LMFDB - Embedded newform 49.5.d.c.19.8

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			19.8
Root			$6.65368 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	49.19
Dual form			49.5.d.c.31.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.49543 - 6.05426i) q^{2} +(6.83370 - 3.94544i) q^{3} +(-16.4360 - 28.4680i) q^{4} +(19.0608 + 11.0048i) q^{5} -55.1639i q^{6} -117.950 q^{8} +(-9.36707 + 16.2242i) q^{9} +O(q^{10})$	\(q+(3.49543 - 6.05426i) q^{2} +(6.83370 - 3.94544i) q^{3} +(-16.4360 - 28.4680i) q^{4} +(19.0608 + 11.0048i) q^{5} -55.1639i q^{6} -117.950 q^{8} +(-9.36707 + 16.2242i) q^{9} +(133.251 - 76.9327i) q^{10} +(-22.3838 - 38.7698i) q^{11} +(-224.638 - 129.695i) q^{12} +311.907i q^{13} +173.674 q^{15} +(-149.310 + 258.612i) q^{16} +(61.9673 - 35.7768i) q^{17} +(65.4838 + 113.421i) q^{18} +(-241.552 - 139.460i) q^{19} -723.499i q^{20} -312.963 q^{22} +(257.422 - 445.867i) q^{23} +(-806.035 + 465.365i) q^{24} +(-70.2902 - 121.746i) q^{25} +(1888.37 + 1090.25i) q^{26} +786.989i q^{27} +866.138 q^{29} +(607.066 - 1051.47i) q^{30} +(591.823 - 341.689i) q^{31} +(100.202 + 173.554i) q^{32} +(-305.928 - 176.627i) q^{33} -500.221i q^{34} +615.830 q^{36} +(-972.097 + 1683.72i) q^{37} +(-1688.65 + 974.945i) q^{38} +(1230.61 + 2131.48i) q^{39} +(-2248.23 - 1298.01i) q^{40} -102.538i q^{41} -885.919 q^{43} +(-735.800 + 1274.44i) q^{44} +(-357.088 + 206.165i) q^{45} +(-1799.60 - 3116.99i) q^{46} +(-2447.98 - 1413.34i) q^{47} +2356.37i q^{48} -982.778 q^{50} +(282.310 - 488.976i) q^{51} +(8879.38 - 5126.52i) q^{52} +(664.901 + 1151.64i) q^{53} +(4764.64 + 2750.86i) q^{54} -985.312i q^{55} -2200.92 q^{57} +(3027.52 - 5243.82i) q^{58} +(-4193.07 + 2420.87i) q^{59} +(-2854.52 - 4944.17i) q^{60} +(340.317 + 196.482i) q^{61} -4777.40i q^{62} -3376.92 q^{64} +(-3432.47 + 5945.20i) q^{65} +(-2138.70 + 1234.78i) q^{66} +(-2123.27 - 3677.61i) q^{67} +(-2036.99 - 1176.06i) q^{68} -4062.56i q^{69} +1188.97 q^{71} +(1104.85 - 1913.65i) q^{72} +(0.185820 - 0.107283i) q^{73} +(6795.79 + 11770.7i) q^{74} +(-960.684 - 554.651i) q^{75} +9168.67i q^{76} +17206.0 q^{78} +(789.481 - 1367.42i) q^{79} +(-5691.93 + 3286.24i) q^{80} +(2346.28 + 4063.88i) q^{81} +(-620.792 - 358.415i) q^{82} +9056.29i q^{83} +1574.86 q^{85} +(-3096.67 + 5363.59i) q^{86} +(5918.92 - 3417.29i) q^{87} +(2640.17 + 4572.90i) q^{88} +(3018.67 + 1742.83i) q^{89} +2882.54i q^{90} -16924.0 q^{92} +(2696.23 - 4670.00i) q^{93} +(-17113.5 + 9880.48i) q^{94} +(-3069.45 - 5316.44i) q^{95} +(1369.49 + 790.678i) q^{96} -7941.40i q^{97} +838.681 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 $

$2$	3.49543	−	6.05426i	0.873857	−	1.51356i	0.0158815	−	0.999874i	$-0.494945\pi$
$2$	3.49543	−	6.05426i	0.873857	−	1.51356i	0.857975	−	0.513691i	$-0.171722\pi$
$3$	6.83370	−	3.94544i	0.759299	−	0.438382i	−0.0697447	−	0.997565i	$-0.522218\pi$
$3$	6.83370	−	3.94544i	0.759299	−	0.438382i	0.829044	+	0.559183i	$0.188885\pi$
$4$	−16.4360	−	28.4680i	−1.02725	−	1.77925i
$5$	19.0608	+	11.0048i	0.762433	+	0.440191i	0.830168	−	0.557513i	$-0.188244\pi$
$5$	19.0608	+	11.0048i	0.762433	+	0.440191i	−0.0677359	+	0.997703i	$0.521578\pi$
$6$		−	55.1639i		−	1.53233i
$7$		0			0
$7$		0			0
$8$	−117.950			−1.84297
$9$	−9.36707	+	16.2242i	−0.115643	+	0.200299i
$10$	133.251	−	76.9327i	1.33251	−	0.769327i
$11$	−22.3838	−	38.7698i	−0.184990	−	0.320412i	0.758583	−	0.651576i	$-0.225892\pi$
$11$	−22.3838	−	38.7698i	−0.184990	−	0.320412i	−0.943573	+	0.331164i	$0.892559\pi$
$12$	−224.638	−	129.695i	−1.55998	−	0.900657i
$13$			311.907i			1.84560i	0.385274	+	0.922802i	$0.374107\pi$
$13$			311.907i			1.84560i	−0.385274	+	0.922802i	$0.625893\pi$
$14$		0			0
$15$	173.674			0.771886
$16$	−149.310	+	258.612i	−0.583241	+	1.01020i
$17$	61.9673	−	35.7768i	0.214420	−	0.123795i	−0.388944	−	0.921261i	$-0.627160\pi$
$17$	61.9673	−	35.7768i	0.214420	−	0.123795i	0.603364	+	0.797466i	$0.293827\pi$
$18$	65.4838	+	113.421i	0.202111	+	0.350066i
$19$	−241.552	−	139.460i	−0.669119	−	0.386316i	0.126624	−	0.991951i	$-0.459586\pi$
$19$	−241.552	−	139.460i	−0.669119	−	0.386316i	−0.795743	+	0.605635i	$0.792919\pi$
$20$		−	723.499i		−	1.80875i
$21$		0			0
$22$	−312.963			−0.646618
$23$	257.422	−	445.867i	0.486619	−	0.842849i	−0.513262	−	0.858232i	$-0.671563\pi$
$23$	257.422	−	445.867i	0.486619	−	0.842849i	0.999882	+	0.0153823i	$0.00489653\pi$
$24$	−806.035	+	465.365i	−1.39937	+	0.807925i
$25$	−70.2902	−	121.746i	−0.112464	−	0.194794i
$26$	1888.37	+	1090.25i	2.79344	+	1.61279i
$27$			786.989i			1.07955i
$28$		0			0
$29$	866.138			1.02989			0.514945	−	0.857223i	$-0.327812\pi$
$29$	866.138			1.02989			0.514945	+	0.857223i	$0.327812\pi$
$30$	607.066	−	1051.47i	0.674518	−	1.16830i
$31$	591.823	−	341.689i	0.615841	−	0.355556i	−0.159407	−	0.987213i	$-0.550958\pi$
$31$	591.823	−	341.689i	0.615841	−	0.355556i	0.775248	+	0.631657i	$0.217625\pi$
$32$	100.202	+	173.554i	0.0978531	+	0.169487i
$33$	−305.928	−	176.627i	−0.280925	−	0.162192i
$34$		−	500.221i		−	0.432717i
$35$		0			0
$36$	615.830			0.475177
$37$	−972.097	+	1683.72i	−0.710078	+	1.22989i	0.254749	+	0.967007i	$0.418007\pi$
$37$	−972.097	+	1683.72i	−0.710078	+	1.22989i	−0.964827	+	0.262884i	$0.915326\pi$
$38$	−1688.65	+	974.945i	−1.16943	+	0.675169i
$39$	1230.61	+	2131.48i	0.809079	+	1.40137i
$40$	−2248.23	−	1298.01i	−1.40514	−	0.811259i
$41$		−	102.538i		−	0.0609983i	−0.999535	−	0.0304991i	$-0.990290\pi$
$41$		−	102.538i		−	0.0609983i	0.999535	−	0.0304991i	$-0.00970969\pi$
$42$		0			0
$43$	−885.919			−0.479134			−0.239567	−	0.970880i	$-0.577006\pi$
$43$	−885.919			−0.479134			−0.239567	+	0.970880i	$0.577006\pi$
$44$	−735.800	+	1274.44i	−0.380062	+	0.658287i
$45$	−357.088	+	206.165i	−0.176340	+	0.101810i
$46$	−1799.60	−	3116.99i	−0.850471	−	1.47306i
$47$	−2447.98	−	1413.34i	−1.10819	−	0.639812i	−0.169827	−	0.985474i	$-0.554321\pi$
$47$	−2447.98	−	1413.34i	−1.10819	−	0.639812i	−0.938359	+	0.345662i	$0.887654\pi$
$48$			2356.37i			1.02273i
$49$		0			0
$50$	−982.778			−0.393111
$51$	282.310	−	488.976i	0.108539	−	0.187995i
$52$	8879.38	−	5126.52i	3.28380	−	1.89590i
$53$	664.901	+	1151.64i	0.236704	+	0.409983i	0.959766	−	0.280799i	$-0.0905996\pi$
$53$	664.901	+	1151.64i	0.236704	+	0.409983i	−0.723063	+	0.690782i	$0.757266\pi$
$54$	4764.64	+	2750.86i	1.63396	+	0.943369i
$55$		−	985.312i		−	0.325723i
$56$		0			0
$57$	−2200.92			−0.677415
$58$	3027.52	−	5243.82i	0.899977	−	1.55881i
$59$	−4193.07	+	2420.87i	−1.20456	+	0.695452i	−0.961565	−	0.274576i	$-0.911463\pi$
$59$	−4193.07	+	2420.87i	−1.20456	+	0.695452i	−0.242993	+	0.970028i	$0.578129\pi$
$60$	−2854.52	−	4944.17i	−0.792922	−	1.37338i
$61$	340.317	+	196.482i	0.0914585	+	0.0528036i	0.545032	−	0.838415i	$-0.316518\pi$
$61$	340.317	+	196.482i	0.0914585	+	0.0528036i	−0.453573	+	0.891219i	$0.649851\pi$
$62$		−	4777.40i		−	1.24282i
$63$		0			0
$64$	−3376.92			−0.824444
$65$	−3432.47	+	5945.20i	−0.812418	+	1.40715i
$66$	−2138.70	+	1234.78i	−0.490977	+	0.283466i
$67$	−2123.27	−	3677.61i	−0.472994	−	0.819249i	0.526529	−	0.850157i	$-0.323493\pi$
$67$	−2123.27	−	3677.61i	−0.472994	−	0.819249i	−0.999522	+	0.0309083i	$0.990160\pi$
$68$	−2036.99	−	1176.06i	−0.440526	−	0.254338i
$69$		−	4062.56i		−	0.853300i
$70$		0			0
$71$	1188.97			0.235860			0.117930	−	0.993022i	$-0.462374\pi$
$71$	1188.97			0.235860			0.117930	+	0.993022i	$0.462374\pi$
$72$	1104.85	−	1913.65i	0.213126	−	0.369146i
$73$	0.185820	−	0.107283i	3.48695e−5	−	2.01319e-5i	−0.499983	−	0.866035i	$-0.666660\pi$
$73$	0.185820	−	0.107283i	3.48695e−5	−	2.01319e-5i	0.500017	+	0.866015i	$0.333327\pi$
$74$	6795.79	+	11770.7i	1.24101	+	2.14950i
$75$	−960.684	−	554.651i	−0.170788	−	0.0986047i
$76$			9168.67i			1.58737i
$77$		0			0
$78$	17206.0			2.82808
$79$	789.481	−	1367.42i	0.126499	−	0.219103i	−0.795819	−	0.605535i	$-0.792959\pi$
$79$	789.481	−	1367.42i	0.126499	−	0.219103i	0.922318	+	0.386432i	$0.126293\pi$
$80$	−5691.93	+	3286.24i	−0.889364	+	0.513475i
$81$	2346.28	+	4063.88i	0.357611	+	0.619400i
$82$	−620.792	−	358.415i	−0.0923249	−	0.0533038i
$83$			9056.29i			1.31460i	0.753628	+	0.657301i	$0.228302\pi$
$83$			9056.29i			1.31460i	−0.753628	+	0.657301i	$0.771698\pi$
$84$		0			0
$85$	1574.86			0.217974
$86$	−3096.67	+	5363.59i	−0.418695	+	0.725201i
$87$	5918.92	−	3417.29i	0.781995	−	0.451485i
$88$	2640.17	+	4572.90i	0.340931	+	0.590509i
$89$	3018.67	+	1742.83i	0.381097	+	0.220026i	0.678295	−	0.734789i	$-0.262719\pi$
$89$	3018.67	+	1742.83i	0.381097	+	0.220026i	−0.297198	+	0.954816i	$0.596052\pi$
$90$			2882.54i			0.355869i
$91$		0			0
$92$	−16924.0			−1.99952
$93$	2696.23	−	4670.00i	0.311738	−	0.539947i
$94$	−17113.5	+	9880.48i	−1.93679	+	1.11821i
$95$	−3069.45	−	5316.44i	−0.340105	−	0.589079i
$96$	1369.49	+	790.678i	0.148600	+	0.0857940i
$97$		−	7941.40i		−	0.844022i	−0.906591	−	0.422011i	$-0.861324\pi$
$97$		−	7941.40i		−	0.844022i	0.906591	−	0.422011i	$-0.138676\pi$
$98$		0			0
$99$	838.681			0.0855710
$100$	−2310.58	+	4002.05i	−0.231058	+	0.400205i
$101$	499.644	−	288.470i	0.0489799	−	0.0282786i	−0.475310	−	0.879818i	$-0.657664\pi$
$101$	499.644	−	288.470i	0.0489799	−	0.0282786i	0.524290	+	0.851540i	$0.324331\pi$
$102$	−1973.59	−	3418.36i	−0.189695	−	0.328562i
$103$	12415.6	+	7168.17i	1.17029	+	0.675669i	0.953749	−	0.300604i	$-0.0971884\pi$
$103$	12415.6	+	7168.17i	1.17029	+	0.675669i	0.216543	+	0.976273i	$0.430522\pi$
$104$		−	36789.5i		−	3.40140i
$105$		0			0
$106$	9296.45			0.827381
$107$	10610.1	−	18377.3i	0.926730	−	1.60514i	0.137976	−	0.990436i	$-0.455940\pi$
$107$	10610.1	−	18377.3i	0.926730	−	1.60514i	0.788755	−	0.614708i	$-0.210726\pi$
$108$	22404.0	−	12935.0i	1.92079	−	1.10897i
$109$	−4030.73	−	6981.42i	−0.339258	−	0.587612i	0.645035	−	0.764153i	$-0.276843\pi$
$109$	−4030.73	−	6981.42i	−0.339258	−	0.587612i	−0.984293	+	0.176541i	$0.943509\pi$
$110$	−5965.33	−	3444.09i	−0.493003	−	0.284635i
$111$			15341.4i			1.24514i
$112$		0			0
$113$	−4563.77			−0.357410			−0.178705	−	0.983903i	$-0.557191\pi$
$113$	−4563.77			−0.357410			−0.178705	+	0.983903i	$0.557191\pi$
$114$	−7693.16	+	13324.9i	−0.591964	+	1.02531i
$115$	9813.33	−	5665.73i	0.742029	−	0.428411i
$116$	−14235.9	−	24657.2i	−1.05796	−	1.83243i
$117$	−5060.46	−	2921.66i	−0.369673	−	0.213431i
$118$			33847.9i			2.43090i
$119$		0			0
$120$	−20484.9			−1.42256
$121$	6318.44	−	10943.9i	0.431558	−	0.747480i
$122$	2379.11	−	1373.58i	0.159843	−	0.0922855i
$123$	−404.558	−	700.714i	−0.0267405	−	0.0463160i
$124$	−19454.4	−	11232.0i	−1.26525	−	0.730491i
$125$		−	16850.1i		−	1.07840i
$126$		0			0
$127$	21712.4			1.34617			0.673085	−	0.739565i	$-0.264969\pi$
$127$	21712.4			1.34617			0.673085	+	0.739565i	$0.264969\pi$
$128$	−13407.0	+	23221.6i	−0.818299	+	1.41734i
$129$	−6054.10	+	3495.34i	−0.363806	+	0.210044i
$130$	23995.9	+	41562.1i	1.41987	+	2.45929i
$131$	−234.269	−	135.255i	−0.0136512	−	0.00788154i	0.493159	−	0.869939i	$-0.335842\pi$
$131$	−234.269	−	135.255i	−0.0136512	−	0.00788154i	−0.506810	+	0.862058i	$0.669175\pi$
$132$			11612.2i			0.666449i
$133$		0			0
$134$	−29686.9			−1.65332
$135$	−8660.63	+	15000.7i	−0.475206	+	0.823081i
$136$	−7309.05	+	4219.88i	−0.395169	+	0.228151i
$137$	4107.78	+	7114.89i	0.218860	+	0.379076i	0.954460	−	0.298340i	$-0.0964329\pi$
$137$	4107.78	+	7114.89i	0.218860	+	0.379076i	−0.735600	+	0.677416i	$0.763100\pi$
$138$	−24595.8	−	14200.4i	−1.29153	−	0.745662i
$139$		−	11669.2i		−	0.603962i	−0.953314	−	0.301981i	$-0.902352\pi$
$139$		−	11669.2i		−	0.603962i	0.953314	−	0.301981i	$-0.0976480\pi$
$140$		0			0
$141$	−22305.0			−1.12193
$142$	4155.95	−	7198.32i	0.206108	−	0.356989i
$143$	12092.6	−	6981.65i	0.591353	−	0.341418i
$144$	−2797.19	−	4844.87i	−0.134895	−	0.233646i
$145$	16509.3	+	9531.64i	0.785222	+	0.453348i
$146$		−	1.50000i		−	7.03698e-5i
$147$		0			0
$148$	63909.7			2.91772
$149$	−14153.8	+	24515.2i	−0.637531	+	1.10424i	0.348442	+	0.937331i	$0.386711\pi$
$149$	−14153.8	+	24515.2i	−0.637531	+	1.10424i	−0.985973	+	0.166906i	$0.946622\pi$
$150$	−6716.00	+	3877.49i	−0.298489	+	0.172333i
$151$	−11067.6	−	19169.7i	−0.485401	−	0.840739i	0.514458	−	0.857515i	$-0.327993\pi$
$151$	−11067.6	−	19169.7i	−0.485401	−	0.840739i	−0.999859	+	0.0167763i	$0.994660\pi$
$152$	28491.1	+	16449.3i	1.23317	+	0.711969i
$153$			1340.50i			0.0572641i
$154$		0			0
$155$	15040.8			0.626049
$156$	40452.7	−	70066.1i	1.66226	−	2.87911i
$157$	−38375.0	+	22155.8i	−1.55686	+	0.898852i	−0.559303	+	0.828964i	$0.688931\pi$
$157$	−38375.0	+	22155.8i	−1.55686	+	0.898852i	−0.997555	+	0.0698885i	$0.977736\pi$
$158$	−5519.15	−	9559.45i	−0.221084	−	0.382929i
$159$	9087.46	+	5246.65i	0.359458	+	0.207533i
$160$			4410.78i			0.172296i
$161$		0			0
$162$	32805.1			1.25000
$163$	12810.8	−	22189.0i	0.482173	−	0.835148i	−0.517618	−	0.855612i	$-0.673181\pi$
$163$	12810.8	−	22189.0i	0.482173	−	0.835148i	0.999791	+	0.0204642i	$0.00651440\pi$
$164$	−2919.06	+	1685.32i	−0.108531	+	0.0626606i
$165$	−3887.49	−	6733.32i	−0.142791	−	0.247321i
$166$	54829.1	+	31655.6i	1.98973	+	1.14877i
$167$			5822.23i			0.208764i	0.994537	+	0.104382i	$0.0332865\pi$
$167$			5822.23i			0.208764i	−0.994537	+	0.104382i	$0.966713\pi$
$168$		0			0
$169$	−68725.1			−2.40626
$170$	5504.82	−	9534.62i	0.190478	−	0.329918i
$171$	4525.27	−	2612.66i	0.154758	−	0.0893493i
$172$	14561.0	+	25220.4i	0.492192	+	0.852501i
$173$	−34244.4	−	19771.0i	−1.14419	−	0.660596i	−0.196723	−	0.980459i	$-0.563030\pi$
$173$	−34244.4	−	19771.0i	−1.14419	−	0.660596i	−0.947464	+	0.319863i	$0.896363\pi$
$174$		−	47779.6i		−	1.57813i
$175$		0			0
$176$	13368.4			0.431574
$177$	−19102.8	+	33087.0i	−0.609747	+	1.05611i
$178$	21103.1	−	12183.9i	0.666049	−	0.384543i
$179$	24041.6	+	41641.2i	0.750338	+	1.29962i	0.947659	+	0.319285i	$0.103443\pi$
$179$	24041.6	+	41641.2i	0.750338	+	1.29962i	−0.197321	+	0.980339i	$0.563224\pi$
$180$	11738.2	+	6777.06i	0.362291	+	0.209169i
$181$		−	47562.9i		−	1.45181i	−0.687793	−	0.725907i	$-0.741420\pi$
$181$		−	47562.9i		−	1.45181i	0.687793	−	0.725907i	$-0.258580\pi$
$182$		0			0
$183$	3100.83			0.0925925
$184$	−30362.9	+	52590.1i	−0.896825	+	1.55335i
$185$	−37057.9	+	21395.4i	−1.08277	+	0.625139i
$186$	−18848.9	−	32647.3i	−0.544829	−	0.943672i
$187$	−2774.12	−	1601.64i	−0.0793309	−	0.0458017i
$188$			92919.0i			2.62899i
$189$		0			0
$190$	−42916.2			−1.18881
$191$	−4912.84	+	8509.29i	−0.134668	+	0.233253i	−0.925471	−	0.378819i	$-0.876330\pi$
$191$	−4912.84	+	8509.29i	−0.134668	+	0.233253i	0.790802	+	0.612072i	$0.209664\pi$
$192$	−23076.9	+	13323.4i	−0.626000	+	0.361421i
$193$	4867.31	+	8430.43i	0.130670	+	0.226326i	0.923935	−	0.382550i	$-0.124954\pi$
$193$	4867.31	+	8430.43i	0.130670	+	0.226326i	−0.793265	+	0.608876i	$0.791621\pi$
$194$	−48079.3	−	27758.6i	−1.27748	−	0.737555i
$195$			54170.3i			1.42460i
$196$		0			0
$197$	58038.9			1.49550			0.747750	−	0.663981i	$-0.231134\pi$
$197$	58038.9			1.49550			0.747750	+	0.663981i	$0.231134\pi$
$198$	2931.55	−	5077.59i	0.0747768	−	0.129517i
$199$	54183.8	−	31283.0i	1.36824	−	0.789955i	0.377539	−	0.925994i	$-0.376770\pi$
$199$	54183.8	−	31283.0i	1.36824	−	0.789955i	0.990704	+	0.136039i	$0.0434371\pi$
$200$	8290.74	+	14360.0i	0.207269	+	0.359000i
$201$	−29019.5	−	16754.4i	−0.718288	−	0.414704i
$202$		−	4033.30i		−	0.0988458i
$203$		0			0
$204$	−18560.2			−0.445988
$205$	1128.41	−	1954.46i	0.0268509	−	0.0465071i
$206$	86795.9	−	50111.6i	2.04534	−	1.18088i
$207$	4822.57	+	8352.94i	0.112548	+	0.194939i
$208$	−80662.9	−	46570.8i	−1.86444	−	1.07643i
$209$			12486.6i			0.285858i
$210$		0			0
$211$	26674.3			0.599140			0.299570	−	0.954074i	$-0.403157\pi$
$211$	26674.3			0.599140			0.299570	+	0.954074i	$0.403157\pi$
$212$	21856.7	−	37856.9i	0.486309	−	0.842312i
$213$	8125.05	−	4691.00i	0.179088	−	0.103397i
$214$	−74173.9	−	128473.i	−1.61966	−	2.80533i
$215$	−16886.3	−	9749.34i	−0.365308	−	0.210910i
$216$		−	92825.5i		−	1.98957i
$217$		0			0
$218$	−56356.4			−1.18585
$219$	0.846557	−	1.46628i	1.76510e−5	−	3.05723e-5i
$220$	−28049.9	+	16194.6i	−0.579543	+	0.334600i
$221$	11159.0	+	19328.0i	0.228477	+	0.395734i
$222$	92880.7	+	53624.7i	1.88460	+	1.08808i
$223$			21285.7i			0.428035i	0.976830	+	0.214017i	$0.0686549\pi$
$223$			21285.7i			0.428035i	−0.976830	+	0.214017i	$0.931345\pi$
$224$		0			0
$225$	2633.65			0.0520228
$226$	−15952.3	+	27630.3i	−0.312326	+	0.540964i
$227$	−18678.4	+	10784.0i	−0.362483	+	0.209280i	−0.670169	−	0.742208i	$-0.733779\pi$
$227$	−18678.4	+	10784.0i	−0.362483	+	0.209280i	0.307686	+	0.951488i	$0.400445\pi$
$228$	36174.4	+	62655.9i	0.695876	+	1.20529i
$229$	17253.3	+	9961.17i	0.329003	+	0.189950i	0.655398	−	0.755283i	$-0.272501\pi$
$229$	17253.3	+	9961.17i	0.329003	+	0.189950i	−0.326395	+	0.945233i	$0.605834\pi$
$230$		−	79216.6i		−	1.49748i
$231$		0			0
$232$	−102161.			−1.89806
$233$	−2013.92	+	3488.22i	−0.0370964	+	0.0642528i	−0.883977	−	0.467529i	$-0.845144\pi$
$233$	−2013.92	+	3488.22i	−0.0370964	+	0.0642528i	0.846881	+	0.531782i	$0.178478\pi$
$234$	−35376.9	+	20424.9i	−0.646083	+	0.373016i
$235$	−31107.0	−	53879.0i	−0.563278	−	0.975626i
$236$	137835.	+	79579.0i	2.47477	+	1.42881i
$237$		−	12459.4i		−	0.221820i
$238$		0			0
$239$	35321.2			0.618358			0.309179	−	0.951004i	$-0.399946\pi$
$239$	35321.2			0.618358			0.309179	+	0.951004i	$0.399946\pi$
$240$	−25931.3	+	44914.3i	−0.450196	+	0.779762i
$241$	68620.0	−	39617.7i	1.18145	−	0.682112i	0.225102	−	0.974335i	$-0.427728\pi$
$241$	68620.0	−	39617.7i	1.18145	−	0.682112i	0.956350	+	0.292223i	$0.0943950\pi$
$242$	−44171.3	−	76506.9i	−0.754239	−	1.30638i
$243$	−23138.2	−	13358.8i	−0.391848	−	0.226233i
$244$		−	12917.5i		−	0.216970i
$245$		0			0
$246$	−5656.41			−0.0934696
$247$	43498.6	−	75341.7i	0.712986	−	1.23493i
$248$	−69805.6	+	40302.3i	−1.13498	+	0.655279i
$249$	35731.0	+	61887.9i	0.576297	+	0.998176i
$250$	−102015.	−	58898.2i	−1.63223	−	0.942371i
$251$			100747.i			1.59914i	0.600575	+	0.799569i	$0.294939\pi$
$251$			100747.i			1.59914i	−0.600575	+	0.799569i	$0.705061\pi$
$252$		0			0
$253$	−23048.3			−0.360078
$254$	75894.0	−	131452.i	1.17636	−	2.03751i
$255$	10762.1	−	6213.52i	0.165508	−	0.0955558i
$256$	66711.1	+	115547.i	1.01793	+	1.76311i
$257$	42453.8	+	24510.7i	0.642763	+	0.371099i	0.785678	−	0.618636i	$-0.212314\pi$
$257$	42453.8	+	24510.7i	0.642763	+	0.371099i	−0.142915	+	0.989735i	$0.545648\pi$
$258$			48870.8i			0.734193i
$259$		0			0
$260$	225664.			3.33823
$261$	−8113.17	+	14052.4i	−0.119099	+	0.206286i
$262$	−1637.74	+	945.549i	−0.0238585	+	0.0137747i
$263$	1435.46	+	2486.30i	0.0207530	+	0.0359453i	0.876215	−	0.481920i	$-0.160060\pi$
$263$	1435.46	+	2486.30i	0.0207530	+	0.0359453i	−0.855462	+	0.517865i	$0.826727\pi$
$264$	36084.2	+	20833.2i	0.517737	+	0.298916i
$265$			29268.3i			0.416779i
$266$		0			0
$267$	27504.9			0.385822
$268$	−69796.2	+	120891.i	−0.971767	+	1.68315i
$269$	−40644.7	+	23466.2i	−0.561693	+	0.324294i	−0.753825	−	0.657076i	$-0.771793\pi$
$269$	−40644.7	+	23466.2i	−0.561693	+	0.324294i	0.192132	+	0.981369i	$0.438460\pi$
$270$	60545.2	+	104867.i	0.830525	+	1.43851i
$271$	−50712.6	−	29278.9i	−0.690521	−	0.398673i	0.113286	−	0.993562i	$-0.463862\pi$
$271$	−50712.6	−	29278.9i	−0.690521	−	0.398673i	−0.803807	+	0.594890i	$0.797196\pi$
$272$			21367.3i			0.288810i
$273$		0			0
$274$	57433.8			0.765009
$275$	−3146.72	+	5450.28i	−0.0416095	+	0.0720698i
$276$	−115653.	+	66772.4i	−1.51824	+	0.876554i
$277$	−29810.0	−	51632.4i	−0.388510	−	0.672919i	0.603739	−	0.797182i	$-0.293677\pi$
$277$	−29810.0	−	51632.4i	−0.388510	−	0.672919i	−0.992249	+	0.124263i	$0.960343\pi$
$278$	−70648.1	−	40788.7i	−0.914136	−	0.527777i
$279$			12802.5i			0.164470i
$280$		0			0
$281$	−47369.7			−0.599912			−0.299956	−	0.953953i	$-0.596972\pi$
$281$	−47369.7			−0.599912			−0.299956	+	0.953953i	$0.596972\pi$
$282$	−77965.6	+	135040.i	−0.980404	+	1.69811i
$283$	−81975.3	+	47328.5i	−1.02355	+	0.590949i	−0.915131	−	0.403156i	$-0.867913\pi$
$283$	−81975.3	+	47328.5i	−1.02355	+	0.590949i	−0.108422	+	0.994105i	$0.534580\pi$
$284$	−19541.9	−	33847.6i	−0.242287	−	0.419654i
$285$	−41951.4	−	24220.6i	−0.516483	−	0.298192i
$286$		−	97615.4i		−	1.19340i
$287$		0			0
$288$	−3754.38			−0.0452640
$289$	−39200.5	+	67897.3i	−0.469349	+	0.812937i
$290$	115414.	−	66634.3i	1.37234	−	0.792323i
$291$	−31332.3	−	54269.1i	−0.370004	−	0.640866i
$292$	−6.10828	−	3.52662i	−7.16396e−5	−	4.13612e-5i
$293$		−	73528.8i		−	0.856490i	−0.903663	−	0.428245i	$-0.859132\pi$
$293$		−	73528.8i		−	0.856490i	0.903663	−	0.428245i	$-0.140868\pi$
$294$		0			0
$295$	−106564.			−1.22453
$296$	114659.	−	198595.i	1.30865	−	2.26665i
$297$	30511.4	−	17615.8i	0.345899	−	0.199705i
$298$	98947.4	+	171382.i	1.11422	+	1.92989i
$299$	139069.	+	80291.6i	1.55557	+	0.898107i
$300$			36465.1i			0.405167i
$301$		0			0
$302$	−154744.			−1.69668
$303$	2276.28	−	3942.63i	0.0247936	−	0.0429438i
$304$	72132.1	−	41645.5i	0.780515	−	0.450630i
$305$	4324.48	+	7490.22i	0.0464873	+	0.0805183i
$306$	8115.71	+	4685.61i	0.0866730	+	0.0500407i
$307$		−	117853.i		−	1.25045i	−0.780445	−	0.625224i	$-0.785008\pi$
$307$		−	117853.i		−	1.25045i	0.780445	−	0.625224i	$-0.214992\pi$
$308$		0			0
$309$	113126.			1.18480
$310$	52574.2	−	91061.1i	0.547078	−	0.947566i
$311$	−3740.82	+	2159.77i	−0.0386764	+	0.0223298i	−0.519214	−	0.854645i	$-0.673775\pi$
$311$	−3740.82	+	2159.77i	−0.0386764	+	0.0223298i	0.480537	+	0.876974i	$0.340442\pi$
$312$	−145151.	−	251408.i	−1.49111	−	2.58268i
$313$	103292.	+	59635.5i	1.05433	+	0.608718i	0.923859	−	0.382734i	$-0.125017\pi$
$313$	103292.	+	59635.5i	1.05433	+	0.608718i	0.130472	+	0.991452i	$0.458351\pi$
$314$			309776.i			3.14187i
$315$		0			0
$316$	−51903.8			−0.519786
$317$	6999.30	−	12123.1i	0.0696524	−	0.120641i	−0.829096	−	0.559106i	$-0.811144\pi$
$317$	6999.30	−	12123.1i	0.0696524	−	0.120641i	0.898748	+	0.438465i	$0.144478\pi$
$318$	63529.1	−	36678.6i	0.628230	−	0.362709i
$319$	−19387.4	−	33580.0i	−0.190519	−	0.329989i
$320$	−64366.9	−	37162.2i	−0.628583	−	0.362912i
$321$		−	167446.i		−	1.62505i
$322$		0			0
$323$	−19957.7			−0.191296
$324$	77127.2	−	133588.i	0.734712	−	1.27256i
$325$	37973.5	−	21924.0i	0.359513	−	0.207565i
$326$	−89558.8	−	155120.i	−0.842700	−	1.45960i
$327$	−55089.5	−	31805.9i	−0.515197	−	0.297449i
$328$			12094.4i			0.112418i
$329$		0			0
$330$	−54353.7			−0.499116
$331$	−15376.5	+	26632.8i	−0.140346	+	0.243087i	−0.927627	−	0.373508i	$-0.878155\pi$
$331$	−15376.5	+	26632.8i	−0.140346	+	0.243087i	0.787281	+	0.616595i	$0.211488\pi$
$332$	257815.	−	148849.i	2.33901	−	1.35043i
$333$	−18211.4	−	31543.1i	−0.164231	−	0.284456i
$334$	35249.3	+	20351.2i	0.315978	+	0.182430i
$335$		−	93464.3i		−	0.832830i
$336$		0			0
$337$	−22396.7			−0.197208			−0.0986040	−	0.995127i	$-0.531438\pi$
$337$	−22396.7			−0.197208			−0.0986040	+	0.995127i	$0.531438\pi$
$338$	−240223.	+	416079.i	−2.10272	+	3.64202i
$339$	−31187.4	+	18006.1i	−0.271382	+	0.156682i
$340$	−25884.5	−	44833.2i	−0.223914	−	0.387831i
$341$	−26494.4	−	15296.6i	−0.227848	−	0.131548i
$342$		−	36529.5i		−	0.312314i
$343$		0			0
$344$	104494.			0.883031
$345$	44707.6	−	77435.8i	0.375615	−	0.650584i
$346$	−239397.	+	138216.i	−1.99971	+	1.15453i
$347$	106902.	+	185159.i	0.887820	+	1.53775i	0.842447	+	0.538780i	$0.181115\pi$
$347$	106902.	+	185159.i	0.887820	+	1.53775i	0.0453739	+	0.998970i	$0.485552\pi$
$348$	−194567.	−	112333.i	−1.60661	−	0.927578i
$349$			63672.4i			0.522758i	0.965236	+	0.261379i	$0.0841772\pi$
$349$			63672.4i			0.522758i	−0.965236	+	0.261379i	$0.915823\pi$
$350$		0			0
$351$	−245468.			−1.99242
$352$	4485.77	−	7769.59i	0.0362036	−	0.0627065i
$353$	−121927.	+	70394.8i	−0.978480	+	0.564926i	−0.901811	−	0.432131i	$-0.857762\pi$
$353$	−121927.	+	70394.8i	−0.978480	+	0.564926i	−0.0766693	+	0.997057i	$0.524429\pi$
$354$	133545.	+	231306.i	1.06566	+	1.84578i
$355$	22662.7	+	13084.3i	0.179827	+	0.103823i
$356$		−	114581.i		−	0.904090i
$357$		0			0
$358$	336142.			2.62275
$359$	18382.6	−	31839.5i	0.142632	−	0.247046i	−0.785855	−	0.618411i	$-0.787777\pi$
$359$	18382.6	−	31839.5i	0.142632	−	0.247046i	0.928487	+	0.371365i	$0.121110\pi$
$360$	42118.6	−	24317.2i	0.324989	−	0.187633i
$361$	−26262.3	−	45487.7i	−0.201520	−	0.349043i
$362$	−287958.	−	166253.i	−2.19741	−	1.26868i
$363$		−	99715.9i		−	0.756748i
$364$		0			0
$365$	4.72250			3.54476e−5
$366$	10838.7	−	18773.2i	0.0809126	−	0.140145i
$367$	21449.9	−	12384.1i	0.159255	−	0.0919459i	−0.418255	−	0.908330i	$-0.637358\pi$
$367$	21449.9	−	12384.1i	0.159255	−	0.0919459i	0.577509	+	0.816384i	$0.304025\pi$
$368$	76871.1	+	133145.i	0.567633	+	0.983169i
$369$	1663.60	+	960.482i	0.0122179	+	0.00705402i
$370$			299144.i			2.18513i
$371$		0			0
$372$	−177261.			−1.28094
$373$	16096.3	−	27879.6i	0.115693	−	0.200387i	−0.802363	−	0.596836i	$-0.796424\pi$
$373$	16096.3	−	27879.6i	0.115693	−	0.200387i	0.918057	+	0.396449i	$0.129758\pi$
$374$	−19393.5	+	11196.8i	−0.138648	+	0.0800482i
$375$	−66480.9	−	115148.i	−0.472753	−	0.818832i
$376$	288740.	+	166704.i	2.04236	+	1.17915i
$377$			270154.i			1.90077i
$378$		0			0
$379$	187516.			1.30545			0.652726	−	0.757594i	$-0.273625\pi$
$379$	187516.			1.30545			0.652726	+	0.757594i	$0.273625\pi$
$380$	−100899.	+	174762.i	−0.698747	+	1.21027i
$381$	148376.	−	85664.8i	1.02215	−	0.590136i
$382$	34345.0	+	59487.2i	0.235362	+	0.407659i
$383$	−22205.2	−	12820.2i	−0.151376	−	0.0873972i	0.422399	−	0.906410i	$-0.361188\pi$
$383$	−22205.2	−	12820.2i	−0.151376	−	0.0873972i	−0.573775	+	0.819013i	$0.694522\pi$
$384$			211586.i			1.43491i
$385$		0			0
$386$	68053.4			0.456746
$387$	8298.47	−	14373.4i	0.0554085	−	0.0959703i
$388$	−226076.	+	130525.i	−1.50173	+	0.867023i
$389$	−36228.0	−	62748.7i	−0.239412	−	0.414673i	0.721134	−	0.692796i	$-0.243621\pi$
$389$	−36228.0	−	62748.7i	−0.239412	−	0.414673i	−0.960546	+	0.278123i	$0.910288\pi$
$390$	327961.	+	189348.i	2.15622	+	1.24489i
$391$		−	36838.9i		−	0.240965i
$392$		0			0
$393$	−2134.56			−0.0138205
$394$	202871.	−	351382.i	1.30685	−	2.26354i
$395$	30096.3	−	17376.1i	0.192894	−	0.111368i
$396$	−13784.6	−	23875.6i	−0.0879029	−	0.152252i
$397$	110506.	+	63800.7i	0.701140	+	0.404803i	0.807772	−	0.589495i	$-0.200673\pi$
$397$	110506.	+	63800.7i	0.701140	+	0.404803i	−0.106632	+	0.994299i	$0.534007\pi$
$398$		−	437390.i		−	2.76123i
$399$		0			0
$400$	41980.1			0.262375
$401$	69224.8	−	119901.i	0.430500	−	0.745648i	−0.566416	−	0.824119i	$-0.691671\pi$
$401$	69224.8	−	119901.i	0.430500	−	0.745648i	0.996916	+	0.0784714i	$0.0250039\pi$
$402$	−202871.	+	117128.i	−1.25536	+	0.724783i
$403$	106575.	+	184594.i	0.656215	+	1.13660i
$404$	−16424.3	−	9482.60i	−0.100629	−	0.0580985i
$405$			103281.i			0.629667i
$406$		0			0
$407$	87036.7			0.525428
$408$	−33298.5	+	57674.8i	−0.200035	+	0.346470i
$409$	66455.9	−	38368.3i	0.397271	−	0.229365i	−0.288035	−	0.957620i	$-0.593002\pi$
$409$	66455.9	−	38368.3i	0.397271	−	0.229365i	0.685306	+	0.728255i	$0.259669\pi$
$410$	−7888.54	−	13663.4i	−0.0469277	−	0.0812811i
$411$	56142.7	+	32414.0i	0.332360	+	0.191888i
$412$		−	471265.i		−	2.77633i
$413$		0			0
$414$	67427.8			0.393404
$415$	−99662.3	+	172620.i	−0.578675	+	1.00229i
$416$	−54132.8	+	31253.6i	−0.312805	+	0.180598i
$417$	−46039.9	−	79743.5i	−0.264766	−	0.458588i
$418$	75596.8	+	43645.8i	0.432664	+	0.249799i
$419$		−	179909.i		−	1.02476i	−0.858757	−	0.512382i	$-0.828763\pi$
$419$		−	179909.i		−	1.02476i	0.858757	−	0.512382i	$-0.171237\pi$
$420$		0			0
$421$	−6114.46			−0.0344980			−0.0172490	−	0.999851i	$-0.505491\pi$
$421$	−6114.46			−0.0344980			−0.0172490	+	0.999851i	$0.505491\pi$
$422$	93238.1	−	161493.i	0.523563	−	0.906837i
$423$	45860.9	−	26477.8i	0.256308	−	0.147979i
$424$	−78425.2	−	135836.i	−0.436238	−	0.755587i
$425$	−8711.39	−	5029.52i	−0.0482291	−	0.0278451i
$426$		−	65588.2i		−	0.361415i
$427$		0			0
$428$	−697554.			−3.80794
$429$	55091.3	−	95421.0i	0.299343	−	0.518477i
$430$	−118050.	+	68156.2i	−0.638453	+	0.368611i
$431$	−112648.	−	195112.i	−0.606412	−	1.05034i	−0.991827	−	0.127593i	$-0.959275\pi$
$431$	−112648.	−	195112.i	−0.606412	−	1.05034i	0.385414	−	0.922744i	$-0.374058\pi$
$432$	−203525.	−	117505.i	−1.09056	−	0.629636i
$433$			291349.i			1.55395i	0.629531	+	0.776976i	$0.283247\pi$
$433$			291349.i			1.55395i	−0.629531	+	0.776976i	$0.716753\pi$
$434$		0			0
$435$	150426.			0.794958
$436$	−132498.	+	229494.i	−0.697007	+	1.20725i
$437$	−124361.	+	71800.0i	−0.651212	+	0.375977i
$438$	−5.91816	−	10.2506i	−3.08488e−5	−	5.34317e-5i
$439$	−234560.	−	135424.i	−1.21710	−	0.702692i	−0.252802	−	0.967518i	$-0.581352\pi$
$439$	−234560.	−	135424.i	−1.21710	−	0.702692i	−0.964296	+	0.264826i	$0.914686\pi$
$440$			116218.i			0.600298i
$441$		0			0
$442$	156023.			0.798625
$443$	−31592.2	+	54719.2i	−0.160980	+	0.278825i	−0.935220	−	0.354066i	$-0.884799\pi$
$443$	−31592.2	+	54719.2i	−0.160980	+	0.278825i	0.774240	+	0.632892i	$0.218132\pi$
$444$	436739.	−	252151.i	2.21542	−	1.27907i
$445$	38358.9	+	66439.5i	0.193707	+	0.335511i
$446$	128869.	+	74402.8i	0.647858	+	0.374041i
$447$			223372.i			1.11793i
$448$		0			0
$449$	328951.			1.63169			0.815846	−	0.578269i	$-0.196272\pi$
$449$	328951.			1.63169			0.815846	+	0.578269i	$0.196272\pi$
$450$	9205.75	−	15944.8i	0.0454605	−	0.0787399i
$451$	−3975.38	+	2295.19i	−0.0195446	+	0.0112841i
$452$	75010.3	+	129922.i	0.367151	+	0.635923i
$453$	−151266.	−	87333.2i	−0.737129	−	0.425582i
$454$			150778.i			0.731522i
$455$		0			0
$456$	259599.			1.24846
$457$	15613.7	−	27043.7i	0.0747607	−	0.129489i	−0.826222	−	0.563345i	$-0.809514\pi$
$457$	15613.7	−	27043.7i	0.0747607	−	0.129489i	0.900982	+	0.433856i	$0.142847\pi$
$458$	120615.	−	69637.1i	0.575003	−	0.331978i
$459$	28156.0	+	48767.6i	0.133643	+	0.231476i
$460$	−322584.	−	186244.i	−1.52450	−	0.880171i
$461$			193095.i			0.908591i	0.890851	+	0.454296i	$0.150109\pi$
$461$			193095.i			0.908591i	−0.890851	+	0.454296i	$0.849891\pi$
$462$		0			0
$463$	−246667.			−1.15067			−0.575333	−	0.817919i	$-0.695127\pi$
$463$	−246667.			−1.15067			−0.575333	+	0.817919i	$0.695127\pi$
$464$	−129323.	+	223994.i	−0.600674	+	1.04040i
$465$	102784.	−	59342.7i	0.475359	−	0.274449i
$466$	14079.1	+	24385.6i	0.0648338	+	0.112295i
$467$	289328.	+	167043.i	1.32665	+	0.765942i	0.984780	−	0.173806i	$-0.0556065\pi$
$467$	289328.	+	167043.i	1.32665	+	0.765942i	0.341870	+	0.939747i	$0.388940\pi$
$468$			192082.i			0.876989i
$469$		0			0
$470$	−434930.			−1.96890
$471$	−174829.	+	302812.i	−0.788081	+	1.36500i
$472$	494573.	−	285542.i	2.21997	−	1.28170i
$473$	19830.2	+	34346.9i	0.0886349	+	0.153520i
$474$	−75432.4	−	43550.9i	−0.335739	−	0.193839i
$475$			39210.7i			0.173787i
$476$		0			0
$477$	−24912.7			−0.109492
$478$	123463.	−	213844.i	0.540356	−	0.935924i
$479$	−130274.	+	75214.0i	−0.567790	+	0.327814i	−0.756266	−	0.654264i	$-0.772979\pi$
$479$	−130274.	+	75214.0i	−0.567790	+	0.327814i	0.188476	+	0.982078i	$0.439645\pi$
$480$	17402.4	+	30141.9i	0.0755314	+	0.130824i
$481$	−525165.	−	303204.i	−2.26989	−	1.31052i
$482$		−	553924.i		−	2.38427i
$483$		0			0
$484$	−415400.			−1.77327
$485$	87393.3	−	151370.i	0.371531	−	0.643510i
$486$	−161756.	+	93389.8i	−0.684837	+	0.395391i
$487$	140032.	+	242542.i	0.590429	+	1.02265i	0.994175	+	0.107782i	$0.0343750\pi$
$487$	140032.	+	242542.i	0.590429	+	1.02265i	−0.403745	+	0.914872i	$0.632292\pi$
$488$	−40140.4	−	23175.1i	−0.168555	−	0.0973154i
$489$		−	202178.i		−	0.845503i
$490$		0			0
$491$	−227539.			−0.943829			−0.471914	−	0.881644i	$-0.656437\pi$
$491$	−227539.			−0.943829			−0.471914	+	0.881644i	$0.656437\pi$
$492$	−13298.6	+	23033.9i	−0.0549385	+	0.0951564i
$493$	53672.2	−	30987.7i	0.220829	−	0.127495i
$494$	−304092.	−	526703.i	−1.24610	−	2.15830i
$495$	15985.9	+	9229.49i	0.0652421	+	0.0376675i
$496$			204070.i			0.829499i
$497$		0			0
$498$	499581.			2.01441
$499$	−115300.	+	199705.i	−0.463049	+	0.802025i	−0.999111	−	0.0421540i	$-0.986578\pi$
$499$	−115300.	+	199705.i	−0.463049	+	0.802025i	0.536062	+	0.844179i	$0.319911\pi$
$500$	−479688.	+	276948.i	−1.91875	+	1.10779i
$501$	22971.2	+	39787.3i	0.0915185	+	0.158515i
$502$	609950.	+	352155.i	2.42040	+	1.39742i
$503$		−	434537.i		−	1.71748i	−0.512415	−	0.858738i	$-0.671249\pi$
$503$		−	434537.i		−	1.71748i	0.512415	−	0.858738i	$-0.328751\pi$
$504$		0			0
$505$	12698.2			0.0497919
$506$	−80563.5	+	139540.i	−0.314657	+	0.545002i
$507$	−469646.	+	271150.i	−1.82707	+	1.05486i
$508$	−356865.	−	618109.i	−1.38286	−	2.39518i
$509$	196800.	+	113622.i	0.759606	+	0.438559i	0.829154	−	0.559020i	$-0.188822\pi$
$509$	196800.	+	113622.i	0.759606	+	0.438559i	−0.0695482	+	0.997579i	$0.522156\pi$
$510$		−	86875.6i		−	0.334009i
$511$		0			0
$512$	503711.			1.92151
$513$	109754.	−	190099.i	0.417046	−	0.722344i
$514$	296789.	−	171351.i	1.12337	−	0.648575i
$515$	157768.	+	273262.i	0.594846	+	1.03030i
$516$	199011.	+	114899.i	0.747442	+	0.431536i
$517$			126544.i			0.473434i
$518$		0			0
$519$	−312021.			−1.15837
$520$	404860.	−	701238.i	1.49726	−	2.59333i
$521$	206209.	−	119055.i	0.759683	−	0.438603i	−0.0694987	−	0.997582i	$-0.522140\pi$
$521$	206209.	−	119055.i	0.759683	−	0.438603i	0.829182	+	0.558979i	$0.188807\pi$
$522$	56718.0	+	98238.5i	0.208152	+	0.360529i
$523$	−172592.	−	99646.0i	−0.630982	−	0.364298i	0.150150	−	0.988663i	$-0.452024\pi$
$523$	−172592.	−	99646.0i	−0.630982	−	0.364298i	−0.781132	+	0.624366i	$0.785358\pi$
$524$			8892.23i			0.0323853i
$525$		0			0
$526$	20070.3			0.0725406
$527$	24449.1	−	42347.1i	0.0880322	−	0.152476i
$528$	91355.9	−	52744.4i	0.327694	−	0.189194i
$529$	7388.68	+	12797.6i	0.0264032	+	0.0457316i
$530$	177198.	+	102305.i	0.630822	+	0.364205i
$531$		−	90705.8i		−	0.321696i
$532$		0			0
$533$	31982.4			0.112579
$534$	96141.4	−	166522.i	0.337154	−	0.583967i
$535$	404476.	−	233524.i	1.41314	−	0.815876i
$536$	250440.	+	433775.i	0.871714	+	1.50985i
$537$	328586.	+	189709.i	1.13946	+	0.657869i
$538$			328098.i			1.13354i
$539$		0			0
$540$	569386.			1.95263
$541$	−139832.	+	242195.i	−0.477761	+	0.827506i	−0.999675	−	0.0254918i	$-0.991885\pi$
$541$	−139832.	+	242195.i	−0.477761	+	0.827506i	0.521914	+	0.852998i	$0.325218\pi$
$542$	−354524.	+	204685.i	−1.20683	+	0.696766i
$543$	−187656.	−	325030.i	−0.636448	−	1.10236i
$544$	12418.4	+	7169.79i	0.0419632	+	0.0242275i
$545$		−	177429.i		−	0.597353i
$546$		0			0
$547$	322945.			1.07933			0.539664	−	0.841881i	$-0.318551\pi$
$547$	322945.			1.07933			0.539664	+	0.841881i	$0.318551\pi$
$548$	135031.	−	233881.i	0.449649	−	0.778814i
$549$	−6375.55	+	3680.92i	−0.0211530	+	0.0122127i
$550$	21998.3	+	38102.1i	0.0727215	+	0.125957i
$551$	−209217.	−	120792.i	−0.689119	−	0.397863i
$552$			479180.i			1.57261i
$553$		0			0
$554$	−416795.			−1.35801
$555$	−168828.	+	292419.i	−0.548099	+	0.949336i
$556$	−332198.	+	191795.i	−1.07460	+	0.620422i
$557$	204004.	+	353346.i	0.657551	+	1.13891i	0.981248	+	0.192751i	$0.0617408\pi$
$557$	204004.	+	353346.i	0.657551	+	1.13891i	−0.323697	+	0.946161i	$0.604926\pi$
$558$	77509.7	+	44750.2i	0.248936	+	0.143723i
$559$		−	276325.i		−	0.884292i
$560$		0			0
$561$	−25276.7			−0.0803145
$562$	−165577.	+	286788.i	−0.524237	+	0.908006i
$563$	−502811.	+	290298.i	−1.58631	+	0.915856i	−0.592401	+	0.805643i	$0.701820\pi$
$563$	−502811.	+	290298.i	−1.58631	+	0.915856i	−0.993908	+	0.110213i	$0.964847\pi$
$564$	366606.	+	634980.i	1.15250	+	1.99619i
$565$	−86989.2	−	50223.3i	−0.272501	−	0.157329i
$566$			661733.i			2.06562i
$567$		0			0
$568$	−140239.			−0.434682
$569$	−168768.	+	292314.i	−0.521273	+	0.902870i	0.478421	+	0.878130i	$0.341209\pi$
$569$	−168768.	+	292314.i	−0.521273	+	0.902870i	−0.999694	+	0.0247401i	$0.992124\pi$
$570$	−293276.	+	169323.i	−0.902665	+	0.521154i
$571$	−109154.	−	189060.i	−0.334786	−	0.579866i	0.648658	−	0.761080i	$-0.275331\pi$
$571$	−109154.	−	189060.i	−0.334786	−	0.579866i	−0.983444	+	0.181214i	$0.941997\pi$
$572$	−397508.	−	229501.i	−1.21494	−	0.701444i
$573$			77533.2i			0.236145i
$574$		0			0
$575$	−72376.9			−0.218909
$576$	31631.9	−	54788.0i	0.0953410	−	0.165136i
$577$	−197760.	+	114177.i	−0.594001	+	0.342947i	−0.766678	−	0.642032i	$-0.778092\pi$
$577$	−197760.	+	114177.i	−0.594001	+	0.342947i	0.172677	+	0.984978i	$0.444758\pi$
$578$	274045.	+	474660.i	0.820289	+	1.42078i
$579$	66523.5	+	38407.3i	0.198435	+	0.114566i
$580$		−	626649.i		−	1.86281i
$581$		0			0
$582$	−438079.			−1.29332
$583$	29766.0	−	51556.2i	0.0875755	−	0.151685i
$584$	−21.9175	+	12.6541i	−6.42636e−5	+	3.71026e-5i
$585$	−64304.3	−	111378.i	−0.187901	−	0.325453i
$586$	−445162.	−	257015.i	−1.29635	−	0.748450i
$587$			235281.i			0.682827i	0.939913	+	0.341413i	$0.110906\pi$
$587$			235281.i			0.682827i	−0.939913	+	0.341413i	$0.889094\pi$
$588$		0			0
$589$	−190608.			−0.549427
$590$	−372488.	+	645168.i	−1.07006	+	1.85340i
$591$	396620.	−	228989.i	1.13553	−	0.655600i
$592$	−290287.	−	502792.i	−0.828293	−	1.43465i
$593$	48847.7	+	28202.2i	0.138910	+	0.0802000i	0.567845	−	0.823136i	$-0.307777\pi$
$593$	48847.7	+	28202.2i	0.138910	+	0.0802000i	−0.428934	+	0.903336i	$0.641111\pi$
$594$		−	246299.i		−	0.698054i
$595$		0			0
$596$	930531.			2.61962
$597$	246850.	−	427557.i	0.692604	−	1.19962i
$598$	972213.	−	561307.i	2.71869	−	1.56963i
$599$	−54321.5	−	94087.6i	−0.151397	−	0.262228i	0.780344	−	0.625350i	$-0.215044\pi$
$599$	−54321.5	−	94087.6i	−0.151397	−	0.262228i	−0.931741	+	0.363123i	$0.881711\pi$
$600$	113313.	+	65421.2i	0.314758	+	0.181726i
$601$			11012.9i			0.0304897i	0.999884	+	0.0152448i	$0.00485277\pi$
$601$			11012.9i			0.0304897i	−0.999884	+	0.0152448i	$0.995147\pi$
$602$		0			0
$603$	79555.2			0.218793
$604$	−363816.	+	630147.i	−0.997258	+	1.72730i
$605$	240869.	−	139066.i	0.658067	−	0.379935i
$606$	−15913.1	−	27562.4i	−0.0433322	−	0.0750535i
$607$	−165640.	−	95632.6i	−0.449561	−	0.259554i	0.258084	−	0.966123i	$-0.416909\pi$
$607$	−165640.	−	95632.6i	−0.449561	−	0.259554i	−0.707645	+	0.706568i	$0.750242\pi$
$608$		−	55896.4i		−	0.151209i
$609$		0			0
$610$	60463.6			0.162493
$611$	440832.	−	763543.i	1.18084	−	2.04527i
$612$	38161.3	−	22032.4i	0.101887	−	0.0588247i
$613$	−155499.	−	269332.i	−0.413816	−	0.716749i	0.581488	−	0.813555i	$-0.302471\pi$
$613$	−155499.	−	269332.i	−0.413816	−	0.716749i	−0.995303	+	0.0968056i	$0.969137\pi$
$614$	−713515.	−	411948.i	−1.89263	−	1.09271i
$615$		−	17808.2i		−	0.0470837i
$616$		0			0
$617$	452960.			1.18984			0.594922	−	0.803784i	$-0.297183\pi$
$617$	452960.			1.18984			0.594922	+	0.803784i	$0.297183\pi$
$618$	395424.	−	684895.i	1.03535	−	1.79328i
$619$	−605159.	+	349389.i	−1.57939	+	0.911859i	−0.584441	+	0.811436i	$0.698686\pi$
$619$	−605159.	+	349389.i	−1.57939	+	0.911859i	−0.994945	+	0.100423i	$0.967981\pi$
$620$	−247212.	−	428183.i	−0.643110	−	1.11390i
$621$	350893.	+	202588.i	0.909895	+	0.525328i
$622$			30197.2i			0.0780524i
$623$		0			0
$624$	−734968.			−1.88755
$625$	141500.	−	245085.i	0.362239	−	0.627417i
$626$	722098.	−	416903.i	1.84267	−	1.06387i
$627$	49264.9	+	85329.3i	0.125315	+	0.217052i
$628$	1.26146e6	+	728307.i	3.19857	+	1.84670i
$629$			139114.i			0.351617i
$630$		0			0
$631$	−401495.			−1.00837			−0.504187	−	0.863595i	$-0.668208\pi$
$631$	−401495.			−1.00837			−0.504187	+	0.863595i	$0.668208\pi$
$632$	−93119.5	+	161288.i	−0.233134	+	0.403801i
$633$	182284.	−	105242.i	0.454927	−	0.262652i
$634$	−48931.1	−	84751.1i	−0.121732	−	0.210847i
$635$	413855.	+	238940.i	1.02636	+	0.592571i
$636$		−	344936.i		−	0.852756i
$637$		0			0
$638$	−271069.			−0.665946
$639$	−11137.2	+	19290.1i	−0.0272755	+	0.0472425i
$640$	−511097.	+	295082.i	−1.24780	+	0.720415i
$641$	−368465.	−	638201.i	−0.896769	−	1.55325i	−0.831599	−	0.555376i	$-0.812574\pi$
$641$	−368465.	−	638201.i	−0.896769	−	1.55325i	−0.0651699	−	0.997874i	$-0.520759\pi$
$642$	−1.01376e6	−	585297.i	−2.45961	−	1.42006i
$643$			328825.i			0.795323i	0.917532	+	0.397661i	$0.130178\pi$
$643$			328825.i			0.795323i	−0.917532	+	0.397661i	$0.869822\pi$
$644$		0			0
$645$	−153862.			−0.369837
$646$	−69760.8	+	120829.i	−0.167166	+	0.289539i
$647$	503584.	−	290745.i	1.20299	−	0.694549i	0.241775	−	0.970332i	$-0.422271\pi$
$647$	503584.	−	290745.i	1.20299	−	0.694549i	0.961220	+	0.275783i	$0.0889372\pi$
$648$	−276744.	−	479335.i	−0.659066	−	1.14154i
$649$	187713.	+	108376.i	0.445662	+	0.257303i
$650$		−	306535.i		−	0.725527i
$651$		0			0
$652$	−842238.			−1.98125
$653$	−298234.	+	516556.i	−0.699407	+	1.21141i	0.269265	+	0.963066i	$0.413219\pi$
$653$	−298234.	+	516556.i	−0.699407	+	1.21141i	−0.968672	+	0.248343i	$0.920114\pi$
$654$	−385123.	+	222351.i	−0.900417	+	0.519856i
$655$	−2976.90	−	5156.15i	−0.00693876	−	0.0120183i
$656$	26517.6	+	15309.9i	0.0616207	+	0.0355767i
$657$			4.01971i			9.31246e-6i
$658$		0			0
$659$	−82075.1			−0.188991			−0.0944954	−	0.995525i	$-0.530124\pi$
$659$	−82075.1			−0.188991			−0.0944954	+	0.995525i	$0.530124\pi$
$660$	−127790.	+	221338.i	−0.293365	+	0.508123i
$661$	133678.	−	77179.0i	0.305955	−	0.176643i	−0.339160	−	0.940729i	$-0.610143\pi$
$661$	133678.	−	77179.0i	0.305955	−	0.176643i	0.645115	+	0.764086i	$0.276810\pi$
$662$	107495.	+	186186.i	0.245285	+	0.424846i
$663$	152515.	+	88054.6i	0.346965	+	0.200320i
$664$		−	1.06819e6i		−	2.42277i
$665$		0			0
$666$	−254627.			−0.574057
$667$	222963.	−	386182.i	0.501164	−	0.868042i
$668$	165747.	−	95694.3i	0.371444	−	0.214454i
$669$	83981.5	+	145460.i	0.187643	+	0.325007i
$670$	−565857.	−	326698.i	−1.26054	−	0.727774i
$671$		−	17592.0i		−	0.0390725i
$672$		0			0
$673$	675260.			1.49087			0.745437	−	0.666576i	$-0.232241\pi$
$673$	675260.			1.49087			0.745437	+	0.666576i	$0.232241\pi$
$674$	−78286.1	+	135595.i	−0.172332	+	0.298487i
$675$	95813.0	−	55317.7i	0.210289	−	0.121411i
$676$	1.12957e6	+	1.95647e6i	2.47183	+	4.28134i
$677$	180907.	+	104447.i	0.394710	+	0.227886i	0.684199	−	0.729295i	$-0.260152\pi$
$677$	180907.	+	104447.i	0.394710	+	0.227886i	−0.289489	+	0.957181i	$0.593485\pi$
$678$			251756.i			0.547671i
$679$		0			0
$680$	−185755.			−0.401720
$681$	−85094.9	+	147389.i	−0.183489	+	0.317812i
$682$	−185219.	+	106936.i	−0.398214	+	0.229909i
$683$	21159.8	+	36649.9i	0.0453598	+	0.0785655i	0.887814	−	0.460203i	$-0.152223\pi$
$683$	21159.8	+	36649.9i	0.0453598	+	0.0785655i	−0.842454	+	0.538768i	$0.818890\pi$
$684$	−148755.	−	85883.6i	−0.317950	−	0.183569i
$685$			180821.i			0.385360i
$686$		0			0
$687$	157205.			0.333083
$688$	132276.	−	229109.i	0.279451	−	0.484023i
$689$	−359205.	+	207387.i	−0.756666	+	0.436862i
$690$	−312544.	−	541342.i	−0.656467	−	1.13703i
$691$	20361.7	+	11755.8i	0.0426439	+	0.0246205i	0.521170	−	0.853453i	$-0.325496\pi$
$691$	20361.7	+	11755.8i	0.0426439	+	0.0246205i	−0.478526	+	0.878073i	$0.658829\pi$
$692$			1.29983e6i			2.71440i
$693$		0			0
$694$	1.49467e6			3.10331
$695$	128416.	−	222424.i	0.265859	−	0.460481i
$696$	−698137.	+	403070.i	−1.44119	+	0.832074i
$697$	−3668.49	−	6354.01i	−0.00755130	−	0.0130792i
$698$	385489.	+	222562.i	0.791227	+	0.456815i
$699$			31783.2i			0.0650495i
$700$		0			0
$701$	−161942.			−0.329552			−0.164776	−	0.986331i	$-0.552690\pi$
$701$	−161942.			−0.329552			−0.164776	+	0.986331i	$0.552690\pi$
$702$	−858014.	+	1.48612e6i	−1.74109	+	3.01565i
$703$	469623.	−	271137.i	0.950253	−	0.548629i
$704$	75588.2	+	130923.i	0.152514	+	0.264161i
$705$	−425152.	−	245462.i	−0.855394	−	0.493862i
$706$			984240.i			1.97466i
$707$		0			0
$708$	1.25589e6			2.50546
$709$	−30803.0	+	53352.3i	−0.0612774	+	0.106136i	−0.895037	−	0.445993i	$-0.852851\pi$
$709$	−30803.0	+	53352.3i	−0.0612774	+	0.106136i	0.833759	+	0.552128i	$0.186184\pi$
$710$	158432.	−	91470.6i	0.314286	−	0.181453i
$711$	14790.3	+	25617.5i	0.0292575	+	0.0506754i
$712$	−356053.	−	205567.i	−0.702351	−	0.405502i
$713$		−	351833.i		−	0.692081i
$714$		0			0
$715$	307326.			0.601156
$716$	790296.	−	1.36883e6i	1.54157	−	2.67008i
$717$	241374.	−	139358.i	0.469519	−	0.271077i
$718$	−128510.	−	222586.i	−0.249280	−	0.431766i
$719$	−209510.	−	120961.i	−0.405272	−	0.233984i	0.283484	−	0.958977i	$-0.408510\pi$
$719$	−209510.	−	120961.i	−0.405272	−	0.233984i	−0.688756	+	0.724993i	$0.741843\pi$
$720$		−	123130.i		−	0.237519i
$721$		0			0
$722$	−367192.			−0.704400
$723$	312619.	−	541471.i	0.598051	−	1.03585i
$724$	−1.35402e6	+	781744.i	−2.58314	+	1.49138i
$725$	−60881.0	−	105449.i	−0.115826	−	0.200616i
$726$	−603706.	−	348550.i	−1.14539	−	0.661289i
$727$			75734.6i			0.143293i	0.997430	+	0.0716466i	$0.0228254\pi$
$727$			75734.6i			0.143293i	−0.997430	+	0.0716466i	$0.977175\pi$
$728$		0			0
$729$	−590924.			−1.11193
$730$	16.5072	−	28.5913i	3.09761e−5	−	5.36522e-5i
$731$	−54898.0	+	31695.4i	−0.102736	+	0.0593146i
$732$	−50965.3	−	88274.5i	−0.0951158	−	0.164745i
$733$	302681.	+	174753.i	0.563349	+	0.325250i	0.754489	−	0.656313i	$-0.227885\pi$
$733$	302681.	+	174753.i	0.563349	+	0.325250i	−0.191140	+	0.981563i	$0.561218\pi$
$734$		−	173151.i		−	0.321390i
$735$		0			0
$736$	103176.			0.190469
$737$	−95053.5	+	164637.i	−0.174998	+	0.303105i
$738$	11630.0	−	6714.59i	0.0213534	−	0.0123284i
$739$	434781.	+	753064.i	0.796127	+	1.37893i	0.922121	+	0.386901i	$0.126454\pi$
$739$	434781.	+	753064.i	0.796127	+	1.37893i	−0.125995	+	0.992031i	$0.540212\pi$
$740$	1.21817e6	+	703311.i	2.22456	+	1.28435i
$741$		−	686483.i		−	1.25024i
$742$		0			0
$743$	95108.3			0.172282			0.0861412	−	0.996283i	$-0.472546\pi$
$743$	95108.3			0.172282			0.0861412	+	0.996283i	$0.472546\pi$
$744$	−318020.	+	550827.i	−0.574525	+	0.995106i
$745$	−539567.	+	311519.i	−0.972149	+	0.561271i
$746$	−112527.	−	194902.i	−0.202199	−	0.350219i
$747$	−146931.	−	84830.9i	−0.263314	−	0.152024i
$748$			105298.i			0.188199i
$749$		0			0
$750$	−929516.			−1.65247
$751$	−376603.	+	652296.i	−0.667735	+	1.15655i	0.310801	+	0.950475i	$0.399403\pi$
$751$	−376603.	+	652296.i	−0.667735	+	1.15655i	−0.978536	+	0.206076i	$0.933931\pi$
$752$	731015.	−	422052.i	1.29268	−	0.746329i
$753$	397492.	+	688476.i	0.701033	+	1.21422i
$754$	1.63558e6	+	944305.i	2.87694	+	1.66100i
$755$		−	487187.i		−	0.854676i
$756$		0			0
$757$	−293022.			−0.511338			−0.255669	−	0.966764i	$-0.582296\pi$
$757$	−293022.			−0.511338			−0.255669	+	0.966764i	$0.582296\pi$
$758$	655450.	−	1.13527e6i	1.14078	−	1.97589i
$759$	−157505.	+	90935.4i	−0.273407	+	0.157852i
$760$	362042.	+	627075.i	0.626804	+	1.08566i
$761$	−451698.	−	260788.i	−0.779972	−	0.450317i	0.0564483	−	0.998406i	$-0.482022\pi$
$761$	−451698.	−	260788.i	−0.779972	−	0.450317i	−0.836420	+	0.548088i	$0.815356\pi$
$762$		−	1.19774e6i		−	2.06278i
$763$		0			0
$764$	322990.			0.553354
$765$	−14751.8	+	25551.0i	−0.0252071	+	0.0436600i
$766$	−155234.	+	89624.2i	−0.264562	+	0.152745i
$767$	−755086.	−	1.30785e6i	−1.28353	−	2.22314i
$768$	911767.	+	526409.i	1.54583	+	0.892485i
$769$		−	920553.i		−	1.55667i	−0.627850	−	0.778334i	$-0.716065\pi$
$769$		−	920553.i		−	1.55667i	0.627850	−	0.778334i	$-0.283935\pi$
$770$		0			0
$771$	386822.			0.650732
$772$	159999.	−	277126.i	0.268461	−	0.464988i
$773$	−395771.	+	228498.i	−0.662346	+	0.382406i	−0.793170	−	0.609000i	$-0.791571\pi$
$773$	−395771.	+	228498.i	−0.662346	+	0.382406i	0.130824	+	0.991406i	$0.458238\pi$
$774$	−58013.4	−	100482.i	−0.0968381	−	0.167729i
$775$	−83198.7	−	48034.8i	−0.138520	−	0.0799747i
$776$			936690.i			1.55551i
$777$		0			0
$778$	−506530.			−0.836846
$779$	−14300.0	+	24768.3i	−0.0235646	+	0.0408151i
$780$	1.54212e6	−	890344.i	2.53472	−	1.46342i
$781$	−26613.6	−	46096.1i	−0.0436316	−	0.0755721i
$782$	−223032.	−	128768.i	−0.364716	−	0.210569i
$783$			681641.i			1.11181i
$784$		0			0
$785$	−975278.			−1.58267
$786$	−7461.21	+	12923.2i	−0.0120771	+	0.0209182i
$787$	−282970.	+	163373.i	−0.456868	+	0.263773i	−0.710726	−	0.703469i	$-0.751634\pi$
$787$	−282970.	+	163373.i	−0.456868	+	0.263773i	0.253859	+	0.967241i	$0.418300\pi$
$788$	−953928.	−	1.65225e6i	−1.53626	−	2.66087i
$789$	19619.1	+	11327.1i	0.0315155	+	0.0181955i
$790$		−	242948.i		−	0.389277i
$791$		0			0
$792$	−98922.5			−0.157705
$793$	−61284.2	+	106147.i	−0.0974545	+	0.168796i
$794$	772531.	−	446021.i	1.22539	−	0.707481i
$795$	115476.	+	200011.i	0.182708	+	0.316460i
$796$	−1.78113e6	−	1.02834e6i	−2.81106	−	1.62297i
$797$			580079.i			0.913210i	0.889669	+	0.456605i	$0.150935\pi$
$797$			580079.i			0.913210i	−0.889669	+	0.456605i	$0.849065\pi$
$798$		0			0
$799$	−202260.			−0.316823
$800$	14086.4	−	24398.3i	0.0220100	−	0.0381224i
$801$	−56552.2	+	32650.4i	−0.0881423	+	0.0508890i
$802$	−483941.	−	838210.i	−0.752391	−	1.30318i
$803$	−8.31869	−	4.80280i	−1.29010e−5	−	7.44840e-6i
$804$			1.10151e6i			1.70402i
$805$		0			0
$806$	1.49010e6			2.29375
$807$	−185169.	+	320722.i	−0.284329	+	0.492472i
$808$	−58933.1	+	34025.1i	−0.0902686	+	0.0521166i
$809$	402559.	+	697253.i	0.615081	+	1.06535i	0.990370	+	0.138444i	$0.0442101\pi$
$809$	402559.	+	697253.i	0.615081	+	1.06535i	−0.375289	+	0.926908i	$0.622457\pi$
$810$	625291.	+	361012.i	0.953042	+	0.550239i
$811$			633160.i			0.962657i	0.876540	+	0.481328i	$0.159846\pi$
$811$			633160.i			0.962657i	−0.876540	+	0.481328i	$0.840154\pi$
$812$		0			0
$813$	−462072.			−0.699083
$814$	304231.	−	526943.i	0.459149	−	0.795270i
$815$	488370.	−	281961.i	0.735249	−	0.424496i
$816$	84303.4	+	146018.i	0.126609	+	0.219293i
$817$	213995.	+	123550.i	0.320598	+	0.185097i
$818$		−	536455.i		−	0.801728i
$819$		0			0
$820$	−74186.2			−0.110330
$821$	−307818.	+	533156.i	−0.456675	+	0.790984i	−0.998783	−	0.0493246i	$-0.984293\pi$
$821$	−307818.	+	533156.i	−0.456675	+	0.790984i	0.542108	+	0.840309i	$0.317626\pi$
$822$	392485.	−	226601.i	0.580871	−	0.335366i
$823$	−64378.0	−	111506.i	−0.0950469	−	0.164626i	0.814581	−	0.580049i	$-0.196967\pi$
$823$	−64378.0	−	111506.i	−0.0950469	−	0.164626i	−0.909628	+	0.415423i	$0.863633\pi$
$824$	−1.46443e6	−	845487.i	−2.15682	−	1.24524i
$825$			49660.7i			0.0729634i
$826$		0			0
$827$	1.05631e6			1.54447			0.772235	−	0.635337i	$-0.219139\pi$
$827$	1.05631e6			1.54447			0.772235	+	0.635337i	$0.219139\pi$
$828$	158528.	−	274578.i	0.231231	−	0.400503i
$829$	−547883.	+	316320.i	−0.797221	+	0.460276i	−0.842498	−	0.538699i	$-0.818916\pi$
$829$	−547883.	+	316320.i	−0.797221	+	0.460276i	0.0452777	+	0.998974i	$0.485583\pi$
$830$	696725.	+	1.20676e6i	1.01136	+	1.75172i
$831$	−407425.	−	235227.i	−0.589991	−	0.340631i
$832$		−	1.05329e6i		−	1.52160i
$833$		0			0
$834$	−643717.			−0.925471
$835$	−64072.3	+	110976.i	−0.0918961	+	0.159169i
$836$	355468.	−	205229.i	0.508613	−	0.293648i
$837$	268906.	+	465758.i	0.383839	+	0.664829i
$838$	−1.08921e6	−	628858.i	−1.55105	−	0.895498i
$839$			249268.i			0.354114i	0.984201	+	0.177057i	$0.0566577\pi$
$839$			249268.i			0.354114i	−0.984201	+	0.177057i	$0.943342\pi$
$840$		0			0
$841$	42913.2			0.0606735
$842$	−21372.6	+	37018.5i	−0.0301463	+	0.0522149i
$843$	−323710.	+	186894.i	−0.455513	+	0.262991i
$844$	−438420.	−	759365.i	−0.615468	−	1.06602i
$845$	−1.30996e6	−	756303.i	−1.83461	−	1.05921i
$846$		−	370205.i		−	0.517251i
$847$		0			0
$848$	−397105.			−0.552222
$849$	−373463.	+	646857.i	−0.518122	+	0.897414i
$850$	−60900.1	+	35160.7i	−0.0842907	+	0.0486653i
$851$	500478.	+	866852.i	0.691075	+	1.19698i
$852$	−267087.	−	154203.i	−0.367937	−	0.212429i
$853$		−	1.16100e6i		−	1.59564i	−0.602898	−	0.797818i	$-0.705988\pi$
$853$		−	1.16100e6i		−	1.59564i	0.602898	−	0.797818i	$-0.294012\pi$
$854$		0			0
$855$	115007.			0.157323
$856$	−1.25147e6	+	2.16760e6i	−1.70794	+	2.95823i
$857$	191594.	−	110617.i	0.260867	−	0.150612i	−0.363863	−	0.931453i	$-0.618542\pi$
$857$	191594.	−	110617.i	0.260867	−	0.150612i	0.624730	+	0.780841i	$0.285209\pi$
$858$	−385135.	−	667074.i	−0.523165	−	0.906149i
$859$	989322.	+	571185.i	1.34076	+	0.774089i	0.986919	−	0.161217i	$-0.0515417\pi$
$859$	989322.	+	571185.i	1.34076	+	0.774089i	0.353842	+	0.935305i	$0.384875\pi$
$860$			640962.i			0.866633i
$861$		0			0
$862$	−1.57501e6			−2.11967
$863$	−560434.	+	970701.i	−0.752494	+	1.30336i	0.194117	+	0.980978i	$0.437816\pi$
$863$	−560434.	+	970701.i	−0.752494	+	1.30336i	−0.946611	+	0.322379i	$0.895517\pi$
$864$	−136585.	+	78857.6i	−0.182969	+	0.105637i
$865$	−435150.	−	753702.i	−0.581577	−	1.00732i
$866$	1.76390e6	+	1.01839e6i	2.35201	+	1.35793i
$867$			618653.i			0.823017i
$868$		0			0
$869$	−70686.2			−0.0936042
$870$	525803.	−	910717.i	0.694680	−	1.20322i
$871$	1.14707e6	−	662263.i	1.51201	−	0.872959i
$872$	475425.	+	823460.i	0.625243	+	1.08295i
$873$	128843.	+	74387.7i	0.169057	+	0.0976051i
$874$			1.00389e6i			1.31420i
$875$		0			0
$876$	−55.6562			−7.25279e−5
$877$	367056.	−	635760.i	0.477236	−	0.826598i	−0.522423	−	0.852686i	$-0.674972\pi$
$877$	367056.	−	635760.i	0.477236	−	0.826598i	0.999660	+	0.0260885i	$0.00830518\pi$
$878$	−1.63978e6	+	946727.i	−2.12714	+	1.22811i
$879$	−290103.	−	502473.i	−0.375470	−	0.650332i
$880$	254814.	+	147117.i	0.329046	+	0.189975i
$881$			567852.i			0.731616i	0.930690	+	0.365808i	$0.119207\pi$
$881$			567852.i			0.731616i	−0.930690	+	0.365808i	$0.880793\pi$
$882$		0			0
$883$	40795.8			0.0523232			0.0261616	−	0.999658i	$-0.491672\pi$
$883$	40795.8			0.0523232			0.0261616	+	0.999658i	$0.491672\pi$
$884$	366821.	−	635352.i	0.469407	−	0.813037i
$885$	−728229.	+	420443.i	−0.929782	+	0.536810i
$886$	220856.	+	382534.i	0.281347	+	0.487307i
$887$	−120455.	−	69544.4i	−0.153100	−	0.0883925i	0.421493	−	0.906832i	$-0.361506\pi$
$887$	−120455.	−	69544.4i	−0.153100	−	0.0883925i	−0.574593	+	0.818439i	$0.694840\pi$
$888$		−	1.80952e6i		−	2.29476i
$889$		0			0
$890$	536323.			0.677090
$891$	105037.	−	181930.i	0.132309	−	0.229165i
$892$	605963.	−	349853.i	0.761582	−	0.439700i
$893$	394210.	+	682791.i	0.494339	+	0.856220i
$894$	1.35235e6	+	780781.i	1.69206	+	0.976909i
$895$			1.05829e6i			1.32117i
$896$		0			0
$897$	1.26714e6			1.57485
$898$	1.14982e6	−	1.99155e6i	1.42587	−	2.46967i
$899$	512600.	−	295950.i	0.634248	−	0.366183i
$900$	−43286.8	−	74975.0i	−0.0534405	−	0.0925617i
$901$	82404.2	+	47576.1i	0.101508	+	0.0586056i
$902$			32090.7i			0.0394426i
$903$		0			0
$904$	538298.			0.658697
$905$	523418.	−	906587.i	0.639075	−	1.10691i
$906$	−1.05748e6	+	610534.i	−1.28829	+	0.743795i
$907$	−371706.	−	643813.i	−0.451840	−	0.782610i	0.546661	−	0.837354i	$-0.315899\pi$
$907$	−371706.	−	643813.i	−0.451840	−	0.782610i	−0.998500	+	0.0547448i	$0.982565\pi$
$908$	613997.	+	354491.i	0.744723	+	0.429966i
$909$			10808.5i			0.0130809i
$910$		0			0
$911$	−549043.			−0.661560			−0.330780	−	0.943708i	$-0.607312\pi$
$911$	−549043.			−0.661560			−0.330780	+	0.943708i	$0.607312\pi$
$912$	328619.	−	569185.i	0.395096	−	0.684327i
$913$	351110.	−	202714.i	0.421213	−	0.243188i
$914$	−109153.	−	189059.i	−0.130660	−	0.226310i
$915$	59104.3	+	34123.9i	0.0705955	+	0.0407583i
$916$		−	654888.i		−	0.780506i
$917$		0			0
$918$	393669.			0.467138
$919$	820048.	−	1.42037e6i	0.970976	−	1.68178i	0.278354	−	0.960479i	$-0.410211\pi$
$919$	820048.	−	1.42037e6i	0.970976	−	1.68178i	0.692622	−	0.721301i	$-0.256455\pi$
$920$	−1.15748e6	+	668274.i	−1.36754	+	0.789548i
$921$	−464983.	−	805375.i	−0.548174	−	0.949464i
$922$	1.16905e6	+	674949.i	1.37521	+	0.793979i
$923$			370848.i			0.435303i
$924$		0			0
$925$	273316.			0.319434
$926$	−862207.	+	1.49339e6i	−1.00552	+	1.74161i
$927$	−232596.	+	134290.i	−0.270672	+	0.156273i
$928$	86788.3	+	150322.i	0.100778	+	0.174552i
$929$	−942167.	−	543960.i	−1.09168	−	0.630283i	−0.157659	−	0.987494i	$-0.550395\pi$
$929$	−942167.	−	543960.i	−1.09168	−	0.630283i	−0.934024	+	0.357210i	$0.883728\pi$
$930$		−	829712.i		−	0.959315i
$931$		0			0
$932$	132404.			0.152429
$933$	−17042.4	+	29518.4i	−0.0195780	+	0.0339101i
$934$	2.02265e6	−	1.16778e6i	2.31860	−	1.33865i
$935$	−35251.3	−	61057.1i	−0.0403230	−	0.0698414i
$936$	596882.	+	344610.i	0.681297	+	0.393347i
$937$		−	347157.i		−	0.395409i	−0.980262	−	0.197704i	$-0.936651\pi$
$937$		−	347157.i		−	0.395409i	0.980262	−	0.197704i	$-0.0633486\pi$
$938$		0			0
$939$	941152.			1.06740
$940$	−1.02255e6	+	1.77111e6i	−1.15726	+	2.00443i
$941$	−144915.	+	83666.7i	−0.163657	+	0.0944873i	−0.579591	−	0.814907i	$-0.696788\pi$
$941$	−144915.	+	83666.7i	−0.163657	+	0.0944873i	0.415935	+	0.909395i	$0.363455\pi$
$942$	1.22220e6	+	2.11692e6i	1.37734	+	2.38562i
$943$	−45718.4	−	26395.5i	−0.0514124	−	0.0296830i
$944$		−	1.44584e6i		−	1.62247i
$945$		0			0
$946$	277260.			0.309817
$947$	263561.	−	456501.i	0.293887	−	0.509028i	−0.680838	−	0.732434i	$-0.738384\pi$
$947$	263561.	−	456501.i	0.293887	−	0.509028i	0.974725	+	0.223406i	$0.0717176\pi$
$948$	−354695.	+	204783.i	−0.394673	+	0.227865i
$949$	33.4624	+	57.9585i	3.71556e−5	+	6.43554e-5i
$950$	237392.	+	137058.i	0.263038	+	0.151865i
$951$		−	110461.i		−	0.122137i
$952$		0			0
$953$	−1.67904e6			−1.84873			−0.924366	−	0.381506i	$-0.875406\pi$
$953$	−1.67904e6			−1.84873			−0.924366	+	0.381506i	$0.875406\pi$
$954$	−87080.5	+	150828.i	−0.0956807	+	0.165724i
$955$	−187285.	+	108129.i	−0.205351	+	0.118560i
$956$	−580540.	−	1.00553e6i	−0.635209	−	1.10021i
$957$	−264975.	−	152984.i	−0.289322	−	0.167040i
$958$			1.05162e6i			1.14585i
$959$		0			0
$960$	−586485.			−0.636377
$961$	−228258.	+	395354.i	−0.247160	+	0.428094i
$962$	−3.67135e6	+	2.11965e6i	−3.96712	+	2.29042i
$963$	198772.	+	344283.i	0.214339	+	0.371247i
$964$	−2.25568e6	−	1.30232e6i	−2.42730	−	1.40140i
$965$			214255.i			0.230078i
$966$		0			0
$967$	797832.			0.853215			0.426608	−	0.904437i	$-0.359709\pi$
$967$	797832.			0.853215			0.426608	+	0.904437i	$0.359709\pi$
$968$	−745260.	+	1.29083e6i	−0.795348	+	1.37758i
$969$	−136385.	+	78742.0i	−0.145251	+	0.0838608i
$970$	−610954.	−	1.05820e6i	−0.649329	−	1.12467i
$971$	808590.	+	466839.i	0.857610	+	0.495141i	0.863211	−	0.504843i	$-0.168450\pi$
$971$	808590.	+	466839.i	0.857610	+	0.495141i	−0.00560133	+	0.999984i	$0.501783\pi$
$972$			878266.i			0.929594i
$973$		0			0
$974$	1.95788e6			2.06380
$975$	173000.	−	299644.i	0.181985	−	0.315208i
$976$	−101625.	+	58673.4i	−0.106685	+	0.0615944i
$977$	719883.	+	1.24687e6i	0.754176	+	1.30627i	0.945783	+	0.324799i	$0.105297\pi$
$977$	719883.	+	1.24687e6i	0.754176	+	1.30627i	−0.191607	+	0.981472i	$0.561370\pi$
$978$	−1.22404e6	−	706697.i	−1.27972	−	0.738849i
$979$		−	156044.i		−	0.162811i
$980$		0			0
$981$	151024.			0.156931
$982$	−795347.	+	1.37758e6i	−0.824772	+	1.42855i
$983$	1.29753e6	−	749128.i	1.34279	−	0.775263i	0.355578	−	0.934647i	$-0.384284\pi$
$983$	1.29753e6	−	749128.i	1.34279	−	0.775263i	0.987217	+	0.159384i	$0.0509509\pi$
$984$	47717.6	+	82649.4i	0.0492820	+	0.0853590i
$985$	1.10627e6	+	638704.i	1.14022	+	0.658305i
$986$		−	433260.i		−	0.445651i
$987$		0			0
$988$	−2.85977e6			−2.92966
$989$	−228055.	+	395003.i	−0.233156	+	0.403838i
$990$	111755.	−	64522.0i	0.114024	−	0.0658321i
$991$	494541.	+	856570.i	0.503564	+	0.872199i	0.999992	+	0.00412045i	$0.00131158\pi$
$991$	494541.	+	856570.i	0.503564	+	0.872199i	−0.496427	+	0.868078i	$0.665355\pi$
$992$	118603.	+	68475.6i	0.120524	+	0.0695845i
$993$			242668.i			0.246101i
$994$		0			0
$995$	1.37705e6			1.39092
$996$	1.17455e6	−	2.03438e6i	1.18400	−	2.05076i
$997$	1.07127e6	−	618500.i	1.07773	−	0.622228i	0.147447	−	0.989070i	$-0.452894\pi$
$997$	1.07127e6	−	618500.i	1.07773	−	0.622228i	0.930283	+	0.366842i	$0.119561\pi$
$998$	806044.	+	1.39611e6i	0.809277	+	1.40171i
$999$	−1.32507e6	−	765030.i	−1.32772	−	0.766562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.5.d.c.19.8		16
7.2	even	3		49.5.b.b.48.2	yes	8
7.3	odd	6	inner	49.5.d.c.31.8		16
7.4	even	3	inner	49.5.d.c.31.7		16
7.5	odd	6		49.5.b.b.48.1	✓	8
7.6	odd	2	inner	49.5.d.c.19.7		16
21.2	odd	6		441.5.d.g.244.8		8
21.5	even	6		441.5.d.g.244.7		8
28.19	even	6		784.5.c.g.97.6		8
28.23	odd	6		784.5.c.g.97.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.5.b.b.48.1	✓	8	7.5	odd	6
49.5.b.b.48.2	yes	8	7.2	even	3
49.5.d.c.19.7		16	7.6	odd	2	inner
49.5.d.c.19.8		16	1.1	even	1	trivial
49.5.d.c.31.7		16	7.4	even	3	inner
49.5.d.c.31.8		16	7.3	odd	6	inner
441.5.d.g.244.7		8	21.5	even	6
441.5.d.g.244.8		8	21.2	odd	6
784.5.c.g.97.3		8	28.23	odd	6
784.5.c.g.97.6		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)

\(f(q)\)	\(=\)	\(q+(3.49543 - 6.05426i) q^{2} +(6.83370 - 3.94544i) q^{3} +(-16.4360 - 28.4680i) q^{4} +(19.0608 + 11.0048i) q^{5} -55.1639i q^{6} -117.950 q^{8} +(-9.36707 + 16.2242i) q^{9} +O(q^{10})\)	\(q+(3.49543 - 6.05426i) q^{2} +(6.83370 - 3.94544i) q^{3} +(-16.4360 - 28.4680i) q^{4} +(19.0608 + 11.0048i) q^{5} -55.1639i q^{6} -117.950 q^{8} +(-9.36707 + 16.2242i) q^{9} +(133.251 - 76.9327i) q^{10} +(-22.3838 - 38.7698i) q^{11} +(-224.638 - 129.695i) q^{12} +311.907i q^{13} +173.674 q^{15} +(-149.310 + 258.612i) q^{16} +(61.9673 - 35.7768i) q^{17} +(65.4838 + 113.421i) q^{18} +(-241.552 - 139.460i) q^{19} -723.499i q^{20} -312.963 q^{22} +(257.422 - 445.867i) q^{23} +(-806.035 + 465.365i) q^{24} +(-70.2902 - 121.746i) q^{25} +(1888.37 + 1090.25i) q^{26} +786.989i q^{27} +866.138 q^{29} +(607.066 - 1051.47i) q^{30} +(591.823 - 341.689i) q^{31} +(100.202 + 173.554i) q^{32} +(-305.928 - 176.627i) q^{33} -500.221i q^{34} +615.830 q^{36} +(-972.097 + 1683.72i) q^{37} +(-1688.65 + 974.945i) q^{38} +(1230.61 + 2131.48i) q^{39} +(-2248.23 - 1298.01i) q^{40} -102.538i q^{41} -885.919 q^{43} +(-735.800 + 1274.44i) q^{44} +(-357.088 + 206.165i) q^{45} +(-1799.60 - 3116.99i) q^{46} +(-2447.98 - 1413.34i) q^{47} +2356.37i q^{48} -982.778 q^{50} +(282.310 - 488.976i) q^{51} +(8879.38 - 5126.52i) q^{52} +(664.901 + 1151.64i) q^{53} +(4764.64 + 2750.86i) q^{54} -985.312i q^{55} -2200.92 q^{57} +(3027.52 - 5243.82i) q^{58} +(-4193.07 + 2420.87i) q^{59} +(-2854.52 - 4944.17i) q^{60} +(340.317 + 196.482i) q^{61} -4777.40i q^{62} -3376.92 q^{64} +(-3432.47 + 5945.20i) q^{65} +(-2138.70 + 1234.78i) q^{66} +(-2123.27 - 3677.61i) q^{67} +(-2036.99 - 1176.06i) q^{68} -4062.56i q^{69} +1188.97 q^{71} +(1104.85 - 1913.65i) q^{72} +(0.185820 - 0.107283i) q^{73} +(6795.79 + 11770.7i) q^{74} +(-960.684 - 554.651i) q^{75} +9168.67i q^{76} +17206.0 q^{78} +(789.481 - 1367.42i) q^{79} +(-5691.93 + 3286.24i) q^{80} +(2346.28 + 4063.88i) q^{81} +(-620.792 - 358.415i) q^{82} +9056.29i q^{83} +1574.86 q^{85} +(-3096.67 + 5363.59i) q^{86} +(5918.92 - 3417.29i) q^{87} +(2640.17 + 4572.90i) q^{88} +(3018.67 + 1742.83i) q^{89} +2882.54i q^{90} -16924.0 q^{92} +(2696.23 - 4670.00i) q^{93} +(-17113.5 + 9880.48i) q^{94} +(-3069.45 - 5316.44i) q^{95} +(1369.49 + 790.678i) q^{96} -7941.40i q^{97} +838.681 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more