LMFDB - Embedded newform 354.6.c.a.353.18

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			353.18
Character	$\chi$	$=$	354.353
Dual form			354.6.c.a.353.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +(-9.68192 + 12.2172i) q^{3} +16.0000 q^{4} +48.6180i q^{5} +(38.7277 - 48.8689i) q^{6} +149.149 q^{7} -64.0000 q^{8} +(-55.5209 - 236.572i) q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +(-9.68192 + 12.2172i) q^{3} +16.0000 q^{4} +48.6180i q^{5} +(38.7277 - 48.8689i) q^{6} +149.149 q^{7} -64.0000 q^{8} +(-55.5209 - 236.572i) q^{9} -194.472i q^{10} +118.353 q^{11} +(-154.911 + 195.476i) q^{12} +964.502i q^{13} -596.595 q^{14} +(-593.977 - 470.716i) q^{15} +256.000 q^{16} -1576.13i q^{17} +(222.084 + 946.289i) q^{18} -2971.66 q^{19} +777.888i q^{20} +(-1444.05 + 1822.18i) q^{21} -473.412 q^{22} +3406.07 q^{23} +(619.643 - 781.902i) q^{24} +761.288 q^{25} -3858.01i q^{26} +(3427.80 + 1612.16i) q^{27} +2386.38 q^{28} +4802.85i q^{29} +(2375.91 + 1882.86i) q^{30} +6759.60i q^{31} -1024.00 q^{32} +(-1145.88 + 1445.94i) q^{33} +6304.52i q^{34} +7251.32i q^{35} +(-888.334 - 3785.16i) q^{36} +5990.82i q^{37} +11886.6 q^{38} +(-11783.5 - 9338.23i) q^{39} -3111.55i q^{40} -7422.97i q^{41} +(5776.19 - 7288.74i) q^{42} +6934.72i q^{43} +1893.65 q^{44} +(11501.7 - 2699.32i) q^{45} -13624.3 q^{46} +26194.3 q^{47} +(-2478.57 + 3127.61i) q^{48} +5438.37 q^{49} -3045.15 q^{50} +(19255.9 + 15260.0i) q^{51} +15432.0i q^{52} +7649.57i q^{53} +(-13711.2 - 6448.65i) q^{54} +5754.09i q^{55} -9545.53 q^{56} +(28771.4 - 36305.4i) q^{57} -19211.4i q^{58} +(-15101.5 - 22065.1i) q^{59} +(-9503.63 - 7531.45i) q^{60} -12209.9i q^{61} -27038.4i q^{62} +(-8280.88 - 35284.5i) q^{63} +4096.00 q^{64} -46892.2 q^{65} +(4583.53 - 5783.78i) q^{66} +38311.8i q^{67} -25218.1i q^{68} +(-32977.3 + 41612.7i) q^{69} -29005.3i q^{70} +44302.6i q^{71} +(3553.34 + 15140.6i) q^{72} +50219.9i q^{73} -23963.3i q^{74} +(-7370.73 + 9300.82i) q^{75} -47546.6 q^{76} +17652.2 q^{77} +(47134.2 + 37352.9i) q^{78} -28462.8 q^{79} +12446.2i q^{80} +(-52883.9 + 26269.4i) q^{81} +29691.9i q^{82} -16275.6 q^{83} +(-23104.7 + 29154.9i) q^{84} +76628.4 q^{85} -27738.9i q^{86} +(-58677.5 - 46500.9i) q^{87} -7574.59 q^{88} +26352.2 q^{89} +(-46006.7 + 10797.3i) q^{90} +143854. i q^{91} +54497.1 q^{92} +(-82583.5 - 65445.9i) q^{93} -104777. q^{94} -144476. i q^{95} +(9914.28 - 12510.4i) q^{96} -42952.2i q^{97} -21753.5 q^{98} +(-6571.06 - 27999.0i) 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
$3$	−9.68192	+	12.2172i	−0.621095	+	0.783735i
$3$	−9.68192	+	12.2172i	−0.621095	+	0.783735i
$4$	16.0000			0.500000
$5$			48.6180i			0.869706i	0.900502	+	0.434853i	$0.143200\pi$
$5$			48.6180i			0.869706i	−0.900502	+	0.434853i	$0.856800\pi$
$6$	38.7277	−	48.8689i	0.439181	−	0.554184i
$7$	149.149			1.15047			0.575234	−	0.817989i	$-0.304911\pi$
$7$	149.149			1.15047			0.575234	+	0.817989i	$0.304911\pi$
$8$	−64.0000			−0.353553
$9$	−55.5209	−	236.572i	−0.228481	−	0.973548i
$10$		−	194.472i		−	0.614975i
$11$	118.353			0.294915			0.147458	−	0.989068i	$-0.452891\pi$
$11$	118.353			0.294915			0.147458	+	0.989068i	$0.452891\pi$
$12$	−154.911	+	195.476i	−0.310548	+	0.391867i
$13$			964.502i			1.58287i	0.611254	+	0.791434i	$0.290665\pi$
$13$			964.502i			1.58287i	−0.611254	+	0.791434i	$0.709335\pi$
$14$	−596.595			−0.813504
$15$	−593.977	−	470.716i	−0.681619	−	0.540170i
$16$	256.000			0.250000
$17$		−	1576.13i		−	1.32273i	−0.750066	−	0.661363i	$-0.769978\pi$
$17$		−	1576.13i		−	1.32273i	0.750066	−	0.661363i	$-0.230022\pi$
$18$	222.084	+	946.289i	0.161561	+	0.688403i
$19$	−2971.66			−1.88849			−0.944246	−	0.329240i	$-0.893208\pi$
$19$	−2971.66			−1.88849			−0.944246	+	0.329240i	$0.893208\pi$
$20$			777.888i			0.434853i
$21$	−1444.05	+	1822.18i	−0.714551	+	0.901662i
$22$	−473.412			−0.208537
$23$	3406.07			1.34256			0.671280	−	0.741204i	$-0.265745\pi$
$23$	3406.07			1.34256			0.671280	+	0.741204i	$0.265745\pi$
$24$	619.643	−	781.902i	0.219590	−	0.277092i
$25$	761.288			0.243612
$26$		−	3858.01i		−	1.11926i
$27$	3427.80	+	1612.16i	0.904912	+	0.425598i
$28$	2386.38			0.575234
$29$			4802.85i			1.06048i	0.847846	+	0.530242i	$0.177899\pi$
$29$			4802.85i			1.06048i	−0.847846	+	0.530242i	$0.822101\pi$
$30$	2375.91	+	1882.86i	0.481977	+	0.381958i
$31$			6759.60i			1.26333i	0.775241	+	0.631665i	$0.217628\pi$
$31$			6759.60i			1.26333i	−0.775241	+	0.631665i	$0.782372\pi$
$32$	−1024.00			−0.176777
$33$	−1145.88	+	1445.94i	−0.183171	+	0.231135i
$34$			6304.52i			0.935309i
$35$			7251.32i			1.00057i
$36$	−888.334	−	3785.16i	−0.114241	−	0.486774i
$37$			5990.82i			0.719420i	0.933064	+	0.359710i	$0.117124\pi$
$37$			5990.82i			0.719420i	−0.933064	+	0.359710i	$0.882876\pi$
$38$	11886.6			1.33537
$39$	−11783.5	−	9338.23i	−1.24055	−	0.983113i
$40$		−	3111.55i		−	0.307487i
$41$		−	7422.97i		−	0.689633i	−0.938670	−	0.344816i	$-0.887941\pi$
$41$		−	7422.97i		−	0.689633i	0.938670	−	0.344816i	$-0.112059\pi$
$42$	5776.19	−	7288.74i	0.505264	−	0.637572i
$43$			6934.72i			0.571949i	0.958237	+	0.285975i	$0.0923173\pi$
$43$			6934.72i			0.571949i	−0.958237	+	0.285975i	$0.907683\pi$
$44$	1893.65			0.147458
$45$	11501.7	−	2699.32i	0.846700	−	0.198711i
$46$	−13624.3			−0.949333
$47$	26194.3			1.72967			0.864834	−	0.502058i	$-0.167424\pi$
$47$	26194.3			1.72967			0.864834	+	0.502058i	$0.167424\pi$
$48$	−2478.57	+	3127.61i	−0.155274	+	0.195934i
$49$	5438.37			0.323578
$50$	−3045.15			−0.172260
$51$	19255.9	+	15260.0i	1.03667	+	0.821539i
$52$			15432.0i			0.791434i
$53$			7649.57i			0.374065i	0.982354	+	0.187033i	$0.0598870\pi$
$53$			7649.57i			0.374065i	−0.982354	+	0.187033i	$0.940113\pi$
$54$	−13711.2	−	6448.65i	−0.639870	−	0.300943i
$55$			5754.09i			0.256490i
$56$	−9545.53			−0.406752
$57$	28771.4	−	36305.4i	1.17293	−	1.48008i
$58$		−	19211.4i		−	0.749876i
$59$	−15101.5	−	22065.1i	−0.564793	−	0.825232i
$59$	−15101.5	−	22065.1i	−0.564793	−	0.825232i
$60$	−9503.63	−	7531.45i	−0.340809	−	0.270085i
$61$		−	12209.9i		−	0.420135i	−0.977687	−	0.210067i	$-0.932632\pi$
$61$		−	12209.9i		−	0.420135i	0.977687	−	0.210067i	$-0.0673684\pi$
$62$		−	27038.4i		−	0.893309i
$63$	−8280.88	−	35284.5i	−0.262860	−	1.12004i
$64$	4096.00			0.125000
$65$	−46892.2			−1.37663
$66$	4583.53	−	5783.78i	0.129521	−	0.163437i
$67$			38311.8i			1.04267i	0.853353	+	0.521334i	$0.174565\pi$
$67$			38311.8i			1.04267i	−0.853353	+	0.521334i	$0.825435\pi$
$68$		−	25218.1i		−	0.661363i
$69$	−32977.3	+	41612.7i	−0.833858	+	1.05221i
$70$		−	29005.3i		−	0.707509i
$71$			44302.6i			1.04300i	0.853252	+	0.521499i	$0.174627\pi$
$71$			44302.6i			1.04300i	−0.853252	+	0.521499i	$0.825373\pi$
$72$	3553.34	+	15140.6i	0.0807803	+	0.344201i
$73$			50219.9i			1.10298i	0.834181	+	0.551491i	$0.185941\pi$
$73$			50219.9i			1.10298i	−0.834181	+	0.551491i	$0.814059\pi$
$74$		−	23963.3i		−	0.508707i
$75$	−7370.73	+	9300.82i	−0.151306	+	0.190927i
$76$	−47546.6			−0.944246
$77$	17652.2			0.339291
$78$	47134.2	+	37352.9i	0.877201	+	0.695166i
$79$	−28462.8			−0.513109			−0.256554	−	0.966530i	$-0.582587\pi$
$79$	−28462.8			−0.513109			−0.256554	+	0.966530i	$0.582587\pi$
$80$			12446.2i			0.217426i
$81$	−52883.9	+	26269.4i	−0.895593	+	0.444875i
$82$			29691.9i			0.487644i
$83$	−16275.6			−0.259324			−0.129662	−	0.991558i	$-0.541389\pi$
$83$	−16275.6			−0.259324			−0.129662	+	0.991558i	$0.541389\pi$
$84$	−23104.7	+	29154.9i	−0.357275	+	0.450831i
$85$	76628.4			1.15038
$86$		−	27738.9i		−	0.404429i
$87$	−58677.5	−	46500.9i	−0.831139	−	0.658662i
$88$	−7574.59			−0.104268
$89$	26352.2			0.352649			0.176324	−	0.984332i	$-0.443579\pi$
$89$	26352.2			0.352649			0.176324	+	0.984332i	$0.443579\pi$
$90$	−46006.7	+	10797.3i	−0.598708	+	0.140510i
$91$			143854.i			1.82104i
$92$	54497.1			0.671280
$93$	−82583.5	−	65445.9i	−0.990116	−	0.784648i
$94$	−104777.			−1.22306
$95$		−	144476.i		−	1.64243i
$96$	9914.28	−	12510.4i	0.109795	−	0.138546i
$97$		−	42952.2i		−	0.463507i	−0.972775	−	0.231753i	$-0.925554\pi$
$97$		−	42952.2i		−	0.463507i	0.972775	−	0.231753i	$-0.0744462\pi$
$98$	−21753.5			−0.228804
$99$	−6571.06	−	27999.0i	−0.0673826	−	0.287114i
$100$	12180.6			0.121806
$101$	−147126.			−1.43511			−0.717555	−	0.696502i	$-0.754739\pi$
$101$	−147126.			−1.43511			−0.717555	+	0.696502i	$0.754739\pi$
$102$	−77023.8	−	61039.9i	−0.733034	−	0.580916i
$103$		−	40078.0i		−	0.372232i	−0.982528	−	0.186116i	$-0.940410\pi$
$103$		−	40078.0i		−	0.372232i	0.982528	−	0.186116i	$-0.0595900\pi$
$104$		−	61728.2i		−	0.559629i
$105$	−88591.0	−	70206.7i	−0.784181	−	0.621449i
$106$		−	30598.3i		−	0.264504i
$107$		−	27896.6i		−	0.235554i	−0.993040	−	0.117777i	$-0.962423\pi$
$107$		−	27896.6i		−	0.235554i	0.993040	−	0.117777i	$-0.0375769\pi$
$108$	54844.9	+	25794.6i	0.452456	+	0.212799i
$109$		−	28350.4i		−	0.228556i	−0.993449	−	0.114278i	$-0.963545\pi$
$109$		−	28350.4i		−	0.228556i	0.993449	−	0.114278i	$-0.0364555\pi$
$110$		−	23016.3i		−	0.181366i
$111$	−73191.2	−	58002.7i	−0.563834	−	0.446828i
$112$	38182.1			0.287617
$113$	−183959.			−1.35526			−0.677632	−	0.735401i	$-0.736994\pi$
$113$	−183959.			−1.35526			−0.677632	+	0.735401i	$0.736994\pi$
$114$	−115086.	+	145222.i	−0.829390	+	1.04657i
$115$			165596.i			1.16763i
$116$			76845.7i			0.530242i
$117$	228175.	−	53550.0i	1.54100	−	0.361656i
$118$	60405.9	+	88260.5i	0.399369	+	0.583527i
$119$		−	235078.i		−	1.52176i
$120$	38014.5	+	30125.8i	0.240989	+	0.190979i
$121$	−147044.			−0.913025
$122$			48839.7i			0.297080i
$123$	90688.0	+	71868.6i	0.540489	+	0.428328i
$124$			108154.i			0.631665i
$125$			188944.i			1.08158i
$126$	33123.5	+	141138.i	0.185870	+	0.791986i
$127$	−70646.1			−0.388668			−0.194334	−	0.980935i	$-0.562255\pi$
$127$	−70646.1			−0.388668			−0.194334	+	0.980935i	$0.562255\pi$
$128$	−16384.0			−0.0883883
$129$	−84723.0	−	67141.4i	−0.448257	−	0.355235i
$130$	187569.			0.973424
$131$	−181316.			−0.923118			−0.461559	−	0.887109i	$-0.652710\pi$
$131$	−181316.			−0.923118			−0.461559	+	0.887109i	$0.652710\pi$
$132$	−18334.1	+	23135.1i	−0.0915853	+	0.115568i
$133$	−443220.			−2.17265
$134$		−	153247.i		−	0.737278i
$135$	−78380.1	+	166653.i	−0.370145	+	0.787007i
$136$			100872.i			0.467654i
$137$			93571.6i			0.425934i	0.977059	+	0.212967i	$0.0683127\pi$
$137$			93571.6i			0.425934i	−0.977059	+	0.212967i	$0.931687\pi$
$138$	131909.	−	166451.i	0.589626	−	0.744026i
$139$	278405.			1.22219			0.611096	−	0.791556i	$-0.290729\pi$
$139$	278405.			1.22219			0.611096	+	0.791556i	$0.290729\pi$
$140$			116021.i			0.500284i
$141$	−253611.	+	320022.i	−1.07429	+	1.35560i
$142$		−	177211.i		−	0.737511i
$143$			114152.i			0.466812i
$144$	−14213.4	−	60562.5i	−0.0571203	−	0.243387i
$145$	−233505.			−0.922310
$146$		−	200880.i		−	0.779926i
$147$	−52653.9	+	66441.8i	−0.200973	+	0.253599i
$148$			95853.2i			0.359710i
$149$	−240122.			−0.886065			−0.443033	−	0.896506i	$-0.646097\pi$
$149$	−240122.			−0.886065			−0.443033	+	0.896506i	$0.646097\pi$
$150$	29482.9	−	37203.3i	0.106990	−	0.135006i
$151$		−	341113.i		−	1.21746i	−0.793377	−	0.608731i	$-0.791679\pi$
$151$		−	341113.i		−	1.21746i	0.793377	−	0.608731i	$-0.208321\pi$
$152$	190186.			0.667683
$153$	−372869.	+	87508.2i	−1.28774	+	0.302218i
$154$	−70608.8			−0.239915
$155$	−328638.			−1.09873
$156$	−188537.	−	149412.i	−0.620275	−	0.491556i
$157$		−	28073.0i		−	0.0908948i	−0.998967	−	0.0454474i	$-0.985529\pi$
$157$		−	28073.0i		−	0.0908948i	0.998967	−	0.0454474i	$-0.0144713\pi$
$158$	113851.			0.362823
$159$	−93456.5	−	74062.5i	−0.293168	−	0.232330i
$160$		−	49784.9i		−	0.153744i
$161$	508011.			1.54457
$162$	211535.	−	105078.i	0.633280	−	0.314574i
$163$	−499270.			−1.47186			−0.735930	−	0.677058i	$-0.763255\pi$
$163$	−499270.			−1.47186			−0.735930	+	0.677058i	$0.763255\pi$
$164$		−	118767.i		−	0.344816i
$165$	−70298.9	−	55710.6i	−0.201020	−	0.159304i
$166$	65102.5			0.183370
$167$		−	318823.i		−	0.884624i	−0.896861	−	0.442312i	$-0.854158\pi$
$167$		−	318823.i		−	0.884624i	0.896861	−	0.442312i	$-0.145842\pi$
$168$	92419.0	−	116620.i	0.252632	−	0.318786i
$169$	−558972.			−1.50547
$170$	−306513.			−0.813443
$171$	164989.	+	703013.i	0.431485	+	1.83854i
$172$			110955.i			0.285975i
$173$	474124.			1.20442			0.602208	−	0.798339i	$-0.294288\pi$
$173$	474124.			1.20442			0.602208	+	0.798339i	$0.294288\pi$
$174$	234710.	+	186003.i	0.587704	+	0.465745i
$175$	113545.			0.280268
$176$	30298.4			0.0737288
$177$	415786.	+	29134.5i	0.997554	+	0.0698996i
$178$	−105409.			−0.249360
$179$	399725.			0.932456			0.466228	−	0.884665i	$-0.345613\pi$
$179$	399725.			0.932456			0.466228	+	0.884665i	$0.345613\pi$
$180$	184027.	−	43189.1i	0.423350	−	0.0993556i
$181$	481995.			1.09357			0.546784	−	0.837274i	$-0.315852\pi$
$181$	481995.			1.09357			0.546784	+	0.837274i	$0.315852\pi$
$182$		−	575418.i		−	1.28767i
$183$	149171.	+	118216.i	0.329274	+	0.260944i
$184$	−217988.			−0.474667
$185$	−291262.			−0.625683
$186$	330334.	+	261784.i	0.700118	+	0.554830i
$187$		−	186540.i		−	0.390092i
$188$	419109.			0.864834
$189$	511253.	+	240452.i	1.04107	+	0.489637i
$190$			577905.i			1.16138i
$191$	−111630.			−0.221411			−0.110705	−	0.993853i	$-0.535311\pi$
$191$	−111630.			−0.221411			−0.110705	+	0.993853i	$0.535311\pi$
$192$	−39657.1	+	50041.7i	−0.0776369	+	0.0979669i
$193$	326703.			0.631335			0.315668	−	0.948870i	$-0.397772\pi$
$193$	326703.			0.631335			0.315668	+	0.948870i	$0.397772\pi$
$194$			171809.i			0.327749i
$195$	454006.	−	572892.i	0.855019	−	1.07891i
$196$	87014.0			0.161789
$197$		−	489424.i		−	0.898503i	−0.893405	−	0.449251i	$-0.851691\pi$
$197$		−	489424.i		−	0.898503i	0.893405	−	0.449251i	$-0.148309\pi$
$198$	26284.3	+	111996.i	0.0476467	+	0.203021i
$199$	−311475.			−0.557558			−0.278779	−	0.960355i	$-0.589930\pi$
$199$	−311475.			−0.557558			−0.278779	+	0.960355i	$0.589930\pi$
$200$	−48722.4			−0.0861299
$201$	−468064.	−	370932.i	−0.817175	−	0.647596i
$202$	588503.			1.01478
$203$			716340.i			1.22005i
$204$	308095.	+	244160.i	0.518333	+	0.410770i
$205$	360890.			0.599777
$206$			160312.i			0.263208i
$207$	−189108.	−	805781.i	−0.306750	−	1.30705i
$208$			246913.i			0.395717i
$209$	−351705.			−0.556946
$210$	354364.	+	280827.i	0.554500	+	0.439431i
$211$			977061.i			1.51083i	0.655247	+	0.755415i	$0.272565\pi$
$211$			977061.i			1.51083i	−0.655247	+	0.755415i	$0.727435\pi$
$212$			122393.i			0.187033i
$213$	−541255.	−	428934.i	−0.817434	−	0.647802i
$214$			111586.i			0.166562i
$215$	−337152.			−0.497428
$216$	−219379.	−	103178.i	−0.319935	−	0.150472i
$217$			1.00819e6i			1.45342i
$218$			113402.i			0.161614i
$219$	−613547.	−	486225.i	−0.864446	−	0.685057i
$220$			92065.4i			0.128245i
$221$	1.52018e6			2.09370
$222$	292765.	+	232011.i	0.398691	+	0.315955i
$223$	−1.20291e6			−1.61983			−0.809915	−	0.586548i	$-0.800487\pi$
$223$	−1.20291e6			−1.61983			−0.809915	+	0.586548i	$0.800487\pi$
$224$	−152728.			−0.203376
$225$	−42267.4	−	180100.i	−0.0556608	−	0.237168i
$226$	735834.			0.958316
$227$	−766381.			−0.987143			−0.493572	−	0.869705i	$-0.664309\pi$
$227$	−766381.			−0.987143			−0.493572	+	0.869705i	$0.664309\pi$
$228$	460342.	−	580887.i	0.586467	−	0.740039i
$229$		−	399242.i		−	0.503092i	−0.967845	−	0.251546i	$-0.919061\pi$
$229$		−	399242.i		−	0.503092i	0.967845	−	0.251546i	$-0.0809389\pi$
$230$		−	662385.i		−	0.825640i
$231$	−170907.	+	215661.i	−0.210732	+	0.265914i
$232$		−	307383.i		−	0.374938i
$233$	1.08621e6			1.31076			0.655379	−	0.755301i	$-0.272509\pi$
$233$	1.08621e6			1.31076			0.655379	+	0.755301i	$0.272509\pi$
$234$	−912698.	+	214200.i	−1.08965	+	0.255729i
$235$			1.27352e6i			1.50430i
$236$	−241624.	−	353042.i	−0.282397	−	0.412616i
$237$	275574.	−	347736.i	0.318689	−	0.402141i
$238$			940312.i			1.07604i
$239$		−	1.12701e6i		−	1.27624i	−0.769938	−	0.638119i	$-0.779713\pi$
$239$		−	1.12701e6i		−	1.27624i	0.769938	−	0.638119i	$-0.220287\pi$
$240$	−152058.	−	120503.i	−0.170405	−	0.135043i
$241$	1.32356e6			1.46792			0.733959	−	0.679194i	$-0.237670\pi$
$241$	1.32356e6			1.46792			0.733959	+	0.679194i	$0.237670\pi$
$242$	588174.			0.645606
$243$	191078.	−	900432.i	0.207585	−	0.978217i
$244$		−	195359.i		−	0.210067i
$245$			264403.i			0.281418i
$246$	−362752.	−	287474.i	−0.382184	−	0.302873i
$247$		−	2.86617e6i		−	2.98924i
$248$		−	432614.i		−	0.446655i
$249$	157579.	−	198843.i	0.161065	−	0.203241i
$250$		−	755775.i		−	0.764790i
$251$			1.14445e6i			1.14660i	0.819345	+	0.573301i	$0.194337\pi$
$251$			1.14445e6i			1.14660i	−0.819345	+	0.573301i	$0.805663\pi$
$252$	−132494.	−	564552.i	−0.131430	−	0.560018i
$253$	403118.			0.395942
$254$	282584.			0.274830
$255$	−741910.	+	936186.i	−0.714497	+	0.901595i
$256$	65536.0			0.0625000
$257$		−	181255.i		−	0.171182i	−0.996330	−	0.0855908i	$-0.972722\pi$
$257$		−	181255.i		−	0.171182i	0.996330	−	0.0855908i	$-0.0272778\pi$
$258$	338892.	+	268565.i	0.316965	+	0.251189i
$259$			893524.i			0.827670i
$260$	−750275.			−0.688315
$261$	1.13622e6	−	266659.i	1.03243	−	0.242301i
$262$	725263.			0.652743
$263$			1.39847e6i			1.24671i	0.781940	+	0.623354i	$0.214230\pi$
$263$			1.39847e6i			1.24671i	−0.781940	+	0.623354i	$0.785770\pi$
$264$	73336.6	−	92540.4i	0.0647606	−	0.0817187i
$265$	−371907.			−0.325327
$266$	1.77288e6			1.53630
$267$	−255140.	+	321951.i	−0.219029	+	0.276383i
$268$			612989.i			0.521334i
$269$	−615833.			−0.518898			−0.259449	−	0.965757i	$-0.583541\pi$
$269$	−615833.			−0.518898			−0.259449	+	0.965757i	$0.583541\pi$
$270$	313521.	−	666612.i	0.261732	−	0.556498i
$271$	−365676.			−0.302463			−0.151232	−	0.988498i	$-0.548324\pi$
$271$	−365676.			−0.302463			−0.151232	+	0.988498i	$0.548324\pi$
$272$		−	403490.i		−	0.330682i
$273$	−1.75750e6	−	1.39279e6i	−1.42721	−	1.13104i
$274$		−	374286.i		−	0.301181i
$275$	90100.7			0.0718449
$276$	−527636.	+	665803.i	−0.416929	+	0.526106i
$277$	−1.09314e6			−0.856002			−0.428001	−	0.903778i	$-0.640782\pi$
$277$	−1.09314e6			−0.856002			−0.428001	+	0.903778i	$0.640782\pi$
$278$	−1.11362e6			−0.864221
$279$	1.59913e6	−	375299.i	1.22991	−	0.288647i
$280$		−	464085.i		−	0.353755i
$281$			786465.i			0.594174i	0.954850	+	0.297087i	$0.0960151\pi$
$281$			786465.i			0.594174i	−0.954850	+	0.297087i	$0.903985\pi$
$282$	1.01445e6	−	1.28009e6i	0.759637	−	0.958555i
$283$		−	1.86804e6i		−	1.38650i	−0.720696	−	0.693251i	$-0.756178\pi$
$283$		−	1.86804e6i		−	1.38650i	0.720696	−	0.693251i	$-0.243822\pi$
$284$			708842.i			0.521499i
$285$	1.76510e6	+	1.39881e6i	1.28723	+	1.02011i
$286$		−	456607.i		−	0.330086i
$287$		−	1.10713e6i		−	0.793401i
$288$	56853.4	+	242250.i	0.0403901	+	0.172101i
$289$	−1.06433e6			−0.749605
$290$	934021.			0.652171
$291$	524756.	+	415860.i	0.363266	+	0.287882i
$292$			803518.i			0.551491i
$293$		−	1.01757e6i		−	0.692464i	−0.938149	−	0.346232i	$-0.887461\pi$
$293$		−	1.01757e6i		−	0.692464i	0.938149	−	0.346232i	$-0.112539\pi$
$294$	210616.	−	265767.i	0.142109	−	0.179322i
$295$	1.07276e6	−	734204.i	0.717709	−	0.491204i
$296$		−	383413.i		−	0.254353i
$297$	405691.	+	190804.i	0.266873	+	0.125515i
$298$	960487.			0.626543
$299$			3.28516e6i			2.12510i
$300$	−117932.	+	148813.i	−0.0756532	+	0.0954637i
$301$			1.03430e6i			0.658010i
$302$			1.36445e6i			0.860875i
$303$	1.42446e6	−	1.79747e6i	0.891340	−	1.12475i
$304$	−760745.			−0.472123
$305$	593623.			0.365394
$306$	1.49148e6	−	350033.i	0.910568	−	0.213700i
$307$	−2.53031e6			−1.53224			−0.766121	−	0.642697i	$-0.777816\pi$
$307$	−2.53031e6			−1.53224			−0.766121	+	0.642697i	$0.777816\pi$
$308$	282435.			0.169645
$309$	489642.	+	388032.i	0.291731	+	0.231191i
$310$	1.31455e6			0.776916
$311$		−	219028.i		−	0.128410i	−0.997937	−	0.0642051i	$-0.979549\pi$
$311$		−	219028.i		−	0.128410i	0.997937	−	0.0642051i	$-0.0204512\pi$
$312$	754146.	+	597647.i	0.438601	+	0.347583i
$313$		−	2.60867e6i		−	1.50507i	−0.658550	−	0.752537i	$-0.728830\pi$
$313$		−	2.60867e6i		−	1.50507i	0.658550	−	0.752537i	$-0.271170\pi$
$314$			112292.i			0.0642724i
$315$	1.71546e6	−	402600.i	0.974102	−	0.228611i
$316$	−455404.			−0.256554
$317$		−	484179.i		−	0.270619i	−0.990803	−	0.135309i	$-0.956797\pi$
$317$		−	484179.i		−	0.270619i	0.990803	−	0.135309i	$-0.0432028\pi$
$318$	373826.	+	296250.i	0.207301	+	0.164282i
$319$			568432.i			0.312753i
$320$			199139.i			0.108713i
$321$	340818.	+	270092.i	0.184612	+	0.146302i
$322$	−2.03204e6			−1.09218
$323$			4.68373e6i			2.49796i
$324$	−846142.	+	420311.i	−0.447796	+	0.222437i
$325$			734264.i			0.385606i
$326$	1.99708e6			1.04076
$327$	346363.	+	274486.i	0.179127	+	0.141955i
$328$			475070.i			0.243822i
$329$	3.90685e6			1.98993
$330$	281196.	+	222842.i	0.142142	+	0.112645i
$331$	−1.45569e6			−0.730298			−0.365149	−	0.930949i	$-0.618982\pi$
$331$	−1.45569e6			−0.730298			−0.365149	+	0.930949i	$0.618982\pi$
$332$	−260410.			−0.129662
$333$	1.41726e6	−	332616.i	0.700390	−	0.164374i
$334$			1.27529e6i			0.625523i
$335$	−1.86265e6			−0.906814
$336$	−369676.	+	466479.i	−0.178638	+	0.225416i
$337$			2.06918e6i			0.992484i	0.868184	+	0.496242i	$0.165287\pi$
$337$			2.06918e6i			0.992484i	−0.868184	+	0.496242i	$0.834713\pi$
$338$	2.23589e6			1.06453
$339$	1.78107e6	−	2.24746e6i	0.841748	−	1.06217i
$340$	1.22605e6			0.575191
$341$			800019.i			0.372575i
$342$	−659957.	−	2.81205e6i	−0.305106	−	1.30004i
$343$	−1.69562e6			−0.778202
$344$		−	443822.i		−	0.202215i
$345$	−2.02313e6	−	1.60329e6i	−0.915114	−	0.725211i
$346$	−1.89649e6			−0.851651
$347$	1.47169e6			0.656134			0.328067	−	0.944654i	$-0.393603\pi$
$347$	1.47169e6			0.656134			0.328067	+	0.944654i	$0.393603\pi$
$348$	−938841.	−	744014.i	−0.415570	−	0.329331i
$349$			3.75943e6i			1.65218i	0.563536	+	0.826091i	$0.309441\pi$
$349$			3.75943e6i			1.65218i	−0.563536	+	0.826091i	$0.690559\pi$
$350$	−454181.			−0.198179
$351$	−1.55493e6	+	3.30613e6i	−0.673665	+	1.43236i
$352$	−121193.			−0.0521342
$353$	−1.11025e6			−0.474224			−0.237112	−	0.971482i	$-0.576201\pi$
$353$	−1.11025e6			−0.474224			−0.237112	+	0.971482i	$0.576201\pi$
$354$	−1.66314e6	−	116538.i	−0.705377	−	0.0494265i
$355$	−2.15391e6			−0.907102
$356$	421636.			0.176324
$357$	2.87200e6	+	2.27601e6i	1.19265	+	0.945155i
$358$	−1.59890e6			−0.659346
$359$		−	2.75407e6i		−	1.12782i	−0.825837	−	0.563909i	$-0.809297\pi$
$359$		−	2.75407e6i		−	1.12782i	0.825837	−	0.563909i	$-0.190703\pi$
$360$	−736107.	+	172756.i	−0.299354	+	0.0702550i
$361$	6.35467e6			2.56641
$362$	−1.92798e6			−0.773270
$363$	1.42366e6	−	1.79646e6i	0.567076	−	0.715570i
$364$			2.30167e6i			0.910520i
$365$	−2.44159e6			−0.959270
$366$	−596686.	−	472862.i	−0.232832	−	0.184515i
$367$			3.31962e6i			1.28654i	0.765639	+	0.643270i	$0.222423\pi$
$367$			3.31962e6i			1.28654i	−0.765639	+	0.643270i	$0.777577\pi$
$368$	871953.			0.335640
$369$	−1.75607e6	+	412130.i	−0.671391	+	0.157568i
$370$	1.16505e6			0.442425
$371$			1.14092e6i			0.430350i
$372$	−1.32134e6	−	1.04713e6i	−0.495058	−	0.392324i
$373$	6734.87			0.00250644			0.00125322	−	0.999999i	$-0.499601\pi$
$373$	6734.87			0.00250644			0.00125322	+	0.999999i	$0.499601\pi$
$374$			746159.i			0.275837i
$375$	−2.30837e6	−	1.82934e6i	−0.847669	−	0.671762i
$376$	−1.67644e6			−0.611530
$377$	−4.63237e6			−1.67861
$378$	−2.04501e6	−	961808.i	−0.736150	−	0.346226i
$379$	−1.92281e6			−0.687606			−0.343803	−	0.939042i	$-0.611715\pi$
$379$	−1.92281e6			−0.687606			−0.343803	+	0.939042i	$0.611715\pi$
$380$		−	2.31162e6i		−	0.821216i
$381$	683990.	−	863099.i	0.241400	−	0.304613i
$382$	446521.			0.156561
$383$			2.89182e6i			1.00734i	0.863897	+	0.503668i	$0.168017\pi$
$383$			2.89182e6i			1.00734i	−0.863897	+	0.503668i	$0.831983\pi$
$384$	158629.	−	200167.i	0.0548976	−	0.0692730i
$385$			858215.i			0.295083i
$386$	−1.30681e6			−0.446421
$387$	1.64056e6	−	385022.i	0.556820	−	0.130680i
$388$		−	687235.i		−	0.231753i
$389$			1.63885e6i			0.549119i	0.961570	+	0.274559i	$0.0885320\pi$
$389$			1.63885e6i			0.549119i	−0.961570	+	0.274559i	$0.911468\pi$
$390$	−1.81603e6	+	2.29157e6i	−0.604589	+	0.762907i
$391$		−	5.36841e6i		−	1.77584i
$392$	−348056.			−0.114402
$393$	1.75549e6	−	2.21518e6i	0.573345	−	0.723480i
$394$			1.95769e6i			0.635337i
$395$		−	1.38380e6i		−	0.446254i
$396$	−105137.	−	447984.i	−0.0336913	−	0.143557i
$397$			3.63179e6i			1.15650i	0.815861	+	0.578249i	$0.196264\pi$
$397$			3.63179e6i			1.15650i	−0.815861	+	0.578249i	$0.803736\pi$
$398$	1.24590e6			0.394253
$399$	4.29122e6	−	5.41491e6i	1.34942	−	1.70278i
$400$	194890.			0.0609030
$401$	3.02104e6			0.938200			0.469100	−	0.883145i	$-0.344578\pi$
$401$	3.02104e6			0.938200			0.469100	+	0.883145i	$0.344578\pi$
$402$	1.87226e6	+	1.48373e6i	0.577830	+	0.457920i
$403$	−6.51965e6			−1.99969
$404$	−2.35401e6			−0.717555
$405$	−1.27717e6	−	2.57111e6i	−0.386910	−	0.778902i
$406$		−	2.86536e6i		−	0.862709i
$407$			709032.i			0.212168i
$408$	−1.23238e6	−	976638.i	−0.366517	−	0.290458i
$409$			5.14602e6i			1.52112i	0.649269	+	0.760559i	$0.275075\pi$
$409$			5.14602e6i			1.52112i	−0.649269	+	0.760559i	$0.724925\pi$
$410$	−1.44356e6			−0.424107
$411$	−1.14318e6	−	905953.i	−0.333820	−	0.264546i
$412$		−	641248.i		−	0.186116i
$413$	−2.25237e6	−	3.29099e6i	−0.649777	−	0.949404i
$414$	756432.	+	3.22312e6i	0.216905	+	0.924222i
$415$		−	791289.i		−	0.225535i
$416$		−	987650.i		−	0.279814i
$417$	−2.69549e6	+	3.40133e6i	−0.759098	+	0.957875i
$418$	1.40682e6			0.393820
$419$	−6.59491e6			−1.83516			−0.917580	−	0.397552i	$-0.869860\pi$
$419$	−6.59491e6			−1.83516			−0.917580	+	0.397552i	$0.869860\pi$
$420$	−1.41746e6	−	1.12331e6i	−0.392090	−	0.310724i
$421$			141184.i			0.0388223i	0.999812	+	0.0194112i	$0.00617915\pi$
$421$			141184.i			0.0388223i	−0.999812	+	0.0194112i	$0.993821\pi$
$422$		−	3.90824e6i		−	1.06832i
$423$	−1.45433e6	−	6.19685e6i	−0.395196	−	1.68391i
$424$		−	489573.i		−	0.132252i
$425$		−	1.19989e6i		−	0.322232i
$426$	2.16502e6	+	1.71574e6i	0.578013	+	0.458065i
$427$		−	1.82110e6i		−	0.483352i
$428$		−	446345.i		−	0.117777i
$429$	−1.39462e6	−	1.10521e6i	−0.365857	−	0.289935i
$430$	1.34861e6			0.351734
$431$	4.22962e6			1.09675			0.548375	−	0.836232i	$-0.315246\pi$
$431$	4.22962e6			1.09675			0.548375	+	0.836232i	$0.315246\pi$
$432$	877518.	+	412714.i	0.226228	+	0.106399i
$433$	5.30206e6			1.35902			0.679509	−	0.733667i	$-0.262193\pi$
$433$	5.30206e6			1.35902			0.679509	+	0.733667i	$0.262193\pi$
$434$		−	4.03275e6i		−	1.02772i
$435$	2.26078e6	−	2.85279e6i	0.572842	−	0.722846i
$436$		−	453606.i		−	0.114278i
$437$	−1.01217e7			−2.53541
$438$	2.45419e6	+	1.94490e6i	0.611255	+	0.484409i
$439$	−59831.6			−0.0148173			−0.00740865	−	0.999973i	$-0.502358\pi$
$439$	−59831.6			−0.0148173			−0.00740865	+	0.999973i	$0.502358\pi$
$440$		−	368262.i		−	0.0906828i
$441$	−301943.	−	1.28657e6i	−0.0739314	−	0.315019i
$442$	−6.08073e6			−1.48047
$443$	−5.07749e6			−1.22925			−0.614624	−	0.788820i	$-0.710692\pi$
$443$	−5.07749e6			−1.22925			−0.614624	+	0.788820i	$0.710692\pi$
$444$	−1.17106e6	−	928043.i	−0.281917	−	0.223414i
$445$			1.28119e6i			0.306701i
$446$	4.81162e6			1.14539
$447$	2.32484e6	−	2.93362e6i	0.550331	−	0.694440i
$448$	610914.			0.143809
$449$			3.48307e6i			0.815354i	0.913126	+	0.407677i	$0.133661\pi$
$449$			3.48307e6i			0.815354i	−0.913126	+	0.407677i	$0.866339\pi$
$450$	169070.	+	720398.i	0.0393581	+	0.167703i
$451$		−	878530.i		−	0.203383i
$452$	−2.94334e6			−0.677632
$453$	4.16745e6	+	3.30262e6i	0.954167	+	0.756160i
$454$	3.06552e6			0.698016
$455$	−6.99392e6			−1.58377
$456$	−1.84137e6	+	2.32355e6i	−0.414695	+	0.523287i
$457$			7.17936e6i			1.60803i	0.594606	+	0.804017i	$0.297308\pi$
$457$			7.17936e6i			1.60803i	−0.594606	+	0.804017i	$0.702692\pi$
$458$			1.59697e6i			0.355739i
$459$	2.54098e6	−	5.40267e6i	0.562949	−	1.19695i
$460$			2.64954e6i			0.583816i
$461$		−	4.63611e6i		−	1.01602i	−0.861352	−	0.508009i	$-0.830382\pi$
$461$		−	4.63611e6i		−	1.01602i	0.861352	−	0.508009i	$-0.169618\pi$
$462$	683629.	−	862643.i	0.149010	−	0.188030i
$463$			1.94274e6i			0.421175i	0.977575	+	0.210588i	$0.0675377\pi$
$463$			1.94274e6i			0.421175i	−0.977575	+	0.210588i	$0.932462\pi$
$464$			1.22953e6i			0.265121i
$465$	3.18185e6	−	4.01505e6i	0.682413	−	0.861109i
$466$	−4.34482e6			−0.926845
$467$	−652283.			−0.138402			−0.0692012	−	0.997603i	$-0.522045\pi$
$467$	−652283.			−0.138402			−0.0692012	+	0.997603i	$0.522045\pi$
$468$	3.65079e6	−	856801.i	0.770500	−	0.180828i
$469$			5.71417e6i			1.19956i
$470$		−	5.09407e6i		−	1.06370i
$471$	342974.	+	271800.i	0.0712375	+	0.0564544i
$472$	966495.	+	1.41217e6i	0.199685	+	0.291764i
$473$			820744.i			0.168677i
$474$	−1.10230e6	+	1.39094e6i	−0.225347	+	0.284357i
$475$	−2.26229e6			−0.460060
$476$		−	3.76125e6i		−	0.760878i
$477$	1.80968e6	−	424711.i	0.364171	−	0.0854668i
$478$			4.50803e6i			0.902437i
$479$		−	8.02216e6i		−	1.59754i	−0.601634	−	0.798772i	$-0.705483\pi$
$479$		−	8.02216e6i		−	1.59754i	0.601634	−	0.798772i	$-0.294517\pi$
$480$	608233.	+	482013.i	0.120494	+	0.0954895i
$481$	−5.77816e6			−1.13875
$482$	−5.29425e6			−1.03797
$483$	−4.91852e6	+	6.20648e6i	−0.959327	+	1.21054i
$484$	−2.35270e6			−0.456512
$485$	2.08825e6			0.403114
$486$	−764312.	+	3.60173e6i	−0.146785	+	0.691704i
$487$	−8.38960e6			−1.60295			−0.801473	−	0.598031i	$-0.795950\pi$
$487$	−8.38960e6			−1.60295			−0.801473	+	0.598031i	$0.795950\pi$
$488$			781436.i			0.148540i
$489$	4.83389e6	−	6.09969e6i	0.914165	−	1.15355i
$490$		−	1.05761e6i		−	0.198992i
$491$			4.71113e6i			0.881904i	0.897531	+	0.440952i	$0.145359\pi$
$491$			4.71113e6i			0.881904i	−0.897531	+	0.440952i	$0.854641\pi$
$492$	1.45101e6	+	1.14990e6i	0.270245	+	0.214164i
$493$	7.56993e6			1.40273
$494$			1.14647e7i			2.11371i
$495$	1.36126e6	−	319472.i	0.249705	−	0.0586030i
$496$			1.73046e6i			0.315833i
$497$			6.60769e6i			1.19994i
$498$	−630317.	+	795371.i	−0.113890	+	0.143713i
$499$	−5.82809e6			−1.04779			−0.523896	−	0.851782i	$-0.675522\pi$
$499$	−5.82809e6			−1.04779			−0.523896	+	0.851782i	$0.675522\pi$
$500$			3.02310e6i			0.540788i
$501$	3.89513e6	+	3.08682e6i	0.693311	+	0.549436i
$502$		−	4.57780e6i		−	0.810770i
$503$	3.72741e6			0.656882			0.328441	−	0.944524i	$-0.393477\pi$
$503$	3.72741e6			0.656882			0.328441	+	0.944524i	$0.393477\pi$
$504$	529976.	+	2.25821e6i	0.0929351	+	0.395993i
$505$		−	7.15296e6i		−	1.24812i
$506$	−1.61247e6			−0.279973
$507$	5.41192e6	−	6.82908e6i	0.935043	−	1.17989i
$508$	−1.13034e6			−0.194334
$509$	383124.			0.0655457			0.0327729	−	0.999463i	$-0.489566\pi$
$509$	383124.			0.0655457			0.0327729	+	0.999463i	$0.489566\pi$
$510$	2.96764e6	−	3.74474e6i	0.505226	−	0.637524i
$511$			7.49024e6i			1.26895i
$512$	−262144.			−0.0441942
$513$	−1.01863e7	−	4.79080e6i	−1.70892	−	0.803738i
$514$			725020.i			0.121044i
$515$	1.94851e6			0.323732
$516$	−1.35557e6	−	1.07426e6i	−0.224128	−	0.177618i
$517$	3.10018e6			0.510105
$518$		−	3.57410e6i		−	0.585251i
$519$	−4.59043e6	+	5.79247e6i	−0.748057	+	0.943943i
$520$	3.00110e6			0.486712
$521$			929559.i			0.150032i	0.997182	+	0.0750158i	$0.0239007\pi$
$521$			929559.i			0.150032i	−0.997182	+	0.0750158i	$0.976099\pi$
$522$	−4.54489e6	+	1.06664e6i	−0.730041	+	0.171332i
$523$	6.21133e6			0.992957			0.496479	−	0.868049i	$-0.334626\pi$
$523$	6.21133e6			0.992957			0.496479	+	0.868049i	$0.334626\pi$
$524$	−2.90105e6			−0.461559
$525$	−1.09934e6	+	1.38721e6i	−0.174073	+	0.219656i
$526$		−	5.59389e6i		−	0.881556i
$527$	1.06540e7			1.67104
$528$	−293346.	+	370162.i	−0.0457926	+	0.0577839i
$529$	5.16495e6			0.802467
$530$	1.48763e6			0.230041
$531$	−4.38155e6	+	4.79767e6i	−0.674359	+	0.738404i
$532$	−7.09152e6			−1.08633
$533$	7.15947e6			1.09160
$534$	1.02056e6	−	1.28780e6i	0.154877	−	0.195432i
$535$	1.35628e6			0.204863
$536$		−	2.45196e6i		−	0.368639i
$537$	−3.87010e6	+	4.88353e6i	−0.579144	+	0.730799i
$538$	2.46333e6			0.366917
$539$	643648.			0.0954281
$540$	−1.25408e6	+	2.66645e6i	−0.185072	+	0.393504i
$541$			252422.i			0.0370795i	0.999828	+	0.0185398i	$0.00590173\pi$
$541$			252422.i			0.0370795i	−0.999828	+	0.0185398i	$0.994098\pi$
$542$	1.46270e6			0.213874
$543$	−4.66664e6	+	5.88864e6i	−0.679210	+	0.857068i
$544$			1.61396e6i			0.233827i
$545$	1.37834e6			0.198777
$546$	7.03000e6	+	5.57115e6i	1.00919	+	0.799766i
$547$	1.34401e7			1.92059			0.960293	−	0.278993i	$-0.0900006\pi$
$547$	1.34401e7			1.92059			0.960293	+	0.278993i	$0.0900006\pi$
$548$			1.49715e6i			0.212967i
$549$	−2.88853e6	+	677907.i	−0.409022	+	0.0959929i
$550$	−360403.			−0.0508020
$551$		−	1.42725e7i		−	2.00272i
$552$	2.11055e6	−	2.66321e6i	0.294813	−	0.372013i
$553$	−4.24519e6			−0.590315
$554$	4.37254e6			0.605285
$555$	2.81998e6	−	3.55841e6i	0.388609	−	0.490370i
$556$	4.45448e6			0.611096
$557$		−	6.05912e6i		−	0.827507i	−0.910389	−	0.413753i	$-0.864218\pi$
$557$		−	6.05912e6i		−	0.827507i	0.910389	−	0.413753i	$-0.135782\pi$
$558$	−6.39654e6	+	1.50120e6i	−0.869680	+	0.204104i
$559$	−6.68855e6			−0.905321
$560$			1.85634e6i			0.250142i
$561$	2.27900e6	+	1.80606e6i	0.305729	+	0.242285i
$562$		−	3.14586e6i		−	0.420144i
$563$	9.23663e6			1.22813			0.614063	−	0.789257i	$-0.289534\pi$
$563$	9.23663e6			1.22813			0.614063	+	0.789257i	$0.289534\pi$
$564$	−4.05778e6	+	5.12035e6i	−0.537144	+	0.677800i
$565$		−	8.94370e6i		−	1.17868i
$566$			7.47217e6i			0.980405i
$567$	−7.88757e6	+	3.91805e6i	−1.03035	+	0.511814i
$568$		−	2.83537e6i		−	0.368756i
$569$	−2.59568e6			−0.336101			−0.168050	−	0.985778i	$-0.553747\pi$
$569$	−2.59568e6			−0.336101			−0.168050	+	0.985778i	$0.553747\pi$
$570$	−7.06040e6	−	5.59523e6i	−0.910211	−	0.721325i
$571$			7.57833e6i			0.972709i	0.873761	+	0.486355i	$0.161674\pi$
$571$			7.57833e6i			0.972709i	−0.873761	+	0.486355i	$0.838326\pi$
$572$			1.82643e6i			0.233406i
$573$	1.08079e6	−	1.36381e6i	0.137517	−	0.173527i
$574$			4.42851e6i			0.561019i
$575$	2.59300e6			0.327064
$576$	−227414.	−	969000.i	−0.0285601	−	0.121694i
$577$	1.98093e6			0.247702			0.123851	−	0.992301i	$-0.460476\pi$
$577$	1.98093e6			0.247702			0.123851	+	0.992301i	$0.460476\pi$
$578$	4.25733e6			0.530051
$579$	−3.16311e6	+	3.99140e6i	−0.392119	+	0.494799i
$580$	−3.73608e6			−0.461155
$581$	−2.42749e6			−0.298344
$582$	−2.09903e6	−	1.66344e6i	−0.256868	−	0.203563i
$583$			905349.i			0.110318i
$584$		−	3.21407e6i		−	0.389963i
$585$	2.60350e6	+	1.10934e7i	0.314534	+	1.34022i
$586$			4.07030e6i			0.489646i
$587$	−7.75742e6			−0.929227			−0.464614	−	0.885513i	$-0.653807\pi$
$587$	−7.75742e6			−0.929227			−0.464614	+	0.885513i	$0.653807\pi$
$588$	−842462.	+	1.06307e6i	−0.100486	+	0.126800i
$589$		−	2.00872e7i		−	2.38579i
$590$	−4.29105e6	+	2.93682e6i	−0.507497	+	0.347334i
$591$	5.97939e6	+	4.73856e6i	0.704188	+	0.558056i
$592$			1.53365e6i			0.179855i
$593$		−	7.05328e6i		−	0.823672i	−0.911258	−	0.411836i	$-0.864888\pi$
$593$		−	7.05328e6i		−	0.823672i	0.911258	−	0.411836i	$-0.135112\pi$
$594$	−1.62276e6	−	763217.i	−0.188707	−	0.0887527i
$595$	1.14290e7			1.32348
$596$	−3.84195e6			−0.443033
$597$	3.01567e6	−	3.80535e6i	0.346297	−	0.436977i
$598$		−	1.31406e7i		−	1.50267i
$599$			8.41296e6i			0.958036i	0.877805	+	0.479018i	$0.159007\pi$
$599$			8.41296e6i			0.958036i	−0.877805	+	0.479018i	$0.840993\pi$
$600$	471726.	−	595252.i	0.0534949	−	0.0675030i
$601$		−	5.27865e6i		−	0.596124i	−0.954547	−	0.298062i	$-0.903660\pi$
$601$		−	5.27865e6i		−	0.596124i	0.954547	−	0.298062i	$-0.0963402\pi$
$602$		−	4.13722e6i		−	0.465283i
$603$	9.06352e6	−	2.12711e6i	1.01509	−	0.238230i
$604$		−	5.45780e6i		−	0.608731i
$605$		−	7.14897e6i		−	0.794063i
$606$	−5.69784e6	+	7.18987e6i	−0.630272	+	0.795315i
$607$	1.33487e7			1.47051			0.735254	−	0.677792i	$-0.237063\pi$
$607$	1.33487e7			1.47051			0.735254	+	0.677792i	$0.237063\pi$
$608$	3.04298e6			0.333842
$609$	−8.75169e6	−	6.93555e6i	−0.956199	−	0.757770i
$610$	−2.37449e6			−0.258372
$611$			2.52645e7i			2.73784i
$612$	−5.96590e6	+	1.40013e6i	−0.643869	+	0.151109i
$613$			9.51734e6i			1.02297i	0.859291	+	0.511487i	$0.170905\pi$
$613$			9.51734e6i			1.02297i	−0.859291	+	0.511487i	$0.829095\pi$
$614$	1.01212e7			1.08346
$615$	−3.49411e6	+	4.40907e6i	−0.372519	+	0.470067i
$616$	−1.12974e6			−0.119957
$617$			2.50921e6i			0.265353i	0.991159	+	0.132677i	$0.0423572\pi$
$617$			2.50921e6i			0.265353i	−0.991159	+	0.132677i	$0.957643\pi$
$618$	−1.95857e6	−	1.55213e6i	−0.206285	−	0.163477i
$619$	1.65298e7			1.73396			0.866982	−	0.498339i	$-0.166057\pi$
$619$	1.65298e7			1.73396			0.866982	+	0.498339i	$0.166057\pi$
$620$	−5.25822e6			−0.549363
$621$	1.16753e7	+	5.49113e6i	1.21490	+	0.571390i
$622$			876113.i			0.0907997i
$623$	3.93040e6			0.405711
$624$	−3.01659e6	−	2.39059e6i	−0.310137	−	0.245778i
$625$	−6.80704e6			−0.697041
$626$			1.04347e7i			1.06425i
$627$	3.40518e6	−	4.29686e6i	0.345916	−	0.436498i
$628$		−	449167.i		−	0.0454474i
$629$	9.44232e6			0.951595
$630$	−6.86185e6	+	1.61040e6i	−0.688794	+	0.161652i
$631$	−1.37345e7			−1.37322			−0.686608	−	0.727028i	$-0.740901\pi$
$631$	−1.37345e7			−1.37322			−0.686608	+	0.727028i	$0.740901\pi$
$632$	1.82162e6			0.181411
$633$	−1.19370e7	−	9.45982e6i	−1.18409	−	0.938369i
$634$			1.93672e6i			0.191356i
$635$		−	3.43467e6i		−	0.338027i
$636$	−1.49530e6	−	1.18500e6i	−0.146584	−	0.116165i
$637$			5.24532e6i			0.512181i
$638$		−	2.27373e6i		−	0.221150i
$639$	1.04808e7	−	2.45972e6i	1.01541	−	0.238305i
$640$		−	796558.i		−	0.0768718i
$641$		−	6.26682e6i		−	0.602424i	−0.953557	−	0.301212i	$-0.902609\pi$
$641$		−	6.26682e6i		−	0.602424i	0.953557	−	0.301212i	$-0.0973912\pi$
$642$	−1.36327e6	−	1.08037e6i	−0.130541	−	0.103451i
$643$	6.58653e6			0.628245			0.314122	−	0.949382i	$-0.398290\pi$
$643$	6.58653e6			0.628245			0.314122	+	0.949382i	$0.398290\pi$
$644$	8.12818e6			0.772286
$645$	3.26428e6	−	4.11906e6i	0.308950	−	0.389851i
$646$		−	1.87349e7i		−	1.76632i
$647$			1.15875e7i			1.08825i	0.839005	+	0.544124i	$0.183138\pi$
$647$			1.15875e7i			1.08825i	−0.839005	+	0.544124i	$0.816862\pi$
$648$	3.38457e6	−	1.68124e6i	0.316640	−	0.157287i
$649$	−1.78731e6	−	2.61147e6i	−0.166566	−	0.243374i
$650$		−	2.93706e6i		−	0.272665i
$651$	−1.23172e7	−	9.76118e6i	−1.13910	−	0.902713i
$652$	−7.98832e6			−0.735930
$653$			1.31530e7i			1.20710i	0.797326	+	0.603549i	$0.206247\pi$
$653$			1.31530e7i			1.20710i	−0.797326	+	0.603549i	$0.793753\pi$
$654$	−1.38545e6	−	1.09794e6i	−0.126662	−	0.100377i
$655$		−	8.81522e6i		−	0.802841i
$656$		−	1.90028e6i		−	0.172408i
$657$	1.18806e7	−	2.78825e6i	1.07381	−	0.252011i
$658$	−1.56274e7			−1.40709
$659$	−1.59847e7			−1.43381			−0.716904	−	0.697172i	$-0.754441\pi$
$659$	−1.59847e7			−1.43381			−0.716904	+	0.697172i	$0.754441\pi$
$660$	−1.12478e6	−	891370.i	−0.100510	−	0.0796522i
$661$	1.52722e7			1.35956			0.679780	−	0.733416i	$-0.262075\pi$
$661$	1.52722e7			1.35956			0.679780	+	0.733416i	$0.262075\pi$
$662$	5.82277e6			0.516399
$663$	−1.47183e7	+	1.85724e7i	−1.30039	+	1.64091i
$664$	1.04164e6			0.0916848
$665$		−	2.15485e7i		−	1.88957i
$666$	−5.66905e6	+	1.33046e6i	−0.495250	+	0.116230i
$667$			1.63588e7i			1.42376i
$668$		−	5.10117e6i		−	0.442312i
$669$	1.16464e7	−	1.46962e7i	1.00607	−	1.26952i
$670$	7.45058e6			0.641214
$671$		−	1.44508e6i		−	0.123904i
$672$	1.47870e6	−	1.86592e6i	0.126316	−	0.159393i
$673$			2.25864e7i			1.92225i	0.276111	+	0.961126i	$0.410954\pi$
$673$			2.25864e7i			1.92225i	−0.276111	+	0.961126i	$0.589046\pi$
$674$		−	8.27672e6i		−	0.701792i
$675$	2.60955e6	+	1.22732e6i	0.220448	+	0.103681i
$676$	−8.94355e6			−0.752737
$677$		−	5.65265e6i		−	0.474003i	−0.971509	−	0.237001i	$-0.923835\pi$
$677$		−	5.65265e6i		−	0.474003i	0.971509	−	0.237001i	$-0.0761646\pi$
$678$	−7.12429e6	+	8.98985e6i	−0.595206	+	0.751066i
$679$		−	6.40627e6i		−	0.533250i
$680$	−4.90422e6			−0.406722
$681$	7.42004e6	−	9.36305e6i	0.613110	−	0.773659i
$682$		−	3.20008e6i		−	0.263451i
$683$	−1.66560e7			−1.36622			−0.683109	−	0.730317i	$-0.739372\pi$
$683$	−1.66560e7			−1.36622			−0.683109	+	0.730317i	$0.739372\pi$
$684$	2.63983e6	+	1.12482e7i	0.215742	+	0.919270i
$685$	−4.54927e6			−0.370437
$686$	6.78247e6			0.550272
$687$	4.87762e6	+	3.86542e6i	0.394290	+	0.312468i
$688$			1.77529e6i			0.142987i
$689$	−7.37803e6			−0.592096
$690$	8.09250e6	+	6.41316e6i	0.647083	+	0.512801i
$691$		−	2.11778e7i		−	1.68728i	−0.536911	−	0.843639i	$-0.680409\pi$
$691$		−	2.11778e7i		−	1.68728i	0.536911	−	0.843639i	$-0.319591\pi$
$692$	7.58598e6			0.602208
$693$	−980066.	−	4.17602e6i	−0.0775215	−	0.330316i
$694$	−5.88676e6			−0.463957
$695$			1.35355e7i			1.06295i
$696$	3.75536e6	+	2.97605e6i	0.293852	+	0.232872i
$697$	−1.16996e7			−0.912195
$698$		−	1.50377e7i		−	1.16827i
$699$	−1.05166e7	+	1.32704e7i	−0.814105	+	1.02729i
$700$	1.81672e6			0.140134
$701$	1.42256e7			1.09339			0.546694	−	0.837333i	$-0.315886\pi$
$701$	1.42256e7			1.09339			0.546694	+	0.837333i	$0.315886\pi$
$702$	6.21974e6	−	1.32245e7i	0.476353	−	1.01283i
$703$		−	1.78027e7i		−	1.35862i
$704$	484774.			0.0368644
$705$	−1.55588e7	−	1.23301e7i	−1.17897	−	0.934315i
$706$	4.44099e6			0.335327
$707$	−2.19436e7			−1.65105
$708$	6.65257e6	+	466153.i	0.498777	+	0.0349498i
$709$	9.18614e6			0.686306			0.343153	−	0.939280i	$-0.388505\pi$
$709$	9.18614e6			0.686306			0.343153	+	0.939280i	$0.388505\pi$
$710$	8.61563e6			0.641418
$711$	1.58028e6	+	6.73350e6i	0.117236	+	0.499536i
$712$	−1.68654e6			−0.124680
$713$			2.30237e7i			1.69610i
$714$	−1.14880e7	−	9.10403e6i	−0.843333	−	0.668326i
$715$	−5.54983e6			−0.405989
$716$	6.39560e6			0.466228
$717$	1.37689e7	+	1.09116e7i	1.00023	+	0.792666i
$718$			1.10163e7i			0.797488i
$719$	1.07825e7			0.777856			0.388928	−	0.921268i	$-0.372845\pi$
$719$	1.07825e7			0.777856			0.388928	+	0.921268i	$0.372845\pi$
$720$	2.94443e6	−	691025.i	0.211675	−	0.0496778i
$721$		−	5.97759e6i		−	0.428241i
$722$	−2.54187e7			−1.81472
$723$	−1.28146e7	+	1.61703e7i	−0.911717	+	1.15046i
$724$	7.71192e6			0.546784
$725$			3.65635e6i			0.258347i
$726$	−5.69466e6	+	7.18585e6i	−0.400983	+	0.505984i
$727$	−5.24483e6			−0.368041			−0.184020	−	0.982922i	$-0.558911\pi$
$727$	−5.24483e6			−0.368041			−0.184020	+	0.982922i	$0.558911\pi$
$728$		−	9.20668e6i		−	0.643835i
$729$	9.15077e6	+	1.10524e7i	0.637733	+	0.770257i
$730$	9.76636e6			0.678306
$731$	1.09300e7			0.756533
$732$	2.38674e6	+	1.89145e6i	0.164637	+	0.130472i
$733$	−3.66211e6			−0.251751			−0.125876	−	0.992046i	$-0.540174\pi$
$733$	−3.66211e6			−0.251751			−0.125876	+	0.992046i	$0.540174\pi$
$734$		−	1.32785e7i		−	0.909722i
$735$	−3.23027e6	−	2.55993e6i	−0.220557	−	0.174787i
$736$	−3.48781e6			−0.237333
$737$			4.53432e6i			0.307499i
$738$	7.02427e6	−	1.64852e6i	0.474745	−	0.111417i
$739$		−	1.61956e7i		−	1.09090i	−0.838143	−	0.545451i	$-0.816359\pi$
$739$		−	1.61956e7i		−	1.09090i	0.838143	−	0.545451i	$-0.183641\pi$
$740$	−4.66019e6			−0.312842
$741$	3.50167e7	+	2.77501e7i	2.34277	+	1.85660i
$742$		−	4.56370e6i		−	0.304304i
$743$			8.89607e6i			0.591189i	0.955314	+	0.295594i	$0.0955177\pi$
$743$			8.89607e6i			0.591189i	−0.955314	+	0.295594i	$0.904482\pi$
$744$	5.28535e6	+	4.18854e6i	0.350059	+	0.277415i
$745$		−	1.16742e7i		−	0.770616i
$746$	−26939.5			−0.00177232
$747$	903637.	+	3.85036e6i	0.0592506	+	0.252464i
$748$		−	2.98464e6i		−	0.195046i
$749$		−	4.16074e6i		−	0.270998i
$750$	9.23346e6	+	7.31735e6i	0.599393	+	0.475008i
$751$			2.86490e7i			1.85357i	0.375592	+	0.926785i	$0.377439\pi$
$751$			2.86490e7i			1.85357i	−0.375592	+	0.926785i	$0.622561\pi$
$752$	6.70575e6			0.432417
$753$	−1.39820e7	−	1.10805e7i	−0.898632	−	0.712149i
$754$	1.85295e7			1.18696
$755$	1.65842e7			1.05883
$756$	8.18005e6	+	3.84723e6i	0.520537	+	0.244818i
$757$	1.40707e7			0.892436			0.446218	−	0.894924i	$-0.352771\pi$
$757$	1.40707e7			0.892436			0.446218	+	0.894924i	$0.352771\pi$
$758$	7.69126e6			0.486211
$759$	−3.90296e6	+	4.92498e6i	−0.245917	+	0.310313i
$760$			9.24648e6i			0.580688i
$761$			1.28884e7i			0.806745i	0.915036	+	0.403373i	$0.132162\pi$
$761$			1.28884e7i			0.806745i	−0.915036	+	0.403373i	$0.867838\pi$
$762$	−2.73596e6	+	3.45239e6i	−0.170695	+	0.215394i
$763$		−	4.22843e6i		−	0.262947i
$764$	−1.78608e6			−0.110705
$765$	−4.25448e6	−	1.81281e7i	−0.262841	−	1.11995i
$766$		−	1.15673e7i		−	0.712295i
$767$	2.12819e7	−	1.45654e7i	1.30623	−	0.893994i
$768$	−634514.	+	800668.i	−0.0388185	+	0.0489834i
$769$		−	1.84314e7i		−	1.12394i	−0.827158	−	0.561969i	$-0.810044\pi$
$769$		−	1.84314e7i		−	1.12394i	0.827158	−	0.561969i	$-0.189956\pi$
$770$		−	3.43286e6i		−	0.208655i
$771$	2.21443e6	+	1.75490e6i	0.134161	+	0.106320i
$772$	5.22725e6			0.315668
$773$	1.96445e6			0.118247			0.0591237	−	0.998251i	$-0.481169\pi$
$773$	1.96445e6			0.118247			0.0591237	+	0.998251i	$0.481169\pi$
$774$	−6.56225e6	+	1.54009e6i	−0.393731	+	0.0924044i
$775$			5.14600e6i			0.307762i
$776$			2.74894e6i			0.163874i
$777$	−1.09164e7	−	8.65103e6i	−0.648674	−	0.514062i
$778$		−	6.55542e6i		−	0.388286i
$779$			2.20585e7i			1.30237i
$780$	7.26410e6	−	9.16628e6i	0.427509	−	0.539457i
$781$			5.24335e6i			0.307596i
$782$			2.14736e7i			1.25571i
$783$	−7.74298e6	+	1.64632e7i	−0.451340	+	0.959646i
$784$	1.39222e6			0.0808945
$785$	1.36485e6			0.0790517
$786$	−7.02194e6	+	8.86070e6i	−0.405416	+	0.511578i
$787$	−6.24666e6			−0.359510			−0.179755	−	0.983711i	$-0.557531\pi$
$787$	−6.24666e6			−0.359510			−0.179755	+	0.983711i	$0.557531\pi$
$788$		−	7.83078e6i		−	0.449251i
$789$	−1.70855e7	−	1.35399e7i	−0.977089	−	0.774325i
$790$			5.53521e6i			0.315549i
$791$	−2.74372e7			−1.55919
$792$	420548.	+	1.79194e6i	0.0238233	+	0.101510i
$793$	1.17765e7			0.665018
$794$		−	1.45272e7i		−	0.817767i
$795$	3.60077e6	−	4.54367e6i	0.202059	−	0.254970i
$796$	−4.98359e6			−0.278779
$797$	1.58383e7			0.883207			0.441604	−	0.897210i	$-0.354410\pi$
$797$	1.58383e7			0.883207			0.441604	+	0.897210i	$0.354410\pi$
$798$	−1.71649e7	+	2.16597e7i	−0.954187	+	1.20405i
$799$		−	4.12857e7i		−	2.28788i
$800$	−779559.			−0.0430649
$801$	−1.46310e6	−	6.23421e6i	−0.0805736	−	0.343321i
$802$	−1.20842e7			−0.663407
$803$			5.94367e6i			0.325286i
$804$	−7.48903e6	−	5.93491e6i	−0.408588	−	0.323798i
$805$			2.46985e7i			1.34332i
$806$	2.60786e7			1.41399
$807$	5.96245e6	−	7.52377e6i	0.322285	−	0.406679i
$808$	9.41604e6			0.507388
$809$	3.27519e7			1.75941			0.879703	−	0.475524i	$-0.157742\pi$
$809$	3.27519e7			1.75941			0.879703	+	0.475524i	$0.157742\pi$
$810$	5.10867e6	+	1.02844e7i	0.273587	+	0.550767i
$811$		−	7.01510e6i		−	0.374526i	−0.982310	−	0.187263i	$-0.940038\pi$
$811$		−	7.01510e6i		−	0.374526i	0.982310	−	0.187263i	$-0.0599616\pi$
$812$			1.14614e7i			0.610027i
$813$	3.54044e6	−	4.46754e6i	0.187859	−	0.237051i
$814$		−	2.83613e6i		−	0.150025i
$815$		−	2.42735e7i		−	1.28008i
$816$	4.92952e6	+	3.90655e6i	0.259167	+	0.205385i
$817$		−	2.06076e7i		−	1.08012i
$818$		−	2.05841e7i		−	1.07559i
$819$	3.40320e7	−	7.98693e6i	1.77287	−	0.416073i
$820$	5.77424e6			0.299889
$821$	1.55129e7			0.803220			0.401610	−	0.915811i	$-0.368451\pi$
$821$	1.55129e7			0.803220			0.401610	+	0.915811i	$0.368451\pi$
$822$	4.57274e6	+	3.62381e6i	0.236046	+	0.187062i
$823$		−	3.21214e7i		−	1.65309i	−0.562874	−	0.826543i	$-0.690304\pi$
$823$		−	3.21214e7i		−	1.65309i	0.562874	−	0.826543i	$-0.309696\pi$
$824$			2.56499e6i			0.131604i
$825$	−872347.	+	1.10078e6i	−0.0446226	+	0.0563074i
$826$	9.00947e6	+	1.31639e7i	0.459462	+	0.671330i
$827$		−	2.82847e7i		−	1.43810i	−0.694960	−	0.719048i	$-0.744578\pi$
$827$		−	2.82847e7i		−	1.43810i	0.694960	−	0.719048i	$-0.255422\pi$
$828$	−3.02573e6	−	1.28925e7i	−0.153375	−	0.653523i
$829$	1.44368e7			0.729602			0.364801	−	0.931086i	$-0.381137\pi$
$829$	1.44368e7			0.729602			0.364801	+	0.931086i	$0.381137\pi$
$830$			3.16515e6i			0.159478i
$831$	1.05836e7	−	1.33551e7i	0.531659	−	0.670878i
$832$			3.95060e6i			0.197859i
$833$		−	8.57159e6i		−	0.428005i
$834$	1.07820e7	−	1.36053e7i	0.536764	−	0.677320i
$835$	1.55005e7			0.769362
$836$	−5.62728e6			−0.278473
$837$	−1.08976e7	+	2.31706e7i	−0.537670	+	1.14320i
$838$	2.63796e7			1.29765
$839$	−3.73880e7			−1.83370			−0.916848	−	0.399237i	$-0.869275\pi$
$839$	−3.73880e7			−1.83370			−0.916848	+	0.399237i	$0.869275\pi$
$840$	5.66982e6	+	4.49323e6i	0.277250	+	0.219715i
$841$	−2.55627e6			−0.124628
$842$		−	564738.i		−	0.0274515i
$843$	−9.60842e6	−	7.61449e6i	−0.465675	−	0.369039i
$844$			1.56330e7i			0.755415i
$845$		−	2.71761e7i		−	1.30932i
$846$	5.81733e6	+	2.47874e7i	0.279446	+	1.19071i
$847$	−2.19314e7			−1.05041
$848$			1.95829e6i			0.0935163i
$849$	2.28223e7	+	1.80862e7i	1.08665	+	0.861150i
$850$			4.79956e6i			0.227853i
$851$			2.04052e7i			0.965864i
$852$	−8.66008e6	−	6.86295e6i	−0.408717	−	0.323901i
$853$	6.58052e6			0.309662			0.154831	−	0.987941i	$-0.450517\pi$
$853$	6.58052e6			0.309662			0.154831	+	0.987941i	$0.450517\pi$
$854$			7.28439e6i			0.341781i
$855$	−3.41791e7	+	8.02145e6i	−1.59899	+	0.375265i
$856$			1.78538e6i			0.0832810i
$857$	−3.95886e7			−1.84127			−0.920637	−	0.390420i	$-0.872330\pi$
$857$	−3.95886e7			−1.84127			−0.920637	+	0.390420i	$0.872330\pi$
$858$	5.57847e6	+	4.42083e6i	0.258700	+	0.205015i
$859$		−	2.72268e6i		−	0.125897i	−0.998017	−	0.0629483i	$-0.979950\pi$
$859$		−	2.72268e6i		−	0.125897i	0.998017	−	0.0629483i	$-0.0200503\pi$
$860$	−5.39444e6			−0.248714
$861$	1.35260e7	+	1.07191e7i	0.621816	+	0.492778i
$862$	−1.69185e7			−0.775520
$863$	3.62841e7			1.65840			0.829201	−	0.558951i	$-0.188796\pi$
$863$	3.62841e7			1.65840			0.829201	+	0.558951i	$0.188796\pi$
$864$	−3.51007e6	−	1.65085e6i	−0.159967	−	0.0752358i
$865$			2.30510e7i			1.04749i
$866$	−2.12082e7			−0.960971
$867$	1.03048e7	−	1.30032e7i	0.465576	−	0.587492i
$868$			1.61310e7i			0.726711i
$869$	−3.36865e6			−0.151324
$870$	−9.04312e6	+	1.14111e7i	−0.405061	+	0.511130i
$871$	−3.69519e7			−1.65041
$872$			1.81443e6i			0.0808068i
$873$	−1.01613e7	+	2.38474e6i	−0.451246	+	0.105903i
$874$	4.04867e7			1.79281
$875$			2.81807e7i			1.24432i
$876$	−9.81676e6	−	7.77960e6i	−0.432223	−	0.342529i
$877$	2.40222e7			1.05466			0.527332	−	0.849659i	$-0.323192\pi$
$877$	2.40222e7			1.05466			0.527332	+	0.849659i	$0.323192\pi$
$878$	239326.			0.0104774
$879$	1.24319e7	+	9.85207e6i	0.542708	+	0.430086i
$880$			1.47305e6i			0.0641224i
$881$	2.74669e7			1.19226			0.596129	−	0.802889i	$-0.296705\pi$
$881$	2.74669e7			1.19226			0.596129	+	0.802889i	$0.296705\pi$
$882$	1.20777e6	+	5.14627e6i	0.0522774	+	0.222752i
$883$	−7.74466e6			−0.334273			−0.167136	−	0.985934i	$-0.553452\pi$
$883$	−7.74466e6			−0.334273			−0.167136	+	0.985934i	$0.553452\pi$
$884$	2.43229e7			1.04685
$885$	−1.41646e6	+	2.02147e7i	−0.0607921	+	0.867578i
$886$	2.03099e7			0.869210
$887$	−2.11251e7			−0.901548			−0.450774	−	0.892638i	$-0.648852\pi$
$887$	−2.11251e7			−0.901548			−0.450774	+	0.892638i	$0.648852\pi$
$888$	4.68424e6	+	3.71217e6i	0.199346	+	0.157978i
$889$	−1.05368e7			−0.447150
$890$		−	5.12477e6i		−	0.216870i
$891$	−6.25896e6	+	3.10906e6i	−0.264124	+	0.131200i
$892$	−1.92465e7			−0.809915
$893$	−7.78407e7			−3.26646
$894$	−9.29935e6	+	1.17345e7i	−0.389143	+	0.491043i
$895$			1.94338e7i			0.810963i
$896$	−2.44365e6			−0.101688
$897$	−4.01355e7	−	3.18067e7i	−1.66551	−	1.31989i
$898$		−	1.39323e7i		−	0.576542i
$899$	−3.24654e7			−1.33974
$900$	−676278.	−	2.88159e6i	−0.0278304	−	0.118584i
$901$	1.20567e7			0.494786
$902$			3.51412e6i			0.143814i
$903$	−1.26363e7	−	1.00141e7i	−0.515705	−	0.408687i
$904$	1.17733e7			0.479158
$905$			2.34336e7i			0.951083i
$906$	−1.66698e7	−	1.32105e7i	−0.674698	−	0.534686i
$907$	1.46459e6			0.0591150			0.0295575	−	0.999563i	$-0.490590\pi$
$907$	1.46459e6			0.0591150			0.0295575	+	0.999563i	$0.490590\pi$
$908$	−1.22621e7			−0.493572
$909$	8.16855e6	+	3.48059e7i	0.327895	+	1.39715i
$910$	2.79757e7			1.11989
$911$			1.00889e7i			0.402761i	0.979513	+	0.201380i	$0.0645427\pi$
$911$			1.00889e7i			0.402761i	−0.979513	+	0.201380i	$0.935457\pi$
$912$	7.36547e6	−	9.29419e6i	0.293234	−	0.370019i
$913$	−1.92627e6			−0.0764786
$914$		−	2.87175e7i		−	1.13705i
$915$	−5.74741e6	+	7.25242e6i	−0.226944	+	0.286372i
$916$		−	6.38787e6i		−	0.251546i
$917$	−2.70430e7			−1.06202
$918$	−1.01639e7	+	2.16107e7i	−0.398065	+	0.846373i
$919$		−	3.71085e7i		−	1.44939i	−0.689071	−	0.724694i	$-0.741981\pi$
$919$		−	3.71085e7i		−	1.44939i	0.689071	−	0.724694i	$-0.258019\pi$
$920$		−	1.05982e7i		−	0.412820i
$921$	2.44982e7	−	3.09133e7i	0.951668	−	1.20087i
$922$			1.85444e7i			0.718433i
$923$	−4.27300e7			−1.65093
$924$	−2.73452e6	+	3.45057e6i	−0.105366	+	0.132957i
$925$			4.56074e6i			0.175259i
$926$		−	7.77097e6i		−	0.297816i
$927$	−9.48135e6	+	2.22517e6i	−0.362386	+	0.0850479i
$928$		−	4.91812e6i		−	0.187469i
$929$	4.31830e7			1.64162			0.820812	−	0.571199i	$-0.193521\pi$
$929$	4.31830e7			1.64162			0.820812	+	0.571199i	$0.193521\pi$
$930$	−1.27274e7	+	1.60602e7i	−0.482539	+	0.608896i
$931$	−1.61610e7			−0.611075
$932$	1.73793e7			0.655379
$933$	2.67592e6	+	2.12061e6i	0.100640	+	0.0797550i
$934$	2.60913e6			0.0978653
$935$	9.06919e6			0.339265
$936$	−1.46032e7	+	3.42720e6i	−0.544826	+	0.127865i
$937$		−	2.52782e7i		−	0.940581i	−0.882512	−	0.470291i	$-0.844149\pi$
$937$		−	2.52782e7i		−	0.940581i	0.882512	−	0.470291i	$-0.155851\pi$
$938$		−	2.28567e7i		−	0.848215i
$939$	3.18706e7	+	2.52569e7i	1.17958	+	0.934794i
$940$			2.03763e7i			0.752151i
$941$	2.58863e7			0.953008			0.476504	−	0.879172i	$-0.341904\pi$
$941$	2.58863e7			0.953008			0.476504	+	0.879172i	$0.341904\pi$
$942$	−1.37189e6	−	1.08720e6i	−0.0503725	−	0.0399193i
$943$		−	2.52831e7i		−	0.925873i
$944$	−3.86598e6	−	5.64867e6i	−0.141198	−	0.206308i
$945$	−1.16903e7	+	2.48561e7i	−0.425840	+	0.905427i
$946$		−	3.28298e6i		−	0.119272i
$947$		−	3.56684e7i		−	1.29243i	−0.763154	−	0.646217i	$-0.776350\pi$
$947$		−	3.56684e7i		−	1.29243i	0.763154	−	0.646217i	$-0.223650\pi$
$948$	4.40919e6	−	5.56377e6i	0.159345	−	0.201071i
$949$	−4.84372e7			−1.74588
$950$	9.04916e6			0.325311
$951$	5.91532e6	+	4.68778e6i	0.212093	+	0.168080i
$952$			1.50450e7i			0.538022i
$953$		−	1.18643e7i		−	0.423165i	−0.977360	−	0.211582i	$-0.932138\pi$
$953$		−	1.18643e7i		−	0.423165i	0.977360	−	0.211582i	$-0.0678616\pi$
$954$	−7.23871e6	+	1.69884e6i	−0.257508	+	0.0604342i
$955$		−	5.42724e6i		−	0.192562i
$956$		−	1.80321e7i		−	0.638119i
$957$	−6.94466e6	−	5.50351e6i	−0.245116	−	0.194250i
$958$			3.20887e7i			1.12963i
$959$			1.39561e7i			0.490024i
$960$	−2.43293e6	−	1.92805e6i	−0.0852023	−	0.0675213i
$961$	−1.70631e7			−0.596003
$962$	2.31127e7			0.805216
$963$	−6.59955e6	+	1.54884e6i	−0.229324	+	0.0538197i
$964$	2.11770e7			0.733959
$965$			1.58837e7i			0.549076i
$966$	1.96741e7	−	2.48259e7i	0.678347	−	0.855978i
$967$			5.39418e7i			1.85507i	0.373741	+	0.927533i	$0.378075\pi$
$967$			5.39418e7i			1.85507i	−0.373741	+	0.927533i	$0.621925\pi$
$968$	9.41079e6			0.322803
$969$	−5.72221e7	−	4.53475e7i	−1.95774	−	1.55147i
$970$	−8.35300e6			−0.285045
$971$			4.78331e7i			1.62810i	0.580797	+	0.814048i	$0.302741\pi$
$971$			4.78331e7i			1.62810i	−0.580797	+	0.814048i	$0.697259\pi$
$972$	3.05725e6	−	1.44069e7i	0.103792	−	0.489109i
$973$	4.15238e7			1.40609
$974$	3.35584e7			1.13345
$975$	−8.97066e6	−	7.10908e6i	−0.302213	−	0.239498i
$976$		−	3.12574e6i		−	0.105034i
$977$	1.36941e7			0.458983			0.229491	−	0.973311i	$-0.426294\pi$
$977$	1.36941e7			0.458983			0.229491	+	0.973311i	$0.426294\pi$
$978$	−1.93356e7	+	2.43988e7i	−0.646412	+	0.815681i
$979$	3.11886e6			0.104002
$980$			4.23045e6i			0.140709i
$981$	−6.70692e6	+	1.57404e6i	−0.222510	+	0.0522207i
$982$		−	1.88445e7i		−	0.623600i
$983$	2.06914e7			0.682976			0.341488	−	0.939886i	$-0.389069\pi$
$983$	2.06914e7			0.682976			0.341488	+	0.939886i	$0.389069\pi$
$984$	−5.80403e6	−	4.59959e6i	−0.191092	−	0.151437i
$985$	2.37948e7			0.781433
$986$	−3.02797e7			−0.991881
$987$	−3.78258e7	+	4.77309e7i	−1.23594	+	1.55958i
$988$		−	4.58588e7i		−	1.49462i
$989$			2.36201e7i			0.767876i
$990$	−5.44503e6	+	1.27789e6i	−0.176568	+	0.0414386i
$991$			1.63554e7i			0.529027i	0.964382	+	0.264514i	$0.0852114\pi$
$991$			1.63554e7i			0.529027i	−0.964382	+	0.264514i	$0.914789\pi$
$992$		−	6.92183e6i		−	0.223327i
$993$	1.40939e7	−	1.77845e7i	0.453585	−	0.572360i
$994$		−	2.64307e7i		−	0.848484i
$995$		−	1.51433e7i		−	0.484911i
$996$	2.52127e6	−	3.18149e6i	0.0805324	−	0.101621i
$997$	−4.67151e7			−1.48840			−0.744199	−	0.667958i	$-0.767169\pi$
$997$	−4.67151e7			−1.48840			−0.744199	+	0.667958i	$0.767169\pi$
$998$	2.33124e7			0.740901
$999$	−9.65818e6	+	2.05354e7i	−0.306183	+	0.651012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.a.353.18	yes	50
3.2	odd	2		354.6.c.b.353.17	yes	50
59.58	odd	2		354.6.c.b.353.18	yes	50
177.176	even	2	inner	354.6.c.a.353.17	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.17	✓	50	177.176	even	2	inner
354.6.c.a.353.18	yes	50	1.1	even	1	trivial
354.6.c.b.353.17	yes	50	3.2	odd	2
354.6.c.b.353.18	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-9.68192 + 12.2172i) q^{3} +16.0000 q^{4} +48.6180i q^{5} +(38.7277 - 48.8689i) q^{6} +149.149 q^{7} -64.0000 q^{8} +(-55.5209 - 236.572i) q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +(-9.68192 + 12.2172i) q^{3} +16.0000 q^{4} +48.6180i q^{5} +(38.7277 - 48.8689i) q^{6} +149.149 q^{7} -64.0000 q^{8} +(-55.5209 - 236.572i) q^{9} -194.472i q^{10} +118.353 q^{11} +(-154.911 + 195.476i) q^{12} +964.502i q^{13} -596.595 q^{14} +(-593.977 - 470.716i) q^{15} +256.000 q^{16} -1576.13i q^{17} +(222.084 + 946.289i) q^{18} -2971.66 q^{19} +777.888i q^{20} +(-1444.05 + 1822.18i) q^{21} -473.412 q^{22} +3406.07 q^{23} +(619.643 - 781.902i) q^{24} +761.288 q^{25} -3858.01i q^{26} +(3427.80 + 1612.16i) q^{27} +2386.38 q^{28} +4802.85i q^{29} +(2375.91 + 1882.86i) q^{30} +6759.60i q^{31} -1024.00 q^{32} +(-1145.88 + 1445.94i) q^{33} +6304.52i q^{34} +7251.32i q^{35} +(-888.334 - 3785.16i) q^{36} +5990.82i q^{37} +11886.6 q^{38} +(-11783.5 - 9338.23i) q^{39} -3111.55i q^{40} -7422.97i q^{41} +(5776.19 - 7288.74i) q^{42} +6934.72i q^{43} +1893.65 q^{44} +(11501.7 - 2699.32i) q^{45} -13624.3 q^{46} +26194.3 q^{47} +(-2478.57 + 3127.61i) q^{48} +5438.37 q^{49} -3045.15 q^{50} +(19255.9 + 15260.0i) q^{51} +15432.0i q^{52} +7649.57i q^{53} +(-13711.2 - 6448.65i) q^{54} +5754.09i q^{55} -9545.53 q^{56} +(28771.4 - 36305.4i) q^{57} -19211.4i q^{58} +(-15101.5 - 22065.1i) q^{59} +(-9503.63 - 7531.45i) q^{60} -12209.9i q^{61} -27038.4i q^{62} +(-8280.88 - 35284.5i) q^{63} +4096.00 q^{64} -46892.2 q^{65} +(4583.53 - 5783.78i) q^{66} +38311.8i q^{67} -25218.1i q^{68} +(-32977.3 + 41612.7i) q^{69} -29005.3i q^{70} +44302.6i q^{71} +(3553.34 + 15140.6i) q^{72} +50219.9i q^{73} -23963.3i q^{74} +(-7370.73 + 9300.82i) q^{75} -47546.6 q^{76} +17652.2 q^{77} +(47134.2 + 37352.9i) q^{78} -28462.8 q^{79} +12446.2i q^{80} +(-52883.9 + 26269.4i) q^{81} +29691.9i q^{82} -16275.6 q^{83} +(-23104.7 + 29154.9i) q^{84} +76628.4 q^{85} -27738.9i q^{86} +(-58677.5 - 46500.9i) q^{87} -7574.59 q^{88} +26352.2 q^{89} +(-46006.7 + 10797.3i) q^{90} +143854. i q^{91} +54497.1 q^{92} +(-82583.5 - 65445.9i) q^{93} -104777. q^{94} -144476. i q^{95} +(9914.28 - 12510.4i) q^{96} -42952.2i q^{97} -21753.5 q^{98} +(-6571.06 - 27999.0i) 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

Introduction

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