LMFDB - Embedded newform 294.6.e.t.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{4705})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 1177x^{2} + 1176x + 1382976 $ x^4 - x^3 + 1177x^2 + 1176x + 1382976
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$-16.8983 + 29.2686i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.6.e.t.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(29.7965 - 51.6091i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(119.186 + 206.436i) q^{10} +(308.169 + 533.764i) q^{11} +(-72.0000 + 124.708i) q^{12} +418.372 q^{13} -536.337 q^{15} +(-128.000 + 221.703i) q^{16} +(-896.948 - 1553.56i) q^{17} +(-162.000 - 280.592i) q^{18} +(-639.965 + 1108.45i) q^{19} -953.488 q^{20} -2465.35 q^{22} +(-2390.84 + 4141.06i) q^{23} +(-288.000 - 498.831i) q^{24} +(-213.163 - 369.209i) q^{25} +(-836.744 + 1449.28i) q^{26} +729.000 q^{27} +1716.02 q^{29} +(1072.67 - 1857.93i) q^{30} +(-321.361 - 556.613i) q^{31} +(-512.000 - 886.810i) q^{32} +(2773.52 - 4803.87i) q^{33} +7175.58 q^{34} +1296.00 q^{36} +(1180.01 - 2043.84i) q^{37} +(-2559.86 - 4433.81i) q^{38} +(-1882.67 - 3260.89i) q^{39} +(1906.98 - 3302.98i) q^{40} +15639.9 q^{41} -1638.61 q^{43} +(4930.70 - 8540.22i) q^{44} +(2413.52 + 4180.33i) q^{45} +(-9563.37 - 16564.2i) q^{46} +(-10367.8 + 17957.5i) q^{47} +2304.00 q^{48} +1705.30 q^{50} +(-8072.53 + 13982.0i) q^{51} +(-3346.98 - 5797.13i) q^{52} +(2673.97 + 4631.45i) q^{53} +(-1458.00 + 2525.33i) q^{54} +36729.4 q^{55} +11519.4 q^{57} +(-3432.04 + 5944.48i) q^{58} +(-8412.46 - 14570.8i) q^{59} +(4290.70 + 7431.70i) q^{60} +(6763.59 - 11714.9i) q^{61} +2570.89 q^{62} +4096.00 q^{64} +(12466.0 - 21591.8i) q^{65} +(11094.1 + 19215.5i) q^{66} +(23241.8 + 40255.9i) q^{67} +(-14351.2 + 24856.9i) q^{68} +43035.2 q^{69} -3273.91 q^{71} +(-2592.00 + 4489.48i) q^{72} +(38379.2 + 66474.7i) q^{73} +(4720.04 + 8175.36i) q^{74} +(-1918.47 + 3322.88i) q^{75} +20478.9 q^{76} +15061.4 q^{78} +(8865.69 - 15355.8i) q^{79} +(7627.90 + 13211.9i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-31279.7 + 54178.1i) q^{82} +78846.7 q^{83} -106904. q^{85} +(3277.22 - 5676.30i) q^{86} +(-7722.10 - 13375.1i) q^{87} +(19722.8 + 34160.9i) q^{88} +(-37080.2 + 64224.8i) q^{89} -19308.1 q^{90} +76507.0 q^{92} +(-2892.25 + 5009.52i) q^{93} +(-41471.1 - 71830.0i) q^{94} +(38137.4 + 66056.0i) q^{95} +(-4608.00 + 7981.29i) q^{96} +24360.2 q^{97} -49923.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} - 18 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} - 72 q^{10} - 2 q^{11} - 288 q^{12} + 576 q^{13} + 324 q^{15} - 512 q^{16} - 1530 q^{17} - 648 q^{18} - 1188 q^{19} + 576 q^{20}+ \cdots + 324 q^{99}+O(q^{100}) $ 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 - 18 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9 - 72 * q^10 - 2 * q^11 - 288 * q^12 + 576 * q^13 + 324 * q^15 - 512 * q^16 - 1530 * q^17 - 648 * q^18 - 1188 * q^19 + 576 * q^20 + 16 * q^22 - 3390 * q^23 - 1152 * q^24 - 3322 * q^25 - 1152 * q^26 + 2916 * q^27 - 7952 * q^29 - 648 * q^30 - 7596 * q^31 - 2048 * q^32 - 18 * q^33 + 12240 * q^34 + 5184 * q^36 - 2688 * q^37 - 4752 * q^38 - 2592 * q^39 - 1152 * q^40 + 73260 * q^41 - 46064 * q^43 - 32 * q^44 - 1458 * q^45 - 13560 * q^46 - 864 * q^47 + 9216 * q^48 + 26576 * q^50 - 13770 * q^51 - 4608 * q^52 + 32920 * q^53 - 5832 * q^54 + 169416 * q^55 + 21384 * q^57 + 15904 * q^58 + 26712 * q^59 - 2592 * q^60 - 20412 * q^61 + 60768 * q^62 + 16384 * q^64 + 35048 * q^65 - 72 * q^66 + 36172 * q^67 - 24480 * q^68 + 61020 * q^69 + 147412 * q^71 - 10368 * q^72 + 74772 * q^73 - 10752 * q^74 - 29898 * q^75 + 38016 * q^76 + 20736 * q^78 + 23116 * q^79 - 4608 * q^80 - 13122 * q^81 - 146520 * q^82 + 295632 * q^83 - 254760 * q^85 + 92128 * q^86 + 35784 * q^87 - 128 * q^88 - 164646 * q^89 + 11664 * q^90 + 108480 * q^92 - 68364 * q^93 - 3456 * q^94 + 83408 * q^95 - 18432 * q^96 + 324072 * q^97 + 324 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$2$	−2.00000	+	3.46410i	−0.353553	+	0.612372i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	29.7965	−	51.6091i	0.533016	−	0.923211i	−0.466241	−	0.884658i	$-0.654392\pi$
$5$	29.7965	−	51.6091i	0.533016	−	0.923211i	0.999257	−	0.0385528i	$-0.0122748\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	64.0000			0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	119.186	+	206.436i	0.376899	+	0.652809i
$11$	308.169	+	533.764i	0.767903	+	1.33005i	0.938698	+	0.344741i	$0.112033\pi$
$11$	308.169	+	533.764i	0.767903	+	1.33005i	−0.170795	+	0.985307i	$0.554633\pi$
$12$	−72.0000	+	124.708i	−0.144338	+	0.250000i
$13$	418.372			0.686601			0.343300	−	0.939226i	$-0.388455\pi$
$13$	418.372			0.686601			0.343300	+	0.939226i	$0.388455\pi$
$14$		0			0
$15$	−536.337			−0.615474
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	−896.948	−	1553.56i	−0.752740	−	1.30378i	−0.946490	−	0.322732i	$-0.895399\pi$
$17$	−896.948	−	1553.56i	−0.752740	−	1.30378i	0.193751	−	0.981051i	$-0.437935\pi$
$18$	−162.000	−	280.592i	−0.117851	−	0.204124i
$19$	−639.965	+	1108.45i	−0.406698	+	0.704422i	−0.994517	−	0.104570i	$-0.966653\pi$
$19$	−639.965	+	1108.45i	−0.406698	+	0.704422i	0.587819	+	0.808992i	$0.299987\pi$
$20$	−953.488			−0.533016
$21$		0			0
$22$	−2465.35			−1.08598
$23$	−2390.84	+	4141.06i	−0.942392	+	1.63227i	−0.181500	+	0.983391i	$0.558095\pi$
$23$	−2390.84	+	4141.06i	−0.942392	+	1.63227i	−0.760892	+	0.648879i	$0.775238\pi$
$24$	−288.000	−	498.831i	−0.102062	−	0.176777i
$25$	−213.163	−	369.209i	−0.0682122	−	0.118147i
$26$	−836.744	+	1449.28i	−0.242750	+	0.420455i
$27$	729.000			0.192450
$28$		0			0
$29$	1716.02			0.378903			0.189451	−	0.981890i	$-0.439329\pi$
$29$	1716.02			0.378903			0.189451	+	0.981890i	$0.439329\pi$
$30$	1072.67	−	1857.93i	0.217603	−	0.376899i
$31$	−321.361	−	556.613i	−0.0600605	−	0.104028i	0.834432	−	0.551111i	$-0.185796\pi$
$31$	−321.361	−	556.613i	−0.0600605	−	0.104028i	−0.894492	+	0.447083i	$0.852463\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	2773.52	−	4803.87i	0.443349	−	0.767903i
$34$	7175.58			1.06453
$35$		0			0
$36$	1296.00			0.166667
$37$	1180.01	−	2043.84i	0.141704	−	0.245438i	−0.786434	−	0.617674i	$-0.788075\pi$
$37$	1180.01	−	2043.84i	0.141704	−	0.245438i	0.928138	+	0.372235i	$0.121409\pi$
$38$	−2559.86	−	4433.81i	−0.287579	−	0.498102i
$39$	−1882.67	−	3260.89i	−0.198205	−	0.343300i
$40$	1906.98	−	3302.98i	0.188450	−	0.326404i
$41$	15639.9			1.45303			0.726513	−	0.687152i	$-0.241140\pi$
$41$	15639.9			1.45303			0.726513	+	0.687152i	$0.241140\pi$
$42$		0			0
$43$	−1638.61			−0.135146			−0.0675731	−	0.997714i	$-0.521526\pi$
$43$	−1638.61			−0.135146			−0.0675731	+	0.997714i	$0.521526\pi$
$44$	4930.70	−	8540.22i	0.383952	−	0.665024i
$45$	2413.52	+	4180.33i	0.177672	+	0.307737i
$46$	−9563.37	−	16564.2i	−0.666371	−	1.15419i
$47$	−10367.8	+	17957.5i	−0.684606	+	1.18577i	0.288955	+	0.957343i	$0.406692\pi$
$47$	−10367.8	+	17957.5i	−0.684606	+	1.18577i	−0.973561	+	0.228429i	$0.926641\pi$
$48$	2304.00			0.144338
$49$		0			0
$50$	1705.30			0.0964666
$51$	−8072.53	+	13982.0i	−0.434594	+	0.752740i
$52$	−3346.98	−	5797.13i	−0.171650	−	0.297307i
$53$	2673.97	+	4631.45i	0.130757	+	0.226478i	0.923969	−	0.382468i	$-0.124926\pi$
$53$	2673.97	+	4631.45i	0.130757	+	0.226478i	−0.793211	+	0.608946i	$0.791592\pi$
$54$	−1458.00	+	2525.33i	−0.0680414	+	0.117851i
$55$	36729.4			1.63722
$56$		0			0
$57$	11519.4			0.469615
$58$	−3432.04	+	5944.48i	−0.133962	+	0.232030i
$59$	−8412.46	−	14570.8i	−0.314625	−	0.544946i	0.664733	−	0.747081i	$-0.268545\pi$
$59$	−8412.46	−	14570.8i	−0.314625	−	0.544946i	−0.979358	+	0.202135i	$0.935212\pi$
$60$	4290.70	+	7431.70i	0.153868	+	0.266508i
$61$	6763.59	−	11714.9i	0.232730	−	0.403100i	−0.725880	−	0.687821i	$-0.758567\pi$
$61$	6763.59	−	11714.9i	0.232730	−	0.403100i	0.958611	+	0.284720i	$0.0919008\pi$
$62$	2570.89			0.0849384
$63$		0			0
$64$	4096.00			0.125000
$65$	12466.0	−	21591.8i	0.365969	−	0.633877i
$66$	11094.1	+	19215.5i	0.313495	+	0.542990i
$67$	23241.8	+	40255.9i	0.632531	+	1.09558i	0.987033	+	0.160520i	$0.0513173\pi$
$67$	23241.8	+	40255.9i	0.632531	+	1.09558i	−0.354501	+	0.935055i	$0.615349\pi$
$68$	−14351.2	+	24856.9i	−0.376370	+	0.651892i
$69$	43035.2			1.08818
$70$		0			0
$71$	−3273.91			−0.0770762			−0.0385381	−	0.999257i	$-0.512270\pi$
$71$	−3273.91			−0.0770762			−0.0385381	+	0.999257i	$0.512270\pi$
$72$	−2592.00	+	4489.48i	−0.0589256	+	0.102062i
$73$	38379.2	+	66474.7i	0.842924	+	1.45999i	0.887412	+	0.460978i	$0.152501\pi$
$73$	38379.2	+	66474.7i	0.842924	+	1.45999i	−0.0444870	+	0.999010i	$0.514165\pi$
$74$	4720.04	+	8175.36i	0.100200	+	0.173551i
$75$	−1918.47	+	3322.88i	−0.0393823	+	0.0682122i
$76$	20478.9			0.406698
$77$		0			0
$78$	15061.4			0.280304
$79$	8865.69	−	15355.8i	0.159825	−	0.276825i	−0.774980	−	0.631985i	$-0.782240\pi$
$79$	8865.69	−	15355.8i	0.159825	−	0.276825i	0.934805	+	0.355160i	$0.115574\pi$
$80$	7627.90	+	13211.9i	0.133254	+	0.230803i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−31279.7	+	54178.1i	−0.513722	+	0.889793i
$83$	78846.7			1.25629			0.628143	−	0.778098i	$-0.283815\pi$
$83$	78846.7			1.25629			0.628143	+	0.778098i	$0.283815\pi$
$84$		0			0
$85$	−106904.			−1.60489
$86$	3277.22	−	5676.30i	0.0477814	−	0.0827598i
$87$	−7722.10	−	13375.1i	−0.109380	−	0.189451i
$88$	19722.8	+	34160.9i	0.271495	+	0.470243i
$89$	−37080.2	+	64224.8i	−0.496212	+	0.859464i	−0.999990	−	0.00436852i	$-0.998609\pi$
$89$	−37080.2	+	64224.8i	−0.496212	+	0.859464i	0.503778	+	0.863833i	$0.331943\pi$
$90$	−19308.1			−0.251266
$91$		0			0
$92$	76507.0			0.942392
$93$	−2892.25	+	5009.52i	−0.0346759	+	0.0600605i
$94$	−41471.1	−	71830.0i	−0.484089	−	0.838467i
$95$	38137.4	+	66056.0i	0.433553	+	0.750936i
$96$	−4608.00	+	7981.29i	−0.0510310	+	0.0883883i
$97$	24360.2			0.262876			0.131438	−	0.991324i	$-0.458041\pi$
$97$	24360.2			0.262876			0.131438	+	0.991324i	$0.458041\pi$
$98$		0			0
$99$	−49923.3			−0.511936
$100$	−3410.61	+	5907.35i	−0.0341061	+	0.0590735i
$101$	74389.9	+	128847.i	0.725622	+	1.25681i	0.958717	+	0.284361i	$0.0917814\pi$
$101$	74389.9	+	128847.i	0.725622	+	1.25681i	−0.233095	+	0.972454i	$0.574885\pi$
$102$	−32290.1	−	55928.1i	−0.307305	−	0.532267i
$103$	−102758.	+	177982.i	−0.954383	+	1.65304i	−0.218610	+	0.975812i	$0.570152\pi$
$103$	−102758.	+	177982.i	−0.954383	+	1.65304i	−0.735773	+	0.677228i	$0.763181\pi$
$104$	26775.8			0.242750
$105$		0			0
$106$	−21391.7			−0.184919
$107$	52288.8	−	90566.9i	0.441519	−	0.764734i	−0.556283	−	0.830993i	$-0.687773\pi$
$107$	52288.8	−	90566.9i	0.441519	−	0.764734i	0.997802	+	0.0662591i	$0.0211064\pi$
$108$	−5832.00	−	10101.3i	−0.0481125	−	0.0833333i
$109$	−106373.	−	184243.i	−0.857560	−	1.48534i	−0.874249	−	0.485478i	$-0.838646\pi$
$109$	−106373.	−	184243.i	−0.857560	−	1.48534i	0.0166886	−	0.999861i	$-0.494688\pi$
$110$	−73458.7	+	127234.i	−0.578844	+	1.00259i
$111$	−21240.2			−0.163626
$112$		0			0
$113$	224886.			1.65678			0.828391	−	0.560150i	$-0.189256\pi$
$113$	224886.			1.65678			0.828391	+	0.560150i	$0.189256\pi$
$114$	−23038.7	+	39904.3i	−0.166034	+	0.287579i
$115$	142477.	+	246778.i	1.00462	+	1.74005i
$116$	−13728.2	−	23777.9i	−0.0947257	−	0.164070i
$117$	−16944.1	+	29348.0i	−0.114433	+	0.198205i
$118$	67299.7			0.444947
$119$		0			0
$120$	−34325.6			−0.217603
$121$	−109410.	+	189504.i	−0.679351	+	1.17667i
$122$	27054.4	+	46859.5i	0.164565	+	0.285035i
$123$	−70379.4	−	121901.i	−0.419453	−	0.726513i
$124$	−5141.78	+	8905.82i	−0.0300302	+	0.0520139i
$125$	160822.			0.920599
$126$		0			0
$127$	−44027.2			−0.242221			−0.121110	−	0.992639i	$-0.538646\pi$
$127$	−44027.2			−0.242221			−0.121110	+	0.992639i	$0.538646\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	7373.73	+	12771.7i	0.0390133	+	0.0675731i
$130$	49864.1	+	86367.1i	0.258779	+	0.448219i
$131$	195566.	−	338730.i	0.995668	−	1.72455i	0.417316	−	0.908762i	$-0.362971\pi$
$131$	195566.	−	338730.i	0.995668	−	1.72455i	0.578353	−	0.815787i	$-0.303696\pi$
$132$	−88752.5			−0.443349
$133$		0			0
$134$	−185934.			−0.894534
$135$	21721.6	−	37623.0i	0.102579	−	0.177672i
$136$	−57404.6	−	99427.8i	−0.266134	−	0.460957i
$137$	−35491.1	−	61472.4i	−0.161554	−	0.279820i	0.773872	−	0.633342i	$-0.218317\pi$
$137$	−35491.1	−	61472.4i	−0.161554	−	0.279820i	−0.935426	+	0.353522i	$0.884984\pi$
$138$	−86070.3	+	149078.i	−0.384730	+	0.666371i
$139$	102764.			0.451133			0.225567	−	0.974228i	$-0.427577\pi$
$139$	102764.			0.451133			0.225567	+	0.974228i	$0.427577\pi$
$140$		0			0
$141$	186620.			0.790515
$142$	6547.81	−	11341.1i	0.0272506	−	0.0471994i
$143$	128929.	+	223312.i	0.527243	+	0.913212i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	51131.5	−	88562.3i	0.201961	−	0.349807i
$146$	−307034.			−1.19208
$147$		0			0
$148$	−37760.4			−0.141704
$149$	113149.	−	195979.i	0.417527	−	0.723177i	−0.578163	−	0.815921i	$-0.696230\pi$
$149$	113149.	−	195979.i	0.417527	−	0.723177i	0.995690	+	0.0927438i	$0.0295637\pi$
$150$	−7673.87	−	13291.5i	−0.0278475	−	0.0482333i
$151$	274112.	+	474776.i	0.978330	+	1.69452i	0.668476	+	0.743733i	$0.266947\pi$
$151$	274112.	+	474776.i	0.978330	+	1.69452i	0.309854	+	0.950784i	$0.399720\pi$
$152$	−40957.8	+	70940.9i	−0.143790	+	0.249051i
$153$	145305.			0.501826
$154$		0			0
$155$	−38301.7			−0.128053
$156$	−30122.8	+	52174.2i	−0.0991023	+	0.171650i
$157$	−120572.	−	208837.i	−0.390389	−	0.676173i	0.602112	−	0.798412i	$-0.294326\pi$
$157$	−120572.	−	208837.i	−0.390389	−	0.676173i	−0.992501	+	0.122238i	$0.960993\pi$
$158$	35462.7	+	61423.3i	0.113013	+	0.195745i
$159$	24065.7	−	41683.0i	0.0754928	−	0.130757i
$160$	−61023.2			−0.188450
$161$		0			0
$162$	26244.0			0.0785674
$163$	−315451.	+	546377.i	−0.929957	+	1.61073i	−0.146569	+	0.989200i	$0.546823\pi$
$163$	−315451.	+	546377.i	−0.929957	+	1.61073i	−0.783388	+	0.621533i	$0.786510\pi$
$164$	−125119.	−	216712.i	−0.363257	−	0.629179i
$165$	−165282.	−	286277.i	−0.472624	−	0.818610i
$166$	−157693.	+	273133.i	−0.444164	+	0.769314i
$167$	239113.			0.663456			0.331728	−	0.943375i	$-0.392368\pi$
$167$	239113.			0.663456			0.331728	+	0.943375i	$0.392368\pi$
$168$		0			0
$169$	−196258.			−0.528579
$170$	213807.	−	370325.i	0.567414	−	0.982790i
$171$	−51837.2	−	89784.6i	−0.135566	−	0.234807i
$172$	13108.9	+	22705.2i	0.0337865	+	0.0585200i
$173$	151470.	−	262353.i	0.384778	−	0.666455i	−0.606961	−	0.794732i	$-0.707611\pi$
$173$	151470.	−	262353.i	0.384778	−	0.666455i	0.991738	+	0.128277i	$0.0409447\pi$
$174$	61776.8			0.154686
$175$		0			0
$176$	−157782.			−0.383952
$177$	−75712.1	+	131137.i	−0.181649	+	0.314625i
$178$	−148321.	−	256899.i	−0.350875	−	0.607733i
$179$	52994.8	+	91789.7i	0.123623	+	0.214122i	0.921194	−	0.389104i	$-0.127215\pi$
$179$	52994.8	+	91789.7i	0.123623	+	0.214122i	−0.797571	+	0.603226i	$0.793882\pi$
$180$	38616.3	−	66885.3i	0.0888360	−	0.153868i
$181$	−473727.			−1.07481			−0.537405	−	0.843324i	$-0.680595\pi$
$181$	−473727.			−1.07481			−0.537405	+	0.843324i	$0.680595\pi$
$182$		0			0
$183$	−121745.			−0.268734
$184$	−153014.	+	265028.i	−0.333186	+	0.577095i
$185$	−70320.4	−	121799.i	−0.151061	−	0.261645i
$186$	−11569.0	−	20038.1i	−0.0245196	−	0.0424692i
$187$	552822.	−	957516.i	1.15606	−	2.00236i
$188$	331768.			0.684606
$189$		0			0
$190$	−305099.			−0.613137
$191$	293907.	−	509061.i	0.582943	−	1.00969i	−0.412185	−	0.911100i	$-0.635234\pi$
$191$	293907.	−	509061.i	0.582943	−	1.00969i	0.995128	−	0.0985869i	$-0.0314322\pi$
$192$	−18432.0	−	31925.2i	−0.0360844	−	0.0625000i
$193$	183430.	+	317711.i	0.354469	+	0.613958i	0.987027	−	0.160555i	$-0.0513283\pi$
$193$	183430.	+	317711.i	0.354469	+	0.613958i	−0.632558	+	0.774513i	$0.717995\pi$
$194$	−48720.4	+	84386.1i	−0.0929407	+	0.160978i
$195$	−224388.			−0.422585
$196$		0			0
$197$	727471.			1.33552			0.667760	−	0.744377i	$-0.267253\pi$
$197$	727471.			1.33552			0.667760	+	0.744377i	$0.267253\pi$
$198$	99846.6	−	172939.i	0.180997	−	0.313495i
$199$	117406.	+	203353.i	0.210163	+	0.364013i	0.951765	−	0.306826i	$-0.0992671\pi$
$199$	117406.	+	203353.i	0.210163	+	0.364013i	−0.741602	+	0.670840i	$0.765934\pi$
$200$	−13642.4	−	23629.4i	−0.0241166	−	0.0417712i
$201$	209176.	−	362303.i	0.365192	−	0.632531i
$202$	−595119.			−1.02619
$203$		0			0
$204$	258321.			0.434594
$205$	466013.	−	807159.i	0.774486	−	1.34145i
$206$	−411032.	−	711929.i	−0.674851	−	1.16888i
$207$	−193658.	−	335426.i	−0.314131	−	0.544090i
$208$	−53551.6	+	92754.1i	−0.0858251	+	0.148653i
$209$	−788868.			−1.24922
$210$		0			0
$211$	−308050.			−0.476337			−0.238169	−	0.971224i	$-0.576547\pi$
$211$	−308050.			−0.476337			−0.238169	+	0.971224i	$0.576547\pi$
$212$	42783.5	−	74103.1i	0.0653787	−	0.113239i
$213$	14732.6	+	25517.6i	0.0222500	+	0.0385381i
$214$	209155.	+	362268.i	0.312201	+	0.540748i
$215$	−48824.8	+	84567.0i	−0.0720351	+	0.124768i
$216$	46656.0			0.0680414
$217$		0			0
$218$	850983.			1.21277
$219$	345413.	−	598272.i	0.486663	−	0.842924i
$220$	−293835.	−	508937.i	−0.409305	−	0.708937i
$221$	−375258.	−	649965.i	−0.516831	−	0.895178i
$222$	42480.4	−	73578.2i	0.0578504	−	0.100200i
$223$	510190.			0.687021			0.343510	−	0.939149i	$-0.388384\pi$
$223$	510190.			0.687021			0.343510	+	0.939149i	$0.388384\pi$
$224$		0			0
$225$	34532.4			0.0454748
$226$	−449771.	+	779027.i	−0.585761	+	1.01457i
$227$	−519016.	−	898962.i	−0.668523	−	1.15791i	−0.978317	−	0.207112i	$-0.933594\pi$
$227$	−519016.	−	898962.i	−0.668523	−	1.15791i	0.309795	−	0.950803i	$-0.399740\pi$
$228$	−92155.0	−	159617.i	−0.117404	−	0.203349i
$229$	519245.	−	899359.i	0.654310	−	1.13330i	−0.327756	−	0.944762i	$-0.606292\pi$
$229$	519245.	−	899359.i	0.654310	−	1.13330i	0.982066	−	0.188536i	$-0.0603742\pi$
$230$	−1.13982e6			−1.42075
$231$		0			0
$232$	109825.			0.133962
$233$	−658726.	+	1.14095e6i	−0.794905	+	1.37682i	0.127994	+	0.991775i	$0.459146\pi$
$233$	−658726.	+	1.14095e6i	−0.794905	+	1.37682i	−0.922899	+	0.385041i	$0.874187\pi$
$234$	−67776.3	−	117392.i	−0.0809167	−	0.140152i
$235$	617846.	+	1.07014e6i	0.729812	+	1.26407i
$236$	−134599.	+	233133.i	−0.157312	+	0.272473i
$237$	−159582.			−0.184550
$238$		0			0
$239$	800669.			0.906689			0.453345	−	0.891335i	$-0.350231\pi$
$239$	800669.			0.906689			0.453345	+	0.891335i	$0.350231\pi$
$240$	68651.1	−	118907.i	0.0769342	−	0.133254i
$241$	−201154.	−	348408.i	−0.223093	−	0.386408i	0.732653	−	0.680602i	$-0.238282\pi$
$241$	−201154.	−	348408.i	−0.223093	−	0.386408i	−0.955745	+	0.294195i	$0.904949\pi$
$242$	−437641.	−	758016.i	−0.480374	−	0.832032i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−216435.			−0.232730
$245$		0			0
$246$	563035.			0.593196
$247$	−267743.	+	463745.i	−0.279239	+	0.483657i
$248$	−20567.1	−	35623.3i	−0.0212346	−	0.0367794i
$249$	−354810.	−	614549.i	−0.362658	−	0.628143i
$250$	−321644.	+	557104.i	−0.325481	+	0.563750i
$251$	−1.29078e6			−1.29320			−0.646601	−	0.762828i	$-0.723810\pi$
$251$	−1.29078e6			−1.29320			−0.646601	+	0.762828i	$0.723810\pi$
$252$		0			0
$253$	−2.94713e6			−2.89466
$254$	88054.4	−	152515.i	0.0856380	−	0.148329i
$255$	481066.	+	833231.i	0.463292	+	0.802444i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	882173.	−	1.52797e6i	0.833146	−	1.44305i	−0.0623853	−	0.998052i	$-0.519871\pi$
$257$	882173.	−	1.52797e6i	0.833146	−	1.44305i	0.895531	−	0.444999i	$-0.146796\pi$
$258$	−58989.9			−0.0551732
$259$		0			0
$260$	−398913.			−0.365969
$261$	−69498.9	+	120376.i	−0.0631505	+	0.109380i
$262$	782263.	+	1.35492e6i	0.704044	+	1.21944i
$263$	−213873.	−	370438.i	−0.190663	−	0.330237i	0.754807	−	0.655947i	$-0.227730\pi$
$263$	−213873.	−	370438.i	−0.190663	−	0.330237i	−0.945470	+	0.325709i	$0.894397\pi$
$264$	177505.	−	307448.i	0.156748	−	0.271495i
$265$	318699.			0.278783
$266$		0			0
$267$	667444.			0.572976
$268$	371868.	−	644094.i	0.316266	−	0.547788i
$269$	633453.	+	1.09717e6i	0.533744	+	0.924473i	0.999223	+	0.0394134i	$0.0125489\pi$
$269$	633453.	+	1.09717e6i	0.533744	+	0.924473i	−0.465479	+	0.885059i	$0.654118\pi$
$270$	86886.6	+	150492.i	0.0725343	+	0.125633i
$271$	156017.	−	270229.i	0.129047	−	0.223516i	−0.794260	−	0.607577i	$-0.792141\pi$
$271$	156017.	−	270229.i	0.129047	−	0.223516i	0.923308	+	0.384061i	$0.125475\pi$
$272$	459237.			0.376370
$273$		0			0
$274$	283929.			0.228472
$275$	131380.	−	227557.i	0.104761	−	0.181451i
$276$	−344281.	−	596313.i	−0.272045	−	0.471196i
$277$	839298.	+	1.45371e6i	0.657229	+	1.13835i	0.981330	+	0.192331i	$0.0616048\pi$
$277$	839298.	+	1.45371e6i	0.657229	+	1.13835i	−0.324101	+	0.946022i	$0.605062\pi$
$278$	−205528.	+	355986.i	−0.159500	+	0.276262i
$279$	52060.5			0.0400403
$280$		0			0
$281$	−765001.			−0.577958			−0.288979	−	0.957335i	$-0.593316\pi$
$281$	−765001.			−0.577958			−0.288979	+	0.957335i	$0.593316\pi$
$282$	−373240.	+	646470.i	−0.279489	+	0.484089i
$283$	42915.8	+	74332.4i	0.0318531	+	0.0551711i	0.881512	−	0.472161i	$-0.156526\pi$
$283$	42915.8	+	74332.4i	0.0318531	+	0.0551711i	−0.849659	+	0.527332i	$0.823192\pi$
$284$	26191.3	+	45364.6i	0.0192691	+	0.0333750i
$285$	343237.	−	594504.i	0.250312	−	0.433553i
$286$	−1.03143e6			−0.745634
$287$		0			0
$288$	82944.0			0.0589256
$289$	−899101.	+	1.55729e6i	−0.633234	+	1.09679i
$290$	204526.	+	354249.i	0.142808	+	0.247351i
$291$	−109621.	−	189869.i	−0.0758858	−	0.131438i
$292$	614067.	−	1.06360e6i	0.421462	−	0.729994i
$293$	−97784.7			−0.0665429			−0.0332715	−	0.999446i	$-0.510593\pi$
$293$	−97784.7			−0.0665429			−0.0332715	+	0.999446i	$0.510593\pi$
$294$		0			0
$295$	−1.00265e6			−0.670800
$296$	75520.7	−	130806.i	0.0500999	−	0.0867756i
$297$	224655.	+	389114.i	0.147783	+	0.255968i
$298$	452595.	+	783918.i	0.295236	+	0.511363i
$299$	−1.00026e6	+	1.73250e6i	−0.647047	+	1.12072i
$300$	61390.9			0.0393823
$301$		0			0
$302$	−2.19289e6			−1.38357
$303$	669509.	−	1.15962e6i	0.418938	−	0.725622i
$304$	−163831.	−	283764.i	−0.101675	−	0.176105i
$305$	−403063.	−	698125.i	−0.248098	−	0.429718i
$306$	−290611.	+	503353.i	−0.177422	+	0.307305i
$307$	−1.75546e6			−1.06303			−0.531514	−	0.847050i	$-0.678377\pi$
$307$	−1.75546e6			−1.06303			−0.531514	+	0.847050i	$0.678377\pi$
$308$		0			0
$309$	1.84965e6			1.10203
$310$	76603.5	−	132681.i	0.0452735	−	0.0784160i
$311$	901978.	+	1.56227e6i	0.528804	+	0.915916i	0.999436	+	0.0335861i	$0.0106928\pi$
$311$	901978.	+	1.56227e6i	0.528804	+	0.915916i	−0.470631	+	0.882330i	$0.655974\pi$
$312$	−120491.	−	208697.i	−0.0700759	−	0.121375i
$313$	−1.23215e6	+	2.13414e6i	−0.710888	+	1.23129i	0.253636	+	0.967300i	$0.418373\pi$
$313$	−1.23215e6	+	2.13414e6i	−0.710888	+	1.23129i	−0.964524	+	0.263994i	$0.914960\pi$
$314$	964576.			0.552093
$315$		0			0
$316$	−283702.			−0.159825
$317$	−826430.	+	1.43142e6i	−0.461911	+	0.800053i	−0.999056	−	0.0434366i	$-0.986169\pi$
$317$	−826430.	+	1.43142e6i	−0.461911	+	0.800053i	0.537145	+	0.843490i	$0.319503\pi$
$318$	96262.8	+	166732.i	0.0533815	+	0.0924595i
$319$	528824.	+	915950.i	0.290961	+	0.503959i
$320$	122046.	−	211391.i	0.0666270	−	0.115401i
$321$	−941199.			−0.509822
$322$		0			0
$323$	2.29606e6			1.22455
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	−89181.4	−	154467.i	−0.0468345	−	0.0811198i
$326$	−1.26180e6	−	2.18551e6i	−0.657579	−	1.13896i
$327$	−957356.	+	1.65819e6i	−0.495113	+	0.857560i
$328$	1.00095e6			0.513722
$329$		0			0
$330$	1.32226e6			0.668392
$331$	834072.	−	1.44465e6i	0.418440	−	0.724760i	−0.577343	−	0.816502i	$-0.695910\pi$
$331$	834072.	−	1.44465e6i	0.418440	−	0.724760i	0.995783	+	0.0917423i	$0.0292436\pi$
$332$	−630774.	−	1.09253e6i	−0.314071	−	0.543987i
$333$	95580.9	+	165551.i	0.0472346	+	0.0818128i
$334$	−478226.	+	828312.i	−0.234567	+	0.406282i
$335$	2.77009e6			1.34860
$336$		0			0
$337$	−524769.			−0.251706			−0.125853	−	0.992049i	$-0.540167\pi$
$337$	−524769.			−0.251706			−0.125853	+	0.992049i	$0.540167\pi$
$338$	392516.	−	679857.i	0.186881	−	0.323688i
$339$	−1.01199e6	−	1.75281e6i	−0.478272	−	0.828391i
$340$	855229.	+	1.48130e6i	0.401222	+	0.694937i
$341$	198067.	−	343061.i	0.0922413	−	0.159767i
$342$	414697.			0.191719
$343$		0			0
$344$	−104871.			−0.0477814
$345$	1.28230e6	−	2.22100e6i	0.580017	−	1.00462i
$346$	605878.	+	1.04941e6i	0.272079	+	0.471255i
$347$	−963184.	−	1.66828e6i	−0.429423	−	0.743783i	0.567399	−	0.823443i	$-0.307950\pi$
$347$	−963184.	−	1.66828e6i	−0.429423	−	0.743783i	−0.996822	+	0.0796604i	$0.974616\pi$
$348$	−123554.	+	214001.i	−0.0546899	+	0.0947257i
$349$	340342.			0.149573			0.0747864	−	0.997200i	$-0.476173\pi$
$349$	340342.			0.149573			0.0747864	+	0.997200i	$0.476173\pi$
$350$		0			0
$351$	304993.			0.132136
$352$	315565.	−	546574.i	0.135747	−	0.235121i
$353$	37395.6	+	64771.1i	0.0159729	+	0.0276659i	0.873901	−	0.486103i	$-0.161582\pi$
$353$	37395.6	+	64771.1i	0.0159729	+	0.0276659i	−0.857928	+	0.513769i	$0.828249\pi$
$354$	−302849.	−	524549.i	−0.128445	−	0.222473i
$355$	−97551.0	+	168963.i	−0.0410829	+	0.0711576i
$356$	1.18657e6			0.496212
$357$		0			0
$358$	−423958.			−0.174830
$359$	−1.20877e6	+	2.09365e6i	−0.495002	+	0.857368i	−0.999983	−	0.00576184i	$-0.998166\pi$
$359$	−1.20877e6	+	2.09365e6i	−0.495002	+	0.857368i	0.504982	+	0.863130i	$0.331499\pi$
$360$	154465.	+	267541.i	0.0628165	+	0.108801i
$361$	418939.	+	725624.i	0.169193	+	0.293051i
$362$	947454.	−	1.64104e6i	0.380003	−	0.658184i
$363$	1.96938e6			0.784447
$364$		0			0
$365$	4.57426e6			1.79717
$366$	243489.	−	421736.i	0.0950117	−	0.164565i
$367$	−80931.9	−	140178.i	−0.0313657	−	0.0543269i	0.849916	−	0.526917i	$-0.176652\pi$
$367$	−80931.9	−	140178.i	−0.0313657	−	0.0543269i	−0.881282	+	0.472591i	$0.843319\pi$
$368$	−612056.	−	1.06011e6i	−0.235598	−	0.408068i
$369$	−633415.	+	1.09711e6i	−0.242171	+	0.419453i
$370$	562563.			0.213632
$371$		0			0
$372$	92552.0			0.0346759
$373$	−38501.2	+	66686.1i	−0.0143286	+	0.0248178i	−0.873101	−	0.487540i	$-0.837894\pi$
$373$	−38501.2	+	66686.1i	−0.0143286	+	0.0248178i	0.858772	+	0.512358i	$0.171228\pi$
$374$	2.21129e6	+	3.83006e6i	0.817460	+	1.41588i
$375$	−723699.	−	1.25348e6i	−0.265754	−	0.460300i
$376$	−663537.	+	1.14928e6i	−0.242045	+	0.419234i
$377$	717936.			0.260155
$378$		0			0
$379$	−774165.			−0.276844			−0.138422	−	0.990373i	$-0.544203\pi$
$379$	−774165.			−0.276844			−0.138422	+	0.990373i	$0.544203\pi$
$380$	610199.	−	1.05690e6i	0.216777	−	0.375468i
$381$	198122.	+	343158.i	0.0699232	+	0.121110i
$382$	1.17563e6	+	2.03625e6i	0.412203	+	0.713956i
$383$	−1.81664e6	+	3.14651e6i	−0.632807	+	1.09605i	0.354168	+	0.935182i	$0.384764\pi$
$383$	−1.81664e6	+	3.14651e6i	−0.632807	+	1.09605i	−0.986975	+	0.160873i	$0.948569\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	−1.46744e6			−0.501295
$387$	66363.6	−	114945.i	0.0225244	−	0.0390133i
$388$	−194881.	−	337545.i	−0.0657190	−	0.113829i
$389$	1.25954e6	+	2.18158e6i	0.422024	+	0.730967i	0.996137	−	0.0878087i	$-0.0279864\pi$
$389$	1.25954e6	+	2.18158e6i	0.422024	+	0.730967i	−0.574113	+	0.818776i	$0.694653\pi$
$390$	448777.	−	777304.i	0.149406	−	0.258779i
$391$	8.57784e6			2.83750
$392$		0			0
$393$	−3.52019e6			−1.14970
$394$	−1.45494e6	+	2.52003e6i	−0.472178	+	0.817836i
$395$	−528333.	−	915099.i	−0.170379	−	0.295104i
$396$	399386.	+	691758.i	0.127984	+	0.221675i
$397$	−2.79639e6	+	4.84349e6i	−0.890474	+	1.54235i	−0.0511664	+	0.998690i	$0.516294\pi$
$397$	−2.79639e6	+	4.84349e6i	−0.890474	+	1.54235i	−0.839308	+	0.543656i	$0.817039\pi$
$398$	−939246.			−0.297216
$399$		0			0
$400$	109139.			0.0341061
$401$	95530.9	−	165464.i	0.0296676	−	0.0513859i	−0.850810	−	0.525473i	$-0.823888\pi$
$401$	95530.9	−	165464.i	0.0296676	−	0.0513859i	0.880478	+	0.474087i	$0.157222\pi$
$402$	836703.	+	1.44921e6i	0.258230	+	0.447267i
$403$	−134448.	−	232871.i	−0.0412376	−	0.0714256i
$404$	1.19024e6	−	2.06155e6i	0.362811	−	0.628407i
$405$	−390990.			−0.118448
$406$		0			0
$407$	1.45457e6			0.435260
$408$	−516642.	+	894850.i	−0.153652	+	0.266134i
$409$	−2.22902e6	−	3.86078e6i	−0.658880	−	1.14121i	−0.980906	−	0.194483i	$-0.937697\pi$
$409$	−2.22902e6	−	3.86078e6i	−0.658880	−	1.14121i	0.322026	−	0.946731i	$-0.395636\pi$
$410$	1.86405e6	+	3.22864e6i	0.547645	+	0.948548i
$411$	−319420.	+	553251.i	−0.0932733	+	0.161554i
$412$	3.28826e6			0.954383
$413$		0			0
$414$	1.54927e6			0.444248
$415$	2.34936e6	−	4.06920e6i	0.669620	−	1.15982i
$416$	−214206.	−	371016.i	−0.0606875	−	0.105114i
$417$	−462439.	−	800968.i	−0.130231	−	0.225567i
$418$	1.57774e6	−	2.73272e6i	0.441666	−	0.764988i
$419$	4.76120e6			1.32489			0.662447	−	0.749109i	$-0.269518\pi$
$419$	4.76120e6			1.32489			0.662447	+	0.749109i	$0.269518\pi$
$420$		0			0
$421$	−1.38498e6			−0.380835			−0.190418	−	0.981703i	$-0.560984\pi$
$421$	−1.38498e6			−0.380835			−0.190418	+	0.981703i	$0.560984\pi$
$422$	616099.	−	1.06711e6i	0.168411	−	0.291696i
$423$	−839789.	−	1.45456e6i	−0.228202	−	0.395257i
$424$	171134.	+	296413.i	0.0462297	+	0.0800722i
$425$	−382392.	+	662322.i	−0.102692	+	0.177868i
$426$	−117861.			−0.0314662
$427$		0			0
$428$	−1.67324e6			−0.441519
$429$	1.16036e6	−	2.00981e6i	0.304404	−	0.527243i
$430$	−195299.	−	338268.i	−0.0509365	−	0.0882246i
$431$	−2.27946e6	−	3.94813e6i	−0.591069	−	1.02376i	−0.994089	−	0.108570i	$-0.965373\pi$
$431$	−2.27946e6	−	3.94813e6i	−0.591069	−	1.02376i	0.403020	−	0.915191i	$-0.367960\pi$
$432$	−93312.0	+	161621.i	−0.0240563	+	0.0416667i
$433$	−6.00870e6			−1.54014			−0.770071	−	0.637958i	$-0.779779\pi$
$433$	−6.00870e6			−1.54014			−0.770071	+	0.637958i	$0.779779\pi$
$434$		0			0
$435$	−920366.			−0.233205
$436$	−1.70197e6	+	2.94789e6i	−0.428780	+	0.742669i
$437$	−3.06011e6	−	5.30027e6i	−0.766538	−	1.32768i
$438$	1.38165e6	+	2.39309e6i	0.344122	+	0.596038i
$439$	−280252.	+	485410.i	−0.0694044	+	0.120212i	−0.898639	−	0.438688i	$-0.855443\pi$
$439$	−280252.	+	485410.i	−0.0694044	+	0.120212i	0.829235	+	0.558900i	$0.188777\pi$
$440$	2.35068e6			0.578844
$441$		0			0
$442$	3.00206e6			0.730910
$443$	−1.67037e6	+	2.89317e6i	−0.404393	+	0.700429i	−0.994251	−	0.107078i	$-0.965850\pi$
$443$	−1.67037e6	+	2.89317e6i	−0.404393	+	0.700429i	0.589858	+	0.807507i	$0.299184\pi$
$444$	169922.	+	294313.i	0.0409064	+	0.0708519i
$445$	2.20972e6	+	3.82735e6i	0.528978	+	0.916217i
$446$	−1.02038e6	+	1.76735e6i	−0.242898	+	0.420713i
$447$	−2.03668e6			−0.482118
$448$		0			0
$449$	−6.47842e6			−1.51654			−0.758269	−	0.651942i	$-0.773955\pi$
$449$	−6.47842e6			−1.51654			−0.758269	+	0.651942i	$0.773955\pi$
$450$	−69064.8	+	119624.i	−0.0160778	+	0.0278475i
$451$	4.81972e6	+	8.34799e6i	1.11578	+	1.93259i
$452$	−1.79908e6	−	3.11611e6i	−0.414196	−	0.717408i
$453$	2.46701e6	−	4.27298e6i	0.564839	−	0.978330i
$454$	4.15213e6			0.945434
$455$		0			0
$456$	737240.			0.166034
$457$	−2.15569e6	+	3.73376e6i	−0.482831	+	0.836289i	−0.999806	−	0.0197123i	$-0.993725\pi$
$457$	−2.15569e6	+	3.73376e6i	−0.482831	+	0.836289i	0.516974	+	0.856001i	$0.327058\pi$
$458$	2.07698e6	+	3.59744e6i	0.462667	+	0.801363i
$459$	−653875.	−	1.13254e6i	−0.144865	−	0.250913i
$460$	2.27964e6	−	3.94845e6i	0.502310	−	0.870026i
$461$	−320951.			−0.0703374			−0.0351687	−	0.999381i	$-0.511197\pi$
$461$	−320951.			−0.0703374			−0.0351687	+	0.999381i	$0.511197\pi$
$462$		0			0
$463$	−3.14239e6			−0.681251			−0.340626	−	0.940199i	$-0.610639\pi$
$463$	−3.14239e6			−0.681251			−0.340626	+	0.940199i	$0.610639\pi$
$464$	−219651.	+	380446.i	−0.0473629	+	0.0820349i
$465$	172358.	+	298532.i	0.0369657	+	0.0640264i
$466$	−2.63491e6	−	4.56379e6i	−0.562083	−	0.973556i
$467$	−2.07293e6	+	3.59043e6i	−0.439839	+	0.761823i	−0.997677	−	0.0681271i	$-0.978298\pi$
$467$	−2.07293e6	+	3.59043e6i	−0.439839	+	0.761823i	0.557838	+	0.829950i	$0.311631\pi$
$468$	542210.			0.114433
$469$		0			0
$470$	−4.94277e6			−1.03211
$471$	−1.08515e6	+	1.87953e6i	−0.225391	+	0.390389i
$472$	−538397.	−	932532.i	−0.111237	−	0.192668i
$473$	−504967.	−	874629.i	−0.103779	−	0.179751i
$474$	319165.	−	552809.i	0.0652483	−	0.113013i
$475$	545667.			0.110967
$476$		0			0
$477$	−433183.			−0.0871716
$478$	−1.60134e6	+	2.77360e6i	−0.320563	+	0.555232i
$479$	128839.	+	223155.i	0.0256571	+	0.0444394i	0.878569	−	0.477616i	$-0.158499\pi$
$479$	128839.	+	223155.i	0.0256571	+	0.0444394i	−0.852912	+	0.522055i	$0.825166\pi$
$480$	274605.	+	475629.i	0.0544007	+	0.0942248i
$481$	493684.	−	855085.i	0.0972940	−	0.168518i
$482$	1.60923e6			0.315501
$483$		0			0
$484$	3.50113e6			0.679351
$485$	725848.	−	1.25721e6i	0.140117	−	0.242690i
$486$	−118098.	−	204552.i	−0.0226805	−	0.0392837i
$487$	−860165.	−	1.48985e6i	−0.164346	−	0.284656i	0.772077	−	0.635529i	$-0.219218\pi$
$487$	−860165.	−	1.48985e6i	−0.164346	−	0.284656i	−0.936423	+	0.350873i	$0.885885\pi$
$488$	432870.	−	749752.i	0.0822825	−	0.142518i
$489$	5.67812e6			1.07382
$490$		0			0
$491$	6.49101e6			1.21509			0.607546	−	0.794285i	$-0.292154\pi$
$491$	6.49101e6			1.21509			0.607546	+	0.794285i	$0.292154\pi$
$492$	−1.12607e6	+	1.95041e6i	−0.209726	+	0.363257i
$493$	−1.53918e6	−	2.66594e6i	−0.285215	−	0.494007i
$494$	−1.07097e6	−	1.85498e6i	−0.197452	−	0.341997i
$495$	−1.48754e6	+	2.57649e6i	−0.272870	+	0.472624i
$496$	164537.			0.0300302
$497$		0			0
$498$	2.83848e6			0.512876
$499$	−189816.	+	328770.i	−0.0341256	+	0.0591073i	−0.882584	−	0.470155i	$-0.844198\pi$
$499$	−189816.	+	328770.i	−0.0341256	+	0.0591073i	0.848458	+	0.529262i	$0.177531\pi$
$500$	−1.28658e6	−	2.22842e6i	−0.230150	−	0.398631i
$501$	−1.07601e6	−	1.86370e6i	−0.191523	−	0.331728i
$502$	2.58155e6	−	4.47138e6i	0.457216	−	0.791922i
$503$	−8.60340e6			−1.51618			−0.758089	−	0.652151i	$-0.773867\pi$
$503$	−8.60340e6			−1.51618			−0.758089	+	0.652151i	$0.773867\pi$
$504$		0			0
$505$	8.86624e6			1.54707
$506$	5.89426e6	−	1.02092e7i	1.02342	−	1.77261i
$507$	883160.	+	1.52968e6i	0.152588	+	0.264290i
$508$	352218.	+	610059.i	0.0605552	+	0.104885i
$509$	−517714.	+	896707.i	−0.0885718	+	0.153411i	−0.906908	−	0.421330i	$-0.861564\pi$
$509$	−517714.	+	896707.i	−0.0885718	+	0.153411i	0.818336	+	0.574740i	$0.194897\pi$
$510$	−3.84853e6			−0.655193
$511$		0			0
$512$	262144.			0.0441942
$513$	−466534.	+	808061.i	−0.0782691	+	0.135566i
$514$	3.52869e6	+	6.11188e6i	0.589123	+	1.02039i
$515$	6.12366e6	+	1.06065e7i	1.01740	+	1.76219i
$516$	117980.	−	204347.i	0.0195067	−	0.0337865i
$517$	−1.27801e7			−2.10284
$518$		0			0
$519$	−2.72645e6			−0.444303
$520$	797825.	−	1.38187e6i	0.129390	−	0.224109i
$521$	−3.21187e6	−	5.56312e6i	−0.518398	−	0.897891i	−0.999772	−	0.0213759i	$-0.993195\pi$
$521$	−3.21187e6	−	5.56312e6i	−0.518398	−	0.897891i	0.481374	−	0.876515i	$-0.340138\pi$
$522$	−277996.	−	481502.i	−0.0446541	−	0.0773432i
$523$	−4.03192e6	+	6.98349e6i	−0.644551	+	1.11640i	0.339854	+	0.940478i	$0.389622\pi$
$523$	−4.03192e6	+	6.98349e6i	−0.644551	+	1.11640i	−0.984405	+	0.175917i	$0.943711\pi$
$524$	−6.25811e6			−0.995668
$525$		0			0
$526$	1.71098e6			0.269638
$527$	−576488.	+	998506.i	−0.0904198	+	0.156612i
$528$	710020.	+	1.22979e6i	0.110837	+	0.191976i
$529$	−8.21408e6	−	1.42272e7i	−1.27620	−	2.21045i
$530$	−637399.	+	1.10401e6i	−0.0985647	+	0.170719i
$531$	1.36282e6			0.209750
$532$		0			0
$533$	6.54329e6			0.997649
$534$	−1.33489e6	+	2.31209e6i	−0.202578	+	0.350875i
$535$	−3.11605e6	−	5.39716e6i	−0.470674	−	0.815231i
$536$	1.48747e6	+	2.57638e6i	0.223633	+	0.387345i
$537$	476953.	−	826107.i	0.0713740	−	0.123623i
$538$	−5.06762e6			−0.754829
$539$		0			0
$540$	−695093.			−0.102579
$541$	4.31107e6	−	7.46699e6i	0.633274	−	1.09686i	−0.353604	−	0.935395i	$-0.615044\pi$
$541$	4.31107e6	−	7.46699e6i	0.633274	−	1.09686i	0.986878	−	0.161467i	$-0.0516226\pi$
$542$	624068.	+	1.08092e6i	0.0912502	+	0.158050i
$543$	2.13177e6	+	3.69234e6i	0.310271	+	0.537405i
$544$	−918474.	+	1.59084e6i	−0.133067	+	0.230478i
$545$	−1.26782e7			−1.82837
$546$		0			0
$547$	−3.51266e6			−0.501958			−0.250979	−	0.967993i	$-0.580753\pi$
$547$	−3.51266e6			−0.501958			−0.250979	+	0.967993i	$0.580753\pi$
$548$	−567857.	+	983558.i	−0.0807770	+	0.139910i
$549$	547851.	+	948905.i	0.0775767	+	0.134367i
$550$	525521.	+	910229.i	0.0740770	+	0.128305i
$551$	−1.09819e6	+	1.90213e6i	−0.154099	+	0.266907i
$552$	2.75425e6			0.384730
$553$		0			0
$554$	−6.71438e6			−0.929462
$555$	−632884.	+	1.09619e6i	−0.0872150	+	0.151061i
$556$	−822114.	−	1.42394e6i	−0.112783	−	0.195347i
$557$	6.10915e6	+	1.05814e7i	0.834340	+	1.44512i	0.894567	+	0.446934i	$0.147484\pi$
$557$	6.10915e6	+	1.05814e7i	0.834340	+	1.44512i	−0.0602274	+	0.998185i	$0.519183\pi$
$558$	−104121.	+	180343.i	−0.0141564	+	0.0245196i
$559$	−685548.			−0.0927915
$560$		0			0
$561$	−9.95080e6			−1.33491
$562$	1.53000e6	−	2.65004e6i	0.204339	−	0.353925i
$563$	−743804.	−	1.28831e6i	−0.0988980	−	0.171296i	0.812331	−	0.583197i	$-0.198198\pi$
$563$	−743804.	−	1.28831e6i	−0.0988980	−	0.171296i	−0.911229	+	0.411901i	$0.864865\pi$
$564$	−1.49296e6	−	2.58588e6i	−0.197629	−	0.342303i
$565$	6.70080e6	−	1.16061e7i	0.883092	−	1.52956i
$566$	−343327.			−0.0450471
$567$		0			0
$568$	−209530.			−0.0272506
$569$	−2.91751e6	+	5.05327e6i	−0.377773	+	0.654322i	−0.990738	−	0.135788i	$-0.956643\pi$
$569$	−2.91751e6	+	5.05327e6i	−0.377773	+	0.654322i	0.612965	+	0.790110i	$0.289977\pi$
$570$	1.37295e6	+	2.37802e6i	0.176997	+	0.306568i
$571$	−4.91614e6	−	8.51500e6i	−0.631006	−	1.09294i	−0.987346	−	0.158579i	$-0.949309\pi$
$571$	−4.91614e6	−	8.51500e6i	−0.631006	−	1.09294i	0.356340	−	0.934356i	$-0.384024\pi$
$572$	2.06287e6	−	3.57299e6i	0.263621	−	0.456606i
$573$	−5.29032e6			−0.673125
$574$		0			0
$575$	2.03856e6			0.257130
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	−162003.	−	280597.i	−0.0202574	−	0.0350868i	0.855719	−	0.517441i	$-0.173115\pi$
$577$	−162003.	−	280597.i	−0.0202574	−	0.0350868i	−0.875976	+	0.482354i	$0.839782\pi$
$578$	−3.59640e6	−	6.22916e6i	−0.447764	−	0.775550i
$579$	1.65087e6	−	2.85940e6i	0.204653	−	0.354469i
$580$	−1.63621e6			−0.201961
$581$		0			0
$582$	876966.			0.107319
$583$	−1.64806e6	+	2.85453e6i	−0.200818	+	0.347827i
$584$	2.45627e6	+	4.25438e6i	0.298019	+	0.516184i
$585$	1.00975e6	+	1.74893e6i	0.121990	+	0.211292i
$586$	195569.	−	338736.i	0.0235265	−	0.0407491i
$587$	4.27646e6			0.512258			0.256129	−	0.966643i	$-0.417553\pi$
$587$	4.27646e6			0.512258			0.256129	+	0.966643i	$0.417553\pi$
$588$		0			0
$589$	822639.			0.0977060
$590$	2.00530e6	−	3.47327e6i	0.237164	−	0.410780i
$591$	−3.27362e6	−	5.67008e6i	−0.385531	−	0.667760i
$592$	302083.	+	523223.i	0.0354260	+	0.0613596i
$593$	7.94651e6	−	1.37638e7i	0.927982	−	1.60731i	0.141289	−	0.989968i	$-0.454875\pi$
$593$	7.94651e6	−	1.37638e7i	0.927982	−	1.60731i	0.786694	−	0.617344i	$-0.211791\pi$
$594$	−1.79724e6			−0.208997
$595$		0			0
$596$	−3.62076e6			−0.417527
$597$	1.05665e6	−	1.83018e6i	0.121338	−	0.210163i
$598$	−4.00105e6	−	6.93002e6i	−0.457531	−	0.792467i
$599$	8.75306e6	+	1.51608e7i	0.996766	+	1.72645i	0.567979	+	0.823043i	$0.307726\pi$
$599$	8.75306e6	+	1.51608e7i	0.996766	+	1.72645i	0.428787	+	0.903406i	$0.358941\pi$
$600$	−122782.	+	212664.i	−0.0139237	+	0.0241166i
$601$	−5.98914e6			−0.676361			−0.338180	−	0.941081i	$-0.609811\pi$
$601$	−5.98914e6			−0.676361			−0.338180	+	0.941081i	$0.609811\pi$
$602$		0			0
$603$	−3.76516e6			−0.421687
$604$	4.38579e6	−	7.59641e6i	0.489165	−	0.847259i
$605$	6.52008e6	+	1.12931e7i	0.724210	+	1.25437i
$606$	2.67804e6	+	4.63850e6i	0.296234	+	0.513093i
$607$	1.63750e6	−	2.83624e6i	0.180389	−	0.312443i	−0.761624	−	0.648019i	$-0.775598\pi$
$607$	1.63750e6	−	2.83624e6i	0.180389	−	0.312443i	0.942013	+	0.335576i	$0.108931\pi$
$608$	1.31065e6			0.143790
$609$		0			0
$610$	3.22450e6			0.350863
$611$	−4.33758e6	+	7.51291e6i	−0.470051	+	0.814152i
$612$	−1.16244e6	−	2.01341e6i	−0.125457	−	0.217297i
$613$	3.81057e6	+	6.60010e6i	0.409580	+	0.709414i	0.994843	−	0.101430i	$-0.0323418\pi$
$613$	3.81057e6	+	6.60010e6i	0.409580	+	0.709414i	−0.585262	+	0.810844i	$0.699009\pi$
$614$	3.51092e6	−	6.08109e6i	0.375837	−	0.650969i
$615$	−8.38824e6			−0.894300
$616$		0			0
$617$	1.28554e7			1.35948			0.679741	−	0.733453i	$-0.262092\pi$
$617$	1.28554e7			1.35948			0.679741	+	0.733453i	$0.262092\pi$
$618$	−3.69929e6	+	6.40736e6i	−0.389625	+	0.674851i
$619$	4.26175e6	+	7.38157e6i	0.447055	+	0.774323i	0.998193	−	0.0600919i	$-0.0191394\pi$
$619$	4.26175e6	+	7.38157e6i	0.447055	+	0.774323i	−0.551138	+	0.834414i	$0.685806\pi$
$620$	306414.	+	530724.i	0.0320132	+	0.0554485i
$621$	−1.74292e6	+	3.01883e6i	−0.181363	+	0.314131i
$622$	−7.21582e6			−0.747842
$623$		0			0
$624$	963929.			0.0991023
$625$	5.45807e6	−	9.45365e6i	0.558906	−	0.968054i
$626$	−4.92858e6	−	8.53655e6i	−0.502674	−	0.870656i
$627$	3.54991e6	+	6.14862e6i	0.360619	+	0.624610i
$628$	−1.92915e6	+	3.34139e6i	−0.195194	+	0.338087i
$629$	−4.23363e6			−0.426664
$630$		0			0
$631$	−1.37373e7			−1.37350			−0.686750	−	0.726894i	$-0.740963\pi$
$631$	−1.37373e7			−1.37350			−0.686750	+	0.726894i	$0.740963\pi$
$632$	567404.	−	982772.i	0.0565067	−	0.0978724i
$633$	1.38622e6	+	2.40101e6i	0.137507	+	0.238169i
$634$	−3.30572e6	−	5.72568e6i	−0.326620	−	0.565723i
$635$	−1.31186e6	+	2.27220e6i	−0.129108	+	0.223621i
$636$	−770102.			−0.0754928
$637$		0			0
$638$	−4.23059e6			−0.411481
$639$	132593.	−	229658.i	0.0128460	−	0.0222500i
$640$	488186.	+	845563.i	0.0471124	+	0.0816011i
$641$	2.52233e6	+	4.36881e6i	0.242470	+	0.419970i	0.961417	−	0.275095i	$-0.0887092\pi$
$641$	2.52233e6	+	4.36881e6i	0.242470	+	0.419970i	−0.718948	+	0.695064i	$0.755376\pi$
$642$	1.88240e6	−	3.26041e6i	0.180249	−	0.312201i
$643$	9.94759e6			0.948835			0.474417	−	0.880300i	$-0.342659\pi$
$643$	9.94759e6			0.948835			0.474417	+	0.880300i	$0.342659\pi$
$644$		0			0
$645$	878846.			0.0831790
$646$	−4.59212e6	+	7.95379e6i	−0.432944	+	0.749881i
$647$	−631379.	−	1.09358e6i	−0.0592966	−	0.102705i	0.834853	−	0.550473i	$-0.185552\pi$
$647$	−631379.	−	1.09358e6i	−0.0592966	−	0.102705i	−0.894150	+	0.447768i	$0.852219\pi$
$648$	−209952.	−	363648.i	−0.0196419	−	0.0340207i
$649$	5.18491e6	−	8.98053e6i	0.483203	−	0.836932i
$650$	713451.			0.0662340
$651$		0			0
$652$	1.00944e7			0.929957
$653$	6.40736e6	−	1.10979e7i	0.588026	−	1.01849i	−0.406465	−	0.913666i	$-0.633239\pi$
$653$	6.40736e6	−	1.10979e7i	0.588026	−	1.01849i	0.994491	−	0.104824i	$-0.0334279\pi$
$654$	−3.82942e6	−	6.63276e6i	−0.350098	−	0.606387i
$655$	−1.16544e7	−	2.01859e7i	−1.06141	−	1.83842i
$656$	−2.00190e6	+	3.46740e6i	−0.181628	+	0.314589i
$657$	−6.21743e6			−0.561950
$658$		0			0
$659$	−3.81355e6			−0.342071			−0.171035	−	0.985265i	$-0.554711\pi$
$659$	−3.81355e6			−0.342071			−0.171035	+	0.985265i	$0.554711\pi$
$660$	−2.64451e6	+	4.58043e6i	−0.236312	+	0.409305i
$661$	−8.31221e6	−	1.43972e7i	−0.739968	−	1.28166i	−0.952509	−	0.304510i	$-0.901507\pi$
$661$	−8.31221e6	−	1.43972e7i	−0.739968	−	1.28166i	0.212541	−	0.977152i	$-0.431826\pi$
$662$	3.33629e6	+	5.77862e6i	0.295882	+	0.512483i
$663$	−3.37732e6	+	5.84969e6i	−0.298393	+	0.516831i
$664$	5.04619e6			0.444164
$665$		0			0
$666$	−764647.			−0.0667999
$667$	−4.10274e6	+	7.10615e6i	−0.357075	+	0.618472i
$668$	−1.91290e6	−	3.31325e6i	−0.165864	−	0.287285i
$669$	−2.29586e6	−	3.97654e6i	−0.198326	−	0.343510i
$670$	−5.54018e6	+	9.59588e6i	−0.476801	+	0.825843i
$671$	8.33730e6			0.714857
$672$		0			0
$673$	1.76139e7			1.49905			0.749527	−	0.661974i	$-0.230281\pi$
$673$	1.76139e7			1.49905			0.749527	+	0.661974i	$0.230281\pi$
$674$	1.04954e6	−	1.81785e6i	0.0889916	−	0.154138i
$675$	−155396.	−	269153.i	−0.0131274	−	0.0227374i
$676$	1.57006e6	+	2.71943e6i	0.132145	+	0.228882i
$677$	8.92151e6	−	1.54525e7i	0.748112	−	1.29577i	−0.200615	−	0.979670i	$-0.564294\pi$
$677$	8.92151e6	−	1.54525e7i	0.748112	−	1.29577i	0.948727	−	0.316098i	$-0.102373\pi$
$678$	8.09588e6			0.676379
$679$		0			0
$680$	−6.84183e6			−0.567414
$681$	−4.67114e6	+	8.09066e6i	−0.385972	+	0.668523i
$682$	792267.	+	1.37225e6i	0.0652244	+	0.112972i
$683$	−7.07658e6	−	1.22570e7i	−0.580459	−	1.00538i	−0.995425	−	0.0955475i	$-0.969540\pi$
$683$	−7.07658e6	−	1.22570e7i	−0.580459	−	1.00538i	0.414966	−	0.909837i	$-0.363794\pi$
$684$	−829395.	+	1.43655e6i	−0.0677830	+	0.117404i
$685$	−4.23004e6			−0.344444
$686$		0			0
$687$	−9.34641e6			−0.755532
$688$	209742.	−	363283.i	0.0168933	−	0.0292600i
$689$	1.11871e6	+	1.93767e6i	0.0897781	+	0.155500i
$690$	5.12919e6	+	8.88402e6i	0.410134	+	0.710373i
$691$	−1.11267e6	+	1.92721e6i	−0.0886487	+	0.153544i	−0.906940	−	0.421259i	$-0.861588\pi$
$691$	−1.11267e6	+	1.92721e6i	−0.0886487	+	0.153544i	0.818291	+	0.574803i	$0.194922\pi$
$692$	−4.84703e6			−0.384778
$693$		0			0
$694$	7.70547e6			0.607296
$695$	3.06201e6	−	5.30357e6i	0.240461	−	0.416491i
$696$	−494214.	−	856004.i	−0.0386716	−	0.0669812i
$697$	−1.40281e7	−	2.42975e7i	−1.09375	−	1.89443i
$698$	−680685.	+	1.17898e6i	−0.0528819	+	0.0915942i
$699$	1.18571e7			0.917877
$700$		0			0
$701$	−4.49378e6			−0.345396			−0.172698	−	0.984975i	$-0.555248\pi$
$701$	−4.49378e6			−0.345396			−0.172698	+	0.984975i	$0.555248\pi$
$702$	−609986.	+	1.05653e6i	−0.0467173	+	0.0809167i
$703$	1.51033e6	+	2.61597e6i	0.115261	+	0.199639i
$704$	1.26226e6	+	2.18630e6i	0.0959879	+	0.166256i
$705$	5.56062e6	−	9.63127e6i	0.421357	−	0.729812i
$706$	−299165.			−0.0225891
$707$		0			0
$708$	2.42279e6			0.181649
$709$	7.71160e6	−	1.33569e7i	0.576141	−	0.997906i	−0.419775	−	0.907628i	$-0.637891\pi$
$709$	7.71160e6	−	1.33569e7i	0.576141	−	0.997906i	0.995917	−	0.0902780i	$-0.0287756\pi$
$710$	−390204.	−	675853.i	−0.0290500	−	0.0503160i
$711$	718120.	+	1.24382e6i	0.0532750	+	0.0922750i
$712$	−2.37313e6	+	4.11039e6i	−0.175437	+	0.303867i
$713$	3.07329e6			0.226402
$714$		0			0
$715$	1.53665e7			1.12412
$716$	847917.	−	1.46863e6i	0.0618117	−	0.107061i
$717$	−3.60301e6	−	6.24060e6i	−0.261739	−	0.453345i
$718$	−4.83507e6	−	8.37459e6i	−0.350019	−	0.606251i
$719$	5.36378e6	−	9.29034e6i	0.386945	−	0.670208i	−0.605092	−	0.796155i	$-0.706864\pi$
$719$	5.36378e6	−	9.29034e6i	0.386945	−	0.670208i	0.992037	+	0.125947i	$0.0401971\pi$
$720$	−1.23572e6			−0.0888360
$721$		0			0
$722$	−3.35151e6			−0.239275
$723$	−1.81038e6	+	3.13567e6i	−0.128803	+	0.223093i
$724$	3.78982e6	+	6.56415e6i	0.268703	+	0.465406i
$725$	−365792.	−	633571.i	−0.0258458	−	0.0447662i
$726$	−3.93877e6	+	6.82214e6i	−0.277344	+	0.480374i
$727$	2.05652e7			1.44310			0.721551	−	0.692362i	$-0.243430\pi$
$727$	2.05652e7			1.44310			0.721551	+	0.692362i	$0.243430\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−9.14853e6	+	1.58457e7i	−0.635395	+	1.10054i
$731$	1.46975e6	+	2.54567e6i	0.101730	+	0.176201i
$732$	973957.	+	1.68694e6i	0.0671834	+	0.116365i
$733$	−1.64661e6	+	2.85201e6i	−0.113196	+	0.196061i	−0.917057	−	0.398756i	$-0.869442\pi$
$733$	−1.64661e6	+	2.85201e6i	−0.113196	+	0.196061i	0.803861	+	0.594817i	$0.202775\pi$
$734$	647455.			0.0443578
$735$		0			0
$736$	4.89645e6			0.333186
$737$	−1.43248e7	+	2.48112e7i	−0.971445	+	1.68259i
$738$	−2.53366e6	−	4.38843e6i	−0.171241	−	0.296598i
$739$	3.85884e6	+	6.68370e6i	0.259923	+	0.450200i	0.966221	−	0.257714i	$-0.0829694\pi$
$739$	3.85884e6	+	6.68370e6i	0.259923	+	0.450200i	−0.706298	+	0.707915i	$0.749636\pi$
$740$	−1.12513e6	+	1.94878e6i	−0.0755304	+	0.130823i
$741$	4.81938e6			0.322438
$742$		0			0
$743$	−8.33553e6			−0.553938			−0.276969	−	0.960879i	$-0.589330\pi$
$743$	−8.33553e6			−0.553938			−0.276969	+	0.960879i	$0.589330\pi$
$744$	−185104.	+	320609.i	−0.0122598	+	0.0212346i
$745$	−6.74287e6	−	1.16790e7i	−0.445097	−	0.770930i
$746$	−154005.	−	266744.i	−0.0101318	−	0.0175488i
$747$	−3.19329e6	+	5.53094e6i	−0.209381	+	0.362658i
$748$	−1.76903e7			−1.15606
$749$		0			0
$750$	5.78960e6			0.375833
$751$	9.03469e6	−	1.56485e7i	0.584539	−	1.01245i	−0.410394	−	0.911908i	$-0.634609\pi$
$751$	9.03469e6	−	1.56485e7i	0.584539	−	1.01245i	0.994933	−	0.100543i	$-0.0320580\pi$
$752$	−2.65415e6	−	4.59712e6i	−0.171151	−	0.296443i
$753$	5.80849e6	+	1.00606e7i	0.373316	+	0.646601i
$754$	−1.43587e6	+	2.48700e6i	−0.0919787	+	0.159312i
$755$	3.26703e7			2.08586
$756$		0			0
$757$	−8.13311e6			−0.515842			−0.257921	−	0.966166i	$-0.583037\pi$
$757$	−8.13311e6			−0.515842			−0.257921	+	0.966166i	$0.583037\pi$
$758$	1.54833e6	−	2.68179e6i	0.0978792	−	0.169532i
$759$	1.32621e7	+	2.29706e7i	0.835617	+	1.44733i
$760$	2.44080e6	+	4.22758e6i	0.153284	+	0.265496i
$761$	−1.00845e6	+	1.74669e6i	−0.0631239	+	0.109334i	−0.895860	−	0.444336i	$-0.853440\pi$
$761$	−1.00845e6	+	1.74669e6i	−0.0631239	+	0.109334i	0.832736	+	0.553670i	$0.186773\pi$
$762$	−1.58498e6			−0.0988863
$763$		0			0
$764$	−9.40501e6			−0.582943
$765$	4.32960e6	−	7.49908e6i	0.267481	−	0.463292i
$766$	−7.26655e6	−	1.25860e7i	−0.447462	−	0.775028i
$767$	−3.51954e6	−	6.09602e6i	−0.216022	−	0.374160i
$768$	−294912.	+	510803.i	−0.0180422	+	0.0312500i
$769$	1.18971e7			0.725478			0.362739	−	0.931891i	$-0.381842\pi$
$769$	1.18971e7			0.725478			0.362739	+	0.931891i	$0.381842\pi$
$770$		0			0

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(29.7965 - 51.6091i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(119.186 + 206.436i) q^{10} +(308.169 + 533.764i) q^{11} +(-72.0000 + 124.708i) q^{12} +418.372 q^{13} -536.337 q^{15} +(-128.000 + 221.703i) q^{16} +(-896.948 - 1553.56i) q^{17} +(-162.000 - 280.592i) q^{18} +(-639.965 + 1108.45i) q^{19} -953.488 q^{20} -2465.35 q^{22} +(-2390.84 + 4141.06i) q^{23} +(-288.000 - 498.831i) q^{24} +(-213.163 - 369.209i) q^{25} +(-836.744 + 1449.28i) q^{26} +729.000 q^{27} +1716.02 q^{29} +(1072.67 - 1857.93i) q^{30} +(-321.361 - 556.613i) q^{31} +(-512.000 - 886.810i) q^{32} +(2773.52 - 4803.87i) q^{33} +7175.58 q^{34} +1296.00 q^{36} +(1180.01 - 2043.84i) q^{37} +(-2559.86 - 4433.81i) q^{38} +(-1882.67 - 3260.89i) q^{39} +(1906.98 - 3302.98i) q^{40} +15639.9 q^{41} -1638.61 q^{43} +(4930.70 - 8540.22i) q^{44} +(2413.52 + 4180.33i) q^{45} +(-9563.37 - 16564.2i) q^{46} +(-10367.8 + 17957.5i) q^{47} +2304.00 q^{48} +1705.30 q^{50} +(-8072.53 + 13982.0i) q^{51} +(-3346.98 - 5797.13i) q^{52} +(2673.97 + 4631.45i) q^{53} +(-1458.00 + 2525.33i) q^{54} +36729.4 q^{55} +11519.4 q^{57} +(-3432.04 + 5944.48i) q^{58} +(-8412.46 - 14570.8i) q^{59} +(4290.70 + 7431.70i) q^{60} +(6763.59 - 11714.9i) q^{61} +2570.89 q^{62} +4096.00 q^{64} +(12466.0 - 21591.8i) q^{65} +(11094.1 + 19215.5i) q^{66} +(23241.8 + 40255.9i) q^{67} +(-14351.2 + 24856.9i) q^{68} +43035.2 q^{69} -3273.91 q^{71} +(-2592.00 + 4489.48i) q^{72} +(38379.2 + 66474.7i) q^{73} +(4720.04 + 8175.36i) q^{74} +(-1918.47 + 3322.88i) q^{75} +20478.9 q^{76} +15061.4 q^{78} +(8865.69 - 15355.8i) q^{79} +(7627.90 + 13211.9i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-31279.7 + 54178.1i) q^{82} +78846.7 q^{83} -106904. q^{85} +(3277.22 - 5676.30i) q^{86} +(-7722.10 - 13375.1i) q^{87} +(19722.8 + 34160.9i) q^{88} +(-37080.2 + 64224.8i) q^{89} -19308.1 q^{90} +76507.0 q^{92} +(-2892.25 + 5009.52i) q^{93} +(-41471.1 - 71830.0i) q^{94} +(38137.4 + 66056.0i) q^{95} +(-4608.00 + 7981.29i) q^{96} +24360.2 q^{97} -49923.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} - 18 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} - 72 q^{10} - 2 q^{11} - 288 q^{12} + 576 q^{13} + 324 q^{15} - 512 q^{16} - 1530 q^{17} - 648 q^{18} - 1188 q^{19} + 576 q^{20}+ \cdots + 324 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 - 18 * q^5 + 144 * q^6 + 256 * q^8 - 162 * q^9 - 72 * q^10 - 2 * q^11 - 288 * q^12 + 576 * q^13 + 324 * q^15 - 512 * q^16 - 1530 * q^17 - 648 * q^18 - 1188 * q^19 + 576 * q^20 + 16 * q^22 - 3390 * q^23 - 1152 * q^24 - 3322 * q^25 - 1152 * q^26 + 2916 * q^27 - 7952 * q^29 - 648 * q^30 - 7596 * q^31 - 2048 * q^32 - 18 * q^33 + 12240 * q^34 + 5184 * q^36 - 2688 * q^37 - 4752 * q^38 - 2592 * q^39 - 1152 * q^40 + 73260 * q^41 - 46064 * q^43 - 32 * q^44 - 1458 * q^45 - 13560 * q^46 - 864 * q^47 + 9216 * q^48 + 26576 * q^50 - 13770 * q^51 - 4608 * q^52 + 32920 * q^53 - 5832 * q^54 + 169416 * q^55 + 21384 * q^57 + 15904 * q^58 + 26712 * q^59 - 2592 * q^60 - 20412 * q^61 + 60768 * q^62 + 16384 * q^64 + 35048 * q^65 - 72 * q^66 + 36172 * q^67 - 24480 * q^68 + 61020 * q^69 + 147412 * q^71 - 10368 * q^72 + 74772 * q^73 - 10752 * q^74 - 29898 * q^75 + 38016 * q^76 + 20736 * q^78 + 23116 * q^79 - 4608 * q^80 - 13122 * q^81 - 146520 * q^82 + 295632 * q^83 - 254760 * q^85 + 92128 * q^86 + 35784 * q^87 - 128 * q^88 - 164646 * q^89 + 11664 * q^90 + 108480 * q^92 - 68364 * q^93 - 3456 * q^94 + 83408 * q^95 - 18432 * q^96 + 324072 * q^97 + 324 * q^99

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