LMFDB - Embedded newform 294.6.e.w.67.1

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			67.1
Root			$-16.8983 - 29.2686i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.6.e.w.79.1

$q$-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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.999257	−	0.0385528i	$-0.987725\pi$
$5$	−29.7965	−	51.6091i	−0.533016	−	0.923211i	0.466241	−	0.884658i	$-0.345608\pi$
$6$	−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	−0.170795	−	0.985307i	$-0.554633\pi$
$11$	308.169	−	533.764i	0.767903	−	1.33005i	0.938698	−	0.344741i	$-0.112033\pi$
$12$	72.0000	+	124.708i	0.144338	+	0.250000i
$13$	−418.372			−0.686601			−0.343300	−	0.939226i	$-0.611545\pi$
$13$	−418.372			−0.686601			−0.343300	+	0.939226i	$0.611545\pi$
$14$		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	−0.193751	−	0.981051i	$-0.562065\pi$
$17$	896.948	−	1553.56i	0.752740	−	1.30378i	0.946490	−	0.322732i	$-0.104601\pi$
$18$	−162.000	+	280.592i	−0.117851	+	0.204124i
$19$	639.965	+	1108.45i	0.406698	+	0.704422i	0.994517	−	0.104570i	$-0.0333467\pi$
$19$	639.965	+	1108.45i	0.406698	+	0.704422i	−0.587819	+	0.808992i	$0.700013\pi$
$20$	953.488			0.533016
$21$		0			0
$22$	−2465.35			−1.08598
$23$	−2390.84	−	4141.06i	−0.942392	−	1.63227i	−0.760892	−	0.648879i	$-0.775238\pi$
$23$	−2390.84	−	4141.06i	−0.942392	−	1.63227i	−0.181500	−	0.983391i	$-0.558095\pi$
$24$	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	$-0.814204\pi$
$31$	321.361	−	556.613i	0.0600605	−	0.104028i	0.894492	+	0.447083i	$0.147537\pi$
$32$	−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	0.928138	−	0.372235i	$-0.121409\pi$
$37$	1180.01	+	2043.84i	0.141704	+	0.245438i	−0.786434	+	0.617674i	$0.788075\pi$
$38$	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	$-0.758860\pi$
$41$	−15639.9			−1.45303			−0.726513	+	0.687152i	$0.758860\pi$
$42$		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	0.973561	+	0.228429i	$0.0733589\pi$
$47$	10367.8	+	17957.5i	0.684606	+	1.18577i	−0.288955	+	0.957343i	$0.593308\pi$
$48$	−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	−0.793211	−	0.608946i	$-0.791592\pi$
$53$	2673.97	−	4631.45i	0.130757	−	0.226478i	0.923969	+	0.382468i	$0.124926\pi$
$54$	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	$-0.731455\pi$
$59$	8412.46	−	14570.8i	0.314625	−	0.544946i	0.979358	+	0.202135i	$0.0647880\pi$
$60$	4290.70	−	7431.70i	0.153868	−	0.266508i
$61$	−6763.59	−	11714.9i	−0.232730	−	0.403100i	0.725880	−	0.687821i	$-0.241433\pi$
$61$	−6763.59	−	11714.9i	−0.232730	−	0.403100i	−0.958611	+	0.284720i	$0.908099\pi$
$62$	−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	−0.354501	−	0.935055i	$-0.615349\pi$
$67$	23241.8	−	40255.9i	0.632531	−	1.09558i	0.987033	−	0.160520i	$-0.0513173\pi$
$68$	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	0.0444870	+	0.999010i	$0.485835\pi$
$73$	−38379.2	+	66474.7i	−0.842924	+	1.45999i	−0.887412	+	0.460978i	$0.847499\pi$
$74$	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	0.934805	−	0.355160i	$-0.115574\pi$
$79$	8865.69	+	15355.8i	0.159825	+	0.276825i	−0.774980	+	0.631985i	$0.782240\pi$
$80$	−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	$-0.716185\pi$
$83$	−78846.7			−1.25629			−0.628143	+	0.778098i	$0.716185\pi$
$84$		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	$-0.00139055\pi$
$89$	37080.2	+	64224.8i	0.496212	+	0.859464i	−0.503778	+	0.863833i	$0.668057\pi$
$90$	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	$-0.541959\pi$
$97$	−24360.2			−0.262876			−0.131438	+	0.991324i	$0.541959\pi$
$98$		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	0.233095	+	0.972454i	$0.425115\pi$
$101$	−74389.9	+	128847.i	−0.725622	+	1.25681i	−0.958717	+	0.284361i	$0.908219\pi$
$102$	−32290.1	+	55928.1i	−0.307305	+	0.532267i
$103$	102758.	+	177982.i	0.954383	+	1.65304i	0.735773	+	0.677228i	$0.236819\pi$
$103$	102758.	+	177982.i	0.954383	+	1.65304i	0.218610	+	0.975812i	$0.429848\pi$
$104$	−26775.8			−0.242750
$105$		0			0
$106$	−21391.7			−0.184919
$107$	52288.8	+	90566.9i	0.441519	+	0.764734i	0.997802	−	0.0662591i	$-0.0211064\pi$
$107$	52288.8	+	90566.9i	0.441519	+	0.764734i	−0.556283	+	0.830993i	$0.687773\pi$
$108$	5832.00	−	10101.3i	0.0481125	−	0.0833333i
$109$	−106373.	+	184243.i	−0.857560	+	1.48534i	0.0166886	+	0.999861i	$0.494688\pi$
$109$	−106373.	+	184243.i	−0.857560	+	1.48534i	−0.874249	+	0.485478i	$0.838646\pi$
$110$	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	−0.578353	−	0.815787i	$-0.696304\pi$
$131$	−195566.	−	338730.i	−0.995668	−	1.72455i	−0.417316	−	0.908762i	$-0.637029\pi$
$132$	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	−0.935426	−	0.353522i	$-0.884984\pi$
$137$	−35491.1	+	61472.4i	−0.161554	+	0.279820i	0.773872	+	0.633342i	$0.218317\pi$
$138$	86070.3	+	149078.i	0.384730	+	0.666371i
$139$	−102764.			−0.451133			−0.225567	−	0.974228i	$-0.572423\pi$
$139$	−102764.			−0.451133			−0.225567	+	0.974228i	$0.572423\pi$
$140$		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	0.995690	−	0.0927438i	$-0.0295637\pi$
$149$	113149.	+	195979.i	0.417527	+	0.723177i	−0.578163	+	0.815921i	$0.696230\pi$
$150$	7673.87	−	13291.5i	0.0278475	−	0.0482333i
$151$	274112.	−	474776.i	0.978330	−	1.69452i	0.309854	−	0.950784i	$-0.399720\pi$
$151$	274112.	−	474776.i	0.978330	−	1.69452i	0.668476	−	0.743733i	$-0.266947\pi$
$152$	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	$-0.705674\pi$
$157$	120572.	−	208837.i	0.390389	−	0.676173i	0.992501	+	0.122238i	$0.0390072\pi$
$158$	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	−0.783388	−	0.621533i	$-0.786510\pi$
$163$	−315451.	−	546377.i	−0.929957	−	1.61073i	−0.146569	−	0.989200i	$-0.546823\pi$
$164$	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	$-0.607632\pi$
$167$	−239113.			−0.663456			−0.331728	+	0.943375i	$0.607632\pi$
$168$		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	$-0.292389\pi$
$173$	−151470.	−	262353.i	−0.384778	−	0.666455i	−0.991738	+	0.128277i	$0.959055\pi$
$174$	−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	−0.797571	−	0.603226i	$-0.793882\pi$
$179$	52994.8	−	91789.7i	0.123623	−	0.214122i	0.921194	+	0.389104i	$0.127215\pi$
$180$	−38616.3	−	66885.3i	−0.0888360	−	0.153868i
$181$	473727.			1.07481			0.537405	−	0.843324i	$-0.319405\pi$
$181$	473727.			1.07481			0.537405	+	0.843324i	$0.319405\pi$
$182$		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	0.995128	+	0.0985869i	$0.0314322\pi$
$191$	293907.	+	509061.i	0.582943	+	1.00969i	−0.412185	+	0.911100i	$0.635234\pi$
$192$	18432.0	−	31925.2i	0.0360844	−	0.0625000i
$193$	183430.	−	317711.i	0.354469	−	0.613958i	−0.632558	−	0.774513i	$-0.717995\pi$
$193$	183430.	−	317711.i	0.354469	−	0.613958i	0.987027	+	0.160555i	$0.0513283\pi$
$194$	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	$-0.900733\pi$
$199$	−117406.	+	203353.i	−0.210163	+	0.364013i	0.741602	+	0.670840i	$0.234066\pi$
$200$	−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	$-0.611616\pi$
$223$	−510190.			−0.687021			−0.343510	+	0.939149i	$0.611616\pi$
$224$		0			0
$225$	34532.4			0.0454748
$226$	−449771.	−	779027.i	−0.585761	−	1.01457i
$227$	519016.	−	898962.i	0.668523	−	1.15791i	−0.309795	−	0.950803i	$-0.600260\pi$
$227$	519016.	−	898962.i	0.668523	−	1.15791i	0.978317	−	0.207112i	$-0.0664063\pi$
$228$	−92155.0	+	159617.i	−0.117404	+	0.203349i
$229$	−519245.	−	899359.i	−0.654310	−	1.13330i	−0.982066	−	0.188536i	$-0.939626\pi$
$229$	−519245.	−	899359.i	−0.654310	−	1.13330i	0.327756	−	0.944762i	$-0.393708\pi$
$230$	1.13982e6			1.42075
$231$		0			0
$232$	109825.			0.133962
$233$	−658726.	−	1.14095e6i	−0.794905	−	1.37682i	−0.922899	−	0.385041i	$-0.874187\pi$
$233$	−658726.	−	1.14095e6i	−0.794905	−	1.37682i	0.127994	−	0.991775i	$-0.459146\pi$
$234$	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	$-0.761718\pi$
$241$	201154.	−	348408.i	0.223093	−	0.386408i	0.955745	+	0.294195i	$0.0950514\pi$
$242$	−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	$-0.276190\pi$
$251$	1.29078e6			1.29320			0.646601	+	0.762828i	$0.276190\pi$
$252$		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	−0.895531	−	0.444999i	$-0.853204\pi$
$257$	−882173.	−	1.52797e6i	−0.833146	−	1.44305i	0.0623853	−	0.998052i	$-0.480129\pi$
$258$	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	−0.945470	−	0.325709i	$-0.894397\pi$
$263$	−213873.	+	370438.i	−0.190663	+	0.330237i	0.754807	+	0.655947i	$0.227730\pi$
$264$	−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	0.465479	+	0.885059i	$0.345882\pi$
$269$	−633453.	+	1.09717e6i	−0.533744	+	0.924473i	−0.999223	+	0.0394134i	$0.987451\pi$
$270$	86886.6	−	150492.i	0.0725343	−	0.125633i
$271$	−156017.	−	270229.i	−0.129047	−	0.223516i	0.794260	−	0.607577i	$-0.207859\pi$
$271$	−156017.	−	270229.i	−0.129047	−	0.223516i	−0.923308	+	0.384061i	$0.874525\pi$
$272$	−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	−0.324101	−	0.946022i	$-0.605062\pi$
$277$	839298.	−	1.45371e6i	0.657229	−	1.13835i	0.981330	−	0.192331i	$-0.0616048\pi$
$278$	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	$-0.843474\pi$
$283$	−42915.8	+	74332.4i	−0.0318531	+	0.0551711i	0.849659	+	0.527332i	$0.176808\pi$
$284$	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	$-0.489407\pi$
$293$	97784.7			0.0665429			0.0332715	+	0.999446i	$0.489407\pi$
$294$		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	$-0.321623\pi$
$307$	1.75546e6			1.06303			0.531514	+	0.847050i	$0.321623\pi$
$308$		0			0
$309$	1.84965e6			1.10203
$310$	76603.5	+	132681.i	0.0452735	+	0.0784160i
$311$	−901978.	+	1.56227e6i	−0.528804	+	0.915916i	0.470631	+	0.882330i	$0.344026\pi$
$311$	−901978.	+	1.56227e6i	−0.528804	+	0.915916i	−0.999436	+	0.0335861i	$0.989307\pi$
$312$	−120491.	+	208697.i	−0.0700759	+	0.121375i
$313$	1.23215e6	+	2.13414e6i	0.710888	+	1.23129i	0.964524	+	0.263994i	$0.0850400\pi$
$313$	1.23215e6	+	2.13414e6i	0.710888	+	1.23129i	−0.253636	+	0.967300i	$0.581627\pi$
$314$	−964576.			−0.552093
$315$		0			0
$316$	−283702.			−0.159825
$317$	−826430.	−	1.43142e6i	−0.461911	−	0.800053i	0.537145	−	0.843490i	$-0.319503\pi$
$317$	−826430.	−	1.43142e6i	−0.461911	−	0.800053i	−0.999056	+	0.0434366i	$0.986169\pi$
$318$	−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	0.995783	−	0.0917423i	$-0.0292436\pi$
$331$	834072.	+	1.44465e6i	0.418440	+	0.724760i	−0.577343	+	0.816502i	$0.695910\pi$
$332$	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	−0.996822	−	0.0796604i	$-0.974616\pi$
$347$	−963184.	+	1.66828e6i	−0.429423	+	0.743783i	0.567399	+	0.823443i	$0.307950\pi$
$348$	123554.	+	214001.i	0.0546899	+	0.0947257i
$349$	−340342.			−0.149573			−0.0747864	−	0.997200i	$-0.523827\pi$
$349$	−340342.			−0.149573			−0.0747864	+	0.997200i	$0.523827\pi$
$350$		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	$-0.838418\pi$
$353$	−37395.6	+	64771.1i	−0.0159729	+	0.0276659i	0.857928	+	0.513769i	$0.171751\pi$
$354$	−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	0.504982	−	0.863130i	$-0.331499\pi$
$359$	−1.20877e6	−	2.09365e6i	−0.495002	−	0.857368i	−0.999983	+	0.00576184i	$0.998166\pi$
$360$	−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	$-0.823348\pi$
$367$	80931.9	−	140178.i	0.0313657	−	0.0543269i	0.881282	+	0.472591i	$0.156681\pi$
$368$	−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	0.858772	−	0.512358i	$-0.171228\pi$
$373$	−38501.2	−	66686.1i	−0.0143286	−	0.0248178i	−0.873101	+	0.487540i	$0.837894\pi$
$374$	−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	0.986975	+	0.160873i	$0.0514309\pi$
$383$	1.81664e6	+	3.14651e6i	0.632807	+	1.09605i	−0.354168	+	0.935182i	$0.615236\pi$
$384$	−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	−0.574113	−	0.818776i	$-0.694653\pi$
$389$	1.25954e6	−	2.18158e6i	0.422024	−	0.730967i	0.996137	+	0.0878087i	$0.0279864\pi$
$390$	−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	0.839308	+	0.543656i	$0.182961\pi$
$397$	2.79639e6	+	4.84349e6i	0.890474	+	1.54235i	0.0511664	+	0.998690i	$0.483706\pi$
$398$	939246.			0.297216
$399$		0			0
$400$	109139.			0.0341061
$401$	95530.9	+	165464.i	0.0296676	+	0.0513859i	0.880478	−	0.474087i	$-0.157222\pi$
$401$	95530.9	+	165464.i	0.0296676	+	0.0513859i	−0.850810	+	0.525473i	$0.823888\pi$
$402$	−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	−0.322026	−	0.946731i	$-0.604364\pi$
$409$	2.22902e6	−	3.86078e6i	0.658880	−	1.14121i	0.980906	−	0.194483i	$-0.0623030\pi$
$410$	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	$-0.730482\pi$
$419$	−4.76120e6			−1.32489			−0.662447	+	0.749109i	$0.730482\pi$
$420$		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	0.403020	+	0.915191i	$0.367960\pi$
$431$	−2.27946e6	+	3.94813e6i	−0.591069	+	1.02376i	−0.994089	+	0.108570i	$0.965373\pi$
$432$	93312.0	+	161621.i	0.0240563	+	0.0416667i
$433$	6.00870e6			1.54014			0.770071	−	0.637958i	$-0.220221\pi$
$433$	6.00870e6			1.54014			0.770071	+	0.637958i	$0.220221\pi$
$434$		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	$-0.144557\pi$
$439$	280252.	+	485410.i	0.0694044	+	0.120212i	−0.829235	+	0.558900i	$0.811223\pi$
$440$	−2.35068e6			−0.578844
$441$		0			0
$442$	3.00206e6			0.730910
$443$	−1.67037e6	−	2.89317e6i	−0.404393	−	0.700429i	0.589858	−	0.807507i	$-0.299184\pi$
$443$	−1.67037e6	−	2.89317e6i	−0.404393	−	0.700429i	−0.994251	+	0.107078i	$0.965850\pi$
$444$	−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	0.516974	−	0.856001i	$-0.327058\pi$
$457$	−2.15569e6	−	3.73376e6i	−0.482831	−	0.836289i	−0.999806	+	0.0197123i	$0.993725\pi$
$458$	−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	$-0.488803\pi$
$461$	320951.			0.0703374			0.0351687	+	0.999381i	$0.488803\pi$
$462$		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	$-0.0217023\pi$
$467$	2.07293e6	+	3.59043e6i	0.439839	+	0.761823i	−0.557838	+	0.829950i	$0.688369\pi$
$468$	−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	$-0.841501\pi$
$479$	−128839.	+	223155.i	−0.0256571	+	0.0444394i	0.852912	+	0.522055i	$0.174834\pi$
$480$	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	−0.936423	−	0.350873i	$-0.885885\pi$
$487$	−860165.	+	1.48985e6i	−0.164346	+	0.284656i	0.772077	+	0.635529i	$0.219218\pi$
$488$	−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	0.848458	−	0.529262i	$-0.177531\pi$
$499$	−189816.	−	328770.i	−0.0341256	−	0.0591073i	−0.882584	+	0.470155i	$0.844198\pi$
$500$	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	$-0.226133\pi$
$503$	8.60340e6			1.51618			0.758089	+	0.652151i	$0.226133\pi$
$504$		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	$-0.138436\pi$
$509$	517714.	+	896707.i	0.0885718	+	0.153411i	−0.818336	+	0.574740i	$0.805103\pi$
$510$	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	−0.481374	−	0.876515i	$-0.659862\pi$
$521$	3.21187e6	−	5.56312e6i	0.518398	−	0.897891i	0.999772	−	0.0213759i	$-0.00680468\pi$
$522$	−277996.	+	481502.i	−0.0446541	+	0.0773432i
$523$	4.03192e6	+	6.98349e6i	0.644551	+	1.11640i	0.984405	+	0.175917i	$0.0562891\pi$
$523$	4.03192e6	+	6.98349e6i	0.644551	+	1.11640i	−0.339854	+	0.940478i	$0.610378\pi$
$524$	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	0.986878	+	0.161467i	$0.0516226\pi$
$541$	4.31107e6	+	7.46699e6i	0.633274	+	1.09686i	−0.353604	+	0.935395i	$0.615044\pi$
$542$	−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	−0.0602274	−	0.998185i	$-0.519183\pi$
$557$	6.10915e6	−	1.05814e7i	0.834340	−	1.44512i	0.894567	−	0.446934i	$-0.147484\pi$
$558$	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	$-0.801802\pi$
$563$	743804.	−	1.28831e6i	0.0988980	−	0.171296i	0.911229	+	0.411901i	$0.135135\pi$
$564$	−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	0.612965	−	0.790110i	$-0.289977\pi$
$569$	−2.91751e6	−	5.05327e6i	−0.377773	−	0.654322i	−0.990738	+	0.135788i	$0.956643\pi$
$570$	−1.37295e6	+	2.37802e6i	−0.176997	+	0.306568i
$571$	−4.91614e6	+	8.51500e6i	−0.631006	+	1.09294i	0.356340	+	0.934356i	$0.384024\pi$
$571$	−4.91614e6	+	8.51500e6i	−0.631006	+	1.09294i	−0.987346	+	0.158579i	$0.949309\pi$
$572$	−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	$-0.826885\pi$
$577$	162003.	−	280597.i	0.0202574	−	0.0350868i	0.875976	+	0.482354i	$0.160218\pi$
$578$	−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	$-0.582447\pi$
$587$	−4.27646e6			−0.512258			−0.256129	+	0.966643i	$0.582447\pi$
$588$		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	−0.786694	−	0.617344i	$-0.788209\pi$
$593$	−7.94651e6	−	1.37638e7i	−0.927982	−	1.60731i	−0.141289	−	0.989968i	$-0.545125\pi$
$594$	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	0.428787	−	0.903406i	$-0.358941\pi$
$599$	8.75306e6	−	1.51608e7i	0.996766	−	1.72645i	0.567979	−	0.823043i	$-0.307726\pi$
$600$	122782.	+	212664.i	0.0139237	+	0.0241166i
$601$	5.98914e6			0.676361			0.338180	−	0.941081i	$-0.390189\pi$
$601$	5.98914e6			0.676361			0.338180	+	0.941081i	$0.390189\pi$
$602$		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	$-0.224402\pi$
$607$	−1.63750e6	−	2.83624e6i	−0.180389	−	0.312443i	−0.942013	+	0.335576i	$0.891069\pi$
$608$	−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	−0.585262	−	0.810844i	$-0.699009\pi$
$613$	3.81057e6	−	6.60010e6i	0.409580	−	0.709414i	0.994843	+	0.101430i	$0.0323418\pi$
$614$	−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	$-0.980861\pi$
$619$	−4.26175e6	+	7.38157e6i	−0.447055	+	0.774323i	0.551138	+	0.834414i	$0.314194\pi$
$620$	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	−0.718948	−	0.695064i	$-0.755376\pi$
$641$	2.52233e6	−	4.36881e6i	0.242470	−	0.419970i	0.961417	+	0.275095i	$0.0887092\pi$
$642$	−1.88240e6	−	3.26041e6i	−0.180249	−	0.312201i
$643$	−9.94759e6			−0.948835			−0.474417	−	0.880300i	$-0.657341\pi$
$643$	−9.94759e6			−0.948835			−0.474417	+	0.880300i	$0.657341\pi$
$644$		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	$-0.814448\pi$
$647$	631379.	−	1.09358e6i	0.0592966	−	0.102705i	0.894150	+	0.447768i	$0.147781\pi$
$648$	−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	0.994491	+	0.104824i	$0.0334279\pi$
$653$	6.40736e6	+	1.10979e7i	0.588026	+	1.01849i	−0.406465	+	0.913666i	$0.633239\pi$
$654$	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	−0.212541	−	0.977152i	$-0.568174\pi$
$661$	8.31221e6	−	1.43972e7i	0.739968	−	1.28166i	0.952509	−	0.304510i	$-0.0984928\pi$
$662$	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	−0.948727	−	0.316098i	$-0.897627\pi$
$677$	−8.92151e6	−	1.54525e7i	−0.748112	−	1.29577i	0.200615	−	0.979670i	$-0.435706\pi$
$678$	−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	0.414966	+	0.909837i	$0.363794\pi$
$683$	−7.07658e6	+	1.22570e7i	−0.580459	+	1.00538i	−0.995425	+	0.0955475i	$0.969540\pi$
$684$	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	$-0.138412\pi$
$691$	1.11267e6	+	1.92721e6i	0.0886487	+	0.153544i	−0.818291	+	0.574803i	$0.805078\pi$
$692$	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	0.995917	+	0.0902780i	$0.0287756\pi$
$709$	7.71160e6	+	1.33569e7i	0.576141	+	0.997906i	−0.419775	+	0.907628i	$0.637891\pi$
$710$	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	$-0.293136\pi$
$719$	−5.36378e6	−	9.29034e6i	−0.386945	−	0.670208i	−0.992037	+	0.125947i	$0.959803\pi$
$720$	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	$-0.756570\pi$
$727$	−2.05652e7			−1.44310			−0.721551	+	0.692362i	$0.756570\pi$
$728$		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	$-0.130558\pi$
$733$	1.64661e6	+	2.85201e6i	0.113196	+	0.196061i	−0.803861	+	0.594817i	$0.797225\pi$
$734$	−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	−0.706298	−	0.707915i	$-0.749636\pi$
$739$	3.85884e6	−	6.68370e6i	0.259923	−	0.450200i	0.966221	+	0.257714i	$0.0829694\pi$
$740$	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	0.994933	+	0.100543i	$0.0320580\pi$
$751$	9.03469e6	+	1.56485e7i	0.584539	+	1.01245i	−0.410394	+	0.911908i	$0.634609\pi$
$752$	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	$-0.146560\pi$
$761$	1.00845e6	+	1.74669e6i	0.0631239	+	0.109334i	−0.832736	+	0.553670i	$0.813227\pi$
$762$	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	$-0.618158\pi$
$769$	−1.18971e7			−0.725478			−0.362739	+	0.931891i	$0.618158\pi$
$770$		0			0
$771$	−1.58791e7			−0.962034

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

Introduction

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