LMFDB - Embedded newform 75.3.k.a.22.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			22.9
Character	$\chi$	$=$	75.22
Dual form			75.3.k.a.58.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.73870 - 1.39544i) q^{2} +(1.71073 - 0.270952i) q^{3} +(3.20210 - 4.40731i) q^{4} +(-4.71895 + 1.65274i) q^{5} +(4.30707 - 3.12927i) q^{6} +(-0.250082 - 0.250082i) q^{7} +(0.696119 - 4.39513i) q^{8} +(2.85317 - 0.927051i) q^{9} +O(q^{10})$	\(q+(2.73870 - 1.39544i) q^{2} +(1.71073 - 0.270952i) q^{3} +(3.20210 - 4.40731i) q^{4} +(-4.71895 + 1.65274i) q^{5} +(4.30707 - 3.12927i) q^{6} +(-0.250082 - 0.250082i) q^{7} +(0.696119 - 4.39513i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-10.6175 + 11.1114i) q^{10} +(-2.45351 + 7.55112i) q^{11} +(4.28374 - 8.40731i) q^{12} +(-10.5776 - 5.38954i) q^{13} +(-1.03387 - 0.335926i) q^{14} +(-7.62501 + 4.10600i) q^{15} +(2.50710 + 7.71607i) q^{16} +(24.0906 + 3.81558i) q^{17} +(6.52034 - 6.52034i) q^{18} +(-15.4606 - 21.2797i) q^{19} +(-7.82638 + 26.0901i) q^{20} +(-0.495582 - 0.360061i) q^{21} +(3.81770 + 24.1040i) q^{22} +(-5.83489 - 11.4516i) q^{23} -7.70747i q^{24} +(19.5369 - 15.5984i) q^{25} -36.4896 q^{26} +(4.62981 - 2.35900i) q^{27} +(-1.90297 + 0.301401i) q^{28} +(-27.7376 + 38.1776i) q^{29} +(-15.1530 + 21.8853i) q^{30} +(27.8697 - 20.2485i) q^{31} +(30.2198 + 30.2198i) q^{32} +(-2.15129 + 13.5827i) q^{33} +(71.3015 - 23.1673i) q^{34} +(1.59344 + 0.766802i) q^{35} +(5.05032 - 15.5433i) q^{36} +(-3.75426 + 7.36815i) q^{37} +(-72.0364 - 36.7044i) q^{38} +(-19.5556 - 6.35401i) q^{39} +(3.97906 + 21.8909i) q^{40} +(-14.5062 - 44.6455i) q^{41} +(-1.85969 - 0.294547i) q^{42} +(1.08084 - 1.08084i) q^{43} +(25.4237 + 34.9928i) q^{44} +(-11.9318 + 9.09025i) q^{45} +(-31.9601 - 23.2203i) q^{46} +(6.73620 + 42.5307i) q^{47} +(6.37966 + 12.5208i) q^{48} -48.8749i q^{49} +(31.7391 - 69.9819i) q^{50} +42.2463 q^{51} +(-57.6237 + 29.3608i) q^{52} +(-28.7572 + 4.55469i) q^{53} +(9.38781 - 12.9212i) q^{54} +(-0.902079 - 39.6884i) q^{55} +(-1.27323 + 0.925055i) q^{56} +(-32.2146 - 32.2146i) q^{57} +(-22.6907 + 143.263i) q^{58} +(71.3918 - 23.1966i) q^{59} +(-6.31962 + 46.7536i) q^{60} +(26.0031 - 80.0294i) q^{61} +(48.0713 - 94.3452i) q^{62} +(-0.945365 - 0.481688i) q^{63} +(94.0684 + 30.5647i) q^{64} +(58.8225 + 7.95096i) q^{65} +(13.0621 + 40.2009i) q^{66} +(-41.9801 - 6.64899i) q^{67} +(93.9570 - 93.9570i) q^{68} +(-13.0848 - 18.0096i) q^{69} +(5.43399 - 0.123510i) q^{70} +(49.0998 + 35.6731i) q^{71} +(-2.08836 - 13.1854i) q^{72} +(43.1099 + 84.6079i) q^{73} +25.4180i q^{74} +(29.1959 - 31.9781i) q^{75} -143.292 q^{76} +(2.50198 - 1.27482i) q^{77} +(-62.4237 + 9.88694i) q^{78} +(-62.3659 + 85.8393i) q^{79} +(-24.5836 - 32.2681i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-102.028 - 102.028i) q^{82} +(-15.0878 + 95.2606i) q^{83} +(-3.17380 + 1.03123i) q^{84} +(-119.989 + 21.8101i) q^{85} +(1.45185 - 4.46832i) q^{86} +(-37.1072 + 72.8270i) q^{87} +(31.4802 + 16.0400i) q^{88} +(-163.312 - 53.0634i) q^{89} +(-19.9927 + 41.5455i) q^{90} +(1.29743 + 3.99309i) q^{91} +(-69.1547 - 10.9530i) q^{92} +(42.1911 - 42.1911i) q^{93} +(77.7974 + 107.079i) q^{94} +(108.127 + 74.8653i) q^{95} +(59.8858 + 43.5096i) q^{96} +(16.8062 + 106.110i) q^{97} +(-68.2019 - 133.854i) q^{98} +23.8192i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	2.73870	−	1.39544i	1.36935	−	0.697719i	0.394151	−	0.919046i	$-0.371039\pi$
$2$	2.73870	−	1.39544i	1.36935	−	0.697719i	0.975200	+	0.221327i	$0.0710388\pi$
$3$	1.71073	−	0.270952i	0.570242	−	0.0903175i
$3$	1.71073	−	0.270952i	0.570242	−	0.0903175i
$4$	3.20210	−	4.40731i	0.800524	−	1.10183i
$5$	−4.71895	+	1.65274i	−0.943789	+	0.330548i
$5$	−4.71895	+	1.65274i	−0.943789	+	0.330548i
$6$	4.30707	−	3.12927i	0.717845	−	0.521545i
$7$	−0.250082	−	0.250082i	−0.0357260	−	0.0357260i	0.689018	−	0.724744i	$-0.258042\pi$
$7$	−0.250082	−	0.250082i	−0.0357260	−	0.0357260i	−0.724744	+	0.689018i	$0.758042\pi$
$8$	0.696119	−	4.39513i	0.0870149	−	0.549391i
$9$	2.85317	−	0.927051i	0.317019	−	0.103006i
$10$	−10.6175	+	11.1114i	−1.06175	+	1.11114i
$11$	−2.45351	+	7.55112i	−0.223046	+	0.686466i	0.775438	+	0.631424i	$0.217529\pi$
$11$	−2.45351	+	7.55112i	−0.223046	+	0.686466i	−0.998484	+	0.0550418i	$0.982471\pi$
$12$	4.28374	−	8.40731i	0.356978	−	0.700609i
$13$	−10.5776	−	5.38954i	−0.813659	−	0.414580i	−0.00292573	−	0.999996i	$-0.500931\pi$
$13$	−10.5776	−	5.38954i	−0.813659	−	0.414580i	−0.810733	+	0.585416i	$0.800931\pi$
$14$	−1.03387	−	0.335926i	−0.0738481	−	0.0239947i
$15$	−7.62501	+	4.10600i	−0.508334	+	0.273733i
$16$	2.50710	+	7.71607i	0.156694	+	0.482254i
$17$	24.0906	+	3.81558i	1.41710	+	0.224446i	0.817533	−	0.575881i	$-0.195341\pi$
$17$	24.0906	+	3.81558i	1.41710	+	0.224446i	0.599563	+	0.800327i	$0.295341\pi$
$18$	6.52034	−	6.52034i	0.362241	−	0.362241i
$19$	−15.4606	−	21.2797i	−0.813715	−	1.11998i	−0.990740	−	0.135776i	$-0.956647\pi$
$19$	−15.4606	−	21.2797i	−0.813715	−	1.11998i	0.177024	−	0.984206i	$-0.443353\pi$
$20$	−7.82638	+	26.0901i	−0.391319	+	1.30450i
$21$	−0.495582	−	0.360061i	−0.0235991	−	0.0171458i
$22$	3.81770	+	24.1040i	0.173532	+	1.09564i
$23$	−5.83489	−	11.4516i	−0.253691	−	0.497897i	0.728676	−	0.684858i	$-0.240136\pi$
$23$	−5.83489	−	11.4516i	−0.253691	−	0.497897i	−0.982367	+	0.186962i	$0.940136\pi$
$24$		−	7.70747i		−	0.321145i
$25$	19.5369	−	15.5984i	0.781476	−	0.623936i
$26$	−36.4896			−1.40344
$27$	4.62981	−	2.35900i	0.171474	−	0.0873705i
$28$	−1.90297	+	0.301401i	−0.0679634	+	0.0107643i
$29$	−27.7376	+	38.1776i	−0.956470	+	1.31647i	−0.00787767	+	0.999969i	$0.502508\pi$
$29$	−27.7376	+	38.1776i	−0.956470	+	1.31647i	−0.948593	+	0.316500i	$0.897492\pi$
$30$	−15.1530	+	21.8853i	−0.505099	+	0.729511i
$31$	27.8697	−	20.2485i	0.899023	−	0.653179i	−0.0391915	−	0.999232i	$-0.512478\pi$
$31$	27.8697	−	20.2485i	0.899023	−	0.653179i	0.938215	+	0.346053i	$0.112478\pi$
$32$	30.2198	+	30.2198i	0.944367	+	0.944367i
$33$	−2.15129	+	13.5827i	−0.0651905	+	0.411597i
$34$	71.3015	−	23.1673i	2.09710	−	0.681390i
$35$	1.59344	+	0.766802i	0.0455270	+	0.0219086i
$36$	5.05032	−	15.5433i	0.140287	−	0.431758i
$37$	−3.75426	+	7.36815i	−0.101466	+	0.199139i	−0.936159	−	0.351577i	$-0.885645\pi$
$37$	−3.75426	+	7.36815i	−0.101466	+	0.199139i	0.834692	+	0.550716i	$0.185645\pi$
$38$	−72.0364	−	36.7044i	−1.89569	−	0.965905i
$39$	−19.5556	−	6.35401i	−0.501426	−	0.162923i
$40$	3.97906	+	21.8909i	0.0994764	+	0.547272i
$41$	−14.5062	−	44.6455i	−0.353810	−	1.08892i	−0.956696	−	0.291088i	$-0.905983\pi$
$41$	−14.5062	−	44.6455i	−0.353810	−	1.08892i	0.602886	−	0.797827i	$-0.294017\pi$
$42$	−1.85969	−	0.294547i	−0.0442784	−	0.00701302i
$43$	1.08084	−	1.08084i	0.0251357	−	0.0251357i	−0.694427	−	0.719563i	$-0.744342\pi$
$43$	1.08084	−	1.08084i	0.0251357	−	0.0251357i	0.719563	+	0.694427i	$0.244342\pi$
$44$	25.4237	+	34.9928i	0.577812	+	0.795291i
$45$	−11.9318	+	9.09025i	−0.265151	+	0.202006i
$46$	−31.9601	−	23.2203i	−0.694784	−	0.504790i
$47$	6.73620	+	42.5307i	0.143323	+	0.904909i	0.949621	+	0.313399i	$0.101468\pi$
$47$	6.73620	+	42.5307i	0.143323	+	0.904909i	−0.806298	+	0.591509i	$0.798532\pi$
$48$	6.37966	+	12.5208i	0.132910	+	0.260850i
$49$		−	48.8749i		−	0.997447i
$50$	31.7391	−	69.9819i	0.634782	−	1.39964i
$51$	42.2463			0.828360
$52$	−57.6237	+	29.3608i	−1.10815	+	0.564630i
$53$	−28.7572	+	4.55469i	−0.542589	+	0.0859376i	−0.421712	−	0.906730i	$-0.638571\pi$
$53$	−28.7572	+	4.55469i	−0.542589	+	0.0859376i	−0.120877	+	0.992668i	$0.538571\pi$
$54$	9.38781	−	12.9212i	0.173848	−	0.239282i
$55$	−0.902079	−	39.6884i	−0.0164014	−	0.721607i
$56$	−1.27323	+	0.925055i	−0.0227362	+	0.0165188i
$57$	−32.2146	−	32.2146i	−0.565169	−	0.565169i
$58$	−22.6907	+	143.263i	−0.391218	+	2.47005i
$59$	71.3918	−	23.1966i	1.21003	−	0.393163i	0.366588	−	0.930383i	$-0.380526\pi$
$59$	71.3918	−	23.1966i	1.21003	−	0.393163i	0.843442	+	0.537221i	$0.180526\pi$
$60$	−6.31962	+	46.7536i	−0.105327	+	0.779226i
$61$	26.0031	−	80.0294i	0.426281	−	1.31196i	−0.475481	−	0.879726i	$-0.657726\pi$
$61$	26.0031	−	80.0294i	0.426281	−	1.31196i	0.901762	−	0.432232i	$-0.142274\pi$
$62$	48.0713	−	94.3452i	0.775343	−	1.52170i
$63$	−0.945365	−	0.481688i	−0.0150058	−	0.00764583i
$64$	94.0684	+	30.5647i	1.46982	+	0.477573i
$65$	58.8225	+	7.95096i	0.904961	+	0.122322i
$66$	13.0621	+	40.2009i	0.197910	+	0.609105i
$67$	−41.9801	−	6.64899i	−0.626568	−	0.0992386i	−0.164927	−	0.986306i	$-0.552739\pi$
$67$	−41.9801	−	6.64899i	−0.626568	−	0.0992386i	−0.461641	+	0.887067i	$0.652739\pi$
$68$	93.9570	−	93.9570i	1.38172	−	1.38172i
$69$	−13.0848	−	18.0096i	−0.189634	−	0.261009i
$70$	5.43399	−	0.123510i	0.0776285	−	0.00176442i
$71$	49.0998	+	35.6731i	0.691546	+	0.502438i	0.877168	−	0.480183i	$-0.159430\pi$
$71$	49.0998	+	35.6731i	0.691546	+	0.502438i	−0.185622	+	0.982621i	$0.559430\pi$
$72$	−2.08836	−	13.1854i	−0.0290050	−	0.183130i
$73$	43.1099	+	84.6079i	0.590547	+	1.15901i	0.972078	+	0.234657i	$0.0753967\pi$
$73$	43.1099	+	84.6079i	0.590547	+	1.15901i	−0.381532	+	0.924356i	$0.624603\pi$
$74$			25.4180i			0.343486i
$75$	29.1959	−	31.9781i	0.389278	−	0.426375i
$76$	−143.292			−1.88543
$77$	2.50198	−	1.27482i	0.0324932	−	0.0165561i
$78$	−62.4237	+	9.88694i	−0.800303	+	0.126756i
$79$	−62.3659	+	85.8393i	−0.789442	+	1.08657i	0.204736	+	0.978817i	$0.434366\pi$
$79$	−62.3659	+	85.8393i	−0.789442	+	1.08657i	−0.994177	+	0.107756i	$0.965634\pi$
$80$	−24.5836	−	32.2681i	−0.307294	−	0.403352i
$81$	7.28115	−	5.29007i	0.0898908	−	0.0653095i
$82$	−102.028	−	102.028i	−1.24425	−	1.24425i
$83$	−15.0878	+	95.2606i	−0.181781	+	1.14772i	0.712984	+	0.701180i	$0.247343\pi$
$83$	−15.0878	+	95.2606i	−0.181781	+	1.14772i	−0.894765	+	0.446538i	$0.852657\pi$
$84$	−3.17380	+	1.03123i	−0.0377834	+	0.0122766i
$85$	−119.989	+	21.8101i	−1.41163	+	0.256589i
$86$	1.45185	−	4.46832i	0.0168819	−	0.0519572i
$87$	−37.1072	+	72.8270i	−0.426520	+	0.837092i
$88$	31.4802	+	16.0400i	0.357730	+	0.182272i
$89$	−163.312	−	53.0634i	−1.83497	−	0.596218i	−0.998864	−	0.0476516i	$-0.984826\pi$
$89$	−163.312	−	53.0634i	−1.83497	−	0.596218i	−0.836107	−	0.548567i	$-0.815174\pi$
$90$	−19.9927	+	41.5455i	−0.222141	+	0.461617i
$91$	1.29743	+	3.99309i	0.0142575	+	0.0438801i
$92$	−69.1547	−	10.9530i	−0.751681	−	0.119055i
$93$	42.1911	−	42.1911i	0.453668	−	0.453668i
$94$	77.7974	+	107.079i	0.827632	+	1.13914i
$95$	108.127	+	74.8653i	1.13818	+	0.788055i
$96$	59.8858	+	43.5096i	0.623811	+	0.453225i
$97$	16.8062	+	106.110i	0.173259	+	1.09392i	0.909044	+	0.416701i	$0.136814\pi$
$97$	16.8062	+	106.110i	0.173259	+	1.09392i	−0.735784	+	0.677216i	$0.763186\pi$
$98$	−68.2019	−	133.854i	−0.695938	−	1.36585i
$99$			23.8192i			0.240598i
$100$	−6.18789	−	136.053i	−0.0618789	−	1.36053i
$101$	−107.110			−1.06049			−0.530247	−	0.847843i	$-0.677901\pi$
$101$	−107.110			−1.06049			−0.530247	+	0.847843i	$0.677901\pi$
$102$	115.700	−	58.9522i	1.13431	−	0.577962i
$103$	94.2525	−	14.9281i	0.915073	−	0.144933i	0.318899	−	0.947789i	$-0.396687\pi$
$103$	94.2525	−	14.9281i	0.915073	−	0.144933i	0.596174	+	0.802855i	$0.296687\pi$
$104$	−31.0510	+	42.7380i	−0.298567	+	0.410942i
$105$	2.93371	+	0.880042i	0.0279401	+	0.00838135i
$106$	−72.4016	+	52.6028i	−0.683034	+	0.496253i
$107$	128.543	+	128.543i	1.20134	+	1.20134i	0.973761	+	0.227575i	$0.0730796\pi$
$107$	128.543	+	128.543i	1.20134	+	1.20134i	0.227575	+	0.973761i	$0.426920\pi$
$108$	4.42823	−	27.9587i	0.0410021	−	0.258877i
$109$	−89.3002	+	29.0154i	−0.819268	+	0.266196i	−0.688518	−	0.725219i	$-0.741738\pi$
$109$	−89.3002	+	29.0154i	−0.819268	+	0.266196i	−0.130750	+	0.991415i	$0.541738\pi$
$110$	−57.8532	−	107.436i	−0.525938	−	0.976689i
$111$	−4.42609	+	13.6221i	−0.0398747	+	0.122722i
$112$	1.30267	−	2.55663i	0.0116310	−	0.0228271i
$113$	−13.1461	−	6.69828i	−0.116337	−	0.0592768i	0.394853	−	0.918744i	$-0.370795\pi$
$113$	−13.1461	−	6.69828i	−0.116337	−	0.0592768i	−0.511191	+	0.859467i	$0.670795\pi$
$114$	−133.180	−	43.2727i	−1.16824	−	0.379585i
$115$	46.4611	+	44.3960i	0.404010	+	0.386052i
$116$	79.4417	+	244.497i	0.684843	+	2.10773i
$117$	−35.1760	−	5.57133i	−0.300649	−	0.0476182i
$118$	163.151	−	163.151i	1.38264	−	1.38264i
$119$	−5.07043	−	6.97885i	−0.0426086	−	0.0586458i
$120$	12.7385	+	36.3711i	0.106154	+	0.303093i
$121$	46.8913	+	34.0685i	0.387531	+	0.281558i
$122$	−40.4613	−	255.462i	−0.331650	−	2.09395i
$123$	−36.9130	−	72.4458i	−0.300105	−	0.588990i
$124$		−	187.668i		−	1.51345i
$125$	−66.4134	+	105.897i	−0.531307	+	0.847179i
$126$	−3.26124			−0.0258828
$127$	36.2034	−	18.4466i	0.285066	−	0.145249i	−0.305611	−	0.952157i	$-0.598861\pi$
$127$	36.2034	−	18.4466i	0.285066	−	0.145249i	0.590677	+	0.806908i	$0.298861\pi$
$128$	131.432	−	20.8168i	1.02681	−	0.162631i
$129$	1.55616	−	2.14187i	0.0120632	−	0.0166036i
$130$	172.192	−	60.3078i	1.32456	−	0.463906i
$131$	121.554	−	88.3139i	0.927890	−	0.674152i	−0.0175852	−	0.999845i	$-0.505598\pi$
$131$	121.554	−	88.3139i	0.927890	−	0.674152i	0.945475	+	0.325694i	$0.105598\pi$
$132$	52.9745	+	52.9745i	0.401322	+	0.401322i
$133$	−1.45525	+	9.18808i	−0.0109417	+	0.0690833i
$134$	−124.249	+	40.3710i	−0.927232	+	0.301276i
$135$	−17.9490	+	18.7839i	−0.132955	+	0.139140i
$136$	33.5399	−	103.225i	0.246617	−	0.759010i
$137$	−7.33780	+	14.4013i	−0.0535606	+	0.105119i	−0.916235	−	0.400641i	$-0.868788\pi$
$137$	−7.33780	+	14.4013i	−0.0535606	+	0.105119i	0.862675	+	0.505759i	$0.168788\pi$
$138$	−60.9665	−	31.0640i	−0.441786	−	0.225101i
$139$	45.4296	+	14.7610i	0.326832	+	0.106194i	0.467837	−	0.883815i	$-0.345033\pi$
$139$	45.4296	+	14.7610i	0.326832	+	0.106194i	−0.141005	+	0.990009i	$0.545033\pi$
$140$	8.48189	−	4.56742i	0.0605849	−	0.0326244i
$141$	23.0476	+	70.9332i	0.163458	+	0.503072i
$142$	184.249	+	29.1822i	1.29753	+	0.205509i
$143$	66.6492	−	66.6492i	0.466079	−	0.466079i
$144$	14.3064	+	19.6910i	0.0993499	+	0.136743i
$145$	67.7947	−	226.001i	0.467550	−	1.55863i
$146$	236.130	+	171.559i	1.61733	+	1.17506i
$147$	−13.2428	−	83.6116i	−0.0900869	−	0.568786i
$148$	20.4522	+	40.1397i	0.138190	+	0.271214i
$149$		−	108.380i		−	0.727379i	−0.931520	−	0.363690i	$-0.881517\pi$
$149$		−	108.380i		−	0.727379i	0.931520	−	0.363690i	$-0.118483\pi$
$150$	35.3352	−	128.320i	0.235568	−	0.855464i
$151$	−59.8487			−0.396349			−0.198175	−	0.980167i	$-0.563501\pi$
$151$	−59.8487			−0.396349			−0.198175	+	0.980167i	$0.563501\pi$
$152$	−104.289	+	53.1380i	−0.686114	+	0.349592i
$153$	72.2719	−	11.4468i	0.472366	−	0.0748154i
$154$	5.07324	−	6.98271i	0.0329431	−	0.0453423i
$155$	−98.0501	+	141.613i	−0.632581	+	0.913634i
$156$	−90.6231	+	65.8415i	−0.580917	+	0.422061i
$157$	−87.1877	−	87.1877i	−0.555336	−	0.555336i	0.372640	−	0.927976i	$-0.378453\pi$
$157$	−87.1877	−	87.1877i	−0.555336	−	0.555336i	−0.927976	+	0.372640i	$0.878453\pi$
$158$	−51.0181	+	322.116i	−0.322900	+	2.03871i
$159$	−47.9616	+	15.5837i	−0.301645	+	0.0980105i
$160$	−192.551	−	92.6599i	−1.20344	−	0.579125i
$161$	−1.40464	+	4.32305i	−0.00872449	+	0.0268512i
$162$	12.5589	−	24.6483i	0.0775243	−	0.152150i
$163$	82.9386	+	42.2593i	0.508826	+	0.259260i	0.689503	−	0.724283i	$-0.257829\pi$
$163$	82.9386	+	42.2593i	0.508826	+	0.259260i	−0.180677	+	0.983542i	$0.557829\pi$
$164$	−243.217	−	79.0259i	−1.48303	−	0.481865i
$165$	−12.2969	−	67.6515i	−0.0745265	−	0.410009i
$166$	91.6093	+	281.944i	0.551863	+	1.69846i
$167$	−234.911	−	37.2062i	−1.40665	−	0.222792i	−0.593495	−	0.804837i	$-0.702252\pi$
$167$	−234.911	−	37.2062i	−1.40665	−	0.222792i	−0.813156	+	0.582046i	$0.802252\pi$
$168$	−1.92750	+	1.92750i	−0.0114732	+	0.0114732i
$169$	−16.4979	−	22.7075i	−0.0976209	−	0.134364i
$170$	−298.178	+	227.168i	−1.75399	+	1.33628i
$171$	−63.8390	−	46.3818i	−0.373328	−	0.271238i
$172$	−1.30263	−	8.22451i	−0.00757346	−	0.0478169i
$173$	15.0135	+	29.4657i	0.0867833	+	0.170322i	0.930319	−	0.366751i	$-0.119530\pi$
$173$	15.0135	+	29.4657i	0.0867833	+	0.170322i	−0.843536	+	0.537073i	$0.819530\pi$
$174$			251.232i			1.44386i
$175$	−8.78670	−	0.984948i	−0.0502097	−	0.00562828i
$176$	−64.4162			−0.366001
$177$	115.847	−	59.0268i	0.654501	−	0.333485i
$178$	−521.311	+	82.5675i	−2.92871	+	0.463862i
$179$	157.338	−	216.558i	0.878985	−	1.20982i	−0.0977154	−	0.995214i	$-0.531153\pi$
$179$	157.338	−	216.558i	0.878985	−	1.20982i	0.976701	−	0.214605i	$-0.0688465\pi$
$180$	1.85685	+	81.6949i	0.0103158	+	0.453860i
$181$	−32.1635	+	23.3682i	−0.177699	+	0.129106i	−0.673079	−	0.739570i	$-0.735029\pi$
$181$	−32.1635	+	23.3682i	−0.177699	+	0.129106i	0.495380	+	0.868676i	$0.335029\pi$
$182$	9.12538	+	9.12538i	0.0501395	+	0.0501395i
$183$	22.8001	−	143.954i	0.124591	−	0.786634i
$184$	−54.3931	+	17.6734i	−0.295615	+	0.0960510i
$185$	5.53850	−	40.9747i	0.0299378	−	0.221485i
$186$	56.6737	−	174.424i	0.304697	−	0.937762i
$187$	−87.9186	+	172.550i	−0.470153	+	0.922727i
$188$	209.016	+	106.499i	1.11179	+	0.566483i
$189$	−1.74778	−	0.567887i	−0.00924749	−	0.00300469i
$190$	400.599	+	54.1484i	2.10841	+	0.284992i
$191$	−40.9280	−	125.963i	−0.214283	−	0.659495i	−0.999204	−	0.0398988i	$-0.987296\pi$
$191$	−40.9280	−	125.963i	−0.214283	−	0.659495i	0.784921	−	0.619596i	$-0.212704\pi$
$192$	169.207	+	26.7997i	0.881286	+	0.139582i
$193$	−31.7199	+	31.7199i	−0.164352	+	0.164352i	−0.784491	−	0.620140i	$-0.787076\pi$
$193$	−31.7199	+	31.7199i	−0.164352	+	0.164352i	0.620140	+	0.784491i	$0.287076\pi$
$194$	194.097	+	267.151i	1.00050	+	1.37707i
$195$	102.783	−	2.33617i	0.527095	−	0.0119804i
$196$	−215.407	−	156.502i	−1.09901	−	0.798480i
$197$	−26.9222	−	169.980i	−0.136661	−	0.862844i	−0.956814	−	0.290700i	$-0.906112\pi$
$197$	−26.9222	−	169.980i	−0.136661	−	0.862844i	0.820153	−	0.572144i	$-0.193888\pi$
$198$	33.2382	+	65.2336i	0.167870	+	0.329462i
$199$		−	26.7052i		−	0.134197i	−0.997746	−	0.0670985i	$-0.978626\pi$
$199$		−	26.7052i		−	0.134197i	0.997746	−	0.0670985i	$-0.0213742\pi$
$200$	−54.9569	−	96.7254i	−0.274784	−	0.483627i
$201$	−73.6179			−0.366258
$202$	−293.342	+	149.465i	−1.45219	+	0.739927i
$203$	16.4842	−	2.61084i	0.0812030	−	0.0128613i
$204$	135.277	−	186.193i	0.663122	−	0.912709i
$205$	142.242	+	186.705i	0.693861	+	0.910755i
$206$	237.298	−	172.407i	1.15193	−	0.836928i
$207$	−27.2642	−	27.2642i	−0.131711	−	0.131711i
$208$	15.0670	−	95.1294i	0.0724376	−	0.457353i
$209$	198.618	−	64.5350i	0.950326	−	0.308780i
$210$	9.26261	−	1.68364i	0.0441077	−	0.00801735i
$211$	4.07202	−	12.5324i	0.0192987	−	0.0593952i	−0.940943	−	0.338564i	$-0.890059\pi$
$211$	4.07202	−	12.5324i	0.0192987	−	0.0593952i	0.960242	+	0.279169i	$0.0900589\pi$
$212$	−72.0094	+	141.326i	−0.339667	+	0.666634i
$213$	93.6620	+	47.7232i	0.439728	+	0.224052i
$214$	531.414	+	172.667i	2.48324	+	0.806855i
$215$	−3.31406	+	6.88674i	−0.0154142	+	0.0320314i
$216$	−7.14522	−	21.9907i	−0.0330797	−	0.101809i
$217$	−12.0335	−	1.90592i	−0.0554540	−	0.00878305i
$218$	−204.077	+	204.077i	−0.936134	+	0.936134i
$219$	96.6740	+	133.060i	0.441434	+	0.607581i
$220$	−177.807	−	123.110i	−0.808215	−	0.559592i
$221$	−234.256	−	170.197i	−1.05998	−	0.770123i
$222$	6.88706	+	43.4832i	0.0310228	+	0.195870i
$223$	−99.4164	−	195.116i	−0.445814	−	0.874958i	−0.999118	−	0.0419796i	$-0.986634\pi$
$223$	−99.4164	−	195.116i	−0.445814	−	0.874958i	0.553305	−	0.832979i	$-0.313366\pi$
$224$		−	15.1148i		−	0.0674769i
$225$	41.2816	−	62.6166i	0.183474	−	0.278296i
$226$	−45.3503			−0.200665
$227$	133.983	−	68.2679i	0.590235	−	0.300740i	−0.133247	−	0.991083i	$-0.542540\pi$
$227$	133.983	−	68.2679i	0.590235	−	0.300740i	0.723482	+	0.690343i	$0.242540\pi$
$228$	−245.134	+	38.8254i	−1.07515	+	0.170287i
$229$	−218.119	+	300.215i	−0.952483	+	1.31098i	−0.00206788	+	0.999998i	$0.500658\pi$
$229$	−218.119	+	300.215i	−0.952483	+	1.31098i	−0.950415	+	0.310983i	$0.899342\pi$
$230$	189.195	+	56.7538i	0.822587	+	0.246756i
$231$	3.93478	−	2.85879i	0.0170337	−	0.0123757i
$232$	148.487	+	148.487i	0.640028	+	0.640028i
$233$	11.6039	−	73.2641i	0.0498021	−	0.314438i	−0.950194	−	0.311659i	$-0.899115\pi$
$233$	11.6039	−	73.2641i	0.0498021	−	0.314438i	0.999996	−	0.00277928i	$-0.000884672\pi$
$234$	−104.111	+	33.8277i	−0.444918	+	0.144563i
$235$	−102.080	−	189.567i	−0.434383	−	0.806668i
$236$	126.369	−	388.923i	0.535461	−	1.64798i
$237$	−83.4326	+	163.746i	−0.352036	+	0.690910i
$238$	−23.6249	−	12.0375i	−0.0992644	−	0.0505777i
$239$	216.055	+	70.2006i	0.903996	+	0.293726i	0.723885	−	0.689920i	$-0.242354\pi$
$239$	216.055	+	70.2006i	0.903996	+	0.293726i	0.180111	+	0.983646i	$0.442354\pi$
$240$	−50.7989	−	48.5410i	−0.211662	−	0.202254i
$241$	−106.433	−	327.566i	−0.441629	−	1.35919i	−0.886139	−	0.463420i	$-0.846622\pi$
$241$	−106.433	−	327.566i	−0.441629	−	1.35919i	0.444510	−	0.895774i	$-0.353378\pi$
$242$	175.962	+	27.8696i	0.727115	+	0.115164i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	−269.450	−	370.866i	−1.10430	−	1.51994i
$245$	80.7776	+	230.638i	0.329704	+	0.941380i
$246$	−202.187	−	146.898i	−0.821899	−	0.597145i
$247$	48.8478	+	308.413i	0.197764	+	1.24863i
$248$	−69.5942	−	136.586i	−0.280622	−	0.550751i
$249$			167.053i			0.670895i
$250$	−34.1133	+	382.697i	−0.136453	+	1.53079i
$251$	−210.120			−0.837130			−0.418565	−	0.908187i	$-0.637467\pi$
$251$	−210.120			−0.837130			−0.418565	+	0.908187i	$0.637467\pi$
$252$	−5.15009	+	2.62410i	−0.0204369	+	0.0104131i
$253$	100.789	−	15.9633i	0.398374	−	0.0630962i
$254$	73.4094	−	101.039i	0.289013	−	0.397793i
$255$	−199.358	+	69.8223i	−0.781797	+	0.273813i
$256$	10.8275	−	7.86664i	0.0422949	−	0.0307290i
$257$	−181.816	−	181.816i	−0.707456	−	0.707456i	0.258544	−	0.966000i	$-0.416757\pi$
$257$	−181.816	−	181.816i	−0.707456	−	0.707456i	−0.966000	+	0.258544i	$0.916757\pi$
$258$	1.27301	−	8.03746i	0.00493414	−	0.0311529i
$259$	2.78151	−	0.903768i	0.0107394	−	0.00348945i
$260$	223.397	−	233.789i	0.859221	−	0.899188i
$261$	−43.7476	+	134.641i	−0.167615	+	0.515867i
$262$	209.662	−	411.486i	0.800238	−	1.57056i
$263$	68.9955	+	35.1550i	0.262340	+	0.133669i	0.580214	−	0.814464i	$-0.302969\pi$
$263$	68.9955	+	35.1550i	0.262340	+	0.133669i	−0.317874	+	0.948133i	$0.602969\pi$
$264$	58.2001	+	18.9104i	0.220455	+	0.0716301i
$265$	128.176	−	69.0216i	0.483683	−	0.260459i
$266$	8.83590	+	27.1941i	0.0332177	+	0.102233i
$267$	−293.761	−	46.5271i	−1.10023	−	0.174259i
$268$	−163.728	+	163.728i	−0.610926	+	0.610926i
$269$	−187.609	−	258.221i	−0.697430	−	0.959931i	−0.999977	−	0.00679606i	$-0.997837\pi$
$269$	−187.609	−	258.221i	−0.697430	−	0.959931i	0.302546	−	0.953135i	$-0.402163\pi$
$270$	−22.9451	+	76.4901i	−0.0849820	+	0.283297i
$271$	286.845	+	208.405i	1.05847	+	0.769022i	0.973804	−	0.227387i	$-0.0730184\pi$
$271$	286.845	+	208.405i	1.05847	+	0.769022i	0.0846638	+	0.996410i	$0.473018\pi$
$272$	30.9564	+	195.451i	0.113810	+	0.718571i
$273$	3.30149	+	6.47953i	0.0120934	+	0.0237346i
$274$			49.6802i			0.181314i
$275$	69.8514	+	185.796i	0.254005	+	0.675623i
$276$	−121.273			−0.439393
$277$	295.312	−	150.469i	1.06611	−	0.543209i	0.169271	−	0.985570i	$-0.445859\pi$
$277$	295.312	−	150.469i	1.06611	−	0.543209i	0.896837	+	0.442360i	$0.145859\pi$
$278$	145.016	−	22.9683i	0.521641	−	0.0826198i
$279$	60.7456	−	83.6092i	0.217726	−	0.299674i
$280$	4.47942	−	6.46960i	0.0159979	−	0.0231057i
$281$	−87.3274	+	63.4471i	−0.310774	+	0.225790i	−0.732228	−	0.681059i	$-0.761520\pi$
$281$	−87.3274	+	63.4471i	−0.310774	+	0.225790i	0.421455	+	0.906849i	$0.361520\pi$
$282$	162.103	+	162.103i	0.574835	+	0.574835i
$283$	20.9100	−	132.020i	0.0738868	−	0.466503i	−0.922808	−	0.385261i	$-0.874111\pi$
$283$	20.9100	−	132.020i	0.0738868	−	0.466503i	0.996694	−	0.0812417i	$-0.0258886\pi$
$284$	314.444	−	102.169i	1.10720	−	0.359751i
$285$	205.261	+	98.7766i	0.720216	+	0.346585i
$286$	89.5275	−	275.537i	0.313033	−	0.963417i
$287$	−7.53730	+	14.7928i	−0.0262624	+	0.0515428i
$288$	114.237	+	58.2068i	0.396657	+	0.202107i
$289$	290.945	+	94.5339i	1.00673	+	0.327107i
$290$	−129.701	−	713.553i	−0.447245	−	2.46053i
$291$	57.5015	+	176.971i	0.197600	+	0.608149i
$292$	510.935	+	80.9242i	1.74978	+	0.277138i
$293$	−255.208	+	255.208i	−0.871017	+	0.871017i	−0.992583	−	0.121566i	$-0.961208\pi$
$293$	−255.208	+	255.208i	−0.871017	+	0.871017i	0.121566	+	0.992583i	$0.461208\pi$
$294$	−152.943	−	210.508i	−0.520214	−	0.716013i
$295$	−298.556	+	227.456i	−1.01205	+	0.771036i
$296$	29.7705	+	21.6295i	0.100576	+	0.0730728i
$297$	6.45386	+	40.7481i	0.0217302	+	0.137199i
$298$	−151.237	−	296.819i	−0.507506	−	0.996037i
$299$			152.578i			0.510293i
$300$	−47.4496	−	231.072i	−0.158165	−	0.770241i
$301$	−0.540595			−0.00179600
$302$	−163.908	+	83.5152i	−0.542741	+	0.276540i
$303$	−183.236	+	29.0217i	−0.604738	+	0.0957811i
$304$	125.434	−	172.645i	0.412612	−	0.567912i
$305$	9.56055	+	420.631i	0.0313461	+	1.37912i
$306$	181.958	−	132.200i	0.594634	−	0.432027i
$307$	−299.563	−	299.563i	−0.975775	−	0.975775i	0.0239382	−	0.999713i	$-0.492380\pi$
$307$	−299.563	−	299.563i	−0.975775	−	0.975775i	−0.999713	+	0.0239382i	$0.992380\pi$
$308$	2.39304	−	15.1091i	0.00776962	−	0.0490555i
$309$	157.195	−	51.0759i	0.508723	−	0.165294i
$310$	−70.9175	+	524.659i	−0.228766	+	1.69245i
$311$	−11.4518	+	35.2451i	−0.0368226	+	0.113328i	−0.967778	−	0.251804i	$-0.918976\pi$
$311$	−11.4518	+	35.2451i	−0.0368226	+	0.113328i	0.930956	+	0.365132i	$0.118976\pi$
$312$	−41.5397	+	81.5263i	−0.133140	+	0.261302i
$313$	374.766	+	190.953i	1.19734	+	0.610073i	0.934912	−	0.354880i	$-0.115478\pi$
$313$	374.766	+	190.953i	1.19734	+	0.610073i	0.262424	+	0.964953i	$0.415478\pi$
$314$	−360.446	−	117.116i	−1.14792	−	0.372981i
$315$	5.25723	+	0.710613i	0.0166896	+	0.00225592i
$316$	178.618	+	549.731i	0.565248	+	1.73966i
$317$	162.025	+	25.6622i	0.511119	+	0.0809533i	0.406667	−	0.913577i	$-0.366691\pi$
$317$	162.025	+	25.6622i	0.511119	+	0.0809533i	0.104452	+	0.994530i	$0.466691\pi$
$318$	−109.606	+	109.606i	−0.344674	+	0.344674i
$319$	−220.229	−	303.119i	−0.690373	−	0.950218i
$320$	−494.419	+	11.2377i	−1.54506	+	0.0351178i
$321$	254.731	+	185.073i	0.793554	+	0.576550i
$322$	2.18565	+	13.7996i	0.00678772	+	0.0428560i
$323$	−291.261	−	571.632i	−0.901738	−	1.76976i
$324$		−	49.0296i		−	0.151326i
$325$	−290.721	+	59.6982i	−0.894526	+	0.183687i
$326$	286.114			0.877652
$327$	−144.906	+	73.8335i	−0.443139	+	0.225790i
$328$	−206.321	+	32.6780i	−0.629027	+	0.0996280i
$329$	8.95156	−	12.3208i	0.0272084	−	0.0374491i
$330$	−128.081	−	168.118i	−0.388124	−	0.509448i
$331$	265.305	−	192.756i	0.801527	−	0.582343i	−0.109835	−	0.993950i	$-0.535032\pi$
$331$	265.305	−	192.756i	0.801527	−	0.582343i	0.911362	+	0.411607i	$0.135032\pi$
$332$	371.530	+	371.530i	1.11907	+	1.11907i
$333$	−3.88089	+	24.5030i	−0.0116543	+	0.0735825i
$334$	−695.269	+	225.907i	−2.08164	+	0.676367i
$335$	209.091	−	38.0060i	0.624151	−	0.113451i
$336$	1.53578	−	4.72666i	0.00457079	−	0.0140674i
$337$	207.965	−	408.154i	0.617107	−	1.21114i	−0.345035	−	0.938590i	$-0.612133\pi$
$337$	207.965	−	408.154i	0.617107	−	1.21114i	0.962142	−	0.272550i	$-0.0878670\pi$
$338$	−76.8697	−	39.1671i	−0.227425	−	0.115879i
$339$	−24.3043	−	7.89696i	−0.0716942	−	0.0232949i
$340$	−288.091	+	598.665i	−0.847328	+	1.76078i
$341$	84.5206	+	260.128i	0.247861	+	0.762838i
$342$	−239.559	−	37.9424i	−0.700465	−	0.110943i
$343$	−24.4768	+	24.4768i	−0.0713608	+	0.0713608i
$344$	−3.99802	−	5.50280i	−0.0116221	−	0.0159965i
$345$	91.5115	+	63.3607i	0.265251	+	0.183654i
$346$	82.2351	+	59.7473i	0.237674	+	0.172680i
$347$	60.7454	+	383.531i	0.175059	+	1.10528i	0.906137	+	0.422984i	$0.139017\pi$
$347$	60.7454	+	383.531i	0.175059	+	1.10528i	−0.731078	+	0.682293i	$0.760983\pi$
$348$	202.150	+	396.742i	0.580891	+	1.14006i
$349$		−	160.925i		−	0.461103i	−0.973060	−	0.230552i	$-0.925947\pi$
$349$		−	160.925i		−	0.461103i	0.973060	−	0.230552i	$-0.0740530\pi$
$350$	−25.4386	+	9.56382i	−0.0726817	+	0.0273252i
$351$	−61.6860			−0.175744
$352$	−302.338	+	154.049i	−0.858913	+	0.437638i
$353$	−70.5532	+	11.1745i	−0.199868	+	0.0316559i	−0.255565	−	0.966792i	$-0.582262\pi$
$353$	−70.5532	+	11.1745i	−0.199868	+	0.0316559i	0.0556979	+	0.998448i	$0.482262\pi$
$354$	234.901	−	323.313i	0.663562	−	0.913315i
$355$	−290.658	−	87.1901i	−0.818754	−	0.245606i
$356$	−756.809	+	549.854i	−2.12587	+	1.54453i
$357$	−10.5650	−	10.5650i	−0.0295940	−	0.0295940i
$358$	128.710	−	812.643i	0.359525	−	2.26995i
$359$	96.8130	−	31.4565i	0.269674	−	0.0876225i	−0.171058	−	0.985261i	$-0.554719\pi$
$359$	96.8130	−	31.4565i	0.269674	−	0.0876225i	0.440733	+	0.897638i	$0.354719\pi$
$360$	31.6469	+	58.7696i	0.0879080	+	0.163249i
$361$	−102.240	+	314.661i	−0.283212	+	0.871638i
$362$	−55.4774	+	108.881i	−0.153253	+	0.300775i
$363$	89.4491	+	45.5766i	0.246416	+	0.125555i
$364$	21.7533	+	7.06806i	0.0597617	+	0.0194177i
$365$	−343.268	−	328.011i	−0.940461	−	0.898660i
$366$	−138.436	−	426.063i	−0.378241	−	1.16411i
$367$	414.375	+	65.6306i	1.12909	+	0.178830i	0.692906	−	0.721028i	$-0.256330\pi$
$367$	414.375	+	65.6306i	1.12909	+	0.178830i	0.436183	+	0.899858i	$0.356330\pi$
$368$	73.7328	−	73.7328i	0.200361	−	0.200361i
$369$	−82.7774	−	113.933i	−0.224329	−	0.308762i
$370$	−42.0093	−	119.946i	−0.113539	−	0.324179i
$371$	8.33070	+	6.05261i	0.0224547	+	0.0163143i
$372$	−50.8492	−	321.049i	−0.136691	−	0.863035i
$373$	179.734	+	352.748i	0.481861	+	0.945705i	0.996115	+	0.0880667i	$0.0280689\pi$
$373$	179.734	+	352.748i	0.481861	+	0.945705i	−0.514254	+	0.857638i	$0.671931\pi$
$374$			595.248i			1.59157i
$375$	−84.9220	+	199.156i	−0.226459	+	0.531084i
$376$	191.617			0.509620
$377$	499.156	−	254.333i	1.32402	−	0.674623i
$378$	−5.57908	+	0.883640i	−0.0147595	+	0.00233767i
$379$	−364.178	+	501.248i	−0.960892	+	1.32255i	−0.0143757	+	0.999897i	$0.504576\pi$
$379$	−364.178	+	501.248i	−0.960892	+	1.32255i	−0.946516	+	0.322657i	$0.895424\pi$
$380$	676.189	−	236.825i	1.77944	−	0.623224i
$381$	56.9360	−	41.3665i	0.149438	−	0.108573i
$382$	−287.864	−	287.864i	−0.753570	−	0.753570i
$383$	38.3398	−	242.068i	0.100104	−	0.632031i	−0.885716	−	0.464227i	$-0.846332\pi$
$383$	38.3398	−	242.068i	0.100104	−	0.632031i	0.985820	−	0.167804i	$-0.0536677\pi$
$384$	219.204	−	71.2237i	0.570844	−	0.185478i
$385$	−9.69975	+	10.1509i	−0.0251942	+	0.0263661i
$386$	−42.6081	+	131.134i	−0.110384	+	0.339726i
$387$	2.08182	−	4.08580i	0.00537937	−	0.0105576i
$388$	521.474	+	265.704i	1.34401	+	0.684805i
$389$	21.1457	+	6.87066i	0.0543591	+	0.0176624i	0.336070	−	0.941837i	$-0.390902\pi$
$389$	21.1457	+	6.87066i	0.0543591	+	0.0176624i	−0.281711	+	0.959499i	$0.590902\pi$
$390$	278.233	−	149.826i	0.713419	−	0.384169i
$391$	−96.8717	−	298.141i	−0.247754	−	0.762508i
$392$	−214.811	−	34.0228i	−0.547988	−	0.0867928i
$393$	184.016	−	184.016i	0.468234	−	0.468234i
$394$	−310.929	−	427.957i	−0.789159	−	1.08618i
$395$	152.431	−	508.145i	0.385901	−	1.28644i
$396$	104.978	+	76.2712i	0.265097	+	0.192604i
$397$	−27.3358	−	172.591i	−0.0688559	−	0.434739i	−0.997900	−	0.0647705i	$-0.979368\pi$
$397$	−27.3358	−	172.591i	−0.0688559	−	0.434739i	0.929044	−	0.369968i	$-0.120632\pi$
$398$	−37.2654	−	73.1375i	−0.0936317	−	0.183763i
$399$			16.1126i			0.0403824i
$400$	169.339	+	111.641i	0.423348	+	0.279103i
$401$	−352.160			−0.878204			−0.439102	−	0.898437i	$-0.644703\pi$
$401$	−352.160			−0.878204			−0.439102	+	0.898437i	$0.644703\pi$
$402$	−201.618	+	102.729i	−0.501536	+	0.255545i
$403$	−403.924	+	63.9753i	−1.00229	+	0.158748i
$404$	−342.976	+	472.066i	−0.848951	+	1.16848i
$405$	−25.6163	+	36.9974i	−0.0632500	+	0.0913516i
$406$	41.5021	−	30.1530i	0.102222	−	0.0742685i
$407$	−46.4267	−	46.4267i	−0.114070	−	0.114070i
$408$	29.4085	−	185.678i	0.0720797	−	0.455093i
$409$	−454.282	+	147.605i	−1.11071	+	0.360893i	−0.806217	−	0.591620i	$-0.798489\pi$
$409$	−454.282	+	147.605i	−1.11071	+	0.360893i	−0.304498	+	0.952513i	$0.598489\pi$
$410$	650.092	+	312.839i	1.58559	+	0.763023i
$411$	−8.65092	+	26.6248i	−0.0210485	+	0.0647805i
$412$	236.013	−	463.201i	0.572846	−	1.12427i
$413$	−23.6548	−	12.0527i	−0.0572756	−	0.0291834i
$414$	−112.714	−	36.6230i	−0.272256	−	0.0884613i
$415$	−86.2426	−	474.466i	−0.207814	−	1.14329i
$416$	−156.781	−	482.522i	−0.376877	−	1.15991i
$417$	81.7172	+	12.9427i	0.195965	+	0.0310377i
$418$	453.901	−	453.901i	1.08589	−	1.08589i
$419$	362.429	+	498.840i	0.864985	+	1.19055i	0.980358	+	0.197227i	$0.0631937\pi$
$419$	362.429	+	498.840i	0.864985	+	1.19055i	−0.115373	+	0.993322i	$0.536806\pi$
$420$	13.2726	−	10.1118i	0.0316015	−	0.0240757i
$421$	374.959	+	272.424i	0.890639	+	0.647087i	0.936044	−	0.351882i	$-0.114458\pi$
$421$	374.959	+	272.424i	0.890639	+	0.647087i	−0.0454057	+	0.998969i	$0.514458\pi$
$422$	−6.33613	−	40.0047i	−0.0150145	−	0.0947980i
$423$	58.6477	+	115.103i	0.138647	+	0.272110i
$424$			129.562i			0.305571i
$425$	530.173	−	301.231i	1.24747	−	0.708778i
$426$	323.107			0.758467
$427$	−26.5168	+	13.5110i	−0.0621003	+	0.0316417i
$428$	978.134	−	154.921i	2.28536	−	0.361966i
$429$	95.9598	−	132.077i	0.223683	−	0.307873i
$430$	0.533799	+	23.4853i	0.00124139	+	0.0546170i
$431$	−19.0751	+	13.8589i	−0.0442578	+	0.0321552i	−0.609694	−	0.792637i	$-0.708708\pi$
$431$	−19.0751	+	13.8589i	−0.0442578	+	0.0321552i	0.565436	+	0.824792i	$0.308708\pi$
$432$	29.8096	+	29.8096i	0.0690038	+	0.0690038i
$433$	−17.5716	+	110.943i	−0.0405810	+	0.256218i	−0.999635	−	0.0270038i	$-0.991403\pi$
$433$	−17.5716	+	110.943i	−0.0405810	+	0.256218i	0.959054	+	0.283222i	$0.0914034\pi$
$434$	−35.6158	+	11.5723i	−0.0820640	+	0.0266642i
$435$	54.7427	−	404.995i	0.125845	−	0.931023i
$436$	−158.068	+	486.483i	−0.362541	+	1.11579i
$437$	−153.476	+	301.213i	−0.351203	+	0.689276i
$438$	450.439	+	229.510i	1.02840	+	0.523995i
$439$	519.678	+	168.854i	1.18378	+	0.384632i	0.833768	−	0.552114i	$-0.186179\pi$
$439$	519.678	+	168.854i	1.18378	+	0.384632i	0.350008	+	0.936747i	$0.386179\pi$
$440$	−175.063	−	23.6631i	−0.397871	−	0.0537797i
$441$	−45.3095	−	139.448i	−0.102743	−	0.316210i
$442$	−879.057	−	139.229i	−1.98882	−	0.314998i
$443$	−165.809	+	165.809i	−0.374287	+	0.374287i	−0.869036	−	0.494749i	$-0.835260\pi$
$443$	−165.809	+	165.809i	−0.374287	+	0.374287i	0.494749	+	0.869036i	$0.335260\pi$
$444$	45.8640	+	63.1264i	0.103297	+	0.142177i
$445$	858.362	−	19.5098i	1.92890	−	0.0438422i
$446$	−544.544	−	395.634i	−1.22095	−	0.887072i
$447$	−29.3657	−	185.408i	−0.0656951	−	0.414782i
$448$	−15.8811	−	31.1685i	−0.0354490	−	0.0695725i
$449$		−	201.205i		−	0.448119i	−0.974576	−	0.224059i	$-0.928069\pi$
$449$		−	201.205i		−	0.448119i	0.974576	−	0.224059i	$-0.0719309\pi$
$450$	25.6804	−	229.094i	0.0570675	−	0.509097i
$451$	372.715			0.826419
$452$	−71.6165	+	36.4904i	−0.158444	+	0.0807311i
$453$	−102.385	+	16.2162i	−0.226015	+	0.0357973i
$454$	271.677	−	373.931i	0.598407	−	0.823636i
$455$	−12.7220	−	16.6988i	−0.0279605	−	0.0367007i
$456$	−164.013	+	119.162i	−0.359677	+	0.261320i
$457$	449.591	+	449.591i	0.983788	+	0.983788i	0.999871	−	0.0160822i	$-0.00511934\pi$
$457$	449.591	+	449.591i	0.983788	+	0.983788i	−0.0160822	+	0.999871i	$0.505119\pi$
$458$	−178.431	+	1126.57i	−0.389587	+	2.45976i
$459$	120.536	−	39.1645i	0.262606	−	0.0853258i
$460$	344.440	−	62.6081i	0.748782	−	0.136105i
$461$	−130.749	+	402.403i	−0.283620	+	0.872892i	0.703189	+	0.711003i	$0.251759\pi$
$461$	−130.749	+	402.403i	−0.283620	+	0.872892i	−0.986809	+	0.161889i	$0.948241\pi$
$462$	6.78694	−	13.3201i	0.0146903	−	0.0288314i
$463$	−585.996	−	298.580i	−1.26565	−	0.644881i	−0.313233	−	0.949676i	$-0.601412\pi$
$463$	−585.996	−	298.580i	−1.26565	−	0.644881i	−0.952418	+	0.304795i	$0.901412\pi$
$464$	−364.122	−	118.310i	−0.784746	−	0.254979i
$465$	−129.366	+	268.828i	−0.278207	+	0.578126i
$466$	−70.4559	−	216.841i	−0.151193	−	0.465324i
$467$	−649.664	−	102.897i	−1.39114	−	0.220335i	−0.584509	−	0.811387i	$-0.698713\pi$
$467$	−649.664	−	102.897i	−1.39114	−	0.220335i	−0.806634	+	0.591052i	$0.798713\pi$
$468$	−137.191	+	137.191i	−0.293144	+	0.293144i
$469$	8.83566	+	12.1612i	0.0188394	+	0.0259302i
$470$	−544.095	−	376.721i	−1.15765	−	0.801533i
$471$	−172.778	−	125.531i	−0.366832	−	0.266519i
$472$	−52.2547	−	329.923i	−0.110709	−	0.698990i
$473$	5.50968	+	10.8134i	0.0116484	+	0.0228612i
$474$			564.875i			1.19172i
$475$	−633.981	−	174.578i	−1.33470	−	0.367533i
$476$	−46.9939			−0.0987267
$477$	−77.8267	+	39.6547i	−0.163159	+	0.0831336i
$478$	689.671	−	109.233i	1.44283	−	0.228521i
$479$	−394.709	+	543.270i	−0.824026	+	1.13418i	0.164979	+	0.986297i	$0.447244\pi$
$479$	−394.709	+	543.270i	−0.824026	+	1.13418i	−0.989006	+	0.147878i	$0.952756\pi$
$480$	−354.508	−	106.344i	−0.738559	−	0.221549i
$481$	79.4218	−	57.7033i	0.165118	−	0.119965i
$482$	−748.584	−	748.584i	−1.55308	−	1.55308i
$483$	−1.23162	+	7.77614i	−0.00254994	+	0.0160997i
$484$	300.301	−	97.5736i	0.620456	−	0.201598i
$485$	−254.680	−	472.951i	−0.525113	−	0.975156i
$486$	14.8064	−	45.5694i	0.0304658	−	0.0937642i
$487$	−47.8556	+	93.9218i	−0.0982660	+	0.192858i	−0.934906	−	0.354895i	$-0.884517\pi$
$487$	−47.8556	+	93.9218i	−0.0982660	+	0.192858i	0.836640	+	0.547753i	$0.184517\pi$
$488$	−333.638	−	169.997i	−0.683685	−	0.348355i
$489$	153.336	+	49.8218i	0.313570	+	0.101885i
$490$	543.067	+	518.929i	1.10830	+	1.05904i
$491$	52.5414	+	161.706i	0.107009	+	0.329340i	0.990197	−	0.139680i	$-0.0446073\pi$
$491$	52.5414	+	161.706i	0.107009	+	0.329340i	−0.883188	+	0.469020i	$0.844607\pi$
$492$	−437.490	−	69.2916i	−0.889207	−	0.140836i
$493$	−813.888	+	813.888i	−1.65089	+	1.65089i
$494$	564.150	+	776.486i	1.14200	+	1.57183i
$495$	−39.3669	−	112.401i	−0.0795291	−	0.227073i
$496$	226.111	+	164.280i	0.455870	+	0.331209i
$497$	−3.35778	−	21.2002i	−0.00675609	−	0.0426563i
$498$	233.112	+	457.508i	0.468096	+	0.918690i
$499$		−	290.197i		−	0.581557i	−0.956790	−	0.290779i	$-0.906086\pi$
$499$		−	290.197i		−	0.581557i	0.956790	−	0.290779i	$-0.0939143\pi$
$500$	254.060	+	631.798i	0.508120	+	1.26360i
$501$	−411.949			−0.822254
$502$	−575.455	+	293.209i	−1.14632	+	0.584081i
$503$	129.151	−	20.4555i	0.256762	−	0.0406671i	−0.0267264	−	0.999643i	$-0.508508\pi$
$503$	129.151	−	20.4555i	0.256762	−	0.0406671i	0.283488	+	0.958976i	$0.408508\pi$
$504$	−2.77516	+	3.81969i	−0.00550628	+	0.00757874i
$505$	505.446	−	177.025i	1.00088	−	0.350544i
$506$	253.754	−	184.363i	0.501490	−	0.364354i
$507$	−34.3761	−	34.3761i	−0.0678029	−	0.0678029i
$508$	34.6272	−	218.627i	0.0681637	−	0.430369i
$509$	−88.4961	+	28.7541i	−0.173863	+	0.0564914i	−0.394655	−	0.918830i	$-0.629136\pi$
$509$	−88.4961	+	28.7541i	−0.173863	+	0.0564914i	0.220792	+	0.975321i	$0.429136\pi$
$510$	−448.550	+	469.414i	−0.879510	+	0.920420i
$511$	10.3779	−	31.9399i	0.0203090	−	0.0625048i
$512$	−222.975	+	437.613i	−0.435498	+	0.854713i
$513$	−121.778	−	62.0492i	−0.237385	−	0.120954i
$514$	−751.653	−	244.227i	−1.46236	−	0.475150i
$515$	−420.100	+	226.220i	−0.815728	+	0.439262i
$516$	−4.45690	−	13.7169i	−0.00863741	−	0.0265832i
$517$	−337.682	−	53.4836i	−0.653157	−	0.103450i
$518$	6.35658	−	6.35658i	0.0122714	−	0.0122714i
$519$	33.6678	+	46.3398i	0.0648706	+	0.0892867i
$520$	75.8929	−	252.997i	0.145948	−	0.486533i
$521$	−55.2207	−	40.1202i	−0.105990	−	0.0770062i	0.533528	−	0.845782i	$-0.320866\pi$
$521$	−55.2207	−	40.1202i	−0.105990	−	0.0770062i	−0.639518	+	0.768776i	$0.720866\pi$
$522$	68.0720	+	429.789i	0.130406	+	0.823351i
$523$	390.574	+	766.544i	0.746795	+	1.46567i	0.880199	+	0.474605i	$0.157409\pi$
$523$	390.574	+	766.544i	0.746795	+	1.46567i	−0.133404	+	0.991062i	$0.542591\pi$
$524$		−	818.513i		−	1.56205i
$525$	−15.2985	+	0.695801i	−0.0291400	+	0.00132534i
$526$	238.015			0.452499
$527$	748.660	−	381.461i	1.42061	−	0.723835i
$528$	−110.199	+	17.4537i	−0.208709	+	0.0330563i
$529$	213.845	−	294.332i	0.404243	−	0.556393i
$530$	254.720	−	367.891i	0.480604	−	0.694134i
$531$	182.188	−	132.368i	0.343104	−	0.249280i
$532$	35.8348	+	35.8348i	0.0673587	+	0.0673587i
$533$	−87.1784	+	550.423i	−0.163562	+	1.03269i
$534$	−869.448	+	282.501i	−1.62818	+	0.529028i
$535$	−819.035	−	394.139i	−1.53091	−	0.736708i
$536$	−58.4463	+	179.879i	−0.109042	+	0.335595i
$537$	210.486	−	413.102i	0.391967	−	0.769278i
$538$	−874.136	−	445.395i	−1.62479	−	0.827871i
$539$	369.061	+	119.915i	0.684713	+	0.222477i
$540$	25.3120	+	139.254i	0.0468740	+	0.257879i
$541$	−6.85938	−	21.1110i	−0.0126791	−	0.0390222i	0.944517	−	0.328463i	$-0.106531\pi$
$541$	−6.85938	−	21.1110i	−0.0126791	−	0.0390222i	−0.957196	+	0.289441i	$0.906531\pi$
$542$	1076.40	+	170.485i	1.98598	+	0.314548i
$543$	−48.6913	+	48.6913i	−0.0896710	+	0.0896710i
$544$	612.707	+	843.319i	1.12630	+	1.55022i
$545$	373.448	−	284.512i	0.685225	−	0.522041i
$546$	18.0836	+	13.1385i	0.0331201	+	0.0240632i
$547$	67.8821	+	428.590i	0.124099	+	0.783529i	0.968718	+	0.248162i	$0.0798266\pi$
$547$	67.8821	+	428.590i	0.124099	+	0.783529i	−0.844620	+	0.535367i	$0.820173\pi$
$548$	39.9744	+	78.4541i	0.0729459	+	0.143164i
$549$		−	252.444i		−	0.459825i
$550$	450.569	+	411.367i	0.819217	+	0.747940i
$551$	1241.25			2.25272
$552$	−88.2631	+	44.9723i	−0.159897	+	0.0814715i
$553$	37.0634	−	5.87027i	0.0670225	−	0.0106153i
$554$	598.801	−	824.179i	1.08087	−	1.48769i
$555$	−1.62734	−	71.5972i	−0.00293214	−	0.129004i
$556$	210.526	−	152.956i	0.378644	−	0.275101i
$557$	−161.067	−	161.067i	−0.289169	−	0.289169i	0.547583	−	0.836752i	$-0.315548\pi$
$557$	−161.067	−	161.067i	−0.289169	−	0.289169i	−0.836752	+	0.547583i	$0.815548\pi$
$558$	49.6927	−	313.747i	0.0890550	−	0.562271i
$559$	−17.2578	+	5.60740i	−0.0308727	+	0.0100311i
$560$	−1.92177	+	14.2176i	−0.00343174	+	0.0253885i
$561$	−103.652	+	319.007i	−0.184763	+	0.568641i
$562$	−150.627	+	295.623i	−0.268020	+	0.526019i
$563$	−169.572	−	86.4014i	−0.301194	−	0.153466i	0.296862	−	0.954920i	$-0.404060\pi$
$563$	−169.572	−	86.4014i	−0.301194	−	0.153466i	−0.598056	+	0.801454i	$0.704060\pi$
$564$	386.425	+	125.557i	0.685151	+	0.222619i
$565$	73.1064	+	9.88170i	0.129392	+	0.0174897i
$566$	−126.960	−	390.743i	−0.224311	−	0.690358i
$567$	−3.14384	−	0.497935i	−0.00554468	−	0.000878192i
$568$	190.967	−	190.967i	0.336210	−	0.336210i
$569$	−249.297	−	343.128i	−0.438132	−	0.603036i	0.531664	−	0.846955i	$-0.321567\pi$
$569$	−249.297	−	343.128i	−0.438132	−	0.603036i	−0.969796	+	0.243919i	$0.921567\pi$
$570$	699.986	−	15.9100i	1.22805	−	0.0279123i
$571$	−148.638	−	107.992i	−0.260312	−	0.189128i	0.449972	−	0.893042i	$-0.351434\pi$
$571$	−148.638	−	107.992i	−0.260312	−	0.189128i	−0.710285	+	0.703914i	$0.751434\pi$
$572$	−80.3264	−	507.161i	−0.140431	−	0.886645i
$573$	−104.147	−	204.400i	−0.181757	−	0.356718i
$574$			51.0308i			0.0889039i
$575$	−292.623	−	132.714i	−0.508909	−	0.230807i
$576$	296.728			0.515153
$577$	675.710	−	344.292i	1.17108	−	0.596693i	0.243343	−	0.969940i	$-0.421756\pi$
$577$	675.710	−	344.292i	1.17108	−	0.596693i	0.927732	+	0.373248i	$0.121756\pi$
$578$	928.728	−	147.096i	1.60680	−	0.254492i
$579$	−45.6694	+	62.8586i	−0.0788764	+	0.108564i
$580$	−778.971	−	1022.47i	−1.34305	−	1.76288i
$581$	27.5961	−	20.0498i	0.0474977	−	0.0345091i
$582$	404.432	+	404.432i	0.694900	+	0.694900i
$583$	36.1630	−	228.324i	0.0620292	−	0.391637i
$584$	401.872	−	130.576i	0.688137	−	0.223589i
$585$	175.201	−	31.8460i	0.299490	−	0.0544376i
$586$	−342.811	+	1055.07i	−0.585002	+	1.80045i
$587$	−123.904	+	243.176i	−0.211081	+	0.414269i	−0.972136	−	0.234418i	$-0.924682\pi$
$587$	−123.904	+	243.176i	−0.211081	+	0.414269i	0.761055	+	0.648687i	$0.224682\pi$
$588$	−410.907	−	209.367i	−0.698821	−	0.356067i
$589$	−861.765	−	280.004i	−1.46310	−	0.475389i
$590$	−500.255	+	1039.55i	−0.847890	+	1.76195i
$591$	−92.1131	−	283.495i	−0.155860	−	0.479687i
$592$	−66.2655	−	10.4954i	−0.111935	−	0.0177287i
$593$	367.718	−	367.718i	0.620098	−	0.620098i	−0.325458	−	0.945556i	$-0.605519\pi$
$593$	367.718	−	367.718i	0.620098	−	0.620098i	0.945556	+	0.325458i	$0.105519\pi$
$594$	74.5366	+	102.591i	0.125482	+	0.172712i
$595$	35.4613	+	24.5527i	0.0595988	+	0.0412650i
$596$	−477.662	−	347.042i	−0.801446	−	0.582284i
$597$	−7.23584	−	45.6853i	−0.0121203	−	0.0765247i
$598$	212.913	+	417.865i	0.356041	+	0.698770i
$599$		−	654.311i		−	1.09234i	−0.837675	−	0.546170i	$-0.816085\pi$
$599$		−	654.311i		−	1.09234i	0.837675	−	0.546170i	$-0.183915\pi$
$600$	−120.224	−	150.580i	−0.200374	−	0.250967i
$601$	−233.449			−0.388434			−0.194217	−	0.980959i	$-0.562217\pi$
$601$	−233.449			−0.388434			−0.194217	+	0.980959i	$0.562217\pi$
$602$	−1.48053	+	0.754367i	−0.00245935	+	0.00125310i
$603$	−125.940	+	19.9470i	−0.208856	+	0.0330795i
$604$	−191.641	+	263.772i	−0.317287	+	0.436708i
$605$	−277.584	−	83.2683i	−0.458816	−	0.137634i
$606$	−461.330	+	335.176i	−0.761270	+	0.553095i
$607$	581.645	+	581.645i	0.958229	+	0.958229i	0.999162	−	0.0409329i	$-0.0130330\pi$
$607$	581.645	+	581.645i	0.958229	+	0.958229i	−0.0409329	+	0.999162i	$0.513033\pi$
$608$	175.851	−	1110.28i	0.289229	−	1.82612i
$609$	27.4926	−	8.93287i	0.0451438	−	0.0146681i
$610$	613.148	+	1138.64i	1.00516	+	1.86663i
$611$	157.968	−	486.176i	0.258541	−	0.795706i
$612$	180.972	−	355.178i	0.295706	−	0.580357i
$613$	−636.056	−	324.087i	−1.03761	−	0.528689i	−0.149713	−	0.988729i	$-0.547835\pi$
$613$	−636.056	−	324.087i	−1.03761	−	0.528689i	−0.887898	+	0.460040i	$0.847835\pi$
$614$	−1238.44	−	402.392i	−2.01700	−	0.655361i
$615$	293.924	+	280.860i	0.477926	+	0.456683i
$616$	−3.86133	−	11.8839i	−0.00626838	−	0.0192921i
$617$	−261.364	−	41.3960i	−0.423605	−	0.0670924i	−0.0590070	−	0.998258i	$-0.518793\pi$
$617$	−261.364	−	41.3960i	−0.423605	−	0.0670924i	−0.364598	+	0.931165i	$0.618793\pi$
$618$	359.238	−	359.238i	0.581291	−	0.581291i
$619$	−159.169	−	219.077i	−0.257138	−	0.353921i	0.660857	−	0.750512i	$-0.270193\pi$
$619$	−159.169	−	219.077i	−0.257138	−	0.353921i	−0.917995	+	0.396591i	$0.870193\pi$
$620$	310.167	+	885.596i	0.500269	+	1.42838i
$621$	−54.0288	−	39.2543i	−0.0870030	−	0.0632114i
$622$	17.8192	+	112.506i	0.0286482	+	0.180878i
$623$	27.5713	+	54.1117i	0.0442557	+	0.0868566i
$624$		−	166.823i		−	0.267344i
$625$	138.380	−	609.488i	0.221409	−	0.975181i
$626$	1292.84			2.06523
$627$	322.295	−	164.218i	0.514028	−	0.261910i
$628$	−663.446	+	105.080i	−1.05644	+	0.167324i
$629$	−118.556	+	163.179i	−0.188484	+	0.259426i
$630$	15.3896	−	5.38998i	0.0244279	−	0.00855553i
$631$	−777.204	+	564.672i	−1.23170	+	0.894884i	−0.997017	−	0.0771869i	$-0.975406\pi$
$631$	−777.204	+	564.672i	−1.23170	+	0.894884i	−0.234686	+	0.972071i	$0.575406\pi$
$632$	333.860	+	333.860i	0.528260	+	0.528260i
$633$	3.57043	−	22.5428i	0.00564049	−	0.0356127i
$634$	479.547	−	155.814i	0.756384	−	0.245764i
$635$	−140.355	+	146.883i	−0.221031	+	0.231312i
$636$	−84.8956	+	261.282i	−0.133484	+	0.410821i
$637$	−263.413	+	516.978i	−0.413522	+	0.811582i
$638$	−1026.13	−	522.837i	−1.60835	−	0.819494i
$639$	173.161	+	56.2634i	0.270987	+	0.0880491i
$640$	−585.816	+	315.457i	−0.915338	+	0.492901i
$641$	252.698	+	777.724i	0.394224	+	1.21330i	0.929564	+	0.368661i	$0.120184\pi$
$641$	252.698	+	777.724i	0.394224	+	1.21330i	−0.535340	+	0.844637i	$0.679816\pi$
$642$	955.889	+	151.398i	1.48892	+	0.235822i
$643$	865.400	−	865.400i	1.34588	−	1.34588i	0.455794	−	0.890085i	$-0.349356\pi$
$643$	865.400	−	865.400i	1.34588	−	1.34588i	0.890085	−	0.455794i	$-0.150644\pi$
$644$	14.5552	+	20.0335i	0.0226012	+	0.0311079i
$645$	−3.80347	+	12.6793i	−0.00589686	+	0.0196578i
$646$	−1595.35	−	1159.09i	−2.46959	−	1.79426i
$647$	26.7458	+	168.866i	0.0413381	+	0.260999i	0.999698	−	0.0245637i	$-0.00781966\pi$
$647$	26.7458	+	168.866i	0.0413381	+	0.260999i	−0.958360	+	0.285562i	$0.907820\pi$
$648$	−18.1820	−	35.6841i	−0.0280586	−	0.0550681i
$649$			596.001i			0.918338i
$650$	−712.893	+	569.178i	−1.09676	+	0.875659i
$651$	−21.1025			−0.0324155
$652$	451.827	−	230.218i	0.692987	−	0.353094i
$653$	774.910	−	122.734i	1.18669	−	0.187954i	0.468286	−	0.883577i	$-0.344872\pi$
$653$	774.910	−	122.734i	1.18669	−	0.187954i	0.718407	+	0.695623i	$0.244872\pi$
$654$	−293.825	+	404.416i	−0.449274	+	0.618373i
$655$	−427.645	+	617.645i	−0.652893	+	0.942969i
$656$	308.119	−	223.862i	0.469694	−	0.341253i
$657$	201.436	+	201.436i	0.306599	+	0.306599i
$658$	7.32278	−	46.2342i	0.0111289	−	0.0702648i
$659$	259.236	−	84.2308i	0.393377	−	0.127816i	−0.105648	−	0.994404i	$-0.533692\pi$
$659$	259.236	−	84.2308i	0.393377	−	0.127816i	0.499025	+	0.866588i	$0.333692\pi$
$660$	−337.537	−	162.430i	−0.511419	−	0.246107i
$661$	212.501	−	654.010i	0.321484	−	0.989426i	−0.651519	−	0.758632i	$-0.725868\pi$
$661$	212.501	−	654.010i	0.321484	−	0.989426i	0.973003	−	0.230793i	$-0.0741321\pi$
$662$	457.613	−	898.117i	0.691259	−	1.35667i
$663$	−446.864	−	227.688i	−0.674002	−	0.343421i
$664$	408.179	+	132.625i	0.614728	+	0.199737i
$665$	−8.31828	−	45.7632i	−0.0125087	−	0.0688168i
$666$	23.5638	+	72.5218i	0.0353810	+	0.108892i
$667$	599.041	+	94.8788i	0.898113	+	0.142247i
$668$	−916.186	+	916.186i	−1.37154	+	1.37154i
$669$	−222.941	−	306.853i	−0.333246	−	0.458673i
$670$	519.602	−	395.860i	0.775525	−	0.590836i
$671$	540.513	+	392.706i	0.805534	+	0.585255i
$672$	−4.09540	−	25.8573i	−0.00609435	−	0.0384782i
$673$	34.3821	+	67.4786i	0.0510878	+	0.100265i	0.915139	−	0.403139i	$-0.132081\pi$
$673$	34.3821	+	67.4786i	0.0510878	+	0.100265i	−0.864051	+	0.503404i	$0.832081\pi$
$674$		−	1408.01i		−	2.08904i
$675$	53.6554	−	118.305i	0.0794894	−	0.175267i
$676$	−152.907			−0.226193
$677$	−753.672	+	384.015i	−1.11325	+	0.567230i	−0.911125	−	0.412129i	$-0.864785\pi$
$677$	−753.672	+	384.015i	−1.11325	+	0.567230i	−0.202127	+	0.979359i	$0.564785\pi$
$678$	−77.5820	+	12.2878i	−0.114428	+	0.0181236i
$679$	22.3333	−	30.7391i	0.0328914	−	0.0452711i
$680$	12.3316	+	542.547i	0.0181347	+	0.797864i
$681$	210.712	−	153.091i	0.309415	−	0.224803i
$682$	594.469	+	594.469i	0.871655	+	0.871655i
$683$	−174.888	+	1104.20i	−0.256059	+	1.61669i	0.439513	+	0.898236i	$0.355151\pi$
$683$	−174.888	+	1104.20i	−0.256059	+	1.61669i	−0.695572	+	0.718457i	$0.744849\pi$
$684$	−408.837	+	132.839i	−0.597715	+	0.194209i
$685$	10.8252	−	80.0862i	0.0158031	−	0.116914i
$686$	−32.8787	+	101.190i	−0.0479282	+	0.147508i
$687$	−291.798	+	572.685i	−0.424742	+	0.833602i
$688$	11.0496	+	5.63004i	0.0160604	+	0.00818319i
$689$	328.729	+	106.811i	0.477110	+	0.155022i
$690$	339.038	+	45.8274i	0.491360	+	0.0664165i
$691$	−326.956	−	1006.27i	−0.473163	−	1.45625i	−0.848419	−	0.529325i	$-0.822445\pi$
$691$	−326.956	−	1006.27i	−0.473163	−	1.45625i	0.375257	−	0.926921i	$-0.377555\pi$
$692$	177.939	+	28.1828i	0.257137	+	0.0407266i
$693$	5.95674	−	5.95674i	0.00859559	−	0.00859559i
$694$	701.558	+	965.611i	1.01089	+	1.39137i
$695$	−238.776	+	5.42716i	−0.343563	+	0.00780886i
$696$	294.253	+	213.787i	0.422777	+	0.307165i
$697$	−179.115	−	1130.89i	−0.256980	−	1.62251i
$698$	−224.561	−	440.725i	−0.321720	−	0.631412i
$699$		−	128.479i		−	0.183804i
$700$	−32.4768	+	35.5718i	−0.0463955	+	0.0508168i
$701$	−406.455			−0.579822			−0.289911	−	0.957054i	$-0.593626\pi$
$701$	−406.455			−0.579822			−0.289911	+	0.957054i	$0.593626\pi$
$702$	−168.940	+	86.0790i	−0.240655	+	0.122620i
$703$	214.835	−	34.0265i	0.305597	−	0.0484018i
$704$	−461.595	+	635.331i	−0.655675	+	0.902459i
$705$	−225.995	−	296.638i	−0.320560	−	0.420763i
$706$	−177.631	+	129.056i	−0.251602	+	0.182799i
$707$	26.7863	+	26.7863i	0.0378872	+	0.0378872i
$708$	110.803	−	699.581i	0.156501	−	0.988109i
$709$	767.230	−	249.288i	1.08213	−	0.351605i	0.286929	−	0.957952i	$-0.407365\pi$
$709$	767.230	−	249.288i	1.08213	−	0.351605i	0.795201	+	0.606346i	$0.207365\pi$
$710$	−917.693	+	166.807i	−1.29252	+	0.234939i
$711$	−98.3631	+	302.730i	−0.138345	+	0.425781i
$712$	−346.905	+	680.840i	−0.487227	+	0.956236i
$713$	−394.496	−	201.006i	−0.553290	−	0.281915i
$714$	−43.6774	−	14.1916i	−0.0611728	−	0.0198762i
$715$	−204.360	+	424.668i	−0.285818	+	0.593941i
$716$	−450.624	−	1386.88i	−0.629363	−	1.93698i
$717$	388.632	+	61.5533i	0.542025	+	0.0858484i
$718$	221.246	−	221.246i	0.308143	−	0.308143i
$719$	189.988	+	261.496i	0.264239	+	0.363694i	0.920434	−	0.390897i	$-0.127835\pi$
$719$	189.988	+	261.496i	0.264239	+	0.363694i	−0.656195	+	0.754591i	$0.727835\pi$
$720$	−100.055	−	69.2762i	−0.138966	−	0.0962170i
$721$	−27.3041	−	19.8376i	−0.0378698	−	0.0275140i
$722$	159.086	+	1004.43i	0.220341	+	1.39118i
$723$	−270.832	−	531.537i	−0.374594	−	0.735182i
$724$			216.582i			0.299146i
$725$	53.6016	+	1178.53i	0.0739333	+	1.62556i
$726$	308.574			0.425033
$727$	596.408	−	303.885i	0.820369	−	0.417999i	0.00716266	−	0.999974i	$-0.497720\pi$
$727$	596.408	−	303.885i	0.820369	−	0.417999i	0.813206	+	0.581975i	$0.197720\pi$
$728$	18.4533	−	2.92271i	0.0253479	−	0.00401471i
$729$	15.8702	−	21.8435i	0.0217698	−	0.0299636i
$730$	−1397.83	−	419.314i	−1.91483	−	0.574402i
$731$	30.1620	−	21.9140i	0.0412613	−	0.0299781i
$732$	−561.442	−	561.442i	−0.766997	−	0.766997i
$733$	−126.562	+	799.081i	−0.172663	+	1.09015i	0.737332	+	0.675531i	$0.236086\pi$
$733$	−126.562	+	799.081i	−0.172663	+	1.09015i	−0.909995	+	0.414620i	$0.863914\pi$
$734$	1226.43	−	398.492i	1.67089	−	0.542905i
$735$	200.680	+	372.672i	0.273034	+	0.507036i
$736$	169.736	−	522.394i	0.230620	−	0.709775i
$737$	153.206	−	300.683i	0.207878	−	0.407983i
$738$	−385.689	−	196.518i	−0.522614	−	0.266285i
$739$	225.122	+	73.1467i	0.304631	+	0.0989806i	0.457344	−	0.889290i	$-0.348801\pi$
$739$	225.122	+	73.1467i	0.304631	+	0.0989806i	−0.152713	+	0.988271i	$0.548801\pi$
$740$	−162.853	−	155.615i	−0.220072	−	0.210290i
$741$	167.130	+	514.374i	0.225547	+	0.694162i
$742$	31.2614	+	4.95131i	0.0421312	+	0.00667293i
$743$	820.748	−	820.748i	1.10464	−	1.10464i	0.110797	−	0.993843i	$-0.464660\pi$
$743$	820.748	−	820.748i	1.10464	−	1.10464i	0.993843	−	0.110797i	$-0.0353404\pi$
$744$	−156.065	−	214.805i	−0.209765	−	0.288717i
$745$	179.123	+	511.437i	0.240434	+	0.686493i
$746$	984.475	+	715.263i	1.31967	+	0.958798i
$747$	45.2634	+	285.782i	0.0605935	+	0.382573i
$748$	478.957	+	940.005i	0.640316	+	1.25669i
$749$		−	64.2925i		−	0.0858378i
$750$	45.3342	+	663.933i	0.0604456	+	0.885244i
$751$	622.914			0.829446			0.414723	−	0.909948i	$-0.363878\pi$
$751$	622.914			0.829446			0.414723	+	0.909948i	$0.363878\pi$
$752$	−311.282	+	158.606i	−0.413938	+	0.210912i
$753$	−359.457	+	56.9324i	−0.477367	+	0.0756075i
$754$	1012.13	−	1393.08i	1.34235	−	1.84759i
$755$	282.423	−	98.9145i	0.374070	−	0.131013i
$756$	−8.09939	+	5.88455i	−0.0107135	+	0.00778380i
$757$	−588.326	−	588.326i	−0.777180	−	0.777180i	0.202170	−	0.979350i	$-0.435201\pi$
$757$	−588.326	−	588.326i	−0.777180	−	0.777180i	−0.979350	+	0.202170i	$0.935201\pi$
$758$	−297.914	+	1880.96i	−0.393027	+	2.48147i
$759$	168.096	−	54.6178i	0.221471	−	0.0719602i
$760$	404.312	−	423.119i	0.531989	−	0.556735i
$761$	−383.044	+	1178.89i	−0.503343	+	1.54913i	0.300194	+	0.953878i	$0.402948\pi$
$761$	−383.044	+	1178.89i	−0.503343	+	1.54913i	−0.803538	+	0.595254i	$0.797052\pi$
$762$	98.2065	−	192.741i	0.128880	−	0.252941i
$763$	29.5886	+	15.0761i	0.0387793	+	0.0197590i
$764$	−686.215	−	222.965i	−0.898187	−	0.291839i
$765$	−322.129	+	173.463i	−0.421083	+	0.226750i
$766$	−232.789	−	716.452i	−0.303903	−	0.935316i
$767$	−880.170	−	139.405i	−1.14755	−	0.181754i
$768$	16.3914	−	16.3914i	0.0213430	−	0.0213430i
$769$	48.2171	+	66.3651i	0.0627010	+	0.0863006i	0.839216	−	0.543798i	$-0.183014\pi$
$769$	48.2171	+	66.3651i	0.0627010	+	0.0863006i	−0.776515	+	0.630099i	$0.783014\pi$
$770$	−12.3997	+	41.3358i	−0.0161035	+	0.0536828i
$771$	−360.301	−	261.774i	−0.467317	−	0.339525i
$772$	38.2291	+	241.369i	0.0495196	+	0.312654i
$773$	340.665	+	668.593i	0.440705	+	0.864933i	0.999368	+	0.0355381i	$0.0113145\pi$
$773$	340.665	+	668.593i	0.440705	+	0.864933i	−0.558663	+	0.829395i	$0.688686\pi$
$774$		−	14.0948i		−	0.0182104i
$775$	228.643	−	830.317i	0.295023	−	1.07138i
$776$	478.066			0.616064
$777$	4.51353	−	2.29976i	0.00580892	−	0.00295979i
$778$	67.4993	−	10.6908i	0.0867601	−	0.0137414i
$779$	−725.768	+	998.934i	−0.931666	+	1.28233i
$780$	318.826	−	460.479i	0.408752	−	0.590358i
$781$	−389.839	+	283.234i	−0.499153	+	0.362656i
$782$	−681.339	−	681.339i	−0.871278	−	0.871278i
$783$	−38.3588	+	242.188i	−0.0489895	+	0.309308i
$784$	377.122	−	122.534i	0.481023	−	0.156294i
$785$	555.533	+	267.335i	0.707685	+	0.340555i
$786$	247.182	−	760.748i	0.314481	−	0.967873i
$787$	−229.977	+	451.355i	−0.292219	+	0.573513i	−0.989711	−	0.143080i	$-0.954299\pi$
$787$	−229.977	+	451.355i	−0.292219	+	0.573513i	0.697492	+	0.716593i	$0.254299\pi$
$788$	−835.363	−	425.638i	−1.06010	−	0.540150i
$789$	127.558	+	41.4460i	0.161670	+	0.0525298i
$790$	−291.622	−	1604.37i	−0.369142	−	2.03084i
$791$	1.61249	+	4.96273i	0.00203854	+	0.00627399i
$792$	104.688	+	16.5810i	0.132182	+	0.0209356i
$793$	−706.372	+	706.372i	−0.890759	+	0.890759i
$794$	−315.705	−	434.531i	−0.397613	−	0.547268i
$795$	200.572	−	152.807i	0.252292	−	0.192210i
$796$	−117.698	−	85.5126i	−0.147862	−	0.107428i
$797$	−171.689	−	1084.00i	−0.215419	−	1.36010i	−0.823990	−	0.566605i	$-0.808257\pi$
$797$	−171.689	−	1084.00i	−0.215419	−	1.36010i	0.608570	−	0.793500i	$-0.291743\pi$
$798$	22.4841	+	44.1276i	0.0281756	+	0.0552977i
$799$			1050.29i			1.31451i
$800$	1061.78	+	119.021i	1.32722	+	0.148776i
$801$	−515.150			−0.643134
$802$	−964.461	+	491.417i	−1.20257	+	0.612740i
$803$	−744.656	+	117.942i	−0.927342	+	0.146877i
$804$	−235.732	+	324.457i	−0.293199	+	0.403553i
$805$	−0.516444	−	22.7217i	−0.000641545	−	0.0282257i
$806$	−1016.95	+	738.860i	−1.26173	+	0.916700i
$807$	−390.913	−	390.913i	−0.484403	−	0.484403i
$808$	−74.5613	+	470.761i	−0.0922788	+	0.582626i
$809$	−67.5579	+	21.9509i	−0.0835079	+	0.0271334i	−0.350473	−	0.936573i	$-0.613979\pi$
$809$	−67.5579	+	21.9509i	−0.0835079	+	0.0271334i	0.266965	+	0.963706i	$0.413979\pi$
$810$	−18.5277	+	137.071i	−0.0228737	+	0.169223i
$811$	−19.2331	+	59.1935i	−0.0237153	+	0.0729882i	−0.962214	−	0.272295i	$-0.912217\pi$
$811$	−19.2331	+	59.1935i	−0.0237153	+	0.0729882i	0.938498	+	0.345284i	$0.112217\pi$
$812$	41.2772	−	81.0111i	0.0508340	−	0.0997674i
$813$	547.181	+	278.803i	0.673039	+	0.342931i
$814$	−191.934	−	62.3633i	−0.235792	−	0.0766133i
$815$	−461.227	−	62.3434i	−0.565922	−	0.0764950i
$816$	105.916	+	325.976i	0.129799	+	0.399480i
$817$	−39.7102	−	6.28947i	−0.0486049	−	0.00769825i
$818$	−1038.17	+	1038.17i	−1.26916	+	1.26916i
$819$	7.40359	+	10.1902i	0.00903979	+	0.0124422i
$820$	1278.34	−	29.0554i	1.55895	−	0.0354334i
$821$	−292.676	−	212.641i	−0.356487	−	0.259003i	0.395099	−	0.918639i	$-0.370710\pi$
$821$	−292.676	−	212.641i	−0.356487	−	0.259003i	−0.751585	+	0.659636i	$0.770710\pi$
$822$	13.4610	+	84.9892i	0.0163759	+	0.103393i
$823$	−5.03504	−	9.88181i	−0.00611791	−	0.0120071i	0.887927	−	0.459984i	$-0.152145\pi$
$823$	−5.03504	−	9.88181i	−0.00611791	−	0.0120071i	−0.894045	+	0.447977i	$0.852145\pi$
$824$		−	424.643i		−	0.515344i
$825$	169.839	+	298.920i	0.205865	+	0.362328i
$826$	−81.6024			−0.0987923
$827$	−1390.02	+	708.250i	−1.68080	+	0.856408i	−0.689571	+	0.724218i	$0.742201\pi$
$827$	−1390.02	+	708.250i	−1.68080	+	0.856408i	−0.991224	+	0.132191i	$0.957799\pi$
$828$	−207.464	+	32.8591i	−0.250560	+	0.0396849i
$829$	−5.75207	+	7.91705i	−0.00693857	+	0.00955012i	−0.812472	−	0.583000i	$-0.801879\pi$
$829$	−5.75207	+	7.91705i	−0.00693857	+	0.00955012i	0.805534	+	0.592550i	$0.201879\pi$
$830$	−898.280	−	1179.07i	−1.08227	−	1.42057i
$831$	464.428	−	337.427i	0.558878	−	0.406049i
$832$	−830.285	−	830.285i	−0.997939	−	0.997939i
$833$	186.486	−	1177.43i	0.223873	−	1.41348i
$834$	241.860	−	78.5850i	0.290000	−	0.0942266i
$835$	1170.02	−	212.673i	1.40123	−	0.254698i
$836$	351.569	−	1082.02i	0.420537	−	1.29428i
$837$	81.2650	−	159.492i	0.0970908	−	0.190552i
$838$	1688.68	+	860.428i	2.01514	+	1.02676i
$839$	576.373	+	187.275i	0.686976	+	0.223212i	0.631647	−	0.775256i	$-0.282379\pi$
$839$	576.373	+	187.275i	0.686976	+	0.223212i	0.0553292	+	0.998468i	$0.482379\pi$
$840$	5.91011	−	12.2814i	0.00703584	−	0.0146207i
$841$	−428.268	−	1318.07i	−0.509237	−	1.56727i
$842$	1407.05	+	222.855i	1.67108	+	0.264673i
$843$	−132.202	+	132.202i	−0.156823	+	0.156823i
$844$	−42.1951	−	58.0766i	−0.0499942	−	0.0688111i
$845$	115.382	+	79.8884i	0.136547	+	0.0945425i
$846$	321.237	+	233.392i	0.379713	+	0.275877i
$847$	−3.20674	−	20.2466i	−0.00378600	−	0.0239039i
$848$	−107.242	−	210.474i	−0.126464	−	0.248200i
$849$		−	231.516i		−	0.272693i
$850$	1031.64	−	1564.80i	1.21369	−	1.84095i
$851$	106.283			0.124892
$852$	510.245	−	259.983i	0.598880	−	0.305144i
$853$	555.263	−	87.9451i	0.650953	−	0.103101i	0.177780	−	0.984070i	$-0.443108\pi$
$853$	555.263	−	87.9451i	0.650953	−	0.103101i	0.473173	+	0.880969i	$0.343108\pi$
$854$	−53.7679	+	74.0052i	−0.0629601	+	0.0866571i
$855$	377.910	+	113.364i	0.442000	+	0.132589i
$856$	654.443	−	475.481i	0.764537	−	0.555468i
$857$	1005.55	+	1005.55i	1.17333	+	1.17333i	0.981410	+	0.191924i	$0.0614726\pi$
$857$	1005.55	+	1005.55i	1.17333	+	1.17333i	0.191924	+	0.981410i	$0.438527\pi$
$858$	78.4995	−	495.626i	0.0914913	−	0.577653i
$859$	1176.31	−	382.208i	1.36940	−	0.444945i	0.470229	−	0.882544i	$-0.344171\pi$
$859$	1176.31	−	382.208i	1.36940	−	0.444945i	0.899170	+	0.437600i	$0.144171\pi$
$860$	19.7400	+	36.6581i	0.0229535	+	0.0426257i
$861$	−8.88612	+	27.3487i	−0.0103207	+	0.0317638i
$862$	−32.9018	+	64.5735i	−0.0381692	+	0.0749112i
$863$	728.140	+	371.006i	0.843731	+	0.429902i	0.821745	−	0.569856i	$-0.193001\pi$
$863$	728.140	+	371.006i	0.843731	+	0.429902i	0.0219863	+	0.999758i	$0.493001\pi$
$864$	211.200	+	68.6231i	0.244445	+	0.0794249i
$865$	−119.547	−	114.234i	−0.138205	−	0.132062i
$866$	106.690	+	328.359i	0.123199	+	0.379167i
$867$	523.342	+	82.8892i	0.603624	+	0.0956047i
$868$	−46.9324	+	46.9324i	−0.0540696	+	0.0540696i
$869$	−495.168	−	681.540i	−0.569813	−	0.784281i
$870$	−415.222	−	1185.55i	−0.477266	−	1.36270i
$871$	408.212	+	296.583i	0.468670	+	0.340509i
$872$	65.3627	+	412.684i	0.0749572	+	0.473261i
$873$	146.320	+	287.170i	0.167606	+	0.328946i
$874$			1039.10i			1.18890i
$875$	43.0918	−	9.87423i	0.0492478	−	0.0112848i
$876$	895.997			1.02283
$877$	−760.694	+	387.593i	−0.867382	+	0.441953i	−0.830272	−	0.557358i	$-0.811815\pi$
$877$	−760.694	+	387.593i	−0.867382	+	0.441953i	−0.0371096	+	0.999311i	$0.511815\pi$
$878$	1658.87	−	262.739i	1.88937	−	0.299247i
$879$	−367.442	+	505.740i	−0.418022	+	0.575359i
$880$	303.977	−	106.463i	0.345428	−	0.120981i
$881$	425.461	−	309.115i	0.482929	−	0.350869i	−0.319529	−	0.947576i	$-0.603525\pi$
$881$	425.461	−	309.115i	0.482929	−	0.350869i	0.802459	+	0.596708i	$0.203525\pi$
$882$	−318.681	−	318.681i	−0.361316	−	0.361316i
$883$	155.162	−	979.657i	0.175722	−	1.10946i	−0.729330	−	0.684163i	$-0.760168\pi$
$883$	155.162	−	979.657i	0.175722	−	1.10946i	0.905051	−	0.425302i	$-0.139832\pi$
$884$	−1500.22	+	487.451i	−1.69708	+	0.551416i
$885$	−449.118	+	470.009i	−0.507478	+	0.531083i
$886$	−222.725	+	685.477i	−0.251383	+	0.773676i
$887$	356.099	−	698.883i	0.401464	−	0.787918i	−0.598448	−	0.801162i	$-0.704216\pi$
$887$	356.099	−	698.883i	0.401464	−	0.787918i	0.999912	+	0.0132438i	$0.00421577\pi$
$888$	56.7898	+	28.9358i	0.0639525	+	0.0325854i
$889$	−13.6670	−	4.44067i	−0.0153734	−	0.00499513i
$890$	2323.57	−	1251.22i	2.61076	−	1.40587i
$891$	22.0816	+	67.9601i	0.0247829	+	0.0762740i
$892$	−1178.28	−	186.621i	−1.32094	−	0.209216i
$893$	800.894	−	800.894i	0.896858	−	0.896858i
$894$	−339.149	−	466.798i	−0.379361	−	0.522146i
$895$	−384.557	+	1281.96i	−0.429673	+	1.43236i
$896$	−38.0747	−	27.6629i	−0.0424941	−	0.0308738i
$897$	41.3413	+	261.019i	0.0460884	+	0.290991i
$898$	−280.769	−	551.041i	−0.312661	−	0.613631i
$899$			1625.65i			1.80828i
$900$	−143.783	−	382.445i	−0.159759	−	0.424939i
$901$	−710.158			−0.788189
$902$	1020.76	−	520.101i	1.13166	−	0.576608i
$903$	−0.924810	+	0.146475i	−0.00102415	+	0.000162210i
$904$	−38.5911	+	53.1160i	−0.0426892	+	0.0587567i
$905$	113.156	−	163.431i	0.125035	−	0.180587i
$906$	−257.773	+	187.283i	−0.284517	+	0.206714i
$907$	249.974	+	249.974i	0.275605	+	0.275605i	0.831352	−	0.555747i	$-0.187568\pi$
$907$	249.974	+	249.974i	0.275605	+	0.275605i	−0.555747	+	0.831352i	$0.687568\pi$
$908$	128.150	−	809.106i	0.141134	−	0.891086i
$909$	−305.603	+	99.2963i	−0.336197	+	0.109237i
$910$	−58.1441	−	27.9803i	−0.0638946	−	0.0307476i
$911$	232.883	−	716.740i	0.255634	−	0.786761i	−0.738070	−	0.674724i	$-0.764262\pi$
$911$	232.883	−	716.740i	0.255634	−	0.786761i	0.993704	−	0.112037i	$-0.0357375\pi$
$912$	167.805	−	329.336i	0.183997	−	0.361114i
$913$	−682.306	−	347.652i	−0.747324	−	0.380780i
$914$	1858.67	+	603.919i	2.03356	+	0.660743i
$915$	130.326	+	716.994i	0.142433	+	0.783600i
$916$	624.701	+	1922.63i	0.681988	+	2.09894i
$917$	−52.4841	−	8.31266i	−0.0572345	−	0.00906506i
$918$	275.460	−	275.460i	0.300066	−	0.300066i
$919$	−548.369	−	754.765i	−0.596701	−	0.821289i	0.398700	−	0.917081i	$-0.369462\pi$
$919$	−548.369	−	754.765i	−0.596701	−	0.821289i	−0.995401	+	0.0957924i	$0.969462\pi$
$920$	227.469	−	173.297i	0.247248	−	0.188367i
$921$	−593.638	−	431.303i	−0.644558	−	0.468299i
$922$	203.447	+	1284.51i	0.220658	+	1.39318i
$923$	−327.095	−	641.960i	−0.354382	−	0.695514i
$924$		−	26.4959i		−	0.0286752i
$925$	41.5847	+	202.511i	0.0449564	+	0.218931i
$926$	−2021.52			−2.18306
$927$	255.079	−	129.969i	0.275166	−	0.140204i
$928$	−1991.94	+	315.493i	−2.14649	+	0.339970i
$929$	−702.940	+	967.513i	−0.756663	+	1.04146i	0.240822	+	0.970569i	$0.422583\pi$
$929$	−702.940	+	967.513i	−0.756663	+	1.04146i	−0.997484	+	0.0708875i	$0.977417\pi$
$930$	20.8372	+	916.763i	0.0224056	+	0.985767i
$931$	−1040.04	+	755.635i	−1.11712	+	0.811638i
$932$	−285.741	−	285.741i	−0.306589	−	0.306589i
$933$	−10.0412	+	63.3975i	−0.0107623	+	0.0679502i
$934$	−1922.82	+	624.762i	−2.05869	+	0.668910i
$935$	129.703	−	959.560i	0.138719	−	1.02627i
$936$	−48.9734	+	150.724i	−0.0523220	+	0.161030i
$937$	−478.587	+	939.280i	−0.510766	+	1.00243i	0.481282	+	0.876566i	$0.340171\pi$
$937$	−478.587	+	939.280i	−0.510766	+	1.00243i	−0.992047	+	0.125868i	$0.959829\pi$
$938$	41.1685	+	20.9764i	0.0438897	+	0.0223629i
$939$	692.861	+	225.124i	0.737872	+	0.239749i
$940$	−1162.35	−	157.113i	−1.23654	−	0.167142i
$941$	179.429	+	552.226i	0.190679	+	0.586850i	1.00000		0.000517053i	$-0.000164583\pi$
$941$	179.429	+	552.226i	0.190679	+	0.586850i	−0.809321	+	0.587367i	$0.800165\pi$
$942$	−648.358	−	102.690i	−0.688278	−	0.109012i
$943$	−426.622	+	426.622i	−0.452409	+	0.452409i
$944$	357.973	+	492.708i	0.379209	+	0.521936i
$945$	9.18623	−	0.208794i	0.00972087	−	0.000220946i
$946$	30.1787	+	21.9261i	0.0319014	+	0.0231777i
$947$	−94.5461	−	596.940i	−0.0998375	−	0.630349i	−0.985971	−	0.166918i	$-0.946618\pi$
$947$	−94.5461	−	596.940i	−0.0998375	−	0.630349i	0.886133	−	0.463431i	$-0.153382\pi$
$948$	454.518	+	892.042i	0.479450	+	0.940973i
$949$		−	1127.29i		−	1.18787i
$950$	−1979.90	+	406.562i	−2.08410	+	0.427960i
$951$	284.133			0.298773
$952$	−34.2025	+	17.4271i	−0.0359270	+	0.0183057i
$953$	−48.1641	+	7.62845i	−0.0505395	+	0.00800467i	−0.181653	−	0.983363i	$-0.558145\pi$
$953$	−48.1641	+	7.62845i	−0.0505395	+	0.00800467i	0.131114	+	0.991367i	$0.458145\pi$
$954$	−157.808	+	217.205i	−0.165418	+	0.227678i
$955$	401.322	+	526.771i	0.420233	+	0.551593i
$956$	1001.22	−	727.432i	1.04731	−	0.760912i
$957$	−458.883	−	458.883i	−0.479501	−	0.479501i
$958$	−322.890	+	2038.65i	−0.337046	+	2.12802i
$959$	5.43655	−	1.76644i	0.00566897	−	0.00184196i
$960$	−842.771	+	153.189i	−0.877886	+	0.159571i
$961$	69.7529	−	214.677i	0.0725837	−	0.223390i
$962$	136.991	−	268.860i	0.142403	−	0.279481i
$963$	485.920	+	247.589i	0.504590	+	0.257102i
$964$	−1784.49	−	579.816i	−1.85113	−	0.601468i
$965$	97.2596	−	202.109i	0.100787	−	0.209439i
$966$	7.47808	+	23.0152i	0.00774129	+	0.0238252i
$967$	−1446.65	−	229.127i	−1.49602	−	0.236946i	−0.645854	−	0.763461i	$-0.723499\pi$
$967$	−1446.65	−	229.127i	−1.49602	−	0.236946i	−0.850166	+	0.526514i	$0.823499\pi$
$968$	182.377	−	182.377i	0.188406	−	0.188406i
$969$	−653.153	−	898.989i	−0.674049	−	0.927749i
$970$	−1357.46	−	939.881i	−1.39945	−	0.968950i
$971$	−676.512	−	491.514i	−0.696716	−	0.506194i	0.182145	−	0.983272i	$-0.441696\pi$
$971$	−676.512	−	491.514i	−0.696716	−	0.506194i	−0.878861	+	0.477078i	$0.841696\pi$
$972$	−13.2847	−	83.8762i	−0.0136674	−	0.0862924i
$973$	−7.66968	−	15.0526i	−0.00788250	−	0.0154703i
$974$			324.003i			0.332652i
$975$	−481.169	+	180.899i	−0.493506	+	0.185537i
$976$	682.705			0.699493
$977$	−468.100	+	238.509i	−0.479120	+	0.244124i	−0.676834	−	0.736136i	$-0.736648\pi$
$977$	−468.100	+	238.509i	−0.479120	+	0.244124i	0.197714	+	0.980260i	$0.436648\pi$
$978$	489.463	−	77.5234i	0.500474	−	0.0792673i
$979$	801.377	−	1103.00i	0.818567	−	1.12666i
$980$	1275.15	+	382.514i	1.30117	+	0.390320i
$981$	−227.890	+	165.572i	−0.232304	+	0.168778i
$982$	369.546	+	369.546i	0.376320	+	0.376320i
$983$	222.203	−	1402.94i	0.226046	−	1.42720i	−0.569842	−	0.821754i	$-0.692996\pi$
$983$	222.203	−	1402.94i	0.226046	−	1.42720i	0.795888	−	0.605443i	$-0.207004\pi$
$984$	−344.104	+	111.806i	−0.349699	+	0.113624i
$985$	407.978	+	757.632i	0.414191	+	0.769170i
$986$	−1093.27	+	3364.72i	−1.10879	+	3.41250i
$987$	11.9753	−	23.5029i	0.0121331	−	0.0238125i
$988$	1515.68	+	772.280i	1.53409	+	0.781660i
$989$	−18.6839	−	6.07076i	−0.0188917	−	0.00613828i
$990$	−264.663	−	252.900i	−0.267337	−	0.255454i
$991$	451.716	+	1390.24i	0.455819	+	1.40287i	0.870171	+	0.492750i	$0.164008\pi$
$991$	451.716	+	1390.24i	0.455819	+	1.40287i	−0.414352	+	0.910117i	$0.635992\pi$
$992$	1454.12	+	230.310i	1.46585	+	0.232168i
$993$	401.637	−	401.637i	0.404468	−	0.404468i
$994$	−38.7795	−	53.3753i	−0.0390135	−	0.0536975i
$995$	44.1368	+	126.020i	0.0443586	+	0.126654i
$996$	736.253	+	534.919i	0.739210	+	0.537067i
$997$	−290.899	−	1836.66i	−0.291774	−	1.84219i	−0.502414	−	0.864627i	$-0.667555\pi$
$997$	−290.899	−	1836.66i	−0.291774	−	1.84219i	0.210639	−	0.977564i	$-0.432445\pi$
$998$	−404.952	−	794.763i	−0.405763	−	0.796355i
$999$			42.9694i			0.0430124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.22.9	✓	80
3.2	odd	2		225.3.r.b.172.2		80
5.2	odd	4		375.3.k.b.118.9		80
5.3	odd	4		375.3.k.c.118.2		80
5.4	even	2		375.3.k.a.7.2		80
25.6	even	5		375.3.k.c.232.2		80
25.8	odd	20	inner	75.3.k.a.58.9	yes	80
25.17	odd	20		375.3.k.a.268.2		80
25.19	even	10		375.3.k.b.232.9		80
75.8	even	20		225.3.r.b.208.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.22.9	✓	80	1.1	even	1	trivial
75.3.k.a.58.9	yes	80	25.8	odd	20	inner
225.3.r.b.172.2		80	3.2	odd	2
225.3.r.b.208.2		80	75.8	even	20
375.3.k.a.7.2		80	5.4	even	2
375.3.k.a.268.2		80	25.17	odd	20
375.3.k.b.118.9		80	5.2	odd	4
375.3.k.b.232.9		80	25.19	even	10
375.3.k.c.118.2		80	5.3	odd	4
375.3.k.c.232.2		80	25.6	even	5

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.73870 - 1.39544i) q^{2} +(1.71073 - 0.270952i) q^{3} +(3.20210 - 4.40731i) q^{4} +(-4.71895 + 1.65274i) q^{5} +(4.30707 - 3.12927i) q^{6} +(-0.250082 - 0.250082i) q^{7} +(0.696119 - 4.39513i) q^{8} +(2.85317 - 0.927051i) q^{9} +O(q^{10})\)	\(q+(2.73870 - 1.39544i) q^{2} +(1.71073 - 0.270952i) q^{3} +(3.20210 - 4.40731i) q^{4} +(-4.71895 + 1.65274i) q^{5} +(4.30707 - 3.12927i) q^{6} +(-0.250082 - 0.250082i) q^{7} +(0.696119 - 4.39513i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-10.6175 + 11.1114i) q^{10} +(-2.45351 + 7.55112i) q^{11} +(4.28374 - 8.40731i) q^{12} +(-10.5776 - 5.38954i) q^{13} +(-1.03387 - 0.335926i) q^{14} +(-7.62501 + 4.10600i) q^{15} +(2.50710 + 7.71607i) q^{16} +(24.0906 + 3.81558i) q^{17} +(6.52034 - 6.52034i) q^{18} +(-15.4606 - 21.2797i) q^{19} +(-7.82638 + 26.0901i) q^{20} +(-0.495582 - 0.360061i) q^{21} +(3.81770 + 24.1040i) q^{22} +(-5.83489 - 11.4516i) q^{23} -7.70747i q^{24} +(19.5369 - 15.5984i) q^{25} -36.4896 q^{26} +(4.62981 - 2.35900i) q^{27} +(-1.90297 + 0.301401i) q^{28} +(-27.7376 + 38.1776i) q^{29} +(-15.1530 + 21.8853i) q^{30} +(27.8697 - 20.2485i) q^{31} +(30.2198 + 30.2198i) q^{32} +(-2.15129 + 13.5827i) q^{33} +(71.3015 - 23.1673i) q^{34} +(1.59344 + 0.766802i) q^{35} +(5.05032 - 15.5433i) q^{36} +(-3.75426 + 7.36815i) q^{37} +(-72.0364 - 36.7044i) q^{38} +(-19.5556 - 6.35401i) q^{39} +(3.97906 + 21.8909i) q^{40} +(-14.5062 - 44.6455i) q^{41} +(-1.85969 - 0.294547i) q^{42} +(1.08084 - 1.08084i) q^{43} +(25.4237 + 34.9928i) q^{44} +(-11.9318 + 9.09025i) q^{45} +(-31.9601 - 23.2203i) q^{46} +(6.73620 + 42.5307i) q^{47} +(6.37966 + 12.5208i) q^{48} -48.8749i q^{49} +(31.7391 - 69.9819i) q^{50} +42.2463 q^{51} +(-57.6237 + 29.3608i) q^{52} +(-28.7572 + 4.55469i) q^{53} +(9.38781 - 12.9212i) q^{54} +(-0.902079 - 39.6884i) q^{55} +(-1.27323 + 0.925055i) q^{56} +(-32.2146 - 32.2146i) q^{57} +(-22.6907 + 143.263i) q^{58} +(71.3918 - 23.1966i) q^{59} +(-6.31962 + 46.7536i) q^{60} +(26.0031 - 80.0294i) q^{61} +(48.0713 - 94.3452i) q^{62} +(-0.945365 - 0.481688i) q^{63} +(94.0684 + 30.5647i) q^{64} +(58.8225 + 7.95096i) q^{65} +(13.0621 + 40.2009i) q^{66} +(-41.9801 - 6.64899i) q^{67} +(93.9570 - 93.9570i) q^{68} +(-13.0848 - 18.0096i) q^{69} +(5.43399 - 0.123510i) q^{70} +(49.0998 + 35.6731i) q^{71} +(-2.08836 - 13.1854i) q^{72} +(43.1099 + 84.6079i) q^{73} +25.4180i q^{74} +(29.1959 - 31.9781i) q^{75} -143.292 q^{76} +(2.50198 - 1.27482i) q^{77} +(-62.4237 + 9.88694i) q^{78} +(-62.3659 + 85.8393i) q^{79} +(-24.5836 - 32.2681i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-102.028 - 102.028i) q^{82} +(-15.0878 + 95.2606i) q^{83} +(-3.17380 + 1.03123i) q^{84} +(-119.989 + 21.8101i) q^{85} +(1.45185 - 4.46832i) q^{86} +(-37.1072 + 72.8270i) q^{87} +(31.4802 + 16.0400i) q^{88} +(-163.312 - 53.0634i) q^{89} +(-19.9927 + 41.5455i) q^{90} +(1.29743 + 3.99309i) q^{91} +(-69.1547 - 10.9530i) q^{92} +(42.1911 - 42.1911i) q^{93} +(77.7974 + 107.079i) q^{94} +(108.127 + 74.8653i) q^{95} +(59.8858 + 43.5096i) q^{96} +(16.8062 + 106.110i) q^{97} +(-68.2019 - 133.854i) q^{98} +23.8192i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more