LMFDB - Embedded newform 136.4.h.a.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(101,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("136.101");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.h (of order $2$, degree $1$, 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:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	136.101
Dual form			136.4.h.a.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.76967 - 0.573530i) q^{2} +3.72680 q^{3} +(7.34213 + 3.17697i) q^{4} -7.30821 q^{5} +(-10.3220 - 2.13743i) q^{6} -5.81849i q^{7} +(-18.5132 - 13.0101i) q^{8} -13.1110 q^{9} +O(q^{10})$	\(q+(-2.76967 - 0.573530i) q^{2} +3.72680 q^{3} +(7.34213 + 3.17697i) q^{4} -7.30821 q^{5} +(-10.3220 - 2.13743i) q^{6} -5.81849i q^{7} +(-18.5132 - 13.0101i) q^{8} -13.1110 q^{9} +(20.2413 + 4.19147i) q^{10} -12.0372 q^{11} +(27.3626 + 11.8399i) q^{12} -56.0136i q^{13} +(-3.33708 + 16.1153i) q^{14} -27.2362 q^{15} +(43.8137 + 46.6515i) q^{16} +(16.9578 - 68.0105i) q^{17} +(36.3131 + 7.51954i) q^{18} +100.291i q^{19} +(-53.6578 - 23.2180i) q^{20} -21.6843i q^{21} +(33.3391 + 6.90370i) q^{22} -188.838i q^{23} +(-68.9948 - 48.4860i) q^{24} -71.5901 q^{25} +(-32.1255 + 155.139i) q^{26} -149.486 q^{27} +(18.4852 - 42.7201i) q^{28} -290.463 q^{29} +(75.4352 + 15.6208i) q^{30} -195.440i q^{31} +(-94.5934 - 154.338i) q^{32} -44.8603 q^{33} +(-85.9737 + 178.641i) q^{34} +42.5227i q^{35} +(-96.2625 - 41.6532i) q^{36} +168.323 q^{37} +(57.5198 - 277.773i) q^{38} -208.751i q^{39} +(135.298 + 95.0804i) q^{40} -55.4431i q^{41} +(-12.4366 + 60.0585i) q^{42} +78.8633i q^{43} +(-88.3788 - 38.2419i) q^{44} +95.8177 q^{45} +(-108.304 + 523.020i) q^{46} -210.230 q^{47} +(163.285 + 173.861i) q^{48} +309.145 q^{49} +(198.281 + 41.0591i) q^{50} +(63.1985 - 253.461i) q^{51} +(177.954 - 411.259i) q^{52} +499.044i q^{53} +(414.025 + 85.7344i) q^{54} +87.9705 q^{55} +(-75.6991 + 107.719i) q^{56} +373.764i q^{57} +(804.485 + 166.589i) q^{58} +442.209i q^{59} +(-199.972 - 86.5287i) q^{60} +444.439 q^{61} +(-112.091 + 541.304i) q^{62} +76.2862i q^{63} +(173.475 + 481.716i) q^{64} +409.359i q^{65} +(124.248 + 25.7287i) q^{66} -675.021i q^{67} +(340.574 - 445.467i) q^{68} -703.763i q^{69} +(24.3881 - 117.774i) q^{70} -789.694i q^{71} +(242.726 + 170.575i) q^{72} +649.239i q^{73} +(-466.198 - 96.5381i) q^{74} -266.802 q^{75} +(-318.622 + 736.348i) q^{76} +70.0385i q^{77} +(-119.725 + 578.172i) q^{78} -65.0808i q^{79} +(-320.199 - 340.939i) q^{80} -203.106 q^{81} +(-31.7982 + 153.559i) q^{82} -377.605i q^{83} +(68.8906 - 159.209i) q^{84} +(-123.931 + 497.035i) q^{85} +(45.2304 - 218.425i) q^{86} -1082.50 q^{87} +(222.847 + 156.605i) q^{88} +792.479 q^{89} +(-265.383 - 54.9543i) q^{90} -325.915 q^{91} +(599.935 - 1386.48i) q^{92} -728.365i q^{93} +(582.267 + 120.573i) q^{94} -732.946i q^{95} +(-352.530 - 575.185i) q^{96} +951.490i q^{97} +(-856.230 - 177.304i) q^{98} +157.820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9}+O(q^{10}) $ 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9	$ 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9} - 232 q^{15} - 78 q^{16} - 28 q^{17} - 2 q^{18} + 1052 q^{25} + 448 q^{26} - 368 q^{30} + 958 q^{32} - 344 q^{33} - 198 q^{34} + 138 q^{36} - 524 q^{38} + 936 q^{47} - 1964 q^{49} - 1038 q^{50} - 1424 q^{52} - 1384 q^{55} + 2320 q^{60} - 2078 q^{64} - 1888 q^{66} - 874 q^{68} + 2472 q^{70} - 4010 q^{72} + 436 q^{76} + 1884 q^{81} - 2264 q^{84} - 1420 q^{86} + 1976 q^{87} - 224 q^{89} + 80 q^{94} + 5746 q^{98}+O(q^{100}) $ 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9 - 232 * q^15 - 78 * q^16 - 28 * q^17 - 2 * q^18 + 1052 * q^25 + 448 * q^26 - 368 * q^30 + 958 * q^32 - 344 * q^33 - 198 * q^34 + 138 * q^36 - 524 * q^38 + 936 * q^47 - 1964 * q^49 - 1038 * q^50 - 1424 * q^52 - 1384 * q^55 + 2320 * q^60 - 2078 * q^64 - 1888 * q^66 - 874 * q^68 + 2472 * q^70 - 4010 * q^72 + 436 * q^76 + 1884 * q^81 - 2264 * q^84 - 1420 * q^86 + 1976 * q^87 - 224 * q^89 + 80 * q^94 + 5746 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.76967	−	0.573530i	−0.979226	−	0.202773i
$2$	−2.76967	−	0.573530i	−0.979226	−	0.202773i
$3$	3.72680			0.717223			0.358611	−	0.933487i	$-0.383250\pi$
$3$	3.72680			0.717223			0.358611	+	0.933487i	$0.383250\pi$
$4$	7.34213	+	3.17697i	0.917766	+	0.397122i
$5$	−7.30821			−0.653666			−0.326833	−	0.945082i	$-0.605981\pi$
$5$	−7.30821			−0.653666			−0.326833	+	0.945082i	$0.605981\pi$
$6$	−10.3220	−	2.13743i	−0.702323	−	0.145434i
$7$		−	5.81849i		−	0.314169i	−0.987585	−	0.157085i	$-0.949790\pi$
$7$		−	5.81849i		−	0.314169i	0.987585	−	0.157085i	$-0.0502095\pi$
$8$	−18.5132	−	13.0101i	−0.818174	−	0.574970i
$9$	−13.1110			−0.485592
$10$	20.2413	+	4.19147i	0.640086	+	0.132546i
$11$	−12.0372			−0.329942			−0.164971	−	0.986298i	$-0.552753\pi$
$11$	−12.0372			−0.329942			−0.164971	+	0.986298i	$0.552753\pi$
$12$	27.3626	+	11.8399i	0.658242	+	0.284825i
$13$		−	56.0136i		−	1.19503i	−0.801858	−	0.597515i	$-0.796155\pi$
$13$		−	56.0136i		−	1.19503i	0.801858	−	0.597515i	$-0.203845\pi$
$14$	−3.33708	+	16.1153i	−0.0637051	+	0.307643i
$15$	−27.2362			−0.468824
$16$	43.8137	+	46.6515i	0.684589	+	0.728930i
$17$	16.9578	−	68.0105i	0.241934	−	0.970293i
$17$	16.9578	−	68.0105i	0.241934	−	0.970293i
$18$	36.3131	+	7.51954i	0.475504	+	0.0984651i
$19$			100.291i			1.21096i	0.795859	+	0.605482i	$0.207020\pi$
$19$			100.291i			1.21096i	−0.795859	+	0.605482i	$0.792980\pi$
$20$	−53.6578	−	23.2180i	−0.599912	−	0.259585i
$21$		−	21.6843i		−	0.225329i
$22$	33.3391	+	6.90370i	0.323087	+	0.0669034i
$23$		−	188.838i		−	1.71198i	−0.516992	−	0.855990i	$-0.672948\pi$
$23$		−	188.838i		−	1.71198i	0.516992	−	0.855990i	$-0.327052\pi$
$24$	−68.9948	−	48.4860i	−0.586813	−	0.412382i
$25$	−71.5901			−0.572721
$26$	−32.1255	+	155.139i	−0.242320	+	1.17020i
$27$	−149.486			−1.06550
$28$	18.4852	−	42.7201i	0.124763	−	0.288334i
$29$	−290.463			−1.85992			−0.929958	−	0.367665i	$-0.880157\pi$
$29$	−290.463			−1.85992			−0.929958	+	0.367665i	$0.880157\pi$
$30$	75.4352	+	15.6208i	0.459084	+	0.0950650i
$31$		−	195.440i		−	1.13232i	−0.824294	−	0.566162i	$-0.808428\pi$
$31$		−	195.440i		−	1.13232i	0.824294	−	0.566162i	$-0.191572\pi$
$32$	−94.5934	−	154.338i	−0.522559	−	0.852603i
$33$	−44.8603			−0.236642
$34$	−85.9737	+	178.641i	−0.433658	+	0.901078i
$35$			42.5227i			0.205362i
$36$	−96.2625	−	41.6532i	−0.445660	−	0.192839i
$37$	168.323			0.747894			0.373947	−	0.927450i	$-0.378004\pi$
$37$	168.323			0.747894			0.373947	+	0.927450i	$0.378004\pi$
$38$	57.5198	−	277.773i	0.245551	−	1.18581i
$39$		−	208.751i		−	0.857102i
$40$	135.298	+	95.0804i	0.534813	+	0.375838i
$41$		−	55.4431i		−	0.211189i	−0.994409	−	0.105595i	$-0.966325\pi$
$41$		−	55.4431i		−	0.211189i	0.994409	−	0.105595i	$-0.0336746\pi$
$42$	−12.4366	+	60.0585i	−0.0456907	+	0.220648i
$43$			78.8633i			0.279687i	0.990174	+	0.139843i	$0.0446599\pi$
$43$			78.8633i			0.279687i	−0.990174	+	0.139843i	$0.955340\pi$
$44$	−88.3788	−	38.2419i	−0.302809	−	0.131027i
$45$	95.8177			0.317415
$46$	−108.304	+	523.020i	−0.347144	+	1.67641i
$47$	−210.230			−0.652450			−0.326225	−	0.945292i	$-0.605777\pi$
$47$	−210.230			−0.652450			−0.326225	+	0.945292i	$0.605777\pi$
$48$	163.285	+	173.861i	0.491002	+	0.522805i
$49$	309.145			0.901298
$50$	198.281	+	41.0591i	0.560823	+	0.116133i
$51$	63.1985	−	253.461i	0.173521	−	0.695916i
$52$	177.954	−	411.259i	0.474572	−	1.09676i
$53$			499.044i			1.29338i	0.762755	+	0.646688i	$0.223846\pi$
$53$			499.044i			1.29338i	−0.762755	+	0.646688i	$0.776154\pi$
$54$	414.025	+	85.7344i	1.04336	+	0.216055i
$55$	87.9705			0.215672
$56$	−75.6991	+	107.719i	−0.180638	+	0.257045i
$57$			373.764i			0.868530i
$58$	804.485	+	166.589i	1.82128	+	0.377141i
$59$			442.209i			0.975775i	0.872906	+	0.487888i	$0.162232\pi$
$59$			442.209i			0.975775i	−0.872906	+	0.487888i	$0.837768\pi$
$60$	−199.972	−	86.5287i	−0.430271	−	0.186180i
$61$	444.439			0.932861			0.466431	−	0.884558i	$-0.345540\pi$
$61$	444.439			0.932861			0.466431	+	0.884558i	$0.345540\pi$
$62$	−112.091	+	541.304i	−0.229605	+	1.10880i
$63$			76.2862i			0.152558i
$64$	173.475	+	481.716i	0.338818	+	0.940852i
$65$			409.359i			0.781150i
$66$	124.248	+	25.7287i	0.231726	+	0.0479846i
$67$		−	675.021i		−	1.23085i	−0.788195	−	0.615425i	$-0.788984\pi$
$67$		−	675.021i		−	1.23085i	0.788195	−	0.615425i	$-0.211016\pi$
$68$	340.574	−	445.467i	0.607363	−	0.794424i
$69$		−	703.763i		−	1.22787i
$70$	24.3881	−	117.774i	0.0416419	−	0.201095i
$71$		−	789.694i		−	1.31999i	−0.751269	−	0.659996i	$-0.770558\pi$
$71$		−	789.694i		−	1.31999i	0.751269	−	0.659996i	$-0.229442\pi$
$72$	242.726	+	170.575i	0.397299	+	0.279201i
$73$			649.239i			1.04093i	0.853884	+	0.520464i	$0.174241\pi$
$73$			649.239i			1.04093i	−0.853884	+	0.520464i	$0.825759\pi$
$74$	−466.198	−	96.5381i	−0.732357	−	0.151653i
$75$	−266.802			−0.410768
$76$	−318.622	+	736.348i	−0.480900	+	1.11138i
$77$			70.0385i			0.103658i
$78$	−119.725	+	578.172i	−0.173797	+	0.839296i
$79$		−	65.0808i		−	0.0926856i	−0.998926	−	0.0463428i	$-0.985243\pi$
$79$		−	65.0808i		−	0.0926856i	0.998926	−	0.0463428i	$-0.0147567\pi$
$80$	−320.199	−	340.939i	−0.447492	−	0.476476i
$81$	−203.106			−0.278609
$82$	−31.7982	+	153.559i	−0.0428235	+	0.206802i
$83$		−	377.605i		−	0.499368i	−0.968327	−	0.249684i	$-0.919673\pi$
$83$		−	377.605i		−	0.499368i	0.968327	−	0.249684i	$-0.0803267\pi$
$84$	68.8906	−	159.209i	0.0894831	−	0.206799i
$85$	−123.931	+	497.035i	−0.158144	+	0.634247i
$86$	45.2304	−	218.425i	0.0567130	−	0.273877i
$87$	−1082.50			−1.33397
$88$	222.847	+	156.605i	0.269950	+	0.189707i
$89$	792.479			0.943849			0.471925	−	0.881639i	$-0.343559\pi$
$89$	792.479			0.943849			0.471925	+	0.881639i	$0.343559\pi$
$90$	−265.383	−	54.9543i	−0.310821	−	0.0643633i
$91$	−325.915			−0.375441
$92$	599.935	−	1386.48i	0.679864	−	1.57120i
$93$		−	728.365i		−	0.812128i
$94$	582.267	+	120.573i	0.638896	+	0.132299i
$95$		−	732.946i		−	0.791565i
$96$	−352.530	−	575.185i	−0.374791	−	0.611506i
$97$			951.490i			0.995971i	0.867185	+	0.497985i	$0.165927\pi$
$97$			951.490i			0.995971i	−0.867185	+	0.497985i	$0.834073\pi$
$98$	−856.230	−	177.304i	−0.882574	−	0.182759i
$99$	157.820			0.160217
$100$	−525.624	−	227.440i	−0.525624	−	0.227440i
$101$			288.283i			0.284012i	0.989866	+	0.142006i	$0.0453553\pi$
$101$			288.283i			0.284012i	−0.989866	+	0.142006i	$0.954645\pi$
$102$	−320.406	+	665.758i	−0.311029	+	0.646273i
$103$	498.770			0.477138			0.238569	−	0.971125i	$-0.423322\pi$
$103$	498.770			0.477138			0.238569	+	0.971125i	$0.423322\pi$
$104$	−728.742	+	1036.99i	−0.687106	+	0.977742i
$105$			158.474i			0.147290i
$106$	286.216	−	1382.19i	0.262262	−	1.26651i
$107$	369.542			0.333878			0.166939	−	0.985967i	$-0.446612\pi$
$107$	369.542			0.333878			0.166939	+	0.985967i	$0.446612\pi$
$108$	−1097.54	−	474.911i	−0.977880	−	0.423133i
$109$	−360.292			−0.316602			−0.158301	−	0.987391i	$-0.550602\pi$
$109$	−360.292			−0.316602			−0.158301	+	0.987391i	$0.550602\pi$
$110$	−243.649	−	50.4537i	−0.211191	−	0.0437325i
$111$	627.305			0.536407
$112$	271.441	−	254.930i	0.229007	−	0.215077i
$113$			452.413i			0.376632i	0.982108	+	0.188316i	$0.0603029\pi$
$113$			452.413i			0.376632i	−0.982108	+	0.188316i	$0.939697\pi$
$114$	214.365	−	1035.20i	0.176115	−	0.850487i
$115$			1380.07i			1.11906i
$116$	−2132.61	−	922.792i	−1.70697	−	0.738613i
$117$			734.393i			0.580296i
$118$	253.620	−	1224.77i	0.197861	−	0.955504i
$119$	−395.719	−	98.6691i	−0.304836	−	0.0760083i
$120$	504.228	+	354.345i	0.383580	+	0.269560i
$121$	−1186.11			−0.891138
$122$	−1230.95	−	254.899i	−0.913482	−	0.189159i
$123$		−	206.625i		−	0.151470i
$124$	620.908	−	1434.95i	0.449671	−	1.03921i
$125$	1436.72			1.02803
$126$	43.7524	−	211.287i	0.0309347	−	0.149389i
$127$	338.477			0.236496			0.118248	−	0.992984i	$-0.462272\pi$
$127$	338.477			0.236496			0.118248	+	0.992984i	$0.462272\pi$
$128$	−204.190	−	1433.69i	−0.141000	−	0.990010i
$129$			293.907i			0.200598i
$130$	234.779	−	1133.79i	0.158396	−	0.764922i
$131$	−2700.02			−1.80078			−0.900389	−	0.435087i	$-0.856718\pi$
$131$	−2700.02			−1.80078			−0.900389	+	0.435087i	$0.856718\pi$
$132$	−329.370	−	142.520i	−0.217182	−	0.0939755i
$133$	583.542			0.380447
$134$	−387.145	+	1869.59i	−0.249584	+	1.20528i
$135$	1092.47			0.696481
$136$	−1198.77	+	1038.47i	−0.755834	+	0.654764i
$137$	1184.49			0.738669			0.369335	−	0.929297i	$-0.379586\pi$
$137$	1184.49			0.738669			0.369335	+	0.929297i	$0.379586\pi$
$138$	−403.629	+	1949.19i	−0.248979	+	1.20236i
$139$	2296.72			1.40147			0.700737	−	0.713419i	$-0.252854\pi$
$139$	2296.72			1.40147			0.700737	+	0.713419i	$0.252854\pi$
$140$	−135.094	+	312.207i	−0.0815536	+	0.188474i
$141$	−783.484			−0.467952
$142$	−452.913	+	2187.19i	−0.267659	+	1.29257i
$143$			674.248i			0.394290i
$144$	−574.440	−	611.647i	−0.332431	−	0.353962i
$145$	2122.76			1.21576
$146$	372.358	−	1798.18i	0.211072	−	1.01930i
$147$	1152.12			0.646431
$148$	1235.85	+	534.757i	0.686392	+	0.297005i
$149$			742.856i			0.408437i	0.978925	+	0.204219i	$0.0654653\pi$
$149$			742.856i			0.408437i	−0.978925	+	0.204219i	$0.934535\pi$
$150$	738.953	+	153.019i	0.402235	+	0.0832929i
$151$	−1768.00			−0.952832			−0.476416	−	0.879220i	$-0.658064\pi$
$151$	−1768.00			−0.952832			−0.476416	+	0.879220i	$0.658064\pi$
$152$	1304.79	−	1856.70i	0.696268	−	0.990779i
$153$	−222.334	+	891.685i	−0.117481	+	0.471166i
$154$	40.1692	−	193.983i	0.0210190	−	0.101504i
$155$			1428.32i			0.740162i
$156$	663.198	−	1532.68i	0.340374	−	0.786619i
$157$		−	3137.50i		−	1.59491i	−0.603381	−	0.797453i	$-0.706180\pi$
$157$		−	3137.50i		−	1.59491i	0.603381	−	0.797453i	$-0.293820\pi$
$158$	−37.3258	+	180.252i	−0.0187942	+	0.0907601i
$159$			1859.84i			0.927638i
$160$	691.308	+	1127.93i	0.341579	+	0.557317i
$161$	−1098.76			−0.537851
$162$	562.535	+	116.487i	0.272821	+	0.0564944i
$163$	1201.94			0.577564			0.288782	−	0.957395i	$-0.406750\pi$
$163$	1201.94			0.577564			0.288782	+	0.957395i	$0.406750\pi$
$164$	176.141	−	407.070i	0.0838678	−	0.193822i
$165$	327.848			0.154685
$166$	−216.568	+	1045.84i	−0.101258	+	0.488994i
$167$			139.410i			0.0645980i	0.999478	+	0.0322990i	$0.0102829\pi$
$167$			139.410i			0.0645980i	−0.999478	+	0.0322990i	$0.989717\pi$
$168$	−282.115	+	401.446i	−0.129558	+	0.184359i
$169$	−940.524			−0.428095
$170$	628.313	−	1305.54i	0.283467	−	0.589004i
$171$		−	1314.91i		−	0.588034i
$172$	−250.546	+	579.024i	−0.111070	+	0.256687i
$173$	−1017.57			−0.447194			−0.223597	−	0.974682i	$-0.571780\pi$
$173$	−1017.57			−0.447194			−0.223597	+	0.974682i	$0.571780\pi$
$174$	2998.15	+	620.843i	1.30626	+	0.270494i
$175$			416.547i			0.179931i
$176$	−527.395	−	561.554i	−0.225874	−	0.240504i
$177$			1648.02i			0.699848i
$178$	−2194.90	−	454.510i	−0.924241	−	0.191387i
$179$		−	3994.95i		−	1.66814i	−0.551662	−	0.834068i	$-0.686006\pi$
$179$		−	3994.95i		−	1.66814i	0.551662	−	0.834068i	$-0.313994\pi$
$180$	703.506	+	304.410i	0.291312	+	0.126052i
$181$	−1222.23			−0.501919			−0.250960	−	0.967998i	$-0.580746\pi$
$181$	−1222.23			−0.501919			−0.250960	+	0.967998i	$0.580746\pi$
$182$	902.676	+	186.922i	0.367642	+	0.0761295i
$183$	1656.33			0.669069
$184$	−2456.81	+	3496.00i	−0.984338	+	1.40070i
$185$	−1230.14			−0.488873
$186$	−417.739	+	2017.33i	−0.164678	+	0.795257i
$187$	−204.125	+	818.658i	−0.0798242	+	0.320140i
$188$	−1543.53	−	667.894i	−0.598796	−	0.259102i
$189$			869.780i			0.334747i
$190$	−420.366	+	2030.02i	−0.160508	+	0.775121i
$191$	−272.533			−0.103245			−0.0516225	−	0.998667i	$-0.516439\pi$
$191$	−272.533			−0.103245			−0.0516225	+	0.998667i	$0.516439\pi$
$192$	646.506	+	1795.26i	0.243008	+	0.674800i
$193$		−	4241.28i		−	1.58183i	−0.611923	−	0.790917i	$-0.709604\pi$
$193$		−	4241.28i		−	1.58183i	0.611923	−	0.790917i	$-0.290396\pi$
$194$	545.707	−	2635.31i	0.201956	−	0.975280i
$195$			1525.60i			0.560258i
$196$	2269.78	+	982.146i	0.827180	+	0.357925i
$197$	2681.84			0.969914			0.484957	−	0.874538i	$-0.338835\pi$
$197$	2681.84			0.969914			0.484957	+	0.874538i	$0.338835\pi$
$198$	−437.109	−	90.5143i	−0.156889	−	0.0324877i
$199$		−	60.1099i		−	0.0214124i	−0.999943	−	0.0107062i	$-0.996592\pi$
$199$		−	60.1099i		−	0.0214124i	0.999943	−	0.0107062i	$-0.00340796\pi$
$200$	1325.36	+	931.394i	0.468586	+	0.329298i
$201$		−	2515.67i		−	0.882794i
$202$	165.339	−	798.448i	0.0575901	−	0.278112i
$203$			1690.06i			0.584328i
$204$	1269.25	−	1660.17i	0.435615	−	0.569779i
$205$			405.189i			0.138047i
$206$	−1381.43	−	286.059i	−0.467226	−	0.0967509i
$207$			2475.86i			0.831324i
$208$	2613.12	−	2454.16i	0.871092	−	0.818103i
$209$		−	1207.22i		−	0.399547i
$210$	90.8893	−	438.920i	0.0298665	−	0.144230i
$211$	−4720.50			−1.54015			−0.770077	−	0.637951i	$-0.779782\pi$
$211$	−4720.50			−1.54015			−0.770077	+	0.637951i	$0.779782\pi$
$212$	−1585.45	+	3664.04i	−0.513628	+	1.18702i
$213$		−	2943.03i		−	0.946727i
$214$	−1023.51	−	211.943i	−0.326942	−	0.0677016i
$215$		−	576.349i		−	0.182822i
$216$	2767.45	+	1944.82i	0.871765	+	0.612631i
$217$	−1137.17			−0.355741
$218$	997.888	+	206.638i	0.310025	+	0.0641985i
$219$			2419.58i			0.746576i
$220$	645.891	+	279.480i	0.197936	+	0.0856479i
$221$	−3809.51	−	949.870i	−1.15953	−	0.289118i
$222$	−1737.43	−	359.778i	−0.525263	−	0.108769i
$223$	−1932.87			−0.580424			−0.290212	−	0.956962i	$-0.593726\pi$
$223$	−1932.87			−0.580424			−0.290212	+	0.956962i	$0.593726\pi$
$224$	−898.012	+	550.391i	−0.267862	+	0.164172i
$225$	938.617			0.278109
$226$	259.472	−	1253.03i	0.0763709	−	0.368808i
$227$	1372.15			0.401201			0.200601	−	0.979673i	$-0.435711\pi$
$227$	1372.15			0.401201			0.200601	+	0.979673i	$0.435711\pi$
$228$	−1187.44	+	2744.22i	−0.344912	+	0.797108i
$229$			5049.41i			1.45709i	0.684995	+	0.728547i	$0.259804\pi$
$229$			5049.41i			1.45709i	−0.684995	+	0.728547i	$0.740196\pi$
$230$	791.511	−	3822.34i	0.226916	−	1.09582i
$231$			261.019i			0.0743455i
$232$	5377.39	+	3778.95i	1.52174	+	1.06940i
$233$		−	2095.36i		−	0.589148i	−0.955629	−	0.294574i	$-0.904822\pi$
$233$		−	2095.36i		−	0.589148i	0.955629	−	0.294574i	$-0.0951777\pi$
$234$	421.196	−	2034.03i	0.117669	−	0.568241i
$235$	1536.40			0.426484
$236$	−1404.89	+	3246.76i	−0.387502	+	0.895533i
$237$		−	242.543i		−	0.0664762i
$238$	1039.42	+	500.237i	0.283091	+	0.136242i
$239$	3347.15			0.905895			0.452947	−	0.891537i	$-0.350373\pi$
$239$	3347.15			0.905895			0.452947	+	0.891537i	$0.350373\pi$
$240$	−1193.32	−	1270.61i	−0.320951	−	0.341740i
$241$		−	5240.94i		−	1.40082i	−0.713739	−	0.700412i	$-0.753000\pi$
$241$		−	5240.94i		−	1.40082i	0.713739	−	0.700412i	$-0.247000\pi$
$242$	3285.12	+	680.266i	0.872626	+	0.180699i
$243$	3279.17			0.865676
$244$	3263.13	+	1411.97i	0.856148	+	0.370459i
$245$	−2259.30			−0.589147
$246$	−118.506	+	572.283i	−0.0307140	+	0.148323i
$247$	5617.65			1.44714
$248$	−2542.69	+	3618.21i	−0.651053	+	0.926439i
$249$		−	1407.26i		−	0.358158i
$250$	−3979.24	−	824.002i	−1.00668	−	0.208458i
$251$		−	5084.71i		−	1.27866i	−0.768932	−	0.639331i	$-0.779211\pi$
$251$		−	5084.71i		−	1.27866i	0.768932	−	0.639331i	$-0.220789\pi$
$252$	−242.359	+	560.103i	−0.0605841	+	0.140013i
$253$			2273.09i			0.564854i
$254$	−937.469	−	194.127i	−0.231583	−	0.0479551i
$255$	−461.867	+	1852.35i	−0.113425	+	0.454896i
$256$	−256.723	+	4087.95i	−0.0626766	+	0.998034i
$257$	−4574.49			−1.11031			−0.555154	−	0.831748i	$-0.687341\pi$
$257$	−4574.49			−1.11031			−0.555154	+	0.831748i	$0.687341\pi$
$258$	168.565	−	814.026i	0.0406759	−	0.196430i
$259$		−	979.385i		−	0.234965i
$260$	−1300.52	+	3005.57i	−0.310211	+	0.716913i
$261$	3808.25			0.903160
$262$	7478.16	+	1548.54i	1.76337	+	0.365150i
$263$	−6138.10			−1.43913			−0.719566	−	0.694424i	$-0.755659\pi$
$263$	−6138.10			−1.43913			−0.719566	+	0.694424i	$0.755659\pi$
$264$	830.506	+	583.637i	0.193614	+	0.136062i
$265$		−	3647.11i		−	0.845436i
$266$	−1616.22	−	334.679i	−0.372544	−	0.0771446i
$267$	2953.41			0.676950
$268$	2144.53	−	4956.09i	0.488797	−	1.12963i
$269$	505.937			0.114675			0.0573374	−	0.998355i	$-0.481739\pi$
$269$	505.937			0.114675			0.0573374	+	0.998355i	$0.481739\pi$
$270$	−3025.78	−	626.564i	−0.682012	−	0.141228i
$271$	−2013.64			−0.451364			−0.225682	−	0.974201i	$-0.572461\pi$
$271$	−2013.64			−0.451364			−0.225682	+	0.974201i	$0.572461\pi$
$272$	3915.78	−	2188.68i	0.872900	−	0.487898i
$273$	−1214.62			−0.269275
$274$	−3280.64	−	679.339i	−0.723324	−	0.149782i
$275$	861.747			0.188965
$276$	2235.84	−	5167.12i	0.487614	−	1.12690i
$277$	−6731.16			−1.46006			−0.730030	−	0.683415i	$-0.760494\pi$
$277$	−6731.16			−1.46006			−0.730030	+	0.683415i	$0.760494\pi$
$278$	−6361.15	−	1317.24i	−1.37236	−	0.284182i
$279$			2562.41i			0.549847i
$280$	553.225	−	787.231i	0.118077	−	0.168022i
$281$	7242.79			1.53761			0.768806	−	0.639482i	$-0.220851\pi$
$281$	7242.79			1.53761			0.768806	+	0.639482i	$0.220851\pi$
$282$	2169.99	+	449.351i	0.458231	+	0.0948882i
$283$	−6740.40			−1.41581			−0.707907	−	0.706306i	$-0.750360\pi$
$283$	−6740.40			−1.41581			−0.707907	+	0.706306i	$0.750360\pi$
$284$	2508.84	−	5798.03i	0.524197	−	1.21144i
$285$		−	2731.54i		−	0.567729i
$286$	386.701	−	1867.44i	0.0799515	−	0.386099i
$287$	−322.595			−0.0663491
$288$	1240.21	+	2023.52i	0.253751	+	0.414017i
$289$	−4337.86	−	2306.62i	−0.882936	−	0.469494i
$290$	−5879.34	−	1217.47i	−1.19051	−	0.246524i
$291$			3546.01i			0.714332i
$292$	−2062.62	+	4766.80i	−0.413375	+	0.955328i
$293$			5846.08i			1.16564i	0.812602	+	0.582819i	$0.198050\pi$
$293$			5846.08i			1.16564i	−0.812602	+	0.582819i	$0.801950\pi$
$294$	−3190.99	−	660.776i	−0.633002	−	0.131079i
$295$		−	3231.76i		−	0.637831i
$296$	−3116.19	−	2189.89i	−0.611908	−	0.430017i
$297$	1799.39			0.351553
$298$	426.050	−	2057.47i	0.0828202	−	0.399952i
$299$	−10577.5			−2.04587
$300$	−1958.89	−	847.623i	−0.376989	−	0.163125i
$301$	458.865			0.0878690
$302$	4896.77	+	1014.00i	0.933037	+	0.193209i
$303$			1074.37i			0.203700i
$304$	−4678.72	+	4394.11i	−0.882707	+	0.829012i
$305$	−3248.05			−0.609779
$306$	1127.20	−	2342.16i	0.210581	−	0.437556i
$307$		−	3423.25i		−	0.636400i	−0.948024	−	0.318200i	$-0.896922\pi$
$307$		−	3423.25i		−	0.636400i	0.948024	−	0.318200i	$-0.103078\pi$
$308$	−222.511	+	514.232i	−0.0411647	+	0.0951334i
$309$	1858.81			0.342214
$310$	819.181	−	3955.96i	0.150085	−	0.724785i
$311$		−	4871.09i		−	0.888148i	−0.895990	−	0.444074i	$-0.853533\pi$
$311$		−	4871.09i		−	0.888148i	0.895990	−	0.444074i	$-0.146467\pi$
$312$	−2715.87	+	3864.65i	−0.492808	+	0.701259i
$313$		−	7615.21i		−	1.37520i	−0.726090	−	0.687599i	$-0.758665\pi$
$313$		−	7615.21i		−	1.37520i	0.726090	−	0.687599i	$-0.241335\pi$
$314$	−1799.45	+	8689.85i	−0.323404	+	1.56177i
$315$		−	557.515i		−	0.0997219i
$316$	206.760	−	477.831i	0.0368075	−	0.0850637i
$317$	2114.40			0.374626			0.187313	−	0.982300i	$-0.440022\pi$
$317$	2114.40			0.374626			0.187313	+	0.982300i	$0.440022\pi$
$318$	1066.67	−	5151.13i	0.188100	−	0.908367i
$319$	3496.36			0.613664
$320$	−1267.79	−	3520.48i	−0.221474	−	0.615003i
$321$	1377.21			0.239465
$322$	3043.19	+	630.169i	0.526678	+	0.109062i
$323$	6820.84	+	1700.72i	1.17499	+	0.292974i
$324$	−1491.23	−	645.261i	−0.255698	−	0.110642i
$325$			4010.02i			0.684418i
$326$	−3328.97	−	689.347i	−0.565566	−	0.117115i
$327$	−1342.73			−0.227074
$328$	−721.320	+	1026.43i	−0.121427	+	0.172790i
$329$			1223.22i			0.204980i
$330$	−908.031	−	188.031i	−0.151471	−	0.0313659i
$331$		−	5136.40i		−	0.852937i	−0.904502	−	0.426468i	$-0.859758\pi$
$331$		−	5136.40i		−	0.852937i	0.904502	−	0.426468i	$-0.140242\pi$
$332$	1199.64	−	2772.42i	0.198310	−	0.458303i
$333$	−2206.88			−0.363171
$334$	79.9557	−	386.119i	0.0130987	−	0.0632560i
$335$			4933.19i			0.804565i
$336$	1011.61	−	950.071i	0.164249	−	0.154258i
$337$			3395.13i			0.548796i	0.961616	+	0.274398i	$0.0884786\pi$
$337$			3395.13i			0.548796i	−0.961616	+	0.274398i	$0.911521\pi$
$338$	2604.94	+	539.418i	0.419201	+	0.0868062i
$339$			1686.05i			0.270129i
$340$	−2488.99	+	3255.57i	−0.397013	+	0.519288i
$341$			2352.55i			0.373601i
$342$	−754.141	+	3641.87i	−0.119238	+	0.575818i
$343$		−	3794.50i		−	0.597329i
$344$	1026.02	−	1460.01i	0.160812	−	0.228833i
$345$			5143.24i			0.802617i
$346$	2818.34	+	583.607i	0.437904	+	0.0906790i
$347$	6394.99			0.989340			0.494670	−	0.869081i	$-0.335289\pi$
$347$	6394.99			0.989340			0.494670	+	0.869081i	$0.335289\pi$
$348$	−7947.82	−	3439.06i	−1.22428	−	0.529750i
$349$		−	8179.53i		−	1.25456i	−0.778795	−	0.627278i	$-0.784169\pi$
$349$		−	8179.53i		−	1.25456i	0.778795	−	0.627278i	$-0.215831\pi$
$350$	238.902	−	1153.70i	0.0364853	−	0.176193i
$351$			8373.22i			1.27330i
$352$	1138.64	+	1857.80i	0.172414	+	0.281309i
$353$	7497.29			1.13043			0.565213	−	0.824945i	$-0.308794\pi$
$353$	7497.29			1.13043			0.565213	+	0.824945i	$0.308794\pi$
$354$	945.191	−	4564.48i	0.141911	−	0.685309i
$355$			5771.24i			0.862833i
$356$	5818.48	+	2517.68i	0.866233	+	0.374823i
$357$	−1474.76	−	367.720i	−0.218635	−	0.0545148i
$358$	−2291.22	+	11064.7i	−0.338253	+	1.63348i
$359$	−2204.88			−0.324148			−0.162074	−	0.986779i	$-0.551818\pi$
$359$	−2204.88			−0.324148			−0.162074	+	0.986779i	$0.551818\pi$
$360$	−1773.89	−	1246.60i	−0.259701	−	0.182504i
$361$	−3199.26			−0.466433
$362$	3385.16	+	700.983i	0.491492	+	0.101776i
$363$	−4420.37			−0.639145
$364$	−2392.91	−	1035.42i	−0.344567	−	0.149096i
$365$		−	4744.77i		−	0.680419i
$366$	−4587.49	−	949.956i	−0.655170	−	0.135669i
$367$			8381.59i			1.19214i	0.802932	+	0.596070i	$0.203272\pi$
$367$			8381.59i			1.19214i	−0.802932	+	0.596070i	$0.796728\pi$
$368$	8809.60	−	8273.71i	1.24791	−	1.17200i
$369$			726.913i			0.102552i
$370$	3407.07	+	705.520i	0.478717	+	0.0991304i
$371$	2903.68			0.406339
$372$	2314.00	−	5347.75i	0.322514	−	0.745344i
$373$		−	1398.31i		−	0.194107i	−0.995279	−	0.0970533i	$-0.969058\pi$
$373$		−	1398.31i		−	0.194107i	0.995279	−	0.0970533i	$-0.0309417\pi$
$374$	1034.88	−	2150.34i	0.143082	−	0.297303i
$375$	5354.37			0.737329
$376$	3892.02	+	2735.11i	0.533818	+	0.375139i
$377$			16269.9i			2.22265i
$378$	498.845	−	2409.00i	0.0678778	−	0.327793i
$379$	12081.4			1.63742			0.818709	−	0.574209i	$-0.194690\pi$
$379$	12081.4			1.63742			0.818709	+	0.574209i	$0.194690\pi$
$380$	2328.55	−	5381.39i	0.314348	−	0.726472i
$381$	1261.44			0.169620
$382$	754.826	+	156.306i	0.101100	+	0.0209353i
$383$	12157.7			1.62201			0.811004	−	0.585041i	$-0.198922\pi$
$383$	12157.7			1.62201			0.811004	+	0.585041i	$0.198922\pi$
$384$	−760.975	−	5343.06i	−0.101128	−	0.710057i
$385$		−	511.856i		−	0.0677574i
$386$	−2432.50	+	11746.9i	−0.320754	+	1.54897i
$387$		−	1033.97i		−	0.135814i
$388$	−3022.86	+	6985.96i	−0.395522	+	0.914068i
$389$		−	11605.5i		−	1.51265i	−0.654195	−	0.756326i	$-0.726992\pi$
$389$		−	11605.5i		−	1.51265i	0.654195	−	0.756326i	$-0.273008\pi$
$390$	874.975	−	4225.40i	0.113605	−	0.548619i
$391$	−12843.0	−	3202.29i	−1.66112	−	0.414187i
$392$	−5723.26	−	4022.01i	−0.737419	−	0.518219i
$393$	−10062.4			−1.29156
$394$	−7427.80	−	1538.11i	−0.949765	−	0.196673i
$395$			475.624i			0.0605854i
$396$	1158.73	+	501.389i	0.147042	+	0.0636257i
$397$	7340.60			0.927995			0.463998	−	0.885836i	$-0.346415\pi$
$397$	7340.60			0.927995			0.463998	+	0.885836i	$0.346415\pi$
$398$	−34.4748	+	166.484i	−0.00434187	+	0.0209676i
$399$	2174.74			0.272865
$400$	−3136.63	−	3339.79i	−0.392078	−	0.417473i
$401$			13980.6i			1.74104i	0.492134	+	0.870520i	$0.336217\pi$
$401$			13980.6i			1.74104i	−0.492134	+	0.870520i	$0.663783\pi$
$402$	−1442.81	+	6967.57i	−0.179007	+	0.864454i
$403$	−10947.3			−1.35316
$404$	−915.867	+	2116.61i	−0.112787	+	0.260657i
$405$	1484.34			0.182117
$406$	969.297	−	4680.89i	0.118486	−	0.572189i
$407$	−2026.14			−0.246762
$408$	−4467.56	+	3870.16i	−0.542101	+	0.469611i
$409$	−1058.88			−0.128015			−0.0640075	−	0.997949i	$-0.520388\pi$
$409$	−1058.88			−0.128015			−0.0640075	+	0.997949i	$0.520388\pi$
$410$	232.388	−	1122.24i	0.0279923	−	0.135179i
$411$	4414.35			0.529790
$412$	3662.03	+	1584.58i	0.437901	+	0.189482i
$413$	2572.99			0.306559
$414$	1419.98	−	6857.30i	0.168570	−	0.814053i
$415$			2759.61i			0.326420i
$416$	−8645.01	+	5298.51i	−1.01889	+	0.624474i
$417$	8559.40			1.00517
$418$	−692.379	+	3343.61i	−0.0810176	+	0.391247i
$419$	−1346.64			−0.157011			−0.0785055	−	0.996914i	$-0.525015\pi$
$419$	−1346.64			−0.157011			−0.0785055	+	0.996914i	$0.525015\pi$
$420$	−503.467	+	1163.53i	−0.0584920	+	0.135178i
$421$			710.544i			0.0822561i	0.999154	+	0.0411280i	$0.0130952\pi$
$421$			710.544i			0.0822561i	−0.999154	+	0.0411280i	$0.986905\pi$
$422$	13074.2	+	2707.34i	1.50816	+	0.312302i
$423$	2756.32			0.316824
$424$	6492.60	−	9238.88i	0.743653	−	1.05821i
$425$	−1214.01	+	4868.88i	−0.138561	+	0.555707i
$426$	−1687.91	+	8151.21i	−0.191971	+	0.927060i
$427$		−	2585.96i		−	0.293076i
$428$	2713.23	+	1174.03i	0.306422	+	0.132590i
$429$			2512.79i			0.282794i
$430$	−330.553	+	1596.30i	−0.0370714	+	0.179024i
$431$			962.297i			0.107546i	0.998553	+	0.0537729i	$0.0171247\pi$
$431$			962.297i			0.107546i	−0.998553	+	0.0537729i	$0.982875\pi$
$432$	−6549.51	−	6973.72i	−0.729429	−	0.776674i
$433$	10376.8			1.15168			0.575842	−	0.817561i	$-0.304674\pi$
$433$	10376.8			1.15168			0.575842	+	0.817561i	$0.304674\pi$
$434$	3149.57	+	652.198i	0.348351	+	0.0721349i
$435$	7911.10			0.871973
$436$	−2645.31	−	1144.64i	−0.290567	−	0.125730i
$437$	18938.8			2.07315
$438$	1387.70	−	6701.44i	0.151386	−	0.731067i
$439$		−	10804.4i		−	1.17464i	−0.809355	−	0.587320i	$-0.800183\pi$
$439$		−	10804.4i		−	1.17464i	0.809355	−	0.587320i	$-0.199817\pi$
$440$	−1628.61	−	1144.50i	−0.176457	−	0.124005i
$441$	−4053.20			−0.437663
$442$	10006.3	+	4815.69i	1.07681	+	0.518234i
$443$			11357.6i			1.21810i	0.793132	+	0.609050i	$0.208449\pi$
$443$			11357.6i			1.21810i	−0.793132	+	0.609050i	$0.791551\pi$
$444$	4605.75	+	1992.93i	0.492296	+	0.213019i
$445$	−5791.60			−0.616962
$446$	5353.41	+	1108.56i	0.568366	+	0.117695i
$447$			2768.47i			0.292940i
$448$	2802.86	−	1009.36i	0.295587	−	0.106446i
$449$			14695.4i			1.54458i	0.635269	+	0.772291i	$0.280889\pi$
$449$			14695.4i			1.54458i	−0.635269	+	0.772291i	$0.719111\pi$
$450$	−2599.66	−	538.325i	−0.272331	−	0.0563930i
$451$			667.381i			0.0696801i
$452$	−1437.30	+	3321.67i	−0.149569	+	0.345660i
$453$	−6588.97			−0.683392
$454$	−3800.40	−	786.968i	−0.392867	−	0.0813529i
$455$	2381.85			0.245413
$456$	4862.70	−	6919.55i	0.499379	−	0.710609i
$457$	12031.7			1.23156			0.615778	−	0.787920i	$-0.288842\pi$
$457$	12031.7			1.23156			0.615778	+	0.787920i	$0.288842\pi$
$458$	2895.99	−	13985.2i	0.295460	−	1.42682i
$459$	−2534.95	+	10166.6i	−0.257781	+	1.03385i
$460$	−4384.45	+	10132.7i	−0.444404	+	1.02704i
$461$			7926.22i			0.800783i	0.916344	+	0.400391i	$0.131126\pi$
$461$			7926.22i			0.800783i	−0.916344	+	0.400391i	$0.868874\pi$
$462$	149.702	−	722.937i	0.0150753	−	0.0728010i
$463$	−8901.77			−0.893521			−0.446761	−	0.894654i	$-0.647422\pi$
$463$	−8901.77			−0.893521			−0.446761	+	0.894654i	$0.647422\pi$
$464$	−12726.2	−	13550.5i	−1.27328	−	1.35575i
$465$			5323.04i			0.530861i
$466$	−1201.75	+	5803.44i	−0.119463	+	0.576909i
$467$			7226.45i			0.716060i	0.933710	+	0.358030i	$0.116551\pi$
$467$			7226.45i			0.716060i	−0.933710	+	0.358030i	$0.883449\pi$
$468$	−2333.15	+	5392.01i	−0.230448	+	0.532576i
$469$	−3927.61			−0.386695
$470$	−4255.32	−	881.172i	−0.417624	−	0.0864796i
$471$		−	11692.8i		−	1.14390i
$472$	5753.18	−	8186.70i	0.561042	−	0.798354i
$473$		−	949.295i		−	0.0922804i
$474$	−139.106	+	671.764i	−0.0134796	+	0.0650952i
$475$		−	7179.84i		−	0.693544i
$476$	−2591.95	−	1981.63i	−0.249584	−	0.190815i
$477$		−	6542.95i		−	0.628053i
$478$	−9270.49	−	1919.69i	−0.887076	−	0.183691i
$479$		−	2585.97i		−	0.246672i	−0.992365	−	0.123336i	$-0.960641\pi$
$479$		−	2585.97i		−	0.246672i	0.992365	−	0.123336i	$-0.0393593\pi$
$480$	2576.36	+	4203.57i	0.244988	+	0.399721i
$481$		−	9428.37i		−	0.893756i
$482$	−3005.83	+	14515.7i	−0.284050	+	1.37172i
$483$	−4094.84			−0.385759
$484$	−8708.54	−	3768.23i	−0.817857	−	0.353890i
$485$		−	6953.68i		−	0.651032i
$486$	−9082.23	−	1880.70i	−0.847692	−	0.175536i
$487$		−	10848.1i		−	1.00939i	−0.863297	−	0.504697i	$-0.831604\pi$
$487$		−	10848.1i		−	1.00939i	0.863297	−	0.504697i	$-0.168396\pi$
$488$	−8227.97	−	5782.19i	−0.763243	−	0.536367i
$489$	4479.38			0.414242
$490$	6257.50	+	1295.77i	0.576908	+	0.119463i
$491$		−	19171.9i		−	1.76215i	−0.472978	−	0.881074i	$-0.656821\pi$
$491$		−	19171.9i		−	1.76215i	0.472978	−	0.881074i	$-0.343179\pi$
$492$	656.443	−	1517.07i	0.0601519	−	0.139014i
$493$	−4925.62	+	19754.5i	−0.449977	+	1.80466i
$494$	−15559.0	−	3221.89i	−1.41707	−	0.293441i
$495$	−1153.38			−0.104728
$496$	9117.57	−	8562.94i	0.825385	−	0.775176i
$497$	−4594.83			−0.414701
$498$	−807.104	+	3897.64i	−0.0726249	+	0.350717i
$499$	−11022.1			−0.988814			−0.494407	−	0.869230i	$-0.664615\pi$
$499$	−11022.1			−0.988814			−0.494407	+	0.869230i	$0.664615\pi$
$500$	10548.6	+	4564.42i	0.943495	+	0.408255i
$501$			519.552i			0.0463311i
$502$	−2916.23	+	14083.0i	−0.259279	+	1.25210i
$503$		−	16741.0i		−	1.48399i	−0.670408	−	0.741993i	$-0.733881\pi$
$503$		−	16741.0i		−	1.48399i	0.670408	−	0.741993i	$-0.266119\pi$
$504$	992.490	−	1412.30i	0.0877163	−	0.124819i
$505$		−	2106.83i		−	0.185649i
$506$	1303.68	−	6295.71i	0.114537	−	0.553119i
$507$	−3505.14			−0.307039
$508$	2485.14	+	1075.33i	0.217048	+	0.0939177i
$509$			11986.6i			1.04380i	0.853006	+	0.521901i	$0.174777\pi$
$509$			11986.6i			1.04380i	−0.853006	+	0.521901i	$0.825223\pi$
$510$	2341.60	−	4865.50i	0.203309	−	0.422447i
$511$	3777.59			0.327027
$512$	3055.60	−	11175.0i	0.263749	−	0.964591i
$513$		−	14992.0i		−	1.29028i
$514$	12669.8	+	2623.61i	1.08724	+	0.225141i
$515$	−3645.11			−0.311889
$516$	−933.736	+	2157.91i	−0.0796617	+	0.184102i
$517$	2530.58			0.215271
$518$	−561.706	+	2712.57i	−0.0476447	+	0.230084i
$519$	−3792.28			−0.320737
$520$	5325.80	−	7578.53i	0.449138	−	0.639117i
$521$			10596.1i			0.891022i	0.895276	+	0.445511i	$0.146978\pi$
$521$			10596.1i			0.891022i	−0.895276	+	0.445511i	$0.853022\pi$
$522$	−10547.6	−	2184.14i	−0.884398	−	0.183137i
$523$		−	6817.11i		−	0.569964i	−0.958533	−	0.284982i	$-0.908012\pi$
$523$		−	6817.11i		−	0.569964i	0.958533	−	0.284982i	$-0.0919877\pi$
$524$	−19823.9	−	8577.89i	−1.65269	−	0.715128i
$525$			1552.39i			0.129051i
$526$	17000.5	+	3520.38i	1.40924	+	0.291818i
$527$	−13292.0	−	3314.24i	−1.09869	−	0.273948i
$528$	−1965.49	−	2092.80i	−0.162002	−	0.172495i
$529$	−23493.0			−1.93088
$530$	−2091.73	+	10101.3i	−0.171432	+	0.827872i
$531$		−	5797.80i		−	0.473829i
$532$	4284.44	+	1853.90i	0.349162	+	0.151084i
$533$	−3105.57			−0.252377
$534$	−8179.96	−	1693.87i	−0.662887	−	0.137267i
$535$	−2700.69			−0.218245
$536$	−8782.09	+	12496.8i	−0.707702	+	1.00705i
$537$		−	14888.4i		−	1.19642i
$538$	−1401.28	−	290.170i	−0.112293	−	0.0232530i
$539$	−3721.25			−0.297376
$540$	8021.06	+	3470.75i	0.639206	+	0.276588i
$541$	−11480.0			−0.912321			−0.456161	−	0.889897i	$-0.650776\pi$
$541$	−11480.0			−0.912321			−0.456161	+	0.889897i	$0.650776\pi$
$542$	5577.11	+	1154.88i	0.441988	+	0.0915247i
$543$	−4554.99			−0.359988
$544$	−12100.7	+	3816.11i	−0.953699	+	0.300762i
$545$	2633.08			0.206952
$546$	3364.09	+	696.620i	0.263681	+	0.0546018i
$547$	−7361.67			−0.575434			−0.287717	−	0.957715i	$-0.592896\pi$
$547$	−7361.67			−0.575434			−0.287717	+	0.957715i	$0.592896\pi$
$548$	8696.66	+	3763.09i	0.677925	+	0.293342i
$549$	−5827.03			−0.452990
$550$	−2386.75	−	494.237i	−0.185039	−	0.0383170i
$551$		−	29130.8i		−	2.25229i
$552$	−9156.02	+	13028.9i	−0.705989	+	1.00461i
$553$	−378.672			−0.0291190
$554$	18643.1	+	3860.52i	1.42973	+	0.296061i
$555$	−4584.47			−0.350631
$556$	16862.8	+	7296.61i	1.28623	+	0.556556i
$557$		−	13342.7i		−	1.01499i	−0.861656	−	0.507494i	$-0.830572\pi$
$557$		−	13342.7i		−	1.01499i	0.861656	−	0.507494i	$-0.169428\pi$
$558$	1469.62	−	7097.02i	0.111494	−	0.538425i
$559$	4417.42			0.334234
$560$	−1983.75	+	1863.08i	−0.149694	+	0.140588i
$561$	−760.734	+	3050.97i	−0.0572517	+	0.229612i
$562$	−20060.1	−	4153.96i	−1.50567	−	0.311787i
$563$			5484.91i			0.410588i	0.978700	+	0.205294i	$0.0658151\pi$
$563$			5484.91i			0.410588i	−0.978700	+	0.205294i	$0.934185\pi$
$564$	−5752.44	−	2489.11i	−0.429470	−	0.185834i
$565$		−	3306.33i		−	0.246191i
$566$	18668.7	+	3865.82i	1.38640	+	0.287089i
$567$			1181.77i			0.0875302i
$568$	−10274.0	+	14619.7i	−0.758956	+	1.07998i
$569$	15357.3			1.13148			0.565740	−	0.824583i	$-0.308590\pi$
$569$	15357.3			1.13148			0.565740	+	0.824583i	$0.308590\pi$
$570$	−1566.62	+	7565.47i	−0.115120	+	0.555934i
$571$	−5145.26			−0.377097			−0.188548	−	0.982064i	$-0.560378\pi$
$571$	−5145.26			−0.377097			−0.188548	+	0.982064i	$0.560378\pi$
$572$	−2142.07	+	4950.42i	−0.156581	+	0.361866i
$573$	−1015.68			−0.0740497
$574$	893.482	+	185.018i	0.0649708	+	0.0134538i
$575$			13519.0i			0.980487i
$576$	−2274.43	−	6315.77i	−0.164527	−	0.456870i
$577$	−9479.65			−0.683956			−0.341978	−	0.939708i	$-0.611097\pi$
$577$	−9479.65			−0.683956			−0.341978	+	0.939708i	$0.611097\pi$
$578$	10691.5	+	8876.48i	0.769392	+	0.638776i
$579$		−	15806.4i		−	1.13453i
$580$	15585.6	+	6743.96i	1.11579	+	0.482806i
$581$	−2197.09			−0.156886
$582$	2033.74	−	9821.27i	0.144848	−	0.699493i
$583$		−	6007.10i		−	0.426739i
$584$	8446.66	−	12019.5i	0.598502	−	0.851660i
$585$		−	5367.10i		−	0.379320i
$586$	3352.90	−	16191.7i	0.236360	−	1.14142i
$587$		−	10181.7i		−	0.715916i	−0.933738	−	0.357958i	$-0.883473\pi$
$587$		−	10181.7i		−	0.715916i	0.933738	−	0.357958i	$-0.116527\pi$
$588$	8459.02	+	3660.26i	0.593272	+	0.256712i
$589$	19600.8			1.37120
$590$	−1853.51	+	8950.89i	−0.129335	+	0.624580i
$591$	9994.67			0.695644
$592$	7374.84	+	7852.51i	0.512000	+	0.545162i
$593$	14555.0			1.00793			0.503965	−	0.863724i	$-0.331874\pi$
$593$	14555.0			1.00793			0.503965	+	0.863724i	$0.331874\pi$
$594$	−4983.72	−	1032.00i	−0.344250	−	0.0712856i
$595$	2891.99	+	721.094i	0.199261	+	0.0496840i
$596$	−2360.03	+	5454.14i	−0.162199	+	0.374850i
$597$		−	224.017i		−	0.0153575i
$598$	29296.2	+	6066.52i	2.00336	+	0.414847i
$599$	−24662.0			−1.68224			−0.841120	−	0.540848i	$-0.818103\pi$
$599$	−24662.0			−1.68224			−0.841120	+	0.540848i	$0.818103\pi$
$600$	4939.35	+	3471.12i	0.336080	+	0.236180i
$601$		−	3957.91i		−	0.268630i	−0.990939	−	0.134315i	$-0.957117\pi$
$601$		−	3957.91i		−	0.268630i	0.990939	−	0.134315i	$-0.0428833\pi$
$602$	−1270.91	−	263.173i	−0.0860436	−	0.0178175i
$603$			8850.19i			0.597691i
$604$	−12980.9	−	5616.88i	−0.874476	−	0.378390i
$605$	8668.30			0.582507
$606$	616.184	−	2975.66i	0.0413049	−	0.199468i
$607$			8629.99i			0.577069i	0.957470	+	0.288534i	$0.0931679\pi$
$607$			8629.99i			0.577069i	−0.957470	+	0.288534i	$0.906832\pi$
$608$	15478.7	−	9486.85i	1.03247	−	0.632800i
$609$			6298.49i			0.419093i
$610$	8996.02	+	1862.85i	0.597112	+	0.123647i
$611$			11775.7i			0.779697i
$612$	−4465.26	+	5840.51i	−0.294931	+	0.385766i
$613$			5474.94i			0.360735i	0.983599	+	0.180368i	$0.0577288\pi$
$613$			5474.94i			0.360735i	−0.983599	+	0.180368i	$0.942271\pi$
$614$	−1963.33	+	9481.26i	−0.129045	+	0.623180i
$615$			1510.06i			0.0990105i
$616$	911.208	−	1296.64i	0.0596000	−	0.0848099i
$617$			17802.6i			1.16160i	0.814047	+	0.580799i	$0.197260\pi$
$617$			17802.6i			1.16160i	−0.814047	+	0.580799i	$0.802740\pi$
$618$	−5148.30	−	1066.09i	−0.335105	−	0.0693920i
$619$	18601.7			1.20786			0.603929	−	0.797038i	$-0.293601\pi$
$619$	18601.7			1.20786			0.603929	+	0.797038i	$0.293601\pi$
$620$	−4537.72	+	10486.9i	−0.293934	+	0.679295i
$621$			28228.6i			1.82411i
$622$	−2793.71	+	13491.3i	−0.180093	+	0.869698i
$623$		−	4611.03i		−	0.296528i
$624$	9738.56	−	9146.16i	0.624767	−	0.586762i
$625$	−1551.09			−0.0992695
$626$	−4367.55	+	21091.6i	−0.278854	+	1.34663i
$627$		−	4499.08i		−	0.286564i
$628$	9967.77	−	23036.0i	0.633372	−	1.46375i
$629$	2854.39	−	11447.7i	0.180941	−	0.725677i
$630$	−319.751	+	1544.13i	−0.0202209	+	0.0976503i
$631$	14688.9			0.926715			0.463358	−	0.886171i	$-0.346645\pi$
$631$	14688.9			0.926715			0.463358	+	0.886171i	$0.346645\pi$
$632$	−846.707	+	1204.85i	−0.0532915	+	0.0758330i
$633$	−17592.3			−1.10463
$634$	−5856.18	−	1212.67i	−0.366843	−	0.0759641i
$635$	−2473.66			−0.154589
$636$	−5908.65	+	13655.1i	−0.368385	+	0.851355i
$637$		−	17316.3i		−	1.07708i
$638$	−9683.77	−	2005.27i	−0.600916	−	0.124435i
$639$			10353.7i			0.640977i
$640$	1492.26	+	10477.7i	0.0921669	+	0.647135i
$641$		−	4288.29i		−	0.264239i	−0.991234	−	0.132119i	$-0.957822\pi$
$641$		−	4288.29i		−	0.264239i	0.991234	−	0.132119i	$-0.0421782\pi$
$642$	−3814.41	−	789.870i	−0.234490	−	0.0485571i
$643$	17779.6			1.09045			0.545223	−	0.838291i	$-0.316445\pi$
$643$	17779.6			1.09045			0.545223	+	0.838291i	$0.316445\pi$
$644$	−8067.20	−	3490.72i	−0.493622	−	0.213592i
$645$		−	2147.94i		−	0.131124i
$646$	−17916.0	−	8622.37i	−1.09117	−	0.525144i
$647$	27669.8			1.68132			0.840658	−	0.541567i	$-0.182169\pi$
$647$	27669.8			1.68132			0.840658	+	0.541567i	$0.182169\pi$
$648$	3760.13	+	2642.42i	0.227950	+	0.160192i
$649$		−	5322.97i		−	0.321949i
$650$	2299.87	−	11106.4i	0.138782	−	0.670200i
$651$	−4237.99			−0.255146
$652$	8824.78	+	3818.52i	0.530069	+	0.229363i
$653$	5881.20			0.352449			0.176224	−	0.984350i	$-0.443612\pi$
$653$	5881.20			0.352449			0.176224	+	0.984350i	$0.443612\pi$
$654$	3718.93	+	770.097i	0.222357	+	0.0460446i
$655$	19732.3			1.17711
$656$	2586.50	−	2429.17i	0.153942	−	0.144578i
$657$		−	8512.16i		−	0.505466i
$658$	701.553	−	3387.91i	0.0415644	−	0.200721i
$659$			12101.0i			0.715307i	0.933854	+	0.357653i	$0.116423\pi$
$659$			12101.0i			0.715307i	−0.933854	+	0.357653i	$0.883577\pi$
$660$	2407.10	+	1041.57i	0.141964	+	0.0614286i
$661$		−	8959.20i		−	0.527190i	−0.964633	−	0.263595i	$-0.915092\pi$
$661$		−	8959.20i		−	0.527190i	0.964633	−	0.263595i	$-0.0849082\pi$
$662$	−2945.88	+	14226.1i	−0.172953	+	0.835218i
$663$	−14197.3	−	3539.97i	−0.831640	−	0.207362i
$664$	−4912.67	+	6990.66i	−0.287122	+	0.408570i
$665$	−4264.64			−0.248685
$666$	6112.32	+	1265.71i	0.355627	+	0.0736415i
$667$			54850.5i			3.18414i
$668$	−442.901	+	1023.56i	−0.0256533	+	0.0592858i
$669$	−7203.42			−0.416293
$670$	2829.33	−	13663.3i	0.163144	−	0.787851i
$671$	−5349.81			−0.307790
$672$	−3346.71	+	2051.20i	−0.192116	+	0.117748i
$673$		−	14016.2i		−	0.802803i	−0.915902	−	0.401402i	$-0.868523\pi$
$673$		−	14016.2i		−	0.802803i	0.915902	−	0.401402i	$-0.131477\pi$
$674$	1947.20	−	9403.37i	0.111281	−	0.537395i
$675$	10701.7			0.610234
$676$	−6905.45	−	2988.02i	−0.392891	−	0.170006i
$677$	−32188.9			−1.82736			−0.913679	−	0.406437i	$-0.866771\pi$
$677$	−32188.9			−1.82736			−0.913679	+	0.406437i	$0.866771\pi$
$678$	967.000	−	4669.80i	0.0547749	−	0.264517i
$679$	5536.24			0.312903
$680$	8760.83	−	7589.33i	0.494063	−	0.427997i
$681$	5113.72			0.287751
$682$	1349.26	−	6515.80i	0.0757563	−	0.365840i
$683$	−12492.7			−0.699884			−0.349942	−	0.936771i	$-0.613799\pi$
$683$	−12492.7			−0.699884			−0.349942	+	0.936771i	$0.613799\pi$
$684$	4177.44	−	9654.25i	0.233521	−	0.539678i
$685$	−8656.48			−0.482843
$686$	−2176.26	+	10509.5i	−0.121122	+	0.584920i
$687$			18818.1i			1.04506i
$688$	−3679.09	+	3455.29i	−0.203872	+	0.191470i
$689$	27953.2			1.54562
$690$	2949.80	−	14245.1i	0.162749	−	0.785943i
$691$	6455.04			0.355371			0.177686	−	0.984087i	$-0.443139\pi$
$691$	6455.04			0.355371			0.177686	+	0.984087i	$0.443139\pi$
$692$	−7471.14	−	3232.80i	−0.410419	−	0.177590i
$693$		−	918.274i		−	0.0503353i
$694$	−17712.0	−	3667.71i	−0.968787	−	0.200612i
$695$	−16784.9			−0.916096
$696$	20040.4	+	14083.4i	1.09142	+	0.766995i
$697$	−3770.71	−	940.195i	−0.204915	−	0.0510939i
$698$	−4691.20	+	22654.6i	−0.254391	+	1.22849i
$699$		−	7808.97i		−	0.422550i
$700$	−1323.36	+	3058.34i	−0.0714546	+	0.165135i
$701$		−	1564.13i		−	0.0842746i	−0.999112	−	0.0421373i	$-0.986583\pi$
$701$		−	1564.13i		−	0.0842746i	0.999112	−	0.0421373i	$-0.0134167\pi$
$702$	4802.29	−	23191.0i	0.258192	−	1.24685i
$703$			16881.2i			0.905673i
$704$	−2088.16	−	5798.52i	−0.111790	−	0.310426i
$705$	5725.86			0.305884
$706$	−20765.0	−	4299.92i	−1.10694	−	0.229220i
$707$	1677.37			0.0892279
$708$	−5235.73	+	12100.0i	−0.277925	+	0.642297i
$709$	−13430.6			−0.711419			−0.355709	−	0.934597i	$-0.615761\pi$
$709$	−13430.6			−0.711419			−0.355709	+	0.934597i	$0.615761\pi$
$710$	3309.98	−	15984.4i	0.174960	−	0.844908i
$711$			853.273i			0.0450074i
$712$	−14671.3	−	10310.2i	−0.772233	−	0.542685i
$713$	−36906.6			−1.93852
$714$	3873.71	+	1864.28i	0.203039	+	0.0977157i
$715$		−	4927.55i		−	0.257734i
$716$	12691.8	−	29331.4i	0.662453	−	1.53096i
$717$	12474.1			0.649728
$718$	6106.78	+	1264.56i	0.317414	+	0.0657285i
$719$			20443.4i			1.06038i	0.847880	+	0.530188i	$0.177878\pi$
$719$			20443.4i			1.06038i	−0.847880	+	0.530188i	$0.822122\pi$
$720$	4198.13	+	4470.04i	0.217299	+	0.231373i
$721$		−	2902.09i		−	0.149902i
$722$	8860.90	+	1834.87i	0.456743	+	0.0945801i
$723$		−	19531.9i		−	1.00470i
$724$	−8973.74	−	3882.98i	−0.460644	−	0.199323i
$725$	20794.3			1.06521
$726$	12243.0	+	2535.22i	0.625867	+	0.129601i
$727$	−8342.06			−0.425571			−0.212785	−	0.977099i	$-0.568253\pi$
$727$	−8342.06			−0.425571			−0.212785	+	0.977099i	$0.568253\pi$
$728$	6033.72	+	4240.18i	0.307176	+	0.215868i
$729$	17704.7			0.899491
$730$	−2721.27	+	13141.4i	−0.137971	+	0.666283i
$731$	5363.53	+	1337.35i	0.271378	+	0.0676658i
$732$	12161.0	+	5262.13i	0.614049	+	0.265702i
$733$		−	4218.64i		−	0.212577i	−0.994335	−	0.106289i	$-0.966103\pi$
$733$		−	4218.64i		−	0.212577i	0.994335	−	0.106289i	$-0.0338968\pi$
$734$	4807.09	−	23214.2i	0.241734	−	1.16737i
$735$	−8419.94			−0.422550
$736$	−29144.9	+	17862.9i	−1.45964	+	0.894611i
$737$			8125.38i			0.406109i
$738$	416.906	−	2013.31i	0.0207948	−	0.100421i
$739$		−	19556.4i		−	0.973467i	−0.873550	−	0.486734i	$-0.838188\pi$
$739$		−	19556.4i		−	0.973467i	0.873550	−	0.486734i	$-0.161812\pi$
$740$	−9031.83	−	3908.11i	−0.448671	−	0.194142i
$741$	20935.9			1.03792
$742$	−8042.24	−	1665.35i	−0.397897	−	0.0823947i
$743$			6026.30i			0.297555i	0.988871	+	0.148778i	$0.0475339\pi$
$743$			6026.30i			0.297555i	−0.988871	+	0.148778i	$0.952466\pi$
$744$	−9476.10	+	13484.3i	−0.466950	+	0.664463i
$745$		−	5428.95i		−	0.266981i
$746$	−801.972	+	3872.86i	−0.0393596	+	0.190074i
$747$			4950.77i			0.242489i
$748$	−4099.57	+	5362.19i	−0.200395	+	0.262114i
$749$		−	2150.18i		−	0.104894i
$750$	−14829.8	−	3070.89i	−0.722012	−	0.149511i
$751$			23393.1i			1.13665i	0.822803	+	0.568327i	$0.192409\pi$
$751$			23393.1i			1.13665i	−0.822803	+	0.568327i	$0.807591\pi$
$752$	−9210.94	−	9807.53i	−0.446660	−	0.475590i
$753$		−	18949.7i		−	0.917085i
$754$	9331.25	−	45062.1i	0.450695	−	2.17648i
$755$	12920.9			0.622833
$756$	−2763.27	+	6386.04i	−0.132935	+	0.307220i
$757$		−	20365.9i		−	0.977824i	−0.872333	−	0.488912i	$-0.837394\pi$
$757$		−	20365.9i		−	0.977824i	0.872333	−	0.488912i	$-0.162606\pi$
$758$	−33461.5	−	6929.05i	−1.60340	−	0.332025i
$759$			8471.35i			0.405126i
$760$	−9535.70	+	13569.2i	−0.455127	+	0.647638i
$761$	−17103.5			−0.814721			−0.407360	−	0.913267i	$-0.633551\pi$
$761$	−17103.5			−0.814721			−0.407360	+	0.913267i	$0.633551\pi$
$762$	−3493.76	−	723.471i	−0.166096	−	0.0343945i
$763$			2096.35i			0.0994667i
$764$	−2000.97	−	865.830i	−0.0947548	−	0.0410008i
$765$	1624.86	−	6516.61i	0.0767935	−	0.307985i
$766$	−33672.8	−	6972.79i	−1.58831	−	0.328900i
$767$	24769.7			1.16608
$768$	−956.756	+	15234.9i	−0.0449531	+	0.715812i
$769$	−8560.73			−0.401441			−0.200720	−	0.979649i	$-0.564328\pi$
$769$	−8560.73			−0.401441			−0.200720	+	0.979649i	$0.564328\pi$
$770$	−293.564	+	1417.67i	−0.0137394	+	0.0663498i
$771$	−17048.2			−0.796337
$772$	13474.4	−	31140.0i	0.628181	−	1.45175i
$773$		−	10883.2i		−	0.506390i	−0.967415	−	0.253195i	$-0.918518\pi$
$773$		−	10883.2i		−	0.506390i	0.967415	−	0.253195i	$-0.0814815\pi$
$774$	−593.015	+	2863.77i	−0.0275394	+	0.132992i
$775$			13991.6i			0.648506i
$776$	12379.0	−	17615.1i	0.572653	−	0.814878i
$777$		−	3649.97i		−	0.168522i
$778$	−6656.09	+	32143.4i	−0.306726	+	1.48123i
$779$	5560.44			0.255742
$780$	−4846.78	+	11201.1i	−0.222491	+	0.514186i
$781$			9505.72i			0.435520i
$782$	33734.3	+	16235.1i	1.54263	+	0.742413i
$783$	43420.0			1.98174
$784$	13544.8	+	14422.1i	0.617018	+	0.656983i
$785$			22929.5i			1.04254i
$786$	27869.6	+	5771.10i	1.26473	+	0.261893i
$787$	−1562.16			−0.0707562			−0.0353781	−	0.999374i	$-0.511264\pi$
$787$	−1562.16			−0.0707562			−0.0353781	+	0.999374i	$0.511264\pi$
$788$	19690.4	+	8520.13i	0.890154	+	0.385174i
$789$	−22875.5			−1.03218
$790$	272.784	−	1317.32i	0.0122851	−	0.0593268i
$791$	2632.36			0.118326
$792$	−2921.75	−	2053.25i	−0.131085	−	0.0921200i
$793$		−	24894.6i		−	1.11480i
$794$	−20331.0	−	4210.05i	−0.908717	−	0.188173i
$795$		−	13592.1i		−	0.606365i
$796$	190.968	−	441.334i	0.00850335	−	0.0196516i
$797$			31111.8i			1.38273i	0.722504	+	0.691366i	$0.242991\pi$
$797$			31111.8i			1.38273i	−0.722504	+	0.691366i	$0.757009\pi$
$798$	−6023.32	−	1247.28i	−0.267197	−	0.0553298i
$799$	−3565.04	+	14297.8i	−0.157850	+	0.633068i
$800$	6771.95	+	11049.1i	0.299281	+	0.488304i
$801$	−10390.2			−0.458325
$802$	8018.28	−	38721.6i	0.353036	−	1.70487i
$803$		−	7815.04i		−	0.343445i
$804$	7992.21	−	18470.4i	0.350577	−	0.810198i
$805$	8029.93			0.351575
$806$	30320.4	+	6278.60i	1.32505	+	0.274385i
$807$	1885.53			0.0822474
$808$	3750.59	−	5337.03i	0.163299	−	0.232371i
$809$			13480.6i			0.585850i	0.956135	+	0.292925i	$0.0946287\pi$
$809$			13480.6i			0.585850i	−0.956135	+	0.292925i	$0.905371\pi$
$810$	−4111.12	−	851.312i	−0.178334	−	0.0369285i
$811$	−20244.4			−0.876543			−0.438271	−	0.898843i	$-0.644409\pi$
$811$	−20244.4			−0.876543			−0.438271	+	0.898843i	$0.644409\pi$
$812$	−5369.26	+	12408.6i	−0.232049	+	0.536277i
$813$	−7504.42			−0.323729
$814$	5611.73	+	1162.05i	0.241635	+	0.0500367i
$815$	−8784.01			−0.377534
$816$	14593.3	−	8156.78i	0.626064	−	0.349932i
$817$	−7909.27			−0.338691
$818$	2932.74	+	607.297i	0.125355	+	0.0259580i
$819$	4273.06			0.182311
$820$	−1287.28	+	2974.95i	−0.0548215	+	0.126695i
$821$	6949.55			0.295422			0.147711	−	0.989031i	$-0.452810\pi$
$821$	6949.55			0.295422			0.147711	+	0.989031i	$0.452810\pi$
$822$	−12226.3	−	2531.76i	−0.518784	−	0.107427i
$823$			13674.7i			0.579184i	0.957150	+	0.289592i	$0.0935196\pi$
$823$			13674.7i			0.579184i	−0.957150	+	0.289592i	$0.906480\pi$
$824$	−9233.81	−	6489.04i	−0.390382	−	0.274340i
$825$	3211.55			0.135530
$826$	−7126.34	−	1475.69i	−0.300190	−	0.0621619i
$827$	20289.8			0.853140			0.426570	−	0.904455i	$-0.359722\pi$
$827$	20289.8			0.853140			0.426570	+	0.904455i	$0.359722\pi$
$828$	−7865.73	+	18178.1i	−0.330137	+	0.762961i
$829$			18898.2i			0.791752i	0.918304	+	0.395876i	$0.129559\pi$
$829$			18898.2i			0.791752i	−0.918304	+	0.395876i	$0.870441\pi$
$830$	1582.72	−	7643.22i	0.0661892	−	0.319638i
$831$	−25085.7			−1.04719
$832$	26982.7	−	9716.96i	1.12435	−	0.404898i
$833$	5242.44	−	21025.1i	0.218055	−	0.874523i
$834$	−23706.7	−	4909.07i	−0.984288	−	0.203822i
$835$		−	1018.84i		−	0.0422255i
$836$	3835.32	−	8863.59i	0.158669	−	0.366691i
$837$			29215.4i			1.20649i
$838$	3729.74	+	772.337i	0.153749	+	0.0318376i
$839$		−	24233.9i		−	0.997198i	−0.866833	−	0.498599i	$-0.833848\pi$
$839$		−	24233.9i		−	0.997198i	0.866833	−	0.498599i	$-0.166152\pi$
$840$	2061.76	−	2933.85i	0.0846873	−	0.120509i
$841$	59979.6			2.45929
$842$	407.518	−	1967.97i	0.0166793	−	0.0805473i
$843$	26992.4			1.10281
$844$	−34658.5	−	14996.9i	−1.41350	−	0.611628i
$845$	6873.54			0.279831
$846$	−7634.09	−	1580.83i	−0.310243	−	0.0642436i
$847$			6901.35i			0.279968i
$848$	−23281.1	+	21864.9i	−0.942780	+	0.885431i
$849$	−25120.1			−1.01545
$850$	6154.87	−	12788.9i	0.248365	−	0.516066i
$851$		−	31785.8i		−	1.28038i
$852$	9349.92	−	21608.1i	0.375966	−	0.868874i
$853$	−14455.1			−0.580225			−0.290112	−	0.956993i	$-0.593693\pi$
$853$	−14455.1			−0.580225			−0.290112	+	0.956993i	$0.593693\pi$
$854$	−1483.13	+	7162.26i	−0.0594280	+	0.286988i
$855$			9609.65i			0.384378i
$856$	−6841.40	−	4807.78i	−0.273171	−	0.191970i
$857$		−	9033.31i		−	0.360061i	−0.983661	−	0.180030i	$-0.942380\pi$
$857$		−	9033.31i		−	0.360061i	0.983661	−	0.180030i	$-0.0576196\pi$
$858$	1441.16	−	6959.59i	0.0573430	−	0.276919i
$859$			17799.1i			0.706981i	0.935438	+	0.353491i	$0.115005\pi$
$859$			17799.1i			0.706981i	−0.935438	+	0.353491i	$0.884995\pi$
$860$	1831.05	−	4231.63i	0.0726025	−	0.167788i
$861$	−1202.25			−0.0475871
$862$	551.906	−	2665.24i	0.0218074	−	0.105312i
$863$	9759.39			0.384952			0.192476	−	0.981302i	$-0.438348\pi$
$863$	9759.39			0.384952			0.192476	+	0.981302i	$0.438348\pi$
$864$	14140.3	+	23071.2i	0.556787	+	0.908448i
$865$	7436.62			0.292315
$866$	−28740.4	−	5951.42i	−1.12776	−	0.233531i
$867$	−16166.3	−	8596.32i	−0.633261	−	0.336732i
$868$	−8349.22	−	3612.75i	−0.326487	−	0.141273i
$869$			783.392i			0.0305808i
$870$	−21911.1	−	4537.25i	−0.853858	−	0.176813i
$871$	−37810.4			−1.47090
$872$	6670.14	+	4687.43i	0.259036	+	0.182037i
$873$		−	12475.0i		−	0.483635i
$874$	−52454.1	−	10861.9i	−2.03008	−	0.420379i
$875$		−	8359.55i		−	0.322977i
$876$	−7686.95	+	17764.9i	−0.296482	+	0.685182i
$877$	−22585.5			−0.869624			−0.434812	−	0.900521i	$-0.643185\pi$
$877$	−22585.5			−0.869624			−0.434812	+	0.900521i	$0.643185\pi$
$878$	−6196.66	+	29924.7i	−0.238186	+	1.15024i
$879$			21787.2i			0.836021i
$880$	3854.31	+	4103.96i	0.147646	+	0.157209i
$881$			17451.7i			0.667382i	0.942682	+	0.333691i	$0.108294\pi$
$881$			17451.7i			0.667382i	−0.942682	+	0.333691i	$0.891706\pi$
$882$	11226.0	+	2324.63i	0.428571	+	0.0887464i
$883$		−	18401.2i		−	0.701300i	−0.936507	−	0.350650i	$-0.885961\pi$
$883$		−	18401.2i		−	0.701300i	0.936507	−	0.350650i	$-0.114039\pi$
$884$	−24952.2	−	19076.8i	−0.949360	−	0.725817i
$885$		−	12044.1i		−	0.457467i
$886$	6513.95	−	31456.9i	0.246998	−	1.19279i
$887$		−	34284.8i		−	1.29783i	−0.760862	−	0.648913i	$-0.775224\pi$
$887$		−	34284.8i		−	1.29783i	0.760862	−	0.648913i	$-0.224776\pi$
$888$	−11613.4	−	8161.29i	−0.438874	−	0.308418i
$889$		−	1969.43i		−	0.0742997i
$890$	16040.8	+	3321.65i	0.604145	+	0.125103i
$891$	2444.83			0.0919246
$892$	−14191.4	−	6140.68i	−0.532694	−	0.230499i
$893$		−	21084.1i		−	0.790093i
$894$	1587.80	−	7667.76i	0.0594005	−	0.286855i
$895$			29195.9i			1.09040i
$896$	−8341.90	+	1188.08i	−0.311030	+	0.0442979i
$897$	−39420.3			−1.46734
$898$	8428.23	−	40701.3i	0.313200	−	1.51249i
$899$			56768.0i			2.10603i
$900$	6891.45	+	2981.96i	0.255239	+	0.110443i
$901$	33940.2	+	8462.71i	1.25495	+	0.312912i
$902$	382.763	−	1848.42i	0.0141293	−	0.0682326i
$903$	1710.10			0.0630216
$904$	5885.93	−	8375.59i	0.216552	−	0.308151i
$905$	8932.28			0.328087
$906$	18249.3	+	3778.97i	0.669195	+	0.138574i
$907$	17165.1			0.628399			0.314199	−	0.949357i	$-0.398264\pi$
$907$	17165.1			0.628399			0.314199	+	0.949357i	$0.398264\pi$
$908$	10074.5	+	4359.28i	0.368209	+	0.159326i
$909$		−	3779.67i		−	0.137914i
$910$	−6596.94	−	1366.06i	−0.240315	−	0.0497632i
$911$		−	9323.86i		−	0.339092i	−0.985522	−	0.169546i	$-0.945770\pi$
$911$		−	9323.86i		−	0.339092i	0.985522	−	0.169546i	$-0.0542302\pi$
$912$	−17436.6	+	16376.0i	−0.633097	+	0.594586i
$913$			4545.32i			0.164762i
$914$	−33323.9	−	6900.56i	−1.20597	−	0.249727i
$915$	−12104.8			−0.437348
$916$	−16041.9	+	37073.4i	−0.578644	+	1.33727i
$917$			15710.0i			0.565749i
$918$	12851.8	−	26704.2i	0.462062	−	0.960098i
$919$	53583.5			1.92335			0.961673	−	0.274199i	$-0.0884127\pi$
$919$	53583.5			1.92335			0.961673	+	0.274199i	$0.0884127\pi$
$920$	17954.8	−	25549.5i	0.643428	−	0.915588i
$921$		−	12757.7i		−	0.456441i
$922$	4545.92	−	21953.0i	0.162377	−	0.784147i
$923$	−44233.6			−1.57743
$924$	−829.252	+	1916.44i	−0.0295242	+	0.0682318i
$925$	−12050.3			−0.428335
$926$	24655.0	+	5105.43i	0.874959	+	0.181182i
$927$	−6539.36			−0.231695
$928$	27475.8	+	44829.3i	0.971917	+	1.58577i
$929$		−	7083.34i		−	0.250158i	−0.992147	−	0.125079i	$-0.960082\pi$
$929$		−	7083.34i		−	0.250158i	0.992147	−	0.125079i	$-0.0399184\pi$
$930$	3052.92	−	14743.1i	0.107644	−	0.519832i
$931$			31004.4i			1.09144i
$932$	6656.89	−	15384.4i	0.233963	−	0.540700i
$933$		−	18153.6i		−	0.637000i
$934$	4144.58	−	20014.9i	0.145198	−	0.701184i
$935$	1491.79	−	5982.92i	0.0521784	−	0.209265i
$936$	9554.52	−	13595.9i	0.333653	−	0.474784i
$937$	−13569.3			−0.473095			−0.236547	−	0.971620i	$-0.576016\pi$
$937$	−13569.3			−0.473095			−0.236547	+	0.971620i	$0.576016\pi$
$938$	10878.2	+	2252.60i	0.378662	+	0.0784115i
$939$		−	28380.3i		−	0.986323i
$940$	11280.5	+	4881.11i	0.391413	+	0.169366i
$941$	−15888.5			−0.550425			−0.275212	−	0.961383i	$-0.588748\pi$
$941$	−15888.5			−0.550425			−0.275212	+	0.961383i	$0.588748\pi$
$942$	−6706.19	+	32385.3i	−0.231953	+	1.12014i
$943$	−10469.8			−0.361552
$944$	−20629.7	+	19374.8i	−0.711272	+	0.668005i
$945$		−	6356.53i		−	0.218813i
$946$	−544.449	+	2629.23i	−0.0187120	+	0.0903633i
$947$	5753.10			0.197414			0.0987068	−	0.995117i	$-0.468529\pi$
$947$	5753.10			0.197414			0.0987068	+	0.995117i	$0.468529\pi$
$948$	770.553	−	1780.78i	0.0263991	−	0.0610096i
$949$	36366.2			1.24394
$950$	−4117.85	+	19885.8i	−0.140632	+	0.679136i
$951$	7879.93			0.268690
$952$	6042.32	+	6975.02i	0.205707	+	0.237460i
$953$	−1956.77			−0.0665120			−0.0332560	−	0.999447i	$-0.510588\pi$
$953$	−1956.77			−0.0665120			−0.0332560	+	0.999447i	$0.510588\pi$
$954$	−3752.58	+	18121.8i	−0.127352	+	0.615006i
$955$	1991.73			0.0674877
$956$	24575.2	+	10633.8i	0.831400	+	0.359751i
$957$	13030.2			0.440134
$958$	−1483.13	+	7162.27i	−0.0500185	+	0.241547i
$959$		−	6891.94i		−	0.232067i
$960$	−4724.80	−	13120.1i	−0.158846	−	0.441094i
$961$	−8405.77			−0.282158
$962$	−5407.45	+	26113.4i	−0.181230	+	0.875189i
$963$	−4845.06			−0.162129
$964$	16650.3	−	38479.6i	0.556297	−	1.28563i
$965$			30996.1i			1.03399i
$966$	11341.3	+	2348.51i	0.377745	+	0.0782217i
$967$	−1299.25			−0.0432070			−0.0216035	−	0.999767i	$-0.506877\pi$
$967$	−1299.25			−0.0432070			−0.0216035	+	0.999767i	$0.506877\pi$
$968$	21958.6	+	15431.3i	0.729107	+	0.512378i
$969$	25419.9	+	6338.23i	0.842729	+	0.210127i
$970$	−3988.14	+	19259.4i	−0.132012	+	0.637507i
$971$		−	27236.6i		−	0.900169i	−0.892986	−	0.450084i	$-0.851394\pi$
$971$		−	27236.6i		−	0.900169i	0.892986	−	0.450084i	$-0.148606\pi$
$972$	24076.1	+	10417.9i	0.794488	+	0.343779i
$973$		−	13363.4i		−	0.440300i
$974$	−6221.71	+	30045.7i	−0.204678	+	0.988424i
$975$			14944.5i			0.490880i
$976$	19472.5	+	20733.7i	0.638626	+	0.679990i
$977$	50368.7			1.64937			0.824686	−	0.565591i	$-0.191352\pi$
$977$	50368.7			1.64937			0.824686	+	0.565591i	$0.191352\pi$
$978$	−12406.4	−	2569.06i	−0.405637	−	0.0839973i
$979$	−9539.24			−0.311415
$980$	−16588.0	−	7177.72i	−0.540699	−	0.233963i
$981$	4723.78			0.153740
$982$	−10995.6	+	53099.8i	−0.357317	+	1.72554i
$983$		−	32918.5i		−	1.06809i	−0.845455	−	0.534047i	$-0.820671\pi$
$983$		−	32918.5i		−	1.06809i	0.845455	−	0.534047i	$-0.179329\pi$
$984$	−2688.21	+	3825.29i	−0.0870905	+	0.123929i
$985$	−19599.4			−0.633999
$986$	24972.1	−	51888.5i	0.806567	−	1.67593i
$987$			4558.69i			0.147016i
$988$	41245.5	+	17847.1i	1.32813	+	0.574689i
$989$	14892.4			0.478818
$990$	3194.48	+	661.497i	0.102553	+	0.0212361i
$991$		−	10192.0i		−	0.326698i	−0.986568	−	0.163349i	$-0.947770\pi$
$991$		−	10192.0i		−	0.326698i	0.986568	−	0.163349i	$-0.0522297\pi$
$992$	−30163.7	+	18487.3i	−0.965423	+	0.591707i
$993$		−	19142.3i		−	0.611745i
$994$	12726.1	+	2635.27i	0.406085	+	0.0840902i
$995$			439.295i			0.0139966i
$996$	4470.82	−	10332.3i	0.142232	−	0.328705i
$997$	−35709.5			−1.13433			−0.567167	−	0.823603i	$-0.691961\pi$
$997$	−35709.5			−1.13433			−0.567167	+	0.823603i	$0.691961\pi$
$998$	30527.6	+	6321.52i	0.968272	+	0.200505i
$999$	−25161.8			−0.796882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.h.a.101.2	yes	52
4.3	odd	2		544.4.h.a.305.17		52
8.3	odd	2		544.4.h.a.305.35		52
8.5	even	2	inner	136.4.h.a.101.3	yes	52
17.16	even	2	inner	136.4.h.a.101.1	✓	52
68.67	odd	2		544.4.h.a.305.36		52
136.67	odd	2		544.4.h.a.305.18		52
136.101	even	2	inner	136.4.h.a.101.4	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.h.a.101.1	✓	52	17.16	even	2	inner
136.4.h.a.101.2	yes	52	1.1	even	1	trivial
136.4.h.a.101.3	yes	52	8.5	even	2	inner
136.4.h.a.101.4	yes	52	136.101	even	2	inner
544.4.h.a.305.17		52	4.3	odd	2
544.4.h.a.305.18		52	136.67	odd	2
544.4.h.a.305.35		52	8.3	odd	2
544.4.h.a.305.36		52	68.67	odd	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.76967 - 0.573530i) q^{2} +3.72680 q^{3} +(7.34213 + 3.17697i) q^{4} -7.30821 q^{5} +(-10.3220 - 2.13743i) q^{6} -5.81849i q^{7} +(-18.5132 - 13.0101i) q^{8} -13.1110 q^{9} +O(q^{10})\)	\(q+(-2.76967 - 0.573530i) q^{2} +3.72680 q^{3} +(7.34213 + 3.17697i) q^{4} -7.30821 q^{5} +(-10.3220 - 2.13743i) q^{6} -5.81849i q^{7} +(-18.5132 - 13.0101i) q^{8} -13.1110 q^{9} +(20.2413 + 4.19147i) q^{10} -12.0372 q^{11} +(27.3626 + 11.8399i) q^{12} -56.0136i q^{13} +(-3.33708 + 16.1153i) q^{14} -27.2362 q^{15} +(43.8137 + 46.6515i) q^{16} +(16.9578 - 68.0105i) q^{17} +(36.3131 + 7.51954i) q^{18} +100.291i q^{19} +(-53.6578 - 23.2180i) q^{20} -21.6843i q^{21} +(33.3391 + 6.90370i) q^{22} -188.838i q^{23} +(-68.9948 - 48.4860i) q^{24} -71.5901 q^{25} +(-32.1255 + 155.139i) q^{26} -149.486 q^{27} +(18.4852 - 42.7201i) q^{28} -290.463 q^{29} +(75.4352 + 15.6208i) q^{30} -195.440i q^{31} +(-94.5934 - 154.338i) q^{32} -44.8603 q^{33} +(-85.9737 + 178.641i) q^{34} +42.5227i q^{35} +(-96.2625 - 41.6532i) q^{36} +168.323 q^{37} +(57.5198 - 277.773i) q^{38} -208.751i q^{39} +(135.298 + 95.0804i) q^{40} -55.4431i q^{41} +(-12.4366 + 60.0585i) q^{42} +78.8633i q^{43} +(-88.3788 - 38.2419i) q^{44} +95.8177 q^{45} +(-108.304 + 523.020i) q^{46} -210.230 q^{47} +(163.285 + 173.861i) q^{48} +309.145 q^{49} +(198.281 + 41.0591i) q^{50} +(63.1985 - 253.461i) q^{51} +(177.954 - 411.259i) q^{52} +499.044i q^{53} +(414.025 + 85.7344i) q^{54} +87.9705 q^{55} +(-75.6991 + 107.719i) q^{56} +373.764i q^{57} +(804.485 + 166.589i) q^{58} +442.209i q^{59} +(-199.972 - 86.5287i) q^{60} +444.439 q^{61} +(-112.091 + 541.304i) q^{62} +76.2862i q^{63} +(173.475 + 481.716i) q^{64} +409.359i q^{65} +(124.248 + 25.7287i) q^{66} -675.021i q^{67} +(340.574 - 445.467i) q^{68} -703.763i q^{69} +(24.3881 - 117.774i) q^{70} -789.694i q^{71} +(242.726 + 170.575i) q^{72} +649.239i q^{73} +(-466.198 - 96.5381i) q^{74} -266.802 q^{75} +(-318.622 + 736.348i) q^{76} +70.0385i q^{77} +(-119.725 + 578.172i) q^{78} -65.0808i q^{79} +(-320.199 - 340.939i) q^{80} -203.106 q^{81} +(-31.7982 + 153.559i) q^{82} -377.605i q^{83} +(68.8906 - 159.209i) q^{84} +(-123.931 + 497.035i) q^{85} +(45.2304 - 218.425i) q^{86} -1082.50 q^{87} +(222.847 + 156.605i) q^{88} +792.479 q^{89} +(-265.383 - 54.9543i) q^{90} -325.915 q^{91} +(599.935 - 1386.48i) q^{92} -728.365i q^{93} +(582.267 + 120.573i) q^{94} -732.946i q^{95} +(-352.530 - 575.185i) q^{96} +951.490i q^{97} +(-856.230 - 177.304i) q^{98} +157.820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9}+O(q^{10}) \) 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9	\( 52 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 428 q^{9} - 232 q^{15} - 78 q^{16} - 28 q^{17} - 2 q^{18} + 1052 q^{25} + 448 q^{26} - 368 q^{30} + 958 q^{32} - 344 q^{33} - 198 q^{34} + 138 q^{36} - 524 q^{38} + 936 q^{47} - 1964 q^{49} - 1038 q^{50} - 1424 q^{52} - 1384 q^{55} + 2320 q^{60} - 2078 q^{64} - 1888 q^{66} - 874 q^{68} + 2472 q^{70} - 4010 q^{72} + 436 q^{76} + 1884 q^{81} - 2264 q^{84} - 1420 q^{86} + 1976 q^{87} - 224 q^{89} + 80 q^{94} + 5746 q^{98}+O(q^{100}) \) 52 * q - 2 * q^2 + 10 * q^4 - 2 * q^8 + 428 * q^9 - 232 * q^15 - 78 * q^16 - 28 * q^17 - 2 * q^18 + 1052 * q^25 + 448 * q^26 - 368 * q^30 + 958 * q^32 - 344 * q^33 - 198 * q^34 + 138 * q^36 - 524 * q^38 + 936 * q^47 - 1964 * q^49 - 1038 * q^50 - 1424 * q^52 - 1384 * q^55 + 2320 * q^60 - 2078 * q^64 - 1888 * q^66 - 874 * q^68 + 2472 * q^70 - 4010 * q^72 + 436 * q^76 + 1884 * q^81 - 2264 * q^84 - 1420 * q^86 + 1976 * q^87 - 224 * q^89 + 80 * q^94 + 5746 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more