LMFDB - Embedded newform 49.6.e.a.15.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(8,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

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

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, 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:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			15.14
Character	$\chi$	$=$	49.15
Dual form			49.6.e.a.36.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.349896 - 1.53300i) q^{2} +(-18.7448 + 23.5052i) q^{3} +(26.6034 + 12.8115i) q^{4} +(-56.1895 + 70.4594i) q^{5} +(29.4746 + 36.9600i) q^{6} +(13.7252 - 128.913i) q^{7} +(60.3208 - 75.6399i) q^{8} +(-147.055 - 644.291i) q^{9} +O(q^{10})$	\(q+(0.349896 - 1.53300i) q^{2} +(-18.7448 + 23.5052i) q^{3} +(26.6034 + 12.8115i) q^{4} +(-56.1895 + 70.4594i) q^{5} +(29.4746 + 36.9600i) q^{6} +(13.7252 - 128.913i) q^{7} +(60.3208 - 75.6399i) q^{8} +(-147.055 - 644.291i) q^{9} +(88.3534 + 110.792i) q^{10} +(-88.9749 + 389.825i) q^{11} +(-799.810 + 385.168i) q^{12} +(26.5719 - 116.419i) q^{13} +(-192.821 - 66.1469i) q^{14} +(-602.902 - 2641.49i) q^{15} +(494.273 + 619.799i) q^{16} +(10.2166 - 4.92007i) q^{17} -1039.15 q^{18} -513.784 q^{19} +(-2397.52 + 1154.58i) q^{20} +(2772.85 + 2739.06i) q^{21} +(566.468 + 272.796i) q^{22} +(-2183.48 - 1051.51i) q^{23} +(647.231 + 2835.70i) q^{24} +(-1111.89 - 4871.50i) q^{25} +(-169.173 - 81.4693i) q^{26} +(11318.6 + 5450.73i) q^{27} +(2016.71 - 3253.68i) q^{28} +(-4930.30 + 2374.31i) q^{29} -4260.34 q^{30} -730.365 q^{31} +(3912.41 - 1884.12i) q^{32} +(-7495.09 - 9398.54i) q^{33} +(-3.96768 - 17.3836i) q^{34} +(8311.93 + 8210.63i) q^{35} +(4342.17 - 19024.3i) q^{36} +(-1661.34 + 800.057i) q^{37} +(-179.771 + 787.629i) q^{38} +(2238.37 + 2806.83i) q^{39} +(1940.14 + 8500.33i) q^{40} +(-6718.10 + 8424.23i) q^{41} +(5169.18 - 3292.39i) q^{42} +(2189.72 + 2745.83i) q^{43} +(-7361.27 + 9230.74i) q^{44} +(53659.3 + 25840.9i) q^{45} +(-2375.95 + 2979.34i) q^{46} +(-2300.75 + 10080.2i) q^{47} -23833.5 q^{48} +(-16430.2 - 3538.71i) q^{49} -7857.03 q^{50} +(-75.8611 + 332.369i) q^{51} +(2198.41 - 2756.71i) q^{52} +(17969.4 + 8653.63i) q^{53} +(12316.3 - 15444.1i) q^{54} +(-22467.3 - 28173.2i) q^{55} +(-8923.07 - 8814.32i) q^{56} +(9630.76 - 12076.6i) q^{57} +(1914.71 + 8388.90i) q^{58} +(-20230.4 - 25368.1i) q^{59} +(17802.2 - 77996.5i) q^{60} +(-45217.6 + 21775.7i) q^{61} +(-255.552 + 1119.65i) q^{62} +(-85076.0 + 10114.4i) q^{63} +(4125.53 + 18075.1i) q^{64} +(6709.76 + 8413.77i) q^{65} +(-17030.4 + 8201.42i) q^{66} -16311.9 q^{67} +334.830 q^{68} +(65644.6 - 31612.8i) q^{69} +(15495.2 - 9869.29i) q^{70} +(51258.9 + 24685.0i) q^{71} +(-57604.6 - 27740.9i) q^{72} +(190.919 + 836.472i) q^{73} +(645.189 + 2826.76i) q^{74} +(135348. + 65179.9i) q^{75} +(-13668.4 - 6582.34i) q^{76} +(49032.4 + 16820.5i) q^{77} +(5086.05 - 2449.31i) q^{78} -3450.59 q^{79} -71443.6 q^{80} +(-195598. + 94195.2i) q^{81} +(10563.7 + 13246.4i) q^{82} +(-15705.9 - 68812.1i) q^{83} +(38675.8 + 108393. i) q^{84} +(-227.402 + 996.313i) q^{85} +(4975.52 - 2396.08i) q^{86} +(36608.8 - 160394. i) q^{87} +(24119.3 + 30244.6i) q^{88} +(18719.8 + 82016.9i) q^{89} +(58389.2 - 73217.8i) q^{90} +(-14643.3 - 5023.34i) q^{91} +(-44616.4 - 55947.2i) q^{92} +(13690.5 - 17167.4i) q^{93} +(14647.9 + 7054.07i) q^{94} +(28869.2 - 36200.9i) q^{95} +(-29050.6 + 127279. i) q^{96} +30628.5 q^{97} +(-11173.7 + 23949.3i) q^{98} +264245. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9}+O(q^{10}) $ 138 * q - 5 * q^2 + 13 * q^3 - 389 * q^4 + 67 * q^5 + 331 * q^6 - 56 * q^7 + 305 * q^8 - 918 * q^9	\( 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9} - 771 q^{10} + 410 q^{11} - 1316 q^{12} + 483 q^{13} + 2597 q^{14} + 2557 q^{15} - 7357 q^{16} - 1422 q^{17} - 2480 q^{18} - 6758 q^{19} - 3647 q^{20} - 399 q^{21} - 857 q^{22} - 2392 q^{23} - 3571 q^{24} - 8066 q^{25} - 343 q^{26} + 16396 q^{27} + 32102 q^{28} + 30341 q^{29} + 13716 q^{30} - 32712 q^{31} - 26993 q^{32} - 16775 q^{33} + 35163 q^{34} - 12019 q^{35} + 35461 q^{36} - 34872 q^{37} + 13383 q^{38} - 20671 q^{39} + 165169 q^{40} + 51233 q^{41} - 13741 q^{42} - 17203 q^{43} - 4267 q^{44} + 30777 q^{45} - 74611 q^{46} + 64264 q^{47} - 247084 q^{48} - 70350 q^{49} - 263036 q^{50} - 57453 q^{51} - 36043 q^{52} + 124590 q^{53} + 144840 q^{54} + 90977 q^{55} + 404404 q^{56} - 103899 q^{57} + 24861 q^{58} - 8079 q^{59} + 72065 q^{60} - 236659 q^{61} - 173227 q^{62} - 119805 q^{63} + 105381 q^{64} - 33383 q^{65} + 536577 q^{66} + 19716 q^{67} - 256340 q^{68} - 202795 q^{69} + 194803 q^{70} + 61778 q^{71} - 392108 q^{72} - 157760 q^{73} - 328319 q^{74} + 355167 q^{75} - 61334 q^{76} - 24402 q^{77} + 497217 q^{78} - 73876 q^{79} - 1340760 q^{80} - 815116 q^{81} + 248976 q^{82} + 303107 q^{83} + 1250354 q^{84} + 205487 q^{85} + 1083219 q^{86} + 197027 q^{87} + 1052915 q^{88} + 219783 q^{89} + 82170 q^{90} - 837235 q^{91} + 35936 q^{92} + 138365 q^{93} - 571908 q^{94} - 610016 q^{95} - 1054494 q^{96} + 762020 q^{97} - 2160767 q^{98} - 1090772 q^{99}+O(q^{100}) \) 138 * q - 5 * q^2 + 13 * q^3 - 389 * q^4 + 67 * q^5 + 331 * q^6 - 56 * q^7 + 305 * q^8 - 918 * q^9 - 771 * q^10 + 410 * q^11 - 1316 * q^12 + 483 * q^13 + 2597 * q^14 + 2557 * q^15 - 7357 * q^16 - 1422 * q^17 - 2480 * q^18 - 6758 * q^19 - 3647 * q^20 - 399 * q^21 - 857 * q^22 - 2392 * q^23 - 3571 * q^24 - 8066 * q^25 - 343 * q^26 + 16396 * q^27 + 32102 * q^28 + 30341 * q^29 + 13716 * q^30 - 32712 * q^31 - 26993 * q^32 - 16775 * q^33 + 35163 * q^34 - 12019 * q^35 + 35461 * q^36 - 34872 * q^37 + 13383 * q^38 - 20671 * q^39 + 165169 * q^40 + 51233 * q^41 - 13741 * q^42 - 17203 * q^43 - 4267 * q^44 + 30777 * q^45 - 74611 * q^46 + 64264 * q^47 - 247084 * q^48 - 70350 * q^49 - 263036 * q^50 - 57453 * q^51 - 36043 * q^52 + 124590 * q^53 + 144840 * q^54 + 90977 * q^55 + 404404 * q^56 - 103899 * q^57 + 24861 * q^58 - 8079 * q^59 + 72065 * q^60 - 236659 * q^61 - 173227 * q^62 - 119805 * q^63 + 105381 * q^64 - 33383 * q^65 + 536577 * q^66 + 19716 * q^67 - 256340 * q^68 - 202795 * q^69 + 194803 * q^70 + 61778 * q^71 - 392108 * q^72 - 157760 * q^73 - 328319 * q^74 + 355167 * q^75 - 61334 * q^76 - 24402 * q^77 + 497217 * q^78 - 73876 * q^79 - 1340760 * q^80 - 815116 * q^81 + 248976 * q^82 + 303107 * q^83 + 1250354 * q^84 + 205487 * q^85 + 1083219 * q^86 + 197027 * q^87 + 1052915 * q^88 + 219783 * q^89 + 82170 * q^90 - 837235 * q^91 + 35936 * q^92 + 138365 * q^93 - 571908 * q^94 - 610016 * q^95 - 1054494 * q^96 + 762020 * q^97 - 2160767 * q^98 - 1090772 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{7}\right)$

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 $

$2$	0.349896	−	1.53300i	0.0618535	−	0.270998i	−0.934539	−	0.355860i	$-0.884188\pi$
$2$	0.349896	−	1.53300i	0.0618535	−	0.270998i	0.996393	+	0.0848623i	$0.0270450\pi$
$3$	−18.7448	+	23.5052i	−1.20248	+	1.50786i	−0.394233	+	0.919010i	$0.628990\pi$
$3$	−18.7448	+	23.5052i	−1.20248	+	1.50786i	−0.808244	+	0.588848i	$0.799582\pi$
$4$	26.6034	+	12.8115i	0.831355	+	0.400359i
$5$	−56.1895	+	70.4594i	−1.00515	+	1.26042i	−0.0398657	+	0.999205i	$0.512693\pi$
$5$	−56.1895	+	70.4594i	−1.00515	+	1.26042i	−0.965282	+	0.261210i	$0.915878\pi$
$6$	29.4746	+	36.9600i	0.334249	+	0.419135i
$7$	13.7252	−	128.913i	0.105870	−	0.994380i
$7$	13.7252	−	128.913i	0.105870	−	0.994380i
$8$	60.3208	−	75.6399i	0.333228	−	0.417855i
$9$	−147.055	−	644.291i	−0.605165	−	2.65140i
$10$	88.3534	+	110.792i	0.279398	+	0.350354i
$11$	−88.9749	+	389.825i	−0.221710	+	0.971376i	0.734480	+	0.678630i	$0.237426\pi$
$11$	−88.9749	+	389.825i	−0.221710	+	0.971376i	−0.956190	+	0.292746i	$0.905431\pi$
$12$	−799.810	+	385.168i	−1.60337	+	0.772142i
$13$	26.5719	−	116.419i	0.0436078	−	0.191058i	−0.948432	−	0.316979i	$-0.897331\pi$
$13$	26.5719	−	116.419i	0.0436078	−	0.191058i	0.992040	+	0.125921i	$0.0401886\pi$
$14$	−192.821	−	66.1469i	−0.262927	−	0.0901964i
$15$	−602.902	−	2641.49i	−0.691861	−	3.03124i
$16$	494.273	+	619.799i	0.482689	+	0.605273i
$17$	10.2166	−	4.92007i	0.00857403	−	0.00412904i	−0.429592	−	0.903023i	$-0.641343\pi$
$17$	10.2166	−	4.92007i	0.00857403	−	0.00412904i	0.438166	+	0.898894i	$0.355628\pi$
$18$	−1039.15			−0.755956
$19$	−513.784			−0.326510			−0.163255	−	0.986584i	$-0.552199\pi$
$19$	−513.784			−0.326510			−0.163255	+	0.986584i	$0.552199\pi$
$20$	−2397.52	+	1154.58i	−1.34025	+	0.645432i
$21$	2772.85	+	2739.06i	1.37208	+	1.35536i
$22$	566.468	+	272.796i	0.249527	+	0.120166i
$23$	−2183.48	−	1051.51i	−0.860654	−	0.414469i	−0.0491332	−	0.998792i	$-0.515646\pi$
$23$	−2183.48	−	1051.51i	−0.860654	−	0.414469i	−0.811521	+	0.584323i	$0.801360\pi$
$24$	647.231	+	2835.70i	0.229367	+	1.00492i
$25$	−1111.89	−	4871.50i	−0.355804	−	1.55888i
$26$	−169.173	−	81.4693i	−0.0490791	−	0.0236353i
$27$	11318.6	+	5450.73i	2.98801	+	1.43895i
$28$	2016.71	−	3253.68i	0.486125	−	0.784297i
$29$	−4930.30	+	2374.31i	−1.08863	+	0.524255i	−0.890065	−	0.455834i	$-0.849341\pi$
$29$	−4930.30	+	2374.31i	−1.08863	+	0.524255i	−0.198561	+	0.980088i	$0.563627\pi$
$30$	−4260.34			−0.864254
$31$	−730.365			−0.136501			−0.0682505	−	0.997668i	$-0.521742\pi$
$31$	−730.365			−0.136501			−0.0682505	+	0.997668i	$0.521742\pi$
$32$	3912.41	−	1884.12i	0.675413	−	0.325262i
$33$	−7495.09	−	9398.54i	−1.19810	−	1.50237i
$34$	−3.96768	−	17.3836i	−0.000588626	−	0.00257894i
$35$	8311.93	+	8210.63i	1.14692	+	1.13294i
$36$	4342.17	−	19024.3i	0.558407	−	2.44654i
$37$	−1661.34	+	800.057i	−0.199505	+	0.0960764i	−0.530969	−	0.847392i	$-0.678172\pi$
$37$	−1661.34	+	800.057i	−0.199505	+	0.0960764i	0.331464	+	0.943468i	$0.392457\pi$
$38$	−179.771	+	787.629i	−0.0201958	+	0.0884835i
$39$	2238.37	+	2806.83i	0.235652	+	0.295498i
$40$	1940.14	+	8500.33i	0.191727	+	0.840013i
$41$	−6718.10	+	8424.23i	−0.624147	+	0.782655i	−0.988921	−	0.148441i	$-0.952575\pi$
$41$	−6718.10	+	8424.23i	−0.624147	+	0.782655i	0.364775	+	0.931096i	$0.381146\pi$
$42$	5169.18	−	3292.39i	0.452167	−	0.287997i
$43$	2189.72	+	2745.83i	0.180600	+	0.226466i	0.863888	−	0.503683i	$-0.168022\pi$
$43$	2189.72	+	2745.83i	0.180600	+	0.226466i	−0.683288	+	0.730149i	$0.739451\pi$
$44$	−7361.27	+	9230.74i	−0.573220	+	0.718795i
$45$	53659.3	+	25840.9i	3.95015	+	1.90229i
$46$	−2375.95	+	2979.34i	−0.165555	+	0.207599i
$47$	−2300.75	+	10080.2i	−0.151923	+	0.665619i	0.840402	+	0.541964i	$0.182319\pi$
$47$	−2300.75	+	10080.2i	−0.151923	+	0.665619i	−0.992325	+	0.123656i	$0.960538\pi$
$48$	−23833.5			−1.49309
$49$	−16430.2	−	3538.71i	−0.977583	−	0.210550i
$50$	−7857.03			−0.444461
$51$	−75.8611	+	332.369i	−0.00408407	+	0.0178935i
$52$	2198.41	−	2756.71i	0.112746	−	0.141379i
$53$	17969.4	+	8653.63i	0.878709	+	0.423164i	0.818153	−	0.575001i	$-0.194998\pi$
$53$	17969.4	+	8653.63i	0.878709	+	0.423164i	0.0605559	+	0.998165i	$0.480713\pi$
$54$	12316.3	−	15444.1i	0.574771	−	0.720740i
$55$	−22467.3	−	28173.2i	−1.00149	−	1.25582i
$56$	−8923.07	−	8814.32i	−0.380228	−	0.375594i
$57$	9630.76	−	12076.6i	0.392621	−	0.492331i
$58$	1914.71	+	8388.90i	0.0747366	+	0.327442i
$59$	−20230.4	−	25368.1i	−0.756615	−	0.948765i	0.243160	−	0.969986i	$-0.421816\pi$
$59$	−20230.4	−	25368.1i	−0.756615	−	0.948765i	−0.999775	+	0.0212214i	$0.993244\pi$
$60$	17802.2	−	77996.5i	0.638404	−	2.79703i
$61$	−45217.6	+	21775.7i	−1.55591	+	0.749285i	−0.996809	−	0.0798179i	$-0.974566\pi$
$61$	−45217.6	+	21775.7i	−1.55591	+	0.749285i	−0.559096	+	0.829103i	$0.688852\pi$
$62$	−255.552	+	1119.65i	−0.00844307	+	0.0369915i
$63$	−85076.0	+	10114.4i	−2.70057	+	0.321061i
$64$	4125.53	+	18075.1i	0.125901	+	0.551609i
$65$	6709.76	+	8413.77i	0.196981	+	0.247006i
$66$	−17030.4	+	8201.42i	−0.481244	+	0.231755i
$67$	−16311.9			−0.443932			−0.221966	−	0.975054i	$-0.571247\pi$
$67$	−16311.9			−0.443932			−0.221966	+	0.975054i	$0.571247\pi$
$68$	334.830			0.00878116
$69$	65644.6	−	31612.8i	1.65988	−	0.799355i
$70$	15495.2	−	9869.29i	0.377965	−	0.240736i
$71$	51258.9	+	24685.0i	1.20677	+	0.581149i	0.925597	−	0.378509i	$-0.123563\pi$
$71$	51258.9	+	24685.0i	1.20677	+	0.581149i	0.281170	+	0.959658i	$0.409277\pi$
$72$	−57604.6	−	27740.9i	−1.30956	−	0.630651i
$73$	190.919	+	836.472i	0.00419317	+	0.0183715i	0.976981	−	0.213325i	$-0.0684294\pi$
$73$	190.919	+	836.472i	0.00419317	+	0.0183715i	−0.972788	+	0.231697i	$0.925572\pi$
$74$	645.189	+	2826.76i	0.0136964	+	0.0600080i
$75$	135348.	+	65179.9i	2.77842	+	1.33801i
$76$	−13668.4	−	6582.34i	−0.271446	−	0.130721i
$77$	49032.4	+	16820.5i	0.942445	+	0.323304i
$78$	5086.05	−	2449.31i	0.0946552	−	0.0455835i
$79$	−3450.59			−0.0622050			−0.0311025	−	0.999516i	$-0.509902\pi$
$79$	−3450.59			−0.0622050			−0.0311025	+	0.999516i	$0.509902\pi$
$80$	−71443.6			−1.24807
$81$	−195598.	+	94195.2i	−3.31248	+	1.59520i
$82$	10563.7	+	13246.4i	0.173492	+	0.217552i
$83$	−15705.9	−	68812.1i	−0.250246	−	1.09640i	−0.931325	−	0.364190i	$-0.881346\pi$
$83$	−15705.9	−	68812.1i	−0.250246	−	1.09640i	0.681078	−	0.732211i	$-0.261511\pi$
$84$	38675.8	+	108393.i	0.598054	+	1.67611i
$85$	−227.402	+	996.313i	−0.00341387	+	0.0149571i
$86$	4975.52	−	2396.08i	0.0725424	−	0.0349346i
$87$	36608.8	−	160394.i	0.518546	−	2.27190i
$88$	24119.3	+	30244.6i	0.332015	+	0.416333i
$89$	18719.8	+	82016.9i	0.250511	+	1.09756i	0.931062	+	0.364860i	$0.118883\pi$
$89$	18719.8	+	82016.9i	0.250511	+	1.09756i	−0.680551	+	0.732701i	$0.738260\pi$
$90$	58389.2	−	73217.8i	0.759848	−	0.952819i
$91$	−14643.3	−	5023.34i	−0.185368	−	0.0635901i
$92$	−44616.4	−	55947.2i	−0.549573	−	0.689142i
$93$	13690.5	−	17167.4i	0.164139	−	0.205824i
$94$	14647.9	+	7054.07i	0.170984	+	0.0823418i
$95$	28869.2	−	36200.9i	0.328191	−	0.411538i
$96$	−29050.6	+	127279.i	−0.321720	+	1.40955i
$97$	30628.5			0.330519			0.165260	−	0.986250i	$-0.447154\pi$
$97$	30628.5			0.330519			0.165260	+	0.986250i	$0.447154\pi$
$98$	−11173.7	+	23949.3i	−0.117526	+	0.251900i
$99$	264245.			2.70968
$100$	32831.3	−	143843.i	0.328313	−	1.43843i
$101$	−50472.5	+	63290.6i	−0.492325	+	0.617356i	−0.964479	−	0.264160i	$-0.914905\pi$
$101$	−50472.5	+	63290.6i	−0.492325	+	0.617356i	0.472154	+	0.881516i	$0.343477\pi$
$102$	482.977	+	232.589i	0.00459649	+	0.00221355i
$103$	88345.2	−	110781.i	0.820521	−	1.02890i	−0.178468	−	0.983946i	$-0.557114\pi$
$103$	88345.2	−	110781.i	0.820521	−	1.02890i	0.998989	−	0.0449555i	$-0.0143146\pi$
$104$	−7203.09	−	9032.39i	−0.0653034	−	0.0818879i
$105$	−348798.	+	41467.2i	−3.08745	+	0.367055i
$106$	19553.4	−	24519.2i	0.169028	−	0.211954i
$107$	6829.71	+	29922.9i	0.0576690	+	0.252664i	0.995543	−	0.0943126i	$-0.0300653\pi$
$107$	6829.71	+	29922.9i	0.0576690	+	0.252664i	−0.937874	+	0.346977i	$0.887208\pi$
$108$	231280.	+	290015.i	1.90800	+	2.39255i
$109$	−11951.5	+	52362.9i	−0.0963508	+	0.422141i	−0.999981	−	0.00617311i	$-0.998035\pi$
$109$	−11951.5	+	52362.9i	−0.0963508	+	0.422141i	0.903630	+	0.428314i	$0.140892\pi$
$110$	−51050.6	+	24584.7i	−0.402271	+	0.193724i
$111$	12335.8	−	54046.9i	0.0950302	−	0.416354i
$112$	86684.3	−	55211.5i	0.652973	−	0.415896i
$113$	31357.9	+	137388.i	0.231021	+	1.01217i	0.948795	+	0.315892i	$0.102304\pi$
$113$	31357.9	+	137388.i	0.231021	+	1.01217i	−0.717775	+	0.696275i	$0.754839\pi$
$114$	−15143.6	−	18989.5i	−0.109136	−	0.136852i
$115$	196777.	−	94762.7i	1.38749	−	0.668179i
$116$	−161581.			−1.11492
$117$	−78915.3			−0.532963
$118$	−45967.8	+	22136.9i	−0.303913	+	0.146357i
$119$	−494.037	−	1384.59i	−0.00319810	−	0.00896299i
$120$	−236169.	−	113733.i	−1.49717	−	0.720998i
$121$	1055.25	+	508.181i	0.00655227	+	0.00315541i
$122$	17560.5	+	76937.7i	0.106816	+	0.467993i
$123$	−72083.9	−	315820.i	−0.429611	−	1.88225i
$124$	−19430.2	−	9357.08i	−0.113481	−	0.0546495i
$125$	151981.	+	73190.2i	0.869990	+	0.418965i
$126$	−14262.5	+	133960.i	−0.0800330	+	0.751708i
$127$	151637.	−	73024.5i	0.834250	−	0.401753i	0.0325424	−	0.999470i	$-0.489640\pi$
$127$	151637.	−	73024.5i	0.834250	−	0.401753i	0.801707	+	0.597717i	$0.203925\pi$
$128$	168111.			0.906924
$129$	−105587.			−0.558646
$130$	15246.0	−	7342.08i	0.0791220	−	0.0381032i
$131$	80679.5	+	101169.i	0.410757	+	0.515073i	0.943576	−	0.331156i	$-0.107439\pi$
$131$	80679.5	+	101169.i	0.410757	+	0.515073i	−0.532819	+	0.846229i	$0.678867\pi$
$132$	−78985.0	−	346056.i	−0.394557	−	1.72867i
$133$	−7051.77	+	66233.5i	−0.0345676	+	0.324675i
$134$	−5707.46	+	25006.0i	−0.0274588	+	0.120305i
$135$	−1.02004e6	+	491225.i	−4.81706	+	2.31977i
$136$	244.122	−	1069.57i	0.00113177	−	0.00495862i
$137$	−3764.84	−	4720.96i	−0.0171374	−	0.0214896i	0.773189	−	0.634176i	$-0.218660\pi$
$137$	−3764.84	−	4720.96i	−0.0171374	−	0.0214896i	−0.790326	+	0.612686i	$0.790089\pi$
$138$	−25493.4	−	111694.i	−0.113954	−	0.499267i
$139$	−30727.1	+	38530.6i	−0.134892	+	0.169149i	−0.844689	−	0.535257i	$-0.820215\pi$
$139$	−30727.1	+	38530.6i	−0.134892	+	0.169149i	0.709798	+	0.704405i	$0.248786\pi$
$140$	115935.	+	324919.i	0.499912	+	1.40105i
$141$	−193811.	−	243031.i	−0.820975	−	1.02947i
$142$	55777.3	−	69942.5i	0.232133	−	0.291085i
$143$	43018.8	+	20716.8i	0.175921	+	0.0847192i
$144$	326645.	−	409600.i	1.31271	−	1.64609i
$145$	109739.	−	480797.i	0.433451	−	1.89907i
$146$	1349.11			0.00523799
$147$	391159.	−	319864.i	1.49300	−	1.22088i
$148$	−54447.0			−0.204324
$149$	−43679.1	+	191370.i	−0.161179	+	0.706170i	0.828155	+	0.560500i	$0.189391\pi$
$149$	−43679.1	+	191370.i	−0.161179	+	0.706170i	−0.989333	+	0.145670i	$0.953466\pi$
$150$	147278.	−	184681.i	0.534454	−	0.670184i
$151$	−455795.	−	219500.i	−1.62678	−	0.783414i	−0.999991	−	0.00422102i	$-0.998656\pi$
$151$	−455795.	−	219500.i	−1.62678	−	0.783414i	−0.626784	−	0.779193i	$-0.715629\pi$
$152$	−30991.9	+	38862.6i	−0.108802	+	0.136434i
$153$	−4672.36	−	5858.95i	−0.0161364	−	0.0202345i
$154$	42941.9	−	69281.0i	0.145908	−	0.235403i
$155$	41038.8	−	51461.1i	0.137204	−	0.172048i
$156$	23588.5	+	103348.i	0.0776048	+	0.340009i
$157$	203074.	+	254646.i	0.657513	+	0.824496i	0.993070	−	0.117524i	$-0.0374958\pi$
$157$	203074.	+	254646.i	0.657513	+	0.824496i	−0.335557	+	0.942020i	$0.608924\pi$
$158$	−1207.35	+	5289.73i	−0.00384760	+	0.0168574i
$159$	−540238.	+	260165.i	−1.69470	+	0.816124i
$160$	−87082.5	+	381533.i	−0.268925	+	1.17824i
$161$	−165522.	+	267047.i	−0.503257	+	0.811938i
$162$	75961.8	+	332810.i	0.227409	+	0.996343i
$163$	−171753.	−	215371.i	−0.506332	−	0.634920i	0.461313	−	0.887238i	$-0.347379\pi$
$163$	−171753.	−	215371.i	−0.506332	−	0.634920i	−0.967644	+	0.252318i	$0.918807\pi$
$164$	−286651.	+	138044.i	−0.832231	+	0.400781i
$165$	1.08336e6			3.09787
$166$	−110984.			−0.312601
$167$	34053.1	−	16399.1i	0.0944855	−	0.0455018i	−0.386044	−	0.922480i	$-0.626159\pi$
$167$	34053.1	−	16399.1i	0.0944855	−	0.0455018i	0.480530	+	0.876979i	$0.340444\pi$
$168$	374443.	−	44516.1i	1.02356	−	0.121687i
$169$	321676.	+	154911.i	0.866367	+	0.417220i
$170$	1447.78	+	697.212i	0.00384219	+	0.00185030i
$171$	75554.6	+	331026.i	0.197593	+	0.865709i
$172$	23075.8	+	101102.i	0.0594753	+	0.260578i
$173$	−603330.	−	290548.i	−1.53264	−	0.738080i	−0.538142	−	0.842854i	$-0.680874\pi$
$173$	−603330.	−	290548.i	−1.53264	−	0.738080i	−0.994496	+	0.104774i	$0.966588\pi$
$174$	−233073.	−	112242.i	−0.583606	−	0.281050i
$175$	−643261.	+	76474.9i	−1.58779	+	0.188766i
$176$	−285591.	+	137533.i	−0.694965	+	0.334677i
$177$	975497.			2.34041
$178$	132282.			0.312932
$179$	−66659.8	+	32101.7i	−0.155500	+	0.0748851i	−0.510015	−	0.860165i	$-0.670360\pi$
$179$	−66659.8	+	32101.7i	−0.155500	+	0.0748851i	0.354515	+	0.935050i	$0.384646\pi$
$180$	1.09646e6	+	1.37491e6i	2.52238	+	3.16296i
$181$	88887.9	+	389443.i	0.201672	+	0.883584i	0.969919	+	0.243430i	$0.0782725\pi$
$181$	88887.9	+	389443.i	0.201672	+	0.883584i	−0.768246	+	0.640154i	$0.778870\pi$
$182$	−12824.4	+	20690.4i	−0.0286984	+	0.0463010i
$183$	335753.	−	1.47103e6i	0.741126	−	3.24708i
$184$	−211245.	+	101730.i	−0.459983	+	0.221516i
$185$	36978.0	−	162011.i	0.0794355	−	0.348030i
$186$	−21527.3	−	26994.3i	−0.0456254	−	0.0572124i
$187$	1008.94	+	4420.45i	0.00210990	+	0.00924406i
$188$	−190350.	+	238692.i	−0.392789	+	0.492542i
$189$	858020.	−	1.38430e6i	1.74720	−	2.81887i
$190$	−45394.6	−	56923.0i	−0.0912262	−	0.114394i
$191$	−41587.7	+	52149.3i	−0.0824862	+	0.103434i	−0.821362	−	0.570407i	$-0.806785\pi$
$191$	−41587.7	+	52149.3i	−0.0824862	+	0.103434i	0.738876	+	0.673841i	$0.235357\pi$
$192$	−502191.	−	241842.i	−0.983141	−	0.473456i
$193$	−498433.	+	625015.i	−0.963193	+	1.20781i	0.0149538	+	0.999888i	$0.495240\pi$
$193$	−498433.	+	625015.i	−0.963193	+	1.20781i	−0.978146	+	0.207917i	$0.933332\pi$
$194$	10716.8	−	46953.4i	0.0204438	−	0.0895701i
$195$	−323540.			−0.609315
$196$	−391763.	−	304638.i	−0.728423	−	0.566426i
$197$	588174.			1.07979			0.539896	−	0.841732i	$-0.318463\pi$
$197$	588174.			1.07979			0.539896	+	0.841732i	$0.318463\pi$
$198$	92458.2	−	405086.i	0.167603	−	0.734318i
$199$	667240.	−	836692.i	1.19440	−	1.49773i	0.372560	−	0.928008i	$-0.378480\pi$
$199$	667240.	−	836692.i	1.19440	−	1.49773i	0.821839	−	0.569720i	$-0.192948\pi$
$200$	−435549.	−	209750.i	−0.769950	−	0.370788i
$201$	305762.	−	383414.i	0.533818	−	0.669387i
$202$	79364.0	+	99519.3i	0.136850	+	0.171605i
$203$	238411.	+	668169.i	0.406056	+	1.13801i
$204$	−6276.31	+	7870.24i	−0.0105591	+	0.0132407i
$205$	−216079.	−	946706.i	−0.359111	−	1.57337i
$206$	−138916.	−	174195.i	−0.228078	−	0.286001i
$207$	−356385.	+	1.56142e6i	−0.578087	+	2.53276i
$208$	85290.3	−	41073.6i	0.136691	−	0.0658271i
$209$	45713.9	−	200286.i	0.0723906	−	0.317164i
$210$	−58473.9	+	549215.i	−0.0914985	+	0.859397i
$211$	229062.	+	1.00358e6i	0.354198	+	1.55184i	0.767379	+	0.641194i	$0.221561\pi$
$211$	229062.	+	1.00358e6i	0.354198	+	1.55184i	−0.413180	+	0.910649i	$0.635582\pi$
$212$	367181.	+	460431.i	0.561101	+	0.703598i
$213$	−1.54106e6	+	742136.i	−2.32740	+	1.12082i
$214$	48261.4			0.0720386
$215$	−316509.			−0.466971
$216$	1.09504e6	−	527342.i	1.59696	−	0.769056i
$217$	−10024.4	+	94153.8i	−0.0144514	+	0.135734i
$218$	76090.3	+	36643.1i	0.108440	+	0.0522218i
$219$	−23240.2	−	11191.9i	−0.0327438	−	0.0157686i
$220$	−236766.	−	1.03734e6i	−0.329809	−	1.44499i
$221$	−301.315	−	1320.15i	−0.000414992	−	0.00181820i
$222$	−78537.4	−	37821.6i	−0.106953	−	0.0515060i
$223$	1.06450e6	+	512638.i	1.43346	+	0.690317i	0.979637	−	0.200775i	$-0.0643460\pi$
$223$	1.06450e6	+	512638.i	1.43346	+	0.690317i	0.453822	+	0.891093i	$0.350060\pi$
$224$	−189189.	−	530221.i	−0.251928	−	0.706052i
$225$	−2.97515e6	+	1.43276e6i	−3.91790	+	1.88676i
$226$	221587.			0.288585
$227$	−506531.			−0.652441			−0.326221	−	0.945294i	$-0.605775\pi$
$227$	−506531.			−0.652441			−0.326221	+	0.945294i	$0.605775\pi$
$228$	410930.	−	197893.i	0.523516	−	0.252112i
$229$	552238.	+	692485.i	0.695885	+	0.872612i	0.996709	−	0.0810674i	$-0.0258329\pi$
$229$	552238.	+	692485.i	0.695885	+	0.872612i	−0.300823	+	0.953680i	$0.597261\pi$
$230$	−76419.4	−	334815.i	−0.0952541	−	0.417336i
$231$	−1.31447e6	+	837219.i	−1.62076	+	1.03231i
$232$	−117807.	+	516148.i	−0.143699	+	0.629585i
$233$	195658.	−	94224.2i	0.236107	−	0.113703i	−0.312090	−	0.950053i	$-0.601029\pi$
$233$	195658.	−	94224.2i	0.236107	−	0.113703i	0.548196	+	0.836350i	$0.315315\pi$
$234$	−27612.2	+	120977.i	−0.0329656	+	0.144432i
$235$	−580969.	−	728512.i	−0.686251	−	0.860532i
$236$	−213193.	−	934059.i	−0.249168	−	1.09168i
$237$	64680.4	−	81106.7i	0.0748000	−	0.0937963i
$238$	−2295.43	+	272.895i	−0.00262676	+	0.000312286i
$239$	954310.	+	1.19667e6i	1.08067	+	1.35512i	0.930429	+	0.366473i	$0.119435\pi$
$239$	954310.	+	1.19667e6i	1.08067	+	1.35512i	0.150245	+	0.988649i	$0.451994\pi$
$240$	1.33919e6	−	1.67930e6i	1.50077	−	1.88191i
$241$	233789.	+	112587.i	0.259288	+	0.124866i	0.559012	−	0.829159i	$-0.311180\pi$
$241$	233789.	+	112587.i	0.259288	+	0.124866i	−0.299724	+	0.954026i	$0.596895\pi$
$242$	1148.27	−	1439.88i	0.00126039	−	0.00158048i
$243$	773074.	−	3.38706e6i	0.839857	−	3.67966i
$244$	−1.48192e6			−1.59349
$245$	1.17254e6	−	958826.i	1.24800	−	1.02053i
$246$	−509373.			−0.536659
$247$	−13652.2	+	59814.3i	−0.0142384	+	0.0623825i
$248$	−44056.2	+	55244.8i	−0.0454860	+	0.0570377i
$249$	1.91184e6	+	920696.i	1.95413	+	0.941061i
$250$	165378.	−	207377.i	0.167351	−	0.209851i
$251$	−706664.	−	886129.i	−0.707993	−	0.887795i	0.289599	−	0.957148i	$-0.406478\pi$
$251$	−706664.	−	886129.i	−0.707993	−	0.887795i	−0.997592	+	0.0693532i	$0.977906\pi$
$252$	−2.39289e6	−	820875.i	−2.37367	−	0.814283i
$253$	604178.	−	757615.i	0.593422	−	0.744127i
$254$	−58889.1	−	258010.i	−0.0572731	−	0.250930i
$255$	−19155.9	−	24020.8i	−0.0184481	−	0.0231332i
$256$	−73195.5	+	320690.i	−0.0698046	+	0.305834i
$257$	−944947.	+	455062.i	−0.892431	+	0.429772i	−0.823149	−	0.567825i	$-0.807785\pi$
$257$	−944947.	+	455062.i	−0.892431	+	0.429772i	−0.0692814	+	0.997597i	$0.522071\pi$
$258$	−36944.5	+	161865.i	−0.0345542	+	0.151392i
$259$	80335.8	+	225149.i	0.0744149	+	0.208555i
$260$	70709.1	+	309797.i	0.0648697	+	0.284213i
$261$	2.25477e6	+	2.82740e6i	2.04881	+	2.56913i
$262$	183321.	−	88282.7i	0.164990	−	0.0794552i
$263$	−1.01253e6			−0.902646			−0.451323	−	0.892361i	$-0.649048\pi$
$263$	−1.01253e6			−0.902646			−0.451323	+	0.892361i	$0.649048\pi$
$264$	−1.16301e6			−1.02701
$265$	−1.61942e6	+	779873.i	−1.41659	+	0.682196i
$266$	99068.3	+	33985.2i	0.0858481	+	0.0294500i
$267$	−2.27872e6	−	1.09737e6i	−1.95620	−	0.942056i
$268$	−433950.	−	208980.i	−0.369065	−	0.177732i
$269$	−164122.	−	719065.i	−0.138288	−	0.605881i	−0.995811	−	0.0914350i	$-0.970855\pi$
$269$	−164122.	−	719065.i	−0.138288	−	0.605881i	0.857523	−	0.514446i	$-0.172003\pi$
$270$	396138.	+	1.73559e6i	0.330702	+	1.44890i
$271$	818209.	+	394029.i	0.676770	+	0.325915i	0.740504	−	0.672052i	$-0.234587\pi$
$271$	818209.	+	394029.i	0.676770	+	0.325915i	−0.0637345	+	0.997967i	$0.520301\pi$
$272$	8099.26	+	3900.40i	0.00663778	+	0.00319659i
$273$	392559.	−	250031.i	0.318785	−	0.203043i
$274$	−8554.51	+	4119.64i	−0.00688365	+	0.00331499i
$275$	1.99796e6			1.59314
$276$	2.15137e6			1.69998
$277$	1.27465e6	−	613841.i	0.998144	−	0.480681i	0.137836	−	0.990455i	$-0.455985\pi$
$277$	1.27465e6	−	613841.i	0.998144	−	0.480681i	0.860308	+	0.509774i	$0.170271\pi$
$278$	48315.9	+	60586.2i	0.0374954	+	0.0470178i
$279$	107404.	+	470568.i	0.0826057	+	0.361919i
$280$	1.12243e6	−	133442.i	0.855590	−	0.101718i
$281$	204970.	−	898032.i	0.154855	−	0.678463i	−0.836578	−	0.547847i	$-0.815447\pi$
$281$	204970.	−	898032.i	0.154855	−	0.678463i	0.991433	−	0.130616i	$-0.0416954\pi$
$282$	−440379.	+	212075.i	−0.329765	+	0.158806i
$283$	102250.	−	447985.i	0.0758920	−	0.332505i	−0.922702	−	0.385514i	$-0.874024\pi$
$283$	102250.	−	447985.i	0.0758920	−	0.332505i	0.998594	+	0.0530094i	$0.0168813\pi$
$284$	1.04741e6	+	1.31341e6i	0.770584	+	0.966281i
$285$	309761.	+	1.35715e6i	0.225900	+	0.989730i
$286$	46810.9	−	58699.0i	0.0338401	−	0.0424341i
$287$	993787.	+	981675.i	0.712178	+	0.703499i
$288$	−1.78926e6	−	2.24366e6i	−1.27114	−	1.59395i
$289$	−885186.	+	1.10999e6i	−0.623433	+	0.781761i
$290$	−698663.	−	336458.i	−0.487835	−	0.234929i
$291$	−574125.	+	719930.i	−0.397442	+	0.498377i
$292$	−5637.36	+	24698.9i	−0.00386918	+	0.0169520i
$293$	428556.			0.291634			0.145817	−	0.989312i	$-0.453419\pi$
$293$	428556.			0.291634			0.145817	+	0.989312i	$0.453419\pi$
$294$	−353484.	−	711564.i	−0.238507	−	0.480116i
$295$	2.92416e6			1.95635
$296$	−39696.9	+	173923.i	−0.0263346	+	0.115379i
$297$	−3.13190e6	+	3.92727e6i	−2.06023	+	2.58345i
$298$	278087.	+	133920.i	0.181401	+	0.0873582i
$299$	−180435.	+	226258.i	−0.116719	+	0.146361i
$300$	2.76565e6	+	3.46801e6i	1.77416	+	2.22473i
$301$	384028.	−	244597.i	0.244313	−	0.155609i
$302$	−495973.	+	621930.i	−0.312925	+	0.392396i
$303$	−541561.	−	2.37273e6i	−0.338876	−	1.48471i
$304$	−253950.	−	318443.i	−0.157603	−	0.197628i
$305$	1.00646e6	−	4.40957e6i	0.619505	−	2.71423i
$306$	−10616.6	+	5112.68i	−0.00648159	+	0.00312137i
$307$	−542751.	+	2.37795e6i	−0.328666	+	1.43998i	0.493010	+	0.870024i	$0.335897\pi$
$307$	−542751.	+	2.37795e6i	−0.328666	+	1.43998i	−0.821676	+	0.569955i	$0.806961\pi$
$308$	1.08893e6	+	1.07566e6i	0.654068	+	0.646097i
$309$	947927.	+	4.15314e6i	0.564779	+	2.47446i
$310$	−64530.3	−	80918.4i	−0.0381381	−	0.0478237i
$311$	1.48851e6	−	716830.i	0.872673	−	0.420257i	0.0567299	−	0.998390i	$-0.481933\pi$
$311$	1.48851e6	−	716830.i	0.872673	−	0.420257i	0.815943	+	0.578133i	$0.196218\pi$
$312$	347328.			0.202001
$313$	−2.10091e6			−1.21213			−0.606063	−	0.795417i	$-0.707252\pi$
$313$	−2.10091e6			−1.21213			−0.606063	+	0.795417i	$0.707252\pi$
$314$	461427.	−	222211.i	0.264106	−	0.127187i
$315$	4.06772e6	−	6.56272e6i	2.30980	−	3.72655i
$316$	−91797.1	−	44207.2i	−0.0517144	−	0.0249043i
$317$	−624296.	−	300645.i	−0.348933	−	0.168037i	0.251205	−	0.967934i	$-0.419173\pi$
$317$	−624296.	−	300645.i	−0.348933	−	0.168037i	−0.600138	+	0.799897i	$0.704888\pi$
$318$	209804.	+	919213.i	0.116345	+	0.509740i
$319$	−486891.	−	2.13321e6i	−0.267889	−	1.17370i
$320$	−1.50537e6	−	724949.i	−0.821805	−	0.395760i
$321$	−831364.	−	400364.i	−0.450328	−	0.216866i
$322$	351466.	+	347183.i	0.188905	+	0.186603i
$323$	−5249.14	+	2527.85i	−0.00279951	+	0.00134817i
$324$	−6.41036e6			−3.39250
$325$	−596681.			−0.313353
$326$	−390259.	+	187939.i	−0.203380	+	0.0979428i
$327$	−1.00677e6	−	1.26245e6i	−0.520669	−	0.652898i
$328$	231967.	+	1.01631e6i	0.119053	+	0.521606i
$329$	1.26790e6	+	434950.i	0.645794	+	0.221538i
$330$	379064.	−	1.66079e6i	0.191614	−	0.839516i
$331$	1.67738e6	−	807782.i	0.841512	−	0.405251i	0.0370922	−	0.999312i	$-0.488190\pi$
$331$	1.67738e6	−	807782.i	0.841512	−	0.405251i	0.804420	+	0.594061i	$0.202476\pi$
$332$	463756.	−	2.03185e6i	0.230911	−	1.01169i
$333$	759777.	+	952731.i	0.375470	+	0.470825i
$334$	−13224.7	−	57941.2i	−0.00648664	−	0.0284198i
$335$	916555.	−	1.14932e6i	0.446218	−	0.559539i
$336$	−327119.	+	3.07246e6i	−0.158073	+	1.48470i
$337$	−1.53645e6	−	1.92664e6i	−0.736958	−	0.924116i	0.262205	−	0.965012i	$-0.415550\pi$
$337$	−1.53645e6	−	1.92664e6i	−0.736958	−	0.924116i	−0.999163	+	0.0408958i	$0.986979\pi$
$338$	350031.	−	438925.i	0.166654	−	0.208977i
$339$	−3.81712e6	−	1.83823e6i	−1.80400	−	0.868761i
$340$	−18813.9	+	23591.9i	−0.00882636	+	0.0110679i
$341$	64984.2	−	284714.i	0.0302637	−	0.132594i
$342$	533898.			0.246827
$343$	−681694.	+	2.06951e6i	−0.312863	+	0.949798i
$344$	339780.			0.154811
$345$	−1.46112e6	+	6.40158e6i	−0.660903	+	2.89561i
$346$	−656513.	+	823241.i	−0.294817	+	0.369689i
$347$	−328749.	−	158317.i	−0.146568	−	0.0705836i	0.359162	−	0.933275i	$-0.383063\pi$
$347$	−328749.	−	158317.i	−0.146568	−	0.0705836i	−0.505730	+	0.862692i	$0.668777\pi$
$348$	3.02880e6	−	3.79799e6i	1.34067	−	1.68115i
$349$	−2.40200e6	−	3.01202e6i	−1.05563	−	1.32371i	−0.943994	−	0.329964i	$-0.892964\pi$
$349$	−2.40200e6	−	3.01202e6i	−1.05563	−	1.32371i	−0.111632	−	0.993750i	$-0.535608\pi$
$350$	−107839.	+	1.01288e6i	−0.0470550	+	0.441963i
$351$	935325.	−	1.17286e6i	0.405224	−	0.508134i
$352$	386369.	+	1.69279e6i	0.166205	+	0.728194i
$353$	81775.4	+	102543.i	0.0349290	+	0.0437996i	0.798989	−	0.601345i	$-0.205368\pi$
$353$	81775.4	+	102543.i	0.0349290	+	0.0437996i	−0.764060	+	0.645145i	$0.776797\pi$
$354$	341323.	−	1.49543e6i	0.144763	−	0.634248i
$355$	−4.61950e6	+	2.22463e6i	−1.94547	+	0.936888i
$356$	−552750.	+	2.42176e6i	−0.231155	+	1.01276i
$357$	41805.6	+	14341.3i	0.0173606	+	0.00595550i
$358$	25887.7	+	113422.i	0.0106755	+	0.0467722i
$359$	−1.32872e6	−	1.66616e6i	−0.544122	−	0.682307i	0.431412	−	0.902155i	$-0.358015\pi$
$359$	−1.32872e6	−	1.66616e6i	−0.544122	−	0.682307i	−0.975534	+	0.219847i	$0.929444\pi$
$360$	5.19138e6	−	2.50003e6i	2.11118	−	1.01669i
$361$	−2.21213e6			−0.893391
$362$	628116.			0.251924
$363$	−31725.3	+	15278.1i	−0.0126369	+	0.00608559i
$364$	−325203.	−	321240.i	−0.128648	−	0.127080i
$365$	−69664.9	−	33548.8i	−0.0273704	−	0.0131809i
$366$	−2.13760e6	−	1.02942e6i	−0.834112	−	0.401687i
$367$	427396.	+	1.87254e6i	0.165640	+	0.725716i	0.987706	+	0.156324i	$0.0499643\pi$
$367$	427396.	+	1.87254e6i	0.165640	+	0.725716i	−0.822066	+	0.569392i	$0.807179\pi$
$368$	−427511.	−	1.87305e6i	−0.164561	−	0.720990i
$369$	6.41558e6	+	3.08958e6i	2.45285	+	1.18123i
$370$	−235424.	−	113374.i	−0.0894020	−	0.0430537i
$371$	1.36220e6	−	2.19773e6i	0.513814	−	0.828970i
$372$	584154.	−	281314.i	0.218862	−	0.105398i
$373$	4.20329e6			1.56429			0.782145	−	0.623097i	$-0.214126\pi$
$373$	4.20329e6			1.56429			0.782145	+	0.623097i	$0.214126\pi$
$374$	7129.56			0.00263563
$375$	−4.56920e6	+	2.20041e6i	−1.67788	+	0.808026i
$376$	623685.	+	782076.i	0.227507	+	0.285285i
$377$	145408.	+	637072.i	0.0526906	+	0.230853i
$378$	−1.82191e6	−	1.79970e6i	−0.655838	−	0.647845i
$379$	−157707.	+	690958.i	−0.0563965	+	0.247089i	−0.995267	−	0.0971825i	$-0.969017\pi$
$379$	−157707.	+	690958.i	−0.0563965	+	0.247089i	0.938870	+	0.344272i	$0.111874\pi$
$380$	1.23181e6	−	593207.i	0.437606	−	0.210740i
$381$	−1.12594e6	+	4.93308e6i	−0.397379	+	1.74103i
$382$	65393.3	+	82000.6i	0.0229285	+	0.0287514i
$383$	−457862.	−	2.00603e6i	−0.159492	−	0.698779i	−0.989917	−	0.141649i	$-0.954760\pi$
$383$	−457862.	−	2.00603e6i	−0.159492	−	0.698779i	0.830425	−	0.557130i	$-0.188097\pi$
$384$	−3.15120e6	+	3.95148e6i	−1.09056	+	1.36751i
$385$	−3.94026e6	+	2.50966e6i	−1.35479	+	0.862904i
$386$	783745.	+	982785.i	0.267736	+	0.335730i
$387$	1.44710e6	−	1.81461e6i	0.491158	−	0.615893i
$388$	814822.	+	392398.i	0.274779	+	0.132327i
$389$	−1.60866e6	+	2.01719e6i	−0.539001	+	0.675886i	−0.974522	−	0.224292i	$-0.927993\pi$
$389$	−1.60866e6	+	2.01719e6i	−0.539001	+	0.675886i	0.435520	+	0.900179i	$0.356564\pi$
$390$	−113205.	+	495986.i	−0.0376882	+	0.165123i
$391$	−27481.2			−0.00909064
$392$	−1.25875e6	+	1.02932e6i	−0.413738	+	0.338327i
$393$	−3.89031e6			−1.27058
$394$	205800.	−	901668.i	0.0667890	−	0.292622i
$395$	193887.	−	243126.i	0.0625252	−	0.0784041i
$396$	7.02979e6	+	3.38537e6i	2.25271	+	1.08485i
$397$	−915158.	+	1.14757e6i	−0.291420	+	0.365430i	−0.905892	−	0.423510i	$-0.860798\pi$
$397$	−915158.	+	1.14757e6i	−0.291420	+	0.365430i	0.614471	+	0.788939i	$0.289369\pi$
$398$	−1.04918e6	−	1.31563e6i	−0.332004	−	0.416319i
$399$	−1.42465e6	−	1.40729e6i	−0.447997	−	0.442537i
$400$	2.46977e6	−	3.09700e6i	0.771804	−	0.967812i
$401$	−1.15889e6	−	5.07742e6i	−0.359899	−	1.57682i	−0.753441	−	0.657515i	$-0.771608\pi$
$401$	−1.15889e6	−	5.07742e6i	−0.359899	−	1.57682i	0.393542	−	0.919307i	$-0.371250\pi$
$402$	−480786.	−	602887.i	−0.148384	−	0.186068i
$403$	−19407.2	+	85028.5i	−0.00595251	+	0.0260797i
$404$	−2.15359e6	+	1.03711e6i	−0.656461	+	0.316135i
$405$	4.35364e6	−	1.90745e7i	1.31891	−	5.77851i
$406$	1.10772e6	−	131693.i	0.333515	−	0.0396503i
$407$	−164065.	−	718814.i	−0.0490941	−	0.215095i
$408$	20564.4	+	25786.9i	0.00611596	+	0.00766917i
$409$	1.00588e6	−	484405.i	0.297329	−	0.143186i	−0.279272	−	0.960212i	$-0.590093\pi$
$409$	1.00588e6	−	484405.i	0.297329	−	0.143186i	0.576601	+	0.817026i	$0.304379\pi$
$410$	−1.52690e6			−0.448592
$411$	181538.			0.0530106
$412$	3.76955e6	−	1.81532e6i	1.09407	−	0.526879i
$413$	−3.54795e6	+	2.25979e6i	−1.02354	+	0.651917i
$414$	2.26896e6	+	1.09267e6i	0.650617	+	0.313321i
$415$	5.73096e6	+	2.75988e6i	1.63345	+	0.786630i
$416$	−115387.	−	505544.i	−0.0326907	−	0.143227i
$417$	−329696.	−	1.44449e6i	−0.0928482	−	0.406795i
$418$	−291042.	−	140158.i	−0.0814732	−	0.0392354i
$419$	3.25126e6	+	1.56572e6i	0.904725	+	0.435692i	0.827593	−	0.561329i	$-0.189710\pi$
$419$	3.25126e6	+	1.56572e6i	0.904725	+	0.435692i	0.0771315	+	0.997021i	$0.475424\pi$
$420$	−9.81044e6	−	3.36545e6i	−2.71372	−	0.930937i
$421$	−3.62987e6	+	1.74805e6i	−0.998127	+	0.480673i	−0.860302	−	0.509784i	$-0.829725\pi$
$421$	−3.62987e6	+	1.74805e6i	−0.998127	+	0.480673i	−0.137825	+	0.990457i	$0.544011\pi$
$422$	1.61864e6			0.442455
$423$	6.83294e6			1.85676
$424$	1.73849e6	−	837213.i	0.469632	−	0.226163i
$425$	−35327.8	−	44299.7i	−0.00948734	−	0.0118967i
$426$	598480.	+	2.62211e6i	0.159781	+	0.700047i
$427$	2.18655e6	+	6.12803e6i	0.580350	+	1.62649i
$428$	−201664.	+	883548.i	−0.0532132	+	0.233142i
$429$	−1.29333e6	+	622835.i	−0.339286	+	0.163391i
$430$	−110745.	+	485206.i	−0.0288838	+	0.126548i
$431$	−1.16193e6	−	1.45702e6i	−0.301292	−	0.377809i	0.608021	−	0.793921i	$-0.291964\pi$
$431$	−1.16193e6	−	1.45702e6i	−0.301292	−	0.377809i	−0.909313	+	0.416112i	$0.863392\pi$
$432$	2.21610e6	+	9.70938e6i	0.571322	+	2.50312i
$433$	1.73531e6	−	2.17601e6i	0.444793	−	0.557752i	−0.508007	−	0.861353i	$-0.669617\pi$
$433$	1.73531e6	−	2.17601e6i	0.444793	−	0.557752i	0.952799	+	0.303601i	$0.0981889\pi$
$434$	140830.	+	48311.4i	0.0358897	+	0.0123119i
$435$	9.24420e6	+	1.15919e7i	2.34232	+	2.93718i
$436$	−988796.	+	1.23991e6i	−0.249110	+	0.312374i
$437$	1.12183e6	+	540247.i	0.281012	+	0.135328i
$438$	−25288.7	+	31711.1i	−0.00629857	+	0.00789815i
$439$	71191.9	−	311912.i	0.0176307	−	0.0772451i	−0.965347	−	0.260969i	$-0.915958\pi$
$439$	71191.9	−	311912.i	0.0176307	−	0.0772451i	0.982978	+	0.183724i	$0.0588152\pi$
$440$	−3.48626e6			−0.858476
$441$	136193.	+	1.11062e7i	0.0333471	+	2.71938i
$442$	−2129.21			−0.000518397
$443$	−371889.	+	1.62935e6i	−0.0900334	+	0.394462i	−0.999786	−	0.0206887i	$-0.993414\pi$
$443$	−371889.	+	1.62935e6i	−0.0900334	+	0.394462i	0.909753	+	0.415151i	$0.136271\pi$
$444$	1.02060e6	−	1.27979e6i	0.245695	−	0.308092i
$445$	−6.83072e6	−	3.28950e6i	−1.63518	−	0.787463i
$446$	1.15834e6	−	1.45251e6i	0.275739	−	0.345766i
$447$	−3.67944e6	−	4.61388e6i	−0.870991	−	1.09219i
$448$	2.38674e6	−	283751.i	0.561838	−	0.0667948i
$449$	−276719.	+	346995.i	−0.0647774	+	0.0812283i	−0.813165	−	0.582034i	$-0.802257\pi$
$449$	−276719.	+	346995.i	−0.0647774	+	0.0812283i	0.748387	+	0.663262i	$0.230829\pi$
$450$	1.15542e6	+	5.06221e6i	0.268972	+	1.17844i
$451$	−2.68623e6	−	3.36842e6i	−0.621873	−	0.779804i
$452$	−925920.	+	4.05672e6i	−0.213171	+	0.933961i
$453$	1.37032e7	−	6.59909e6i	3.13744	−	1.51091i
$454$	−177233.	+	776510.i	−0.0403558	+	0.176810i
$455$	1.17674e6	−	749496.i	0.266472	−	0.169723i
$456$	−332537.	−	1.45694e6i	−0.0748906	−	0.328117i
$457$	−2.65433e6	−	3.32842e6i	−0.594516	−	0.745500i	0.389996	−	0.920817i	$-0.372476\pi$
$457$	−2.65433e6	−	3.32842e6i	−0.594516	−	0.745500i	−0.984512	+	0.175317i	$0.943905\pi$
$458$	1.25480e6	−	604281.i	0.279519	−	0.134609i
$459$	142455.			0.0315607
$460$	6.44898e6			1.42101
$461$	346322.	−	166780.i	0.0758976	−	0.0365504i	−0.395550	−	0.918444i	$-0.629446\pi$
$461$	346322.	−	166780.i	0.0758976	−	0.0365504i	0.471447	+	0.881894i	$0.343732\pi$
$462$	823526.	+	2.30801e6i	0.179503	+	0.503076i
$463$	−128120.	−	61699.2i	−0.0277756	−	0.0133760i	0.419944	−	0.907550i	$-0.362050\pi$
$463$	−128120.	−	61699.2i	−0.0277756	−	0.0133760i	−0.447720	+	0.894174i	$0.647764\pi$
$464$	−3.90851e6	−	1.88224e6i	−0.842785	−	0.405864i
$465$	440339.	+	1.92925e6i	0.0944397	+	0.413768i
$466$	−75985.1	−	332912.i	−0.0162093	−	0.0710174i
$467$	−5.41353e6	−	2.60702e6i	−1.14865	−	0.553161i	−0.240023	−	0.970767i	$-0.577155\pi$
$467$	−5.41353e6	−	2.60702e6i	−1.14865	−	0.553161i	−0.908628	+	0.417606i	$0.862869\pi$
$468$	−2.09941e6	−	1.01102e6i	−0.443081	−	0.213377i
$469$	−223883.	+	2.10282e6i	−0.0469991	+	0.441437i
$470$	−1.32008e6	+	635719.i	−0.275649	+	0.132746i
$471$	−9.79208e6			−2.03387
$472$	−3.13916e6			−0.648572
$473$	−1.26522e6	+	609299.i	−0.260024	+	0.125221i
$474$	−101705.	−	127534.i	−0.0207920	−	0.0260723i
$475$	571270.	+	2.50290e6i	0.116174	+	0.508990i
$476$	4595.60	−	43164.0i	0.000929661	−	0.00873181i
$477$	2.93295e6	−	1.28501e7i	0.590213	−	2.58589i
$478$	2.16839e6	−	1.04424e6i	0.434079	−	0.209041i
$479$	369228.	−	1.61769e6i	0.0735286	−	0.322150i	−0.924765	−	0.380538i	$-0.875739\pi$
$479$	369228.	−	1.61769e6i	0.0735286	−	0.322150i	0.998294	+	0.0583880i	$0.0185961\pi$
$480$	−7.33567e6	−	9.19864e6i	−1.45324	−	1.82230i
$481$	48997.1	+	214670.i	0.00965623	+	0.0423067i
$482$	254397.	−	319004.i	0.0498764	−	0.0625430i
$483$	−3.17432e6	−	8.89635e6i	−0.619132	−	1.73518i
$484$	21562.6	+	27038.7i	0.00418396	+	0.00524653i
$485$	−1.72100e6	+	2.15807e6i	−0.332221	+	0.416592i
$486$	−4.92185e6	−	2.37024e6i	−0.945231	−	0.455199i
$487$	1.25466e6	−	1.57329e6i	0.239719	−	0.300598i	−0.647389	−	0.762160i	$-0.724139\pi$
$487$	1.25466e6	−	1.57329e6i	0.239719	−	0.300598i	0.887108	+	0.461561i	$0.152711\pi$
$488$	−1.08046e6	+	4.73378e6i	−0.205380	+	0.899827i
$489$	8.28181e6			1.56622
$490$	−1.05961e6	−	2.13299e6i	−0.199368	−	0.401327i
$491$	−222277.			−0.0416094			−0.0208047	−	0.999784i	$-0.506623\pi$
$491$	−222277.			−0.0416094			−0.0208047	+	0.999784i	$0.506623\pi$
$492$	2.12846e6	−	9.32538e6i	0.396417	−	1.73682i
$493$	−38689.3	+	48514.9i	−0.00716925	+	0.00898995i
$494$	86918.2	+	41857.6i	0.0160248	+	0.00771715i
$495$	−1.48478e7	+	1.86185e7i	−2.72363	+	3.41532i
$496$	−361000.	−	452680.i	−0.0658875	−	0.0826203i
$497$	3.88576e6	−	6.26915e6i	0.705643	−	1.13846i
$498$	2.08037e6	−	2.60870e6i	0.375895	−	0.471358i
$499$	44625.5	+	195517.i	0.00802290	+	0.0351506i	0.978781	−	0.204909i	$-0.0656900\pi$
$499$	44625.5	+	195517.i	0.00802290	+	0.0351506i	−0.970758	+	0.240060i	$0.922833\pi$
$500$	3.10553e6	+	3.89421e6i	0.555534	+	0.696617i
$501$	−252853.	+	1.10782e6i	−0.0450063	+	0.197186i
$502$	−1.60569e6	+	773260.i	−0.284382	+	0.136951i
$503$	−1.61030e6	+	7.05517e6i	−0.283783	+	1.24333i	0.609118	+	0.793080i	$0.291524\pi$
$503$	−1.61030e6	+	7.05517e6i	−0.283783	+	1.24333i	−0.892901	+	0.450254i	$0.851333\pi$
$504$	−4.36680e6	+	7.04524e6i	−0.765750	+	1.23543i
$505$	−1.62339e6	−	7.11253e6i	−0.283266	−	1.24107i
$506$	−950021.	−	1.19129e6i	−0.164952	−	0.206843i
$507$	−9.67095e6	+	4.65729e6i	−1.67090	+	0.804661i
$508$	4.96961e6			0.854403
$509$	−286868.			−0.0490781			−0.0245390	−	0.999699i	$-0.507812\pi$
$509$	−286868.			−0.0490781			−0.0245390	+	0.999699i	$0.507812\pi$
$510$	−43526.3	+	20961.2i	−0.00741014	+	0.00356854i
$511$	110453.	−	13131.3i	0.0187122	−	0.00222462i
$512$	5.31281e6	+	2.55851e6i	0.895673	+	0.431333i
$513$	−5.81529e6	−	2.80050e6i	−0.975614	−	0.469831i
$514$	366975.	+	1.60782e6i	0.0612673	+	0.268430i
$515$	2.84152e6	+	1.24495e7i	0.472098	+	2.06840i
$516$	−2.80897e6	−	1.35273e6i	−0.464433	−	0.223659i
$517$	−3.72481e6	−	1.79378e6i	−0.612884	−	0.295149i
$518$	373262.	−	44375.7i	0.0611208	−	0.00726642i
$519$	1.81387e7	−	8.73513e6i	2.95588	−	1.42348i
$520$	1.04115e6			0.168852
$521$	1.21143e7			1.95526			0.977629	−	0.210336i	$-0.0674558\pi$
$521$	1.21143e7			1.95526			0.977629	+	0.210336i	$0.0674558\pi$
$522$	5.12332e6	−	2.46726e6i	0.822954	−	0.396314i
$523$	550184.	+	689909.i	0.0879536	+	0.110290i	0.823861	−	0.566792i	$-0.191816\pi$
$523$	550184.	+	689909.i	0.0879536	+	0.110290i	−0.735907	+	0.677082i	$0.763244\pi$
$524$	850220.	+	3.72506e6i	0.135271	+	0.592659i
$525$	1.02602e7	−	1.65535e7i	1.62465	−	2.62114i
$526$	−354280.	+	1.55220e6i	−0.0558318	+	0.244615i
$527$	−7461.87	+	3593.45i	−0.00117036	+	0.000563618i
$528$	2.12059e6	−	9.29090e6i	0.331033	−	1.45035i
$529$	−351093.	−	440257.i	−0.0545486	−	0.0684018i
$530$	628912.	+	2.75544e6i	0.0972523	+	0.426090i
$531$	−1.33695e7	+	1.67648e7i	−2.05768	+	2.58025i
$532$	−1.03615e6	+	1.67169e6i	−0.158725	+	0.256081i
$533$	802229.	+	1.00596e6i	0.122315	+	0.153378i
$534$	−2.47959e6	+	3.10930e6i	−0.376293	+	0.471857i
$535$	−2.49211e6	−	1.20013e6i	−0.376428	−	0.181278i
$536$	−983945.	+	1.23383e6i	−0.147931	+	0.185499i
$537$	494967.	−	2.16859e6i	0.0740696	−	0.324520i
$538$	−1.15975e6			−0.172746
$539$	2.84136e6	−	6.09006e6i	0.421263	−	0.902920i
$540$	−3.34298e7			−4.93343
$541$	−2.67484e6	+	1.17192e7i	−0.392921	+	1.72150i	0.261356	+	0.965242i	$0.415830\pi$
$541$	−2.67484e6	+	1.17192e7i	−0.392921	+	1.72150i	−0.654277	+	0.756255i	$0.727027\pi$
$542$	890332.	−	1.11644e6i	0.130183	−	0.163244i
$543$	−1.08201e7	−	5.21070e6i	−1.57483	−	0.758396i
$544$	30701.6	−	38498.6i	0.00444799	−	0.00557761i
$545$	−3.01791e6	−	3.78433e6i	−0.435226	−	0.545756i
$546$	−245942.	−	689277.i	−0.0353062	−	0.0989491i
$547$	4.15120e6	−	5.20544e6i	0.593205	−	0.743856i	−0.391097	−	0.920350i	$-0.627904\pi$
$547$	4.15120e6	−	5.20544e6i	0.593205	−	0.743856i	0.984302	+	0.176494i	$0.0564756\pi$
$548$	−39674.8	−	173827.i	−0.00564369	−	0.0247266i
$549$	2.06794e7	+	2.59311e7i	2.92824	+	3.67189i
$550$	699079.	−	3.06286e6i	0.0985415	−	0.431739i
$551$	2.53311e6	−	1.21988e6i	0.355447	−	0.171174i
$552$	1.56855e6	−	6.87226e6i	0.219104	−	0.959957i
$553$	−47359.9	+	444826.i	−0.00658563	+	0.0618554i
$554$	−495019.	−	2.16882e6i	−0.0685248	−	0.300227i
$555$	3.11496e6	+	3.90604e6i	0.429260	+	0.538275i
$556$	−1.31108e6	+	631382.i	−0.179863	+	0.0866174i
$557$	1.34399e7			1.83551			0.917756	−	0.397145i	$-0.129999\pi$
$557$	1.34399e7			1.83551			0.917756	+	0.397145i	$0.129999\pi$
$558$	758959.			0.103189
$559$	377852.	−	181964.i	0.0511437	−	0.0246295i
$560$	−980575.	+	9.21003e6i	−0.132133	+	1.24105i
$561$	−122816.	−	59145.0i	−0.0164758	−	0.00793435i
$562$	−1.30496e6	−	628436.i	−0.174284	−	0.0839306i
$563$	−3.15621e6	−	1.38282e7i	−0.419657	−	1.83864i	−0.534385	−	0.845241i	$-0.679457\pi$
$563$	−3.15621e6	−	1.38282e7i	−0.419657	−	1.83864i	0.114728	−	0.993397i	$-0.463400\pi$
$564$	−2.04242e6	−	8.94845e6i	−0.270364	−	1.18454i
$565$	−1.14422e7	−	5.51029e6i	−1.50796	−	0.726196i
$566$	−650983.	−	313497.i	−0.0854139	−	0.0411331i
$567$	9.45839e6	+	2.65081e7i	1.23555	+	3.46274i
$568$	4.95915e6	−	2.38820e6i	0.644965	−	0.310599i
$569$	−4.60425e6			−0.596182			−0.298091	−	0.954538i	$-0.596350\pi$
$569$	−4.60425e6			−0.596182			−0.298091	+	0.954538i	$0.596350\pi$
$570$	2.18890e6			0.282188
$571$	8.51060e6	−	4.09849e6i	1.09237	−	0.526058i	0.201119	−	0.979567i	$-0.435542\pi$
$571$	8.51060e6	−	4.09849e6i	1.09237	−	0.526058i	0.891252	+	0.453509i	$0.149828\pi$
$572$	879032.	+	1.10227e6i	0.112335	+	0.140863i
$573$	−446228.	−	1.95505e6i	−0.0567767	−	0.248755i
$574$	1.85263e6	−	1.17999e6i	0.234697	−	0.149485i
$575$	−2.69463e6	+	1.18060e7i	−0.339883	+	1.48913i
$576$	1.10389e7	−	5.31608e6i	1.38635	−	0.667629i
$577$	1.60258e6	−	7.02137e6i	0.200392	−	0.877976i	−0.770306	−	0.637674i	$-0.779897\pi$
$577$	1.60258e6	−	7.02137e6i	0.200392	−	0.877976i	0.970698	−	0.240301i	$-0.0772462\pi$
$578$	1.39188e6	+	1.74537e6i	0.173294	+	0.217304i
$579$	−5.34809e6	−	2.34315e7i	−0.662983	−	2.90472i
$580$	9.07916e6	−	1.13849e7i	1.12066	−	1.40527i
$581$	−9.08635e6	+	1.08024e6i	−1.11673	+	0.132764i
$582$	902765.	+	1.13203e6i	0.110476	+	0.138532i
$583$	−4.97223e6	+	6.23497e6i	−0.605870	+	0.759737i
$584$	74787.0	+	36015.5i	0.00907390	+	0.00436976i
$585$	4.43421e6	−	5.56032e6i	0.535706	−	0.671754i
$586$	149950.	−	656974.i	0.0180386	−	0.0790322i
$587$	766664.			0.0918353			0.0459176	−	0.998945i	$-0.485379\pi$
$587$	766664.			0.0918353			0.0459176	+	0.998945i	$0.485379\pi$
$588$	1.45041e7	−	3.49811e6i	1.73000	−	0.417244i
$589$	375250.			0.0445690
$590$	1.02315e6	−	4.48272e6i	0.121007	−	0.530166i
$591$	−1.10252e7	+	1.38251e7i	−1.29843	+	1.62817i
$592$	−1.31703e6	−	634248.i	−0.154451	−	0.0743797i
$593$	−1.03710e6	+	1.30049e6i	−0.121112	+	0.151869i	−0.838691	−	0.544608i	$-0.816679\pi$
$593$	−1.03710e6	+	1.30049e6i	−0.121112	+	0.151869i	0.717579	+	0.696477i	$0.245250\pi$
$594$	4.92466e6	+	6.17532e6i	0.572677	+	0.718114i
$595$	125317.	+	42989.7i	0.0145116	+	0.00497819i
$596$	−3.61375e6	+	4.53150e6i	−0.416718	+	0.522548i
$597$	7.15936e6	+	3.13672e7i	0.822126	+	3.60197i
$598$	283719.	+	355772.i	0.0324441	+	0.0406836i
$599$	−302123.	+	1.32369e6i	−0.0344046	+	0.150737i	−0.989213	−	0.146487i	$-0.953203\pi$
$599$	−302123.	+	1.32369e6i	−0.0344046	+	0.150737i	0.954808	+	0.297223i	$0.0960606\pi$
$600$	1.30945e7	−	6.30597e6i	1.48494	−	0.715111i
$601$	−867225.	+	3.79956e6i	−0.0979368	+	0.429089i	−0.999997	−	0.00252156i	$-0.999197\pi$
$601$	−867225.	+	3.79956e6i	−0.0979368	+	0.429089i	0.902060	+	0.431611i	$0.142055\pi$
$602$	−240597.	−	674297.i	−0.0270582	−	0.0758333i
$603$	2.39874e6	+	1.05096e7i	0.268652	+	1.17704i
$604$	−9.31357e6	−	1.16788e7i	−1.03878	−	1.30259i
$605$	−95100.1	+	45797.8i	−0.0105631	+	0.00508693i
$606$	−3.82688e6			−0.423315
$607$	1.38193e7			1.52234			0.761172	−	0.648550i	$-0.224624\pi$
$607$	1.38193e7			1.52234			0.761172	+	0.648550i	$0.224624\pi$
$608$	−2.01013e6	+	968029.i	−0.220529	+	0.106201i
$609$	−2.01744e7	−	6.92079e6i	−2.20423	−	0.756157i
$610$	−6.40770e6	−	3.08578e6i	−0.697232	−	0.335769i
$611$	1.11240e6	+	535702.i	0.120547	+	0.0580524i
$612$	−49238.5	−	215728.i	−0.00531405	−	0.0232824i
$613$	−397713.	−	1.74249e6i	−0.0427483	−	0.187292i	0.949046	−	0.315138i	$-0.102051\pi$
$613$	−397713.	−	1.74249e6i	−0.0427483	−	0.187292i	−0.991794	+	0.127846i	$0.959194\pi$
$614$	3.45547e6	+	1.66407e6i	0.369902	+	0.178135i
$615$	2.63028e7	+	1.26668e7i	2.80424	+	1.35045i
$616$	4.22997e6	−	2.69418e6i	0.449144	−	0.286071i
$617$	−1.13328e7	+	5.45761e6i	−1.19847	+	0.577151i	−0.923238	−	0.384227i	$-0.874468\pi$
$617$	−1.13328e7	+	5.45761e6i	−1.19847	+	0.577151i	−0.275229	+	0.961379i	$0.588754\pi$
$618$	6.69842e6			0.705507
$619$	441351.			0.0462975			0.0231487	−	0.999732i	$-0.492631\pi$
$619$	441351.			0.0462975			0.0231487	+	0.999732i	$0.492631\pi$
$620$	1.75106e6	−	843268.i	0.182946	−	0.0881021i
$621$	−1.89823e7	−	2.38031e7i	−1.97524	−	2.47687i
$622$	−578072.	−	2.53270e6i	−0.0599109	−	0.262487i
$623$	1.08300e7	−	1.28754e6i	1.11791	−	0.132905i
$624$	−633303.	+	2.77468e6i	−0.0651103	+	0.285267i
$625$	371899.	−	179097.i	0.0380824	−	0.0183395i
$626$	−735102.	+	3.22069e6i	−0.0749742	+	0.328483i
$627$	3.85085e6	+	4.82882e6i	0.391190	+	0.490537i
$628$	2.14004e6	+	9.37613e6i	0.216532	+	0.948690i
$629$	−13036.9	+	16347.8i	−0.00131386	+	0.00164752i
$630$	−8.63734e6	−	8.53207e6i	−0.867019	−	0.856452i
$631$	1.15398e7	+	1.44704e7i	1.15378	+	1.44680i	0.873462	+	0.486892i	$0.161869\pi$
$631$	1.15398e7	+	1.44704e7i	1.15378	+	1.44680i	0.280321	+	0.959906i	$0.409559\pi$
$632$	−208142.	+	261002.i	−0.0207285	+	0.0259927i
$633$	−2.78832e7	−	1.34278e7i	−2.76588	−	1.33198i
$634$	−679326.	+	851848.i	−0.0671205	+	0.0841664i
$635$	−3.37514e6	+	1.47875e7i	−0.332168	+	1.45532i
$636$	−1.77052e7			−1.73564
$637$	−848557.	+	1.81876e6i	−0.0828576	+	0.177594i
$638$	−3.44056e6			−0.334640
$639$	8.36643e6	−	3.66557e7i	0.810565	−	3.55132i
$640$	−9.44606e6	+	1.18450e7i	−0.911592	+	1.14310i
$641$	1.38882e7	+	6.68821e6i	1.33506	+	0.642931i	0.958932	−	0.283636i	$-0.0915407\pi$
$641$	1.38882e7	+	6.68821e6i	1.33506	+	0.642931i	0.376129	+	0.926567i	$0.377255\pi$
$642$	−904648.	+	1.13439e6i	−0.0866247	+	0.108624i
$643$	2.52070e6	+	3.16086e6i	0.240433	+	0.301493i	0.887377	−	0.461044i	$-0.152525\pi$
$643$	2.52070e6	+	3.16086e6i	0.240433	+	0.301493i	−0.646944	+	0.762537i	$0.723953\pi$
$644$	−7.82470e6	+	4.98376e6i	−0.743452	+	0.473525i
$645$	5.93288e6	−	7.43960e6i	0.561521	−	0.704125i
$646$	2038.53	+	8931.39i	0.000192192	+	0.000842050i
$647$	3.79281e6	+	4.75603e6i	0.356205	+	0.446667i	0.927357	−	0.374177i	$-0.122075\pi$
$647$	3.79281e6	+	4.75603e6i	0.356205	+	0.446667i	−0.571152	+	0.820844i	$0.693503\pi$
$648$	−4.67374e6	+	2.04770e7i	−0.437247	+	1.91570i
$649$	1.16891e7	−	5.62918e6i	1.08936	−	0.524607i
$650$	−208776.	+	914709.i	−0.0193820	+	0.0849180i
$651$	−2.02520e6	−	2.00051e6i	−0.187290	−	0.185007i
$652$	−1.80997e6	−	7.93001e6i	−0.166745	−	0.730558i
$653$	−5.37401e6	−	6.73880e6i	−0.493192	−	0.618443i	0.471487	−	0.881873i	$-0.343718\pi$
$653$	−5.37401e6	−	6.73880e6i	−0.493192	−	0.618443i	−0.964678	+	0.263430i	$0.915146\pi$
$654$	−2.28760e6	+	1.10165e6i	−0.209139	+	0.100716i
$655$	−1.16616e7			−1.06208
$656$	−8.54191e6			−0.774988
$657$	510855.	−	246015.i	0.0461726	−	0.0222356i
$658$	1.11041e6	−	1.79149e6i	0.0999811	−	0.161306i
$659$	−1.00962e7	−	4.86206e6i	−0.905614	−	0.436121i	−0.0777010	−	0.996977i	$-0.524758\pi$
$659$	−1.00962e7	−	4.86206e6i	−0.905614	−	0.436121i	−0.827914	+	0.560856i	$0.810472\pi$
$660$	2.88210e7	+	1.38795e7i	2.57543	+	1.24026i
$661$	1.99769e6	+	8.75244e6i	0.177838	+	0.779158i	0.982626	+	0.185596i	$0.0594216\pi$
$661$	1.99769e6	+	8.75244e6i	0.177838	+	0.779158i	−0.804788	+	0.593562i	$0.797721\pi$
$662$	−651418.	−	2.85405e6i	−0.0577717	−	0.253114i
$663$	36678.4	+	17663.4i	0.00324061	+	0.00156059i
$664$	−6.15233e6	−	2.96281e6i	−0.541526	−	0.260785i
$665$	−4.27054e6	−	4.21849e6i	−0.374480	−	0.369916i
$666$	1.72638e6	−	831379.i	0.150817	−	0.0726295i
$667$	1.32618e7			1.15422
$668$	1.11602e6			0.0967681
$669$	−3.20035e7	+	1.54121e7i	−2.76460	+	1.33136i
$670$	−1.44121e6	−	1.80722e6i	−0.124034	−	0.155533i
$671$	−4.46546e6	−	1.95644e7i	−0.382877	−	1.67749i
$672$	1.60092e7	+	5.49194e6i	1.36756	+	0.469140i
$673$	−638367.	+	2.79687e6i	−0.0543292	+	0.238032i	−0.994801	−	0.101841i	$-0.967527\pi$
$673$	−638367.	+	2.79687e6i	−0.0543292	+	0.238032i	0.940472	+	0.339872i	$0.110384\pi$
$674$	−3.49113e6	+	1.68124e6i	−0.296017	+	0.142554i
$675$	1.39683e7	−	6.11989e7i	1.18000	−	5.16993i
$676$	6.57302e6	+	8.24231e6i	0.553220	+	0.693716i
$677$	−299647.	−	1.31284e6i	−0.0251269	−	0.110088i	0.960809	−	0.277210i	$-0.0894098\pi$
$677$	−299647.	−	1.31284e6i	−0.0251269	−	0.110088i	−0.985936	+	0.167122i	$0.946553\pi$
$678$	−4.15360e6	+	5.20844e6i	−0.347016	+	0.435145i
$679$	420382.	−	3.94842e6i	0.0349921	−	0.328662i
$680$	61643.9	+	77299.0i	0.00511232	+	0.00641064i
$681$	9.49480e6	−	1.19061e7i	0.784545	−	0.983789i
$682$	−413728.	−	199241.i	−0.0340608	−	0.0164028i
$683$	−1.06212e7	+	1.33186e7i	−0.871209	+	1.09246i	0.123764	+	0.992312i	$0.460504\pi$
$683$	−1.06212e7	+	1.33186e7i	−0.871209	+	1.09246i	−0.994972	+	0.100150i	$0.968068\pi$
$684$	−2.23094e6	+	9.77438e6i	−0.182325	+	0.798820i
$685$	544180.			0.0443115
$686$	2.93402e6	+	1.76915e6i	0.238042	+	0.143534i
$687$	−2.66286e7			−2.15256
$688$	−619539.	+	2.71438e6i	−0.0498997	+	0.218625i
$689$	1.48493e6	−	1.86204e6i	0.119168	−	0.149431i
$690$	9.30236e6	+	4.47978e6i	0.743824	+	0.358207i
$691$	7.78918e6	−	9.76733e6i	0.620579	−	0.778181i	−0.367847	−	0.929886i	$-0.619905\pi$
$691$	7.78918e6	−	9.76733e6i	0.620579	−	0.778181i	0.988426	+	0.151705i	$0.0484765\pi$
$692$	−1.23282e7	−	1.54591e7i	−0.978669	−	1.22721i
$693$	3.62680e6	−	3.40646e7i	0.286874	−	2.69445i
$694$	−357727.	+	448576.i	−0.0281938	+	0.0353539i
$695$	−988300.	−	4.33002e6i	−0.0776116	−	0.340039i
$696$	−9.92388e6	−	1.24442e7i	−0.776531	−	0.973738i
$697$	−27188.5	+	119121.i	−0.00211984	+	0.00928763i
$698$	−5.45786e6	+	2.62837e6i	−0.424018	+	0.204196i
$699$	−1.45281e6	+	6.36520e6i	−0.112465	+	0.492741i
$700$	−1.80927e7	−	6.20665e6i	−1.39559	−	0.478754i
$701$	−1.64221e6	−	7.19500e6i	−0.126222	−	0.553014i	−0.998006	−	0.0631232i	$-0.979894\pi$
$701$	−1.64221e6	−	7.19500e6i	−0.126222	−	0.553014i	0.871784	−	0.489891i	$-0.162963\pi$
$702$	−1.47072e6	−	1.84423e6i	−0.112639	−	0.141245i
$703$	853567.	−	411056.i	0.0651403	−	0.0313699i
$704$	−7.41319e6			−0.563733
$705$	2.80139e7			2.12276
$706$	185811.	−	89481.9i	0.0140301	−	0.00675653i
$707$	7.46625e6	+	7.37525e6i	0.561764	+	0.554917i
$708$	2.59515e7	+	1.24976e7i	1.94571	+	0.937007i
$709$	−1.97661e6	−	951883.i	−0.147674	−	0.0711161i	0.358587	−	0.933496i	$-0.383259\pi$
$709$	−1.97661e6	−	951883.i	−0.147674	−	0.0711161i	−0.506261	+	0.862380i	$0.668973\pi$
$710$	1.79401e6	+	7.86007e6i	0.133561	+	0.585168i
$711$	507426.	+	2.22318e6i	0.0376443	+	0.164930i
$712$	7.33295e6	+	3.53136e6i	0.542099	+	0.261061i
$713$	1.59474e6	+	767984.i	0.117480	+	0.0565755i
$714$	36612.8	−	59069.8i	0.00268774	−	0.00433631i
$715$	−3.87690e6	+	1.86701e6i	−0.283608	+	0.136579i
$716$	−2.18465e6			−0.159257
$717$	−4.60162e7			−3.34282
$718$	−3.01913e6	+	1.45393e6i	−0.218560	+	0.105253i
$719$	−1.00507e7	−	1.26032e7i	−0.725060	−	0.909196i	0.273553	−	0.961857i	$-0.411801\pi$
$719$	−1.00507e7	−	1.26032e7i	−0.725060	−	0.909196i	−0.998612	+	0.0526610i	$0.983230\pi$
$720$	1.05062e7	+	4.60305e7i	0.755288	+	3.30913i
$721$	−1.30686e7	−	1.29094e7i	−0.936250	−	0.924840i
$722$	−774014.	+	3.39118e6i	−0.0552594	+	0.242107i
$723$	−7.02870e6	+	3.38485e6i	−0.500069	+	0.240820i
$724$	−2.62464e6	+	1.14993e7i	−0.186090	+	0.815313i
$725$	1.70484e7	+	2.13780e7i	1.20459	+	1.51050i
$726$	12320.7	+	53980.5i	0.000867549	+	0.00380098i
$727$	352724.	−	442302.i	0.0247513	−	0.0310372i	−0.769302	−	0.638886i	$-0.779396\pi$
$727$	352724.	−	442302.i	0.0247513	−	0.0310372i	0.794053	+	0.607848i	$0.207967\pi$
$728$	−1.26326e6	+	804603.i	−0.0883413	+	0.0562669i
$729$	3.22303e7	+	4.04155e7i	2.24619	+	2.81663i
$730$	−75805.7	+	95057.4i	−0.00526496	+	0.00660205i
$731$	35881.2	+	17279.5i	0.00248356	+	0.00119602i
$732$	2.77782e7	−	3.48328e7i	1.91614	−	2.40276i
$733$	−1.64217e6	+	7.19484e6i	−0.112891	+	0.494608i	0.886595	+	0.462547i	$0.153064\pi$
$733$	−1.64217e6	+	7.19484e6i	−0.112891	+	0.494608i	−0.999486	+	0.0320611i	$0.989793\pi$
$734$	3.02014e6			0.206913
$735$	558368.	+	4.55338e7i	0.0381243	+	3.10896i
$736$	−1.05238e7			−0.716108
$737$	1.45135e6	−	6.35877e6i	0.0984244	−	0.431225i
$738$	6.98110e6	−	8.75403e6i	0.471827	−	0.591653i
$739$	−1.71752e7	−	8.27113e6i	−1.15689	−	0.557127i	−0.245790	−	0.969323i	$-0.579047\pi$
$739$	−1.71752e7	−	8.27113e6i	−1.15689	−	0.557127i	−0.911095	+	0.412196i	$0.864762\pi$
$740$	3.05935e6	−	3.83630e6i	0.205376	−	0.257533i
$741$	−1.15004e6	−	1.44210e6i	−0.0769426	−	0.0964830i
$742$	−2.89248e6	−	2.85722e6i	−0.192868	−	0.190517i
$743$	964578.	−	1.20954e6i	0.0641011	−	0.0803802i	−0.748747	−	0.662856i	$-0.769344\pi$
$743$	964578.	−	1.20954e6i	0.0641011	−	0.0803802i	0.812848	+	0.582475i	$0.197916\pi$
$744$	−472715.	−	2.07110e6i	−0.0313088	−	0.137173i
$745$	−1.10295e7	−	1.38306e7i	−0.728059	−	0.912957i
$746$	1.47071e6	−	6.44362e6i	0.0967568	−	0.423919i
$747$	−4.20253e7	+	2.02383e7i	−2.75556	+	1.32701i
$748$	−29791.5	+	130525.i	−0.00194687	+	0.00852981i
$749$	3.95120e6	−	469743.i	0.257350	−	0.0305954i
$750$	1.77447e6	+	7.77447e6i	0.115190	+	0.504682i
$751$	1.32969e7	+	1.66738e7i	0.860301	+	1.07878i	0.996116	+	0.0880487i	$0.0280631\pi$
$751$	1.32969e7	+	1.66738e7i	0.860301	+	1.07878i	−0.135816	+	0.990734i	$0.543365\pi$
$752$	−7.38492e6	+	3.55639e6i	−0.476213	+	0.229332i
$753$	3.40749e7			2.19001
$754$	1.02751e6			0.0658197
$755$	4.10767e7	−	1.97815e7i	2.62258	−	1.26297i
$756$	4.05612e7	−	2.58345e7i	2.58111	−	1.64398i
$757$	−6.80028e6	−	3.27484e6i	−0.431308	−	0.207707i	0.205618	−	0.978632i	$-0.434080\pi$
$757$	−6.80028e6	−	3.27484e6i	−0.431308	−	0.207707i	−0.636925	+	0.770926i	$0.719794\pi$
$758$	1.00405e6	+	483527.i	0.0634723	+	0.0305667i
$759$	6.48271e6	+	2.84026e7i	0.408463	+	1.78959i
$760$	−996815.	−	4.36733e6i	−0.0626009	−	0.274272i
$761$	1.83035e7	+	8.81450e6i	1.14570	+	0.551742i	0.907740	−	0.419532i	$-0.137806\pi$
$761$	1.83035e7	+	8.81450e6i	1.14570	+	0.551742i	0.237963	+	0.971274i	$0.423520\pi$
$762$	7.16843e6	+	3.45214e6i	0.447236	+	0.215378i
$763$	6.58623e6	+	2.25939e6i	0.409567	+	0.140501i
$764$	−1.77448e6	+	854546.i	−0.109986	+	0.0529666i
$765$	675356.			0.0417233
$766$	−3.23543e6			−0.199233
$767$	−3.49090e6	+	1.68113e6i	−0.214264	+	0.103184i
$768$	−6.16585e6	−	7.73174e6i	−0.377216	−	0.473014i
$769$	5.59931e6	+	2.45322e7i	0.341444	+	1.49596i	0.796029	+	0.605259i	$0.206930\pi$
$769$	5.59931e6	+	2.45322e7i	0.341444	+	1.49596i	−0.454585	+	0.890703i	$0.650213\pi$
$770$	2.46861e6	+	6.91852e6i	0.150046	+	0.420520i
$771$	7.01647e6	−	3.07412e7i	0.425092	−	1.86245i
$772$	−2.12674e7	+	1.02418e7i	−1.28431	+	0.618492i
$773$	−3.13989e6	+	1.37568e7i	−0.189002	+	0.828071i	0.788142	+	0.615493i	$0.211043\pi$
$773$	−3.13989e6	+	1.37568e7i	−0.189002	+	0.828071i	−0.977144	+	0.212578i	$0.931814\pi$
$774$	−2.27545e6	−	2.85332e6i	−0.136526	−	0.171198i
$775$	812084.	+	3.55797e6i	0.0485676	+	0.212789i
$776$	1.84754e6	−	2.31674e6i	0.110139	−	0.138109i
$777$	−6.79805e6	−	2.33206e6i	−0.403954	−	0.138576i
$778$	2.52949e6	+	3.17188e6i	0.149825	+	0.187874i
$779$	3.45165e6	−	4.32823e6i	0.203790	−	0.255545i
$780$	−8.60725e6	−	4.14503e6i	−0.506557	−	0.243945i
$781$	−1.41836e7	+	1.77856e7i	−0.832067	+	1.04338i
$782$	−9615.58	+	42128.6i	−0.000562288	+	0.00246354i
$783$	−6.87457e7			−4.00720
$784$	−5.92774e6	−	1.19325e7i	−0.344428	−	0.693334i
$785$	−2.93528e7			−1.70010
$786$	−1.36121e6	+	5.96383e6i	−0.0785900	+	0.344325i
$787$	−7.87817e6	+	9.87891e6i	−0.453407	+	0.568555i	−0.955021	−	0.296537i	$-0.904168\pi$
$787$	−7.87817e6	+	9.87891e6i	−0.453407	+	0.568555i	0.501614	+	0.865091i	$0.332740\pi$
$788$	1.56474e7	+	7.53539e6i	0.897691	+	0.432305i
$789$	1.89796e7	−	2.37997e7i	1.08541	−	1.36106i
$790$	−304871.	−	382296.i	−0.0173799	−	0.0217938i
$791$	1.81415e7	−	2.15677e6i	1.03094	−	0.122564i
$792$	1.59394e7	−	1.99874e7i	0.902943	−	1.13225i
$793$	1.33359e6	+	5.84282e6i	0.0753075	+	0.329944i
$794$	1.43901e6	+	1.80447e6i	0.0810053	+	0.101577i
$795$	1.20246e7	−	5.26833e7i	0.674767	−	2.95635i
$796$	2.84701e7	−	1.37105e7i	1.59260	−	0.766955i
$797$	4.67283e6	−	2.04730e7i	0.260576	−	1.14166i	−0.660053	−	0.751219i	$-0.729466\pi$
$797$	4.67283e6	−	2.04730e7i	0.260576	−	1.14166i	0.920629	−	0.390439i	$-0.127677\pi$
$798$	−2.65584e6	+	1.69158e6i	−0.147637	+	0.0940338i
$799$	26089.5	+	114306.i	0.00144577	+	0.00633434i
$800$	−1.35286e7	−	1.69644e7i	−0.747358	−	0.937157i
$801$	5.00899e7	−	2.41220e7i	2.75847	−	1.32841i
$802$	−8.18916e6			−0.449576
$803$	−343064.			−0.0187753
$804$	1.30464e7	−	6.28282e6i	0.711788	−	0.342779i
$805$	−9.51537e6	−	2.66678e7i	−0.517531	−	1.45043i
$806$	123558.	+	59502.3i	0.00669935	+	0.00322624i
$807$	1.99782e7	+	9.62099e6i	1.07987	+	0.520039i
$808$	1.74275e6	+	7.63548e6i	0.0939088	+	0.411441i
$809$	−56656.2	−	248227.i	−0.00304352	−	0.0133345i	0.973383	−	0.229183i	$-0.0736054\pi$
$809$	−56656.2	−	248227.i	−0.00304352	−	0.0133345i	−0.976427	+	0.215848i	$0.930748\pi$
$810$	−2.77178e7	−	1.33482e7i	−1.48439	−	0.714843i
$811$	3.80736e6	+	1.83353e6i	0.203269	+	0.0978892i	0.532749	−	0.846273i	$-0.321159\pi$
$811$	3.80736e6	+	1.83353e6i	0.203269	+	0.0978892i	−0.329480	+	0.944163i	$0.606873\pi$
$812$	−2.21773e6	+	2.08299e7i	−0.118037	+	1.10866i
$813$	−2.45988e7	+	1.18462e7i	−1.30523	+	0.628567i
$814$	−1.15935e6			−0.0613270
$815$	2.48256e7			1.30920
$816$	−243498.	+	117263.i	−0.0128018	+	0.00616501i
$817$	−1.12505e6	−	1.41076e6i	−0.0589678	−	0.0739433i
$818$	−390638.	−	1.71150e6i	−0.0204123	−	0.0894320i
$819$	−1.08313e6	+	1.01732e7i	−0.0564247	+	0.529967i
$820$	6.38028e6	−	2.79538e7i	0.331364	−	1.45180i
$821$	1.26743e6	−	610363.i	0.0656246	−	0.0316032i	−0.400784	−	0.916173i	$-0.631262\pi$
$821$	1.26743e6	−	610363.i	0.0656246	−	0.0316032i	0.466408	+	0.884570i	$0.345548\pi$
$822$	63519.5	−	278297.i	0.00327889	−	0.0143658i
$823$	6.18438e6	+	7.75496e6i	0.318270	+	0.399098i	0.915072	−	0.403290i	$-0.132134\pi$
$823$	6.18438e6	+	7.75496e6i	0.318270	+	0.399098i	−0.596802	+	0.802389i	$0.703562\pi$
$824$	−3.05044e6	−	1.33648e7i	−0.156511	−	0.685718i
$825$	−3.74513e7	+	4.69624e7i	−1.91572	+	2.40224i
$826$	2.22283e6	+	6.22969e6i	0.113359	+	0.317699i
$827$	−1.80149e7	−	2.25900e7i	−0.915942	−	1.14855i	−0.988505	−	0.151191i	$-0.951689\pi$
$827$	−1.80149e7	−	2.25900e7i	−0.915942	−	1.14855i	0.0725627	−	0.997364i	$-0.476882\pi$
$828$	−2.94852e7	+	3.69733e7i	−1.49461	+	1.87418i
$829$	2.90117e7	+	1.39713e7i	1.46618	+	0.706074i	0.985319	−	0.170723i	$-0.0546105\pi$
$829$	2.90117e7	+	1.39713e7i	1.46618	+	0.706074i	0.480859	+	0.876798i	$0.340325\pi$
$830$	6.23613e6	−	7.81986e6i	0.314210	−	0.394007i
$831$	−9.46464e6	+	4.14673e7i	−0.475447	+	2.08307i
$832$	2.21391e6			0.110880
$833$	−185272.	+	44684.2i	−0.00925120	+	0.00223121i
$834$	−2.32976e6			−0.115983
$835$	−757954.	+	3.32081e6i	−0.0376207	+	0.164827i
$836$	3.78210e6	−	4.74261e6i	0.187162	−	0.234694i
$837$	−8.26668e6	−	3.98102e6i	−0.407866	−	0.196418i
$838$	3.53785e6	−	4.43632e6i	0.174032	−	0.218229i
$839$	−1.01397e6	−	1.27148e6i	−0.0497302	−	0.0623597i	0.756344	−	0.654174i	$-0.226983\pi$
$839$	−1.01397e6	−	1.27148e6i	−0.0497302	−	0.0623597i	−0.806075	+	0.591814i	$0.798412\pi$
$840$	−1.79032e7	+	2.88843e7i	−0.875451	+	1.41242i
$841$	5.88207e6	−	7.37588e6i	0.286774	−	0.359603i
$842$	1.40968e6	+	6.17621e6i	0.0685236	+	0.300222i
$843$	1.72663e7	+	2.16513e7i	0.836817	+	1.04934i
$844$	−6.76362e6	+	2.96333e7i	−0.326831	+	1.43194i
$845$	−2.89897e7	+	1.39607e7i	−1.39670	+	0.672614i
$846$	2.39082e6	−	1.04749e7i	0.114847	−	0.503179i
$847$	79994.8	−	129061.i	0.00383136	−	0.00618138i
$848$	3.51831e6	+	1.54147e7i	0.168013	+	0.736115i
$849$	8.61333e6	+	1.08008e7i	0.410111	+	0.514263i
$850$	−80272.3	+	38657.1i	−0.00381082	+	0.00183519i
$851$	4.46875e6			0.211525
$852$	−5.05053e7			−2.38362
$853$	−2.65837e7	+	1.28020e7i	−1.25096	+	0.602429i	−0.937768	−	0.347262i	$-0.887111\pi$
$853$	−2.65837e7	+	1.28020e7i	−1.25096	+	0.602429i	−0.313188	+	0.949691i	$0.601397\pi$
$854$	1.01593e7	−	1.20780e6i	0.476672	−	0.0566697i
$855$	−2.75693e7	−	1.32767e7i	−1.28976	−	0.621117i
$856$	2.67534e6	+	1.28837e6i	0.124794	+	0.0600977i
$857$	−4.45680e6	−	1.95265e7i	−0.207286	−	0.908181i	−0.966363	−	0.257180i	$-0.917207\pi$
$857$	−4.45680e6	−	1.95265e7i	−0.207286	−	0.908181i	0.759077	−	0.651001i	$-0.225651\pi$
$858$	502272.	+	2.20060e6i	0.0232927	+	0.102052i
$859$	1.92166e6	+	925424.i	0.0888576	+	0.0427915i	0.477785	−	0.878477i	$-0.341440\pi$
$859$	1.92166e6	+	925424.i	0.0888576	+	0.0427915i	−0.388927	+	0.921269i	$0.627154\pi$
$860$	−8.42019e6	−	4.05495e6i	−0.388218	−	0.186956i
$861$	−4.17028e7	+	4.95788e6i	−1.91715	+	0.227923i
$862$	−2.64016e6	+	1.27143e6i	−0.121021	+	0.0582808i
$863$	−2.38483e7			−1.09001			−0.545004	−	0.838433i	$-0.683472\pi$
$863$	−2.38483e7			−1.09001			−0.545004	+	0.838433i	$0.683472\pi$
$864$	5.45526e7			2.48617
$865$	5.43726e7	−	2.61845e7i	2.47081	−	1.18988i
$866$	−2.72864e6	−	3.42160e6i	−0.123638	−	0.155037i
$867$	−9.49788e6	−	4.16129e7i	−0.429120	−	1.88010i
$868$	−1.47293e6	+	2.37638e6i	−0.0663565	+	0.107057i
$869$	307016.	−	1.34512e6i	0.0137915	−	0.0604244i
$870$	2.10048e7	−	1.01154e7i	0.940850	−	0.453089i
$871$	−433438.	+	1.89901e6i	−0.0193589	+	0.0848170i
$872$	3.23980e6	+	4.06258e6i	0.144287	+	0.180930i
$873$	−4.50409e6	−	1.97337e7i	−0.200019	−	0.876340i
$874$	1.22072e6	−	1.53074e6i	0.0540553	−	0.0677832i
$875$	1.15211e7	−	1.85878e7i	0.508716	−	0.820745i
$876$	−474881.	−	595482.i	−0.0209086	−	0.0262186i
$877$	1.22859e7	−	1.54060e7i	0.539395	−	0.676380i	−0.435205	−	0.900331i	$-0.643324\pi$
$877$	1.22859e7	−	1.54060e7i	0.539395	−	0.676380i	0.974600	+	0.223951i	$0.0718956\pi$
$878$	−453250.	−	218274.i	−0.0198427	−	0.00955576i
$879$	−8.03318e6	+	1.00733e7i	−0.350683	+	0.439743i
$880$	6.35669e6	−	2.78505e7i	0.276710	−	1.21234i
$881$	4.16515e7			1.80797			0.903985	−	0.427564i	$-0.140628\pi$
$881$	4.16515e7			1.80797			0.903985	+	0.427564i	$0.140628\pi$
$882$	1.70735e7	+	3.67725e6i	0.739010	+	0.159166i
$883$	4.06209e7			1.75326			0.876632	−	0.481161i	$-0.159785\pi$
$883$	4.06209e7			1.75326			0.876632	+	0.481161i	$0.159785\pi$
$884$	8897.07	−	38980.6i	0.000382927	−	0.00167771i
$885$	−5.48127e7	+	6.87329e7i	−2.35246	+	2.94989i
$886$	2.36767e6	+	1.14021e6i	0.101330	+	0.0487978i
$887$	−997359.	+	1.25065e6i	−0.0425640	+	0.0533736i	−0.802658	−	0.596440i	$-0.796581\pi$
$887$	−997359.	+	1.25065e6i	−0.0425640	+	0.0533736i	0.760094	+	0.649813i	$0.225153\pi$
$888$	−3.34399e6	−	4.19323e6i	−0.142309	−	0.178450i
$889$	−7.33259e6	−	2.05503e7i	−0.311174	−	0.872095i
$890$	−7.43283e6	+	9.32048e6i	−0.314543	+	0.394424i
$891$	−1.93163e7	−	8.46301e7i	−0.815134	−	3.57134i
$892$	2.17517e7	+	2.72758e7i	0.915338	+	1.14780i
$893$	1.18209e6	−	5.17906e6i	0.0496044	−	0.217331i
$894$	−8.36048e6	+	4.02619e6i	−0.349854	+	0.168481i
$895$	1.48372e6	−	6.50059e6i	0.0619146	−	0.271266i
$896$	2.30735e6	−	2.16717e7i	0.0960159	−	0.901827i
$897$	−1.93603e6	−	8.48230e6i	−0.0803398	−	0.351992i
$898$	435119.	+	545622.i	0.0180060	+	0.0225788i
$899$	3.60092e6	−	1.73411e6i	0.148599	−	0.0715613i
$900$	−9.75048e7			−4.01254
$901$	226163.			0.00928133
$902$	−6.10368e6	+	2.93938e6i	−0.249790	+	0.120293i
$903$	−1.44920e6	+	1.36116e7i	−0.0591438	+	0.555506i
$904$	1.22835e7	+	5.91544e6i	0.499922	+	0.240750i
$905$	−3.24345e7	−	1.56196e7i	−1.31639	−	0.633941i
$906$	−5.32170e6	−	2.33159e7i	−0.215392	−	0.943694i
$907$	−4.95265e6	−	2.16990e7i	−0.199903	−	0.875833i	−0.970993	−	0.239107i	$-0.923145\pi$
$907$	−4.95265e6	−	2.16990e7i	−0.199903	−	0.875833i	0.771090	−	0.636726i	$-0.219712\pi$
$908$	−1.34754e7	−	6.48942e6i	−0.542410	−	0.261211i
$909$	4.81998e7	+	2.32118e7i	1.93480	+	0.931749i
$910$	−737238.	−	2.06618e6i	−0.0295124	−	0.0827113i
$911$	1.85772e6	−	894630.i	0.0741624	−	0.0357148i	−0.396435	−	0.918063i	$-0.629753\pi$
$911$	1.85772e6	−	894630.i	0.0741624	−	0.0357148i	0.470597	+	0.882348i	$0.344038\pi$
$912$	1.22453e7			0.487508
$913$	2.82221e7			1.12050
$914$	−6.03119e6	+	2.90447e6i	−0.238802	+	0.115001i
$915$	8.47820e7	+	1.06313e8i	3.34773	+	4.19792i
$916$	5.81962e6	+	2.54974e7i	0.229169	+	1.00405i
$917$	1.41494e7	−	9.01210e6i	0.555665	−	0.353918i
$918$	49844.6	−	218384.i	0.00195214	−	0.00855290i
$919$	−3.72791e7	+	1.79527e7i	−1.45605	+	0.701197i	−0.983634	−	0.180179i	$-0.942332\pi$
$919$	−3.72791e7	+	1.79527e7i	−1.45605	+	0.701197i	−0.472416	+	0.881376i	$0.656618\pi$
$920$	4.70189e6	−	2.06003e7i	0.183148	−	0.802426i
$921$	−4.57203e7	−	5.73315e7i	−1.77607	−	2.22712i
$922$	−134496.	−	589266.i	−0.00521054	−	0.0228289i
$923$	4.23585e6	−	5.31159e6i	0.163658	−	0.205220i
$924$	−4.56953e7	+	5.43254e6i	−1.76072	+	0.209326i
$925$	5.74469e6	+	7.20362e6i	0.220756	+	0.276819i
$926$	−139413.	+	174819.i	−0.00534290	+	0.00669978i
$927$	−8.43670e7	−	4.06290e7i	−3.22458	−	1.55288i
$928$	−1.48159e7	+	1.85785e7i	−0.564752	+	0.708177i
$929$	1.06419e7	−	4.66250e7i	0.404556	−	1.77247i	−0.204008	−	0.978969i	$-0.565397\pi$
$929$	1.06419e7	−	4.66250e7i	0.404556	−	1.77247i	0.608563	−	0.793505i	$-0.291746\pi$
$930$	3.11161e6			0.117972
$931$	8.44159e6	+	1.81813e6i	0.319191	+	0.0687466i
$932$	6.41232e6			0.241811
$933$	−1.10526e7	+	4.84246e7i	−0.415681	+	1.82122i
$934$	−5.89072e6	+	7.38673e6i	−0.220954	+	0.277067i
$935$	−368154.	−	177294.i	−0.0137721	−	0.00663230i
$936$	−4.76024e6	+	5.96915e6i	−0.177598	+	0.222701i
$937$	1.53550e7	+	1.92545e7i	0.571347	+	0.716447i	0.980610	−	0.195970i	$-0.0627855\pi$
$937$	1.53550e7	+	1.92545e7i	0.571347	+	0.716447i	−0.409263	+	0.912417i	$0.634214\pi$
$938$	3.14527e6	+	1.07898e6i	0.116722	+	0.0400411i
$939$	3.93811e7	−	4.93824e7i	1.45755	−	1.82771i
$940$	−6.12239e6	−	2.68239e7i	−0.225996	−	0.990154i
$941$	−1.22725e7	−	1.53892e7i	−0.451812	−	0.566554i	0.502802	−	0.864402i	$-0.332303\pi$
$941$	−1.22725e7	−	1.53892e7i	−0.451812	−	0.566554i	−0.954613	+	0.297848i	$0.903731\pi$
$942$	−3.42621e6	+	1.50112e7i	−0.125802	+	0.551174i
$943$	2.35269e7	−	1.13300e7i	0.861561	−	0.414906i
$944$	5.72380e6	−	2.50776e7i	0.209052	−	0.915916i
$945$	4.93252e7	+	1.38239e8i	1.79676	+	5.03558i
$946$	491356.	+	2.15277e6i	0.0178512	+	0.0782114i
$947$	2.41260e7	+	3.02530e7i	0.874199	+	1.09621i	0.994631	+	0.103489i	$0.0330007\pi$
$947$	2.41260e7	+	3.02530e7i	0.874199	+	1.09621i	−0.120432	+	0.992722i	$0.538428\pi$
$948$	2.75981e6	−	1.32906e6i	0.0997376	−	0.0480311i
$949$	102454.			0.00369288
$950$	4.03682e6			0.145121
$951$	1.87690e7	−	9.03867e6i	0.672961	−	0.324081i
$952$	−134531.	−	46150.5i	−0.00481093	−	0.00165038i
$953$	−9.06080e6	−	4.36345e6i	−0.323172	−	0.155632i	0.265262	−	0.964176i	$-0.414541\pi$
$953$	−9.06080e6	−	4.36345e6i	−0.323172	−	0.155632i	−0.588435	+	0.808545i	$0.700256\pi$
$954$	−1.86729e7	−	8.99241e6i	−0.664265	−	0.319893i
$955$	−1.33762e6	−	5.86048e6i	−0.0474595	−	0.207934i
$956$	1.00567e7	+	4.40615e7i	0.355888	+	1.55925i
$957$	5.92681e7	+	2.85420e7i	2.09190	+	1.00741i
$958$	−2.35073e6	−	1.13205e6i	−0.0827539	−	0.0398522i
$959$	−660267.	+	420542.i	−0.0231832	+	0.0147660i
$960$	4.52579e7	−	2.17951e7i	1.58495	−	0.763273i
$961$	−2.80957e7			−0.981367
$962$	346233.			0.0120623
$963$	1.82747e7	−	8.80063e6i	0.635016	−	0.305808i
$964$	4.77717e6	+	5.99038e6i	0.165569	+	0.207617i
$965$	−1.60315e7	−	7.02385e7i	−0.554186	−	2.42805i
$966$	−1.47487e7	+	1.75342e6i	−0.508525	+	0.0604566i
$967$	−8.65533e6	+	3.79215e7i	−0.297658	+	1.30413i	0.575946	+	0.817488i	$0.304634\pi$
$967$	−8.65533e6	+	3.79215e7i	−0.297658	+	1.30413i	−0.873604	+	0.486637i	$0.838223\pi$
$968$	102092.	−	49165.1i	0.00350191	−	0.00168643i
$969$	38976.2	−	170766.i	0.00133349	−	0.00584241i
$970$	2.70614e6	+	3.39339e6i	0.0923465	+	0.115799i
$971$	1.09593e7	+	4.80157e7i	0.373021	+	1.63431i	0.718244	+	0.695791i	$0.244946\pi$
$971$	1.09593e7	+	4.80157e7i	0.373021	+	1.63431i	−0.345223	+	0.938521i	$0.612197\pi$
$972$	6.39597e7	−	8.02029e7i	2.17140	−	2.72285i
$973$	4.54537e6	+	4.48997e6i	0.153917	+	0.152041i
$974$	−1.97285e6	−	2.47387e6i	−0.0666340	−	0.0835564i
$975$	1.11846e7	−	1.40251e7i	0.376799	−	0.472492i
$976$	−3.58464e7	−	1.72627e7i	−1.20454	−	0.580076i
$977$	1.96015e6	−	2.45795e6i	0.0656980	−	0.0823827i	−0.747897	−	0.663815i	$-0.768936\pi$
$977$	1.96015e6	−	2.45795e6i	0.0656980	−	0.0823827i	0.813595	+	0.581433i	$0.197508\pi$
$978$	2.89777e6	−	1.26960e7i	0.0968763	−	0.424443i
$979$	−3.36378e7			−1.12169
$980$	4.34775e7	−	1.04860e7i	1.44610	−	0.348773i
$981$	3.54944e7			1.17757
$982$	−77773.9	+	340750.i	−0.00257368	+	0.0112760i
$983$	1.90616e6	−	2.39025e6i	0.0629181	−	0.0788968i	−0.749377	−	0.662144i	$-0.769647\pi$
$983$	1.90616e6	−	2.39025e6i	0.0629181	−	0.0788968i	0.812295	+	0.583247i	$0.198218\pi$
$984$	−2.82368e7	−	1.35981e7i	−0.929667	−	0.447704i
$985$	−3.30492e7	+	4.14424e7i	−1.08535	+	1.36099i
$986$	60835.8	+	76285.7i	0.00199282	+	0.00249891i
$987$	−3.39900e7	+	2.16491e7i	−1.11060	+	0.707371i
$988$	−1.12951e6	+	1.41636e6i	−0.0368126	+	0.0461615i
$989$	−1.89395e6	−	8.29796e6i	−0.0615714	−	0.269762i
$990$	2.33469e7	+	2.92761e7i	0.757080	+	0.949348i
$991$	207466.	−	908967.i	0.00671062	−	0.0294011i	−0.971462	−	0.237196i	$-0.923772\pi$
$991$	207466.	−	908967.i	0.00671062	−	0.0294011i	0.978172	+	0.207795i	$0.0666287\pi$
$992$	−2.85749e6	+	1.37609e6i	−0.0921945	+	0.0443986i
$993$	−1.24550e7	+	5.45687e7i	−0.400838	+	1.75619i
$994$	−8.25096e6	−	8.15041e6i	−0.264874	−	0.261645i
$995$	2.14610e7	+	9.40266e7i	0.687213	+	3.01088i
$996$	3.90660e7	+	4.89872e7i	1.24782	+	1.56471i
$997$	1.66912e6	−	803805.i	0.0531801	−	0.0256102i	−0.407105	−	0.913382i	$-0.633462\pi$
$997$	1.66912e6	−	803805.i	0.0531801	−	0.0256102i	0.460285	+	0.887771i	$0.347747\pi$
$998$	315341.			0.0100220
$999$	−2.31648e7			−0.734370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.e.a.15.14	✓	138
49.36	even	7	inner	49.6.e.a.36.14	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.e.a.15.14	✓	138	1.1	even	1	trivial
49.6.e.a.36.14	yes	138	49.36	even	7	inner

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.349896 - 1.53300i) q^{2} +(-18.7448 + 23.5052i) q^{3} +(26.6034 + 12.8115i) q^{4} +(-56.1895 + 70.4594i) q^{5} +(29.4746 + 36.9600i) q^{6} +(13.7252 - 128.913i) q^{7} +(60.3208 - 75.6399i) q^{8} +(-147.055 - 644.291i) q^{9} +O(q^{10})\)	\(q+(0.349896 - 1.53300i) q^{2} +(-18.7448 + 23.5052i) q^{3} +(26.6034 + 12.8115i) q^{4} +(-56.1895 + 70.4594i) q^{5} +(29.4746 + 36.9600i) q^{6} +(13.7252 - 128.913i) q^{7} +(60.3208 - 75.6399i) q^{8} +(-147.055 - 644.291i) q^{9} +(88.3534 + 110.792i) q^{10} +(-88.9749 + 389.825i) q^{11} +(-799.810 + 385.168i) q^{12} +(26.5719 - 116.419i) q^{13} +(-192.821 - 66.1469i) q^{14} +(-602.902 - 2641.49i) q^{15} +(494.273 + 619.799i) q^{16} +(10.2166 - 4.92007i) q^{17} -1039.15 q^{18} -513.784 q^{19} +(-2397.52 + 1154.58i) q^{20} +(2772.85 + 2739.06i) q^{21} +(566.468 + 272.796i) q^{22} +(-2183.48 - 1051.51i) q^{23} +(647.231 + 2835.70i) q^{24} +(-1111.89 - 4871.50i) q^{25} +(-169.173 - 81.4693i) q^{26} +(11318.6 + 5450.73i) q^{27} +(2016.71 - 3253.68i) q^{28} +(-4930.30 + 2374.31i) q^{29} -4260.34 q^{30} -730.365 q^{31} +(3912.41 - 1884.12i) q^{32} +(-7495.09 - 9398.54i) q^{33} +(-3.96768 - 17.3836i) q^{34} +(8311.93 + 8210.63i) q^{35} +(4342.17 - 19024.3i) q^{36} +(-1661.34 + 800.057i) q^{37} +(-179.771 + 787.629i) q^{38} +(2238.37 + 2806.83i) q^{39} +(1940.14 + 8500.33i) q^{40} +(-6718.10 + 8424.23i) q^{41} +(5169.18 - 3292.39i) q^{42} +(2189.72 + 2745.83i) q^{43} +(-7361.27 + 9230.74i) q^{44} +(53659.3 + 25840.9i) q^{45} +(-2375.95 + 2979.34i) q^{46} +(-2300.75 + 10080.2i) q^{47} -23833.5 q^{48} +(-16430.2 - 3538.71i) q^{49} -7857.03 q^{50} +(-75.8611 + 332.369i) q^{51} +(2198.41 - 2756.71i) q^{52} +(17969.4 + 8653.63i) q^{53} +(12316.3 - 15444.1i) q^{54} +(-22467.3 - 28173.2i) q^{55} +(-8923.07 - 8814.32i) q^{56} +(9630.76 - 12076.6i) q^{57} +(1914.71 + 8388.90i) q^{58} +(-20230.4 - 25368.1i) q^{59} +(17802.2 - 77996.5i) q^{60} +(-45217.6 + 21775.7i) q^{61} +(-255.552 + 1119.65i) q^{62} +(-85076.0 + 10114.4i) q^{63} +(4125.53 + 18075.1i) q^{64} +(6709.76 + 8413.77i) q^{65} +(-17030.4 + 8201.42i) q^{66} -16311.9 q^{67} +334.830 q^{68} +(65644.6 - 31612.8i) q^{69} +(15495.2 - 9869.29i) q^{70} +(51258.9 + 24685.0i) q^{71} +(-57604.6 - 27740.9i) q^{72} +(190.919 + 836.472i) q^{73} +(645.189 + 2826.76i) q^{74} +(135348. + 65179.9i) q^{75} +(-13668.4 - 6582.34i) q^{76} +(49032.4 + 16820.5i) q^{77} +(5086.05 - 2449.31i) q^{78} -3450.59 q^{79} -71443.6 q^{80} +(-195598. + 94195.2i) q^{81} +(10563.7 + 13246.4i) q^{82} +(-15705.9 - 68812.1i) q^{83} +(38675.8 + 108393. i) q^{84} +(-227.402 + 996.313i) q^{85} +(4975.52 - 2396.08i) q^{86} +(36608.8 - 160394. i) q^{87} +(24119.3 + 30244.6i) q^{88} +(18719.8 + 82016.9i) q^{89} +(58389.2 - 73217.8i) q^{90} +(-14643.3 - 5023.34i) q^{91} +(-44616.4 - 55947.2i) q^{92} +(13690.5 - 17167.4i) q^{93} +(14647.9 + 7054.07i) q^{94} +(28869.2 - 36200.9i) q^{95} +(-29050.6 + 127279. i) q^{96} +30628.5 q^{97} +(-11173.7 + 23949.3i) q^{98} +264245. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9}+O(q^{10}) \) 138 * q - 5 * q^2 + 13 * q^3 - 389 * q^4 + 67 * q^5 + 331 * q^6 - 56 * q^7 + 305 * q^8 - 918 * q^9	\( 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9} - 771 q^{10} + 410 q^{11} - 1316 q^{12} + 483 q^{13} + 2597 q^{14} + 2557 q^{15} - 7357 q^{16} - 1422 q^{17} - 2480 q^{18} - 6758 q^{19} - 3647 q^{20} - 399 q^{21} - 857 q^{22} - 2392 q^{23} - 3571 q^{24} - 8066 q^{25} - 343 q^{26} + 16396 q^{27} + 32102 q^{28} + 30341 q^{29} + 13716 q^{30} - 32712 q^{31} - 26993 q^{32} - 16775 q^{33} + 35163 q^{34} - 12019 q^{35} + 35461 q^{36} - 34872 q^{37} + 13383 q^{38} - 20671 q^{39} + 165169 q^{40} + 51233 q^{41} - 13741 q^{42} - 17203 q^{43} - 4267 q^{44} + 30777 q^{45} - 74611 q^{46} + 64264 q^{47} - 247084 q^{48} - 70350 q^{49} - 263036 q^{50} - 57453 q^{51} - 36043 q^{52} + 124590 q^{53} + 144840 q^{54} + 90977 q^{55} + 404404 q^{56} - 103899 q^{57} + 24861 q^{58} - 8079 q^{59} + 72065 q^{60} - 236659 q^{61} - 173227 q^{62} - 119805 q^{63} + 105381 q^{64} - 33383 q^{65} + 536577 q^{66} + 19716 q^{67} - 256340 q^{68} - 202795 q^{69} + 194803 q^{70} + 61778 q^{71} - 392108 q^{72} - 157760 q^{73} - 328319 q^{74} + 355167 q^{75} - 61334 q^{76} - 24402 q^{77} + 497217 q^{78} - 73876 q^{79} - 1340760 q^{80} - 815116 q^{81} + 248976 q^{82} + 303107 q^{83} + 1250354 q^{84} + 205487 q^{85} + 1083219 q^{86} + 197027 q^{87} + 1052915 q^{88} + 219783 q^{89} + 82170 q^{90} - 837235 q^{91} + 35936 q^{92} + 138365 q^{93} - 571908 q^{94} - 610016 q^{95} - 1054494 q^{96} + 762020 q^{97} - 2160767 q^{98} - 1090772 q^{99}+O(q^{100}) \) 138 * q - 5 * q^2 + 13 * q^3 - 389 * q^4 + 67 * q^5 + 331 * q^6 - 56 * q^7 + 305 * q^8 - 918 * q^9 - 771 * q^10 + 410 * q^11 - 1316 * q^12 + 483 * q^13 + 2597 * q^14 + 2557 * q^15 - 7357 * q^16 - 1422 * q^17 - 2480 * q^18 - 6758 * q^19 - 3647 * q^20 - 399 * q^21 - 857 * q^22 - 2392 * q^23 - 3571 * q^24 - 8066 * q^25 - 343 * q^26 + 16396 * q^27 + 32102 * q^28 + 30341 * q^29 + 13716 * q^30 - 32712 * q^31 - 26993 * q^32 - 16775 * q^33 + 35163 * q^34 - 12019 * q^35 + 35461 * q^36 - 34872 * q^37 + 13383 * q^38 - 20671 * q^39 + 165169 * q^40 + 51233 * q^41 - 13741 * q^42 - 17203 * q^43 - 4267 * q^44 + 30777 * q^45 - 74611 * q^46 + 64264 * q^47 - 247084 * q^48 - 70350 * q^49 - 263036 * q^50 - 57453 * q^51 - 36043 * q^52 + 124590 * q^53 + 144840 * q^54 + 90977 * q^55 + 404404 * q^56 - 103899 * q^57 + 24861 * q^58 - 8079 * q^59 + 72065 * q^60 - 236659 * q^61 - 173227 * q^62 - 119805 * q^63 + 105381 * q^64 - 33383 * q^65 + 536577 * q^66 + 19716 * q^67 - 256340 * q^68 - 202795 * q^69 + 194803 * q^70 + 61778 * q^71 - 392108 * q^72 - 157760 * q^73 - 328319 * q^74 + 355167 * q^75 - 61334 * q^76 - 24402 * q^77 + 497217 * q^78 - 73876 * q^79 - 1340760 * q^80 - 815116 * q^81 + 248976 * q^82 + 303107 * q^83 + 1250354 * q^84 + 205487 * q^85 + 1083219 * q^86 + 197027 * q^87 + 1052915 * q^88 + 219783 * q^89 + 82170 * q^90 - 837235 * q^91 + 35936 * q^92 + 138365 * q^93 - 571908 * q^94 - 610016 * q^95 - 1054494 * q^96 + 762020 * q^97 - 2160767 * q^98 - 1090772 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more