986999i	−0.869746	−	0.493499i	$-0.835718\pi$
$251$		−	62181.9i		−	0.986999i	0.869746	−	0.493499i	$-0.164282\pi$
$252$		0			0
$253$	6504.64			0.101621
$254$	7256.22	−	12568.1i	0.112472	−	0.194807i
$255$	37846.7	−	21850.8i	0.582033	−	0.336037i
$256$	12326.8	+	21350.6i	0.188092	+	0.325785i
$257$	−99319.1	−	57341.9i	−1.50372	−	0.868172i	−0.999991	−	0.00430917i	$-0.998628\pi$
$257$	−99319.1	−	57341.9i	−1.50372	−	0.868172i	−0.503727	−	0.863863i	$-0.668038\pi$
$258$		−	40752.3i		−	0.612228i
$259$		0			0
$260$	−16601.0			−0.245577
$261$	−90695.9	+	157090.i	−1.33139	+	2.30604i
$262$	−1191.31	+	687.803i	−0.0173549	+	0.0100199i
$263$	41795.8	+	72392.5i	0.604256	+	1.04660i	0.992169	+	0.124906i	$0.0398630\pi$
$263$	41795.8	+	72392.5i	0.604256	+	1.04660i	−0.387912	+	0.921696i	$0.626804\pi$
$264$	21268.4	+	12279.3i	0.305159	+	0.176184i
$265$		−	25131.1i		−	0.357866i
$266$		0			0
$267$	168293.			2.36071
$268$	−45152.2	+	78205.9i	−0.628651	+	1.08886i
$269$	−5939.83	+	3429.36i	−0.0820861	+	0.0473924i	−0.540481	−	0.841356i	$-0.681758\pi$
$269$	−5939.83	+	3429.36i	−0.0820861	+	0.0473924i	0.458395	+	0.888748i	$0.348424\pi$
$270$	10671.8	+	18484.2i	0.146390	+	0.253555i
$271$	43609.6	+	25178.0i	0.593804	+	0.342833i	0.766600	−	0.642125i	$-0.221947\pi$
$271$	43609.6	+	25178.0i	0.593804	+	0.342833i	−0.172796	+	0.984958i	$0.555280\pi$
$272$			42563.4i			0.575305i
$273$		0			0
$274$	39167.9			0.521710
$275$	−8598.11	+	14892.4i	−0.113694	+	0.196924i
$276$	−38874.0	+	22443.9i	−0.510318	+	0.294632i
$277$	−42152.8	−	73010.8i	−0.549373	−	0.951541i	−0.998318	−	0.0579819i	$-0.981533\pi$
$277$	−42152.8	−	73010.8i	−0.549373	−	0.951541i	0.448945	−	0.893559i	$-0.351800\pi$
$278$	−48920.3	−	28244.2i	−0.632994	−	0.365459i
$279$			49092.2i			0.630672i
$280$		0			0
$281$	9852.07			0.124771			0.0623857	−	0.998052i	$-0.480129\pi$
$281$	9852.07			0.124771			0.0623857	+	0.998052i	$0.480129\pi$
$282$	−33018.9	+	57190.3i	−0.415206	+	0.719158i
$283$	27481.8	−	15866.6i	0.343141	−	0.198112i	−0.318519	−	0.947916i	$-0.603186\pi$
$283$	27481.8	−	15866.6i	0.343141	−	0.198112i	0.661660	+	0.749804i	$0.269852\pi$
$284$	55989.8	+	96977.2i	0.694180	+	1.20236i
$285$	−28897.2	−	16683.8i	−0.355767	−	0.205402i
$286$			8504.07i			0.103967i
$287$		0			0
$288$	−181032.			−2.18258
$289$	17965.8	−	31117.7i	0.215105	−	0.372573i
$290$	11791.3	−	6807.74i	0.140206	−	0.0809481i
$291$	11324.7	+	19615.0i	0.133734	+	0.231634i
$292$	4060.87	+	2344.54i	0.0476270	+	0.0274974i
$293$			17750.9i			0.206769i	0.994641	+	0.103384i	$0.0329672\pi$
$293$			17750.9i			0.206769i	−0.994641	+	0.103384i	$0.967033\pi$
$294$		0			0
$295$	24440.5			0.280845
$296$	38562.9	−	66792.8i	0.440135	−	0.762336i
$297$	−41907.3	+	24195.2i	−0.475091	+	0.274294i
$298$	−25725.6	−	44558.0i	−0.289689	−	0.501756i
$299$	−29963.8	−	17299.6i	−0.335161	−	0.193505i
$300$		−	118669.i		−	1.31855i
$301$		0			0
$302$	−7757.74			−0.0850592
$303$	113352.	−	196332.i	1.23465	−	2.13848i
$304$	28144.6	−	16249.3i	0.304542	−	0.175828i
$305$	−15457.6	−	26773.3i	−0.166166	−	0.287807i
$306$	92157.3	+	53207.0i	0.984208	+	0.568233i
$307$		−	5360.84i		−	0.0568795i	−0.999596	−	0.0284398i	$-0.990946\pi$
$307$		−	5360.84i		−	0.0568795i	0.999596	−	0.0284398i	$-0.00905388\pi$
$308$		0			0
$309$	28211.8			0.295470
$310$	1842.46	−	3191.23i	0.0191723	−	0.0332074i
$311$	−119842.	+	69190.9i	−1.23905	+	0.715365i	−0.968900	−	0.247453i	$-0.920406\pi$
$311$	−119842.	+	69190.9i	−1.23905	+	0.715365i	−0.270149	+	0.962818i	$0.587073\pi$
$312$	−65315.5	−	113130.i	−0.670976	−	1.16216i
$313$	39630.0	+	22880.4i	0.404515	+	0.233547i	0.688430	−	0.725302i	$-0.258300\pi$
$313$	39630.0	+	22880.4i	0.404515	+	0.233547i	−0.283915	+	0.958849i	$0.591633\pi$
$314$			54462.0i			0.552375i
$315$		0			0
$316$	−27239.9			−0.272792
$317$	−19719.4	+	34154.9i	−0.196234	+	0.339887i	−0.947304	−	0.320335i	$-0.896205\pi$
$317$	−19719.4	+	34154.9i	−0.196234	+	0.339887i	0.751070	+	0.660222i	$0.229538\pi$
$318$	76937.8	−	44420.1i	0.760826	−	0.439263i
$319$	15434.5	+	26733.3i	0.151674	+	0.262707i
$320$	−1605.78	−	927.097i	−0.0156814	−	0.00905368i
$321$			136546.i			1.32516i
$322$		0			0
$323$	−91206.0			−0.874215
$324$	72196.4	−	125048.i	0.687742	−	1.19120i
$325$	79214.7	−	45734.6i	0.749961	−	0.432990i
$326$	−11595.7	−	20084.3i	−0.109109	−	0.188983i
$327$	153031.	+	88352.6i	1.43115	+	0.826274i
$328$		−	26521.4i		−	0.246518i
$329$		0			0
$330$	6625.29			0.0608383
$331$	−19903.6	+	34474.0i	−0.181667	+	0.314656i	−0.942448	−	0.334352i	$-0.891483\pi$
$331$	−19903.6	+	34474.0i	−0.181667	+	0.314656i	0.760782	+	0.649008i	$0.224816\pi$
$332$	119742.	−	69133.2i	1.08635	−	0.627206i
$333$	138597.	+	240058.i	1.24987	+	2.16485i
$334$	−37127.4	−	21435.5i	−0.332814	−	0.192150i
$335$			54228.1i			0.483209i
$336$		0			0
$337$	−71094.3			−0.626001			−0.313001	−	0.949753i	$-0.601334\pi$
$337$	−71094.3			−0.626001			−0.313001	+	0.949753i	$0.601334\pi$
$338$	−1905.57	+	3300.54i	−0.0166798	+	0.0288902i
$339$	82220.8	−	47470.2i	0.715455	−	0.413068i
$340$	17675.9	+	30615.5i	0.152906	+	0.264840i
$341$	7235.14	+	4177.21i	0.0622212	+	0.0359234i
$342$		−	81250.6i		−	0.694664i
$343$		0			0
$344$	73380.5			0.620103
$345$	−13477.6	+	23344.0i	−0.113234	+	0.196126i
$346$	37815.7	−	21832.9i	0.315879	−	0.182373i
$347$	−33129.0	−	57381.1i	−0.275137	−	0.476552i	0.695032	−	0.718978i	$-0.255390\pi$
$347$	−33129.0	−	57381.1i	−0.275137	−	0.476552i	−0.970170	+	0.242427i	$0.922057\pi$
$348$	−184483.	−	106512.i	−1.52335	−	0.879505i
$349$			225684.i			1.85289i	0.376429	+	0.926445i	$0.377152\pi$
$349$			225684.i			1.85289i	−0.376429	+	0.926445i	$0.622848\pi$
$350$		0			0
$351$	257395.			2.08923
$352$	−15403.9	+	26680.3i	−0.124321	+	0.215330i
$353$	−115180.	+	66499.3i	−0.924333	+	0.533664i	−0.885015	−	0.465563i	$-0.845852\pi$
$353$	−115180.	+	66499.3i	−0.924333	+	0.533664i	−0.0393184	+	0.999227i	$0.512519\pi$
$354$	43199.4	+	74823.6i	0.344724	+	0.597079i
$355$	58235.1	+	33622.1i	0.462092	+	0.266789i
$356$			136138.i			1.07419i
$357$		0			0
$358$	−6203.58			−0.0484034
$359$	−116365.	+	201550.i	−0.902888	+	1.56385i	−0.0791611	+	0.996862i	$0.525224\pi$
$359$	−116365.	+	201550.i	−0.902888	+	1.56385i	−0.823727	+	0.566986i	$0.808109\pi$
$360$	−60709.9	+	35050.9i	−0.468440	+	0.270454i
$361$	−30341.1	−	52552.3i	−0.232818	−	0.403253i
$362$	22988.7	+	13272.5i	0.175427	+	0.101283i
$363$		−	221193.i		−	1.67865i
$364$		0			0
$365$	2815.81			0.0211357
$366$	54643.4	−	94645.2i	0.407921	−	0.706540i
$367$	−94025.0	+	54285.3i	−0.698089	+	0.403042i	−0.806635	−	0.591049i	$-0.798714\pi$
$367$	−94025.0	+	54285.3i	−0.698089	+	0.403042i	0.108546	+	0.994091i	$0.465381\pi$
$368$	−13126.6	−	22736.0i	−0.0969297	−	0.167887i
$369$	82549.3	+	47659.9i	0.606262	+	0.350026i
$370$		−	20806.5i		−	0.151984i
$371$		0			0
$372$	−57652.9			−0.416615
$373$	84941.4	−	147123.i	0.610523	−	1.05746i	−0.380630	−	0.924728i	$-0.624293\pi$
$373$	84941.4	−	147123.i	0.610523	−	1.05746i	0.991152	−	0.132729i	$-0.0423739\pi$
$374$	15683.2	−	9054.68i	0.112122	−	0.0647336i
$375$	−75144.5	−	130154.i	−0.534361	−	0.925540i
$376$	−102979.	−	59455.2i	−0.728409	−	0.420547i
$377$		−	164197.i		−	1.15526i
$378$		0			0
$379$	−224839.			−1.56528			−0.782641	−	0.622474i	$-0.786128\pi$
$379$	−224839.			−1.56528			−0.782641	+	0.622474i	$0.786128\pi$
$380$	13496.1	−	23376.0i	0.0934634	−	0.161883i
$381$	−118081.	+	68174.2i	−0.813449	+	0.469645i
$382$	−11484.4	−	19891.6i	−0.0787015	−	0.136315i
$383$	21284.9	+	12288.9i	0.145103	+	0.0837750i	0.570794	−	0.821094i	$-0.306636\pi$
$383$	21284.9	+	12288.9i	0.145103	+	0.0837750i	−0.425691	+	0.904869i	$0.639969\pi$
$384$		−	267192.i		−	1.81201i
$385$		0			0
$386$	23635.1			0.158629
$387$	−131867.	+	228400.i	−0.880470	+	1.52502i
$388$	−15867.2	+	9160.96i	−0.105399	+	0.0608524i
$389$	−72068.1	−	124826.i	−0.476260	−	0.824906i	0.523370	−	0.852105i	$-0.324675\pi$
$389$	−72068.1	−	124826.i	−0.476260	−	0.824906i	−0.999630	+	0.0271990i	$0.991341\pi$
$390$	−30519.5	−	17620.4i	−0.200654	−	0.115848i
$391$			73678.7i			0.481935i
$392$		0			0
$393$	12924.2			0.0836793
$394$	−21594.4	+	37402.6i	−0.139107	+	0.240940i
$395$	−14166.1	+	8178.81i	−0.0907939	+	0.0524199i
$396$	−35700.4	−	61834.9i	−0.227658	−	0.394315i
$397$	−132716.	−	76623.7i	−0.842060	−	0.486164i	0.0159040	−	0.999874i	$-0.494937\pi$
$397$	−132716.	−	76623.7i	−0.842060	−	0.486164i	−0.857964	+	0.513710i	$0.828271\pi$
$398$			73480.8i			0.463882i
$399$		0			0
$400$	69405.2			0.433782
$401$	22713.1	−	39340.3i	0.141250	−	0.244652i	−0.786718	−	0.617313i	$-0.788221\pi$
$401$	22713.1	−	39340.3i	0.141250	−	0.244652i	0.927968	+	0.372661i	$0.121555\pi$
$402$	−166017.	+	95849.9i	−1.02731	+	0.593116i
$403$	−22219.2	−	38484.8i	−0.136810	−	0.236962i
$404$	158819.	+	91694.5i	0.973063	+	0.561798i
$405$		−	86708.3i		−	0.528629i
$406$		0			0
$407$	47172.5			0.284774
$408$	−139089.	+	240909.i	−0.835550	+	1.44721i
$409$	9025.43	−	5210.83i	0.0539537	−	0.0311502i	−0.472781	−	0.881180i	$-0.656750\pi$
$409$	9025.43	−	5210.83i	0.0539537	−	0.0311502i	0.526734	+	0.850030i	$0.323416\pi$
$410$	−3577.40	−	6196.24i	−0.0212814	−	0.0368605i
$411$	−318691.	−	183996.i	−1.88663	−	1.08925i
$412$			22821.5i			0.134447i
$413$		0			0
$414$	−65636.5			−0.382952
$415$	41514.7	−	71905.6i	0.241049	−	0.417510i
$416$	141916.	−	81935.5i	0.820061	−	0.473462i
$417$	265362.	+	459620.i	1.52604	+	2.64318i
$418$	−11974.6	−	6913.55i	−0.0685345	−	0.0395684i
$419$		−	148730.i		−	0.847167i	−0.905857	−	0.423584i	$-0.860772\pi$
$419$		−	148730.i		−	0.847167i	0.905857	−	0.423584i	$-0.139228\pi$
$420$		0			0
$421$	238275.			1.34436			0.672178	−	0.740389i	$-0.265359\pi$
$421$	238275.			1.34436			0.672178	+	0.740389i	$0.265359\pi$
$422$	3019.41	−	5229.76i	0.0169550	−	0.0293668i
$423$	370115.	−	213686.i	2.06850	−	1.19425i
$424$	79984.8	+	138538.i	0.444913	+	0.770613i
$425$	−168687.	−	97391.6i	−0.933908	−	0.539192i
$426$			237712.i			1.30988i
$427$		0			0
$428$	−110457.			−0.602983
$429$	39949.0	−	69193.7i	0.217066	−	0.375969i
$430$	17144.0	−	9898.09i	0.0927204	−	0.0535321i
$431$	−140052.	−	242578.i	−0.753938	−	1.30586i	−0.945900	−	0.324457i	$-0.894818\pi$
$431$	−140052.	−	242578.i	−0.753938	−	1.30586i	0.191962	−	0.981402i	$-0.438515\pi$
$432$	169141.	+	97653.5i	0.906319	+	0.523263i
$433$		−	78101.0i		−	0.416563i	−0.978069	−	0.208281i	$-0.933213\pi$
$433$		−	78101.0i		−	0.416563i	0.978069	−	0.208281i	$-0.0667870\pi$
$434$		0			0
$435$	−127921.			−0.676026
$436$	−71471.5	+	123792.i	−0.375976	+	0.651209i
$437$	48719.3	−	28128.1i	0.255116	−	0.147291i
$438$	4977.03	+	8620.47i	0.0259431	+	0.0449348i
$439$	269003.	+	155309.i	1.39581	+	0.805874i	0.993951	−	0.109826i	$-0.0350294\pi$
$439$	269003.	+	155309.i	1.39581	+	0.805874i	0.401863	+	0.915700i	$0.368363\pi$
$440$			11929.8i			0.0616208i
$441$		0			0
$442$	−96326.4			−0.493061
$443$	2691.42	−	4661.68i	0.0137143	−	0.0237539i	−0.859087	−	0.511830i	$-0.828968\pi$
$443$	2691.42	−	4661.68i	0.0137143	−	0.0237539i	0.872801	+	0.488076i	$0.162301\pi$
$444$	−281919.	+	162766.i	−1.43007	+	0.825654i
$445$	40875.6	+	70798.7i	0.206417	+	0.357524i
$446$	100059.	+	57768.8i	0.503019	+	0.290418i
$447$			483397.i			2.41930i
$448$		0			0
$449$	167992.			0.833292			0.416646	−	0.909069i	$-0.363206\pi$
$449$	167992.			0.833292			0.416646	+	0.909069i	$0.363206\pi$
$450$	86761.0	−	150274.i	0.428449	−	0.742096i
$451$	14048.1	−	8110.67i	0.0690660	−	0.0398753i
$452$	38400.3	+	66511.2i	0.187957	+	0.325550i
$453$	63121.2	+	36443.0i	0.307595	+	0.177590i
$454$		−	127643.i		−	0.619279i
$455$		0			0
$456$	212398.			1.02146
$457$	97823.6	−	169435.i	0.468394	−	0.811282i	−0.530954	−	0.847401i	$-0.678166\pi$
$457$	97823.6	−	169435.i	0.468394	−	0.811282i	0.999347	+	0.0361191i	$0.0114996\pi$
$458$	−41588.4	+	24011.0i	−0.198263	+	0.114467i
$459$	−274061.	−	474688.i	−1.30083	−	2.25311i
$460$	−18883.7	−	10902.5i	−0.0892426	−	0.0515243i
$461$		−	355715.i		−	1.67379i	−0.547365	−	0.836894i	$-0.684369\pi$
$461$		−	355715.i		−	1.67379i	0.547365	−	0.836894i	$-0.315631\pi$
$462$		0			0
$463$	−103798.			−0.484205			−0.242102	−	0.970251i	$-0.577837\pi$
$463$	−103798.			−0.484205			−0.242102	+	0.970251i	$0.577837\pi$
$464$	62294.7	−	107898.i	0.289344	−	0.501159i
$465$	−29982.5	+	17310.4i	−0.138663	+	0.0800572i
$466$	34242.1	+	59309.0i	0.157684	+	0.273117i
$467$	254709.	+	147056.i	1.16791	+	0.674295i	0.953187	−	0.302380i	$-0.0977812\pi$
$467$	254709.	+	147056.i	1.16791	+	0.674295i	0.214725	+	0.976675i	$0.431115\pi$
$468$			379792.i			1.73402i
$469$		0			0
$470$	−32079.0			−0.145220
$471$	255843.	−	443132.i	1.15327	−	1.99752i
$472$	−134731.	+	77786.8i	−0.604759	+	0.349158i
$473$	22440.9	+	38868.8i	0.100304	+	0.173732i
$474$	−50078.1	−	28912.6i	−0.222890	−	0.128686i
$475$			148723.i			0.659162i
$476$		0			0
$477$	−574941.			−2.52689
$478$	25523.5	−	44207.9i	0.111708	−	0.193484i
$479$	318478.	−	183873.i	1.38806	−	0.801397i	0.394964	−	0.918697i	$-0.370757\pi$
$479$	318478.	−	183873.i	1.38806	−	0.801397i	0.993097	+	0.117300i	$0.0374238\pi$
$480$	−63833.8	−	110563.i	−0.277056	−	0.479875i
$481$	−217301.	−	125459.i	−0.939229	−	0.542264i
$482$		−	107890.i		−	0.464396i
$483$		0			0
$484$	178931.			0.763827
$485$	−5501.18	+	9528.33i	−0.0233869	+	0.0405073i
$486$	74414.9	−	42963.5i	0.315056	−	0.181898i
$487$	171157.	+	296453.i	0.721667	+	1.24996i	0.960331	+	0.278862i	$0.0899571\pi$
$487$	171157.	+	296453.i	0.721667	+	1.24996i	−0.238664	+	0.971102i	$0.576710\pi$
$488$	170422.	+	98393.4i	0.715628	+	0.413168i
$489$			217889.i			0.911209i
$490$		0			0
$491$	41579.7			0.172472			0.0862360	−	0.996275i	$-0.472516\pi$
$491$	41579.7			0.172472			0.0862360	+	0.996275i	$0.472516\pi$
$492$	−55970.8	+	96944.3i	−0.231223	+	0.400491i
$493$	−302811.	+	174828.i	−1.24588	+	0.719311i
$494$	36774.2	+	63694.8i	0.150692	+	0.261006i
$495$	−37132.1	−	21438.2i	−0.151544	−	0.0874940i
$496$		−	33719.1i		−	0.137060i
$497$		0			0
$498$	293514.			1.18351
$499$	−177988.	+	308284.i	−0.714807	+	1.23808i	0.248227	+	0.968702i	$0.420152\pi$
$499$	−177988.	+	308284.i	−0.714807	+	1.23808i	−0.963034	+	0.269380i	$0.913181\pi$
$500$	105286.	−	60787.0i	0.421145	−	0.243148i
$501$	201392.	+	348822.i	0.802357	+	1.38972i
$502$	92474.2	+	53390.0i	0.366955	+	0.211862i
$503$		−	196448.i		−	0.776446i	−0.921566	−	0.388223i	$-0.873089\pi$
$503$		−	196448.i		−	0.776446i	0.921566	−	0.388223i	$-0.126911\pi$
$504$		0			0
$505$	110126.			0.431823
$506$	−5584.95	+	9673.42i	−0.0218132	+	0.0377815i
$507$	31009.4	−	17903.3i	0.120636	−	0.0696494i
$508$	−55148.5	−	95519.9i	−0.213701	−	0.370140i
$509$	−115675.	−	66784.7i	−0.446480	−	0.257776i	0.259862	−	0.965646i	$-0.416323\pi$
$509$	−115675.	−	66784.7i	−0.446480	−	0.257776i	−0.706343	+	0.707870i	$0.749656\pi$
$510$			75045.3i			0.288525i
$511$		0			0
$512$	222641.			0.849308
$513$	−209255.	+	362440.i	−0.795134	+	1.37721i
$514$	170553.	−	98468.6i	0.645554	−	0.372711i
$515$	6852.19	+	11868.3i	0.0258354	+	0.0447482i
$516$	−268229.	−	154862.i	−1.00741	−	0.581629i
$517$		−	72729.4i		−	0.272100i
$518$		0			0
$519$	−410253.			−1.52306
$520$	31728.2	−	54954.8i	0.117338	−	0.203235i
$521$	311261.	−	179707.i	1.14670	−	0.662046i	0.198618	−	0.980077i	$-0.436355\pi$
$521$	311261.	−	179707.i	1.14670	−	0.662046i	0.948080	+	0.318031i	$0.103022\pi$
$522$	−155745.	−	269758.i	−0.571574	−	0.989996i
$523$	−129840.	−	74963.2i	−0.474685	−	0.274060i	0.243514	−	0.969897i	$-0.421700\pi$
$523$	−129840.	−	74963.2i	−0.474685	−	0.274060i	−0.718199	+	0.695838i	$0.755033\pi$
$524$			10454.8i			0.0380763i
$525$		0			0
$526$	−143545.			−0.518821
$527$	−47315.7	+	81953.1i	−0.170366	+	0.295083i
$528$	52502.9	−	30312.6i	0.188328	−	0.108731i
$529$	117198.	+	202993.i	0.418802	+	0.725386i
$530$	37373.9	+	21577.8i	0.133051	+	0.0768168i
$531$		−	559142.i		−	1.98305i
$532$		0			0
$533$	−86283.7			−0.303721
$534$	−144498.	+	250278.i	−0.506733	+	0.877687i
$535$	−57443.1	+	33164.8i	−0.200692	+	0.115870i
$536$	−172592.	−	298937.i	−0.600745	−	1.04052i
$537$	50475.7	+	29142.2i	0.175039	+	0.101059i
$538$		−	11777.9i		−	0.0406916i
$539$		0			0
$540$	162216.			0.556295
$541$	84120.9	−	145702.i	0.287415	−	0.497818i	−0.685777	−	0.727812i	$-0.740537\pi$
$541$	84120.9	−	145702.i	0.287415	−	0.497818i	0.973192	+	0.229994i	$0.0738707\pi$
$542$	−74887.3	+	43236.2i	−0.254923	+	0.147180i
$543$	−124699.	−	215985.i	−0.422925	−	0.732528i
$544$	−302210.	−	174481.i	−1.02120	−	0.589591i
$545$			85837.7i			0.288992i
$546$		0			0
$547$	297422.			0.994027			0.497013	−	0.867743i	$-0.334430\pi$
$547$	297422.			0.994027			0.497013	+	0.867743i	$0.334430\pi$
$548$	148841.	−	257801.i	0.495635	−	0.858465i
$549$	−612509.	+	353632.i	−2.03221	+	1.17330i
$550$	−14764.8	−	25573.5i	−0.0488094	−	0.0845403i
$551$	231206.	+	133487.i	0.761545	+	0.439678i
$552$		−	171581.i		−	0.563107i
$553$		0			0
$554$	144771.			0.471697
$555$	−97741.6	+	169293.i	−0.317317	+	0.549609i
$556$	−371803.	+	214660.i	−1.20272	+	0.694388i
$557$	−225833.	−	391154.i	−0.727909	−	1.26077i	−0.957766	−	0.287550i	$-0.907159\pi$
$557$	−225833.	−	391154.i	−0.727909	−	1.26077i	0.229857	−	0.973224i	$-0.426174\pi$
$558$	−73007.7	−	42151.0i	−0.234477	−	0.135375i
$559$		−	238733.i		−	0.763992i
$560$		0			0
$561$	−170142.			−0.540613
$562$	−8459.09	+	14651.6i	−0.0267825	+	0.0463886i
$563$	−477175.	+	275497.i	−1.50543	+	0.869160i	−0.505450	+	0.862856i	$0.668673\pi$
$563$	−477175.	+	275497.i	−1.50543	+	0.869160i	−0.999980	+	0.00630406i	$0.997993\pi$
$564$	250949.	+	434656.i	0.788909	+	1.36643i
$565$	39940.2	+	23059.5i	0.125116	+	0.0722359i
$566$			54493.0i			0.170101i
$567$		0			0
$568$	−428035.			−1.32673
$569$	−71871.0	+	124484.i	−0.221988	+	0.384494i	−0.955411	−	0.295278i	$-0.904588\pi$
$569$	−71871.0	+	124484.i	−0.221988	+	0.384494i	0.733424	+	0.679772i	$0.237921\pi$
$570$	49622.9	−	28649.8i	0.152733	−	0.0881803i
$571$	−59122.3	−	102403.i	−0.181334	−	0.314080i	0.761001	−	0.648751i	$-0.224708\pi$
$571$	−59122.3	−	102403.i	−0.181334	−	0.314080i	−0.942335	+	0.334671i	$0.891375\pi$
$572$	55973.2	+	32316.1i	0.171076	+	0.0987706i
$573$			215799.i			0.657264i
$574$		0			0
$575$	120143.			0.363381
$576$	−21209.8	+	36736.4i	−0.0639280	+	0.110727i
$577$	391392.	−	225971.i	1.17560	−	0.678735i	0.220610	−	0.975362i	$-0.429195\pi$
$577$	391392.	−	225971.i	1.17560	−	0.678735i	0.954993	+	0.296627i	$0.0958619\pi$
$578$	30851.2	+	53435.9i	0.0923458	+	0.159948i
$579$	−192308.	−	111029.i	−0.573640	−	0.331191i
$580$		−	103480.i		−	0.307609i
$581$		0			0
$582$	−38894.0			−0.114825
$583$	−48921.2	+	84734.0i	−0.143933	+	0.249299i
$584$	−15522.4	+	8961.87i	−0.0455128	+	0.0262768i
$585$	114033.	+	197511.i	0.333211	+	0.577138i
$586$	−26398.4	−	15241.1i	−0.0768744	−	0.0443835i
$587$			59990.7i			0.174104i	0.996204	+	0.0870518i	$0.0277446\pi$
$587$			59990.7i			0.174104i	−0.996204	+	0.0870518i	$0.972255\pi$
$588$		0			0
$589$	72254.1			0.208273
$590$	−20984.9	+	36346.9i	−0.0602841	+	0.104415i
$591$	351408.	−	202885.i	1.00609	−	0.580866i
$592$	−95195.9	−	164884.i	−0.271628	−	0.470474i
$593$	−67071.2	−	38723.6i	−0.190734	−	0.110120i	0.401592	−	0.915819i	$-0.368457\pi$
$593$	−67071.2	−	38723.6i	−0.190734	−	0.110120i	−0.592326	+	0.805698i	$0.701790\pi$
$594$		−	83096.9i		−	0.235511i
$595$		0			0
$596$	−391037.			−1.10084
$597$	345186.	−	597880.i	0.968512	−	1.67751i
$598$	51454.4	−	29707.2i	0.143886	−	0.0830729i
$599$	203526.	+	352517.i	0.567238	+	0.982485i	0.996838	+	0.0794655i	$0.0253214\pi$
$599$	203526.	+	352517.i	0.567238	+	0.982485i	−0.429600	+	0.903019i	$0.641345\pi$
$600$	392834.	+	226803.i	1.09121	+	0.630008i
$601$			681741.i			1.88743i	0.330761	+	0.943715i	$0.392695\pi$
$601$			681741.i			1.88743i	−0.330761	+	0.943715i	$0.607305\pi$
$602$		0			0
$603$	1.24061e6			3.41193
$604$	−29480.1	+	51061.0i	−0.0808080	+	0.139964i
$605$	93053.3	−	53724.3i	0.254227	−	0.146778i
$606$	194650.	+	337145.i	0.530042	+	0.918060i
$607$	−83818.8	−	48392.8i	−0.227491	−	0.131342i	0.381923	−	0.924194i	$-0.375262\pi$
$607$	−83818.8	−	48392.8i	−0.227491	−	0.131342i	−0.609414	+	0.792852i	$0.708595\pi$
$608$			266444.i			0.720774i
$609$		0			0
$610$	53088.1			0.142672
$611$	−193429.	+	335029.i	−0.518131	+	0.897430i
$612$	700410.	−	404382.i	1.87003	−	1.07967i
$613$	−239048.	−	414043.i	−0.636156	−	1.10185i	−0.986269	−	0.165147i	$-0.947190\pi$
$613$	−239048.	−	414043.i	−0.636156	−	1.10185i	0.350113	−	0.936707i	$-0.386143\pi$
$614$	7972.40	+	4602.87i	0.0211472	+	0.0122093i
$615$			67221.3i			0.177728i
$616$		0			0
$617$	−55323.0			−0.145323			−0.0726617	−	0.997357i	$-0.523149\pi$
$617$	−55323.0			−0.145323			−0.0726617	+	0.997357i	$0.523149\pi$
$618$	−24222.9	+	41955.4i	−0.0634234	+	0.109853i
$619$	123599.	−	71359.7i	0.322576	−	0.186239i	−0.329964	−	0.943993i	$-0.607037\pi$
$619$	123599.	−	71359.7i	0.322576	−	0.186239i	0.652540	+	0.757754i	$0.273703\pi$
$620$	−14003.0	−	24253.9i	−0.0364281	−	0.0630954i
$621$	292789.	+	169042.i	0.759226	+	0.438339i
$622$		−	237632.i		−	0.614220i
$623$		0			0
$624$	−322474.			−0.828182
$625$	−139615.	+	241821.i	−0.357415	+	0.619061i
$626$	−68053.4	+	39290.6i	−0.173660	+	0.100263i
$627$	64954.7	+	112505.i	0.165225	+	0.286178i
$628$	358465.	+	206960.i	0.908925	+	0.524768i
$629$			534328.i			1.35054i
$630$		0			0
$631$	−667428.			−1.67628			−0.838138	−	0.545459i	$-0.816356\pi$
$631$	−667428.			−1.67628			−0.838138	+	0.545459i	$0.816356\pi$
$632$	52061.4	−	90172.9i	0.130341	−	0.225757i
$633$	−49135.1	+	28368.1i	−0.122626	+	0.0707984i
$634$	−33862.5	−	58651.5i	−0.0842442	−	0.145915i
$635$	−57360.0	−	33116.8i	−0.142253	−	0.0821299i
$636$		−	675200.i		−	1.66924i
$637$		0			0
$638$	−53008.8			−0.130229
$639$	769193.	−	1.33228e6i	1.88379	−	3.26283i
$640$	112404.	−	64896.6i	0.274424	−	0.158439i
$641$	−5549.50	−	9612.01i	−0.0135063	−	0.0233937i	0.859193	−	0.511651i	$-0.170966\pi$
$641$	−5549.50	−	9612.01i	−0.0135063	−	0.0233937i	−0.872700	+	0.488258i	$0.837633\pi$
$642$	−203065.	−	117240.i	−0.492680	−	0.284449i
$643$		−	136149.i		−	0.329300i	−0.986352	−	0.164650i	$-0.947351\pi$
$643$		−	136149.i		−	0.329300i	0.986352	−	0.164650i	$-0.0526494\pi$
$644$		0			0
$645$	−185991.			−0.447066
$646$	78310.4	−	135638.i	0.187653	−	0.325024i
$647$	−95977.3	+	55412.5i	−0.229277	+	0.132373i	−0.610238	−	0.792218i	$-0.708926\pi$
$647$	−95977.3	+	55412.5i	−0.229277	+	0.132373i	0.380962	+	0.924591i	$0.375593\pi$
$648$	275966.	+	477987.i	0.657213	+	1.13833i
$649$	−82405.6	−	47576.9i	−0.195644	−	0.112955i
$650$			157073.i			0.371770i
$651$		0			0
$652$	−176258.			−0.414624
$653$	44159.1	−	76485.8i	0.103560	−	0.179372i	−0.809589	−	0.586998i	$-0.800310\pi$
$653$	44159.1	−	76485.8i	0.103560	−	0.179372i	0.913149	+	0.407626i	$0.133643\pi$
$654$	−262788.	+	151721.i	−0.614399	+	0.354723i
$655$	3139.08	+	5437.04i	0.00731677	+	0.0126730i
$656$	−56699.2	−	32735.3i	−0.131756	−	0.0760691i
$657$		−	64419.0i		−	0.149239i
$658$		0			0
$659$	136014.			0.313194			0.156597	−	0.987663i	$-0.449948\pi$
$659$	136014.			0.313194			0.156597	+	0.987663i	$0.449948\pi$
$660$	25176.6	−	43607.2i	0.0577976	−	0.100108i
$661$	−119626.	+	69066.3i	−0.273794	+	0.158075i	−0.630611	−	0.776099i	$-0.717195\pi$
$661$	−119626.	+	69066.3i	−0.273794	+	0.158075i	0.356817	+	0.934174i	$0.383862\pi$
$662$	−34178.8	−	59199.5i	−0.0779904	−	0.135083i
$663$	783764.	+	452506.i	1.78303	+	1.02943i
$664$			528515.i			1.19873i
$665$		0			0
$666$	−476004.			−1.07316
$667$	107834.	−	186774.i	0.242385	−	0.419823i
$668$	−282174.	+	162913.i	−0.632360	+	0.365093i
$669$	−542754.	−	940077.i	−1.21269	−	2.10045i
$670$	−80645.7	−	46560.8i	−0.179652	−	0.103722i
$671$			120361.i			0.267326i
$672$		0			0
$673$	752500.			1.66141			0.830704	−	0.556714i	$-0.187938\pi$
$673$	752500.			1.66141			0.830704	+	0.556714i	$0.187938\pi$
$674$	61042.3	−	105728.i	0.134373	−	0.232740i
$675$	−774040.	+	446892.i	−1.69885	+	0.980834i
$676$	14482.6	+	25084.6i	0.0316923	+	0.0548927i
$677$	−670735.	−	387249.i	−1.46343	−	0.844914i	−0.464267	−	0.885695i	$-0.653682\pi$
$677$	−670735.	−	387249.i	−1.46343	−	0.844914i	−0.999168	+	0.0407809i	$0.987015\pi$
$678$			163033.i			0.354664i
$679$		0			0
$680$	−135130.			−0.292236
$681$	−599622.	+	1.03857e6i	−1.29295	+	2.23946i
$682$	−12424.3	+	7173.19i	−0.0267119	+	0.0154221i
$683$	165044.	+	285864.i	0.353800	+	0.612799i	0.986912	−	0.161261i	$-0.0515560\pi$
$683$	165044.	+	285864.i	0.353800	+	0.612799i	−0.633112	+	0.774060i	$0.718223\pi$
$684$	−534787.	−	308759.i	−1.14306	−	0.659945i
$685$		−	178759.i		−	0.380967i
$686$		0			0
$687$	451181.			0.955954
$688$	90573.2	−	156877.i	0.191347	−	0.331424i
$689$	450713.	−	260219.i	0.949427	−	0.548152i
$690$	−23144.1	−	40086.7i	−0.0486118	−	0.0841981i
$691$	611381.	+	352981.i	1.28043	+	0.739257i	0.976927	−	0.213574i	$-0.0685103\pi$
$691$	611381.	+	352981.i	1.28043	+	0.739257i	0.303503	+	0.952830i	$0.401844\pi$
$692$		−	331868.i		−	0.693031i
$693$		0			0
$694$	113780.			0.236236
$695$	−128904.	+	223269.i	−0.266869	+	0.462230i
$696$	705177.	−	407134.i	1.45573	−	0.840463i
$697$	91870.4	+	159124.i	0.189108	+	0.327545i
$698$	−335627.	−	193774.i	−0.688884	−	0.397728i
$699$		−	643427.i		−	1.31688i
$700$		0			0
$701$	−387191.			−0.787933			−0.393966	−	0.919125i	$-0.628897\pi$
$701$	−387191.			−0.787933			−0.393966	+	0.919125i	$0.628897\pi$
$702$	−221002.	+	382787.i	−0.448459	+	0.776754i
$703$	353318.	−	203988.i	0.714917	−	0.412757i
$704$	3609.44	+	6251.74i	0.00728274	+	0.0126141i
$705$	261012.	+	150696.i	0.525149	+	0.303195i
$706$		−	228388.i		−	0.458209i
$707$		0			0
$708$	656645.			1.30998
$709$	−325367.	+	563553.i	−0.647264	+	1.12109i	0.336509	+	0.941680i	$0.390754\pi$
$709$	−325367.	+	563553.i	−0.647264	+	1.12109i	−0.983774	+	0.179415i	$0.942580\pi$
$710$	−100002.	+	57736.5i	−0.198378	+	0.114534i
$711$	187112.	+	324087.i	0.370137	+	0.641095i
$712$	−450661.	−	260189.i	−0.888976	−	0.513251i
$713$		−	58368.9i		−	0.114816i
$714$		0			0
$715$	38811.9			0.0759194
$716$	−23574.1	+	40831.6i	−0.0459843	+	0.0796471i
$717$	−415346.	+	239800.i	−0.807925	+	0.466456i
$718$	−199825.	−	346106.i	−0.387614	−	0.671368i
$719$	−73352.4	−	42350.1i	−0.141892	−	0.0819212i	0.427374	−	0.904075i	$-0.359439\pi$
$719$	−73352.4	−	42350.1i	−0.141892	−	0.0819212i	−0.569265	+	0.822154i	$0.692772\pi$
$720$			173052.i			0.333820i
$721$		0			0
$722$	104205.			0.199900
$723$	−506830.	+	877855.i	−0.969584	+	1.67937i
$724$	174718.	−	100874.i	0.333319	−	0.192442i
$725$	285080.	+	493772.i	0.542363	+	0.939400i
$726$	328949.	+	189919.i	0.624102	+	0.360325i
$727$			602305.i			1.13959i	0.821788	+	0.569794i	$0.192977\pi$
$727$			602305.i			1.13959i	−0.821788	+	0.569794i	$0.807023\pi$
$728$		0			0
$729$	88844.8			0.167177
$730$	−2417.68	+	4187.55i	−0.00453684	+	0.00785804i
$731$	−440271.	+	254190.i	−0.823920	+	0.475690i
$732$	−415299.	−	719319.i	−0.775066	−	1.34245i
$733$	408604.	+	235907.i	0.760491	+	0.439070i	0.829472	−	0.558548i	$-0.188641\pi$
$733$	408604.	+	235907.i	0.760491	+	0.439070i	−0.0689807	+	0.997618i	$0.521975\pi$
$734$		−	186440.i		−	0.346056i
$735$		0			0
$736$	215241.			0.397347
$737$	105562.	−	182840.i	0.194345	−	0.336616i
$738$	−141755.	+	81842.5i	−0.260271	+	0.150268i
$739$	164051.	+	284145.i	0.300393	+	0.520296i	0.976225	−	0.216760i	$-0.0695488\pi$
$739$	164051.	+	284145.i	0.300393	+	0.520296i	−0.675832	+	0.737056i	$0.736215\pi$
$740$	−136947.	−	79066.6i	−0.250086	−	0.144387i
$741$		−	691007.i		−	1.25848i
$742$		0			0
$743$	−237585.			−0.430370			−0.215185	−	0.976573i	$-0.569035\pi$
$743$	−237585.			−0.430370			−0.215185	+	0.976573i	$0.569035\pi$
$744$	110187.	−	190850.i	0.199061	−	0.344783i
$745$	−203359.	+	117409.i	−0.366396	+	0.211539i
$746$	145863.	+	252642.i	0.262100	+	0.453971i
$747$	−1.64503e6	−	949758.i	−2.94803	−	1.70205i
$748$		−	137634.i		−	0.245993i
$749$		0			0
$750$	258079.			0.458807
$751$	182142.	−	315480.i	0.322947	−	0.559361i	−0.658148	−	0.752889i	$-0.728660\pi$
$751$	182142.	−	315480.i	0.322947	−	0.559361i	0.981095	+	0.193528i	$0.0619931\pi$
$752$	−254214.	+	146771.i	−0.449536	+	0.259540i
$753$	−501614.	−	868820.i	−0.884666	−	1.53229i
$754$	244186.	+	140981.i	0.429514	+	0.247980i
$755$			35405.7i			0.0621126i
$756$		0			0
$757$	−590661.			−1.03073			−0.515367	−	0.856969i	$-0.672345\pi$
$757$	−590661.			−1.03073			−0.515367	+	0.856969i	$0.672345\pi$
$758$	193049.	−	334370.i	0.335992	−	0.581954i
$759$	90884.4	−	52472.1i	0.157763	−	0.0910847i
$760$	51588.1	+	89353.2i	0.0893145	+	0.154697i
$761$	−236178.	−	136358.i	−0.407822	−	0.235456i	0.282031	−	0.959405i	$-0.408992\pi$
$761$	−236178.	−	136358.i	−0.407822	−	0.235456i	−0.689854	+	0.723949i	$0.742325\pi$
$762$		−	234140.i		−	0.403242i
$763$		0			0
$764$	−174567.			−0.299072
$765$	242833.	−	420599.i	0.414939	−	0.718696i
$766$	−36550.9	+	21102.7i	−0.0622933	+	0.0359650i
$767$	253068.	+	438327.i	0.430177	+	0.745089i
$768$	344465.	+	198877.i	0.584014	+	0.337181i
$769$		−	725929.i		−	1.22756i	−0.789478	−	0.613778i	$-0.789649\pi$
$769$		−	725929.i		−	1.22756i	0.789478	−	0.613778i	$-0.210351\pi$
$770$		0			0
$771$	−1.85028e6			−3.11264
$772$	89815.2	−	155564.i	0.150701	−	0.261021i
$773$	−340019.	+	196310.i	−0.569042	+	0.328536i	−0.756767	−	0.653685i	$-0.773222\pi$
$773$	−340019.	+	196310.i	−0.569042	+	0.328536i	0.187725	+	0.982222i	$0.439889\pi$
$774$	−226445.	−	392214.i	−0.377990	−	0.654698i
$775$	133635.	+	77154.4i	0.222494	+	0.128457i
$776$		−	70034.4i		−	0.116302i
$777$		0			0
$778$	247514.			0.408922
$779$	70146.1	−	121497.i	0.115592	−	0.200211i
$780$	−231953.	+	133918.i	−0.381251	+	0.220116i
$781$	−130900.	−	226725.i	−0.214604	−	0.371705i
$782$	−109572.	−	63261.3i	−0.179178	−	0.103449i
$783$			1.60443e6i			2.61697i
$784$		0			0
$785$	248560.			0.403360
$786$	−11096.8	+	19220.3i	−0.0179620	+	0.0311110i
$787$	280834.	−	162139.i	0.453419	−	0.261782i	−0.255854	−	0.966715i	$-0.582357\pi$
$787$	280834.	−	162139.i	0.453419	−	0.261782i	0.709273	+	0.704934i	$0.249023\pi$
$788$	164121.	+	284266.i	0.264309	+	0.457797i
$789$	1.16796e6	+	674323.i	1.87618	+	1.08321i
$790$		−	28089.6i		−	0.0450082i
$791$		0			0
$792$	272925.			0.435104
$793$	320109.	−	554445.i	0.509040	−	0.881683i
$794$	227903.	−	131580.i	0.361501	−	0.208712i
$795$	−202730.	−	351138.i	−0.320762	−	0.555576i
$796$	483646.	+	279233.i	0.763311	+	0.440698i
$797$		−	179577.i		−	0.282706i	−0.989959	−	0.141353i	$-0.954855\pi$
$797$		−	179577.i		−	0.282706i	0.989959	−	0.141353i	$-0.0451453\pi$
$798$		0			0
$799$	823813.			1.29043
$800$	−284514.	+	492794.i	−0.444554	+	0.769990i
$801$	1.61971e6	−	935137.i	2.52447	−	1.45751i
$802$	39003.4	+	67555.9i	0.0606393	+	0.105030i
$803$	−9493.99	−	5481.36i	−0.0147237	−	0.00850075i
$804$			1.45695e6i			2.25389i
$805$		0			0
$806$	76310.5			0.117467
$807$	−55328.5	+	95831.7i	−0.0849575	+	0.147151i
$808$	−607078.	+	350496.i	−0.929868	+	0.536860i
$809$	491309.	+	850972.i	0.750685	+	1.30022i	0.947491	+	0.319782i	$0.103610\pi$
$809$	491309.	+	850972.i	0.750685	+	1.30022i	−0.196806	+	0.980442i	$0.563057\pi$
$810$	128949.	+	74448.6i	0.196538	+	0.113471i
$811$		−	994497.i		−	1.51203i	−0.654552	−	0.756017i	$-0.727143\pi$
$811$		−	994497.i		−	1.51203i	0.654552	−	0.756017i	$-0.272857\pi$
$812$		0			0
$813$	812431.			1.22915
$814$	−40502.8	+	70152.9i	−0.0611274	+	0.105876i
$815$	−91663.2	+	52921.8i	−0.138000	+	0.0796745i
$816$	343354.	+	594706.i	0.515657	+	0.893145i
$817$	336161.	+	194083.i	0.503621	+	0.290765i
$818$			17896.3i			0.0267459i
$819$		0			0
$820$	−54377.7			−0.0808710
$821$	511373.	−	885725.i	0.758668	−	1.31405i	−0.184862	−	0.982765i	$-0.559184\pi$
$821$	511373.	−	885725.i	0.758668	−	1.31405i	0.943530	−	0.331287i	$-0.107483\pi$
$822$	547263.	−	315962.i	0.809939	−	0.467619i
$823$	−158856.	−	275146.i	−0.234532	−	0.406222i	0.724604	−	0.689165i	$-0.242023\pi$
$823$	−158856.	−	275146.i	−0.234532	−	0.406222i	−0.959137	+	0.282943i	$0.908689\pi$
$824$	−75546.7	−	43616.9i	−0.111266	−	0.0642392i
$825$			277439.i			0.407624i
$826$		0			0
$827$	−50540.8			−0.0738977			−0.0369489	−	0.999317i	$-0.511764\pi$
$827$	−50540.8			−0.0738977			−0.0369489	+	0.999317i	$0.511764\pi$
$828$	−249424.	+	432015.i	−0.363813	+	0.630142i
$829$	931232.	−	537647.i	1.35503	−	0.782327i	0.366081	−	0.930583i	$-0.380699\pi$
$829$	931232.	−	537647.i	1.35503	−	0.782327i	0.988949	+	0.148256i	$0.0473660\pi$
$830$	71289.9	+	123478.i	0.103484	+	0.179239i
$831$	−1.17794e6	−	680083.i	−1.70577	−	0.984827i
$832$		−	38398.3i		−	0.0554710i
$833$		0			0
$834$	−911369.			−1.31027
$835$	−97829.9	+	169446.i	−0.140313	+	0.243030i
$836$	−91009.0	+	52544.1i	−0.130218	+	0.0751816i
$837$	217113.	+	376051.i	0.309910	+	0.536780i
$838$	221184.	+	127701.i	0.314968	+	0.181847i
$839$			966211.i			1.37261i	0.727312	+	0.686307i	$0.240769\pi$
$839$			966211.i			1.37261i	−0.727312	+	0.686307i	$0.759231\pi$
$840$		0			0
$841$	316212.			0.447082
$842$	−204585.	+	354352.i	−0.288570	+	0.499817i
$843$	137655.	−	79475.4i	0.193704	−	0.111835i
$844$	−22948.0	−	39747.1i	−0.0322151	−	0.0557982i
$845$	15063.4	+	8696.86i	0.0210965	+	0.0121800i
$846$			733892.i			1.02539i
$847$		0			0
$848$	394899.			0.549155
$849$	255988.	−	443384.i	0.355144	−	0.615127i
$850$	289673.	−	167243.i	0.400931	−	0.231478i
$851$	−164787.	−	285420.i	−0.227544	−	0.394117i
$852$	1.56461e6	+	903326.i	2.15539	+	1.24441i
$853$			395709.i			0.543848i	0.962319	+	0.271924i	$0.0876600\pi$
$853$			395709.i			0.543848i	−0.962319	+	0.271924i	$0.912340\pi$
$854$		0			0
$855$	−370822.			−0.507263
$856$	211107.	−	365648.i	0.288108	−	0.499018i
$857$	−681620.	+	393534.i	−0.928070	+	0.535822i	−0.886201	−	0.463301i	$-0.846665\pi$
$857$	−681620.	+	393534.i	−0.928070	+	0.535822i	−0.0418697	+	0.999123i	$0.513331\pi$
$858$	68601.2	+	118821.i	0.0931874	+	0.161405i
$859$	−1.14415e6	−	660578.i	−1.55059	−	0.895236i	−0.998093	−	0.0617241i	$-0.980340\pi$
$859$	−1.14415e6	−	660578.i	−1.55059	−	0.895236i	−0.552501	−	0.833512i	$-0.686327\pi$
$860$		−	150454.i		−	0.203426i
$861$		0			0
$862$	481001.			0.647339
$863$	324056.	−	561282.i	0.435110	−	0.753632i	−0.562195	−	0.827005i	$-0.690043\pi$
$863$	324056.	−	561282.i	0.435110	−	0.753632i	0.997305	+	0.0733726i	$0.0233762\pi$
$864$	−1.38673e6	+	800627.i	−1.85765	+	1.07251i
$865$	−99643.8	−	172588.i	−0.133174	−	0.230663i
$866$	116148.	+	67058.3i	0.154874	+	0.0894163i
$867$		−	579712.i		−	0.771212i
$868$		0			0
$869$	63684.7			0.0843327
$870$	109834.	−	190239.i	0.145111	−	0.251339i
$871$	−972551.	+	561502.i	−1.28196	+	0.740142i
$872$	−273195.	−	473188.i	−0.359286	−	0.622302i
$873$	217986.	+	125854.i	0.286022	+	0.165135i
$874$			96604.2i			0.126466i
$875$		0			0
$876$	75652.5			0.0985860
$877$	−17919.5	+	31037.5i	−0.0232985	+	0.0403541i	−0.877440	−	0.479687i	$-0.840750\pi$
$877$	−17919.5	+	31037.5i	−0.0232985	+	0.0403541i	0.854141	+	0.520041i	$0.174083\pi$
$878$	−461937.	+	266699.i	−0.599230	+	0.345966i
$879$	143194.	+	248020.i	0.185331	+	0.321003i
$880$	25504.2	+	14724.9i	0.0329342	+	0.0190146i
$881$		−	830960.i		−	1.07060i	−0.844661	−	0.535302i	$-0.820198\pi$
$881$		−	830960.i		−	1.07060i	0.844661	−	0.535302i	$-0.179802\pi$
$882$		0			0
$883$	−1.54585e6			−1.98265			−0.991327	−	0.131415i	$-0.958048\pi$
$883$	−1.54585e6			−1.98265			−0.991327	+	0.131415i	$0.958048\pi$
$884$	−366048.	+	634014.i	−0.468418	+	0.811324i
$885$	341489.	−	197159.i	0.436004	−	0.251727i
$886$	4621.76	+	8005.12i	0.00588762	+	0.0101977i
$887$	739331.	+	426853.i	0.939705	+	0.542539i	0.889868	−	0.456219i	$-0.150796\pi$
$887$	739331.	+	426853.i	0.939705	+	0.542539i	0.0498370	+	0.998757i	$0.484130\pi$
$888$		−	1.24433e6i		−	1.57801i
$889$		0			0
$890$	−140385.			−0.177231
$891$	−168790.	+	292352.i	−0.212613	+	0.368257i
$892$	760462.	−	439053.i	0.955757	−	0.551807i
$893$	−314504.	−	544737.i	−0.394388	−	0.683100i
$894$	−718887.	−	415050.i	−0.899468	−	0.519308i
$895$			28312.7i			0.0353455i
$896$		0			0
$897$	−558214.			−0.693771
$898$	−144240.	+	249831.i	−0.178868	+	0.309809i
$899$	239889.	−	138500.i	0.296818	−	0.171368i
$900$	−659398.	−	1.14211e6i	−0.814072	−	1.41001i
$901$	−959790.	−	554135.i	−1.18230	−	0.682600i
$902$			27855.6i			0.0342373i
$903$		0			0
$904$	−293565.			−0.359226
$905$	60574.9	−	104919.i	0.0739597	−	0.128102i
$906$	−108393.	+	62580.7i	−0.132052	+	0.0762402i
$907$	−97196.7	−	168350.i	−0.118151	−	0.204643i	0.800884	−	0.598819i	$-0.204363\pi$
$907$	−97196.7	−	168350.i	−0.118151	−	0.204643i	−0.919035	+	0.394176i	$0.871030\pi$
$908$	−840140.	−	485055.i	−1.01901	−	0.588327i
$909$		−	2.51941e6i		−	3.04910i
$910$		0			0
$911$	433279.			0.522072			0.261036	−	0.965329i	$-0.415936\pi$
$911$	433279.			0.522072			0.261036	+	0.965329i	$0.415936\pi$
$912$	262162.	−	454078.i	0.315195	−	0.545934i
$913$	−279948.	+	161628.i	−0.335843	+	0.193899i
$914$	167985.	+	290958.i	0.201084	+	0.348287i
$915$	−431953.	−	249388.i	−0.515935	−	0.297875i
$916$			364976.i			0.434984i
$917$		0			0
$918$	941246.			1.11691
$919$	−467629.	+	809958.i	−0.553695	+	0.959028i	0.444309	+	0.895874i	$0.353449\pi$
$919$	−467629.	+	809958.i	−0.553695	+	0.959028i	−0.998004	+	0.0631545i	$0.979884\pi$
$920$	72181.9	−	41674.3i	0.0852811	−	0.0492371i
$921$	−43245.2	−	74902.9i	−0.0509822	−	0.0883038i
$922$	529004.	+	305421.i	0.622296	+	0.359283i
$923$			1.39255e6i			1.63459i
$924$		0			0
$925$	871291.			1.01831
$926$	89122.4	−	154365.i	0.103936	−	0.180022i
$927$	271520.	−	156762.i	0.315967	−	0.182424i
$928$	510732.	+	884614.i	0.593058	+	1.02721i
$929$	1.01219e6	+	584387.i	1.17282	+	0.677126i	0.954342	−	0.298717i	$-0.0965586\pi$
$929$	1.01219e6	+	584387.i	1.17282	+	0.677126i	0.218475	+	0.975843i	$0.429892\pi$
$930$		−	59451.5i		−	0.0687380i
$931$		0			0
$932$	520491.			0.599213
$933$	−1.11631e6	+	1.93350e6i	−1.28239	+	2.22117i
$934$	−437391.	+	252528.i	−0.501391	+	0.289478i
$935$	−41324.9	−	71576.7i	−0.0472703	−	0.0818745i
$936$	−1.25724e6	−	725865.i	−1.43504	−	0.828522i
$937$		−	695595.i		−	0.792277i	−0.918191	−	0.396139i	$-0.870350\pi$
$937$		−	695595.i		−	0.792277i	0.918191	−	0.396139i	$-0.129650\pi$
$938$		0			0
$939$	738292.			0.837331
$940$	−121903.	+	211142.i	−0.137962	+	0.238957i
$941$	1.34501e6	−	776541.i	1.51896	−	0.876971i	0.519208	−	0.854648i	$-0.326227\pi$
$941$	1.34501e6	−	776541.i	1.51896	−	0.876971i	0.999751	−	0.0223233i	$-0.00710633\pi$
$942$	439338.	+	760956.i	0.495105	+	0.857547i
$943$	−98148.2	−	56665.9i	−0.110372	−	0.0637233i
$944$			384048.i			0.430964i
$945$		0			0
$946$	−77072.0			−0.0861220
$947$	−522505.	+	905005.i	−0.582627	+	1.00914i	0.412540	+	0.910940i	$0.364642\pi$
$947$	−522505.	+	905005.i	−0.582627	+	1.00914i	−0.995167	+	0.0981999i	$0.968692\pi$
$948$	−380602.	+	219741.i	−0.423501	+	0.244508i
$949$	29156.2	+	50500.0i	0.0323741	+	0.0560736i
$950$	−221175.	−	127695.i	−0.245069	−	0.141491i
$951$			636294.i			0.703553i
$952$		0			0
$953$	−855805.			−0.942300			−0.471150	−	0.882053i	$-0.656161\pi$
$953$	−855805.			−0.942300			−0.471150	+	0.882053i	$0.656161\pi$
$954$	493650.	−	855027.i	0.542403	−	0.939470i
$955$	−90783.9	+	52414.1i	−0.0995410	+	0.0574700i
$956$	−193983.	−	335988.i	−0.212250	−	0.367627i
$957$	431308.	+	249016.i	0.470938	+	0.271896i
$958$			631502.i			0.688087i
$959$		0			0
$960$	−29915.1			−0.0324600
$961$	−424277.	+	734869.i	−0.459412	+	0.795725i
$962$	373154.	−	215440.i	0.403216	−	0.232797i
$963$	758732.	+	1.31416e6i	0.818156	+	1.41709i
$964$	−710127.	−	409992.i	−0.764156	−	0.441186i
$965$		−	107869.i		−	0.115835i
$966$		0			0
$967$	−1.73940e6			−1.86015			−0.930074	−	0.367371i	$-0.880258\pi$
$967$	−1.73940e6			−1.86015			−0.930074	+	0.367371i	$0.880258\pi$
$968$	−341976.	+	592321.i	−0.364960	+	0.632130i
$969$	−1.27435e6	+	735748.i	−1.35719	+	0.783576i
$970$	−9446.74	−	16362.2i	−0.0100401	−	0.0173900i
$971$	80831.8	+	46668.3i	0.0857322	+	0.0494975i	0.542253	−	0.840215i	$-0.317571\pi$
$971$	80831.8	+	46668.3i	0.0857322	+	0.0494975i	−0.456521	+	0.889713i	$0.650905\pi$
$972$		−	653059.i		−	0.691226i
$973$		0			0
$974$	−587829.			−0.619630
$975$	737871.	−	1.27803e6i	0.776195	−	1.34441i
$976$	420703.	−	242893.i	0.441648	−	0.254986i
$977$	−525949.	−	910971.i	−0.551004	−	0.954367i	−0.998202	−	0.0599319i	$-0.980912\pi$
$977$	−525949.	−	910971.i	−0.551004	−	0.954367i	0.447199	−	0.894435i	$-0.352422\pi$
$978$	−324035.	−	187082.i	−0.338778	−	0.195593i
$979$		−	318280.i		−	0.332081i
$980$		0			0
$981$	1.96376e6			2.04057
$982$	−35700.8	+	61835.5i	−0.0370215	+	0.0641232i
$983$	28554.3	−	16485.8i	0.0295505	−	0.0170610i	−0.485152	−	0.874430i	$-0.661236\pi$
$983$	28554.3	−	16485.8i	0.0295505	−	0.0170610i	0.514702	+	0.857369i	$0.327902\pi$
$984$	−213945.	−	370564.i	−0.220959	−	0.382713i
$985$	170703.	+	98555.2i	0.175941	+	0.101580i
$986$		−	600435.i		−	0.617607i
$987$		0			0
$988$	558980.			0.572641
$989$	156785.	−	271560.i	0.160292	−	0.277635i
$990$	63764.0	−	36814.1i	0.0650586	−	0.0375616i
$991$	−319010.	−	552542.i	−0.324831	−	0.562623i	0.656647	−	0.754198i	$-0.271974\pi$
$991$	−319010.	−	552542.i	−0.324831	−	0.562623i	−0.981478	+	0.191574i	$0.938641\pi$
$992$	239413.	+	138225.i	0.243290	+	0.140464i
$993$			642239.i			0.651325i
$994$		0			0
$995$	335361.			0.338740
$996$	1.11538e6	−	1.93189e6i	1.12435	−	1.94744i
$997$	−1.49099e6	+	860822.i	−1.49997	+	0.866010i	−1.00000		3.04581e-5i	$-0.999990\pi$
$997$	−1.49099e6	+	860822.i	−1.49997	+	0.866010i	−0.499974	+	0.866041i	$0.666657\pi$
$998$	−305644.	−	529391.i	−0.306870	−	0.531515i
$999$	2.12334e6	+	1.22591e6i	2.12760	+	1.22837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.5.d.c.19.4		16
7.2	even	3		49.5.b.b.48.6	yes	8
7.3	odd	6	inner	49.5.d.c.31.4		16
7.4	even	3	inner	49.5.d.c.31.3		16
7.5	odd	6		49.5.b.b.48.5	✓	8
7.6	odd	2	inner	49.5.d.c.19.3		16
21.2	odd	6		441.5.d.g.244.4		8
21.5	even	6		441.5.d.g.244.3		8
28.19	even	6		784.5.c.g.97.8		8
28.23	odd	6		784.5.c.g.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.5.b.b.48.5	✓	8	7.5	odd	6
49.5.b.b.48.6	yes	8	7.2	even	3
49.5.d.c.19.3		16	7.6	odd	2	inner
49.5.d.c.19.4		16	1.1	even	1	trivial
49.5.d.c.31.3		16	7.4	even	3	inner
49.5.d.c.31.4		16	7.3	odd	6	inner
441.5.d.g.244.3		8	21.5	even	6
441.5.d.g.244.4		8	21.2	odd	6
784.5.c.g.97.1		8	28.23	odd	6
784.5.c.g.97.8		8	28.19	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	49.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.858610 + 1.48716i) q^{2} +(13.9722 - 8.06687i) q^{3} +(6.52558 + 11.3026i) q^{4} +(6.78727 + 3.91863i) q^{5} +27.7052i q^{6} -49.8872 q^{8} +(89.6489 - 155.277i) q^{9} +O(q^{10})\)	\(q+(-0.858610 + 1.48716i) q^{2} +(13.9722 - 8.06687i) q^{3} +(6.52558 + 11.3026i) q^{4} +(6.78727 + 3.91863i) q^{5} +27.7052i q^{6} -49.8872 q^{8} +(89.6489 - 155.277i) q^{9} +(-11.6552 + 6.72915i) q^{10} +(-15.2563 - 26.4247i) q^{11} +(182.354 + 105.282i) q^{12} +162.301i q^{13} +126.444 q^{15} +(-61.5756 + 106.652i) q^{16} +(299.315 - 172.810i) q^{17} +(153.947 + 266.644i) q^{18} +(-228.537 - 131.946i) q^{19} +102.285i q^{20} +52.3969 q^{22} +(-106.589 + 184.618i) q^{23} +(-697.036 + 402.434i) q^{24} +(-281.789 - 488.072i) q^{25} +(-241.367 - 139.353i) q^{26} -1585.91i q^{27} -1011.68 q^{29} +(-108.566 + 188.043i) q^{30} +(-237.120 + 136.901i) q^{31} +(-504.837 - 874.403i) q^{32} +(-426.329 - 246.141i) q^{33} +593.504i q^{34} +2340.04 q^{36} +(-773.001 + 1338.88i) q^{37} +(392.448 - 226.580i) q^{38} +(1309.26 + 2267.71i) q^{39} +(-338.598 - 195.490i) q^{40} +531.628i q^{41} -1470.93 q^{43} +(199.112 - 344.873i) q^{44} +(1216.94 - 702.602i) q^{45} +(-183.038 - 317.030i) q^{46} +(2064.25 + 1191.79i) q^{47} +1986.89i q^{48} +967.786 q^{50} +(2788.07 - 4829.07i) q^{51} +(-1834.43 + 1059.11i) q^{52} +(-1603.31 - 2777.02i) q^{53} +(2358.50 + 1361.68i) q^{54} -239.135i q^{55} -4257.56 q^{57} +(868.637 - 1504.52i) q^{58} +(2700.71 - 1559.25i) q^{59} +(825.123 + 1429.15i) q^{60} +(-3416.15 - 1972.32i) q^{61} -470.179i q^{62} -236.587 q^{64} +(-635.998 + 1101.58i) q^{65} +(732.101 - 422.679i) q^{66} +(3459.63 + 5992.26i) q^{67} +(3906.41 + 2255.36i) q^{68} +3439.38i q^{69} +8580.05 q^{71} +(-4472.34 + 7746.32i) q^{72} +(311.150 - 179.642i) q^{73} +(-1327.41 - 2299.15i) q^{74} +(-7874.44 - 4546.31i) q^{75} -3444.09i q^{76} -4496.58 q^{78} +(-1043.58 + 1807.53i) q^{79} +(-835.859 + 482.584i) q^{80} +(-5531.80 - 9581.36i) q^{81} +(-790.613 - 456.461i) q^{82} -10594.2i q^{83} +2708.71 q^{85} +(1262.95 - 2187.50i) q^{86} +(-14135.4 + 8161.08i) q^{87} +(761.095 + 1318.25i) q^{88} +(9033.60 + 5215.55i) q^{89} +2413.04i q^{90} -2782.23 q^{92} +(-2208.73 + 3825.63i) q^{93} +(-3544.76 + 2046.57i) q^{94} +(-1034.09 - 1791.10i) q^{95} +(-14107.4 - 8144.91i) q^{96} +1403.85i q^{97} -5470.85 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{2} - 52 q^{4} - 744 q^{8} + 352 q^{9}+O(q^{10}) \) 16 * q + 12 * q^2 - 52 * q^4 - 744 * q^8 + 352 * q^9	\( 16 q + 12 q^{2} - 52 q^{4} - 744 q^{8} + 352 q^{9} - 120 q^{11} - 1264 q^{15} + 300 q^{16} - 340 q^{18} + 3904 q^{22} - 1752 q^{23} + 2192 q^{25} + 2496 q^{29} - 456 q^{30} - 3156 q^{32} + 9880 q^{36} - 2368 q^{37} + 7672 q^{39} - 17104 q^{43} - 264 q^{44} - 7208 q^{46} - 11112 q^{50} + 11976 q^{51} - 5496 q^{53} - 18400 q^{57} + 17496 q^{58} - 2856 q^{60} + 7960 q^{64} - 30240 q^{65} + 7440 q^{67} + 19968 q^{71} + 1508 q^{72} + 1080 q^{74} + 44912 q^{78} + 14096 q^{79} - 3432 q^{81} + 23824 q^{85} - 44496 q^{86} + 44464 q^{88} - 64464 q^{92} - 9584 q^{93} - 22488 q^{95} + 60288 q^{99}+O(q^{100}) \) 16 * q + 12 * q^2 - 52 * q^4 - 744 * q^8 + 352 * q^9 - 120 * q^11 - 1264 * q^15 + 300 * q^16 - 340 * q^18 + 3904 * q^22 - 1752 * q^23 + 2192 * q^25 + 2496 * q^29 - 456 * q^30 - 3156 * q^32 + 9880 * q^36 - 2368 * q^37 + 7672 * q^39 - 17104 * q^43 - 264 * q^44 - 7208 * q^46 - 11112 * q^50 + 11976 * q^51 - 5496 * q^53 - 18400 * q^57 + 17496 * q^58 - 2856 * q^60 + 7960 * q^64 - 30240 * q^65 + 7440 * q^67 + 19968 * q^71 + 1508 * q^72 + 1080 * q^74 + 44912 * q^78 + 14096 * q^79 - 3432 * q^81 + 23824 * q^85 - 44496 * q^86 + 44464 * q^88 - 64464 * q^92 - 9584 * q^93 - 22488 * q^95 + 60288 * q^99

Introduction

L-functions

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