LMFDB - Embedded newform 147.6.e.m.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(67,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, 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("147.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$-3.22311 + 5.58259i$ of defining polynomial
Character	$\chi$	$=$	147.79
Dual form			147.6.e.m.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72311 + 4.71657i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(1.16933 + 2.02534i) q^{4} +(18.0000 - 31.1769i) q^{5} +49.0160 q^{6} -187.016 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-2.72311 + 4.71657i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(1.16933 + 2.02534i) q^{4} +(18.0000 - 31.1769i) q^{5} +49.0160 q^{6} -187.016 q^{8} +(-40.5000 + 70.1481i) q^{9} +(98.0320 + 169.796i) q^{10} +(-92.2151 - 159.721i) q^{11} +(10.5240 - 18.2281i) q^{12} -147.872 q^{13} -324.000 q^{15} +(471.847 - 817.262i) q^{16} +(984.192 + 1704.67i) q^{17} +(-220.572 - 382.042i) q^{18} +(946.256 - 1638.96i) q^{19} +84.1920 q^{20} +1004.45 q^{22} +(-68.4942 + 118.635i) q^{23} +(841.572 + 1457.65i) q^{24} +(914.500 + 1583.96i) q^{25} +(402.672 - 697.448i) q^{26} +729.000 q^{27} -1259.58 q^{29} +(882.288 - 1528.17i) q^{30} +(4484.51 + 7767.40i) q^{31} +(-422.474 - 731.747i) q^{32} +(-829.936 + 1437.49i) q^{33} -10720.3 q^{34} -189.432 q^{36} +(-6448.61 + 11169.3i) q^{37} +(5153.52 + 8926.16i) q^{38} +(665.424 + 1152.55i) q^{39} +(-3366.29 + 5830.58i) q^{40} -8975.62 q^{41} +13538.9 q^{43} +(215.660 - 373.535i) q^{44} +(1458.00 + 2525.33i) q^{45} +(-373.035 - 646.115i) q^{46} +(-10023.1 + 17360.5i) q^{47} -8493.24 q^{48} -9961.14 q^{50} +(8857.73 - 15342.0i) q^{51} +(-172.912 - 299.492i) q^{52} +(-4667.16 - 8083.76i) q^{53} +(-1985.15 + 3438.38i) q^{54} -6639.49 q^{55} -17032.6 q^{57} +(3429.98 - 5940.90i) q^{58} +(4433.23 + 7678.58i) q^{59} +(-378.864 - 656.212i) q^{60} +(-20574.2 + 35635.5i) q^{61} -48847.3 q^{62} +34800.0 q^{64} +(-2661.70 + 4610.19i) q^{65} +(-4520.02 - 7828.90i) q^{66} +(27675.8 + 47935.8i) q^{67} +(-2301.70 + 3986.65i) q^{68} +1232.90 q^{69} -63866.8 q^{71} +(7574.15 - 13118.8i) q^{72} +(20649.7 + 35766.3i) q^{73} +(-35120.5 - 60830.6i) q^{74} +(8230.50 - 14255.6i) q^{75} +4425.95 q^{76} -7248.09 q^{78} +(-8481.76 + 14690.8i) q^{79} +(-16986.5 - 29421.4i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(24441.6 - 42334.1i) q^{82} +101693. q^{83} +70861.8 q^{85} +(-36868.0 + 63857.3i) q^{86} +(5668.12 + 9817.47i) q^{87} +(17245.7 + 29870.4i) q^{88} +(43551.3 - 75433.0i) q^{89} -15881.2 q^{90} -320.370 q^{92} +(40360.6 - 69906.6i) q^{93} +(-54587.9 - 94549.0i) q^{94} +(-34065.2 - 59002.7i) q^{95} +(-3802.27 + 6585.72i) q^{96} +118107. q^{97} +14938.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 18 * q^3 - 37 * q^4 + 72 * q^5 - 54 * q^6 - 498 * q^8 - 162 * q^9	\( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9} - 108 q^{10} - 480 q^{11} - 333 q^{12} - 2592 q^{13} - 1296 q^{15} + 1679 q^{16} + 936 q^{17} + 243 q^{18} - 216 q^{19} - 2664 q^{20} - 2984 q^{22} + 504 q^{23} + 2241 q^{24} + 3658 q^{25} - 8892 q^{26} + 2916 q^{27} + 12744 q^{29} - 972 q^{30} + 9936 q^{31} - 9039 q^{32} - 4320 q^{33} - 38880 q^{34} + 5994 q^{36} - 11124 q^{37} + 28116 q^{38} + 11664 q^{39} - 8964 q^{40} - 41904 q^{41} - 12528 q^{43} - 11196 q^{44} + 5832 q^{45} - 6160 q^{46} + 7920 q^{47} - 30222 q^{48} + 10974 q^{50} + 8424 q^{51} + 44820 q^{52} - 2220 q^{53} + 2187 q^{54} - 34560 q^{55} + 3888 q^{57} + 71318 q^{58} + 29736 q^{59} + 11988 q^{60} - 17280 q^{61} - 81360 q^{62} - 21758 q^{64} - 46656 q^{65} + 13428 q^{66} + 20680 q^{67} - 45216 q^{68} - 9072 q^{69} - 184560 q^{71} + 20169 q^{72} + 56592 q^{73} - 85218 q^{74} + 32922 q^{75} + 174744 q^{76} + 160056 q^{78} + 56096 q^{79} - 60444 q^{80} - 13122 q^{81} - 52272 q^{82} + 142704 q^{83} + 67392 q^{85} - 240996 q^{86} - 57348 q^{87} + 52812 q^{88} + 123192 q^{89} + 17496 q^{90} - 51072 q^{92} + 89424 q^{93} - 345384 q^{94} + 7776 q^{95} - 81351 q^{96} - 71712 q^{97} + 77760 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 18 * q^3 - 37 * q^4 + 72 * q^5 - 54 * q^6 - 498 * q^8 - 162 * q^9 - 108 * q^10 - 480 * q^11 - 333 * q^12 - 2592 * q^13 - 1296 * q^15 + 1679 * q^16 + 936 * q^17 + 243 * q^18 - 216 * q^19 - 2664 * q^20 - 2984 * q^22 + 504 * q^23 + 2241 * q^24 + 3658 * q^25 - 8892 * q^26 + 2916 * q^27 + 12744 * q^29 - 972 * q^30 + 9936 * q^31 - 9039 * q^32 - 4320 * q^33 - 38880 * q^34 + 5994 * q^36 - 11124 * q^37 + 28116 * q^38 + 11664 * q^39 - 8964 * q^40 - 41904 * q^41 - 12528 * q^43 - 11196 * q^44 + 5832 * q^45 - 6160 * q^46 + 7920 * q^47 - 30222 * q^48 + 10974 * q^50 + 8424 * q^51 + 44820 * q^52 - 2220 * q^53 + 2187 * q^54 - 34560 * q^55 + 3888 * q^57 + 71318 * q^58 + 29736 * q^59 + 11988 * q^60 - 17280 * q^61 - 81360 * q^62 - 21758 * q^64 - 46656 * q^65 + 13428 * q^66 + 20680 * q^67 - 45216 * q^68 - 9072 * q^69 - 184560 * q^71 + 20169 * q^72 + 56592 * q^73 - 85218 * q^74 + 32922 * q^75 + 174744 * q^76 + 160056 * q^78 + 56096 * q^79 - 60444 * q^80 - 13122 * q^81 - 52272 * q^82 + 142704 * q^83 + 67392 * q^85 - 240996 * q^86 - 57348 * q^87 + 52812 * q^88 + 123192 * q^89 + 17496 * q^90 - 51072 * q^92 + 89424 * q^93 - 345384 * q^94 + 7776 * q^95 - 81351 * q^96 - 71712 * q^97 + 77760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.72311	+	4.71657i	−0.481383	+	0.833779i	−0.999772	−	0.0213658i	$-0.993199\pi$
$2$	−2.72311	+	4.71657i	−0.481383	+	0.833779i	0.518389	+	0.855145i	$0.326532\pi$
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	1.16933	+	2.02534i	0.0365417	+	0.0632920i
$5$	18.0000	−	31.1769i	0.321994	−	0.557710i	−0.658906	−	0.752226i	$-0.728980\pi$
$5$	18.0000	−	31.1769i	0.321994	−	0.557710i	0.980899	+	0.194516i	$0.0623136\pi$
$6$	49.0160			0.555853
$7$		0			0
$7$		0			0
$8$	−187.016			−1.03313
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	98.0320	+	169.796i	0.310004	+	0.536943i
$11$	−92.2151	−	159.721i	−0.229784	−	0.397998i	0.727960	−	0.685620i	$-0.240469\pi$
$11$	−92.2151	−	159.721i	−0.229784	−	0.397998i	−0.957744	+	0.287622i	$0.907135\pi$
$12$	10.5240	−	18.2281i	0.0210973	−	0.0365417i
$13$	−147.872			−0.242676			−0.121338	−	0.992611i	$-0.538719\pi$
$13$	−147.872			−0.242676			−0.121338	+	0.992611i	$0.538719\pi$
$14$		0			0
$15$	−324.000			−0.371806
$16$	471.847	−	817.262i	0.460788	−	0.798108i
$17$	984.192	+	1704.67i	0.825957	+	1.43060i	0.901186	+	0.433433i	$0.142698\pi$
$17$	984.192	+	1704.67i	0.825957	+	1.43060i	−0.0752284	+	0.997166i	$0.523969\pi$
$18$	−220.572	−	382.042i	−0.160461	−	0.277926i
$19$	946.256	−	1638.96i	0.601346	−	1.04156i	−0.391271	−	0.920275i	$-0.627965\pi$
$19$	946.256	−	1638.96i	0.601346	−	1.04156i	0.992617	−	0.121287i	$-0.0387021\pi$
$20$	84.1920			0.0470647
$21$		0			0
$22$	1004.45			0.442457
$23$	−68.4942	+	118.635i	−0.0269982	+	0.0467622i	−0.879209	−	0.476437i	$-0.841928\pi$
$23$	−68.4942	+	118.635i	−0.0269982	+	0.0467622i	0.852211	+	0.523199i	$0.175261\pi$
$24$	841.572	+	1457.65i	0.298238	+	0.516564i
$25$	914.500	+	1583.96i	0.292640	+	0.506867i
$26$	402.672	−	697.448i	0.116820	−	0.202339i
$27$	729.000			0.192450
$28$		0			0
$29$	−1259.58			−0.278120			−0.139060	−	0.990284i	$-0.544408\pi$
$29$	−1259.58			−0.278120			−0.139060	+	0.990284i	$0.544408\pi$
$30$	882.288	−	1528.17i	0.178981	−	0.310004i
$31$	4484.51	+	7767.40i	0.838129	+	1.45168i	0.891457	+	0.453105i	$0.149684\pi$
$31$	4484.51	+	7767.40i	0.838129	+	1.45168i	−0.0533279	+	0.998577i	$0.516983\pi$
$32$	−422.474	−	731.747i	−0.0729332	−	0.126324i
$33$	−829.936	+	1437.49i	−0.132666	+	0.229784i
$34$	−10720.3			−1.59041
$35$		0			0
$36$	−189.432			−0.0243611
$37$	−6448.61	+	11169.3i	−0.774393	+	1.34129i	0.160742	+	0.986996i	$0.448611\pi$
$37$	−6448.61	+	11169.3i	−0.774393	+	1.34129i	−0.935135	+	0.354292i	$0.884722\pi$
$38$	5153.52	+	8926.16i	0.578955	+	1.00278i
$39$	665.424	+	1152.55i	0.0700547	+	0.121338i
$40$	−3366.29	+	5830.58i	−0.332661	+	0.576185i
$41$	−8975.62			−0.833882			−0.416941	−	0.908934i	$-0.636898\pi$
$41$	−8975.62			−0.833882			−0.416941	+	0.908934i	$0.636898\pi$
$42$		0			0
$43$	13538.9			1.11664			0.558320	−	0.829626i	$-0.311446\pi$
$43$	13538.9			1.11664			0.558320	+	0.829626i	$0.311446\pi$
$44$	215.660	−	373.535i	0.0167934	−	0.0290870i
$45$	1458.00	+	2525.33i	0.107331	+	0.185903i
$46$	−373.035	−	646.115i	−0.0259929	−	0.0450210i
$47$	−10023.1	+	17360.5i	−0.661845	+	1.14635i	0.318286	+	0.947995i	$0.396893\pi$
$47$	−10023.1	+	17360.5i	−0.661845	+	1.14635i	−0.980130	+	0.198354i	$0.936440\pi$
$48$	−8493.24			−0.532072
$49$		0			0
$50$	−9961.14			−0.563487
$51$	8857.73	−	15342.0i	0.476867	−	0.825957i
$52$	−172.912	−	299.492i	−0.00886780	−	0.0153595i
$53$	−4667.16	−	8083.76i	−0.228225	−	0.395297i	0.729057	−	0.684453i	$-0.239959\pi$
$53$	−4667.16	−	8083.76i	−0.228225	−	0.395297i	−0.957282	+	0.289155i	$0.906626\pi$
$54$	−1985.15	+	3438.38i	−0.0926421	+	0.160461i
$55$	−6639.49			−0.295956
$56$		0			0
$57$	−17032.6			−0.694375
$58$	3429.98	−	5940.90i	0.133882	−	0.231890i
$59$	4433.23	+	7678.58i	0.165802	+	0.287178i	0.936940	−	0.349491i	$-0.113645\pi$
$59$	4433.23	+	7678.58i	0.165802	+	0.287178i	−0.771138	+	0.636668i	$0.780312\pi$
$60$	−378.864	−	656.212i	−0.0135864	−	0.0235324i
$61$	−20574.2	+	35635.5i	−0.707942	+	1.22619i	0.257678	+	0.966231i	$0.417043\pi$
$61$	−20574.2	+	35635.5i	−0.707942	+	1.22619i	−0.965619	+	0.259960i	$0.916291\pi$
$62$	−48847.3			−1.61384
$63$		0			0
$64$	34800.0			1.06201
$65$	−2661.70	+	4610.19i	−0.0781403	+	0.135343i
$66$	−4520.02	−	7828.90i	−0.127726	−	0.221228i
$67$	27675.8	+	47935.8i	0.753204	+	1.30459i	0.946262	+	0.323400i	$0.104826\pi$
$67$	27675.8	+	47935.8i	0.753204	+	1.30459i	−0.193058	+	0.981187i	$0.561841\pi$
$68$	−2301.70	+	3986.65i	−0.0603637	+	0.104553i
$69$	1232.90			0.0311748
$70$		0			0
$71$	−63866.8			−1.50359			−0.751794	−	0.659398i	$-0.770811\pi$
$71$	−63866.8			−1.50359			−0.751794	+	0.659398i	$0.770811\pi$
$72$	7574.15	−	13118.8i	0.172188	−	0.298238i
$73$	20649.7	+	35766.3i	0.453530	+	0.785537i	0.998602	−	0.0528522i	$-0.0168312\pi$
$73$	20649.7	+	35766.3i	0.453530	+	0.785537i	−0.545073	+	0.838389i	$0.683498\pi$
$74$	−35120.5	−	60830.6i	−0.745559	−	1.29135i
$75$	8230.50	−	14255.6i	0.168956	−	0.292640i
$76$	4425.95			0.0878968
$77$		0			0
$78$	−7248.09			−0.134892
$79$	−8481.76	+	14690.8i	−0.152904	+	0.264837i	−0.932294	−	0.361702i	$-0.882196\pi$
$79$	−8481.76	+	14690.8i	−0.152904	+	0.264837i	0.779390	+	0.626539i	$0.215529\pi$
$80$	−16986.5	−	29421.4i	−0.296742	−	0.513972i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	24441.6	−	42334.1i	0.401416	−	0.695273i
$83$	101693.			1.62030			0.810150	−	0.586223i	$-0.199386\pi$
$83$	101693.			1.62030			0.810150	+	0.586223i	$0.199386\pi$
$84$		0			0
$85$	70861.8			1.06381
$86$	−36868.0	+	63857.3i	−0.537531	+	0.931031i
$87$	5668.12	+	9817.47i	0.0802862	+	0.139060i
$88$	17245.7	+	29870.4i	0.237396	+	0.411183i
$89$	43551.3	−	75433.0i	0.582808	−	1.00945i	−0.412336	−	0.911032i	$-0.635287\pi$
$89$	43551.3	−	75433.0i	0.582808	−	1.00945i	0.995145	−	0.0984220i	$-0.0313795\pi$
$90$	−15881.2			−0.206670
$91$		0			0
$92$	−320.370			−0.00394623
$93$	40360.6	−	69906.6i	0.483894	−	0.838129i
$94$	−54587.9	−	94549.0i	−0.637201	−	1.10366i
$95$	−34065.2	−	59002.7i	−0.387260	−	0.670753i
$96$	−3802.27	+	6585.72i	−0.0421080	+	0.0729332i
$97$	118107.			1.27452			0.637258	−	0.770650i	$-0.280068\pi$
$97$	118107.			1.27452			0.637258	+	0.770650i	$0.280068\pi$
$98$		0			0
$99$	14938.8			0.153190
$100$	−2138.71	+	3704.35i	−0.0213871	+	0.0370435i
$101$	11116.4	+	19254.1i	0.108432	+	0.187811i	0.915135	−	0.403147i	$-0.132084\pi$
$101$	11116.4	+	19254.1i	0.108432	+	0.187811i	−0.806703	+	0.590957i	$0.798750\pi$
$102$	48241.2	+	83556.1i	0.459111	+	0.795203i
$103$	67965.3	−	117719.i	0.631239	−	1.09334i	−0.356059	−	0.934463i	$-0.615880\pi$
$103$	67965.3	−	117719.i	0.631239	−	1.09334i	0.987299	−	0.158875i	$-0.0507868\pi$
$104$	27654.4			0.250716
$105$		0			0
$106$	50836.8			0.439454
$107$	−58813.1	+	101867.i	−0.496609	+	0.860152i	−0.999992	−	0.00391112i	$-0.998755\pi$
$107$	−58813.1	+	101867.i	−0.496609	+	0.860152i	0.503383	+	0.864063i	$0.332088\pi$
$108$	852.444	+	1476.48i	0.00703244	+	0.0121806i
$109$	17332.1	+	30020.1i	0.139729	+	0.242017i	0.927394	−	0.374086i	$-0.122044\pi$
$109$	17332.1	+	30020.1i	0.139729	+	0.242017i	−0.787665	+	0.616103i	$0.788710\pi$
$110$	18080.1	−	31315.6i	0.142468	−	0.246762i
$111$	116075.			0.894192
$112$		0			0
$113$	−26584.5			−0.195854			−0.0979269	−	0.995194i	$-0.531221\pi$
$113$	−26584.5			−0.195854			−0.0979269	+	0.995194i	$0.531221\pi$
$114$	46381.7	−	80335.4i	0.334260	−	0.578955i
$115$	2465.79	+	4270.88i	0.0173865	+	0.0301143i
$116$	−1472.87	−	2551.09i	−0.0101629	−	0.0176027i
$117$	5988.82	−	10372.9i	0.0404461	−	0.0700547i
$118$	−48288.7			−0.319257
$119$		0			0
$120$	60593.2			0.384123
$121$	63518.2	−	110017.i	0.394398	−	0.683118i
$122$	−112051.	−	194079.i	−0.681582	−	1.18053i
$123$	40390.3	+	69958.0i	0.240721	+	0.416941i
$124$	−10487.8	+	18165.4i	−0.0612533	+	0.106094i
$125$	178344.			1.02090
$126$		0			0
$127$	−137111.			−0.754334			−0.377167	−	0.926145i	$-0.623102\pi$
$127$	−137111.			−0.754334			−0.377167	+	0.926145i	$0.623102\pi$
$128$	−81245.0	+	140720.i	−0.438300	+	0.759158i
$129$	−60925.2	−	105526.i	−0.322346	−	0.558320i
$130$	−14496.2	−	25108.1i	−0.0752308	−	0.130304i
$131$	−27044.6	+	46842.6i	−0.137690	+	0.238486i	−0.926622	−	0.375995i	$-0.877301\pi$
$131$	−27044.6	+	46842.6i	−0.137690	+	0.238486i	0.788932	+	0.614481i	$0.210634\pi$
$132$	−3881.89			−0.0193913
$133$		0			0
$134$	−301457.			−1.45032
$135$	13122.0	−	22728.0i	0.0619677	−	0.107331i
$136$	−184060.	−	318801.i	−0.853319	−	1.47799i
$137$	−211424.	−	366198.i	−0.962395	−	1.66692i	−0.716456	−	0.697632i	$-0.754237\pi$
$137$	−211424.	−	366198.i	−0.962395	−	1.66692i	−0.245939	−	0.969285i	$-0.579096\pi$
$138$	−3357.31	+	5815.04i	−0.0150070	+	0.0259929i
$139$	9913.38			0.0435196			0.0217598	−	0.999763i	$-0.493073\pi$
$139$	9913.38			0.0435196			0.0217598	+	0.999763i	$0.493073\pi$
$140$		0			0
$141$	180415.			0.764233
$142$	173916.	−	301232.i	0.723801	−	1.25366i
$143$	13636.0	+	23618.3i	0.0557632	+	0.0965848i
$144$	38219.6	+	66198.3i	0.153596	+	0.266036i
$145$	−22672.5	+	39269.9i	−0.0895528	+	0.155110i
$146$	−224925.			−0.873285
$147$		0			0
$148$	−30162.3			−0.113190
$149$	−252731.	+	437743.i	−0.932595	+	1.61530i	−0.153727	+	0.988113i	$0.549128\pi$
$149$	−252731.	+	437743.i	−0.932595	+	1.61530i	−0.778868	+	0.627188i	$0.784206\pi$
$150$	44825.1	+	77639.4i	0.162665	+	0.281744i
$151$	96551.4	+	167232.i	0.344601	+	0.596866i	0.985281	−	0.170942i	$-0.0546810\pi$
$151$	96551.4	+	167232.i	0.344601	+	0.596866i	−0.640680	+	0.767808i	$0.721348\pi$
$152$	−176965.	+	306512.i	−0.621267	+	1.07607i
$153$	−159439.			−0.550638
$154$		0			0
$155$	322885.			1.07949
$156$	−1556.20	+	2695.43i	−0.00511983	+	0.00886780i
$157$	132462.	+	229430.i	0.428885	+	0.742850i	0.996774	−	0.0802545i	$-0.0255733\pi$
$157$	132462.	+	229430.i	0.428885	+	0.742850i	−0.567890	+	0.823105i	$0.692240\pi$
$158$	−46193.5	−	80009.6i	−0.147210	−	0.254976i
$159$	−42004.5	+	72753.9i	−0.131766	+	0.228225i
$160$	−30418.1			−0.0939362
$161$		0			0
$162$	35732.7			0.106974
$163$	269546.	−	466868.i	0.794629	−	1.37634i	−0.128446	−	0.991717i	$-0.540999\pi$
$163$	269546.	−	466868.i	0.794629	−	1.37634i	0.923075	−	0.384621i	$-0.125668\pi$
$164$	−10495.5	−	18178.7i	−0.0304714	−	0.0527781i
$165$	29877.7	+	51749.7i	0.0854353	+	0.147978i
$166$	−276921.	+	479641.i	−0.779984	+	1.35097i
$167$	−218748.			−0.606949			−0.303475	−	0.952840i	$-0.598147\pi$
$167$	−218748.			−0.606949			−0.303475	+	0.952840i	$0.598147\pi$
$168$		0			0
$169$	−349427.			−0.941108
$170$	−192965.	+	334225.i	−0.512101	+	0.886984i
$171$	76646.7	+	132756.i	0.200449	+	0.347187i
$172$	15831.5	+	27421.0i	0.0408039	+	0.0706744i
$173$	295101.	−	511129.i	0.749644	−	1.29842i	−0.198350	−	0.980131i	$-0.563558\pi$
$173$	295101.	−	511129.i	0.749644	−	1.29842i	0.947994	−	0.318289i	$-0.103108\pi$
$174$	−61739.7			−0.154593
$175$		0			0
$176$	−174046.			−0.423527
$177$	39899.1	−	69107.2i	0.0957260	−	0.165802i
$178$	237190.	+	410825.i	0.561108	+	0.971867i
$179$	108676.	+	188232.i	0.253513	+	0.439098i	0.964491	−	0.264117i	$-0.0850805\pi$
$179$	108676.	+	188232.i	0.253513	+	0.439098i	−0.710977	+	0.703215i	$0.751747\pi$
$180$	−3409.78	+	5905.90i	−0.00784412	+	0.0135864i
$181$	−188109.			−0.426790			−0.213395	−	0.976966i	$-0.568452\pi$
$181$	−188109.			−0.426790			−0.213395	+	0.976966i	$0.568452\pi$
$182$		0			0
$183$	370335.			0.817461
$184$	12809.5	−	22186.7i	0.0278925	−	0.0483113i
$185$	232150.	+	402095.i	0.498700	+	0.863773i
$186$	219813.	+	380727.i	0.465876	+	0.806922i
$187$	181515.	−	314393.i	0.379584	−	0.657459i
$188$	−46881.2			−0.0967396
$189$		0			0
$190$	371053.			0.745680
$191$	−86761.3	+	150275.i	−0.172085	+	0.298060i	−0.939149	−	0.343511i	$-0.888384\pi$
$191$	−86761.3	+	150275.i	−0.172085	+	0.298060i	0.767064	+	0.641571i	$0.221717\pi$
$192$	−156600.	−	271239.i	−0.306576	−	0.531005i
$193$	−58890.7	−	102002.i	−0.113803	−	0.197113i	0.803498	−	0.595308i	$-0.202970\pi$
$193$	−58890.7	−	102002.i	−0.113803	−	0.197113i	−0.917301	+	0.398195i	$0.869637\pi$
$194$	−321618.	+	557059.i	−0.613530	+	1.06267i
$195$	47910.5			0.0902287
$196$		0			0
$197$	224734.			0.412575			0.206288	−	0.978491i	$-0.433862\pi$
$197$	224734.			0.412575			0.206288	+	0.978491i	$0.433862\pi$
$198$	−40680.1	+	70460.1i	−0.0737428	+	0.127726i
$199$	370137.	+	641096.i	0.662567	+	1.14760i	0.979939	+	0.199298i	$0.0638661\pi$
$199$	370137.	+	641096.i	0.662567	+	1.14760i	−0.317372	+	0.948301i	$0.602801\pi$
$200$	−171026.	−	296226.i	−0.302334	−	0.523658i
$201$	249082.	−	431422.i	0.434862	−	0.753204i
$202$	−121084.			−0.208790
$203$		0			0
$204$	41430.5			0.0697020
$205$	−161561.	+	279832.i	−0.268505	+	0.465064i
$206$	370154.	+	641126.i	0.607735	+	1.05263i
$207$	−5548.03	−	9609.47i	−0.00899939	−	0.0155874i
$208$	−69772.9	+	120850.i	−0.111822	+	0.193682i
$209$	−349036.			−0.552720
$210$		0			0
$211$	−705896.			−1.09153			−0.545763	−	0.837939i	$-0.683760\pi$
$211$	−705896.			−1.09153			−0.545763	+	0.837939i	$0.683760\pi$
$212$	10914.9	−	18905.2i	0.0166794	−	0.0288896i
$213$	287400.	+	497792.i	0.434049	+	0.751794i
$214$	−320309.	−	554792.i	−0.478118	−	0.828124i
$215$	243701.	−	422102.i	0.359551	−	0.622761i
$216$	−136335.			−0.198825
$217$		0			0
$218$	−188789.			−0.269052
$219$	185847.	−	321896.i	0.261846	−	0.453530i
$220$	−7763.77	−	13447.2i	−0.0108147	−	0.0187317i
$221$	−145534.	−	252073.i	−0.200440	−	0.347173i
$222$	−316085.	+	547475.i	−0.430449	+	0.745559i
$223$	−42214.3			−0.0568456			−0.0284228	−	0.999596i	$-0.509048\pi$
$223$	−42214.3			−0.0568456			−0.0284228	+	0.999596i	$0.509048\pi$
$224$		0			0
$225$	−148149.			−0.195093
$226$	72392.5	−	125387.i	0.0942806	−	0.163299i
$227$	371201.	+	642940.i	0.478129	+	0.828144i	0.999686	−	0.0250731i	$-0.00798184\pi$
$227$	371201.	+	642940.i	0.478129	+	0.828144i	−0.521557	+	0.853217i	$0.674649\pi$
$228$	−19916.8	−	34496.9i	−0.0253736	−	0.0439484i
$229$	470618.	−	815134.i	0.593034	−	1.02717i	−0.400787	−	0.916171i	$-0.631263\pi$
$229$	470618.	−	815134.i	0.593034	−	1.02717i	0.993821	−	0.110994i	$-0.0354035\pi$
$230$	−26858.5			−0.0334782
$231$		0			0
$232$	235562.			0.287333
$233$	256166.	−	443692.i	0.309123	−	0.535416i	−0.669048	−	0.743219i	$-0.733298\pi$
$233$	256166.	−	443692.i	0.309123	−	0.535416i	0.978171	+	0.207803i	$0.0666313\pi$
$234$	32616.4	+	56493.3i	0.0389401	+	0.0674462i
$235$	360831.	+	624977.i	0.426220	+	0.738234i
$236$	−10367.8	+	17957.6i	−0.0121174	+	0.0209879i
$237$	152672.			0.176558
$238$		0			0
$239$	−115323.			−0.130593			−0.0652966	−	0.997866i	$-0.520799\pi$
$239$	−115323.			−0.130593			−0.0652966	+	0.997866i	$0.520799\pi$
$240$	−152878.	+	264793.i	−0.171324	+	0.296742i
$241$	−454932.	−	787965.i	−0.504549	−	0.873905i	−0.999986	−	0.00526118i	$-0.998325\pi$
$241$	−454932.	−	787965.i	−0.504549	−	0.873905i	0.495437	−	0.868644i	$-0.335008\pi$
$242$	345934.	+	599176.i	0.379713	+	0.657682i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−96232.2			−0.103477
$245$		0			0
$246$	−439949.			−0.463516
$247$	−139925.	+	242357.i	−0.145933	+	0.252763i
$248$	−838675.	−	1.45263e6i	−0.865894	−	1.49977i
$249$	−457618.	−	792618.i	−0.467740	−	0.810150i
$250$	−485651.	+	841171.i	−0.491444	+	0.851206i
$251$	321264.			0.321868			0.160934	−	0.986965i	$-0.448549\pi$
$251$	321264.			0.321868			0.160934	+	0.986965i	$0.448549\pi$
$252$		0			0
$253$	25264.8			0.0248150
$254$	373369.	−	646694.i	0.363123	−	0.628948i
$255$	−318878.	−	552313.i	−0.307096	−	0.531906i
$256$	114321.	+	198010.i	0.109025	+	0.188837i
$257$	−278246.	+	481936.i	−0.262782	+	0.455152i	−0.966980	−	0.254851i	$-0.917973\pi$
$257$	−278246.	+	481936.i	−0.262782	+	0.455152i	0.704198	+	0.710004i	$0.251307\pi$
$258$	663624.			0.620688
$259$		0			0
$260$	−12449.6			−0.0114215
$261$	51013.1	−	88357.2i	0.0463533	−	0.0802862i
$262$	−147291.	−	255115.i	−0.132563	−	0.229606i
$263$	116690.	+	202112.i	0.104026	+	0.180179i	0.913340	−	0.407198i	$-0.133494\pi$
$263$	116690.	+	202112.i	0.104026	+	0.180179i	−0.809314	+	0.587377i	$0.800161\pi$
$264$	155211.	−	268834.i	0.137061	−	0.237396i
$265$	−336036.			−0.293948
$266$		0			0
$267$	−783923.			−0.672969
$268$	−64724.4	+	112106.i	−0.0550466	+	0.0953436i
$269$	−739286.	−	1.28048e6i	−0.622919	−	1.07893i	−0.988939	−	0.148321i	$-0.952613\pi$
$269$	−739286.	−	1.28048e6i	−0.622919	−	1.07893i	0.366020	−	0.930607i	$-0.380720\pi$
$270$	71465.3	+	123782.i	0.0596604	+	0.103335i
$271$	88880.8	−	153946.i	0.0735165	−	0.127334i	−0.826924	−	0.562314i	$-0.809911\pi$
$271$	88880.8	−	153946.i	0.0735165	−	0.127334i	0.900440	+	0.434980i	$0.143245\pi$
$272$	1.85755e6			1.52236
$273$		0			0
$274$	2.30293e6			1.85312
$275$	168661.	−	292130.i	0.134488	−	0.232940i
$276$	1441.67	+	2497.04i	0.00113918	+	0.00197312i
$277$	611259.	+	1.05873e6i	0.478659	+	0.829062i	0.999701	−	0.0244697i	$-0.00778972\pi$
$277$	611259.	+	1.05873e6i	0.478659	+	0.829062i	−0.521042	+	0.853531i	$0.674456\pi$
$278$	−26995.2	+	46757.1i	−0.0209496	+	0.0362857i
$279$	−726491.			−0.558753
$280$		0			0
$281$	177799.			0.134327			0.0671636	−	0.997742i	$-0.478605\pi$
$281$	177799.			0.134327			0.0671636	+	0.997742i	$0.478605\pi$
$282$	−491291.	+	850941.i	−0.367888	+	0.637201i
$283$	−545259.	−	944416.i	−0.404703	−	0.700966i	0.589584	−	0.807707i	$-0.299292\pi$
$283$	−545259.	−	944416.i	−0.404703	−	0.700966i	−0.994287	+	0.106741i	$0.965958\pi$
$284$	−74681.5	−	129352.i	−0.0549436	−	0.0951651i
$285$	−306587.	+	531024.i	−0.223584	+	0.387260i
$286$	−148530.			−0.107374
$287$		0			0
$288$	68440.8			0.0486221
$289$	−1.22734e6	+	2.12581e6i	−0.864410	+	1.49720i
$290$	−123479.	−	213872.i	−0.0862183	−	0.149334i
$291$	−531481.	−	920551.i	−0.367921	−	0.637258i
$292$	−48292.7	+	83645.4i	−0.0331455	+	0.0574096i
$293$	−545742.			−0.371380			−0.185690	−	0.982608i	$-0.559452\pi$
$293$	−545742.			−0.371380			−0.185690	+	0.982608i	$0.559452\pi$
$294$		0			0
$295$	319193.			0.213549
$296$	1.20599e6	−	2.08884e6i	0.800047	−	1.38572i
$297$	−67224.8	−	116437.i	−0.0442220	−	0.0765948i
$298$	−1.37643e6	−	2.38405e6i	−0.897870	−	1.55516i
$299$	10128.4	−	17542.9i	0.00655182	−	0.0113481i
$300$	38496.8			0.0246957
$301$		0			0
$302$	−1.05168e6			−0.663539
$303$	100047.	−	173287.i	0.0626035	−	0.108432i
$304$	−892975.	−	1.54668e6i	−0.554186	−	0.959878i
$305$	740670.	+	1.28288e6i	0.455906	+	0.789652i
$306$	434170.	−	752005.i	0.265068	−	0.459111i
$307$	3.29000e6			1.99228			0.996138	−	0.0878052i	$-0.0279853\pi$
$307$	3.29000e6			1.99228			0.996138	+	0.0878052i	$0.0279853\pi$
$308$		0			0
$309$	−1.22338e6			−0.728892
$310$	−879251.	+	1.52291e6i	−0.519647	+	0.900056i
$311$	−349856.	−	605968.i	−0.205111	−	0.355262i	0.745057	−	0.667000i	$-0.232422\pi$
$311$	−349856.	−	605968.i	−0.205111	−	0.355262i	−0.950168	+	0.311738i	$0.899089\pi$
$312$	−124445.	−	215545.i	−0.0723754	−	0.125358i
$313$	311609.	−	539723.i	0.179783	−	0.311394i	−0.762023	−	0.647550i	$-0.775794\pi$
$313$	311609.	−	539723.i	0.179783	−	0.311394i	0.941806	+	0.336156i	$0.109127\pi$
$314$	−1.44283e6			−0.825831
$315$		0			0
$316$	−39672.0			−0.0223494
$317$	319622.	−	553601.i	0.178644	−	0.309420i	−0.762772	−	0.646667i	$-0.776162\pi$
$317$	319622.	−	553601.i	0.178644	−	0.309420i	0.941416	+	0.337247i	$0.109496\pi$
$318$	−228766.	−	396234.i	−0.126860	−	0.219727i
$319$	116153.	+	201182.i	0.0639075	+	0.110691i
$320$	626399.	−	1.08496e6i	0.341961	−	0.592294i
$321$	1.05864e6			0.573435
$322$		0			0
$323$	3.72519e6			1.98675
$324$	7671.99	−	13288.3i	0.00406018	−	0.00703244i
$325$	−135229.	−	234223.i	−0.0710168	−	0.123005i
$326$	1.46801e6	+	2.54267e6i	0.765041	+	1.32509i
$327$	155989.	−	270181.i	0.0806724	−	0.139729i
$328$	1.67858e6			0.861506
$329$		0			0
$330$	−325441.			−0.164508
$331$	−704817.	+	1.22078e6i	−0.353595	+	0.612445i	−0.986876	−	0.161477i	$-0.948374\pi$
$331$	−704817.	+	1.22078e6i	−0.353595	+	0.612445i	0.633281	+	0.773922i	$0.281708\pi$
$332$	118913.	+	205963.i	0.0592084	+	0.102552i
$333$	−522337.	−	904714.i	−0.258131	−	0.447096i
$334$	595674.	−	1.03174e6i	0.292175	−	0.506062i
$335$	1.99265e6			0.970108
$336$		0			0
$337$	−1.55677e6			−0.746704			−0.373352	−	0.927690i	$-0.621792\pi$
$337$	−1.55677e6			−0.746704			−0.373352	+	0.927690i	$0.621792\pi$
$338$	951528.	−	1.64810e6i	0.453033	−	0.784676i
$339$	119630.	+	207205.i	0.0565381	+	0.0979269i
$340$	82861.1	+	143520.i	0.0388735	+	0.0673308i
$341$	827080.	−	1.43254e6i	0.385178	−	0.667148i
$342$	−834870.			−0.385970
$343$		0			0
$344$	−2.53200e6			−1.15363
$345$	22192.1	−	38437.9i	0.0100381	−	0.0173865i
$346$	1.60718e6	+	2.78372e6i	0.721731	+	1.25007i
$347$	−124148.	−	215031.i	−0.0553500	−	0.0958690i	0.837023	−	0.547168i	$-0.184294\pi$
$347$	−124148.	−	215031.i	−0.0553500	−	0.0958690i	−0.892373	+	0.451299i	$0.850961\pi$
$348$	−13255.8	+	22959.8i	−0.00586758	+	0.0101629i
$349$	−1.86169e6			−0.818171			−0.409086	−	0.912496i	$-0.634152\pi$
$349$	−1.86169e6			−0.818171			−0.409086	+	0.912496i	$0.634152\pi$
$350$		0			0
$351$	−107799.			−0.0467031
$352$	−77917.0	+	134956.i	−0.0335178	+	0.0580546i
$353$	885642.	+	1.53398e6i	0.378287	+	0.655212i	0.990813	−	0.135238i	$-0.0431799\pi$
$353$	885642.	+	1.53398e6i	0.378287	+	0.655212i	−0.612526	+	0.790450i	$0.709847\pi$
$354$	217299.	+	376373.i	0.0921616	+	0.159629i
$355$	−1.14960e6	+	1.99117e6i	−0.484146	+	0.838566i
$356$	203704.			0.0851871
$357$		0			0
$358$	−1.18375e6			−0.488147
$359$	2.23780e6	−	3.87599e6i	0.916401	−	1.58725i	0.111563	−	0.993757i	$-0.464414\pi$
$359$	2.23780e6	−	3.87599e6i	0.916401	−	1.58725i	0.804837	−	0.593495i	$-0.202253\pi$
$360$	−272669.	−	472277.i	−0.110887	−	0.192062i
$361$	−552751.	−	957393.i	−0.223235	−	0.386654i
$362$	512243.	−	887230.i	0.205449	−	0.355848i
$363$	−1.14333e6			−0.455412
$364$		0			0
$365$	1.48678e6			0.584135
$366$	−1.00846e6	+	1.74671e6i	−0.393511	+	0.681582i
$367$	1.58548e6	+	2.74614e6i	0.614465	+	1.06428i	0.990478	+	0.137670i	$0.0439613\pi$
$367$	1.58548e6	+	2.74614e6i	0.614465	+	1.06428i	−0.376014	+	0.926614i	$0.622705\pi$
$368$	64637.5	+	111955.i	0.0248809	+	0.0430949i
$369$	363512.	−	629622.i	0.138980	−	0.240721i
$370$	−2.52868e6			−0.960261
$371$		0			0
$372$	188780.			0.0707292
$373$	1.15590e6	−	2.00207e6i	0.430177	−	0.745088i	−0.566712	−	0.823916i	$-0.691785\pi$
$373$	1.15590e6	−	2.00207e6i	0.430177	−	0.745088i	0.996888	+	0.0788285i	$0.0251179\pi$
$374$	988570.	+	1.71225e6i	0.365450	+	0.632978i
$375$	−802548.	−	1.39005e6i	−0.294709	−	0.510450i
$376$	1.87447e6	−	3.24669e6i	0.683770	−	1.18432i
$377$	186257.			0.0674931
$378$		0			0
$379$	−591840.			−0.211644			−0.105822	−	0.994385i	$-0.533747\pi$
$379$	−591840.			−0.211644			−0.105822	+	0.994385i	$0.533747\pi$
$380$	79667.2	−	137988.i	0.0283022	−	0.0490209i
$381$	617000.	+	1.06868e6i	0.217757	+	0.377167i
$382$	−472521.	−	818431.i	−0.165677	−	0.286961i
$383$	−1.79883e6	+	3.11567e6i	−0.626605	+	1.08531i	0.361623	+	0.932324i	$0.382223\pi$
$383$	−1.79883e6	+	3.11567e6i	−0.626605	+	1.08531i	−0.988228	+	0.152987i	$0.951111\pi$
$384$	1.46241e6			0.506105
$385$		0			0
$386$	641464.			0.219131
$387$	−548327.	+	949730.i	−0.186107	+	0.322346i
$388$	138106.	+	239207.i	0.0465730	+	0.0806667i
$389$	1.12373e6	+	1.94636e6i	0.376520	+	0.652152i	0.990553	−	0.137128i	$-0.0437873\pi$
$389$	1.12373e6	+	1.94636e6i	0.376520	+	0.652152i	−0.614033	+	0.789280i	$0.710454\pi$
$390$	−130466.	+	225973.i	−0.0434345	+	0.0752308i
$391$	−269646.			−0.0891973
$392$		0			0
$393$	486803.			0.158991
$394$	−611976.	+	1.05997e6i	−0.198607	+	0.343997i
$395$	305343.	+	528870.i	0.0984681	+	0.170552i
$396$	17468.5	+	30256.3i	0.00559780	+	0.00969567i
$397$	−2.29335e6	+	3.97220e6i	−0.730288	+	1.26490i	0.226471	+	0.974018i	$0.427281\pi$
$397$	−2.29335e6	+	3.97220e6i	−0.730288	+	1.26490i	−0.956760	+	0.290879i	$0.906052\pi$
$398$	−4.03169e6			−1.27579
$399$		0			0
$400$	1.72602e6			0.539380
$401$	−3.00216e6	+	5.19990e6i	−0.932338	+	1.61486i	−0.153023	+	0.988223i	$0.548901\pi$
$401$	−3.00216e6	+	5.19990e6i	−0.932338	+	1.61486i	−0.779314	+	0.626633i	$0.784432\pi$
$402$	1.35655e6	+	2.34962e6i	0.418670	+	0.725158i
$403$	−663134.	−	1.14858e6i	−0.203394	−	0.352289i
$404$	−25997.5	+	45028.9i	−0.00792461	+	0.0137258i
$405$	−236196.			−0.0715542
$406$		0			0
$407$	2.37864e6			0.711774
$408$	−1.65654e6	+	2.86921e6i	−0.492664	+	0.853319i
$409$	−1.77670e6	−	3.07733e6i	−0.525177	−	0.909633i	−0.999570	−	0.0293196i	$-0.990666\pi$
$409$	−1.77670e6	−	3.07733e6i	−0.525177	−	0.909633i	0.474393	−	0.880313i	$-0.342667\pi$
$410$	−879898.	−	1.52403e6i	−0.258507	−	0.447747i
$411$	−1.90282e6	+	3.29578e6i	−0.555639	+	0.962395i
$412$	317896.			0.0922661
$413$		0			0
$414$	60431.6			0.0173286
$415$	1.83047e6	−	3.17047e6i	0.521726	−	0.903657i
$416$	62472.1	+	108205.i	0.0176992	+	0.0306559i
$417$	−44610.2	−	77267.1i	−0.0125630	−	0.0217598i
$418$	950465.	−	1.64625e6i	0.266070	−	0.460846i
$419$	−2.01375e6			−0.560365			−0.280182	−	0.959947i	$-0.590395\pi$
$419$	−2.01375e6			−0.560365			−0.280182	+	0.959947i	$0.590395\pi$
$420$		0			0
$421$	−5.89987e6			−1.62232			−0.811161	−	0.584823i	$-0.801164\pi$
$421$	−5.89987e6			−1.62232			−0.811161	+	0.584823i	$0.801164\pi$
$422$	1.92223e6	−	3.32940e6i	0.525442	−	0.910092i
$423$	−811869.	−	1.40620e6i	−0.220615	−	0.382116i
$424$	872834.	+	1.51179e6i	0.235786	+	0.408392i
$425$	−1.80009e6	+	3.11784e6i	−0.483416	+	0.837301i
$426$	−3.13049e6			−0.835774
$427$		0			0
$428$	−275088.			−0.0725877
$429$	122724.	−	212565.i	0.0321949	−	0.0557632i
$430$	1.32725e6	+	2.29886e6i	0.346163	+	0.599573i
$431$	1.90524e6	+	3.29997e6i	0.494033	+	0.855690i	0.999976	−	0.00687645i	$-0.00218886\pi$
$431$	1.90524e6	+	3.29997e6i	0.494033	+	0.855690i	−0.505943	+	0.862567i	$0.668856\pi$
$432$	343976.	−	595784.i	0.0886786	−	0.153596i
$433$	−6.59449e6			−1.69029			−0.845146	−	0.534536i	$-0.820487\pi$
$433$	−6.59449e6			−1.69029			−0.845146	+	0.534536i	$0.820487\pi$
$434$		0			0
$435$	408105.			0.103407
$436$	−40534.0	+	70207.0i	−0.0102118	+	0.0176874i
$437$	129626.	+	224519.i	0.0324705	+	0.0562406i
$438$	1.01216e6	+	1.75312e6i	0.252096	+	0.436643i
$439$	−2.27514e6	+	3.94065e6i	−0.563438	+	0.975904i	0.433755	+	0.901031i	$0.357188\pi$
$439$	−2.27514e6	+	3.94065e6i	−0.563438	+	0.975904i	−0.997193	+	0.0748729i	$0.976145\pi$
$440$	1.24169e6			0.305761
$441$		0			0
$442$	1.58523e6			0.385954
$443$	−2.55769e6	+	4.43004e6i	−0.619210	+	1.07250i	0.370420	+	0.928864i	$0.379214\pi$
$443$	−2.55769e6	+	4.43004e6i	−0.619210	+	1.07250i	−0.989630	+	0.143639i	$0.954120\pi$
$444$	135730.	+	235092.i	0.0326753	+	0.0565952i
$445$	−1.56785e6	−	2.71559e6i	−0.375321	−	0.650076i
$446$	114954.	−	199106.i	0.0273645	−	0.0473967i
$447$	4.54916e6			1.07687
$448$		0			0
$449$	5.95600e6			1.39424			0.697122	−	0.716953i	$-0.254464\pi$
$449$	5.95600e6			1.39424			0.697122	+	0.716953i	$0.254464\pi$
$450$	403426.	−	698755.i	0.0939145	−	0.162665i
$451$	827687.	+	1.43360e6i	0.191613	+	0.331883i
$452$	−31086.1	−	53842.7i	−0.00715682	−	0.0123960i
$453$	868962.	−	1.50509e6i	0.198955	−	0.344601i
$454$	−4.04329e6			−0.920652
$455$		0			0
$456$	3.18537e6			0.717378
$457$	1.29917e6	−	2.25022e6i	0.290988	−	0.504006i	−0.683056	−	0.730366i	$-0.739349\pi$
$457$	1.29917e6	−	2.25022e6i	0.290988	−	0.504006i	0.974044	+	0.226361i	$0.0726828\pi$
$458$	2.56309e6	+	4.43940e6i	0.570953	+	0.988919i
$459$	717476.	+	1.24270e6i	0.158956	+	0.275319i
$460$	−5766.66	+	9988.15i	−0.00127066	+	0.00220085i
$461$	−4.51513e6			−0.989505			−0.494752	−	0.869034i	$-0.664741\pi$
$461$	−4.51513e6			−0.989505			−0.494752	+	0.869034i	$0.664741\pi$
$462$		0			0
$463$	−5.55129e6			−1.20349			−0.601744	−	0.798689i	$-0.705527\pi$
$463$	−5.55129e6			−1.20349			−0.601744	+	0.798689i	$0.705527\pi$
$464$	−594330.	+	1.02941e6i	−0.128154	+	0.221969i
$465$	−1.45298e6	−	2.51664e6i	−0.311622	−	0.539745i
$466$	1.39513e6	+	2.41644e6i	0.297613	+	0.515480i
$467$	−3.97675e6	+	6.88794e6i	−0.843794	+	1.46149i	0.0428708	+	0.999081i	$0.486350\pi$
$467$	−3.97675e6	+	6.88794e6i	−0.843794	+	1.46149i	−0.886665	+	0.462413i	$0.846984\pi$
$468$	28011.7			0.00591187
$469$		0			0
$470$	−3.93033e6			−0.820699
$471$	1.19215e6	−	2.06487e6i	0.247617	−	0.428885i
$472$	−829085.	−	1.43602e6i	−0.171295	−	0.296691i
$473$	−1.24849e6	−	2.16246e6i	−0.256586	−	0.444421i
$474$	−415742.	+	720086.i	−0.0849920	+	0.147210i
$475$	3.46140e6			0.703912
$476$		0			0
$477$	756080.			0.152150
$478$	314037.	−	543928.i	0.0628653	−	0.108886i
$479$	−3.28185e6	−	5.68433e6i	−0.653552	−	1.13199i	−0.982255	−	0.187552i	$-0.939945\pi$
$479$	−3.28185e6	−	5.68433e6i	−0.653552	−	1.13199i	0.328703	−	0.944433i	$-0.393389\pi$
$480$	136882.	+	237086.i	0.0271170	+	0.0469681i
$481$	953568.	−	1.65163e6i	0.187927	−	0.325499i
$482$	4.95532e6			0.971525
$483$		0			0
$484$	297096.			0.0576479
$485$	2.12592e6	−	3.68221e6i	0.410387	−	0.710810i
$486$	−160797.	−	278509.i	−0.0308807	−	0.0534870i
$487$	−2.33185e6	−	4.03888e6i	−0.445531	−	0.771683i	0.552558	−	0.833475i	$-0.313652\pi$
$487$	−2.33185e6	−	4.03888e6i	−0.445531	−	0.771683i	−0.998089	+	0.0617918i	$0.980319\pi$
$488$	3.84770e6	−	6.66441e6i	0.731394	−	1.26681i
$489$	−4.85183e6			−0.917558
$490$		0			0
$491$	−917227.			−0.171701			−0.0858506	−	0.996308i	$-0.527361\pi$
$491$	−917227.			−0.171701			−0.0858506	+	0.996308i	$0.527361\pi$
$492$	−94459.4	+	163608.i	−0.0175927	+	0.0304714i
$493$	−1.23967e6	−	2.14717e6i	−0.229715	−	0.397878i
$494$	−762061.	−	1.31993e6i	−0.140499	−	0.243351i
$495$	268899.	−	465747.i	0.0493261	−	0.0854353i
$496$	8.46401e6			1.54480
$497$		0			0
$498$	4.98458e6			0.900648
$499$	−156718.	+	271443.i	−0.0281752	+	0.0488009i	−0.879769	−	0.475401i	$-0.842303\pi$
$499$	−156718.	+	271443.i	−0.0281752	+	0.0488009i	0.851594	+	0.524202i	$0.175636\pi$
$500$	208544.	+	361208.i	0.0373054	+	0.0646148i
$501$	984365.	+	1.70497e6i	0.175211	+	0.303475i
$502$	−874837.	+	1.51526e6i	−0.154942	+	0.268367i
$503$	3.74110e6			0.659294			0.329647	−	0.944104i	$-0.393070\pi$
$503$	3.74110e6			0.659294			0.329647	+	0.944104i	$0.393070\pi$
$504$		0			0
$505$	800378.			0.139658
$506$	−68798.9	+	119163.i	−0.0119455	+	0.0206902i
$507$	1.57242e6	+	2.72351e6i	0.271675	+	0.470554i
$508$	−160329.	−	277697.i	−0.0275646	−	0.0477433i
$509$	5.15085e6	−	8.92153e6i	0.881220	−	1.52632i	0.0312337	−	0.999512i	$-0.490056\pi$
$509$	5.15085e6	−	8.92153e6i	0.881220	−	1.52632i	0.849986	−	0.526805i	$-0.176610\pi$
$510$	3.47336e6			0.591323
$511$		0			0
$512$	−6.44492e6			−1.08653
$513$	689821.	−	1.19480e6i	0.115729	−	0.200449i
$514$	−1.51539e6	−	2.62473e6i	−0.252998	−	0.438205i
$515$	−2.44675e6	−	4.23790e6i	−0.406510	−	0.704096i
$516$	142484.	−	246789.i	0.0235581	−	0.0408039i
$517$	3.69711e6			0.608326
$518$		0			0
$519$	−5.31181e6			−0.865614
$520$	497780.	−	862180.i	0.0807289	−	0.139827i
$521$	−3.28663e6	−	5.69260e6i	−0.530464	−	0.918791i	−0.999368	−	0.0355415i	$-0.988684\pi$
$521$	−3.28663e6	−	5.69260e6i	−0.530464	−	0.918791i	0.468904	−	0.883249i	$-0.344649\pi$
$522$	277829.	+	481213.i	0.0446273	+	0.0772967i
$523$	4.18266e6	−	7.24458e6i	0.668650	−	1.15814i	−0.309632	−	0.950856i	$-0.600206\pi$
$523$	4.18266e6	−	7.24458e6i	0.668650	−	1.15814i	0.978282	−	0.207279i	$-0.0664607\pi$
$524$	−126497.			−0.0201257
$525$		0			0
$526$	−1.27103e6			−0.200306
$527$	−8.82724e6	+	1.52892e7i	−1.38452	+	2.39805i
$528$	783205.	+	1.35655e6i	0.122262	+	0.211764i
$529$	3.20879e6	+	5.55778e6i	0.498542	+	0.863500i
$530$	915063.	−	1.58494e6i	0.141502	−	0.245088i
$531$	−718184.			−0.110535
$532$		0			0
$533$	1.32724e6			0.202364
$534$	2.13471e6	−	3.69742e6i	0.323956	−	0.561108i
$535$	2.11727e6	+	3.66722e6i	0.319810	+	0.553927i
$536$	−5.17581e6	−	8.96477e6i	−0.778155	−	1.34780i
$537$	978083.	−	1.69409e6i	0.146366	−	0.253513i
$538$	8.05263e6			1.19945
$539$		0			0
$540$	61376.0			0.00905761
$541$	4.03311e6	−	6.98556e6i	0.592444	−	1.02614i	−0.401458	−	0.915877i	$-0.631496\pi$
$541$	4.03311e6	−	6.98556e6i	0.592444	−	1.02614i	0.993902	−	0.110266i	$-0.0351702\pi$
$542$	484064.	+	838424.i	0.0707791	+	0.122593i
$543$	846492.	+	1.46617e6i	0.123204	+	0.213395i
$544$	831592.	−	1.44036e6i	0.120479	−	0.208676i
$545$	1.24791e6			0.179967
$546$		0			0
$547$	3.90775e6			0.558416			0.279208	−	0.960231i	$-0.409928\pi$
$547$	3.90775e6			0.558416			0.279208	+	0.960231i	$0.409928\pi$
$548$	494451.	−	856414.i	0.0703350	−	0.121824i
$549$	−1.66651e6	−	2.88647e6i	−0.235981	−	0.408730i
$550$	918568.	+	1.59101e6i	0.129481	+	0.224267i
$551$	−1.19189e6	+	2.06441e6i	−0.167246	+	0.289679i
$552$	−230571.			−0.0322075
$553$		0			0
$554$	−6.65811e6			−0.921672
$555$	2.08935e6	−	3.61886e6i	0.287924	−	0.498700i
$556$	11592.0	+	20078.0i	0.00159028	+	0.00275444i
$557$	5.79311e6	+	1.00340e7i	0.791177	+	1.37036i	0.925239	+	0.379385i	$0.123864\pi$
$557$	5.79311e6	+	1.00340e7i	0.791177	+	1.37036i	−0.134062	+	0.990973i	$0.542802\pi$
$558$	1.97832e6	−	3.42654e6i	0.268974	−	0.465876i
$559$	−2.00203e6			−0.270982
$560$		0			0
$561$	−3.26727e6			−0.438306
$562$	−484167.	+	838602.i	−0.0646628	+	0.111999i
$563$	955879.	+	1.65563e6i	0.127096	+	0.220137i	0.922550	−	0.385877i	$-0.126101\pi$
$563$	955879.	+	1.65563e6i	0.127096	+	0.220137i	−0.795454	+	0.606014i	$0.792768\pi$
$564$	210966.	+	365403.i	0.0279263	+	0.0483698i
$565$	−478520.	+	828822.i	−0.0630637	+	0.109230i
$566$	5.93920e6			0.779268
$567$		0			0
$568$	1.19441e7			1.55340
$569$	−4.08409e6	+	7.07385e6i	−0.528828	+	0.915957i	0.470607	+	0.882343i	$0.344035\pi$
$569$	−4.08409e6	+	7.07385e6i	−0.528828	+	0.915957i	−0.999435	+	0.0336138i	$0.989298\pi$
$570$	−1.66974e6	−	2.89208e6i	−0.215259	−	0.372840i
$571$	3.73297e6	+	6.46569e6i	0.479141	+	0.829897i	0.999714	−	0.0239203i	$-0.00761479\pi$
$571$	3.73297e6	+	6.46569e6i	0.479141	+	0.829897i	−0.520573	+	0.853817i	$0.674281\pi$
$572$	−31890.1	+	55235.3i	−0.00407536	+	0.00705873i
$573$	1.56170e6			0.198706
$574$		0			0
$575$	−250552.			−0.0316030
$576$	−1.40940e6	+	2.44115e6i	−0.177002	+	0.306576i
$577$	−3.44219e6	−	5.96205e6i	−0.430423	−	0.745514i	0.566487	−	0.824071i	$-0.308302\pi$
$577$	−3.44219e6	−	5.96205e6i	−0.430423	−	0.745514i	−0.996910	+	0.0785568i	$0.974969\pi$
$578$	−6.68436e6	−	1.15777e7i	−0.832224	−	1.44145i
$579$	−530017.	+	918016.i	−0.0657042	+	0.113803i
$580$	−106047.			−0.0130896
$581$		0			0
$582$	5.78912e6			0.708444
$583$	−860766.	+	1.49089e6i	−0.104885	+	0.181666i
$584$	−3.86182e6	−	6.68886e6i	−0.468554	−	0.811559i
$585$	−215597.	−	373426.i	−0.0260468	−	0.0451143i
$586$	1.48612e6	−	2.57403e6i	0.178776	−	0.309649i
$587$	8.91086e6			1.06739			0.533696	−	0.845676i	$-0.320803\pi$
$587$	8.91086e6			1.06739			0.533696	+	0.845676i	$0.320803\pi$
$588$		0			0
$589$	1.69740e7			2.01602
$590$	−869197.	+	1.50549e6i	−0.102799	+	0.178053i
$591$	−1.01130e6	−	1.75163e6i	−0.119100	−	0.206288i
$592$	6.08551e6	+	1.05404e7i	0.713662	+	1.23610i
$593$	6.17151e6	−	1.06894e7i	0.720700	−	1.24829i	−0.240019	−	0.970768i	$-0.577154\pi$
$593$	6.17151e6	−	1.06894e7i	0.720700	−	1.24829i	0.960720	−	0.277521i	$-0.0895128\pi$
$594$	732243.			0.0851508
$595$		0			0
$596$	−1.18211e6			−0.136314
$597$	3.33123e6	−	5.76986e6i	0.382533	−	0.662567i
$598$	55161.4	+	95542.3i	0.00630786	+	0.0109255i
$599$	−4.52866e6	−	7.84387e6i	−0.515707	−	0.893230i	−0.999834	−	0.0182325i	$-0.994196\pi$
$599$	−4.52866e6	−	7.84387e6i	−0.515707	−	0.893230i	0.484127	−	0.874998i	$-0.339137\pi$
$600$	−1.53924e6	+	2.66603e6i	−0.174553	+	0.302334i
$601$	−7.41700e6			−0.837611			−0.418805	−	0.908076i	$-0.637551\pi$
$601$	−7.41700e6			−0.837611			−0.418805	+	0.908076i	$0.637551\pi$
$602$		0			0
$603$	−4.48347e6			−0.502136
$604$	−225801.	+	391100.i	−0.0251846	+	0.0436209i
$605$	−2.28666e6	−	3.96061e6i	−0.253988	−	0.439919i
$606$	544880.	+	943760.i	0.0602725	+	0.104395i
$607$	−2.88907e6	+	5.00401e6i	−0.318263	+	0.551247i	−0.980126	−	0.198378i	$-0.936433\pi$
$607$	−2.88907e6	+	5.00401e6i	−0.318263	+	0.551247i	0.661863	+	0.749625i	$0.269766\pi$
$608$	−1.59908e6			−0.175432
$609$		0			0
$610$	−8.06770e6			−0.877860
$611$	1.48213e6	−	2.56713e6i	0.160614	−	0.278192i
$612$	−186437.	−	322919.i	−0.0201212	−	0.0348510i
$613$	−3.14632e6	−	5.44959e6i	−0.338183	−	0.585750i	0.645908	−	0.763415i	$-0.276479\pi$
$613$	−3.14632e6	−	5.44959e6i	−0.338183	−	0.585750i	−0.984091	+	0.177665i	$0.943146\pi$
$614$	−8.95902e6	+	1.55175e7i	−0.959047	+	1.66112i
$615$	2.90810e6			0.310043
$616$		0			0
$617$	−9.79133e6			−1.03545			−0.517725	−	0.855547i	$-0.673221\pi$
$617$	−9.79133e6			−1.03545			−0.517725	+	0.855547i	$0.673221\pi$
$618$	3.33139e6	−	5.77013e6i	0.350876	−	0.607735i
$619$	−6.63386e6	−	1.14902e7i	−0.695889	−	1.20531i	−0.969880	−	0.243583i	$-0.921677\pi$
$619$	−6.63386e6	−	1.14902e7i	−0.695889	−	1.20531i	0.273991	−	0.961732i	$-0.411656\pi$
$620$	377560.	+	653953.i	0.0394463	+	0.0683231i
$621$	−49932.3	+	86485.3i	−0.00519580	+	0.00899939i
$622$	3.81079e6			0.394947
$623$		0			0
$624$	1.25591e6			0.129121
$625$	352380.	−	610339.i	0.0360837	−	0.0624987i
$626$	1.69709e6	+	2.93945e6i	0.173089	+	0.299799i
$627$	1.57066e6	+	2.72047e6i	0.159556	+	0.276360i
$628$	−309783.	+	536560.i	−0.0313443	+	0.0542900i
$629$	−2.53867e7			−2.55846
$630$		0			0
$631$	4.41233e6			0.441158			0.220579	−	0.975369i	$-0.429205\pi$
$631$	4.41233e6			0.441158			0.220579	+	0.975369i	$0.429205\pi$
$632$	1.58622e6	−	2.74742e6i	0.157969	−	0.273610i
$633$	3.17653e6	+	5.50191e6i	0.315097	+	0.545763i
$634$	1.74073e6	+	3.01504e6i	0.171992	+	0.297899i
$635$	−2.46800e6	+	4.27470e6i	−0.242891	+	0.420699i
$636$	−196469.			−0.0192598
$637$		0			0
$638$	−1.26518e6			−0.123056
$639$	2.58660e6	−	4.48013e6i	0.250598	−	0.434049i
$640$	2.92482e6	+	5.06594e6i	0.282260	+	0.488888i
$641$	−4.06518e6	−	7.04109e6i	−0.390782	−	0.676854i	0.601771	−	0.798669i	$-0.294462\pi$
$641$	−4.06518e6	−	7.04109e6i	−0.390782	−	0.676854i	−0.992553	+	0.121815i	$0.961129\pi$
$642$	−2.88278e6	+	4.99313e6i	−0.276041	+	0.478118i
$643$	3.12961e6			0.298513			0.149256	−	0.988799i	$-0.452312\pi$
$643$	3.12961e6			0.298513			0.149256	+	0.988799i	$0.452312\pi$
$644$		0			0
$645$	−4.38661e6			−0.415174
$646$	−1.01441e7	+	1.75701e7i	−0.956384	+	1.65651i
$647$	6.73300e6	+	1.16619e7i	0.632336	+	1.09524i	0.987073	+	0.160271i	$0.0512370\pi$
$647$	6.73300e6	+	1.16619e7i	0.632336	+	1.09524i	−0.354737	+	0.934966i	$0.615430\pi$
$648$	613506.	+	1.06262e6i	0.0573960	+	0.0994127i
$649$	817622.	−	1.41616e6i	0.0761975	−	0.131978i
$650$	1.47297e6			0.136745
$651$		0			0
$652$	1.26076e6			0.116148
$653$	−7.23861e6	+	1.25376e7i	−0.664312	+	1.15062i	0.315159	+	0.949039i	$0.397942\pi$
$653$	−7.23861e6	+	1.25376e7i	−0.664312	+	1.15062i	−0.979471	+	0.201584i	$0.935391\pi$
$654$	849551.	+	1.47147e6i	0.0776685	+	0.134526i
$655$	973605.	+	1.68633e6i	0.0886706	+	0.153582i
$656$	−4.23511e6	+	7.33543e6i	−0.384243	+	0.665528i
$657$	−3.34525e6			−0.302353
$658$		0			0
$659$	432708.			0.0388134			0.0194067	−	0.999812i	$-0.493822\pi$
$659$	432708.			0.0388134			0.0194067	+	0.999812i	$0.493822\pi$
$660$	−69874.0	+	121025.i	−0.00624389	+	0.0108147i
$661$	−14982.6	−	25950.6i	−0.00133378	−	0.00231017i	0.865358	−	0.501155i	$-0.167091\pi$
$661$	−14982.6	−	25950.6i	−0.00133378	−	0.00231017i	−0.866692	+	0.498844i	$0.833758\pi$
$662$	−3.83859e6	−	6.64863e6i	−0.340429	−	0.589640i
$663$	−1.30981e6	+	2.26866e6i	−0.115724	+	0.200440i
$664$	−1.90182e7			−1.67398
$665$		0			0
$666$	5.68953e6			0.497039
$667$	86274.1	−	149431.i	0.00750872	−	0.0130055i
$668$	−255789.	−	443039.i	−0.0221789	−	0.0384150i
$669$	189964.	+	329028.i	0.0164099	+	0.0284228i
$670$	−5.42622e6	+	9.39849e6i	−0.466993	+	0.808856i
$671$	7.58899e6			0.650696
$672$		0			0
$673$	−6.71329e6			−0.571344			−0.285672	−	0.958327i	$-0.592217\pi$
$673$	−6.71329e6			−0.571344			−0.285672	+	0.958327i	$0.592217\pi$
$674$	4.23925e6	−	7.34259e6i	0.359450	−	0.622586i
$675$	666670.	+	1.15471e6i	0.0563186	+	0.0975467i
$676$	−408596.	−	707710.i	−0.0343897	−	0.0595646i
$677$	−2.22965e6	+	3.86186e6i	−0.186967	+	0.323836i	−0.944237	−	0.329265i	$-0.893199\pi$
$677$	−2.22965e6	+	3.86186e6i	−0.186967	+	0.323836i	0.757271	+	0.653101i	$0.226532\pi$
$678$	−1.30306e6			−0.108866
$679$		0			0
$680$	−1.32523e7			−1.09905
$681$	3.34081e6	−	5.78646e6i	0.276048	−	0.478129i
$682$	4.50446e6	+	7.80195e6i	0.370836	+	0.642306i
$683$	8.99196e6	+	1.55745e7i	0.737569	+	1.27751i	0.953587	+	0.301117i	$0.0973596\pi$
$683$	8.99196e6	+	1.55745e7i	0.737569	+	1.27751i	−0.216018	+	0.976389i	$0.569307\pi$
$684$	−179251.	+	310472.i	−0.0146495	+	0.0253736i
$685$	−1.52225e7			−1.23954
$686$		0			0
$687$	−8.47112e6			−0.684777
$688$	6.38830e6	−	1.10649e7i	0.514534	−	0.891199i
$689$	690143.	+	1.19536e6i	0.0553848	+	0.0959294i
$690$	120863.	+	209341.i	0.00966432	+	0.0167391i
$691$	1.25468e6	−	2.17316e6i	0.0999624	−	0.173140i	−0.811706	−	0.584066i	$-0.801461\pi$
$691$	1.25468e6	−	2.17316e6i	0.0999624	−	0.173140i	0.911669	+	0.410926i	$0.134794\pi$
$692$	1.38028e6			0.109573
$693$		0			0
$694$	1.35228e6			0.106578
$695$	178441.	−	309069.i	0.0140130	−	0.0242713i
$696$	−1.06003e6	−	1.83602e6i	−0.0829458	−	0.143666i
$697$	−8.83373e6	−	1.53005e7i	−0.688751	−	1.19295i
$698$	5.06959e6	−	8.78079e6i	0.393853	−	0.682174i
$699$	−4.61098e6			−0.356944
$700$		0			0
$701$	9.68649e6			0.744512			0.372256	−	0.928130i	$-0.378584\pi$
$701$	9.68649e6			0.744512			0.372256	+	0.928130i	$0.378584\pi$
$702$	293548.	−	508440.i	0.0224821	−	0.0389401i
$703$	1.22041e7	+	2.11381e7i	0.931357	+	1.61316i
$704$	−3.20908e6	−	5.55829e6i	−0.244033	−	0.422678i
$705$	3.24748e6	−	5.62479e6i	0.246078	−	0.426220i
$706$	−9.64681e6			−0.728403
$707$		0			0
$708$	186621.			0.0139919
$709$	4.76360e6	−	8.25079e6i	0.355893	−	0.616425i	−0.631377	−	0.775476i	$-0.717510\pi$
$709$	4.76360e6	−	8.25079e6i	0.355893	−	0.616425i	0.987270	+	0.159051i	$0.0508434\pi$
$710$	−6.26099e6	−	1.08443e7i	−0.466119	−	0.807342i
$711$	−687023.	−	1.18996e6i	−0.0509679	−	0.0882790i
$712$	−8.14478e6	+	1.41072e7i	−0.602115	+	1.04289i
$713$	−1.22865e6			−0.0905118
$714$		0			0
$715$	981794.			0.0718217
$716$	−254157.	+	440212.i	−0.0185276	+	0.0320907i
$717$	518953.	+	898853.i	0.0376990	+	0.0652966i
$718$	1.21876e7	+	2.11095e7i	0.882279	+	1.52815i
$719$	378588.	−	655734.i	0.0273114	−	0.0473048i	−0.852047	−	0.523466i	$-0.824639\pi$
$719$	378588.	−	655734.i	0.0273114	−	0.0473048i	0.879358	+	0.476161i	$0.157972\pi$
$720$	2.75181e6			0.197828
$721$		0			0
$722$	6.02081e6			0.429845
$723$	−4.09439e6	+	7.09169e6i	−0.291302	+	0.504549i
$724$	−219962.	−	380986.i	−0.0155956	−	0.0270124i
$725$	−1.15189e6	−	1.99513e6i	−0.0813889	−	0.140970i
$726$	3.11341e6	−	5.39258e6i	0.219227	−	0.379713i
$727$	2.66570e7			1.87058			0.935288	−	0.353888i	$-0.115141\pi$
$727$	2.66570e7			1.87058			0.935288	+	0.353888i	$0.115141\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	−4.04866e6	+	7.01248e6i	−0.281192	+	0.487040i
$731$	1.33249e7	+	2.30794e7i	0.922297	+	1.59747i
$732$	433045.	+	750056.i	0.0298714	+	0.0517387i
$733$	1.35429e7	−	2.34569e7i	0.931001	−	1.61254i	0.149387	−	0.988779i	$-0.452270\pi$
$733$	1.35429e7	−	2.34569e7i	0.931001	−	1.61254i	0.781614	−	0.623762i	$-0.214397\pi$
$734$	−1.72698e7			−1.18317
$735$		0			0
$736$	115748.			0.00787625
$737$	5.10425e6	−	8.84081e6i	0.346149	−	0.599547i
$738$	1.97977e6	+	3.42906e6i	0.133805	+	0.231758i
$739$	−1.09753e7	−	1.90098e7i	−0.739276	−	1.28046i	−0.952822	−	0.303531i	$-0.901834\pi$
$739$	−1.09753e7	−	1.90098e7i	−0.739276	−	1.28046i	0.213545	−	0.976933i	$-0.431499\pi$
$740$	−542921.	+	940366.i	−0.0364466	+	0.0631274i
$741$	2.51865e6			0.168508
$742$		0			0
$743$	5.77370e6			0.383691			0.191846	−	0.981425i	$-0.438553\pi$
$743$	5.77370e6			0.383691			0.191846	+	0.981425i	$0.438553\pi$
$744$	−7.54808e6	+	1.30737e7i	−0.499924	+	0.865894i
$745$	9.09832e6	+	1.57587e7i	0.600579	+	1.04023i
$746$	6.29527e6	+	1.09037e7i	0.414159	+	0.717345i
$747$	−4.11856e6	+	7.13356e6i	−0.270050	+	0.467740i
$748$	849005.			0.0554825
$749$		0			0
$750$	8.74171e6			0.567470
$751$	4.18875e6	−	7.25512e6i	0.271009	−	0.469402i	−0.698111	−	0.715989i	$-0.745976\pi$
$751$	4.18875e6	−	7.25512e6i	0.271009	−	0.469402i	0.969121	+	0.246587i	$0.0793093\pi$
$752$	9.45871e6	+	1.63830e7i	0.609940	+	1.05645i
$753$	−1.44569e6	−	2.50400e6i	−0.0929153	−	0.160934i
$754$	−507198.	+	878493.i	−0.0324900	+	0.0562743i
$755$	6.95170e6			0.443837
$756$		0			0
$757$	1.18828e7			0.753665			0.376833	−	0.926281i	$-0.377013\pi$
$757$	1.18828e7			0.753665			0.376833	+	0.926281i	$0.377013\pi$
$758$	1.61165e6	−	2.79145e6i	0.101882	−	0.176465i
$759$	−113692.	−	196920.i	−0.00716348	−	0.0124075i
$760$	6.37074e6	+	1.10344e7i	0.400088	+	0.692973i
$761$	8.84701e6	−	1.53235e7i	0.553777	−	0.959170i	−0.444221	−	0.895917i	$-0.646519\pi$
$761$	8.84701e6	−	1.53235e7i	0.553777	−	0.959170i	0.997998	−	0.0632523i	$-0.0201473\pi$
$762$	−6.72064e6			−0.419298
$763$		0			0
$764$	−405811.			−0.0251531
$765$	−2.86990e6	+	4.97082e6i	−0.177302	+	0.307096i
$766$	−9.79684e6	−	1.69686e7i	−0.603273	−	1.04490i
$767$	−655551.	−	1.13545e6i	−0.0402363	−	0.0696913i
$768$	1.02889e6	−	1.78209e6i	0.0629457	−	0.109025i
$769$	4.12006e6			0.251239			0.125620	−	0.992078i	$-0.459908\pi$
$769$	4.12006e6			0.251239			0.125620	+	0.992078i	$0.459908\pi$
$770$		0			0
$771$	5.00843e6			0.303435
$772$	137726.	−	238548.i	0.00831710	−	0.0144056i
$773$	6.34320e6	+	1.09868e7i	0.381821	+	0.661334i	0.991323	−	0.131451i	$-0.0419637\pi$
$773$	6.34320e6	+	1.09868e7i	0.381821	+	0.661334i	−0.609502	+	0.792785i	$0.708630\pi$
$774$	−2.98631e6	−	5.17244e6i	−0.179177	−	0.310344i
$775$	−8.20217e6	+	1.42066e7i	−0.490540	+	0.849641i
$776$	−2.20879e7			−1.31674
$777$		0			0
$778$	−1.22402e7			−0.725001
$779$	−8.49323e6	+	1.47107e7i	−0.501452	+	0.868540i
$780$	56023.4	+	97035.3i	0.00329710	+	0.00571075i
$781$	5.88948e6	+	1.02009e7i	0.345501	+	0.598425i
$782$	734276.	−	1.27180e6i	0.0429380	−	0.0743709i
$783$	−918235.			−0.0535241
$784$		0			0
$785$	9.53723e6			0.552393
$786$	−1.32562e6	+	2.29604e6i	−0.0765353	+	0.132563i
$787$	4.57405e6	+	7.92248e6i	0.263247	+	0.455957i	0.967103	−	0.254385i	$-0.0818732\pi$
$787$	4.57405e6	+	7.92248e6i	0.263247	+	0.455957i	−0.703856	+	0.710343i	$0.748540\pi$
$788$	262789.	+	455164.i	0.0150762	+	0.0261127i
$789$	1.05021e6	−	1.81901e6i	0.0600596	−	0.104026i
$790$	−3.32594e6			−0.189603
$791$		0			0
$792$	−2.79380e6			−0.158264
$793$	3.04234e6	−	5.26949e6i	0.171801	−	0.297568i
$794$	−1.24901e7	−	2.16335e7i	−0.703096	−	1.21780i
$795$	1.51216e6	+	2.61914e6i	0.0848555	+	0.146974i
$796$	−865626.	+	1.49931e6i	−0.0484226	+	0.0838703i
$797$	1.10180e7			0.614408			0.307204	−	0.951644i	$-0.400607\pi$
$797$	1.10180e7			0.614408			0.307204	+	0.951644i	$0.400607\pi$
$798$		0			0
$799$	−3.94585e7			−2.18662
$800$	772705.	−	1.33837e6i	0.0426863	−	0.0739349i
$801$	3.52765e6	+	6.11007e6i	0.194269	+	0.336485i
$802$	−1.63504e7	−	2.83198e7i	−0.897622	−	1.55473i
$803$	3.80842e6	−	6.59638e6i	0.208428	−	0.361008i
$804$	1.16504e6			0.0635624
$805$		0			0
$806$	7.22315e6			0.391642
$807$	−6.65357e6	+	1.15243e7i	−0.359643	+	0.622919i
$808$	−2.07894e6	−	3.60083e6i	−0.112025	−	0.194032i
$809$	1.55136e7	+	2.68704e7i	0.833378	+	1.44345i	0.895344	+	0.445375i	$0.146930\pi$
$809$	1.55136e7	+	2.68704e7i	0.833378	+	1.44345i	−0.0619660	+	0.998078i	$0.519737\pi$
$810$	643188.	−	1.11403e6i	0.0344449	−	0.0596604i
$811$	2.94456e7			1.57206			0.786028	−	0.618191i	$-0.212134\pi$
$811$	2.94456e7			1.57206			0.786028	+	0.618191i	$0.212134\pi$
$812$		0			0
$813$	−1.59985e6			−0.0848895
$814$	−6.47729e6	+	1.12190e7i	−0.342635	+	0.593462i
$815$	−9.70367e6	−	1.68072e7i	−0.511731	−	0.886344i
$816$	−8.35898e6	−	1.44782e7i	−0.439469	−	0.761182i
$817$	1.28113e7	−	2.21898e7i	0.671487	−	1.16305i
$818$	1.93526e7			1.01124
$819$		0			0
$820$	−755675.			−0.0392464
$821$	2.61656e6	−	4.53201e6i	0.135479	−	0.234657i	−0.790301	−	0.612718i	$-0.790076\pi$
$821$	2.61656e6	−	4.53201e6i	0.135479	−	0.234657i	0.925780	+	0.378062i	$0.123409\pi$
$822$	−1.03632e7	−	1.79495e7i	−0.534950	−	0.926561i
$823$	−7.08154e6	−	1.22656e7i	−0.364442	−	0.631232i	0.624245	−	0.781229i	$-0.285407\pi$
$823$	−7.08154e6	−	1.22656e7i	−0.364442	−	0.631232i	−0.988686	+	0.149997i	$0.952074\pi$
$824$	−1.27106e7	+	2.20154e7i	−0.652151	+	1.12956i
$825$	−3.03591e6			−0.155294
$826$		0			0
$827$	2.98006e7			1.51517			0.757585	−	0.652737i	$-0.226379\pi$
$827$	2.98006e7			1.51517			0.757585	+	0.652737i	$0.226379\pi$
$828$	12975.0	−	22473.3i	0.000657705	−	0.00113918i
$829$	−9.96521e6	−	1.72602e7i	−0.503617	−	0.872289i	−0.999991	−	0.00418109i	$-0.998669\pi$
$829$	−9.96521e6	−	1.72602e7i	−0.503617	−	0.872289i	0.496375	−	0.868108i	$-0.334664\pi$
$830$	9.96916e6	+	1.72671e7i	0.502300	+	0.870009i
$831$	5.50134e6	−	9.52859e6i	0.276354	−	0.478659i
$832$	−5.14594e6			−0.257725
$833$		0			0
$834$	485914.			0.0241905
$835$	−3.93746e6	+	6.81988e6i	−0.195434	+	0.338501i
$836$	−408140.	−	706919.i	−0.0201973	−	0.0349827i
$837$	3.26921e6	+	5.66244e6i	0.161298	+	0.279376i
$838$	5.48367e6	−	9.49799e6i	0.269750	−	0.467220i
$839$	1.88103e7			0.922552			0.461276	−	0.887257i	$-0.347392\pi$
$839$	1.88103e7			0.922552			0.461276	+	0.887257i	$0.347392\pi$
$840$		0			0
$841$	−1.89246e7			−0.922650
$842$	1.60660e7	−	2.78271e7i	0.780957	−	1.35266i
$843$	−800096.	−	1.38581e6i	−0.0387769	−	0.0671636i
$844$	−825427.	−	1.42968e6i	−0.0398862	−	0.0690849i
$845$	−6.28968e6	+	1.08941e7i	−0.303031	+	0.524865i
$846$	8.84324e6			0.424801
$847$		0			0
$848$	−8.80874e6			−0.420653
$849$	−4.90733e6	+	8.49974e6i	−0.233655	+	0.404703i
$850$	−9.80367e6	−	1.69805e7i	−0.465416	−	0.806125i
$851$	−883384.	−	1.53007e6i	−0.0418144	−	0.0724247i
$852$	−672134.	+	1.16417e6i	−0.0317217	+	0.0549436i
$853$	−2.05980e7			−0.969285			−0.484643	−	0.874712i	$-0.661050\pi$
$853$	−2.05980e7			−0.969285			−0.484643	+	0.874712i	$0.661050\pi$
$854$		0			0
$855$	5.51856e6			0.258173
$856$	1.09990e7	−	1.90508e7i	0.513060	−	0.888647i
$857$	−1.23786e7	−	2.14404e7i	−0.575731	−	0.997195i	−0.995962	−	0.0897778i	$-0.971384\pi$
$857$	−1.23786e7	−	2.14404e7i	−0.575731	−	0.997195i	0.420231	−	0.907417i	$-0.361949\pi$
$858$	668384.	+	1.15767e6i	0.0309961	+	0.0536869i
$859$	−1.95533e7	+	3.38672e7i	−0.904141	+	1.56602i	−0.0820751	+	0.996626i	$0.526155\pi$
$859$	−1.95533e7	+	3.38672e7i	−0.904141	+	1.56602i	−0.822066	+	0.569392i	$0.807179\pi$
$860$	1.13987e6			0.0525544
$861$		0			0
$862$	−2.07527e7			−0.951275
$863$	1.96681e7	−	3.40662e7i	0.898952	−	1.55703i	0.0701154	−	0.997539i	$-0.477663\pi$
$863$	1.96681e7	−	3.40662e7i	0.898952	−	1.55703i	0.828836	−	0.559491i	$-0.189003\pi$
$864$	−307984.	−	533444.i	−0.0140360	−	0.0243111i
$865$	−1.06236e7	−	1.84007e7i	−0.482761	−	0.836167i
$866$	1.79575e7	−	3.11034e7i	0.813677	−	1.40933i
$867$	2.20921e7			0.998135
$868$		0			0
$869$	3.12859e6			0.140540
$870$	−1.11131e6	+	1.92485e6i	−0.0497781	+	0.0862183i
$871$	−4.09247e6	−	7.08837e6i	−0.182785	−	0.316593i
$872$	−3.24138e6	−	5.61424e6i	−0.144357	−	0.250034i
$873$	−4.78333e6	+	8.28496e6i	−0.212419	+	0.367921i
$874$	−1.41195e6			−0.0625229
$875$		0			0
$876$	869268.			0.0382731
$877$	−4.04626e6	+	7.00833e6i	−0.177646	+	0.307692i	−0.941074	−	0.338201i	$-0.890182\pi$
$877$	−4.04626e6	+	7.00833e6i	−0.177646	+	0.307692i	0.763428	+	0.645893i	$0.223515\pi$
$878$	−1.23909e7	−	2.14617e7i	−0.542459	−	0.939566i
$879$	2.45584e6	+	4.25364e6i	0.107208	+	0.185690i
$880$	−3.13282e6	+	5.42620e6i	−0.136373	+	0.236205i
$881$	4.05755e6			0.176126			0.0880631	−	0.996115i	$-0.471932\pi$
$881$	4.05755e6			0.176126			0.0880631	+	0.996115i	$0.471932\pi$
$882$		0			0
$883$	1.79813e7			0.776102			0.388051	−	0.921638i	$-0.373148\pi$
$883$	1.79813e7			0.776102			0.388051	+	0.921638i	$0.373148\pi$
$884$	340356.	−	589515.i	0.0146488	−	0.0253725i
$885$	−1.43637e6	−	2.48786e6i	−0.0616463	−	0.106775i
$886$	−1.39297e7	−	2.41270e7i	−0.596154	−	1.03257i
$887$	−7.65695e6	+	1.32622e7i	−0.326773	+	0.565988i	−0.981870	−	0.189557i	$-0.939295\pi$
$887$	−7.65695e6	+	1.32622e7i	−0.326773	+	0.565988i	0.655096	+	0.755545i	$0.272628\pi$
$888$	−2.17079e7			−0.923814
$889$		0			0
$890$	1.70777e7			0.722693
$891$	−605023.	+	1.04793e6i	−0.0255316	+	0.0442220i
$892$	−49362.5	−	85498.4i	−0.00207723	−	0.00359787i
$893$	1.89688e7	+	3.28549e7i	0.795996	+	1.37871i
$894$	−1.23879e7	+	2.14564e7i	−0.518385	+	0.897870i
$895$	7.82466e6			0.326519
$896$		0			0
$897$	−182311.			−0.00756539
$898$	−1.62188e7	+	2.80919e7i	−0.671165	+	1.16249i
$899$	−5.64861e6	−	9.78368e6i	−0.233100	−	0.403741i
$900$	−173236.	−	300053.i	−0.00712903	−	0.0123478i
$901$	9.18677e6	−	1.59120e7i	0.377008	−	0.652997i
$902$	−9.01554e6			−0.368957
$903$		0			0
$904$	4.97172e6			0.202342
$905$	−3.38597e6	+	5.86467e6i	−0.137424	+	0.238025i
$906$	4.73256e6	+	8.19704e6i	0.191547	+	0.331769i
$907$	1.08879e7	+	1.88583e7i	0.439465	+	0.761176i	0.997648	−	0.0685419i	$-0.0218347\pi$
$907$	1.08879e7	+	1.88583e7i	0.439465	+	0.761176i	−0.558183	+	0.829718i	$0.688501\pi$
$908$	−868116.	+	1.50362e6i	−0.0349432	+	0.0605235i
$909$	−1.80085e6			−0.0722883
$910$		0			0
$911$	−5.35112e6			−0.213623			−0.106812	−	0.994279i	$-0.534064\pi$
$911$	−5.35112e6			−0.213623			−0.106812	+	0.994279i	$0.534064\pi$
$912$	−8.03678e6	+	1.39201e7i	−0.319959	+	0.554186i
$913$	−9.37762e6	−	1.62425e7i	−0.372319	−	0.644876i
$914$	7.07556e6	+	1.22552e7i	0.280153	+	0.485239i
$915$	6.66603e6	−	1.15459e7i	0.263217	−	0.455906i
$916$	2.20124e6			0.0866818
$917$		0			0
$918$	−7.81507e6			−0.306074
$919$	1.33929e7	−	2.31972e7i	0.523102	−	0.906040i	−0.476536	−	0.879155i	$-0.658108\pi$
$919$	1.33929e7	−	2.31972e7i	0.523102	−	0.906040i	0.999639	−	0.0268850i	$-0.00855878\pi$
$920$	−461143.	−	798722.i	−0.0179625	−	0.0311119i
$921$	−1.48050e7	−	2.56430e7i	−0.575120	−	0.996138i
$922$	1.22952e7	−	2.12959e7i	0.476330	−	0.825028i
$923$	9.44411e6			0.364886
$924$		0			0
$925$	−2.35890e7			−0.906474
$926$	1.51168e7	−	2.61830e7i	0.579338	−	1.00344i
$927$	5.50519e6	+	9.53526e6i	0.210413	+	0.364446i
$928$	532141.	+	921695.i	0.0202841	+	0.0351332i
$929$	369987.	−	640836.i	0.0140652	−	0.0243617i	−0.858907	−	0.512131i	$-0.828856\pi$
$929$	369987.	−	640836.i	0.0140652	−	0.0243617i	0.872972	+	0.487770i	$0.162189\pi$
$930$	1.58265e7			0.600037
$931$		0			0
$932$	1.19817e6			0.0451834
$933$	−3.14870e6	+	5.45371e6i	−0.118421	+	0.205111i
$934$	−2.16583e7	−	3.75132e7i	−0.812375	−	1.40708i
$935$	−6.53453e6	−	1.13181e7i	−0.244447	−	0.423395i
$936$	−1.12000e6	+	1.93990e6i	−0.0417859	+	0.0723754i
$937$	122654.			0.00456385			0.00228193	−	0.999997i	$-0.499274\pi$
$937$	122654.			0.00456385			0.00228193	+	0.999997i	$0.499274\pi$
$938$		0			0
$939$	−5.60897e6			−0.207596
$940$	−843862.	+	1.46161e6i	−0.0311496	+	0.0539526i
$941$	6.12332e6	+	1.06059e7i	0.225431	+	0.390457i	0.956449	−	0.291901i	$-0.0942878\pi$
$941$	6.12332e6	+	1.06059e7i	0.225431	+	0.390457i	−0.731018	+	0.682358i	$0.760954\pi$
$942$	6.49273e6	+	1.12457e7i	0.238397	+	0.412915i
$943$	614778.	−	1.06483e6i	0.0225133	−	0.0389942i
$944$	8.36722e6			0.305599
$945$		0			0
$946$	1.35992e7			0.494065
$947$	1.85587e6	−	3.21446e6i	0.0672470	−	0.116475i	−0.830442	−	0.557106i	$-0.811912\pi$
$947$	1.85587e6	−	3.21446e6i	0.0672470	−	0.116475i	0.897689	+	0.440631i	$0.145245\pi$
$948$	178524.	+	309213.i	0.00645172	+	0.0111747i
$949$	−3.05351e6	−	5.28883e6i	−0.110061	−	0.190631i
$950$	−9.42579e6	+	1.63259e7i	−0.338851	+	0.586907i
$951$	−5.75319e6			−0.206280
$952$		0			0
$953$	−2.32857e7			−0.830533			−0.415266	−	0.909700i	$-0.636312\pi$
$953$	−2.32857e7			−0.830533			−0.415266	+	0.909700i	$0.636312\pi$
$954$	−2.05889e6	+	3.56610e6i	−0.0732424	+	0.126860i
$955$	3.12341e6	+	5.40990e6i	0.110820	+	0.191947i
$956$	−134851.	−	233568.i	−0.00477209	−	0.00826551i
$957$	1.04537e6	−	1.81064e6i	0.0368970	−	0.0639075i
$958$	3.57474e7			1.25843
$959$		0			0
$960$	−1.12752e7			−0.394862
$961$	−2.59071e7	+	4.48724e7i	−0.904921	+	1.56737i
$962$	5.19334e6	+	8.99514e6i	0.180930	+	0.313379i
$963$	−4.76386e6	−	8.25125e6i	−0.165536	−	0.286717i
$964$	1.06393e6	−	1.84279e6i	0.0368741	−	0.0638679i
$965$	−4.24013e6			−0.146575
$966$		0			0
$967$	2.25257e7			0.774661			0.387330	−	0.921941i	$-0.373397\pi$
$967$	2.25257e7			0.774661			0.387330	+	0.921941i	$0.373397\pi$
$968$	−1.18789e7	+	2.05749e7i	−0.407464	+	0.705748i
$969$	−1.67634e7	−	2.90350e7i	−0.573524	−	0.993373i
$970$	1.15782e7	+	2.00541e7i	0.395106	+	0.684343i
$971$	9.97281e6	−	1.72734e7i	0.339445	−	0.587936i	−0.644883	−	0.764281i	$-0.723094\pi$
$971$	9.97281e6	−	1.72734e7i	0.339445	−	0.587936i	0.984328	+	0.176345i	$0.0564274\pi$
$972$	−138096.			−0.00468830
$973$		0			0
$974$	2.53995e7			0.857884
$975$	−1.21706e6	+	2.10801e6i	−0.0410016	+	0.0710168i
$976$	1.94157e7	+	3.36290e7i	0.652422	+	1.13003i
$977$	479671.	+	830815.i	0.0160771	+	0.0278463i	0.873952	−	0.486012i	$-0.161549\pi$
$977$	479671.	+	830815.i	0.0160771	+	0.0278463i	−0.857875	+	0.513859i	$0.828216\pi$
$978$	1.32121e7	−	2.28840e7i	0.441697	−	0.765041i
$979$	−1.60643e7			−0.535681
$980$		0			0
$981$	−2.80780e6			−0.0931524
$982$	2.49771e6	−	4.32616e6i	0.0826539	−	0.143161i
$983$	2.61049e7	+	4.52149e7i	0.861663	+	1.49244i	0.870323	+	0.492482i	$0.163910\pi$
$983$	2.61049e7	+	4.52149e7i	0.861663	+	1.49244i	−0.00865985	+	0.999963i	$0.502757\pi$
$984$	−7.55363e6	−	1.30833e7i	−0.248695	−	0.430753i
$985$	4.04521e6	−	7.00651e6i	0.132847	−	0.230097i
$986$	1.35030e7			0.442323
$987$		0			0
$988$	−654475.			−0.0213305
$989$	−927339.	+	1.60620e6i	−0.0301472	+	0.0522166i
$990$	1.46449e6	+	2.53656e6i	0.0474894	+	0.0822541i
$991$	8.81523e6	+	1.52684e7i	0.285134	+	0.493867i	0.972642	−	0.232310i	$-0.0746285\pi$
$991$	8.81523e6	+	1.52684e7i	0.285134	+	0.493867i	−0.687507	+	0.726177i	$0.741295\pi$
$992$	3.78918e6	−	6.56306e6i	0.122255	−	0.211752i
$993$	1.26867e7			0.408296
$994$		0			0
$995$	2.66498e7			0.853369
$996$	1.07022e6	−	1.85367e6i	0.0341840	−	0.0592084i
$997$	2.02437e7	+	3.50632e7i	0.644990	+	1.11716i	0.984304	+	0.176482i	$0.0564717\pi$
$997$	2.02437e7	+	3.50632e7i	0.644990	+	1.11716i	−0.339314	+	0.940673i	$0.610195\pi$
$998$	−853521.	−	1.47834e6i	−0.0271261	−	0.0469838i
$999$	−4.70103e6	+	8.14243e6i	−0.149032	+	0.258131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.e.m.79.1		4
7.2	even	3		147.6.a.j.1.2	yes	2
7.3	odd	6		147.6.e.n.67.1		4
7.4	even	3	inner	147.6.e.m.67.1		4
7.5	odd	6		147.6.a.h.1.2	✓	2
7.6	odd	2		147.6.e.n.79.1		4
21.2	odd	6		441.6.a.r.1.1		2
21.5	even	6		441.6.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.h.1.2	✓	2	7.5	odd	6
147.6.a.j.1.2	yes	2	7.2	even	3
147.6.e.m.67.1		4	7.4	even	3	inner
147.6.e.m.79.1		4	1.1	even	1	trivial
147.6.e.n.67.1		4	7.3	odd	6
147.6.e.n.79.1		4	7.6	odd	2
441.6.a.q.1.1		2	21.5	even	6
441.6.a.r.1.1		2	21.2	odd	6

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.72311 + 4.71657i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(1.16933 + 2.02534i) q^{4} +(18.0000 - 31.1769i) q^{5} +49.0160 q^{6} -187.016 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-2.72311 + 4.71657i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(1.16933 + 2.02534i) q^{4} +(18.0000 - 31.1769i) q^{5} +49.0160 q^{6} -187.016 q^{8} +(-40.5000 + 70.1481i) q^{9} +(98.0320 + 169.796i) q^{10} +(-92.2151 - 159.721i) q^{11} +(10.5240 - 18.2281i) q^{12} -147.872 q^{13} -324.000 q^{15} +(471.847 - 817.262i) q^{16} +(984.192 + 1704.67i) q^{17} +(-220.572 - 382.042i) q^{18} +(946.256 - 1638.96i) q^{19} +84.1920 q^{20} +1004.45 q^{22} +(-68.4942 + 118.635i) q^{23} +(841.572 + 1457.65i) q^{24} +(914.500 + 1583.96i) q^{25} +(402.672 - 697.448i) q^{26} +729.000 q^{27} -1259.58 q^{29} +(882.288 - 1528.17i) q^{30} +(4484.51 + 7767.40i) q^{31} +(-422.474 - 731.747i) q^{32} +(-829.936 + 1437.49i) q^{33} -10720.3 q^{34} -189.432 q^{36} +(-6448.61 + 11169.3i) q^{37} +(5153.52 + 8926.16i) q^{38} +(665.424 + 1152.55i) q^{39} +(-3366.29 + 5830.58i) q^{40} -8975.62 q^{41} +13538.9 q^{43} +(215.660 - 373.535i) q^{44} +(1458.00 + 2525.33i) q^{45} +(-373.035 - 646.115i) q^{46} +(-10023.1 + 17360.5i) q^{47} -8493.24 q^{48} -9961.14 q^{50} +(8857.73 - 15342.0i) q^{51} +(-172.912 - 299.492i) q^{52} +(-4667.16 - 8083.76i) q^{53} +(-1985.15 + 3438.38i) q^{54} -6639.49 q^{55} -17032.6 q^{57} +(3429.98 - 5940.90i) q^{58} +(4433.23 + 7678.58i) q^{59} +(-378.864 - 656.212i) q^{60} +(-20574.2 + 35635.5i) q^{61} -48847.3 q^{62} +34800.0 q^{64} +(-2661.70 + 4610.19i) q^{65} +(-4520.02 - 7828.90i) q^{66} +(27675.8 + 47935.8i) q^{67} +(-2301.70 + 3986.65i) q^{68} +1232.90 q^{69} -63866.8 q^{71} +(7574.15 - 13118.8i) q^{72} +(20649.7 + 35766.3i) q^{73} +(-35120.5 - 60830.6i) q^{74} +(8230.50 - 14255.6i) q^{75} +4425.95 q^{76} -7248.09 q^{78} +(-8481.76 + 14690.8i) q^{79} +(-16986.5 - 29421.4i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(24441.6 - 42334.1i) q^{82} +101693. q^{83} +70861.8 q^{85} +(-36868.0 + 63857.3i) q^{86} +(5668.12 + 9817.47i) q^{87} +(17245.7 + 29870.4i) q^{88} +(43551.3 - 75433.0i) q^{89} -15881.2 q^{90} -320.370 q^{92} +(40360.6 - 69906.6i) q^{93} +(-54587.9 - 94549.0i) q^{94} +(-34065.2 - 59002.7i) q^{95} +(-3802.27 + 6585.72i) q^{96} +118107. q^{97} +14938.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 18 * q^3 - 37 * q^4 + 72 * q^5 - 54 * q^6 - 498 * q^8 - 162 * q^9	\( 4 q + 3 q^{2} - 18 q^{3} - 37 q^{4} + 72 q^{5} - 54 q^{6} - 498 q^{8} - 162 q^{9} - 108 q^{10} - 480 q^{11} - 333 q^{12} - 2592 q^{13} - 1296 q^{15} + 1679 q^{16} + 936 q^{17} + 243 q^{18} - 216 q^{19} - 2664 q^{20} - 2984 q^{22} + 504 q^{23} + 2241 q^{24} + 3658 q^{25} - 8892 q^{26} + 2916 q^{27} + 12744 q^{29} - 972 q^{30} + 9936 q^{31} - 9039 q^{32} - 4320 q^{33} - 38880 q^{34} + 5994 q^{36} - 11124 q^{37} + 28116 q^{38} + 11664 q^{39} - 8964 q^{40} - 41904 q^{41} - 12528 q^{43} - 11196 q^{44} + 5832 q^{45} - 6160 q^{46} + 7920 q^{47} - 30222 q^{48} + 10974 q^{50} + 8424 q^{51} + 44820 q^{52} - 2220 q^{53} + 2187 q^{54} - 34560 q^{55} + 3888 q^{57} + 71318 q^{58} + 29736 q^{59} + 11988 q^{60} - 17280 q^{61} - 81360 q^{62} - 21758 q^{64} - 46656 q^{65} + 13428 q^{66} + 20680 q^{67} - 45216 q^{68} - 9072 q^{69} - 184560 q^{71} + 20169 q^{72} + 56592 q^{73} - 85218 q^{74} + 32922 q^{75} + 174744 q^{76} + 160056 q^{78} + 56096 q^{79} - 60444 q^{80} - 13122 q^{81} - 52272 q^{82} + 142704 q^{83} + 67392 q^{85} - 240996 q^{86} - 57348 q^{87} + 52812 q^{88} + 123192 q^{89} + 17496 q^{90} - 51072 q^{92} + 89424 q^{93} - 345384 q^{94} + 7776 q^{95} - 81351 q^{96} - 71712 q^{97} + 77760 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 18 * q^3 - 37 * q^4 + 72 * q^5 - 54 * q^6 - 498 * q^8 - 162 * q^9 - 108 * q^10 - 480 * q^11 - 333 * q^12 - 2592 * q^13 - 1296 * q^15 + 1679 * q^16 + 936 * q^17 + 243 * q^18 - 216 * q^19 - 2664 * q^20 - 2984 * q^22 + 504 * q^23 + 2241 * q^24 + 3658 * q^25 - 8892 * q^26 + 2916 * q^27 + 12744 * q^29 - 972 * q^30 + 9936 * q^31 - 9039 * q^32 - 4320 * q^33 - 38880 * q^34 + 5994 * q^36 - 11124 * q^37 + 28116 * q^38 + 11664 * q^39 - 8964 * q^40 - 41904 * q^41 - 12528 * q^43 - 11196 * q^44 + 5832 * q^45 - 6160 * q^46 + 7920 * q^47 - 30222 * q^48 + 10974 * q^50 + 8424 * q^51 + 44820 * q^52 - 2220 * q^53 + 2187 * q^54 - 34560 * q^55 + 3888 * q^57 + 71318 * q^58 + 29736 * q^59 + 11988 * q^60 - 17280 * q^61 - 81360 * q^62 - 21758 * q^64 - 46656 * q^65 + 13428 * q^66 + 20680 * q^67 - 45216 * q^68 - 9072 * q^69 - 184560 * q^71 + 20169 * q^72 + 56592 * q^73 - 85218 * q^74 + 32922 * q^75 + 174744 * q^76 + 160056 * q^78 + 56096 * q^79 - 60444 * q^80 - 13122 * q^81 - 52272 * q^82 + 142704 * q^83 + 67392 * q^85 - 240996 * q^86 - 57348 * q^87 + 52812 * q^88 + 123192 * q^89 + 17496 * q^90 - 51072 * q^92 + 89424 * q^93 - 345384 * q^94 + 7776 * q^95 - 81351 * q^96 - 71712 * q^97 + 77760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more