LMFDB - Embedded newform 115.5.f.a.47.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,5,Mod(47,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("115.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	115.f (of order $4$, degree $2$, 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:	$11.8875457546$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.19
Character	$\chi$	$=$	115.47
Dual form			115.5.f.a.93.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05609 - 1.05609i) q^{2} +(11.5301 - 11.5301i) q^{3} -13.7694i q^{4} +(-24.8276 + 2.93067i) q^{5} -24.3536 q^{6} +(12.8452 + 12.8452i) q^{7} +(-31.4390 + 31.4390i) q^{8} -184.888i q^{9} +(29.3151 + 23.1251i) q^{10} -169.793 q^{11} +(-158.763 - 158.763i) q^{12} +(94.6983 - 94.6983i) q^{13} -27.1313i q^{14} +(-252.475 + 320.057i) q^{15} -153.905 q^{16} +(341.866 + 341.866i) q^{17} +(-195.258 + 195.258i) q^{18} -355.531i q^{19} +(40.3535 + 341.861i) q^{20} +296.215 q^{21} +(179.316 + 179.316i) q^{22} +(-77.9968 + 77.9968i) q^{23} +724.992i q^{24} +(607.822 - 145.523i) q^{25} -200.019 q^{26} +(-1197.85 - 1197.85i) q^{27} +(176.871 - 176.871i) q^{28} -161.329i q^{29} +(604.643 - 71.3725i) q^{30} -560.870 q^{31} +(665.561 + 665.561i) q^{32} +(-1957.74 + 1957.74i) q^{33} -722.079i q^{34} +(-356.562 - 281.272i) q^{35} -2545.79 q^{36} +(-1477.25 - 1477.25i) q^{37} +(-375.471 + 375.471i) q^{38} -2183.77i q^{39} +(688.418 - 872.693i) q^{40} +1424.88 q^{41} +(-312.828 - 312.828i) q^{42} +(-129.853 + 129.853i) q^{43} +2337.94i q^{44} +(541.847 + 4590.34i) q^{45} +164.743 q^{46} +(-2121.12 - 2121.12i) q^{47} +(-1774.55 + 1774.55i) q^{48} -2071.00i q^{49} +(-795.597 - 488.227i) q^{50} +7883.52 q^{51} +(-1303.94 - 1303.94i) q^{52} +(1870.71 - 1870.71i) q^{53} +2530.06i q^{54} +(4215.56 - 497.608i) q^{55} -807.683 q^{56} +(-4099.32 - 4099.32i) q^{57} +(-170.377 + 170.377i) q^{58} -1498.79i q^{59} +(4406.98 + 3476.42i) q^{60} +2380.94 q^{61} +(592.327 + 592.327i) q^{62} +(2374.93 - 2374.93i) q^{63} +1056.71i q^{64} +(-2073.60 + 2628.66i) q^{65} +4135.08 q^{66} +(6207.79 + 6207.79i) q^{67} +(4707.27 - 4707.27i) q^{68} +1798.63i q^{69} +(79.5130 + 673.607i) q^{70} -7191.70 q^{71} +(5812.70 + 5812.70i) q^{72} +(3233.16 - 3233.16i) q^{73} +3120.20i q^{74} +(5330.37 - 8686.18i) q^{75} -4895.43 q^{76} +(-2181.03 - 2181.03i) q^{77} +(-2306.25 + 2306.25i) q^{78} +4602.86i q^{79} +(3821.10 - 451.046i) q^{80} -12646.7 q^{81} +(-1504.79 - 1504.79i) q^{82} +(2921.41 - 2921.41i) q^{83} -4078.69i q^{84} +(-9489.61 - 7485.82i) q^{85} +274.271 q^{86} +(-1860.15 - 1860.15i) q^{87} +(5338.12 - 5338.12i) q^{88} -1513.75i q^{89} +(4275.55 - 5420.03i) q^{90} +2432.84 q^{91} +(1073.97 + 1073.97i) q^{92} +(-6466.91 + 6466.91i) q^{93} +4480.18i q^{94} +(1041.94 + 8826.99i) q^{95} +15348.0 q^{96} +(-10904.0 - 10904.0i) q^{97} +(-2187.15 + 2187.15i) q^{98} +31392.7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 48 q^{5} + 160 q^{7} + 180 q^{8} + 16 q^{10} + 312 q^{11} - 720 q^{12} - 760 q^{13} - 60 q^{15} - 4528 q^{16} + 420 q^{17} + 980 q^{18} + 1344 q^{20} + 1976 q^{21} + 720 q^{22} - 1176 q^{25} + 1872 q^{26}+ \cdots - 22320 q^{98}+O(q^{100}) $ 88 * q - 48 * q^5 + 160 * q^7 + 180 * q^8 + 16 * q^10 + 312 * q^11 - 720 * q^12 - 760 * q^13 - 60 * q^15 - 4528 * q^16 + 420 * q^17 + 980 * q^18 + 1344 * q^20 + 1976 * q^21 + 720 * q^22 - 1176 * q^25 + 1872 * q^26 + 2820 * q^27 - 1140 * q^28 - 1160 * q^30 - 820 * q^31 - 3720 * q^32 + 820 * q^33 - 1728 * q^35 + 9504 * q^36 + 180 * q^37 + 3180 * q^38 + 8560 * q^40 + 1956 * q^41 + 5320 * q^42 - 8960 * q^43 + 2064 * q^45 - 5640 * q^47 + 3820 * q^48 - 5448 * q^50 - 6648 * q^51 - 2800 * q^52 - 2160 * q^53 - 11796 * q^55 - 1464 * q^56 - 160 * q^57 + 3740 * q^58 - 6700 * q^60 - 4496 * q^61 - 30300 * q^62 - 2740 * q^63 - 3336 * q^65 - 4104 * q^66 + 640 * q^67 + 13440 * q^68 + 6508 * q^70 + 14916 * q^71 + 44280 * q^72 + 3660 * q^73 + 15732 * q^75 - 53552 * q^76 + 10980 * q^77 + 4340 * q^78 + 10404 * q^80 - 35864 * q^81 + 32860 * q^82 + 7920 * q^83 + 14216 * q^85 + 59352 * q^86 - 38440 * q^87 - 19140 * q^88 + 7160 * q^90 + 52584 * q^91 - 20960 * q^93 + 28224 * q^95 - 26624 * q^96 + 13480 * q^97 - 22320 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.05609	−	1.05609i	−0.264021	−	0.264021i	0.562664	−	0.826686i	$-0.309776\pi$
$2$	−1.05609	−	1.05609i	−0.264021	−	0.264021i	−0.826686	+	0.562664i	$0.809776\pi$
$3$	11.5301	−	11.5301i	1.28113	−	1.28113i	0.341100	−	0.940027i	$-0.389201\pi$
$3$	11.5301	−	11.5301i	1.28113	−	1.28113i	0.940027	−	0.341100i	$-0.110799\pi$
$4$		−	13.7694i		−	0.860585i
$5$	−24.8276	+	2.93067i	−0.993105	+	0.117227i
$5$	−24.8276	+	2.93067i	−0.993105	+	0.117227i
$6$	−24.3536			−0.676490
$7$	12.8452	+	12.8452i	0.262148	+	0.262148i	0.825926	−	0.563778i	$-0.190653\pi$
$7$	12.8452	+	12.8452i	0.262148	+	0.262148i	−0.563778	+	0.825926i	$0.690653\pi$
$8$	−31.4390	+	31.4390i	−0.491234	+	0.491234i
$9$		−	184.888i		−	2.28257i
$10$	29.3151	+	23.1251i	0.293151	+	0.231251i
$11$	−169.793			−1.40325			−0.701624	−	0.712547i	$-0.747541\pi$
$11$	−169.793			−1.40325			−0.701624	+	0.712547i	$0.747541\pi$
$12$	−158.763	−	158.763i	−1.10252	−	1.10252i
$13$	94.6983	−	94.6983i	0.560345	−	0.560345i	−0.369060	−	0.929405i	$-0.620320\pi$
$13$	94.6983	−	94.6983i	0.560345	−	0.560345i	0.929405	+	0.369060i	$0.120320\pi$
$14$		−	27.1313i		−	0.138425i
$15$	−252.475	+	320.057i	−1.12211	+	1.42248i
$16$	−153.905			−0.601193
$17$	341.866	+	341.866i	1.18293	+	1.18293i	0.978983	+	0.203943i	$0.0653758\pi$
$17$	341.866	+	341.866i	1.18293	+	1.18293i	0.203943	+	0.978983i	$0.434624\pi$
$18$	−195.258	+	195.258i	−0.602648	+	0.602648i
$19$		−	355.531i		−	0.984850i	−0.870355	−	0.492425i	$-0.836111\pi$
$19$		−	355.531i		−	0.984850i	0.870355	−	0.492425i	$-0.163889\pi$
$20$	40.3535	+	341.861i	0.100884	+	0.854652i
$21$	296.215			0.671689
$22$	179.316	+	179.316i	0.370488	+	0.370488i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$23$	−77.9968	+	77.9968i	−0.147442	+	0.147442i
$24$			724.992i			1.25867i
$25$	607.822	−	145.523i	0.972516	−	0.232837i
$26$	−200.019			−0.295886
$27$	−1197.85	−	1197.85i	−1.64314	−	1.64314i
$28$	176.871	−	176.871i	0.225600	−	0.225600i
$29$		−	161.329i		−	0.191830i	−0.995390	−	0.0959151i	$-0.969422\pi$
$29$		−	161.329i		−	0.191830i	0.995390	−	0.0959151i	$-0.0305777\pi$
$30$	604.643	−	71.3725i	0.671826	−	0.0793028i
$31$	−560.870			−0.583632			−0.291816	−	0.956475i	$-0.594259\pi$
$31$	−560.870			−0.583632			−0.291816	+	0.956475i	$0.594259\pi$
$32$	665.561	+	665.561i	0.649962	+	0.649962i
$33$	−1957.74	+	1957.74i	−1.79774	+	1.79774i
$34$		−	722.079i		−	0.624636i
$35$	−356.562	−	281.272i	−0.291071	−	0.229609i
$36$	−2545.79			−1.96435
$37$	−1477.25	−	1477.25i	−1.07907	−	1.07907i	−0.996593	−	0.0824767i	$-0.973717\pi$
$37$	−1477.25	−	1477.25i	−1.07907	−	1.07907i	−0.0824767	−	0.996593i	$-0.526283\pi$
$38$	−375.471	+	375.471i	−0.260021	+	0.260021i
$39$		−	2183.77i		−	1.43575i
$40$	688.418	−	872.693i	0.430262	−	0.545433i
$41$	1424.88			0.847636			0.423818	−	0.905747i	$-0.360690\pi$
$41$	1424.88			0.847636			0.423818	+	0.905747i	$0.360690\pi$
$42$	−312.828	−	312.828i	−0.177340	−	0.177340i
$43$	−129.853	+	129.853i	−0.0702286	+	0.0702286i	−0.741349	−	0.671120i	$-0.765814\pi$
$43$	−129.853	+	129.853i	−0.0702286	+	0.0702286i	0.671120	+	0.741349i	$0.265814\pi$
$44$			2337.94i			1.20762i
$45$	541.847	+	4590.34i	0.267579	+	2.26683i
$46$	164.743			0.0778557
$47$	−2121.12	−	2121.12i	−0.960219	−	0.960219i	0.0390193	−	0.999238i	$-0.487577\pi$
$47$	−2121.12	−	2121.12i	−0.960219	−	0.960219i	−0.999238	+	0.0390193i	$0.987577\pi$
$48$	−1774.55	+	1774.55i	−0.770204	+	0.770204i
$49$		−	2071.00i		−	0.862557i
$50$	−795.597	−	488.227i	−0.318239	−	0.195291i
$51$	7883.52			3.03096
$52$	−1303.94	−	1303.94i	−0.482225	−	0.482225i
$53$	1870.71	−	1870.71i	0.665970	−	0.665970i	−0.290811	−	0.956781i	$-0.593925\pi$
$53$	1870.71	−	1870.71i	0.665970	−	0.665970i	0.956781	+	0.290811i	$0.0939250\pi$
$54$			2530.06i			0.867647i
$55$	4215.56	−	497.608i	1.39357	−	0.164498i
$56$	−807.683			−0.257552
$57$	−4099.32	−	4099.32i	−1.26172	−	1.26172i
$58$	−170.377	+	170.377i	−0.0506473	+	0.0506473i
$59$		−	1498.79i		−	0.430563i	−0.976552	−	0.215282i	$-0.930933\pi$
$59$		−	1498.79i		−	0.430563i	0.976552	−	0.215282i	$-0.0690669\pi$
$60$	4406.98	+	3476.42i	1.22416	+	0.965672i
$61$	2380.94			0.639866			0.319933	−	0.947440i	$-0.396340\pi$
$61$	2380.94			0.639866			0.319933	+	0.947440i	$0.396340\pi$
$62$	592.327	+	592.327i	0.154091	+	0.154091i
$63$	2374.93	−	2374.93i	0.598371	−	0.598371i
$64$			1056.71i			0.257985i
$65$	−2073.60	+	2628.66i	−0.490794	+	0.622169i
$66$	4135.08			0.949283
$67$	6207.79	+	6207.79i	1.38289	+	1.38289i	0.839445	+	0.543444i	$0.182880\pi$
$67$	6207.79	+	6207.79i	1.38289	+	1.38289i	0.543444	+	0.839445i	$0.317120\pi$
$68$	4707.27	−	4707.27i	1.01801	−	1.01801i
$69$			1798.63i			0.377784i
$70$	79.5130	+	673.607i	0.0162272	+	0.137471i
$71$	−7191.70			−1.42664			−0.713321	−	0.700838i	$-0.752810\pi$
$71$	−7191.70			−1.42664			−0.713321	+	0.700838i	$0.752810\pi$
$72$	5812.70	+	5812.70i	1.12128	+	1.12128i
$73$	3233.16	−	3233.16i	0.606711	−	0.606711i	−0.335374	−	0.942085i	$-0.608863\pi$
$73$	3233.16	−	3233.16i	0.606711	−	0.606711i	0.942085	+	0.335374i	$0.108863\pi$
$74$			3120.20i			0.569795i
$75$	5330.37	−	8686.18i	0.947622	−	1.54421i
$76$	−4895.43			−0.847547
$77$	−2181.03	−	2181.03i	−0.367858	−	0.367858i
$78$	−2306.25	+	2306.25i	−0.379068	+	0.379068i
$79$			4602.86i			0.737519i	0.929525	+	0.368760i	$0.120217\pi$
$79$			4602.86i			0.737519i	−0.929525	+	0.368760i	$0.879783\pi$
$80$	3821.10	−	451.046i	0.597047	−	0.0704759i
$81$	−12646.7			−1.92756
$82$	−1504.79	−	1504.79i	−0.223794	−	0.223794i
$83$	2921.41	−	2921.41i	0.424068	−	0.424068i	−0.462533	−	0.886602i	$-0.653059\pi$
$83$	2921.41	−	2921.41i	0.424068	−	0.424068i	0.886602	+	0.462533i	$0.153059\pi$
$84$		−	4078.69i		−	0.578046i
$85$	−9489.61	−	7485.82i	−1.31344	−	1.03610i
$86$	274.271			0.0370837
$87$	−1860.15	−	1860.15i	−0.245759	−	0.245759i
$88$	5338.12	−	5338.12i	0.689324	−	0.689324i
$89$		−	1513.75i		−	0.191106i	−0.995424	−	0.0955529i	$-0.969538\pi$
$89$		−	1513.75i		−	0.191106i	0.995424	−	0.0955529i	$-0.0304619\pi$
$90$	4275.55	−	5420.03i	0.527846	−	0.669139i
$91$	2432.84			0.293786
$92$	1073.97	+	1073.97i	0.126886	+	0.126886i
$93$	−6466.91	+	6466.91i	−0.747706	+	0.747706i
$94$			4480.18i			0.507037i
$95$	1041.94	+	8826.99i	0.115451	+	0.978059i
$96$	15348.0			1.66537
$97$	−10904.0	−	10904.0i	−1.15889	−	1.15889i	−0.984714	−	0.174180i	$-0.944273\pi$
$97$	−10904.0	−	10904.0i	−1.15889	−	1.15889i	−0.174180	−	0.984714i	$-0.555727\pi$
$98$	−2187.15	+	2187.15i	−0.227734	+	0.227734i
$99$			31392.7i			3.20301i
$100$	−2003.76	−	8369.33i	−0.200376	−	0.836933i
$101$	10387.8			1.01832			0.509158	−	0.860673i	$-0.329957\pi$
$101$	10387.8			1.01832			0.509158	+	0.860673i	$0.329957\pi$
$102$	−8325.67	−	8325.67i	−0.800237	−	0.800237i
$103$	5186.69	−	5186.69i	0.488896	−	0.488896i	−0.419062	−	0.907958i	$-0.637641\pi$
$103$	5186.69	−	5186.69i	0.488896	−	0.488896i	0.907958	+	0.419062i	$0.137641\pi$
$104$			5954.44i			0.550521i
$105$	−7354.31	+	868.108i	−0.667058	+	0.0787400i
$106$	−3951.26			−0.351661
$107$	11702.6	+	11702.6i	1.02215	+	1.02215i	0.999749	+	0.0224031i	$0.00713172\pi$
$107$	11702.6	+	11702.6i	1.02215	+	1.02215i	0.0224031	+	0.999749i	$0.492868\pi$
$108$	−16493.6	+	16493.6i	−1.41406	+	1.41406i
$109$		−	7134.42i		−	0.600490i	−0.953862	−	0.300245i	$-0.902932\pi$
$109$		−	7134.42i		−	0.600490i	0.953862	−	0.300245i	$-0.0970684\pi$
$110$	−4977.51	−	3926.48i	−0.411364	−	0.324502i
$111$	−34065.7			−2.76485
$112$	−1976.95	−	1976.95i	−0.157601	−	0.157601i
$113$	8202.79	−	8202.79i	0.642399	−	0.642399i	−0.308746	−	0.951145i	$-0.599909\pi$
$113$	8202.79	−	8202.79i	0.642399	−	0.642399i	0.951145	+	0.308746i	$0.0999092\pi$
$114$			8658.47i			0.666241i
$115$	1707.89	−	2165.06i	0.129141	−	0.163710i
$116$	−2221.40			−0.165086
$117$	−17508.6	−	17508.6i	−1.27903	−	1.27903i
$118$	−1582.85	+	1582.85i	−0.113678	+	0.113678i
$119$			8782.69i			0.620202i
$120$	−2124.71	−	17999.8i	−0.147550	−	1.24999i
$121$	14188.7			0.969106
$122$	−2514.48	−	2514.48i	−0.168938	−	0.168938i
$123$	16429.0	−	16429.0i	1.08593	−	1.08593i
$124$			7722.82i			0.502265i
$125$	−14664.3	+	5394.33i	−0.938516	+	0.345237i
$126$	−5016.27			−0.315965
$127$	2245.94	+	2245.94i	0.139248	+	0.139248i	0.773295	−	0.634046i	$-0.218607\pi$
$127$	2245.94	+	2245.94i	0.139248	+	0.139248i	−0.634046	+	0.773295i	$0.718607\pi$
$128$	11765.0	−	11765.0i	0.718076	−	0.718076i
$129$			2994.44i			0.179944i
$130$	4966.00	−	586.190i	0.293846	−	0.0346858i
$131$	19045.1			1.10979			0.554894	−	0.831921i	$-0.312759\pi$
$131$	19045.1			1.10979			0.554894	+	0.831921i	$0.312759\pi$
$132$	26956.8	+	26956.8i	1.54711	+	1.54711i
$133$	4566.88	−	4566.88i	0.258176	−	0.258176i
$134$		−	13111.9i		−	0.730225i
$135$	33250.2	+	26229.2i	1.82443	+	1.43919i
$136$	−21495.8			−1.16219
$137$	−7329.71	−	7329.71i	−0.390522	−	0.390522i	0.484351	−	0.874874i	$-0.339056\pi$
$137$	−7329.71	−	7329.71i	−0.390522	−	0.390522i	−0.874874	+	0.484351i	$0.839056\pi$
$138$	1899.51	−	1899.51i	0.0997430	−	0.0997430i
$139$		−	5122.73i		−	0.265138i	−0.991174	−	0.132569i	$-0.957677\pi$
$139$		−	5122.73i		−	0.265138i	0.991174	−	0.132569i	$-0.0423226\pi$
$140$	−3872.93	+	4909.63i	−0.197599	+	0.250491i
$141$	−48913.7			−2.46032
$142$	7595.05	+	7595.05i	0.376664	+	0.376664i
$143$	−16079.1	+	16079.1i	−0.786303	+	0.786303i
$144$			28455.3i			1.37227i
$145$	472.803	+	4005.42i	0.0224876	+	0.190508i
$146$	−6828.99			−0.320369
$147$	−23878.9	−	23878.9i	−1.10505	−	1.10505i
$148$	−20340.7	+	20340.7i	−0.928632	+	0.928632i
$149$			14038.1i			0.632316i	0.948707	+	0.316158i	$0.102393\pi$
$149$			14038.1i			0.632316i	−0.948707	+	0.316158i	$0.897607\pi$
$150$	−14802.7	+	3544.02i	−0.657897	+	0.157512i
$151$	−2527.99			−0.110872			−0.0554359	−	0.998462i	$-0.517655\pi$
$151$	−2527.99			−0.110872			−0.0554359	+	0.998462i	$0.517655\pi$
$152$	11177.5	+	11177.5i	0.483792	+	0.483792i
$153$	63206.9	−	63206.9i	2.70011	−	2.70011i
$154$			4606.71i			0.194245i
$155$	13925.1	−	1643.73i	0.579607	−	0.0684173i
$156$	−30069.1			−1.23558
$157$	5260.65	+	5260.65i	0.213422	+	0.213422i	0.805720	−	0.592297i	$-0.201779\pi$
$157$	5260.65	+	5260.65i	0.213422	+	0.213422i	−0.592297	+	0.805720i	$0.701779\pi$
$158$	4861.01	−	4861.01i	0.194721	−	0.194721i
$159$		−	43139.1i		−	1.70638i
$160$	−18474.8	−	14573.8i	−0.721674	−	0.569288i
$161$	−2003.77			−0.0773031
$162$	13356.0	+	13356.0i	0.508917	+	0.508917i
$163$	−6146.58	+	6146.58i	−0.231344	+	0.231344i	−0.813254	−	0.581909i	$-0.802306\pi$
$163$	−6146.58	+	6146.58i	−0.231344	+	0.231344i	0.581909	+	0.813254i	$0.302306\pi$
$164$		−	19619.6i		−	0.729463i
$165$	42868.5	−	54343.5i	1.57460	−	1.99609i
$166$	−6170.51			−0.223926
$167$	−7173.14	−	7173.14i	−0.257203	−	0.257203i	0.566712	−	0.823916i	$-0.308215\pi$
$167$	−7173.14	−	7173.14i	−0.257203	−	0.257203i	−0.823916	+	0.566712i	$0.808215\pi$
$168$	−9312.70	+	9312.70i	−0.329957	+	0.329957i
$169$			10625.5i			0.372027i
$170$	2116.18	+	17927.5i	0.0732241	+	0.620329i
$171$	−65733.5			−2.24799
$172$	1787.99	+	1787.99i	0.0604377	+	0.0604377i
$173$	−23063.9	+	23063.9i	−0.770621	+	0.770621i	−0.978215	−	0.207594i	$-0.933437\pi$
$173$	−23063.9	+	23063.9i	−0.770621	+	0.770621i	0.207594	+	0.978215i	$0.433437\pi$
$174$			3928.95i			0.129771i
$175$	9676.90	+	5938.34i	0.315980	+	0.193905i
$176$	26132.1			0.843623
$177$	−17281.3	−	17281.3i	−0.551606	−	0.551606i
$178$	−1598.65	+	1598.65i	−0.0504560	+	0.0504560i
$179$			46399.3i			1.44812i	0.689735	+	0.724062i	$0.257727\pi$
$179$			46399.3i			1.44812i	−0.689735	+	0.724062i	$0.742273\pi$
$180$	63206.0	−	7460.89i	1.95080	−	0.230274i
$181$	4651.45			0.141981			0.0709906	−	0.997477i	$-0.477384\pi$
$181$	4651.45			0.141981			0.0709906	+	0.997477i	$0.477384\pi$
$182$	−2569.29	−	2569.29i	−0.0775658	−	0.0775658i
$183$	27452.6	−	27452.6i	0.819749	−	0.819749i
$184$		−	4904.28i		−	0.144857i
$185$	41005.9	+	32347.2i	1.19813	+	0.945134i
$186$	13659.2			0.394821
$187$	−58046.4	−	58046.4i	−1.65994	−	1.65994i
$188$	−29206.5	+	29206.5i	−0.826351	+	0.826351i
$189$		−	30773.2i		−	0.861489i
$190$	8221.67	−	10422.4i	0.227747	−	0.288710i
$191$	6413.60			0.175807			0.0879033	−	0.996129i	$-0.471983\pi$
$191$	6413.60			0.175807			0.0879033	+	0.996129i	$0.471983\pi$
$192$	12184.0	+	12184.0i	0.330511	+	0.330511i
$193$	8454.64	−	8454.64i	0.226976	−	0.226976i	−0.584452	−	0.811428i	$-0.698690\pi$
$193$	8454.64	−	8454.64i	0.226976	−	0.226976i	0.811428	+	0.584452i	$0.198690\pi$
$194$			23031.2i			0.611945i
$195$	6399.91	+	54217.8i	0.168308	+	1.42585i
$196$	−28516.4			−0.742304
$197$	20732.3	+	20732.3i	0.534214	+	0.534214i	0.921823	−	0.387610i	$-0.126699\pi$
$197$	20732.3	+	20732.3i	0.534214	+	0.534214i	−0.387610	+	0.921823i	$0.626699\pi$
$198$	33153.4	−	33153.4i	0.845665	−	0.845665i
$199$			56203.7i			1.41925i	0.704580	+	0.709624i	$0.251135\pi$
$199$			56203.7i			1.41925i	−0.704580	+	0.709624i	$0.748865\pi$
$200$	−14534.2	+	23684.4i	−0.363356	+	0.592111i
$201$	143153.			3.54331
$202$	−10970.5	−	10970.5i	−0.268857	−	0.268857i
$203$	2072.31	−	2072.31i	0.0502878	−	0.0502878i
$204$		−	108551.i		−	2.60840i
$205$	−35376.3	+	4175.84i	−0.841792	+	0.0993657i
$206$	−10955.2			−0.258158
$207$	14420.7	+	14420.7i	0.336547	+	0.336547i
$208$	−14574.6	+	14574.6i	−0.336875	+	0.336875i
$209$			60366.7i			1.38199i
$210$	8683.58	+	6849.98i	0.196907	+	0.155328i
$211$	87727.9			1.97048			0.985242	−	0.171166i	$-0.0547535\pi$
$211$	87727.9			1.97048			0.985242	+	0.171166i	$0.0547535\pi$
$212$	−25758.5	−	25758.5i	−0.573124	−	0.573124i
$213$	−82921.3	+	82921.3i	−1.82771	+	1.82771i
$214$		−	24717.9i		−	0.539740i
$215$	2843.38	−	3604.49i	0.0615117	−	0.0779771i
$216$	75318.2			1.61433
$217$	−7204.51	−	7204.51i	−0.152998	−	0.152998i
$218$	−7534.56	+	7534.56i	−0.158542	+	0.158542i
$219$		−	74557.6i		−	1.55455i
$220$	−6851.74	−	58045.6i	−0.141565	−	1.19929i
$221$	64748.2			1.32569
$222$	35976.3	+	35976.3i	0.729980	+	0.729980i
$223$	43071.8	−	43071.8i	0.866131	−	0.866131i	−0.125910	−	0.992042i	$-0.540185\pi$
$223$	43071.8	−	43071.8i	0.866131	−	0.866131i	0.992042	+	0.125910i	$0.0401852\pi$
$224$			17098.6i			0.340772i
$225$	−26905.5	−	112379.i	−0.531468	−	2.21984i
$226$	−17325.7			−0.339214
$227$	43149.9	+	43149.9i	0.837390	+	0.837390i	0.988515	−	0.151125i	$-0.0482895\pi$
$227$	43149.9	+	43149.9i	0.837390	+	0.837390i	−0.151125	+	0.988515i	$0.548289\pi$
$228$	−56445.0	+	56445.0i	−1.08582	+	1.08582i
$229$			36914.1i			0.703916i	0.936016	+	0.351958i	$0.114484\pi$
$229$			36914.1i			0.703916i	−0.936016	+	0.351958i	$0.885516\pi$
$230$	−4090.17	+	482.806i	−0.0773189	+	0.00912678i
$231$	−50295.2			−0.942546
$232$	5072.03	+	5072.03i	0.0942336	+	0.0942336i
$233$	−70155.1	+	70155.1i	−1.29225	+	1.29225i	−0.358862	+	0.933391i	$0.616835\pi$
$233$	−70155.1	+	70155.1i	−1.29225	+	1.29225i	−0.933391	+	0.358862i	$0.883165\pi$
$234$			36981.2i			0.675381i
$235$	58878.8	+	46446.2i	1.06616	+	0.841035i
$236$	−20637.4			−0.370536
$237$	53071.6	+	53071.6i	0.944856	+	0.944856i
$238$	9275.27	−	9275.27i	0.163747	−	0.163747i
$239$		−	29058.5i		−	0.508718i	−0.967110	−	0.254359i	$-0.918135\pi$
$239$		−	29058.5i		−	0.508718i	0.967110	−	0.254359i	$-0.0818645\pi$
$240$	38857.2	−	49258.5i	0.674605	−	0.855182i
$241$	2245.85			0.0386676			0.0193338	−	0.999813i	$-0.493845\pi$
$241$	2245.85			0.0386676			0.0193338	+	0.999813i	$0.493845\pi$
$242$	−14984.5	−	14984.5i	−0.255865	−	0.255865i
$243$	−48793.0	+	48793.0i	−0.826314	+	0.826314i
$244$		−	32784.0i		−	0.550659i
$245$	6069.42	+	51418.0i	0.101115	+	0.856610i
$246$	−34700.9			−0.573417
$247$	−33668.2	−	33668.2i	−0.551856	−	0.551856i
$248$	17633.2	−	17633.2i	0.286700	−	0.286700i
$249$		−	67368.5i		−	1.08657i
$250$	21183.6	+	9789.89i	0.338938	+	0.156638i
$251$	870.147			0.0138116			0.00690582	−	0.999976i	$-0.497802\pi$
$251$	870.147			0.0138116			0.00690582	+	0.999976i	$0.497802\pi$
$252$	−32701.3	−	32701.3i	−0.514949	−	0.514949i
$253$	13243.3	−	13243.3i	0.206898	−	0.206898i
$254$		−	4743.81i		−	0.0735292i
$255$	−195729.	+	23104.0i	−3.01006	+	0.355309i
$256$	−7942.30			−0.121190
$257$	−60122.7	−	60122.7i	−0.910274	−	0.910274i	0.0860194	−	0.996293i	$-0.472585\pi$
$257$	−60122.7	−	60122.7i	−0.910274	−	0.910274i	−0.996293	+	0.0860194i	$0.972585\pi$
$258$	3162.39	−	3162.39i	0.0475090	−	0.0475090i
$259$		−	37951.2i		−	0.565751i
$260$	36195.0	+	28552.2i	0.535429	+	0.422370i
$261$	−29827.9			−0.437866
$262$	−20113.2	−	20113.2i	−0.293008	−	0.293008i
$263$	−47771.1	+	47771.1i	−0.690643	+	0.690643i	−0.962374	−	0.271730i	$-0.912404\pi$
$263$	−47771.1	+	47771.1i	−0.690643	+	0.690643i	0.271730	+	0.962374i	$0.412404\pi$
$264$		−	123099.i		−	1.76622i
$265$	−40962.8	+	51927.7i	−0.583309	+	0.739448i
$266$	−9646.03			−0.136328
$267$	−17453.7	−	17453.7i	−0.244831	−	0.244831i
$268$	85477.3	−	85477.3i	1.19009	−	1.19009i
$269$		−	105129.i		−	1.45283i	−0.687254	−	0.726417i	$-0.741184\pi$
$269$		−	105129.i		−	1.45283i	0.687254	−	0.726417i	$-0.258816\pi$
$270$	−7414.77	−	62815.3i	−0.101711	−	0.861664i
$271$	−76148.8			−1.03687			−0.518435	−	0.855117i	$-0.673485\pi$
$271$	−76148.8			−1.03687			−0.518435	+	0.855117i	$0.673485\pi$
$272$	−52614.9	−	52614.9i	−0.711166	−	0.711166i
$273$	28051.0	−	28051.0i	0.376377	−	0.376377i
$274$			15481.6i			0.206213i
$275$	−103204.	+	24708.8i	−1.36468	+	0.326728i
$276$	24766.0			0.325115
$277$	−60434.6	−	60434.6i	−0.787637	−	0.787637i	0.193470	−	0.981106i	$-0.438026\pi$
$277$	−60434.6	−	60434.6i	−0.787637	−	0.787637i	−0.981106	+	0.193470i	$0.938026\pi$
$278$	−5410.04	+	5410.04i	−0.0700021	+	0.0700021i
$279$			103698.i			1.33218i
$280$	20052.8	−	2367.05i	0.255776	−	0.0301920i
$281$	12271.1			0.155406			0.0777032	−	0.996977i	$-0.475241\pi$
$281$	12271.1			0.155406			0.0777032	+	0.996977i	$0.475241\pi$
$282$	51657.1	+	51657.1i	0.649578	+	0.649578i
$283$	−34586.4	+	34586.4i	−0.431849	+	0.431849i	−0.889257	−	0.457408i	$-0.848778\pi$
$283$	−34586.4	+	34586.4i	−0.431849	+	0.431849i	0.457408	+	0.889257i	$0.348778\pi$
$284$			99025.1i			1.22775i
$285$	113790.	+	89762.6i	1.40093	+	1.10511i
$286$	33961.8			0.415202
$287$	18302.9	+	18302.9i	0.222206	+	0.222206i
$288$	123054.	−	123054.i	1.48358	−	1.48358i
$289$			150223.i			1.79863i
$290$	3730.75	−	4729.39i	0.0443608	−	0.0562353i
$291$	−251450.			−2.96938
$292$	−44518.6	−	44518.6i	−0.522126	−	0.522126i
$293$	−81499.3	+	81499.3i	−0.949333	+	0.949333i	−0.998777	−	0.0494436i	$-0.984255\pi$
$293$	−81499.3	+	81499.3i	−0.949333	+	0.949333i	0.0494436	+	0.998777i	$0.484255\pi$
$294$			50436.4i			0.583511i
$295$	4392.46	+	37211.4i	0.0504736	+	0.427594i
$296$	92886.3			1.06015
$297$	203386.	+	203386.i	2.30573	+	2.30573i
$298$	14825.4	−	14825.4i	0.166945	−	0.166945i
$299$			14772.3i			0.165237i
$300$	−119603.	−	73395.9i	−1.32892	−	0.815510i
$301$	−3335.98			−0.0368205
$302$	2669.77	+	2669.77i	0.0292725	+	0.0292725i
$303$	119773.	−	119773.i	1.30459	−	1.30459i
$304$			54718.1i			0.592084i
$305$	−59113.1	+	6977.75i	−0.635454	+	0.0750094i
$306$	−133504.			−1.42578
$307$	48666.0	+	48666.0i	0.516355	+	0.516355i	0.916467	−	0.400111i	$-0.131029\pi$
$307$	48666.0	+	48666.0i	0.516355	+	0.516355i	−0.400111	+	0.916467i	$0.631029\pi$
$308$	−30031.4	+	30031.4i	−0.316573	+	0.316573i
$309$		−	119607.i		−	1.25267i
$310$	−16442.0	−	12970.2i	−0.171092	−	0.134965i
$311$	14980.4			0.154882			0.0774411	−	0.996997i	$-0.475325\pi$
$311$	14980.4			0.154882			0.0774411	+	0.996997i	$0.475325\pi$
$312$	68655.5	+	68655.5i	0.705288	+	0.705288i
$313$	69736.2	−	69736.2i	0.711819	−	0.711819i	−0.255097	−	0.966915i	$-0.582107\pi$
$313$	69736.2	−	69736.2i	0.711819	−	0.711819i	0.966915	+	0.255097i	$0.0821074\pi$
$314$		−	11111.4i		−	0.112696i
$315$	−52003.8	+	65924.1i	−0.524100	+	0.664390i
$316$	63378.4			0.634698
$317$	122186.	+	122186.i	1.21591	+	1.21591i	0.969050	+	0.246863i	$0.0793999\pi$
$317$	122186.	+	122186.i	1.21591	+	1.21591i	0.246863	+	0.969050i	$0.420600\pi$
$318$	−45558.6	+	45558.6i	−0.450522	+	0.450522i
$319$			27392.6i			0.269185i
$320$	−3096.86	−	26235.5i	−0.0302427	−	0.256206i
$321$	269866.			2.61901
$322$	2116.16	+	2116.16i	0.0204097	+	0.0204097i
$323$	121544.	−	121544.i	1.16500	−	1.16500i
$324$			174137.i			1.65883i
$325$	43778.9	−	71340.5i	0.414475	−	0.675413i
$326$	12982.6			0.122160
$327$	−82260.9	−	82260.9i	−0.769304	−	0.769304i
$328$	−44796.7	+	44796.7i	−0.416388	+	0.416388i
$329$		−	54492.7i		−	0.503438i
$330$	−102664.	+	12118.6i	−0.942738	+	0.111282i
$331$	86751.3			0.791808			0.395904	−	0.918292i	$-0.370431\pi$
$331$	86751.3			0.791808			0.395904	+	0.918292i	$0.370431\pi$
$332$	−40225.9	−	40225.9i	−0.364947	−	0.364947i
$333$	−273126.	+	273126.i	−2.46305	+	2.46305i
$334$			15150.9i			0.135814i
$335$	−172318.	−	135932.i	−1.53547	−	1.21124i
$336$	−45589.0			−0.403814
$337$	−31939.9	−	31939.9i	−0.281238	−	0.281238i	0.552365	−	0.833603i	$-0.313726\pi$
$337$	−31939.9	−	31939.9i	−0.281238	−	0.281238i	−0.833603	+	0.552365i	$0.813726\pi$
$338$	11221.4	−	11221.4i	0.0982232	−	0.0982232i
$339$		−	189159.i		−	1.64599i
$340$	−103075.	+	130666.i	−0.891652	+	1.13033i
$341$	95231.8			0.818980
$342$	69420.2	+	69420.2i	0.593518	+	0.593518i
$343$	57443.9	−	57443.9i	0.488265	−	0.488265i
$344$		−	8164.88i		−	0.0689974i
$345$	−5271.19	−	44655.7i	−0.0442864	−	0.375179i
$346$	48715.0			0.406921
$347$	−32993.9	−	32993.9i	−0.274016	−	0.274016i	0.556699	−	0.830714i	$-0.312068\pi$
$347$	−32993.9	−	32993.9i	−0.274016	−	0.274016i	−0.830714	+	0.556699i	$0.812068\pi$
$348$	−25613.1	+	25613.1i	−0.211496	+	0.211496i
$349$		−	162122.i		−	1.33104i	−0.746381	−	0.665519i	$-0.768210\pi$
$349$		−	162122.i		−	1.33104i	0.746381	−	0.665519i	$-0.231790\pi$
$350$	−3948.24	−	16491.0i	−0.0322305	−	0.134621i
$351$	−226868.			−1.84145
$352$	−113008.	−	113008.i	−0.912058	−	0.912058i
$353$	88849.7	−	88849.7i	0.713028	−	0.713028i	−0.254140	−	0.967168i	$-0.581792\pi$
$353$	88849.7	−	88849.7i	0.713028	−	0.713028i	0.967168	+	0.254140i	$0.0817923\pi$
$354$			36501.0i			0.291272i
$355$	178553.	−	21076.5i	1.41681	−	0.167241i
$356$	−20843.4			−0.164463
$357$	101266.	+	101266.i	0.794558	+	0.794558i
$358$	49001.7	−	49001.7i	0.382336	−	0.382336i
$359$			192000.i			1.48974i	0.667207	+	0.744872i	$0.267490\pi$
$359$			192000.i			1.48974i	−0.667207	+	0.744872i	$0.732510\pi$
$360$	−161351.	−	127281.i	−1.24499	−	0.982103i
$361$	3918.87			0.0300709
$362$	−4912.33	−	4912.33i	−0.0374861	−	0.0374861i
$363$	163598.	−	163598.i	1.24155	−	1.24155i
$364$		−	33498.7i		−	0.252828i
$365$	−70796.4	+	89747.0i	−0.531405	+	0.673650i
$366$	−57984.5			−0.432863
$367$	82175.5	+	82175.5i	0.610113	+	0.610113i	0.942975	−	0.332862i	$-0.108014\pi$
$367$	82175.5	+	82175.5i	0.610113	+	0.610113i	−0.332862	+	0.942975i	$0.608014\pi$
$368$	12004.1	−	12004.1i	0.0886410	−	0.0886410i
$369$		−	263443.i		−	1.93479i
$370$	−9144.28	−	77467.1i	−0.0667953	−	0.565866i
$371$	48059.4			0.349165
$372$	89045.2	+	89045.2i	0.643465	+	0.643465i
$373$	28967.5	−	28967.5i	0.208206	−	0.208206i	−0.595299	−	0.803505i	$-0.702966\pi$
$373$	28967.5	−	28967.5i	0.208206	−	0.208206i	0.803505	+	0.595299i	$0.202966\pi$
$374$			122604.i			0.876519i
$375$	−106884.	+	231279.i	−0.760065	+	1.64465i
$376$	133372.			0.943385
$377$	−15277.6	−	15277.6i	−0.107491	−	0.107491i
$378$	−32499.2	+	32499.2i	−0.227452	+	0.227452i
$379$		−	13961.6i		−	0.0971981i	−0.998818	−	0.0485990i	$-0.984524\pi$
$379$		−	13961.6i		−	0.0971981i	0.998818	−	0.0485990i	$-0.0154757\pi$
$380$	121542.	−	14346.9i	0.841704	−	0.0993553i
$381$	51792.0			0.356790
$382$	−6773.31	−	6773.31i	−0.0464167	−	0.0464167i
$383$	25812.0	−	25812.0i	0.175964	−	0.175964i	−0.613630	−	0.789594i	$-0.710291\pi$
$383$	25812.0	−	25812.0i	0.175964	−	0.175964i	0.789594	+	0.613630i	$0.210291\pi$
$384$		−	271303.i		−	1.83989i
$385$	60541.7	+	47758.0i	0.408445	+	0.322199i
$386$	−17857.7			−0.119853
$387$	24008.3	+	24008.3i	0.160302	+	0.160302i
$388$	−150142.	+	150142.i	−0.997327	+	0.997327i
$389$		−	41207.1i		−	0.272316i	−0.990687	−	0.136158i	$-0.956525\pi$
$389$		−	41207.1i		−	0.272316i	0.990687	−	0.136158i	$-0.0434755\pi$
$390$	50499.8	−	64017.5i	0.332017	−	0.420891i
$391$	−53328.8			−0.348826
$392$	65110.2	+	65110.2i	0.423718	+	0.423718i
$393$	219592.	−	219592.i	1.42178	−	1.42178i
$394$		−	43790.2i		−	0.282088i
$395$	−13489.5	−	114278.i	−0.0864571	−	0.732434i
$396$	432258.			2.75647
$397$	120824.	+	120824.i	0.766605	+	0.766605i	0.977507	−	0.210902i	$-0.0676401\pi$
$397$	120824.	+	120824.i	0.766605	+	0.766605i	−0.210902	+	0.977507i	$0.567640\pi$
$398$	59355.9	−	59355.9i	0.374712	−	0.374712i
$399$		−	105313.i		−	0.661513i
$400$	−93547.1	+	22396.8i	−0.584669	+	0.139980i
$401$	−127947.			−0.795683			−0.397842	−	0.917454i	$-0.630241\pi$
$401$	−127947.			−0.795683			−0.397842	+	0.917454i	$0.630241\pi$
$402$	−151182.	−	151182.i	−0.935511	−	0.935511i
$403$	−53113.4	+	53113.4i	−0.327035	+	0.327035i
$404$		−	143034.i		−	0.876348i
$405$	313988.	−	37063.4i	1.91427	−	0.225962i
$406$	−4377.08			−0.0265541
$407$	250826.	+	250826.i	1.51420	+	1.51420i
$408$	−247850.	+	247850.i	−1.48891	+	1.48891i
$409$		−	29709.4i		−	0.177602i	−0.996049	−	0.0888010i	$-0.971696\pi$
$409$		−	29709.4i		−	0.177602i	0.996049	−	0.0888010i	$-0.0283035\pi$
$410$	41770.4	+	32950.3i	0.248486	+	0.196016i
$411$	−169025.			−1.00062
$412$	−71417.5	−	71417.5i	−0.420736	−	0.420736i
$413$	19252.3	−	19252.3i	0.112871	−	0.112871i
$414$		−	30459.0i		−	0.177711i
$415$	−63969.9	+	81093.3i	−0.371432	+	0.470857i
$416$	126055.			0.728406
$417$	−59065.8	−	59065.8i	−0.339675	−	0.339675i
$418$	63752.4	−	63752.4i	0.364875	−	0.364875i
$419$		−	261626.i		−	1.49023i	−0.666936	−	0.745115i	$-0.732394\pi$
$419$		−	261626.i		−	1.49023i	0.666936	−	0.745115i	$-0.267606\pi$
$420$	11953.3	+	101264.i	0.0677625	+	0.574060i
$421$	199824.			1.12742			0.563708	−	0.825974i	$-0.309374\pi$
$421$	199824.			1.12742			0.563708	+	0.825974i	$0.309374\pi$
$422$	−92648.2	−	92648.2i	−0.520250	−	0.520250i
$423$	−392171.	+	392171.i	−2.19177	+	2.19177i
$424$			117626.i			0.654295i
$425$	257543.	+	158044.i	1.42584	+	0.874985i
$426$	175144.			0.965108
$427$	30583.7	+	30583.7i	0.167739	+	0.167739i
$428$	161138.	−	161138.i	0.879649	−	0.879649i
$429$			370789.i			2.01471i
$430$	−6809.50	+	803.799i	−0.0368280	+	0.00434721i
$431$	−189060.			−1.01776			−0.508878	−	0.860838i	$-0.669940\pi$
$431$	−189060.			−1.01776			−0.508878	+	0.860838i	$0.669940\pi$
$432$	184355.	+	184355.i	0.987842	+	0.987842i
$433$	29097.9	−	29097.9i	0.155198	−	0.155198i	−0.625237	−	0.780435i	$-0.714998\pi$
$433$	29097.9	−	29097.9i	0.155198	−	0.155198i	0.780435	+	0.625237i	$0.214998\pi$
$434$			15217.2i			0.0807893i
$435$	51634.5	+	40731.6i	0.272874	+	0.215255i
$436$	−98236.4			−0.516773
$437$	27730.3	+	27730.3i	0.145208	+	0.145208i
$438$	−78739.2	+	78739.2i	−0.410434	+	0.410434i
$439$			197259.i			1.02355i	0.859121	+	0.511773i	$0.171011\pi$
$439$			197259.i			1.02355i	−0.859121	+	0.511773i	$0.828989\pi$
$440$	−116889.	+	148177.i	−0.603764	+	0.765378i
$441$	−382904.			−1.96885
$442$	−68379.6	−	68379.6i	−0.350011	−	0.350011i
$443$	24825.7	−	24825.7i	0.126501	−	0.126501i	−0.641022	−	0.767523i	$-0.721489\pi$
$443$	24825.7	−	24825.7i	0.126501	−	0.126501i	0.767523	+	0.641022i	$0.221489\pi$
$444$			469063.i			2.37939i
$445$	4436.30	+	37582.8i	0.0224027	+	0.189788i
$446$	−90975.1			−0.457354
$447$	161861.	+	161861.i	0.810077	+	0.810077i
$448$	−13573.6	+	13573.6i	−0.0676301	+	0.0676301i
$449$		−	120871.i		−	0.599557i	−0.954009	−	0.299778i	$-0.903087\pi$
$449$		−	120871.i		−	0.599557i	0.954009	−	0.299778i	$-0.0969127\pi$
$450$	−90267.5	+	147097.i	−0.445766	+	0.726403i
$451$	−241934.			−1.18944
$452$	−112947.	−	112947.i	−0.552839	−	0.552839i
$453$	−29148.1	+	29148.1i	−0.142041	+	0.142041i
$454$		−	91139.9i		−	0.442178i
$455$	−60401.7	+	7129.87i	−0.291761	+	0.0344396i
$456$	257757.			1.23960
$457$	−255165.	−	255165.i	−1.22177	−	1.22177i	−0.967003	−	0.254767i	$-0.918001\pi$
$457$	−255165.	−	255165.i	−1.22177	−	1.22177i	−0.254767	−	0.967003i	$-0.581999\pi$
$458$	38984.4	−	38984.4i	0.185849	−	0.185849i
$459$		−	819005.i		−	3.88742i
$460$	−29811.5	−	23516.6i	−0.140886	−	0.111137i
$461$	402093.			1.89202			0.946008	−	0.324143i	$-0.105076\pi$
$461$	402093.			1.89202			0.946008	+	0.324143i	$0.105076\pi$
$462$	53116.0	+	53116.0i	0.248852	+	0.248852i
$463$	−58516.3	+	58516.3i	−0.272970	+	0.272970i	−0.830295	−	0.557325i	$-0.811828\pi$
$463$	−58516.3	+	58516.3i	−0.272970	+	0.272970i	0.557325	+	0.830295i	$0.311828\pi$
$464$			24829.4i			0.115327i
$465$	141606.	−	179510.i	0.654899	−	0.830202i
$466$	148180.			0.682365
$467$	−192768.	−	192768.i	−0.883895	−	0.883895i	0.110033	−	0.993928i	$-0.464904\pi$
$467$	−192768.	−	192768.i	−0.883895	−	0.883895i	−0.993928	+	0.110033i	$0.964904\pi$
$468$	−241082.	+	241082.i	−1.10071	+	1.10071i
$469$			159481.i			0.725043i
$470$	−13129.9	−	111232.i	−0.0594383	−	0.503541i
$471$	121312.			0.546843
$472$	47120.5	+	47120.5i	0.211507	+	0.211507i
$473$	22048.1	−	22048.1i	0.0985482	−	0.0985482i
$474$		−	112096.i		−	0.498924i
$475$	−51738.0	−	216100.i	−0.229310	−	0.957782i
$476$	120932.			0.533737
$477$	−345872.	−	345872.i	−1.52012	−	1.52012i
$478$	−30688.3	+	30688.3i	−0.134313	+	0.134313i
$479$		−	81215.4i		−	0.353971i	−0.984213	−	0.176985i	$-0.943365\pi$
$479$		−	81215.4i		−	0.353971i	0.984213	−	0.176985i	$-0.0566345\pi$
$480$	−381055.	+	44980.0i	−1.65389	+	0.195226i
$481$	−279785.			−1.20930
$482$	−2371.81	−	2371.81i	−0.0102091	−	0.0102091i
$483$	−23103.8	+	23103.8i	−0.0990351	+	0.0990351i
$484$		−	195369.i		−	0.833999i
$485$	302677.	+	238765.i	1.28676	+	1.01505i
$486$	103059.			0.436329
$487$	−122211.	−	122211.i	−0.515289	−	0.515289i	0.400853	−	0.916142i	$-0.368714\pi$
$487$	−122211.	−	122211.i	−0.515289	−	0.515289i	−0.916142	+	0.400853i	$0.868714\pi$
$488$	−74854.4	+	74854.4i	−0.314324	+	0.314324i
$489$			141742.i			0.592763i
$490$	47892.0	−	60711.7i	0.199467	−	0.252860i
$491$	−188082.			−0.780159			−0.390079	−	0.920781i	$-0.627552\pi$
$491$	−188082.			−0.780159			−0.390079	+	0.920781i	$0.627552\pi$
$492$	−226217.	−	226217.i	−0.934535	−	0.934535i
$493$	55152.9	−	55152.9i	0.226921	−	0.226921i
$494$			71112.9i			0.291403i
$495$	−92001.8	−	779408.i	−0.375479	−	3.18093i
$496$	86320.9			0.350875
$497$	−92379.1	−	92379.1i	−0.373991	−	0.373991i
$498$	−71146.9	+	71146.9i	−0.286878	+	0.286878i
$499$			240448.i			0.965651i	0.875717	+	0.482825i	$0.160389\pi$
$499$			240448.i			0.965651i	−0.875717	+	0.482825i	$0.839611\pi$
$500$	74276.4	+	201918.i	0.297106	+	0.807673i
$501$	−165415.			−0.659020
$502$	−918.950	−	918.950i	−0.00364657	−	0.00364657i
$503$	−350867.	+	350867.i	−1.38678	+	1.38678i	−0.554782	+	0.831996i	$0.687198\pi$
$503$	−350867.	+	350867.i	−1.38678	+	1.38678i	−0.831996	+	0.554782i	$0.812802\pi$
$504$			149331.i			0.587881i
$505$	−257906.	+	30443.4i	−1.01130	+	0.119374i
$506$	−27972.1			−0.109251
$507$	122513.	+	122513.i	0.476614	+	0.476614i
$508$	30925.2	−	30925.2i	0.119835	−	0.119835i
$509$		−	376542.i		−	1.45338i	−0.686968	−	0.726688i	$-0.741059\pi$
$509$		−	376542.i		−	1.45338i	0.686968	−	0.726688i	$-0.258941\pi$
$510$	231106.	+	182307.i	0.888529	+	0.700910i
$511$	83061.4			0.318096
$512$	−179851.	−	179851.i	−0.686079	−	0.686079i
$513$	−425871.	+	425871.i	−1.61824	+	1.61824i
$514$			126989.i			0.480664i
$515$	−113573.	+	143974.i	−0.428213	+	0.542836i
$516$	41231.6			0.154857
$517$	360152.	+	360152.i	1.34743	+	1.34743i
$518$	−40079.7	+	40079.7i	−0.149370	+	0.149370i
$519$			531861.i			1.97453i
$520$	−17450.5	−	147835.i	−0.0645359	−	0.546726i
$521$	−160724.			−0.592112			−0.296056	−	0.955171i	$-0.595672\pi$
$521$	−160724.			−0.592112			−0.296056	+	0.955171i	$0.595672\pi$
$522$	31500.8	+	31500.8i	0.115606	+	0.115606i
$523$	70717.0	−	70717.0i	0.258536	−	0.258536i	−0.565923	−	0.824458i	$-0.691480\pi$
$523$	70717.0	−	70717.0i	0.258536	−	0.258536i	0.824458	+	0.565923i	$0.191480\pi$
$524$		−	262239.i		−	0.955068i
$525$	180046.	−	43106.1i	0.653228	−	0.156394i
$526$	100901.			0.364689
$527$	−191742.	−	191742.i	−0.690393	−	0.690393i
$528$	301306.	−	301306.i	1.08079	−	1.08079i
$529$		−	12167.0i		−	0.0434783i
$530$	98100.4	−	11579.8i	0.349236	−	0.0412241i
$531$	−277109.			−0.982791
$532$	−62883.0	−	62883.0i	−0.222183	−	0.222183i
$533$	134933.	−	134933.i	0.474968	−	0.474968i
$534$			36865.3i			0.129281i
$535$	−324845.	−	256252.i	−1.13493	−	0.895281i
$536$	−390334.			−1.35865
$537$	534991.	+	534991.i	1.85523	+	1.85523i
$538$	−111025.	+	111025.i	−0.383579	+	0.383579i
$539$			351641.i			1.21038i
$540$	361159.	−	457834.i	1.23854	−	1.57008i
$541$	568133.			1.94114			0.970568	−	0.240829i	$-0.0774192\pi$
$541$	568133.			1.94114			0.970568	+	0.240829i	$0.0774192\pi$
$542$	80419.7	+	80419.7i	0.273756	+	0.273756i
$543$	53631.8	−	53631.8i	0.181896	−	0.181896i
$544$			455065.i			1.53771i
$545$	20908.6	+	177131.i	0.0703935	+	0.596350i
$546$	−59248.6			−0.198743
$547$	−237299.	−	237299.i	−0.793089	−	0.793089i	0.188906	−	0.981995i	$-0.439506\pi$
$547$	−237299.	−	237299.i	−0.793089	−	0.793089i	−0.981995	+	0.188906i	$0.939506\pi$
$548$	−100926.	+	100926.i	−0.336078	+	0.336078i
$549$		−	440208.i		−	1.46054i
$550$	135087.	+	82897.6i	0.446568	+	0.274042i
$551$	−57357.5			−0.188924
$552$	−56547.1	−	56547.1i	−0.185580	−	0.185580i
$553$	−59124.8	+	59124.8i	−0.193339	+	0.193339i
$554$			127648.i			0.415906i
$555$	845771.	−	99835.4i	2.74579	−	0.324115i
$556$	−70536.7			−0.228174
$557$	−135982.	−	135982.i	−0.438299	−	0.438299i	0.453140	−	0.891439i	$-0.350304\pi$
$557$	−135982.	−	135982.i	−0.438299	−	0.438299i	−0.891439	+	0.453140i	$0.850304\pi$
$558$	109514.	−	109514.i	0.351724	−	0.351724i
$559$			24593.7i			0.0787045i
$560$	54876.8	+	43289.2i	0.174990	+	0.138039i
$561$	−1.33857e6			−4.25318
$562$	−12959.3	−	12959.3i	−0.0410306	−	0.0410306i
$563$	377692.	−	377692.i	1.19157	−	1.19157i	0.214947	−	0.976626i	$-0.431042\pi$
$563$	377692.	−	377692.i	1.19157	−	1.19157i	0.976626	−	0.214947i	$-0.0689578\pi$
$564$			673511.i			2.11732i
$565$	−179616.	+	227696.i	−0.562663	+	0.713276i
$566$	73052.4			0.228035
$567$	−162450.	−	162450.i	−0.505306	−	0.505306i
$568$	226100.	−	226100.i	0.700815	−	0.700815i
$569$		−	362550.i		−	1.11981i	−0.828557	−	0.559904i	$-0.810838\pi$
$569$		−	362550.i		−	1.11981i	0.828557	−	0.559904i	$-0.189162\pi$
$570$	−25375.1	−	214969.i	−0.0781013	−	0.661647i
$571$	371039.			1.13801			0.569007	−	0.822333i	$-0.307328\pi$
$571$	371039.			1.13801			0.569007	+	0.822333i	$0.307328\pi$
$572$	221399.	+	221399.i	0.676681	+	0.676681i
$573$	73949.7	−	73949.7i	0.225230	−	0.225230i
$574$		−	38658.8i		−	0.117334i
$575$	−36057.8	+	58758.5i	−0.109060	+	0.177720i
$576$	195372.			0.588869
$577$	−69605.5	−	69605.5i	−0.209070	−	0.209070i	0.594802	−	0.803872i	$-0.297230\pi$
$577$	−69605.5	−	69605.5i	−0.209070	−	0.209070i	−0.803872	+	0.594802i	$0.797230\pi$
$578$	158649.	−	158649.i	0.474876	−	0.474876i
$579$		−	194966.i		−	0.581571i
$580$	55152.1	−	6510.20i	0.163948	−	0.0193525i
$581$	75052.3			0.222337
$582$	265553.	+	265553.i	0.783980	+	0.783980i
$583$	−317634.	+	317634.i	−0.934521	+	0.934521i
$584$			203295.i			0.596074i
$585$	486009.	+	383385.i	1.42014	+	1.12027i
$586$	172141.			0.501289
$587$	−63668.7	−	63668.7i	−0.184778	−	0.184778i	0.608656	−	0.793434i	$-0.291709\pi$
$587$	−63668.7	−	63668.7i	−0.184778	−	0.184778i	−0.793434	+	0.608656i	$0.791709\pi$
$588$	−328798.	+	328798.i	−0.950986	+	0.950986i
$589$			199407.i			0.574789i
$590$	34659.6	−	43937.3i	0.0995680	−	0.126220i
$591$	478093.			1.36879
$592$	227356.	+	227356.i	0.648729	+	0.648729i
$593$	3270.06	−	3270.06i	0.00929923	−	0.00929923i	−0.702442	−	0.711741i	$-0.747907\pi$
$593$	3270.06	−	3270.06i	0.00929923	−	0.00929923i	0.711741	+	0.702442i	$0.247907\pi$
$594$		−	429586.i		−	1.21752i
$595$	−25739.2	−	218053.i	−0.0727044	−	0.615926i
$596$	193295.			0.544162
$597$	648036.	+	648036.i	1.81824	+	1.81824i
$598$	15600.8	−	15600.8i	0.0436260	−	0.0436260i
$599$			338288.i			0.942830i	0.881912	+	0.471415i	$0.156257\pi$
$599$			338288.i			0.942830i	−0.881912	+	0.471415i	$0.843743\pi$
$600$	105503.	+	440666.i	0.293065	+	1.22407i
$601$	−166645.			−0.461364			−0.230682	−	0.973029i	$-0.574096\pi$
$601$	−166645.			−0.461364			−0.230682	+	0.973029i	$0.574096\pi$
$602$	3523.08	+	3523.08i	0.00972141	+	0.00972141i
$603$	1.14775e6	−	1.14775e6i	3.15654	−	3.15654i
$604$			34808.8i			0.0954147i
$605$	−352271.	+	41582.4i	−0.962424	+	0.113605i
$606$	−252982.			−0.688881
$607$	−17707.8	−	17707.8i	−0.0480603	−	0.0480603i	0.682668	−	0.730728i	$-0.260819\pi$
$607$	−17707.8	−	17707.8i	−0.0480603	−	0.0480603i	−0.730728	+	0.682668i	$0.760819\pi$
$608$	236627.	−	236627.i	0.640115	−	0.640115i
$609$		−	47788.1i		−	0.128850i
$610$	69797.6	+	55059.4i	0.187578	+	0.147969i
$611$	−401734.			−1.07611
$612$	−870320.	−	870320.i	−2.32368	−	2.32368i
$613$	77407.4	−	77407.4i	0.205997	−	0.205997i	−0.596566	−	0.802564i	$-0.703469\pi$
$613$	77407.4	−	77407.4i	0.205997	−	0.205997i	0.802564	+	0.596566i	$0.203469\pi$
$614$		−	102791.i		−	0.272658i
$615$	−359746.	+	456042.i	−0.951142	+	1.20574i
$616$	137139.			0.361409
$617$	−303587.	−	303587.i	−0.797466	−	0.797466i	0.185229	−	0.982695i	$-0.440697\pi$
$617$	−303587.	−	303587.i	−0.797466	−	0.797466i	−0.982695	+	0.185229i	$0.940697\pi$
$618$	−126315.	+	126315.i	−0.330733	+	0.330733i
$619$			34541.1i			0.0901478i	0.998984	+	0.0450739i	$0.0143523\pi$
$619$			34541.1i			0.0901478i	−0.998984	+	0.0450739i	$0.985648\pi$
$620$	−22633.1	−	191739.i	−0.0588789	−	0.498802i
$621$	186856.			0.484535
$622$	−15820.5	−	15820.5i	−0.0408922	−	0.0408922i
$623$	19444.5	−	19444.5i	0.0500979	−	0.0500979i
$624$			336094.i			0.863160i
$625$	348271.	−	176905.i	0.891574	−	0.452876i
$626$	−147295.			−0.375871
$627$	696036.	+	696036.i	1.77050	+	1.77050i
$628$	72435.8	−	72435.8i	0.183668	−	0.183668i
$629$		−	1.01004e6i		−	2.55292i
$630$	124542.	−	14701.0i	0.313787	−	0.0370396i
$631$	−419828.			−1.05442			−0.527209	−	0.849735i	$-0.676762\pi$
$631$	−419828.			−1.05442			−0.527209	+	0.849735i	$0.676762\pi$
$632$	−144709.	−	144709.i	−0.362295	−	0.362295i
$633$	1.01152e6	−	1.01152e6i	2.52444	−	2.52444i
$634$		−	258078.i		−	0.642054i
$635$	−62343.4	−	49179.2i	−0.154612	−	0.121965i
$636$	−593998.			−1.46849
$637$	−196120.	−	196120.i	−0.483330	−	0.483330i
$638$	28928.9	−	28928.9i	0.0710707	−	0.0710707i
$639$			1.32966e6i			3.25641i
$640$	−257617.	+	326575.i	−0.628947	+	0.797302i
$641$	80309.1			0.195456			0.0977279	−	0.995213i	$-0.468843\pi$
$641$	80309.1			0.195456			0.0977279	+	0.995213i	$0.468843\pi$
$642$	−285001.	−	285001.i	−0.691475	−	0.691475i
$643$	−232755.	+	232755.i	−0.562960	+	0.562960i	−0.930147	−	0.367187i	$-0.880321\pi$
$643$	−232755.	+	232755.i	−0.562960	+	0.562960i	0.367187	+	0.930147i	$0.380321\pi$
$644$			27590.7i			0.0665259i
$645$	−8775.72	−	74344.9i	−0.0210942	−	0.178703i
$646$	−256721.			−0.615172
$647$	397665.	+	397665.i	0.949968	+	0.949968i	0.998807	−	0.0488387i	$-0.0155520\pi$
$647$	397665.	+	397665.i	0.949968	+	0.949968i	−0.0488387	+	0.998807i	$0.515552\pi$
$648$	397601.	−	397601.i	0.946884	−	0.946884i
$649$			254484.i			0.604187i
$650$	−121576.	+	29107.4i	−0.287754	+	0.0688933i
$651$	−166138.			−0.392019
$652$	84634.6	+	84634.6i	0.199091	+	0.199091i
$653$	−54870.1	+	54870.1i	−0.128679	+	0.128679i	−0.768513	−	0.639834i	$-0.779003\pi$
$653$	−54870.1	+	54870.1i	−0.128679	+	0.128679i	0.639834	+	0.768513i	$0.279003\pi$
$654$			173749.i			0.406225i
$655$	−472844.	+	55814.9i	−1.10214	+	0.130097i
$656$	−219296.			−0.509592
$657$	−597774.	−	597774.i	−1.38486	−	1.38486i
$658$	−57548.9	+	57548.9i	−0.132919	+	0.132919i
$659$			779685.i			1.79535i	0.440661	+	0.897674i	$0.354744\pi$
$659$			779685.i			1.79535i	−0.440661	+	0.897674i	$0.645256\pi$
$660$	−748275.	−	590272.i	−1.71780	−	1.35508i
$661$	−602854.			−1.37978			−0.689889	−	0.723915i	$-0.742341\pi$
$661$	−602854.			−1.37978			−0.689889	+	0.723915i	$0.742341\pi$
$662$	−91616.8	−	91616.8i	−0.209054	−	0.209054i
$663$	746555.	−	746555.i	1.69838	−	1.69838i
$664$			183692.i			0.416634i
$665$	−100001.	+	126769.i	−0.226131	+	0.286661i
$666$	576888.			1.30060
$667$	12583.2	+	12583.2i	0.0282838	+	0.0282838i
$668$	−98769.6	+	98769.6i	−0.221345	+	0.221345i
$669$		−	993249.i		−	2.21925i
$670$	38426.7	+	325538.i	0.0856020	+	0.725190i
$671$	−404267.			−0.897890
$672$	197149.	+	197149.i	0.436572	+	0.436572i
$673$	−259051.	+	259051.i	−0.571946	+	0.571946i	−0.932672	−	0.360726i	$-0.882529\pi$
$673$	−259051.	+	259051.i	−0.571946	+	0.571946i	0.360726	+	0.932672i	$0.382529\pi$
$674$			67462.5i			0.148506i
$675$	−902392.	−	553763.i	−1.98056	−	1.21539i
$676$	146306.			0.320161
$677$	−61018.4	−	61018.4i	−0.133132	−	0.133132i	0.637400	−	0.770533i	$-0.280010\pi$
$677$	−61018.4	−	61018.4i	−0.133132	−	0.133132i	−0.770533	+	0.637400i	$0.780010\pi$
$678$	−199768.	+	199768.i	−0.434576	+	0.434576i
$679$		−	280130.i		−	0.607602i
$680$	533690.	−	62997.2i	1.15417	−	0.136240i
$681$	995048.			2.14561
$682$	−100573.	−	100573.i	−0.216228	−	0.216228i
$683$	150510.	−	150510.i	0.322644	−	0.322644i	−0.527137	−	0.849780i	$-0.676734\pi$
$683$	150510.	−	150510.i	0.322644	−	0.322644i	0.849780	+	0.527137i	$0.176734\pi$
$684$			905108.i			1.93459i
$685$	203460.	+	160498.i	0.433609	+	0.342050i
$686$	−121331.			−0.257825
$687$	425624.	+	425624.i	0.901806	+	0.901806i
$688$	19985.0	−	19985.0i	0.0422209	−	0.0422209i
$689$		−	354306.i		−	0.746346i
$690$	−41593.4	+	52727.0i	−0.0873627	+	0.110748i
$691$	806137.			1.68831			0.844156	−	0.536098i	$-0.180102\pi$
$691$	806137.			1.68831			0.844156	+	0.536098i	$0.180102\pi$
$692$	317576.	+	317576.i	0.663186	+	0.663186i
$693$	−403247.	+	403247.i	−0.839663	+	0.839663i
$694$			69688.9i			0.144692i
$695$	15013.0	+	127185.i	0.0310813	+	0.263310i
$696$	116962.			0.241450
$697$	487116.	+	487116.i	1.00269	+	1.00269i
$698$	−171214.	+	171214.i	−0.351423	+	0.351423i
$699$			1.61780e6i			3.31108i
$700$	81767.2	−	133245.i	0.166872	−	0.271928i
$701$	−600505.			−1.22203			−0.611014	−	0.791620i	$-0.709238\pi$
$701$	−600505.			−1.22203			−0.611014	+	0.791620i	$0.709238\pi$
$702$	239592.	+	239592.i	0.486181	+	0.486181i
$703$	−525207.	+	525207.i	−1.06272	+	1.06272i
$704$		−	179421.i		−	0.362017i
$705$	1.21441e6	−	143350.i	2.44336	−	0.288416i
$706$	−187666.			−0.376509
$707$	133434.	+	133434.i	0.266949	+	0.266949i
$708$	−237952.	+	237952.i	−0.474704	+	0.474704i
$709$			81715.0i			0.162558i	0.996691	+	0.0812792i	$0.0259005\pi$
$709$			81715.0i			0.162558i	−0.996691	+	0.0812792i	$0.974099\pi$
$710$	−210826.	−	166309.i	−0.418222	−	0.329912i
$711$	851014.			1.68344
$712$	47590.7	+	47590.7i	0.0938777	+	0.0938777i
$713$	43746.1	−	43746.1i	0.0860518	−	0.0860518i
$714$		−	213890.i		−	0.419561i
$715$	352084.	−	446329.i	0.688706	−	0.873057i
$716$	638889.			1.24623
$717$	−335049.	−	335049.i	−0.651733	−	0.651733i
$718$	202768.	−	202768.i	0.393324	−	0.393324i
$719$		−	758162.i		−	1.46657i	−0.679919	−	0.733287i	$-0.737985\pi$
$719$		−	758162.i		−	1.46657i	0.679919	−	0.733287i	$-0.262015\pi$
$720$	−83393.1	−	706477.i	−0.160866	−	1.36280i
$721$	133249.			0.256326
$722$	−4138.66	−	4138.66i	−0.00793936	−	0.00793936i
$723$	25895.0	−	25895.0i	0.0495381	−	0.0495381i
$724$		−	64047.5i		−	0.122187i
$725$	−23477.1	−	98059.5i	−0.0446652	−	0.186558i
$726$	−345546.			−0.655590
$727$	150377.	+	150377.i	0.284520	+	0.284520i	0.834909	−	0.550389i	$-0.185520\pi$
$727$	150377.	+	150377.i	0.284520	+	0.284520i	−0.550389	+	0.834909i	$0.685520\pi$
$728$	−76486.2	+	76486.2i	−0.144318	+	0.144318i
$729$			100795.i			0.189664i
$730$	169548.	−	20013.5i	0.318160	−	0.0375559i
$731$	−88784.4			−0.166151
$732$	−378005.	−	378005.i	−0.705464	−	0.705464i
$733$	382106.	−	382106.i	0.711175	−	0.711175i	−0.255606	−	0.966781i	$-0.582275\pi$
$733$	382106.	−	382106.i	0.711175	−	0.711175i	0.966781	+	0.255606i	$0.0822750\pi$
$734$		−	173569.i		−	0.322166i
$735$	662838.	+	522876.i	1.22697	+	0.967885i
$736$	−103823.			−0.191663
$737$	−1.05404e6	−	1.05404e6i	−1.94054	−	1.94054i
$738$	−278218.	+	278218.i	−0.510826	+	0.510826i
$739$			975534.i			1.78630i	0.449762	+	0.893148i	$0.351509\pi$
$739$			975534.i			1.78630i	−0.449762	+	0.893148i	$0.648491\pi$
$740$	445400.	−	564625.i	0.813368	−	1.03109i
$741$	−776397.			−1.41399
$742$	−50754.9	−	50754.9i	−0.0921870	−	0.0921870i
$743$	−7337.78	+	7337.78i	−0.0132919	+	0.0132919i	−0.713721	−	0.700430i	$-0.752992\pi$
$743$	−7337.78	+	7337.78i	−0.0132919	+	0.0132919i	0.700430	+	0.713721i	$0.252992\pi$
$744$		−	406626.i		−	0.734598i
$745$	−41140.9	−	348532.i	−0.0741245	−	0.627957i
$746$	−61184.3			−0.109942
$747$	−540134.	−	540134.i	−0.967967	−	0.967967i
$748$	−799262.	+	799262.i	−1.42852	+	1.42852i
$749$			300646.i			0.535910i
$750$	357129.	−	131371.i	0.634896	−	0.233549i
$751$	76363.4			0.135396			0.0676979	−	0.997706i	$-0.478435\pi$
$751$	76363.4			0.135396			0.0676979	+	0.997706i	$0.478435\pi$
$752$	326452.	+	326452.i	0.577277	+	0.577277i
$753$	10032.9	−	10032.9i	0.0176945	−	0.0176945i
$754$			32268.9i			0.0567599i
$755$	62764.0	−	7408.71i	0.110107	−	0.0129972i
$756$	−423728.			−0.741385
$757$	−445831.	−	445831.i	−0.777999	−	0.777999i	0.201492	−	0.979490i	$-0.435421\pi$
$757$	−445831.	−	445831.i	−0.777999	−	0.777999i	−0.979490	+	0.201492i	$0.935421\pi$
$758$	−14744.7	+	14744.7i	−0.0256624	+	0.0256624i
$759$		−	305395.i		−	0.530124i
$760$	−310269.	−	244754.i	−0.537170	−	0.423743i
$761$	585037.			1.01022			0.505108	−	0.863056i	$-0.331453\pi$
$761$	585037.			1.01022			0.505108	+	0.863056i	$0.331453\pi$
$762$	−54696.8	−	54696.8i	−0.0942002	−	0.0942002i
$763$	91643.3	−	91643.3i	0.157417	−	0.157417i
$764$		−	88311.2i		−	0.151297i
$765$	−1.38404e6	+	1.75452e6i	−2.36497	+	2.99802i
$766$	−54519.5			−0.0929167
$767$	−141933.	−	141933.i	−0.241264	−	0.241264i
$768$	−91575.9	+	91575.9i	−0.155260	+	0.155260i
$769$			730416.i			1.23514i	0.786515	+	0.617572i	$0.211883\pi$
$769$			730416.i			1.23514i	−0.786515	+	0.617572i	$0.788117\pi$
$770$	−13500.8	−	114374.i	−0.0227707	−	0.192906i
$771$	−1.38645e6			−2.33235
$772$	−116415.	−	116415.i	−0.195332	−	0.195332i
$773$	−172500.	+	172500.i	−0.288688	+	0.288688i	−0.836561	−	0.547873i	$-0.815438\pi$
$773$	−172500.	+	172500.i	−0.288688	+	0.288688i	0.547873	+	0.836561i	$0.315438\pi$
$774$		−	50709.5i		−	0.0846463i
$775$	−340909.	+	81619.6i	−0.567591	+	0.135891i
$776$	685624.			1.13858
$777$	−437582.	−	437582.i	−0.724799	−	0.724799i
$778$	−43518.3	+	43518.3i	−0.0718973	+	0.0718973i
$779$		−	506587.i		−	0.834794i
$780$	746545.	−	88122.7i	1.22706	−	0.144843i
$781$	1.22110e6			2.00193
$782$	56319.8	+	56319.8i	0.0920975	+	0.0920975i
$783$	−193248.	+	193248.i	−0.315203	+	0.315203i
$784$			318738.i			0.518563i
$785$	−146027.	−	115192.i	−0.236970	−	0.186932i
$786$	−463817.			−0.750760
$787$	641643.	+	641643.i	1.03596	+	1.03596i	0.999329	+	0.0366343i	$0.0116637\pi$
$787$	641643.	+	641643.i	1.03596	+	1.03596i	0.0366343	+	0.999329i	$0.488336\pi$
$788$	285471.	−	285471.i	0.459736	−	0.459736i
$789$			1.10162e6i			1.76960i
$790$	−106441.	+	134933.i	−0.170552	+	0.216205i
$791$	210734.			0.336807
$792$	−986957.	−	986957.i	−1.57343	−	1.57343i
$793$	225471.	−	225471.i	0.358545	−	0.358545i
$794$		−	255201.i		−	0.404800i
$795$	126427.	+	1.07104e6i	0.200034	+	1.69462i
$796$	773889.			1.22138
$797$	−402737.	−	402737.i	−0.634022	−	0.634022i	0.315052	−	0.949074i	$-0.397978\pi$
$797$	−402737.	−	402737.i	−0.634022	−	0.634022i	−0.949074	+	0.315052i	$0.897978\pi$
$798$	−111220.	+	111220.i	−0.174653	+	0.174653i
$799$		−	1.45028e6i		−	2.27174i
$800$	501398.	+	307688.i	0.783434	+	0.480763i
$801$	−279874.			−0.436212
$802$	135123.	+	135123.i	0.210077	+	0.210077i
$803$	−548968.	+	548968.i	−0.851366	+	0.851366i
$804$		−	1.97113e6i		−	3.04932i
$805$	49749.0	−	5872.41i	0.0767701	−	0.00906200i
$806$	112185.			0.172688
$807$	−1.21215e6	−	1.21215e6i	−1.86126	−	1.86126i
$808$	−326583.	+	326583.i	−0.500232	+	0.500232i
$809$			650724.i			0.994260i	0.867676	+	0.497130i	$0.165613\pi$
$809$			650724.i			0.994260i	−0.867676	+	0.497130i	$0.834387\pi$
$810$	−370741.	−	292456.i	−0.565067	−	0.445750i
$811$	−472879.			−0.718967			−0.359483	−	0.933152i	$-0.617047\pi$
$811$	−472879.			−0.718967			−0.359483	+	0.933152i	$0.617047\pi$
$812$	−28534.4	−	28534.4i	−0.0432770	−	0.0432770i
$813$	−878007.	+	878007.i	−1.32836	+	1.32836i
$814$		−	529788.i		−	0.799564i
$815$	134591.	−	170619.i	0.202629	−	0.256869i
$816$	−1.21331e6			−1.82219
$817$	46166.6	+	46166.6i	0.0691647	+	0.0691647i
$818$	−31375.7	+	31375.7i	−0.0468907	+	0.0468907i
$819$		−	449804.i		−	0.670588i
$820$	57498.7	+	487109.i	0.0855127	+	0.724434i
$821$	−473443.			−0.702395			−0.351197	−	0.936301i	$-0.614225\pi$
$821$	−473443.			−0.702395			−0.351197	+	0.936301i	$0.614225\pi$
$822$	178505.	+	178505.i	0.264184	+	0.264184i
$823$	379914.	−	379914.i	0.560900	−	0.560900i	−0.368663	−	0.929563i	$-0.620184\pi$
$823$	379914.	−	379914.i	0.560900	−	0.560900i	0.929563	+	0.368663i	$0.120184\pi$
$824$			326129.i			0.480325i
$825$	−905060.	+	1.47485e6i	−1.32975	+	2.16691i
$826$	−40664.2			−0.0596008
$827$	−249150.	−	249150.i	−0.364293	−	0.364293i	0.501098	−	0.865391i	$-0.332930\pi$
$827$	−249150.	−	249150.i	−0.364293	−	0.364293i	−0.865391	+	0.501098i	$0.832930\pi$
$828$	198564.	−	198564.i	0.289627	−	0.289627i
$829$		−	26540.9i		−	0.0386194i	−0.999814	−	0.0193097i	$-0.993853\pi$
$829$		−	26540.9i		−	0.0386194i	0.999814	−	0.0193097i	$-0.00614685\pi$
$830$	153199.	−	18083.7i	0.222382	−	0.0262502i
$831$	−1.39364e6			−2.01812
$832$	100068.	+	100068.i	0.144560	+	0.144560i
$833$	708004.	−	708004.i	1.02034	−	1.02034i
$834$			124757.i			0.179363i
$835$	199114.	+	157070.i	0.285581	+	0.225279i
$836$	831211.			1.18932
$837$	671836.	+	671836.i	0.958986	+	0.958986i
$838$	−276300.	+	276300.i	−0.393453	+	0.393453i
$839$			1.27974e6i			1.81801i	0.416781	+	0.909007i	$0.363158\pi$
$839$			1.27974e6i			1.81801i	−0.416781	+	0.909007i	$0.636842\pi$
$840$	203920.	−	258505.i	0.289002	−	0.366361i
$841$	681254.			0.963201
$842$	−211032.	−	211032.i	−0.297662	−	0.297662i
$843$	141487.	−	141487.i	0.199095	−	0.199095i
$844$		−	1.20796e6i		−	1.69577i
$845$	−31139.8	−	263805.i	−0.0436116	−	0.369462i
$846$	828332.			1.15735
$847$	182257.	+	182257.i	0.254049	+	0.254049i
$848$	−287912.	+	287912.i	−0.400376	+	0.400376i
$849$			797572.i			1.10651i
$850$	−105079.	−	438896.i	−0.145438	−	0.607468i
$851$	230441.			0.318200
$852$	1.14177e6	+	1.14177e6i	1.57290	+	1.57290i
$853$	−621058.	+	621058.i	−0.853560	+	0.853560i	−0.990570	−	0.137010i	$-0.956251\pi$
$853$	−621058.	+	621058.i	−0.853560	+	0.853560i	0.137010	+	0.990570i	$0.456251\pi$
$854$		−	64598.1i		−	0.0885735i
$855$	1.63201e6	−	192643.i	2.23249	−	0.263525i
$856$	−735837.			−1.00423
$857$	−33448.8	−	33448.8i	−0.0455427	−	0.0455427i	0.683969	−	0.729511i	$-0.260252\pi$
$857$	−33448.8	−	33448.8i	−0.0455427	−	0.0455427i	−0.729511	+	0.683969i	$0.760252\pi$
$858$	391585.	−	391585.i	0.531926	−	0.531926i
$859$		−	1.08045e6i		−	1.46425i	−0.681168	−	0.732127i	$-0.738528\pi$
$859$		−	1.08045e6i		−	1.46425i	0.681168	−	0.732127i	$-0.261472\pi$
$860$	−49631.6	−	39151.5i	−0.0671060	−	0.0529361i
$861$	422069.			0.569348
$862$	199663.	+	199663.i	0.268710	+	0.268710i
$863$	482586.	−	482586.i	0.647967	−	0.647967i	−0.304534	−	0.952501i	$-0.598501\pi$
$863$	482586.	−	482586.i	0.647967	−	0.647967i	0.952501	+	0.304534i	$0.0985008\pi$
$864$		−	1.59448e6i		−	2.13595i
$865$	505030.	−	640215.i	0.674971	−	0.855646i
$866$	−61459.7			−0.0819510
$867$	1.73209e6	+	1.73209e6i	2.30427	+	2.30427i
$868$	−99201.5	+	99201.5i	−0.131668	+	0.131668i
$869$		−	781533.i		−	1.03492i
$870$	−11514.5	−	97546.5i	−0.0152127	−	0.128876i
$871$	1.17573e6			1.54979
$872$	224299.	+	224299.i	0.294981	+	0.294981i
$873$	−2.01603e6	+	2.01603e6i	−2.64526	+	2.64526i
$874$		−	58571.1i		−	0.0766761i
$875$	−257658.	−	119075.i	−0.336533	−	0.155527i
$876$	−1.02661e6			−1.33782
$877$	98483.4	+	98483.4i	0.128045	+	0.128045i	0.768225	−	0.640180i	$-0.221140\pi$
$877$	98483.4	+	98483.4i	0.128045	+	0.128045i	−0.640180	+	0.768225i	$0.721140\pi$
$878$	208322.	−	208322.i	0.270238	−	0.270238i
$879$			1.87940e6i			2.43243i
$880$	−648797.	+	76584.5i	−0.837806	+	0.0988952i
$881$	256457.			0.330417			0.165209	−	0.986259i	$-0.447170\pi$
$881$	256457.			0.330417			0.165209	+	0.986259i	$0.447170\pi$
$882$	404379.	+	404379.i	0.519818	+	0.519818i
$883$	665916.	−	665916.i	0.854079	−	0.854079i	−0.136554	−	0.990633i	$-0.543603\pi$
$883$	665916.	−	665916.i	0.854079	−	0.854079i	0.990633	+	0.136554i	$0.0436026\pi$
$884$		−	891541.i		−	1.14087i
$885$	479699.	+	378407.i	0.612466	+	0.483140i
$886$	−52436.1			−0.0667979
$887$	180619.	+	180619.i	0.229570	+	0.229570i	0.812513	−	0.582943i	$-0.198099\pi$
$887$	180619.	+	180619.i	0.229570	+	0.229570i	−0.582943	+	0.812513i	$0.698099\pi$
$888$	1.07099e6	−	1.07099e6i	1.35819	−	1.35819i
$889$			57699.2i			0.0730073i
$890$	35005.5	−	44375.8i	0.0441933	−	0.0560229i
$891$	2.14733e6			2.70485
$892$	−593072.	−	593072.i	−0.745380	−	0.745380i
$893$	−754125.	+	754125.i	−0.945672	+	0.945672i
$894$		−	341878.i		−	0.427756i
$895$	−135981.	−	1.15199e6i	−0.169759	−	1.43814i
$896$	302247.			0.376484
$897$	170327.	+	170327.i	0.211689	+	0.211689i
$898$	−127650.	+	127650.i	−0.158296	+	0.158296i
$899$			90484.7i			0.111958i
$900$	−1.54739e6	+	370472.i	−1.91036	+	0.457373i
$901$	1.27906e6			1.57559
$902$	255503.	+	255503.i	0.314039	+	0.314039i
$903$	−38464.3	+	38464.3i	−0.0471718	+	0.0471718i
$904$			515775.i			0.631137i
$905$	−115484.	+	13631.9i	−0.141002	+	0.0166440i
$906$	61565.7			0.0750037
$907$	−327921.	−	327921.i	−0.398616	−	0.398616i	0.479129	−	0.877745i	$-0.340953\pi$
$907$	−327921.	−	327921.i	−0.398616	−	0.398616i	−0.877745	+	0.479129i	$0.840953\pi$
$908$	594146.	−	594146.i	0.720646	−	0.720646i
$909$		−	1.92059e6i		−	2.32438i
$910$	71319.2	+	56259.7i	0.0861238	+	0.0679382i
$911$	−1.46844e6			−1.76938			−0.884688	−	0.466183i	$-0.845629\pi$
$911$	−1.46844e6			−1.76938			−0.884688	+	0.466183i	$0.845629\pi$
$912$	630907.	+	630907.i	0.758535	+	0.758535i
$913$	−496035.	+	496035.i	−0.595073	+	0.595073i
$914$			538953.i			0.645146i
$915$	−601128.	+	762037.i	−0.718000	+	0.910193i
$916$	508283.			0.605780
$917$	244638.	+	244638.i	0.290928	+	0.290928i
$918$	−864940.	+	864940.i	−1.02636	+	1.02636i
$919$		−	750514.i		−	0.888644i	−0.895867	−	0.444322i	$-0.853445\pi$
$919$		−	750514.i		−	0.888644i	0.895867	−	0.444322i	$-0.146555\pi$
$920$	14372.8	+	121762.i	0.0169811	+	0.143858i
$921$	1.12225e6			1.32303
$922$	−424645.	−	424645.i	−0.499533	−	0.499533i
$923$	−681042.	+	681042.i	−0.799411	+	0.799411i
$924$			692533.i			0.811141i
$925$	−1.11288e6	−	682930.i	−1.30066	−	0.798165i
$926$	123596.			0.144140
$927$	−958959.	−	958959.i	−1.11594	−	1.11594i
$928$	107374.	−	107374.i	0.124682	−	0.124682i
$929$			73235.6i			0.0848576i	0.999099	+	0.0424288i	$0.0135096\pi$
$929$			73235.6i			0.0848576i	−0.999099	+	0.0424288i	$0.986490\pi$
$930$	−339126.	+	40030.7i	−0.392099	+	0.0462836i
$931$	−736304.			−0.849489
$932$	965991.	+	965991.i	1.11209	+	1.11209i
$933$	172726.	−	172726.i	0.198424	−	0.198424i
$934$			407159.i			0.466734i
$935$	1.61127e6	+	1.27104e6i	1.84308	+	1.45390i
$936$	1.10091e6			1.25660
$937$	239757.	+	239757.i	0.273082	+	0.273082i	0.830340	−	0.557258i	$-0.188146\pi$
$937$	239757.	+	239757.i	0.273082	+	0.273082i	−0.557258	+	0.830340i	$0.688146\pi$
$938$	168426.	−	168426.i	0.191427	−	0.191427i
$939$		−	1.60814e6i		−	1.82386i
$940$	639534.	−	810724.i	0.723783	−	0.917524i
$941$	104090.			0.117552			0.0587760	−	0.998271i	$-0.481280\pi$
$941$	104090.			0.117552			0.0587760	+	0.998271i	$0.481280\pi$
$942$	−128116.	−	128116.i	−0.144378	−	0.144378i
$943$	−111136.	+	111136.i	−0.124977	+	0.124977i
$944$			230672.i			0.258851i
$945$	90186.3	+	764027.i	0.100990	+	0.855549i
$946$	−46569.4			−0.0520377
$947$	−228741.	−	228741.i	−0.255062	−	0.255062i	0.567980	−	0.823042i	$-0.307725\pi$
$947$	−228741.	−	228741.i	−0.255062	−	0.255062i	−0.823042	+	0.567980i	$0.807725\pi$
$948$	730762.	−	730762.i	0.813129	−	0.813129i
$949$		−	612350.i		−	0.679934i
$950$	−173580.	+	282859.i	−0.192332	+	0.313418i
$951$	2.81764e6			3.11548
$952$	−276119.	−	276119.i	−0.304665	−	0.304665i
$953$	−76233.1	+	76233.1i	−0.0839379	+	0.0839379i	−0.747829	−	0.663891i	$-0.768904\pi$
$953$	−76233.1	+	76233.1i	−0.0839379	+	0.0839379i	0.663891	+	0.747829i	$0.268904\pi$
$954$			730542.i			0.802691i
$955$	−159234.	+	18796.2i	−0.174594	+	0.0206093i
$956$	−400117.			−0.437796
$957$	315840.	+	315840.i	0.344861	+	0.344861i
$958$	−85770.4	+	85770.4i	−0.0934559	+	0.0934559i
$959$		−	188304.i		−	0.204749i
$960$	−338206.	−	266792.i	−0.366977	−	0.289488i
$961$	−608946.			−0.659374
$962$	295477.	+	295477.i	0.319282	+	0.319282i
$963$	2.16368e6	−	2.16368e6i	2.33314	−	2.33314i
$964$		−	30924.0i		−	0.0332768i
$965$	−185131.	+	234686.i	−0.198804	+	0.252019i
$966$	48799.2			0.0522948
$967$	506003.	+	506003.i	0.541128	+	0.541128i	0.923860	−	0.382732i	$-0.125017\pi$
$967$	506003.	+	506003.i	0.541128	+	0.541128i	−0.382732	+	0.923860i	$0.625017\pi$
$968$	−446078.	+	446078.i	−0.476058	+	0.476058i
$969$		−	2.80283e6i		−	2.98504i
$970$	−67496.8	−	571810.i	−0.0717364	−	0.607726i
$971$	−1.09552e6			−1.16194			−0.580970	−	0.813925i	$-0.697326\pi$
$971$	−1.09552e6			−1.16194			−0.580970	+	0.813925i	$0.697326\pi$
$972$	671849.	+	671849.i	0.711113	+	0.711113i
$973$	65802.7	−	65802.7i	0.0695053	−	0.0695053i
$974$			258130.i			0.272095i
$975$	−317789.	−	1.32734e6i	−0.334295	−	1.39629i
$976$	−366439.			−0.384682
$977$	859403.	+	859403.i	0.900343	+	0.900343i	0.995466	−	0.0951227i	$-0.0303244\pi$
$977$	859403.	+	859403.i	0.900343	+	0.900343i	−0.0951227	+	0.995466i	$0.530324\pi$
$978$	149692.	−	149692.i	0.156502	−	0.156502i
$979$			257024.i			0.268169i
$980$	707993.	−	83572.1i	0.737186	−	0.0870180i
$981$	−1.31907e6			−1.37066
$982$	198630.	+	198630.i	0.205979	+	0.205979i
$983$	431066.	−	431066.i	0.446105	−	0.446105i	−0.447953	−	0.894057i	$-0.647847\pi$
$983$	431066.	−	431066.i	0.446105	−	0.446105i	0.894057	+	0.447953i	$0.147847\pi$
$984$			1.03302e6i			1.06689i
$985$	−575493.	−	453974.i	−0.593154	−	0.467906i
$986$	−116492.			−0.119824
$987$	−628308.	−	628308.i	−0.644968	−	0.644968i
$988$	−463589.	+	463589.i	−0.474919	+	0.474919i
$989$		−	20256.2i		−	0.0207093i
$990$	−725959.	+	920283.i	−0.740699	+	0.938968i
$991$	−1.40874e6			−1.43444			−0.717220	−	0.696847i	$-0.754586\pi$
$991$	−1.40874e6			−1.43444			−0.717220	+	0.696847i	$0.754586\pi$
$992$	−373293.	−	373293.i	−0.379338	−	0.379338i
$993$	1.00025e6	−	1.00025e6i	1.01441	−	1.01441i
$994$			195120.i			0.197483i
$995$	−164714.	−	1.39540e6i	−0.166374	−	1.40946i
$996$	−927621.			−0.935087
$997$	896520.	+	896520.i	0.901923	+	0.901923i	0.995602	−	0.0936791i	$-0.0298628\pi$
$997$	896520.	+	896520.i	0.901923	+	0.901923i	−0.0936791	+	0.995602i	$0.529863\pi$
$998$	253934.	−	253934.i	0.254952	−	0.254952i
$999$			3.53903e6i			3.54612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.5.f.a.47.19	✓	88
5.3	odd	4	inner	115.5.f.a.93.19	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.5.f.a.47.19	✓	88	1.1	even	1	trivial
115.5.f.a.93.19	yes	88	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05609 - 1.05609i) q^{2} +(11.5301 - 11.5301i) q^{3} -13.7694i q^{4} +(-24.8276 + 2.93067i) q^{5} -24.3536 q^{6} +(12.8452 + 12.8452i) q^{7} +(-31.4390 + 31.4390i) q^{8} -184.888i q^{9} +(29.3151 + 23.1251i) q^{10} -169.793 q^{11} +(-158.763 - 158.763i) q^{12} +(94.6983 - 94.6983i) q^{13} -27.1313i q^{14} +(-252.475 + 320.057i) q^{15} -153.905 q^{16} +(341.866 + 341.866i) q^{17} +(-195.258 + 195.258i) q^{18} -355.531i q^{19} +(40.3535 + 341.861i) q^{20} +296.215 q^{21} +(179.316 + 179.316i) q^{22} +(-77.9968 + 77.9968i) q^{23} +724.992i q^{24} +(607.822 - 145.523i) q^{25} -200.019 q^{26} +(-1197.85 - 1197.85i) q^{27} +(176.871 - 176.871i) q^{28} -161.329i q^{29} +(604.643 - 71.3725i) q^{30} -560.870 q^{31} +(665.561 + 665.561i) q^{32} +(-1957.74 + 1957.74i) q^{33} -722.079i q^{34} +(-356.562 - 281.272i) q^{35} -2545.79 q^{36} +(-1477.25 - 1477.25i) q^{37} +(-375.471 + 375.471i) q^{38} -2183.77i q^{39} +(688.418 - 872.693i) q^{40} +1424.88 q^{41} +(-312.828 - 312.828i) q^{42} +(-129.853 + 129.853i) q^{43} +2337.94i q^{44} +(541.847 + 4590.34i) q^{45} +164.743 q^{46} +(-2121.12 - 2121.12i) q^{47} +(-1774.55 + 1774.55i) q^{48} -2071.00i q^{49} +(-795.597 - 488.227i) q^{50} +7883.52 q^{51} +(-1303.94 - 1303.94i) q^{52} +(1870.71 - 1870.71i) q^{53} +2530.06i q^{54} +(4215.56 - 497.608i) q^{55} -807.683 q^{56} +(-4099.32 - 4099.32i) q^{57} +(-170.377 + 170.377i) q^{58} -1498.79i q^{59} +(4406.98 + 3476.42i) q^{60} +2380.94 q^{61} +(592.327 + 592.327i) q^{62} +(2374.93 - 2374.93i) q^{63} +1056.71i q^{64} +(-2073.60 + 2628.66i) q^{65} +4135.08 q^{66} +(6207.79 + 6207.79i) q^{67} +(4707.27 - 4707.27i) q^{68} +1798.63i q^{69} +(79.5130 + 673.607i) q^{70} -7191.70 q^{71} +(5812.70 + 5812.70i) q^{72} +(3233.16 - 3233.16i) q^{73} +3120.20i q^{74} +(5330.37 - 8686.18i) q^{75} -4895.43 q^{76} +(-2181.03 - 2181.03i) q^{77} +(-2306.25 + 2306.25i) q^{78} +4602.86i q^{79} +(3821.10 - 451.046i) q^{80} -12646.7 q^{81} +(-1504.79 - 1504.79i) q^{82} +(2921.41 - 2921.41i) q^{83} -4078.69i q^{84} +(-9489.61 - 7485.82i) q^{85} +274.271 q^{86} +(-1860.15 - 1860.15i) q^{87} +(5338.12 - 5338.12i) q^{88} -1513.75i q^{89} +(4275.55 - 5420.03i) q^{90} +2432.84 q^{91} +(1073.97 + 1073.97i) q^{92} +(-6466.91 + 6466.91i) q^{93} +4480.18i q^{94} +(1041.94 + 8826.99i) q^{95} +15348.0 q^{96} +(-10904.0 - 10904.0i) q^{97} +(-2187.15 + 2187.15i) q^{98} +31392.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 48 q^{5} + 160 q^{7} + 180 q^{8} + 16 q^{10} + 312 q^{11} - 720 q^{12} - 760 q^{13} - 60 q^{15} - 4528 q^{16} + 420 q^{17} + 980 q^{18} + 1344 q^{20} + 1976 q^{21} + 720 q^{22} - 1176 q^{25} + 1872 q^{26}+ \cdots - 22320 q^{98}+O(q^{100}) \) 88 * q - 48 * q^5 + 160 * q^7 + 180 * q^8 + 16 * q^10 + 312 * q^11 - 720 * q^12 - 760 * q^13 - 60 * q^15 - 4528 * q^16 + 420 * q^17 + 980 * q^18 + 1344 * q^20 + 1976 * q^21 + 720 * q^22 - 1176 * q^25 + 1872 * q^26 + 2820 * q^27 - 1140 * q^28 - 1160 * q^30 - 820 * q^31 - 3720 * q^32 + 820 * q^33 - 1728 * q^35 + 9504 * q^36 + 180 * q^37 + 3180 * q^38 + 8560 * q^40 + 1956 * q^41 + 5320 * q^42 - 8960 * q^43 + 2064 * q^45 - 5640 * q^47 + 3820 * q^48 - 5448 * q^50 - 6648 * q^51 - 2800 * q^52 - 2160 * q^53 - 11796 * q^55 - 1464 * q^56 - 160 * q^57 + 3740 * q^58 - 6700 * q^60 - 4496 * q^61 - 30300 * q^62 - 2740 * q^63 - 3336 * q^65 - 4104 * q^66 + 640 * q^67 + 13440 * q^68 + 6508 * q^70 + 14916 * q^71 + 44280 * q^72 + 3660 * q^73 + 15732 * q^75 - 53552 * q^76 + 10980 * q^77 + 4340 * q^78 + 10404 * q^80 - 35864 * q^81 + 32860 * q^82 + 7920 * q^83 + 14216 * q^85 + 59352 * q^86 - 38440 * q^87 - 19140 * q^88 + 7160 * q^90 + 52584 * q^91 - 20960 * q^93 + 28224 * q^95 - 26624 * q^96 + 13480 * q^97 - 22320 * q^98

Introduction

L-functions

Modular forms

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