LMFDB - Embedded newform 354.6.c.a.353.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, 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:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.10
Character	$\chi$	$=$	354.353
Dual form			354.6.c.a.353.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +(-12.9095 + 8.73750i) q^{3} +16.0000 q^{4} +27.1818i q^{5} +(51.6381 - 34.9500i) q^{6} -249.363 q^{7} -64.0000 q^{8} +(90.3121 - 225.594i) q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +(-12.9095 + 8.73750i) q^{3} +16.0000 q^{4} +27.1818i q^{5} +(51.6381 - 34.9500i) q^{6} -249.363 q^{7} -64.0000 q^{8} +(90.3121 - 225.594i) q^{9} -108.727i q^{10} -19.0816 q^{11} +(-206.553 + 139.800i) q^{12} -831.209i q^{13} +997.454 q^{14} +(-237.501 - 350.905i) q^{15} +256.000 q^{16} +32.0791i q^{17} +(-361.248 + 902.377i) q^{18} -1974.78 q^{19} +434.909i q^{20} +(3219.16 - 2178.81i) q^{21} +76.3264 q^{22} +2858.56 q^{23} +(826.210 - 559.200i) q^{24} +2386.15 q^{25} +3324.84i q^{26} +(805.242 + 3701.42i) q^{27} -3989.81 q^{28} -5589.10i q^{29} +(950.005 + 1403.62i) q^{30} -735.144i q^{31} -1024.00 q^{32} +(246.335 - 166.726i) q^{33} -128.316i q^{34} -6778.15i q^{35} +(1444.99 - 3609.51i) q^{36} +12608.3i q^{37} +7899.11 q^{38} +(7262.69 + 10730.5i) q^{39} -1739.64i q^{40} +553.165i q^{41} +(-12876.7 + 8715.25i) q^{42} -13179.3i q^{43} -305.306 q^{44} +(6132.06 + 2454.85i) q^{45} -11434.2 q^{46} -25841.7 q^{47} +(-3304.84 + 2236.80i) q^{48} +45375.1 q^{49} -9544.59 q^{50} +(-280.291 - 414.126i) q^{51} -13299.3i q^{52} -31787.2i q^{53} +(-3220.97 - 14805.7i) q^{54} -518.673i q^{55} +15959.3 q^{56} +(25493.5 - 17254.6i) q^{57} +22356.4i q^{58} +(5198.86 - 26227.8i) q^{59} +(-3800.02 - 5614.47i) q^{60} -48642.8i q^{61} +2940.58i q^{62} +(-22520.5 + 56254.9i) q^{63} +4096.00 q^{64} +22593.8 q^{65} +(-985.339 + 666.902i) q^{66} -21463.9i q^{67} +513.265i q^{68} +(-36902.7 + 24976.7i) q^{69} +27112.6i q^{70} +48557.5i q^{71} +(-5779.97 + 14438.0i) q^{72} +57551.1i q^{73} -50433.4i q^{74} +(-30804.1 + 20849.0i) q^{75} -31596.4 q^{76} +4758.26 q^{77} +(-29050.8 - 42922.1i) q^{78} +15793.3 q^{79} +6958.55i q^{80} +(-42736.4 - 40747.8i) q^{81} -2212.66i q^{82} -117424. q^{83} +(51506.6 - 34861.0i) q^{84} -871.968 q^{85} +52717.2i q^{86} +(48834.8 + 72152.7i) q^{87} +1221.22 q^{88} +37701.5 q^{89} +(-24528.2 - 9819.39i) q^{90} +207273. i q^{91} +45736.9 q^{92} +(6423.33 + 9490.37i) q^{93} +103367. q^{94} -53678.0i q^{95} +(13219.4 - 8947.20i) q^{96} +64760.2i q^{97} -181500. q^{98} +(-1723.30 + 4304.70i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9}+O(q^{10}) $ 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9	$ 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9} - 652 q^{11} - 208 q^{12} - 152 q^{14} - 2107 q^{15} + 12800 q^{16} - 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} + 2456 q^{23} + 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} + 8428 q^{30} - 51200 q^{32} - 9744 q^{33} + 816 q^{36} + 3576 q^{38} + 1388 q^{39} + 15204 q^{42} - 10432 q^{44} + 33067 q^{45} - 9824 q^{46} - 27144 q^{47} - 3328 q^{48} + 85768 q^{49} + 95824 q^{50} + 3338 q^{51} - 39560 q^{54} - 2432 q^{56} - 63969 q^{57} - 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} - 9400 q^{65} + 38976 q^{66} - 115930 q^{69} - 3264 q^{72} + 24248 q^{75} - 14304 q^{76} - 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} - 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} + 104908 q^{89} - 132268 q^{90} + 39296 q^{92} - 91204 q^{93} + 108576 q^{94} + 13312 q^{96} - 343072 q^{98} - 111406 q^{99}+O(q^{100}) $ 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9 - 652 * q^11 - 208 * q^12 - 152 * q^14 - 2107 * q^15 + 12800 * q^16 - 204 * q^18 - 894 * q^19 - 3801 * q^21 + 2608 * q^22 + 2456 * q^23 + 832 * q^24 - 23956 * q^25 + 9890 * q^27 + 608 * q^28 + 8428 * q^30 - 51200 * q^32 - 9744 * q^33 + 816 * q^36 + 3576 * q^38 + 1388 * q^39 + 15204 * q^42 - 10432 * q^44 + 33067 * q^45 - 9824 * q^46 - 27144 * q^47 - 3328 * q^48 + 85768 * q^49 + 95824 * q^50 + 3338 * q^51 - 39560 * q^54 - 2432 * q^56 - 63969 * q^57 - 23840 * q^59 - 33712 * q^60 + 94781 * q^63 + 204800 * q^64 - 9400 * q^65 + 38976 * q^66 - 115930 * q^69 - 3264 * q^72 + 24248 * q^75 - 14304 * q^76 - 150240 * q^77 - 5552 * q^78 - 68658 * q^79 + 47095 * q^81 - 175140 * q^83 - 60816 * q^84 - 138524 * q^85 + 138261 * q^87 + 41728 * q^88 + 104908 * q^89 - 132268 * q^90 + 39296 * q^92 - 91204 * q^93 + 108576 * q^94 + 13312 * q^96 - 343072 * q^98 - 111406 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−4.00000			−0.707107
$2$	−4.00000			−0.707107
$3$	−12.9095	+	8.73750i	−0.828147	+	0.560511i
$3$	−12.9095	+	8.73750i	−0.828147	+	0.560511i
$4$	16.0000			0.500000
$5$			27.1818i			0.486243i	0.969996	+	0.243122i	$0.0781714\pi$
$5$			27.1818i			0.486243i	−0.969996	+	0.243122i	$0.921829\pi$
$6$	51.6381	−	34.9500i	0.585588	−	0.396341i
$7$	−249.363			−1.92348			−0.961740	−	0.273965i	$-0.911665\pi$
$7$	−249.363			−1.92348			−0.961740	+	0.273965i	$0.911665\pi$
$8$	−64.0000			−0.353553
$9$	90.3121	−	225.594i	0.371655	−	0.928371i
$10$		−	108.727i		−	0.343826i
$11$	−19.0816			−0.0475481			−0.0237741	−	0.999717i	$-0.507568\pi$
$11$	−19.0816			−0.0475481			−0.0237741	+	0.999717i	$0.507568\pi$
$12$	−206.553	+	139.800i	−0.414073	+	0.280256i
$13$		−	831.209i		−	1.36412i	−0.731297	−	0.682059i	$-0.761085\pi$
$13$		−	831.209i		−	1.36412i	0.731297	−	0.682059i	$-0.238915\pi$
$14$	997.454			1.36011
$15$	−237.501	−	350.905i	−0.272545	−	0.402681i
$16$	256.000			0.250000
$17$			32.0791i			0.0269215i	0.999909	+	0.0134608i	$0.00428482\pi$
$17$			32.0791i			0.0269215i	−0.999909	+	0.0134608i	$0.995715\pi$
$18$	−361.248	+	902.377i	−0.262800	+	0.656457i
$19$	−1974.78			−1.25497			−0.627486	−	0.778628i	$-0.715916\pi$
$19$	−1974.78			−1.25497			−0.627486	+	0.778628i	$0.715916\pi$
$20$			434.909i			0.243122i
$21$	3219.16	−	2178.81i	1.59292	−	1.07813i
$22$	76.3264			0.0336216
$23$	2858.56			1.12675			0.563375	−	0.826201i	$-0.309503\pi$
$23$	2858.56			1.12675			0.563375	+	0.826201i	$0.309503\pi$
$24$	826.210	−	559.200i	0.292794	−	0.198171i
$25$	2386.15			0.763568
$26$			3324.84i			0.964577i
$27$	805.242	+	3701.42i	0.212577	+	0.977144i
$28$	−3989.81			−0.961740
$29$		−	5589.10i		−	1.23409i	−0.786928	−	0.617045i	$-0.788329\pi$
$29$		−	5589.10i		−	1.23409i	0.786928	−	0.617045i	$-0.211671\pi$
$30$	950.005	+	1403.62i	0.192718	+	0.284738i
$31$		−	735.144i		−	0.137394i	−0.997638	−	0.0686971i	$-0.978116\pi$
$31$		−	735.144i		−	0.137394i	0.997638	−	0.0686971i	$-0.0218842\pi$
$32$	−1024.00			−0.176777
$33$	246.335	−	166.726i	0.0393768	−	0.0266512i
$34$		−	128.316i		−	0.0190364i
$35$		−	6778.15i		−	0.935279i
$36$	1444.99	−	3609.51i	0.185827	−	0.464186i
$37$			12608.3i			1.51410i	0.653359	+	0.757048i	$0.273359\pi$
$37$			12608.3i			1.51410i	−0.653359	+	0.757048i	$0.726641\pi$
$38$	7899.11			0.887399
$39$	7262.69	+	10730.5i	0.764603	+	1.12969i
$40$		−	1739.64i		−	0.171913i
$41$			553.165i			0.0513919i	0.999670	+	0.0256960i	$0.00818018\pi$
$41$			553.165i			0.0513919i	−0.999670	+	0.0256960i	$0.991820\pi$
$42$	−12876.7	+	8715.25i	−1.12637	+	0.762354i
$43$		−	13179.3i		−	1.08698i	−0.839416	−	0.543490i	$-0.817103\pi$
$43$		−	13179.3i		−	1.08698i	0.839416	−	0.543490i	$-0.182897\pi$
$44$	−305.306			−0.0237741
$45$	6132.06	+	2454.85i	0.451414	+	0.180715i
$46$	−11434.2			−0.796733
$47$	−25841.7			−1.70638			−0.853192	−	0.521598i	$-0.825336\pi$
$47$	−25841.7			−1.70638			−0.853192	+	0.521598i	$0.825336\pi$
$48$	−3304.84	+	2236.80i	−0.207037	+	0.140128i
$49$	45375.1			2.69977
$50$	−9544.59			−0.539924
$51$	−280.291	−	414.126i	−0.0150898	−	0.0222950i
$52$		−	13299.3i		−	0.682059i
$53$		−	31787.2i		−	1.55440i	−0.629253	−	0.777200i	$-0.716639\pi$
$53$		−	31787.2i		−	1.55440i	0.629253	−	0.777200i	$-0.283361\pi$
$54$	−3220.97	−	14805.7i	−0.150315	−	0.690945i
$55$		−	518.673i		−	0.0231199i
$56$	15959.3			0.680053
$57$	25493.5	−	17254.6i	1.03930	−	0.703426i
$58$			22356.4i			0.872634i
$59$	5198.86	−	26227.8i	0.194437	−	0.980915i
$59$	5198.86	−	26227.8i	0.194437	−	0.980915i
$60$	−3800.02	−	5614.47i	−0.136272	−	0.201340i
$61$		−	48642.8i		−	1.67376i	−0.547385	−	0.836881i	$-0.684377\pi$
$61$		−	48642.8i		−	1.67376i	0.547385	−	0.836881i	$-0.315623\pi$
$62$			2940.58i			0.0971524i
$63$	−22520.5	+	56254.9i	−0.714870	+	1.78570i
$64$	4096.00			0.125000
$65$	22593.8			0.663293
$66$	−985.339	+	666.902i	−0.0278436	+	0.0188453i
$67$		−	21463.9i		−	0.584147i	−0.956396	−	0.292074i	$-0.905655\pi$
$67$		−	21463.9i		−	0.584147i	0.956396	−	0.292074i	$-0.0943452\pi$
$68$			513.265i			0.0134608i
$69$	−36902.7	+	24976.7i	−0.933115	+	0.631556i
$70$			27112.6i			0.661342i
$71$			48557.5i			1.14317i	0.820543	+	0.571585i	$0.193671\pi$
$71$			48557.5i			1.14317i	−0.820543	+	0.571585i	$0.806329\pi$
$72$	−5779.97	+	14438.0i	−0.131400	+	0.328229i
$73$			57551.1i			1.26400i	0.774969	+	0.631999i	$0.217765\pi$
$73$			57551.1i			1.26400i	−0.774969	+	0.631999i	$0.782235\pi$
$74$		−	50433.4i		−	1.07063i
$75$	−30804.1	+	20849.0i	−0.632346	+	0.427988i
$76$	−31596.4			−0.627486
$77$	4758.26			0.0914578
$78$	−29050.8	−	42922.1i	−0.540656	−	0.798811i
$79$	15793.3			0.284711			0.142355	−	0.989816i	$-0.454532\pi$
$79$	15793.3			0.284711			0.142355	+	0.989816i	$0.454532\pi$
$80$			6958.55i			0.121561i
$81$	−42736.4	−	40747.8i	−0.723746	−	0.690067i
$82$		−	2212.66i		−	0.0363396i
$83$	−117424.			−1.87095			−0.935475	−	0.353394i	$-0.885028\pi$
$83$	−117424.			−1.87095			−0.935475	+	0.353394i	$0.885028\pi$
$84$	51506.6	−	34861.0i	0.796462	−	0.539066i
$85$	−871.968			−0.0130904
$86$			52717.2i			0.768610i
$87$	48834.8	+	72152.7i	0.691722	+	1.02201i
$88$	1221.22			0.0168108
$89$	37701.5			0.504527			0.252263	−	0.967659i	$-0.418825\pi$
$89$	37701.5			0.504527			0.252263	+	0.967659i	$0.418825\pi$
$90$	−24528.2	−	9819.39i	−0.319198	−	0.127785i
$91$			207273.i			2.62385i
$92$	45736.9			0.563375
$93$	6423.33	+	9490.37i	0.0770110	+	0.113783i
$94$	103367.			1.20660
$95$		−	53678.0i		−	0.610222i
$96$	13219.4	−	8947.20i	0.146397	−	0.0990853i
$97$			64760.2i			0.698842i	0.936966	+	0.349421i	$0.113622\pi$
$97$			64760.2i			0.698842i	−0.936966	+	0.349421i	$0.886378\pi$
$98$	−181500.			−1.90903
$99$	−1723.30	+	4304.70i	−0.0176715	+	0.0441423i
$100$	38178.4			0.381784
$101$	−125668.			−1.22581			−0.612903	−	0.790158i	$-0.709998\pi$
$101$	−125668.			−1.22581			−0.612903	+	0.790158i	$0.709998\pi$
$102$	1121.16	+	1656.50i	0.0106701	+	0.0157649i
$103$			170320.i			1.58187i	0.611899	+	0.790936i	$0.290406\pi$
$103$			170320.i			1.58187i	−0.611899	+	0.790936i	$0.709594\pi$
$104$			53197.4i			0.482288i
$105$	59224.1	+	87502.8i	0.524234	+	0.774548i
$106$			127149.i			1.09913i
$107$			30453.1i			0.257142i	0.991700	+	0.128571i	$0.0410389\pi$
$107$			30453.1i			0.257142i	−0.991700	+	0.128571i	$0.958961\pi$
$108$	12883.9	+	59222.7i	0.106289	+	0.488572i
$109$			185355.i			1.49430i	0.664655	+	0.747151i	$0.268579\pi$
$109$			185355.i			1.49430i	−0.664655	+	0.747151i	$0.731421\pi$
$110$			2074.69i			0.0163483i
$111$	−110165.	−	162768.i	−0.848668	−	1.25389i
$112$	−63837.0			−0.480870
$113$	−160899.			−1.18538			−0.592688	−	0.805432i	$-0.701933\pi$
$113$	−160899.			−1.18538			−0.592688	+	0.805432i	$0.701933\pi$
$114$	−101974.	+	69018.5i	−0.734897	+	0.497397i
$115$			77700.8i			0.547875i
$116$		−	89425.6i		−	0.617045i
$117$	−187516.	−	75068.2i	−1.26641	−	0.506981i
$118$	−20795.4	+	104911.i	−0.137487	+	0.693612i
$119$		−	7999.35i		−	0.0517830i
$120$	15200.1	+	22457.9i	0.0963591	+	0.142369i
$121$	−160687.			−0.997739
$122$			194571.i			1.18353i
$123$	−4833.28	−	7141.10i	−0.0288058	−	0.0425601i
$124$		−	11762.3i		−	0.0686971i
$125$			149803.i			0.857523i
$126$	90082.1	−	225020.i	0.505490	−	1.26268i
$127$	−33339.5			−0.183421			−0.0917106	−	0.995786i	$-0.529233\pi$
$127$	−33339.5			−0.183421			−0.0917106	+	0.995786i	$0.529233\pi$
$128$	−16384.0			−0.0883883
$129$	115154.	+	170139.i	0.609264	+	0.900179i
$130$	−90375.1			−0.469019
$131$	207958.			1.05876			0.529379	−	0.848385i	$-0.322425\pi$
$131$	207958.			1.05876			0.529379	+	0.848385i	$0.322425\pi$
$132$	3941.36	−	2667.61i	0.0196884	−	0.0133256i
$133$	492437.			2.41391
$134$			85855.7i			0.413054i
$135$	−100611.	+	21888.0i	−0.475130	+	0.103364i
$136$		−	2053.06i		−	0.00951820i
$137$		−	321269.i		−	1.46240i	−0.682161	−	0.731202i	$-0.738960\pi$
$137$		−	321269.i		−	1.46240i	0.682161	−	0.731202i	$-0.261040\pi$
$138$	147611.	−	99906.7i	0.659812	−	0.446577i
$139$	−270868.			−1.18911			−0.594553	−	0.804057i	$-0.702671\pi$
$139$	−270868.			−1.18911			−0.594553	+	0.804057i	$0.702671\pi$
$140$		−	108450.i		−	0.467639i
$141$	333604.	−	225792.i	1.41314	−	0.956447i
$142$		−	194230.i		−	0.808343i
$143$			15860.8i			0.0648612i
$144$	23119.9	−	57752.1i	0.0929137	−	0.232093i
$145$	151922.			0.600068
$146$		−	230204.i		−	0.893782i
$147$	−585771.	+	396465.i	−2.23581	+	1.51325i
$148$			201733.i			0.757048i
$149$	366442.			1.35219			0.676097	−	0.736812i	$-0.263670\pi$
$149$	366442.			1.35219			0.676097	+	0.736812i	$0.263670\pi$
$150$	123216.	−	83395.9i	0.447136	−	0.302633i
$151$			116689.i			0.416475i	0.978078	+	0.208237i	$0.0667726\pi$
$151$			116689.i			0.416475i	−0.978078	+	0.208237i	$0.933227\pi$
$152$	126386.			0.443700
$153$	7236.86	+	2897.13i	0.0249932	+	0.0100055i
$154$	−19033.0			−0.0646705
$155$	19982.6			0.0668070
$156$	116203.	+	171688.i	0.382301	+	0.564845i
$157$		−	273349.i		−	0.885050i	−0.896756	−	0.442525i	$-0.854083\pi$
$157$		−	273349.i		−	0.885050i	0.896756	−	0.442525i	$-0.145917\pi$
$158$	−63173.1			−0.201321
$159$	277741.	+	410358.i	0.871259	+	1.28727i
$160$		−	27834.2i		−	0.0859565i
$161$	−712820.			−2.16728
$162$	170946.	+	162991.i	0.511765	+	0.487951i
$163$	−130770.			−0.385512			−0.192756	−	0.981247i	$-0.561743\pi$
$163$	−130770.			−0.385512			−0.192756	+	0.981247i	$0.561743\pi$
$164$			8850.64i			0.0256960i
$165$	4531.91	+	6695.83i	0.0129590	+	0.0191467i
$166$	469696.			1.32296
$167$			67427.2i			0.187087i	0.995615	+	0.0935436i	$0.0298194\pi$
$167$			67427.2i			0.187087i	−0.995615	+	0.0935436i	$0.970181\pi$
$168$	−206027.	+	139444.i	−0.563184	+	0.381177i
$169$	−319615.			−0.860816
$170$	3487.87			0.00925632
$171$	−178346.	+	445498.i	−0.466416	+	1.16508i
$172$		−	210869.i		−	0.543490i
$173$	−61414.8			−0.156012			−0.0780060	−	0.996953i	$-0.524855\pi$
$173$	−61414.8			−0.156012			−0.0780060	+	0.996953i	$0.524855\pi$
$174$	−195339.	−	288611.i	−0.489121	−	0.722669i
$175$	−595018.			−1.46871
$176$	−4884.89			−0.0118870
$177$	162050.	+	384013.i	0.388792	+	0.921326i
$178$	−150806.			−0.356754
$179$	369202.			0.861254			0.430627	−	0.902530i	$-0.358292\pi$
$179$	369202.			0.861254			0.430627	+	0.902530i	$0.358292\pi$
$180$	98113.0	+	39277.6i	0.225707	+	0.0903573i
$181$	158624.			0.359891			0.179946	−	0.983677i	$-0.442408\pi$
$181$	158624.			0.359891			0.179946	+	0.983677i	$0.442408\pi$
$182$		−	829092.i		−	1.85534i
$183$	425016.	+	627955.i	0.938162	+	1.38612i
$184$	−182948.			−0.398366
$185$	−342718.			−0.736219
$186$	−25693.3	−	37961.5i	−0.0544550	−	0.0804564i
$187$		−	612.121i		−	0.00128007i
$188$	−413467.			−0.853192
$189$	−200798.	−	922998.i	−0.408888	−	1.87952i
$190$			214712.i			0.431492i
$191$	591614.			1.17342			0.586712	−	0.809796i	$-0.300422\pi$
$191$	591614.			1.17342			0.586712	+	0.809796i	$0.300422\pi$
$192$	−52877.4	+	35788.8i	−0.103518	+	0.0700639i
$193$	−236469.			−0.456962			−0.228481	−	0.973548i	$-0.573376\pi$
$193$	−236469.			−0.456962			−0.228481	+	0.973548i	$0.573376\pi$
$194$		−	259041.i		−	0.494156i
$195$	−291675.	+	197413.i	−0.549304	+	0.371783i
$196$	726002.			1.34989
$197$			614717.i			1.12852i	0.825597	+	0.564261i	$0.190839\pi$
$197$			614717.i			1.12852i	−0.825597	+	0.564261i	$0.809161\pi$
$198$	6893.20	−	17218.8i	0.0124956	−	0.0312133i
$199$	313102.			0.560471			0.280236	−	0.959931i	$-0.409587\pi$
$199$	313102.			0.560471			0.280236	+	0.959931i	$0.409587\pi$
$200$	−152714.			−0.269962
$201$	187541.	+	277089.i	0.327421	+	0.483760i
$202$	502673.			0.866776
$203$			1.39372e6i			2.37375i
$204$	−4484.66	−	6626.02i	−0.00754491	−	0.0111475i
$205$	−15036.0			−0.0249890
$206$		−	681278.i		−	1.11855i
$207$	258162.	−	644874.i	0.418762	−	1.04604i
$208$		−	212789.i		−	0.341029i
$209$	37681.9			0.0596716
$210$	−236896.	−	350011.i	−0.370690	−	0.547688i
$211$			143690.i			0.222187i	0.993810	+	0.111094i	$0.0354354\pi$
$211$			143690.i			0.222187i	−0.993810	+	0.111094i	$0.964565\pi$
$212$		−	508596.i		−	0.777200i
$213$	−424271.	−	626855.i	−0.640759	−	0.946712i
$214$		−	121812.i		−	0.181827i
$215$	358237.			0.528536
$216$	−51535.5	−	236891.i	−0.0751575	−	0.345473i
$217$			183318.i			0.264275i
$218$		−	741420.i		−	1.05663i
$219$	−502853.	−	742958.i	−0.708485	−	1.04678i
$220$		−	8298.77i		−	0.0115600i
$221$	26664.4			0.0367241
$222$	440662.	+	651071.i	0.600099	+	0.886638i
$223$	61539.3			0.0828686			0.0414343	−	0.999141i	$-0.486807\pi$
$223$	61539.3			0.0828686			0.0414343	+	0.999141i	$0.486807\pi$
$224$	255348.			0.340026
$225$	215498.	−	538301.i	0.283783	−	0.708874i
$226$	643595.			0.838188
$227$	−861447.			−1.10959			−0.554797	−	0.831986i	$-0.687204\pi$
$227$	−861447.			−1.10959			−0.554797	+	0.831986i	$0.687204\pi$
$228$	407895.	−	276074.i	0.519651	−	0.351713i
$229$		−	28004.2i		−	0.0352886i	−0.999844	−	0.0176443i	$-0.994383\pi$
$229$		−	28004.2i		−	0.0352886i	0.999844	−	0.0176443i	$-0.00561665\pi$
$230$		−	310803.i		−	0.387406i
$231$	−61426.9	+	41575.3i	−0.0757405	+	0.0512631i
$232$			357703.i			0.436317i
$233$	233617.			0.281913			0.140957	−	0.990016i	$-0.454982\pi$
$233$	233617.			0.281913			0.140957	+	0.990016i	$0.454982\pi$
$234$	750063.	+	300273.i	0.895485	+	0.358489i
$235$		−	702425.i		−	0.829717i
$236$	83181.8	−	419644.i	0.0972183	−	0.490458i
$237$	−203884.	+	137994.i	−0.235783	+	0.159584i
$238$			31997.4i			0.0366161i
$239$		−	1.29212e6i		−	1.46321i	−0.681728	−	0.731606i	$-0.738771\pi$
$239$		−	1.29212e6i		−	1.46321i	0.681728	−	0.731606i	$-0.261229\pi$
$240$	−60800.3	−	89831.6i	−0.0681362	−	0.100670i
$241$	−1.10894e6			−1.22988			−0.614941	−	0.788573i	$-0.710820\pi$
$241$	−1.10894e6			−1.22988			−0.614941	+	0.788573i	$0.710820\pi$
$242$	642748.			0.705508
$243$	907741.	+	152625.i	0.986158	+	0.165809i
$244$		−	778284.i		−	0.836881i
$245$			1.23338e6i			1.31275i
$246$	19333.1	+	28564.4i	0.0203687	+	0.0300945i
$247$			1.64145e6i			1.71193i
$248$			47049.2i			0.0485762i
$249$	1.51589e6	−	1.02599e6i	1.54942	−	1.04869i
$250$		−	599212.i		−	0.606360i
$251$		−	431414.i		−	0.432225i	−0.976368	−	0.216113i	$-0.930662\pi$
$251$		−	431414.i		−	0.432225i	0.976368	−	0.216113i	$-0.0693379\pi$
$252$	−360328.	+	900079.i	−0.357435	+	0.892851i
$253$	−54545.9			−0.0535748
$254$	133358.			0.129698
$255$	11256.7	−	7618.82i	0.0108408	−	0.00733732i
$256$	65536.0			0.0625000
$257$			915310.i			0.864441i	0.901768	+	0.432221i	$0.142270\pi$
$257$			915310.i			0.864441i	−0.901768	+	0.432221i	$0.857730\pi$
$258$	−460617.	−	680555.i	−0.430815	−	0.636522i
$259$		−	3.14406e6i		−	2.91233i
$260$	361500.			0.331646
$261$	−1.26087e6	−	504764.i	−1.14569	−	0.458656i
$262$	−831831.			−0.748655
$263$			777783.i			0.693377i	0.937980	+	0.346688i	$0.112694\pi$
$263$			777783.i			0.693377i	−0.937980	+	0.346688i	$0.887306\pi$
$264$	−15765.4	+	10670.4i	−0.0139218	+	0.00942264i
$265$	864035.			0.755817
$266$	−1.96975e6			−1.70689
$267$	−486709.	+	329417.i	−0.417822	+	0.282793i
$268$		−	343423.i		−	0.292074i
$269$	924524.			0.779000			0.389500	−	0.921026i	$-0.372648\pi$
$269$	924524.			0.779000			0.389500	+	0.921026i	$0.372648\pi$
$270$	402445.	−	87551.8i	0.335967	−	0.0730896i
$271$	−1.81247e6			−1.49915			−0.749577	−	0.661917i	$-0.769743\pi$
$271$	−1.81247e6			−1.49915			−0.749577	+	0.661917i	$0.769743\pi$
$272$			8212.25i			0.00673038i
$273$	−1.81105e6	−	2.67580e6i	−1.47070	−	2.17293i
$274$			1.28508e6i			1.03408i
$275$	−45531.6			−0.0363062
$276$	−590443.	+	399627.i	−0.466557	+	0.315778i
$277$	510011.			0.399374			0.199687	−	0.979860i	$-0.436007\pi$
$277$	510011.			0.399374			0.199687	+	0.979860i	$0.436007\pi$
$278$	1.08347e6			0.840824
$279$	−165844.	−	66392.4i	−0.127553	−	0.0510632i
$280$			433802.i			0.330671i
$281$		−	2.48579e6i		−	1.87801i	−0.343903	−	0.939005i	$-0.611749\pi$
$281$		−	2.48579e6i		−	1.87801i	0.343903	−	0.939005i	$-0.388251\pi$
$282$	−1.33442e6	+	903168.i	−0.999238	+	0.676310i
$283$			2.27300e6i			1.68707i	0.537073	+	0.843536i	$0.319530\pi$
$283$			2.27300e6i			1.68707i	−0.537073	+	0.843536i	$0.680470\pi$
$284$			776920.i			0.571585i
$285$	469012.	+	692958.i	0.342036	+	0.505353i
$286$		−	63443.2i		−	0.0458638i
$287$		−	137939.i		−	0.0988514i
$288$	−92479.6	+	231008.i	−0.0656999	+	0.164114i
$289$	1.41883e6			0.999275
$290$	−607688.			−0.424312
$291$	−565843.	−	836024.i	−0.391709	−	0.578744i
$292$			920818.i			0.631999i
$293$			912407.i			0.620897i	0.950590	+	0.310449i	$0.100479\pi$
$293$			912407.i			0.620897i	−0.950590	+	0.310449i	$0.899521\pi$
$294$	2.34309e6	−	1.58586e6i	1.58096	−	1.07003i
$295$	712919.	+	141314.i	0.476963	+	0.0945435i
$296$		−	806934.i		−	0.535314i
$297$	−15365.3	−	70629.0i	−0.0101077	−	0.0464614i
$298$	−1.46577e6			−0.956146
$299$		−	2.37606e6i		−	1.53702i
$300$	−492865.	+	333584.i	−0.316173	+	0.213994i
$301$			3.28644e6i			2.09078i
$302$		−	466757.i		−	0.294492i
$303$	1.62232e6	−	1.09803e6i	1.01515	−	0.687078i
$304$	−505543.			−0.313743
$305$	1.32220e6			0.813855
$306$	−28947.4	−	11588.5i	−0.0176728	−	0.00707497i
$307$	2.74142e6			1.66008			0.830042	−	0.557700i	$-0.188316\pi$
$307$	2.74142e6			1.66008			0.830042	+	0.557700i	$0.188316\pi$
$308$	76132.1			0.0457289
$309$	−1.48817e6	−	2.19875e6i	−0.886657	−	1.31002i
$310$	−79930.3			−0.0472397
$311$			823152.i			0.482591i	0.970452	+	0.241296i	$0.0775723\pi$
$311$			823152.i			0.482591i	−0.970452	+	0.241296i	$0.922428\pi$
$312$	−464812.	−	686753.i	−0.270328	−	0.399406i
$313$			2.69455e6i			1.55463i	0.629114	+	0.777313i	$0.283418\pi$
$313$			2.69455e6i			1.55463i	−0.629114	+	0.777313i	$0.716582\pi$
$314$			1.09339e6i			0.625825i
$315$	−1.52911e6	−	612149.i	−0.868286	−	0.347601i
$316$	252692.			0.142355
$317$			3.11997e6i			1.74382i	0.489663	+	0.871912i	$0.337120\pi$
$317$			3.11997e6i			1.74382i	−0.489663	+	0.871912i	$0.662880\pi$
$318$	−1.11096e6	−	1.64143e6i	−0.616073	−	0.910239i
$319$			106649.i			0.0586787i
$320$			111337.i			0.0607804i
$321$	−266084.	−	393135.i	−0.144131	−	0.212951i
$322$	2.85128e6			1.53250
$323$		−	63349.1i		−	0.0337858i
$324$	−683783.	−	651964.i	−0.361873	−	0.345033i
$325$		−	1.98339e6i		−	1.04160i
$326$	523079.			0.272598
$327$	−1.61954e6	−	2.39285e6i	−0.837572	−	1.23750i
$328$		−	35402.6i		−	0.0181698i
$329$	6.44398e6			3.28219
$330$	−18127.6	−	26783.3i	−0.00916339	−	0.0135388i
$331$	1.37132e6			0.687968			0.343984	−	0.938975i	$-0.388223\pi$
$331$	1.37132e6			0.687968			0.343984	+	0.938975i	$0.388223\pi$
$332$	−1.87879e6			−0.935475
$333$	2.84437e6	+	1.13869e6i	1.40564	+	0.562721i
$334$		−	269709.i		−	0.132291i
$335$	583429.			0.284038
$336$	824106.	−	557776.i	0.398231	−	0.269533i
$337$		−	1.50392e6i		−	0.721358i	−0.932690	−	0.360679i	$-0.882545\pi$
$337$		−	1.50392e6i		−	0.721358i	0.932690	−	0.360679i	$-0.117455\pi$
$338$	1.27846e6			0.608689
$339$	2.07713e6	−	1.40585e6i	0.981666	−	0.664417i
$340$	−13951.5			−0.00654521
$341$			14027.7i			0.00653284i
$342$	713385.	−	1.78199e6i	0.329806	−	0.823836i
$343$	−7.12384e6			−3.26948
$344$			843475.i			0.384305i
$345$	−678911.	−	1.00308e6i	−0.307090	−	0.453721i
$346$	245659.			0.110317
$347$	1.20439e6			0.536963			0.268482	−	0.963285i	$-0.413478\pi$
$347$	1.20439e6			0.536963			0.268482	+	0.963285i	$0.413478\pi$
$348$	781357.	+	1.15444e6i	0.345861	+	0.511004i
$349$			864403.i			0.379885i	0.981795	+	0.189943i	$0.0608302\pi$
$349$			864403.i			0.379885i	−0.981795	+	0.189943i	$0.939170\pi$
$350$	2.38007e6			1.03853
$351$	3.07665e6	−	669325.i	1.33294	−	0.289981i
$352$	19539.6			0.00840540
$353$	−548637.			−0.234341			−0.117170	−	0.993112i	$-0.537382\pi$
$353$	−548637.			−0.234341			−0.117170	+	0.993112i	$0.537382\pi$
$354$	−648202.	−	1.53605e6i	−0.274917	−	0.651476i
$355$	−1.31988e6			−0.555858
$356$	603225.			0.252263
$357$	69894.3	+	103268.i	0.0290250	+	0.0428839i
$358$	−1.47681e6			−0.608999
$359$			1.47880e6i			0.605583i	0.953057	+	0.302791i	$0.0979185\pi$
$359$			1.47880e6i			0.605583i	−0.953057	+	0.302791i	$0.902081\pi$
$360$	−392452.	−	157110.i	−0.159599	−	0.0638923i
$361$	1.42365e6			0.574955
$362$	−634495.			−0.254482
$363$	2.07439e6	−	1.40400e6i	0.826275	−	0.559244i
$364$			3.31637e6i			1.31193i
$365$	−1.56434e6			−0.614611
$366$	−1.70007e6	−	2.51182e6i	−0.663381	−	0.980135i
$367$			3.76658e6i			1.45976i	0.683574	+	0.729881i	$0.260425\pi$
$367$			3.76658e6i			1.45976i	−0.683574	+	0.729881i	$0.739575\pi$
$368$	731791.			0.281687
$369$	124791.	+	49957.5i	0.0477108	+	0.0191001i
$370$	1.37087e6			0.520586
$371$			7.92657e6i			2.98986i
$372$	102773.	+	151846.i	0.0385055	+	0.0568913i
$373$	1.36999e6			0.509853			0.254927	−	0.966960i	$-0.417949\pi$
$373$	1.36999e6			0.509853			0.254927	+	0.966960i	$0.417949\pi$
$374$			2448.48i			0.000905145i
$375$	−1.30890e6	−	1.93389e6i	−0.480651	−	0.710155i
$376$	1.65387e6			0.603298
$377$	−4.64571e6			−1.68344
$378$	803192.	+	3.69199e6i	0.289128	+	1.32902i
$379$	−1.03832e6			−0.371308			−0.185654	−	0.982615i	$-0.559440\pi$
$379$	−1.03832e6			−0.371308			−0.185654	+	0.982615i	$0.559440\pi$
$380$		−	858849.i		−	0.305111i
$381$	430397.	−	291304.i	0.151900	−	0.102810i
$382$	−2.36646e6			−0.829736
$383$		−	5.23290e6i		−	1.82283i	−0.411492	−	0.911413i	$-0.634992\pi$
$383$		−	5.23290e6i		−	1.82283i	0.411492	−	0.911413i	$-0.365008\pi$
$384$	211510.	−	143155.i	0.0731985	−	0.0495426i
$385$			129338.i			0.0444707i
$386$	945874.			0.323121
$387$	−2.97317e6	−	1.19025e6i	−1.00912	−	0.403981i
$388$			1.03616e6i			0.349421i
$389$		−	1.85039e6i		−	0.619995i	−0.950737	−	0.309998i	$-0.899672\pi$
$389$		−	1.85039e6i		−	0.619995i	0.950737	−	0.309998i	$-0.100328\pi$
$390$	1.16670e6	−	789652.i	0.388416	−	0.262890i
$391$			91700.0i			0.0303338i
$392$	−2.90401e6			−0.954514
$393$	−2.68464e6	+	1.81703e6i	−0.876808	+	0.593446i
$394$		−	2.45887e6i		−	0.797985i
$395$			429290.i			0.138439i
$396$	−27572.8	+	68875.2i	−0.00883574	+	0.0220711i
$397$		−	3.40062e6i		−	1.08288i	−0.840739	−	0.541441i	$-0.817879\pi$
$397$		−	3.40062e6i		−	1.08288i	0.840739	−	0.541441i	$-0.182121\pi$
$398$	−1.25241e6			−0.396313
$399$	−6.35713e6	+	4.30267e6i	−1.99908	+	1.35303i
$400$	610854.			0.190892
$401$	−2.05659e6			−0.638686			−0.319343	−	0.947639i	$-0.603462\pi$
$401$	−2.05659e6			−0.638686			−0.319343	+	0.947639i	$0.603462\pi$
$402$	−750165.	−	1.10836e6i	−0.231522	−	0.342070i
$403$	−611058.			−0.187422
$404$	−2.01069e6			−0.612903
$405$	1.10760e6	−	1.16165e6i	0.335540	−	0.351916i
$406$		−	5.57487e6i		−	1.67849i
$407$		−	240587.i		−	0.0719925i
$408$	17938.6	+	26504.1i	0.00533506	+	0.00788247i
$409$			1.02814e6i			0.303910i	0.988387	+	0.151955i	$0.0485568\pi$
$409$			1.02814e6i			0.303910i	−0.988387	+	0.151955i	$0.951443\pi$
$410$	60144.1			0.0176699
$411$	2.80709e6	+	4.14743e6i	0.819693	+	1.21108i
$412$			2.72511e6i			0.790936i
$413$	−1.29641e6	+	6.54025e6i	−0.373995	+	1.88677i
$414$	−1.03265e6	+	2.57950e6i	−0.296109	+	0.739663i
$415$		−	3.19180e6i		−	0.909736i
$416$			851158.i			0.241144i
$417$	3.49678e6	−	2.36671e6i	0.984754	−	0.666506i
$418$	−150728.			−0.0421942
$419$	3.99798e6			1.11251			0.556257	−	0.831010i	$-0.312237\pi$
$419$	3.99798e6			1.11251			0.556257	+	0.831010i	$0.312237\pi$
$420$	947586.	+	1.40004e6i	0.262117	+	0.387274i
$421$			1.14747e6i			0.315526i	0.987477	+	0.157763i	$0.0504282\pi$
$421$			1.14747e6i			0.315526i	−0.987477	+	0.157763i	$0.949572\pi$
$422$		−	574759.i		−	0.157110i
$423$	−2.33382e6	+	5.82974e6i	−0.634185	+	1.58416i
$424$			2.03438e6i			0.549564i
$425$			76545.5i			0.0205564i
$426$	1.69709e6	+	2.50742e6i	0.453085	+	0.669427i
$427$			1.21297e7i			3.21945i
$428$			487250.i			0.128571i
$429$	−138584.	−	204756.i	−0.0363554	−	0.0537146i
$430$	−1.43295e6			−0.373732
$431$	−2.60282e6			−0.674919			−0.337459	−	0.941340i	$-0.609568\pi$
$431$	−2.60282e6			−0.674919			−0.337459	+	0.941340i	$0.609568\pi$
$432$	206142.	+	947563.i	0.0531444	+	0.244286i
$433$	6.20147e6			1.58955			0.794777	−	0.606902i	$-0.207588\pi$
$433$	6.20147e6			1.58955			0.794777	+	0.606902i	$0.207588\pi$
$434$		−	733272.i		−	0.186871i
$435$	−1.96124e6	+	1.32742e6i	−0.496945	+	0.336345i
$436$			2.96568e6i			0.747151i
$437$	−5.64502e6			−1.41404
$438$	2.01141e6	+	2.97183e6i	0.500975	+	0.740183i
$439$	−1.47136e6			−0.364383			−0.182192	−	0.983263i	$-0.558319\pi$
$439$	−1.47136e6			−0.364383			−0.182192	+	0.983263i	$0.558319\pi$
$440$			33195.1i			0.00817414i
$441$	4.09792e6	−	1.02364e7i	1.00338	−	2.50639i
$442$	−106658.			−0.0259679
$443$	−4.29034e6			−1.03868			−0.519340	−	0.854567i	$-0.673822\pi$
$443$	−4.29034e6			−1.03868			−0.519340	+	0.854567i	$0.673822\pi$
$444$	−1.76265e6	−	2.60429e6i	−0.424334	−	0.626947i
$445$			1.02480e6i			0.245323i
$446$	−246157.			−0.0585970
$447$	−4.73059e6	+	3.20179e6i	−1.11982	+	0.757920i
$448$	−1.02139e6			−0.240435
$449$			694825.i			0.162652i	0.996688	+	0.0813260i	$0.0259155\pi$
$449$			694825.i			0.162652i	−0.996688	+	0.0813260i	$0.974085\pi$
$450$	−861992.	+	2.15320e6i	−0.200665	+	0.501250i
$451$		−	10555.3i		−	0.00244359i
$452$	−2.57438e6			−0.592688
$453$	−1.01957e6	−	1.50640e6i	−0.233439	−	0.344902i
$454$	3.44579e6			0.784602
$455$	−5.63406e6			−1.27583
$456$	−1.63158e6	+	1.10430e6i	−0.367449	+	0.248699i
$457$		−	859411.i		−	0.192491i	−0.995358	−	0.0962455i	$-0.969317\pi$
$457$		−	859411.i		−	0.192491i	0.995358	−	0.0962455i	$-0.0306834\pi$
$458$			112017.i			0.0249528i
$459$	−118738.	+	25831.4i	−0.0263062	+	0.00572291i
$460$			1.24321e6i			0.273937i
$461$			3.46831e6i			0.760091i	0.924968	+	0.380046i	$0.124092\pi$
$461$			3.46831e6i			0.760091i	−0.924968	+	0.380046i	$0.875908\pi$
$462$	245707.	−	166301.i	0.0535566	−	0.0362485i
$463$			7.91320e6i			1.71553i	0.514038	+	0.857767i	$0.328149\pi$
$463$			7.91320e6i			1.71553i	−0.514038	+	0.857767i	$0.671851\pi$
$464$		−	1.43081e6i		−	0.308523i
$465$	−257966.	+	174598.i	−0.0553260	+	0.0374461i
$466$	−934469.			−0.199343
$467$	−3.07470e6			−0.652395			−0.326197	−	0.945302i	$-0.605767\pi$
$467$	−3.07470e6			−0.652395			−0.326197	+	0.945302i	$0.605767\pi$
$468$	−3.00025e6	−	1.20109e6i	−0.633204	−	0.253490i
$469$			5.35232e6i			1.12360i
$470$			2.80970e6i			0.586699i
$471$	2.38838e6	+	3.52880e6i	0.496080	+	0.732951i
$472$	−332727.	+	1.67858e6i	−0.0687437	+	0.346806i
$473$			251482.i			0.0516838i
$474$	815535.	−	551975.i	0.166723	−	0.112843i
$475$	−4.71211e6			−0.958256
$476$		−	127990.i		−	0.0258915i
$477$	−7.17101e6	−	2.87077e6i	−1.44306	−	0.577700i
$478$			5.16847e6i			1.03465i
$479$		−	3.10651e6i		−	0.618633i	−0.950959	−	0.309317i	$-0.899900\pi$
$479$		−	3.10651e6i		−	0.618633i	0.950959	−	0.309317i	$-0.100100\pi$
$480$	243201.	+	359326.i	0.0481795	+	0.0711846i
$481$	1.04802e7			2.06541
$482$	4.43574e6			0.869658
$483$	9.20217e6	−	6.22827e6i	1.79483	−	1.21478i
$484$	−2.57099e6			−0.498870
$485$	−1.76030e6			−0.339807
$486$	−3.63097e6	−	610499.i	−0.697319	−	0.117245i
$487$	244673.			0.0467481			0.0233740	−	0.999727i	$-0.492559\pi$
$487$	244673.			0.0467481			0.0233740	+	0.999727i	$0.492559\pi$
$488$			3.11314e6i			0.591764i
$489$	1.68818e6	−	1.14260e6i	0.319261	−	0.216084i
$490$		−	4.93351e6i		−	0.928252i
$491$		−	7.22347e6i		−	1.35220i	−0.736808	−	0.676102i	$-0.763668\pi$
$491$		−	7.22347e6i		−	1.35220i	0.736808	−	0.676102i	$-0.236332\pi$
$492$	−77332.5	−	114258.i	−0.0144029	−	0.0212800i
$493$	179293.			0.0332236
$494$		−	6.56581e6i		−	1.21052i
$495$	−117010.	−	46842.4i	−0.0214639	−	0.00859264i
$496$		−	188197.i		−	0.0343486i
$497$		−	1.21085e7i		−	2.19886i
$498$	−6.06356e6	+	4.10397e6i	−1.09561	+	0.741534i
$499$	6.58867e6			1.18453			0.592265	−	0.805743i	$-0.298234\pi$
$499$	6.58867e6			1.18453			0.592265	+	0.805743i	$0.298234\pi$
$500$			2.39685e6i			0.428761i
$501$	−589145.	−	870453.i	−0.104864	−	0.154936i
$502$			1.72566e6i			0.305630i
$503$	7.55097e6			1.33071			0.665354	−	0.746528i	$-0.268281\pi$
$503$	7.55097e6			1.33071			0.665354	+	0.746528i	$0.268281\pi$
$504$	1.44131e6	−	3.60032e6i	0.252745	−	0.631341i
$505$		−	3.41589e6i		−	0.596040i
$506$	218184.			0.0378831
$507$	4.12608e6	−	2.79264e6i	0.712882	−	0.482497i
$508$	−533432.			−0.0917106
$509$	1.10535e7			1.89106			0.945531	−	0.325533i	$-0.105544\pi$
$509$	1.10535e7			1.89106			0.945531	+	0.325533i	$0.105544\pi$
$510$	−45026.8	+	30475.3i	−0.00766559	+	0.00518827i
$511$		−	1.43511e7i		−	2.43127i
$512$	−262144.			−0.0441942
$513$	−1.59017e6	−	7.30948e6i	−0.266779	−	1.22629i
$514$		−	3.66124e6i		−	0.611252i
$515$	−4.62960e6			−0.769175
$516$	1.84247e6	+	2.72222e6i	0.304632	+	0.450089i
$517$	493101.			0.0811353
$518$			1.25762e7i			2.05933i
$519$	792837.	−	536612.i	0.129201	−	0.0874464i
$520$	−1.44600e6			−0.234509
$521$			4.07215e6i			0.657248i	0.944461	+	0.328624i	$0.106585\pi$
$521$			4.07215e6i			0.657248i	−0.944461	+	0.328624i	$0.893415\pi$
$522$	5.04348e6	+	2.01905e6i	0.810128	+	0.324319i
$523$	8.02958e6			1.28363			0.641813	−	0.766861i	$-0.278182\pi$
$523$	8.02958e6			1.28363			0.641813	+	0.766861i	$0.278182\pi$
$524$	3.32732e6			0.529379
$525$	7.68141e6	−	5.19897e6i	1.21630	−	0.823226i
$526$		−	3.11113e6i		−	0.490291i
$527$	23582.8			0.00369886
$528$	63061.7	−	42681.8i	0.00984421	−	0.00666281i
$529$	1.73502e6			0.269566
$530$	−3.45614e6			−0.534443
$531$	−5.44731e6	−	3.54152e6i	−0.838390	−	0.545071i
$532$	7.87899e6			1.20696
$533$	459796.			0.0701046
$534$	1.94684e6	−	1.31767e6i	0.295445	−	0.199965i
$535$	−827771.			−0.125033
$536$			1.37369e6i			0.206527i
$537$	−4.76622e6	+	3.22590e6i	−0.713245	+	0.482742i
$538$	−3.69809e6			−0.550836
$539$	−865830.			−0.128369
$540$	−1.60978e6	+	350207.i	−0.237565	+	0.0516822i
$541$			5.05013e6i			0.741838i	0.928665	+	0.370919i	$0.120957\pi$
$541$			5.05013e6i			0.741838i	−0.928665	+	0.370919i	$0.879043\pi$
$542$	7.24986e6			1.06006
$543$	−2.04776e6	+	1.38597e6i	−0.298043	+	0.201723i
$544$		−	32849.0i		−	0.00475910i
$545$	−5.03829e6			−0.726594
$546$	7.24419e6	+	1.07032e7i	1.03994	+	1.53650i
$547$	−2.55185e6			−0.364659			−0.182330	−	0.983237i	$-0.558364\pi$
$547$	−2.55185e6			−0.364659			−0.182330	+	0.983237i	$0.558364\pi$
$548$		−	5.14030e6i		−	0.731202i
$549$	−1.09735e7	−	4.39303e6i	−1.55387	−	0.622061i
$550$	182126.			0.0256724
$551$			1.10372e7i			1.54875i
$552$	2.36177e6	−	1.59851e6i	0.329906	−	0.223289i
$553$	−3.93826e6			−0.547636
$554$	−2.04004e6			−0.282400
$555$	4.42433e6	−	2.99450e6i	0.609698	−	0.412659i
$556$	−4.33388e6			−0.594553
$557$		−	821859.i		−	0.112243i	−0.998424	−	0.0561215i	$-0.982127\pi$
$557$		−	821859.i		−	0.112243i	0.998424	−	0.0561215i	$-0.0178734\pi$
$558$	663377.	+	265570.i	0.0901934	+	0.0361071i
$559$	−1.09548e7			−1.48277
$560$		−	1.73521e6i		−	0.233820i
$561$	5348.41	+	7902.19i	0.000717492	+	0.00106008i
$562$			9.94315e6i			1.32795i
$563$	−7.46240e6			−0.992219			−0.496110	−	0.868260i	$-0.665239\pi$
$563$	−7.46240e6			−0.992219			−0.496110	+	0.868260i	$0.665239\pi$
$564$	5.33767e6	−	3.61267e6i	0.706568	−	0.478223i
$565$		−	4.37352e6i		−	0.576381i
$566$		−	9.09200e6i		−	1.19294i
$567$	1.06569e7	+	1.01610e7i	1.39211	+	1.32733i
$568$		−	3.10768e6i		−	0.404171i
$569$	−5.27703e6			−0.683296			−0.341648	−	0.939828i	$-0.610985\pi$
$569$	−5.27703e6			−0.683296			−0.341648	+	0.939828i	$0.610985\pi$
$570$	−1.87605e6	−	2.77183e6i	−0.241856	−	0.357339i
$571$			5.93463e6i			0.761734i	0.924630	+	0.380867i	$0.124375\pi$
$571$			5.93463e6i			0.761734i	−0.924630	+	0.380867i	$0.875625\pi$
$572$			253773.i			0.0324306i
$573$	−7.63746e6	+	5.16923e6i	−0.971768	+	0.657717i
$574$			551756.i			0.0698985i
$575$	6.82095e6			0.860350
$576$	369918.	−	924034.i	0.0464568	−	0.116046i
$577$	−3.50046e6			−0.437709			−0.218855	−	0.975757i	$-0.570232\pi$
$577$	−3.50046e6			−0.437709			−0.218855	+	0.975757i	$0.570232\pi$
$578$	−5.67531e6			−0.706594
$579$	3.05270e6	−	2.06615e6i	0.378432	−	0.256132i
$580$	2.43075e6			0.300034
$581$	2.92813e7			3.59873
$582$	2.26337e6	+	3.34410e6i	0.276980	+	0.409234i
$583$			606551.i			0.0739088i
$584$		−	3.68327e6i		−	0.446891i
$585$	2.04049e6	−	5.09702e6i	0.246516	−	0.615782i
$586$		−	3.64963e6i		−	0.439041i
$587$	8.90956e6			1.06724			0.533619	−	0.845725i	$-0.320832\pi$
$587$	8.90956e6			1.06724			0.533619	+	0.845725i	$0.320832\pi$
$588$	−9.37234e6	+	6.34344e6i	−1.11790	+	0.756627i
$589$			1.45175e6i			0.172426i
$590$	−2.85167e6	−	565258.i	−0.337264	−	0.0668523i
$591$	−5.37109e6	−	7.93571e6i	−0.632548	−	0.934581i
$592$			3.22774e6i			0.378524i
$593$		−	8.64554e6i		−	1.00961i	−0.863232	−	0.504807i	$-0.831564\pi$
$593$		−	8.64554e6i		−	1.00961i	0.863232	−	0.504807i	$-0.168436\pi$
$594$	61461.3	+	282516.i	0.00714719	+	0.0328531i
$595$	217437.			0.0251791
$596$	5.86307e6			0.676097
$597$	−4.04200e6	+	2.73573e6i	−0.464153	+	0.314150i
$598$			9.50424e6i			1.08684i
$599$			1.27001e7i			1.44623i	0.690726	+	0.723117i	$0.257291\pi$
$599$			1.27001e7i			1.44623i	−0.690726	+	0.723117i	$0.742709\pi$
$600$	1.97146e6	−	1.33433e6i	0.223568	−	0.151317i
$601$			264815.i			0.0299058i	0.999888	+	0.0149529i	$0.00475984\pi$
$601$			264815.i			0.0299058i	−0.999888	+	0.0149529i	$0.995240\pi$
$602$		−	1.31457e7i		−	1.47841i
$603$	−4.84214e6	−	1.93845e6i	−0.542305	−	0.217101i
$604$			1.86703e6i			0.208237i
$605$		−	4.36776e6i		−	0.485144i
$606$	−6.48927e6	+	4.39210e6i	−0.717818	+	0.485838i
$607$	−9.08359e6			−1.00066			−0.500329	−	0.865835i	$-0.666788\pi$
$607$	−9.08359e6			−1.00066			−0.500329	+	0.865835i	$0.666788\pi$
$608$	2.02217e6			0.221850
$609$	−1.21776e7	−	1.79922e7i	−1.33051	−	1.96581i
$610$	−5.28880e6			−0.575483
$611$			2.14799e7i			2.32771i
$612$	115790.	+	46354.1i	0.0124966	+	0.00500276i
$613$			1.44109e7i			1.54896i	0.632599	+	0.774480i	$0.281988\pi$
$613$			1.44109e7i			1.54896i	−0.632599	+	0.774480i	$0.718012\pi$
$614$	−1.09657e7			−1.17386
$615$	194108.	−	131377.i	0.0206945	−	0.0140066i
$616$	−304528.			−0.0323352
$617$			3.21358e6i			0.339841i	0.985458	+	0.169921i	$0.0543511\pi$
$617$			3.21358e6i			0.339841i	−0.985458	+	0.169921i	$0.945649\pi$
$618$	5.95267e6	+	8.79498e6i	0.626961	+	0.926326i
$619$	1.14962e6			0.120594			0.0602972	−	0.998180i	$-0.480795\pi$
$619$	1.14962e6			0.120594			0.0602972	+	0.998180i	$0.480795\pi$
$620$	319721.			0.0334035
$621$	2.30183e6	+	1.05807e7i	0.239522	+	1.10100i
$622$		−	3.29261e6i		−	0.341243i
$623$	−9.40138e6			−0.970447
$624$	1.85925e6	+	2.74701e6i	0.191151	+	0.282422i
$625$	3.38479e6			0.346603
$626$		−	1.07782e7i		−	1.09929i
$627$	−486456.	+	329246.i	−0.0494168	+	0.0334466i
$628$		−	4.37358e6i		−	0.442525i
$629$	−404464.			−0.0407618
$630$	6.11644e6	+	2.44860e6i	0.613971	+	0.245791i
$631$	1.22280e7			1.22259			0.611297	−	0.791401i	$-0.290648\pi$
$631$	1.22280e7			1.22259			0.611297	+	0.791401i	$0.290648\pi$
$632$	−1.01077e6			−0.100661
$633$	−1.25549e6	−	1.85497e6i	−0.124538	−	0.184004i
$634$		−	1.24799e7i		−	1.23307i
$635$		−	906228.i		−	0.0891873i
$636$	4.44386e6	+	6.56573e6i	0.435629	+	0.643636i
$637$		−	3.77162e7i		−	3.68281i
$638$		−	426596.i		−	0.0414921i
$639$	1.09543e7	+	4.38533e6i	1.06129	+	0.424864i
$640$		−	445347.i		−	0.0429782i
$641$		−	1.13066e7i		−	1.08689i	−0.839443	−	0.543447i	$-0.817119\pi$
$641$		−	1.13066e7i		−	1.08689i	0.839443	−	0.543447i	$-0.182881\pi$
$642$	1.06434e6	+	1.57254e6i	0.101916	+	0.150579i
$643$	−1.33986e6			−0.127801			−0.0639003	−	0.997956i	$-0.520354\pi$
$643$	−1.33986e6			−0.127801			−0.0639003	+	0.997956i	$0.520354\pi$
$644$	−1.14051e7			−1.08364
$645$	−4.62468e6	+	3.13010e6i	−0.437706	+	0.296250i
$646$			253396.i			0.0238901i
$647$		−	6.13593e6i		−	0.576261i	−0.957591	−	0.288131i	$-0.906966\pi$
$647$		−	6.13593e6i		−	0.576261i	0.957591	−	0.288131i	$-0.0930337\pi$
$648$	2.73513e6	+	2.60786e6i	0.255883	+	0.243976i
$649$	−99202.6	+	500468.i	−0.00924509	+	0.0466407i
$650$			7.93355e6i			0.736519i
$651$	−1.60174e6	−	2.36655e6i	−0.148129	−	0.218858i
$652$	−2.09232e6			−0.192756
$653$		−	6.51370e6i		−	0.597785i	−0.954287	−	0.298892i	$-0.903383\pi$
$653$		−	6.51370e6i		−	0.597785i	0.954287	−	0.298892i	$-0.0966172\pi$
$654$	6.47816e6	+	9.57139e6i	0.592253	+	0.875045i
$655$			5.65267e6i			0.514814i
$656$			141610.i			0.0128480i
$657$	1.29832e7	+	5.19756e6i	1.17346	+	0.469771i
$658$	−2.57759e7			−2.32086
$659$	−1.08066e6			−0.0969338			−0.0484669	−	0.998825i	$-0.515434\pi$
$659$	−1.08066e6			−0.0969338			−0.0484669	+	0.998825i	$0.515434\pi$
$660$	72510.5	+	107133.i	0.00647949	+	0.00957336i
$661$	1.26714e7			1.12803			0.564016	−	0.825764i	$-0.309256\pi$
$661$	1.26714e7			1.12803			0.564016	+	0.825764i	$0.309256\pi$
$662$	−5.48528e6			−0.486467
$663$	−344225.	+	232980.i	−0.0304130	+	0.0205843i
$664$	7.51514e6			0.661481
$665$			1.33853e7i			1.17375i
$666$	−1.13775e7	−	4.55474e6i	−0.993940	−	0.397904i
$667$		−	1.59768e7i		−	1.39051i
$668$			1.07883e6i			0.0935436i
$669$	−794443.	+	537700.i	−0.0686274	+	0.0464488i
$670$	−2.33372e6			−0.200845
$671$			928182.i			0.0795842i
$672$	−3.29642e6	+	2.23110e6i	−0.281592	+	0.190589i
$673$			1.22706e7i			1.04431i	0.852850	+	0.522156i	$0.174872\pi$
$673$			1.22706e7i			1.04431i	−0.852850	+	0.522156i	$0.825128\pi$
$674$			6.01569e6i			0.510077i
$675$	1.92143e6	+	8.83213e6i	0.162317	+	0.746116i
$676$	−5.11384e6			−0.430408
$677$			4.72780e6i			0.396449i	0.980157	+	0.198224i	$0.0635175\pi$
$677$			4.72780e6i			0.396449i	−0.980157	+	0.198224i	$0.936482\pi$
$678$	−8.30851e6	+	5.62341e6i	−0.694143	+	0.469814i
$679$		−	1.61488e7i		−	1.34421i
$680$	55806.0			0.00462816
$681$	1.11209e7	−	7.52690e6i	0.918907	−	0.621940i
$682$		−	56111.0i		−	0.00461941i
$683$	6.14881e6			0.504359			0.252179	−	0.967680i	$-0.418853\pi$
$683$	6.14881e6			0.504359			0.252179	+	0.967680i	$0.418853\pi$
$684$	−2.85354e6	+	7.12797e6i	−0.233208	+	0.582540i
$685$	8.73267e6			0.711084
$686$	2.84954e7			2.31187
$687$	244687.	+	361521.i	0.0197796	+	0.0292241i
$688$		−	3.37390e6i		−	0.271745i
$689$	−2.64218e7			−2.12038
$690$	2.71564e6	+	4.01233e6i	0.217145	+	0.320829i
$691$			6.35626e6i			0.506415i	0.967412	+	0.253207i	$0.0814855\pi$
$691$			6.35626e6i			0.506415i	−0.967412	+	0.253207i	$0.918515\pi$
$692$	−982637.			−0.0780060
$693$	429728.	−	1.07343e6i	0.0339907	−	0.0849068i
$694$	−4.81757e6			−0.379691
$695$		−	7.36268e6i		−	0.578194i
$696$	−3.12543e6	−	4.61777e6i	−0.244560	−	0.361335i
$697$	−17745.0			−0.00138355
$698$		−	3.45761e6i		−	0.268620i
$699$	−3.01589e6	+	2.04123e6i	−0.233465	+	0.158015i
$700$	−9.52029e6			−0.734353
$701$	6.10135e6			0.468955			0.234477	−	0.972122i	$-0.424662\pi$
$701$	6.10135e6			0.468955			0.234477	+	0.972122i	$0.424662\pi$
$702$	−1.23066e7	+	2.67730e6i	−0.942530	+	0.205047i
$703$		−	2.48987e7i		−	1.90015i
$704$	−78158.3			−0.00594351
$705$	6.13744e6	+	9.06798e6i	0.465066	+	0.687128i
$706$	2.19455e6			0.165704
$707$	3.13370e7			2.35781
$708$	2.59281e6	+	6.14421e6i	0.194396	+	0.460663i
$709$	−1.11383e6			−0.0832152			−0.0416076	−	0.999134i	$-0.513248\pi$
$709$	−1.11383e6			−0.0832152			−0.0416076	+	0.999134i	$0.513248\pi$
$710$	5.27953e6			0.393051
$711$	1.42632e6	−	3.56287e6i	0.105814	−	0.264317i
$712$	−2.41290e6			−0.178377
$713$		−	2.10145e6i		−	0.154809i
$714$	−279577.	−	413072.i	−0.0205237	−	0.0303235i
$715$	−431125.			−0.0315383
$716$	5.90723e6			0.430627
$717$	1.12899e7	+	1.66806e7i	0.820146	+	1.21175i
$718$		−	5.91520e6i		−	0.428212i
$719$	−7.45716e6			−0.537961			−0.268981	−	0.963146i	$-0.586687\pi$
$719$	−7.45716e6			−0.537961			−0.268981	+	0.963146i	$0.586687\pi$
$720$	1.56981e6	+	628441.i	0.112854	+	0.0451786i
$721$		−	4.24715e7i		−	3.04270i
$722$	−5.69459e6			−0.406555
$723$	1.43158e7	−	9.68932e6i	1.01852	−	0.689363i
$724$	2.53798e6			0.179946
$725$		−	1.33364e7i		−	0.942312i
$726$	−8.29757e6	+	5.61601e6i	−0.584264	+	0.395445i
$727$	1.44480e6			0.101385			0.0506924	−	0.998714i	$-0.483857\pi$
$727$	1.44480e6			0.101385			0.0506924	+	0.998714i	$0.483857\pi$
$728$		−	1.32655e7i		−	0.927672i
$729$	−1.30521e7	+	5.96108e6i	−0.909622	+	0.415438i
$730$	6.25737e6			0.434595
$731$	422780.			0.0292631
$732$	6.80026e6	+	1.00473e7i	0.469081	+	0.693060i
$733$	2.12581e6			0.146139			0.0730694	−	0.997327i	$-0.476721\pi$
$733$	2.12581e6			0.146139			0.0730694	+	0.997327i	$0.476721\pi$
$734$		−	1.50663e7i		−	1.03221i
$735$	−1.07766e7	−	1.59223e7i	−0.735809	−	1.08715i
$736$	−2.92716e6			−0.199183
$737$			409566.i			0.0277751i
$738$	−499163.	−	199830.i	−0.0337366	−	0.0135058i
$739$			2.67233e7i			1.80003i	0.435860	+	0.900014i	$0.356444\pi$
$739$			2.67233e7i			1.80003i	−0.435860	+	0.900014i	$0.643556\pi$
$740$	−5.48348e6			−0.368110
$741$	−1.43422e7	−	2.11904e7i	−0.959555	−	1.41773i
$742$		−	3.17063e7i		−	2.11415i
$743$			1.48655e7i			0.987885i	0.869494	+	0.493943i	$0.164445\pi$
$743$			1.48655e7i			0.987885i	−0.869494	+	0.493943i	$0.835555\pi$
$744$	−411093.	−	607384.i	−0.0272275	−	0.0402282i
$745$			9.96055e6i			0.657496i
$746$	−5.47996e6			−0.360521
$747$	−1.06048e7	+	2.64902e7i	−0.695347	+	1.73694i
$748$		−	9793.93i		−	0.000640034i
$749$		−	7.59389e6i		−	0.494606i
$750$	5.23562e6	+	7.73555e6i	0.339872	+	0.502155i
$751$		−	1.28094e6i		−	0.0828758i	−0.999141	−	0.0414379i	$-0.986806\pi$
$751$		−	1.28094e6i		−	0.0828758i	0.999141	−	0.0414379i	$-0.0131939\pi$
$752$	−6.61548e6			−0.426596
$753$	3.76948e6	+	5.56936e6i	0.242267	+	0.357946i
$754$	1.85828e7			1.19038
$755$	−3.17183e6			−0.202508
$756$	−3.21277e6	−	1.47680e7i	−0.204444	−	0.939758i
$757$	−1.46658e7			−0.930178			−0.465089	−	0.885264i	$-0.653978\pi$
$757$	−1.46658e7			−0.930178			−0.465089	+	0.885264i	$0.653978\pi$
$758$	4.15329e6			0.262555
$759$	704162.	−	476595.i	0.0443678	−	0.0300293i
$760$			3.43539e6i			0.215746i
$761$			8.27138e6i			0.517745i	0.965911	+	0.258873i	$0.0833510\pi$
$761$			8.27138e6i			0.517745i	−0.965911	+	0.258873i	$0.916649\pi$
$762$	−1.72159e6	+	1.16522e6i	−0.107409	+	0.0726974i
$763$		−	4.62208e7i		−	2.87426i
$764$	9.46582e6			0.586712
$765$	−78749.3	+	196711.i	−0.00486511	+	0.0121528i
$766$			2.09316e7i			1.28893i
$767$	−2.18008e7	−	4.32134e6i	−1.33808	−	0.265234i
$768$	−846039.	+	572621.i	−0.0517592	+	0.0350319i
$769$		−	7.12105e6i		−	0.434238i	−0.976145	−	0.217119i	$-0.930334\pi$
$769$		−	7.12105e6i		−	0.434238i	0.976145	−	0.217119i	$-0.0696660\pi$
$770$		−	517352.i		−	0.0314456i
$771$	−7.99753e6	−	1.18162e7i	−0.484529	−	0.715884i
$772$	−3.78350e6			−0.228481
$773$	−1.74787e6			−0.105211			−0.0526054	−	0.998615i	$-0.516753\pi$
$773$	−1.74787e6			−0.105211			−0.0526054	+	0.998615i	$0.516753\pi$
$774$	1.18927e7	+	4.76100e6i	0.713556	+	0.285658i
$775$		−	1.75416e6i		−	0.104910i
$776$		−	4.14465e6i		−	0.247078i
$777$	2.74712e7	+	4.05883e7i	1.63240	+	2.41184i
$778$			7.40154e6i			0.438403i
$779$		−	1.09238e6i		−	0.0644955i
$780$	−4.66680e6	+	3.15861e6i	−0.274652	+	0.185891i
$781$		−	926555.i		−	0.0543555i
$782$		−	366800.i		−	0.0214493i
$783$	2.06876e7	−	4.50058e6i	1.20588	−	0.262340i
$784$	1.16160e7			0.674943
$785$	7.43011e6			0.430350
$786$	1.07386e7	−	7.26813e6i	0.619997	−	0.419630i
$787$	−8.32100e6			−0.478893			−0.239447	−	0.970910i	$-0.576966\pi$
$787$	−8.32100e6			−0.478893			−0.239447	+	0.970910i	$0.576966\pi$
$788$			9.83547e6i			0.564261i
$789$	−6.79588e6	−	1.00408e7i	−0.388645	−	0.574218i
$790$		−	1.71716e6i		−	0.0978910i
$791$	4.01222e7			2.28005
$792$	110291.	−	275501.i	0.00624781	−	0.0156067i
$793$	−4.04323e7			−2.28321
$794$			1.36025e7i			0.765713i
$795$	−1.11543e7	+	7.54951e6i	−0.625927	+	0.423644i
$796$	5.00964e6			0.280236
$797$	−2.62306e7			−1.46272			−0.731362	−	0.681990i	$-0.761115\pi$
$797$	−2.62306e7			−1.46272			−0.731362	+	0.681990i	$0.761115\pi$
$798$	2.54285e7	−	1.72107e7i	1.41356	−	0.956733i
$799$		−	828979.i		−	0.0459384i
$800$	−2.44342e6			−0.134981
$801$	3.40491e6	−	8.50525e6i	0.187510	−	0.468388i
$802$	8.22637e6			0.451619
$803$		−	1.09817e6i		−	0.0601007i
$804$	3.00066e6	+	4.43343e6i	0.163710	+	0.241880i
$805$		−	1.93757e7i		−	1.05383i
$806$	2.44423e6			0.132527
$807$	−1.19352e7	+	8.07803e6i	−0.645126	+	0.436638i
$808$	8.04276e6			0.433388
$809$	1.64514e7			0.883755			0.441877	−	0.897075i	$-0.354313\pi$
$809$	1.64514e7			0.883755			0.441877	+	0.897075i	$0.354313\pi$
$810$	−4.43039e6	+	4.64662e6i	−0.237263	+	0.248842i
$811$		−	6.45007e6i		−	0.344360i	−0.985066	−	0.172180i	$-0.944919\pi$
$811$		−	6.45007e6i		−	0.344360i	0.985066	−	0.172180i	$-0.0550810\pi$
$812$			2.22995e7i			1.18687i
$813$	2.33981e7	−	1.58364e7i	1.24152	−	0.840293i
$814$			962350.i			0.0509064i
$815$		−	3.55456e6i		−	0.187453i
$816$	−71754.5	−	106016.i	−0.00377245	−	0.00557375i
$817$			2.60262e7i			1.36413i
$818$		−	4.11256e6i		−	0.214897i
$819$	4.67596e7	+	1.87193e7i	2.43591	+	0.975167i
$820$	−240576.			−0.0124945
$821$	−5.68974e6			−0.294601			−0.147301	−	0.989092i	$-0.547058\pi$
$821$	−5.68974e6			−0.294601			−0.147301	+	0.989092i	$0.547058\pi$
$822$	−1.12283e7	−	1.65897e7i	−0.579611	−	0.856366i
$823$			1.81413e7i			0.933619i	0.884358	+	0.466810i	$0.154597\pi$
$823$			1.81413e7i			0.933619i	−0.884358	+	0.466810i	$0.845403\pi$
$824$		−	1.09005e7i		−	0.559276i
$825$	587791.	−	397832.i	0.0300669	−	0.0203500i
$826$	5.18562e6	−	2.61610e7i	0.264454	−	1.33415i
$827$			1.18723e7i			0.603632i	0.953366	+	0.301816i	$0.0975929\pi$
$827$			1.18723e7i			0.603632i	−0.953366	+	0.301816i	$0.902407\pi$
$828$	4.13060e6	−	1.03180e7i	0.209381	−	0.523021i
$829$	−2.37256e7			−1.19903			−0.599517	−	0.800362i	$-0.704640\pi$
$829$	−2.37256e7			−1.19903			−0.599517	+	0.800362i	$0.704640\pi$
$830$			1.27672e7i			0.643281i
$831$	−6.58400e6	+	4.45622e6i	−0.330740	+	0.223854i
$832$		−	3.40463e6i		−	0.170515i
$833$			1.45559e6i			0.0726820i
$834$	−1.39871e7	+	9.46683e6i	−0.696326	+	0.471291i
$835$	−1.83279e6			−0.0909698
$836$	602911.			0.0298358
$837$	2.72108e6	−	591969.i	0.134254	−	0.0292069i
$838$	−1.59919e7			−0.786667
$839$	−3.05279e7			−1.49724			−0.748622	−	0.662997i	$-0.769284\pi$
$839$	−3.05279e7			−1.49724			−0.748622	+	0.662997i	$0.769284\pi$
$840$	−3.79034e6	−	5.60018e6i	−0.185345	−	0.273844i
$841$	−1.07269e7			−0.522980
$842$		−	4.58987e6i		−	0.223111i
$843$	2.17196e7	+	3.20903e7i	1.05265	+	1.55527i
$844$			2.29903e6i			0.111094i
$845$		−	8.68772e6i		−	0.418566i
$846$	9.33528e6	−	2.33190e7i	0.448437	−	1.12017i
$847$	4.00694e7			1.91913
$848$		−	8.13753e6i		−	0.388600i
$849$	−1.98603e7	−	2.93434e7i	−0.945622	−	1.39714i
$850$		−	306182.i		−	0.0145356i
$851$			3.60417e7i			1.70601i
$852$	−6.78834e6	−	1.00297e7i	−0.320379	−	0.473356i
$853$	−1.24002e7			−0.583522			−0.291761	−	0.956491i	$-0.594241\pi$
$853$	−1.24002e7			−0.583522			−0.291761	+	0.956491i	$0.594241\pi$
$854$		−	4.85189e7i		−	2.27649i
$855$	−1.21095e7	−	4.84778e6i	−0.566512	−	0.226792i
$856$		−	1.94900e6i		−	0.0909133i
$857$	−9.18455e6			−0.427175			−0.213587	−	0.976924i	$-0.568515\pi$
$857$	−9.18455e6			−0.427175			−0.213587	+	0.976924i	$0.568515\pi$
$858$	554335.	+	819022.i	0.0257072	+	0.0379820i
$859$		−	9.49362e6i		−	0.438984i	−0.975614	−	0.219492i	$-0.929560\pi$
$859$		−	9.49362e6i		−	0.438984i	0.975614	−	0.219492i	$-0.0704401\pi$
$860$	5.73180e6			0.264268
$861$	1.20524e6	+	1.78073e6i	0.0554073	+	0.0818634i
$862$	1.04113e7			0.477240
$863$	1.36883e7			0.625637			0.312819	−	0.949813i	$-0.398727\pi$
$863$	1.36883e7			0.625637			0.312819	+	0.949813i	$0.398727\pi$
$864$	−824568.	−	3.79025e6i	−0.0375787	−	0.172736i
$865$		−	1.66937e6i		−	0.0758597i
$866$	−2.48059e7			−1.12398
$867$	−1.83164e7	+	1.23970e7i	−0.827547	+	0.560105i
$868$			2.93309e6i			0.132137i
$869$	−301361.			−0.0135375
$870$	7.84497e6	−	5.30967e6i	0.351393	−	0.237832i
$871$	−1.78410e7			−0.796845
$872$		−	1.18627e7i		−	0.528315i
$873$	1.46095e7	+	5.84863e6i	0.648785	+	0.259728i
$874$	2.25801e7			0.999877
$875$		−	3.73554e7i		−	1.64943i
$876$	−8.04565e6	−	1.18873e7i	−0.354243	−	0.523388i
$877$	−2.54146e7			−1.11580			−0.557898	−	0.829909i	$-0.688392\pi$
$877$	−2.54146e7			−1.11580			−0.557898	+	0.829909i	$0.688392\pi$
$878$	5.88545e6			0.257658
$879$	−7.97216e6	−	1.17788e7i	−0.348020	−	0.514194i
$880$		−	132780.i		−	0.00577999i
$881$	−2.07015e7			−0.898592			−0.449296	−	0.893383i	$-0.648325\pi$
$881$	−2.07015e7			−0.898592			−0.449296	+	0.893383i	$0.648325\pi$
$882$	−1.63917e7	+	4.09454e7i	−0.709499	+	1.77229i
$883$	6.76406e6			0.291948			0.145974	−	0.989288i	$-0.453368\pi$
$883$	6.76406e6			0.291948			0.145974	+	0.989288i	$0.453368\pi$
$884$	426631.			0.0183621
$885$	−1.04382e7	+	4.40482e6i	−0.447988	+	0.189047i
$886$	1.71614e7			0.734458
$887$	1.88153e7			0.802974			0.401487	−	0.915865i	$-0.368494\pi$
$887$	1.88153e7			0.802974			0.401487	+	0.915865i	$0.368494\pi$
$888$	7.05059e6	+	1.04171e7i	0.300049	+	0.443319i
$889$	8.31365e6			0.352807
$890$		−	4.09919e6i		−	0.173469i
$891$	815480.	+	777533.i	0.0344127	+	0.0328114i
$892$	984628.			0.0414343
$893$	5.10316e7			2.14146
$894$	1.89224e7	−	1.28071e7i	0.791830	−	0.535930i
$895$			1.00356e7i			0.418779i
$896$	4.08557e6			0.170013
$897$	2.07608e7	+	3.06738e7i	0.861516	+	1.27288i
$898$		−	2.77930e6i		−	0.115012i
$899$	−4.10880e6			−0.169557
$900$	3.44797e6	−	8.61282e6i	0.141892	−	0.354437i
$901$	1.01971e6			0.0418468
$902$			42221.1i			0.00172788i
$903$	−2.87152e7	−	4.24263e7i	−1.17191	−	1.73148i
$904$	1.02975e7			0.419094
$905$			4.31168e6i			0.174995i
$906$	4.07829e6	+	6.02562e6i	0.165066	+	0.243883i
$907$	2.29799e7			0.927535			0.463768	−	0.885957i	$-0.346497\pi$
$907$	2.29799e7			0.927535			0.463768	+	0.885957i	$0.346497\pi$
$908$	−1.37832e7			−0.554797
$909$	−1.13494e7	+	2.83500e7i	−0.455577	+	1.13800i
$910$	2.25362e7			0.902148
$911$			5.58414e6i			0.222926i	0.993769	+	0.111463i	$0.0355536\pi$
$911$			5.58414e6i			0.222926i	−0.993769	+	0.111463i	$0.964446\pi$
$912$	6.52632e6	−	4.41718e6i	0.259825	−	0.175856i
$913$	2.24064e6			0.0889601
$914$			3.43765e6i			0.136112i
$915$	−1.70690e7	+	1.15527e7i	−0.673992	+	0.456175i
$916$		−	448067.i		−	0.0176443i
$917$	−5.18571e7			−2.03650
$918$	474952.	−	103326.i	0.0186013	−	0.00404671i
$919$			2.30946e7i			0.902031i	0.892516	+	0.451016i	$0.148938\pi$
$919$			2.30946e7i			0.902031i	−0.892516	+	0.451016i	$0.851062\pi$
$920$		−	4.97285e6i		−	0.193703i
$921$	−3.53905e7	+	2.39532e7i	−1.37479	+	0.930496i
$922$		−	1.38732e7i		−	0.537466i
$923$	4.03614e7			1.55942
$924$	−982830.	+	665204.i	−0.0378703	+	0.0256316i
$925$			3.00854e7i			1.15612i
$926$		−	3.16528e7i		−	1.21307i
$927$	3.84231e7	+	1.53819e7i	1.46856	+	0.587910i
$928$			5.72324e6i			0.218158i
$929$	−1.43249e7			−0.544569			−0.272285	−	0.962217i	$-0.587779\pi$
$929$	−1.43249e7			−0.544569			−0.272285	+	0.962217i	$0.587779\pi$
$930$	1.03186e6	−	698391.i	0.0391214	−	0.0264784i
$931$	−8.96057e7			−3.38814
$932$	3.73788e6			0.140957
$933$	−7.19230e6	−	1.06265e7i	−0.270498	−	0.399656i
$934$	1.22988e7			0.461313
$935$	16638.6			0.000622424
$936$	1.20010e7	+	4.80437e6i	0.447743	+	0.179245i
$937$			4.01098e6i			0.149246i	0.997212	+	0.0746228i	$0.0237753\pi$
$937$			4.01098e6i			0.149246i	−0.997212	+	0.0746228i	$0.976225\pi$
$938$		−	2.14093e7i		−	0.794502i
$939$	−2.35437e7	−	3.47854e7i	−0.871385	−	1.28746i
$940$		−	1.12388e7i		−	0.414859i
$941$	3.06044e7			1.12670			0.563352	−	0.826217i	$-0.309511\pi$
$941$	3.06044e7			1.12670			0.563352	+	0.826217i	$0.309511\pi$
$942$	−9.55354e6	−	1.41152e7i	−0.350782	−	0.518275i
$943$			1.58125e6i			0.0579059i
$944$	1.33091e6	−	6.71431e6i	0.0486092	−	0.245229i
$945$	2.50888e7	−	5.45805e6i	0.913902	−	0.198819i
$946$		−	1.00593e6i		−	0.0365460i
$947$			1.79280e7i			0.649616i	0.945780	+	0.324808i	$0.105300\pi$
$947$			1.79280e7i			0.649616i	−0.945780	+	0.324808i	$0.894700\pi$
$948$	−3.26214e6	+	2.20790e6i	−0.117891	+	0.0797918i
$949$	4.78370e7			1.72424
$950$	1.88484e7			0.677589
$951$	−2.72608e7	−	4.02774e7i	−0.977433	−	1.44414i
$952$			511958.i			0.0183081i
$953$			1.94055e7i			0.692137i	0.938209	+	0.346068i	$0.112483\pi$
$953$			1.94055e7i			0.692137i	−0.938209	+	0.346068i	$0.887517\pi$
$954$	2.86841e7	+	1.14831e7i	1.02040	+	0.408496i
$955$			1.60811e7i			0.570569i
$956$		−	2.06739e7i		−	0.731606i
$957$	−931847.	−	1.37679e6i	−0.0328901	−	0.0485946i
$958$			1.24260e7i			0.437440i
$959$			8.01127e7i			2.81290i
$960$	−972805.	−	1.43731e6i	−0.0340681	−	0.0503351i
$961$	2.80887e7			0.981123
$962$	−4.19207e7			−1.46046
$963$	6.87004e6	+	2.75028e6i	0.238723	+	0.0955679i
$964$	−1.77430e7			−0.614941
$965$		−	6.42765e6i		−	0.222195i
$966$	−3.68087e7	+	2.49131e7i	−1.26913	+	0.858983i
$967$		−	2.83777e7i		−	0.975913i	−0.872868	−	0.487956i	$-0.837743\pi$
$967$		−	2.83777e7i		−	0.975913i	0.872868	−	0.487956i	$-0.162257\pi$
$968$	1.02840e7			0.352754
$969$	553513.	+	817807.i	0.0189373	+	0.0279796i
$970$	7.04120e6			0.240280
$971$			9.55316e6i			0.325161i	0.986695	+	0.162581i	$0.0519818\pi$
$971$			9.55316e6i			0.325161i	−0.986695	+	0.162581i	$0.948018\pi$
$972$	1.45239e7	+	2.44200e6i	0.493079	+	0.0829047i
$973$	6.75445e7			2.28722
$974$	−978692.			−0.0330559
$975$	1.73299e7	+	2.56046e7i	0.583826	+	0.862594i
$976$		−	1.24525e7i		−	0.418440i
$977$	−3.28138e7			−1.09981			−0.549907	−	0.835226i	$-0.685337\pi$
$977$	−3.28138e7			−1.09981			−0.549907	+	0.835226i	$0.685337\pi$
$978$	−6.75271e6	+	4.57041e6i	−0.225752	+	0.152794i
$979$	−719406.			−0.0239893
$980$			1.97340e7i			0.656373i
$981$	4.18150e7	+	1.67398e7i	1.38727	+	0.555364i
$982$			2.88939e7i			0.956153i
$983$	−1.58210e6			−0.0522215			−0.0261108	−	0.999659i	$-0.508312\pi$
$983$	−1.58210e6			−0.0522215			−0.0261108	+	0.999659i	$0.508312\pi$
$984$	309330.	+	457030.i	0.0101844	+	0.0150473i
$985$	−1.67091e7			−0.548736
$986$	−717173.			−0.0234926
$987$	−8.31887e7	+	5.63043e7i	−2.71814	+	1.83971i
$988$			2.62632e7i			0.855965i
$989$		−	3.76738e7i		−	1.22475i
$990$	468038.	+	187370.i	0.0151773	+	0.00607591i
$991$			4.25936e7i			1.37772i	0.724896	+	0.688859i	$0.241888\pi$
$991$			4.25936e7i			1.37772i	−0.724896	+	0.688859i	$0.758112\pi$
$992$			752788.i			0.0242881i
$993$	−1.77031e7	+	1.19819e7i	−0.569739	+	0.385614i
$994$			4.84339e7i			1.55483i
$995$			8.51069e6i			0.272525i
$996$	2.42542e7	−	1.64159e7i	0.774711	−	0.524344i
$997$	4.18235e7			1.33255			0.666273	−	0.745708i	$-0.267889\pi$
$997$	4.18235e7			1.33255			0.666273	+	0.745708i	$0.267889\pi$
$998$	−2.63547e7			−0.837590
$999$	−4.66687e7	+	1.01528e7i	−1.47949	+	0.321863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.a.353.10	yes	50
3.2	odd	2		354.6.c.b.353.9	yes	50
59.58	odd	2		354.6.c.b.353.10	yes	50
177.176	even	2	inner	354.6.c.a.353.9	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.9	✓	50	177.176	even	2	inner
354.6.c.a.353.10	yes	50	1.1	even	1	trivial
354.6.c.b.353.9	yes	50	3.2	odd	2
354.6.c.b.353.10	yes	50	59.58	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-12.9095 + 8.73750i) q^{3} +16.0000 q^{4} +27.1818i q^{5} +(51.6381 - 34.9500i) q^{6} -249.363 q^{7} -64.0000 q^{8} +(90.3121 - 225.594i) q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +(-12.9095 + 8.73750i) q^{3} +16.0000 q^{4} +27.1818i q^{5} +(51.6381 - 34.9500i) q^{6} -249.363 q^{7} -64.0000 q^{8} +(90.3121 - 225.594i) q^{9} -108.727i q^{10} -19.0816 q^{11} +(-206.553 + 139.800i) q^{12} -831.209i q^{13} +997.454 q^{14} +(-237.501 - 350.905i) q^{15} +256.000 q^{16} +32.0791i q^{17} +(-361.248 + 902.377i) q^{18} -1974.78 q^{19} +434.909i q^{20} +(3219.16 - 2178.81i) q^{21} +76.3264 q^{22} +2858.56 q^{23} +(826.210 - 559.200i) q^{24} +2386.15 q^{25} +3324.84i q^{26} +(805.242 + 3701.42i) q^{27} -3989.81 q^{28} -5589.10i q^{29} +(950.005 + 1403.62i) q^{30} -735.144i q^{31} -1024.00 q^{32} +(246.335 - 166.726i) q^{33} -128.316i q^{34} -6778.15i q^{35} +(1444.99 - 3609.51i) q^{36} +12608.3i q^{37} +7899.11 q^{38} +(7262.69 + 10730.5i) q^{39} -1739.64i q^{40} +553.165i q^{41} +(-12876.7 + 8715.25i) q^{42} -13179.3i q^{43} -305.306 q^{44} +(6132.06 + 2454.85i) q^{45} -11434.2 q^{46} -25841.7 q^{47} +(-3304.84 + 2236.80i) q^{48} +45375.1 q^{49} -9544.59 q^{50} +(-280.291 - 414.126i) q^{51} -13299.3i q^{52} -31787.2i q^{53} +(-3220.97 - 14805.7i) q^{54} -518.673i q^{55} +15959.3 q^{56} +(25493.5 - 17254.6i) q^{57} +22356.4i q^{58} +(5198.86 - 26227.8i) q^{59} +(-3800.02 - 5614.47i) q^{60} -48642.8i q^{61} +2940.58i q^{62} +(-22520.5 + 56254.9i) q^{63} +4096.00 q^{64} +22593.8 q^{65} +(-985.339 + 666.902i) q^{66} -21463.9i q^{67} +513.265i q^{68} +(-36902.7 + 24976.7i) q^{69} +27112.6i q^{70} +48557.5i q^{71} +(-5779.97 + 14438.0i) q^{72} +57551.1i q^{73} -50433.4i q^{74} +(-30804.1 + 20849.0i) q^{75} -31596.4 q^{76} +4758.26 q^{77} +(-29050.8 - 42922.1i) q^{78} +15793.3 q^{79} +6958.55i q^{80} +(-42736.4 - 40747.8i) q^{81} -2212.66i q^{82} -117424. q^{83} +(51506.6 - 34861.0i) q^{84} -871.968 q^{85} +52717.2i q^{86} +(48834.8 + 72152.7i) q^{87} +1221.22 q^{88} +37701.5 q^{89} +(-24528.2 - 9819.39i) q^{90} +207273. i q^{91} +45736.9 q^{92} +(6423.33 + 9490.37i) q^{93} +103367. q^{94} -53678.0i q^{95} +(13219.4 - 8947.20i) q^{96} +64760.2i q^{97} -181500. q^{98} +(-1723.30 + 4304.70i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9}+O(q^{10}) \) 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9	\( 50 q - 200 q^{2} - 13 q^{3} + 800 q^{4} + 52 q^{6} + 38 q^{7} - 3200 q^{8} + 51 q^{9} - 652 q^{11} - 208 q^{12} - 152 q^{14} - 2107 q^{15} + 12800 q^{16} - 204 q^{18} - 894 q^{19} - 3801 q^{21} + 2608 q^{22} + 2456 q^{23} + 832 q^{24} - 23956 q^{25} + 9890 q^{27} + 608 q^{28} + 8428 q^{30} - 51200 q^{32} - 9744 q^{33} + 816 q^{36} + 3576 q^{38} + 1388 q^{39} + 15204 q^{42} - 10432 q^{44} + 33067 q^{45} - 9824 q^{46} - 27144 q^{47} - 3328 q^{48} + 85768 q^{49} + 95824 q^{50} + 3338 q^{51} - 39560 q^{54} - 2432 q^{56} - 63969 q^{57} - 23840 q^{59} - 33712 q^{60} + 94781 q^{63} + 204800 q^{64} - 9400 q^{65} + 38976 q^{66} - 115930 q^{69} - 3264 q^{72} + 24248 q^{75} - 14304 q^{76} - 150240 q^{77} - 5552 q^{78} - 68658 q^{79} + 47095 q^{81} - 175140 q^{83} - 60816 q^{84} - 138524 q^{85} + 138261 q^{87} + 41728 q^{88} + 104908 q^{89} - 132268 q^{90} + 39296 q^{92} - 91204 q^{93} + 108576 q^{94} + 13312 q^{96} - 343072 q^{98} - 111406 q^{99}+O(q^{100}) \) 50 * q - 200 * q^2 - 13 * q^3 + 800 * q^4 + 52 * q^6 + 38 * q^7 - 3200 * q^8 + 51 * q^9 - 652 * q^11 - 208 * q^12 - 152 * q^14 - 2107 * q^15 + 12800 * q^16 - 204 * q^18 - 894 * q^19 - 3801 * q^21 + 2608 * q^22 + 2456 * q^23 + 832 * q^24 - 23956 * q^25 + 9890 * q^27 + 608 * q^28 + 8428 * q^30 - 51200 * q^32 - 9744 * q^33 + 816 * q^36 + 3576 * q^38 + 1388 * q^39 + 15204 * q^42 - 10432 * q^44 + 33067 * q^45 - 9824 * q^46 - 27144 * q^47 - 3328 * q^48 + 85768 * q^49 + 95824 * q^50 + 3338 * q^51 - 39560 * q^54 - 2432 * q^56 - 63969 * q^57 - 23840 * q^59 - 33712 * q^60 + 94781 * q^63 + 204800 * q^64 - 9400 * q^65 + 38976 * q^66 - 115930 * q^69 - 3264 * q^72 + 24248 * q^75 - 14304 * q^76 - 150240 * q^77 - 5552 * q^78 - 68658 * q^79 + 47095 * q^81 - 175140 * q^83 - 60816 * q^84 - 138524 * q^85 + 138261 * q^87 + 41728 * q^88 + 104908 * q^89 - 132268 * q^90 + 39296 * q^92 - 91204 * q^93 + 108576 * q^94 + 13312 * q^96 - 343072 * q^98 - 111406 * q^99

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