LMFDB - Embedded newform 161.4.c.c.160.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(160,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("161.160");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.2
Character	$\chi$	$=$	161.160
Dual form			161.4.c.c.160.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.29875 q^{2} -6.28001i q^{3} +20.0768 q^{4} +10.4216 q^{5} +33.2762i q^{6} +(-11.5274 + 14.4955i) q^{7} -63.9920 q^{8} -12.4385 q^{9} -55.2216 q^{10} +47.9270i q^{11} -126.082i q^{12} -43.6247i q^{13} +(61.0808 - 76.8080i) q^{14} -65.4478i q^{15} +178.463 q^{16} -89.5819 q^{17} +65.9086 q^{18} -94.5661 q^{19} +209.233 q^{20} +(91.0318 + 72.3921i) q^{21} -253.953i q^{22} +(-54.9894 + 95.6199i) q^{23} +401.870i q^{24} -16.3899 q^{25} +231.157i q^{26} -91.4463i q^{27} +(-231.433 + 291.023i) q^{28} -231.117 q^{29} +346.792i q^{30} +91.7580i q^{31} -433.697 q^{32} +300.982 q^{33} +474.672 q^{34} +(-120.134 + 151.066i) q^{35} -249.725 q^{36} +74.6290i q^{37} +501.082 q^{38} -273.964 q^{39} -666.900 q^{40} +377.735i q^{41} +(-482.355 - 383.588i) q^{42} -305.195i q^{43} +962.221i q^{44} -129.629 q^{45} +(291.375 - 506.666i) q^{46} +87.3335i q^{47} -1120.75i q^{48} +(-77.2383 - 334.190i) q^{49} +86.8462 q^{50} +562.575i q^{51} -875.844i q^{52} +118.644i q^{53} +484.552i q^{54} +499.477i q^{55} +(737.661 - 927.595i) q^{56} +593.876i q^{57} +1224.63 q^{58} +440.635i q^{59} -1313.98i q^{60} +470.158 q^{61} -486.203i q^{62} +(143.384 - 180.302i) q^{63} +870.349 q^{64} -454.640i q^{65} -1594.83 q^{66} +207.499i q^{67} -1798.52 q^{68} +(600.494 + 345.334i) q^{69} +(636.561 - 800.464i) q^{70} +393.876 q^{71} +795.964 q^{72} -397.322i q^{73} -395.441i q^{74} +102.929i q^{75} -1898.58 q^{76} +(-694.726 - 552.474i) q^{77} +1451.67 q^{78} -574.659i q^{79} +1859.88 q^{80} -910.123 q^{81} -2001.52i q^{82} -1080.93 q^{83} +(1827.63 + 1453.40i) q^{84} -933.588 q^{85} +1617.15i q^{86} +1451.42i q^{87} -3066.94i q^{88} +559.712 q^{89} +686.874 q^{90} +(632.362 + 502.879i) q^{91} +(-1104.01 + 1919.74i) q^{92} +576.241 q^{93} -462.759i q^{94} -985.531 q^{95} +2723.62i q^{96} -697.226 q^{97} +(409.267 + 1770.79i) q^{98} -596.140i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{2} + 184 q^{4} - 228 q^{8} - 436 q^{9} + 168 q^{16} - 404 q^{18} + 204 q^{23} - 140 q^{25} + 256 q^{29} + 1008 q^{32} - 2040 q^{35} - 4412 q^{36} + 1296 q^{39} - 888 q^{46} + 1916 q^{49} + 4080 q^{50}+ \cdots + 6884 q^{98}+O(q^{100}) $ 36 * q - 8 * q^2 + 184 * q^4 - 228 * q^8 - 436 * q^9 + 168 * q^16 - 404 * q^18 + 204 * q^23 - 140 * q^25 + 256 * q^29 + 1008 * q^32 - 2040 * q^35 - 4412 * q^36 + 1296 * q^39 - 888 * q^46 + 1916 * q^49 + 4080 * q^50 + 6020 * q^58 + 3988 * q^64 - 1712 * q^70 - 5040 * q^71 - 8636 * q^72 - 2864 * q^77 + 8820 * q^78 + 9380 * q^81 - 5032 * q^85 - 3672 * q^92 - 5352 * q^93 - 3840 * q^95 + 6884 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−5.29875			−1.87339			−0.936696	−	0.350143i	$-0.886133\pi$
$2$	−5.29875			−1.87339			−0.936696	+	0.350143i	$0.886133\pi$
$3$		−	6.28001i		−	1.20859i	−0.796761	−	0.604294i	$-0.793455\pi$
$3$		−	6.28001i		−	1.20859i	0.796761	−	0.604294i	$-0.206545\pi$
$4$	20.0768			2.50960
$5$	10.4216			0.932138			0.466069	−	0.884748i	$-0.345670\pi$
$5$	10.4216			0.932138			0.466069	+	0.884748i	$0.345670\pi$
$6$			33.2762i			2.26416i
$7$	−11.5274	+	14.4955i	−0.622421	+	0.782683i
$7$	−11.5274	+	14.4955i	−0.622421	+	0.782683i
$8$	−63.9920			−2.82807
$9$	−12.4385			−0.460685
$10$	−55.2216			−1.74626
$11$			47.9270i			1.31369i	0.754028	+	0.656843i	$0.228108\pi$
$11$			47.9270i			1.31369i	−0.754028	+	0.656843i	$0.771892\pi$
$12$		−	126.082i		−	3.03307i
$13$		−	43.6247i		−	0.930717i	−0.885122	−	0.465358i	$-0.845925\pi$
$13$		−	43.6247i		−	0.930717i	0.885122	−	0.465358i	$-0.154075\pi$
$14$	61.0808	−	76.8080i	1.16604	−	1.46627i
$15$		−	65.4478i		−	1.12657i
$16$	178.463			2.78849
$17$	−89.5819			−1.27805			−0.639023	−	0.769187i	$-0.720661\pi$
$17$	−89.5819			−1.27805			−0.639023	+	0.769187i	$0.720661\pi$
$18$	65.9086			0.863044
$19$	−94.5661			−1.14184			−0.570920	−	0.821006i	$-0.693413\pi$
$19$	−94.5661			−1.14184			−0.570920	+	0.821006i	$0.693413\pi$
$20$	209.233			2.33929
$21$	91.0318	+	72.3921i	0.945941	+	0.752250i
$22$		−	253.953i		−	2.46105i
$23$	−54.9894	+	95.6199i	−0.498525	+	0.866875i
$23$	−54.9894	+	95.6199i	−0.498525	+	0.866875i
$24$			401.870i			3.41797i
$25$	−16.3899			−0.131119
$26$			231.157i			1.74360i
$27$		−	91.4463i		−	0.651809i
$28$	−231.433	+	291.023i	−1.56203	+	1.96422i
$29$	−231.117			−1.47991			−0.739955	−	0.672657i	$-0.765153\pi$
$29$	−231.117			−1.47991			−0.739955	+	0.672657i	$0.765153\pi$
$30$			346.792i			2.11051i
$31$			91.7580i			0.531620i	0.964025	+	0.265810i	$0.0856394\pi$
$31$			91.7580i			0.531620i	−0.964025	+	0.265810i	$0.914361\pi$
$32$	−433.697			−2.39586
$33$	300.982			1.58770
$34$	474.672			2.39428
$35$	−120.134	+	151.066i	−0.580182	+	0.729568i
$36$	−249.725			−1.15614
$37$			74.6290i			0.331593i	0.986160	+	0.165796i	$0.0530195\pi$
$37$			74.6290i			0.331593i	−0.986160	+	0.165796i	$0.946981\pi$
$38$	501.082			2.13911
$39$	−273.964			−1.12485
$40$	−666.900			−2.63615
$41$			377.735i			1.43884i	0.694577	+	0.719418i	$0.255591\pi$
$41$			377.735i			1.43884i	−0.694577	+	0.719418i	$0.744409\pi$
$42$	−482.355	−	383.588i	−1.77212	−	1.40926i
$43$		−	305.195i		−	1.08237i	−0.840904	−	0.541184i	$-0.817976\pi$
$43$		−	305.195i		−	1.08237i	0.840904	−	0.541184i	$-0.182024\pi$
$44$			962.221i			3.29682i
$45$	−129.629			−0.429422
$46$	291.375	−	506.666i	0.933934	−	1.62400i
$47$			87.3335i			0.271040i	0.990775	+	0.135520i	$0.0432706\pi$
$47$			87.3335i			0.271040i	−0.990775	+	0.135520i	$0.956729\pi$
$48$		−	1120.75i		−	3.37013i
$49$	−77.2383	−	334.190i	−0.225185	−	0.974316i
$50$	86.8462			0.245638
$51$			562.575i			1.54463i
$52$		−	875.844i		−	2.33573i
$53$			118.644i			0.307490i	0.988111	+	0.153745i	$0.0491335\pi$
$53$			118.644i			0.307490i	−0.988111	+	0.153745i	$0.950867\pi$
$54$			484.552i			1.22109i
$55$			499.477i			1.22454i
$56$	737.661	−	927.595i	1.76025	−	2.21348i
$57$			593.876i			1.38001i
$58$	1224.63			2.77245
$59$			440.635i			0.972301i	0.873875	+	0.486151i	$0.161599\pi$
$59$			440.635i			0.972301i	−0.873875	+	0.486151i	$0.838401\pi$
$60$		−	1313.98i		−	2.82724i
$61$	470.158			0.986845			0.493422	−	0.869790i	$-0.335746\pi$
$61$	470.158			0.986845			0.493422	+	0.869790i	$0.335746\pi$
$62$		−	486.203i		−	0.995933i
$63$	143.384	−	180.302i	0.286740	−	0.360570i
$64$	870.349			1.69990
$65$		−	454.640i		−	0.867556i
$66$	−1594.83			−2.97439
$67$			207.499i			0.378358i	0.981943	+	0.189179i	$0.0605827\pi$
$67$			207.499i			0.378358i	−0.981943	+	0.189179i	$0.939417\pi$
$68$	−1798.52			−3.20739
$69$	600.494	+	345.334i	1.04769	+	0.602512i
$70$	636.561	−	800.464i	1.08691	−	1.36677i
$71$	393.876			0.658373			0.329186	−	0.944265i	$-0.393226\pi$
$71$	393.876			0.658373			0.329186	+	0.944265i	$0.393226\pi$
$72$	795.964			1.30285
$73$		−	397.322i		−	0.637028i	−0.947918	−	0.318514i	$-0.896816\pi$
$73$		−	397.322i		−	0.637028i	0.947918	−	0.318514i	$-0.103184\pi$
$74$		−	395.441i		−	0.621204i
$75$			102.929i			0.158469i
$76$	−1898.58			−2.86556
$77$	−694.726	−	552.474i	−1.02820	−	0.817665i
$78$	1451.67			2.10729
$79$		−	574.659i		−	0.818407i	−0.912443	−	0.409203i	$-0.865807\pi$
$79$		−	574.659i		−	0.818407i	0.912443	−	0.409203i	$-0.134193\pi$
$80$	1859.88			2.59926
$81$	−910.123			−1.24845
$82$		−	2001.52i		−	2.69550i
$83$	−1080.93			−1.42948			−0.714742	−	0.699388i	$-0.753456\pi$
$83$	−1080.93			−1.42948			−0.714742	+	0.699388i	$0.753456\pi$
$84$	1827.63	+	1453.40i	2.37393	+	1.88785i
$85$	−933.588			−1.19132
$86$			1617.15i			2.02770i
$87$			1451.42i			1.78860i
$88$		−	3066.94i		−	3.71520i
$89$	559.712			0.666622			0.333311	−	0.942817i	$-0.391834\pi$
$89$	559.712			0.666622			0.333311	+	0.942817i	$0.391834\pi$
$90$	686.874			0.804476
$91$	632.362	+	502.879i	0.728456	+	0.579298i
$92$	−1104.01	+	1919.74i	−1.25110	+	2.17551i
$93$	576.241			0.642510
$94$		−	462.759i		−	0.507765i
$95$	−985.531			−1.06435
$96$			2723.62i			2.89561i
$97$	−697.226			−0.729821			−0.364910	−	0.931043i	$-0.618900\pi$
$97$	−697.226			−0.729821			−0.364910	+	0.931043i	$0.618900\pi$
$98$	409.267	+	1770.79i	0.421859	+	1.82528i
$99$		−	596.140i		−	0.605196i
$100$	−329.057			−0.329057
$101$		−	1725.47i		−	1.69991i	−0.526859	−	0.849953i	$-0.676631\pi$
$101$		−	1725.47i		−	1.69991i	0.526859	−	0.849953i	$-0.323369\pi$
$102$		−	2980.95i		−	2.89370i
$103$	1392.83			1.33243			0.666213	−	0.745761i	$-0.267914\pi$
$103$	1392.83			1.33243			0.666213	+	0.745761i	$0.267914\pi$
$104$			2791.63i			2.63213i
$105$	948.698	+	754.443i	0.881747	+	0.701201i
$106$		−	628.665i		−	0.576050i
$107$			2181.41i			1.97088i	0.170010	+	0.985442i	$0.445620\pi$
$107$			2181.41i			1.97088i	−0.170010	+	0.985442i	$0.554380\pi$
$108$		−	1835.95i		−	1.63578i
$109$			1010.52i			0.887982i	0.896031	+	0.443991i	$0.146438\pi$
$109$			1010.52i			0.887982i	−0.896031	+	0.443991i	$0.853562\pi$
$110$		−	2646.61i		−	2.29404i
$111$	468.671			0.400759
$112$	−2057.22	+	2586.91i	−1.73561	+	2.18250i
$113$		−	1020.13i		−	0.849251i	−0.905369	−	0.424625i	$-0.860406\pi$
$113$		−	1020.13i		−	0.849251i	0.905369	−	0.424625i	$-0.139594\pi$
$114$		−	3146.80i		−	2.58531i
$115$	−573.078	+	996.514i	−0.464694	+	0.808047i
$116$	−4640.09			−3.71398
$117$			542.626i			0.428768i
$118$		−	2334.82i		−	1.82150i
$119$	1032.65	−	1298.53i	0.795483	−	1.00031i
$120$			4188.13i			3.18602i
$121$	−965.999			−0.725770
$122$	−2491.25			−1.84875
$123$	2372.18			1.73896
$124$			1842.21i			1.33415i
$125$	−1473.51			−1.05436
$126$	−759.754	+	955.377i	−0.537177	+	0.675490i
$127$	266.210			0.186002			0.0930012	−	0.995666i	$-0.470354\pi$
$127$	266.210			0.186002			0.0930012	+	0.995666i	$0.470354\pi$
$128$	−1142.19			−0.788720
$129$	−1916.63			−1.30814
$130$			2409.03i			1.62527i
$131$			1981.22i			1.32138i	0.750661	+	0.660688i	$0.229735\pi$
$131$			1981.22i			1.32138i	−0.750661	+	0.660688i	$0.770265\pi$
$132$	6042.76			3.98450
$133$	1090.10	−	1370.78i	0.710705	−	0.893698i
$134$		−	1099.49i		−	0.708814i
$135$		−	953.018i		−	0.607576i
$136$	5732.52			3.61441
$137$		−	1780.13i		−	1.11012i	−0.831810	−	0.555061i	$-0.812695\pi$
$137$		−	1780.13i		−	1.11012i	0.831810	−	0.555061i	$-0.187305\pi$
$138$	−3181.87	−	1829.84i	−1.96274	−	1.12874i
$139$			780.661i			0.476365i	0.971220	+	0.238183i	$0.0765517\pi$
$139$			780.661i			0.476365i	−0.971220	+	0.238183i	$0.923448\pi$
$140$	−2411.91	+	3032.93i	−1.45602	+	1.83092i
$141$	548.455			0.327576
$142$	−2087.05			−1.23339
$143$	2090.80			1.22267
$144$	−2219.82			−1.28462
$145$	−2408.61			−1.37948
$146$			2105.31i			1.19340i
$147$	−2098.72	+	485.057i	−1.17755	+	0.272156i
$148$			1498.31i			0.832165i
$149$		−	913.349i		−	0.502178i	−0.967964	−	0.251089i	$-0.919211\pi$
$149$		−	913.349i		−	0.502178i	0.967964	−	0.251089i	$-0.0807886\pi$
$150$		−	545.395i		−	0.296875i
$151$	456.923			0.246251			0.123125	−	0.992391i	$-0.460708\pi$
$151$	456.923			0.246251			0.123125	+	0.992391i	$0.460708\pi$
$152$	6051.47			3.22920
$153$	1114.26			0.588777
$154$	3681.18	+	2927.42i	1.92622	+	1.53181i
$155$			956.266i			0.495543i
$156$	−5500.31			−2.82293
$157$	−1411.70			−0.717616			−0.358808	−	0.933411i	$-0.616817\pi$
$157$	−1411.70			−0.717616			−0.358808	+	0.933411i	$0.616817\pi$
$158$			3044.97i			1.53320i
$159$	745.084			0.371629
$160$	−4519.83			−2.23327
$161$	−752.173	−	1899.35i	−0.368196	−	0.929748i
$162$	4822.52			2.33884
$163$	−1005.07			−0.482963			−0.241481	−	0.970405i	$-0.577633\pi$
$163$	−1005.07			−0.482963			−0.241481	+	0.970405i	$0.577633\pi$
$164$			7583.70i			3.61090i
$165$	3136.72			1.47996
$166$	5727.57			2.67798
$167$		−	2879.54i		−	1.33429i	−0.744930	−	0.667143i	$-0.767517\pi$
$167$		−	2879.54i		−	1.33429i	0.744930	−	0.667143i	$-0.232483\pi$
$168$	−5825.30	−	4632.51i	−2.67519	−	2.12742i
$169$	293.884			0.133766
$170$	4946.85			2.23180
$171$	1176.26			0.526029
$172$		−	6127.34i		−	2.71631i
$173$			358.433i			0.157521i	0.996894	+	0.0787606i	$0.0250963\pi$
$173$			358.433i			0.157521i	−0.996894	+	0.0787606i	$0.974904\pi$
$174$		−	7690.70i		−	3.35075i
$175$	188.933	−	237.580i	0.0816115	−	0.102625i
$176$			8553.21i			3.66320i
$177$	2767.19			1.17511
$178$	−2965.78			−1.24884
$179$	1662.36			0.694140			0.347070	−	0.937839i	$-0.387177\pi$
$179$	1662.36			0.694140			0.347070	+	0.937839i	$0.387177\pi$
$180$	−2602.54			−1.07768
$181$	−506.312			−0.207922			−0.103961	−	0.994581i	$-0.533152\pi$
$181$	−506.312			−0.207922			−0.103961	+	0.994581i	$0.533152\pi$
$182$	−3350.73	−	2664.63i	−1.36468	−	1.08525i
$183$		−	2952.59i		−	1.19269i
$184$	3518.88	−	6118.90i	1.40987	−	2.45158i
$185$			777.755i			0.309090i
$186$	−3053.36			−1.20367
$187$		−	4293.39i		−	1.67895i
$188$			1753.38i			0.680203i
$189$	1325.56	+	1054.14i	0.510160	+	0.405700i
$190$	5222.09			1.99395
$191$			1517.23i			0.574781i	0.957814	+	0.287390i	$0.0927877\pi$
$191$			1517.23i			0.574781i	−0.957814	+	0.287390i	$0.907212\pi$
$192$		−	5465.80i		−	2.05448i
$193$	−2118.34			−0.790059			−0.395029	−	0.918668i	$-0.629266\pi$
$193$	−2118.34			−0.790059			−0.395029	+	0.918668i	$0.629266\pi$
$194$	3694.43			1.36724
$195$	−2855.14			−1.04852
$196$	−1550.70	−	6709.47i	−0.565123	−	2.44514i
$197$	−2452.11			−0.886832			−0.443416	−	0.896316i	$-0.646233\pi$
$197$	−2452.11			−0.886832			−0.443416	+	0.896316i	$0.646233\pi$
$198$			3158.80i			1.13377i
$199$	−899.046			−0.320260			−0.160130	−	0.987096i	$-0.551191\pi$
$199$	−899.046			−0.320260			−0.160130	+	0.987096i	$0.551191\pi$
$200$	1048.82			0.370815
$201$	1303.09			0.457279
$202$			9142.83i			3.18459i
$203$	2664.18	−	3350.16i	0.921126	−	1.15830i
$204$			11294.7i			3.87641i
$205$			3936.61i			1.34119i
$206$	−7380.28			−2.49616
$207$	683.986	−	1189.37i	0.229663	−	0.399357i
$208$		−	7785.41i		−	2.59529i
$209$		−	4532.27i		−	1.50002i
$210$	−5026.92	−	3997.61i	−1.65186	−	1.31362i
$211$	−4959.66			−1.61818			−0.809092	−	0.587682i	$-0.800041\pi$
$211$	−4959.66			−1.61818			−0.809092	+	0.587682i	$0.800041\pi$
$212$			2381.99i			0.771678i
$213$		−	2473.54i		−	0.795701i
$214$		−	11558.7i		−	3.69224i
$215$		−	3180.63i		−	1.00892i
$216$			5851.83i			1.84336i
$217$	−1330.08	−	1057.73i	−0.416090	−	0.330891i
$218$		−	5354.48i		−	1.66354i
$219$	−2495.18			−0.769904
$220$			10027.9i			3.07309i
$221$			3907.98i			1.18950i
$222$	−2483.37			−0.750779
$223$			4634.33i			1.39165i	0.718212	+	0.695824i	$0.244961\pi$
$223$			4634.33i			1.39165i	−0.718212	+	0.695824i	$0.755039\pi$
$224$	4999.40	−	6286.66i	1.49123	−	1.87520i
$225$	203.866			0.0604048
$226$			5405.39i			1.59098i
$227$	4129.30			1.20736			0.603681	−	0.797226i	$-0.293700\pi$
$227$	4129.30			1.20736			0.603681	+	0.797226i	$0.293700\pi$
$228$			11923.1i			3.46328i
$229$	−5674.46			−1.63746			−0.818732	−	0.574176i	$-0.805322\pi$
$229$	−5674.46			−1.63746			−0.818732	+	0.574176i	$0.805322\pi$
$230$	3036.60	−	5280.28i	0.870555	−	1.51379i
$231$	−3469.54	+	4362.88i	−0.988220	+	1.24267i
$232$	14789.6			4.18529
$233$	5713.00			1.60631			0.803157	−	0.595767i	$-0.203152\pi$
$233$	5713.00			1.60631			0.803157	+	0.595767i	$0.203152\pi$
$234$		−	2875.24i		−	0.803250i
$235$			910.156i			0.252647i
$236$			8846.54i			2.44009i
$237$	−3608.86			−0.989117
$238$	−5471.73	+	6880.61i	−1.49025	+	1.87396i
$239$	1879.68			0.508730			0.254365	−	0.967108i	$-0.418134\pi$
$239$	1879.68			0.508730			0.254365	+	0.967108i	$0.418134\pi$
$240$		−	11680.0i		−	3.14143i
$241$	4685.18			1.25228			0.626138	−	0.779712i	$-0.284634\pi$
$241$	4685.18			1.25228			0.626138	+	0.779712i	$0.284634\pi$
$242$	5118.59			1.35965
$243$			3246.53i			0.857058i
$244$	9439.26			2.47658
$245$	−804.948	−	3482.80i	−0.209903	−	0.908197i
$246$	−12569.6			−3.25775
$247$			4125.42i			1.06273i
$248$		−	5871.77i		−	1.50346i
$249$			6788.23i			1.72766i
$250$	7807.77			1.97523
$251$	−4651.56			−1.16974			−0.584868	−	0.811129i	$-0.698854\pi$
$251$	−4651.56			−1.16974			−0.584868	+	0.811129i	$0.698854\pi$
$252$	2878.68	−	3619.89i	0.719603	−	0.904887i
$253$	−4582.78	−	2635.48i	−1.13880	−	0.654906i
$254$	−1410.58			−0.348456
$255$			5862.94i			1.43981i
$256$	−910.619			−0.222319
$257$			971.769i			0.235865i	0.993022	+	0.117932i	$0.0376266\pi$
$257$			971.769i			0.235865i	−0.993022	+	0.117932i	$0.962373\pi$
$258$	10155.7			2.45065
$259$	−1081.78	−	860.278i	−0.259532	−	0.206390i
$260$		−	9127.71i		−	2.17722i
$261$	2874.75			0.681772
$262$		−	10498.0i		−	2.47546i
$263$			7180.14i			1.68345i	0.539909	+	0.841723i	$0.318459\pi$
$263$			7180.14i			1.68345i	−0.539909	+	0.841723i	$0.681541\pi$
$264$	−19260.4			−4.49014
$265$			1236.46i			0.286623i
$266$	−5776.18	+	7263.43i	−1.33143	+	1.67425i
$267$		−	3515.00i		−	0.805672i
$268$			4165.91i			0.949528i
$269$		−	6468.84i		−	1.46622i	−0.680112	−	0.733108i	$-0.738069\pi$
$269$		−	6468.84i		−	1.46622i	0.680112	−	0.733108i	$-0.261931\pi$
$270$			5049.81i			1.13823i
$271$		−	634.490i		−	0.142223i	−0.997468	−	0.0711116i	$-0.977345\pi$
$271$		−	634.490i		−	0.142223i	0.997468	−	0.0711116i	$-0.0226547\pi$
$272$	−15987.1			−3.56382
$273$	3158.09	−	3971.24i	0.700132	−	0.880403i
$274$			9432.46i			2.07969i
$275$		−	785.521i		−	0.172250i
$276$	12056.0	+	6933.20i	2.62929	+	1.51206i
$277$	1288.44			0.279476			0.139738	−	0.990188i	$-0.455374\pi$
$277$	1288.44			0.279476			0.139738	+	0.990188i	$0.455374\pi$
$278$		−	4136.53i		−	0.892419i
$279$		−	1141.33i		−	0.244909i
$280$	7687.61	−	9667.03i	1.64080	−	2.06327i
$281$		−	4383.66i		−	0.930630i	−0.885145	−	0.465315i	$-0.845941\pi$
$281$		−	4383.66i		−	0.930630i	0.885145	−	0.465315i	$-0.154059\pi$
$282$	−2906.13			−0.613679
$283$	864.804			0.181651			0.0908256	−	0.995867i	$-0.471049\pi$
$283$	864.804			0.181651			0.0908256	+	0.995867i	$0.471049\pi$
$284$	7907.76			1.65225
$285$			6189.15i			1.28636i
$286$	−11078.6			−2.29054
$287$	−5475.45	−	4354.30i	−1.12615	−	0.895561i
$288$	5394.55			1.10374
$289$	3111.91			0.633404
$290$	12762.7			2.58431
$291$			4378.59i			0.882052i
$292$		−	7976.95i		−	1.59868i
$293$	−3793.25			−0.756328			−0.378164	−	0.925739i	$-0.623444\pi$
$293$	−3793.25			−0.756328			−0.378164	+	0.925739i	$0.623444\pi$
$294$	11120.6	−	2570.20i	2.20601	−	0.509854i
$295$			4592.13i			0.906319i
$296$		−	4775.66i		−	0.937769i
$297$	4382.75			0.856273
$298$			4839.61i			0.940776i
$299$	4171.39	+	2398.90i	0.806815	+	0.463986i
$300$			2066.48i			0.397695i
$301$	4423.95	+	3518.11i	0.847151	+	0.673688i
$302$	−2421.12			−0.461324
$303$	−10835.9			−2.05449
$304$	−16876.6			−3.18401
$305$	4899.80			0.919875
$306$	−5904.21			−1.10301
$307$			1137.77i			0.211519i	0.994392	+	0.105759i	$0.0337273\pi$
$307$			1137.77i			0.211519i	−0.994392	+	0.105759i	$0.966273\pi$
$308$	−13947.9	−	11091.9i	−2.58037	−	2.05201i
$309$		−	8747.00i		−	1.61035i
$310$		−	5067.02i		−	0.928346i
$311$		−	4686.11i		−	0.854421i	−0.904152	−	0.427210i	$-0.859496\pi$
$311$		−	4686.11i		−	0.854421i	0.904152	−	0.427210i	$-0.140504\pi$
$312$	17531.5			3.18117
$313$	−5048.25			−0.911642			−0.455821	−	0.890071i	$-0.650654\pi$
$313$	−5048.25			−0.911642			−0.455821	+	0.890071i	$0.650654\pi$
$314$	7480.24			1.34438
$315$	1494.29	−	1879.04i	0.267281	−	0.336101i
$316$		−	11537.3i		−	2.05387i
$317$	1339.33			0.237301			0.118650	−	0.992936i	$-0.462143\pi$
$317$	1339.33			0.237301			0.118650	+	0.992936i	$0.462143\pi$
$318$	−3948.02			−0.696207
$319$		−	11076.8i		−	1.94414i
$320$	9070.45			1.58454
$321$	13699.3			2.38199
$322$	3985.58	+	10064.2i	0.689775	+	1.74178i
$323$	8471.41			1.45932
$324$	−18272.4			−3.13312
$325$			715.006i			0.122035i
$326$	5325.61			0.904779
$327$	6346.06			1.07320
$328$		−	24172.0i		−	4.06913i
$329$	−1265.94	−	1006.73i	−0.212139	−	0.168701i
$330$	−16620.7			−2.77254
$331$	10115.1			1.67968			0.839840	−	0.542833i	$-0.182648\pi$
$331$	10115.1			1.67968			0.839840	+	0.542833i	$0.182648\pi$
$332$	−21701.6			−3.58743
$333$		−	928.273i		−	0.152760i
$334$			15258.0i			2.49964i
$335$			2162.47i			0.352682i
$336$	16245.8	+	12919.3i	2.63775	+	2.09764i
$337$			2949.04i			0.476689i	0.971181	+	0.238345i	$0.0766048\pi$
$337$			2949.04i			0.476689i	−0.971181	+	0.238345i	$0.923395\pi$
$338$	−1557.22			−0.250596
$339$	−6406.39			−1.02639
$340$	−18743.4			−2.98972
$341$	−4397.69			−0.698381
$342$	−6232.72			−0.985458
$343$	5734.61	+	2732.74i	0.902740	+	0.430186i
$344$			19530.0i			3.06101i
$345$	6258.12	+	3598.94i	0.976596	+	0.561624i
$346$		−	1899.25i		−	0.295099i
$347$	−9464.27			−1.46418			−0.732088	−	0.681211i	$-0.761454\pi$
$347$	−9464.27			−1.46418			−0.732088	+	0.681211i	$0.761454\pi$
$348$			29139.8i			4.48867i
$349$			2632.49i			0.403764i	0.979410	+	0.201882i	$0.0647058\pi$
$349$			2632.49i			0.403764i	−0.979410	+	0.201882i	$0.935294\pi$
$350$	−1001.11	+	1258.88i	−0.152890	+	0.192257i
$351$	−3989.32			−0.606650
$352$		−	20785.8i		−	3.14741i
$353$			3385.70i			0.510489i	0.966877	+	0.255245i	$0.0821560\pi$
$353$			3385.70i			0.510489i	−0.966877	+	0.255245i	$0.917844\pi$
$354$	−14662.7			−2.20145
$355$	4104.82			0.613694
$356$	11237.2			1.67295
$357$	−8154.80	−	6485.02i	−1.20896	−	0.961411i
$358$	−8808.46			−1.30040
$359$			4929.56i			0.724713i	0.932040	+	0.362356i	$0.118028\pi$
$359$			4929.56i			0.724713i	−0.932040	+	0.362356i	$0.881972\pi$
$360$	8295.23			1.21444
$361$	2083.75			0.303797
$362$	2682.83			0.389520
$363$			6066.48i			0.877157i
$364$	12695.8	+	10096.2i	1.82813	+	1.45380i
$365$		−	4140.74i		−	0.593797i
$366$			15645.1i			2.23437i
$367$	7489.07			1.06519			0.532597	−	0.846369i	$-0.321216\pi$
$367$	7489.07			1.06519			0.532597	+	0.846369i	$0.321216\pi$
$368$	−9813.59	+	17064.6i	−1.39013	+	2.41727i
$369$		−	4698.46i		−	0.662851i
$370$		−	4121.13i		−	0.579047i
$371$	−1719.80	−	1367.65i	−0.240667	−	0.191388i
$372$	11569.1			1.61244
$373$			876.538i			0.121677i	0.998148	+	0.0608383i	$0.0193774\pi$
$373$			876.538i			0.121677i	−0.998148	+	0.0608383i	$0.980623\pi$
$374$			22749.6i			3.14534i
$375$			9253.66i			1.27429i
$376$		−	5588.64i		−	0.766522i
$377$			10082.4i			1.37738i
$378$	−7023.81	−	5585.62i	−0.955730	−	0.760035i
$379$			1013.71i			0.137389i	0.997638	+	0.0686947i	$0.0218834\pi$
$379$			1013.71i			0.137389i	−0.997638	+	0.0686947i	$0.978117\pi$
$380$	−19786.3			−2.67110
$381$		−	1671.80i		−	0.224800i
$382$		−	8039.44i		−	1.07679i
$383$	−10199.9			−1.36081			−0.680404	−	0.732837i	$-0.738196\pi$
$383$	−10199.9			−1.36081			−0.680404	+	0.732837i	$0.738196\pi$
$384$			7172.95i			0.953238i
$385$	−7240.16	−	5757.67i	−0.958423	−	0.762176i
$386$	11224.6			1.48009
$387$			3796.17i			0.498631i
$388$	−13998.1			−1.83156
$389$			4076.15i			0.531283i	0.964072	+	0.265641i	$0.0855837\pi$
$389$			4076.15i			0.531283i	−0.964072	+	0.265641i	$0.914416\pi$
$390$	15128.7			1.96429
$391$	4926.05	−	8565.81i	0.637139	−	1.10791i
$392$	4942.63	+	21385.5i	0.636838	+	2.75544i
$393$	12442.1			1.59700
$394$	12993.1			1.66138
$395$		−	5988.87i		−	0.762868i
$396$		−	11968.6i		−	1.51880i
$397$		−	9867.65i		−	1.24746i	−0.781638	−	0.623732i	$-0.785616\pi$
$397$		−	9867.65i		−	1.24746i	0.781638	−	0.623732i	$-0.214384\pi$
$398$	4763.82			0.599972
$399$	−8608.52	−	6845.84i	−1.08011	−	0.858949i
$400$	−2925.00			−0.365625
$401$		−	8945.57i		−	1.11402i	−0.830507	−	0.557008i	$-0.811949\pi$
$401$		−	8945.57i		−	1.11402i	0.830507	−	0.557008i	$-0.188051\pi$
$402$	−6904.78			−0.856664
$403$	4002.92			0.494788
$404$		−	34641.8i		−	4.26608i
$405$	−9484.95			−1.16373
$406$	−14116.8	+	17751.7i	−1.72563	+	2.16995i
$407$	−3576.75			−0.435609
$408$		−	36000.3i		−	4.36833i
$409$		−	10016.8i		−	1.21099i	−0.795848	−	0.605497i	$-0.792974\pi$
$409$		−	10016.8i		−	1.21099i	0.795848	−	0.605497i	$-0.207026\pi$
$410$		−	20859.1i		−	2.51258i
$411$	−11179.2			−1.34168
$412$	27963.6			3.34386
$413$	−6387.22	−	5079.37i	−0.761004	−	0.605181i
$414$	−3624.27	+	6302.17i	−0.430249	+	0.748152i
$415$	−11265.0			−1.33248
$416$			18919.9i			2.22987i
$417$	4902.55			0.575729
$418$			24015.4i			2.81012i
$419$	2444.90			0.285063			0.142531	−	0.989790i	$-0.454476\pi$
$419$	2444.90			0.285063			0.142531	+	0.989790i	$0.454476\pi$
$420$	19046.8	+	15146.8i	2.21283	+	1.75973i
$421$			1860.40i			0.215369i	0.994185	+	0.107684i	$0.0343436\pi$
$421$			1860.40i			0.215369i	−0.994185	+	0.107684i	$0.965656\pi$
$422$	26280.0			3.03149
$423$		−	1086.30i		−	0.124864i
$424$		−	7592.25i		−	0.869605i
$425$	1468.24			0.167577
$426$			13106.7i			1.49066i
$427$	−5419.69	+	6815.16i	−0.614233	+	0.772386i
$428$			43795.7i			4.94613i
$429$		−	13130.3i		−	1.47770i
$430$			16853.4i			1.89010i
$431$		−	12526.2i		−	1.39992i	−0.714183	−	0.699959i	$-0.753202\pi$
$431$		−	12526.2i		−	1.39992i	0.714183	−	0.699959i	$-0.246798\pi$
$432$		−	16319.8i		−	1.81756i
$433$	13473.0			1.49531			0.747657	−	0.664085i	$-0.231179\pi$
$433$	13473.0			1.49531			0.747657	+	0.664085i	$0.231179\pi$
$434$	7047.75	+	5604.65i	0.779499	+	0.619889i
$435$			15126.1i			1.66722i
$436$			20288.0i			2.22848i
$437$	5200.13	−	9042.40i	0.569236	−	0.989832i
$438$	13221.4			1.44233
$439$			1417.33i			0.154089i	0.997028	+	0.0770447i	$0.0245484\pi$
$439$			1417.33i			0.154089i	−0.997028	+	0.0770447i	$0.975452\pi$
$440$		−	31962.5i		−	3.46307i
$441$	960.729	+	4156.83i	0.103739	+	0.448853i
$442$		−	20707.4i		−	2.22840i
$443$	−3245.54			−0.348082			−0.174041	−	0.984738i	$-0.555683\pi$
$443$	−3245.54			−0.348082			−0.174041	+	0.984738i	$0.555683\pi$
$444$	9409.41			1.00575
$445$	5833.10			0.621384
$446$		−	24556.2i		−	2.60710i
$447$	−5735.84			−0.606926
$448$	−10032.9	+	12616.1i	−1.05805	+	1.33048i
$449$	14035.4			1.47521			0.737605	−	0.675232i	$-0.235957\pi$
$449$	14035.4			1.47521			0.737605	+	0.675232i	$0.235957\pi$
$450$	−1080.24			−0.113162
$451$	−18103.7			−1.89018
$452$		−	20480.8i		−	2.13128i
$453$		−	2869.48i		−	0.297616i
$454$	−21880.1			−2.26186
$455$	6590.23	+	5240.81i	0.679021	+	0.539985i
$456$		−	38003.3i		−	3.90278i
$457$			3867.75i			0.395899i	0.980212	+	0.197950i	$0.0634282\pi$
$457$			3867.75i			0.395899i	−0.980212	+	0.197950i	$0.936572\pi$
$458$	30067.6			3.06761
$459$			8191.93i			0.833043i
$460$	−11505.6	+	20006.8i	−1.16620	+	2.02787i
$461$		−	12035.2i		−	1.21591i	−0.793970	−	0.607957i	$-0.791989\pi$
$461$		−	12035.2i		−	1.21591i	0.793970	−	0.607957i	$-0.208011\pi$
$462$	18384.2	−	23117.8i	1.85132	−	2.32801i
$463$	−17921.7			−1.79890			−0.899451	−	0.437021i	$-0.856033\pi$
$463$	−17921.7			−1.79890			−0.899451	+	0.437021i	$0.856033\pi$
$464$	−41245.9			−4.12671
$465$	6005.36			0.598907
$466$	−30271.8			−3.00926
$467$	−10655.0			−1.05579			−0.527897	−	0.849309i	$-0.677019\pi$
$467$	−10655.0			−1.05579			−0.527897	+	0.849309i	$0.677019\pi$
$468$			10894.2i			1.07603i
$469$	−3007.80	−	2391.92i	−0.296135	−	0.235498i
$470$		−	4822.69i		−	0.473307i
$471$			8865.47i			0.867302i
$472$		−	28197.1i		−	2.74974i
$473$	14627.1			1.42189
$474$	19122.5			1.85300
$475$	1549.93			0.149717
$476$	20732.2	−	26070.4i	1.99634	−	2.51037i
$477$		−	1475.75i		−	0.141656i
$478$	−9959.96			−0.953050
$479$	−4391.21			−0.418871			−0.209436	−	0.977822i	$-0.567163\pi$
$479$	−4391.21			−0.418871			−0.209436	+	0.977822i	$0.567163\pi$
$480$			28384.6i			2.69911i
$481$	3255.67			0.308619
$482$	−24825.6			−2.34601
$483$	−11927.9	+	4723.65i	−1.12368	+	0.444997i
$484$	−19394.2			−1.82139
$485$	−7266.22			−0.680293
$486$		−	17202.6i		−	1.60561i
$487$	6792.51			0.632029			0.316014	−	0.948754i	$-0.397655\pi$
$487$	6792.51			0.632029			0.316014	+	0.948754i	$0.397655\pi$
$488$	−30086.3			−2.79087
$489$			6311.83i			0.583703i
$490$	4265.22	+	18454.5i	0.393231	+	1.70141i
$491$	−11228.3			−1.03203			−0.516014	−	0.856580i	$-0.672585\pi$
$491$	−11228.3			−1.03203			−0.516014	+	0.856580i	$0.672585\pi$
$492$	47625.7			4.36409
$493$	20703.9			1.89139
$494$		−	21859.6i		−	1.99091i
$495$		−	6212.75i		−	0.564126i
$496$			16375.4i			1.48242i
$497$	−4540.36	+	5709.42i	−0.409785	+	0.515297i
$498$		−	35969.2i		−	3.23658i
$499$	17063.0			1.53075			0.765375	−	0.643584i	$-0.222553\pi$
$499$	17063.0			1.53075			0.765375	+	0.643584i	$0.222553\pi$
$500$	−29583.4			−2.64602
$501$	−18083.6			−1.61260
$502$	24647.5			2.19137
$503$	2795.65			0.247817			0.123909	−	0.992294i	$-0.460457\pi$
$503$	2795.65			0.247817			0.123909	+	0.992294i	$0.460457\pi$
$504$	−9175.39	+	11537.9i	−0.810922	+	1.01972i
$505$		−	17982.2i		−	1.58455i
$506$	24283.0	+	13964.8i	2.13342	+	1.22690i
$507$		−	1845.59i		−	0.161668i
$508$	5344.64			0.466792
$509$			21726.4i			1.89195i	0.324236	+	0.945976i	$0.394893\pi$
$509$			21726.4i			1.89195i	−0.324236	+	0.945976i	$0.605107\pi$
$510$		−	31066.3i		−	2.69733i
$511$	5759.37	+	4580.09i	0.498590	+	0.396499i
$512$	13962.7			1.20521
$513$			8647.72i			0.744262i
$514$		−	5149.17i		−	0.441868i
$515$	14515.6			1.24200
$516$	−38479.7			−3.28290
$517$	−4185.63			−0.356062
$518$	5732.11	+	4558.40i	0.486205	+	0.386650i
$519$	2250.96			0.190378
$520$			29093.3i			2.45351i
$521$	−18173.2			−1.52818			−0.764092	−	0.645108i	$-0.776813\pi$
$521$	−18173.2			−1.52818			−0.764092	+	0.645108i	$0.776813\pi$
$522$	−15232.6			−1.27723
$523$	7338.81			0.613583			0.306791	−	0.951777i	$-0.400745\pi$
$523$	7338.81			0.613583			0.306791	+	0.951777i	$0.400745\pi$
$524$			39776.6i			3.31612i
$525$	−1492.00	−	1186.50i	−0.124031	−	0.0986347i
$526$		−	38045.8i		−	3.15376i
$527$		−	8219.85i		−	0.679435i
$528$	53714.3			4.42730
$529$	−6119.33	−	10516.2i	−0.502945	−	0.864318i
$530$		−	6551.70i		−	0.536958i
$531$		−	5480.84i		−	0.447925i
$532$	21885.7	−	27520.9i	1.78358	−	2.24282i
$533$	16478.6			1.33915
$534$			18625.1i			1.50934i
$535$			22733.8i			1.83714i
$536$		−	13278.3i		−	1.07002i
$537$		−	10439.7i		−	0.838929i
$538$			34276.8i			2.74680i
$539$	16016.8	−	3701.80i	1.27994	−	0.295822i
$540$		−	19133.6i		−	1.52477i
$541$	2587.58			0.205635			0.102818	−	0.994700i	$-0.467214\pi$
$541$	2587.58			0.205635			0.102818	+	0.994700i	$0.467214\pi$
$542$			3362.00i			0.266440i
$543$			3179.65i			0.251292i
$544$	38851.4			3.06202
$545$			10531.2i			0.827721i
$546$	−16733.9	+	21042.6i	−1.31162	+	1.64934i
$547$	−903.404			−0.0706157			−0.0353078	−	0.999376i	$-0.511241\pi$
$547$	−903.404			−0.0706157			−0.0353078	+	0.999376i	$0.511241\pi$
$548$		−	35739.3i		−	2.78596i
$549$	−5848.06			−0.454625
$550$			4162.28i			0.322691i
$551$	21855.8			1.68982
$552$	−38426.8	−	22098.6i	−2.96296	−	1.70395i
$553$	8329.96	+	6624.32i	0.640553	+	0.509393i
$554$	−6827.14			−0.523569
$555$	4884.31			0.373563
$556$			15673.2i			1.19549i
$557$			13166.5i			1.00158i	0.865568	+	0.500791i	$0.166957\pi$
$557$			13166.5i			1.00158i	−0.865568	+	0.500791i	$0.833043\pi$
$558$			6047.64i			0.458812i
$559$	−13314.1			−1.00738
$560$	−21439.5	+	26959.8i	−1.61783	+	2.03439i
$561$	−26962.5			−2.02916
$562$			23227.9i			1.74344i
$563$	3702.82			0.277185			0.138592	−	0.990349i	$-0.455742\pi$
$563$	3702.82			0.277185			0.138592	+	0.990349i	$0.455742\pi$
$564$	11011.2			0.822085
$565$		−	10631.4i		−	0.791618i
$566$	−4582.38			−0.340304
$567$	10491.3	−	13192.7i	0.777064	−	0.977144i
$568$	−25204.9			−1.86192
$569$			20116.4i			1.48211i	0.671443	+	0.741056i	$0.265675\pi$
$569$			20116.4i			1.48211i	−0.671443	+	0.741056i	$0.734325\pi$
$570$		−	32794.8i		−	2.40986i
$571$			21657.8i			1.58730i	0.608372	+	0.793652i	$0.291823\pi$
$571$			21657.8i			1.58730i	−0.608372	+	0.793652i	$0.708177\pi$
$572$	41976.6			3.06841
$573$	9528.23			0.694673
$574$	29013.1	+	23072.4i	2.10972	+	1.67774i
$575$	901.273	−	1567.20i	0.0653664	−	0.113664i
$576$	−10825.8			−0.783120
$577$			801.281i			0.0578124i	0.999582	+	0.0289062i	$0.00920241\pi$
$577$			801.281i			0.0578124i	−0.999582	+	0.0289062i	$0.990798\pi$
$578$	−16489.3			−1.18661
$579$			13303.2i			0.954856i
$580$	−48357.2			−3.46194
$581$	12460.3	−	15668.6i	0.889741	−	1.11883i
$582$		−	23201.1i		−	1.65243i
$583$	−5686.25			−0.403946
$584$			25425.4i			1.80156i
$585$			5655.04i			0.399670i
$586$	20099.5			1.41690
$587$		−	19033.1i		−	1.33829i	−0.743130	−	0.669147i	$-0.766660\pi$
$587$		−	19033.1i		−	1.33829i	0.743130	−	0.669147i	$-0.233340\pi$
$588$	−42135.5	+	9738.40i	−2.95517	+	0.683001i
$589$		−	8677.19i		−	0.607025i
$590$		−	24332.6i		−	1.69789i
$591$			15399.3i			1.07181i
$592$			13318.5i			0.924643i
$593$		−	5571.59i		−	0.385831i	−0.981215	−	0.192915i	$-0.938206\pi$
$593$		−	5571.59i		−	0.385831i	0.981215	−	0.192915i	$-0.0617943\pi$
$594$	−23223.1			−1.60413
$595$	10761.8	−	13532.8i	0.741500	−	0.932422i
$596$		−	18337.1i		−	1.26026i
$597$			5646.02i			0.387062i
$598$	−22103.2	−	12711.2i	−1.51148	−	0.869228i
$599$	−10548.2			−0.719509			−0.359754	−	0.933047i	$-0.617140\pi$
$599$	−10548.2			−0.719509			−0.359754	+	0.933047i	$0.617140\pi$
$600$		−	6586.62i		−	0.448163i
$601$			8239.33i			0.559217i	0.960114	+	0.279608i	$0.0902046\pi$
$601$			8239.33i			0.559217i	−0.960114	+	0.279608i	$0.909795\pi$
$602$	−23441.4	−	18641.6i	−1.58705	−	1.26208i
$603$		−	2580.97i		−	0.174304i
$604$	9173.55			0.617991
$605$	−10067.3			−0.676517
$606$	57417.0			3.84886
$607$		−	2964.72i		−	0.198245i	−0.995075	−	0.0991223i	$-0.968397\pi$
$607$		−	2964.72i		−	0.198245i	0.995075	−	0.0991223i	$-0.0316035\pi$
$608$	41013.1			2.73569
$609$	−21039.0	−	16731.1i	−1.39991	−	1.11326i
$610$	−25962.8			−1.72329
$611$	3809.90			0.252262
$612$	22370.9			1.47760
$613$			18386.0i			1.21143i	0.795683	+	0.605713i	$0.207112\pi$
$613$			18386.0i			1.21143i	−0.795683	+	0.605713i	$0.792888\pi$
$614$		−	6028.79i		−	0.396258i
$615$	24721.9			1.62095
$616$	44456.8	+	35353.9i	2.90782	+	2.31242i
$617$			29618.3i			1.93255i	0.257504	+	0.966277i	$0.417100\pi$
$617$			29618.3i			1.93255i	−0.257504	+	0.966277i	$0.582900\pi$
$618$			46348.2i			3.01683i
$619$	−12876.2			−0.836086			−0.418043	−	0.908427i	$-0.637284\pi$
$619$	−12876.2			−0.836086			−0.418043	+	0.908427i	$0.637284\pi$
$620$			19198.8i			1.24361i
$621$	8744.09	+	5028.58i	0.565037	+	0.324943i
$622$			24830.5i			1.60067i
$623$	−6452.02	+	8113.30i	−0.414919	+	0.521754i
$624$	−48892.4			−3.13664
$625$	−13307.6			−0.851688
$626$	26749.4			1.70786
$627$	−28462.7			−1.81290
$628$	−28342.4			−1.80093
$629$		−	6685.41i		−	0.423791i
$630$	−7917.86	+	9956.57i	−0.500723	+	0.629650i
$631$		−	9606.63i		−	0.606076i	−0.952978	−	0.303038i	$-0.901999\pi$
$631$		−	9606.63i		−	0.606076i	0.952978	−	0.303038i	$-0.0980009\pi$
$632$			36773.5i			2.31451i
$633$			31146.7i			1.95572i
$634$	−7096.78			−0.444557
$635$	2774.34			0.173380
$636$	14958.9			0.932640
$637$	−14579.0	+	3369.50i	−0.906812	+	0.209583i
$638$			58693.0i			3.64213i
$639$	−4899.22			−0.303303
$640$	−11903.5			−0.735196
$641$		−	18771.9i		−	1.15670i	−0.815789	−	0.578350i	$-0.803697\pi$
$641$		−	18771.9i		−	1.15670i	0.815789	−	0.578350i	$-0.196303\pi$
$642$	−72589.0			−4.46240
$643$	−773.918			−0.0474655			−0.0237328	−	0.999718i	$-0.507555\pi$
$643$	−773.918			−0.0474655			−0.0237328	+	0.999718i	$0.507555\pi$
$644$	−15101.2	−	38132.8i	−0.924024	−	2.33330i
$645$	−19974.4			−1.21936
$646$	−44887.9			−2.73389
$647$			18640.8i			1.13268i	0.824170	+	0.566342i	$0.191642\pi$
$647$			18640.8i			1.13268i	−0.824170	+	0.566342i	$0.808358\pi$
$648$	58240.6			3.53072
$649$	−21118.3			−1.27730
$650$		−	3788.64i		−	0.228620i
$651$	−6642.55	+	8352.89i	−0.399911	+	0.502881i
$652$	−20178.5			−1.21204
$653$	−22227.7			−1.33207			−0.666033	−	0.745922i	$-0.732009\pi$
$653$	−22227.7			−1.33207			−0.666033	+	0.745922i	$0.732009\pi$
$654$	−33626.2			−2.01053
$655$			20647.5i			1.23170i
$656$			67411.8i			4.01218i
$657$			4942.09i			0.293469i
$658$	6707.91	+	5334.40i	0.397419	+	0.316043i
$659$		−	16967.7i		−	1.00298i	−0.865163	−	0.501492i	$-0.832785\pi$
$659$		−	16967.7i		−	1.00298i	0.865163	−	0.501492i	$-0.167215\pi$
$660$	62975.3			3.71410
$661$	−453.229			−0.0266695			−0.0133348	−	0.999911i	$-0.504245\pi$
$661$	−453.229			−0.0266695			−0.0133348	+	0.999911i	$0.504245\pi$
$662$	−53597.3			−3.14670
$663$	24542.2			1.43762
$664$	69170.6			4.04268
$665$	11360.6	−	14285.8i	0.662475	−	0.833050i
$666$			4918.69i			0.286179i
$667$	12709.0	−	22099.4i	0.737772	−	1.28290i
$668$		−	57812.0i		−	3.34852i
$669$	29103.6			1.68193
$670$		−	11458.4i		−	0.660712i
$671$			22533.3i			1.29640i
$672$	−39480.2	−	31396.3i	−2.26634	−	1.80229i
$673$	7504.04			0.429806			0.214903	−	0.976635i	$-0.431056\pi$
$673$	7504.04			0.429806			0.214903	+	0.976635i	$0.431056\pi$
$674$		−	15626.2i		−	0.893026i
$675$			1498.80i			0.0854649i
$676$	5900.25			0.335699
$677$	5278.65			0.299668			0.149834	−	0.988711i	$-0.452126\pi$
$677$	5278.65			0.299668			0.149834	+	0.988711i	$0.452126\pi$
$678$	33945.9			1.92284
$679$	8037.20	−	10106.6i	0.454256	−	0.571218i
$680$	59742.1			3.36913
$681$		−	25932.0i		−	1.45920i
$682$	23302.3			1.30834
$683$	−26270.0			−1.47173			−0.735867	−	0.677126i	$-0.763225\pi$
$683$	−26270.0			−1.47173			−0.735867	+	0.677126i	$0.763225\pi$
$684$	23615.5			1.32012
$685$		−	18551.8i		−	1.03479i
$686$	−30386.3	−	14480.1i	−1.69119	−	0.805908i
$687$			35635.7i			1.97902i
$688$		−	54466.1i		−	3.01817i
$689$	5175.80			0.286186
$690$	−33160.2	−	19069.9i	−1.82955	−	1.05214i
$691$		−	3209.75i		−	0.176707i	−0.996089	−	0.0883537i	$-0.971839\pi$
$691$		−	3209.75i		−	0.176707i	0.996089	−	0.0883537i	$-0.0281606\pi$
$692$			7196.19i			0.395315i
$693$	8641.35	+	6871.95i	0.473676	+	0.376686i
$694$	50148.8			2.74297
$695$			8135.74i			0.444038i
$696$		−	92879.0i		−	5.05829i
$697$		−	33838.2i		−	1.83890i
$698$		−	13948.9i		−	0.756409i
$699$		−	35877.7i		−	1.94137i
$700$	3793.17	−	4769.85i	0.204812	−	0.257547i
$701$			26555.0i			1.43077i	0.698732	+	0.715384i	$0.253748\pi$
$701$			26555.0i			1.43077i	−0.698732	+	0.715384i	$0.746252\pi$
$702$	21138.4			1.13649
$703$		−	7057.38i		−	0.378626i
$704$			41713.3i			2.23314i
$705$	5715.79			0.305346
$706$		−	17940.0i		−	0.956347i
$707$	25011.5	+	19890.1i	1.33049	+	1.05806i
$708$	55556.3			2.94906
$709$			24535.2i			1.29963i	0.760092	+	0.649815i	$0.225154\pi$
$709$			24535.2i			1.29963i	−0.760092	+	0.649815i	$0.774846\pi$
$710$	−21750.4			−1.14969
$711$			7147.89i			0.377028i
$712$	−35817.1			−1.88526
$713$	−8773.89	−	5045.72i	−0.460848	−	0.265026i
$714$	43210.3	+	34362.5i	2.26485	+	1.80110i
$715$	21789.5			1.13970
$716$	33375.0			1.74201
$717$		−	11804.4i		−	0.614845i
$718$		−	26120.5i		−	1.35767i
$719$		−	1509.08i		−	0.0782744i	−0.999234	−	0.0391372i	$-0.987539\pi$
$719$		−	1509.08i		−	0.0782744i	0.999234	−	0.0391372i	$-0.0124609\pi$
$720$	−23134.1			−1.19744
$721$	−16055.7	+	20189.8i	−0.829330	+	1.04287i
$722$	−11041.3			−0.569132
$723$		−	29422.9i		−	1.51349i
$724$	−10165.1			−0.521801
$725$	3787.99			0.194045
$726$		−	32144.8i		−	1.64326i
$727$	−16361.6			−0.834687			−0.417343	−	0.908749i	$-0.637039\pi$
$727$	−16361.6			−0.834687			−0.417343	+	0.908749i	$0.637039\pi$
$728$	−40466.1	−	32180.2i	−2.06013	−	1.63830i
$729$	−4185.09			−0.212625
$730$			21940.7i			1.11242i
$731$			27340.0i			1.38332i
$732$		−	59278.6i		−	2.99317i
$733$	−24970.5			−1.25826			−0.629131	−	0.777299i	$-0.716589\pi$
$733$	−24970.5			−1.25826			−0.629131	+	0.777299i	$0.716589\pi$
$734$	−39682.8			−1.99553
$735$	−21872.0	+	5055.08i	−1.09764	+	0.253686i
$736$	23848.8	−	41470.1i	1.19440	−	2.07691i
$737$	−9944.80			−0.497044
$738$			24896.0i			1.24178i
$739$	26596.0			1.32388			0.661941	−	0.749556i	$-0.269733\pi$
$739$	26596.0			1.32388			0.661941	+	0.749556i	$0.269733\pi$
$740$			15614.8i			0.775693i
$741$	25907.7			1.28440
$742$	9112.80	+	7246.87i	0.450864	+	0.358546i
$743$			20527.4i			1.01356i	0.862075	+	0.506782i	$0.169165\pi$
$743$			20527.4i			1.01356i	−0.862075	+	0.506782i	$0.830835\pi$
$744$	−36874.8			−1.81706
$745$		−	9518.57i		−	0.468099i
$746$		−	4644.56i		−	0.227948i
$747$	13445.1			0.658542
$748$		−	86197.6i		−	4.21350i
$749$	−31620.6	−	25146.0i	−1.54258	−	1.22672i
$750$		−	49032.9i		−	2.38724i
$751$			4277.52i			0.207842i	0.994586	+	0.103921i	$0.0331389\pi$
$751$			4277.52i			0.207842i	−0.994586	+	0.103921i	$0.966861\pi$
$752$			15585.8i			0.755793i
$753$			29211.8i			1.41373i
$754$		−	53424.3i		−	2.58037i
$755$	4761.88			0.229540
$756$	26613.0	+	21163.7i	1.28030	+	1.01814i
$757$			9903.01i			0.475470i	0.971330	+	0.237735i	$0.0764050\pi$
$757$			9903.01i			0.475470i	−0.971330	+	0.237735i	$0.923595\pi$
$758$		−	5371.38i		−	0.257384i
$759$	−16550.8	+	28779.9i	−0.791511	+	1.37634i
$760$	63066.1			3.01006
$761$			13640.8i			0.649776i	0.945753	+	0.324888i	$0.105327\pi$
$761$			13640.8i			0.649776i	−0.945753	+	0.324888i	$0.894673\pi$
$762$			8858.46i			0.421139i
$763$	−14647.9	−	11648.6i	−0.695008	−	0.552699i
$764$			30461.2i			1.44247i
$765$	11612.4			0.548822
$766$	54046.6			2.54933
$767$	19222.6			0.904937
$768$			5718.70i			0.268692i
$769$	7455.44			0.349610			0.174805	−	0.984603i	$-0.444071\pi$
$769$	7455.44			0.349610			0.174805	+	0.984603i	$0.444071\pi$
$770$	38363.8	+	30508.5i	1.79550	+	1.42786i
$771$	6102.72			0.285064
$772$	−42529.4			−1.98273
$773$	−13983.5			−0.650651			−0.325325	−	0.945602i	$-0.605474\pi$
$773$	−13983.5			−0.650651			−0.325325	+	0.945602i	$0.605474\pi$
$774$		−	20115.0i		−	0.934132i
$775$		−	1503.91i		−	0.0697057i
$776$	44616.9			2.06398
$777$	−5402.56	+	6793.61i	−0.249441	+	0.313667i
$778$		−	21598.5i		−	0.995301i
$779$		−	35720.9i		−	1.64292i
$780$	−57322.1			−2.63136
$781$			18877.3i			0.864894i
$782$	−26101.9	+	45388.1i	−1.19361	+	2.07554i
$783$			21134.8i			0.964619i
$784$	−13784.2	−	59640.7i	−0.627925	−	2.71687i
$785$	−14712.2			−0.668917
$786$	−65927.6			−2.99181
$787$	−18558.6			−0.840588			−0.420294	−	0.907388i	$-0.638073\pi$
$787$	−18558.6			−0.840588			−0.420294	+	0.907388i	$0.638073\pi$
$788$	−49230.6			−2.22559
$789$	45091.3			2.03459
$790$			31733.5i			1.42915i
$791$	14787.2	+	11759.4i	0.664694	+	0.528591i
$792$			38148.2i			1.71154i
$793$		−	20510.5i		−	0.918473i
$794$			52286.3i			2.33699i
$795$	7764.98			0.346410
$796$	−18050.0			−0.803724
$797$	−9082.85			−0.403677			−0.201839	−	0.979419i	$-0.564692\pi$
$797$	−9082.85			−0.403677			−0.201839	+	0.979419i	$0.564692\pi$
$798$	45614.4	+	36274.4i	2.02348	+	1.60915i
$799$		−	7823.50i		−	0.346402i
$800$	7108.27			0.314144
$801$	−6961.98			−0.307103
$802$			47400.4i			2.08699i
$803$	19042.5			0.836854
$804$	26162.0			1.14759
$805$	−7838.85	−	19794.3i	−0.343209	−	0.866653i
$806$	−21210.5			−0.926931
$807$	−40624.4			−1.77205
$808$			110416.i			4.80745i
$809$	10645.8			0.462655			0.231327	−	0.972876i	$-0.425693\pi$
$809$	10645.8			0.462655			0.231327	+	0.972876i	$0.425693\pi$
$810$	50258.4			2.18013
$811$			10303.3i			0.446114i	0.974805	+	0.223057i	$0.0716036\pi$
$811$			10303.3i			0.446114i	−0.974805	+	0.223057i	$0.928396\pi$
$812$	53488.2	−	67260.4i	2.31166	−	2.90687i
$813$	−3984.60			−0.171889
$814$	18952.3			0.816066
$815$	−10474.4			−0.450188
$816$			100399.i			4.30719i
$817$			28861.1i			1.23589i
$818$			53076.3i			2.26867i
$819$	−7865.63	−	6255.07i	−0.335589	−	0.266874i
$820$			79034.5i			3.36586i
$821$	−4318.02			−0.183557			−0.0917784	−	0.995779i	$-0.529255\pi$
$821$	−4318.02			−0.183557			−0.0917784	+	0.995779i	$0.529255\pi$
$822$	59236.0			2.51349
$823$	10086.5			0.427209			0.213604	−	0.976920i	$-0.431480\pi$
$823$	10086.5			0.427209			0.213604	+	0.976920i	$0.431480\pi$
$824$	−89130.1			−3.76820
$825$	−4933.08			−0.208179
$826$	33844.3	+	26914.3i	1.42566	+	1.13374i
$827$		−	7232.54i		−	0.304111i	−0.988372	−	0.152056i	$-0.951411\pi$
$827$		−	7232.54i		−	0.304111i	0.988372	−	0.152056i	$-0.0485893\pi$
$828$	13732.2	−	23878.7i	0.576363	−	1.00223i
$829$		−	32215.2i		−	1.34967i	−0.737967	−	0.674837i	$-0.764214\pi$
$829$		−	32215.2i		−	1.34967i	0.737967	−	0.674837i	$-0.235786\pi$
$830$	59690.5			2.49625
$831$		−	8091.43i		−	0.337772i
$832$		−	37968.8i		−	1.58213i
$833$	6919.16	+	29937.4i	0.287797	+	1.24522i
$834$	−25977.4			−1.07857
$835$		−	30009.5i		−	1.24374i
$836$		−	90993.5i		−	3.76444i
$837$	8390.93			0.346515
$838$	−12954.9			−0.534035
$839$	−19927.4			−0.819988			−0.409994	−	0.912088i	$-0.634469\pi$
$839$	−19927.4			−0.819988			−0.409994	+	0.912088i	$0.634469\pi$
$840$	−60709.1	−	48278.3i	−2.49364	−	1.98305i
$841$	29026.1			1.19013
$842$		−	9857.78i		−	0.403470i
$843$	−27529.4			−1.12475
$844$	−99574.0			−4.06099
$845$	3062.75			0.124688
$846$			5756.02i			0.233920i
$847$	11135.5	−	14002.6i	0.451734	−	0.568047i
$848$			21173.6i			0.857433i
$849$		−	5430.98i		−	0.219541i
$850$	−7779.85			−0.313937
$851$	−7136.02	−	4103.81i	−0.287450	−	0.165307i
$852$		−	49660.8i		−	1.99689i
$853$		−	8219.46i		−	0.329928i	−0.986300	−	0.164964i	$-0.947249\pi$
$853$		−	8219.46i		−	0.329928i	0.986300	−	0.164964i	$-0.0527509\pi$
$854$	28717.6	−	36111.9i	1.15070	−	1.44698i
$855$	12258.5			0.490331
$856$		−	139593.i		−	5.57380i
$857$		−	28865.8i		−	1.15057i	−0.817954	−	0.575284i	$-0.804892\pi$
$857$		−	28865.8i		−	1.15057i	0.817954	−	0.575284i	$-0.195108\pi$
$858$			69574.0i			2.76832i
$859$		−	18669.4i		−	0.741550i	−0.928723	−	0.370775i	$-0.879092\pi$
$859$		−	18669.4i		−	0.741550i	0.928723	−	0.370775i	$-0.120908\pi$
$860$		−	63856.8i		−	2.53197i
$861$	−27345.0	+	34385.9i	−1.08236	+	1.36105i
$862$			66373.1i			2.62260i
$863$	−27583.1			−1.08800			−0.543998	−	0.839086i	$-0.683090\pi$
$863$	−27583.1			−1.08800			−0.543998	+	0.839086i	$0.683090\pi$
$864$			39660.0i			1.56165i
$865$			3735.45i			0.146831i
$866$	−71390.1			−2.80131
$867$		−	19542.8i		−	0.765524i
$868$	−26703.7	−	21235.8i	−1.04422	−	0.830405i
$869$	27541.7			1.07513
$870$		−	80149.6i		−	3.12336i
$871$	9052.08			0.352145
$872$		−	64665.0i		−	2.51128i
$873$	8672.45			0.336218
$874$	−27554.2	+	47913.5i	−1.06640	+	1.85434i
$875$	16985.7	−	21359.3i	0.656255	−	0.825229i
$876$	−50095.3			−1.93215
$877$	−10367.1			−0.399170			−0.199585	−	0.979881i	$-0.563959\pi$
$877$	−10367.1			−0.399170			−0.199585	+	0.979881i	$0.563959\pi$
$878$		−	7510.06i		−	0.288670i
$879$			23821.7i			0.914089i
$880$			89138.3i			3.41460i
$881$	−11497.0			−0.439663			−0.219832	−	0.975538i	$-0.570551\pi$
$881$	−11497.0			−0.439663			−0.219832	+	0.975538i	$0.570551\pi$
$882$	−5090.67	−	22026.0i	−0.194344	−	0.840878i
$883$	41511.5			1.58208			0.791038	−	0.611767i	$-0.209541\pi$
$883$	41511.5			1.58208			0.791038	+	0.611767i	$0.209541\pi$
$884$			78459.8i			2.98517i
$885$	28838.6			1.09537
$886$	17197.3			0.652094
$887$			22852.5i			0.865065i	0.901618	+	0.432532i	$0.142380\pi$
$887$			22852.5i			0.865065i	−0.901618	+	0.432532i	$0.857620\pi$
$888$	−29991.2			−1.13338
$889$	−3068.71	+	3858.84i	−0.115772	+	0.145581i
$890$	−30908.2			−1.16410
$891$		−	43619.5i		−	1.64008i
$892$			93042.4i			3.49248i
$893$		−	8258.79i		−	0.309485i
$894$	30392.8			1.13701
$895$	17324.5			0.647034
$896$	13166.5	−	16556.6i	0.490916	−	0.617318i
$897$	15065.1	−	26196.4i	0.560768	−	0.975107i
$898$	−74369.9			−2.76365
$899$		−	21206.8i		−	0.786749i
$900$	4092.98			0.151592
$901$		−	10628.3i		−	0.392987i
$902$	95927.1			3.54104
$903$	22093.7	−	27782.5i	0.814212	−	1.02386i
$904$			65279.8i			2.40174i
$905$	−5276.59			−0.193812
$906$			15204.7i			0.557551i
$907$			27053.3i			0.990396i	0.868780	+	0.495198i	$0.164905\pi$
$907$			27053.3i			0.990396i	−0.868780	+	0.495198i	$0.835095\pi$
$908$	82903.1			3.03000
$909$			21462.2i			0.783121i
$910$	−34920.0	−	27769.8i	−1.27207	−	1.01160i
$911$		−	42965.1i		−	1.56257i	−0.624176	−	0.781284i	$-0.714565\pi$
$911$		−	42965.1i		−	1.56257i	0.624176	−	0.781284i	$-0.285435\pi$
$912$			105985.i			3.84815i
$913$		−	51805.6i		−	1.87789i
$914$		−	20494.3i		−	0.741674i
$915$		−	30770.8i		−	1.11175i
$916$	−113925.			−4.10938
$917$	−28718.8	−	22838.3i	−1.03422	−	0.822452i
$918$		−	43407.0i		−	1.56062i
$919$		−	20887.7i		−	0.749753i	−0.927075	−	0.374876i	$-0.877685\pi$
$919$		−	20887.7i		−	0.749753i	0.927075	−	0.374876i	$-0.122315\pi$
$920$	36672.4	−	63768.9i	1.31419	−	2.28521i
$921$	7145.23			0.255639
$922$			63771.6i			2.27788i
$923$		−	17182.7i		−	0.612758i
$924$	−69657.2	+	87592.7i	−2.48004	+	3.11860i
$925$		−	1223.16i		−	0.0434783i
$926$	94962.6			3.37005
$927$	−17324.8			−0.613829
$928$	100235.			3.54566
$929$		−	18239.3i		−	0.644146i	−0.946715	−	0.322073i	$-0.895620\pi$
$929$		−	18239.3i		−	0.644146i	0.946715	−	0.322073i	$-0.104380\pi$
$930$	−31820.9			−1.12199
$931$	7304.13	+	31603.1i	0.257125	+	1.11251i
$932$	114699.			4.03121
$933$	−29428.8			−1.03264
$934$	56458.3			1.97792
$935$		−	44744.1i		−	1.56501i
$936$		−	34723.7i		−	1.21259i
$937$	26881.3			0.937218			0.468609	−	0.883406i	$-0.344755\pi$
$937$	26881.3			0.937218			0.468609	+	0.883406i	$0.344755\pi$
$938$	15937.6	+	12674.2i	0.554776	+	0.441180i
$939$			31703.0i			1.10180i
$940$			18273.0i			0.634043i
$941$	55079.6			1.90812			0.954061	−	0.299611i	$-0.0968569\pi$
$941$	55079.6			1.90812			0.954061	+	0.299611i	$0.0968569\pi$
$942$		−	46975.9i		−	1.62480i
$943$	−36119.0	−	20771.4i	−1.24729	−	0.717296i
$944$			78637.2i			2.71125i
$945$	13814.5	+	10985.8i	0.475539	+	0.378168i
$946$	−77505.4			−2.66376
$947$	13265.5			0.455195			0.227598	−	0.973755i	$-0.426913\pi$
$947$	13265.5			0.455195			0.227598	+	0.973755i	$0.426913\pi$
$948$	−72454.3			−2.48229
$949$	−17333.1			−0.592892
$950$	−8212.71			−0.280479
$951$		−	8411.01i		−	0.286799i
$952$	−66081.0	+	83095.7i	−2.24968	+	2.82893i
$953$			13566.7i			0.461143i	0.973055	+	0.230572i	$0.0740596\pi$
$953$			13566.7i			0.461143i	−0.973055	+	0.230572i	$0.925940\pi$
$954$			7819.65i			0.265378i
$955$			15812.0i			0.535775i
$956$	37738.0			1.27671
$957$	−69562.1			−2.34966
$958$	23267.9			0.784710
$959$	25803.8	+	20520.2i	0.868873	+	0.690963i
$960$		−	56962.5i		−	1.91506i
$961$	21371.5			0.717380
$962$	−17251.0			−0.578165
$963$		−	27133.4i		−	0.907958i
$964$	94063.3			3.14271
$965$	−22076.5			−0.736444
$966$	63203.1	−	25029.5i	2.10510	−	0.833654i
$967$	3115.45			0.103605			0.0518025	−	0.998657i	$-0.483503\pi$
$967$	3115.45			0.103605			0.0518025	+	0.998657i	$0.483503\pi$
$968$	61816.2			2.05253
$969$		−	53200.5i		−	1.76372i
$970$	38501.9			1.27446
$971$	−14345.0			−0.474103			−0.237051	−	0.971497i	$-0.576181\pi$
$971$	−14345.0			−0.474103			−0.237051	+	0.971497i	$0.576181\pi$
$972$			65179.9i			2.15087i
$973$	−11316.1	−	8998.98i	−0.372843	−	0.296500i
$974$	−35991.8			−1.18404
$975$	4490.24			0.147490
$976$	83905.9			2.75181
$977$			34346.8i			1.12472i	0.826893	+	0.562360i	$0.190106\pi$
$977$			34346.8i			1.12472i	−0.826893	+	0.562360i	$0.809894\pi$
$978$		−	33444.8i		−	1.09351i
$979$			26825.3i			0.875732i
$980$	−16160.8	−	69923.5i	−0.526773	−	2.27921i
$981$		−	12569.3i		−	0.409080i
$982$	59496.0			1.93339
$983$	30929.3			1.00355			0.501776	−	0.864998i	$-0.332680\pi$
$983$	30929.3			1.00355			0.501776	+	0.864998i	$0.332680\pi$
$984$	−151800.			−4.91790
$985$	−25555.0			−0.826649
$986$	−109705.			−3.54332
$987$	−6322.26	+	7950.12i	−0.203890	+	0.256388i
$988$			82825.2i			2.66702i
$989$	29182.7	+	16782.5i	0.938278	+	0.539588i
$990$			32919.8i			1.05683i
$991$	−1742.50			−0.0558551			−0.0279276	−	0.999610i	$-0.508891\pi$
$991$	−1742.50			−0.0558551			−0.0279276	+	0.999610i	$0.508891\pi$
$992$		−	39795.2i		−	1.27369i
$993$		−	63522.7i		−	2.03004i
$994$	24058.3	−	30252.8i	0.767688	−	0.965353i
$995$	−9369.51			−0.298526
$996$			136286.i			4.33573i
$997$			55769.5i			1.77155i	0.464112	+	0.885777i	$0.346374\pi$
$997$			55769.5i			1.77155i	−0.464112	+	0.885777i	$0.653626\pi$
$998$	−90412.6			−2.86770
$999$	6824.55			0.216135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.c.c.160.2	yes	36
7.6	odd	2	inner	161.4.c.c.160.3	yes	36
23.22	odd	2	inner	161.4.c.c.160.1	✓	36
161.160	even	2	inner	161.4.c.c.160.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.c.c.160.1	✓	36	23.22	odd	2	inner
161.4.c.c.160.2	yes	36	1.1	even	1	trivial
161.4.c.c.160.3	yes	36	7.6	odd	2	inner
161.4.c.c.160.4	yes	36	161.160	even	2	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.29875 q^{2} -6.28001i q^{3} +20.0768 q^{4} +10.4216 q^{5} +33.2762i q^{6} +(-11.5274 + 14.4955i) q^{7} -63.9920 q^{8} -12.4385 q^{9} -55.2216 q^{10} +47.9270i q^{11} -126.082i q^{12} -43.6247i q^{13} +(61.0808 - 76.8080i) q^{14} -65.4478i q^{15} +178.463 q^{16} -89.5819 q^{17} +65.9086 q^{18} -94.5661 q^{19} +209.233 q^{20} +(91.0318 + 72.3921i) q^{21} -253.953i q^{22} +(-54.9894 + 95.6199i) q^{23} +401.870i q^{24} -16.3899 q^{25} +231.157i q^{26} -91.4463i q^{27} +(-231.433 + 291.023i) q^{28} -231.117 q^{29} +346.792i q^{30} +91.7580i q^{31} -433.697 q^{32} +300.982 q^{33} +474.672 q^{34} +(-120.134 + 151.066i) q^{35} -249.725 q^{36} +74.6290i q^{37} +501.082 q^{38} -273.964 q^{39} -666.900 q^{40} +377.735i q^{41} +(-482.355 - 383.588i) q^{42} -305.195i q^{43} +962.221i q^{44} -129.629 q^{45} +(291.375 - 506.666i) q^{46} +87.3335i q^{47} -1120.75i q^{48} +(-77.2383 - 334.190i) q^{49} +86.8462 q^{50} +562.575i q^{51} -875.844i q^{52} +118.644i q^{53} +484.552i q^{54} +499.477i q^{55} +(737.661 - 927.595i) q^{56} +593.876i q^{57} +1224.63 q^{58} +440.635i q^{59} -1313.98i q^{60} +470.158 q^{61} -486.203i q^{62} +(143.384 - 180.302i) q^{63} +870.349 q^{64} -454.640i q^{65} -1594.83 q^{66} +207.499i q^{67} -1798.52 q^{68} +(600.494 + 345.334i) q^{69} +(636.561 - 800.464i) q^{70} +393.876 q^{71} +795.964 q^{72} -397.322i q^{73} -395.441i q^{74} +102.929i q^{75} -1898.58 q^{76} +(-694.726 - 552.474i) q^{77} +1451.67 q^{78} -574.659i q^{79} +1859.88 q^{80} -910.123 q^{81} -2001.52i q^{82} -1080.93 q^{83} +(1827.63 + 1453.40i) q^{84} -933.588 q^{85} +1617.15i q^{86} +1451.42i q^{87} -3066.94i q^{88} +559.712 q^{89} +686.874 q^{90} +(632.362 + 502.879i) q^{91} +(-1104.01 + 1919.74i) q^{92} +576.241 q^{93} -462.759i q^{94} -985.531 q^{95} +2723.62i q^{96} -697.226 q^{97} +(409.267 + 1770.79i) q^{98} -596.140i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} + 184 q^{4} - 228 q^{8} - 436 q^{9} + 168 q^{16} - 404 q^{18} + 204 q^{23} - 140 q^{25} + 256 q^{29} + 1008 q^{32} - 2040 q^{35} - 4412 q^{36} + 1296 q^{39} - 888 q^{46} + 1916 q^{49} + 4080 q^{50}+ \cdots + 6884 q^{98}+O(q^{100}) \) 36 * q - 8 * q^2 + 184 * q^4 - 228 * q^8 - 436 * q^9 + 168 * q^16 - 404 * q^18 + 204 * q^23 - 140 * q^25 + 256 * q^29 + 1008 * q^32 - 2040 * q^35 - 4412 * q^36 + 1296 * q^39 - 888 * q^46 + 1916 * q^49 + 4080 * q^50 + 6020 * q^58 + 3988 * q^64 - 1712 * q^70 - 5040 * q^71 - 8636 * q^72 - 2864 * q^77 + 8820 * q^78 + 9380 * q^81 - 5032 * q^85 - 3672 * q^92 - 5352 * q^93 - 3840 * q^95 + 6884 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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