LMFDB - Embedded newform 49.6.e.a.15.6

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			15.6
Character	$\chi$	$=$	49.15
Dual form			49.6.e.a.36.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68439 + 7.37980i) q^{2} +(-6.81157 + 8.54144i) q^{3} +(-22.7933 - 10.9767i) q^{4} +(-28.2340 + 35.4043i) q^{5} +(-51.5608 - 64.6552i) q^{6} +(-64.4638 - 112.479i) q^{7} +(-31.6272 + 39.6593i) q^{8} +(27.5139 + 120.546i) q^{9} +O(q^{10})$	\(q+(-1.68439 + 7.37980i) q^{2} +(-6.81157 + 8.54144i) q^{3} +(-22.7933 - 10.9767i) q^{4} +(-28.2340 + 35.4043i) q^{5} +(-51.5608 - 64.6552i) q^{6} +(-64.4638 - 112.479i) q^{7} +(-31.6272 + 39.6593i) q^{8} +(27.5139 + 120.546i) q^{9} +(-213.720 - 267.996i) q^{10} +(143.435 - 628.430i) q^{11} +(249.015 - 119.919i) q^{12} +(-171.334 + 750.664i) q^{13} +(938.652 - 286.272i) q^{14} +(-110.086 - 482.317i) q^{15} +(-744.157 - 933.143i) q^{16} +(1096.10 - 527.852i) q^{17} -935.952 q^{18} +1082.77 q^{19} +(1032.17 - 497.066i) q^{20} +(1399.83 + 215.542i) q^{21} +(4396.09 + 2117.04i) q^{22} +(-3672.42 - 1768.55i) q^{23} +(-123.316 - 540.284i) q^{24} +(239.072 + 1047.44i) q^{25} +(-5251.16 - 2528.83i) q^{26} +(-3608.90 - 1737.96i) q^{27} +(234.702 + 3271.36i) q^{28} +(-4582.59 + 2206.86i) q^{29} +3744.83 q^{30} -7210.41 q^{31} +(6677.38 - 3215.65i) q^{32} +(4390.67 + 5505.73i) q^{33} +(2049.19 + 8978.08i) q^{34} +(5802.29 + 893.422i) q^{35} +(696.066 - 3049.66i) q^{36} +(-14838.3 + 7145.77i) q^{37} +(-1823.81 + 7990.65i) q^{38} +(-5244.70 - 6576.64i) q^{39} +(-511.147 - 2239.48i) q^{40} +(8608.85 - 10795.2i) q^{41} +(-3948.52 + 9967.40i) q^{42} +(6714.27 + 8419.43i) q^{43} +(-10167.4 + 12749.6i) q^{44} +(-5044.68 - 2429.39i) q^{45} +(19237.3 - 24122.8i) q^{46} +(372.089 - 1630.23i) q^{47} +13039.3 q^{48} +(-8495.84 + 14501.6i) q^{49} -8132.62 q^{50} +(-2957.52 + 12957.7i) q^{51} +(12145.1 - 15229.5i) q^{52} +(-11888.2 - 5725.05i) q^{53} +(18904.6 - 23705.6i) q^{54} +(18199.4 + 22821.3i) q^{55} +(6499.63 + 1000.80i) q^{56} +(-7375.38 + 9248.44i) q^{57} +(-8567.30 - 37535.8i) q^{58} +(7909.80 + 9918.58i) q^{59} +(-2785.03 + 12202.0i) q^{60} +(20563.3 - 9902.76i) q^{61} +(12145.2 - 53211.4i) q^{62} +(11785.2 - 10865.6i) q^{63} +(3984.82 + 17458.6i) q^{64} +(-21739.3 - 27260.2i) q^{65} +(-48026.8 + 23128.5i) q^{66} -37235.9 q^{67} -30777.7 q^{68} +(40120.9 - 19321.2i) q^{69} +(-16366.6 + 41314.9i) q^{70} +(-605.367 - 291.530i) q^{71} +(-5650.97 - 2721.36i) q^{72} +(6594.29 + 28891.5i) q^{73} +(-27740.8 - 121540. i) q^{74} +(-10575.1 - 5092.72i) q^{75} +(-24680.0 - 11885.3i) q^{76} +(-79931.2 + 24377.6i) q^{77} +(57368.4 - 27627.2i) q^{78} +17613.2 q^{79} +54047.7 q^{80} +(12356.3 - 5950.50i) q^{81} +(65165.5 + 81714.9i) q^{82} +(16882.5 + 73967.1i) q^{83} +(-29540.8 - 20278.4i) q^{84} +(-12258.9 + 53709.8i) q^{85} +(-73443.2 + 35368.4i) q^{86} +(12364.9 - 54174.0i) q^{87} +(20386.6 + 25564.0i) q^{88} +(8870.89 + 38865.9i) q^{89} +(26425.6 - 33136.7i) q^{90} +(95478.5 - 29119.2i) q^{91} +(64294.0 + 80622.1i) q^{92} +(49114.2 - 61587.3i) q^{93} +(11404.0 + 5491.89i) q^{94} +(-30571.0 + 38334.8i) q^{95} +(-18017.1 + 78938.0i) q^{96} +76835.1 q^{97} +(-92708.5 - 87124.0i) q^{98} +79701.3 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 $

$2$	−1.68439	+	7.37980i	−0.297761	+	1.30458i	0.575691	+	0.817667i	$0.304733\pi$
$2$	−1.68439	+	7.37980i	−0.297761	+	1.30458i	−0.873452	+	0.486910i	$0.838124\pi$
$3$	−6.81157	+	8.54144i	−0.436962	+	0.547933i	−0.950740	−	0.309990i	$-0.899674\pi$
$3$	−6.81157	+	8.54144i	−0.436962	+	0.547933i	0.513777	+	0.857924i	$0.328246\pi$
$4$	−22.7933	−	10.9767i	−0.712292	−	0.343022i
$5$	−28.2340	+	35.4043i	−0.505064	+	0.633331i	−0.967363	−	0.253393i	$-0.918453\pi$
$5$	−28.2340	+	35.4043i	−0.505064	+	0.633331i	0.462299	+	0.886724i	$0.347025\pi$
$6$	−51.5608	−	64.6552i	−0.584711	−	0.733205i
$7$	−64.4638	−	112.479i	−0.497245	−	0.867610i
$7$	−64.4638	−	112.479i	−0.497245	−	0.867610i
$8$	−31.6272	+	39.6593i	−0.174718	+	0.219089i
$9$	27.5139	+	120.546i	0.113226	+	0.496075i
$10$	−213.720	−	267.996i	−0.675840	−	0.847477i
$11$	143.435	−	628.430i	0.357415	−	1.56594i	−0.402191	−	0.915556i	$-0.631751\pi$
$11$	143.435	−	628.430i	0.357415	−	1.56594i	0.759606	−	0.650383i	$-0.225392\pi$
$12$	249.015	−	119.919i	0.499198	−	0.240401i
$13$	−171.334	+	750.664i	−0.281181	+	1.23193i	0.615101	+	0.788448i	$0.289115\pi$
$13$	−171.334	+	750.664i	−0.281181	+	1.23193i	−0.896282	+	0.443485i	$0.853742\pi$
$14$	938.652	−	286.272i	1.27992	−	0.390354i
$15$	−110.086	−	482.317i	−0.126329	−	0.553483i
$16$	−744.157	−	933.143i	−0.726715	−	0.911272i
$17$	1096.10	−	527.852i	0.919869	−	0.442985i	0.0868445	−	0.996222i	$-0.472322\pi$
$17$	1096.10	−	527.852i	0.919869	−	0.442985i	0.833024	+	0.553236i	$0.186607\pi$
$18$	−935.952			−0.680883
$19$	1082.77			0.688103			0.344051	−	0.938951i	$-0.388201\pi$
$19$	1082.77			0.688103			0.344051	+	0.938951i	$0.388201\pi$
$20$	1032.17	−	497.066i	0.576999	−	0.277868i
$21$	1399.83	+	215.542i	0.692670	+	0.106656i
$22$	4396.09	+	2117.04i	1.93646	+	0.932552i
$23$	−3672.42	−	1768.55i	−1.44755	−	0.697102i	−0.465381	−	0.885111i	$-0.654083\pi$
$23$	−3672.42	−	1768.55i	−1.44755	−	0.697102i	−0.982167	+	0.188008i	$0.939797\pi$
$24$	−123.316	−	540.284i	−0.0437011	−	0.191467i
$25$	239.072	+	1047.44i	0.0765031	+	0.335182i
$26$	−5251.16	−	2528.83i	−1.52343	−	0.733644i
$27$	−3608.90	−	1737.96i	−0.952721	−	0.458806i
$28$	234.702	+	3271.36i	0.0565747	+	0.788557i
$29$	−4582.59	+	2206.86i	−1.01185	+	0.487281i	−0.864943	−	0.501870i	$-0.832646\pi$
$29$	−4582.59	+	2206.86i	−1.01185	+	0.487281i	−0.146906	+	0.989151i	$0.546931\pi$
$30$	3744.83			0.759678
$31$	−7210.41			−1.34758			−0.673792	−	0.738921i	$-0.735336\pi$
$31$	−7210.41			−1.34758			−0.673792	+	0.738921i	$0.735336\pi$
$32$	6677.38	−	3215.65i	1.15274	−	0.555130i
$33$	4390.67	+	5505.73i	0.701853	+	0.880096i
$34$	2049.19	+	8978.08i	0.304008	+	1.33194i
$35$	5802.29	+	893.422i	0.800625	+	0.123278i
$36$	696.066	−	3049.66i	0.0895146	−	0.392189i
$37$	−14838.3	+	7145.77i	−1.78189	+	0.858114i	−0.826406	+	0.563074i	$0.809619\pi$
$37$	−14838.3	+	7145.77i	−1.78189	+	0.858114i	−0.955485	+	0.295040i	$0.904667\pi$
$38$	−1823.81	+	7990.65i	−0.204890	+	0.897683i
$39$	−5244.70	−	6576.64i	−0.552152	−	0.692377i
$40$	−511.147	−	2239.48i	−0.0505121	−	0.221308i
$41$	8608.85	−	10795.2i	0.799808	−	1.00293i	−0.199925	−	0.979811i	$-0.564070\pi$
$41$	8608.85	−	10795.2i	0.799808	−	1.00293i	0.999733	−	0.0231161i	$-0.00735872\pi$
$42$	−3948.52	+	9967.40i	−0.345391	+	0.871884i
$43$	6714.27	+	8419.43i	0.553768	+	0.694403i	0.977392	−	0.211435i	$-0.0678137\pi$
$43$	6714.27	+	8419.43i	0.553768	+	0.694403i	−0.423624	+	0.905838i	$0.639242\pi$
$44$	−10167.4	+	12749.6i	−0.791735	+	0.992804i
$45$	−5044.68	−	2429.39i	−0.371366	−	0.178841i
$46$	19237.3	−	24122.8i	1.34045	−	1.68087i
$47$	372.089	−	1630.23i	0.0245698	−	0.107647i	−0.961156	−	0.276005i	$-0.910989\pi$
$47$	372.089	−	1630.23i	0.0245698	−	0.107647i	0.985726	+	0.168358i	$0.0538464\pi$
$48$	13039.3			0.816864
$49$	−8495.84	+	14501.6i	−0.505494	+	0.862830i
$50$	−8132.62			−0.460051
$51$	−2957.52	+	12957.7i	−0.159221	+	0.697595i
$52$	12145.1	−	15229.5i	0.622863	−	0.781045i
$53$	−11888.2	−	5725.05i	−0.581335	−	0.279956i	0.120016	−	0.992772i	$-0.461705\pi$
$53$	−11888.2	−	5725.05i	−0.581335	−	0.279956i	−0.701351	+	0.712816i	$0.747420\pi$
$54$	18904.6	−	23705.6i	0.882231	−	1.10628i
$55$	18199.4	+	22821.3i	0.811240	+	1.01726i
$56$	6499.63	+	1000.80i	0.276961	+	0.0426458i
$57$	−7375.38	+	9248.44i	−0.300675	+	0.377035i
$58$	−8567.30	−	37535.8i	−0.334406	−	1.46513i
$59$	7909.80	+	9918.58i	0.295826	+	0.370953i	0.907425	−	0.420214i	$-0.138045\pi$
$59$	7909.80	+	9918.58i	0.295826	+	0.370953i	−0.611599	+	0.791168i	$0.709474\pi$
$60$	−2785.03	+	12202.0i	−0.0998737	+	0.437575i
$61$	20563.3	−	9902.76i	0.707568	−	0.340747i	−0.0452499	−	0.998976i	$-0.514408\pi$
$61$	20563.3	−	9902.76i	0.707568	−	0.340747i	0.752818	+	0.658229i	$0.228694\pi$
$62$	12145.2	−	53211.4i	0.401258	−	1.75803i
$63$	11785.2	−	10865.6i	0.374099	−	0.344907i
$64$	3984.82	+	17458.6i	0.121607	+	0.532795i
$65$	−21739.3	−	27260.2i	−0.638207	−	0.800286i
$66$	−48026.8	+	23128.5i	−1.35714	+	0.653563i
$67$	−37235.9			−1.01339			−0.506693	−	0.862127i	$-0.669132\pi$
$67$	−37235.9			−1.01339			−0.506693	+	0.862127i	$0.669132\pi$
$68$	−30777.7			−0.807168
$69$	40120.9	−	19321.2i	1.01449	−	0.488552i
$70$	−16366.6	+	41314.9i	−0.399221	+	1.00777i
$71$	−605.367	−	291.530i	−0.0142519	−	0.00686336i	0.426744	−	0.904372i	$-0.359660\pi$
$71$	−605.367	−	291.530i	−0.0142519	−	0.00686336i	−0.440996	+	0.897509i	$0.645375\pi$
$72$	−5650.97	−	2721.36i	−0.128467	−	0.0618665i
$73$	6594.29	+	28891.5i	0.144831	+	0.634546i	0.994274	+	0.106865i	$0.0340812\pi$
$73$	6594.29	+	28891.5i	0.144831	+	0.634546i	−0.849443	+	0.527681i	$0.823062\pi$
$74$	−27740.8	−	121540.i	−0.588897	−	2.58013i
$75$	−10575.1	−	5092.72i	−0.217087	−	0.104543i
$76$	−24680.0	−	11885.3i	−0.490130	−	0.236034i
$77$	−79931.2	+	24377.6i	−1.53635	+	0.468559i
$78$	57368.4	−	27627.2i	1.06767	−	0.514162i
$79$	17613.2			0.317520			0.158760	−	0.987317i	$-0.449250\pi$
$79$	17613.2			0.317520			0.158760	+	0.987317i	$0.449250\pi$
$80$	54047.7			0.944175
$81$	12356.3	−	5950.50i	0.209256	−	0.100772i
$82$	65165.5	+	81714.9i	1.07024	+	1.34204i
$83$	16882.5	+	73967.1i	0.268994	+	1.17854i	0.911186	+	0.411995i	$0.135168\pi$
$83$	16882.5	+	73967.1i	0.268994	+	1.17854i	−0.642193	+	0.766543i	$0.721975\pi$
$84$	−29540.8	−	20278.4i	−0.456798	−	0.313571i
$85$	−12258.9	+	53709.8i	−0.184037	+	0.806317i
$86$	−73443.2	+	35368.4i	−1.07079	+	0.515667i
$87$	12364.9	−	54174.0i	0.175142	−	0.767349i
$88$	20386.6	+	25564.0i	0.280633	+	0.351903i
$89$	8870.89	+	38865.9i	0.118711	+	0.520108i	0.998960	+	0.0455957i	$0.0145186\pi$
$89$	8870.89	+	38865.9i	0.118711	+	0.520108i	−0.880249	+	0.474513i	$0.842624\pi$
$90$	26425.6	−	33136.7i	0.343890	−	0.431224i
$91$	95478.5	−	29119.2i	1.20865	−	0.368618i
$92$	64294.0	+	80622.1i	0.791955	+	0.993080i
$93$	49114.2	−	61587.3i	0.588844	−	0.738387i
$94$	11404.0	+	5491.89i	0.133118	+	0.0641065i
$95$	−30571.0	+	38334.8i	−0.347536	+	0.435797i
$96$	−18017.1	+	78938.0i	−0.199529	+	0.874195i
$97$	76835.1			0.829145			0.414572	−	0.910016i	$-0.363931\pi$
$97$	76835.1			0.829145			0.414572	+	0.910016i	$0.363931\pi$
$98$	−92708.5	−	87124.0i	−0.975112	−	0.916374i
$99$	79701.3			0.817292
$100$	6048.22	−	26499.0i	0.0604822	−	0.264990i
$101$	−51040.2	+	64002.4i	−0.497862	+	0.624299i	−0.965746	−	0.259491i	$-0.916445\pi$
$101$	−51040.2	+	64002.4i	−0.497862	+	0.624299i	0.467884	+	0.883790i	$0.345017\pi$
$102$	−90643.9	−	43651.8i	−0.862657	−	0.415434i
$103$	−91157.6	+	114308.i	−0.846642	+	1.06166i	0.150684	+	0.988582i	$0.451852\pi$
$103$	−91157.6	+	114308.i	−0.846642	+	1.06166i	−0.997327	+	0.0730737i	$0.976719\pi$
$104$	−24352.0	−	30536.4i	−0.220776	−	0.276844i
$105$	−47153.8	+	43474.3i	−0.417391	+	0.384821i
$106$	62274.2	−	78089.3i	0.538323	−	0.675036i
$107$	19548.8	+	85648.7i	0.165067	+	0.723205i	0.987922	+	0.154953i	$0.0495228\pi$
$107$	19548.8	+	85648.7i	0.165067	+	0.723205i	−0.822855	+	0.568251i	$0.807620\pi$
$108$	63181.9	+	79227.6i	0.521235	+	0.653607i
$109$	2635.72	−	11547.8i	0.0212487	−	0.0930966i	−0.963192	−	0.268815i	$-0.913368\pi$
$109$	2635.72	−	11547.8i	0.0212487	−	0.0930966i	0.984440	+	0.175719i	$0.0562250\pi$
$110$	−199071.	+	95867.7i	−1.56865	+	0.755424i
$111$	40037.3	−	175415.i	0.308430	−	1.35132i
$112$	−56987.4	+	143856.i	−0.429273	+	1.08363i
$113$	−22453.0	−	98373.0i	−0.165416	−	0.724736i	−0.987790	−	0.155789i	$-0.950208\pi$
$113$	−22453.0	−	98373.0i	−0.165416	−	0.724736i	0.822374	−	0.568947i	$-0.192649\pi$
$114$	−55828.6	−	70006.9i	−0.402341	−	0.504520i
$115$	166301.	−	80086.4i	1.17260	−	0.564695i
$116$	128676.			0.887879
$117$	−95203.9			−0.642969
$118$	−86520.4	+	41666.0i	−0.572023	+	0.275472i
$119$	−130030.	−	89259.9i	−0.841739	−	0.577815i
$120$	22610.1	+	10888.4i	0.143334	+	0.0690260i
$121$	−229248.	−	110400.i	−1.42345	−	0.685498i
$122$	38443.8	+	168433.i	0.233844	+	1.02454i
$123$	33566.4	+	147064.i	0.200052	+	0.876483i
$124$	164349.	+	79146.5i	0.959873	+	0.462250i
$125$	−171332.	−	82509.0i	−0.980759	−	0.472309i
$126$	60335.0	+	105275.i	0.338566	+	0.590741i
$127$	−30236.9	+	14561.3i	−0.166352	+	0.0801108i	−0.515207	−	0.857066i	$-0.672285\pi$
$127$	−30236.9	+	14561.3i	−0.166352	+	0.0801108i	0.348855	+	0.937177i	$0.386571\pi$
$128$	101609.			0.548161
$129$	−117649.			−0.622463
$130$	237792.	−	114515.i	1.23407	−	0.594296i
$131$	−138522.	−	173702.i	−0.705248	−	0.884353i	0.292156	−	0.956371i	$-0.405628\pi$
$131$	−138522.	−	173702.i	−0.705248	−	0.884353i	−0.997403	+	0.0720181i	$0.977056\pi$
$132$	−39643.4	−	173689.i	−0.198032	−	0.867636i
$133$	−69799.6	−	121789.i	−0.342156	−	0.597005i
$134$	62719.8	−	274794.i	0.301747	−	1.32204i
$135$	163425.	−	78701.1i	0.771761	−	0.371661i
$136$	−13732.2	+	60164.9i	−0.0636640	+	0.278930i
$137$	31418.3	+	39397.3i	0.143015	+	0.179335i	0.848180	−	0.529708i	$-0.177699\pi$
$137$	31418.3	+	39397.3i	0.143015	+	0.179335i	−0.705165	+	0.709043i	$0.749127\pi$
$138$	75007.3	+	328629.i	0.335279	+	1.46895i
$139$	101154.	−	126843.i	0.444063	−	0.556837i	−0.508546	−	0.861035i	$-0.669817\pi$
$139$	101154.	−	126843.i	0.444063	−	0.556837i	0.952609	+	0.304198i	$0.0983883\pi$
$140$	−122447.	−	84054.0i	−0.527991	−	0.362442i
$141$	11390.0	+	14282.6i	0.0482475	+	0.0605005i
$142$	3171.11	−	3976.44i	0.0131974	−	0.0165491i
$143$	447164.	+	215343.i	1.82863	+	0.880624i
$144$	92012.2	−	115380.i	0.369777	−	0.463685i
$145$	51252.4	−	224551.i	0.202439	−	0.886943i
$146$	−224321.			−0.870939
$147$	−65994.4	−	171345.i	−0.251891	−	0.654001i
$148$	416652.			1.56358
$149$	18852.4	−	82597.6i	0.0695665	−	0.304791i	−0.928160	−	0.372181i	$-0.878610\pi$
$149$	18852.4	−	82597.6i	0.0695665	−	0.304791i	0.997727	+	0.0673901i	$0.0214672\pi$
$150$	55395.9	−	69464.3i	0.201025	−	0.252077i
$151$	−222217.	−	107014.i	−0.793113	−	0.381943i	−0.00696060	−	0.999976i	$-0.502216\pi$
$151$	−222217.	−	107014.i	−0.793113	−	0.381943i	−0.786152	+	0.618033i	$0.787930\pi$
$152$	−34245.1	+	42942.0i	−0.120224	+	0.150756i
$153$	93788.4	+	117607.i	0.323907	+	0.406167i
$154$	−45266.4	−	630938.i	−0.153806	−	2.14380i
$155$	203579.	−	255279.i	0.680617	−	0.853467i
$156$	47354.4	+	207473.i	0.155793	+	0.682574i
$157$	313060.	+	392565.i	1.01363	+	1.27105i	0.962192	+	0.272372i	$0.0878082\pi$
$157$	313060.	+	392565.i	1.01363	+	1.27105i	0.0514353	+	0.998676i	$0.483620\pi$
$158$	−29667.6	+	129982.i	−0.0945452	+	0.414229i
$159$	129877.	−	62545.7i	0.407419	−	0.196203i
$160$	−74680.9	+	327198.i	−0.230627	+	1.01044i
$161$	37814.8	+	527076.i	0.114973	+	1.60254i
$162$	23100.6	+	101210.i	0.0691570	+	0.302996i
$163$	−60607.1	−	75998.8i	−0.178671	−	0.224046i	0.684429	−	0.729080i	$-0.260052\pi$
$163$	−60607.1	−	75998.8i	−0.178671	−	0.224046i	−0.863100	+	0.505033i	$0.831480\pi$
$164$	−314720.	+	151561.i	−0.913722	+	0.440025i
$165$	−318893.			−0.911873
$166$	−574300.			−1.61759
$167$	−85488.4	+	41169.0i	−0.237201	+	0.114230i	−0.548708	−	0.836014i	$-0.684880\pi$
$167$	−85488.4	+	41169.0i	−0.237201	+	0.114230i	0.311508	+	0.950244i	$0.399166\pi$
$168$	−52821.0	+	48699.2i	−0.144389	+	0.133122i
$169$	−199618.	−	96130.9i	−0.537629	−	0.258908i
$170$	−375719.	−	180937.i	−0.997105	−	0.480180i
$171$	29791.3	+	130524.i	0.0779111	+	0.341351i
$172$	−60623.2	−	265607.i	−0.156249	−	0.684572i
$173$	296870.	+	142965.i	0.754137	+	0.363173i	0.771126	−	0.636682i	$-0.219694\pi$
$173$	296870.	+	142965.i	0.754137	+	0.363173i	−0.0169890	+	0.999856i	$0.505408\pi$
$174$	378966.	+	182501.i	0.948916	+	0.456974i
$175$	102403.	−	94412.7i	0.252767	−	0.233043i
$176$	−693152.	+	333805.i	−1.68674	+	0.812289i
$177$	−138597.			−0.332522
$178$	−301765.			−0.713869
$179$	−283860.	+	136700.i	−0.662174	+	0.318886i	−0.734613	−	0.678487i	$-0.762636\pi$
$179$	−283860.	+	136700.i	−0.662174	+	0.318886i	0.0724386	+	0.997373i	$0.476922\pi$
$180$	88318.4	+	110748.i	0.203175	+	0.254773i
$181$	86847.1	+	380502.i	0.197042	+	0.863298i	0.972686	+	0.232127i	$0.0745683\pi$
$181$	86847.1	+	380502.i	0.197042	+	0.863298i	−0.775644	+	0.631171i	$0.782575\pi$
$182$	54071.1	+	753661.i	0.121000	+	1.68654i
$183$	−55484.5	+	243093.i	−0.122474	+	0.536594i
$184$	186288.	−	89711.5i	0.405639	−	0.195346i
$185$	165955.	−	727094.i	0.356500	−	1.56193i
$186$	371775.	+	466191.i	0.787948	+	0.988055i
$187$	−174499.	−	764531.i	−0.364913	−	1.59879i
$188$	−26375.6	+	33074.0i	−0.0544263	+	0.0682484i
$189$	37160.8	+	517959.i	0.0756711	+	1.05473i
$190$	−231410.	−	290179.i	−0.465048	−	0.583151i
$191$	408613.	−	512384.i	0.810454	−	1.01628i	−0.188958	−	0.981985i	$-0.560511\pi$
$191$	408613.	−	512384.i	0.810454	−	1.01628i	0.999412	−	0.0342919i	$-0.0109176\pi$
$192$	−176265.	−	84884.6i	−0.345074	−	0.166179i
$193$	141391.	−	177299.i	0.273231	−	0.342620i	−0.626217	−	0.779649i	$-0.715398\pi$
$193$	141391.	−	177299.i	0.273231	−	0.342620i	0.899448	+	0.437028i	$0.143969\pi$
$194$	−129420.	+	567028.i	−0.246887	+	1.08168i
$195$	380920.			0.717376
$196$	352828.	−	237283.i	0.656029	−	0.441191i
$197$	44274.1			0.0812801			0.0406401	−	0.999174i	$-0.487060\pi$
$197$	44274.1			0.0812801			0.0406401	+	0.999174i	$0.487060\pi$
$198$	−134248.	+	588180.i	−0.243358	+	1.06622i
$199$	−290439.	+	364199.i	−0.519904	+	0.651938i	−0.970588	−	0.240745i	$-0.922608\pi$
$199$	−290439.	+	364199.i	−0.519904	+	0.651938i	0.450685	+	0.892683i	$0.351180\pi$
$200$	−49102.1	−	23646.3i	−0.0868011	−	0.0418012i
$201$	253635.	−	318048.i	0.442811	−	0.555268i
$202$	−386353.	−	484472.i	−0.666202	−	0.835391i
$203$	543635.	+	373180.i	0.925907	+	0.635592i
$204$	209645.	−	262886.i	0.352702	−	0.442275i
$205$	139133.	+	609580.i	0.231230	+	1.01309i
$206$	−690026.	−	865265.i	−1.13291	−	1.42063i
$207$	112149.	−	491356.i	0.181915	−	0.797023i
$208$	827976.	−	398732.i	1.32697	−	0.639033i
$209$	155307.	−	680446.i	0.245939	−	1.07753i
$210$	−241406.	−	421214.i	−0.377746	−	0.659104i
$211$	267426.	+	1.17167e6i	0.413521	+	1.81175i	0.567136	+	0.823624i	$0.308051\pi$
$211$	267426.	+	1.17167e6i	0.413521	+	1.81175i	−0.153615	+	0.988131i	$0.549091\pi$
$212$	208129.	+	260986.i	0.318049	+	0.398821i
$213$	6613.58	−	3184.93i	0.00998821	−	0.00481007i
$214$	−664998.			−0.992627
$215$	−487654.			−0.719475
$216$	183066.	−	88159.8i	0.266976	−	0.128569i
$217$	464810.	+	811017.i	0.670080	+	1.16918i
$218$	80781.1	+	38902.1i	0.115125	+	0.0554411i
$219$	−291692.	−	140472.i	−0.410974	−	0.197915i
$220$	−164322.	−	719941.i	−0.228896	−	1.00286i
$221$	208441.	+	913238.i	0.287079	+	1.25778i
$222$	1.22709e6	+	590934.i	1.67106	+	0.804742i
$223$	38216.0	+	18403.8i	0.0514615	+	0.0247826i	0.459438	−	0.888210i	$-0.348051\pi$
$223$	38216.0	+	18403.8i	0.0514615	+	0.0247826i	−0.407976	+	0.912993i	$0.633765\pi$
$224$	−792141.	−	543768.i	−1.05483	−	0.724092i
$225$	−119688.	+	57638.6i	−0.157613	+	0.0759026i
$226$	763793.			0.994729
$227$	−245152.			−0.315770			−0.157885	−	0.987458i	$-0.550467\pi$
$227$	−245152.			−0.315770			−0.157885	+	0.987458i	$0.550467\pi$
$228$	269627.	−	129845.i	0.343499	−	0.165421i
$229$	−481873.	−	604249.i	−0.607217	−	0.761426i	0.379267	−	0.925287i	$-0.376176\pi$
$229$	−481873.	−	604249.i	−0.607217	−	0.761426i	−0.986483	+	0.163862i	$0.947605\pi$
$230$	310906.	+	1.36217e6i	0.387533	+	1.69789i
$231$	336237.	−	848777.i	0.414587	−	1.04656i
$232$	57412.1	−	251539.i	0.0700299	−	0.306821i
$233$	−553894.	+	266742.i	−0.668401	+	0.321885i	−0.737131	−	0.675750i	$-0.763820\pi$
$233$	−553894.	+	266742.i	−0.668401	+	0.321885i	0.0687294	+	0.997635i	$0.478105\pi$
$234$	160361.	−	702586.i	0.191451	−	0.838803i
$235$	47211.5	+	59201.3i	0.0557671	+	0.0699297i
$236$	−71417.6	−	312901.i	−0.0834690	−	0.365702i
$237$	−119974.	+	150442.i	−0.138744	+	0.173980i
$238$	877742.	−	809250.i	1.00444	−	0.926063i
$239$	−460870.	−	577912.i	−0.521895	−	0.654436i	0.449115	−	0.893474i	$-0.351739\pi$
$239$	−460870.	−	577912.i	−0.521895	−	0.654436i	−0.971010	+	0.239038i	$0.923168\pi$
$240$	−368150.	+	461645.i	−0.412569	+	0.517345i
$241$	−1.43408e6	−	690616.i	−1.59049	−	0.765938i	−0.591308	−	0.806446i	$-0.701388\pi$
$241$	−1.43408e6	−	690616.i	−1.59049	−	0.765938i	−0.999179	+	0.0405074i	$0.987103\pi$
$242$	1.20087e6	−	1.50585e6i	1.31813	−	1.65289i
$243$	183252.	−	802878.i	0.199082	−	0.872236i
$244$	−577406.			−0.620878
$245$	−273547.	−	710226.i	−0.291150	−	0.755930i
$246$	−1.14184e6			−1.20301
$247$	−185516.	+	812799.i	−0.193481	+	0.847697i
$248$	228046.	−	285960.i	0.235447	−	0.295241i
$249$	−746782.	−	359631.i	−0.763300	−	0.367586i
$250$	897490.	−	1.12542e6i	0.908196	−	1.13884i
$251$	288249.	+	361453.i	0.288791	+	0.362132i	0.904971	−	0.425473i	$-0.139892\pi$
$251$	288249.	+	361453.i	0.288791	+	0.362132i	−0.616180	+	0.787605i	$0.711321\pi$
$252$	−387893.	+	118300.i	−0.384778	+	0.117350i
$253$	−1.63816e6	+	2.05419e6i	−1.60900	+	2.01762i
$254$	−56528.9	−	247669.i	−0.0549777	−	0.240873i
$255$	−375256.	−	470557.i	−0.361391	−	0.453170i
$256$	−298664.	+	1.30853e6i	−0.284828	+	1.24791i
$257$	−822476.	+	396084.i	−0.776767	+	0.374071i	−0.779884	−	0.625924i	$-0.784722\pi$
$257$	−822476.	+	396084.i	−0.776767	+	0.374071i	0.00311741	+	0.999995i	$0.499008\pi$
$258$	198167.	−	868225.i	0.185345	−	0.812051i
$259$	1.76028e6	+	1.20835e6i	1.63055	+	1.11929i
$260$	196284.	+	859976.i	0.180074	+	0.788956i
$261$	−392113.	−	491694.i	−0.356295	−	0.446780i
$262$	1.51521e6	−	729687.i	1.36370	−	0.656724i
$263$	−235249.			−0.209719			−0.104860	−	0.994487i	$-0.533439\pi$
$263$	−235249.			−0.209719			−0.104860	+	0.994487i	$0.533439\pi$
$264$	−357219.			−0.315445
$265$	538342.	−	259252.i	0.470916	−	0.226781i
$266$	1.01635e6	−	309968.i	0.880720	−	0.268604i
$267$	−392395.	−	188968.i	−0.336857	−	0.162222i
$268$	848730.	+	408727.i	0.721826	+	0.347613i
$269$	285296.	+	1.24996e6i	0.240389	+	1.05321i	0.940664	+	0.339341i	$0.110204\pi$
$269$	285296.	+	1.24996e6i	0.240389	+	1.05321i	−0.700274	+	0.713874i	$0.746939\pi$
$270$	305528.	+	1.33861e6i	0.255059	+	1.11749i
$271$	791346.	+	381092.i	0.654550	+	0.315215i	0.731521	−	0.681819i	$-0.238811\pi$
$271$	791346.	+	381092.i	0.654550	+	0.315215i	−0.0769711	+	0.997033i	$0.524525\pi$
$272$	−1.30823e6	−	630009.i	−1.07216	−	0.516327i
$273$	−401638.	+	1.01387e6i	−0.326158	+	0.823334i
$274$	−343665.	+	165500.i	−0.276540	+	0.133175i
$275$	692536.			0.552218
$276$	−1.12657e6			−0.890197
$277$	747.651	−	360.050i	0.000585463	−	0.000281944i	−0.433591	−	0.901110i	$-0.642754\pi$
$277$	747.651	−	360.050i	0.000585463	−	0.000281944i	0.434176	+	0.900828i	$0.357039\pi$
$278$	765691.	+	960147.i	0.594213	+	0.745119i
$279$	−198387.	−	869189.i	−0.152582	−	0.668503i
$280$	−218943.	+	201858.i	−0.166892	+	0.153869i
$281$	290351.	−	1.27211e6i	0.219360	−	0.961080i	−0.738592	−	0.674153i	$-0.764509\pi$
$281$	290351.	−	1.27211e6i	0.219360	−	0.961080i	0.957952	−	0.286928i	$-0.0926339\pi$
$282$	−124588.	+	59998.3i	−0.0932938	+	0.0449279i
$283$	−13522.5	+	59246.0i	−0.0100367	+	0.0439737i	−0.979698	−	0.200477i	$-0.935751\pi$
$283$	−13522.5	+	59246.0i	−0.0100367	+	0.0439737i	0.969662	+	0.244451i	$0.0786078\pi$
$284$	10598.3	+	13289.9i	0.00779724	+	0.00977742i
$285$	−119198.	−	522240.i	−0.0869273	−	0.380854i
$286$	−2.34239e6	+	2.93726e6i	−1.69334	+	2.12338i
$287$	−1.76918e6	−	272414.i	−1.26785	−	0.195220i
$288$	571356.	+	716458.i	0.405906	+	0.508990i
$289$	37530.7	−	47062.0i	0.0264327	−	0.0331456i
$290$	1.57082e6	+	756465.i	1.09681	+	0.528195i
$291$	−523368.	+	656282.i	−0.362305	+	0.454316i
$292$	166827.	−	730917.i	0.114501	−	0.501662i
$293$	2.44911e6			1.66663			0.833316	−	0.552797i	$-0.186440\pi$
$293$	2.44911e6			1.66663			0.833316	+	0.552797i	$0.186440\pi$
$294$	1.37565e6	−	198413.i	0.928199	−	0.133876i
$295$	−574485.			−0.384347
$296$	185900.	−	814480.i	0.123325	−	0.540320i
$297$	−1.60982e6	+	2.01866e6i	−1.05898	+	1.32792i
$298$	577800.	+	278254.i	0.376909	+	0.181510i
$299$	1.95679e6	−	2.45374e6i	1.26581	−	1.58727i
$300$	185141.	+	232160.i	0.118768	+	0.148931i
$301$	514178.	−	1.29796e6i	0.327113	−	0.825743i
$302$	1.16404e6	−	1.45966e6i	0.734433	−	0.920949i
$303$	−199009.	−	871913.i	−0.124527	−	0.545590i
$304$	−805752.	−	1.01038e6i	−0.500055	−	0.627049i
$305$	−229983.	+	1.00762e6i	−0.141562	+	0.620224i
$306$	−1.02589e6	+	494044.i	−0.626323	+	0.301621i
$307$	−439541.	+	1.92576e6i	−0.266167	+	1.16615i	0.648266	+	0.761414i	$0.275495\pi$
$307$	−439541.	+	1.92576e6i	−0.266167	+	1.16615i	−0.914433	+	0.404738i	$0.867363\pi$
$308$	2.08948e6	+	321733.i	1.25505	+	0.193250i
$309$	−355428.	−	1.55723e6i	−0.211766	−	0.927807i
$310$	1.54101e6	+	1.93236e6i	0.910752	+	1.14205i
$311$	1.69459e6	−	816073.i	0.993492	−	0.478441i	0.134767	−	0.990877i	$-0.456971\pi$
$311$	1.69459e6	−	816073.i	0.993492	−	0.478441i	0.858725	+	0.512437i	$0.171257\pi$
$312$	426700.			0.248163
$313$	−2.85673e6			−1.64819			−0.824097	−	0.566449i	$-0.808317\pi$
$313$	−2.85673e6			−1.64819			−0.824097	+	0.566449i	$0.808317\pi$
$314$	−3.42437e6	+	1.64909e6i	−1.96000	+	0.943886i
$315$	51944.9	+	724026.i	0.0294962	+	0.411129i
$316$	−401464.	−	193335.i	−0.226167	−	0.108916i
$317$	1.46176e6	+	703945.i	0.817010	+	0.393451i	0.795227	−	0.606312i	$-0.207352\pi$
$317$	1.46176e6	+	703945.i	0.817010	+	0.393451i	0.0217825	+	0.999763i	$0.493066\pi$
$318$	242810.	+	1.06382e6i	0.134648	+	0.589931i
$319$	729551.	+	3.19637e6i	0.401402	+	1.75866i
$320$	−730617.	−	351847.i	−0.398855	−	0.192078i
$321$	−864721.	−	416428.i	−0.468396	−	0.225568i
$322$	−3.95341e6	−	608736.i	−2.12487	−	0.327182i
$323$	1.18682e6	−	571543.i	0.632964	−	0.304820i
$324$	−346959.			−0.183618
$325$	−827240.			−0.434433
$326$	662943.	−	319256.i	0.345487	−	0.166378i
$327$	80681.7	+	101172.i	0.0417259	+	0.0523226i
$328$	155854.	+	682842.i	0.0799897	+	0.350458i
$329$	−207352.	+	63238.6i	−0.105613	+	0.0322101i
$330$	537140.	−	2.35336e6i	0.271521	−	1.18961i
$331$	1.05848e6	−	509736.i	0.531021	−	0.255726i	−0.149105	−	0.988821i	$-0.547639\pi$
$331$	1.05848e6	−	509736.i	0.531021	−	0.255726i	0.680126	+	0.733095i	$0.261925\pi$
$332$	427106.	−	1.87127e6i	0.212662	−	0.931733i
$333$	−1.26966e6	−	1.59210e6i	−0.627445	−	0.786792i
$334$	−159823.	−	700232.i	−0.0783925	−	0.343460i
$335$	1.05132e6	−	1.31831e6i	0.511825	−	0.641808i
$336$	−840560.	−	1.46664e6i	−0.406182	−	0.708719i
$337$	36750.8	+	46084.1i	0.0176276	+	0.0221043i	0.790567	−	0.612375i	$-0.209786\pi$
$337$	36750.8	+	46084.1i	0.0176276	+	0.0221043i	−0.772940	+	0.634480i	$0.781214\pi$
$338$	1.04566e6	−	1.31122e6i	0.497851	−	0.624286i
$339$	993187.	+	478294.i	0.469388	+	0.226045i
$340$	868977.	−	1.08966e6i	0.407672	−	0.511205i
$341$	−1.03423e6	+	4.53124e6i	−0.481647	+	2.11023i
$342$	−1.01342e6			−0.468517
$343$	2.17879e6	+	20773.0i	0.999955	+	0.00953376i
$344$	−546263.			−0.248889
$345$	−448718.	+	1.96596e6i	−0.202967	+	0.889258i
$346$	−1.55510e6	+	1.95003e6i	−0.698341	+	0.875691i
$347$	−2.77128e6	−	1.33458e6i	−1.23554	−	0.595004i	−0.301941	−	0.953327i	$-0.597635\pi$
$347$	−2.77128e6	−	1.33458e6i	−1.23554	−	0.595004i	−0.933598	+	0.358322i	$0.883349\pi$
$348$	−876488.	+	1.09908e6i	−0.387970	+	0.486499i
$349$	−1.58397e6	−	1.98624e6i	−0.696121	−	0.872908i	0.300606	−	0.953748i	$-0.402811\pi$
$349$	−1.58397e6	−	1.98624e6i	−0.696121	−	0.872908i	−0.996727	+	0.0808405i	$0.974240\pi$
$350$	524260.	+	914746.i	0.228758	+	0.399145i
$351$	1.92295e6	−	2.41130e6i	0.833105	−	1.04468i
$352$	−1.06304e6	−	4.65750e6i	−0.457293	−	2.00353i
$353$	753466.	+	944817.i	0.321830	+	0.403562i	0.916259	−	0.400586i	$-0.131193\pi$
$353$	753466.	+	944817.i	0.321830	+	0.403562i	−0.594429	+	0.804148i	$0.702622\pi$
$354$	233452.	−	1.02282e6i	0.0990123	−	0.433801i
$355$	27413.3	−	13201.6i	0.0115449	−	0.00555974i
$356$	224422.	−	983257.i	0.0938513	−	0.411189i
$357$	1.64812e6	−	502647.i	0.684412	−	0.208734i
$358$	−530687.	−	2.32509e6i	−0.218842	−	0.958809i
$359$	392029.	+	491589.i	0.160539	+	0.201310i	0.855595	−	0.517646i	$-0.173192\pi$
$359$	392029.	+	491589.i	0.160539	+	0.201310i	−0.695055	+	0.718956i	$0.744620\pi$
$360$	255897.	−	123234.i	0.104066	−	0.0501156i
$361$	−1.30370e6			−0.526515
$362$	−2.95432e6			−1.18491
$363$	2.50452e6	−	1.20611e6i	0.997602	−	0.480420i
$364$	−2.49590e6	−	384313.i	−0.987358	−	0.152031i
$365$	−1.20907e6	−	582255.i	−0.475026	−	0.228761i
$366$	−1.70052e6	−	818929.i	−0.663560	−	0.319554i
$367$	−192845.	−	844909.i	−0.0747383	−	0.327450i	0.923713	−	0.383086i	$-0.125139\pi$
$367$	−192845.	−	844909.i	−0.0747383	−	0.327450i	−0.998451	+	0.0556357i	$0.982281\pi$
$368$	1.08255e6	+	4.74297e6i	0.416705	+	1.82571i
$369$	1.53818e6	+	740748.i	0.588086	+	0.283208i
$370$	5.08628e6	+	2.44942e6i	1.93151	+	0.930164i
$371$	122412.	+	1.70623e6i	0.0461733	+	0.643579i
$372$	−1.79550e6	+	864668.i	−0.672711	+	0.323960i
$373$	3.07088e6			1.14285			0.571427	−	0.820653i	$-0.306390\pi$
$373$	3.07088e6			1.14285			0.571427	+	0.820653i	$0.306390\pi$
$374$	5.93601e6			2.19440
$375$	1.87178e6	−	901403.i	0.687349	−	0.331010i
$376$	52885.6	+	66316.4i	0.0192916	+	0.0241909i
$377$	−871455.	−	3.81809e6i	−0.315785	−	1.38354i
$378$	−3.88503e6	−	598207.i	−1.39851	−	0.215339i
$379$	−414961.	+	1.81806e6i	−0.148392	+	0.650147i	0.844941	+	0.534860i	$0.179636\pi$
$379$	−414961.	+	1.81806e6i	−0.148392	+	0.650147i	−0.993332	+	0.115286i	$0.963221\pi$
$380$	1.11760e6	−	538209.i	0.397035	−	0.191202i
$381$	81586.1	−	357452.i	0.0287941	−	0.126155i
$382$	3.09303e6	+	3.87854e6i	1.08449	+	1.35991i
$383$	−601153.	−	2.63382e6i	−0.209406	−	0.917466i	−0.964964	−	0.262384i	$-0.915491\pi$
$383$	−601153.	−	2.63382e6i	−0.209406	−	0.917466i	0.755558	−	0.655082i	$-0.227366\pi$
$384$	−692118.	+	867889.i	−0.239526	+	0.300356i
$385$	1.39370e6	−	3.51818e6i	0.479202	−	1.20967i
$386$	1.07027e6	+	1.34208e6i	0.365617	+	0.458470i
$387$	−830196.	+	1.04103e6i	−0.281775	+	0.353335i
$388$	−1.75133e6	−	843395.i	−0.590593	−	0.284415i
$389$	1.89729e6	−	2.37912e6i	0.635710	−	0.797155i	−0.354750	−	0.934961i	$-0.615434\pi$
$389$	1.89729e6	−	2.37912e6i	0.635710	−	0.797155i	0.990459	+	0.137807i	$0.0440053\pi$
$390$	−641618.	+	2.81111e6i	−0.213607	+	0.935873i
$391$	−4.95885e6			−1.64036
$392$	−306423.	−	795584.i	−0.100718	−	0.261500i
$393$	2.42722e6			0.792733
$394$	−74575.0	+	326734.i	−0.0242021	+	0.106036i
$395$	−497291.	+	623583.i	−0.160368	+	0.201095i
$396$	−1.81666e6	−	874857.i	−0.582151	−	0.280349i
$397$	1.30376e6	−	1.63486e6i	0.415166	−	0.520601i	−0.529644	−	0.848220i	$-0.677675\pi$
$397$	1.30376e6	−	1.63486e6i	0.415166	−	0.520601i	0.944810	+	0.327618i	$0.106246\pi$
$398$	−2.19851e6	−	2.75684e6i	−0.695697	−	0.872377i
$399$	1.51570e6	+	233383.i	0.476628	+	0.0733900i
$400$	799508.	−	1.00255e6i	0.249846	−	0.313297i
$401$	458181.	+	2.00742e6i	0.142291	+	0.623416i	0.994900	+	0.100867i	$0.0321617\pi$
$401$	458181.	+	2.00742e6i	0.142291	+	0.623416i	−0.852609	+	0.522549i	$0.824981\pi$
$402$	1.91991e6	+	2.40749e6i	0.592538	+	0.743019i
$403$	1.23539e6	−	5.41260e6i	0.378915	−	1.66013i
$404$	1.86591e6	−	898575.i	0.568771	−	0.273906i
$405$	−138195.	+	605474.i	−0.0418655	+	0.183425i
$406$	−3.66969e6	+	3.38334e6i	−1.10488	+	1.01866i
$407$	2.36228e6	+	1.03498e7i	0.706878	+	3.09704i
$408$	−420356.	−	527110.i	−0.125016	−	0.156766i
$409$	−517664.	+	249294.i	−0.153017	+	0.0736891i	−0.508825	−	0.860870i	$-0.669920\pi$
$409$	−517664.	+	249294.i	−0.153017	+	0.0736891i	0.355808	+	0.934559i	$0.384206\pi$
$410$	−4.73294e6			−1.39050
$411$	−550517.			−0.160756
$412$	3.33251e6	−	1.60485e6i	0.967227	−	0.465792i
$413$	605732.	−	1.52907e6i	0.174745	−	0.441116i
$414$	3.43721e6	+	1.65527e6i	0.985611	+	0.474645i
$415$	−3.09541e6	−	1.49067e6i	−0.882264	−	0.424876i
$416$	1.26981e6	+	5.56342e6i	0.359755	+	1.57619i
$417$	394404.	+	1.72799e6i	0.111071	+	0.486634i
$418$	4.75996e6	+	2.29228e6i	1.33249	+	0.641692i
$419$	3.25249e6	+	1.56631e6i	0.905066	+	0.435857i	0.827716	−	0.561147i	$-0.189640\pi$
$419$	3.25249e6	+	1.56631e6i	0.905066	+	0.435857i	0.0773500	+	0.997004i	$0.475354\pi$
$420$	1.55200e6	−	473331.i	0.429306	−	0.130931i
$421$	−187591.	+	90339.3i	−0.0515831	+	0.0248411i	−0.459497	−	0.888179i	$-0.651970\pi$
$421$	−187591.	+	90339.3i	−0.0515831	+	0.0248411i	0.407914	+	0.913020i	$0.366256\pi$
$422$	−9.09715e6			−2.48671
$423$	206756.			0.0561832
$424$	603043.	−	290410.i	0.162905	−	0.0784507i
$425$	814941.	+	1.02190e6i	0.218854	+	0.274434i
$426$	12364.3	+	54171.6i	0.00330101	+	0.0144626i
$427$	−2.43944e6	−	1.67456e6i	−0.647470	−	0.444458i
$428$	494558.	−	2.16680e6i	0.130499	−	0.571754i
$429$	−4.88523e6	+	2.35260e6i	−1.28157	+	0.617171i
$430$	821401.	−	3.59879e6i	0.214232	−	0.938611i
$431$	−2.18532e6	−	2.74030e6i	−0.566658	−	0.710567i	0.413115	−	0.910679i	$-0.364441\pi$
$431$	−2.18532e6	−	2.74030e6i	−0.566658	−	0.710567i	−0.979773	+	0.200112i	$0.935869\pi$
$432$	1.06383e6	+	4.66093e6i	0.274259	+	1.20161i
$433$	−291945.	+	366087.i	−0.0748310	+	0.0938351i	−0.817838	−	0.575449i	$-0.804827\pi$
$433$	−291945.	+	366087.i	−0.0748310	+	0.0938351i	0.743007	+	0.669284i	$0.233399\pi$
$434$	−6.76807e6	+	2.06414e6i	−1.72481	+	0.526035i
$435$	1.56888e6	+	1.96732e6i	0.397528	+	0.498484i
$436$	−186834.	+	234282.i	−0.0470694	+	0.0590232i
$437$	−3.97640e6	−	1.91493e6i	−0.996062	−	0.479678i
$438$	1.52798e6	−	1.91602e6i	0.380568	−	0.477217i
$439$	−1.43195e6	+	6.27380e6i	−0.354624	+	1.55371i	0.411740	+	0.911301i	$0.364921\pi$
$439$	−1.43195e6	+	6.27380e6i	−0.354624	+	1.55371i	−0.766364	+	0.642407i	$0.777936\pi$
$440$	−1.48067e6			−0.364609
$441$	−1.98187e6	−	625147.i	−0.485264	−	0.153068i
$442$	−7.09062e6			−1.72635
$443$	1.09541e6	−	4.79932e6i	0.265197	−	1.16190i	−0.650331	−	0.759651i	$-0.725370\pi$
$443$	1.09541e6	−	4.79932e6i	0.265197	−	1.16190i	0.915528	−	0.402253i	$-0.131773\pi$
$444$	−2.83806e6	+	3.55881e6i	−0.683225	+	0.856737i
$445$	−1.62648e6	−	783271.i	−0.389358	−	0.187505i
$446$	−200187.	+	251027.i	−0.0476540	+	0.0597563i
$447$	577088.	+	723646.i	0.136607	+	0.171300i
$448$	1.70685e6	−	1.57366e6i	0.401790	−	0.370437i
$449$	−95273.5	+	119469.i	−0.0223026	+	0.0279666i	−0.792858	−	0.609407i	$-0.791408\pi$
$449$	−95273.5	+	119469.i	−0.0223026	+	0.0279666i	0.770555	+	0.637373i	$0.219979\pi$
$450$	−223760.	−	980358.i	−0.0520897	−	0.228220i
$451$	−5.54919e6	−	6.95846e6i	−1.28466	−	1.61091i
$452$	−568032.	+	2.48871e6i	−0.130775	+	0.572965i
$453$	2.42770e6	−	1.16912e6i	0.555840	−	0.267678i
$454$	412932.	−	1.80917e6i	0.0940240	−	0.411946i
$455$	−1.66479e6	+	4.20250e6i	−0.376991	+	0.951653i
$456$	−133524.	−	585005.i	−0.0300709	−	0.131749i
$457$	3.81535e6	+	4.78429e6i	0.854562	+	1.07159i	0.996654	+	0.0817330i	$0.0260455\pi$
$457$	3.81535e6	+	4.78429e6i	0.854562	+	1.07159i	−0.142093	+	0.989853i	$0.545383\pi$
$458$	5.27091e6	−	2.53833e6i	1.17414	−	0.565438i
$459$	−4.87308e6			−1.07962
$460$	−4.66964e6			−1.02894
$461$	6.83710e6	−	3.29258e6i	1.49837	−	0.721578i	0.508175	−	0.861254i	$-0.330320\pi$
$461$	6.83710e6	−	3.29258e6i	1.49837	−	0.721578i	0.990197	+	0.139675i	$0.0446058\pi$
$462$	5.69745e6	+	3.91104e6i	1.24187	+	0.852486i
$463$	2.64758e6	+	1.27501e6i	0.573979	+	0.276414i	0.698273	−	0.715832i	$-0.253952\pi$
$463$	2.64758e6	+	1.27501e6i	0.573979	+	0.276414i	−0.124294	+	0.992245i	$0.539666\pi$
$464$	5.46947e6	+	2.63396e6i	1.17937	+	0.567955i
$465$	793764.	+	3.47771e6i	0.170239	+	0.745866i
$466$	−1.03552e6	−	4.53693e6i	−0.220900	−	0.967826i
$467$	995722.	+	479514.i	0.211274	+	0.101744i	0.536528	−	0.843882i	$-0.319736\pi$
$467$	995722.	+	479514.i	0.211274	+	0.101744i	−0.325254	+	0.945627i	$0.605450\pi$
$468$	2.17001e6	+	1.04502e6i	0.457981	+	0.220552i
$469$	2.40037e6	+	4.18824e6i	0.503901	+	0.879223i
$470$	−516417.	+	248693.i	−0.107834	+	0.0519301i
$471$	−5.48550e6			−1.13937
$472$	−643529.			−0.132958
$473$	6.25408e6	−	3.01181e6i	1.28532	−	0.618977i
$474$	−908152.	−	1.13879e6i	−0.185657	−	0.232807i
$475$	258861.	+	1.13414e6i	0.0526420	+	0.230640i
$476$	1.98405e6	+	3.46183e6i	0.401361	+	0.700307i
$477$	363043.	−	1.59060e6i	0.0730571	−	0.320084i
$478$	5.04116e6	−	2.42770e6i	1.00916	−	0.485987i
$479$	−81410.3	+	356682.i	−0.0162122	+	0.0710301i	−0.982387	−	0.186858i	$-0.940170\pi$
$479$	−81410.3	+	356682.i	−0.0162122	+	0.0710301i	0.966175	+	0.257888i	$0.0830267\pi$
$480$	−2.28605e6	−	2.86662e6i	−0.452879	−	0.567893i
$481$	−2.82176e6	−	1.23629e7i	−0.556105	−	2.43646i
$482$	7.51216e6	−	9.41995e6i	1.47281	−	1.84685i
$483$	−4.75956e6	−	3.26722e6i	−0.928323	−	0.637251i
$484$	4.01350e6	+	5.03277e6i	0.778772	+	0.976549i
$485$	−2.16936e6	+	2.72029e6i	−0.418772	+	0.525123i
$486$	5.61642e6	+	2.70472e6i	1.07862	+	0.519436i
$487$	2.96479e6	−	3.71772e6i	0.566462	−	0.710321i	−0.413275	−	0.910606i	$-0.635615\pi$
$487$	2.96479e6	−	3.71772e6i	0.566462	−	0.710321i	0.979738	+	0.200285i	$0.0641867\pi$
$488$	−257624.	+	1.12872e6i	−0.0489707	+	0.214555i
$489$	1.06197e6			0.200835
$490$	5.70209e6	−	822421.i	1.07286	−	0.154741i
$491$	1.80332e6			0.337574			0.168787	−	0.985653i	$-0.446015\pi$
$491$	1.80332e6			0.337574			0.168787	+	0.985653i	$0.446015\pi$
$492$	849186.	−	3.72053e6i	0.158158	−	0.692933i
$493$	−3.85806e6	+	4.83785e6i	−0.714910	+	0.896469i
$494$	−5.68581e6	−	2.73814e6i	−1.04828	−	0.504823i
$495$	−2.25028e6	+	2.82177e6i	−0.412785	+	0.517616i
$496$	5.36568e6	+	6.72834e6i	0.979310	+	1.22802i
$497$	6233.45	+	86883.9i	0.00113198	+	0.0157779i
$498$	3.91188e6	−	4.90535e6i	0.706826	−	0.886332i
$499$	1.08666e6	+	4.76096e6i	0.195363	+	0.855940i	0.973653	+	0.228035i	$0.0732302\pi$
$499$	1.08666e6	+	4.76096e6i	0.195363	+	0.855940i	−0.778290	+	0.627905i	$0.783913\pi$
$500$	2.99954e6	+	3.76131e6i	0.536575	+	0.672843i
$501$	230667.	−	1.01062e6i	0.0410574	−	0.179884i
$502$	−3.15297e6	+	1.51839e6i	−0.558420	+	0.268921i
$503$	332265.	−	1.45575e6i	0.0585551	−	0.256547i	−0.937175	−	0.348860i	$-0.886569\pi$
$503$	332265.	−	1.45575e6i	0.0585551	−	0.256547i	0.995730	+	0.0923131i	$0.0294261\pi$
$504$	58187.9	+	811043.i	0.0102037	+	0.142222i
$505$	−824891.	−	3.61408e6i	−0.143935	−	0.630623i
$506$	−1.24002e7	−	1.55494e7i	−2.15304	−	2.69983i
$507$	2.18081e6	−	1.05022e6i	0.376788	−	0.181452i
$508$	849034.			0.145971
$509$	8.19665e6			1.40230			0.701152	−	0.713012i	$-0.252670\pi$
$509$	8.19665e6			1.40230			0.701152	+	0.713012i	$0.252670\pi$
$510$	4.10469e6	−	1.97672e6i	0.698804	−	0.336526i
$511$	2.82458e6	−	2.60417e6i	0.478522	−	0.441182i
$512$	−6.22415e6	−	2.99739e6i	−1.04931	−	0.505323i
$513$	−3.90762e6	−	1.88181e6i	−0.655570	−	0.315706i
$514$	−1.53765e6	−	6.73687e6i	−0.256714	−	1.12474i
$515$	−1.47325e6	−	6.45474e6i	−0.244770	−	1.07241i
$516$	2.68161e6	+	1.29139e6i	0.443375	+	0.213518i
$517$	−971113.	−	467663.i	−0.159788	−	0.0769497i
$518$	−1.18824e7	+	1.09552e7i	−1.94572	+	1.79389i
$519$	−3.24327e6	+	1.56188e6i	−0.528524	+	0.254524i
$520$	1.76867e6			0.286840
$521$	−9.16660e6			−1.47950			−0.739749	−	0.672883i	$-0.765056\pi$
$521$	−9.16660e6			−1.47950			−0.739749	+	0.672883i	$0.765056\pi$
$522$	4.28908e6	−	2.06551e6i	0.688951	−	0.331781i
$523$	−5.04043e6	−	6.32050e6i	−0.805775	−	1.01041i	−0.999569	−	0.0293672i	$-0.990651\pi$
$523$	−5.04043e6	−	6.32050e6i	−0.805775	−	1.01041i	0.193794	−	0.981042i	$-0.437921\pi$
$524$	1.25072e6	+	5.47976e6i	0.198990	+	0.871832i
$525$	108892.	+	1.51777e6i	0.0172424	+	0.240330i
$526$	396252.	−	1.73609e6i	0.0624463	−	0.273595i
$527$	−7.90330e6	+	3.80603e6i	−1.23960	+	0.596960i
$528$	1.87028e6	−	8.19425e6i	0.291960	−	1.27916i
$529$	6.34594e6	+	7.95755e6i	0.985954	+	1.23635i
$530$	1.00645e6	+	4.40954e6i	0.155633	+	0.681874i
$531$	−978018.	+	1.22640e6i	−0.150526	+	0.188753i
$532$	254129.	+	3.54214e6i	0.0389292	+	0.542608i
$533$	6.62855e6	+	8.31194e6i	1.01065	+	1.26731i
$534$	2.05549e6	−	2.57751e6i	0.311934	−	0.391153i
$535$	−3.58427e6	−	1.72609e6i	−0.541397	−	0.260723i
$536$	1.17767e6	−	1.47675e6i	0.177056	−	0.222021i
$537$	765921.	−	3.35572e6i	0.114617	−	0.502169i
$538$	−9.70504e6			−1.44558
$539$	7.89462e6	+	7.41907e6i	1.17047	+	1.09996i
$540$	−4.58887e6			−0.677207
$541$	−427713.	+	1.87393e6i	−0.0628288	+	0.275271i	−0.996578	−	0.0826567i	$-0.973659\pi$
$541$	−427713.	+	1.87393e6i	−0.0628288	+	0.275271i	0.933749	+	0.357928i	$0.116517\pi$
$542$	−4.14532e6	+	5.19807e6i	−0.606122	+	0.760053i
$543$	−3.84160e6	−	1.85002e6i	−0.559130	−	0.269263i
$544$	5.62165e6	−	7.04933e6i	0.814454	−	1.02129i
$545$	334426.	+	419356.i	0.0482290	+	0.0604773i
$546$	−6.80565e6	−	4.67177e6i	−0.976986	−	0.670656i
$547$	3.09576e6	−	3.88196e6i	0.442383	−	0.554731i	−0.509786	−	0.860301i	$-0.670276\pi$
$547$	3.09576e6	−	3.88196e6i	0.442383	−	0.554731i	0.952170	+	0.305570i	$0.0988470\pi$
$548$	−283676.	−	1.24286e6i	−0.0403525	−	0.176796i
$549$	1.75952e6	+	2.20637e6i	0.249151	+	0.312426i
$550$	−1.16650e6	+	5.11078e6i	−0.164429	+	0.720411i
$551$	−4.96190e6	+	2.38952e6i	−0.696256	+	0.335299i
$552$	−502647.	+	2.20224e6i	−0.0702127	+	0.307622i
$553$	−1.13541e6	−	1.98111e6i	−0.157885	−	0.275484i
$554$	1397.76	+	6123.98i	0.000193490	+	0.000847733i
$555$	5.08002e6	+	6.37014e6i	0.700056	+	0.877843i
$556$	−3.69794e6	+	1.78083e6i	−0.507309	+	0.244307i
$557$	−5.97202e6			−0.815611			−0.407806	−	0.913069i	$-0.633706\pi$
$557$	−5.97202e6			−0.815611			−0.407806	+	0.913069i	$0.633706\pi$
$558$	6.74860e6			0.917547
$559$	−7.47055e6	+	3.59763e6i	−1.01117	+	0.486953i
$560$	−3.48412e6	−	6.07921e6i	−0.469486	−	0.819176i
$561$	7.71881e6	+	3.71718e6i	1.03548	+	0.498662i
$562$	8.89887e6	+	4.28547e6i	1.18849	+	0.572345i
$563$	2.84087e6	+	1.24467e7i	0.377729	+	1.65494i	0.704401	+	0.709802i	$0.251216\pi$
$563$	2.84087e6	+	1.24467e7i	0.377729	+	1.65494i	−0.326671	+	0.945138i	$0.605927\pi$
$564$	−102840.	−	450572.i	−0.0136133	−	0.0596439i
$565$	4.11676e6	+	1.98253e6i	0.542544	+	0.261275i
$566$	−414447.	−	199587.i	−0.0543786	−	0.0261873i
$567$	−1.46584e6	−	1.00623e6i	−0.191482	−	0.131444i
$568$	30708.0	−	14788.2i	0.00399374	−	0.00192329i
$569$	1.24856e6			0.161669			0.0808347	−	0.996728i	$-0.474241\pi$
$569$	1.24856e6			0.161669			0.0808347	+	0.996728i	$0.474241\pi$
$570$	4.05481e6			0.522737
$571$	−6.59742e6	+	3.17715e6i	−0.846806	+	0.407800i	−0.806391	−	0.591383i	$-0.798582\pi$
$571$	−6.59742e6	+	3.17715e6i	−0.846806	+	0.407800i	−0.0404151	+	0.999183i	$0.512868\pi$
$572$	−7.82861e6	−	9.81677e6i	−1.00045	−	1.25452i
$573$	1.59320e6	+	6.98028e6i	0.202714	+	0.888150i
$574$	4.99036e6	−	1.25974e7i	0.632197	−	1.59588i
$575$	974478.	−	4.26947e6i	0.122914	−	0.538523i
$576$	−1.99494e6	+	960710.i	−0.250537	+	0.120652i
$577$	536102.	−	2.34882e6i	0.0670360	−	0.293704i	−0.930286	−	0.366834i	$-0.880442\pi$
$577$	536102.	−	2.34882e6i	0.0670360	−	0.293704i	0.997322	+	0.0731301i	$0.0232988\pi$
$578$	284092.	+	356240.i	0.0353703	+	0.0443530i
$579$	551292.	+	2.41537e6i	0.0683417	+	0.299424i
$580$	−3.63304e6	+	4.55569e6i	−0.448436	+	0.562321i
$581$	7.23140e6	−	6.66712e6i	0.888756	−	0.819404i
$582$	−3.96168e6	−	4.96779e6i	−0.484810	−	0.607933i
$583$	−5.30298e6	+	6.64972e6i	−0.646172	+	0.810274i
$584$	−1.35438e6	−	652233.i	−0.164326	−	0.0791354i
$585$	2.68798e6	−	3.37062e6i	0.324741	−	0.407212i
$586$	−4.12527e6	+	1.80740e7i	−0.496258	+	2.17425i
$587$	−4.15560e6			−0.497782			−0.248891	−	0.968532i	$-0.580066\pi$
$587$	−4.15560e6			−0.497782			−0.248891	+	0.968532i	$0.580066\pi$
$588$	−376572.	+	4.62993e6i	−0.0449164	+	0.552244i
$589$	−7.80724e6			−0.927277
$590$	967658.	−	4.23959e6i	0.114444	−	0.501411i
$591$	−301576.	+	378165.i	−0.0355164	+	0.0445361i
$592$	1.77101e7	+	8.52872e6i	2.07690	+	1.00018i
$593$	−2.03881e6	+	2.55659e6i	−0.238090	+	0.298555i	−0.886493	−	0.462742i	$-0.846866\pi$
$593$	−2.03881e6	+	2.55659e6i	−0.238090	+	0.298555i	0.648403	+	0.761297i	$0.275437\pi$
$594$	−1.21857e7	−	1.52804e7i	−1.41705	−	1.77692i
$595$	6.83145e6	−	2.08347e6i	0.791081	−	0.241265i
$596$	−1.33636e6	+	1.67574e6i	−0.154101	+	0.193237i
$597$	−1.13244e6	−	4.96154e6i	−0.130041	−	0.569745i
$598$	1.48121e7	+	1.85738e7i	1.69381	+	2.12397i
$599$	−1.58284e6	+	6.93486e6i	−0.180247	+	0.789715i	0.801264	+	0.598311i	$0.204161\pi$
$599$	−1.58284e6	+	6.93486e6i	−0.180247	+	0.789715i	−0.981511	+	0.191404i	$0.938696\pi$
$600$	536436.	−	258334.i	0.0608331	−	0.0292957i
$601$	2.84729e6	−	1.24748e7i	0.321547	−	1.40879i	−0.513252	−	0.858238i	$-0.671559\pi$
$601$	2.84729e6	−	1.24748e7i	0.321547	−	1.40879i	0.834800	−	0.550554i	$-0.185583\pi$
$602$	8.71261e6	+	5.98081e6i	0.979845	+	0.672618i
$603$	−1.02450e6	−	4.48865e6i	−0.114742	−	0.502715i
$604$	3.89041e6	+	4.87842e6i	0.433913	+	0.544110i
$605$	1.03812e7	−	4.99933e6i	1.15308	−	0.555295i
$606$	6.76976e6			0.748844
$607$	1.28807e6			0.141895			0.0709477	−	0.997480i	$-0.477398\pi$
$607$	1.28807e6			0.141895			0.0709477	+	0.997480i	$0.477398\pi$
$608$	7.23008e6	−	3.48182e6i	0.793203	−	0.381986i
$609$	−6.89050e6	+	2.10148e6i	−0.752849	+	0.229605i
$610$	−7.04868e6	−	3.39446e6i	−0.766978	−	0.369357i
$611$	1.16000e6	+	558627.i	0.125706	+	0.0605368i
$612$	−846815.	−	3.71014e6i	−0.0913924	−	0.400416i
$613$	1.05868e6	+	4.63837e6i	0.113792	+	0.498556i	0.999417	+	0.0341539i	$0.0108736\pi$
$613$	1.05868e6	+	4.63837e6i	0.113792	+	0.498556i	−0.885624	+	0.464402i	$0.846269\pi$
$614$	−1.34713e7	−	6.48746e6i	−1.44208	−	0.694470i
$615$	−6.15440e6	−	2.96380e6i	−0.656143	−	0.315982i
$616$	1.56121e6	−	3.94101e6i	0.165771	−	0.418462i
$617$	5.59655e6	−	2.69516e6i	0.591844	−	0.285017i	−0.113890	−	0.993493i	$-0.536331\pi$
$617$	5.59655e6	−	2.69516e6i	0.591844	−	0.285017i	0.705735	+	0.708476i	$0.250617\pi$
$618$	1.20908e7			1.27345
$619$	7.31696e6			0.767545			0.383772	−	0.923428i	$-0.374625\pi$
$619$	7.31696e6			0.767545			0.383772	+	0.923428i	$0.374625\pi$
$620$	−7.44236e6	+	3.58405e6i	−0.777555	+	0.374451i
$621$	1.01798e7	+	1.27650e7i	1.05927	+	1.32829i
$622$	3.16810e6	+	1.38803e7i	0.328339	+	1.43855i
$623$	3.79973e6	−	3.50323e6i	0.392223	−	0.361617i
$624$	−2.23407e6	+	9.78810e6i	−0.229686	+	1.00632i
$625$	4.73359e6	−	2.27958e6i	0.484720	−	0.233429i
$626$	4.81185e6	−	2.10821e7i	0.490768	−	2.15020i
$627$	4.75410e6	+	5.96146e6i	0.482947	+	0.605597i
$628$	−2.82662e6	−	1.23842e7i	−0.286001	−	1.25305i
$629$	−1.24923e7	+	1.56649e7i	−1.25897	+	1.57870i
$630$	−5.43066e6	−	836200.i	−0.545132	−	0.0839380i
$631$	9.45830e6	+	1.18603e7i	0.945670	+	1.18583i	0.982453	+	0.186509i	$0.0597174\pi$
$631$	9.45830e6	+	1.18603e7i	0.945670	+	1.18583i	−0.0367834	+	0.999323i	$0.511711\pi$
$632$	−557058.	+	698528.i	−0.0554763	+	0.0695651i
$633$	−1.18293e7	−	5.69671e6i	−1.17341	−	0.565087i
$634$	−7.65715e6	+	9.60176e6i	−0.756561	+	0.948698i
$635$	338174.	−	1.48164e6i	0.0332818	−	0.145817i
$636$	−3.64689e6			−0.357503
$637$	−9.43019e6	−	8.86214e6i	−0.920814	−	0.865347i
$638$	−2.48175e7			−2.41382
$639$	18486.8	−	80995.9i	0.00179106	−	0.00784713i
$640$	−2.86883e6	+	3.59740e6i	−0.276857	+	0.347167i
$641$	−2.01520e6	−	970471.i	−0.193720	−	0.0932905i	0.334509	−	0.942392i	$-0.391429\pi$
$641$	−2.01520e6	−	970471.i	−0.193720	−	0.0932905i	−0.528229	+	0.849102i	$0.677144\pi$
$642$	4.52968e6	−	5.68004e6i	0.433741	−	0.543894i
$643$	3.22396e6	+	4.04272e6i	0.307512	+	0.385608i	0.911441	−	0.411430i	$-0.134970\pi$
$643$	3.22396e6	+	4.04272e6i	0.307512	+	0.385608i	−0.603929	+	0.797038i	$0.706399\pi$
$644$	4.92362e6	−	1.24289e7i	0.467810	−	1.18091i
$645$	3.32169e6	−	4.16527e6i	0.314384	−	0.394225i
$646$	2.21880e6	+	9.72122e6i	0.209188	+	0.916514i
$647$	−2.85963e6	−	3.58586e6i	−0.268564	−	0.336769i	0.629201	−	0.777242i	$-0.283382\pi$
$647$	−2.85963e6	−	3.58586e6i	−0.268564	−	0.336769i	−0.897766	+	0.440473i	$0.854811\pi$
$648$	−154804.	+	678242.i	−0.0144826	+	0.0634523i
$649$	7.36767e6	−	3.54808e6i	0.686623	−	0.330660i
$650$	1.39340e6	−	6.10487e6i	0.129357	−	0.566752i
$651$	−1.00933e7	−	1.55415e6i	−0.933431	−	0.143727i
$652$	547221.	+	2.39753e6i	0.0504131	+	0.220874i
$653$	−1.06182e7	−	1.33148e7i	−0.974467	−	1.22194i	−0.975060	−	0.221943i	$-0.928760\pi$
$653$	−1.06182e7	−	1.33148e7i	−0.974467	−	1.22194i	0.000592803	−	1.00000i	$-0.499811\pi$
$654$	−882526.	+	425002.i	−0.0806832	+	0.0388550i
$655$	1.00608e7			0.916283
$656$	−1.64798e7			−1.49517
$657$	−3.30133e6	+	1.58984e6i	−0.298384	+	0.143694i
$658$	−117427.	−	1.63673e6i	−0.0105731	−	0.147372i
$659$	−1.30737e7	−	6.29595e6i	−1.17269	−	0.564739i	−0.256918	−	0.966433i	$-0.582707\pi$
$659$	−1.30737e7	−	6.29595e6i	−1.17269	−	0.564739i	−0.915774	+	0.401694i	$0.868421\pi$
$660$	7.26862e6	+	3.50038e6i	0.649520	+	0.312792i
$661$	−677280.	−	2.96736e6i	−0.0602927	−	0.264159i	0.935793	−	0.352549i	$-0.114685\pi$
$661$	−677280.	−	2.96736e6i	−0.0602927	−	0.264159i	−0.996086	+	0.0883897i	$0.971828\pi$
$662$	1.97886e6	+	8.66995e6i	0.175497	+	0.768903i
$663$	−9.22018e6	−	4.44020e6i	−0.814621	−	0.392301i
$664$	−3.46743e6	−	1.66983e6i	−0.305202	−	0.146978i
$665$	6.28256e6	+	967373.i	0.550912	+	0.0848281i
$666$	1.38880e7	−	6.68810e6i	1.21326	−	0.584275i
$667$	2.07321e7			1.80438
$668$	2.40046e6			0.208139
$669$	−417506.	+	201060.i	−0.0360660	+	0.0173685i
$670$	7.95803e6	+	9.97906e6i	0.684887	+	0.858821i
$671$	−3.27369e6	−	1.43430e7i	−0.280693	−	1.22980i
$672$	1.00403e7	−	3.06211e6i	0.857675	−	0.261576i
$673$	1.63113e6	−	7.14644e6i	0.138820	−	0.608208i	−0.856876	−	0.515523i	$-0.827598\pi$
$673$	1.63113e6	−	7.14644e6i	0.138820	−	0.608208i	0.995695	−	0.0926855i	$-0.0295451\pi$
$674$	−401994.	+	193590.i	−0.0340855	+	0.0164147i
$675$	957623.	−	4.19562e6i	0.0808975	−	0.354435i
$676$	3.49476e6	+	4.38229e6i	0.294137	+	0.368837i
$677$	2.35159e6	+	1.03030e7i	0.197192	+	0.863954i	0.972598	+	0.232492i	$0.0746878\pi$
$677$	2.35159e6	+	1.03030e7i	0.197192	+	0.863954i	−0.775407	+	0.631462i	$0.782455\pi$
$678$	−5.20263e6	+	6.52389e6i	−0.434659	+	0.545045i
$679$	−4.95308e6	−	8.64230e6i	−0.412288	−	0.719374i
$680$	−1.74238e6	−	2.18487e6i	−0.144501	−	0.181198i
$681$	1.66987e6	−	2.09395e6i	0.137979	−	0.173021i
$682$	−3.16976e7	−	1.52648e7i	−2.60955	−	1.25669i
$683$	−1.38384e7	+	1.73528e7i	−1.13510	+	1.42337i	−0.243874	+	0.969807i	$0.578418\pi$
$683$	−1.38384e7	+	1.73528e7i	−1.13510	+	1.42337i	−0.891225	+	0.453562i	$0.850153\pi$
$684$	753681.	−	3.30209e6i	0.0615953	−	0.269867i
$685$	−2.28189e6			−0.185810
$686$	−3.82324e6	+	1.60441e7i	−0.310185	+	1.30168i
$687$	8.44347e6			0.682541
$688$	2.86006e6	−	1.25308e7i	0.230359	−	1.00927i
$689$	6.33445e6	−	7.94315e6i	0.508348	−	0.637448i
$690$	−1.37526e7	−	6.62291e6i	−1.09967	−	0.529573i
$691$	−2.44909e6	+	3.07107e6i	−0.195124	+	0.244677i	−0.869762	−	0.493471i	$-0.835728\pi$
$691$	−2.44909e6	+	3.07107e6i	−0.195124	+	0.244677i	0.674639	+	0.738148i	$0.264299\pi$
$692$	−5.19736e6	−	6.51729e6i	−0.412589	−	0.517371i
$693$	−5.13785e6	−	8.96469e6i	−0.406395	−	0.709091i
$694$	1.45168e7	−	1.82035e7i	1.14413	−	1.43469i
$695$	1.63480e6	+	7.16254e6i	0.128382	+	0.562477i
$696$	1.75744e6	+	2.20376e6i	0.137517	+	0.172441i
$697$	3.73788e6	−	1.63767e7i	0.291436	−	1.27686i
$698$	1.73261e7	−	8.34381e6i	1.34605	−	0.648225i
$699$	1.49453e6	−	6.54798e6i	0.115695	−	0.506891i
$700$	−3.37046e6	+	1.02793e6i	−0.259982	+	0.0792899i
$701$	−1.50957e6	−	6.61384e6i	−0.116026	−	0.508345i	−0.999226	−	0.0393470i	$-0.987472\pi$
$701$	−1.50957e6	−	6.61384e6i	−0.116026	−	0.508345i	0.883199	−	0.468998i	$-0.155385\pi$
$702$	1.45559e7	+	1.82526e7i	1.11480	+	1.39792i
$703$	−1.60666e7	+	7.73725e6i	−1.22612	+	0.590470i
$704$	1.15431e7			0.877789
$705$	−827249.			−0.0626849
$706$	−8.24169e6	+	3.96899e6i	−0.622307	+	0.299687i
$707$	1.04891e7	+	1.61509e6i	0.789208	+	0.121520i
$708$	3.15909e6	+	1.52134e6i	0.236853	+	0.114062i
$709$	−4.33972e6	−	2.08990e6i	−0.324225	−	0.156139i	0.264690	−	0.964334i	$-0.414730\pi$
$709$	−4.33972e6	−	2.08990e6i	−0.324225	−	0.156139i	−0.588915	+	0.808195i	$0.700445\pi$
$710$	51250.1	+	224541.i	0.00381548	+	0.0167167i
$711$	484609.	+	2.12321e6i	0.0359515	+	0.157514i
$712$	−1.82196e6	−	877408.i	−0.134691	−	0.0648637i
$713$	2.64797e7	+	1.27519e7i	1.95069	+	0.939404i
$714$	933357.	+	1.30094e7i	0.0685176	+	0.955022i
$715$	−2.02493e7	+	9.75154e6i	−1.48130	+	0.713359i
$716$	7.97064e6			0.581046
$717$	8.07545e6			0.586636
$718$	−4.28816e6	+	2.06507e6i	−0.310427	+	0.149494i
$719$	−1.08033e7	−	1.35469e7i	−0.779353	−	0.977278i	−0.999998	−	0.00192386i	$-0.999388\pi$
$719$	−1.08033e7	−	1.35469e7i	−0.779353	−	0.977278i	0.220645	−	0.975354i	$-0.429184\pi$
$720$	1.48706e6	+	6.51525e6i	0.106905	+	0.468382i
$721$	1.87336e7	+	2.88455e6i	1.34209	+	0.206652i
$722$	2.19595e6	−	9.62107e6i	0.156776	−	0.686879i
$723$	1.56672e7	−	7.54491e6i	1.11467	−	0.536795i
$724$	2.19712e6	−	9.62620e6i	0.155778	−	0.682509i
$725$	−3.40713e6	−	4.27240e6i	−0.240737	−	0.301875i
$726$	4.68228e6	+	2.05144e7i	0.329697	+	1.44450i
$727$	−8.94451e6	+	1.12161e7i	−0.627654	+	0.787053i	−0.989399	−	0.145224i	$-0.953610\pi$
$727$	−8.94451e6	+	1.12161e7i	−0.627654	+	0.787053i	0.361745	+	0.932277i	$0.382181\pi$
$728$	−1.86487e6	+	4.70757e6i	−0.130413	+	0.329207i
$729$	7.68736e6	+	9.63965e6i	0.535745	+	0.671803i
$730$	6.33347e6	−	7.94192e6i	0.439880	−	0.551592i
$731$	1.18037e7	+	5.68436e6i	0.817004	+	0.393449i
$732$	3.93304e6	−	4.93187e6i	0.271300	−	0.340200i
$733$	5.67682e6	−	2.48718e7i	0.390252	−	1.70981i	−0.273515	−	0.961868i	$-0.588186\pi$
$733$	5.67682e6	−	2.48718e7i	0.390252	−	1.70981i	0.663767	−	0.747939i	$-0.268957\pi$
$734$	6.56009e6			0.449438
$735$	7.92963e6	+	2.50127e6i	0.541421	+	0.170782i
$736$	−3.02092e7			−2.05563
$737$	−5.34093e6	+	2.34001e7i	−0.362200	+	1.58690i
$738$	−8.05748e6	+	1.01038e7i	−0.544575	+	0.682876i
$739$	6.33343e6	+	3.05002e6i	0.426607	+	0.205443i	0.634852	−	0.772633i	$-0.281061\pi$
$739$	6.33343e6	+	3.05002e6i	0.426607	+	0.205443i	−0.208245	+	0.978077i	$0.566775\pi$
$740$	−1.17637e7	+	1.47513e7i	−0.789708	+	0.990262i
$741$	−5.67881e6	−	7.12101e6i	−0.379937	−	0.476427i
$742$	−1.27978e7	−	1.97057e6i	−0.853347	−	0.131396i
$743$	−7.22795e6	+	9.06356e6i	−0.480334	+	0.602319i	−0.961668	−	0.274218i	$-0.911581\pi$
$743$	−7.22795e6	+	9.06356e6i	−0.480334	+	0.602319i	0.481334	+	0.876537i	$0.340152\pi$
$744$	889162.	+	3.89567e6i	0.0588910	+	0.258018i
$745$	2.39203e6	+	2.99951e6i	0.157898	+	0.197998i
$746$	−5.17257e6	+	2.26625e7i	−0.340298	+	1.49094i
$747$	−8.45196e6	+	4.07025e6i	−0.554187	+	0.266882i
$748$	−4.41460e6	+	1.93416e7i	−0.288494	+	1.26398i
$749$	8.37345e6	−	7.72005e6i	0.545381	−	0.502824i
$750$	3.49936e6	+	1.53317e7i	0.227162	+	0.995262i
$751$	−9.93071e6	−	1.24527e7i	−0.642511	−	0.805683i	0.348804	−	0.937196i	$-0.386588\pi$
$751$	−9.93071e6	−	1.24527e7i	−0.642511	−	0.805683i	−0.991314	+	0.131513i	$0.958017\pi$
$752$	−1.79813e6	+	865933.i	−0.115951	+	0.0558392i
$753$	−5.05075e6			−0.324615
$754$	2.96447e7			1.89897
$755$	1.00628e7	−	4.84600e6i	0.642470	−	0.309397i
$756$	4.83846e6	−	1.22139e7i	0.307895	−	0.777232i
$757$	−8.32053e6	−	4.00696e6i	−0.527729	−	0.254141i	0.150994	−	0.988535i	$-0.451752\pi$
$757$	−8.32053e6	−	4.00696e6i	−0.527729	−	0.254141i	−0.678724	+	0.734393i	$0.737467\pi$
$758$	−1.27180e7	−	6.12467e6i	−0.803981	−	0.387177i
$759$	−6.38727e6	−	2.79845e7i	−0.402449	−	1.76325i
$760$	−553456.	−	2.42485e6i	−0.0347575	−	0.152283i
$761$	−3.60044e6	−	1.73388e6i	−0.225369	−	0.108532i	0.317793	−	0.948160i	$-0.397058\pi$
$761$	−3.60044e6	−	1.73388e6i	−0.225369	−	0.108532i	−0.543161	+	0.839628i	$0.682773\pi$
$762$	2.50050e6	+	1.20418e6i	0.156005	+	0.0751283i
$763$	−1.46879e6	+	447955.i	−0.0913374	+	0.0278563i
$764$	−1.49379e7	+	7.19372e6i	−0.925885	+	0.445883i
$765$	−6.81181e6			−0.420832
$766$	2.04497e7			1.25926
$767$	−8.80074e6	+	4.23821e6i	−0.540171	+	0.260132i
$768$	−9.14238e6	−	1.14642e7i	−0.559314	−	0.701358i
$769$	3.59864e6	+	1.57667e7i	0.219444	+	0.961445i	0.957891	+	0.287134i	$0.0927024\pi$
$769$	3.59864e6	+	1.57667e7i	0.219444	+	0.961445i	−0.738447	+	0.674312i	$0.764440\pi$
$770$	2.36159e7	+	1.62113e7i	1.43542	+	0.985348i
$771$	2.21923e6	−	9.72308e6i	0.134452	−	0.589071i
$772$	−5.16894e6	+	2.48923e6i	−0.312146	+	0.150322i
$773$	−4.80294e6	+	2.10431e7i	−0.289107	+	1.26666i	0.596646	+	0.802504i	$0.296500\pi$
$773$	−4.80294e6	+	2.10431e7i	−0.289107	+	1.26666i	−0.885753	+	0.464156i	$0.846358\pi$
$774$	−6.28424e6	−	7.88019e6i	−0.377051	−	0.472807i
$775$	−1.72381e6	−	7.55251e6i	−0.103094	−	0.451686i
$776$	−2.43008e6	+	3.04723e6i	−0.144866	+	0.181656i
$777$	−2.23113e7	+	6.80456e6i	−1.32579	+	0.404341i
$778$	1.43617e7	+	1.80090e7i	0.850660	+	1.06669i
$779$	9.32143e6	−	1.16887e7i	0.550350	−	0.690117i
$780$	−8.68243e6	−	4.18124e6i	−0.510981	−	0.246075i
$781$	−270037.	+	338615.i	−0.0158415	+	0.0198646i
$782$	8.35265e6	−	3.65954e7i	0.488436	−	2.13998i
$783$	2.03735e7			1.18758
$784$	1.98543e7	−	2.86361e6i	1.15362	−	0.166389i
$785$	−2.27374e7			−1.31694
$786$	−4.08838e6	+	1.79124e7i	−0.236045	+	1.03418i
$787$	−3.80915e6	+	4.77652e6i	−0.219225	+	0.274900i	−0.879267	−	0.476329i	$-0.841967\pi$
$787$	−3.80915e6	+	4.77652e6i	−0.219225	+	0.274900i	0.660042	+	0.751229i	$0.270539\pi$
$788$	−1.00915e6	−	485983.i	−0.0578952	−	0.0278808i
$789$	1.60242e6	−	2.00937e6i	0.0916395	−	0.114912i
$790$	−3.76429e6	−	4.72027e6i	−0.214593	−	0.269091i
$791$	−9.61745e6	+	8.86698e6i	−0.546536	+	0.503888i
$792$	−2.52073e6	+	3.16090e6i	−0.142795	+	0.179060i
$793$	3.91045e6	+	1.71328e7i	0.220823	+	0.967488i
$794$	9.86893e6	+	1.23752e7i	0.555545	+	0.696631i
$795$	−1.45257e6	+	6.36413e6i	−0.0815116	+	0.357126i
$796$	1.06178e7	−	5.11326e6i	0.593952	−	0.286032i
$797$	4.76479e6	−	2.08759e7i	0.265704	−	1.16413i	−0.649252	−	0.760573i	$-0.724918\pi$
$797$	4.76479e6	−	2.08759e7i	0.265704	−	1.16413i	0.914956	−	0.403553i	$-0.132225\pi$
$798$	−4.27535e6	+	1.07924e7i	−0.237664	+	0.599946i
$799$	−452673.	−	1.98329e6i	−0.0250852	−	0.109906i
$800$	4.96459e6	+	6.22540e6i	0.274258	+	0.343908i
$801$	−4.44107e6	+	2.13871e6i	−0.244572	+	0.117780i
$802$	−1.55862e7			−0.855664
$803$	1.91021e7			1.04542
$804$	−9.27230e6	+	4.46530e6i	−0.505880	+	0.243619i
$805$	−1.97284e7	−	1.35426e7i	−1.07301	−	0.736569i
$806$	3.78630e7	+	1.82339e7i	2.05295	+	0.988647i
$807$	−1.26198e7	−	6.07738e6i	−0.682133	−	0.328498i
$808$	−924030.	−	4.04844e6i	−0.0497918	−	0.218152i
$809$	−1.37180e6	−	6.01024e6i	−0.0736918	−	0.322865i	0.924624	−	0.380882i	$-0.124379\pi$
$809$	−1.37180e6	−	6.01024e6i	−0.0736918	−	0.322865i	−0.998316	+	0.0580167i	$0.981522\pi$
$810$	−4.23550e6	−	2.03971e6i	−0.226826	−	0.109234i
$811$	3.43328e6	+	1.65338e6i	0.183298	+	0.0882715i	0.523282	−	0.852160i	$-0.324707\pi$
$811$	3.43328e6	+	1.65338e6i	0.183298	+	0.0882715i	−0.339984	+	0.940431i	$0.610422\pi$
$812$	−8.29497e6	−	1.44733e7i	−0.441494	−	0.770333i
$813$	−8.64538e6	+	4.16340e6i	−0.458731	+	0.220913i
$814$	−8.03586e7			−4.25080
$815$	4.40186e6			0.232136
$816$	1.42923e7	−	6.88279e6i	0.751408	−	0.361859i
$817$	7.27003e6	+	9.11633e6i	0.381049	+	0.477821i
$818$	−967790.	−	4.24017e6i	−0.0505706	−	0.221564i
$819$	6.13720e6	+	1.07084e7i	0.319713	+	0.557846i
$820$	3.51988e6	−	1.54216e7i	0.182807	−	0.800930i
$821$	2.08589e7	−	1.00451e7i	1.08003	−	0.520113i	0.192700	−	0.981258i	$-0.438275\pi$
$821$	2.08589e7	−	1.00451e7i	1.08003	−	0.520113i	0.887325	+	0.461145i	$0.152561\pi$
$822$	927287.	−	4.06271e6i	0.0478668	−	0.209718i
$823$	−2.23888e7	−	2.80747e7i	−1.15221	−	1.44483i	−0.875070	−	0.483996i	$-0.839185\pi$
$823$	−2.23888e7	−	2.80747e7i	−1.15221	−	1.44483i	−0.277140	−	0.960830i	$-0.589386\pi$
$824$	−1.65031e6	−	7.23050e6i	−0.0846737	−	0.370980i
$825$	−4.71726e6	+	5.91525e6i	−0.241299	+	0.302579i
$826$	1.02640e7	+	7.04574e6i	0.523438	+	0.359316i
$827$	2.55805e6	+	3.20770e6i	0.130061	+	0.163091i	0.842598	−	0.538544i	$-0.181025\pi$
$827$	2.55805e6	+	3.20770e6i	0.130061	+	0.163091i	−0.712537	+	0.701635i	$0.752454\pi$
$828$	−7.94971e6	+	9.96863e6i	−0.402973	+	0.505312i
$829$	−1.03092e7	−	4.96465e6i	−0.521001	−	0.250901i	0.154852	−	0.987938i	$-0.450510\pi$
$829$	−1.03092e7	−	4.96465e6i	−0.521001	−	0.250901i	−0.675852	+	0.737037i	$0.736224\pi$
$830$	1.62148e7	−	2.03327e7i	0.816987	−	1.02447i
$831$	−2017.33	+	8838.51i	−0.000101339	+	0.000443994i
$832$	−1.37883e7			−0.690562
$833$	−1.65757e6	+	2.03797e7i	−0.0827673	+	1.01762i
$834$	−1.34166e7			−0.667924
$835$	956116.	−	4.18902e6i	0.0474564	−	0.207920i
$836$	−1.10090e7	+	1.38049e7i	−0.544795	+	0.683151i
$837$	2.60217e7	+	1.25314e7i	1.28387	+	0.618280i
$838$	−1.70376e7	+	2.13644e7i	−0.838103	+	1.05095i
$839$	−5.90656e6	−	7.40659e6i	−0.289687	−	0.363257i	0.615598	−	0.788060i	$-0.288915\pi$
$839$	−5.90656e6	−	7.40659e6i	−0.289687	−	0.363257i	−0.905285	+	0.424804i	$0.860343\pi$
$840$	−232815.	−	3.24506e6i	−0.0113845	−	0.158681i
$841$	3.34138e6	−	4.18996e6i	0.162906	−	0.204277i
$842$	−350709.	−	1.53656e6i	−0.0170477	−	0.0746909i
$843$	8.88792e6	+	1.11451e7i	0.430756	+	0.540151i
$844$	6.76553e6	−	2.96417e7i	0.326923	−	1.43234i
$845$	9.03944e6	−	4.35317e6i	0.435512	−	0.209731i
$846$	−348257.	+	1.52582e6i	−0.0167292	+	0.0732953i
$847$	2.36056e6	+	3.29023e7i	0.113059	+	1.57586i
$848$	3.50439e6	+	1.53537e7i	0.167349	+	0.733203i
$849$	−413937.	−	519060.i	−0.0197090	−	0.0247143i
$850$	−8.91413e6	+	4.29282e6i	−0.423186	+	0.203796i
$851$	6.71303e7			3.17757
$852$	−185706.			−0.00876448
$853$	7.32862e6	−	3.52928e6i	0.344865	−	0.166078i	−0.253431	−	0.967354i	$-0.581559\pi$
$853$	7.32862e6	−	3.52928e6i	0.344865	−	0.166078i	0.598296	+	0.801275i	$0.295845\pi$
$854$	1.64669e7	−	1.51819e7i	0.772622	−	0.712332i
$855$	−5.46224e6	−	2.63048e6i	−0.255538	−	0.123061i
$856$	−4.01504e6	−	1.93354e6i	−0.187286	−	0.0901923i
$857$	591131.	+	2.58992e6i	0.0274936	+	0.120457i	0.986813	−	0.161867i	$-0.0517516\pi$
$857$	591131.	+	2.58992e6i	0.0274936	+	0.120457i	−0.959319	+	0.282325i	$0.908894\pi$
$858$	−9.13310e6	−	4.00147e7i	−0.423545	−	1.85567i
$859$	8.85621e6	+	4.26492e6i	0.409510	+	0.197210i	0.627286	−	0.778789i	$-0.284166\pi$
$859$	8.85621e6	+	4.26492e6i	0.409510	+	0.197210i	−0.217776	+	0.975999i	$0.569880\pi$
$860$	1.11153e7	+	5.35283e6i	0.512476	+	0.246796i
$861$	1.43777e7	−	1.32558e7i	0.660971	−	0.609394i
$862$	2.39038e7	−	1.15115e7i	1.09572	−	0.527670i
$863$	1.21981e7			0.557528			0.278764	−	0.960360i	$-0.410075\pi$
$863$	1.21981e7			0.557528			0.278764	+	0.960360i	$0.410075\pi$
$864$	−2.96867e7			−1.35293
$865$	−1.34434e7	+	6.47398e6i	−0.610897	+	0.294192i
$866$	−2.20990e6	−	2.77113e6i	−0.100133	−	0.125563i
$867$	146334.	+	641132.i	0.00661147	+	0.0289667i
$868$	−1.69230e6	−	2.35879e7i	−0.0762392	−	1.06265i
$869$	2.52635e6	−	1.10687e7i	0.113487	−	0.497217i
$870$	−1.71610e7	+	8.26431e6i	−0.768679	+	0.370176i
$871$	6.37978e6	−	2.79516e7i	0.284945	−	1.24842i
$872$	374618.	+	469757.i	0.0166839	+	0.0209210i
$873$	2.11403e6	+	9.26219e6i	0.0938807	+	0.411318i
$874$	2.08296e7	−	2.61195e7i	0.922366	−	1.15661i
$875$	1.76420e6	+	2.45900e7i	0.0778981	+	1.08577i
$876$	5.10673e6	+	6.40363e6i	0.224845	+	0.281946i
$877$	−2.25790e6	+	2.83132e6i	−0.0991302	+	0.124305i	−0.828922	−	0.559364i	$-0.811045\pi$
$877$	−2.25790e6	+	2.83132e6i	−0.0991302	+	0.124305i	0.729792	+	0.683669i	$0.239617\pi$
$878$	−4.38875e7	−	2.11351e7i	−1.92134	−	0.925268i
$879$	−1.66823e7	+	2.09189e7i	−0.728255	+	0.913203i
$880$	7.75233e6	−	3.39652e7i	0.337463	−	1.47852i
$881$	−7.61008e6			−0.330331			−0.165165	−	0.986266i	$-0.552816\pi$
$881$	−7.61008e6			−0.330331			−0.165165	+	0.986266i	$0.552816\pi$
$882$	7.95170e6	−	1.35728e7i	0.344182	−	0.587486i
$883$	1.48687e7			0.641756			0.320878	−	0.947120i	$-0.396022\pi$
$883$	1.48687e7			0.641756			0.320878	+	0.947120i	$0.396022\pi$
$884$	5.27328e6	−	2.31037e7i	0.226960	−	0.994378i
$885$	3.91315e6	−	4.90693e6i	0.167945	−	0.210597i
$886$	3.35729e7	+	1.61679e7i	1.43683	+	0.691940i
$887$	−1.99257e7	+	2.49861e7i	−0.850364	+	1.06632i	0.146656	+	0.989187i	$0.453149\pi$
$887$	−1.99257e7	+	2.49861e7i	−0.850364	+	1.06632i	−0.997021	+	0.0771355i	$0.975423\pi$
$888$	5.69056e6	+	7.13574e6i	0.242171	+	0.303673i
$889$	3.58702e6	+	2.46232e6i	0.152223	+	0.104494i
$890$	8.52002e6	−	1.06838e7i	0.360550	−	0.452115i
$891$	−1.96714e6	−	8.61860e6i	−0.0830120	−	0.363699i
$892$	−669056.	−	838970.i	−0.0281547	−	0.0353048i
$893$	402888.	−	1.76517e6i	0.0169066	−	0.0740725i
$894$	−6.31241e6	+	3.03990e6i	−0.264150	+	0.127208i
$895$	3.17474e6	−	1.39095e7i	0.132480	−	0.580433i
$896$	−6.55011e6	−	1.14289e7i	−0.272570	−	0.475590i
$897$	7.62965e6	+	3.34277e7i	0.316609	+	1.38716i
$898$	−721181.	−	904333.i	−0.0298438	−	0.0374229i
$899$	3.30423e7	−	1.59124e7i	1.36355	−	0.656652i
$900$	3.36076e6			0.138303
$901$	−1.60526e7			−0.658768
$902$	6.06991e7	−	2.92311e7i	2.48408	−	1.19627i
$903$	7.58409e6	+	1.32330e7i	0.309517	+	0.540055i
$904$	4.61153e6	+	2.22080e6i	0.187683	+	0.0903832i
$905$	−1.59234e7	−	7.66832e6i	−0.646272	−	0.311228i
$906$	4.53867e6	+	1.98852e7i	0.183700	+	0.804841i
$907$	−1.03565e7	−	4.53748e7i	−0.418018	−	1.83146i	−0.543563	−	0.839368i	$-0.682925\pi$
$907$	−1.03565e7	−	4.53748e7i	−0.418018	−	1.83146i	0.125545	−	0.992088i	$-0.459932\pi$
$908$	5.58783e6	+	2.69095e6i	0.224920	+	0.108316i
$909$	−9.11956e6	−	4.39175e6i	−0.366070	−	0.176290i
$910$	−2.82094e7	−	1.93645e7i	−1.12925	−	0.775179i
$911$	−2.38556e7	+	1.14882e7i	−0.952345	+	0.458625i	−0.844508	−	0.535544i	$-0.820107\pi$
$911$	−2.38556e7	+	1.14882e7i	−0.952345	+	0.458625i	−0.107837	+	0.994169i	$0.534392\pi$
$912$	1.41185e7			0.562086
$913$	4.89047e7			1.94166
$914$	−4.17337e7	+	2.00979e7i	−1.65242	+	0.795765i
$915$	−7.04000e6	−	8.82788e6i	−0.277984	−	0.348581i
$916$	4.35083e6	+	1.90622e7i	0.171330	+	0.750646i
$917$	−1.06080e7	+	2.67783e7i	−0.416592	+	1.05162i
$918$	8.20818e6	−	3.59624e7i	0.321470	−	1.40845i
$919$	6.50822e6	−	3.13419e6i	0.254199	−	0.122416i	−0.302445	−	0.953167i	$-0.597803\pi$
$919$	6.50822e6	−	3.13419e6i	0.254199	−	0.122416i	0.556644	+	0.830751i	$0.312089\pi$
$920$	−2.08347e6	+	9.12830e6i	−0.0811556	+	0.355566i
$921$	−1.34548e7	−	1.68717e7i	−0.522669	−	0.655406i
$922$	1.27822e7	+	5.60025e7i	0.495197	+	2.16960i
$923$	322561.	−	404479.i	0.0124626	−	0.0156276i
$924$	−1.69807e7	+	1.56557e7i	−0.654299	+	0.603243i
$925$	−1.10322e7	−	1.38340e7i	−0.423945	−	0.531610i
$926$	−1.38689e7	+	1.73910e7i	−0.531512	+	0.666495i
$927$	−1.62875e7	−	7.84365e6i	−0.622523	−	0.299791i
$928$	−2.35032e7	+	2.94720e7i	−0.895893	+	1.12341i
$929$	−4.74386e6	+	2.07842e7i	−0.180340	+	0.790122i	0.801127	+	0.598494i	$0.204234\pi$
$929$	−4.74386e6	+	2.07842e7i	−0.180340	+	0.790122i	−0.981468	+	0.191628i	$0.938623\pi$
$930$	−2.70018e7			−1.02373
$931$	−9.19907e6	+	1.57019e7i	−0.347832	+	0.593716i
$932$	1.55530e7			0.586510
$933$	−4.57240e6	+	2.00330e7i	−0.171965	+	0.753428i
$934$	−5.21591e6	+	6.54054e6i	−0.195642	+	0.245328i
$935$	3.19945e7	+	1.54077e7i	1.19687	+	0.576381i
$936$	3.01104e6	−	3.77572e6i	0.112338	−	0.140867i
$937$	−2.91348e6	−	3.65338e6i	−0.108408	−	0.135940i	0.724667	−	0.689099i	$-0.241993\pi$
$937$	−2.91348e6	−	3.65338e6i	−0.108408	−	0.135940i	−0.833075	+	0.553159i	$0.813422\pi$
$938$	−3.49515e7	+	1.06596e7i	−1.29706	+	0.395579i
$939$	1.94588e7	−	2.44006e7i	0.720198	−	0.903100i
$940$	−426272.	−	1.86762e6i	−0.0157350	−	0.0689397i
$941$	2.45939e7	+	3.08398e7i	0.905428	+	1.13537i	0.990295	+	0.138979i	$0.0443821\pi$
$941$	2.45939e7	+	3.08398e7i	0.905428	+	1.13537i	−0.0848668	+	0.996392i	$0.527046\pi$
$942$	9.23973e6	−	4.04819e7i	0.339259	−	1.48639i
$943$	−5.07071e7	+	2.44192e7i	−1.85690	+	0.894237i
$944$	3.36932e6	−	1.47620e7i	0.123059	−	0.539155i
$945$	−1.93872e7	−	1.33084e7i	−0.706211	−	0.484781i
$946$	1.16922e7	+	5.12270e7i	0.424785	+	1.86110i
$947$	−3.10592e7	−	3.89471e7i	−1.12542	−	1.41124i	−0.899407	−	0.437112i	$-0.856001\pi$
$947$	−3.10592e7	−	3.89471e7i	−1.12542	−	1.41124i	−0.226016	−	0.974124i	$-0.572570\pi$
$948$	4.38596e6	−	2.11217e6i	0.158505	−	0.0763321i
$949$	−2.28176e7			−0.822442
$950$	−8.80578e6			−0.316562
$951$	−1.59696e7	+	7.69054e6i	−0.572587	+	0.275744i
$952$	7.65249e6	−	2.33387e6i	0.273659	−	0.0834612i
$953$	−3.62726e7	−	1.74680e7i	−1.29374	−	0.623032i	−0.344855	−	0.938656i	$-0.612072\pi$
$953$	−3.62726e7	−	1.74680e7i	−1.29374	−	0.623032i	−0.948884	+	0.315624i	$0.897786\pi$
$954$	1.11268e7	+	5.35838e6i	0.395821	+	0.190617i
$955$	6.60383e6	+	2.89333e7i	0.234308	+	1.02657i
$956$	4.16119e6	+	1.82314e7i	0.147256	+	0.645170i
$957$	−3.22710e7	−	1.55409e7i	−1.13902	−	0.548525i
$958$	−2.49512e6	−	1.20158e6i	−0.0878369	−	0.0423000i
$959$	2.40601e6	−	6.07358e6i	0.0844793	−	0.213254i
$960$	7.98193e6	−	3.84389e6i	0.279531	−	0.134615i
$961$	2.33609e7			0.815983
$962$	9.59890e7			3.34413
$963$	−9.78677e6	+	4.71306e6i	−0.340074	+	0.163771i
$964$	2.51067e7	+	3.14829e7i	0.870157	+	1.09114i
$965$	2.28511e6	+	1.00117e7i	0.0789930	+	0.346091i
$966$	3.21284e7	−	2.96214e7i	1.10776	−	1.02132i
$967$	−4.56953e6	+	2.00204e7i	−0.157147	+	0.688505i	0.833553	+	0.552440i	$0.186303\pi$
$967$	−4.56953e6	+	2.00204e7i	−0.157147	+	0.688505i	−0.990700	+	0.136066i	$0.956554\pi$
$968$	1.16289e7	−	5.60017e6i	0.398887	−	0.192094i
$969$	−3.20232e6	+	1.40303e7i	−0.109561	+	0.480017i
$970$	−1.64212e7	−	2.05915e7i	−0.560370	−	0.702681i
$971$	−3.73081e6	−	1.63458e7i	−0.126986	−	0.556361i	−0.997891	−	0.0649105i	$-0.979324\pi$
$971$	−3.73081e6	−	1.63458e7i	−0.126986	−	0.556361i	0.870905	−	0.491451i	$-0.163533\pi$
$972$	−1.29899e7	+	1.62888e7i	−0.441000	+	0.552997i
$973$	−2.07878e7	−	3.20086e6i	−0.703926	−	0.108389i
$974$	2.24422e7	+	2.81417e7i	0.757999	+	0.950500i
$975$	5.63480e6	−	7.06582e6i	0.189831	−	0.238041i
$976$	−2.45430e7	−	1.18193e7i	−0.824713	−	0.397161i
$977$	−3.32787e7	+	4.17302e7i	−1.11540	+	1.39866i	−0.208135	+	0.978100i	$0.566739\pi$
$977$	−3.32787e7	+	4.17302e7i	−1.11540	+	1.39866i	−0.907263	+	0.420565i	$0.861832\pi$
$978$	−1.78877e6	+	7.83712e6i	−0.0598009	+	0.262005i
$979$	2.56969e7			0.856887
$980$	−1.56089e6	+	1.91911e7i	−0.0519168	+	0.638313i
$981$	1.46457e6			0.0485888
$982$	−3.03750e6	+	1.33081e7i	−0.100516	+	0.440392i
$983$	−9.55021e6	+	1.19756e7i	−0.315231	+	0.395287i	−0.914053	−	0.405595i	$-0.867064\pi$
$983$	−9.55021e6	+	1.19756e7i	−0.315231	+	0.395287i	0.598822	+	0.800882i	$0.295636\pi$
$984$	−6.89407e6	−	3.32001e6i	−0.226980	−	0.109308i
$985$	−1.25003e6	+	1.56749e6i	−0.0410517	+	0.0514772i
$986$	−2.92039e7	−	3.66205e7i	−0.956640	−	1.19959i
$987$	872243.	−	2.20184e6i	0.0285000	−	0.0719436i
$988$	1.31504e7	−	1.64900e7i	0.428593	−	0.537439i
$989$	−9.76750e6	−	4.27942e7i	−0.317536	−	1.39121i
$990$	−1.70337e7	−	2.13596e7i	−0.552359	−	0.692637i
$991$	−3.40860e6	+	1.49340e7i	−0.110253	+	0.483051i	0.889410	+	0.457110i	$0.151115\pi$
$991$	−3.40860e6	+	1.49340e7i	−0.110253	+	0.483051i	−0.999663	+	0.0259413i	$0.991742\pi$
$992$	−4.81466e7	+	2.31862e7i	−1.55341	+	0.748084i
$993$	−2.85601e6	+	1.25130e7i	−0.0919152	+	0.402707i
$994$	−651686.	−	100345.i	−0.0209205	−	0.00322129i
$995$	−4.69396e6	−	2.05656e7i	−0.150308	−	0.658542i
$996$	1.30741e7	+	1.63944e7i	0.417603	+	0.523657i
$997$	−4.54891e7	+	2.19064e7i	−1.44934	+	0.697964i	−0.982480	−	0.186368i	$-0.940328\pi$
$997$	−4.54891e7	+	2.19064e7i	−1.44934	+	0.697964i	−0.466858	+	0.884332i	$0.654614\pi$
$998$	−3.69653e7			−1.17481
$999$	6.59692e7			2.09135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.e.a.15.6	✓	138
49.36	even	7	inner	49.6.e.a.36.6	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.e.a.15.6	✓	138	1.1	even	1	trivial
49.6.e.a.36.6	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)

\(f(q)\)	\(=\)	\(q+(-1.68439 + 7.37980i) q^{2} +(-6.81157 + 8.54144i) q^{3} +(-22.7933 - 10.9767i) q^{4} +(-28.2340 + 35.4043i) q^{5} +(-51.5608 - 64.6552i) q^{6} +(-64.4638 - 112.479i) q^{7} +(-31.6272 + 39.6593i) q^{8} +(27.5139 + 120.546i) q^{9} +O(q^{10})\)	\(q+(-1.68439 + 7.37980i) q^{2} +(-6.81157 + 8.54144i) q^{3} +(-22.7933 - 10.9767i) q^{4} +(-28.2340 + 35.4043i) q^{5} +(-51.5608 - 64.6552i) q^{6} +(-64.4638 - 112.479i) q^{7} +(-31.6272 + 39.6593i) q^{8} +(27.5139 + 120.546i) q^{9} +(-213.720 - 267.996i) q^{10} +(143.435 - 628.430i) q^{11} +(249.015 - 119.919i) q^{12} +(-171.334 + 750.664i) q^{13} +(938.652 - 286.272i) q^{14} +(-110.086 - 482.317i) q^{15} +(-744.157 - 933.143i) q^{16} +(1096.10 - 527.852i) q^{17} -935.952 q^{18} +1082.77 q^{19} +(1032.17 - 497.066i) q^{20} +(1399.83 + 215.542i) q^{21} +(4396.09 + 2117.04i) q^{22} +(-3672.42 - 1768.55i) q^{23} +(-123.316 - 540.284i) q^{24} +(239.072 + 1047.44i) q^{25} +(-5251.16 - 2528.83i) q^{26} +(-3608.90 - 1737.96i) q^{27} +(234.702 + 3271.36i) q^{28} +(-4582.59 + 2206.86i) q^{29} +3744.83 q^{30} -7210.41 q^{31} +(6677.38 - 3215.65i) q^{32} +(4390.67 + 5505.73i) q^{33} +(2049.19 + 8978.08i) q^{34} +(5802.29 + 893.422i) q^{35} +(696.066 - 3049.66i) q^{36} +(-14838.3 + 7145.77i) q^{37} +(-1823.81 + 7990.65i) q^{38} +(-5244.70 - 6576.64i) q^{39} +(-511.147 - 2239.48i) q^{40} +(8608.85 - 10795.2i) q^{41} +(-3948.52 + 9967.40i) q^{42} +(6714.27 + 8419.43i) q^{43} +(-10167.4 + 12749.6i) q^{44} +(-5044.68 - 2429.39i) q^{45} +(19237.3 - 24122.8i) q^{46} +(372.089 - 1630.23i) q^{47} +13039.3 q^{48} +(-8495.84 + 14501.6i) q^{49} -8132.62 q^{50} +(-2957.52 + 12957.7i) q^{51} +(12145.1 - 15229.5i) q^{52} +(-11888.2 - 5725.05i) q^{53} +(18904.6 - 23705.6i) q^{54} +(18199.4 + 22821.3i) q^{55} +(6499.63 + 1000.80i) q^{56} +(-7375.38 + 9248.44i) q^{57} +(-8567.30 - 37535.8i) q^{58} +(7909.80 + 9918.58i) q^{59} +(-2785.03 + 12202.0i) q^{60} +(20563.3 - 9902.76i) q^{61} +(12145.2 - 53211.4i) q^{62} +(11785.2 - 10865.6i) q^{63} +(3984.82 + 17458.6i) q^{64} +(-21739.3 - 27260.2i) q^{65} +(-48026.8 + 23128.5i) q^{66} -37235.9 q^{67} -30777.7 q^{68} +(40120.9 - 19321.2i) q^{69} +(-16366.6 + 41314.9i) q^{70} +(-605.367 - 291.530i) q^{71} +(-5650.97 - 2721.36i) q^{72} +(6594.29 + 28891.5i) q^{73} +(-27740.8 - 121540. i) q^{74} +(-10575.1 - 5092.72i) q^{75} +(-24680.0 - 11885.3i) q^{76} +(-79931.2 + 24377.6i) q^{77} +(57368.4 - 27627.2i) q^{78} +17613.2 q^{79} +54047.7 q^{80} +(12356.3 - 5950.50i) q^{81} +(65165.5 + 81714.9i) q^{82} +(16882.5 + 73967.1i) q^{83} +(-29540.8 - 20278.4i) q^{84} +(-12258.9 + 53709.8i) q^{85} +(-73443.2 + 35368.4i) q^{86} +(12364.9 - 54174.0i) q^{87} +(20386.6 + 25564.0i) q^{88} +(8870.89 + 38865.9i) q^{89} +(26425.6 - 33136.7i) q^{90} +(95478.5 - 29119.2i) q^{91} +(64294.0 + 80622.1i) q^{92} +(49114.2 - 61587.3i) q^{93} +(11404.0 + 5491.89i) q^{94} +(-30571.0 + 38334.8i) q^{95} +(-18017.1 + 78938.0i) q^{96} +76835.1 q^{97} +(-92708.5 - 87124.0i) q^{98} +79701.3 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