LMFDB - Embedded newform 161.4.c.c.160.12

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			160.12
Character	$\chi$	$=$	161.160
Dual form			161.4.c.c.160.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.36931 q^{2} +9.90574i q^{3} +3.35226 q^{4} +8.06501 q^{5} -33.3755i q^{6} +(-16.4867 + 8.43733i) q^{7} +15.6597 q^{8} -71.1238 q^{9} -27.1735 q^{10} +67.8577i q^{11} +33.2067i q^{12} -7.51672i q^{13} +(55.5489 - 28.4280i) q^{14} +79.8899i q^{15} -79.5804 q^{16} -88.2202 q^{17} +239.638 q^{18} +92.8569 q^{19} +27.0360 q^{20} +(-83.5780 - 163.313i) q^{21} -228.634i q^{22} +(91.6350 - 61.4006i) q^{23} +155.121i q^{24} -59.9556 q^{25} +25.3262i q^{26} -437.079i q^{27} +(-55.2678 + 28.2842i) q^{28} +109.684 q^{29} -269.174i q^{30} -60.4173i q^{31} +142.854 q^{32} -672.181 q^{33} +297.241 q^{34} +(-132.965 + 68.0471i) q^{35} -238.426 q^{36} +224.309i q^{37} -312.864 q^{38} +74.4587 q^{39} +126.295 q^{40} -188.711i q^{41} +(281.600 + 550.253i) q^{42} -93.3679i q^{43} +227.477i q^{44} -573.614 q^{45} +(-308.747 + 206.878i) q^{46} +50.8467i q^{47} -788.303i q^{48} +(200.623 - 278.208i) q^{49} +202.009 q^{50} -873.887i q^{51} -25.1980i q^{52} -223.248i q^{53} +1472.65i q^{54} +547.273i q^{55} +(-258.176 + 132.126i) q^{56} +919.816i q^{57} -369.559 q^{58} -301.444i q^{59} +267.812i q^{60} +244.869 q^{61} +203.565i q^{62} +(1172.60 - 600.094i) q^{63} +155.324 q^{64} -60.6224i q^{65} +2264.79 q^{66} +476.214i q^{67} -295.737 q^{68} +(608.218 + 907.713i) q^{69} +(448.002 - 229.272i) q^{70} -574.349 q^{71} -1113.77 q^{72} +806.456i q^{73} -755.766i q^{74} -593.905i q^{75} +311.281 q^{76} +(-572.538 - 1118.75i) q^{77} -250.875 q^{78} +825.242i q^{79} -641.817 q^{80} +2409.25 q^{81} +635.827i q^{82} -1377.06 q^{83} +(-280.176 - 547.469i) q^{84} -711.497 q^{85} +314.585i q^{86} +1086.50i q^{87} +1062.63i q^{88} -414.720 q^{89} +1932.68 q^{90} +(63.4210 + 123.926i) q^{91} +(307.185 - 205.831i) q^{92} +598.479 q^{93} -171.318i q^{94} +748.892 q^{95} +1415.07i q^{96} -325.780 q^{97} +(-675.961 + 937.368i) q^{98} -4826.29i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.36931			−1.19123			−0.595616	−	0.803269i	$-0.703092\pi$
$2$	−3.36931			−1.19123			−0.595616	+	0.803269i	$0.703092\pi$
$3$			9.90574i			1.90636i	0.302402	+	0.953181i	$0.402212\pi$
$3$			9.90574i			1.90636i	−0.302402	+	0.953181i	$0.597788\pi$
$4$	3.35226			0.419033
$5$	8.06501			0.721357			0.360678	−	0.932690i	$-0.382545\pi$
$5$	8.06501			0.721357			0.360678	+	0.932690i	$0.382545\pi$
$6$		−	33.3755i		−	2.27092i
$7$	−16.4867	+	8.43733i	−0.890198	+	0.455573i
$7$	−16.4867	+	8.43733i	−0.890198	+	0.455573i
$8$	15.6597			0.692066
$9$	−71.1238			−2.63421
$10$	−27.1735			−0.859303
$11$			67.8577i			1.85999i	0.367575	+	0.929994i	$0.380188\pi$
$11$			67.8577i			1.85999i	−0.367575	+	0.929994i	$0.619812\pi$
$12$			33.2067i			0.798828i
$13$		−	7.51672i		−	0.160366i	−0.996780	−	0.0801832i	$-0.974449\pi$
$13$		−	7.51672i		−	0.160366i	0.996780	−	0.0801832i	$-0.0255505\pi$
$14$	55.5489	−	28.4280i	1.06043	−	0.542693i
$15$			79.8899i			1.37517i
$16$	−79.5804			−1.24344
$17$	−88.2202			−1.25862			−0.629310	−	0.777154i	$-0.716662\pi$
$17$	−88.2202			−1.25862			−0.629310	+	0.777154i	$0.716662\pi$
$18$	239.638			3.13796
$19$	92.8569			1.12120			0.560601	−	0.828086i	$-0.310570\pi$
$19$	92.8569			1.12120			0.560601	+	0.828086i	$0.310570\pi$
$20$	27.0360			0.302272
$21$	−83.5780	−	163.313i	−0.868487	−	1.69704i
$22$		−	228.634i		−	2.21568i
$23$	91.6350	−	61.4006i	0.830748	−	0.556648i
$23$	91.6350	−	61.4006i	0.830748	−	0.556648i
$24$			155.121i			1.31933i
$25$	−59.9556			−0.479645
$26$			25.3262i			0.191034i
$27$		−	437.079i		−	3.11540i
$28$	−55.2678	+	28.2842i	−0.373023	+	0.190900i
$29$	109.684			0.702338			0.351169	−	0.936312i	$-0.385784\pi$
$29$	109.684			0.702338			0.351169	+	0.936312i	$0.385784\pi$
$30$		−	269.174i		−	1.63814i
$31$		−	60.4173i		−	0.350041i	−0.984565	−	0.175021i	$-0.944001\pi$
$31$		−	60.4173i		−	0.350041i	0.984565	−	0.175021i	$-0.0559992\pi$
$32$	142.854			0.789164
$33$	−672.181			−3.54581
$34$	297.241			1.49931
$35$	−132.965	+	68.0471i	−0.642150	+	0.328630i
$36$	−238.426			−1.10382
$37$			224.309i			0.996652i	0.866990	+	0.498326i	$0.166052\pi$
$37$			224.309i			0.996652i	−0.866990	+	0.498326i	$0.833948\pi$
$38$	−312.864			−1.33561
$39$	74.4587			0.305716
$40$	126.295			0.499227
$41$		−	188.711i		−	0.718823i	−0.933179	−	0.359412i	$-0.882977\pi$
$41$		−	188.711i		−	0.718823i	0.933179	−	0.359412i	$-0.117023\pi$
$42$	281.600	+	550.253i	1.03457	+	2.02157i
$43$		−	93.3679i		−	0.331127i	−0.986199	−	0.165564i	$-0.947056\pi$
$43$		−	93.3679i		−	0.331127i	0.986199	−	0.165564i	$-0.0529443\pi$
$44$			227.477i			0.779396i
$45$	−573.614			−1.90021
$46$	−308.747	+	206.878i	−0.989614	+	0.663097i
$47$			50.8467i			0.157803i	0.996882	+	0.0789016i	$0.0251413\pi$
$47$			50.8467i			0.157803i	−0.996882	+	0.0789016i	$0.974859\pi$
$48$		−	788.303i		−	2.37045i
$49$	200.623	−	278.208i	0.584907	−	0.811101i
$50$	202.009			0.571368
$51$		−	873.887i		−	2.39938i
$52$		−	25.1980i		−	0.0671988i
$53$		−	223.248i		−	0.578595i	−0.957239	−	0.289298i	$-0.906578\pi$
$53$		−	223.248i		−	0.578595i	0.957239	−	0.289298i	$-0.0934217\pi$
$54$			1472.65i			3.71116i
$55$			547.273i			1.34171i
$56$	−258.176	+	132.126i	−0.616076	+	0.315287i
$57$			919.816i			2.13742i
$58$	−369.559			−0.836647
$59$		−	301.444i		−	0.665163i	−0.943074	−	0.332582i	$-0.892080\pi$
$59$		−	301.444i		−	0.665163i	0.943074	−	0.332582i	$-0.107920\pi$
$60$			267.812i			0.576240i
$61$	244.869			0.513971			0.256985	−	0.966415i	$-0.417271\pi$
$61$	244.869			0.513971			0.256985	+	0.966415i	$0.417271\pi$
$62$			203.565i			0.416980i
$63$	1172.60	−	600.094i	2.34497	−	1.20008i
$64$	155.324			0.303367
$65$		−	60.6224i		−	0.115681i
$66$	2264.79			4.22388
$67$			476.214i			0.868340i	0.900831	+	0.434170i	$0.142958\pi$
$67$			476.214i			0.868340i	−0.900831	+	0.434170i	$0.857042\pi$
$68$	−295.737			−0.527403
$69$	608.218	+	907.713i	1.06117	+	1.58371i
$70$	448.002	−	229.272i	0.764950	−	0.391475i
$71$	−574.349			−0.960038			−0.480019	−	0.877258i	$-0.659370\pi$
$71$	−574.349			−0.960038			−0.480019	+	0.877258i	$0.659370\pi$
$72$	−1113.77			−1.82305
$73$			806.456i			1.29299i	0.762916	+	0.646497i	$0.223767\pi$
$73$			806.456i			1.29299i	−0.762916	+	0.646497i	$0.776233\pi$
$74$		−	755.766i		−	1.18724i
$75$		−	593.905i		−	0.914376i
$76$	311.281			0.469820
$77$	−572.538	−	1118.75i	−0.847360	−	1.65576i
$78$	−250.875			−0.364179
$79$			825.242i			1.17528i	0.809123	+	0.587639i	$0.199943\pi$
$79$			825.242i			1.17528i	−0.809123	+	0.587639i	$0.800057\pi$
$80$	−641.817			−0.896967
$81$	2409.25			3.30487
$82$			635.827i			0.856285i
$83$	−1377.06			−1.82111			−0.910553	−	0.413393i	$-0.864344\pi$
$83$	−1377.06			−1.82111			−0.910553	+	0.413393i	$0.864344\pi$
$84$	−280.176	−	547.469i	−0.363925	−	0.711116i
$85$	−711.497			−0.907914
$86$			314.585i			0.394449i
$87$			1086.50i			1.33891i
$88$			1062.63i			1.28723i
$89$	−414.720			−0.493935			−0.246968	−	0.969024i	$-0.579434\pi$
$89$	−414.720			−0.493935			−0.246968	+	0.969024i	$0.579434\pi$
$90$	1932.68			2.26359
$91$	63.4210	+	123.926i	0.0730586	+	0.142758i
$92$	307.185	−	205.831i	0.348111	−	0.233254i
$93$	598.479			0.667305
$94$		−	171.318i		−	0.187980i
$95$	748.892			0.808786
$96$			1415.07i			1.50443i
$97$	−325.780			−0.341010			−0.170505	−	0.985357i	$-0.554540\pi$
$97$	−325.780			−0.341010			−0.170505	+	0.985357i	$0.554540\pi$
$98$	−675.961	+	937.368i	−0.696759	+	0.966209i
$99$		−	4826.29i		−	4.89960i
$100$	−200.987			−0.200987
$101$		−	953.898i		−	0.939767i	−0.882729	−	0.469883i	$-0.844296\pi$
$101$		−	953.898i		−	0.939767i	0.882729	−	0.469883i	$-0.155704\pi$
$102$			2944.40i			2.85822i
$103$	−319.597			−0.305736			−0.152868	−	0.988247i	$-0.548851\pi$
$103$	−319.597			−0.305736			−0.152868	+	0.988247i	$0.548851\pi$
$104$		−	117.709i		−	0.110984i
$105$	−674.058	−	1317.12i	−0.626488	−	1.22417i
$106$			752.194i			0.689241i
$107$			780.974i			0.705603i	0.935698	+	0.352802i	$0.114771\pi$
$107$			780.974i			0.705603i	−0.935698	+	0.352802i	$0.885229\pi$
$108$		−	1465.20i		−	1.30546i
$109$			1008.11i			0.885863i	0.896555	+	0.442932i	$0.146062\pi$
$109$			1008.11i			0.885863i	−0.896555	+	0.442932i	$0.853938\pi$
$110$		−	1843.93i		−	1.59829i
$111$	−2221.94			−1.89998
$112$	1312.02	−	671.446i	1.10691	−	0.566480i
$113$			1478.56i			1.23090i	0.788176	+	0.615449i	$0.211025\pi$
$113$			1478.56i			1.23090i	−0.788176	+	0.615449i	$0.788975\pi$
$114$		−	3099.15i		−	2.54616i
$115$	739.037	−	495.196i	0.599266	−	0.401542i
$116$	367.689			0.294303
$117$			534.617i			0.422439i
$118$			1015.66i			0.792364i
$119$	1454.46	−	744.343i	1.12042	−	0.573393i
$120$			1251.05i			0.951706i
$121$	−3273.67			−2.45955
$122$	−825.039			−0.612258
$123$	1869.33			1.37034
$124$		−	202.535i		−	0.146679i
$125$	−1491.67			−1.06735
$126$	−3950.84	+	2021.91i	−2.79341	+	1.42957i
$127$	−1397.50			−0.976439			−0.488220	−	0.872721i	$-0.662353\pi$
$127$	−1397.50			−0.976439			−0.488220	+	0.872721i	$0.662353\pi$
$128$	−1666.17			−1.15054
$129$	924.878			0.631248
$130$			204.256i			0.137803i
$131$		−	1642.65i		−	1.09556i	−0.836622	−	0.547781i	$-0.815473\pi$
$131$		−	1642.65i		−	1.09556i	0.836622	−	0.547781i	$-0.184527\pi$
$132$	−2253.33			−1.48581
$133$	−1530.90	+	783.464i	−0.998092	+	0.510789i
$134$		−	1604.51i		−	1.03439i
$135$		−	3525.04i		−	2.24731i
$136$	−1381.50			−0.871049
$137$		−	622.288i		−	0.388071i	−0.980995	−	0.194035i	$-0.937842\pi$
$137$		−	622.288i		−	0.388071i	0.980995	−	0.194035i	$-0.0621576\pi$
$138$	−2049.28	−	3058.37i	−1.26410	−	1.88656i
$139$			12.1176i			0.00739428i	0.999993	+	0.00369714i	$0.00117684\pi$
$139$			12.1176i			0.00739428i	−0.999993	+	0.00369714i	$0.998823\pi$
$140$	−445.735	+	228.112i	−0.269082	+	0.137707i
$141$	−503.674			−0.300830
$142$	1935.16			1.14363
$143$	510.067			0.298280
$144$	5660.06			3.27550
$145$	884.602			0.506636
$146$		−	2717.20i		−	1.54026i
$147$	2755.85	+	1987.32i	1.54625	+	1.11504i
$148$			751.942i			0.417630i
$149$			1325.66i			0.728874i	0.931228	+	0.364437i	$0.118739\pi$
$149$			1325.66i			0.728874i	−0.931228	+	0.364437i	$0.881261\pi$
$150$			2001.05i			1.08923i
$151$	1872.71			1.00926			0.504632	−	0.863334i	$-0.331628\pi$
$151$	1872.71			1.00926			0.504632	+	0.863334i	$0.331628\pi$
$152$	1454.11			0.775946
$153$	6274.55			3.31547
$154$	1929.06	+	3769.42i	1.00940	+	1.97239i
$155$		−	487.267i		−	0.252504i
$156$	249.605			0.128105
$157$	464.472			0.236108			0.118054	−	0.993007i	$-0.462334\pi$
$157$	464.472			0.236108			0.118054	+	0.993007i	$0.462334\pi$
$158$		−	2780.50i		−	1.40003i
$159$	2211.44			1.10301
$160$	1152.12			0.569269
$161$	−992.702	+	1785.45i	−0.485937	+	0.873994i
$162$	−8117.51			−3.93686
$163$	1403.71			0.674522			0.337261	−	0.941411i	$-0.390500\pi$
$163$	1403.71			0.674522			0.337261	+	0.941411i	$0.390500\pi$
$164$		−	632.610i		−	0.301211i
$165$	−5421.15			−2.55779
$166$	4639.74			2.16936
$167$			3655.37i			1.69378i	0.531769	+	0.846889i	$0.321527\pi$
$167$			3655.37i			1.69378i	−0.531769	+	0.846889i	$0.678473\pi$
$168$	−1308.80	−	2557.43i	−0.601050	−	1.17446i
$169$	2140.50			0.974283
$170$	2397.26			1.08154
$171$	−6604.33			−2.95348
$172$		−	312.994i		−	0.138753i
$173$		−	494.053i		−	0.217122i	−0.994090	−	0.108561i	$-0.965376\pi$
$173$		−	494.053i		−	0.217122i	0.994090	−	0.108561i	$-0.0346243\pi$
$174$		−	3660.76i		−	1.59495i
$175$	988.470	−	505.865i	0.426979	−	0.218513i
$176$		−	5400.14i		−	2.31279i
$177$	2986.02			1.26804
$178$	1397.32			0.588392
$179$	529.860			0.221249			0.110625	−	0.993862i	$-0.464715\pi$
$179$	529.860			0.221249			0.110625	+	0.993862i	$0.464715\pi$
$180$	−1922.91			−0.796249
$181$	−3305.77			−1.35755			−0.678773	−	0.734348i	$-0.737488\pi$
$181$	−3305.77			−1.35755			−0.678773	+	0.734348i	$0.737488\pi$
$182$	−213.685	−	417.545i	−0.0870297	−	0.170058i
$183$			2425.61i			0.979814i
$184$	1434.97	−	961.513i	0.574933	−	0.385237i
$185$			1809.05i			0.718941i
$186$	−2016.46			−0.794915
$187$		−	5986.42i		−	2.34102i
$188$			170.452i			0.0661248i
$189$	3687.78	+	7205.99i	1.41929	+	2.77332i
$190$	−2523.25			−0.963452
$191$		−	75.4008i		−	0.0285645i	−0.999898	−	0.0142822i	$-0.995454\pi$
$191$		−	75.4008i		−	0.0285645i	0.999898	−	0.0142822i	$-0.00454633\pi$
$192$			1538.60i			0.578327i
$193$	−3548.13			−1.32332			−0.661658	−	0.749805i	$-0.730147\pi$
$193$	−3548.13			−1.32332			−0.661658	+	0.749805i	$0.730147\pi$
$194$	1097.66			0.406222
$195$	600.510			0.220530
$196$	672.541	−	932.625i	0.245095	−	0.339878i
$197$	−891.499			−0.322420			−0.161210	−	0.986920i	$-0.551540\pi$
$197$	−891.499			−0.322420			−0.161210	+	0.986920i	$0.551540\pi$
$198$			16261.3i			5.83656i
$199$	3989.79			1.42125			0.710625	−	0.703571i	$-0.248412\pi$
$199$	3989.79			1.42125			0.710625	+	0.703571i	$0.248412\pi$
$200$	−938.885			−0.331946
$201$	−4717.25			−1.65537
$202$			3213.98i			1.11948i
$203$	−1808.33	+	925.439i	−0.625220	+	0.319966i
$204$		−	2929.50i		−	1.00542i
$205$		−	1521.96i		−	0.518528i
$206$	1076.82			0.364203
$207$	−6517.42	+	4367.04i	−2.18837	+	1.46633i
$208$			598.184i			0.199407i
$209$			6301.05i			2.08542i
$210$	2271.11	+	4437.79i	0.746293	+	1.45827i
$211$	191.719			0.0625520			0.0312760	−	0.999511i	$-0.490043\pi$
$211$	191.719			0.0625520			0.0312760	+	0.999511i	$0.490043\pi$
$212$		−	748.388i		−	0.242450i
$213$		−	5689.36i		−	1.83018i
$214$		−	2631.34i		−	0.840537i
$215$		−	753.013i		−	0.238861i
$216$		−	6844.51i		−	2.15606i
$217$	509.761	+	996.083i	0.159469	+	0.311606i
$218$		−	3396.63i		−	1.05527i
$219$	−7988.55			−2.46491
$220$			1834.60i			0.562222i
$221$			663.127i			0.201840i
$222$	7486.42			2.26331
$223$			2347.92i			0.705058i	0.935801	+	0.352529i	$0.114678\pi$
$223$			2347.92i			0.705058i	−0.935801	+	0.352529i	$0.885322\pi$
$224$	−2355.19	+	1205.31i	−0.702513	+	0.359522i
$225$	4264.27			1.26349
$226$		−	4981.74i		−	1.46629i
$227$	−2146.23			−0.627535			−0.313767	−	0.949500i	$-0.601591\pi$
$227$	−2146.23			−0.627535			−0.313767	+	0.949500i	$0.601591\pi$
$228$			3083.47i			0.895647i
$229$	3282.28			0.947159			0.473579	−	0.880751i	$-0.342962\pi$
$229$	3282.28			0.947159			0.473579	+	0.880751i	$0.342962\pi$
$230$	−2490.05	+	1668.47i	−0.713864	+	0.478329i
$231$	11082.0	−	5671.41i	3.15647	−	1.61537i
$232$	1717.61			0.486064
$233$	−2099.94			−0.590438			−0.295219	−	0.955430i	$-0.595393\pi$
$233$	−2099.94			−0.590438			−0.295219	+	0.955430i	$0.595393\pi$
$234$		−	1801.29i		−	0.503223i
$235$			410.079i			0.113832i
$236$		−	1010.52i		−	0.278725i
$237$	−8174.64			−2.24051
$238$	−4900.53	+	2507.92i	−1.33468	+	0.683044i
$239$	−450.171			−0.121837			−0.0609187	−	0.998143i	$-0.519403\pi$
$239$	−450.171			−0.121837			−0.0609187	+	0.998143i	$0.519403\pi$
$240$		−	6357.68i		−	1.70994i
$241$	−1116.97			−0.298548			−0.149274	−	0.988796i	$-0.547694\pi$
$241$	−1116.97			−0.298548			−0.149274	+	0.988796i	$0.547694\pi$
$242$	11030.0			2.92990
$243$			12064.3i			3.18487i
$244$	820.864			0.215371
$245$	1618.03	−	2243.75i	0.421926	−	0.585093i
$246$	−6298.34			−1.63239
$247$		−	697.979i		−	0.179803i
$248$		−	946.116i		−	0.242252i
$249$		−	13640.8i		−	3.47169i
$250$	5025.90			1.27146
$251$	5048.97			1.26967			0.634837	−	0.772646i	$-0.281067\pi$
$251$	5048.97			1.26967			0.634837	+	0.772646i	$0.281067\pi$
$252$	3930.85	−	2011.68i	0.982621	−	0.502872i
$253$	4166.50	+	6218.14i	1.03536	+	1.54518i
$254$	4708.60			1.16317
$255$		−	7047.91i		−	1.73081i
$256$	4371.24			1.06720
$257$		−	4733.73i		−	1.14896i	−0.818520	−	0.574479i	$-0.805205\pi$
$257$		−	4733.73i		−	1.14896i	0.818520	−	0.574479i	$-0.194795\pi$
$258$	−3116.20			−0.751963
$259$	−1892.57	−	3698.11i	−0.454047	−	0.887218i
$260$		−	203.222i		−	0.0484743i
$261$	−7801.13			−1.85011
$262$			5534.59i			1.30507i
$263$			2940.09i			0.689330i	0.938726	+	0.344665i	$0.112007\pi$
$263$			2940.09i			0.689330i	−0.938726	+	0.344665i	$0.887993\pi$
$264$	−10526.1			−2.45393
$265$		−	1800.50i		−	0.417373i
$266$	5158.09	−	2639.73i	1.18896	−	0.608468i
$267$		−	4108.11i		−	0.941619i
$268$			1596.40i			0.363863i
$269$		−	311.175i		−	0.0705304i	−0.999378	−	0.0352652i	$-0.988772\pi$
$269$		−	311.175i		−	0.0705304i	0.999378	−	0.0352652i	$-0.0112276\pi$
$270$			11877.0i			2.67707i
$271$			6023.16i			1.35011i	0.737766	+	0.675057i	$0.235881\pi$
$271$			6023.16i			1.35011i	−0.737766	+	0.675057i	$0.764119\pi$
$272$	7020.60			1.56502
$273$	−1227.58	+	628.233i	−0.272148	+	0.139276i
$274$			2096.68i			0.462282i
$275$		−	4068.45i		−	0.892133i
$276$	2038.91	+	3042.89i	0.444666	+	0.663625i
$277$	−4369.29			−0.947745			−0.473873	−	0.880593i	$-0.657144\pi$
$277$	−4369.29			−0.947745			−0.473873	+	0.880593i	$0.657144\pi$
$278$		−	40.8281i		−	0.00880830i
$279$			4297.11i			0.922083i
$280$	−2082.20	+	1065.60i	−0.444411	+	0.227434i
$281$			4029.59i			0.855464i	0.903906	+	0.427732i	$0.140687\pi$
$281$			4029.59i			0.855464i	−0.903906	+	0.427732i	$0.859313\pi$
$282$	1697.04			0.358358
$283$	3085.19			0.648041			0.324020	−	0.946050i	$-0.394965\pi$
$283$	3085.19			0.648041			0.324020	+	0.946050i	$0.394965\pi$
$284$	−1925.37			−0.402288
$285$			7418.33i			1.54184i
$286$	−1718.58			−0.355320
$287$	1592.22	+	3111.23i	0.327476	+	0.639895i
$288$	−10160.3			−2.07883
$289$	2869.81			0.584125
$290$	−2980.50			−0.603521
$291$		−	3227.10i		−	0.650089i
$292$			2703.45i			0.541807i
$293$	3065.80			0.611282			0.305641	−	0.952147i	$-0.401129\pi$
$293$	3065.80			0.611282			0.305641	+	0.952147i	$0.401129\pi$
$294$	−9285.33	−	6695.90i	−1.84194	−	1.32828i
$295$		−	2431.15i		−	0.479820i
$296$			3512.60i			0.689749i
$297$	29659.1			5.79461
$298$		−	4466.56i		−	0.868258i
$299$	−461.531	−	688.795i	−0.0892677	−	0.133224i
$300$		−	1990.93i		−	0.383154i
$301$	787.775	+	1539.33i	0.150853	+	0.294769i
$302$	−6309.74			−1.20227
$303$	9449.07			1.79153
$304$	−7389.59			−1.39415
$305$	1974.87			0.370756
$306$	−21140.9			−3.94950
$307$			2161.68i			0.401869i	0.979605	+	0.200934i	$0.0643978\pi$
$307$			2161.68i			0.401869i	−0.979605	+	0.200934i	$0.935602\pi$
$308$	−1919.30	−	3750.34i	−0.355072	−	0.693817i
$309$		−	3165.85i		−	0.582844i
$310$			1641.75i			0.300791i
$311$		−	2228.78i		−	0.406375i	−0.979140	−	0.203187i	$-0.934870\pi$
$311$		−	2228.78i		−	0.406375i	0.979140	−	0.203187i	$-0.0651301\pi$
$312$	1166.00			0.211576
$313$	1089.24			0.196700			0.0983502	−	0.995152i	$-0.468643\pi$
$313$	1089.24			0.196700			0.0983502	+	0.995152i	$0.468643\pi$
$314$	−1564.95			−0.281259
$315$	9457.00	−	4839.77i	1.69156	−	0.865683i
$316$			2766.43i			0.492481i
$317$	2372.67			0.420386			0.210193	−	0.977660i	$-0.432591\pi$
$317$	2372.67			0.420386			0.210193	+	0.977660i	$0.432591\pi$
$318$	−7451.04			−1.31394
$319$			7442.90i			1.30634i
$320$	1252.69			0.218836
$321$	−7736.12			−1.34514
$322$	3344.72	−	6015.73i	0.578864	−	1.04113i
$323$	−8191.85			−1.41117
$324$	8076.43			1.38485
$325$			450.670i			0.0769189i
$326$	−4729.54			−0.803512
$327$	−9986.05			−1.68878
$328$		−	2955.16i		−	0.497473i
$329$	−429.010	−	838.294i	−0.0718909	−	0.140476i
$330$	18265.5			3.04692
$331$	−2835.12			−0.470793			−0.235396	−	0.971899i	$-0.575639\pi$
$331$	−2835.12			−0.470793			−0.235396	+	0.971899i	$0.575639\pi$
$332$	−4616.26			−0.763103
$333$		−	15953.7i		−	2.62539i
$334$		−	12316.1i		−	2.01768i
$335$			3840.67i			0.626383i
$336$	6651.17	+	12996.5i	1.07991	+	2.11017i
$337$		−	7618.13i		−	1.23141i	−0.787976	−	0.615706i	$-0.788871\pi$
$337$		−	7618.13i		−	1.23141i	0.787976	−	0.615706i	$-0.211129\pi$
$338$	−7212.01			−1.16060
$339$	−14646.3			−2.34654
$340$	−2385.13			−0.380446
$341$	4099.78			0.651072
$342$	22252.0			3.51828
$343$	−960.284	+	6279.45i	−0.151168	+	0.988508i
$344$		−	1462.11i		−	0.229162i
$345$	4905.29	+	7320.71i	0.765484	+	1.14242i
$346$			1664.62i			0.258643i
$347$	−5534.30			−0.856187			−0.428093	−	0.903735i	$-0.640815\pi$
$347$	−5534.30			−0.856187			−0.428093	+	0.903735i	$0.640815\pi$
$348$			3642.24i			0.561047i
$349$			1830.97i			0.280830i	0.990093	+	0.140415i	$0.0448437\pi$
$349$			1830.97i			0.280830i	−0.990093	+	0.140415i	$0.955156\pi$
$350$	−3330.47	+	1704.42i	−0.508631	+	0.260300i
$351$	−3285.40			−0.499606
$352$			9693.74i			1.46784i
$353$			2261.42i			0.340973i	0.985360	+	0.170486i	$0.0545339\pi$
$353$			2261.42i			0.340973i	−0.985360	+	0.170486i	$0.945466\pi$
$354$	−10060.8			−1.51053
$355$	−4632.13			−0.692530
$356$	−1390.25			−0.206975
$357$	7373.27	+	14407.5i	1.09309	+	2.13593i
$358$	−1785.26			−0.263559
$359$		−	6807.82i		−	1.00084i	−0.865781	−	0.500422i	$-0.833178\pi$
$359$		−	6807.82i		−	1.00084i	0.865781	−	0.500422i	$-0.166822\pi$
$360$	−8982.61			−1.31507
$361$	1763.40			0.257093
$362$	11138.2			1.61715
$363$		−	32428.1i		−	4.68880i
$364$	212.604	+	415.433i	0.0306140	+	0.0598203i
$365$			6504.08i			0.932710i
$366$		−	8172.62i		−	1.16719i
$367$	−6996.02			−0.995066			−0.497533	−	0.867445i	$-0.665761\pi$
$367$	−6996.02			−0.995066			−0.497533	+	0.867445i	$0.665761\pi$
$368$	−7292.35	+	4886.28i	−1.03299	+	0.692161i
$369$			13421.9i			1.89353i
$370$		−	6095.26i		−	0.856425i
$371$	1883.62	+	3680.63i	0.263592	+	0.515064i
$372$	2006.26			0.279623
$373$			3079.09i			0.427424i	0.976897	+	0.213712i	$0.0685553\pi$
$373$			3079.09i			0.427424i	−0.976897	+	0.213712i	$0.931445\pi$
$374$			20170.1i			2.78869i
$375$		−	14776.1i		−	2.03476i
$376$			796.243i			0.109210i
$377$		−	824.464i		−	0.112631i
$378$	−12425.3	−	24279.2i	−1.69071	−	3.30367i
$379$			3233.11i			0.438189i	0.975704	+	0.219094i	$0.0703102\pi$
$379$			3233.11i			0.438189i	−0.975704	+	0.219094i	$0.929690\pi$
$380$	2510.48			0.338908
$381$		−	13843.2i		−	1.86145i
$382$			254.049i			0.0340269i
$383$	−7710.24			−1.02865			−0.514327	−	0.857594i	$-0.671958\pi$
$383$	−7710.24			−1.02865			−0.514327	+	0.857594i	$0.671958\pi$
$384$		−	16504.6i		−	2.19335i
$385$	−4617.52	−	9022.73i	−0.611249	−	1.19439i
$386$	11954.8			1.57638
$387$			6640.67i			0.872259i
$388$	−1092.10			−0.142895
$389$			14944.3i			1.94783i	0.226921	+	0.973913i	$0.427134\pi$
$389$			14944.3i			1.94783i	−0.226921	+	0.973913i	$0.572866\pi$
$390$	−2023.31			−0.262703
$391$	−8084.06	+	5416.77i	−1.04560	+	0.700609i
$392$	3141.69	−	4356.64i	0.404794	−	0.561335i
$393$	16271.6			2.08854
$394$	3003.74			0.384077
$395$			6655.59i			0.847795i
$396$		−	16179.0i		−	2.05310i
$397$		−	1656.68i		−	0.209437i	−0.994502	−	0.104719i	$-0.966606\pi$
$397$		−	1656.68i		−	0.209437i	0.994502	−	0.104719i	$-0.0333942\pi$
$398$	−13442.8			−1.69304
$399$	−7760.79	−	15164.7i	−0.973748	−	1.90272i
$400$	4771.29			0.596412
$401$		−	1230.25i		−	0.153207i	−0.997062	−	0.0766034i	$-0.975592\pi$
$401$		−	1230.25i		−	0.153207i	0.997062	−	0.0766034i	$-0.0244075\pi$
$402$	15893.9			1.97193
$403$	−454.140			−0.0561348
$404$		−	3197.72i		−	0.393793i
$405$	19430.6			2.38399
$406$	6092.82	−	3118.09i	0.744782	−	0.381154i
$407$	−15221.1			−1.85376
$408$		−	13684.8i		−	1.66053i
$409$			11828.0i			1.42997i	0.699138	+	0.714987i	$0.253567\pi$
$409$			11828.0i			1.42997i	−0.699138	+	0.714987i	$0.746433\pi$
$410$			5127.95i			0.617687i
$411$	6164.23			0.739803
$412$	−1071.37			−0.128114
$413$	2543.38	+	4969.82i	0.303030	+	0.592127i
$414$	21959.2	−	14713.9i	2.60685	−	1.74674i
$415$	−11106.0			−1.31367
$416$		−	1073.79i		−	0.126555i
$417$	−120.034			−0.0140962
$418$		−	21230.2i		−	2.48422i
$419$	10137.7			1.18200			0.591001	−	0.806670i	$-0.298733\pi$
$419$	10137.7			1.18200			0.591001	+	0.806670i	$0.298733\pi$
$420$	−2259.62	−	4415.34i	−0.262519	−	0.512968i
$421$			4015.66i			0.464873i	0.972612	+	0.232436i	$0.0746697\pi$
$421$			4015.66i			0.464873i	−0.972612	+	0.232436i	$0.925330\pi$
$422$	−645.961			−0.0745139
$423$		−	3616.41i		−	0.415687i
$424$		−	3496.00i		−	0.400426i
$425$	5289.30			0.603691
$426$			19169.2i			2.18017i
$427$	−4037.08	+	2066.04i	−0.457536	+	0.234151i
$428$			2618.03i			0.295671i
$429$			5052.60i			0.568629i
$430$			2537.14i			0.284538i
$431$		−	9835.32i		−	1.09919i	−0.835432	−	0.549595i	$-0.814782\pi$
$431$		−	9835.32i		−	1.09919i	0.835432	−	0.549595i	$-0.185218\pi$
$432$			34782.9i			3.87383i
$433$	2225.85			0.247038			0.123519	−	0.992342i	$-0.460582\pi$
$433$	2225.85			0.247038			0.123519	+	0.992342i	$0.460582\pi$
$434$	−1717.54	−	3356.11i	−0.189965	−	0.371195i
$435$			8762.64i			0.965831i
$436$			3379.44i			0.371206i
$437$	8508.94	−	5701.47i	0.931436	−	0.624115i
$438$	26915.9			2.93628
$439$		−	7601.42i		−	0.826415i	−0.910637	−	0.413207i	$-0.864408\pi$
$439$		−	7601.42i		−	0.826415i	0.910637	−	0.413207i	$-0.135592\pi$
$440$			8570.12i			0.928555i
$441$	−14269.1	+	19787.2i	−1.54077	+	2.13661i
$442$		−	2234.28i		−	0.240439i
$443$	11039.7			1.18400			0.592001	−	0.805938i	$-0.298338\pi$
$443$	11039.7			1.18400			0.592001	+	0.805938i	$0.298338\pi$
$444$	−7448.54			−0.796153
$445$	−3344.72			−0.356304
$446$		−	7910.86i		−	0.839888i
$447$	−13131.6			−1.38950
$448$	−2560.78	+	1310.52i	−0.270057	+	0.138206i
$449$	−12986.9			−1.36501			−0.682506	−	0.730880i	$-0.739110\pi$
$449$	−12986.9			−1.36501			−0.682506	+	0.730880i	$0.739110\pi$
$450$	−14367.6			−1.50511
$451$	12805.5			1.33700
$452$			4956.54i			0.515787i
$453$			18550.6i			1.92402i
$454$	7231.32			0.747539
$455$	511.491	+	999.464i	0.0527013	+	0.102979i
$456$			14404.0i			1.47923i
$457$			14410.2i			1.47501i	0.675343	+	0.737504i	$0.263996\pi$
$457$			14410.2i			1.47501i	−0.675343	+	0.737504i	$0.736004\pi$
$458$	−11059.0			−1.12829
$459$			38559.2i			3.92111i
$460$	2477.45	−	1660.03i	0.251112	−	0.168259i
$461$		−	15237.1i		−	1.53940i	−0.638406	−	0.769700i	$-0.720406\pi$
$461$		−	15237.1i		−	1.53940i	0.638406	−	0.769700i	$-0.279594\pi$
$462$	−37338.9	+	19108.8i	−3.76009	+	1.92428i
$463$	9399.65			0.943496			0.471748	−	0.881733i	$-0.343623\pi$
$463$	9399.65			0.943496			0.471748	+	0.881733i	$0.343623\pi$
$464$	−8728.70			−0.873318
$465$	4826.74			0.481365
$466$	7075.37			0.703348
$467$	7176.84			0.711145			0.355573	−	0.934649i	$-0.384286\pi$
$467$	7176.84			0.711145			0.355573	+	0.934649i	$0.384286\pi$
$468$			1792.18i			0.177016i
$469$	−4017.97	−	7851.20i	−0.395592	−	0.772995i
$470$		−	1381.68i		−	0.135601i
$471$			4600.95i			0.450107i
$472$		−	4720.51i		−	0.460337i
$473$	6335.73			0.615892
$474$	27542.9			2.66896
$475$	−5567.29			−0.537778
$476$	4875.74	−	2495.23i	0.469494	−	0.240271i
$477$			15878.3i			1.52414i
$478$	1516.77			0.145137
$479$	−8380.58			−0.799413			−0.399706	−	0.916643i	$-0.630888\pi$
$479$	−8380.58			−0.799413			−0.399706	+	0.916643i	$0.630888\pi$
$480$			11412.6i			1.08523i
$481$	1686.07			0.159829
$482$	3763.41			0.355640
$483$	−17686.2	−	9833.45i	−1.66615	−	0.926372i
$484$	−10974.2			−1.03063
$485$	−2627.42			−0.245990
$486$		−	40648.3i		−	3.79392i
$487$	16070.0			1.49528			0.747642	−	0.664102i	$-0.231186\pi$
$487$	16070.0			1.49528			0.747642	+	0.664102i	$0.231186\pi$
$488$	3834.56			0.355702
$489$			13904.8i			1.28588i
$490$	−5451.64	+	7559.88i	−0.502612	+	0.696981i
$491$	7915.47			0.727536			0.363768	−	0.931490i	$-0.381490\pi$
$491$	7915.47			0.727536			0.363768	+	0.931490i	$0.381490\pi$
$492$	6266.47			0.574216
$493$	−9676.34			−0.883976
$494$			2351.71i			0.214187i
$495$		−	38924.1i		−	3.53436i
$496$			4808.04i			0.435257i
$497$	9469.13	−	4845.97i	0.854625	−	0.437368i
$498$			45960.1i			4.13558i
$499$	2712.80			0.243370			0.121685	−	0.992569i	$-0.461170\pi$
$499$	2712.80			0.243370			0.121685	+	0.992569i	$0.461170\pi$
$500$	−5000.47			−0.447255
$501$	−36209.2			−3.22895
$502$	−17011.6			−1.51248
$503$	−14344.1			−1.27152			−0.635758	−	0.771889i	$-0.719312\pi$
$503$	−14344.1			−1.27152			−0.635758	+	0.771889i	$0.719312\pi$
$504$	18362.5	−	9397.28i	1.62288	−	0.830532i
$505$		−	7693.20i		−	0.677907i
$506$	−14038.2	−	20950.8i	−1.23335	−	1.84067i
$507$			21203.2i			1.85733i
$508$	−4684.78			−0.409160
$509$		−	9221.60i		−	0.803026i	−0.915853	−	0.401513i	$-0.868484\pi$
$509$		−	9221.60i		−	0.803026i	0.915853	−	0.401513i	$-0.131516\pi$
$510$			23746.6i			2.06180i
$511$	−6804.34	−	13295.8i	−0.589053	−	1.15102i
$512$	−1398.75			−0.120736
$513$		−	40585.8i		−	3.49299i
$514$			15949.4i			1.36867i
$515$	−2577.56			−0.220545
$516$	3100.44			0.264514
$517$	−3450.34			−0.293512
$518$	6376.64	+	12460.1i	0.540876	+	1.05688i
$519$	4893.96			0.413913
$520$		−	949.328i		−	0.0800592i
$521$	9512.86			0.799935			0.399967	−	0.916529i	$-0.369021\pi$
$521$	9512.86			0.799935			0.399967	+	0.916529i	$0.369021\pi$
$522$	26284.5			2.20391
$523$	14365.7			1.20108			0.600541	−	0.799594i	$-0.294952\pi$
$523$	14365.7			1.20108			0.600541	+	0.799594i	$0.294952\pi$
$524$		−	5506.58i		−	0.459077i
$525$	5010.97	+	9791.53i	0.416565	+	0.813976i
$526$		−	9906.08i		−	0.821152i
$527$			5330.03i			0.440569i
$528$	53492.4			4.40901
$529$	4626.94	−	11252.9i	0.380286	−	0.924869i
$530$			6066.45i			0.497188i
$531$			21439.8i			1.75218i
$532$	−5131.99	+	2626.38i	−0.418233	+	0.214037i
$533$	−1418.49			−0.115275
$534$			13841.5i			1.12169i
$535$			6298.56i			0.508992i
$536$			7457.36i			0.600949i
$537$			5248.66i			0.421781i
$538$			1048.45i			0.0840181i
$539$	18878.5	+	13613.8i	1.50864	+	1.08792i
$540$		−	11816.9i		−	0.941699i
$541$	4703.19			0.373764			0.186882	−	0.982382i	$-0.440162\pi$
$541$	4703.19			0.373764			0.186882	+	0.982382i	$0.440162\pi$
$542$		−	20293.9i		−	1.60830i
$543$		−	32746.1i		−	2.58797i
$544$	−12602.6			−0.993258
$545$			8130.39i			0.639023i
$546$	4136.10	−	2116.71i	0.324192	−	0.165910i
$547$	6975.55			0.545252			0.272626	−	0.962120i	$-0.412108\pi$
$547$	6975.55			0.545252			0.272626	+	0.962120i	$0.412108\pi$
$548$		−	2086.07i		−	0.162614i
$549$	−17416.0			−1.35391
$550$			13707.9i			1.06274i
$551$	10184.9			0.787462
$552$	9524.50	+	14214.5i	0.734402	+	1.09603i
$553$	−6962.84	−	13605.5i	−0.535425	−	1.04623i
$554$	14721.5			1.12898
$555$	−17920.0			−1.37056
$556$			40.6215i			0.00309845i
$557$		−	12020.5i		−	0.914404i	−0.889363	−	0.457202i	$-0.848852\pi$
$557$		−	12020.5i		−	0.914404i	0.889363	−	0.457202i	$-0.151148\pi$
$558$		−	14478.3i		−	1.09841i
$559$	−701.820			−0.0531017
$560$	10581.5	−	5415.22i	0.798478	−	0.408634i
$561$	59299.9			4.46283
$562$		−	13577.0i		−	1.01906i
$563$	−12048.9			−0.901954			−0.450977	−	0.892536i	$-0.648924\pi$
$563$	−12048.9			−0.901954			−0.450977	+	0.892536i	$0.648924\pi$
$564$	−1688.45			−0.126058
$565$			11924.6i			0.887917i
$566$	−10395.0			−0.771967
$567$	−39720.6	+	20327.6i	−2.94199	+	1.50561i
$568$	−8994.12			−0.664410
$569$		−	17880.9i		−	1.31741i	−0.752400	−	0.658706i	$-0.771104\pi$
$569$		−	17880.9i		−	1.31741i	0.752400	−	0.658706i	$-0.228896\pi$
$570$		−	24994.7i		−	1.83669i
$571$		−	8109.37i		−	0.594337i	−0.954825	−	0.297169i	$-0.903958\pi$
$571$		−	8109.37i		−	0.594337i	0.954825	−	0.297169i	$-0.0960423\pi$
$572$	1709.88			0.124989
$573$	746.901			0.0544542
$574$	−5364.68	−	10482.7i	−0.390100	−	0.762264i
$575$	−5494.03	+	3681.31i	−0.398464	+	0.266993i
$576$	−11047.2			−0.799134
$577$		−	20562.4i		−	1.48358i	−0.670635	−	0.741788i	$-0.733978\pi$
$577$		−	20562.4i		−	1.48358i	0.670635	−	0.741788i	$-0.266022\pi$
$578$	−9669.27			−0.695828
$579$		−	35146.9i		−	2.52272i
$580$	2965.42			0.212297
$581$	22703.2	−	11618.7i	1.62115	−	0.829646i
$582$			10873.1i			0.774406i
$583$	15149.1			1.07618
$584$			12628.8i			0.894838i
$585$			4311.70i			0.304729i
$586$	−10329.6			−0.728179
$587$			16711.5i			1.17505i	0.809205	+	0.587526i	$0.199898\pi$
$587$			16711.5i			1.17505i	−0.809205	+	0.587526i	$0.800102\pi$
$588$	9238.34	+	6662.02i	0.647930	+	0.467240i
$589$		−	5610.17i		−	0.392467i
$590$			8191.29i			0.571577i
$591$		−	8830.96i		−	0.614649i
$592$		−	17850.6i		−	1.23928i
$593$			27240.2i			1.88638i	0.332261	+	0.943188i	$0.392189\pi$
$593$			27240.2i			1.88638i	−0.332261	+	0.943188i	$0.607811\pi$
$594$	−99930.9			−6.90272
$595$	11730.2	−	6003.13i	0.808224	−	0.413621i
$596$			4443.96i			0.305422i
$597$			39521.8i			2.70942i
$598$	1555.04	+	2320.76i	0.106338	+	0.158701i
$599$	19766.7			1.34832			0.674161	−	0.738584i	$-0.264505\pi$
$599$	19766.7			1.34832			0.674161	+	0.738584i	$0.264505\pi$
$600$		−	9300.35i		−	0.632809i
$601$		−	7070.92i		−	0.479915i	−0.970783	−	0.239958i	$-0.922866\pi$
$601$		−	7070.92i		−	0.479915i	0.970783	−	0.239958i	$-0.0771335\pi$
$602$	−2654.26	−	5186.48i	−0.179700	−	0.351138i
$603$		−	33870.1i		−	2.28739i
$604$	6277.82			0.422915
$605$	−26402.1			−1.77421
$606$	−31836.9			−2.13413
$607$			7616.64i			0.509308i	0.967032	+	0.254654i	$0.0819616\pi$
$607$			7616.64i			0.509308i	−0.967032	+	0.254654i	$0.918038\pi$
$608$	13265.0			0.884812
$609$	−9167.16	−	17912.8i	−0.609971	−	1.19190i
$610$	−6653.95			−0.441657
$611$	382.200			0.0253063
$612$	21034.0			1.38929
$613$			18919.1i			1.24655i	0.782003	+	0.623275i	$0.214198\pi$
$613$			18919.1i			1.24655i	−0.782003	+	0.623275i	$0.785802\pi$
$614$		−	7283.38i		−	0.478719i
$615$	15076.1			0.988501
$616$	−8965.75	−	17519.3i	−0.586429	−	1.14589i
$617$		−	8779.01i		−	0.572819i	−0.958107	−	0.286410i	$-0.907538\pi$
$617$		−	8779.01i		−	0.572819i	0.958107	−	0.286410i	$-0.0924618\pi$
$618$			10666.7i			0.694302i
$619$	−15250.5			−0.990255			−0.495127	−	0.868820i	$-0.664879\pi$
$619$	−15250.5			−0.990255			−0.495127	+	0.868820i	$0.664879\pi$
$620$		−	1633.45i		−	0.105808i
$621$	−26836.9	−	40051.7i	−1.73418	−	2.58811i
$622$			7509.46i			0.484086i
$623$	6837.37	−	3499.13i	0.439701	−	0.225024i
$624$	−5925.46			−0.380141
$625$	−4535.88			−0.290296
$626$	−3669.97			−0.234316
$627$	−62416.6			−3.97556
$628$	1557.03			0.0989370
$629$		−	19788.6i		−	1.25441i
$630$	−31863.6	+	16306.7i	−2.01504	+	1.03123i
$631$			17396.6i			1.09754i	0.835974	+	0.548769i	$0.184903\pi$
$631$			17396.6i			1.09754i	−0.835974	+	0.548769i	$0.815097\pi$
$632$			12923.0i			0.813371i
$633$			1899.12i			0.119247i
$634$	−7994.25			−0.500777
$635$	−11270.8			−0.704361
$636$	7413.34			0.462198
$637$	−2091.21	−	1508.03i	−0.130073	−	0.0937994i
$638$		−	25077.4i		−	1.55615i
$639$	40849.9			2.52895
$640$	−13437.7			−0.829953
$641$			1156.57i			0.0712663i	0.999365	+	0.0356331i	$0.0113448\pi$
$641$			1156.57i			0.0712663i	−0.999365	+	0.0356331i	$0.988655\pi$
$642$	26065.4			1.60237
$643$	26432.2			1.62113			0.810564	−	0.585650i	$-0.199161\pi$
$643$	26432.2			1.62113			0.810564	+	0.585650i	$0.199161\pi$
$644$	−3327.80	+	5985.29i	−0.203624	+	0.366232i
$645$	7459.15			0.455355
$646$	27600.9			1.68103
$647$			5345.62i			0.324819i	0.986723	+	0.162410i	$0.0519266\pi$
$647$			5345.62i			0.324819i	−0.986723	+	0.162410i	$0.948073\pi$
$648$	37728.0			2.28719
$649$	20455.3			1.23720
$650$		−	1518.45i		−	0.0916283i
$651$	−9866.94	+	5049.56i	−0.594034	+	0.304006i
$652$	4705.61			0.282647
$653$	−31697.8			−1.89959			−0.949793	−	0.312877i	$-0.898707\pi$
$653$	−31697.8			−1.89959			−0.949793	+	0.312877i	$0.898707\pi$
$654$	33646.1			2.01172
$655$		−	13248.0i		−	0.790291i
$656$			15017.7i			0.893817i
$657$		−	57358.2i		−	3.40602i
$658$	1445.47	+	2824.48i	0.0856387	+	0.167340i
$659$		−	17246.0i		−	1.01944i	−0.860341	−	0.509719i	$-0.829750\pi$
$659$		−	17246.0i		−	1.01944i	0.860341	−	0.509719i	$-0.170250\pi$
$660$	−18173.1			−1.07180
$661$	13420.7			0.789719			0.394860	−	0.918741i	$-0.370793\pi$
$661$	13420.7			0.789719			0.394860	+	0.918741i	$0.370793\pi$
$662$	9552.41			0.560823
$663$	−6568.76			−0.384781
$664$	−21564.3			−1.26033
$665$	−12346.8	+	6318.65i	−0.719980	+	0.368461i
$666$			53752.9i			3.12745i
$667$	10050.9	−	6734.66i	0.583466	−	0.390955i
$668$			12253.8i			0.709749i
$669$	−23257.8			−1.34410
$670$		−	12940.4i		−	0.746167i
$671$			16616.2i			0.955979i
$672$	−11939.4	−	23329.9i	−0.685378	−	1.33924i
$673$	−19234.2			−1.10167			−0.550836	−	0.834613i	$-0.685691\pi$
$673$	−19234.2			−1.10167			−0.550836	+	0.834613i	$0.685691\pi$
$674$			25667.9i			1.46690i
$675$			26205.3i			1.49429i
$676$	7175.52			0.408257
$677$	−26407.7			−1.49916			−0.749579	−	0.661915i	$-0.769744\pi$
$677$	−26407.7			−1.49916			−0.749579	+	0.661915i	$0.769744\pi$
$678$	49347.9			2.79527
$679$	5371.05	−	2748.72i	0.303567	−	0.155355i
$680$	−11141.8			−0.628337
$681$		−	21260.0i		−	1.19631i
$682$	−13813.4			−0.775578
$683$	26736.7			1.49788			0.748940	−	0.662638i	$-0.230563\pi$
$683$	26736.7			1.49788			0.748940	+	0.662638i	$0.230563\pi$
$684$	−22139.5			−1.23761
$685$		−	5018.76i		−	0.279937i
$686$	3235.50	−	21157.4i	0.180076	−	1.17754i
$687$			32513.4i			1.80563i
$688$			7430.26i			0.411738i
$689$	−1678.10			−0.0927872
$690$	−16527.4	−	24665.8i	−0.911868	−	1.36088i
$691$			17045.2i			0.938393i	0.883094	+	0.469197i	$0.155456\pi$
$691$			17045.2i			0.938393i	−0.883094	+	0.469197i	$0.844544\pi$
$692$		−	1656.20i		−	0.0909814i
$693$	40721.0	+	79569.7i	2.23213	+	4.36162i
$694$	18646.8			1.01992
$695$			97.7290i			0.00533391i
$696$			17014.2i			0.926614i
$697$			16648.1i			0.904725i
$698$		−	6169.11i		−	0.334533i
$699$		−	20801.5i		−	1.12559i
$700$	3313.61	−	1695.79i	0.178918	−	0.0915642i
$701$		−	8327.36i		−	0.448673i	−0.974512	−	0.224337i	$-0.927978\pi$
$701$		−	8327.36i		−	0.448673i	0.974512	−	0.224337i	$-0.0720215\pi$
$702$	11069.5			0.595146
$703$			20828.6i			1.11745i
$704$			10539.9i			0.564259i
$705$	−4062.14			−0.217006
$706$		−	7619.44i		−	0.406178i
$707$	8048.35	+	15726.6i	0.428132	+	0.836579i
$708$	10009.9			0.531351
$709$			20960.5i			1.11028i	0.831757	+	0.555139i	$0.187335\pi$
$709$			20960.5i			1.11028i	−0.831757	+	0.555139i	$0.812665\pi$
$710$	15607.1			0.824964
$711$		−	58694.3i		−	3.09593i
$712$	−6494.38			−0.341836
$713$	−3709.66	−	5536.34i	−0.194850	−	0.290796i
$714$	−24842.8	−	48543.4i	−1.30213	−	2.54439i
$715$	4113.70			0.215166
$716$	1776.23			0.0927107
$717$		−	4459.28i		−	0.232266i
$718$			22937.7i			1.19224i
$719$		−	36435.9i		−	1.88989i	−0.327231	−	0.944944i	$-0.606115\pi$
$719$		−	36435.9i		−	1.88989i	0.327231	−	0.944944i	$-0.393885\pi$
$720$	45648.4			2.36280
$721$	5269.11	−	2696.55i	0.272166	−	0.139285i
$722$	−5941.44			−0.306257
$723$		−	11064.4i		−	0.569141i
$724$	−11081.8			−0.568857
$725$	−6576.17			−0.336873
$726$			109260.i			5.58544i
$727$	−7126.48			−0.363558			−0.181779	−	0.983339i	$-0.558185\pi$
$727$	−7126.48			−0.363558			−0.181779	+	0.983339i	$0.558185\pi$
$728$	993.153	+	1940.64i	0.0505614	+	0.0987980i
$729$	−54455.8			−2.76664
$730$		−	21914.3i		−	1.11107i
$731$			8236.93i			0.416763i
$732$			8131.27i			0.410574i
$733$	−10100.3			−0.508953			−0.254476	−	0.967079i	$-0.581903\pi$
$733$	−10100.3			−0.508953			−0.254476	+	0.967079i	$0.581903\pi$
$734$	23571.8			1.18535
$735$	22226.0	+	16027.8i	1.11540	+	0.804344i
$736$	13090.4	−	8771.32i	0.655597	−	0.439287i
$737$	−32314.8			−1.61510
$738$		−	45222.4i		−	2.25564i
$739$	−17113.1			−0.851845			−0.425923	−	0.904760i	$-0.640050\pi$
$739$	−17113.1			−0.851845			−0.425923	+	0.904760i	$0.640050\pi$
$740$			6064.42i			0.301260i
$741$	6914.00			0.342770
$742$	−6346.51	−	12401.2i	−0.313999	−	0.613561i
$743$		−	15753.2i		−	0.777831i	−0.921273	−	0.388915i	$-0.872850\pi$
$743$		−	15753.2i		−	0.777831i	0.921273	−	0.388915i	$-0.127150\pi$
$744$	9371.98			0.461819
$745$			10691.5i			0.525778i
$746$		−	10374.4i		−	0.509161i
$747$	97941.6			4.79718
$748$		−	20068.1i		−	0.980964i
$749$	−6589.33	−	12875.7i	−0.321454	−	0.628127i
$750$			49785.3i			2.42387i
$751$		−	20389.3i		−	0.990702i	−0.868693	−	0.495351i	$-0.835040\pi$
$751$		−	20389.3i		−	0.990702i	0.868693	−	0.495351i	$-0.164960\pi$
$752$		−	4046.40i		−	0.196220i
$753$			50013.8i			2.42046i
$754$			2777.88i			0.134170i
$755$	15103.4			0.728039
$756$	12362.4	+	24156.4i	0.594730	+	1.16211i
$757$			34888.3i			1.67508i	0.546373	+	0.837542i	$0.316008\pi$
$757$			34888.3i			1.67508i	−0.546373	+	0.837542i	$0.683992\pi$
$758$		−	10893.3i		−	0.521984i
$759$	−61595.3	+	41272.3i	−2.94567	+	1.97377i
$760$	11727.4			0.559734
$761$			22458.1i			1.06978i	0.844921	+	0.534891i	$0.179647\pi$
$761$			22458.1i			1.06978i	−0.844921	+	0.534891i	$0.820353\pi$
$762$			46642.2i			2.21741i
$763$	−8505.73	−	16620.4i	−0.403575	−	0.788594i
$764$		−	252.763i		−	0.0119695i
$765$	50604.3			2.39164
$766$	25978.2			1.22537
$767$	−2265.87			−0.106670
$768$			43300.4i			2.03447i
$769$	−6671.74			−0.312860			−0.156430	−	0.987689i	$-0.549999\pi$
$769$	−6671.74			−0.312860			−0.156430	+	0.987689i	$0.549999\pi$
$770$	15557.9	+	30400.4i	0.728139	+	1.42280i
$771$	46891.1			2.19033
$772$	−11894.3			−0.554513
$773$	31728.6			1.47632			0.738162	−	0.674623i	$-0.235694\pi$
$773$	31728.6			1.47632			0.738162	+	0.674623i	$0.235694\pi$
$774$		−	22374.5i		−	1.03906i
$775$			3622.36i			0.167895i
$776$	−5101.61			−0.236002
$777$	36632.5	−	18747.3i	1.69136	−	0.865578i
$778$		−	50351.9i		−	2.32031i
$779$		−	17523.1i		−	0.805946i
$780$	2013.07			0.0924095
$781$		−	38974.0i		−	1.78566i
$782$	27237.7	−	18250.8i	1.24555	−	0.834587i
$783$		−	47940.5i		−	2.18806i
$784$	−15965.7	+	22139.9i	−0.727299	+	1.00856i
$785$	3745.98			0.170318
$786$	−54824.2			−2.48793
$787$	−28178.3			−1.27630			−0.638151	−	0.769912i	$-0.720300\pi$
$787$	−28178.3			−1.27630			−0.638151	+	0.769912i	$0.720300\pi$
$788$	−2988.54			−0.135105
$789$	−29123.8			−1.31411
$790$		−	22424.8i		−	1.00992i
$791$	−12475.1	−	24376.6i	−0.560764	−	1.09574i
$792$		−	75578.2i		−	3.39085i
$793$		−	1840.61i		−	0.0824237i
$794$			5581.89i			0.249488i
$795$	17835.3			0.795664
$796$	13374.8			0.595551
$797$	−3409.52			−0.151533			−0.0757663	−	0.997126i	$-0.524140\pi$
$797$	−3409.52			−0.151533			−0.0757663	+	0.997126i	$0.524140\pi$
$798$	26148.5	+	51094.8i	1.15996	+	2.26658i
$799$		−	4485.71i		−	0.198614i
$800$	−8564.89			−0.378518
$801$	29496.5			1.30113
$802$			4145.11i			0.182505i
$803$	−54724.3			−2.40495
$804$	−15813.5			−0.693655
$805$	−8006.15	+	14399.7i	−0.350534	+	0.630461i
$806$	1530.14			0.0668696
$807$	3082.42			0.134456
$808$		−	14937.7i		−	0.650381i
$809$	11902.6			0.517273			0.258636	−	0.965975i	$-0.416727\pi$
$809$	11902.6			0.517273			0.258636	+	0.965975i	$0.416727\pi$
$810$	−65467.8			−2.83988
$811$			10425.1i			0.451387i	0.974198	+	0.225693i	$0.0724648\pi$
$811$			10425.1i			0.451387i	−0.974198	+	0.225693i	$0.927535\pi$
$812$	−6061.99	+	3102.32i	−0.261988	+	0.134076i
$813$	−59663.8			−2.57380
$814$	51284.5			2.20826
$815$	11320.9			0.486571
$816$			69544.3i			2.98350i
$817$		−	8669.85i		−	0.371260i
$818$		−	39852.4i		−	1.70343i
$819$	−4510.74	−	8814.08i	−0.192452	−	0.376055i
$820$		−	5102.01i		−	0.217280i
$821$	34524.3			1.46761			0.733804	−	0.679361i	$-0.237743\pi$
$821$	34524.3			1.46761			0.733804	+	0.679361i	$0.237743\pi$
$822$	−20769.2			−0.881276
$823$	−36056.2			−1.52715			−0.763573	−	0.645722i	$-0.776557\pi$
$823$	−36056.2			−1.52715			−0.763573	+	0.645722i	$0.776557\pi$
$824$	−5004.79			−0.211590
$825$	40301.0			1.70073
$826$	−8569.44	−	16744.9i	−0.360979	−	0.705361i
$827$		−	25269.4i		−	1.06252i	−0.847209	−	0.531260i	$-0.821719\pi$
$827$		−	25269.4i		−	1.06252i	0.847209	−	0.531260i	$-0.178281\pi$
$828$	−21848.1	+	14639.5i	−0.916999	+	0.614441i
$829$			24092.6i			1.00937i	0.863303	+	0.504686i	$0.168392\pi$
$829$			24092.6i			1.00937i	−0.863303	+	0.504686i	$0.831608\pi$
$830$	37419.5			1.56488
$831$		−	43281.1i		−	1.80674i
$832$		−	1167.53i		−	0.0486499i
$833$	−17699.0	+	24543.5i	−0.736175	+	1.02087i
$834$	404.433			0.0167918
$835$			29480.6i			1.22182i
$836$			21122.8i			0.873860i
$837$	−26407.1			−1.09052
$838$	−34157.1			−1.40804
$839$	34087.4			1.40265			0.701327	−	0.712840i	$-0.252591\pi$
$839$	34087.4			1.40265			0.701327	+	0.712840i	$0.252591\pi$
$840$	−10555.5	−	20625.7i	−0.433572	−	0.847207i
$841$	−12358.4			−0.506722
$842$		−	13530.0i		−	0.553771i
$843$	−39916.1			−1.63082
$844$	642.692			0.0262114
$845$	17263.1			0.702805
$846$			12184.8i			0.495180i
$847$	53972.0	−	27621.0i	2.18949	−	1.12051i
$848$			17766.2i			0.719451i
$849$			30561.1i			1.23540i
$850$	−17821.3			−0.719135
$851$	13772.7	+	20554.5i	0.554784	+	0.827967i
$852$		−	19072.2i		−	0.766906i
$853$		−	12972.1i		−	0.520699i	−0.965514	−	0.260350i	$-0.916162\pi$
$853$		−	12972.1i		−	0.520699i	0.965514	−	0.260350i	$-0.0838379\pi$
$854$	13602.2	−	6961.13i	0.545031	−	0.278928i
$855$	−53264.0			−2.13051
$856$			12229.8i			0.488324i
$857$			31008.7i			1.23598i	0.786185	+	0.617991i	$0.212053\pi$
$857$			31008.7i			1.23598i	−0.786185	+	0.617991i	$0.787947\pi$
$858$		−	17023.8i		−	0.677368i
$859$			43254.4i			1.71807i	0.511919	+	0.859034i	$0.328935\pi$
$859$			43254.4i			1.71807i	−0.511919	+	0.859034i	$0.671065\pi$
$860$		−	2524.30i		−	0.100091i
$861$	−30819.0	+	15772.1i	−1.21987	+	0.624288i
$862$			33138.2i			1.30939i
$863$	−610.927			−0.0240976			−0.0120488	−	0.999927i	$-0.503835\pi$
$863$	−610.927			−0.0240976			−0.0120488	+	0.999927i	$0.503835\pi$
$864$		−	62438.4i		−	2.45856i
$865$		−	3984.54i		−	0.156623i
$866$	−7499.59			−0.294280
$867$			28427.6i			1.11355i
$868$	1708.85	+	3339.13i	0.0668229	+	0.130573i
$869$	−55999.0			−2.18600
$870$		−	29524.1i		−	1.15053i
$871$	3579.57			0.139253
$872$			15786.6i			0.613076i
$873$	23170.7			0.898293
$874$	−28669.3	+	19210.0i	−1.10956	+	0.743465i
$875$	24592.7	−	12585.7i	0.950155	−	0.486256i
$876$	−26779.7			−1.03288
$877$	13040.9			0.502121			0.251061	−	0.967971i	$-0.419221\pi$
$877$	13040.9			0.502121			0.251061	+	0.967971i	$0.419221\pi$
$878$			25611.6i			0.984451i
$879$			30369.0i			1.16533i
$880$		−	43552.2i		−	1.66835i
$881$	−46396.5			−1.77428			−0.887138	−	0.461505i	$-0.847310\pi$
$881$	−46396.5			−1.77428			−0.887138	+	0.461505i	$0.847310\pi$
$882$	48076.9	−	66669.1i	1.83541	−	2.54520i
$883$	4692.24			0.178830			0.0894148	−	0.995994i	$-0.471500\pi$
$883$	4692.24			0.178830			0.0894148	+	0.995994i	$0.471500\pi$
$884$			2222.98i			0.0845778i
$885$	24082.3			0.914710
$886$	−37196.2			−1.41042
$887$			46924.2i			1.77628i	0.459572	+	0.888140i	$0.348003\pi$
$887$			46924.2i			1.77628i	−0.459572	+	0.888140i	$0.651997\pi$
$888$	−34794.9			−1.31491
$889$	23040.1	−	11791.1i	0.869225	−	0.444839i
$890$	11269.4			0.424440
$891$			163486.i			6.14701i
$892$			7870.83i			0.295443i
$893$			4721.46i			0.176929i
$894$	44244.6			1.65521
$895$	4273.33			0.159599
$896$	27469.6	−	14058.0i	1.02421	−	0.524157i
$897$	6823.02	−	4571.81i	0.253973	−	0.170176i
$898$	43757.0			1.62605
$899$		−	6626.81i		−	0.245847i
$900$	14294.9			0.529443
$901$			19695.0i			0.728231i
$902$	−43145.8			−1.59268
$903$	−15248.2	+	7803.50i	−0.561936	+	0.287579i
$904$			23153.8i			0.851863i
$905$	−26661.1			−0.979275
$906$		−	62502.7i		−	2.29196i
$907$		−	35941.0i		−	1.31577i	−0.753120	−	0.657883i	$-0.771452\pi$
$907$		−	35941.0i		−	1.31577i	0.753120	−	0.657883i	$-0.228548\pi$
$908$	−7194.73			−0.262958
$909$			67844.8i			2.47555i
$910$	−1723.37	−	3367.51i	−0.0627795	−	0.122672i
$911$		−	12203.7i		−	0.443827i	−0.975066	−	0.221913i	$-0.928770\pi$
$911$		−	12203.7i		−	0.443827i	0.975066	−	0.221913i	$-0.0712302\pi$
$912$		−	73199.4i		−	2.65776i
$913$		−	93444.0i		−	3.38723i
$914$		−	48552.3i		−	1.75708i
$915$			19562.5i			0.706795i
$916$	11003.1			0.396891
$917$	13859.5	+	27081.8i	0.499109	+	0.975268i
$918$		−	129918.i		−	4.67095i
$919$			29157.4i			1.04659i	0.852152	+	0.523295i	$0.175297\pi$
$919$			29157.4i			1.04659i	−0.852152	+	0.523295i	$0.824703\pi$
$920$	11573.1	−	7754.61i	0.414732	−	0.277893i
$921$	−21413.1			−0.766107
$922$			51338.6i			1.83378i
$923$			4317.22i			0.153958i
$924$	37150.0	−	19012.1i	1.32267	−	0.676895i
$925$		−	13448.6i		−	0.478039i
$926$	−31670.4			−1.12392
$927$	22731.0			0.805375
$928$	15668.8			0.554260
$929$		−	425.736i		−	0.0150355i	−0.999972	−	0.00751773i	$-0.997607\pi$
$929$		−	425.736i		−	0.0150355i	0.999972	−	0.00751773i	$-0.00239299\pi$
$930$	−16262.8			−0.573417
$931$	18629.2	−	25833.5i	0.655798	−	0.909407i
$932$	−7039.57			−0.247413
$933$	22077.7			0.774697
$934$	−24181.0			−0.847139
$935$		−	48280.5i		−	1.68871i
$936$			8371.93i			0.292356i
$937$	25134.9			0.876330			0.438165	−	0.898894i	$-0.355628\pi$
$937$	25134.9			0.876330			0.438165	+	0.898894i	$0.355628\pi$
$938$	13537.8	+	26453.1i	0.471242	+	0.920816i
$939$			10789.7i			0.374982i
$940$			1374.69i			0.0476995i
$941$	21103.7			0.731094			0.365547	−	0.930793i	$-0.380882\pi$
$941$	21103.7			0.731094			0.365547	+	0.930793i	$0.380882\pi$
$942$		−	15502.0i		−	0.536182i
$943$	−11587.0	−	17292.6i	−0.400132	−	0.597161i
$944$			23989.0i			0.827094i
$945$	29742.0	+	58116.4i	1.02382	+	2.00056i
$946$	−21347.0			−0.733670
$947$	49604.3			1.70214			0.851069	−	0.525054i	$-0.175955\pi$
$947$	49604.3			1.70214			0.851069	+	0.525054i	$0.175955\pi$
$948$	−27403.5			−0.938846
$949$	6061.91			0.207353
$950$	18757.9			0.640619
$951$			23503.0i			0.801407i
$952$	22776.4	−	11656.2i	0.775406	−	0.396826i
$953$			53062.7i			1.80364i	0.432111	+	0.901820i	$0.357769\pi$
$953$			53062.7i			1.80364i	−0.432111	+	0.901820i	$0.642231\pi$
$954$		−	53498.9i		−	1.81561i
$955$		−	608.109i		−	0.0206052i
$956$	−1509.09			−0.0510539
$957$	−73727.4			−2.49035
$958$	28236.8			0.952286
$959$	5250.45	+	10259.5i	0.176794	+	0.345460i
$960$			12408.8i			0.417180i
$961$	26140.7			0.877471
$962$	−5680.88			−0.190394
$963$		−	55545.8i		−	1.85871i
$964$	−3744.37			−0.125102
$965$	−28615.7			−0.954583
$966$	59590.3	+	33132.0i	1.98477	+	1.10352i
$967$	6990.74			0.232479			0.116239	−	0.993221i	$-0.462916\pi$
$967$	6990.74			0.232479			0.116239	+	0.993221i	$0.462916\pi$
$968$	−51264.5			−1.70217
$969$		−	81146.4i		−	2.69019i
$970$	8852.61			0.293031
$971$	−9987.36			−0.330082			−0.165041	−	0.986287i	$-0.552776\pi$
$971$	−9987.36			−0.330082			−0.165041	+	0.986287i	$0.552776\pi$
$972$			40442.6i			1.33456i
$973$	−102.241	−	199.780i	−0.00336864	−	0.00658238i
$974$	−54145.0			−1.78123
$975$	−4464.22			−0.146635
$976$	−19486.8			−0.639094
$977$		−	19527.2i		−	0.639439i	−0.947512	−	0.319720i	$-0.896411\pi$
$977$		−	19527.2i		−	0.639439i	0.947512	−	0.319720i	$-0.103589\pi$
$978$		−	46849.6i		−	1.53178i
$979$		−	28142.0i		−	0.918714i
$980$	5424.05	−	7521.63i	0.176801	−	0.245173i
$981$		−	71700.3i		−	2.33355i
$982$	−26669.7			−0.866664
$983$	25517.2			0.827947			0.413973	−	0.910289i	$-0.364141\pi$
$983$	25517.2			0.827947			0.413973	+	0.910289i	$0.364141\pi$
$984$	29273.0			0.948364
$985$	−7189.95			−0.232580
$986$	32602.6			1.05302
$987$	8303.93	−	4249.67i	0.267798	−	0.137050i
$988$		−	2339.81i		−	0.0753434i
$989$	−5732.84	−	8555.76i	−0.184321	−	0.275083i
$990$			131147.i			4.21024i
$991$	−16634.8			−0.533221			−0.266611	−	0.963804i	$-0.585904\pi$
$991$	−16634.8			−0.533221			−0.266611	+	0.963804i	$0.585904\pi$
$992$		−	8630.86i		−	0.276240i
$993$		−	28084.0i		−	0.897501i
$994$	−31904.5	+	16327.6i	−1.01806	+	0.521006i
$995$	32177.7			1.02523
$996$		−	45727.5i		−	1.45475i
$997$		−	14480.9i		−	0.459995i	−0.973191	−	0.229997i	$-0.926128\pi$
$997$		−	14480.9i		−	0.459995i	0.973191	−	0.229997i	$-0.0738717\pi$
$998$	−9140.29			−0.289910
$999$	98040.5			3.10497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.c.c.160.12	yes	36
7.6	odd	2	inner	161.4.c.c.160.9	✓	36
23.22	odd	2	inner	161.4.c.c.160.11	yes	36
161.160	even	2	inner	161.4.c.c.160.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.c.c.160.9	✓	36	7.6	odd	2	inner
161.4.c.c.160.10	yes	36	161.160	even	2	inner
161.4.c.c.160.11	yes	36	23.22	odd	2	inner
161.4.c.c.160.12	yes	36	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-3.36931 q^{2} +9.90574i q^{3} +3.35226 q^{4} +8.06501 q^{5} -33.3755i q^{6} +(-16.4867 + 8.43733i) q^{7} +15.6597 q^{8} -71.1238 q^{9} -27.1735 q^{10} +67.8577i q^{11} +33.2067i q^{12} -7.51672i q^{13} +(55.5489 - 28.4280i) q^{14} +79.8899i q^{15} -79.5804 q^{16} -88.2202 q^{17} +239.638 q^{18} +92.8569 q^{19} +27.0360 q^{20} +(-83.5780 - 163.313i) q^{21} -228.634i q^{22} +(91.6350 - 61.4006i) q^{23} +155.121i q^{24} -59.9556 q^{25} +25.3262i q^{26} -437.079i q^{27} +(-55.2678 + 28.2842i) q^{28} +109.684 q^{29} -269.174i q^{30} -60.4173i q^{31} +142.854 q^{32} -672.181 q^{33} +297.241 q^{34} +(-132.965 + 68.0471i) q^{35} -238.426 q^{36} +224.309i q^{37} -312.864 q^{38} +74.4587 q^{39} +126.295 q^{40} -188.711i q^{41} +(281.600 + 550.253i) q^{42} -93.3679i q^{43} +227.477i q^{44} -573.614 q^{45} +(-308.747 + 206.878i) q^{46} +50.8467i q^{47} -788.303i q^{48} +(200.623 - 278.208i) q^{49} +202.009 q^{50} -873.887i q^{51} -25.1980i q^{52} -223.248i q^{53} +1472.65i q^{54} +547.273i q^{55} +(-258.176 + 132.126i) q^{56} +919.816i q^{57} -369.559 q^{58} -301.444i q^{59} +267.812i q^{60} +244.869 q^{61} +203.565i q^{62} +(1172.60 - 600.094i) q^{63} +155.324 q^{64} -60.6224i q^{65} +2264.79 q^{66} +476.214i q^{67} -295.737 q^{68} +(608.218 + 907.713i) q^{69} +(448.002 - 229.272i) q^{70} -574.349 q^{71} -1113.77 q^{72} +806.456i q^{73} -755.766i q^{74} -593.905i q^{75} +311.281 q^{76} +(-572.538 - 1118.75i) q^{77} -250.875 q^{78} +825.242i q^{79} -641.817 q^{80} +2409.25 q^{81} +635.827i q^{82} -1377.06 q^{83} +(-280.176 - 547.469i) q^{84} -711.497 q^{85} +314.585i q^{86} +1086.50i q^{87} +1062.63i q^{88} -414.720 q^{89} +1932.68 q^{90} +(63.4210 + 123.926i) q^{91} +(307.185 - 205.831i) q^{92} +598.479 q^{93} -171.318i q^{94} +748.892 q^{95} +1415.07i q^{96} -325.780 q^{97} +(-675.961 + 937.368i) q^{98} -4826.29i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} + 184 q^{4} - 228 q^{8} - 436 q^{9} + 168 q^{16} - 404 q^{18} + 204 q^{23} - 140 q^{25} + 256 q^{29} + 1008 q^{32} - 2040 q^{35} - 4412 q^{36} + 1296 q^{39} - 888 q^{46} + 1916 q^{49} + 4080 q^{50}+ \cdots + 6884 q^{98}+O(q^{100}) \) 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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