LMFDB - Embedded newform 49.4.e.a.15.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,4,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, 4, names="a")

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
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:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			15.7
Character	$\chi$	$=$	49.15
Dual form			49.4.e.a.36.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0613960 - 0.268993i) q^{2} +(2.25069 - 2.82228i) q^{3} +(7.13916 + 3.43804i) q^{4} +(-2.36861 + 2.97014i) q^{5} +(-0.620990 - 0.778697i) q^{6} +(9.47466 - 15.9132i) q^{7} +(2.73935 - 3.43503i) q^{8} +(3.10843 + 13.6189i) q^{9} +O(q^{10})$	\(q+(0.0613960 - 0.268993i) q^{2} +(2.25069 - 2.82228i) q^{3} +(7.13916 + 3.43804i) q^{4} +(-2.36861 + 2.97014i) q^{5} +(-0.620990 - 0.778697i) q^{6} +(9.47466 - 15.9132i) q^{7} +(2.73935 - 3.43503i) q^{8} +(3.10843 + 13.6189i) q^{9} +(0.653525 + 0.819495i) q^{10} +(12.3443 - 54.0839i) q^{11} +(25.7711 - 12.4107i) q^{12} +(-10.7609 + 47.1465i) q^{13} +(-3.69885 - 3.52563i) q^{14} +(3.05155 + 13.3697i) q^{15} +(38.7678 + 48.6133i) q^{16} +(-51.6949 + 24.8950i) q^{17} +3.85424 q^{18} -112.013 q^{19} +(-27.1213 + 13.0609i) q^{20} +(-23.5870 - 62.5559i) q^{21} +(-13.7903 - 6.64106i) q^{22} +(-108.715 - 52.3546i) q^{23} +(-3.52919 - 15.4624i) q^{24} +(24.6037 + 107.796i) q^{25} +(12.0214 + 5.78922i) q^{26} +(133.246 + 64.1677i) q^{27} +(122.351 - 81.0329i) q^{28} +(-154.212 + 74.2644i) q^{29} +3.78372 q^{30} -75.8179 q^{31} +(47.1246 - 22.6940i) q^{32} +(-124.856 - 156.565i) q^{33} +(3.52272 + 15.4340i) q^{34} +(24.8228 + 65.8333i) q^{35} +(-24.6308 + 107.915i) q^{36} +(358.390 - 172.591i) q^{37} +(-6.87715 + 30.1307i) q^{38} +(108.841 + 136.483i) q^{39} +(3.71409 + 16.2725i) q^{40} +(-53.9698 + 67.6759i) q^{41} +(-18.2753 + 2.50407i) q^{42} +(29.5287 + 37.0279i) q^{43} +(274.070 - 343.673i) q^{44} +(-47.8127 - 23.0254i) q^{45} +(-20.7577 + 26.0294i) q^{46} +(92.7165 - 406.217i) q^{47} +224.455 q^{48} +(-163.462 - 301.545i) q^{49} +30.5069 q^{50} +(-46.0888 + 201.928i) q^{51} +(-238.915 + 299.591i) q^{52} +(284.334 + 136.928i) q^{53} +(25.4414 - 31.9026i) q^{54} +(131.398 + 164.768i) q^{55} +(-28.7081 - 76.1376i) q^{56} +(-252.107 + 316.132i) q^{57} +(10.5087 + 46.0415i) q^{58} +(-429.962 - 539.155i) q^{59} +(-24.1801 + 105.940i) q^{60} +(-221.533 + 106.685i) q^{61} +(-4.65492 + 20.3945i) q^{62} +(246.172 + 79.5694i) q^{63} +(107.477 + 470.889i) q^{64} +(-114.544 - 143.633i) q^{65} +(-49.7806 + 23.9731i) q^{66} +367.091 q^{67} -454.648 q^{68} +(-392.444 + 188.991i) q^{69} +(19.2327 - 2.63527i) q^{70} +(-82.7389 - 39.8450i) q^{71} +(55.2965 + 26.6294i) q^{72} +(12.3116 + 53.9406i) q^{73} +(-24.4222 - 107.001i) q^{74} +(359.605 + 173.177i) q^{75} +(-799.679 - 385.105i) q^{76} +(-743.691 - 708.863i) q^{77} +(43.3953 - 20.8981i) q^{78} +436.724 q^{79} -236.214 q^{80} +(141.178 - 67.9878i) q^{81} +(14.8909 + 18.6725i) q^{82} +(289.021 + 1266.28i) q^{83} +(46.6779 - 527.690i) q^{84} +(48.5035 - 212.508i) q^{85} +(11.7732 - 5.66967i) q^{86} +(-137.488 + 602.374i) q^{87} +(-151.965 - 190.557i) q^{88} +(17.1743 + 75.2457i) q^{89} +(-9.12919 + 11.4476i) q^{90} +(648.298 + 617.938i) q^{91} +(-596.140 - 747.535i) q^{92} +(-170.643 + 213.979i) q^{93} +(-103.577 - 49.8802i) q^{94} +(265.315 - 332.694i) q^{95} +(42.0141 - 184.076i) q^{96} +1261.25 q^{97} +(-91.1494 + 25.4565i) q^{98} +774.935 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) $ 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * 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 $

$2$	0.0613960	−	0.268993i	0.0217068	−	0.0951035i	−0.962914	−	0.269808i	$-0.913040\pi$
$2$	0.0613960	−	0.268993i	0.0217068	−	0.0951035i	0.984621	+	0.174704i	$0.0558970\pi$
$3$	2.25069	−	2.82228i	0.433146	−	0.543147i	−0.516577	−	0.856241i	$-0.672794\pi$
$3$	2.25069	−	2.82228i	0.433146	−	0.543147i	0.949722	+	0.313094i	$0.101365\pi$
$4$	7.13916	+	3.43804i	0.892395	+	0.429755i
$5$	−2.36861	+	2.97014i	−0.211855	+	0.265657i	−0.876393	−	0.481597i	$-0.840057\pi$
$5$	−2.36861	+	2.97014i	−0.211855	+	0.265657i	0.664538	+	0.747254i	$0.268628\pi$
$6$	−0.620990	−	0.778697i	−0.0422530	−	0.0529836i
$7$	9.47466	−	15.9132i	0.511583	−	0.859234i
$7$	9.47466	−	15.9132i	0.511583	−	0.859234i
$8$	2.73935	−	3.43503i	0.121063	−	0.151808i
$9$	3.10843	+	13.6189i	0.115127	+	0.504404i
$10$	0.653525	+	0.819495i	0.0206663	+	0.0259147i
$11$	12.3443	−	54.0839i	0.338358	−	1.48244i	−0.464125	−	0.885770i	$-0.653631\pi$
$11$	12.3443	−	54.0839i	0.338358	−	1.48244i	0.802483	−	0.596675i	$-0.203512\pi$
$12$	25.7711	−	12.4107i	0.619957	−	0.298556i
$13$	−10.7609	+	47.1465i	−0.229580	+	1.00585i	0.720404	+	0.693554i	$0.243956\pi$
$13$	−10.7609	+	47.1465i	−0.229580	+	1.00585i	−0.949984	+	0.312299i	$0.898901\pi$
$14$	−3.69885	−	3.52563i	−0.0706113	−	0.0673045i
$15$	3.05155	+	13.3697i	0.0525272	+	0.230137i
$16$	38.7678	+	48.6133i	0.605747	+	0.759583i
$17$	−51.6949	+	24.8950i	−0.737521	+	0.355172i	−0.764637	−	0.644461i	$-0.777082\pi$
$17$	−51.6949	+	24.8950i	−0.737521	+	0.355172i	0.0271161	+	0.999632i	$0.491368\pi$
$18$	3.85424			0.0504696
$19$	−112.013			−1.35250			−0.676251	−	0.736671i	$-0.736396\pi$
$19$	−112.013			−1.35250			−0.676251	+	0.736671i	$0.736396\pi$
$20$	−27.1213	+	13.0609i	−0.303226	+	0.146026i
$21$	−23.5870	−	62.5559i	−0.245100	−	0.650038i
$22$	−13.7903	−	6.64106i	−0.133641	−	0.0643581i
$23$	−108.715	−	52.3546i	−0.985596	−	0.474638i	−0.129570	−	0.991570i	$-0.541360\pi$
$23$	−108.715	−	52.3546i	−0.985596	−	0.474638i	−0.856026	+	0.516932i	$0.827074\pi$
$24$	−3.52919	−	15.4624i	−0.0300164	−	0.131510i
$25$	24.6037	+	107.796i	0.196829	+	0.862366i
$26$	12.0214	+	5.78922i	0.0906768	+	0.0436677i
$27$	133.246	+	64.1677i	0.949746	+	0.457374i
$28$	122.351	−	81.0329i	0.825795	−	0.546921i
$29$	−154.212	+	74.2644i	−0.987462	+	0.475536i	−0.856665	−	0.515873i	$-0.827468\pi$
$29$	−154.212	+	74.2644i	−0.987462	+	0.475536i	−0.130796	+	0.991409i	$0.541753\pi$
$30$	3.78372			0.0230270
$31$	−75.8179			−0.439268			−0.219634	−	0.975582i	$-0.570486\pi$
$31$	−75.8179			−0.439268			−0.219634	+	0.975582i	$0.570486\pi$
$32$	47.1246	−	22.6940i	0.260329	−	0.125368i
$33$	−124.856	−	156.565i	−0.658628	−	0.825893i
$34$	3.52272	+	15.4340i	0.0177689	+	0.0778505i
$35$	24.8228	+	65.8333i	0.119880	+	0.317939i
$36$	−24.6308	+	107.915i	−0.114031	+	0.499604i
$37$	358.390	−	172.591i	1.59240	−	0.766861i	0.593134	−	0.805104i	$-0.297890\pi$
$37$	358.390	−	172.591i	1.59240	−	0.766861i	0.999268	+	0.0382431i	$0.0121761\pi$
$38$	−6.87715	+	30.1307i	−0.0293584	+	0.128628i
$39$	108.841	+	136.483i	0.446886	+	0.560377i
$40$	3.71409	+	16.2725i	0.0146812	+	0.0643227i
$41$	−53.9698	+	67.6759i	−0.205577	+	0.257786i	−0.873922	−	0.486066i	$-0.838432\pi$
$41$	−53.9698	+	67.6759i	−0.205577	+	0.257786i	0.668345	+	0.743851i	$0.267003\pi$
$42$	−18.2753	+	2.50407i	−0.0671413	+	0.00919969i
$43$	29.5287	+	37.0279i	0.104723	+	0.131319i	0.831431	−	0.555628i	$-0.187522\pi$
$43$	29.5287	+	37.0279i	0.104723	+	0.131319i	−0.726708	+	0.686946i	$0.758951\pi$
$44$	274.070	−	343.673i	0.939038	−	1.17752i
$45$	−47.8127	−	23.0254i	−0.158389	−	0.0762761i
$46$	−20.7577	+	26.0294i	−0.0665339	+	0.0834308i
$47$	92.7165	−	406.217i	0.287747	−	1.26070i	−0.599863	−	0.800103i	$-0.704778\pi$
$47$	92.7165	−	406.217i	0.287747	−	1.26070i	0.887609	−	0.460597i	$-0.152365\pi$
$48$	224.455			0.674942
$49$	−163.462	−	301.545i	−0.476565	−	0.879139i
$50$	30.5069			0.0862866
$51$	−46.0888	+	201.928i	−0.126544	+	0.554424i
$52$	−238.915	+	299.591i	−0.637146	+	0.798956i
$53$	284.334	+	136.928i	0.736912	+	0.354878i	0.764399	−	0.644744i	$-0.223036\pi$
$53$	284.334	+	136.928i	0.736912	+	0.354878i	−0.0274864	+	0.999622i	$0.508750\pi$
$54$	25.4414	−	31.9026i	0.0641137	−	0.0803961i
$55$	131.398	+	164.768i	0.322140	+	0.403950i
$56$	−28.7081	−	76.1376i	−0.0685050	−	0.181684i
$57$	−252.107	+	316.132i	−0.585830	+	0.734608i
$58$	10.5087	+	46.0415i	0.0237906	+	0.104233i
$59$	−429.962	−	539.155i	−0.948751	−	1.18970i	−0.981738	−	0.190240i	$-0.939073\pi$
$59$	−429.962	−	539.155i	−0.948751	−	1.18970i	0.0329867	−	0.999456i	$-0.489498\pi$
$60$	−24.1801	+	105.940i	−0.0520274	+	0.227947i
$61$	−221.533	+	106.685i	−0.464989	+	0.223927i	−0.651684	−	0.758491i	$-0.725937\pi$
$61$	−221.533	+	106.685i	−0.464989	+	0.223927i	0.186694	+	0.982418i	$0.440223\pi$
$62$	−4.65492	+	20.3945i	−0.00953508	+	0.0417759i
$63$	246.172	+	79.5694i	0.492298	+	0.159124i
$64$	107.477	+	470.889i	0.209917	+	0.919705i
$65$	−114.544	−	143.633i	−0.218575	−	0.274084i
$66$	−49.7806	+	23.9731i	−0.0928420	+	0.0447103i
$67$	367.091			0.669363			0.334682	−	0.942331i	$-0.391371\pi$
$67$	367.091			0.669363			0.334682	+	0.942331i	$0.391371\pi$
$68$	−454.648			−0.810797
$69$	−392.444	+	188.991i	−0.684705	+	0.329737i
$70$	19.2327	−	2.63527i	0.0328393	−	0.00449964i
$71$	−82.7389	−	39.8450i	−0.138300	−	0.0666018i	0.363454	−	0.931612i	$-0.381597\pi$
$71$	−82.7389	−	39.8450i	−0.138300	−	0.0666018i	−0.501754	+	0.865010i	$0.667312\pi$
$72$	55.2965	+	26.6294i	0.0905105	+	0.0435875i
$73$	12.3116	+	53.9406i	0.0197392	+	0.0864832i	0.983838	−	0.179060i	$-0.0573057\pi$
$73$	12.3116	+	53.9406i	0.0197392	+	0.0864832i	−0.964099	+	0.265544i	$0.914449\pi$
$74$	−24.4222	−	107.001i	−0.0383652	−	0.168089i
$75$	359.605	+	173.177i	0.553648	+	0.266623i
$76$	−799.679	−	385.105i	−1.20697	−	0.581244i
$77$	−743.691	−	708.863i	−1.10067	−	1.04912i
$78$	43.3953	−	20.8981i	0.0629942	−	0.0303364i
$79$	436.724			0.621965			0.310983	−	0.950416i	$-0.399342\pi$
$79$	436.724			0.621965			0.310983	+	0.950416i	$0.399342\pi$
$80$	−236.214			−0.330119
$81$	141.178	−	67.9878i	0.193660	−	0.0932618i
$82$	14.8909	+	18.6725i	0.0200539	+	0.0251468i
$83$	289.021	+	1266.28i	0.382219	+	1.67461i	0.690512	+	0.723320i	$0.257385\pi$
$83$	289.021	+	1266.28i	0.382219	+	1.67461i	−0.308293	+	0.951291i	$0.599758\pi$
$84$	46.6779	−	527.690i	0.0606307	−	0.685424i
$85$	48.5035	−	212.508i	0.0618934	−	0.271173i
$86$	11.7732	−	5.66967i	0.0147621	−	0.00710903i
$87$	−137.488	+	602.374i	−0.169428	+	0.742314i
$88$	−151.965	−	190.557i	−0.184085	−	0.230835i
$89$	17.1743	+	75.2457i	0.0204548	+	0.0896183i	0.984125	−	0.177477i	$-0.0567934\pi$
$89$	17.1743	+	75.2457i	0.0204548	+	0.0896183i	−0.963670	+	0.267095i	$0.913936\pi$
$90$	−9.12919	+	11.4476i	−0.0106922	+	0.0134076i
$91$	648.298	+	617.938i	0.746814	+	0.711841i
$92$	−596.140	−	747.535i	−0.675564	−	0.847130i
$93$	−170.643	+	213.979i	−0.190267	+	0.238587i
$94$	−103.577	−	49.8802i	−0.113651	−	0.0547314i
$95$	265.315	−	332.694i	0.286534	−	0.359302i
$96$	42.0141	−	184.076i	0.0446672	−	0.195700i
$97$	1261.25			1.32021			0.660103	−	0.751175i	$-0.270512\pi$
$97$	1261.25			1.32021			0.660103	+	0.751175i	$0.270512\pi$
$98$	−91.1494	+	25.4565i	−0.0939539	+	0.0262398i
$99$	774.935			0.786706
$100$	−194.956	+	854.160i	−0.194956	+	0.854160i
$101$	908.876	−	1139.70i	0.895412	−	1.12281i	−0.0964305	−	0.995340i	$-0.530743\pi$
$101$	908.876	−	1139.70i	0.895412	−	1.12281i	0.991842	−	0.127471i	$-0.0406860\pi$
$102$	51.4877	+	24.7952i	0.0499808	+	0.0240695i
$103$	66.7048	−	83.6452i	0.0638119	−	0.0800176i	−0.748901	−	0.662682i	$-0.769418\pi$
$103$	66.7048	−	83.6452i	0.0638119	−	0.0800176i	0.812713	+	0.582664i	$0.197990\pi$
$104$	132.472	+	166.115i	0.124903	+	0.156624i
$105$	241.668	+	78.1135i	0.224613	+	0.0726010i
$106$	54.2898	−	68.0772i	0.0497461	−	0.0623797i
$107$	−150.142	−	657.814i	−0.135652	−	0.594330i	−0.996361	−	0.0852330i	$-0.972837\pi$
$107$	−150.142	−	657.814i	−0.135652	−	0.594330i	0.860709	−	0.509097i	$-0.170021\pi$
$108$	730.651	+	916.208i	0.650990	+	0.816316i
$109$	−20.7014	+	90.6988i	−0.0181911	+	0.0797006i	−0.983209	−	0.182485i	$-0.941586\pi$
$109$	−20.7014	+	90.6988i	−0.0181911	+	0.0797006i	0.965018	+	0.262185i	$0.0844432\pi$
$110$	52.3887	−	25.2291i	0.0454097	−	0.0218682i
$111$	319.524	−	1399.92i	0.273224	−	1.19707i
$112$	1140.91	−	156.327i	0.962549	−	0.131888i
$113$	−68.6897	−	300.949i	−0.0571839	−	0.250539i	0.938254	−	0.345946i	$-0.112442\pi$
$113$	−68.6897	−	300.949i	−0.0571839	−	0.250539i	−0.995438	+	0.0954068i	$0.969585\pi$
$114$	69.5590	+	87.2242i	0.0571473	+	0.0716605i
$115$	413.004	−	198.892i	0.334894	−	0.161277i
$116$	−1356.27			−1.08557
$117$	−675.534			−0.533788
$118$	−171.427	+	82.5550i	−0.133739	+	0.0644051i
$119$	−93.6323	+	1058.50i	−0.0721282	+	0.815403i
$120$	54.2847	+	26.1422i	0.0412958	+	0.0198870i
$121$	−1573.49	−	757.754i	−1.18219	−	0.569312i
$122$	15.0962	+	66.1408i	0.0112028	+	0.0490829i
$123$	69.5310	+	304.635i	0.0509707	+	0.223317i
$124$	−541.277	−	260.665i	−0.392001	−	0.188778i
$125$	−806.287	−	388.288i	−0.576932	−	0.277836i
$126$	36.5176	−	61.3334i	0.0258194	−	0.0433652i
$127$	−1036.08	+	498.948i	−0.723912	+	0.348618i	−0.759287	−	0.650756i	$-0.774452\pi$
$127$	−1036.08	+	498.948i	−0.723912	+	0.348618i	0.0353745	+	0.999374i	$0.488738\pi$
$128$	551.700			0.380967
$129$	170.963			0.116686
$130$	−45.6689	+	21.9930i	−0.0308110	+	0.0148378i
$131$	1434.69	+	1799.04i	0.956864	+	1.19987i	0.979769	+	0.200132i	$0.0641371\pi$
$131$	1434.69	+	1799.04i	0.956864	+	1.19987i	−0.0229048	+	0.999738i	$0.507291\pi$
$132$	−353.094	−	1547.00i	−0.232825	−	1.02007i
$133$	−1061.28	+	1782.49i	−0.691917	+	1.16212i
$134$	22.5379	−	98.7451i	0.0145297	−	0.0636588i
$135$	−506.194	+	243.770i	−0.322713	+	0.155410i
$136$	−56.0953	+	245.770i	−0.0353686	+	0.154960i
$137$	−360.581	−	452.154i	−0.224865	−	0.281972i	0.656582	−	0.754254i	$-0.272002\pi$
$137$	−360.581	−	452.154i	−0.224865	−	0.281972i	−0.881447	+	0.472283i	$0.843430\pi$
$138$	26.7428	+	117.168i	0.0164964	+	0.0722754i
$139$	−44.7782	+	56.1501i	−0.0273240	+	0.0342632i	−0.795306	−	0.606209i	$-0.792690\pi$
$139$	−44.7782	+	56.1501i	−0.0273240	+	0.0342632i	0.767982	+	0.640472i	$0.221261\pi$
$140$	−49.1234	+	555.336i	−0.0296549	+	0.335246i
$141$	−937.782	−	1175.94i	−0.560110	−	0.702355i
$142$	−15.7979	+	19.8099i	−0.00933611	+	0.0117071i
$143$	2417.03	+	1163.98i	1.41344	+	0.680678i
$144$	−541.553	+	679.086i	−0.313399	+	0.392990i
$145$	144.691	−	633.934i	0.0828686	−	0.363071i
$146$	15.2655			0.00865333
$147$	−1218.94	−	217.349i	−0.683924	−	0.121950i
$148$	3151.98			1.75061
$149$	−219.530	+	961.823i	−0.120702	+	0.528830i	0.878036	+	0.478595i	$0.158854\pi$
$149$	−219.530	+	961.823i	−0.120702	+	0.528830i	−0.998737	+	0.0502342i	$0.984003\pi$
$150$	68.6616	−	86.0990i	0.0373747	−	0.0468663i
$151$	−2509.25	−	1208.39i	−1.35232	−	0.651242i	−0.389408	−	0.921065i	$-0.627320\pi$
$151$	−2509.25	−	1208.39i	−1.35232	−	0.651242i	−0.962910	+	0.269824i	$0.913035\pi$
$152$	−306.842	+	384.768i	−0.163738	+	0.205321i
$153$	−499.732	−	626.644i	−0.264059	−	0.331119i
$154$	−236.339	+	156.527i	−0.123667	+	0.0819044i
$155$	179.583	−	225.190i	0.0930610	−	0.116695i
$156$	307.803	+	1348.57i	0.157974	+	0.692129i
$157$	−1489.03	−	1867.19i	−0.756929	−	0.949159i	0.242853	−	0.970063i	$-0.421917\pi$
$157$	−1489.03	−	1867.19i	−0.756929	−	0.949159i	−0.999781	+	0.0209045i	$0.993345\pi$
$158$	26.8131	−	117.476i	0.0135008	−	0.0591511i
$159$	1026.40	−	494.287i	0.511941	−	0.246538i
$160$	−44.2153	+	193.720i	−0.0218471	+	0.0957182i
$161$	−1863.17	+	1233.97i	−0.912040	+	0.604041i
$162$	−9.62050	−	42.1502i	−0.00466579	−	0.0204422i
$163$	−88.4816	−	110.952i	−0.0425179	−	0.0533157i	0.760118	−	0.649785i	$-0.225141\pi$
$163$	−88.4816	−	110.952i	−0.0425179	−	0.0533157i	−0.802636	+	0.596469i	$0.796570\pi$
$164$	−617.972	+	297.599i	−0.294241	+	0.141699i
$165$	760.756			0.358938
$166$	358.367			0.167558
$167$	−1088.62	+	524.253i	−0.504432	+	0.242921i	−0.668752	−	0.743486i	$-0.733171\pi$
$167$	−1088.62	+	524.253i	−0.504432	+	0.242921i	0.164320	+	0.986407i	$0.447457\pi$
$168$	−279.494	−	90.3400i	−0.128354	−	0.0414874i
$169$	−127.572	−	61.4353i	−0.0580663	−	0.0279633i
$170$	−54.1852	−	26.0942i	−0.0244460	−	0.0117726i
$171$	−348.184	−	1525.49i	−0.155709	−	0.682208i
$172$	83.5072	+	365.869i	0.0370196	+	0.162193i
$173$	3398.17	+	1636.47i	1.49340	+	0.719183i	0.989494	−	0.144575i	$-0.0461816\pi$
$173$	3398.17	+	1636.47i	1.49340	+	0.719183i	0.503906	+	0.863759i	$0.331896\pi$
$174$	153.593	+	73.9667i	0.0669189	+	0.0322264i
$175$	1948.49	+	629.804i	0.841669	+	0.272050i
$176$	3107.76	−	1496.62i	1.33100	−	0.640976i
$177$	−2489.36			−1.05713
$178$	21.2950			0.00896703
$179$	−81.1272	+	39.0688i	−0.0338756	+	0.0163136i	−0.450745	−	0.892653i	$-0.648842\pi$
$179$	−81.1272	+	39.0688i	−0.0338756	+	0.0163136i	0.416869	+	0.908966i	$0.363127\pi$
$180$	−262.181	−	328.764i	−0.108566	−	0.136137i
$181$	−767.575	−	3362.97i	−0.315212	−	1.38104i	−0.845843	−	0.533432i	$-0.820902\pi$
$181$	−767.575	−	3362.97i	−0.315212	−	1.38104i	0.530630	−	0.847603i	$-0.321955\pi$
$182$	206.024	−	136.449i	0.0839095	−	0.0555729i
$183$	−197.508	+	865.340i	−0.0797827	+	0.349551i
$184$	−477.649	+	230.024i	−0.191374	+	0.0921606i
$185$	−336.264	+	1473.27i	−0.133636	+	0.585497i
$186$	47.0822	+	59.0392i	0.0185604	+	0.0232740i
$187$	708.279	+	3103.17i	0.276976	+	1.21351i
$188$	2058.51	−	2581.29i	0.798576	−	1.00138i
$189$	2283.57	−	1512.40i	0.878865	−	0.582069i
$190$	−73.2033	−	91.7940i	−0.0279512	−	0.0350497i
$191$	609.678	−	764.512i	0.230967	−	0.289624i	−0.652820	−	0.757513i	$-0.726414\pi$
$191$	609.678	−	764.512i	0.230967	−	0.289624i	0.883787	+	0.467889i	$0.154985\pi$
$192$	1570.88	+	756.494i	0.590460	+	0.284350i
$193$	301.934	−	378.614i	0.112610	−	0.141208i	−0.722332	−	0.691546i	$-0.756930\pi$
$193$	301.934	−	378.614i	0.112610	−	0.141208i	0.834942	+	0.550338i	$0.185501\pi$
$194$	77.4354	−	339.267i	0.0286574	−	0.125556i
$195$	−663.174			−0.243543
$196$	−130.258	−	2714.77i	−0.0474700	−	0.989346i
$197$	1683.13			0.608721			0.304360	−	0.952557i	$-0.401557\pi$
$197$	1683.13			0.608721			0.304360	+	0.952557i	$0.401557\pi$
$198$	47.5779	−	208.452i	0.0170768	−	0.0748185i
$199$	1959.24	−	2456.81i	0.697925	−	0.875170i	−0.298942	−	0.954271i	$-0.596634\pi$
$199$	1959.24	−	2456.81i	0.697925	−	0.875170i	0.996867	+	0.0791012i	$0.0252050\pi$
$200$	437.680	+	210.776i	0.154743	+	0.0745204i
$201$	826.209	−	1036.03i	0.289932	−	0.363563i
$202$	−250.769	−	314.454i	−0.0873468	−	0.109529i
$203$	−279.315	+	3157.64i	−0.0965719	+	1.09174i
$204$	−1023.27	+	1283.14i	−0.351193	+	0.440382i
$205$	−73.1739	−	320.596i	−0.0249302	−	0.109226i
$206$	−18.4046	−	23.0786i	−0.00622480	−	0.00780566i
$207$	375.078	−	1643.33i	0.125941	−	0.551783i
$208$	−2709.13	+	1304.65i	−0.903097	+	0.434908i
$209$	−1382.72	+	6058.09i	−0.457630	+	2.00501i
$210$	35.8495	−	60.2113i	0.0117802	−	0.0197856i
$211$	−568.748	−	2491.85i	−0.185565	−	0.813013i	−0.978918	−	0.204252i	$-0.934524\pi$
$211$	−568.748	−	2491.85i	−0.185565	−	0.813013i	0.793353	−	0.608761i	$-0.208333\pi$
$212$	1559.15	+	1955.11i	0.505106	+	0.633383i
$213$	−298.673	+	143.833i	−0.0960787	+	0.0462690i
$214$	−186.166			−0.0594675
$215$	−179.920			−0.0570718
$216$	585.425	−	281.926i	0.184412	−	0.0888084i
$217$	−718.349	+	1206.51i	−0.224722	+	0.377434i
$218$	23.1264	+	11.1371i	0.00718494	+	0.00346008i
$219$	179.945	+	86.6569i	0.0555231	+	0.0267385i
$220$	371.593	+	1628.05i	0.113876	+	0.498925i
$221$	−617.428	−	2705.13i	−0.187931	−	0.823379i
$222$	−356.953	−	171.899i	−0.107915	−	0.0519691i
$223$	1271.66	+	612.401i	0.381869	+	0.183899i	0.614963	−	0.788556i	$-0.289171\pi$
$223$	1271.66	+	612.401i	0.381869	+	0.183899i	−0.233094	+	0.972454i	$0.574885\pi$
$224$	85.3543	−	964.923i	0.0254597	−	0.287820i
$225$	−1391.58	+	670.151i	−0.412321	+	0.198563i
$226$	−85.1706			−0.0250684
$227$	−3830.05			−1.11986			−0.559932	−	0.828539i	$-0.689173\pi$
$227$	−3830.05			−1.11986			−0.559932	+	0.828539i	$0.689173\pi$
$228$	−2886.70	+	1390.16i	−0.838494	+	0.403797i
$229$	−1281.95	−	1607.52i	−0.369930	−	0.463877i	0.561671	−	0.827361i	$-0.310159\pi$
$229$	−1281.95	−	1607.52i	−0.369930	−	0.463877i	−0.931601	+	0.363483i	$0.881587\pi$
$230$	−28.1439	−	123.307i	−0.00806851	−	0.0353504i
$231$	−3674.43	+	503.470i	−1.04658	+	0.143402i
$232$	−167.339	+	733.158i	−0.0473548	+	0.207475i
$233$	−1660.14	+	799.483i	−0.466779	+	0.224789i	−0.652463	−	0.757820i	$-0.726264\pi$
$233$	−1660.14	+	799.483i	−0.466779	+	0.224789i	0.185684	+	0.982610i	$0.440550\pi$
$234$	−41.4751	+	181.714i	−0.0115868	+	0.0507651i
$235$	986.914	+	1237.55i	0.273954	+	0.343527i
$236$	−1215.93	−	5327.35i	−0.335383	−	1.46941i
$237$	982.930	−	1232.55i	0.269401	−	0.337819i
$238$	278.982	+	90.1744i	0.0759820	+	0.0245594i
$239$	−3512.96	−	4405.11i	−0.950771	−	1.19223i	−0.981259	−	0.192694i	$-0.938277\pi$
$239$	−3512.96	−	4405.11i	−0.950771	−	1.19223i	0.0304875	−	0.999535i	$-0.490294\pi$
$240$	−531.645	+	666.662i	−0.142990	+	0.179303i
$241$	3871.19	+	1864.27i	1.03471	+	0.498290i	0.872576	−	0.488478i	$-0.162448\pi$
$241$	3871.19	+	1864.27i	1.03471	+	0.498290i	0.162135	+	0.986769i	$0.448162\pi$
$242$	−300.437	+	376.736i	−0.0798050	+	0.100072i
$243$	−762.674	+	3341.49i	−0.201340	+	0.882127i
$244$	−1948.34			−0.511188
$245$	1282.81	+	228.737i	0.334512	+	0.0596467i
$246$	86.2138			0.0223447
$247$	1205.36	−	5281.02i	0.310507	−	1.36042i
$248$	−207.692	+	260.437i	−0.0531792	+	0.0666846i
$249$	4224.30	+	2034.32i	1.07512	+	0.517749i
$250$	−153.950	+	193.047i	−0.0389465	+	0.0488374i
$251$	4519.99	+	5667.89i	1.13665	+	1.42531i	0.889853	+	0.456247i	$0.150807\pi$
$251$	4519.99	+	5667.89i	1.13665	+	1.42531i	0.246797	+	0.969067i	$0.420622\pi$
$252$	1483.90	+	1414.41i	0.370940	+	0.353569i
$253$	−4173.55	+	5233.47i	−1.03711	+	1.30049i
$254$	70.6027	+	309.331i	0.0174410	+	0.0764139i
$255$	−490.589	−	615.179i	−0.120478	−	0.151075i
$256$	−825.946	+	3618.71i	−0.201647	+	0.883473i
$257$	142.633	−	68.6883i	0.0346194	−	0.0166718i	−0.416494	−	0.909138i	$-0.636741\pi$
$257$	142.633	−	68.6883i	0.0346194	−	0.0166718i	0.451113	+	0.892467i	$0.351027\pi$
$258$	10.4964	−	45.9879i	0.00253287	−	0.0110972i
$259$	649.132	−	7338.38i	0.155734	−	1.76056i
$260$	−323.929	−	1419.23i	−0.0772662	−	0.338525i
$261$	−1490.76	−	1869.35i	−0.353546	−	0.443333i
$262$	572.014	−	275.467i	0.134882	−	0.0649559i
$263$	−515.650			−0.120899			−0.0604493	−	0.998171i	$-0.519253\pi$
$263$	−515.650			−0.120899			−0.0604493	+	0.998171i	$0.519253\pi$
$264$	−879.831			−0.205113
$265$	−1080.17	+	520.184i	−0.250394	+	0.120584i
$266$	414.319	+	394.916i	0.0955020	+	0.0910295i
$267$	251.018	+	120.884i	0.0575359	+	0.0277078i
$268$	2620.72	+	1262.07i	0.597337	+	0.287662i
$269$	127.001	+	556.427i	0.0287858	+	0.126119i	0.987279	−	0.158996i	$-0.0508255\pi$
$269$	127.001	+	556.427i	0.0287858	+	0.126119i	−0.958493	+	0.285114i	$0.907968\pi$
$270$	34.4943	+	151.129i	0.00777502	+	0.0340646i
$271$	−6725.52	−	3238.84i	−1.50755	−	0.725998i	−0.516106	−	0.856525i	$-0.672619\pi$
$271$	−6725.52	−	3238.84i	−1.50755	−	0.725998i	−0.991445	+	0.130526i	$0.958333\pi$
$272$	−3214.33	−	1547.94i	−0.716534	−	0.345064i
$273$	3203.11	−	438.890i	0.710114	−	0.0972997i
$274$	−143.765	+	69.2334i	−0.0316976	+	0.0152647i
$275$	6133.73			1.34501
$276$	−3451.48			−0.752734
$277$	5246.78	−	2526.72i	1.13808	−	0.548071i	0.232649	−	0.972561i	$-0.425261\pi$
$277$	5246.78	−	2526.72i	1.13808	−	0.548071i	0.905433	+	0.424489i	$0.139546\pi$
$278$	12.3548	+	15.4924i	0.00266544	+	0.00334235i
$279$	−235.675	−	1032.56i	−0.0505716	−	0.221569i
$280$	294.138	+	95.0731i	0.0627789	+	0.0202918i
$281$	−1938.60	+	8493.57i	−0.411556	+	1.80315i	0.165236	+	0.986254i	$0.447162\pi$
$281$	−1938.60	+	8493.57i	−0.411556	+	1.80315i	−0.576792	+	0.816891i	$0.695696\pi$
$282$	−373.896	+	180.059i	−0.0789546	+	0.0380226i
$283$	−603.995	+	2646.27i	−0.126868	+	0.555847i	0.871041	+	0.491211i	$0.163446\pi$
$283$	−603.995	+	2646.27i	−0.126868	+	0.555847i	−0.997909	+	0.0646356i	$0.979411\pi$
$284$	−453.698	−	568.920i	−0.0947959	−	0.118870i
$285$	−341.814	−	1497.58i	−0.0710431	−	0.311260i
$286$	461.499	−	578.702i	0.0954162	−	0.119648i
$287$	565.598	+	1500.04i	0.116328	+	0.308518i
$288$	455.551	+	571.243i	0.0932070	+	0.116878i
$289$	−1010.60	+	1267.25i	−0.205699	+	0.257938i
$290$	−161.640	−	77.8420i	−0.0327305	−	0.0157622i
$291$	2838.67	−	3559.58i	0.571842	−	0.717067i
$292$	−97.5555	+	427.419i	−0.0195514	+	0.0856602i
$293$	5752.13			1.14691			0.573453	−	0.819239i	$-0.305604\pi$
$293$	5752.13			1.14691			0.573453	+	0.819239i	$0.305604\pi$
$294$	−133.304	+	314.544i	−0.0264437	+	0.0623965i
$295$	2619.78			0.517049
$296$	388.897	−	1703.87i	0.0763654	−	0.334579i
$297$	5115.26	−	6414.33i	0.999386	−	1.25319i
$298$	245.246	+	118.104i	0.0476735	+	0.0229584i
$299$	3638.21	−	4562.17i	0.703690	−	0.882399i
$300$	1971.89	+	2472.67i	0.379490	+	0.475866i
$301$	869.008	−	119.071i	0.166408	−	0.0228012i
$302$	−479.107	+	600.782i	−0.0912898	+	0.114474i
$303$	−1170.94	−	5130.20i	−0.222008	−	0.972681i
$304$	−4342.50	−	5445.32i	−0.819274	−	1.02734i
$305$	207.856	−	910.677i	0.0390223	−	0.170968i
$306$	−199.245	+	95.9512i	−0.0372224	+	0.0179254i
$307$	−1390.57	+	6092.51i	−0.258516	+	1.13263i	0.664323	+	0.747445i	$0.268720\pi$
$307$	−1390.57	+	6092.51i	−0.258516	+	1.13263i	−0.922839	+	0.385186i	$0.874137\pi$
$308$	−2872.23	−	7617.53i	−0.531365	−	1.40925i
$309$	−85.9380	−	376.519i	−0.0158215	−	0.0693185i
$310$	−49.5489	−	62.1324i	−0.00907803	−	0.0113835i
$311$	−8139.46	+	3919.76i	−1.48407	+	0.714691i	−0.988124	−	0.153660i	$-0.950894\pi$
$311$	−8139.46	+	3919.76i	−1.48407	+	0.714691i	−0.495948	+	0.868352i	$0.665180\pi$
$312$	766.976			0.139171
$313$	7433.40			1.34237			0.671183	−	0.741292i	$-0.265787\pi$
$313$	7433.40			1.34237			0.671183	+	0.741292i	$0.265787\pi$
$314$	−593.682	+	285.902i	−0.106699	+	0.0513834i
$315$	−819.418	+	542.697i	−0.146568	+	0.0970715i
$316$	3117.84	+	1501.47i	0.555039	+	0.267293i
$317$	9006.37	+	4337.24i	1.59574	+	0.768466i	0.999412	−	0.0342783i	$-0.0109133\pi$
$317$	9006.37	+	4337.24i	1.59574	+	0.768466i	0.596324	+	0.802744i	$0.296628\pi$
$318$	−69.9433	−	306.442i	−0.0123340	−	0.0540390i
$319$	2112.87	+	9257.10i	0.370841	+	1.62476i
$320$	−1653.18	−	796.128i	−0.288798	−	0.139078i
$321$	−2194.46	−	1056.79i	−0.381566	−	0.183752i
$322$	217.539	+	576.941i	0.0376490	+	0.0998500i
$323$	5790.50	−	2788.56i	0.997499	−	0.480370i
$324$	1241.64			0.212901
$325$	−5346.96			−0.912603
$326$	−35.2779	+	16.9889i	−0.00599344	+	0.00288629i
$327$	209.385	+	262.560i	0.0354098	+	0.0444025i
$328$	84.6272	+	370.776i	0.0142462	+	0.0624167i
$329$	−5585.78	−	5324.19i	−0.936030	−	0.892195i
$330$	46.7074	−	204.638i	0.00779138	−	0.0341363i
$331$	−821.418	+	395.574i	−0.136403	+	0.0656880i	−0.500840	−	0.865540i	$-0.666976\pi$
$331$	−821.418	+	395.574i	−0.136403	+	0.0656880i	0.364438	+	0.931228i	$0.381261\pi$
$332$	−2290.17	+	10033.9i	−0.378582	+	1.65868i
$333$	3464.53	+	4344.39i	0.570136	+	0.714928i
$334$	74.1835	+	325.019i	0.0121531	+	0.0532463i
$335$	−869.495	+	1090.31i	−0.141808	+	0.177821i
$336$	2126.63	−	3571.80i	0.345289	−	0.579933i
$337$	−3199.37	−	4011.88i	−0.517153	−	0.648490i	0.452848	−	0.891588i	$-0.350408\pi$
$337$	−3199.37	−	4011.88i	−0.517153	−	0.648490i	−0.970002	+	0.243098i	$0.921836\pi$
$338$	−24.3581	+	30.5441i	−0.00391984	+	0.00491532i
$339$	−1003.96	−	483.482i	−0.160849	−	0.0774606i
$340$	1076.88	−	1350.37i	0.171771	−	0.215394i
$341$	−935.918	+	4100.53i	−0.148630	+	0.651190i
$342$	−431.725			−0.0682603
$343$	−6347.30	−	255.827i	−0.999189	−	0.0402721i
$344$	208.081			0.0326134
$345$	368.216	−	1613.26i	0.0574611	−	0.251753i
$346$	648.834	−	813.612i	0.100814	−	0.126416i
$347$	−6451.18	−	3106.72i	−0.998033	−	0.480627i	−0.137762	−	0.990465i	$-0.543991\pi$
$347$	−6451.18	−	3106.72i	−0.998033	−	0.480627i	−0.860270	+	0.509838i	$0.829705\pi$
$348$	−3052.54	+	3827.76i	−0.470210	+	0.589625i
$349$	364.681	+	457.295i	0.0559339	+	0.0701389i	0.809011	−	0.587793i	$-0.200003\pi$
$349$	364.681	+	457.295i	0.0559339	+	0.0701389i	−0.753078	+	0.657932i	$0.771432\pi$
$350$	289.043	−	485.464i	0.0441428	−	0.0741404i
$351$	−4459.13	+	5591.57i	−0.678093	+	0.850302i
$352$	−645.660	−	2828.82i	−0.0977665	−	0.428343i
$353$	−3638.13	−	4562.07i	−0.548550	−	0.687859i	0.427845	−	0.903852i	$-0.359273\pi$
$353$	−3638.13	−	4562.07i	−0.548550	−	0.687859i	−0.976395	+	0.215992i	$0.930701\pi$
$354$	−152.837	+	669.621i	−0.0229468	+	0.100537i
$355$	314.321	−	151.369i	0.0469928	−	0.0226305i
$356$	−136.087	+	596.238i	−0.0202602	+	0.0887655i
$357$	2776.66	+	2646.62i	0.411642	+	0.392364i
$358$	5.52836	+	24.2213i	0.000816154	+	0.00357580i
$359$	2.56248	+	3.21324i	0.000376719	+	0.000472391i	0.782020	−	0.623254i	$-0.214190\pi$
$359$	2.56248	+	3.21324i	0.000376719	+	0.000472391i	−0.781643	+	0.623726i	$0.785618\pi$
$360$	−210.069	+	101.164i	−0.0307544	+	0.0148105i
$361$	5687.90			0.829261
$362$	−951.742			−0.138184
$363$	−5680.03	+	2735.36i	−0.821280	+	0.395507i
$364$	2503.81	+	6640.43i	0.360537	+	0.956190i
$365$	−189.373	−	91.1970i	−0.0271567	−	0.0130780i
$366$	220.645	+	106.257i	0.0315117	+	0.0151752i
$367$	−1803.34	−	7900.94i	−0.256494	−	1.12378i	−0.924970	−	0.380041i	$-0.875910\pi$
$367$	−1803.34	−	7900.94i	−0.256494	−	1.12378i	0.668475	−	0.743734i	$-0.266947\pi$
$368$	−1669.53	−	7314.68i	−0.236495	−	1.03615i
$369$	−1089.43	−	524.644i	−0.153696	−	0.0740159i
$370$	375.654	+	180.906i	0.0527820	+	0.0254185i
$371$	4872.94	−	3227.33i	0.681915	−	0.451630i
$372$	−1953.92	+	940.956i	−0.272327	+	0.131146i
$373$	−9756.61			−1.35437			−0.677183	−	0.735815i	$-0.736799\pi$
$373$	−9756.61			−1.35437			−0.677183	+	0.735815i	$0.736799\pi$
$374$	878.218			0.121421
$375$	−2910.56	+	1401.65i	−0.400802	+	0.193016i
$376$	−1141.39	−	1431.25i	−0.156549	−	0.196307i
$377$	−1841.86	−	8069.70i	−0.251619	−	1.10242i
$378$	−266.624	−	707.121i	−0.0362795	−	0.0962180i
$379$	−3126.64	+	13698.7i	−0.423759	+	1.85661i	0.0860049	+	0.996295i	$0.472590\pi$
$379$	−3126.64	+	13698.7i	−0.423759	+	1.85661i	−0.509764	+	0.860314i	$0.670267\pi$
$380$	3037.94	−	1463.00i	0.410113	−	0.197500i
$381$	−923.717	+	4047.07i	−0.124209	+	0.544193i
$382$	−168.217	−	210.937i	−0.0225307	−	0.0282526i
$383$	−2004.46	−	8782.12i	−0.267424	−	1.17166i	−0.912999	−	0.407962i	$-0.866239\pi$
$383$	−2004.46	−	8782.12i	−0.267424	−	1.17166i	0.645575	−	0.763697i	$-0.276618\pi$
$384$	1241.71	−	1557.05i	0.165014	−	0.206921i
$385$	3866.94	−	529.847i	0.511889	−	0.0701390i
$386$	−83.3070	−	104.464i	−0.0109850	−	0.0137748i
$387$	−412.491	+	517.248i	−0.0541812	+	0.0679411i
$388$	9004.23	+	4336.21i	1.17815	+	0.567365i
$389$	−7021.72	+	8804.96i	−0.915206	+	1.14763i	0.0734291	+	0.997300i	$0.476606\pi$
$389$	−7021.72	+	8804.96i	−0.915206	+	1.14763i	−0.988636	+	0.150332i	$0.951966\pi$
$390$	−40.7162	+	178.389i	−0.00528653	+	0.0231618i
$391$	6923.40			0.895476
$392$	−1483.59	−	264.539i	−0.191155	−	0.0340848i
$393$	8306.43			1.06617
$394$	103.337	−	452.751i	0.0132134	−	0.0578915i
$395$	−1034.43	+	1297.13i	−0.131766	+	0.165230i
$396$	5532.38	+	2664.26i	0.702052	+	0.338091i
$397$	−4607.50	+	5777.62i	−0.582478	+	0.730404i	−0.982533	−	0.186087i	$-0.940419\pi$
$397$	−4607.50	+	5777.62i	−0.582478	+	0.730404i	0.400055	+	0.916491i	$0.368991\pi$
$398$	−540.577	−	677.862i	−0.0680821	−	0.0853722i
$399$	2642.05	+	7007.07i	0.331499	+	0.879178i
$400$	−4286.48	+	5375.07i	−0.535810	+	0.671884i
$401$	1907.38	+	8356.78i	0.237531	+	1.04069i	0.943220	+	0.332170i	$0.107781\pi$
$401$	1907.38	+	8356.78i	0.237531	+	1.04069i	−0.705688	+	0.708522i	$0.749362\pi$
$402$	−227.960	−	285.853i	−0.0282826	−	0.0354653i
$403$	815.869	−	3574.55i	0.100847	−	0.441839i
$404$	10406.9	−	5011.72i	1.28159	−	0.617184i
$405$	−132.462	+	580.355i	−0.0162521	+	0.0712052i
$406$	832.234	+	269.000i	0.101732	+	0.0328824i
$407$	−4910.34	−	21513.6i	−0.598026	−	2.62012i
$408$	567.377	+	711.468i	0.0688464	+	0.0863307i
$409$	5580.48	−	2687.42i	0.674663	−	0.324900i	−0.0649933	−	0.997886i	$-0.520703\pi$
$409$	5580.48	−	2687.42i	0.674663	−	0.324900i	0.739656	+	0.672985i	$0.234988\pi$
$410$	−90.7307			−0.0109289
$411$	−2087.66			−0.250551
$412$	763.792	−	367.823i	0.0913334	−	0.0439838i
$413$	−12653.4	+	1733.77i	−1.50759	+	0.206570i
$414$	−419.015	−	201.787i	−0.0497427	−	0.0239548i
$415$	−4445.62	−	2140.90i	−0.525848	−	0.253235i
$416$	562.842	+	2465.97i	0.0663356	+	0.290635i
$417$	57.6892	+	252.753i	0.00677470	+	0.0296819i
$418$	1544.69	+	743.885i	0.180750	+	0.0870445i
$419$	2949.44	+	1420.38i	0.343889	+	0.165608i	0.597854	−	0.801605i	$-0.296020\pi$
$419$	2949.44	+	1420.38i	0.343889	+	0.165608i	−0.253964	+	0.967214i	$0.581735\pi$
$420$	1456.75	+	1388.53i	0.169243	+	0.161317i
$421$	8386.32	−	4038.64i	0.970841	−	0.467532i	0.119896	−	0.992787i	$-0.461744\pi$
$421$	8386.32	−	4038.64i	0.970841	−	0.467532i	0.850945	+	0.525254i	$0.176030\pi$
$422$	−705.209			−0.0813484
$423$	5820.44			0.669030
$424$	1249.24	−	601.604i	0.143086	−	0.0689068i
$425$	−3955.46	−	4959.99i	−0.451454	−	0.566105i
$426$	20.3529	+	89.1719i	0.00231479	+	0.0101418i
$427$	−401.250	+	4536.10i	−0.0454751	+	0.514092i
$428$	1189.71	−	5212.44i	0.134361	−	0.588675i
$429$	8725.07	−	4201.77i	0.981935	−	0.472875i
$430$	−11.0464	+	48.3973i	−0.00123884	+	0.00542773i
$431$	−9615.10	−	12057.0i	−1.07458	−	1.34748i	−0.933945	−	0.357416i	$-0.883658\pi$
$431$	−9615.10	−	12057.0i	−1.07458	−	1.34748i	−0.140633	−	0.990062i	$-0.544914\pi$
$432$	2046.24	+	8965.16i	0.227893	+	0.998464i
$433$	4357.12	−	5463.66i	0.483580	−	0.606390i	−0.478858	−	0.877892i	$-0.658949\pi$
$433$	4357.12	−	5463.66i	0.483580	−	0.606390i	0.962438	+	0.271503i	$0.0875206\pi$
$434$	280.439	+	267.306i	0.0310173	+	0.0295647i
$435$	−1463.48	−	1835.15i	−0.161307	−	0.202273i
$436$	−459.617	+	576.341i	−0.0504854	+	0.0633067i
$437$	12177.5	+	5864.39i	1.33302	+	0.641949i
$438$	34.3580	−	43.0836i	0.00374815	−	0.00470003i
$439$	1257.65	−	5510.14i	0.136730	−	0.599054i	−0.859411	−	0.511286i	$-0.829169\pi$
$439$	1257.65	−	5510.14i	0.136730	−	0.599054i	0.996141	−	0.0877682i	$-0.0279735\pi$
$440$	925.927			0.100322
$441$	3598.60	−	3163.50i	0.388576	−	0.341594i
$442$	−765.570			−0.0823856
$443$	−1816.11	+	7956.88i	−0.194776	+	0.853370i	0.779210	+	0.626763i	$0.215621\pi$
$443$	−1816.11	+	7956.88i	−0.194776	+	0.853370i	−0.973986	+	0.226607i	$0.927237\pi$
$444$	7094.13	−	8895.75i	0.758271	−	0.950842i
$445$	−264.170	−	127.217i	−0.0281412	−	0.0135521i
$446$	242.807	−	304.470i	0.0257786	−	0.0323253i
$447$	2220.44	+	2784.34i	0.234951	+	0.294619i
$448$	8511.67	+	2751.20i	0.897631	+	0.290138i
$449$	1985.34	−	2489.54i	0.208673	−	0.261668i	−0.666470	−	0.745532i	$-0.732196\pi$
$449$	1985.34	−	2489.54i	0.208673	−	0.261668i	0.875143	+	0.483864i	$0.160767\pi$
$450$	94.8286	+	415.471i	0.00993391	+	0.0435233i
$451$	2993.96	+	3754.30i	0.312594	+	0.391981i
$452$	544.288	−	2384.68i	0.0566398	−	0.248155i
$453$	−9057.96	+	4362.08i	−0.939471	+	0.452425i
$454$	−235.149	+	1030.26i	−0.0243086	+	0.106503i
$455$	−3370.93	+	461.884i	−0.347322	+	0.0475900i
$456$	395.315	+	1731.99i	0.0405972	+	0.177868i
$457$	−2637.35	−	3307.14i	−0.269957	−	0.338515i	0.628312	−	0.777961i	$-0.283746\pi$
$457$	−2637.35	−	3307.14i	−0.269957	−	0.338515i	−0.898269	+	0.439446i	$0.855175\pi$
$458$	−511.119	+	246.142i	−0.0521464	+	0.0251124i
$459$	−8485.58			−0.862904
$460$	3632.31			0.368168
$461$	−5763.67	+	2775.64i	−0.582301	+	0.280421i	−0.701755	−	0.712418i	$-0.747600\pi$
$461$	−5763.67	+	2775.64i	−0.582301	+	0.280421i	0.119454	+	0.992840i	$0.461886\pi$
$462$	−90.1650	+	1019.31i	−0.00907978	+	0.102646i
$463$	−4446.66	−	2141.40i	−0.446337	−	0.214944i	0.197194	−	0.980364i	$-0.436817\pi$
$463$	−4446.66	−	2141.40i	−0.446337	−	0.214944i	−0.643531	+	0.765420i	$0.722531\pi$
$464$	−9588.69	−	4617.67i	−0.959361	−	0.462004i
$465$	−231.363	−	1013.67i	−0.0230735	−	0.101092i
$466$	113.129	+	495.653i	0.0112460	+	0.0492718i
$467$	10802.7	+	5202.30i	1.07043	+	0.515490i	0.884244	−	0.467025i	$-0.154674\pi$
$467$	10802.7	+	5202.30i	1.07043	+	0.515490i	0.186182	+	0.982515i	$0.440388\pi$
$468$	−4822.75	−	2322.51i	−0.476350	−	0.229398i
$469$	3478.06	−	5841.61i	0.342435	−	0.575139i
$470$	393.486	−	189.493i	0.0386173	−	0.0185971i
$471$	−8621.08			−0.843393
$472$	−3029.83			−0.295465
$473$	2367.12	−	1139.95i	0.230106	−	0.110813i
$474$	−271.201	−	340.076i	−0.0262799	−	0.0329540i
$475$	−2755.93	−	12074.5i	−0.266212	−	1.16635i
$476$	−4307.64	+	7234.92i	−0.414790	+	0.696664i
$477$	−980.981	+	4297.96i	−0.0941636	+	0.412558i
$478$	−1400.63	+	674.506i	−0.134023	+	0.0645423i
$479$	−2185.14	+	9573.72i	−0.208438	+	0.913224i	0.757170	+	0.653218i	$0.226582\pi$
$479$	−2185.14	+	9573.72i	−0.208438	+	0.913224i	−0.965607	+	0.260006i	$0.916275\pi$
$480$	447.216	+	560.792i	0.0425261	+	0.0533261i
$481$	4280.49	+	18754.1i	0.405767	+	1.77778i
$482$	739.151	−	926.866i	0.0698494	−	0.0875884i
$483$	−710.812	+	8035.67i	−0.0669629	+	0.757010i
$484$	−8628.23	−	10819.5i	−0.810314	−	1.01610i
$485$	−2987.40	+	3746.08i	−0.279692	+	0.350723i
$486$	852.015	+	410.309i	0.0795230	+	0.0382962i
$487$	1306.14	−	1637.84i	0.121533	−	0.152398i	−0.717343	−	0.696720i	$-0.754642\pi$
$487$	1306.14	−	1637.84i	0.121533	−	0.152398i	0.838876	+	0.544323i	$0.183213\pi$
$488$	−240.390	+	1053.22i	−0.0222991	+	0.0976986i
$489$	−512.283			−0.0473747
$490$	140.288	−	331.023i	0.0129338	−	0.0305186i
$491$	14911.0			1.37051			0.685256	−	0.728302i	$-0.259690\pi$
$491$	14911.0			1.37051			0.685256	+	0.728302i	$0.259690\pi$
$492$	−550.955	+	2413.89i	−0.0504857	+	0.221192i
$493$	6123.15	−	7678.19i	0.559377	−	0.701436i
$494$	−1346.56	−	648.467i	−0.122641	−	0.0590606i
$495$	−1835.52	+	2301.66i	−0.166667	+	0.208994i
$496$	−2939.30	−	3685.76i	−0.266085	−	0.333660i
$497$	−1417.99	+	939.126i	−0.127979	+	0.0847597i
$498$	806.573	−	1011.41i	0.0725771	−	0.0910088i
$499$	3489.93	+	15290.4i	0.313088	+	1.37173i	0.849419	+	0.527719i	$0.176953\pi$
$499$	3489.93	+	15290.4i	0.313088	+	1.37173i	−0.536331	+	0.844008i	$0.680190\pi$
$500$	−4421.27	−	5544.10i	−0.395450	−	0.495879i
$501$	−970.565	+	4252.32i	−0.0865502	+	0.379201i
$502$	1802.13	−	867.862i	0.160225	−	0.0771605i
$503$	655.625	−	2872.48i	0.0581170	−	0.254627i	−0.937521	−	0.347929i	$-0.886885\pi$
$503$	655.625	−	2872.48i	0.0581170	−	0.254627i	0.995638	+	0.0933017i	$0.0297421\pi$
$504$	947.675	−	627.641i	0.0837555	−	0.0554710i
$505$	1232.28	+	5398.98i	0.108586	+	0.475746i
$506$	1151.53	+	1443.97i	0.101169	+	0.126862i
$507$	−460.512	+	221.771i	−0.0403393	+	0.0194264i
$508$	−9112.11			−0.795836
$509$	518.395			0.0451423			0.0225712	−	0.999745i	$-0.492815\pi$
$509$	518.395			0.0451423			0.0225712	+	0.999745i	$0.492815\pi$
$510$	−195.599	+	94.1957i	−0.0169829	+	0.00817854i
$511$	975.017	+	315.151i	0.0844075	+	0.0272827i
$512$	4899.21	+	2359.34i	0.422884	+	0.203650i
$513$	−14925.2	−	7187.62i	−1.28453	−	0.618599i
$514$	−9.71963	−	42.5845i	−0.000834074	−	0.00365432i
$515$	90.4404	+	396.245i	0.00773841	+	0.0339042i
$516$	1220.53	+	587.778i	0.104130	+	0.0501462i
$517$	−20825.3	−	10028.9i	−1.77156	−	0.853137i
$518$	−1934.12	−	625.159i	−0.164055	−	0.0530269i
$519$	12266.8	−	5907.38i	1.03748	−	0.499625i
$520$	−807.159			−0.0680697
$521$	−9518.96			−0.800448			−0.400224	−	0.916417i	$-0.631068\pi$
$521$	−9518.96			−0.800448			−0.400224	+	0.916417i	$0.631068\pi$
$522$	−594.369	+	286.233i	−0.0498368	+	0.0240002i
$523$	−46.1753	−	57.9020i	−0.00386062	−	0.00484106i	0.779897	−	0.625907i	$-0.215271\pi$
$523$	−46.1753	−	57.9020i	−0.00386062	−	0.00484106i	−0.783758	+	0.621066i	$0.786700\pi$
$524$	4057.29	+	17776.2i	0.338251	+	1.48198i
$525$	6162.93	−	4081.69i	0.512328	−	0.339313i
$526$	−31.6588	+	138.706i	−0.00262432	+	0.0114979i
$527$	3919.40	−	1887.49i	0.323969	−	0.156015i
$528$	2770.73	−	12139.4i	0.228372	−	1.00056i
$529$	1492.03	+	1870.94i	0.122629	+	0.153772i
$530$	73.6077	+	322.497i	0.00603267	+	0.0264309i
$531$	6006.20	−	7531.54i	0.490861	−	0.615520i
$532$	−13704.9	+	9076.74i	−1.11689	+	0.739711i
$533$	−2609.92	−	3272.74i	−0.212098	−	0.265963i
$534$	47.9285	−	60.1005i	0.00388403	−	0.00487042i
$535$	2309.43	+	1112.16i	0.186627	+	0.0898747i
$536$	1005.59	−	1260.97i	0.0810352	−	0.101615i
$537$	−72.3293	+	316.895i	−0.00581236	+	0.0254656i
$538$	157.473			0.0126192
$539$	−18326.5	+	5118.29i	−1.46453	+	0.409017i
$540$	−4451.89			−0.354776
$541$	−2384.88	+	10448.9i	−0.189527	+	0.830373i	0.787339	+	0.616520i	$0.211458\pi$
$541$	−2384.88	+	10448.9i	−0.189527	+	0.830373i	−0.976866	+	0.213852i	$0.931399\pi$
$542$	−1284.15	+	1610.27i	−0.101769	+	0.127614i
$543$	−11218.8	−	5402.69i	−0.886639	−	0.426983i
$544$	−1871.14	+	2346.33i	−0.147471	+	0.184923i
$545$	−220.355	−	276.316i	−0.0173192	−	0.0217176i
$546$	78.5996	−	888.561i	0.00616072	−	0.0696464i
$547$	285.516	−	358.026i	0.0223177	−	0.0279855i	−0.770547	−	0.637383i	$-0.780017\pi$
$547$	285.516	−	358.026i	0.0223177	−	0.0279855i	0.792865	+	0.609397i	$0.208588\pi$
$548$	−1019.72	−	4467.69i	−0.0794897	−	0.348267i
$549$	−2141.55	−	2685.41i	−0.166483	−	0.208763i
$550$	376.586	−	1649.93i	0.0291958	−	0.127915i
$551$	17273.7	−	8318.58i	1.33554	−	0.643164i
$552$	−425.850	+	1865.77i	−0.0328358	+	0.143863i
$553$	4137.81	−	6949.68i	0.318187	−	0.534413i
$554$	−357.539	−	1566.48i	−0.0274194	−	0.120132i
$555$	3401.15	+	4264.90i	0.260127	+	0.326189i
$556$	−512.725	+	246.915i	−0.0391086	+	0.0188337i
$557$	8614.08			0.655279			0.327639	−	0.944803i	$-0.393747\pi$
$557$	8614.08			0.655279			0.327639	+	0.944803i	$0.393747\pi$
$558$	−292.221			−0.0221697
$559$	−2063.49	+	993.726i	−0.156130	+	0.0751880i
$560$	−2238.05	+	3758.93i	−0.168883	+	0.283650i
$561$	10352.1	+	4985.32i	0.779086	+	0.375188i
$562$	2165.69	+	1042.94i	0.162552	+	0.0782809i
$563$	2109.52	+	9242.42i	0.157914	+	0.691868i	0.990447	+	0.137892i	$0.0440327\pi$
$563$	2109.52	+	9242.42i	0.157914	+	0.691868i	−0.832533	+	0.553975i	$0.813110\pi$
$564$	−2652.04	−	11619.4i	−0.197999	−	0.867489i
$565$	1056.56	+	508.813i	0.0786723	+	0.0378866i
$566$	674.747	+	324.941i	0.0501091	+	0.0241313i
$567$	255.709	−	2890.76i	0.0189396	−	0.214110i
$568$	−363.520	+	175.062i	−0.0268538	+	0.0129321i
$569$	13190.6			0.971842			0.485921	−	0.874003i	$-0.338484\pi$
$569$	13190.6			0.971842			0.485921	+	0.874003i	$0.338484\pi$
$570$	−423.826			−0.0311441
$571$	−14188.6	+	6832.87i	−1.03989	+	0.500783i	−0.874286	−	0.485411i	$-0.838670\pi$
$571$	−14188.6	+	6832.87i	−1.03989	+	0.500783i	−0.165599	+	0.986193i	$0.552956\pi$
$572$	13253.8	+	16619.7i	0.968825	+	1.21487i
$573$	−785.468	−	3441.36i	−0.0572660	−	0.250899i
$574$	438.226	−	60.0457i	0.0318662	−	0.00436631i
$575$	2968.80	−	13007.2i	0.215318	−	0.943368i
$576$	−6078.91	+	2927.45i	−0.439736	+	0.211766i
$577$	−3006.51	+	13172.4i	−0.216920	+	0.950388i	0.742819	+	0.669493i	$0.233488\pi$
$577$	−3006.51	+	13172.4i	−0.216920	+	0.950388i	−0.959739	+	0.280895i	$0.909369\pi$
$578$	278.835	+	349.649i	0.0200658	+	0.0251617i
$579$	−388.992	−	1704.28i	−0.0279205	−	0.122328i
$580$	3212.46	−	4028.30i	0.229983	−	0.288390i
$581$	22889.1	+	7398.35i	1.63442	+	0.528288i
$582$	−783.221	−	982.128i	−0.0557827	−	0.0699493i
$583$	10915.5	−	13687.6i	0.775428	−	0.972356i
$584$	219.014	+	105.471i	0.0155186	+	0.00747335i
$585$	1600.08	−	2006.43i	0.113085	−	0.141805i
$586$	353.158	−	1547.29i	0.0248956	−	0.109075i
$587$	14319.0			1.00683			0.503416	−	0.864044i	$-0.332076\pi$
$587$	14319.0			1.00683			0.503416	+	0.864044i	$0.332076\pi$
$588$	−7954.99	−	5742.47i	−0.557922	−	0.402748i
$589$	8492.59			0.594111
$590$	160.844	−	704.703i	0.0112235	−	0.0491732i
$591$	3788.20	−	4750.26i	0.263665	−	0.330625i
$592$	22284.2	+	10731.5i	1.54709	+	0.745038i
$593$	5226.83	−	6554.23i	0.361956	−	0.453879i	−0.567192	−	0.823585i	$-0.691970\pi$
$593$	5226.83	−	6554.23i	0.361956	−	0.453879i	0.929149	+	0.369707i	$0.120542\pi$
$594$	−1411.36	−	1769.79i	−0.0974894	−	0.122248i
$595$	−2922.13	−	2785.28i	−0.201337	−	0.191908i
$596$	−4874.05	+	6111.86i	−0.334981	+	0.420053i
$597$	−2524.16	−	11059.1i	−0.173043	−	0.758152i
$598$	−1003.82	−	1258.75i	−0.0686444	−	0.0860774i
$599$	−893.485	+	3914.62i	−0.0609463	+	0.267023i	−0.996216	−	0.0869129i	$-0.972300\pi$
$599$	−893.485	+	3914.62i	−0.0609463	+	0.267023i	0.935270	+	0.353936i	$0.115157\pi$
$600$	1579.95	−	760.864i	0.107502	−	0.0517702i
$601$	5194.81	−	22760.0i	0.352580	−	1.54476i	−0.418619	−	0.908162i	$-0.637486\pi$
$601$	5194.81	−	22760.0i	0.352580	−	1.54476i	0.771199	−	0.636594i	$-0.219657\pi$
$602$	21.3242	−	241.068i	0.00144370	−	0.0163209i
$603$	1141.08	+	4999.38i	0.0770617	+	0.337630i
$604$	−13759.5	−	17253.8i	−0.926928	−	1.16233i
$605$	5977.62	−	2878.67i	0.401694	−	0.193446i
$606$	−1451.88			−0.0973245
$607$	−14674.0			−0.981217			−0.490608	−	0.871380i	$-0.663225\pi$
$607$	−14674.0			−0.981217			−0.490608	+	0.871380i	$0.663225\pi$
$608$	−5278.57	+	2542.02i	−0.352096	+	0.169560i
$609$	8283.07	+	7895.17i	0.551144	+	0.525334i
$610$	−232.205	−	111.824i	−0.0154126	−	0.00742232i
$611$	18154.0	+	8742.52i	1.20202	+	0.578862i
$612$	−1413.24	−	6191.82i	−0.0933446	−	0.408970i
$613$	674.548	+	2955.39i	0.0444449	+	0.194726i	0.992277	−	0.124046i	$-0.0395869\pi$
$613$	674.548	+	2955.39i	0.0444449	+	0.194726i	−0.947832	+	0.318772i	$0.896730\pi$
$614$	1553.47	+	748.111i	0.102106	+	0.0491715i
$615$	−1069.50	−	515.045i	−0.0701243	−	0.0337701i
$616$	−4472.20	+	612.780i	−0.292516	+	0.0400805i
$617$	−26939.7	+	12973.5i	−1.75778	+	0.846503i	−0.783427	+	0.621484i	$0.786530\pi$
$617$	−26939.7	+	12973.5i	−1.75778	+	0.846503i	−0.974355	+	0.225018i	$0.927756\pi$
$618$	−106.557			−0.00693587
$619$	18888.3			1.22647			0.613235	−	0.789901i	$-0.289868\pi$
$619$	18888.3			1.22647			0.613235	+	0.789901i	$0.289868\pi$
$620$	2056.28	−	990.254i	0.133197	−	0.0641445i
$621$	−11126.4	−	13952.0i	−0.718979	−	0.901572i
$622$	554.659	+	2430.12i	0.0357553	+	0.156654i
$623$	1360.12	+	439.628i	0.0874674	+	0.0282718i
$624$	−2415.33	+	10582.3i	−0.154953	+	0.678893i
$625$	−9389.24	+	4521.62i	−0.600911	+	0.289384i
$626$	456.381	−	1999.53i	0.0291384	−	0.127664i
$627$	13985.5	+	17537.3i	0.890795	+	1.11702i
$628$	−4210.98	−	18449.5i	−0.267574	−	1.17232i
$629$	−14230.3	+	17844.2i	−0.902064	+	1.13115i
$630$	95.6730	+	253.737i	0.00605033	+	0.0160462i
$631$	2776.99	+	3482.24i	0.175199	+	0.219692i	0.861676	−	0.507459i	$-0.169415\pi$
$631$	2776.99	+	3482.24i	0.175199	+	0.219692i	−0.686477	+	0.727151i	$0.740844\pi$
$632$	1196.34	−	1500.16i	0.0752971	−	0.0944196i
$633$	−8312.76	−	4003.21i	−0.521963	−	0.251364i
$634$	1719.64	−	2156.37i	0.107722	−	0.135079i
$635$	972.112	−	4259.10i	0.0607513	−	0.266169i
$636$	9027.00			0.562805
$637$	15975.8	−	4461.77i	0.993695	−	0.277522i
$638$	2619.82			0.162570
$639$	285.457	−	1250.67i	0.0176722	−	0.0774268i
$640$	−1306.76	+	1638.63i	−0.0807098	+	0.101207i
$641$	−14167.4	−	6822.68i	−0.872981	−	0.420405i	−0.0569249	−	0.998378i	$-0.518130\pi$
$641$	−14167.4	−	6822.68i	−0.872981	−	0.420405i	−0.816056	+	0.577973i	$0.803844\pi$
$642$	−419.002	+	525.411i	−0.0257581	+	0.0322996i
$643$	2317.55	+	2906.12i	0.142139	+	0.178237i	0.847805	−	0.530308i	$-0.177924\pi$
$643$	2317.55	+	2906.12i	0.142139	+	0.178237i	−0.705666	+	0.708544i	$0.749352\pi$
$644$	−17543.9	+	2403.87i	−1.07349	+	0.147089i
$645$	−404.944	+	507.784i	−0.0247204	+	0.0309984i
$646$	−394.590	−	1728.81i	−0.0240324	−	0.105293i
$647$	3305.02	+	4144.37i	0.200825	+	0.251827i	0.872038	−	0.489438i	$-0.162798\pi$
$647$	3305.02	+	4144.37i	0.200825	+	0.251827i	−0.671213	+	0.741264i	$0.734226\pi$
$648$	153.196	−	671.194i	0.00928718	−	0.0406898i
$649$	−34467.2	+	16598.5i	−2.08468	+	1.00393i
$650$	−328.282	+	1438.30i	−0.0198096	+	0.0867917i
$651$	1788.32	+	4742.86i	0.107665	+	0.285541i
$652$	−250.226	−	1096.31i	−0.0150301	−	0.0658510i
$653$	947.444	+	1188.06i	0.0567785	+	0.0711980i	0.809410	−	0.587244i	$-0.199787\pi$
$653$	947.444	+	1188.06i	0.0567785	+	0.0711980i	−0.752631	+	0.658442i	$0.771216\pi$
$654$	83.4823	−	40.2029i	0.00499146	−	0.00240376i
$655$	−8741.62			−0.521471
$656$	−5382.24			−0.320337
$657$	−696.343	+	335.341i	−0.0413499	+	0.0199131i
$658$	−1775.12	+	1175.65i	−0.105169	+	0.0696531i
$659$	−16036.4	−	7722.71i	−0.947934	−	0.456501i	−0.104973	−	0.994475i	$-0.533476\pi$
$659$	−16036.4	−	7722.71i	−0.947934	−	0.456501i	−0.842961	+	0.537974i	$0.819190\pi$
$660$	5431.16	+	2615.51i	0.320315	+	0.154255i
$661$	−1857.70	−	8139.10i	−0.109313	−	0.478932i	−0.999718	−	0.0237622i	$-0.992436\pi$
$661$	−1857.70	−	8139.10i	−0.109313	−	0.478932i	0.890404	−	0.455170i	$-0.150422\pi$
$662$	55.9751	+	245.243i	0.00328630	+	0.0143982i
$663$	−9024.26	−	4345.86i	−0.528617	−	0.254569i
$664$	5141.46	+	2476.00i	0.300493	+	0.144710i
$665$	−2780.47	−	7374.18i	−0.162139	−	0.430013i
$666$	1381.32	−	665.209i	0.0803680	−	0.0387032i
$667$	20653.3			1.19895
$668$	−9574.25			−0.554549
$669$	4590.48	−	2210.66i	0.265289	−	0.127756i
$670$	239.903	+	300.829i	0.0138332	+	0.0173463i
$671$	3035.25	+	13298.3i	0.174627	+	0.765089i
$672$	−2531.17	−	2412.64i	−0.145301	−	0.138496i
$673$	717.915	−	3145.39i	0.0411197	−	0.180157i	−0.950198	−	0.311648i	$-0.899119\pi$
$673$	717.915	−	3145.39i	0.0411197	−	0.180157i	0.991317	+	0.131490i	$0.0419763\pi$
$674$	−1275.60	+	614.296i	−0.0728994	+	0.0351065i
$675$	−3638.68	+	15942.1i	−0.207486	+	0.909054i
$676$	−699.538	−	877.193i	−0.0398008	−	0.0499086i
$677$	202.577	+	887.550i	0.0115003	+	0.0503860i	0.980352	−	0.197254i	$-0.0632023\pi$
$677$	202.577	+	887.550i	0.0115003	+	0.0503860i	−0.968852	+	0.247640i	$0.920345\pi$
$678$	−191.693	+	240.375i	−0.0108583	+	0.0136158i
$679$	11949.9	−	20070.5i	0.675396	−	1.13437i
$680$	−597.103	−	748.743i	−0.0336733	−	0.0422250i
$681$	−8620.25	+	10809.4i	−0.485064	+	0.608251i
$682$	1045.55	+	503.512i	0.0587042	+	0.0282705i
$683$	−496.921	+	623.120i	−0.0278392	+	0.0349092i	−0.795556	−	0.605880i	$-0.792821\pi$
$683$	−496.921	+	623.120i	−0.0278392	+	0.0349092i	0.767717	+	0.640789i	$0.221393\pi$
$684$	2758.97	−	12087.8i	0.154228	−	0.675716i
$685$	2197.03			0.122547
$686$	−458.514	+	1691.67i	−0.0255192	+	0.0941522i
$687$	−7422.15			−0.412187
$688$	−655.282	+	2870.98i	−0.0363116	+	0.159092i
$689$	−9515.39	+	11931.9i	−0.526136	+	0.659753i
$690$	−411.349	−	198.095i	−0.0226953	−	0.0109295i
$691$	11406.8	−	14303.7i	0.627981	−	0.787464i	−0.361461	−	0.932387i	$-0.617722\pi$
$691$	11406.8	−	14303.7i	0.627981	−	0.787464i	0.989443	+	0.144923i	$0.0462935\pi$
$692$	18633.8	+	23366.1i	1.02363	+	1.28359i
$693$	7342.24	−	12331.7i	0.402465	−	0.675964i
$694$	−1231.76	+	1544.58i	−0.0673734	+	0.0844836i
$695$	−60.7116	−	265.995i	−0.00331356	−	0.0145176i
$696$	1692.55	+	2122.39i	0.0921780	+	0.115588i
$697$	1105.17	−	4842.08i	0.0600594	−	0.263137i
$698$	145.399	−	70.0206i	0.00788459	−	0.00379702i
$699$	−1480.11	+	6484.77i	−0.0800898	+	0.350896i
$700$	11745.3	+	11195.3i	0.634187	+	0.604487i
$701$	3300.46	+	14460.2i	0.177827	+	0.779110i	0.982631	+	0.185570i	$0.0594130\pi$
$701$	3300.46	+	14460.2i	0.177827	+	0.779110i	−0.804804	+	0.593540i	$0.797730\pi$
$702$	1230.32	+	1542.78i	0.0661475	+	0.0829464i
$703$	−40144.3	+	19332.5i	−2.15373	+	1.03718i
$704$	26794.2			1.43444
$705$	5713.95			0.305248
$706$	−1450.53	+	698.540i	−0.0773251	+	0.0372378i
$707$	−9524.94	−	25261.4i	−0.506679	−	1.34378i
$708$	−17771.9	−	8558.51i	−0.943376	−	0.454306i
$709$	−17576.1	−	8464.22i	−0.931009	−	0.448350i	−0.0940203	−	0.995570i	$-0.529972\pi$
$709$	−17576.1	−	8464.22i	−0.931009	−	0.448350i	−0.836989	+	0.547220i	$0.815686\pi$
$710$	−21.4192	−	93.8438i	−0.00113218	−	0.00496042i
$711$	1357.52	+	5947.70i	0.0716050	+	0.313722i
$712$	305.518	+	147.130i	0.0160811	+	0.00774427i
$713$	8242.57	+	3969.41i	0.432941	+	0.208493i
$714$	882.399	−	584.410i	0.0462507	−	0.0306316i
$715$	−9182.19	+	4421.91i	−0.480272	+	0.231287i
$716$	−713.500			−0.0372413
$717$	−20339.0			−1.05938
$718$	1.02167	−	0.492009i	5.31034e−5	−	2.55733e-5i
$719$	5497.54	+	6893.70i	0.285151	+	0.357568i	0.903691	−	0.428185i	$-0.140847\pi$
$719$	5497.54	+	6893.70i	0.285151	+	0.357568i	−0.618540	+	0.785753i	$0.712275\pi$
$720$	−734.254	−	3216.98i	−0.0380056	−	0.166514i
$721$	−699.060	−	1854.00i	−0.0361087	−	0.0957650i
$722$	349.214	−	1530.01i	0.0180006	−	0.0788657i
$723$	13974.3	−	6729.68i	0.718826	−	0.346168i
$724$	6082.17	−	26647.7i	0.312213	−	1.36789i
$725$	−11799.6	−	14796.2i	−0.604448	−	0.757954i
$726$	387.063	+	1695.83i	0.0197868	+	0.0866918i
$727$	−12532.0	+	15714.6i	−0.639320	+	0.801682i	−0.990918	−	0.134469i	$-0.957067\pi$
$727$	−12532.0	+	15714.6i	−0.639320	+	0.801682i	0.351598	+	0.936151i	$0.385638\pi$
$728$	3898.55	−	534.179i	0.198475	−	0.0271951i
$729$	10351.9	+	12980.9i	0.525933	+	0.659499i
$730$	−36.1581	+	45.3408i	−0.00183325	+	0.00229882i
$731$	−2448.29	−	1179.04i	−0.123876	−	0.0596556i
$732$	−4385.12	+	5498.76i	−0.221419	+	0.277651i
$733$	1031.93	−	4521.17i	0.0519988	−	0.227821i	−0.942251	−	0.334908i	$-0.891295\pi$
$733$	1031.93	−	4521.17i	0.0519988	−	0.227821i	0.994250	+	0.107086i	$0.0341521\pi$
$734$	−2236.02			−0.112443
$735$	3532.76	−	3105.62i	0.177290	−	0.155854i
$736$	−6311.31			−0.316084
$737$	4531.48	−	19853.7i	0.226485	−	0.992294i
$738$	−208.013	+	260.839i	−0.0103754	+	0.0130103i
$739$	7018.83	+	3380.09i	0.349380	+	0.168253i	0.600340	−	0.799745i	$-0.295032\pi$
$739$	7018.83	+	3380.09i	0.349380	+	0.168253i	−0.250960	+	0.967997i	$0.580746\pi$
$740$	−7465.80	+	9361.82i	−0.370876	+	0.465064i
$741$	−12191.6	−	15287.8i	−0.604413	−	0.757911i
$742$	−568.952	−	1508.93i	−0.0281494	−	0.0746560i
$743$	6638.25	−	8324.11i	0.327771	−	0.411012i	−0.590454	−	0.807071i	$-0.701051\pi$
$743$	6638.25	−	8324.11i	0.327771	−	0.411012i	0.918225	+	0.396060i	$0.129623\pi$
$744$	267.576	+	1172.33i	0.0131852	+	0.0577683i
$745$	−2336.77	−	2930.22i	−0.114916	−	0.144100i
$746$	−599.017	+	2624.46i	−0.0293989	+	0.128805i
$747$	−16347.0	+	7872.31i	−0.800677	+	0.385586i
$748$	−5612.31	+	24589.1i	−0.274340	+	1.20196i
$749$	−11890.5	−	3843.32i	−0.580066	−	0.187493i
$750$	198.338	+	868.977i	0.00965638	+	0.0423074i
$751$	20888.6	+	26193.5i	1.01496	+	1.27272i	0.961689	+	0.274141i	$0.0883936\pi$
$751$	20888.6	+	26193.5i	1.01496	+	1.27272i	0.0532721	+	0.998580i	$0.483035\pi$
$752$	23342.0	−	11240.9i	1.13191	−	0.545098i
$753$	26169.4			1.26649
$754$	−2283.78			−0.110305
$755$	9532.53	−	4590.62i	0.459502	−	0.221285i
$756$	21502.5	−	2946.27i	1.03444	−	0.141739i
$757$	17907.2	+	8623.65i	0.859773	+	0.414045i	0.811196	−	0.584774i	$-0.198817\pi$
$757$	17907.2	+	8623.65i	0.859773	+	0.414045i	0.0485773	+	0.998819i	$0.484531\pi$
$758$	3492.90	+	1682.09i	0.167372	+	0.0806019i
$759$	5376.92	+	23557.8i	0.257141	+	1.12661i
$760$	−416.026	−	1822.73i	−0.0198564	−	0.0869966i
$761$	−16285.3	−	7842.59i	−0.775745	−	0.373579i	0.00374575	−	0.999993i	$-0.498808\pi$
$761$	−16285.3	−	7842.59i	−0.775745	−	0.373579i	−0.779491	+	0.626414i	$0.784522\pi$
$762$	1031.92	+	496.947i	0.0490585	+	0.0236253i
$763$	1247.17	+	1188.77i	0.0591752	+	0.0564040i
$764$	6981.02	−	3361.88i	0.330582	−	0.159200i
$765$	3044.89			0.143906
$766$	−2485.40			−0.117234
$767$	30046.1	−	14469.4i	1.41447	−	0.681175i

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0613960 - 0.268993i) q^{2} +(2.25069 - 2.82228i) q^{3} +(7.13916 + 3.43804i) q^{4} +(-2.36861 + 2.97014i) q^{5} +(-0.620990 - 0.778697i) q^{6} +(9.47466 - 15.9132i) q^{7} +(2.73935 - 3.43503i) q^{8} +(3.10843 + 13.6189i) q^{9} +O(q^{10})\)	\(q+(0.0613960 - 0.268993i) q^{2} +(2.25069 - 2.82228i) q^{3} +(7.13916 + 3.43804i) q^{4} +(-2.36861 + 2.97014i) q^{5} +(-0.620990 - 0.778697i) q^{6} +(9.47466 - 15.9132i) q^{7} +(2.73935 - 3.43503i) q^{8} +(3.10843 + 13.6189i) q^{9} +(0.653525 + 0.819495i) q^{10} +(12.3443 - 54.0839i) q^{11} +(25.7711 - 12.4107i) q^{12} +(-10.7609 + 47.1465i) q^{13} +(-3.69885 - 3.52563i) q^{14} +(3.05155 + 13.3697i) q^{15} +(38.7678 + 48.6133i) q^{16} +(-51.6949 + 24.8950i) q^{17} +3.85424 q^{18} -112.013 q^{19} +(-27.1213 + 13.0609i) q^{20} +(-23.5870 - 62.5559i) q^{21} +(-13.7903 - 6.64106i) q^{22} +(-108.715 - 52.3546i) q^{23} +(-3.52919 - 15.4624i) q^{24} +(24.6037 + 107.796i) q^{25} +(12.0214 + 5.78922i) q^{26} +(133.246 + 64.1677i) q^{27} +(122.351 - 81.0329i) q^{28} +(-154.212 + 74.2644i) q^{29} +3.78372 q^{30} -75.8179 q^{31} +(47.1246 - 22.6940i) q^{32} +(-124.856 - 156.565i) q^{33} +(3.52272 + 15.4340i) q^{34} +(24.8228 + 65.8333i) q^{35} +(-24.6308 + 107.915i) q^{36} +(358.390 - 172.591i) q^{37} +(-6.87715 + 30.1307i) q^{38} +(108.841 + 136.483i) q^{39} +(3.71409 + 16.2725i) q^{40} +(-53.9698 + 67.6759i) q^{41} +(-18.2753 + 2.50407i) q^{42} +(29.5287 + 37.0279i) q^{43} +(274.070 - 343.673i) q^{44} +(-47.8127 - 23.0254i) q^{45} +(-20.7577 + 26.0294i) q^{46} +(92.7165 - 406.217i) q^{47} +224.455 q^{48} +(-163.462 - 301.545i) q^{49} +30.5069 q^{50} +(-46.0888 + 201.928i) q^{51} +(-238.915 + 299.591i) q^{52} +(284.334 + 136.928i) q^{53} +(25.4414 - 31.9026i) q^{54} +(131.398 + 164.768i) q^{55} +(-28.7081 - 76.1376i) q^{56} +(-252.107 + 316.132i) q^{57} +(10.5087 + 46.0415i) q^{58} +(-429.962 - 539.155i) q^{59} +(-24.1801 + 105.940i) q^{60} +(-221.533 + 106.685i) q^{61} +(-4.65492 + 20.3945i) q^{62} +(246.172 + 79.5694i) q^{63} +(107.477 + 470.889i) q^{64} +(-114.544 - 143.633i) q^{65} +(-49.7806 + 23.9731i) q^{66} +367.091 q^{67} -454.648 q^{68} +(-392.444 + 188.991i) q^{69} +(19.2327 - 2.63527i) q^{70} +(-82.7389 - 39.8450i) q^{71} +(55.2965 + 26.6294i) q^{72} +(12.3116 + 53.9406i) q^{73} +(-24.4222 - 107.001i) q^{74} +(359.605 + 173.177i) q^{75} +(-799.679 - 385.105i) q^{76} +(-743.691 - 708.863i) q^{77} +(43.3953 - 20.8981i) q^{78} +436.724 q^{79} -236.214 q^{80} +(141.178 - 67.9878i) q^{81} +(14.8909 + 18.6725i) q^{82} +(289.021 + 1266.28i) q^{83} +(46.6779 - 527.690i) q^{84} +(48.5035 - 212.508i) q^{85} +(11.7732 - 5.66967i) q^{86} +(-137.488 + 602.374i) q^{87} +(-151.965 - 190.557i) q^{88} +(17.1743 + 75.2457i) q^{89} +(-9.12919 + 11.4476i) q^{90} +(648.298 + 617.938i) q^{91} +(-596.140 - 747.535i) q^{92} +(-170.643 + 213.979i) q^{93} +(-103.577 - 49.8802i) q^{94} +(265.315 - 332.694i) q^{95} +(42.0141 - 184.076i) q^{96} +1261.25 q^{97} +(-91.1494 + 25.4565i) q^{98} +774.935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more