LMFDB - Embedded newform 147.6.e.n.67.1

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			67.1
Root			$-3.22311 - 5.58259i$ of defining polynomial
Character	$\chi$	$=$	147.67
Dual form			147.6.e.n.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72311 - 4.71657i) q^{2} +(4.50000 - 7.79423i) q^{3} +(1.16933 - 2.02534i) q^{4} +(-18.0000 - 31.1769i) q^{5} -49.0160 q^{6} -187.016 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.72311	−	4.71657i	−0.481383	−	0.833779i	0.518389	−	0.855145i	$-0.326532\pi$
$2$	−2.72311	−	4.71657i	−0.481383	−	0.833779i	−0.999772	+	0.0213658i	$0.993199\pi$
$3$	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	$-0.271020\pi$
$5$	−18.0000	−	31.1769i	−0.321994	−	0.557710i	−0.980899	+	0.194516i	$0.937686\pi$
$6$	−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	−0.957744	−	0.287622i	$-0.907135\pi$
$11$	−92.2151	+	159.721i	−0.229784	+	0.397998i	0.727960	+	0.685620i	$0.240469\pi$
$12$	−10.5240	−	18.2281i	−0.0210973	−	0.0365417i
$13$	147.872			0.242676			0.121338	−	0.992611i	$-0.461281\pi$
$13$	147.872			0.242676			0.121338	+	0.992611i	$0.461281\pi$
$14$		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	0.0752284	+	0.997166i	$0.476031\pi$
$17$	−984.192	+	1704.67i	−0.825957	+	1.43060i	−0.901186	+	0.433433i	$0.857302\pi$
$18$	−220.572	+	382.042i	−0.160461	+	0.277926i
$19$	−946.256	−	1638.96i	−0.601346	−	1.04156i	−0.992617	−	0.121287i	$-0.961298\pi$
$19$	−946.256	−	1638.96i	−0.601346	−	1.04156i	0.391271	−	0.920275i	$-0.372035\pi$
$20$	−84.1920			−0.0470647
$21$		0			0
$22$	1004.45			0.442457
$23$	−68.4942	−	118.635i	−0.0269982	−	0.0467622i	0.852211	−	0.523199i	$-0.175261\pi$
$23$	−68.4942	−	118.635i	−0.0269982	−	0.0467622i	−0.879209	+	0.476437i	$0.841928\pi$
$24$	−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	0.0533279	+	0.998577i	$0.483017\pi$
$31$	−4484.51	+	7767.40i	−0.838129	+	1.45168i	−0.891457	+	0.453105i	$0.850316\pi$
$32$	−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	−0.935135	−	0.354292i	$-0.884722\pi$
$37$	−6448.61	−	11169.3i	−0.774393	−	1.34129i	0.160742	−	0.986996i	$-0.448611\pi$
$38$	−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	$-0.363102\pi$
$41$	8975.62			0.833882			0.416941	+	0.908934i	$0.363102\pi$
$42$		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	0.980130	+	0.198354i	$0.0635596\pi$
$47$	10023.1	+	17360.5i	0.661845	+	1.14635i	−0.318286	+	0.947995i	$0.603107\pi$
$48$	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	−0.957282	−	0.289155i	$-0.906626\pi$
$53$	−4667.16	+	8083.76i	−0.228225	+	0.395297i	0.729057	+	0.684453i	$0.239959\pi$
$54$	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	$-0.886355\pi$
$59$	−4433.23	+	7678.58i	−0.165802	+	0.287178i	0.771138	+	0.636668i	$0.219688\pi$
$60$	−378.864	+	656.212i	−0.0135864	+	0.0235324i
$61$	20574.2	+	35635.5i	0.707942	+	1.22619i	0.965619	+	0.259960i	$0.0837094\pi$
$61$	20574.2	+	35635.5i	0.707942	+	1.22619i	−0.257678	+	0.966231i	$0.582957\pi$
$62$	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	−0.193058	−	0.981187i	$-0.561841\pi$
$67$	27675.8	−	47935.8i	0.753204	−	1.30459i	0.946262	−	0.323400i	$-0.104826\pi$
$68$	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	$-0.983169\pi$
$73$	−20649.7	+	35766.3i	−0.453530	+	0.785537i	0.545073	+	0.838389i	$0.316502\pi$
$74$	−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	0.779390	−	0.626539i	$-0.215529\pi$
$79$	−8481.76	−	14690.8i	−0.152904	−	0.264837i	−0.932294	+	0.361702i	$0.882196\pi$
$80$	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	$-0.800614\pi$
$83$	−101693.			−1.62030			−0.810150	+	0.586223i	$0.800614\pi$
$84$		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	−0.995145	−	0.0984220i	$-0.968621\pi$
$89$	−43551.3	−	75433.0i	−0.582808	−	1.00945i	0.412336	−	0.911032i	$-0.364713\pi$
$90$	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	$-0.719932\pi$
$97$	−118107.			−1.27452			−0.637258	+	0.770650i	$0.719932\pi$
$98$		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	$-0.867916\pi$
$101$	−11116.4	+	19254.1i	−0.108432	+	0.187811i	0.806703	+	0.590957i	$0.201250\pi$
$102$	48241.2	−	83556.1i	0.459111	−	0.795203i
$103$	−67965.3	−	117719.i	−0.631239	−	1.09334i	−0.987299	−	0.158875i	$-0.949213\pi$
$103$	−67965.3	−	117719.i	−0.631239	−	1.09334i	0.356059	−	0.934463i	$-0.384120\pi$
$104$	−27654.4			−0.250716
$105$		0			0
$106$	50836.8			0.439454
$107$	−58813.1	−	101867.i	−0.496609	−	0.860152i	0.503383	−	0.864063i	$-0.332088\pi$
$107$	−58813.1	−	101867.i	−0.496609	−	0.860152i	−0.999992	+	0.00391112i	$0.998755\pi$
$108$	−852.444	+	1476.48i	−0.00703244	+	0.0121806i
$109$	17332.1	−	30020.1i	0.139729	−	0.242017i	−0.787665	−	0.616103i	$-0.788710\pi$
$109$	17332.1	−	30020.1i	0.139729	−	0.242017i	0.927394	+	0.374086i	$0.122044\pi$
$110$	−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	$-0.122699\pi$
$131$	27044.6	+	46842.6i	0.137690	+	0.238486i	−0.788932	+	0.614481i	$0.789366\pi$
$132$	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	−0.245939	+	0.969285i	$0.579096\pi$
$137$	−211424.	+	366198.i	−0.962395	+	1.66692i	−0.716456	+	0.697632i	$0.754237\pi$
$138$	3357.31	+	5815.04i	0.0150070	+	0.0259929i
$139$	−9913.38			−0.0435196			−0.0217598	−	0.999763i	$-0.506927\pi$
$139$	−9913.38			−0.0435196			−0.0217598	+	0.999763i	$0.506927\pi$
$140$		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	−0.778868	−	0.627188i	$-0.784206\pi$
$149$	−252731.	−	437743.i	−0.932595	−	1.61530i	−0.153727	−	0.988113i	$-0.549128\pi$
$150$	−44825.1	+	77639.4i	−0.162665	+	0.281744i
$151$	96551.4	−	167232.i	0.344601	−	0.596866i	−0.640680	−	0.767808i	$-0.721348\pi$
$151$	96551.4	−	167232.i	0.344601	−	0.596866i	0.985281	+	0.170942i	$0.0546810\pi$
$152$	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	$-0.974427\pi$
$157$	−132462.	+	229430.i	−0.428885	+	0.742850i	0.567890	+	0.823105i	$0.307760\pi$
$158$	−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	0.923075	+	0.384621i	$0.125668\pi$
$163$	269546.	+	466868.i	0.794629	+	1.37634i	−0.128446	+	0.991717i	$0.540999\pi$
$164$	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	$-0.401853\pi$
$167$	218748.			0.606949			0.303475	+	0.952840i	$0.401853\pi$
$168$		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	−0.947994	−	0.318289i	$-0.896892\pi$
$173$	−295101.	−	511129.i	−0.749644	−	1.29842i	0.198350	−	0.980131i	$-0.436442\pi$
$174$	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	−0.710977	−	0.703215i	$-0.751747\pi$
$179$	108676.	−	188232.i	0.253513	−	0.439098i	0.964491	+	0.264117i	$0.0850805\pi$
$180$	3409.78	+	5905.90i	0.00784412	+	0.0135864i
$181$	188109.			0.426790			0.213395	−	0.976966i	$-0.431548\pi$
$181$	188109.			0.426790			0.213395	+	0.976966i	$0.431548\pi$
$182$		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	0.767064	−	0.641571i	$-0.221717\pi$
$191$	−86761.3	−	150275.i	−0.172085	−	0.298060i	−0.939149	+	0.343511i	$0.888384\pi$
$192$	156600.	−	271239.i	0.306576	−	0.531005i
$193$	−58890.7	+	102002.i	−0.113803	+	0.197113i	−0.917301	−	0.398195i	$-0.869637\pi$
$193$	−58890.7	+	102002.i	−0.113803	+	0.197113i	0.803498	+	0.595308i	$0.202970\pi$
$194$	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	0.317372	+	0.948301i	$0.397199\pi$
$199$	−370137.	+	641096.i	−0.662567	+	1.14760i	−0.979939	+	0.199298i	$0.936134\pi$
$200$	−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	$-0.490952\pi$
$223$	42214.3			0.0568456			0.0284228	+	0.999596i	$0.490952\pi$
$224$		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	$-0.992018\pi$
$227$	−371201.	+	642940.i	−0.478129	+	0.828144i	0.521557	+	0.853217i	$0.325351\pi$
$228$	−19916.8	+	34496.9i	−0.0253736	+	0.0439484i
$229$	−470618.	−	815134.i	−0.593034	−	1.02717i	−0.993821	−	0.110994i	$-0.964596\pi$
$229$	−470618.	−	815134.i	−0.593034	−	1.02717i	0.400787	−	0.916171i	$-0.368737\pi$
$230$	26858.5			0.0334782
$231$		0			0
$232$	235562.			0.287333
$233$	256166.	+	443692.i	0.309123	+	0.535416i	0.978171	−	0.207803i	$-0.0666313\pi$
$233$	256166.	+	443692.i	0.309123	+	0.535416i	−0.669048	+	0.743219i	$0.733298\pi$
$234$	−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	−0.495437	−	0.868644i	$-0.664992\pi$
$241$	454932.	−	787965.i	0.504549	−	0.873905i	0.999986	−	0.00526118i	$-0.00167469\pi$
$242$	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	$-0.551451\pi$
$251$	−321264.			−0.321868			−0.160934	+	0.986965i	$0.551451\pi$
$252$		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	$-0.0820265\pi$
$257$	278246.	+	481936.i	0.262782	+	0.455152i	−0.704198	+	0.710004i	$0.748693\pi$
$258$	−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	−0.809314	−	0.587377i	$-0.800161\pi$
$263$	116690.	−	202112.i	0.104026	−	0.180179i	0.913340	+	0.407198i	$0.133494\pi$
$264$	−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	−0.366020	−	0.930607i	$-0.619280\pi$
$269$	739286.	−	1.28048e6i	0.622919	−	1.07893i	0.988939	−	0.148321i	$-0.0473868\pi$
$270$	71465.3	−	123782.i	0.0596604	−	0.103335i
$271$	−88880.8	−	153946.i	−0.0735165	−	0.127334i	0.826924	−	0.562314i	$-0.190089\pi$
$271$	−88880.8	−	153946.i	−0.0735165	−	0.127334i	−0.900440	+	0.434980i	$0.856755\pi$
$272$	−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	−0.521042	−	0.853531i	$-0.674456\pi$
$277$	611259.	−	1.05873e6i	0.478659	−	0.829062i	0.999701	+	0.0244697i	$0.00778972\pi$
$278$	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	$-0.700708\pi$
$283$	545259.	−	944416.i	0.404703	−	0.700966i	0.994287	+	0.106741i	$0.0340415\pi$
$284$	−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	$-0.440548\pi$
$293$	545742.			0.371380			0.185690	+	0.982608i	$0.440548\pi$
$294$		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	$-0.972015\pi$
$307$	−3.29000e6			−1.99228			−0.996138	+	0.0878052i	$0.972015\pi$
$308$		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	$-0.767578\pi$
$311$	349856.	−	605968.i	0.205111	−	0.355262i	0.950168	+	0.311738i	$0.100911\pi$
$312$	−124445.	+	215545.i	−0.0723754	+	0.125358i
$313$	−311609.	−	539723.i	−0.179783	−	0.311394i	0.762023	−	0.647550i	$-0.224206\pi$
$313$	−311609.	−	539723.i	−0.179783	−	0.311394i	−0.941806	+	0.336156i	$0.890873\pi$
$314$	1.44283e6			0.825831
$315$		0			0
$316$	−39672.0			−0.0223494
$317$	319622.	+	553601.i	0.178644	+	0.309420i	0.941416	−	0.337247i	$-0.109496\pi$
$317$	319622.	+	553601.i	0.178644	+	0.309420i	−0.762772	+	0.646667i	$0.776162\pi$
$318$	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	0.633281	−	0.773922i	$-0.281708\pi$
$331$	−704817.	−	1.22078e6i	−0.353595	−	0.612445i	−0.986876	+	0.161477i	$0.948374\pi$
$332$	−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	−0.892373	−	0.451299i	$-0.850961\pi$
$347$	−124148.	+	215031.i	−0.0553500	+	0.0958690i	0.837023	+	0.547168i	$0.184294\pi$
$348$	13255.8	+	22959.8i	0.00586758	+	0.0101629i
$349$	1.86169e6			0.818171			0.409086	−	0.912496i	$-0.365848\pi$
$349$	1.86169e6			0.818171			0.409086	+	0.912496i	$0.365848\pi$
$350$		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	$-0.956820\pi$
$353$	−885642.	+	1.53398e6i	−0.378287	+	0.655212i	0.612526	+	0.790450i	$0.290153\pi$
$354$	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	0.804837	+	0.593495i	$0.202253\pi$
$359$	2.23780e6	+	3.87599e6i	0.916401	+	1.58725i	0.111563	+	0.993757i	$0.464414\pi$
$360$	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	0.376014	+	0.926614i	$0.377295\pi$
$367$	−1.58548e6	+	2.74614e6i	−0.614465	+	1.06428i	−0.990478	+	0.137670i	$0.956039\pi$
$368$	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	0.996888	−	0.0788285i	$-0.0251179\pi$
$373$	1.15590e6	+	2.00207e6i	0.430177	+	0.745088i	−0.566712	+	0.823916i	$0.691785\pi$
$374$	−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	0.988228	+	0.152987i	$0.0488893\pi$
$383$	1.79883e6	+	3.11567e6i	0.626605	+	1.08531i	−0.361623	+	0.932324i	$0.617777\pi$
$384$	−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	−0.614033	−	0.789280i	$-0.710454\pi$
$389$	1.12373e6	−	1.94636e6i	0.376520	−	0.652152i	0.990553	+	0.137128i	$0.0437873\pi$
$390$	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	0.956760	+	0.290879i	$0.0939477\pi$
$397$	2.29335e6	+	3.97220e6i	0.730288	+	1.26490i	−0.226471	+	0.974018i	$0.572719\pi$
$398$	4.03169e6			1.27579
$399$		0			0
$400$	1.72602e6			0.539380
$401$	−3.00216e6	−	5.19990e6i	−0.932338	−	1.61486i	−0.779314	−	0.626633i	$-0.784432\pi$
$401$	−3.00216e6	−	5.19990e6i	−0.932338	−	1.61486i	−0.153023	−	0.988223i	$-0.548901\pi$
$402$	−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	−0.474393	−	0.880313i	$-0.657333\pi$
$409$	1.77670e6	−	3.07733e6i	0.525177	−	0.909633i	0.999570	−	0.0293196i	$-0.00933407\pi$
$410$	−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	$-0.409605\pi$
$419$	2.01375e6			0.560365			0.280182	+	0.959947i	$0.409605\pi$
$420$		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	−0.505943	−	0.862567i	$-0.668856\pi$
$431$	1.90524e6	−	3.29997e6i	0.494033	−	0.855690i	0.999976	+	0.00687645i	$0.00218886\pi$
$432$	−343976.	−	595784.i	−0.0886786	−	0.153596i
$433$	6.59449e6			1.69029			0.845146	−	0.534536i	$-0.179513\pi$
$433$	6.59449e6			1.69029			0.845146	+	0.534536i	$0.179513\pi$
$434$		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	0.997193	+	0.0748729i	$0.0238551\pi$
$439$	2.27514e6	+	3.94065e6i	0.563438	+	0.975904i	−0.433755	+	0.901031i	$0.642812\pi$
$440$	−1.24169e6			−0.305761
$441$		0			0
$442$	1.58523e6			0.385954
$443$	−2.55769e6	−	4.43004e6i	−0.619210	−	1.07250i	−0.989630	−	0.143639i	$-0.954120\pi$
$443$	−2.55769e6	−	4.43004e6i	−0.619210	−	1.07250i	0.370420	−	0.928864i	$-0.379214\pi$
$444$	−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	0.974044	−	0.226361i	$-0.0726828\pi$
$457$	1.29917e6	+	2.25022e6i	0.290988	+	0.504006i	−0.683056	+	0.730366i	$0.739349\pi$
$458$	−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	$-0.335259\pi$
$461$	4.51513e6			0.989505			0.494752	+	0.869034i	$0.335259\pi$
$462$		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	0.886665	+	0.462413i	$0.153016\pi$
$467$	3.97675e6	+	6.88794e6i	0.843794	+	1.46149i	−0.0428708	+	0.999081i	$0.513650\pi$
$468$	−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	−0.328703	−	0.944433i	$-0.606611\pi$
$479$	3.28185e6	−	5.68433e6i	0.653552	−	1.13199i	0.982255	−	0.187552i	$-0.0600553\pi$
$480$	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	−0.998089	−	0.0617918i	$-0.980319\pi$
$487$	−2.33185e6	+	4.03888e6i	−0.445531	+	0.771683i	0.552558	+	0.833475i	$0.313652\pi$
$488$	−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	0.851594	−	0.524202i	$-0.175636\pi$
$499$	−156718.	−	271443.i	−0.0281752	−	0.0488009i	−0.879769	+	0.475401i	$0.842303\pi$
$500$	−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	$-0.606930\pi$
$503$	−3.74110e6			−0.659294			−0.329647	+	0.944104i	$0.606930\pi$
$504$		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	−0.849986	−	0.526805i	$-0.823390\pi$
$509$	−5.15085e6	−	8.92153e6i	−0.881220	−	1.52632i	−0.0312337	−	0.999512i	$-0.509944\pi$
$510$	−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	−0.468904	−	0.883249i	$-0.655351\pi$
$521$	3.28663e6	−	5.69260e6i	0.530464	−	0.918791i	0.999368	−	0.0355415i	$-0.0113156\pi$
$522$	277829.	−	481213.i	0.0446273	−	0.0772967i
$523$	−4.18266e6	−	7.24458e6i	−0.668650	−	1.15814i	−0.978282	−	0.207279i	$-0.933539\pi$
$523$	−4.18266e6	−	7.24458e6i	−0.668650	−	1.15814i	0.309632	−	0.950856i	$-0.399794\pi$
$524$	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	0.993902	+	0.110266i	$0.0351702\pi$
$541$	4.03311e6	+	6.98556e6i	0.592444	+	1.02614i	−0.401458	+	0.915877i	$0.631496\pi$
$542$	−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	−0.134062	−	0.990973i	$-0.542802\pi$
$557$	5.79311e6	−	1.00340e7i	0.791177	−	1.37036i	0.925239	−	0.379385i	$-0.123864\pi$
$558$	−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	$-0.873899\pi$
$563$	−955879.	+	1.65563e6i	−0.127096	+	0.220137i	0.795454	+	0.606014i	$0.207232\pi$
$564$	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	−0.999435	−	0.0336138i	$-0.989298\pi$
$569$	−4.08409e6	−	7.07385e6i	−0.528828	−	0.915957i	0.470607	−	0.882343i	$-0.344035\pi$
$570$	1.66974e6	−	2.89208e6i	0.215259	−	0.372840i
$571$	3.73297e6	−	6.46569e6i	0.479141	−	0.829897i	−0.520573	−	0.853817i	$-0.674281\pi$
$571$	3.73297e6	−	6.46569e6i	0.479141	−	0.829897i	0.999714	+	0.0239203i	$0.00761479\pi$
$572$	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	$-0.691698\pi$
$577$	3.44219e6	−	5.96205e6i	0.430423	−	0.745514i	0.996910	+	0.0785568i	$0.0250312\pi$
$578$	−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	$-0.679197\pi$
$587$	−8.91086e6			−1.06739			−0.533696	+	0.845676i	$0.679197\pi$
$588$		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	−0.960720	−	0.277521i	$-0.910487\pi$
$593$	−6.17151e6	−	1.06894e7i	−0.720700	−	1.24829i	0.240019	−	0.970768i	$-0.422846\pi$
$594$	−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	0.484127	+	0.874998i	$0.339137\pi$
$599$	−4.52866e6	+	7.84387e6i	−0.515707	+	0.893230i	−0.999834	+	0.0182325i	$0.994196\pi$
$600$	1.53924e6	+	2.66603e6i	0.174553	+	0.302334i
$601$	7.41700e6			0.837611			0.418805	−	0.908076i	$-0.362449\pi$
$601$	7.41700e6			0.837611			0.418805	+	0.908076i	$0.362449\pi$
$602$		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	$-0.0635673\pi$
$607$	2.88907e6	+	5.00401e6i	0.318263	+	0.551247i	−0.661863	+	0.749625i	$0.730234\pi$
$608$	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	−0.984091	−	0.177665i	$-0.943146\pi$
$613$	−3.14632e6	+	5.44959e6i	−0.338183	+	0.585750i	0.645908	+	0.763415i	$0.276479\pi$
$614$	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	−0.273991	−	0.961732i	$-0.588344\pi$
$619$	6.63386e6	−	1.14902e7i	0.695889	−	1.20531i	0.969880	−	0.243583i	$-0.0783227\pi$
$620$	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	−0.992553	−	0.121815i	$-0.961129\pi$
$641$	−4.06518e6	+	7.04109e6i	−0.390782	+	0.676854i	0.601771	+	0.798669i	$0.294462\pi$
$642$	2.88278e6	+	4.99313e6i	0.276041	+	0.478118i
$643$	−3.12961e6			−0.298513			−0.149256	−	0.988799i	$-0.547688\pi$
$643$	−3.12961e6			−0.298513			−0.149256	+	0.988799i	$0.547688\pi$
$644$		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	0.354737	+	0.934966i	$0.384570\pi$
$647$	−6.73300e6	+	1.16619e7i	−0.632336	+	1.09524i	−0.987073	+	0.160271i	$0.948763\pi$
$648$	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	−0.979471	−	0.201584i	$-0.935391\pi$
$653$	−7.23861e6	−	1.25376e7i	−0.664312	−	1.15062i	0.315159	−	0.949039i	$-0.397942\pi$
$654$	−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	$-0.832909\pi$
$661$	14982.6	−	25950.6i	0.00133378	−	0.00231017i	0.866692	+	0.498844i	$0.166242\pi$
$662$	−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	$-0.106801\pi$
$677$	2.22965e6	+	3.86186e6i	0.186967	+	0.323836i	−0.757271	+	0.653101i	$0.773468\pi$
$678$	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	−0.216018	−	0.976389i	$-0.569307\pi$
$683$	8.99196e6	−	1.55745e7i	0.737569	−	1.27751i	0.953587	−	0.301117i	$-0.0973596\pi$
$684$	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	$-0.198539\pi$
$691$	−1.25468e6	−	2.17316e6i	−0.0999624	−	0.173140i	−0.911669	+	0.410926i	$0.865206\pi$
$692$	−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	0.987270	−	0.159051i	$-0.0508434\pi$
$709$	4.76360e6	+	8.25079e6i	0.355893	+	0.616425i	−0.631377	+	0.775476i	$0.717510\pi$
$710$	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	$-0.175361\pi$
$719$	−378588.	−	655734.i	−0.0273114	−	0.0473048i	−0.879358	+	0.476161i	$0.842028\pi$
$720$	−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	$-0.884859\pi$
$727$	−2.66570e7			−1.87058			−0.935288	+	0.353888i	$0.884859\pi$
$728$		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	−0.781614	−	0.623762i	$-0.785603\pi$
$733$	−1.35429e7	−	2.34569e7i	−0.931001	−	1.61254i	−0.149387	−	0.988779i	$-0.547730\pi$
$734$	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	0.213545	+	0.976933i	$0.431499\pi$
$739$	−1.09753e7	+	1.90098e7i	−0.739276	+	1.28046i	−0.952822	+	0.303531i	$0.901834\pi$
$740$	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	0.969121	−	0.246587i	$-0.0793093\pi$
$751$	4.18875e6	+	7.25512e6i	0.271009	+	0.469402i	−0.698111	+	0.715989i	$0.745976\pi$
$752$	−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	−0.997998	−	0.0632523i	$-0.979853\pi$
$761$	−8.84701e6	−	1.53235e7i	−0.553777	−	0.959170i	0.444221	−	0.895917i	$-0.353481\pi$
$762$	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	$-0.540092\pi$
$769$	−4.12006e6			−0.251239			−0.125620	+	0.992078i	$0.540092\pi$
$770$		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	$-0.958036\pi$
$773$	−6.34320e6	+	1.09868e7i	−0.381821	+	0.661334i	0.609502	+	0.792785i	$0.291370\pi$
$774$	−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	$-0.918127\pi$
$787$	−4.57405e6	+	7.92248e6i	−0.263247	+	0.455957i	0.703856	+	0.710343i	$0.251460\pi$
$788$	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	$-0.599393\pi$
$797$	−1.10180e7			−0.614408			−0.307204	+	0.951644i	$0.599393\pi$
$798$		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	−0.0619660	−	0.998078i	$-0.519737\pi$
$809$	1.55136e7	−	2.68704e7i	0.833378	−	1.44345i	0.895344	−	0.445375i	$-0.146930\pi$
$810$	−643188.	−	1.11403e6i	−0.0344449	−	0.0596604i
$811$	−2.94456e7			−1.57206			−0.786028	−	0.618191i	$-0.787866\pi$
$811$	−2.94456e7			−1.57206			−0.786028	+	0.618191i	$0.787866\pi$
$812$		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	0.925780	−	0.378062i	$-0.123409\pi$
$821$	2.61656e6	+	4.53201e6i	0.135479	+	0.234657i	−0.790301	+	0.612718i	$0.790076\pi$
$822$	1.03632e7	−	1.79495e7i	0.534950	−	0.926561i
$823$	−7.08154e6	+	1.22656e7i	−0.364442	+	0.631232i	−0.988686	−	0.149997i	$-0.952074\pi$
$823$	−7.08154e6	+	1.22656e7i	−0.364442	+	0.631232i	0.624245	+	0.781229i	$0.285407\pi$
$824$	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	−0.496375	−	0.868108i	$-0.665336\pi$
$829$	9.96521e6	−	1.72602e7i	0.503617	−	0.872289i	0.999991	−	0.00418109i	$-0.00133089\pi$
$830$	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	$-0.652608\pi$
$839$	−1.88103e7			−0.922552			−0.461276	+	0.887257i	$0.652608\pi$
$840$		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	$-0.338950\pi$
$853$	2.05980e7			0.969285			0.484643	+	0.874712i	$0.338950\pi$
$854$		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	−0.420231	−	0.907417i	$-0.638051\pi$
$857$	1.23786e7	−	2.14404e7i	0.575731	−	0.997195i	0.995962	−	0.0897778i	$-0.0286157\pi$
$858$	668384.	−	1.15767e6i	0.0309961	−	0.0536869i
$859$	1.95533e7	+	3.38672e7i	0.904141	+	1.56602i	0.822066	+	0.569392i	$0.192821\pi$
$859$	1.95533e7	+	3.38672e7i	0.904141	+	1.56602i	0.0820751	+	0.996626i	$0.473845\pi$
$860$	−1.13987e6			−0.0525544
$861$		0			0
$862$	−2.07527e7			−0.951275
$863$	1.96681e7	+	3.40662e7i	0.898952	+	1.55703i	0.828836	+	0.559491i	$0.189003\pi$
$863$	1.96681e7	+	3.40662e7i	0.898952	+	1.55703i	0.0701154	+	0.997539i	$0.477663\pi$
$864$	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	0.763428	−	0.645893i	$-0.223515\pi$
$877$	−4.04626e6	−	7.00833e6i	−0.177646	−	0.307692i	−0.941074	+	0.338201i	$0.890182\pi$
$878$	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	$-0.528068\pi$
$881$	−4.05755e6			−0.176126			−0.0880631	+	0.996115i	$0.528068\pi$
$882$		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	$-0.0607053\pi$
$887$	7.65695e6	+	1.32622e7i	0.326773	+	0.565988i	−0.655096	+	0.755545i	$0.727372\pi$
$888$	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	−0.558183	−	0.829718i	$-0.688501\pi$
$907$	1.08879e7	−	1.88583e7i	0.439465	−	0.761176i	0.997648	+	0.0685419i	$0.0218347\pi$
$908$	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	0.999639	+	0.0268850i	$0.00855878\pi$
$919$	1.33929e7	+	2.31972e7i	0.523102	+	0.906040i	−0.476536	+	0.879155i	$0.658108\pi$
$920$	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	$-0.171144\pi$
$929$	−369987.	−	640836.i	−0.0140652	−	0.0243617i	−0.872972	+	0.487770i	$0.837811\pi$
$930$	−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	$-0.500726\pi$
$937$	−122654.			−0.00456385			−0.00228193	+	0.999997i	$0.500726\pi$
$938$		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	$-0.905712\pi$
$941$	−6.12332e6	+	1.06059e7i	−0.225431	+	0.390457i	0.731018	+	0.682358i	$0.239046\pi$
$942$	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	0.897689	−	0.440631i	$-0.145245\pi$
$947$	1.85587e6	+	3.21446e6i	0.0672470	+	0.116475i	−0.830442	+	0.557106i	$0.811912\pi$
$948$	−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	$-0.276906\pi$
$971$	−9.97281e6	−	1.72734e7i	−0.339445	−	0.587936i	−0.984328	+	0.176345i	$0.943573\pi$
$972$	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	−0.857875	−	0.513859i	$-0.828216\pi$
$977$	479671.	−	830815.i	0.0160771	−	0.0278463i	0.873952	+	0.486012i	$0.161549\pi$
$978$	−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	0.00865985	+	0.999963i	$0.497243\pi$
$983$	−2.61049e7	+	4.52149e7i	−0.861663	+	1.49244i	−0.870323	+	0.492482i	$0.836090\pi$
$984$	−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	−0.687507	−	0.726177i	$-0.741295\pi$
$991$	8.81523e6	−	1.52684e7i	0.285134	−	0.493867i	0.972642	+	0.232310i	$0.0746285\pi$
$992$	−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	0.339314	+	0.940673i	$0.389805\pi$
$997$	−2.02437e7	+	3.50632e7i	−0.644990	+	1.11716i	−0.984304	+	0.176482i	$0.943528\pi$
$998$	−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.n.67.1		4
7.2	even	3	inner	147.6.e.n.79.1		4
7.3	odd	6		147.6.a.j.1.2	yes	2
7.4	even	3		147.6.a.h.1.2	✓	2
7.5	odd	6		147.6.e.m.79.1		4
7.6	odd	2		147.6.e.m.67.1		4
21.11	odd	6		441.6.a.q.1.1		2
21.17	even	6		441.6.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.h.1.2	✓	2	7.4	even	3
147.6.a.j.1.2	yes	2	7.3	odd	6
147.6.e.m.67.1		4	7.6	odd	2
147.6.e.m.79.1		4	7.5	odd	6
147.6.e.n.67.1		4	1.1	even	1	trivial
147.6.e.n.79.1		4	7.2	even	3	inner
441.6.a.q.1.1		2	21.11	odd	6
441.6.a.r.1.1		2	21.17	even	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

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