LMFDB - Embedded newform 354.6.c.a.353.20

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			353.20
Character	$\chi$	$=$	354.353
Dual form			354.6.c.a.353.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +(-4.24050 + 15.0006i) q^{3} +16.0000 q^{4} -2.81364i q^{5} +(16.9620 - 60.0024i) q^{6} -187.063 q^{7} -64.0000 q^{8} +(-207.036 - 127.220i) q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +(-4.24050 + 15.0006i) q^{3} +16.0000 q^{4} -2.81364i q^{5} +(16.9620 - 60.0024i) q^{6} -187.063 q^{7} -64.0000 q^{8} +(-207.036 - 127.220i) q^{9} +11.2546i q^{10} +666.690 q^{11} +(-67.8480 + 240.010i) q^{12} -37.6073i q^{13} +748.250 q^{14} +(42.2063 + 11.9312i) q^{15} +256.000 q^{16} -547.530i q^{17} +(828.145 + 508.880i) q^{18} +2120.27 q^{19} -45.0183i q^{20} +(793.238 - 2806.05i) q^{21} -2666.76 q^{22} -3663.00 q^{23} +(271.392 - 960.039i) q^{24} +3117.08 q^{25} +150.429i q^{26} +(2786.32 - 2566.19i) q^{27} -2993.00 q^{28} +7843.11i q^{29} +(-168.825 - 47.7250i) q^{30} +9408.50i q^{31} -1024.00 q^{32} +(-2827.10 + 10000.8i) q^{33} +2190.12i q^{34} +526.327i q^{35} +(-3312.58 - 2035.52i) q^{36} -2007.07i q^{37} -8481.06 q^{38} +(564.133 + 159.474i) q^{39} +180.073i q^{40} -6359.63i q^{41} +(-3172.95 + 11224.2i) q^{42} -10978.9i q^{43} +10667.0 q^{44} +(-357.952 + 582.526i) q^{45} +14652.0 q^{46} +5896.12 q^{47} +(-1085.57 + 3840.16i) q^{48} +18185.4 q^{49} -12468.3 q^{50} +(8213.28 + 2321.80i) q^{51} -601.717i q^{52} +10521.2i q^{53} +(-11145.3 + 10264.8i) q^{54} -1875.83i q^{55} +11972.0 q^{56} +(-8990.98 + 31805.3i) q^{57} -31372.5i q^{58} +(113.139 - 26737.8i) q^{59} +(675.301 + 190.900i) q^{60} +37521.9i q^{61} -37634.0i q^{62} +(38728.7 + 23798.1i) q^{63} +4096.00 q^{64} -105.814 q^{65} +(11308.4 - 40003.0i) q^{66} +10868.6i q^{67} -8760.48i q^{68} +(15532.9 - 54947.2i) q^{69} -2105.31i q^{70} -54026.4i q^{71} +(13250.3 + 8142.09i) q^{72} -5462.57i q^{73} +8028.29i q^{74} +(-13218.0 + 46758.1i) q^{75} +33924.2 q^{76} -124713. q^{77} +(-2256.53 - 637.895i) q^{78} -33666.4 q^{79} -720.292i q^{80} +(26679.1 + 52678.4i) q^{81} +25438.5i q^{82} +13880.4 q^{83} +(12691.8 - 44896.8i) q^{84} -1540.55 q^{85} +43915.5i q^{86} +(-117651. - 33258.7i) q^{87} -42668.2 q^{88} -66534.7 q^{89} +(1431.81 - 2330.11i) q^{90} +7034.92i q^{91} -58607.9 q^{92} +(-141133. - 39896.7i) q^{93} -23584.5 q^{94} -5965.67i q^{95} +(4342.27 - 15360.6i) q^{96} +145432. i q^{97} -72741.6 q^{98} +(-138029. - 84816.4i) 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
$3$	−4.24050	+	15.0006i	−0.272028	+	0.962289i
$3$	−4.24050	+	15.0006i	−0.272028	+	0.962289i
$4$	16.0000			0.500000
$5$		−	2.81364i		−	0.0503320i	−0.999683	−	0.0251660i	$-0.991989\pi$
$5$		−	2.81364i		−	0.0503320i	0.999683	−	0.0251660i	$-0.00801143\pi$
$6$	16.9620	−	60.0024i	0.192353	−	0.680441i
$7$	−187.063			−1.44292			−0.721459	−	0.692457i	$-0.756528\pi$
$7$	−187.063			−1.44292			−0.721459	+	0.692457i	$0.756528\pi$
$8$	−64.0000			−0.353553
$9$	−207.036	−	127.220i	−0.852001	−	0.523539i
$10$			11.2546i			0.0355901i
$11$	666.690			1.66128			0.830639	−	0.556812i	$-0.187975\pi$
$11$	666.690			1.66128			0.830639	+	0.556812i	$0.187975\pi$
$12$	−67.8480	+	240.010i	−0.136014	+	0.481145i
$13$		−	37.6073i		−	0.0617183i	−0.999524	−	0.0308592i	$-0.990176\pi$
$13$		−	37.6073i		−	0.0617183i	0.999524	−	0.0308592i	$-0.00982433\pi$
$14$	748.250			1.02030
$15$	42.2063	+	11.9312i	0.0484339	+	0.0136917i
$16$	256.000			0.250000
$17$		−	547.530i		−	0.459500i	−0.973250	−	0.229750i	$-0.926209\pi$
$17$		−	547.530i		−	0.459500i	0.973250	−	0.229750i	$-0.0737908\pi$
$18$	828.145	+	508.880i	0.602456	+	0.370198i
$19$	2120.27			1.34743			0.673715	−	0.738991i	$-0.264698\pi$
$19$	2120.27			1.34743			0.673715	+	0.738991i	$0.264698\pi$
$20$		−	45.0183i		−	0.0251660i
$21$	793.238	−	2806.05i	0.392514	−	1.38850i
$22$	−2666.76			−1.17470
$23$	−3663.00			−1.44383			−0.721916	−	0.691980i	$-0.756738\pi$
$23$	−3663.00			−1.44383			−0.721916	+	0.691980i	$0.756738\pi$
$24$	271.392	−	960.039i	0.0961765	−	0.340221i
$25$	3117.08			0.997467
$26$			150.429i			0.0436414i
$27$	2786.32	−	2566.19i	0.735565	−	0.677454i
$28$	−2993.00			−0.721459
$29$			7843.11i			1.73178i	0.500231	+	0.865892i	$0.333248\pi$
$29$			7843.11i			1.73178i	−0.500231	+	0.865892i	$0.666752\pi$
$30$	−168.825	−	47.7250i	−0.0342479	−	0.00968150i
$31$			9408.50i			1.75839i	0.476459	+	0.879197i	$0.341920\pi$
$31$			9408.50i			1.75839i	−0.476459	+	0.879197i	$0.658080\pi$
$32$	−1024.00			−0.176777
$33$	−2827.10	+	10000.8i	−0.451914	+	1.59863i
$34$			2190.12i			0.324915i
$35$			526.327i			0.0726249i
$36$	−3312.58	−	2035.52i	−0.426001	−	0.261770i
$37$		−	2007.07i		−	0.241023i	−0.992712	−	0.120512i	$-0.961547\pi$
$37$		−	2007.07i		−	0.241023i	0.992712	−	0.120512i	$-0.0384535\pi$
$38$	−8481.06			−0.952777
$39$	564.133	+	159.474i	0.0593909	+	0.0167891i
$40$			180.073i			0.0177950i
$41$		−	6359.63i		−	0.590843i	−0.955367	−	0.295421i	$-0.904540\pi$
$41$		−	6359.63i		−	0.590843i	0.955367	−	0.295421i	$-0.0954600\pi$
$42$	−3172.95	+	11224.2i	−0.277550	+	0.981821i
$43$		−	10978.9i		−	0.905497i	−0.891638	−	0.452748i	$-0.850444\pi$
$43$		−	10978.9i		−	0.905497i	0.891638	−	0.452748i	$-0.149556\pi$
$44$	10667.0			0.830639
$45$	−357.952	+	582.526i	−0.0263508	+	0.0428829i
$46$	14652.0			1.02094
$47$	5896.12			0.389333			0.194667	−	0.980869i	$-0.437637\pi$
$47$	5896.12			0.389333			0.194667	+	0.980869i	$0.437637\pi$
$48$	−1085.57	+	3840.16i	−0.0680070	+	0.240572i
$49$	18185.4			1.08201
$50$	−12468.3			−0.705315
$51$	8213.28	+	2321.80i	0.442172	+	0.124997i
$52$		−	601.717i		−	0.0308592i
$53$			10521.2i			0.514489i	0.966346	+	0.257244i	$0.0828145\pi$
$53$			10521.2i			0.514489i	−0.966346	+	0.257244i	$0.917185\pi$
$54$	−11145.3	+	10264.8i	−0.520123	+	0.479033i
$55$		−	1875.83i		−	0.0836154i
$56$	11972.0			0.510149
$57$	−8990.98	+	31805.3i	−0.366539	+	1.29662i
$58$		−	31372.5i		−	1.22456i
$59$	113.139	−	26737.8i	0.00423139	−	0.999991i
$59$	113.139	−	26737.8i	0.00423139	−	0.999991i
$60$	675.301	+	190.900i	0.0242170	+	0.00684585i
$61$			37521.9i			1.29110i	0.763717	+	0.645551i	$0.223372\pi$
$61$			37521.9i			1.29110i	−0.763717	+	0.645551i	$0.776628\pi$
$62$		−	37634.0i		−	1.24337i
$63$	38728.7	+	23798.1i	1.22937	+	0.755425i
$64$	4096.00			0.125000
$65$	−105.814			−0.00310640
$66$	11308.4	−	40003.0i	0.319552	−	1.13040i
$67$			10868.6i			0.295793i	0.989003	+	0.147897i	$0.0472503\pi$
$67$			10868.6i			0.295793i	−0.989003	+	0.147897i	$0.952750\pi$
$68$		−	8760.48i		−	0.229750i
$69$	15532.9	−	54947.2i	0.392763	−	1.38938i
$70$		−	2105.31i		−	0.0513536i
$71$		−	54026.4i		−	1.27192i	−0.771722	−	0.635960i	$-0.780604\pi$
$71$		−	54026.4i		−	1.27192i	0.771722	−	0.635960i	$-0.219396\pi$
$72$	13250.3	+	8142.09i	0.301228	+	0.185099i
$73$		−	5462.57i		−	0.119975i	−0.998199	−	0.0599874i	$-0.980894\pi$
$73$		−	5462.57i		−	0.119975i	0.998199	−	0.0599874i	$-0.0191060\pi$
$74$			8028.29i			0.170429i
$75$	−13218.0	+	46758.1i	−0.271339	+	0.959852i
$76$	33924.2			0.673715
$77$	−124713.			−2.39709
$78$	−2256.53	−	637.895i	−0.0419957	−	0.0118717i
$79$	−33666.4			−0.606917			−0.303459	−	0.952845i	$-0.598141\pi$
$79$	−33666.4			−0.606917			−0.303459	+	0.952845i	$0.598141\pi$
$80$		−	720.292i		−	0.0125830i
$81$	26679.1	+	52678.4i	0.451813	+	0.892113i
$82$			25438.5i			0.417789i
$83$	13880.4			0.221160			0.110580	−	0.993867i	$-0.464729\pi$
$83$	13880.4			0.221160			0.110580	+	0.993867i	$0.464729\pi$
$84$	12691.8	−	44896.8i	0.196257	−	0.694252i
$85$	−1540.55			−0.0231275
$86$			43915.5i			0.640283i
$87$	−117651.	−	33258.7i	−1.66648	−	0.471094i
$88$	−42668.2			−0.587350
$89$	−66534.7			−0.890376			−0.445188	−	0.895437i	$-0.646863\pi$
$89$	−66534.7			−0.890376			−0.445188	+	0.895437i	$0.646863\pi$
$90$	1431.81	−	2330.11i	0.0186328	−	0.0303228i
$91$			7034.92i			0.0890545i
$92$	−58607.9			−0.721916
$93$	−141133.	−	39896.7i	−1.69208	−	0.478332i
$94$	−23584.5			−0.275300
$95$		−	5965.67i		−	0.0678188i
$96$	4342.27	−	15360.6i	0.0480882	−	0.170110i
$97$			145432.i			1.56939i	0.619882	+	0.784695i	$0.287180\pi$
$97$			145432.i			1.56939i	−0.619882	+	0.784695i	$0.712820\pi$
$98$	−72741.6			−0.765099
$99$	−138029.	−	84816.4i	−1.41541	−	0.869744i
$100$	49873.3			0.498733
$101$	−67535.6			−0.658763			−0.329382	−	0.944197i	$-0.606840\pi$
$101$	−67535.6			−0.658763			−0.329382	+	0.944197i	$0.606840\pi$
$102$	−32853.1	−	9287.20i	−0.312663	−	0.0883861i
$103$			2682.23i			0.0249116i	0.999922	+	0.0124558i	$0.00396491\pi$
$103$			2682.23i			0.0249116i	−0.999922	+	0.0124558i	$0.996035\pi$
$104$			2406.87i			0.0218207i
$105$	−7895.23	−	2231.89i	−0.0698862	−	0.0197560i
$106$		−	42084.8i		−	0.363798i
$107$			68251.5i			0.576306i	0.957584	+	0.288153i	$0.0930411\pi$
$107$			68251.5i			0.576306i	−0.957584	+	0.288153i	$0.906959\pi$
$108$	44581.1	−	41059.1i	0.367782	−	0.338727i
$109$		−	30197.3i		−	0.243445i	−0.992564	−	0.121723i	$-0.961158\pi$
$109$		−	30197.3i		−	0.243445i	0.992564	−	0.121723i	$-0.0388419\pi$
$110$			7503.31i			0.0591250i
$111$	30107.3	+	8510.99i	0.231934	+	0.0655651i
$112$	−47888.0			−0.360730
$113$	−103210.			−0.760368			−0.380184	−	0.924911i	$-0.624139\pi$
$113$	−103210.			−0.760368			−0.380184	+	0.924911i	$0.624139\pi$
$114$	35963.9	−	127221.i	0.259182	−	0.916847i
$115$			10306.4i			0.0726709i
$116$			125490.i			0.865892i
$117$	−4784.41	+	7786.08i	−0.0323120	+	0.0525841i
$118$	−452.557	+	106951.i	−0.00299204	+	0.707100i
$119$			102422.i			0.663021i
$120$	−2701.21	−	763.600i	−0.0171240	−	0.00484075i
$121$	283424.			1.75984
$122$		−	150088.i		−	0.912947i
$123$	95398.2	+	26968.0i	0.568562	+	0.160726i
$124$			150536.i			0.879197i
$125$		−	17563.0i		−	0.100536i
$126$	−154915.	−	95192.4i	−0.869295	−	0.534166i
$127$	−170663.			−0.938922			−0.469461	−	0.882953i	$-0.655552\pi$
$127$	−170663.			−0.938922			−0.469461	+	0.882953i	$0.655552\pi$
$128$	−16384.0			−0.0883883
$129$	164690.	+	46555.9i	0.871350	+	0.246321i
$130$	423.254			0.00219656
$131$	−194297.			−0.989209			−0.494605	−	0.869118i	$-0.664687\pi$
$131$	−194297.			−0.989209			−0.494605	+	0.869118i	$0.664687\pi$
$132$	−45233.6	+	160012.i	−0.225957	+	0.799315i
$133$	−396622.			−1.94423
$134$		−	43474.6i		−	0.209157i
$135$	−7220.35	−	7839.70i	−0.0340976	−	0.0370224i
$136$			35041.9i			0.162458i
$137$		−	207514.i		−	0.944594i	−0.881439	−	0.472297i	$-0.843425\pi$
$137$		−	207514.i		−	0.944594i	0.881439	−	0.472297i	$-0.156575\pi$
$138$	−62131.7	+	219789.i	−0.277725	+	0.982443i
$139$	−146549.			−0.643350			−0.321675	−	0.946850i	$-0.604246\pi$
$139$	−146549.			−0.643350			−0.321675	+	0.946850i	$0.604246\pi$
$140$			8421.23i			0.0363125i
$141$	−25002.5	+	88445.4i	−0.105910	+	0.374651i
$142$			216106.i			0.899384i
$143$		−	25072.4i		−	0.102531i
$144$	−53001.3	−	32568.3i	−0.213000	−	0.130885i
$145$	22067.7			0.0871641
$146$			21850.3i			0.0848349i
$147$	−77115.1	+	272792.i	−0.294338	+	1.04121i
$148$		−	32113.2i		−	0.120512i
$149$	−18570.8			−0.0685277			−0.0342638	−	0.999413i	$-0.510909\pi$
$149$	−18570.8			−0.0685277			−0.0342638	+	0.999413i	$0.510909\pi$
$150$	52872.0	−	187033.i	0.191866	−	0.678718i
$151$			530293.i			1.89266i	0.323198	+	0.946331i	$0.395242\pi$
$151$			530293.i			1.89266i	−0.323198	+	0.946331i	$0.604758\pi$
$152$	−135697.			−0.476388
$153$	−69656.8	+	113359.i	−0.240566	+	0.391495i
$154$	498851.			1.69500
$155$	26472.1			0.0885034
$156$	9026.12	+	2551.58i	0.0296954	+	0.00839456i
$157$			39623.2i			0.128292i	0.997941	+	0.0641461i	$0.0204324\pi$
$157$			39623.2i			0.128292i	−0.997941	+	0.0641461i	$0.979568\pi$
$158$	134666.			0.429155
$159$	−157824.	−	44615.2i	−0.495087	−	0.139955i
$160$			2881.17i			0.00889752i
$161$	685209.			2.08333
$162$	−106716.	−	210713.i	−0.319480	−	0.630819i
$163$	−542846.			−1.60032			−0.800162	−	0.599784i	$-0.795253\pi$
$163$	−542846.			−1.60032			−0.800162	+	0.599784i	$0.795253\pi$
$164$		−	101754.i		−	0.295421i
$165$	28138.5	+	7954.44i	0.0804622	+	0.0227457i
$166$	−55521.6			−0.156384
$167$		−	416409.i		−	1.15539i	−0.816252	−	0.577695i	$-0.803952\pi$
$167$		−	416409.i		−	1.15539i	0.816252	−	0.577695i	$-0.196048\pi$
$168$	−50767.3	+	179587.i	−0.138775	+	0.490911i
$169$	369879.			0.996191
$170$	6162.21			0.0163536
$171$	−438972.	−	269740.i	−1.14801	−	0.705433i
$172$		−	175662.i		−	0.452748i
$173$	−494194.			−1.25540			−0.627700	−	0.778456i	$-0.716003\pi$
$173$	−494194.			−1.25540			−0.627700	+	0.778456i	$0.716003\pi$
$174$	470606.	+	133035.i	1.17838	+	0.333114i
$175$	−583089.			−1.43926
$176$	170673.			0.415319
$177$	400604.	+	115079.i	0.961130	+	0.276097i
$178$	266139.			0.629591
$179$	−15411.4			−0.0359510			−0.0179755	−	0.999838i	$-0.505722\pi$
$179$	−15411.4			−0.0359510			−0.0179755	+	0.999838i	$0.505722\pi$
$180$	−5727.23	+	9320.42i	−0.0131754	+	0.0214415i
$181$	−179894.			−0.408150			−0.204075	−	0.978955i	$-0.565419\pi$
$181$	−179894.			−0.408150			−0.204075	+	0.978955i	$0.565419\pi$
$182$		−	28139.7i		−	0.0629710i
$183$	−562852.	−	159112.i	−1.24241	−	0.351216i
$184$	234432.			0.510472
$185$	−5647.19			−0.0121312
$186$	564533.	+	159587.i	1.19648	+	0.338232i
$187$		−	365033.i		−	0.763357i
$188$	94337.9			0.194667
$189$	−521215.	+	480039.i	−1.06136	+	0.977511i
$190$			23862.7i			0.0479551i
$191$	−742679.			−1.47305			−0.736526	−	0.676410i	$-0.763535\pi$
$191$	−742679.			−1.47305			−0.736526	+	0.676410i	$0.763535\pi$
$192$	−17369.1	+	61442.5i	−0.0340035	+	0.120286i
$193$	−302492.			−0.584549			−0.292275	−	0.956334i	$-0.594412\pi$
$193$	−302492.			−0.584549			−0.292275	+	0.956334i	$0.594412\pi$
$194$		−	581728.i		−	1.10973i
$195$	448.702	−	1587.27i	0.000845029	−	0.00298926i
$196$	290966.			0.541006
$197$			798096.i			1.46518i	0.680672	+	0.732588i	$0.261688\pi$
$197$			798096.i			1.46518i	−0.680672	+	0.732588i	$0.738312\pi$
$198$	552116.	+	339265.i	1.00085	+	0.615002i
$199$	478448.			0.856450			0.428225	−	0.903672i	$-0.359139\pi$
$199$	478448.			0.856450			0.428225	+	0.903672i	$0.359139\pi$
$200$	−199493.			−0.352658
$201$	−163036.	−	46088.5i	−0.284639	−	0.0804641i
$202$	270142.			0.465816
$203$		−	1.46715e6i		−	2.49882i
$204$	131412.	+	37148.8i	0.221086	+	0.0624984i
$205$	−17893.7			−0.0297383
$206$		−	10728.9i		−	0.0176152i
$207$	758373.	+	466007.i	1.23015	+	0.755903i
$208$		−	9627.47i		−	0.0154296i
$209$	1.41356e6			2.23846
$210$	31580.9	+	8927.56i	0.0494170	+	0.0139696i
$211$			811479.i			1.25479i	0.778701	+	0.627395i	$0.215879\pi$
$211$			811479.i			1.25479i	−0.778701	+	0.627395i	$0.784121\pi$
$212$			168339.i			0.257244i
$213$	810429.	+	229099.i	1.22396	+	0.345998i
$214$		−	273006.i		−	0.407510i
$215$	−30890.6			−0.0455754
$216$	−178324.	+	164236.i	−0.260061	+	0.239516i
$217$		−	1.75998e6i		−	2.53722i
$218$			120789.i			0.172142i
$219$	81941.8	+	23164.0i	0.115450	+	0.0326365i
$220$		−	30013.2i		−	0.0418077i
$221$	−20591.1			−0.0283596
$222$	−120429.	−	34044.0i	−0.164002	−	0.0463615i
$223$	151447.			0.203938			0.101969	−	0.994788i	$-0.467486\pi$
$223$	151447.			0.203938			0.101969	+	0.994788i	$0.467486\pi$
$224$	191552.			0.255074
$225$	−645350.	−	396556.i	−0.849843	−	0.522213i
$226$	412838.			0.537661
$227$	457515.			0.589306			0.294653	−	0.955604i	$-0.404796\pi$
$227$	457515.			0.589306			0.294653	+	0.955604i	$0.404796\pi$
$228$	−143856.	+	508884.i	−0.183269	+	0.648309i
$229$			735864.i			0.927276i	0.886025	+	0.463638i	$0.153456\pi$
$229$			735864.i			0.927276i	−0.886025	+	0.463638i	$0.846544\pi$
$230$		−	41225.4i		−	0.0513861i
$231$	528844.	−	1.87077e6i	0.652075	−	2.30669i
$232$		−	501959.i		−	0.612278i
$233$	6075.49			0.00733148			0.00366574	−	0.999993i	$-0.498833\pi$
$233$	6075.49			0.00733148			0.00366574	+	0.999993i	$0.498833\pi$
$234$	19137.6	−	31144.3i	0.0228480	−	0.0371826i
$235$		−	16589.6i		−	0.0195959i
$236$	1810.23	−	427805.i	0.00211569	−	0.499996i
$237$	142762.	−	505017.i	0.165098	−	0.584030i
$238$		−	409689.i		−	0.468826i
$239$			1.09274e6i			1.23743i	0.785616	+	0.618714i	$0.212346\pi$
$239$			1.09274e6i			1.23743i	−0.785616	+	0.618714i	$0.787654\pi$
$240$	10804.8	+	3054.40i	0.0121085	+	0.00342293i
$241$	1.20235e6			1.33349			0.666745	−	0.745286i	$-0.267687\pi$
$241$	1.20235e6			1.33349			0.666745	+	0.745286i	$0.267687\pi$
$242$	−1.13370e6			−1.24440
$243$	−903340.	+	176820.i	−0.981376	+	0.192095i
$244$			600351.i			0.645551i
$245$		−	51167.2i		−	0.0544598i
$246$	−381593.	−	107872.i	−0.402034	−	0.113650i
$247$		−	79737.5i		−	0.0831611i
$248$		−	602144.i		−	0.621686i
$249$	−58859.9	+	208215.i	−0.0601618	+	0.212820i
$250$			70252.0i			0.0710900i
$251$			1.36387e6i			1.36643i	0.730216	+	0.683216i	$0.239419\pi$
$251$			1.36387e6i			1.36643i	−0.730216	+	0.683216i	$0.760581\pi$
$252$	619660.	+	380770.i	0.614684	+	0.377712i
$253$	−2.44208e6			−2.39861
$254$	682651.			0.663918
$255$	6532.71	−	23109.2i	0.00629134	−	0.0222554i
$256$	65536.0			0.0625000
$257$			1.36597e6i			1.29005i	0.764160	+	0.645026i	$0.223154\pi$
$257$			1.36597e6i			1.29005i	−0.764160	+	0.645026i	$0.776846\pi$
$258$	−658759.	−	186224.i	−0.616137	−	0.174175i
$259$			375448.i			0.347777i
$260$	−1693.02			−0.00155320
$261$	997802.	−	1.62381e6i	0.906657	−	1.47548i
$262$	777189.			0.699477
$263$		−	1.56382e6i		−	1.39411i	−0.717017	−	0.697056i	$-0.754493\pi$
$263$		−	1.56382e6i		−	1.39411i	0.717017	−	0.697056i	$-0.245507\pi$
$264$	180934.	−	640048.i	0.159776	−	0.565201i
$265$	29602.9			0.0258952
$266$	1.58649e6			1.37478
$267$	282140.	−	998061.i	0.242207	−	0.856799i
$268$			173898.i			0.147897i
$269$	−88015.3			−0.0741613			−0.0370807	−	0.999312i	$-0.511806\pi$
$269$	−88015.3			−0.0741613			−0.0370807	+	0.999312i	$0.511806\pi$
$270$	28881.4	+	31358.8i	0.0241107	+	0.0261788i
$271$	256158.			0.211878			0.105939	−	0.994373i	$-0.466215\pi$
$271$	256158.			0.211878			0.105939	+	0.994373i	$0.466215\pi$
$272$		−	140168.i		−	0.114875i
$273$	−105528.	−	29831.6i	−0.0856962	−	0.0242253i
$274$			830055.i			0.667929i
$275$	2.07813e6			1.65707
$276$	248527.	−	879154.i	0.196382	−	0.694692i
$277$	124238.			0.0972872			0.0486436	−	0.998816i	$-0.484510\pi$
$277$	124238.			0.0972872			0.0486436	+	0.998816i	$0.484510\pi$
$278$	586198.			0.454917
$279$	1.19695e6	−	1.94790e6i	0.920588	−	1.49815i
$280$		−	33684.9i		−	0.0256768i
$281$		−	290534.i		−	0.219499i	−0.993959	−	0.109749i	$-0.964995\pi$
$281$		−	290534.i		−	0.219499i	0.993959	−	0.109749i	$-0.0350048\pi$
$282$	100010.	−	353782.i	0.0748894	−	0.264919i
$283$			1.86911e6i			1.38730i	0.720313	+	0.693649i	$0.243998\pi$
$283$			1.86911e6i			1.38730i	−0.720313	+	0.693649i	$0.756002\pi$
$284$		−	864422.i		−	0.635960i
$285$	89488.6	+	25297.4i	0.0652613	+	0.0184486i
$286$			100290.i			0.0725005i
$287$			1.18965e6i			0.852538i
$288$	212005.	+	130273.i	0.150614	+	0.0925496i
$289$	1.12007e6			0.788860
$290$	−88270.9			−0.0616343
$291$	−2.18157e6	−	616704.i	−1.51021	−	0.426918i
$292$		−	87401.1i		−	0.0599874i
$293$			1.12457e6i			0.765276i	0.923898	+	0.382638i	$0.124984\pi$
$293$			1.12457e6i			0.765276i	−0.923898	+	0.382638i	$0.875016\pi$
$294$	308460.	−	1.09117e6i	0.208128	−	0.736246i
$295$	−75230.7	−	318.333i	−0.0503315	−	0.000212974i
$296$			128453.i			0.0852146i
$297$	1.85761e6	−	1.71086e6i	1.22198	−	1.12544i
$298$	74283.4			0.0484564
$299$			137755.i			0.0891109i
$300$	−211488.	+	748130.i	−0.135669	+	0.479926i
$301$			2.05374e6i			1.30656i
$302$		−	2.12117e6i		−	1.33831i
$303$	286385.	−	1.01308e6i	0.179202	−	0.633921i
$304$	542788.			0.336857
$305$	105573.			0.0649837
$306$	278627.	−	453434.i	0.170106	−	0.276828i
$307$	−604748.			−0.366208			−0.183104	−	0.983094i	$-0.558615\pi$
$307$	−604748.			−0.366208			−0.183104	+	0.983094i	$0.558615\pi$
$308$	−1.99540e6			−1.19854
$309$	−40235.0	−	11374.0i	−0.0239722	−	0.00677667i
$310$	−105889.			−0.0625813
$311$			191045.i			0.112004i	0.998431	+	0.0560020i	$0.0178353\pi$
$311$			191045.i			0.112004i	−0.998431	+	0.0560020i	$0.982165\pi$
$312$	−36104.5	−	10206.3i	−0.0209978	−	0.00593585i
$313$			1.00241e6i			0.578343i	0.957277	+	0.289171i	$0.0933797\pi$
$313$			1.00241e6i			0.578343i	−0.957277	+	0.289171i	$0.906620\pi$
$314$		−	158493.i		−	0.0907162i
$315$	66959.4	−	108969.i	0.0380220	−	0.0618765i
$316$	−538663.			−0.303459
$317$			684667.i			0.382676i	0.981524	+	0.191338i	$0.0612827\pi$
$317$			684667.i			0.382676i	−0.981524	+	0.191338i	$0.938717\pi$
$318$	631298.	+	178461.i	0.350079	+	0.0989634i
$319$			5.22893e6i			2.87697i
$320$		−	11524.7i		−	0.00629150i
$321$	−1.02381e6	−	289421.i	−0.554573	−	0.156771i
$322$	−2.74084e6			−1.47314
$323$		−	1.16091e6i		−	0.619144i
$324$	426866.	+	842854.i	0.225906	+	0.446056i
$325$		−	117225.i		−	0.0615620i
$326$	2.17139e6			1.13160
$327$	452977.	+	128052.i	0.234265	+	0.0662240i
$328$			407016.i			0.208894i
$329$	−1.10294e6			−0.561776
$330$	−112554.	−	31817.8i	−0.0568953	−	0.0160837i
$331$	−1.82831e6			−0.917235			−0.458617	−	0.888634i	$-0.651655\pi$
$331$	−1.82831e6			−0.917235			−0.458617	+	0.888634i	$0.651655\pi$
$332$	222087.			0.110580
$333$	−255340.	+	415537.i	−0.126185	+	0.205352i
$334$			1.66564e6i			0.816985i
$335$	30580.5			0.0148879
$336$	203069.	−	718349.i	0.0981286	−	0.347126i
$337$			2.14517e6i			1.02893i	0.857510	+	0.514467i	$0.172010\pi$
$337$			2.14517e6i			1.02893i	−0.857510	+	0.514467i	$0.827990\pi$
$338$	−1.47951e6			−0.704413
$339$	437660.	−	1.54821e6i	0.206841	−	0.731694i
$340$	−24648.8			−0.0115638
$341$			6.27255e6i			2.92118i
$342$	1.75589e6	+	1.07896e6i	0.811767	+	0.498816i
$343$	−257845.			−0.118338
$344$			702648.i			0.320141i
$345$	−154602.	−	43704.1i	−0.0699305	−	0.0197685i
$346$	1.97677e6			0.887702
$347$	3.89417e6			1.73617			0.868084	−	0.496418i	$-0.165352\pi$
$347$	3.89417e6			1.73617			0.868084	+	0.496418i	$0.165352\pi$
$348$	−1.88242e6	−	532139.i	−0.833238	−	0.235547i
$349$		−	3.92695e6i		−	1.72581i	−0.505370	−	0.862903i	$-0.668644\pi$
$349$		−	3.92695e6i		−	1.72581i	0.505370	−	0.862903i	$-0.331356\pi$
$350$	2.33236e6			1.01771
$351$	−96507.7	−	104786.i	−0.0418113	−	0.0453978i
$352$	−682691.			−0.293675
$353$	1.74908e6			0.747090			0.373545	−	0.927612i	$-0.378142\pi$
$353$	1.74908e6			0.747090			0.373545	+	0.927612i	$0.378142\pi$
$354$	−1.60242e6	−	460316.i	−0.679621	−	0.195230i
$355$	−152011.			−0.0640183
$356$	−1.06456e6			−0.445188
$357$	−1.53640e6	−	434322.i	−0.638018	−	0.180360i
$358$	61645.7			0.0254212
$359$		−	4.32594e6i		−	1.77151i	−0.464149	−	0.885757i	$-0.653640\pi$
$359$		−	4.32594e6i		−	1.77151i	0.464149	−	0.885757i	$-0.346360\pi$
$360$	22908.9	−	37281.7i	0.00931640	−	0.0151614i
$361$	2.01943e6			0.815567
$362$	719575.			0.288605
$363$	−1.20186e6	+	4.25154e6i	−0.478727	+	1.69348i
$364$			112559.i			0.0445272i
$365$	−15369.7			−0.00603856
$366$	2.25141e6	+	636447.i	0.878519	+	0.248347i
$367$		−	2.32078e6i		−	0.899432i	−0.893172	−	0.449716i	$-0.851525\pi$
$367$		−	2.32078e6i		−	0.899432i	0.893172	−	0.449716i	$-0.148475\pi$
$368$	−937727.			−0.360958
$369$	−809072.	+	1.31667e6i	−0.309329	+	0.503399i
$370$	22588.7			0.00857803
$371$		−	1.96812e6i		−	0.742365i
$372$	−2.25813e6	−	638347.i	−0.846041	−	0.239166i
$373$	−1.12473e6			−0.418578			−0.209289	−	0.977854i	$-0.567115\pi$
$373$	−1.12473e6			−0.418578			−0.209289	+	0.977854i	$0.567115\pi$
$374$			1.46013e6i			0.539775i
$375$	263456.	+	74475.8i	0.0967451	+	0.0273487i
$376$	−377352.			−0.137650
$377$	294959.			0.106883
$378$	2.08486e6	−	1.92015e6i	0.750495	−	0.691205i
$379$	−2.81110e6			−1.00526			−0.502630	−	0.864501i	$-0.667634\pi$
$379$	−2.81110e6			−1.00526			−0.502630	+	0.864501i	$0.667634\pi$
$380$		−	95450.7i		−	0.0339094i
$381$	723695.	−	2.56004e6i	0.255413	−	0.903514i
$382$	2.97072e6			1.04160
$383$		−	762361.i		−	0.265561i	−0.991145	−	0.132780i	$-0.957609\pi$
$383$		−	762361.i		−	0.265561i	0.991145	−	0.132780i	$-0.0423905\pi$
$384$	69476.3	−	245770.i	0.0240441	−	0.0850552i
$385$			350897.i			0.120650i
$386$	1.20997e6			0.413339
$387$	−1.39673e6	+	2.27303e6i	−0.474063	+	0.771485i
$388$			2.32691e6i			0.784695i
$389$			2.93019e6i			0.981798i	0.871216	+	0.490899i	$0.163332\pi$
$389$			2.93019e6i			0.981798i	−0.871216	+	0.490899i	$0.836668\pi$
$390$	−1794.81	+	6349.07i	−0.000597526	+	0.00211373i
$391$			2.00560e6i			0.663441i
$392$	−1.16386e6			−0.382549
$393$	823917.	−	2.91458e6i	0.269093	−	0.951906i
$394$		−	3.19239e6i		−	1.03604i
$395$			94725.3i			0.0305473i
$396$	−2.20846e6	−	1.35706e6i	−0.707705	−	0.434872i
$397$			1.36287e6i			0.433989i	0.976173	+	0.216994i	$0.0696253\pi$
$397$			1.36287e6i			0.433989i	−0.976173	+	0.216994i	$0.930375\pi$
$398$	−1.91379e6			−0.605602
$399$	1.68188e6	−	5.94957e6i	0.528885	−	1.87091i
$400$	797973.			0.249367
$401$	−4.68537e6			−1.45507			−0.727534	−	0.686072i	$-0.759334\pi$
$401$	−4.68537e6			−1.45507			−0.727534	+	0.686072i	$0.759334\pi$
$402$	652145.	+	184354.i	0.201270	+	0.0568967i
$403$	353828.			0.108525
$404$	−1.08057e6			−0.329382
$405$	148218.	−	75065.4i	0.0449018	−	0.0227406i
$406$			5.86861e6i			1.76693i
$407$		−	1.33810e6i		−	0.400406i
$408$	−525650.	−	148595.i	−0.156331	−	0.0441931i
$409$			2.60459e6i			0.769894i	0.922939	+	0.384947i	$0.125780\pi$
$409$			2.60459e6i			0.769894i	−0.922939	+	0.384947i	$0.874220\pi$
$410$	71574.9			0.0210281
$411$	3.11283e6	+	879962.i	0.908973	+	0.256956i
$412$			42915.6i			0.0124558i
$413$	−21164.1	+	5.00165e6i	−0.00610555	+	1.44291i
$414$	−3.03349e6	−	1.86403e6i	−0.869846	−	0.534504i
$415$		−	39054.5i		−	0.0111314i
$416$			38509.9i			0.0109104i
$417$	621443.	−	2.19833e6i	0.175009	−	0.619088i
$418$	−5.65424e6			−1.58283
$419$	−1.40864e6			−0.391980			−0.195990	−	0.980606i	$-0.562792\pi$
$419$	−1.40864e6			−0.391980			−0.195990	+	0.980606i	$0.562792\pi$
$420$	−126324.	−	35710.2i	−0.0349431	−	0.00987801i
$421$			2.26263e6i			0.622168i	0.950382	+	0.311084i	$0.100692\pi$
$421$			2.26263e6i			0.622168i	−0.950382	+	0.311084i	$0.899308\pi$
$422$		−	3.24592e6i		−	0.887271i
$423$	−1.22071e6	−	750105.i	−0.331713	−	0.203831i
$424$		−	673357.i		−	0.181899i
$425$		−	1.70670e6i		−	0.458336i
$426$	−3.24171e6	−	916395.i	−0.865468	−	0.244658i
$427$		−	7.01895e6i		−	1.86295i
$428$			1.09202e6i			0.288153i
$429$	376101.	+	106320.i	0.0986647	+	0.0278914i
$430$	123563.			0.0322267
$431$	−2.83049e6			−0.733954			−0.366977	−	0.930230i	$-0.619607\pi$
$431$	−2.83049e6			−0.733954			−0.366977	+	0.930230i	$0.619607\pi$
$432$	713297.	−	656946.i	0.183891	−	0.169364i
$433$	6.36161e6			1.63060			0.815300	−	0.579038i	$-0.196572\pi$
$433$	6.36161e6			1.63060			0.815300	+	0.579038i	$0.196572\pi$
$434$			7.03991e6i			1.79408i
$435$	−93578.1	+	331029.i	−0.0237111	+	0.0838771i
$436$		−	483156.i		−	0.121723i
$437$	−7.76652e6			−1.94546
$438$	−327767.	−	92656.1i	−0.0816358	−	0.0230775i
$439$	−6.33927e6			−1.56992			−0.784960	−	0.619546i	$-0.787317\pi$
$439$	−6.33927e6			−1.56992			−0.784960	+	0.619546i	$0.787317\pi$
$440$			120053.i			0.0295625i
$441$	−3.76504e6	−	2.31355e6i	−0.921876	−	0.566476i
$442$	82364.5			0.0200532
$443$	−5.59851e6			−1.35539			−0.677693	−	0.735345i	$-0.737020\pi$
$443$	−5.59851e6			−1.35539			−0.677693	+	0.735345i	$0.737020\pi$
$444$	481717.	+	136176.i	0.115967	+	0.0327825i
$445$			187205.i			0.0448144i
$446$	−605787.			−0.144206
$447$	78749.6	−	278574.i	0.0186414	−	0.0659434i
$448$	−766208.			−0.180365
$449$			5.17357e6i			1.21108i	0.795813	+	0.605542i	$0.207044\pi$
$449$			5.17357e6i			1.21108i	−0.795813	+	0.605542i	$0.792956\pi$
$450$	2.58140e6	+	1.58622e6i	0.600930	+	0.369260i
$451$		−	4.23990e6i		−	0.981554i
$452$	−1.65135e6			−0.380184
$453$	−7.95471e6	−	2.24871e6i	−1.82129	−	0.514858i
$454$	−1.83006e6			−0.416702
$455$	19793.7			0.00448229
$456$	575423.	−	2.03554e6i	0.129591	−	0.458423i
$457$			656578.i			0.147060i	0.997293	+	0.0735302i	$0.0234265\pi$
$457$			656578.i			0.147060i	−0.997293	+	0.0735302i	$0.976573\pi$
$458$		−	2.94346e6i		−	0.655683i
$459$	−1.40507e6	−	1.52559e6i	−0.311290	−	0.337992i
$460$			164902.i			0.0363355i
$461$		−	6.76467e6i		−	1.48250i	−0.671230	−	0.741249i	$-0.734234\pi$
$461$		−	6.76467e6i		−	1.48250i	0.671230	−	0.741249i	$-0.265766\pi$
$462$	−2.11538e6	+	7.48306e6i	−0.461087	+	1.63108i
$463$			7.11188e6i			1.54181i	0.636947	+	0.770907i	$0.280197\pi$
$463$			7.11188e6i			1.54181i	−0.636947	+	0.770907i	$0.719803\pi$
$464$			2.00784e6i			0.432946i
$465$	−112255.	+	397098.i	−0.0240754	+	0.0851659i
$466$	−24302.0			−0.00518414
$467$	−5.81485e6			−1.23381			−0.616903	−	0.787039i	$-0.711613\pi$
$467$	−5.81485e6			−1.23381			−0.616903	+	0.787039i	$0.711613\pi$
$468$	−76550.5	+	124577.i	−0.0161560	+	0.0262920i
$469$		−	2.03312e6i		−	0.426806i
$470$			66358.3i			0.0138564i
$471$	−594372.	−	168022.i	−0.123454	−	0.0348991i
$472$	−7240.90	+	1.71122e6i	−0.00149602	+	0.353550i
$473$		−	7.31951e6i		−	1.50428i
$474$	−571050.	+	2.02007e6i	−0.116742	+	0.412971i
$475$	6.60904e6			1.34402
$476$			1.63876e6i			0.331510i
$477$	1.33851e6	−	2.17827e6i	0.269355	−	0.438345i
$478$		−	4.37094e6i		−	0.874994i
$479$		−	1.11117e6i		−	0.221281i	−0.993861	−	0.110640i	$-0.964710\pi$
$479$		−	1.11117e6i		−	0.221281i	0.993861	−	0.110640i	$-0.0352902\pi$
$480$	−43219.3	−	12217.6i	−0.00856199	−	0.00242038i
$481$	−75480.6			−0.0148755
$482$	−4.80942e6			−0.942920
$483$	−2.90563e6	+	1.02786e7i	−0.566725	+	2.00477i
$484$	4.53479e6			0.879922
$485$	409194.			0.0789905
$486$	3.61336e6	−	707280.i	0.693938	−	0.135832i
$487$	9.75184e6			1.86322			0.931610	−	0.363460i	$-0.118405\pi$
$487$	9.75184e6			1.86322			0.931610	+	0.363460i	$0.118405\pi$
$488$		−	2.40140e6i		−	0.456473i
$489$	2.30194e6	−	8.14303e6i	0.435333	−	1.53998i
$490$			204669.i			0.0385089i
$491$			3.42199e6i			0.640582i	0.947319	+	0.320291i	$0.103781\pi$
$491$			3.42199e6i			0.640582i	−0.947319	+	0.320291i	$0.896219\pi$
$492$	1.52637e6	+	431488.i	0.284281	+	0.0803629i
$493$	4.29434e6			0.795754
$494$			318950.i			0.0588038i
$495$	−238643.	+	388364.i	−0.0437759	+	0.0712404i
$496$			2.40857e6i			0.439598i
$497$			1.01063e7i			1.83528i
$498$	235439.	−	832858.i	0.0425408	−	0.150487i
$499$	1.67419e6			0.300991			0.150495	−	0.988611i	$-0.451913\pi$
$499$	1.67419e6			0.300991			0.150495	+	0.988611i	$0.451913\pi$
$500$		−	281008.i		−	0.0502682i
$501$	6.24639e6	+	1.76578e6i	1.11182	+	0.314299i
$502$		−	5.45547e6i		−	0.966213i
$503$	−4.46014e6			−0.786010			−0.393005	−	0.919536i	$-0.628565\pi$
$503$	−4.46014e6			−0.786010			−0.393005	+	0.919536i	$0.628565\pi$
$504$	−2.47864e6	−	1.52308e6i	−0.434647	−	0.267083i
$505$			190021.i			0.0331569i
$506$	9.76833e6			1.69607
$507$	−1.56847e6	+	5.54840e6i	−0.270992	+	0.958624i
$508$	−2.73060e6			−0.469461
$509$	1.16377e7			1.99101			0.995506	−	0.0947009i	$-0.0301895\pi$
$509$	1.16377e7			1.99101			0.995506	+	0.0947009i	$0.0301895\pi$
$510$	−26130.9	+	92436.9i	−0.00444865	+	0.0157369i
$511$			1.02184e6i			0.173114i
$512$	−262144.			−0.0441942
$513$	5.90773e6	−	5.44101e6i	0.991122	−	0.912822i
$514$		−	5.46387e6i		−	0.912205i
$515$	7546.82			0.00125385
$516$	2.63504e6	+	744895.i	0.435675	+	0.123160i
$517$	3.93088e6			0.646791
$518$		−	1.50179e6i		−	0.245915i
$519$	2.09563e6	−	7.41321e6i	0.341504	−	1.20806i
$520$	6772.07			0.00109828
$521$			2.64005e6i			0.426106i	0.977041	+	0.213053i	$0.0683407\pi$
$521$			2.64005e6i			0.426106i	−0.977041	+	0.213053i	$0.931659\pi$
$522$	−3.99121e6	+	6.49524e6i	−0.641103	+	1.04332i
$523$	−7.92048e6			−1.26619			−0.633093	−	0.774076i	$-0.718215\pi$
$523$	−7.92048e6			−1.26619			−0.633093	+	0.774076i	$0.718215\pi$
$524$	−3.10875e6			−0.494605
$525$	2.47259e6	−	8.74670e6i	0.391520	−	1.38499i
$526$			6.25528e6i			0.985786i
$527$	5.15143e6			0.807981
$528$	−723737.	+	2.56019e6i	−0.112979	+	0.399657i
$529$	6.98119e6			1.08465
$530$	−118412.			−0.0183107
$531$	−3.42501e6	+	5.52131e6i	−0.527140	+	0.849778i
$532$	−6.34595e6			−0.972116
$533$	−239168.			−0.0364658
$534$	−1.12856e6	+	3.99224e6i	−0.171266	+	0.605848i
$535$	192035.			0.0290066
$536$		−	695593.i		−	0.104579i
$537$	65352.2	−	231181.i	0.00977967	−	0.0345952i
$538$	352061.			0.0524400
$539$	1.21240e7			1.79752
$540$	−115526.	−	125435.i	−0.0170488	−	0.0185112i
$541$			7.64287e6i			1.12270i	0.827579	+	0.561350i	$0.189718\pi$
$541$			7.64287e6i			1.12270i	−0.827579	+	0.561350i	$0.810282\pi$
$542$	−1.02463e6			−0.149820
$543$	762839.	−	2.69851e6i	0.111028	−	0.392758i
$544$			560670.i			0.0812289i
$545$	−84964.3			−0.0122531
$546$	422112.	+	119326.i	0.0605963	+	0.0171299i
$547$	−1.02646e7			−1.46681			−0.733407	−	0.679790i	$-0.762071\pi$
$547$	−1.02646e7			−1.46681			−0.733407	+	0.679790i	$0.762071\pi$
$548$		−	3.32022e6i		−	0.472297i
$549$	4.77354e6	−	7.76840e6i	0.675943	−	1.10002i
$550$	−8.31251e6			−1.17172
$551$			1.66295e7i			2.33346i
$552$	−994107.	+	3.51662e6i	−0.138863	+	0.491222i
$553$	6.29773e6			0.875732
$554$	−496953.			−0.0687925
$555$	23946.9	−	84711.2i	0.00330002	−	0.0116737i
$556$	−2.34479e6			−0.321675
$557$		−	6.55629e6i		−	0.895407i	−0.894182	−	0.447703i	$-0.852242\pi$
$557$		−	6.55629e6i		−	0.895407i	0.894182	−	0.447703i	$-0.147758\pi$
$558$	−4.78780e6	+	7.79160e6i	−0.650954	+	1.05935i
$559$	−412886.			−0.0558857
$560$			134740.i			0.0181562i
$561$	5.47571e6	+	1.54792e6i	0.734570	+	0.207655i
$562$			1.16214e6i			0.155209i
$563$	−1.51505e6			−0.201445			−0.100723	−	0.994915i	$-0.532115\pi$
$563$	−1.51505e6			−0.201445			−0.100723	+	0.994915i	$0.532115\pi$
$564$	−400040.	+	1.41513e6i	−0.0529548	+	0.187326i
$565$			290395.i			0.0382708i
$566$		−	7.47646e6i		−	0.980968i
$567$	−4.99066e6	−	9.85415e6i	−0.651929	−	1.28725i
$568$			3.45769e6i			0.449692i
$569$	8.81006e6			1.14077			0.570385	−	0.821377i	$-0.306794\pi$
$569$	8.81006e6			1.14077			0.570385	+	0.821377i	$0.306794\pi$
$570$	−357955.	−	101190.i	−0.0461467	−	0.0130451i
$571$		−	174406.i		−	0.0223857i	−0.999937	−	0.0111929i	$-0.996437\pi$
$571$		−	174406.i		−	0.0223857i	0.999937	−	0.0111929i	$-0.00356287\pi$
$572$		−	401159.i		−	0.0512656i
$573$	3.14933e6	−	1.11406e7i	0.400711	−	1.41750i
$574$		−	4.75859e6i		−	0.602835i
$575$	−1.14179e7			−1.44017
$576$	−848021.	−	521093.i	−0.106500	−	0.0654424i
$577$	4.60760e6			0.576149			0.288075	−	0.957608i	$-0.406985\pi$
$577$	4.60760e6			0.576149			0.288075	+	0.957608i	$0.406985\pi$
$578$	−4.48027e6			−0.557808
$579$	1.28272e6	−	4.53757e6i	0.159014	−	0.562506i
$580$	353084.			0.0435820
$581$	−2.59650e6			−0.319116
$582$	8.72627e6	+	2.46682e6i	1.06788	+	0.301877i
$583$			7.01438e6i			0.854708i
$584$			349604.i			0.0424175i
$585$	21907.2	+	13461.6i	0.00264666	+	0.00162632i
$586$		−	4.49829e6i		−	0.541132i
$587$	−1.53559e7			−1.83942			−0.919709	−	0.392600i	$-0.871576\pi$
$587$	−1.53559e7			−1.83942			−0.919709	+	0.392600i	$0.871576\pi$
$588$	−1.23384e6	+	4.36467e6i	−0.147169	+	0.520605i
$589$			1.99485e7i			2.36931i
$590$	300923.	+	1273.33i	0.0355898	+	0.000150595i
$591$	−1.19719e7	−	3.38433e6i	−1.40992	−	0.398569i
$592$		−	513811.i		−	0.0602558i
$593$		−	1.21186e7i		−	1.41520i	−0.706615	−	0.707598i	$-0.749779\pi$
$593$		−	1.21186e7i		−	1.41520i	0.706615	−	0.707598i	$-0.250221\pi$
$594$	−7.43043e6	+	6.84342e6i	−0.864068	+	0.795806i
$595$	288180.			0.0333711
$596$	−297133.			−0.0342638
$597$	−2.02886e6	+	7.17701e6i	−0.232978	+	0.824153i
$598$		−	551022.i		−	0.0630109i
$599$			597022.i			0.0679866i	0.999422	+	0.0339933i	$0.0108225\pi$
$599$			597022.i			0.0679866i	−0.999422	+	0.0339933i	$0.989178\pi$
$600$	845951.	−	2.99252e6i	0.0959328	−	0.339359i
$601$			9.83823e6i			1.11104i	0.831502	+	0.555521i	$0.187481\pi$
$601$			9.83823e6i			1.11104i	−0.831502	+	0.555521i	$0.812519\pi$
$602$		−	8.21495e6i		−	0.923876i
$603$	1.38271e6	−	2.25020e6i	0.154859	−	0.252016i
$604$			8.48468e6i			0.946331i
$605$		−	797455.i		−	0.0885764i
$606$	−1.14554e6	+	4.05230e6i	−0.126715	+	0.448250i
$607$	−6.42666e6			−0.707968			−0.353984	−	0.935251i	$-0.615173\pi$
$607$	−6.42666e6			−0.707968			−0.353984	+	0.935251i	$0.615173\pi$
$608$	−2.17115e6			−0.238194
$609$	2.20082e7	+	6.22146e6i	2.40459	+	0.679750i
$610$	−422293.			−0.0459504
$611$		−	221737.i		−	0.0240290i
$612$	−1.11451e6	+	1.81374e6i	−0.120283	+	0.195747i
$613$		−	1.83620e7i		−	1.97365i	−0.161806	−	0.986823i	$-0.551732\pi$
$613$		−	1.83620e7i		−	1.97365i	0.161806	−	0.986823i	$-0.448268\pi$
$614$	2.41899e6			0.258948
$615$	75878.3	−	268417.i	0.00808965	−	0.0286168i
$616$	7.98161e6			0.847498
$617$		−	7.41933e6i		−	0.784606i	−0.919836	−	0.392303i	$-0.871678\pi$
$617$		−	7.41933e6i		−	0.784606i	0.919836	−	0.392303i	$-0.128322\pi$
$618$	160940.	+	45495.9i	0.0169509	+	0.00479183i
$619$	−1.65346e6			−0.173447			−0.0867236	−	0.996232i	$-0.527640\pi$
$619$	−1.65346e6			−0.173447			−0.0867236	+	0.996232i	$0.527640\pi$
$620$	423554.			0.0442517
$621$	−1.02063e7	+	9.39996e6i	−1.06203	+	0.978131i
$622$		−	764178.i		−	0.0791988i
$623$	1.24462e7			1.28474
$624$	144418.	+	40825.3i	0.0148477	+	0.00419728i
$625$	9.69147e6			0.992406
$626$		−	4.00965e6i		−	0.408950i
$627$	−5.99420e6	+	2.12042e7i	−0.608923	+	2.15404i
$628$			633971.i			0.0641461i
$629$	−1.09893e6			−0.110750
$630$	−267838.	+	435875.i	−0.0268856	+	0.0437533i
$631$	−8.23874e6			−0.823735			−0.411868	−	0.911244i	$-0.635123\pi$
$631$	−8.23874e6			−0.823735			−0.411868	+	0.911244i	$0.635123\pi$
$632$	2.15465e6			0.214578
$633$	−1.21727e7	−	3.44108e6i	−1.20747	−	0.341338i
$634$		−	2.73867e6i		−	0.270593i
$635$			480184.i			0.0472578i
$636$	−2.52519e6	−	713842.i	−0.247543	−	0.0699777i
$637$		−	683904.i		−	0.0667800i
$638$		−	2.09157e7i		−	2.03433i
$639$	−6.87324e6	+	1.11854e7i	−0.665901	+	1.08368i
$640$			46098.7i			0.00444876i
$641$		−	4.64496e6i		−	0.446516i	−0.974759	−	0.223258i	$-0.928331\pi$
$641$		−	4.64496e6i		−	0.446516i	0.974759	−	0.223258i	$-0.0716692\pi$
$642$	4.09526e6	+	1.15768e6i	0.392142	+	0.110854i
$643$	8.01063e6			0.764080			0.382040	−	0.924146i	$-0.375222\pi$
$643$	8.01063e6			0.764080			0.382040	+	0.924146i	$0.375222\pi$
$644$	1.09633e7			1.04167
$645$	130992.	−	463378.i	0.0123978	−	0.0438568i
$646$			4.64363e6i			0.437801i
$647$			1.33654e7i			1.25523i	0.778525	+	0.627613i	$0.215968\pi$
$647$			1.33654e7i			1.25523i	−0.778525	+	0.627613i	$0.784032\pi$
$648$	−1.70746e6	−	3.37142e6i	−0.159740	−	0.315409i
$649$	75428.7	−	1.78258e7i	0.00702951	−	1.66126i
$650$			468901.i			0.0435309i
$651$	2.64007e7	+	7.46318e6i	2.44154	+	0.690194i
$652$	−8.68554e6			−0.800162
$653$			1.23117e7i			1.12988i	0.825131	+	0.564942i	$0.191101\pi$
$653$			1.23117e7i			1.12988i	−0.825131	+	0.564942i	$0.808899\pi$
$654$	−1.81191e6	−	512206.i	−0.165650	−	0.0468274i
$655$			546683.i			0.0497889i
$656$		−	1.62806e6i		−	0.147711i
$657$	−694949.	+	1.13095e6i	−0.0628115	+	0.102219i
$658$	4.41177e6			0.397236
$659$	−2.14518e6			−0.192420			−0.0962100	−	0.995361i	$-0.530672\pi$
$659$	−2.14518e6			−0.192420			−0.0962100	+	0.995361i	$0.530672\pi$
$660$	450217.	+	127271.i	0.0402311	+	0.0113729i
$661$	−2.16697e7			−1.92907			−0.964537	−	0.263948i	$-0.914975\pi$
$661$	−2.16697e7			−1.92907			−0.964537	+	0.263948i	$0.914975\pi$
$662$	7.31325e6			0.648583
$663$	87316.6	−	308879.i	0.00771460	−	0.0272901i
$664$	−888346.			−0.0781920
$665$			1.11595e6i			0.0978570i
$666$	1.02136e6	−	1.66215e6i	0.0892264	−	0.145206i
$667$		−	2.87293e7i		−	2.50041i
$668$		−	6.66254e6i		−	0.577695i
$669$	−642210.	+	2.27179e6i	−0.0554769	+	0.196247i
$670$	−122322.			−0.0105273
$671$			2.50155e7i			2.14488i
$672$	−812276.	+	2.87340e6i	−0.0693874	+	0.245455i
$673$		−	1.42022e7i		−	1.20869i	−0.796721	−	0.604347i	$-0.793434\pi$
$673$		−	1.42022e7i		−	1.20869i	0.796721	−	0.604347i	$-0.206566\pi$
$674$		−	8.58069e6i		−	0.727566i
$675$	8.68518e6	−	7.99904e6i	0.733701	−	0.675738i
$676$	5.91806e6			0.498095
$677$			371656.i			0.0311652i	0.999879	+	0.0155826i	$0.00496029\pi$
$677$			371656.i			0.0311652i	−0.999879	+	0.0155826i	$0.995040\pi$
$678$	−1.75064e6	+	6.19282e6i	−0.146259	+	0.517386i
$679$		−	2.72049e7i		−	2.26450i
$680$	98595.4			0.00817682
$681$	−1.94009e6	+	6.86300e6i	−0.160308	+	0.567083i
$682$		−	2.50902e7i		−	2.06559i
$683$	2.17625e7			1.78507			0.892537	−	0.450974i	$-0.148923\pi$
$683$	2.17625e7			1.78507			0.892537	+	0.450974i	$0.148923\pi$
$684$	−7.02355e6	−	4.31585e6i	−0.574006	−	0.352716i
$685$	−583869.			−0.0475433
$686$	1.03138e6			0.0836774
$687$	−1.10384e7	−	3.12043e6i	−0.892308	−	0.252245i
$688$		−	2.81059e6i		−	0.226374i
$689$	395674.			0.0317534
$690$	618407.	+	174816.i	0.0494483	+	0.0139785i
$691$			7.73330e6i			0.616126i	0.951366	+	0.308063i	$0.0996808\pi$
$691$			7.73330e6i			0.616126i	−0.951366	+	0.308063i	$0.900319\pi$
$692$	−7.90710e6			−0.627700
$693$	2.58201e7	+	1.58660e7i	2.04232	+	1.25497i
$694$	−1.55767e7			−1.22766
$695$			412338.i			0.0323811i
$696$	7.52969e6	+	2.12856e6i	0.589188	+	0.166557i
$697$	−3.48208e6			−0.271492
$698$			1.57078e7i			1.22033i
$699$	−25763.1	+	91136.1i	−0.00199437	+	0.00705501i
$700$	−9.32943e6			−0.719631
$701$	−2.49208e6			−0.191543			−0.0957715	−	0.995403i	$-0.530532\pi$
$701$	−2.49208e6			−0.191543			−0.0957715	+	0.995403i	$0.530532\pi$
$702$	386031.	+	419143.i	0.0295651	+	0.0321011i
$703$		−	4.25553e6i		−	0.324762i
$704$	2.73076e6			0.207660
$705$	248854.	+	70348.1i	0.0188569	+	0.00533064i
$706$	−6.99632e6			−0.528272
$707$	1.26334e7			0.950542
$708$	6.40966e6	+	1.84126e6i	0.480565	+	0.138049i
$709$	9.23865e6			0.690229			0.345114	−	0.938561i	$-0.387840\pi$
$709$	9.23865e6			0.690229			0.345114	+	0.938561i	$0.387840\pi$
$710$	608044.			0.0452678
$711$	6.97017e6	+	4.28305e6i	0.517094	+	0.317745i
$712$	4.25822e6			0.314795
$713$		−	3.44633e7i		−	2.53883i
$714$	6.14559e6	+	1.73729e6i	0.451147	+	0.127534i
$715$	−70544.8			−0.00516060
$716$	−246583.			−0.0179755
$717$	−1.63917e7	−	4.63374e6i	−1.19076	−	0.336615i
$718$			1.73038e7i			1.25265i
$719$	1.96582e7			1.41815			0.709075	−	0.705133i	$-0.249113\pi$
$719$	1.96582e7			1.41815			0.709075	+	0.705133i	$0.249113\pi$
$720$	−91635.7	+	149127.i	−0.00658769	+	0.0107207i
$721$		−	501744.i		−	0.0359455i
$722$	−8.07770e6			−0.576693
$723$	−5.09858e6	+	1.80360e7i	−0.362747	+	1.28320i
$724$	−2.87830e6			−0.204075
$725$			2.44476e7i			1.72740i
$726$	4.80744e6	−	1.70062e7i	0.338511	−	1.19747i
$727$	7.21876e6			0.506555			0.253278	−	0.967394i	$-0.418491\pi$
$727$	7.21876e6			0.506555			0.253278	+	0.967394i	$0.418491\pi$
$728$		−	450235.i		−	0.0314855i
$729$	1.17820e6	−	1.43005e7i	0.0821111	−	0.996623i
$730$	61478.9			0.00426991
$731$	−6.01126e6			−0.416076
$732$	−9.00563e6	−	2.54579e6i	−0.621207	−	0.175608i
$733$	−1.75023e6			−0.120319			−0.0601597	−	0.998189i	$-0.519161\pi$
$733$	−1.75023e6			−0.120319			−0.0601597	+	0.998189i	$0.519161\pi$
$734$			9.28311e6i			0.635995i
$735$	767539.	+	216974.i	0.0524061	+	0.0148146i
$736$	3.75091e6			0.255236
$737$			7.24602e6i			0.491395i
$738$	3.23629e6	−	5.26669e6i	0.218729	−	0.355957i
$739$		−	2.37481e7i		−	1.59963i	−0.600249	−	0.799813i	$-0.704932\pi$
$739$		−	2.37481e7i		−	1.59963i	0.600249	−	0.799813i	$-0.295068\pi$
$740$	−90355.0			−0.00606559
$741$	1.19611e6	+	338127.i	0.0800250	+	0.0226222i
$742$			7.87249e6i			0.524931i
$743$			2.09336e7i			1.39114i	0.718457	+	0.695571i	$0.244849\pi$
$743$			2.09336e7i			1.39114i	−0.718457	+	0.695571i	$0.755151\pi$
$744$	9.03252e6	+	2.55339e6i	0.598242	+	0.169116i
$745$			52251.7i			0.00344913i
$746$	4.49892e6			0.295979
$747$	−2.87375e6	−	1.76587e6i	−0.188429	−	0.115786i
$748$		−	5.84052e6i		−	0.381678i
$749$		−	1.27673e7i		−	0.831562i
$750$	−1.05382e6	−	297903.i	−0.0684091	−	0.0193385i
$751$		−	1.51513e7i		−	0.980279i	−0.871644	−	0.490139i	$-0.836946\pi$
$751$		−	1.51513e7i		−	0.980279i	0.871644	−	0.490139i	$-0.163054\pi$
$752$	1.50941e6			0.0973334
$753$	−2.04588e7	−	5.78348e6i	−1.31490	−	0.371708i
$754$	−1.17983e6			−0.0755775
$755$	1.49205e6			0.0952615
$756$	−8.33944e6	+	7.68062e6i	−0.530680	+	0.488756i
$757$	2.21987e7			1.40795			0.703977	−	0.710223i	$-0.251406\pi$
$757$	2.21987e7			1.40795			0.703977	+	0.710223i	$0.251406\pi$
$758$	1.12444e7			0.710827
$759$	1.03556e7	−	3.66327e7i	0.652488	−	2.30815i
$760$			381803.i			0.0239776i
$761$		−	6.46127e6i		−	0.404442i	−0.979340	−	0.202221i	$-0.935184\pi$
$761$		−	6.46127e6i		−	0.404442i	0.979340	−	0.202221i	$-0.0648160\pi$
$762$	−2.89478e6	+	1.02402e7i	−0.180604	+	0.638881i
$763$			5.64878e6i			0.351272i
$764$	−1.18829e7			−0.736526
$765$	318950.	+	195989.i	0.0197047	+	0.0121082i
$766$			3.04945e6i			0.187780i
$767$	−1.00554e6	−	4254.86i	−0.0617177	−	0.000261154i
$768$	−277905.	+	983080.i	−0.0170018	+	0.0601431i
$769$			1.92562e7i			1.17424i	0.809501	+	0.587118i	$0.199738\pi$
$769$			1.92562e7i			1.17424i	−0.809501	+	0.587118i	$0.800262\pi$
$770$		−	1.40359e6i		−	0.0853125i
$771$	−2.04903e7	−	5.79238e6i	−1.24140	−	0.350931i
$772$	−4.83988e6			−0.292275
$773$	2.22585e6			0.133982			0.0669910	−	0.997754i	$-0.478660\pi$
$773$	2.22585e6			0.133982			0.0669910	+	0.997754i	$0.478660\pi$
$774$	5.58694e6	−	9.09211e6i	0.335213	−	0.545522i
$775$			2.93271e7i			1.75394i
$776$		−	9.30765e6i		−	0.554863i
$777$	−5.63195e6	−	1.59209e6i	−0.334662	−	0.0946051i
$778$		−	1.17208e7i		−	0.694236i
$779$		−	1.34841e7i		−	0.796119i
$780$	7179.23	−	25396.3i	0.000422515	−	0.00149463i
$781$		−	3.60189e7i		−	2.11301i
$782$		−	8.02240e6i		−	0.469124i
$783$	2.01270e7	+	2.18534e7i	1.17320	+	1.27384i
$784$	4.65546e6			0.270503
$785$	111485.			0.00645720
$786$	−3.29567e6	+	1.16583e7i	−0.190277	+	0.673099i
$787$	1.37892e7			0.793603			0.396801	−	0.917905i	$-0.370120\pi$
$787$	1.37892e7			0.793603			0.396801	+	0.917905i	$0.370120\pi$
$788$			1.27695e7i			0.732588i
$789$	2.34583e7	+	6.63138e6i	1.34154	+	0.379238i
$790$		−	378901.i		−	0.0216002i
$791$	1.93066e7			1.09715
$792$	8.83386e6	+	5.42825e6i	0.500423	+	0.307501i
$793$	1.41110e6			0.0796846
$794$		−	5.45148e6i		−	0.306876i
$795$	−125531.	+	444062.i	−0.00704423	+	0.0249187i
$796$	7.65517e6			0.428225
$797$	−9.94985e6			−0.554844			−0.277422	−	0.960748i	$-0.589480\pi$
$797$	−9.94985e6			−0.554844			−0.277422	+	0.960748i	$0.589480\pi$
$798$	−6.72750e6	+	2.37983e7i	−0.373979	+	1.32294i
$799$		−	3.22830e6i		−	0.178899i
$800$	−3.19189e6			−0.176329
$801$	1.37751e7	+	8.46455e6i	0.758601	+	0.466147i
$802$	1.87415e7			1.02889
$803$		−	3.64184e6i		−	0.199311i
$804$	−2.60858e6	−	737416.i	−0.142319	−	0.0402321i
$805$		−	1.92793e6i		−	0.104858i
$806$	−1.41531e6			−0.0767388
$807$	373229.	−	1.32028e6i	0.0201740	−	0.0713647i
$808$	4.32228e6			0.232908
$809$	−2.88876e7			−1.55181			−0.775907	−	0.630847i	$-0.782708\pi$
$809$	−2.88876e7			−1.55181			−0.775907	+	0.630847i	$0.782708\pi$
$810$	−592872.	+	300262.i	−0.0317504	+	0.0160801i
$811$			2.59400e7i			1.38490i	0.721468	+	0.692448i	$0.243468\pi$
$811$			2.59400e7i			1.38490i	−0.721468	+	0.692448i	$0.756532\pi$
$812$		−	2.34744e7i		−	1.24941i
$813$	−1.08624e6	+	3.84253e6i	−0.0576367	+	0.203888i
$814$			5.35238e6i			0.283130i
$815$			1.52738e6i			0.0805475i
$816$	2.10260e6	+	594381.i	0.110543	+	0.0312492i
$817$		−	2.32781e7i		−	1.22009i
$818$		−	1.04184e7i		−	0.544397i
$819$	894983.	−	1.45648e6i	0.0466235	−	0.0758745i
$820$	−286299.			−0.0148691
$821$	2.29003e7			1.18572			0.592862	−	0.805304i	$-0.297998\pi$
$821$	2.29003e7			1.18572			0.592862	+	0.805304i	$0.297998\pi$
$822$	−1.24513e7	−	3.51985e6i	−0.642741	−	0.181696i
$823$			2.82547e7i			1.45409i	0.686591	+	0.727044i	$0.259106\pi$
$823$			2.82547e7i			1.45409i	−0.686591	+	0.727044i	$0.740894\pi$
$824$		−	171662.i		−	0.00880759i
$825$	−8.81230e6	+	3.11732e7i	−0.450769	+	1.59458i
$826$	84656.4	−	2.00066e7i	0.00431727	−	1.02029i
$827$		−	2.32919e7i		−	1.18425i	−0.805848	−	0.592123i	$-0.798290\pi$
$827$		−	2.32919e7i		−	1.18425i	0.805848	−	0.592123i	$-0.201710\pi$
$828$	1.21340e7	+	7.45611e6i	0.615074	+	0.377952i
$829$	7.31413e6			0.369638			0.184819	−	0.982773i	$-0.440830\pi$
$829$	7.31413e6			0.369638			0.184819	+	0.982773i	$0.440830\pi$
$830$			156218.i			0.00787111i
$831$	−526832.	+	1.86365e6i	−0.0264649	+	0.0936185i
$832$		−	154040.i		−	0.00771479i
$833$		−	9.95704e6i		−	0.497185i
$834$	−2.48577e6	+	8.79332e6i	−0.123750	+	0.437762i
$835$	−1.17163e6			−0.0581531
$836$	2.26170e7			1.11923
$837$	2.41440e7	+	2.62150e7i	1.19123	+	1.29341i
$838$	5.63455e6			0.277172
$839$	2.21954e7			1.08858			0.544288	−	0.838899i	$-0.316800\pi$
$839$	2.21954e7			1.08858			0.544288	+	0.838899i	$0.316800\pi$
$840$	505294.	+	142841.i	0.0247085	+	0.00698481i
$841$	−4.10033e7			−1.99907
$842$		−	9.05050e6i		−	0.439939i
$843$	4.35819e6	+	1.23201e6i	0.211221	+	0.0597098i
$844$			1.29837e7i			0.627395i
$845$		−	1.04071e6i		−	0.0501402i
$846$	4.88285e6	+	3.00042e6i	0.234556	+	0.144131i
$847$	−5.30181e7			−2.53931
$848$			2.69343e6i			0.128622i
$849$	−2.80378e7	−	7.92597e6i	−1.33498	−	0.377384i
$850$			6.82678e6i			0.324092i
$851$			7.35190e6i			0.347997i
$852$	1.29669e7	+	3.66558e6i	0.611978	+	0.172999i
$853$	−1.45570e7			−0.685016			−0.342508	−	0.939515i	$-0.611276\pi$
$853$	−1.45570e7			−0.685016			−0.342508	+	0.939515i	$0.611276\pi$
$854$			2.80758e7i			1.31731i
$855$	−758953.	+	1.23511e6i	−0.0355058	+	0.0577817i
$856$		−	4.36810e6i		−	0.203755i
$857$	−2.82987e6			−0.131618			−0.0658090	−	0.997832i	$-0.520963\pi$
$857$	−2.82987e6			−0.131618			−0.0658090	+	0.997832i	$0.520963\pi$
$858$	−1.50441e6	−	425278.i	−0.0697665	−	0.0197222i
$859$		−	3.03820e7i		−	1.40486i	−0.711751	−	0.702431i	$-0.752098\pi$
$859$		−	3.03820e7i		−	1.40486i	0.711751	−	0.702431i	$-0.247902\pi$
$860$	−494250.			−0.0227877
$861$	−1.78454e7	−	5.04470e6i	−0.820388	−	0.231914i
$862$	1.13220e7			0.518984
$863$	−4.65291e6			−0.212666			−0.106333	−	0.994331i	$-0.533911\pi$
$863$	−4.65291e6			−0.212666			−0.106333	+	0.994331i	$0.533911\pi$
$864$	−2.85319e6	+	2.62778e6i	−0.130031	+	0.119758i
$865$			1.39048e6i			0.0631867i
$866$	−2.54465e7			−1.15301
$867$	−4.74965e6	+	1.68017e7i	−0.214592	+	0.759111i
$868$		−	2.81596e7i		−	1.26861i
$869$	−2.24451e7			−1.00826
$870$	374313.	−	1.32412e6i	0.0167663	−	0.0593100i
$871$	408741.			0.0182559
$872$			1.93263e6i			0.0860709i
$873$	1.85019e7	−	3.01097e7i	0.821637	−	1.33712i
$874$	3.10661e7			1.37565
$875$			3.28538e6i			0.145066i
$876$	1.31107e6	+	370624.i	0.0577252	+	0.0163182i
$877$	2.30388e7			1.01149			0.505743	−	0.862684i	$-0.331218\pi$
$877$	2.30388e7			1.01149			0.505743	+	0.862684i	$0.331218\pi$
$878$	2.53571e7			1.11010
$879$	−1.68693e7	−	4.76874e6i	−0.736417	−	0.208177i
$880$		−	480212.i		−	0.0209038i
$881$	1.66897e7			0.724450			0.362225	−	0.932091i	$-0.382017\pi$
$881$	1.66897e7			0.724450			0.362225	+	0.932091i	$0.382017\pi$
$882$	1.50601e7	+	9.25419e6i	0.651865	+	0.400559i
$883$	−2.64559e7			−1.14188			−0.570940	−	0.820992i	$-0.693421\pi$
$883$	−2.64559e7			−1.14188			−0.570940	+	0.820992i	$0.693421\pi$
$884$	−329458.			−0.0141798
$885$	323791.	−	1.12716e6i	0.0138965	−	0.0483755i
$886$	2.23940e7			0.958403
$887$	−2.69988e7			−1.15222			−0.576110	−	0.817372i	$-0.695430\pi$
$887$	−2.69988e7			−1.15222			−0.576110	+	0.817372i	$0.695430\pi$
$888$	−1.92687e6	−	544703.i	−0.0820011	−	0.0231808i
$889$	3.19246e7			1.35479
$890$		−	748820.i		−	0.0316885i
$891$	1.77867e7	+	3.51201e7i	0.750587	+	1.48205i
$892$	2.42315e6			0.101969
$893$	1.25013e7			0.524600
$894$	−314998.	+	1.11430e6i	−0.0131815	+	0.0466290i
$895$			43362.3i			0.00180948i
$896$	3.06483e6			0.127537
$897$	−2.06641e6	−	584152.i	−0.0857505	−	0.0242407i
$898$		−	2.06943e7i		−	0.856366i
$899$	−7.37919e7			−3.04516
$900$	−1.03256e7	−	6.34489e6i	−0.424922	−	0.261107i
$901$	5.76067e6			0.236407
$902$			1.69596e7i			0.694063i
$903$	−3.08073e7	−	8.70887e6i	−1.25729	−	0.355420i
$904$	6.60541e6			0.268831
$905$			506157.i			0.0205430i
$906$	3.18188e7	+	8.99482e6i	1.28785	+	0.364059i
$907$	−4.18266e7			−1.68824			−0.844120	−	0.536155i	$-0.819876\pi$
$907$	−4.18266e7			−1.68824			−0.844120	+	0.536155i	$0.819876\pi$
$908$	7.32024e6			0.294653
$909$	1.39823e7	+	8.59189e6i	0.561267	+	0.344889i
$910$	−79175.0			−0.00316945
$911$		−	4.16398e6i		−	0.166231i	−0.996540	−	0.0831157i	$-0.973513\pi$
$911$		−	4.16398e6i		−	0.166231i	0.996540	−	0.0831157i	$-0.0264871\pi$
$912$	−2.30169e6	+	8.14215e6i	−0.0916347	+	0.324154i
$913$	9.25393e6			0.367409
$914$		−	2.62631e6i		−	0.103987i
$915$	−447683.	+	1.58366e6i	−0.0176774	+	0.0625331i
$916$			1.17738e7i			0.463638i
$917$	3.63457e7			1.42735
$918$	5.62027e6	+	6.10236e6i	0.220115	+	0.238996i
$919$			1.89847e7i			0.741505i	0.928732	+	0.370753i	$0.120900\pi$
$919$			1.89847e7i			0.741505i	−0.928732	+	0.370753i	$0.879100\pi$
$920$		−	659607.i		−	0.0256931i
$921$	2.56443e6	−	9.07158e6i	0.0996190	−	0.352398i
$922$			2.70587e7i			1.04828i
$923$	−2.03179e6			−0.0785008
$924$	8.46150e6	−	2.99323e7i	0.326038	−	1.15335i
$925$		−	6.25621e6i		−	0.240413i
$926$		−	2.84475e7i		−	1.09023i
$927$	341233.	−	555318.i	0.0130422	−	0.0212248i
$928$		−	8.03135e6i		−	0.306139i
$929$	−2.52966e7			−0.961661			−0.480831	−	0.876814i	$-0.659665\pi$
$929$	−2.52966e7			−0.961661			−0.480831	+	0.876814i	$0.659665\pi$
$930$	449020.	−	1.58839e6i	0.0170239	−	0.0602214i
$931$	3.85578e7			1.45794
$932$	97207.9			0.00366574
$933$	−2.86579e6	−	810124.i	−0.107780	−	0.0304683i
$934$	2.32594e7			0.872432
$935$	−1.02707e6			−0.0384213
$936$	306202.	−	498309.i	0.0114240	−	0.0185913i
$937$			3.77578e7i			1.40494i	0.711713	+	0.702471i	$0.247920\pi$
$937$			3.77578e7i			1.40494i	−0.711713	+	0.702471i	$0.752080\pi$
$938$			8.13246e6i			0.301797i
$939$	−1.50368e7	−	4.25072e6i	−0.556533	−	0.157325i
$940$		−	265433.i		−	0.00979796i
$941$	4.65375e7			1.71328			0.856641	−	0.515914i	$-0.172547\pi$
$941$	4.65375e7			1.71328			0.856641	+	0.515914i	$0.172547\pi$
$942$	2.37749e6	+	672088.i	0.0872953	+	0.0246774i
$943$			2.32953e7i			0.853078i
$944$	28963.6	−	6.84488e6i	0.00105785	−	0.249998i
$945$	1.35066e6	+	1.46651e6i	0.0492001	+	0.0534203i
$946$			2.92780e7i			1.06369i
$947$		−	5.94048e6i		−	0.215252i	−0.994191	−	0.107626i	$-0.965675\pi$
$947$		−	5.94048e6i		−	0.215252i	0.994191	−	0.107626i	$-0.0343248\pi$
$948$	2.28420e6	−	8.08027e6i	0.0825492	−	0.292015i
$949$	−205433.			−0.00740464
$950$	−2.64362e7			−0.950363
$951$	−1.02704e7	−	2.90333e6i	−0.368245	−	0.104099i
$952$		−	6.55503e6i		−	0.234413i
$953$			4.07813e7i			1.45455i	0.686346	+	0.727275i	$0.259214\pi$
$953$			4.07813e7i			1.45455i	−0.686346	+	0.727275i	$0.740786\pi$
$954$	−5.35403e6	+	8.71309e6i	−0.190463	+	0.309957i
$955$			2.08963e6i			0.0741416i
$956$			1.74838e7i			0.618714i
$957$	−7.84371e7	−	2.21733e7i	−2.76848	−	0.782618i
$958$			4.44470e6i			0.156469i
$959$			3.88180e7i			1.36297i
$960$	172877.	+	48870.4i	0.00605424	+	0.00171146i
$961$	−5.98906e7			−2.09195
$962$	301923.			0.0105186
$963$	8.68297e6	−	1.41305e7i	0.301719	−	0.491013i
$964$	1.92377e7			0.666745
$965$			851105.i			0.0294215i
$966$	1.16225e7	−	4.11142e7i	0.400735	−	1.41759i
$967$		−	2.05359e7i		−	0.706233i	−0.935579	−	0.353116i	$-0.885122\pi$
$967$		−	2.05359e7i		−	0.706233i	0.935579	−	0.353116i	$-0.114878\pi$
$968$	−1.81392e7			−0.622198
$969$	1.74143e7	+	4.92283e6i	0.595796	+	0.168425i
$970$	−1.63678e6			−0.0558547
$971$		−	2.42845e7i		−	0.826572i	−0.910601	−	0.413286i	$-0.864381\pi$
$971$		−	2.42845e7i		−	0.826572i	0.910601	−	0.413286i	$-0.135619\pi$
$972$	−1.44534e7	+	2.82912e6i	−0.490688	+	0.0960475i
$973$	2.74139e7			0.928301
$974$	−3.90073e7			−1.31750
$975$	1.75845e6	+	497093.i	0.0592404	+	0.0167466i
$976$			9.60561e6i			0.322776i
$977$	−4.03057e7			−1.35092			−0.675461	−	0.737395i	$-0.736056\pi$
$977$	−4.03057e7			−1.35092			−0.675461	+	0.737395i	$0.736056\pi$
$978$	−9.20776e6	+	3.25721e7i	−0.307827	+	1.08893i
$979$	−4.43580e7			−1.47916
$980$		−	818675.i		−	0.0272299i
$981$	−3.84170e6	+	6.25193e6i	−0.127453	+	0.207416i
$982$		−	1.36880e7i		−	0.452960i
$983$	−5.59941e7			−1.84824			−0.924120	−	0.382101i	$-0.875201\pi$
$983$	−5.59941e7			−1.84824			−0.924120	+	0.382101i	$0.875201\pi$
$984$	−6.10549e6	−	1.72595e6i	−0.201017	−	0.0568252i
$985$	2.24556e6			0.0737452
$986$	−1.71774e7			−0.562683
$987$	4.67703e6	−	1.65448e7i	0.152819	−	0.540591i
$988$		−	1.27580e6i		−	0.0415805i
$989$			4.02156e7i			1.30739i
$990$	954572.	−	1.55346e6i	0.0309543	−	0.0503746i
$991$		−	3.11669e7i		−	1.00811i	−0.863670	−	0.504057i	$-0.831840\pi$
$991$		−	3.11669e7i		−	1.00811i	0.863670	−	0.504057i	$-0.168160\pi$
$992$		−	9.63430e6i		−	0.310843i
$993$	7.75296e6	−	2.74258e7i	0.249514	−	0.882645i
$994$		−	4.04253e7i		−	1.29774i
$995$		−	1.34618e6i		−	0.0431068i
$996$	−941758.	+	3.33143e6i	−0.0300809	+	0.106410i
$997$	1.43887e7			0.458443			0.229221	−	0.973374i	$-0.426382\pi$
$997$	1.43887e7			0.458443			0.229221	+	0.973374i	$0.426382\pi$
$998$	−6.69676e6			−0.212833
$999$	−5.15054e6	−	5.59234e6i	−0.163282	−	0.177288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.c.a.353.20	yes	50
3.2	odd	2		354.6.c.b.353.19	yes	50
59.58	odd	2		354.6.c.b.353.20	yes	50
177.176	even	2	inner	354.6.c.a.353.19	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.c.a.353.19	✓	50	177.176	even	2	inner
354.6.c.a.353.20	yes	50	1.1	even	1	trivial
354.6.c.b.353.19	yes	50	3.2	odd	2
354.6.c.b.353.20	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +(-4.24050 + 15.0006i) q^{3} +16.0000 q^{4} -2.81364i q^{5} +(16.9620 - 60.0024i) q^{6} -187.063 q^{7} -64.0000 q^{8} +(-207.036 - 127.220i) q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +(-4.24050 + 15.0006i) q^{3} +16.0000 q^{4} -2.81364i q^{5} +(16.9620 - 60.0024i) q^{6} -187.063 q^{7} -64.0000 q^{8} +(-207.036 - 127.220i) q^{9} +11.2546i q^{10} +666.690 q^{11} +(-67.8480 + 240.010i) q^{12} -37.6073i q^{13} +748.250 q^{14} +(42.2063 + 11.9312i) q^{15} +256.000 q^{16} -547.530i q^{17} +(828.145 + 508.880i) q^{18} +2120.27 q^{19} -45.0183i q^{20} +(793.238 - 2806.05i) q^{21} -2666.76 q^{22} -3663.00 q^{23} +(271.392 - 960.039i) q^{24} +3117.08 q^{25} +150.429i q^{26} +(2786.32 - 2566.19i) q^{27} -2993.00 q^{28} +7843.11i q^{29} +(-168.825 - 47.7250i) q^{30} +9408.50i q^{31} -1024.00 q^{32} +(-2827.10 + 10000.8i) q^{33} +2190.12i q^{34} +526.327i q^{35} +(-3312.58 - 2035.52i) q^{36} -2007.07i q^{37} -8481.06 q^{38} +(564.133 + 159.474i) q^{39} +180.073i q^{40} -6359.63i q^{41} +(-3172.95 + 11224.2i) q^{42} -10978.9i q^{43} +10667.0 q^{44} +(-357.952 + 582.526i) q^{45} +14652.0 q^{46} +5896.12 q^{47} +(-1085.57 + 3840.16i) q^{48} +18185.4 q^{49} -12468.3 q^{50} +(8213.28 + 2321.80i) q^{51} -601.717i q^{52} +10521.2i q^{53} +(-11145.3 + 10264.8i) q^{54} -1875.83i q^{55} +11972.0 q^{56} +(-8990.98 + 31805.3i) q^{57} -31372.5i q^{58} +(113.139 - 26737.8i) q^{59} +(675.301 + 190.900i) q^{60} +37521.9i q^{61} -37634.0i q^{62} +(38728.7 + 23798.1i) q^{63} +4096.00 q^{64} -105.814 q^{65} +(11308.4 - 40003.0i) q^{66} +10868.6i q^{67} -8760.48i q^{68} +(15532.9 - 54947.2i) q^{69} -2105.31i q^{70} -54026.4i q^{71} +(13250.3 + 8142.09i) q^{72} -5462.57i q^{73} +8028.29i q^{74} +(-13218.0 + 46758.1i) q^{75} +33924.2 q^{76} -124713. q^{77} +(-2256.53 - 637.895i) q^{78} -33666.4 q^{79} -720.292i q^{80} +(26679.1 + 52678.4i) q^{81} +25438.5i q^{82} +13880.4 q^{83} +(12691.8 - 44896.8i) q^{84} -1540.55 q^{85} +43915.5i q^{86} +(-117651. - 33258.7i) q^{87} -42668.2 q^{88} -66534.7 q^{89} +(1431.81 - 2330.11i) q^{90} +7034.92i q^{91} -58607.9 q^{92} +(-141133. - 39896.7i) q^{93} -23584.5 q^{94} -5965.67i q^{95} +(4342.27 - 15360.6i) q^{96} +145432. i q^{97} -72741.6 q^{98} +(-138029. - 84816.4i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more