LMFDB - Embedded newform 161.4.c.c.160.1

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			160.1
Character	$\chi$	$=$	161.160
Dual form			161.4.c.c.160.3

$q$-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	$-0.654330\pi$
$5$	−10.4216			−0.932138			−0.466069	+	0.884748i	$0.654330\pi$
$6$			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	$-0.771892\pi$
$11$		−	47.9270i		−	1.31369i	0.754028	−	0.656843i	$-0.228108\pi$
$12$		−	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	$-0.279339\pi$
$17$	89.5819			1.27805			0.639023	+	0.769187i	$0.279339\pi$
$18$	65.9086			0.863044
$19$	94.5661			1.14184			0.570920	−	0.821006i	$-0.306587\pi$
$19$	94.5661			1.14184			0.570920	+	0.821006i	$0.306587\pi$
$20$	−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	$-0.946981\pi$
$37$		−	74.6290i		−	0.331593i	0.986160	−	0.165796i	$-0.0530195\pi$
$38$	−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	$0.182024\pi$
$43$			305.195i			1.08237i	−0.840904	+	0.541184i	$0.817976\pi$
$44$		−	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	$-0.950867\pi$
$53$		−	118.644i		−	0.307490i	0.988111	−	0.153745i	$-0.0491335\pi$
$54$			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	$-0.664254\pi$
$61$	−470.158			−0.986845			−0.493422	+	0.869790i	$0.664254\pi$
$62$		−	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	$-0.939417\pi$
$67$		−	207.499i		−	0.378358i	0.981943	−	0.189179i	$-0.0605827\pi$
$68$	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	$0.134193\pi$
$79$			574.659i			0.818407i	−0.912443	+	0.409203i	$0.865807\pi$
$80$	−1859.88			−2.59926
$81$	−910.123			−1.24845
$82$		−	2001.52i		−	2.69550i
$83$	1080.93			1.42948			0.714742	−	0.699388i	$-0.246544\pi$
$83$	1080.93			1.42948			0.714742	+	0.699388i	$0.246544\pi$
$84$	−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	$-0.608166\pi$
$89$	−559.712			−0.666622			−0.333311	+	0.942817i	$0.608166\pi$
$90$	−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	$-0.381100\pi$
$97$	697.226			0.729821			0.364910	+	0.931043i	$0.381100\pi$
$98$	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	$-0.732086\pi$
$103$	−1392.83			−1.33243			−0.666213	+	0.745761i	$0.732086\pi$
$104$			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	$-0.554380\pi$
$107$		−	2181.41i		−	1.97088i	0.170010	−	0.985442i	$-0.445620\pi$
$108$		−	1835.95i		−	1.63578i
$109$		−	1010.52i		−	0.887982i	−0.896031	−	0.443991i	$-0.853562\pi$
$109$		−	1010.52i		−	0.887982i	0.896031	−	0.443991i	$-0.146438\pi$
$110$		−	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	$0.139594\pi$
$113$			1020.13i			0.849251i	−0.905369	+	0.424625i	$0.860406\pi$
$114$			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	$0.187305\pi$
$137$			1780.13i			1.11012i	−0.831810	+	0.555061i	$0.812695\pi$
$138$	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	$0.0807886\pi$
$149$			913.349i			0.502178i	−0.967964	+	0.251089i	$0.919211\pi$
$150$		−	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	$-0.383183\pi$
$157$	1411.70			0.717616			0.358808	+	0.933411i	$0.383183\pi$
$158$		−	3044.97i		−	1.53320i
$159$	−745.084			−0.371629
$160$	4519.83			2.23327
$161$	−2019.94	−	305.150i	−0.988781	−	0.149374i
$162$	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	$-0.466848\pi$
$181$	506.312			0.207922			0.103961	+	0.994581i	$0.466848\pi$
$182$	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	$-0.907212\pi$
$191$		−	1517.23i		−	0.574781i	0.957814	−	0.287390i	$-0.0927877\pi$
$192$		−	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	$-0.448809\pi$
$199$	899.046			0.320260			0.160130	+	0.987096i	$0.448809\pi$
$200$	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	$-0.706300\pi$
$227$	−4129.30			−1.20736			−0.603681	+	0.797226i	$0.706300\pi$
$228$		−	11923.1i		−	3.46328i
$229$	5674.46			1.63746			0.818732	−	0.574176i	$-0.194678\pi$
$229$	5674.46			1.63746			0.818732	+	0.574176i	$0.194678\pi$
$230$	−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	$-0.715366\pi$
$241$	−4685.18			−1.25228			−0.626138	+	0.779712i	$0.715366\pi$
$242$	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	$-0.301146\pi$
$251$	4651.56			1.16974			0.584868	+	0.811129i	$0.301146\pi$
$252$	−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	$-0.681541\pi$
$263$		−	7180.14i		−	1.68345i	0.539909	−	0.841723i	$-0.318459\pi$
$264$	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	$0.154059\pi$
$281$			4383.66i			0.930630i	−0.885145	+	0.465315i	$0.845941\pi$
$282$	−2906.13			−0.613679
$283$	−864.804			−0.181651			−0.0908256	−	0.995867i	$-0.528951\pi$
$283$	−864.804			−0.181651			−0.0908256	+	0.995867i	$0.528951\pi$
$284$	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	$-0.376556\pi$
$293$	3793.25			0.756328			0.378164	+	0.925739i	$0.376556\pi$
$294$	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	$-0.349346\pi$
$313$	5048.25			0.911642			0.455821	+	0.890071i	$0.349346\pi$
$314$	−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
$322$	10703.2	+	1616.92i	1.85237	+	0.279836i
$323$	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	$-0.923395\pi$
$337$		−	2949.04i		−	0.476689i	0.971181	−	0.238345i	$-0.0766048\pi$
$338$	−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	$-0.881972\pi$
$359$		−	4929.56i		−	0.724713i	0.932040	−	0.362356i	$-0.118028\pi$
$360$	−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	$-0.678784\pi$
$367$	−7489.07			−1.06519			−0.532597	+	0.846369i	$0.678784\pi$
$368$	−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	$-0.980623\pi$
$373$		−	876.538i		−	0.121677i	0.998148	−	0.0608383i	$-0.0193774\pi$
$374$			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	$-0.978117\pi$
$379$		−	1013.71i		−	0.137389i	0.997638	−	0.0686947i	$-0.0218834\pi$
$380$	−19786.3			−2.67110
$381$		−	1671.80i		−	0.224800i
$382$			8039.44i			1.07679i
$383$	10199.9			1.36081			0.680404	−	0.732837i	$-0.261804\pi$
$383$	10199.9			1.36081			0.680404	+	0.732837i	$0.261804\pi$
$384$			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	$-0.914416\pi$
$389$		−	4076.15i		−	0.531283i	0.964072	−	0.265641i	$-0.0855837\pi$
$390$	−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	$0.188051\pi$
$401$			8945.57i			1.11402i	−0.830507	+	0.557008i	$0.811949\pi$
$402$	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	$-0.545524\pi$
$419$	−2444.90			−0.285063			−0.142531	+	0.989790i	$0.545524\pi$
$420$	19046.8	+	15146.8i	2.21283	+	1.75973i
$421$		−	1860.40i		−	0.215369i	−0.994185	−	0.107684i	$-0.965656\pi$
$421$		−	1860.40i		−	0.215369i	0.994185	−	0.107684i	$-0.0343436\pi$
$422$	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	$0.246798\pi$
$431$			12526.2i			1.39992i	−0.714183	+	0.699959i	$0.753202\pi$
$432$		−	16319.8i		−	1.81756i
$433$	−13473.0			−1.49531			−0.747657	−	0.664085i	$-0.768821\pi$
$433$	−13473.0			−1.49531			−0.747657	+	0.664085i	$0.768821\pi$
$434$	−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	$-0.936572\pi$
$457$		−	3867.75i		−	0.395899i	0.980212	−	0.197950i	$-0.0634282\pi$
$458$	−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	$-0.322981\pi$
$467$	10655.0			1.05579			0.527897	+	0.849309i	$0.322981\pi$
$468$			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	$-0.432837\pi$
$479$	4391.21			0.418871			0.209436	+	0.977822i	$0.432837\pi$
$480$		−	28384.6i		−	2.69911i
$481$	−3255.67			−0.308619
$482$	24825.6			2.34601
$483$	−1916.35	+	12685.3i	−0.180532	+	1.19503i
$484$	−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	$-0.539543\pi$
$503$	−2795.65			−0.247817			−0.123909	+	0.992294i	$0.539543\pi$
$504$	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	$-0.223187\pi$
$521$	18173.2			1.52818			0.764092	+	0.645108i	$0.223187\pi$
$522$	−15232.6			−1.27723
$523$	−7338.81			−0.613583			−0.306791	−	0.951777i	$-0.599255\pi$
$523$	−7338.81			−0.613583			−0.306791	+	0.951777i	$0.599255\pi$
$524$			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	$-0.833043\pi$
$557$		−	13166.5i		−	1.00158i	0.865568	−	0.500791i	$-0.166957\pi$
$558$			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	$-0.544258\pi$
$563$	−3702.82			−0.277185			−0.138592	+	0.990349i	$0.544258\pi$
$564$	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	$-0.734325\pi$
$569$		−	20116.4i		−	1.48211i	0.671443	−	0.741056i	$-0.265675\pi$
$570$		−	32794.8i		−	2.40986i
$571$		−	21657.8i		−	1.58730i	−0.608372	−	0.793652i	$-0.708177\pi$
$571$		−	21657.8i		−	1.58730i	0.608372	−	0.793652i	$-0.291823\pi$
$572$	−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	$-0.792888\pi$
$613$		−	18386.0i		−	1.21143i	0.795683	−	0.605713i	$-0.207112\pi$
$614$		−	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	$-0.582900\pi$
$617$		−	29618.3i		−	1.93255i	0.257504	−	0.966277i	$-0.417100\pi$
$618$		−	46348.2i		−	3.01683i
$619$	12876.2			0.836086			0.418043	−	0.908427i	$-0.362716\pi$
$619$	12876.2			0.836086			0.418043	+	0.908427i	$0.362716\pi$
$620$		−	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	$0.0980009\pi$
$631$			9606.63i			0.606076i	−0.952978	+	0.303038i	$0.901999\pi$
$632$		−	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	$0.196303\pi$
$641$			18771.9i			1.15670i	−0.815789	+	0.578350i	$0.803697\pi$
$642$	72589.0			4.46240
$643$	773.918			0.0474655			0.0237328	−	0.999718i	$-0.492445\pi$
$643$	773.918			0.0474655			0.0237328	+	0.999718i	$0.492445\pi$
$644$	−40554.0	−	6126.44i	−2.48144	−	0.374869i
$645$	−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	$0.167215\pi$
$659$			16967.7i			1.00298i	−0.865163	+	0.501492i	$0.832785\pi$
$660$	62975.3			3.71410
$661$	453.229			0.0266695			0.0133348	−	0.999911i	$-0.495755\pi$
$661$	453.229			0.0266695			0.0133348	+	0.999911i	$0.495755\pi$
$662$	−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	$-0.547874\pi$
$677$	−5278.65			−0.299668			−0.149834	+	0.988711i	$0.547874\pi$
$678$	−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	$-0.746252\pi$
$701$		−	26555.0i		−	1.43077i	0.698732	−	0.715384i	$-0.253748\pi$
$702$	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	$-0.774846\pi$
$709$		−	24535.2i		−	1.29963i	0.760092	−	0.649815i	$-0.225154\pi$
$710$	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	$-0.362961\pi$
$727$	16361.6			0.834687			0.417343	+	0.908749i	$0.362961\pi$
$728$	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	$-0.283411\pi$
$733$	24970.5			1.25826			0.629131	+	0.777299i	$0.283411\pi$
$734$	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	$-0.830835\pi$
$743$		−	20527.4i		−	1.01356i	0.862075	−	0.506782i	$-0.169165\pi$
$744$	−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	$-0.966861\pi$
$751$		−	4277.52i		−	0.207842i	0.994586	−	0.103921i	$-0.0331389\pi$
$752$			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	$-0.923595\pi$
$757$		−	9903.01i		−	0.475470i	0.971330	−	0.237735i	$-0.0764050\pi$
$758$			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	$-0.555929\pi$
$769$	−7455.44			−0.349610			−0.174805	+	0.984603i	$0.555929\pi$
$770$	−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	$-0.394526\pi$
$773$	13983.5			0.650651			0.325325	+	0.945602i	$0.394526\pi$
$774$			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	$-0.361927\pi$
$787$	18558.6			0.840588			0.420294	+	0.907388i	$0.361927\pi$
$788$	−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	$-0.435308\pi$
$797$	9082.85			0.403677			0.201839	+	0.979419i	$0.435308\pi$
$798$	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
$805$	21051.1	+	3180.16i	0.921680	+	0.139237i
$806$	−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	$0.0485893\pi$
$827$			7232.54i			0.304111i	−0.988372	+	0.152056i	$0.951411\pi$
$828$	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	$-0.365531\pi$
$839$	19927.4			0.819988			0.409994	+	0.912088i	$0.365531\pi$
$840$	−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	$-0.429449\pi$
$881$	11497.0			0.439663			0.219832	+	0.975538i	$0.429449\pi$
$882$	−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	$-0.835095\pi$
$907$		−	27053.3i		−	0.990396i	0.868780	−	0.495198i	$-0.164905\pi$
$908$	−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	$0.285435\pi$
$911$			42965.1i			1.56257i	−0.624176	+	0.781284i	$0.714565\pi$
$912$		−	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	$0.122315\pi$
$919$			20887.7i			0.749753i	−0.927075	+	0.374876i	$0.877685\pi$
$920$	−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	$-0.655245\pi$
$937$	−26881.3			−0.937218			−0.468609	+	0.883406i	$0.655245\pi$
$938$	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	$-0.903143\pi$
$941$	−55079.6			−1.90812			−0.954061	+	0.299611i	$0.903143\pi$
$942$			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	$-0.925940\pi$
$953$		−	13566.7i		−	0.461143i	0.973055	−	0.230572i	$-0.0740596\pi$
$954$		−	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
$966$	10154.2	−	67216.0i	0.338206	−	2.23876i
$967$	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	$-0.423819\pi$
$971$	14345.0			0.474103			0.237051	+	0.971497i	$0.423819\pi$
$972$			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	$-0.809894\pi$
$977$		−	34346.8i		−	1.12472i	0.826893	−	0.562360i	$-0.190106\pi$
$978$		−	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	$-0.667320\pi$
$983$	−30929.3			−1.00355			−0.501776	+	0.864998i	$0.667320\pi$
$984$	−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.160.1	✓	36
7.6	odd	2	inner	161.4.c.c.160.4	yes	36
23.22	odd	2	inner	161.4.c.c.160.2	yes	36
161.160	even	2	inner	161.4.c.c.160.3	yes	36

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