LMFDB - Embedded newform 49.6.e.a.15.9

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			15.9
Character	$\chi$	$=$	49.15
Dual form			49.6.e.a.36.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.769126 + 3.36976i) q^{2} +(18.8003 - 23.5748i) q^{3} +(18.0673 + 8.70074i) q^{4} +(-1.58408 + 1.98637i) q^{5} +(64.9817 + 81.4844i) q^{6} +(112.806 + 63.8895i) q^{7} +(-112.177 + 140.665i) q^{8} +(-148.248 - 649.518i) q^{9} +O(q^{10})$	\(q+(-0.769126 + 3.36976i) q^{2} +(18.8003 - 23.5748i) q^{3} +(18.0673 + 8.70074i) q^{4} +(-1.58408 + 1.98637i) q^{5} +(64.9817 + 81.4844i) q^{6} +(112.806 + 63.8895i) q^{7} +(-112.177 + 140.665i) q^{8} +(-148.248 - 649.518i) q^{9} +(-5.47525 - 6.86574i) q^{10} +(92.7358 - 406.302i) q^{11} +(544.788 - 262.356i) q^{12} +(-97.0314 + 425.122i) q^{13} +(-302.054 + 330.989i) q^{14} +(17.0472 + 74.6887i) q^{15} +(12.3637 + 15.5036i) q^{16} +(205.487 - 98.9574i) q^{17} +2302.74 q^{18} +388.164 q^{19} +(-45.9029 + 22.1057i) q^{20} +(3626.96 - 1458.23i) q^{21} +(1297.82 + 624.995i) q^{22} +(-1552.39 - 747.591i) q^{23} +(1207.20 + 5289.09i) q^{24} +(693.942 + 3040.36i) q^{25} +(-1357.93 - 653.945i) q^{26} +(-11497.7 - 5537.02i) q^{27} +(1482.20 + 2135.80i) q^{28} +(5797.22 - 2791.79i) q^{29} -264.795 q^{30} -4575.25 q^{31} +(-5248.96 + 2527.77i) q^{32} +(-7835.03 - 9824.82i) q^{33} +(175.417 + 768.553i) q^{34} +(-305.602 + 122.868i) q^{35} +(2972.85 - 13024.9i) q^{36} +(-8795.79 + 4235.83i) q^{37} +(-298.547 + 1308.02i) q^{38} +(8197.96 + 10279.9i) q^{39} +(-101.717 - 445.650i) q^{40} +(-8828.56 + 11070.7i) q^{41} +(2124.30 + 13343.6i) q^{42} +(-407.134 - 510.530i) q^{43} +(5210.61 - 6533.90i) q^{44} +(1525.02 + 734.412i) q^{45} +(3713.19 - 4656.19i) q^{46} +(-1724.96 + 7557.55i) q^{47} +597.934 q^{48} +(8643.26 + 14414.2i) q^{49} -10779.0 q^{50} +(1530.31 - 6704.74i) q^{51} +(-5451.97 + 6836.55i) q^{52} +(27533.3 + 13259.4i) q^{53} +(27501.7 - 34486.0i) q^{54} +(660.166 + 827.822i) q^{55} +(-21641.2 + 8700.92i) q^{56} +(7297.60 - 9150.90i) q^{57} +(4948.89 + 21682.5i) q^{58} +(-16731.8 - 20981.1i) q^{59} +(-341.850 + 1497.74i) q^{60} +(-25728.5 + 12390.2i) q^{61} +(3518.95 - 15417.5i) q^{62} +(24774.2 - 82740.9i) q^{63} +(-4339.65 - 19013.3i) q^{64} +(-690.746 - 866.168i) q^{65} +(39133.4 - 18845.7i) q^{66} -61268.0 q^{67} +4573.59 q^{68} +(-46809.7 + 22542.4i) q^{69} +(-178.990 - 1124.31i) q^{70} +(6417.17 + 3090.35i) q^{71} +(107995. + 52007.5i) q^{72} +(14434.0 + 63239.4i) q^{73} +(-7508.66 - 32897.6i) q^{74} +(84722.1 + 40800.0i) q^{75} +(7013.07 + 3377.31i) q^{76} +(36419.6 - 39908.3i) q^{77} +(-40946.1 + 19718.6i) q^{78} +58738.5 q^{79} -50.3809 q^{80} +(-200836. + 96717.3i) q^{81} +(-30515.2 - 38264.9i) q^{82} +(-11619.9 - 50910.1i) q^{83} +(78217.0 + 5210.99i) q^{84} +(-128.942 + 564.930i) q^{85} +(2033.50 - 979.283i) q^{86} +(43173.3 - 189155. i) q^{87} +(46749.8 + 58622.4i) q^{88} +(-2654.51 - 11630.2i) q^{89} +(-3647.73 + 4574.11i) q^{90} +(-38106.6 + 41756.9i) q^{91} +(-21542.8 - 27013.9i) q^{92} +(-86016.0 + 107861. i) q^{93} +(-24140.4 - 11625.4i) q^{94} +(-614.883 + 771.039i) q^{95} +(-39090.3 + 171266. i) q^{96} +62352.4 q^{97} +(-55220.2 + 18039.4i) q^{98} -277648. 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 $

$2$	−0.769126	+	3.36976i	−0.135964	+	0.595695i	0.860335	+	0.509730i	$0.170255\pi$
$2$	−0.769126	+	3.36976i	−0.135964	+	0.595695i	−0.996298	+	0.0859655i	$0.972603\pi$
$3$	18.8003	−	23.5748i	1.20604	−	1.51232i	0.404325	−	0.914615i	$-0.367506\pi$
$3$	18.8003	−	23.5748i	1.20604	−	1.51232i	0.801713	−	0.597709i	$-0.203922\pi$
$4$	18.0673	+	8.70074i	0.564602	+	0.271898i
$5$	−1.58408	+	1.98637i	−0.0283369	+	0.0355333i	−0.795798	−	0.605562i	$-0.792948\pi$
$5$	−1.58408	+	1.98637i	−0.0283369	+	0.0355333i	0.767461	+	0.641095i	$0.221520\pi$
$6$	64.9817	+	81.4844i	0.736907	+	0.924052i
$7$	112.806	+	63.8895i	0.870134	+	0.492816i
$7$	112.806	+	63.8895i	0.870134	+	0.492816i
$8$	−112.177	+	140.665i	−0.619695	+	0.777073i
$9$	−148.248	−	649.518i	−0.610075	−	2.67291i
$10$	−5.47525	−	6.86574i	−0.0173142	−	0.0217114i
$11$	92.7358	−	406.302i	0.231082	−	1.01244i	−0.717663	−	0.696391i	$-0.754788\pi$
$11$	92.7358	−	406.302i	0.231082	−	1.01244i	0.948744	−	0.316044i	$-0.102355\pi$
$12$	544.788	−	262.356i	1.09213	−	0.525942i
$13$	−97.0314	+	425.122i	−0.159241	+	0.697679i	0.830762	+	0.556628i	$0.187905\pi$
$13$	−97.0314	+	425.122i	−0.159241	+	0.697679i	−0.990002	+	0.141051i	$0.954952\pi$
$14$	−302.054	+	330.989i	−0.411875	+	0.451330i
$15$	17.0472	+	74.6887i	0.0195625	+	0.0857091i
$16$	12.3637	+	15.5036i	0.0120739	+	0.0151402i
$17$	205.487	−	98.9574i	0.172450	−	0.0830474i	−0.345667	−	0.938357i	$-0.612347\pi$
$17$	205.487	−	98.9574i	0.172450	−	0.0830474i	0.518117	+	0.855310i	$0.326633\pi$
$18$	2302.74			1.67519
$19$	388.164			0.246679			0.123339	−	0.992365i	$-0.460640\pi$
$19$	388.164			0.246679			0.123339	+	0.992365i	$0.460640\pi$
$20$	−45.9029	+	22.1057i	−0.0256605	+	0.0123574i
$21$	3626.96	−	1458.23i	1.79471	−	0.721570i
$22$	1297.82	+	624.995i	0.571684	+	0.275309i
$23$	−1552.39	−	747.591i	−0.611901	−	0.294676i	0.102151	−	0.994769i	$-0.467428\pi$
$23$	−1552.39	−	747.591i	−0.611901	−	0.294676i	−0.714052	+	0.700093i	$0.753142\pi$
$24$	1207.20	+	5289.09i	0.427810	+	1.87436i
$25$	693.942	+	3040.36i	0.222061	+	0.972914i
$26$	−1357.93	−	653.945i	−0.393953	−	0.189718i
$27$	−11497.7	−	5537.02i	−3.03531	−	1.46173i
$28$	1482.20	+	2135.80i	0.357284	+	0.514832i
$29$	5797.22	−	2791.79i	1.28004	−	0.616436i	0.334642	−	0.942345i	$-0.391385\pi$
$29$	5797.22	−	2791.79i	1.28004	−	0.616436i	0.945401	+	0.325909i	$0.105670\pi$
$30$	−264.795			−0.0537163
$31$	−4575.25			−0.855088			−0.427544	−	0.903995i	$-0.640621\pi$
$31$	−4575.25			−0.855088			−0.427544	+	0.903995i	$0.640621\pi$
$32$	−5248.96	+	2527.77i	−0.906146	+	0.436377i
$33$	−7835.03	−	9824.82i	−1.25244	−	1.57051i
$34$	175.417	+	768.553i	0.0260241	+	0.114019i
$35$	−305.602	+	122.868i	−0.0421683	+	0.0169539i
$36$	2972.85	−	13024.9i	0.382310	−	1.67501i
$37$	−8795.79	+	4235.83i	−1.05626	+	0.508668i	−0.879654	−	0.475614i	$-0.842226\pi$
$37$	−8795.79	+	4235.83i	−1.05626	+	0.508668i	−0.176605	+	0.984282i	$0.556512\pi$
$38$	−298.547	+	1308.02i	−0.0335393	+	0.146945i
$39$	8197.96	+	10279.9i	0.863066	+	1.08225i
$40$	−101.717	−	445.650i	−0.0100518	−	0.0440397i
$41$	−8828.56	+	11070.7i	−0.820220	+	1.02852i	0.178783	+	0.983889i	$0.442784\pi$
$41$	−8828.56	+	11070.7i	−0.820220	+	1.02852i	−0.999003	+	0.0446351i	$0.985787\pi$
$42$	2124.30	+	13343.6i	0.185820	+	1.16721i
$43$	−407.134	−	510.530i	−0.0335789	−	0.0421066i	0.764759	−	0.644317i	$-0.222858\pi$
$43$	−407.134	−	510.530i	−0.0335789	−	0.0421066i	−0.798337	+	0.602210i	$0.794287\pi$
$44$	5210.61	−	6533.90i	0.405748	−	0.508792i
$45$	1525.02	+	734.412i	0.112265	+	0.0540640i
$46$	3713.19	−	4656.19i	0.258733	−	0.324441i
$47$	−1724.96	+	7557.55i	−0.113903	+	0.499041i	0.885505	+	0.464630i	$0.153813\pi$
$47$	−1724.96	+	7557.55i	−0.113903	+	0.499041i	−0.999408	+	0.0344111i	$0.989044\pi$
$48$	597.934			0.0374585
$49$	8643.26	+	14414.2i	0.514265	+	0.857631i
$50$	−10779.0			−0.609753
$51$	1530.31	−	6704.74i	0.0823863	−	0.360958i
$52$	−5451.97	+	6836.55i	−0.279605	+	0.350614i
$53$	27533.3	+	13259.4i	1.34638	+	0.648385i	0.961557	−	0.274604i	$-0.0885468\pi$
$53$	27533.3	+	13259.4i	1.34638	+	0.648385i	0.384827	+	0.922989i	$0.374261\pi$
$54$	27501.7	−	34486.0i	1.28344	−	1.60938i
$55$	660.166	+	827.822i	0.0294270	+	0.0369003i
$56$	−21641.2	+	8700.92i	−0.922171	+	0.370762i
$57$	7297.60	−	9150.90i	0.297504	−	0.373058i
$58$	4948.89	+	21682.5i	0.193169	+	0.846329i
$59$	−16731.8	−	20981.1i	−0.625769	−	0.784689i	0.363375	−	0.931643i	$-0.381624\pi$
$59$	−16731.8	−	20981.1i	−0.625769	−	0.784689i	−0.989143	+	0.146954i	$0.953053\pi$
$60$	−341.850	+	1497.74i	−0.0122591	+	0.0537105i
$61$	−25728.5	+	12390.2i	−0.885297	+	0.426337i	−0.820556	−	0.571565i	$-0.806336\pi$
$61$	−25728.5	+	12390.2i	−0.885297	+	0.426337i	−0.0647407	+	0.997902i	$0.520622\pi$
$62$	3518.95	−	15417.5i	0.116261	−	0.509372i
$63$	24774.2	−	82740.9i	0.786407	−	2.62645i
$64$	−4339.65	−	19013.3i	−0.132436	−	0.580239i
$65$	−690.746	−	866.168i	−0.0202785	−	0.0254284i
$66$	39133.4	−	18845.7i	1.10583	−	0.532539i
$67$	−61268.0			−1.66743			−0.833713	−	0.552197i	$-0.813789\pi$
$67$	−61268.0			−1.66743			−0.833713	+	0.552197i	$0.813789\pi$
$68$	4573.59			0.119946
$69$	−46809.7	+	22542.4i	−1.18362	+	0.570002i
$70$	−178.990	−	1124.31i	−0.00436600	−	0.0274245i
$71$	6417.17	+	3090.35i	0.151077	+	0.0727547i	0.507894	−	0.861419i	$-0.330424\pi$
$71$	6417.17	+	3090.35i	0.151077	+	0.0727547i	−0.356818	+	0.934174i	$0.616138\pi$
$72$	107995.	+	52007.5i	2.45511	+	1.18232i
$73$	14434.0	+	63239.4i	0.317014	+	1.38893i	0.842761	+	0.538288i	$0.180929\pi$
$73$	14434.0	+	63239.4i	0.317014	+	1.38893i	−0.525746	+	0.850641i	$0.676214\pi$
$74$	−7508.66	−	32897.6i	−0.159398	−	0.698369i
$75$	84722.1	+	40800.0i	1.73918	+	0.837543i
$76$	7013.07	+	3377.31i	0.139275	+	0.0670714i
$77$	36419.6	−	39908.3i	0.700016	−	0.767073i
$78$	−40946.1	+	19718.6i	−0.762037	+	0.366978i
$79$	58738.5			1.05890			0.529450	−	0.848341i	$-0.322398\pi$
$79$	58738.5			1.05890			0.529450	+	0.848341i	$0.322398\pi$
$80$	−50.3809			−0.000880119
$81$	−200836.	+	96717.3i	−3.40117	+	1.63792i
$82$	−30515.2	−	38264.9i	−0.501167	−	0.628443i
$83$	−11619.9	−	50910.1i	−0.185143	−	0.811165i	−0.979131	−	0.203231i	$-0.934856\pi$
$83$	−11619.9	−	50910.1i	−0.185143	−	0.811165i	0.793988	−	0.607934i	$-0.208001\pi$
$84$	78217.0	+	5210.99i	1.20949	+	0.0805790i
$85$	−128.942	+	564.930i	−0.00193574	+	0.00848101i
$86$	2033.50	−	979.283i	0.0296482	−	0.0142778i
$87$	43173.3	−	189155.i	0.611530	−	2.67929i
$88$	46749.8	+	58622.4i	0.643536	+	0.806968i
$89$	−2654.51	−	11630.2i	−0.0355230	−	0.155637i	0.954056	−	0.299629i	$-0.0968630\pi$
$89$	−2654.51	−	11630.2i	−0.0355230	−	0.155637i	−0.989579	+	0.143993i	$0.954006\pi$
$90$	−3647.73	+	4574.11i	−0.0474697	+	0.0595251i
$91$	−38106.6	+	41756.9i	−0.482388	+	0.528597i
$92$	−21542.8	−	27013.9i	−0.265359	−	0.332749i
$93$	−86016.0	+	107861.i	−1.03127	+	1.29317i
$94$	−24140.4	−	11625.4i	−0.281790	−	0.135703i
$95$	−614.883	+	771.039i	−0.00699010	+	0.00876531i
$96$	−39090.3	+	171266.i	−0.432903	+	1.89667i
$97$	62352.4			0.672859			0.336429	−	0.941709i	$-0.390781\pi$
$97$	62352.4			0.672859			0.336429	+	0.941709i	$0.390781\pi$
$98$	−55220.2	+	18039.4i	−0.580808	+	0.189739i
$99$	−277648.			−2.84713
$100$	−13915.7	+	60968.7i	−0.139157	+	0.609687i
$101$	52395.5	−	65701.8i	0.511082	−	0.640876i	−0.457607	−	0.889154i	$-0.651293\pi$
$101$	52395.5	−	65701.8i	0.511082	−	0.640876i	0.968689	+	0.248279i	$0.0798648\pi$
$102$	21416.4	+	10313.6i	0.203819	+	0.0981543i
$103$	109747.	−	137618.i	1.01929	−	1.27815i	0.0592669	−	0.998242i	$-0.481124\pi$
$103$	109747.	−	137618.i	1.01929	−	1.27815i	0.960026	−	0.279911i	$-0.0903049\pi$
$104$	−48915.3	−	61337.8i	−0.443467	−	0.556090i
$105$	−2848.80	+	9514.45i	−0.0252168	+	0.0842191i
$106$	−65857.5	+	82582.6i	−0.569299	+	0.713878i
$107$	3280.61	+	14373.3i	0.0277009	+	0.121366i	0.986888	−	0.161407i	$-0.0516030\pi$
$107$	3280.61	+	14373.3i	0.0277009	+	0.121366i	−0.959187	+	0.282772i	$0.908746\pi$
$108$	−159557.	−	200078.i	−1.31630	−	1.65059i
$109$	40338.4	−	176734.i	0.325201	−	1.42480i	−0.502959	−	0.864310i	$-0.667755\pi$
$109$	40338.4	−	176734.i	0.325201	−	1.42480i	0.828161	−	0.560491i	$-0.189387\pi$
$110$	−3297.32	+	1587.90i	−0.0259824	+	0.0125124i
$111$	−65504.4	+	286994.i	−0.504619	+	2.21088i
$112$	404.178	+	2538.80i	0.00304458	+	0.0191242i
$113$	−1149.53	−	5036.44i	−0.00846888	−	0.0371046i	0.970517	−	0.241033i	$-0.0774862\pi$
$113$	−1149.53	−	5036.44i	−0.00846888	−	0.0371046i	−0.978986	+	0.203928i	$0.934629\pi$
$114$	25223.6	+	31629.3i	0.181779	+	0.227944i
$115$	3944.10	−	1899.38i	0.0278102	−	0.0133927i
$116$	129031.			0.890323
$117$	290509.			1.96198
$118$	83570.1	−	40245.2i	0.552517	−	0.266078i
$119$	29502.5	+	1965.52i	0.190981	+	0.0127236i
$120$	−12418.4	−	5980.39i	−0.0787250	−	0.0379120i
$121$	−11379.4	−	5480.03i	−0.0706571	−	0.0340267i
$122$	−21963.5	−	96228.4i	−0.133599	−	0.585334i
$123$	95009.4	+	416263.i	0.566244	+	2.48088i
$124$	−82662.3	−	39808.1i	−0.482784	−	0.232497i
$125$	−14291.9	−	6882.60i	−0.0818114	−	0.0393983i
$126$	259763.	+	147121.i	1.45764	+	0.825560i
$127$	271848.	−	130915.i	1.49560	−	0.720245i	0.505795	−	0.862653i	$-0.331199\pi$
$127$	271848.	−	130915.i	1.49560	−	0.720245i	0.989808	+	0.142409i	$0.0454848\pi$
$128$	−119021.			−0.642094
$129$	−19689.9			−0.104176
$130$	3450.05	−	1661.46i	0.0179047	−	0.00862245i
$131$	−203791.	−	255546.i	−1.03754	−	1.30104i	−0.952460	−	0.304664i	$-0.901456\pi$
$131$	−203791.	−	255546.i	−1.03754	−	1.30104i	−0.0850836	−	0.996374i	$-0.527116\pi$
$132$	−56074.4	−	245678.i	−0.280111	−	1.22725i
$133$	43787.1	+	24799.6i	0.214643	+	0.121567i
$134$	47122.8	−	206459.i	0.226709	−	0.993278i
$135$	29211.9	−	14067.7i	0.137951	−	0.0664339i
$136$	−9131.02	+	40005.6i	−0.0423323	+	0.185470i
$137$	−111955.	−	140387.i	−0.509613	−	0.639034i	0.458754	−	0.888563i	$-0.348296\pi$
$137$	−111955.	−	140387.i	−0.509613	−	0.639034i	−0.968367	+	0.249529i	$0.919724\pi$
$138$	−39959.8	−	175075.i	−0.178618	−	0.782577i
$139$	−206715.	+	259213.i	−0.907476	+	1.13794i	0.0824839	+	0.996592i	$0.473715\pi$
$139$	−206715.	+	259213.i	−0.907476	+	1.13794i	−0.989960	+	0.141347i	$0.954857\pi$
$140$	−6590.43	−	439.069i	−0.0284180	−	0.00189327i
$141$	145738.	+	182750.i	0.617341	+	0.774121i
$142$	−15349.3	+	19247.5i	−0.0638806	+	0.0801037i
$143$	163730.	+	78848.1i	0.669557	+	0.322442i
$144$	8236.96	−	10328.8i	0.0331025	−	0.0415092i
$145$	−3637.71	+	15937.9i	−0.0143684	+	0.0629521i
$146$	−224203.			−0.870481
$147$	502308.	+	67228.1i	1.91724	+	0.256600i
$148$	−195771.			−0.734672
$149$	75279.6	−	329821.i	0.277787	−	1.21706i	−0.622798	−	0.782383i	$-0.714004\pi$
$149$	75279.6	−	329821.i	0.277787	−	1.21706i	0.900585	−	0.434680i	$-0.143139\pi$
$150$	−202648.	+	254113.i	−0.735385	+	0.922144i
$151$	4342.49	+	2091.23i	0.0154987	+	0.00746380i	0.441617	−	0.897204i	$-0.354405\pi$
$151$	4342.49	+	2091.23i	0.0154987	+	0.00746380i	−0.426118	+	0.904667i	$0.640119\pi$
$152$	−43543.0	+	54601.2i	−0.152866	+	0.191687i
$153$	−94737.7	−	118797.i	−0.327186	−	0.410278i
$154$	106470.	+	153420.i	0.361765	+	0.521290i
$155$	7247.56	−	9088.16i	0.0242305	−	0.0303841i
$156$	58671.8	+	257058.i	0.193027	+	0.845707i
$157$	227540.	+	285326.i	0.736731	+	0.923831i	0.999154	−	0.0411218i	$-0.0130932\pi$
$157$	227540.	+	285326.i	0.736731	+	0.923831i	−0.262424	+	0.964953i	$0.584522\pi$
$158$	−45177.3	+	197935.i	−0.143972	+	0.630782i
$159$	830221.	−	399813.i	2.60436	−	1.25419i
$160$	3293.68	−	14430.6i	0.0101714	−	0.0445639i
$161$	−127355.	−	183514.i	−0.387215	−	0.557962i
$162$	−171446.	−	751156.i	−0.513264	−	2.24876i
$163$	−51619.0	−	64728.2i	−0.152174	−	0.190820i	0.699901	−	0.714240i	$-0.253227\pi$
$163$	−51619.0	−	64728.2i	−0.152174	−	0.190820i	−0.852075	+	0.523420i	$0.824656\pi$
$164$	−255831.	+	123202.i	−0.742752	+	0.357690i
$165$	31927.1			0.0912954
$166$	180492.			0.508380
$167$	−581998.	+	280275.i	−1.61484	+	0.777667i	−0.999940	−	0.0109359i	$-0.996519\pi$
$167$	−581998.	+	280275.i	−1.61484	+	0.777667i	−0.614903	+	0.788603i	$0.710805\pi$
$168$	−201738.	+	673767.i	−0.551462	+	1.84178i
$169$	163210.	+	78597.6i	0.439571	+	0.211686i
$170$	−1804.51	−	869.005i	−0.00478891	−	0.00230622i
$171$	−57544.7	−	252120.i	−0.150493	−	0.659351i
$172$	−2913.81	−	12766.3i	−0.00751001	−	0.0329035i
$173$	−194808.	−	93814.5i	−0.494870	−	0.238317i	0.169766	−	0.985484i	$-0.445699\pi$
$173$	−194808.	−	93814.5i	−0.494870	−	0.238317i	−0.664636	+	0.747168i	$0.731413\pi$
$174$	604201.	+	290968.i	1.51289	+	0.728571i
$175$	−115966.	+	387305.i	−0.286244	+	0.956001i
$176$	7445.69	−	3585.65i	0.0181185	−	0.00872543i
$177$	−809188.			−1.94141
$178$	41232.6			0.0975418
$179$	552373.	−	266009.i	1.28855	−	0.620531i	0.340974	−	0.940073i	$-0.389243\pi$
$179$	552373.	−	266009.i	1.28855	−	0.620531i	0.947572	+	0.319541i	$0.103529\pi$
$180$	21163.1	+	26537.6i	0.0486852	+	0.0610493i
$181$	−40149.1	−	175905.i	−0.0910919	−	0.399099i	0.908741	−	0.417360i	$-0.137044\pi$
$181$	−40149.1	−	175905.i	−0.0910919	−	0.399099i	−0.999833	+	0.0182601i	$0.994187\pi$
$182$	−111402.	−	160526.i	−0.249296	−	0.359226i
$183$	−191606.	+	839482.i	−0.422943	+	1.85303i
$184$	279302.	−	134505.i	0.608177	−	0.292883i
$185$	5519.29	−	24181.6i	0.0118564	−	0.0519464i
$186$	−297308.	−	372812.i	−0.630120	−	0.790146i
$187$	−21150.6	−	92666.7i	−0.0442301	−	0.193785i
$188$	−96921.6	+	121536.i	−0.199998	+	0.250790i
$189$	−943254.	−	1.35919e6i	−1.92076	−	2.76775i
$190$	−2125.29	−	2665.04i	−0.00427106	−	0.00535573i
$191$	−286734.	+	359553.i	−0.568716	+	0.713147i	−0.980142	−	0.198296i	$-0.936459\pi$
$191$	−286734.	+	359553.i	−0.568716	+	0.713147i	0.411427	+	0.911443i	$0.365031\pi$
$192$	−529821.	−	255148.i	−1.03723	−	0.499504i
$193$	180053.	−	225779.i	0.347941	−	0.436305i	−0.576809	−	0.816879i	$-0.695702\pi$
$193$	180053.	−	225779.i	0.347941	−	0.436305i	0.924750	+	0.380574i	$0.124274\pi$
$194$	−47956.9	+	210113.i	−0.0914843	+	0.400819i
$195$	−33406.0			−0.0629126
$196$	30745.8	+	335628.i	0.0571670	+	0.624048i
$197$	−381975.			−0.701244			−0.350622	−	0.936517i	$-0.614030\pi$
$197$	−381975.			−0.701244			−0.350622	+	0.936517i	$0.614030\pi$
$198$	213547.	−	935609.i	0.387106	−	1.69602i
$199$	184388.	−	231215.i	0.330065	−	0.413889i	−0.588913	−	0.808196i	$-0.700444\pi$
$199$	184388.	−	231215.i	0.330065	−	0.413889i	0.918979	+	0.394307i	$0.129015\pi$
$200$	−505517.	−	243444.i	−0.893636	−	0.430352i
$201$	−1.15186e6	+	1.44438e6i	−2.01098	+	2.52169i
$202$	181101.	+	227093.i	0.312278	+	0.391585i
$203$	832326.	+	55451.4i	1.41760	+	0.0944435i
$204$	85984.8	−	107822.i	0.144659	−	0.181397i
$205$	−8005.33	−	35073.6i	−0.0133044	−	0.0582903i
$206$	379331.	+	475666.i	0.622803	+	0.780970i
$207$	−255435.	+	1.11913e6i	−0.414338	+	1.81533i
$208$	−7790.58	+	3751.74i	−0.0124857	+	0.00601277i
$209$	35996.7	−	157712.i	0.0570029	−	0.249746i
$210$	−29870.3	−	16917.6i	−0.0467404	−	0.0264722i
$211$	−9228.59	−	40433.1i	−0.0142702	−	0.0625217i	0.967292	−	0.253667i	$-0.0816369\pi$
$211$	−9228.59	−	40433.1i	−0.0142702	−	0.0625217i	−0.981562	+	0.191146i	$0.938780\pi$
$212$	382086.	+	479121.i	0.583877	+	0.732159i
$213$	193499.	−	93184.1i	0.292233	−	0.140732i
$214$	−50957.7			−0.0760633
$215$	1659.04			0.00244771
$216$	2.06865e6	−	996208.i	3.01684	−	1.45283i
$217$	−516115.	−	292311.i	−0.744041	−	0.421401i
$218$	564526.	+	271862.i	0.804531	+	0.387442i
$219$	1.76222e6	+	848639.i	2.48284	+	1.19567i
$220$	4724.74	+	20700.4i	0.00658144	+	0.0288352i
$221$	22130.3	+	96959.1i	0.0304794	+	0.133539i
$222$	−916719.	−	441469.i	−1.24840	−	0.601198i
$223$	−144744.	−	69705.1i	−0.194912	−	0.0938647i	0.333882	−	0.942615i	$-0.391641\pi$
$223$	−144744.	−	69705.1i	−0.194912	−	0.0938647i	−0.528794	+	0.848750i	$0.677356\pi$
$224$	−753610.	−	50207.2i	−1.00352	−	0.0668568i
$225$	1.87189e6	−	901455.i	2.46504	−	1.18710i
$226$	17855.7			0.0232545
$227$	494158.			0.636504			0.318252	−	0.948006i	$-0.396904\pi$
$227$	494158.			0.636504			0.318252	+	0.948006i	$0.396904\pi$
$228$	211467.	−	101837.i	0.269405	−	0.129739i
$229$	−188240.	−	236045.i	−0.237204	−	0.297445i	0.648954	−	0.760828i	$-0.275207\pi$
$229$	−188240.	−	236045.i	−0.237204	−	0.297445i	−0.886158	+	0.463383i	$0.846635\pi$
$230$	3366.95	+	14751.6i	0.00419678	+	0.0183873i
$231$	−256133.	−	1.60887e6i	−0.315817	−	1.98377i
$232$	−257605.	+	1.12864e6i	−0.314221	+	1.37669i
$233$	296745.	−	142905.i	0.358091	−	0.172448i	−0.246185	−	0.969223i	$-0.579177\pi$
$233$	296745.	−	142905.i	0.358091	−	0.172448i	0.604275	+	0.796775i	$0.293463\pi$
$234$	−223438.	+	978947.i	−0.266758	+	1.16874i
$235$	−12279.6	−	15398.2i	−0.0145049	−	0.0181886i
$236$	−119748.	−	524650.i	−0.139955	−	0.613182i
$237$	1.10430e6	−	1.38475e6i	1.27707	−	1.60140i
$238$	−29314.4	+	97904.5i	−0.0335459	+	0.112037i
$239$	388559.	+	487238.i	0.440010	+	0.551755i	0.951546	−	0.307507i	$-0.0994947\pi$
$239$	388559.	+	487238.i	0.440010	+	0.551755i	−0.511536	+	0.859262i	$0.670923\pi$
$240$	−947.176	+	1187.72i	−0.00106146	+	0.00133102i
$241$	325823.	+	156908.i	0.361359	+	0.174022i	0.605749	−	0.795655i	$-0.292873\pi$
$241$	325823.	+	156908.i	0.361359	+	0.174022i	−0.244390	+	0.969677i	$0.578588\pi$
$242$	27218.6	−	34131.0i	0.0298763	−	0.0374637i
$243$	−805623.	+	3.52967e6i	−0.875218	+	3.83458i
$244$	−572646.			−0.615761
$245$	−42323.6	−	5664.52i	−0.0450472	−	0.00602904i
$246$	−1.47578e6			−1.55484
$247$	−37664.1	+	165017.i	−0.0392813	+	0.172102i
$248$	513237.	−	643579.i	0.529894	−	0.664466i
$249$	−1.41865e6	−	683188.i	−1.45003	−	0.698299i
$250$	34184.9	−	42866.6i	0.0345927	−	0.0433779i
$251$	−514512.	−	645177.i	−0.515479	−	0.646390i	0.454163	−	0.890919i	$-0.349938\pi$
$251$	−514512.	−	645177.i	−0.515479	−	0.646390i	−0.969642	+	0.244528i	$0.921367\pi$
$252$	1.16751e6	−	1.27935e6i	1.15813	−	1.26908i
$253$	−447710.	+	561410.i	−0.439739	+	0.551416i
$254$	232067.	+	1.01675e6i	0.225699	+	0.988851i
$255$	10894.0	+	13660.6i	0.0104915	+	0.0131559i
$256$	230411.	−	1.00950e6i	0.219737	−	0.962731i
$257$	235780.	−	113546.i	0.222677	−	0.107235i	−0.319220	−	0.947681i	$-0.603421\pi$
$257$	235780.	−	113546.i	0.222677	−	0.107235i	0.541896	+	0.840445i	$0.317706\pi$
$258$	15144.0	−	66350.2i	0.0141642	−	0.0620573i
$259$	−1.26284e6	−	84133.2i	−1.16977	−	0.0779324i
$260$	−4943.59	−	21659.3i	−0.00453533	−	0.0198706i
$261$	−2.67275e6	−	3.35152e6i	−2.42860	−	3.04537i
$262$	1.01787e6	−	490180.i	0.916090	−	0.441166i
$263$	212493.			0.189433			0.0947165	−	0.995504i	$-0.469806\pi$
$263$	212493.			0.189433			0.0947165	+	0.995504i	$0.469806\pi$
$264$	2.26092e6			1.99653
$265$	−69953.0	+	33687.6i	−0.0611916	+	0.0294683i
$266$	−117247.	+	128478.i	−0.101601	+	0.111333i
$267$	−324085.	−	156071.i	−0.278215	−	0.133981i
$268$	−1.10695e6	−	533077.i	−0.941433	−	0.453370i
$269$	143497.	+	628699.i	0.120910	+	0.529739i	0.998713	+	0.0507184i	$0.0161511\pi$
$269$	143497.	+	628699.i	0.120910	+	0.529739i	−0.877803	+	0.479021i	$0.840992\pi$
$270$	24937.2	+	109257.i	0.0208180	+	0.0912096i
$271$	−443703.	−	213676.i	−0.367003	−	0.176739i	0.241288	−	0.970454i	$-0.422430\pi$
$271$	−443703.	−	213676.i	−0.367003	−	0.176739i	−0.608291	+	0.793714i	$0.708144\pi$
$272$	4074.77	+	1962.31i	0.00333950	+	0.00160822i
$273$	267997.	+	1.68340e6i	0.217633	+	1.36704i
$274$	559177.	−	269285.i	0.449959	−	0.216689i
$275$	1.29966e6			1.03633
$276$	−1.04186e6			−0.823258
$277$	1.23517e6	−	594826.i	0.967224	−	0.465791i	0.117532	−	0.993069i	$-0.462502\pi$
$277$	1.23517e6	−	594826.i	0.967224	−	0.465791i	0.849693	+	0.527279i	$0.176788\pi$
$278$	−714495.	−	895948.i	−0.554481	−	0.695298i
$279$	678273.	+	2.97171e6i	0.521668	+	2.28558i
$280$	16998.1	−	56770.5i	0.0129571	−	0.0432740i
$281$	−70394.7	+	308419.i	−0.0531831	+	0.233011i	−0.994533	−	0.104421i	$-0.966701\pi$
$281$	−70394.7	+	308419.i	−0.0531831	+	0.233011i	0.941350	+	0.337432i	$0.109558\pi$
$282$	−727914.	+	350545.i	−0.545076	+	0.262495i
$283$	114085.	−	499838.i	0.0846762	−	0.370991i	−0.914780	−	0.403951i	$-0.867637\pi$
$283$	114085.	−	499838.i	0.0846762	−	0.370991i	0.999457	+	0.0329608i	$0.0104936\pi$
$284$	89052.4	+	111668.i	0.0655164	+	0.0821549i
$285$	6617.12	+	28991.5i	0.00482566	+	0.0211426i
$286$	−391628.	+	491086.i	−0.283112	+	0.355012i
$287$	−1.70321e6	+	684782.i	−1.22057	+	0.490736i
$288$	2.41998e6	+	3.03456e6i	1.71922	+	2.15583i
$289$	−852834.	+	1.06942e6i	−0.600648	+	0.753189i
$290$	−50908.9	−	24516.5i	−0.0355467	−	0.0171184i
$291$	1.17224e6	−	1.46995e6i	0.811494	−	1.01758i
$292$	−289447.	+	1.26815e6i	−0.198660	+	0.870388i
$293$	−850323.			−0.578648			−0.289324	−	0.957231i	$-0.593431\pi$
$293$	−850323.			−0.578648			−0.289324	+	0.957231i	$0.593431\pi$
$294$	−612881.	+	1.64095e6i	−0.413530	+	1.10720i
$295$	68180.8			0.0456149
$296$	390849.	−	1.71242e6i	0.259287	−	1.13601i
$297$	−3.31596e6	+	4.15808e6i	−2.18131	+	2.73528i
$298$	1.05352e6	+	507348.i	0.687230	+	0.330952i
$299$	468448.	−	587415.i	0.303029	−	0.379986i
$300$	1.17571e6	+	1.47429e6i	0.754216	+	0.945757i
$301$	−13309.5	−	83602.3i	−0.00846733	−	0.0531866i
$302$	−10386.9	+	13024.7i	−0.00655341	+	0.00821772i
$303$	−563858.	−	2.47042e6i	−0.352828	−	1.54584i
$304$	4799.14	+	6017.93i	0.00297838	+	0.00373476i
$305$	16144.4	−	70733.3i	0.00993740	−	0.0435386i
$306$	473184.	−	227873.i	0.288886	−	0.139120i
$307$	423175.	−	1.85405e6i	0.256256	−	1.12273i	−0.668962	−	0.743296i	$-0.733261\pi$
$307$	423175.	−	1.85405e6i	0.256256	−	1.12273i	0.925218	−	0.379435i	$-0.123882\pi$
$308$	1.00523e6	−	404157.i	0.603796	−	0.242758i
$309$	−1.18105e6	−	5.17452e6i	−0.703675	−	3.08300i
$310$	25050.6	+	31412.5i	0.0148052	+	0.0185651i
$311$	532630.	−	256501.i	0.312266	−	0.150379i	−0.271186	−	0.962527i	$-0.587416\pi$
$311$	532630.	−	256501.i	0.312266	−	0.150379i	0.583452	+	0.812148i	$0.301702\pi$
$312$	−2.36565e6			−1.37583
$313$	−1.37249e6			−0.791861			−0.395931	−	0.918280i	$-0.629578\pi$
$313$	−1.37249e6			−0.791861			−0.395931	+	0.918280i	$0.629578\pi$
$314$	−1.13649e6	+	547304.i	−0.650490	+	0.313260i
$315$	125110.	+	180279.i	0.0710421	+	0.102369i
$316$	1.06124e6	+	511068.i	0.597857	+	0.287913i
$317$	2.20790e6	+	1.06327e6i	1.23405	+	0.594286i	0.933190	−	0.359383i	$-0.117013\pi$
$317$	2.20790e6	+	1.06327e6i	1.23405	+	0.594286i	0.300858	+	0.953669i	$0.402727\pi$
$318$	708731.	+	3.10515e6i	0.393019	+	1.72193i
$319$	−596702.	−	2.61432e6i	−0.328307	−	1.43841i
$320$	44641.8	+	21498.4i	0.0243706	+	0.0117363i
$321$	400523.	+	192882.i	0.216953	+	0.104479i
$322$	716351.	−	288011.i	0.385022	−	0.154799i
$323$	79762.7	−	38411.7i	0.0425396	−	0.0204860i
$324$	−4.47006e6			−2.36565
$325$	−1.35986e6			−0.714143
$326$	257820.	−	124160.i	0.134361	−	0.0647048i
$327$	−3.40810e6	−	4.27362e6i	−1.76256	−	2.21017i
$328$	−566899.	−	2.48374e6i	−0.290952	−	1.27474i
$329$	−677434.	+	742328.i	−0.345046	+	0.378099i
$330$	−24555.9	+	107587.i	−0.0124129	+	0.0543843i
$331$	1.70311e6	−	820175.i	0.854423	−	0.411468i	0.0452055	−	0.998978i	$-0.485606\pi$
$331$	1.70311e6	−	820175.i	0.854423	−	0.411468i	0.809217	+	0.587509i	$0.199891\pi$
$332$	233016.	−	1.02091e6i	0.116022	−	0.508325i
$333$	4.05521e6	+	5.08507e6i	2.00402	+	2.51296i
$334$	−496832.	−	2.17676e6i	−0.243693	−	1.06769i
$335$	97053.4	−	121701.i	0.0472497	−	0.0592492i
$336$	67450.4	+	38201.7i	0.0325939	+	0.0184601i
$337$	472340.	+	592295.i	0.226558	+	0.284095i	0.882098	−	0.471065i	$-0.156130\pi$
$337$	472340.	+	592295.i	0.226558	+	0.284095i	−0.655540	+	0.755160i	$0.727559\pi$
$338$	−390384.	+	489526.i	−0.185866	+	0.233069i
$339$	−140345.	−	67586.4i	−0.0663280	−	0.0319419i
$340$	−7244.93	+	9084.86i	−0.00339889	+	0.00426207i
$341$	−424289.	+	1.85893e6i	−0.197595	+	0.865721i
$342$	893843.			0.413234
$343$	54091.5	+	2.17822e6i	0.0248253	+	0.999692i
$344$	117485.			0.0535286
$345$	29372.7	−	128690.i	0.0132861	−	0.0582101i
$346$	465964.	−	584301.i	0.209249	−	0.262389i
$347$	2.90912e6	+	1.40096e6i	1.29699	+	0.624600i	0.949701	−	0.313157i	$-0.101387\pi$
$347$	2.90912e6	+	1.40096e6i	1.29699	+	0.624600i	0.347293	+	0.937757i	$0.387101\pi$
$348$	2.42581e6	−	3.04187e6i	1.07376	−	1.34646i
$349$	−4363.55	−	5471.72i	−0.00191768	−	0.00240470i	0.780872	−	0.624691i	$-0.214775\pi$
$349$	−4363.55	−	5471.72i	−0.00191768	−	0.00240470i	−0.782789	+	0.622287i	$0.786204\pi$
$350$	−1.21593e6	−	688666.i	−0.530566	−	0.300496i
$351$	3.46955e6	−	4.35068e6i	1.50316	−	1.88491i
$352$	540270.	+	2.36708e6i	0.232410	+	1.01825i
$353$	−246843.	−	309532.i	−0.105435	−	0.132211i	0.726314	−	0.687363i	$-0.241232\pi$
$353$	−246843.	−	309532.i	−0.105435	−	0.132211i	−0.831749	+	0.555151i	$0.812660\pi$
$354$	622367.	−	2.72677e6i	0.263960	−	1.15649i
$355$	−16303.9	+	7851.54i	−0.00686626	+	0.00330662i
$356$	53231.4	−	233222.i	0.0222609	−	0.0975314i
$357$	600991.	−	658562.i	0.249573	−	0.273480i
$358$	471542.	+	2.06596e6i	0.194452	+	0.851951i
$359$	1.53836e6	+	1.92904e6i	0.629973	+	0.789961i	0.989709	−	0.143093i	$-0.0457048\pi$
$359$	1.53836e6	+	1.92904e6i	0.629973	+	0.789961i	−0.359736	+	0.933054i	$0.617133\pi$
$360$	−274378.	+	132134.i	−0.111582	+	0.0537350i
$361$	−2.32543e6			−0.939150
$362$	623637.			0.250127
$363$	−343127.	+	165241.i	−0.136675	+	0.0658190i
$364$	−1.05180e6	+	422878.i	−0.416082	+	0.167287i
$365$	−148482.	−	71504.9i	−0.0583365	−	0.0280934i
$366$	−2.68148e6	−	1.29133e6i	−1.04634	−	0.503890i
$367$	99077.4	+	434086.i	0.0383981	+	0.168233i	0.990491	−	0.137575i	$-0.0439307\pi$
$367$	99077.4	+	434086.i	0.0383981	+	0.168233i	−0.952093	+	0.305808i	$0.901074\pi$
$368$	−7602.92	−	33310.6i	−0.00292658	−	0.0128222i
$369$	8.49942e6	+	4.09311e6i	3.24955	+	1.56490i
$370$	77241.2	+	37197.4i	0.0293322	+	0.0141256i
$371$	2.25878e6	+	3.25482e6i	0.852000	+	1.22770i
$372$	−2.49254e6	+	1.20034e6i	−0.933867	+	0.449727i
$373$	−206503.			−0.0768518			−0.0384259	−	0.999261i	$-0.512234\pi$
$373$	−206503.			−0.0768518			−0.0384259	+	0.999261i	$0.512234\pi$
$374$	328532.			0.121450
$375$	−430947.	+	207533.i	−0.158251	+	0.0762095i
$376$	−869584.	−	1.09042e6i	−0.317206	−	0.397764i
$377$	624341.	+	2.73542e6i	0.226240	+	0.991221i
$378$	5.30564e6	−	2.13315e6i	1.90989	−	0.767877i
$379$	−13389.1	+	58661.5i	−0.00478800	+	0.0209776i	−0.977265	−	0.212019i	$-0.931996\pi$
$379$	−13389.1	+	58661.5i	−0.00478800	+	0.0209776i	0.972477	+	0.232997i	$0.0748532\pi$
$380$	−17817.9	+	8580.63i	−0.00632990	+	0.00304832i
$381$	2.02452e6	−	8.86999e6i	0.714512	−	3.13048i
$382$	−991072.	−	1.24276e6i	−0.347494	−	0.435743i
$383$	899249.	+	3.93987e6i	0.313244	+	1.37241i	0.849158	+	0.528139i	$0.177110\pi$
$383$	899249.	+	3.93987e6i	0.313244	+	1.37241i	−0.535914	+	0.844273i	$0.680033\pi$
$384$	−2.23763e6	+	2.80590e6i	−0.774390	+	0.971055i
$385$	21581.3	+	135561.i	0.00742039	+	0.0466103i
$386$	622337.	+	780386.i	0.212597	+	0.266589i
$387$	−271242.	+	340126.i	−0.0920617	+	0.115442i
$388$	1.12654e6	+	542512.i	0.379898	+	0.182949i
$389$	484355.	−	607362.i	0.162289	−	0.203504i	−0.694037	−	0.719939i	$-0.744170\pi$
$389$	484355.	−	607362.i	0.162289	−	0.203504i	0.856327	+	0.516435i	$0.172741\pi$
$390$	25693.4	−	112570.i	0.00855382	−	0.0374767i
$391$	−392976.			−0.129994
$392$	−2.99715e6	−	401134.i	−0.985130	−	0.131848i
$393$	−9.85576e6			−3.21891
$394$	293787.	−	1.28716e6i	0.0953436	−	0.417728i
$395$	−93046.4	+	116677.i	−0.0300059	+	0.0376262i
$396$	−5.01635e6	−	2.41575e6i	−1.60750	−	0.774129i
$397$	−783774.	+	982821.i	−0.249583	+	0.312967i	−0.890803	−	0.454390i	$-0.849857\pi$
$397$	−783774.	+	982821.i	−0.249583	+	0.312967i	0.641220	+	0.767357i	$0.278429\pi$
$398$	637323.	+	799177.i	0.201675	+	0.252892i
$399$	1.40786e6	−	566033.i	0.442717	−	0.177996i
$400$	−38556.7	+	48348.6i	−0.0120490	+	0.0151089i
$401$	404692.	+	1.77307e6i	0.125679	+	0.550637i	0.998085	+	0.0618548i	$0.0197016\pi$
$401$	404692.	+	1.77307e6i	0.125679	+	0.550637i	−0.872406	+	0.488782i	$0.837441\pi$
$402$	−3.98130e6	−	4.99239e6i	−1.22874	−	1.54079i
$403$	443943.	−	1.94504e6i	0.136165	−	0.596577i
$404$	1.51830e6	−	731173.i	0.462811	−	0.222878i
$405$	126023.	−	552142.i	0.0381779	−	0.167268i
$406$	−827021.	+	2.76209e6i	−0.249001	+	0.831616i
$407$	905341.	+	3.96656e6i	0.270911	+	1.18694i
$408$	771459.	+	967379.i	0.229436	+	0.287704i
$409$	911281.	−	438850.i	0.269367	−	0.129720i	−0.294325	−	0.955705i	$-0.595095\pi$
$409$	911281.	−	438850.i	0.269367	−	0.129720i	0.563692	+	0.825985i	$0.309381\pi$
$410$	124347.			0.0365322
$411$	−5.41436e6			−1.58104
$412$	3.18021e6	−	1.53151e6i	0.923022	−	0.444504i
$413$	−546977.	−	3.43577e6i	−0.157795	−	0.991173i
$414$	−3.57475e6	−	1.72151e6i	−1.02505	−	0.493638i
$415$	119533.	+	57564.2i	0.0340697	+	0.0164071i
$416$	−565295.	−	2.47672e6i	−0.160156	−	0.701688i
$417$	2.22458e6	+	9.74654e6i	0.626482	+	2.74480i
$418$	503765.	+	242601.i	0.141022	+	0.0679127i
$419$	−3.92922e6	−	1.89221e6i	−1.09338	−	0.526545i	−0.201810	−	0.979425i	$-0.564682\pi$
$419$	−3.92922e6	−	1.89221e6i	−1.09338	−	0.526545i	−0.891571	+	0.452880i	$0.850397\pi$
$420$	−134253.	+	147113.i	−0.0371364	+	0.0406939i
$421$	−1.73795e6	+	836954.i	−0.477895	+	0.230142i	−0.657294	−	0.753634i	$-0.728299\pi$
$421$	−1.73795e6	+	836954.i	−0.477895	+	0.230142i	0.179399	+	0.983776i	$0.442585\pi$
$422$	143348.			0.0391841
$423$	5.16449e6			1.40338
$424$	−4.95373e6	+	2.38559e6i	−1.33819	+	0.644438i
$425$	443462.	+	556083.i	0.119092	+	0.149337i
$426$	165183.	+	723715.i	0.0441004	+	0.193216i
$427$	−3.69392e6	−	246097.i	−0.980432	−	0.0653186i
$428$	−65786.5	+	288229.i	−0.0173591	+	0.0760552i
$429$	4.93699e6	−	2.37753e6i	1.29515	−	0.623710i
$430$	−1276.01	+	5590.56i	−0.000332799	+	0.00145809i
$431$	−2.15691e6	−	2.70468e6i	−0.559292	−	0.701331i	0.419134	−	0.907924i	$-0.362334\pi$
$431$	−2.15691e6	−	2.70468e6i	−0.559292	−	0.701331i	−0.978427	+	0.206594i	$0.933762\pi$
$432$	−56310.9	−	246714.i	−0.0145172	−	0.0636040i
$433$	1.80090e6	−	2.25826e6i	0.461605	−	0.578835i	−0.495488	−	0.868615i	$-0.665011\pi$
$433$	1.80090e6	−	2.25826e6i	0.461605	−	0.578835i	0.957093	+	0.289780i	$0.0935822\pi$
$434$	1.38197e6	−	1.51436e6i	0.352189	−	0.385926i
$435$	307342.	+	385395.i	0.0778751	+	0.0976523i
$436$	2.26652e6	−	2.84213e6i	0.571010	−	0.716024i
$437$	−602582.	−	290188.i	−0.150943	−	0.0726903i
$438$	−4.21508e6	+	5.28554e6i	−1.04983	+	1.31645i
$439$	−219262.	+	960648.i	−0.0543002	+	0.237905i	−0.994794	−	0.101906i	$-0.967506\pi$
$439$	−219262.	+	960648.i	−0.0543002	+	0.237905i	0.940494	+	0.339811i	$0.110363\pi$
$440$	−190501.			−0.0469101
$441$	8.08094e6	−	7.75083e6i	1.97863	−	1.89781i
$442$	−343750.			−0.0836926
$443$	−1.65893e6	+	7.26826e6i	−0.401624	+	1.75963i	0.219201	+	0.975680i	$0.429655\pi$
$443$	−1.65893e6	+	7.26826e6i	−0.401624	+	1.75963i	−0.620825	+	0.783949i	$0.713202\pi$
$444$	−3.68054e6	+	4.61525e6i	−0.886042	+	1.11106i
$445$	27306.9	+	13150.3i	0.00653690	+	0.00314800i
$446$	346216.	−	434141.i	0.0824157	−	0.103346i
$447$	−6.36020e6	−	7.97543e6i	−1.50557	−	1.88793i
$448$	725211.	−	2.42206e6i	0.170714	−	0.570152i
$449$	−2.86050e6	+	3.58695e6i	−0.669616	+	0.839672i	−0.994352	−	0.106133i	$-0.966153\pi$
$449$	−2.86050e6	+	3.58695e6i	−0.669616	+	0.839672i	0.324736	+	0.945805i	$0.394725\pi$
$450$	1.59797e6	+	7.00116e6i	0.371995	+	1.62982i
$451$	3.67931e6	+	4.61371e6i	0.851775	+	1.06809i
$452$	23051.8	−	100997.i	0.00530712	−	0.0232520i
$453$	130940.	−	63057.6i	0.0299798	−	0.0144375i
$454$	−380070.	+	1.66520e6i	−0.0865414	+	0.379163i
$455$	−22581.0	−	141840.i	−0.00511346	−	0.0321196i
$456$	468592.	+	2.05304e6i	0.105532	+	0.462365i
$457$	2.54068e6	+	3.18592e6i	0.569063	+	0.713582i	0.980204	−	0.197990i	$-0.0634412\pi$
$457$	2.54068e6	+	3.18592e6i	0.569063	+	0.713582i	−0.411141	+	0.911572i	$0.634870\pi$
$458$	940196.	−	452774.i	0.209438	−	0.100860i
$459$	−2.91057e6			−0.644831
$460$	87785.2			0.0193431
$461$	−4.04023e6	+	1.94567e6i	−0.885428	+	0.426400i	−0.820604	−	0.571497i	$-0.806363\pi$
$461$	−4.04023e6	+	1.94567e6i	−0.885428	+	0.426400i	−0.0648241	+	0.997897i	$0.520649\pi$
$462$	5.61851e6	+	374318.i	1.22466	+	0.0815897i
$463$	998294.	+	480753.i	0.216424	+	0.104224i	0.538955	−	0.842335i	$-0.318819\pi$
$463$	998294.	+	480753.i	0.216424	+	0.104224i	−0.322531	+	0.946559i	$0.604534\pi$
$464$	114958.	+	55360.7i	0.0247881	+	0.0119373i
$465$	−77995.3	−	341720.i	−0.0167277	−	0.0732888i
$466$	253321.	+	1.10987e6i	0.0540389	+	0.236760i
$467$	−4.92199e6	−	2.37031e6i	−1.04436	−	0.502936i	−0.168598	−	0.985685i	$-0.553924\pi$
$467$	−4.92199e6	−	2.37031e6i	−1.04436	−	0.502936i	−0.875759	+	0.482749i	$0.839638\pi$
$468$	5.24871e6	+	2.52765e6i	1.10774	+	0.533460i
$469$	−6.91138e6	−	3.91438e6i	−1.45088	−	0.821734i
$470$	61332.8	−	29536.3i	0.0128070	−	0.00616753i
$471$	1.10043e7			2.28566
$472$	4.82823e6			0.997546
$473$	−245185.	+	118075.i	−0.0503897	+	0.0242664i
$474$	3.81693e6	+	4.78627e6i	0.780311	+	0.978479i
$475$	269363.	+	1.18016e6i	0.0547778	+	0.239997i
$476$	515927.	+	292205.i	0.104369	+	0.0591112i
$477$	4.53042e6	−	1.98491e7i	0.911681	−	3.99433i
$478$	−1.94073e6	+	934605.i	−0.388503	+	0.187093i
$479$	1.00297e6	−	4.39430e6i	0.199733	−	0.875086i	−0.771363	−	0.636395i	$-0.780425\pi$
$479$	1.00297e6	−	4.39430e6i	0.199733	−	0.875086i	0.971096	−	0.238690i	$-0.0767181\pi$
$480$	−278276.	−	348947.i	−0.0551280	−	0.0691283i
$481$	−947277.	−	4.15029e6i	−0.186687	−	0.817930i
$482$	−779342.	+	977264.i	−0.152796	+	0.191600i
$483$	−6.72062e6	−	447742.i	−1.31082	−	0.0873294i
$484$	−157914.	−	198018.i	−0.0306414	−	0.0384231i
$485$	−98771.2	+	123855.i	−0.0190667	+	0.0239089i
$486$	−1.12745e7	−	5.42952e6i	−2.16524	−	1.04273i
$487$	3.49825e6	−	4.38666e6i	0.668387	−	0.838131i	−0.325840	−	0.945425i	$-0.605647\pi$
$487$	3.49825e6	−	4.38666e6i	0.668387	−	0.838131i	0.994227	+	0.107294i	$0.0342185\pi$
$488$	1.14327e6	−	5.00899e6i	0.217320	−	0.952139i
$489$	−2.49641e6			−0.472110
$490$	51640.3	−	138264.i	0.00971624	−	0.0260146i
$491$	4.02638e6			0.753722			0.376861	−	0.926270i	$-0.377003\pi$
$491$	4.02638e6			0.753722			0.376861	+	0.926270i	$0.377003\pi$
$492$	−1.90524e6	+	8.34739e6i	−0.354843	+	1.55467i
$493$	914985.	−	1.14736e6i	0.169550	−	0.212608i
$494$	−527100.	−	253838.i	−0.0971798	−	0.0467993i
$495$	439817.	−	551513.i	0.0806788	−	0.101168i
$496$	−56567.0	−	70932.7i	−0.0103243	−	0.0129462i
$497$	526453.	+	758599.i	0.0956023	+	0.137759i
$498$	3.39330e6	−	4.25507e6i	0.613125	−	0.768835i
$499$	−1.66541e6	−	7.29663e6i	−0.299412	−	1.31181i	−0.871006	−	0.491273i	$-0.836532\pi$
$499$	−1.66541e6	−	7.29663e6i	−0.299412	−	1.31181i	0.571593	−	0.820537i	$-0.306325\pi$
$500$	−198331.	−	248699.i	−0.0354786	−	0.0444887i
$501$	−4.33428e6	+	1.89897e7i	−0.771477	+	3.38006i
$502$	2.56982e6	−	1.23756e6i	0.455138	−	0.219183i
$503$	−150864.	+	660979.i	−0.0265868	+	0.116484i	−0.986480	−	0.163881i	$-0.947599\pi$
$503$	−150864.	+	660979.i	−0.0265868	+	0.116484i	0.959893	+	0.280366i	$0.0904557\pi$
$504$	8.85968e6	+	1.27665e7i	1.55361	+	2.23869i
$505$	47509.8	+	208154.i	0.00829000	+	0.0363208i
$506$	−1.54747e6	−	1.94047e6i	−0.268687	−	0.336923i
$507$	4.92131e6	−	2.36998e6i	0.850278	−	0.409472i
$508$	6.05060e6			1.04025
$509$	1.72338e6			0.294840			0.147420	−	0.989074i	$-0.452903\pi$
$509$	1.72338e6			0.294840			0.147420	+	0.989074i	$0.452903\pi$
$510$	−54411.9	+	26203.4i	−0.00926336	+	0.00446100i
$511$	−2.41210e6	+	8.05594e6i	−0.408642	+	1.36478i
$512$	−206947.	−	99660.5i	−0.0348887	−	0.0168015i
$513$	−4.46301e6	−	2.14927e6i	−0.748747	−	0.360577i
$514$	201278.	+	881855.i	0.0336037	+	0.147228i
$515$	99513.3	+	435996.i	0.0165334	+	0.0724377i
$516$	−355742.	−	171317.i	−0.0588182	−	0.0283253i
$517$	2.91068e6	+	1.40171e6i	0.478926	+	0.230639i
$518$	1.25479e6	−	4.19076e6i	0.205469	−	0.686228i
$519$	−5.87410e6	+	2.82882e6i	−0.957245	+	0.460985i
$520$	199325.			0.0323262
$521$	−7.22785e6			−1.16658			−0.583291	−	0.812263i	$-0.698235\pi$
$521$	−7.22785e6			−1.16658			−0.583291	+	0.812263i	$0.698235\pi$
$522$	1.33495e7	−	6.42878e6i	2.14432	−	1.03265i
$523$	5.44261e6	+	6.82482e6i	0.870068	+	1.09103i	0.995100	+	0.0988783i	$0.0315255\pi$
$523$	5.44261e6	+	6.82482e6i	0.870068	+	1.09103i	−0.125031	+	0.992153i	$0.539903\pi$
$524$	−1.45851e6	−	6.39014e6i	−0.232049	−	1.01667i
$525$	6.95044e6	+	1.00153e7i	1.10056	+	1.58587i
$526$	−163434.	+	716051.i	−0.0257560	+	0.112844i
$527$	−940155.	+	452755.i	−0.147460	+	0.0710128i
$528$	55449.9	−	242942.i	0.00865597	−	0.0379243i
$529$	−2.16197e6	−	2.71103e6i	−0.335901	−	0.421206i
$530$	−59716.5	−	261635.i	−0.00923431	−	0.0404582i
$531$	−1.11471e7	+	1.39780e7i	−1.71564	+	2.15135i
$532$	575339.	+	829042.i	0.0881342	+	0.126998i
$533$	−3.84974e6	−	4.82742e6i	−0.586967	−	0.736033i
$534$	775185.	−	972051.i	0.117639	−	0.147515i
$535$	−33747.4	−	16251.9i	−0.00509749	−	0.00245482i
$536$	6.87285e6	−	8.61828e6i	1.03330	−	1.29571i
$537$	4.11366e6	−	1.80231e7i	0.615592	−	2.69709i
$538$	−2.22893e6			−0.332003
$539$	6.65806e6	−	2.17506e6i	0.987133	−	0.322477i
$540$	650179.			0.0959509
$541$	806435.	−	3.53322e6i	0.118461	−	0.519013i	−0.880525	−	0.473999i	$-0.842810\pi$
$541$	806435.	−	3.53322e6i	0.118461	−	0.519013i	0.998986	−	0.0450132i	$-0.0143330\pi$
$542$	1.06130e6	−	1.33083e6i	0.155182	−	0.194592i
$543$	−4.90173e6	−	2.36055e6i	−0.713428	−	0.343569i
$544$	−828452.	+	1.03885e6i	−0.120025	+	0.150506i
$545$	287161.	+	360088.i	0.0414127	+	0.0519299i
$546$	−5.87877e6	−	391656.i	−0.843927	−	0.0562242i
$547$	5.62201e6	−	7.04978e6i	0.803385	−	1.00741i	−0.196255	−	0.980553i	$-0.562878\pi$
$547$	5.62201e6	−	7.04978e6i	0.803385	−	1.00741i	0.999639	−	0.0268595i	$-0.00855067\pi$
$548$	−801246.	−	3.51049e6i	−0.113976	−	0.499363i
$549$	1.18618e7	+	1.48743e7i	1.67966	+	2.10623i
$550$	−999599.	+	4.37953e6i	−0.140903	+	0.617335i
$551$	2.25027e6	−	1.08367e6i	0.315759	−	0.152062i
$552$	2.08003e6	−	9.11322e6i	0.290551	−	1.27299i
$553$	6.62604e6	+	3.75277e6i	0.921385	+	0.521843i
$554$	1.05442e6	+	4.61972e6i	0.145962	+	0.639501i
$555$	−466312.	−	584737.i	−0.0642605	−	0.0805802i
$556$	−5.99012e6	+	2.88469e6i	−0.821766	+	0.395742i
$557$	2.67171e6			0.364882			0.182441	−	0.983217i	$-0.441600\pi$
$557$	2.67171e6			0.364882			0.182441	+	0.983217i	$0.441600\pi$
$558$	−1.05356e7			−1.43244
$559$	256543.	−	123544.i	0.0347240	−	0.0167222i
$560$	−5683.26	−	3218.81i	−0.000765821	−	0.000433736i
$561$	−2.58224e6	−	1.24354e6i	−0.346409	−	0.166822i
$562$	−985157.	−	474427.i	−0.131572	−	0.0633619i
$563$	269882.	+	1.18243e6i	0.0358841	+	0.157219i	0.989696	−	0.143187i	$-0.0457351\pi$
$563$	269882.	+	1.18243e6i	0.0358841	+	0.157219i	−0.953811	+	0.300406i	$0.902878\pi$
$564$	1.04303e6	+	4.56981e6i	0.138070	+	0.604924i
$565$	11825.2	+	5694.72i	0.00155843	+	0.000750501i
$566$	1.59659e6	+	768876.i	0.209484	+	0.100882i
$567$	−2.88346e7	−	1.92103e6i	−3.76666	−	0.250943i
$568$	−1.15456e6	+	556008.i	−0.150157	+	0.0723119i
$569$	−8.77727e6			−1.13652			−0.568262	−	0.822847i	$-0.692384\pi$
$569$	−8.77727e6			−1.13652			−0.568262	+	0.822847i	$0.692384\pi$
$570$	−102784.			−0.0132507
$571$	−6.58867e6	+	3.17294e6i	−0.845683	+	0.407259i	−0.805973	−	0.591952i	$-0.798358\pi$
$571$	−6.58867e6	+	3.17294e6i	−0.845683	+	0.407259i	−0.0397096	+	0.999211i	$0.512643\pi$
$572$	2.27211e6	+	2.84914e6i	0.290362	+	0.364102i
$573$	3.08571e6	+	1.35194e7i	0.392616	+	1.72016i
$574$	−997567.	−	6.26610e6i	−0.126375	−	0.793812i
$575$	1.19568e6	−	5.23860e6i	0.150815	−	0.660763i
$576$	−1.17061e7	+	5.63737e6i	−1.47013	+	0.707979i
$577$	−3.25307e6	+	1.42526e7i	−0.406774	+	1.78220i	0.192124	+	0.981371i	$0.438462\pi$
$577$	−3.25307e6	+	1.42526e7i	−0.406774	+	1.78220i	−0.598899	+	0.800825i	$0.704395\pi$
$578$	−2.94775e6	−	3.69637e6i	−0.367005	−	0.460209i
$579$	−1.93765e6	−	8.48941e6i	−0.240203	−	1.05240i
$580$	−204395.	+	256303.i	−0.0252290	+	0.0316361i
$581$	1.94183e6	−	6.48534e6i	0.238656	−	0.797063i
$582$	4.05177e6	+	5.08075e6i	0.495835	+	0.621757i
$583$	7.94063e6	−	9.95723e6i	0.967572	−	1.21330i
$584$	−1.05147e7	−	5.06363e6i	−1.27575	−	0.614370i
$585$	−460190.	+	577060.i	−0.0555965	+	0.0697158i
$586$	654005.	−	2.86539e6i	0.0786751	−	0.344698i
$587$	−5.63807e6			−0.675359			−0.337680	−	0.941261i	$-0.609642\pi$
$587$	−5.63807e6			−0.675359			−0.337680	+	0.941261i	$0.609642\pi$
$588$	8.49039e6	+	5.58507e6i	1.01271	+	0.666171i
$589$	−1.77595e6			−0.210932
$590$	−52439.6	+	229753.i	−0.00620197	+	0.0271726i
$591$	−7.18123e6	+	9.00498e6i	−0.845727	+	1.06051i
$592$	−174419.	−	83995.7i	−0.0204545	−	0.00985037i
$593$	1.22897e6	−	1.54109e6i	0.143518	−	0.179966i	−0.704877	−	0.709329i	$-0.748998\pi$
$593$	1.22897e6	−	1.54109e6i	0.143518	−	0.179966i	0.848395	+	0.529364i	$0.177569\pi$
$594$	−1.14613e7	−	1.43721e7i	−1.33281	−	1.67129i
$595$	−50638.5	+	55489.3i	−0.00586392	+	0.00642565i
$596$	4.22978e6	−	5.30398e6i	0.487756	−	0.611627i
$597$	−1.98431e6	−	8.69382e6i	−0.227863	−	0.998332i
$598$	1.61915e6	+	2.03036e6i	0.185155	+	0.232177i
$599$	370563.	−	1.62354e6i	0.0421983	−	0.184883i	−0.949436	−	0.313960i	$-0.898344\pi$
$599$	370563.	−	1.62354e6i	0.0421983	−	0.184883i	0.991635	+	0.129077i	$0.0412014\pi$
$600$	−1.52430e7	+	7.34064e6i	−1.72859	+	0.832446i
$601$	1.35040e6	−	5.91650e6i	0.152502	−	0.668157i	−0.839650	−	0.543127i	$-0.817240\pi$
$601$	1.35040e6	−	5.91650e6i	0.152502	−	0.668157i	0.992153	−	0.125030i	$-0.0399027\pi$
$602$	291957.	+	19450.8i	0.0328343	+	0.00218749i
$603$	9.08288e6	+	3.97947e7i	1.01726	+	4.45689i
$604$	60261.6	+	75565.7i	0.00672123	+	0.00842815i
$605$	28911.3	−	13922.9i	0.00321128	−	0.00154647i
$606$	8.75842e6			0.968823
$607$	−1.33808e7			−1.47404			−0.737020	−	0.675871i	$-0.763768\pi$
$607$	−1.33808e7			−1.47404			−0.737020	+	0.675871i	$0.763768\pi$
$608$	−2.03746e6	+	981188.i	−0.223527	+	0.107645i
$609$	1.69552e7	−	1.85794e7i	1.85251	−	2.02997i
$610$	225937.	+	108806.i	0.0245846	+	0.0118393i
$611$	−3.04551e6	−	1.46664e6i	−0.330032	−	0.158935i
$612$	−678027.	−	2.97063e6i	−0.0731760	−	0.320605i
$613$	−528642.	−	2.31613e6i	−0.0568212	−	0.248950i	0.938538	−	0.345175i	$-0.112180\pi$
$613$	−528642.	−	2.31613e6i	−0.0568212	−	0.248950i	−0.995360	+	0.0962249i	$0.969323\pi$
$614$	5.92223e6	+	2.85200e6i	0.633964	+	0.305301i
$615$	−977357.	−	470670.i	−0.104199	−	0.0501798i
$616$	1.52829e6	+	9.59976e6i	0.162275	+	1.01932i
$617$	−3.26427e6	+	1.57199e6i	−0.345202	+	0.166240i	−0.598449	−	0.801161i	$-0.704216\pi$
$617$	−3.26427e6	+	1.57199e6i	−0.345202	+	0.166240i	0.253247	+	0.967402i	$0.418502\pi$
$618$	1.83453e7			1.93220
$619$	1.83157e7			1.92131			0.960656	−	0.277740i	$-0.0895855\pi$
$619$	1.83157e7			1.92131			0.960656	+	0.277740i	$0.0895855\pi$
$620$	210017.	−	101139.i	0.0219420	−	0.0105667i
$621$	1.37096e7	+	1.71912e7i	1.42657	+	1.78887i
$622$	454688.	+	1.99212e6i	0.0471235	+	0.206461i
$623$	443603.	−	1.48155e6i	0.0457904	−	0.152931i
$624$	−58018.4	+	254195.i	−0.00596491	+	0.0261340i
$625$	−8.74404e6	+	4.21091e6i	−0.895390	+	0.431197i
$626$	1.05562e6	−	4.62497e6i	0.107664	−	0.471708i
$627$	−3.04128e6	−	3.81364e6i	−0.308949	−	0.387410i
$628$	1.62848e6	+	7.13483e6i	0.164772	+	0.721912i
$629$	−1.38825e6	+	1.74082e6i	−0.139908	+	0.175439i
$630$	−703722.	+	282934.i	−0.0706399	+	0.0284010i
$631$	−5.66152e6	−	7.09932e6i	−0.566056	−	0.709812i	0.413608	−	0.910455i	$-0.364268\pi$
$631$	−5.66152e6	−	7.09932e6i	−0.566056	−	0.709812i	−0.979664	+	0.200643i	$0.935697\pi$
$632$	−6.58909e6	+	8.26246e6i	−0.656195	+	0.822843i
$633$	−1.12670e6	−	542591.i	−0.111763	−	0.0538225i
$634$	−5.28113e6	+	6.62232e6i	−0.521799	+	0.654315i
$635$	−170582.	+	747371.i	−0.0167880	+	0.0735532i
$636$	1.84785e7			1.81144
$637$	−6.96647e6	+	2.27581e6i	−0.680243	+	0.222222i
$638$	9.26858e6			0.901491
$639$	1.05590e6	−	4.62621e6i	0.102299	−	0.448201i
$640$	188539.	−	236420.i	0.0181949	−	0.0228157i
$641$	652519.	+	314237.i	0.0627261	+	0.0302073i	0.464984	−	0.885319i	$-0.346060\pi$
$641$	652519.	+	314237.i	0.0627261	+	0.0302073i	−0.402258	+	0.915526i	$0.631774\pi$
$642$	−958019.	+	1.20132e6i	−0.0917353	+	0.115032i
$643$	9.21268e6	+	1.15523e7i	0.878736	+	1.10190i	0.994088	+	0.108576i	$0.0346290\pi$
$643$	9.21268e6	+	1.15523e7i	0.878736	+	1.10190i	−0.115352	+	0.993325i	$0.536800\pi$
$644$	−704252.	−	4.42368e6i	−0.0669134	−	0.420309i
$645$	31190.3	−	39111.5i	0.00295203	−	0.00370173i
$646$	68090.7	+	298325.i	0.00641958	+	0.0281260i
$647$	−1.20125e7	−	1.50632e7i	−1.12816	−	1.41467i	−0.897153	−	0.441721i	$-0.854368\pi$
$647$	−1.20125e7	−	1.50632e7i	−1.12816	−	1.41467i	−0.231010	−	0.972951i	$-0.574203\pi$
$648$	8.92432e6	−	3.91000e7i	0.834906	−	3.65796i
$649$	−1.00763e7	+	4.85248e6i	−0.939050	+	0.452223i
$650$	1.04590e6	−	4.58239e6i	0.0970974	−	0.425411i
$651$	−1.65943e7	+	6.67178e6i	−1.53464	+	0.617005i
$652$	−369432.	−	1.61859e6i	−0.0340342	−	0.149113i
$653$	−1.41125e6	−	1.76965e6i	−0.129515	−	0.162407i	0.712846	−	0.701321i	$-0.247406\pi$
$653$	−1.41125e6	−	1.76965e6i	−0.129515	−	0.162407i	−0.842360	+	0.538914i	$0.818835\pi$
$654$	1.70223e7	−	8.19753e6i	1.55623	−	0.749443i
$655$	830430.			0.0756309
$656$	−280788.			−0.0254753
$657$	3.89353e7	−	1.87503e7i	3.51909	−	1.69470i
$658$	−1.98044e6	−	2.85373e6i	−0.178318	−	0.256950i
$659$	4.48786e6	+	2.16124e6i	0.402555	+	0.193860i	0.624196	−	0.781268i	$-0.285427\pi$
$659$	4.48786e6	+	2.16124e6i	0.402555	+	0.193860i	−0.221640	+	0.975128i	$0.571141\pi$
$660$	576835.	+	277789.i	0.0515456	+	0.0248230i
$661$	240091.	+	1.05191e6i	0.0213734	+	0.0936429i	0.984490	−	0.175443i	$-0.0561357\pi$
$661$	240091.	+	1.05191e6i	0.0213734	+	0.0936429i	−0.963116	+	0.269086i	$0.913279\pi$
$662$	1.45389e6	+	6.36989e6i	0.128939	+	0.564920i
$663$	2.70185e6	+	1.30114e6i	0.238713	+	0.114958i
$664$	8.46477e6	+	4.07642e6i	0.745066	+	0.358805i
$665$	−118624.	+	47693.0i	−0.0104020	+	0.00418216i
$666$	−2.02544e7	+	9.75402e6i	−1.76944	+	0.852115i
$667$	−1.10867e7			−0.964909
$668$	−1.29537e7			−1.12319
$669$	−4.36451e6	+	2.10184e6i	−0.377025	+	0.181566i
$670$	335457.	+	420650.i	0.0288702	+	0.0362021i
$671$	2.64820e6	+	1.16025e7i	0.227062	+	0.994825i
$672$	−1.53517e7	+	1.68223e7i	−1.31139	+	1.43702i
$673$	2.61179e6	−	1.14430e7i	0.222280	−	0.973872i	−0.733477	−	0.679714i	$-0.762104\pi$
$673$	2.61179e6	−	1.14430e7i	0.222280	−	0.973872i	0.955757	−	0.294158i	$-0.0950392\pi$
$674$	−2.35918e6	+	1.13612e6i	−0.200038	+	0.0963331i
$675$	8.85576e6	−	3.87996e7i	0.748112	−	3.27769i
$676$	2.26489e6	+	2.84009e6i	0.190626	+	0.239037i
$677$	4.64406e6	+	2.03469e7i	0.389427	+	1.70619i	0.666638	+	0.745381i	$0.267733\pi$
$677$	4.64406e6	+	2.03469e7i	0.389427	+	1.70619i	−0.277211	+	0.960809i	$0.589410\pi$
$678$	335693.	−	420946.i	0.0280458	−	0.0351683i
$679$	7.03371e6	+	3.98367e6i	0.585477	+	0.331596i
$680$	−65001.8	−	81509.7i	−0.00539080	−	0.00675985i
$681$	9.29031e6	−	1.16497e7i	0.767649	−	0.962601i
$682$	−5.93783e6	−	2.85951e6i	−0.488840	−	0.235413i
$683$	6.39218e6	−	8.01554e6i	0.524321	−	0.657478i	−0.447199	−	0.894434i	$-0.647579\pi$
$683$	6.39218e6	−	8.01554e6i	0.524321	−	0.657478i	0.971520	+	0.236957i	$0.0761500\pi$
$684$	1.15395e6	−	5.05580e6i	0.0943078	−	0.413189i
$685$	456205.			0.0371479
$686$	−7.38168e6	−	1.49305e6i	−0.598887	−	0.121133i
$687$	−9.10368e6			−0.735910
$688$	2881.36	−	12624.1i	0.000232074	−	0.00101678i
$689$	−8.30844e6	+	1.04185e7i	−0.666763	+	0.836095i
$690$	411064.	+	197958.i	0.0328691	+	0.0158289i
$691$	1.14076e7	−	1.43047e7i	0.908866	−	1.13968i	−0.0808635	−	0.996725i	$-0.525768\pi$
$691$	1.14076e7	−	1.43047e7i	0.908866	−	1.13968i	0.989729	−	0.142956i	$-0.0456608\pi$
$692$	−2.70339e6	−	3.38994e6i	−0.214607	−	0.269108i
$693$	−3.13203e7	−	1.77388e7i	−2.47738	−	1.40311i
$694$	−6.95838e6	+	8.72553e6i	−0.548415	+	0.687691i
$695$	−187440.	−	821227.i	−0.0147197	−	0.0644913i
$696$	2.17645e7	+	2.72918e7i	1.70304	+	2.13554i
$697$	−718632.	+	3.14853e6i	−0.0560305	+	0.245486i
$698$	21794.5	−	10495.7i	0.00169320	−	0.000815403i
$699$	2.20993e6	−	9.68235e6i	0.171075	−	0.749528i
$700$	−5.46504e6	+	5.98855e6i	−0.421549	+	0.461931i
$701$	1.35993e6	+	5.95826e6i	0.104526	+	0.457957i	0.999920	+	0.0126819i	$0.00403689\pi$
$701$	1.35993e6	+	5.95826e6i	0.104526	+	0.457957i	−0.895394	+	0.445275i	$0.853106\pi$
$702$	1.19922e7	+	1.50378e7i	0.918454	+	1.15171i
$703$	−3.41421e6	+	1.64420e6i	−0.260557	+	0.125477i
$704$	−8.12757e6			−0.618058
$705$	−593870.			−0.0450006
$706$	1.23290e6	−	593734.i	0.0930930	−	0.0448312i
$707$	1.01082e7	−	4.06402e6i	0.760543	−	0.305779i
$708$	−1.46198e7	−	7.04053e6i	−1.09612	−	0.527864i
$709$	−1.58528e7	−	7.63432e6i	−1.18438	−	0.570368i	−0.265196	−	0.964195i	$-0.585437\pi$
$709$	−1.58528e7	−	7.63432e6i	−1.18438	−	0.570368i	−0.919185	+	0.393827i	$0.871151\pi$
$710$	−13918.1	−	60979.0i	−0.00103617	−	0.00453978i
$711$	−8.70788e6	−	3.81517e7i	−0.646009	−	2.83035i
$712$	1.93374e6	+	931239.i	0.142954	+	0.0688432i
$713$	7.10257e6	+	3.42042e6i	0.523229	+	0.251974i
$714$	1.75696e6	+	2.53171e6i	0.128978	+	0.185853i
$715$	−415983.	+	200327.i	−0.0304306	+	0.0146546i
$716$	1.22944e7			0.896237
$717$	1.87916e7			1.36510
$718$	−7.68361e6	+	3.70023e6i	−0.556229	+	0.267866i
$719$	−689596.	−	864726.i	−0.0497476	−	0.0623816i	0.756335	−	0.654184i	$-0.226988\pi$
$719$	−689596.	−	864726.i	−0.0497476	−	0.0623816i	−0.806083	+	0.591803i	$0.798416\pi$
$720$	7468.89	+	32723.3i	0.000536939	+	0.00235248i
$721$	2.11724e7	−	8.51244e6i	1.51681	−	0.609840i
$722$	1.78855e6	−	7.83614e6i	0.127690	−	0.559447i
$723$	9.82465e6	−	4.73130e6i	0.698990	−	0.336616i
$724$	805116.	−	3.52745e6i	0.0570837	−	0.250100i
$725$	1.25110e7	+	1.56883e7i	0.883988	+	1.10849i
$726$	−292915.	−	1.28335e6i	−0.0206253	−	0.0903654i
$727$	4.44474e6	−	5.57353e6i	0.311896	−	0.391106i	−0.601032	−	0.799225i	$-0.705244\pi$
$727$	4.44474e6	−	5.57353e6i	0.311896	−	0.391106i	0.912929	+	0.408119i	$0.133815\pi$
$728$	−1.59908e6	−	1.00444e7i	−0.111826	−	0.702420i
$729$	3.42925e7	+	4.30014e7i	2.38990	+	2.99684i
$730$	355156.	−	445351.i	0.0246667	−	0.0309311i
$731$	−134182.	−	64618.4i	−0.00928751	−	0.00447263i
$732$	−1.07659e7	+	1.35000e7i	−0.742631	+	0.931230i
$733$	−6.32174e6	+	2.76974e7i	−0.434587	+	1.90405i	−0.00721589	+	0.999974i	$0.502297\pi$
$733$	−6.32174e6	+	2.76974e7i	−0.434587	+	1.90405i	−0.427371	+	0.904076i	$0.640560\pi$
$734$	−1.53897e6			−0.105436
$735$	−929235.	+	891276.i	−0.0634465	+	0.0608547i
$736$	1.00382e7			0.683061
$737$	−5.68174e6	+	2.48933e7i	−0.385312	+	1.68816i
$738$	−2.03299e7	+	2.54929e7i	−1.37403	+	1.72297i
$739$	1.61421e7	+	7.77361e6i	1.08730	+	0.523615i	0.889643	−	0.456657i	$-0.150953\pi$
$739$	1.61421e7	+	7.77361e6i	1.08730	+	0.523615i	0.197654	+	0.980272i	$0.436668\pi$
$740$	310116.	−	388874.i	0.0208183	−	0.0261053i
$741$	3.18215e6	+	3.99029e6i	0.212900	+	0.266968i
$742$	−1.27053e7	+	5.10819e6i	−0.847177	+	0.340610i
$743$	1.14479e7	−	1.43552e7i	0.760771	−	0.953977i	−0.239084	−	0.970999i	$-0.576847\pi$
$743$	1.14479e7	−	1.43552e7i	0.760771	−	0.953977i	0.999855	+	0.0170222i	$0.00541860\pi$
$744$	−5.52325e6	−	2.41989e7i	−0.365816	−	1.60274i
$745$	535899.	+	671997.i	0.0353747	+	0.0443584i
$746$	158827.	−	695866.i	0.0104490	−	0.0457803i
$747$	−3.13444e7	+	1.50947e7i	−2.05522	+	0.989743i
$748$	424136.	−	1.85826e6i	0.0277173	−	0.121437i
$749$	−548231.	+	1.83098e6i	−0.0357074	+	0.119256i
$750$	−367884.	−	1.61181e6i	−0.0238813	−	0.104631i
$751$	9.51635e6	+	1.19331e7i	0.615702	+	0.772066i	0.987733	−	0.156155i	$-0.0499098\pi$
$751$	9.51635e6	+	1.19331e7i	0.615702	+	0.772066i	−0.372031	+	0.928220i	$0.621338\pi$
$752$	−138496.	+	66696.1i	−0.00893084	+	0.00430087i
$753$	−2.48829e7			−1.59924
$754$	−9.69790e6			−0.621226
$755$	−11032.8	+	5313.12i	−0.000704399	+	0.000339221i
$756$	−5.21603e6	−	3.27639e7i	−0.331922	−	2.08493i
$757$	−1.81990e6	−	876418.i	−0.115427	−	0.0555868i	0.375279	−	0.926912i	$-0.377547\pi$
$757$	−1.81990e6	−	876418.i	−0.115427	−	0.0555868i	−0.490706	+	0.871325i	$0.663261\pi$
$758$	−187377.	−	90236.2i	−0.0118453	−	0.00570437i
$759$	4.81807e6	+	2.11093e7i	0.303577	+	1.33006i
$760$	−39482.8	−	172985.i	−0.00247956	−	0.0108636i
$761$	−1.86205e6	−	896715.i	−0.116555	−	0.0561297i	0.374698	−	0.927147i	$-0.377746\pi$
$761$	−1.86205e6	−	896715.i	−0.116555	−	0.0561297i	−0.491252	+	0.871017i	$0.663461\pi$
$762$	2.83327e7	+	1.36443e7i	1.76766	+	0.851262i
$763$	1.58419e7	−	1.73594e7i	0.985133	−	1.07950i
$764$	−8.30886e6	+	4.00134e6i	−0.515001	+	0.248011i
$765$	386048.			0.0238500
$766$	−1.39680e7			−0.860129
$767$	1.05430e7	−	5.07726e6i	0.647109	−	0.311631i
$768$	−1.94669e7	−	2.44107e7i	−1.19095	−	1.49340i
$769$	−5.06957e6	−	2.22112e7i	−0.309140	−	1.35443i	−0.855900	−	0.517142i	$-0.826996\pi$
$769$	−5.06957e6	−	2.22112e7i	−0.309140	−	1.35443i	0.546760	−	0.837290i	$-0.315861\pi$
$770$	−473406.	−	31539.4i	−0.0287745	−	0.00191702i
$771$	1.75592e6	−	7.69317e6i	0.106382	−	0.466090i
$772$	5.21750e6	−	2.51261e6i	0.315079	−	0.151734i
$773$	−4.34818e6	+	1.90506e7i	−0.261733	+	1.14673i	0.657637	+	0.753335i	$0.271556\pi$
$773$	−4.34818e6	+	1.90506e7i	−0.261733	+	1.14673i	−0.919371	+	0.393393i	$0.871301\pi$
$774$	−937526.	−	1.17562e6i	−0.0562511	−	0.0705366i
$775$	−3.17496e6	−	1.39104e7i	−0.189882	−	0.831927i
$776$	−6.99450e6	+	8.77082e6i	−0.416967	+	0.522861i
$777$	−2.57252e7	+	2.81895e7i	−1.52864	+	1.67508i
$778$	1.67414e6	+	2.09930e6i	0.0991612	+	0.124344i
$779$	−3.42693e6	+	4.29724e6i	−0.202331	+	0.253715i
$780$	−603554.	−	290656.i	−0.0355206	−	0.0171058i
$781$	1.85071e6	−	2.32072e6i	0.108571	−	0.136143i
$782$	302248.	−	1.32423e6i	0.0176745	−	0.0774369i
$783$	−8.21132e7			−4.78639
$784$	−116609.	+	312214.i	−0.00677552	+	0.0181410i
$785$	−927206.			−0.0537034
$786$	7.58032e6	−	3.32116e7i	0.437654	−	1.91749i
$787$	−8.54873e6	+	1.07198e7i	−0.492000	+	0.616948i	−0.964404	−	0.264434i	$-0.914815\pi$
$787$	−8.54873e6	+	1.07198e7i	−0.492000	+	0.616948i	0.472404	+	0.881382i	$0.343386\pi$
$788$	−6.90124e6	−	3.32346e6i	−0.395924	−	0.190667i
$789$	3.99493e6	−	5.00948e6i	0.228463	−	0.286484i
$790$	−321608.	−	403283.i	−0.0183341	−	0.0229902i
$791$	192102.	−	641582.i	0.0109167	−	0.0364595i
$792$	3.11457e7	−	3.90555e7i	1.76435	−	2.21243i
$793$	−2.77087e6	−	1.21400e7i	−0.156471	−	0.685543i
$794$	−2.70905e6	−	3.39704e6i	−0.152499	−	0.191227i
$795$	−520958.	+	2.28246e6i	−0.0292338	+	0.128081i
$796$	5.34313e6	−	2.57312e6i	0.298891	−	0.143938i
$797$	−2.62543e6	+	1.15027e7i	−0.146404	+	0.641439i	0.847462	+	0.530855i	$0.178129\pi$
$797$	−2.62543e6	+	1.15027e7i	−0.146404	+	0.641439i	−0.993867	+	0.110584i	$0.964728\pi$
$798$	824578.	+	5.17949e6i	0.0458379	+	0.287925i
$799$	393418.	+	1.72368e6i	0.0218015	+	0.0955188i
$800$	−1.13278e7	−	1.42046e7i	−0.625777	−	0.784700i
$801$	−7.16049e6	+	3.44831e6i	−0.394332	+	0.189900i
$802$	−6.28609e6			−0.345100
$803$	2.70328e7			1.47946
$804$	−3.33781e7	+	1.60740e7i	−1.82105	+	0.876970i
$805$	566268.	+	37726.0i	0.0307987	+	0.00205188i
$806$	6.21288e6	+	2.99196e6i	0.336864	+	0.162225i
$807$	1.75192e7	+	8.43682e6i	0.946960	+	0.456032i
$808$	3.36441e6	+	1.47404e7i	0.181293	+	0.794295i
$809$	−4.19566e6	−	1.83824e7i	−0.225387	−	0.987486i	−0.953349	−	0.301869i	$-0.902390\pi$
$809$	−4.19566e6	−	1.83824e7i	−0.225387	−	0.987486i	0.727962	−	0.685617i	$-0.240468\pi$
$810$	1.76366e6	+	849334.i	0.0944501	+	0.0454848i
$811$	−7.73343e6	−	3.72422e6i	−0.412876	−	0.198831i	0.215903	−	0.976415i	$-0.430731\pi$
$811$	−7.73343e6	−	3.72422e6i	−0.412876	−	0.198831i	−0.628779	+	0.777584i	$0.716445\pi$
$812$	1.45554e7	+	8.24370e6i	0.774700	+	0.438765i
$813$	−1.33791e7	+	6.44304e6i	−0.709906	+	0.341873i
$814$	−1.40627e7			−0.743887
$815$	210343.			0.0110926
$816$	122868.	−	59170.0i	0.00645970	−	0.00311083i
$817$	−158035.	−	198170.i	−0.00828320	−	0.0103868i
$818$	777929.	+	3.40833e6i	0.0406497	+	0.178098i
$819$	3.27711e7	+	1.85605e7i	1.70719	+	0.966897i
$820$	160532.	−	703337.i	0.00833734	−	0.0365283i
$821$	−1.47977e7	+	7.12618e6i	−0.766188	+	0.368977i	−0.775801	−	0.630977i	$-0.782654\pi$
$821$	−1.47977e7	+	7.12618e6i	−0.766188	+	0.368977i	0.00961360	+	0.999954i	$0.496940\pi$
$822$	4.16433e6	−	1.82451e7i	0.214964	−	0.941818i
$823$	8.35701e6	+	1.04794e7i	0.430082	+	0.539306i	0.948899	−	0.315579i	$-0.102199\pi$
$823$	8.35701e6	+	1.04794e7i	0.430082	+	0.539306i	−0.518817	+	0.854885i	$0.673627\pi$
$824$	7.04705e6	+	3.08751e7i	0.361567	+	1.58413i
$825$	2.44339e7	−	3.06391e7i	1.24985	−	1.56726i
$826$	1.19984e7	+	799362.i	0.611891	+	0.0407656i
$827$	−425274.	−	533277.i	−0.0216225	−	0.0271137i	0.770903	−	0.636953i	$-0.219805\pi$
$827$	−425274.	−	533277.i	−0.0216225	−	0.0271137i	−0.792525	+	0.609839i	$0.791234\pi$
$828$	−1.43523e7	+	1.79972e7i	−0.727522	+	0.912283i
$829$	−1.97609e6	−	951635.i	−0.0998667	−	0.0480933i	0.383284	−	0.923631i	$-0.374793\pi$
$829$	−1.97609e6	−	951635.i	−0.0998667	−	0.0480933i	−0.483150	+	0.875537i	$0.660508\pi$
$830$	−285914.	+	358525.i	−0.0144059	+	0.0180644i
$831$	9.19862e6	−	4.03018e7i	0.462083	−	2.02452i
$832$	8.50404e6			0.425909
$833$	3.20247e6	+	2.10662e6i	0.159909	+	0.105190i
$834$	−3.45545e7			−1.72024
$835$	365199.	−	1.60004e6i	0.0181265	−	0.0794174i
$836$	2.02257e6	−	2.53622e6i	0.100089	−	0.125508i
$837$	5.26051e7	+	2.53333e7i	2.59546	+	1.24991i
$838$	9.39838e6	−	1.17852e7i	0.462320	−	0.579731i
$839$	−1.56591e6	−	1.96359e6i	−0.0768000	−	0.0963041i	0.741947	−	0.670458i	$-0.233902\pi$
$839$	−1.56591e6	−	1.96359e6i	−0.0768000	−	0.0963041i	−0.818747	+	0.574154i	$0.805331\pi$
$840$	−1.01878e6	−	1.46803e6i	−0.0498177	−	0.0717854i
$841$	1.30251e7	−	1.63330e7i	0.635028	−	0.796299i
$842$	−1.48363e6	−	6.50021e6i	−0.0721183	−	0.315971i
$843$	5.94748e6	+	7.45791e6i	0.288247	+	0.361450i
$844$	185062.	−	810811.i	0.00894256	−	0.0391799i
$845$	−414661.	+	199690.i	−0.0199780	+	0.00962089i
$846$	−3.97214e6	+	1.74031e7i	−0.190809	+	0.835989i
$847$	−933545.	−	1.34520e6i	−0.0447123	−	0.0644287i
$848$	134846.	+	590799.i	0.00643945	+	0.0282131i
$849$	−9.63875e6	−	1.20866e7i	−0.458935	−	0.575487i
$850$	−2.21495e6	+	1.06666e6i	−0.105152	+	0.0506383i
$851$	1.68212e7			0.796218
$852$	4.30677e6			0.203260
$853$	2.62780e7	−	1.26548e7i	1.23657	−	0.595501i	0.302691	−	0.953089i	$-0.402115\pi$
$853$	2.62780e7	−	1.26548e7i	1.23657	−	0.595501i	0.933880	+	0.357588i	$0.116401\pi$
$854$	3.67038e6	−	1.22583e7i	0.172213	−	0.575158i
$855$	591959.	+	285073.i	0.0276934	+	0.0133364i
$856$	−2.38983e6	−	1.15088e6i	−0.111476	−	0.0536841i
$857$	−4.84296e6	−	2.12184e7i	−0.225247	−	0.986872i	−0.953460	−	0.301520i	$-0.902506\pi$
$857$	−4.84296e6	−	2.12184e7i	−0.225247	−	0.986872i	0.728213	−	0.685351i	$-0.240351\pi$
$858$	4.21454e6	+	1.84651e7i	0.195448	+	0.856315i
$859$	−1.42835e7	−	6.87856e6i	−0.660467	−	0.318064i	0.0734544	−	0.997299i	$-0.476598\pi$
$859$	−1.42835e7	−	6.87856e6i	−0.660467	−	0.318064i	−0.733921	+	0.679234i	$0.762312\pi$
$860$	29974.3	+	14434.8i	0.00138198	+	0.000665527i
$861$	−1.58773e7	+	5.30270e7i	−0.729908	+	2.43775i
$862$	1.07731e7	−	5.18803e6i	0.493823	−	0.237812i
$863$	−8.71179e6			−0.398181			−0.199090	−	0.979981i	$-0.563799\pi$
$863$	−8.71179e6			−0.398181			−0.199090	+	0.979981i	$0.563799\pi$
$864$	7.43475e7			3.38830
$865$	494942.	−	238351.i	0.0224913	−	0.0108312i
$866$	6.22468e6	+	7.80550e6i	0.282048	+	0.353676i
$867$	9.17785e6	+	4.02108e7i	0.414661	+	1.81675i
$868$	−6.78146e6	−	9.77183e6i	−0.305509	−	0.440227i
$869$	5.44716e6	−	2.38656e7i	0.244692	−	1.07207i
$870$	−1.53507e6	+	739252.i	−0.0687592	+	0.0331127i
$871$	5.94492e6	−	2.60464e7i	0.265522	−	1.16333i
$872$	2.03353e7	+	2.54997e7i	0.905648	+	1.13565i
$873$	−9.24364e6	−	4.04990e7i	−0.410495	−	1.79849i
$874$	1.44133e6	−	1.80737e6i	0.0638240	−	0.0800327i
$875$	−1.17248e6	−	1.68950e6i	−0.0517707	−	0.0745997i
$876$	2.44547e7	+	3.06652e7i	1.07672	+	1.35016i
$877$	1.41651e7	−	1.77624e7i	0.621899	−	0.779836i	−0.366711	−	0.930335i	$-0.619516\pi$
$877$	1.41651e7	−	1.77624e7i	0.621899	−	0.779836i	0.988610	+	0.150498i	$0.0480878\pi$
$878$	−3.06851e6	−	1.47772e6i	−0.134336	−	0.0646927i
$879$	−1.59863e7	+	2.00462e7i	−0.697872	+	0.875104i
$880$	−4672.11	+	20469.9i	−0.000203379	+	0.000891063i
$881$	−7.85974e6			−0.341168			−0.170584	−	0.985343i	$-0.554565\pi$
$881$	−7.85974e6			−0.341168			−0.170584	+	0.985343i	$0.554565\pi$
$882$	1.99032e7	+	3.31922e7i	0.861492	+	1.43670i
$883$	−4.24134e7			−1.83063			−0.915316	−	0.402736i	$-0.868059\pi$
$883$	−4.24134e7			−1.83063			−0.915316	+	0.402736i	$0.868059\pi$
$884$	−443782.	+	1.94434e6i	−0.0191002	+	0.0836836i
$885$	1.28182e6	−	1.60735e6i	0.0550134	−	0.0689846i
$886$	−2.32164e7	−	1.11804e7i	−0.993597	−	0.478491i
$887$	−2.05635e7	+	2.57859e7i	−0.877584	+	1.10046i	0.116644	+	0.993174i	$0.462786\pi$
$887$	−2.05635e7	+	2.57859e7i	−0.877584	+	1.10046i	−0.994229	+	0.107282i	$0.965785\pi$
$888$	−3.30220e7	−	4.14082e7i	−1.40530	−	1.76220i
$889$	3.90301e7	+	2.60027e6i	1.65632	+	0.110348i
$890$	−65315.7	+	81903.4i	−0.00276403	+	0.00346598i
$891$	2.06718e7	+	9.05690e7i	0.872336	+	3.82195i
$892$	−2.00864e6	−	2.51876e6i	−0.0845261	−	0.105992i
$893$	−669568.	+	2.93357e6i	−0.0280974	+	0.123103i
$894$	3.17671e7	−	1.52982e7i	1.32933	−	0.640173i
$895$	−346610.	+	1.51860e6i	−0.0144638	+	0.0633703i
$896$	−1.34263e7	−	7.60420e6i	−0.558708	−	0.316434i
$897$	−5.04125e6	−	2.20871e7i	−0.209198	−	0.916555i
$898$	−9.88709e6	−	1.23980e7i	−0.409145	−	0.513052i
$899$	−2.65237e7	+	1.27732e7i	−1.09455	+	0.527107i
$900$	4.16633e7			1.71454
$901$	6.96985e6			0.286030
$902$	−1.83770e7	+	8.84988e6i	−0.752068	+	0.362177i
$903$	−2.22113e6	−	1.25798e6i	−0.0906473	−	0.0513397i
$904$	837403.	+	403272.i	0.0340811	+	0.0164126i
$905$	413012.	+	198896.i	0.0167626	+	0.00807244i
$906$	111779.	+	489737.i	0.00452419	+	0.0198218i
$907$	−2.15496e6	−	9.44150e6i	−0.0869803	−	0.381086i	0.912636	−	0.408773i	$-0.134043\pi$
$907$	−2.15496e6	−	9.44150e6i	−0.0869803	−	0.381086i	−0.999617	+	0.0276868i	$0.991186\pi$
$908$	8.92809e6	+	4.29954e6i	0.359372	+	0.173064i
$909$	−5.04421e7	−	2.42916e7i	−2.02480	−	0.975095i
$910$	495335.	+	33000.3i	0.0198288	+	0.00132104i
$911$	3.23671e7	−	1.55872e7i	1.29213	−	0.622258i	0.343653	−	0.939097i	$-0.388335\pi$
$911$	3.23671e7	−	1.55872e7i	1.29213	−	0.622258i	0.948480	+	0.316838i	$0.102621\pi$
$912$	232097.			0.00924021
$913$	−2.17625e7			−0.864035
$914$	−1.26899e7	+	6.11113e6i	−0.502449	+	0.241967i
$915$	−1.36400e6	−	1.71041e6i	−0.0538596	−	0.0675378i
$916$	−1.34721e6	−	5.90251e6i	−0.0530514	−	0.232433i
$917$	−6.66208e6	−	4.18471e7i	−0.261629	−	1.64339i
$918$	2.23859e6	−	9.80792e6i	0.0876735	−	0.384123i
$919$	1.81877e7	−	8.75874e6i	0.710378	−	0.342100i	−0.0435555	−	0.999051i	$-0.513869\pi$
$919$	1.81877e7	−	8.75874e6i	0.710378	−	0.342100i	0.753933	+	0.656951i	$0.228154\pi$
$920$	−175260.	+	767865.i	−0.00682674	+	0.0299099i
$921$	−3.57531e7	−	4.48329e7i	−1.38888	−	1.74160i
$922$	−3.44900e6	−	1.51111e7i	−0.133618	−	0.585420i
$923$	−1.93644e6	+	2.42822e6i	−0.0748170	+	0.0938175i
$924$	9.37074e6	−	3.12965e7i	0.361072	−	1.20591i
$925$	−1.89822e7	−	2.38029e7i	−0.729444	−	0.914694i
$926$	−2.38784e6	+	2.99425e6i	−0.0915119	+	0.114752i
$927$	−1.05655e8	−	5.08809e7i	−4.03824	−	1.94471i
$928$	−2.33724e7	+	2.93080e7i	−0.890908	+	1.11716i
$929$	−4.75042e6	+	2.08129e7i	−0.180589	+	0.791214i	0.800761	+	0.598985i	$0.204429\pi$
$929$	−4.75042e6	+	2.08129e7i	−0.180589	+	0.791214i	−0.981350	+	0.192229i	$0.938428\pi$
$930$	1.21150e6			0.0459322
$931$	3.35500e6	+	5.59508e6i	0.126858	+	0.211559i
$932$	6.60474e6			0.249067
$933$	3.96663e6	−	1.73789e7i	0.149182	−	0.653610i
$934$	1.17730e7	−	1.47629e7i	0.441591	−	0.553738i
$935$	217575.	+	104778.i	0.00813916	+	0.00391961i
$936$	−3.25884e7	+	4.08646e7i	−1.21583	+	1.52461i
$937$	2.58636e7	+	3.24320e7i	0.962367	+	1.20677i	0.978362	+	0.206898i	$0.0663369\pi$
$937$	2.58636e7	+	3.24320e7i	0.962367	+	1.20677i	−0.0159953	+	0.999872i	$0.505092\pi$
$938$	1.85063e7	−	2.02791e7i	0.686771	−	0.752559i
$939$	−2.58032e7	+	3.23562e7i	−0.955015	+	1.19755i
$940$	−87884.0	−	385045.i	−0.00324407	−	0.0142132i
$941$	1.83619e7	+	2.30250e7i	0.675993	+	0.847669i	0.994978	−	0.100091i	$-0.0319133\pi$
$941$	1.83619e7	+	2.30250e7i	0.675993	+	0.847669i	−0.318985	+	0.947760i	$0.603342\pi$
$942$	−8.46371e6	+	3.70820e7i	−0.310766	+	1.36156i
$943$	2.19817e7	−	1.05858e7i	0.804975	−	0.387655i
$944$	118414.	−	518807.i	0.00432488	−	0.0189485i
$945$	4.19405e6	+	279417.i	0.152776	+	0.0101783i
$946$	−209306.	−	917031.i	−0.00760421	−	0.0333162i
$947$	3.18221e7	+	3.99036e7i	1.15306	+	1.44590i	0.874200	+	0.485567i	$0.161387\pi$
$947$	3.18221e7	+	3.99036e7i	1.15306	+	1.44590i	0.278865	+	0.960330i	$0.410042\pi$
$948$	3.20000e7	−	1.54104e7i	1.15646	−	0.556920i
$949$	−2.82850e7			−1.01951
$950$	−4.18402e6			−0.150413
$951$	6.65756e7	−	3.20611e7i	2.38706	−	1.14955i
$952$	−3.58597e6	+	3.92949e6i	−0.128237	+	0.140522i
$953$	3.59001e7	+	1.72886e7i	1.28045	+	0.616634i	0.945506	−	0.325603i	$-0.105567\pi$
$953$	3.59001e7	+	1.72886e7i	1.28045	+	0.616634i	0.334947	+	0.942237i	$0.391282\pi$
$954$	6.34022e7	+	3.05329e7i	2.25545	+	1.08617i
$955$	−259997.	−	1.13912e6i	−0.00922485	−	0.0404167i
$956$	2.78087e6	+	1.21838e7i	0.0984094	+	0.431160i
$957$	−7.28502e7	−	3.50828e7i	−2.57129	−	1.23827i
$958$	1.40363e7	+	6.75954e6i	0.494128	+	0.237960i
$959$	−3.65988e6	−	2.29891e7i	−0.128505	−	0.807191i
$960$	1.34610e6	−	648246.i	0.0471410	−	0.0227019i
$961$	−7.69622e6			−0.268825
$962$	1.47141e7			0.512620
$963$	8.84936e6	−	4.26163e6i	0.307501	−	0.148085i
$964$	4.52152e6	+	5.66980e6i	0.156708	+	0.196506i
$965$	163263.	+	715303.i	0.00564378	+	0.0247270i
$966$	6.67779e6	−	2.23025e7i	0.230245	−	0.768973i
$967$	−2.71210e6	+	1.18825e7i	−0.0932695	+	0.408640i	−0.999912	−	0.0132592i	$-0.995779\pi$
$967$	−2.71210e6	+	1.18825e7i	−0.0932695	+	0.408640i	0.906643	+	0.421899i	$0.138636\pi$
$968$	2.04736e6	−	985954.i	0.0702271	−	0.0338196i
$969$	594013.	−	2.60254e6i	0.0203229	−	0.0890406i
$970$	−341395.	−	428096.i	−0.0116500	−	0.0146087i
$971$	9.08089e6	+	3.97860e7i	0.309087	+	1.35420i	0.855986	+	0.516999i	$0.172951\pi$
$971$	9.08089e6	+	3.97860e7i	0.309087	+	1.35420i	−0.546899	+	0.837199i	$0.684192\pi$
$972$	−4.52661e7	+	5.67619e7i	−1.53676	+	1.92704i
$973$	−3.98796e7	+	1.60337e7i	−1.35042	+	0.542941i
$974$	1.20914e7	+	1.51622e7i	0.408395	+	0.512111i
$975$	−2.55657e7	+	3.20584e7i	−0.861283	+	1.08002i
$976$	−510190.	−	245695.i	−0.0171438	−	0.00825603i
$977$	8.84341e6	−	1.10893e7i	0.296403	−	0.371678i	−0.611222	−	0.791459i	$-0.709322\pi$
$977$	8.84341e6	−	1.10893e7i	0.296403	−	0.371678i	0.907625	+	0.419781i	$0.137893\pi$
$978$	1.92005e6	−	8.41230e6i	0.0641898	−	0.281234i
$979$	−4.97154e6			−0.165781
$980$	−715386.	−	470589.i	−0.0237944	−	0.0156522i
$981$	−1.20772e8			−4.00677
$982$	−3.09680e6	+	1.35680e7i	−0.102479	+	0.448989i
$983$	2.00546e7	−	2.51476e7i	0.661956	−	0.830067i	−0.331598	−	0.943421i	$-0.607588\pi$
$983$	2.00546e7	−	2.51476e7i	0.661956	−	0.830067i	0.993555	+	0.113354i	$0.0361593\pi$
$984$	−6.92116e7	−	3.33306e7i	−2.27872	−	1.09737i
$985$	605078.	−	758744.i	0.0198711	−	0.0249175i
$986$	3.16257e6	+	3.96574e6i	0.103597	+	0.129907i
$987$	4.76429e6	+	2.99263e7i	0.155670	+	0.977824i
$988$	−2.11626e6	+	2.65371e6i	−0.0689726	+	0.0864889i
$989$	250363.	+	1.09691e6i	0.00813916	+	0.0356600i
$990$	1.52019e6	+	1.90626e6i	0.0492959	+	0.0618151i
$991$	−1.02285e7	+	4.48142e7i	−0.330849	+	1.44954i	0.486641	+	0.873602i	$0.338222\pi$
$991$	−1.02285e7	+	4.48142e7i	−0.330849	+	1.44954i	−0.817490	+	0.575942i	$0.804635\pi$
$992$	2.40153e7	−	1.15652e7i	0.774834	−	0.373141i
$993$	1.26835e7	−	5.55700e7i	0.408193	−	1.78841i
$994$	−2.96120e6	+	1.19056e6i	−0.0950610	+	0.0382196i
$995$	167194.	+	732527.i	0.00535382	+	0.0234566i
$996$	−1.96870e7	−	2.46867e7i	−0.628826	−	0.788522i
$997$	2.94373e7	−	1.41763e7i	0.937908	−	0.451673i	0.0984775	−	0.995139i	$-0.468603\pi$
$997$	2.94373e7	−	1.41763e7i	0.937908	−	0.451673i	0.839431	+	0.543466i	$0.182888\pi$
$998$	2.58688e7			0.822148
$999$	1.24586e8			3.94961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.e.a.15.9	✓	138
49.36	even	7	inner	49.6.e.a.36.9	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.e.a.15.9	✓	138	1.1	even	1	trivial
49.6.e.a.36.9	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)

\(f(q)\)	\(=\)	\(q+(-0.769126 + 3.36976i) q^{2} +(18.8003 - 23.5748i) q^{3} +(18.0673 + 8.70074i) q^{4} +(-1.58408 + 1.98637i) q^{5} +(64.9817 + 81.4844i) q^{6} +(112.806 + 63.8895i) q^{7} +(-112.177 + 140.665i) q^{8} +(-148.248 - 649.518i) q^{9} +O(q^{10})\)	\(q+(-0.769126 + 3.36976i) q^{2} +(18.8003 - 23.5748i) q^{3} +(18.0673 + 8.70074i) q^{4} +(-1.58408 + 1.98637i) q^{5} +(64.9817 + 81.4844i) q^{6} +(112.806 + 63.8895i) q^{7} +(-112.177 + 140.665i) q^{8} +(-148.248 - 649.518i) q^{9} +(-5.47525 - 6.86574i) q^{10} +(92.7358 - 406.302i) q^{11} +(544.788 - 262.356i) q^{12} +(-97.0314 + 425.122i) q^{13} +(-302.054 + 330.989i) q^{14} +(17.0472 + 74.6887i) q^{15} +(12.3637 + 15.5036i) q^{16} +(205.487 - 98.9574i) q^{17} +2302.74 q^{18} +388.164 q^{19} +(-45.9029 + 22.1057i) q^{20} +(3626.96 - 1458.23i) q^{21} +(1297.82 + 624.995i) q^{22} +(-1552.39 - 747.591i) q^{23} +(1207.20 + 5289.09i) q^{24} +(693.942 + 3040.36i) q^{25} +(-1357.93 - 653.945i) q^{26} +(-11497.7 - 5537.02i) q^{27} +(1482.20 + 2135.80i) q^{28} +(5797.22 - 2791.79i) q^{29} -264.795 q^{30} -4575.25 q^{31} +(-5248.96 + 2527.77i) q^{32} +(-7835.03 - 9824.82i) q^{33} +(175.417 + 768.553i) q^{34} +(-305.602 + 122.868i) q^{35} +(2972.85 - 13024.9i) q^{36} +(-8795.79 + 4235.83i) q^{37} +(-298.547 + 1308.02i) q^{38} +(8197.96 + 10279.9i) q^{39} +(-101.717 - 445.650i) q^{40} +(-8828.56 + 11070.7i) q^{41} +(2124.30 + 13343.6i) q^{42} +(-407.134 - 510.530i) q^{43} +(5210.61 - 6533.90i) q^{44} +(1525.02 + 734.412i) q^{45} +(3713.19 - 4656.19i) q^{46} +(-1724.96 + 7557.55i) q^{47} +597.934 q^{48} +(8643.26 + 14414.2i) q^{49} -10779.0 q^{50} +(1530.31 - 6704.74i) q^{51} +(-5451.97 + 6836.55i) q^{52} +(27533.3 + 13259.4i) q^{53} +(27501.7 - 34486.0i) q^{54} +(660.166 + 827.822i) q^{55} +(-21641.2 + 8700.92i) q^{56} +(7297.60 - 9150.90i) q^{57} +(4948.89 + 21682.5i) q^{58} +(-16731.8 - 20981.1i) q^{59} +(-341.850 + 1497.74i) q^{60} +(-25728.5 + 12390.2i) q^{61} +(3518.95 - 15417.5i) q^{62} +(24774.2 - 82740.9i) q^{63} +(-4339.65 - 19013.3i) q^{64} +(-690.746 - 866.168i) q^{65} +(39133.4 - 18845.7i) q^{66} -61268.0 q^{67} +4573.59 q^{68} +(-46809.7 + 22542.4i) q^{69} +(-178.990 - 1124.31i) q^{70} +(6417.17 + 3090.35i) q^{71} +(107995. + 52007.5i) q^{72} +(14434.0 + 63239.4i) q^{73} +(-7508.66 - 32897.6i) q^{74} +(84722.1 + 40800.0i) q^{75} +(7013.07 + 3377.31i) q^{76} +(36419.6 - 39908.3i) q^{77} +(-40946.1 + 19718.6i) q^{78} +58738.5 q^{79} -50.3809 q^{80} +(-200836. + 96717.3i) q^{81} +(-30515.2 - 38264.9i) q^{82} +(-11619.9 - 50910.1i) q^{83} +(78217.0 + 5210.99i) q^{84} +(-128.942 + 564.930i) q^{85} +(2033.50 - 979.283i) q^{86} +(43173.3 - 189155. i) q^{87} +(46749.8 + 58622.4i) q^{88} +(-2654.51 - 11630.2i) q^{89} +(-3647.73 + 4574.11i) q^{90} +(-38106.6 + 41756.9i) q^{91} +(-21542.8 - 27013.9i) q^{92} +(-86016.0 + 107861. i) q^{93} +(-24140.4 - 11625.4i) q^{94} +(-614.883 + 771.039i) q^{95} +(-39090.3 + 171266. i) q^{96} +62352.4 q^{97} +(-55220.2 + 18039.4i) q^{98} -277648. 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

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