LMFDB - Embedded newform 177.4.d.c.176.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(176,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, 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("177.176");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.d (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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.1
Character	$\chi$	$=$	177.176
Dual form			177.4.d.c.176.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.56568 q^{2} +(-1.93387 - 4.82288i) q^{3} +22.9768 q^{4} -10.3188i q^{5} +(10.7633 + 26.8426i) q^{6} -5.13468 q^{7} -83.3558 q^{8} +(-19.5203 + 18.6536i) q^{9} +O(q^{10})$	\(q-5.56568 q^{2} +(-1.93387 - 4.82288i) q^{3} +22.9768 q^{4} -10.3188i q^{5} +(10.7633 + 26.8426i) q^{6} -5.13468 q^{7} -83.3558 q^{8} +(-19.5203 + 18.6536i) q^{9} +57.4309i q^{10} +8.23442 q^{11} +(-44.4341 - 110.814i) q^{12} -53.3544i q^{13} +28.5780 q^{14} +(-49.7661 + 19.9551i) q^{15} +280.117 q^{16} -93.0677i q^{17} +(108.644 - 103.820i) q^{18} -84.1079 q^{19} -237.092i q^{20} +(9.92981 + 24.7639i) q^{21} -45.8301 q^{22} -138.110 q^{23} +(161.199 + 402.015i) q^{24} +18.5232 q^{25} +296.953i q^{26} +(127.714 + 58.0703i) q^{27} -117.978 q^{28} +249.312i q^{29} +(276.982 - 111.064i) q^{30} -203.586i q^{31} -892.196 q^{32} +(-15.9243 - 39.7136i) q^{33} +517.985i q^{34} +52.9836i q^{35} +(-448.513 + 428.600i) q^{36} -60.4290i q^{37} +468.118 q^{38} +(-257.322 + 103.180i) q^{39} +860.128i q^{40} -36.5916i q^{41} +(-55.2661 - 137.828i) q^{42} +368.769i q^{43} +189.200 q^{44} +(192.482 + 201.425i) q^{45} +768.675 q^{46} +112.441 q^{47} +(-541.711 - 1350.97i) q^{48} -316.635 q^{49} -103.094 q^{50} +(-448.854 + 179.981i) q^{51} -1225.91i q^{52} +318.575i q^{53} +(-710.814 - 323.200i) q^{54} -84.9689i q^{55} +428.006 q^{56} +(162.654 + 405.642i) q^{57} -1387.59i q^{58} +(453.071 + 10.2958i) q^{59} +(-1143.46 + 458.504i) q^{60} +214.084i q^{61} +1133.09i q^{62} +(100.231 - 95.7805i) q^{63} +2724.74 q^{64} -550.551 q^{65} +(88.6295 + 221.033i) q^{66} +309.301i q^{67} -2138.39i q^{68} +(267.087 + 666.087i) q^{69} -294.889i q^{70} +830.490i q^{71} +(1627.13 - 1554.89i) q^{72} -110.548i q^{73} +336.328i q^{74} +(-35.8216 - 89.3354i) q^{75} -1932.53 q^{76} -42.2811 q^{77} +(1432.17 - 574.269i) q^{78} -180.521 q^{79} -2890.46i q^{80} +(33.0838 - 728.249i) q^{81} +203.657i q^{82} +339.217 q^{83} +(228.155 + 568.995i) q^{84} -960.343 q^{85} -2052.45i q^{86} +(1202.40 - 482.137i) q^{87} -686.386 q^{88} +743.168 q^{89} +(-1071.29 - 1121.07i) q^{90} +273.958i q^{91} -3173.32 q^{92} +(-981.870 + 393.709i) q^{93} -625.813 q^{94} +867.889i q^{95} +(1725.39 + 4302.95i) q^{96} +439.178i q^{97} +1762.29 q^{98} +(-160.738 + 153.602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	$ 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) $ 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−5.56568			−1.96776			−0.983882	−	0.178819i	$-0.942772\pi$
$2$	−5.56568			−1.96776			−0.983882	+	0.178819i	$0.942772\pi$
$3$	−1.93387	−	4.82288i	−0.372173	−	0.928163i
$3$	−1.93387	−	4.82288i	−0.372173	−	0.928163i
$4$	22.9768			2.87209
$5$		−	10.3188i		−	0.922938i	−0.887156	−	0.461469i	$-0.847323\pi$
$5$		−	10.3188i		−	0.922938i	0.887156	−	0.461469i	$-0.152677\pi$
$6$	10.7633	+	26.8426i	0.732349	+	1.82641i
$7$	−5.13468			−0.277247			−0.138623	−	0.990345i	$-0.544268\pi$
$7$	−5.13468			−0.277247			−0.138623	+	0.990345i	$0.544268\pi$
$8$	−83.3558			−3.68384
$9$	−19.5203	+	18.6536i	−0.722974	+	0.690875i
$10$			57.4309i			1.81612i
$11$	8.23442			0.225706			0.112853	−	0.993612i	$-0.464001\pi$
$11$	8.23442			0.225706			0.112853	+	0.993612i	$0.464001\pi$
$12$	−44.4341	−	110.814i	−1.06892	−	2.66577i
$13$		−	53.3544i		−	1.13830i	−0.822235	−	0.569148i	$-0.807273\pi$
$13$		−	53.3544i		−	1.13830i	0.822235	−	0.569148i	$-0.192727\pi$
$14$	28.5780			0.545556
$15$	−49.7661	+	19.9551i	−0.856637	+	0.343493i
$16$	280.117			4.37683
$17$		−	93.0677i		−	1.32778i	−0.747831	−	0.663889i	$-0.768905\pi$
$17$		−	93.0677i		−	1.32778i	0.747831	−	0.663889i	$-0.231095\pi$
$18$	108.644	−	103.820i	1.42264	−	1.35948i
$19$	−84.1079			−1.01556			−0.507781	−	0.861486i	$-0.669534\pi$
$19$	−84.1079			−1.01556			−0.507781	+	0.861486i	$0.669534\pi$
$20$		−	237.092i		−	2.65076i
$21$	9.92981	+	24.7639i	0.103184	+	0.257330i
$22$	−45.8301			−0.444137
$23$	−138.110			−1.25208			−0.626041	−	0.779790i	$-0.715326\pi$
$23$	−138.110			−1.25208			−0.626041	+	0.779790i	$0.715326\pi$
$24$	161.199	+	402.015i	1.37103	+	3.41921i
$25$	18.5232			0.148186
$26$			296.953i			2.23990i
$27$	127.714	+	58.0703i	0.910317	+	0.413912i
$28$	−117.978			−0.796279
$29$			249.312i			1.59642i	0.602383	+	0.798208i	$0.294218\pi$
$29$			249.312i			1.59642i	−0.602383	+	0.798208i	$0.705782\pi$
$30$	276.982	−	111.064i	1.68566	−	0.675913i
$31$		−	203.586i		−	1.17952i	−0.807579	−	0.589760i	$-0.799222\pi$
$31$		−	203.586i		−	1.17952i	0.807579	−	0.589760i	$-0.200778\pi$
$32$	−892.196			−4.92874
$33$	−15.9243	−	39.7136i	−0.0840019	−	0.209492i
$34$			517.985i			2.61275i
$35$			52.9836i			0.255882i
$36$	−448.513	+	428.600i	−2.07645	+	1.98426i
$37$		−	60.4290i		−	0.268499i	−0.990948	−	0.134249i	$-0.957138\pi$
$37$		−	60.4290i		−	0.268499i	0.990948	−	0.134249i	$-0.0428624\pi$
$38$	468.118			1.99839
$39$	−257.322	+	103.180i	−1.05652	+	0.423644i
$40$			860.128i			3.39996i
$41$		−	36.5916i		−	0.139382i	−0.997569	−	0.0696908i	$-0.977799\pi$
$41$		−	36.5916i		−	0.139382i	0.997569	−	0.0696908i	$-0.0222013\pi$
$42$	−55.2661	−	137.828i	−0.203042	−	0.506365i
$43$			368.769i			1.30783i	0.756568	+	0.653915i	$0.226875\pi$
$43$			368.769i			1.30783i	−0.756568	+	0.653915i	$0.773125\pi$
$44$	189.200			0.648250
$45$	192.482	+	201.425i	0.637635	+	0.667260i
$46$	768.675			2.46380
$47$	112.441			0.348963			0.174482	−	0.984660i	$-0.444175\pi$
$47$	112.441			0.348963			0.174482	+	0.984660i	$0.444175\pi$
$48$	−541.711	−	1350.97i	−1.62894	−	4.06242i
$49$	−316.635			−0.923134
$50$	−103.094			−0.291595
$51$	−448.854	+	179.981i	−1.23240	+	0.494164i
$52$		−	1225.91i		−	3.26929i
$53$			318.575i			0.825655i	0.910809	+	0.412827i	$0.135459\pi$
$53$			318.575i			0.825655i	−0.910809	+	0.412827i	$0.864541\pi$
$54$	−710.814	−	323.200i	−1.79129	−	0.814482i
$55$		−	84.9689i		−	0.208313i
$56$	428.006			1.02133
$57$	162.654	+	405.642i	0.377965	+	0.942608i
$58$		−	1387.59i		−	3.14137i
$59$	453.071	+	10.2958i	0.999742	+	0.0227186i
$59$	453.071	+	10.2958i	0.999742	+	0.0227186i
$60$	−1143.46	+	458.504i	−2.46034	+	0.986544i
$61$			214.084i			0.449355i	0.974433	+	0.224678i	$0.0721329\pi$
$61$			214.084i			0.449355i	−0.974433	+	0.224678i	$0.927867\pi$
$62$			1133.09i			2.32102i
$63$	100.231	−	95.7805i	0.200442	−	0.191543i
$64$	2724.74			5.32175
$65$	−550.551			−1.05058
$66$	88.6295	+	221.033i	0.165296	+	0.412231i
$67$			309.301i			0.563987i	0.959416	+	0.281993i	$0.0909956\pi$
$67$			309.301i			0.563987i	−0.959416	+	0.281993i	$0.909004\pi$
$68$		−	2138.39i		−	3.81351i
$69$	267.087	+	666.087i	0.465992	+	1.16214i
$70$		−	294.889i		−	0.503515i
$71$			830.490i			1.38818i	0.719886	+	0.694092i	$0.244194\pi$
$71$			830.490i			1.38818i	−0.719886	+	0.694092i	$0.755806\pi$
$72$	1627.13	−	1554.89i	2.66332	−	2.54507i
$73$		−	110.548i		−	0.177243i	−0.996065	−	0.0886214i	$-0.971754\pi$
$73$		−	110.548i		−	0.177243i	0.996065	−	0.0886214i	$-0.0282461\pi$
$74$			336.328i			0.528343i
$75$	−35.8216	−	89.3354i	−0.0551509	−	0.137541i
$76$	−1932.53			−2.91679
$77$	−42.2811			−0.0625764
$78$	1432.17	−	574.269i	2.07899	−	0.833631i
$79$	−180.521			−0.257091			−0.128546	−	0.991704i	$-0.541031\pi$
$79$	−180.521			−0.257091			−0.128546	+	0.991704i	$0.541031\pi$
$80$		−	2890.46i		−	4.03955i
$81$	33.0838	−	728.249i	0.0453824	−	0.998970i
$82$			203.657i			0.274270i
$83$	339.217			0.448602			0.224301	−	0.974520i	$-0.427990\pi$
$83$	339.217			0.448602			0.224301	+	0.974520i	$0.427990\pi$
$84$	228.155	+	568.995i	0.296354	+	0.739077i
$85$	−960.343			−1.22546
$86$		−	2052.45i		−	2.57350i
$87$	1202.40	−	482.137i	1.48173	−	0.594143i
$88$	−686.386			−0.831466
$89$	743.168			0.885120			0.442560	−	0.896739i	$-0.354070\pi$
$89$	743.168			0.885120			0.442560	+	0.896739i	$0.354070\pi$
$90$	−1071.29	−	1121.07i	−1.25472	−	1.31301i
$91$			273.958i			0.315589i
$92$	−3173.32			−3.59610
$93$	−981.870	+	393.709i	−1.09479	+	0.438986i
$94$	−625.813			−0.686677
$95$			867.889i			0.937301i
$96$	1725.39	+	4302.95i	1.83434	+	4.57467i
$97$			439.178i			0.459709i	0.973225	+	0.229854i	$0.0738250\pi$
$97$			439.178i			0.459709i	−0.973225	+	0.229854i	$0.926175\pi$
$98$	1762.29			1.81651
$99$	−160.738	+	153.602i	−0.163180	+	0.155935i
$100$	425.604			0.425604
$101$	−1299.12			−1.27988			−0.639939	−	0.768426i	$-0.721040\pi$
$101$	−1299.12			−1.27988			−0.639939	+	0.768426i	$0.721040\pi$
$102$	2498.18	−	1001.72i	2.42506	−	0.972398i
$103$			1553.76i			1.48638i	0.669083	+	0.743188i	$0.266687\pi$
$103$			1553.76i			1.48638i	−0.669083	+	0.743188i	$0.733313\pi$
$104$			4447.40i			4.19330i
$105$	255.533	−	102.463i	0.237500	−	0.0952323i
$106$		−	1773.09i		−	1.62469i
$107$		−	1293.66i		−	1.16881i	−0.811462	−	0.584406i	$-0.801328\pi$
$107$		−	1293.66i		−	1.16881i	0.811462	−	0.584406i	$-0.198672\pi$
$108$	2934.45	+	1334.27i	2.61452	+	1.18880i
$109$		−	1671.05i		−	1.46841i	−0.678926	−	0.734207i	$-0.737554\pi$
$109$		−	1671.05i		−	1.46841i	0.678926	−	0.734207i	$-0.262446\pi$
$110$			472.910i			0.409911i
$111$	−291.442	+	116.862i	−0.249211	+	0.0999282i
$112$	−1438.31			−1.21346
$113$	−121.231			−0.100924			−0.0504621	−	0.998726i	$-0.516069\pi$
$113$	−121.231			−0.100924			−0.0504621	+	0.998726i	$0.516069\pi$
$114$	−905.279	−	2257.67i	−0.743747	−	1.85483i
$115$			1425.12i			1.15559i
$116$			5728.38i			4.58506i
$117$	995.254	+	1041.49i	0.786421	+	0.822958i
$118$	−2521.64	−	57.3030i	−1.96726	−	0.0447048i
$119$			477.873i			0.368122i
$120$	4148.29	−	1663.38i	3.15571	−	1.26537i
$121$	−1263.19			−0.949057
$122$		−	1191.52i		−	0.884225i
$123$	−176.477	+	70.7634i	−0.129369	+	0.0518741i
$124$		−	4677.74i		−	3.38769i
$125$		−	1480.98i		−	1.05970i
$126$	−557.851	+	533.083i	−0.394423	+	0.376911i
$127$	−1216.64			−0.850071			−0.425035	−	0.905177i	$-0.639738\pi$
$127$	−1216.64			−0.850071			−0.425035	+	0.905177i	$0.639738\pi$
$128$	−8027.44			−5.54322
$129$	1778.53	−	713.151i	1.21388	−	0.486740i
$130$	3064.19			2.06729
$131$	−1764.68			−1.17695			−0.588477	−	0.808514i	$-0.700272\pi$
$131$	−1764.68			−1.17695			−0.588477	+	0.808514i	$0.700272\pi$
$132$	−365.889	−	912.489i	−0.241261	−	0.601682i
$133$	431.868			0.281561
$134$		−	1721.47i		−	1.10979i
$135$	599.213	−	1317.85i	0.382015	−	0.840166i
$136$			7757.73i			4.89132i
$137$		−	1726.01i		−	1.07637i	−0.842826	−	0.538186i	$-0.819110\pi$
$137$		−	1726.01i		−	1.07637i	0.842826	−	0.538186i	$-0.180890\pi$
$138$	−1486.52	−	3707.23i	−0.916962	−	2.28681i
$139$	−720.662			−0.439754			−0.219877	−	0.975528i	$-0.570566\pi$
$139$	−720.662			−0.439754			−0.219877	+	0.975528i	$0.570566\pi$
$140$			1217.39i			0.734916i
$141$	−217.447	−	542.291i	−0.129875	−	0.323895i
$142$		−	4622.24i		−	2.73162i
$143$		−	439.342i		−	0.256921i
$144$	−5467.97	+	5225.21i	−3.16434	+	3.02385i
$145$	2572.59			1.47339
$146$			615.277i			0.348772i
$147$	612.331	+	1527.09i	0.343566	+	0.856819i
$148$		−	1388.46i		−	0.771155i
$149$	1960.40			1.07787			0.538933	−	0.842348i	$-0.318827\pi$
$149$	1960.40			1.07787			0.538933	+	0.842348i	$0.318827\pi$
$150$	199.371	+	497.212i	0.108524	+	0.270648i
$151$			2940.00i			1.58446i	0.610221	+	0.792231i	$0.291080\pi$
$151$			2940.00i			1.58446i	−0.610221	+	0.792231i	$0.708920\pi$
$152$	7010.89			3.74117
$153$	1736.05	+	1816.71i	0.917329	+	0.959949i
$154$	235.323			0.123136
$155$	−2100.75			−1.08862
$156$	−5912.42	+	2370.75i	−3.03444	+	1.21674i
$157$		−	2907.11i		−	1.47779i	−0.673821	−	0.738895i	$-0.735348\pi$
$157$		−	2907.11i		−	1.47779i	0.673821	−	0.738895i	$-0.264652\pi$
$158$	1004.72			0.505895
$159$	1536.45	−	616.083i	0.766342	−	0.307287i
$160$			9206.36i			4.54892i
$161$	709.151			0.347136
$162$	−184.134	+	4053.20i	−0.0893019	+	1.96574i
$163$	−1619.97			−0.778442			−0.389221	−	0.921144i	$-0.627256\pi$
$163$	−1619.97			−0.778442			−0.389221	+	0.921144i	$0.627256\pi$
$164$		−	840.756i		−	0.400317i
$165$	−409.795	+	164.319i	−0.193348	+	0.0775285i
$166$	−1887.97			−0.882742
$167$		−	1514.57i		−	0.701804i	−0.936412	−	0.350902i	$-0.885875\pi$
$167$		−	1514.57i		−	0.701804i	0.936412	−	0.350902i	$-0.114125\pi$
$168$	−827.707	−	2064.22i	−0.380113	−	0.947964i
$169$	−649.693			−0.295718
$170$	5344.96			2.41141
$171$	1641.81	−	1568.92i	0.734225	−	0.701627i
$172$			8473.11i			3.75621i
$173$	−1756.60			−0.771977			−0.385989	−	0.922503i	$-0.626140\pi$
$173$	−1756.60			−0.771977			−0.385989	+	0.922503i	$0.626140\pi$
$174$	−6692.17	+	2683.42i	−2.91570	+	1.16913i
$175$	−95.1110			−0.0410841
$176$	2306.60			0.987879
$177$	−826.524	−	2205.01i	−0.350991	−	0.936379i
$178$	−4136.23			−1.74171
$179$	−2833.03			−1.18296			−0.591481	−	0.806319i	$-0.701457\pi$
$179$	−2833.03			−1.18296			−0.591481	+	0.806319i	$0.701457\pi$
$180$	4422.62	+	4628.10i	1.83135	+	1.91643i
$181$	344.955			0.141659			0.0708295	−	0.997488i	$-0.477435\pi$
$181$	344.955			0.141659			0.0708295	+	0.997488i	$0.477435\pi$
$182$		−	1524.76i		−	0.621005i
$183$	1032.50	−	414.011i	0.417075	−	0.167238i
$184$	11512.3			4.61247
$185$	−623.552			−0.247808
$186$	5464.77	−	2191.26i	2.15428	−	0.863821i
$187$		−	766.358i		−	0.299688i
$188$	2583.54			1.00226
$189$	−655.770	−	298.173i	−0.252382	−	0.114756i
$190$		−	4830.39i		−	1.84439i
$191$	4289.37			1.62496			0.812482	−	0.582986i	$-0.198116\pi$
$191$	4289.37			1.62496			0.812482	+	0.582986i	$0.198116\pi$
$192$	−5269.29	−	13141.1i	−1.98062	−	4.93946i
$193$	−1977.19			−0.737415			−0.368708	−	0.929545i	$-0.620200\pi$
$193$	−1977.19			−0.737415			−0.368708	+	0.929545i	$0.620200\pi$
$194$		−	2444.32i		−	0.904598i
$195$	1064.69	+	2655.24i	0.390997	+	0.975107i
$196$	−7275.25			−2.65133
$197$			13.2281i			0.00478408i	0.999997	+	0.00239204i	$0.000761410\pi$
$197$			13.2281i			0.00478408i	−0.999997	+	0.00239204i	$0.999239\pi$
$198$	894.617	−	854.898i	0.321099	−	0.306843i
$199$	4236.79			1.50924			0.754618	−	0.656164i	$-0.227822\pi$
$199$	4236.79			1.50924			0.754618	+	0.656164i	$0.227822\pi$
$200$	−1544.02			−0.545894
$201$	1491.72	−	598.148i	0.523472	−	0.209901i
$202$	7230.50			2.51850
$203$		−	1280.14i		−	0.442601i
$204$	−10313.2	+	4135.38i	−3.53956	+	1.41929i
$205$	−377.580			−0.128641
$206$		−	8647.74i		−	2.92484i
$207$	2695.95	−	2576.25i	0.905223	−	0.865033i
$208$		−	14945.5i		−	4.98213i
$209$	−692.580			−0.229219
$210$	−1422.22	+	570.278i	−0.467344	+	0.187395i
$211$			2664.87i			0.869466i	0.900559	+	0.434733i	$0.143157\pi$
$211$			2664.87i			0.869466i	−0.900559	+	0.434733i	$0.856843\pi$
$212$			7319.83i			2.37136i
$213$	4005.35	−	1606.06i	1.28846	−	0.516645i
$214$			7200.09i			2.29995i
$215$	3805.24			1.20705
$216$	−10645.7	−	4840.50i	−3.35346	−	1.52479i
$217$			1045.35i			0.327018i
$218$			9300.50i			2.88949i
$219$	−533.162	+	213.786i	−0.164510	+	0.0659650i
$220$		−	1952.31i		−	0.598294i
$221$	−4965.57			−1.51141
$222$	1622.07	−	650.415i	0.490388	−	0.196635i
$223$	−4836.11			−1.45224			−0.726120	−	0.687567i	$-0.758679\pi$
$223$	−4836.11			−1.45224			−0.726120	+	0.687567i	$0.758679\pi$
$224$	4581.15			1.36648
$225$	−361.579	+	345.526i	−0.107135	+	0.102378i
$226$	674.731			0.198595
$227$	−2329.04			−0.680986			−0.340493	−	0.940247i	$-0.610594\pi$
$227$	−2329.04			−0.680986			−0.340493	+	0.940247i	$0.610594\pi$
$228$	3737.26	+	9320.35i	1.08555	+	2.70726i
$229$		−	4734.44i		−	1.36620i	−0.730323	−	0.683102i	$-0.760630\pi$
$229$		−	4734.44i		−	1.36620i	0.730323	−	0.683102i	$-0.239370\pi$
$230$		−	7931.77i		−	2.27394i
$231$	81.7662	+	203.917i	0.0232893	+	0.0580811i
$232$		−	20781.6i		−	5.88094i
$233$	−2827.38			−0.794971			−0.397485	−	0.917609i	$-0.630117\pi$
$233$	−2827.38			−0.794971			−0.397485	+	0.917609i	$0.630117\pi$
$234$	−5539.26	−	5796.62i	−1.54749	−	1.61939i
$235$		−	1160.26i		−	0.322071i
$236$	10410.1	+	236.564i	2.87135	+	0.0652500i
$237$	349.105	+	870.632i	0.0956826	+	0.238623i
$238$		−	2659.69i		−	0.724378i
$239$			640.800i			0.173431i	0.996233	+	0.0867153i	$0.0276371\pi$
$239$			640.800i			0.173431i	−0.996233	+	0.0867153i	$0.972363\pi$
$240$	−13940.4	+	5589.78i	−3.74936	+	1.50341i
$241$	−1123.12			−0.300194			−0.150097	−	0.988671i	$-0.547959\pi$
$241$	−1123.12			−0.300194			−0.150097	+	0.988671i	$0.547959\pi$
$242$	7030.53			1.86752
$243$	−3576.23	+	1248.78i	−0.944097	+	0.329668i
$244$			4918.96i			1.29059i
$245$			3267.28i			0.851995i
$246$	982.213	−	393.846i	0.254567	−	0.102076i
$247$			4487.53i			1.15601i
$248$			16970.1i			4.34516i
$249$	−656.002	−	1636.00i	−0.166958	−	0.416376i
$250$			8242.66i			2.08525i
$251$		−	4798.42i		−	1.20667i	−0.797489	−	0.603333i	$-0.793839\pi$
$251$		−	4798.42i		−	1.20667i	0.797489	−	0.603333i	$-0.206161\pi$
$252$	2302.97	−	2200.73i	0.575689	−	0.550130i
$253$	−1137.25			−0.282603
$254$	6771.40			1.67274
$255$	1857.18	+	4631.62i	0.456082	+	1.13742i
$256$	22880.2			5.58599
$257$			719.646i			0.174670i	0.996179	+	0.0873351i	$0.0278351\pi$
$257$			719.646i			0.174670i	−0.996179	+	0.0873351i	$0.972165\pi$
$258$	−9898.71	+	3969.17i	−2.38863	+	0.957789i
$259$			310.284i			0.0744405i
$260$	−12649.9			−3.01736
$261$	−4650.57	−	4866.64i	−1.10292	−	1.15417i
$262$	9821.64			2.31597
$263$			1763.93i			0.413569i	0.978386	+	0.206785i	$0.0663000\pi$
$263$			1763.93i			0.413569i	−0.978386	+	0.206785i	$0.933700\pi$
$264$	1327.38	+	3310.36i	0.309450	+	0.771736i
$265$	3287.30			0.762028
$266$	−2403.64			−0.554047
$267$	−1437.19	−	3584.21i	−0.329418	−	0.821536i
$268$			7106.73i			1.61982i
$269$	−4111.19			−0.931834			−0.465917	−	0.884828i	$-0.654276\pi$
$269$	−4111.19			−0.931834			−0.465917	+	0.884828i	$0.654276\pi$
$270$	−3335.03	+	7334.72i	−0.751716	+	1.65325i
$271$	−4331.06			−0.970824			−0.485412	−	0.874286i	$-0.661330\pi$
$271$	−4331.06			−0.970824			−0.485412	+	0.874286i	$0.661330\pi$
$272$		−	26069.9i		−	5.81147i
$273$	1321.27	−	529.799i	0.292918	−	0.117454i
$274$			9606.41i			2.11805i
$275$	152.528			0.0334465
$276$	6136.78	+	15304.5i	1.33837	+	3.33777i
$277$	−2518.92			−0.546381			−0.273190	−	0.961960i	$-0.588079\pi$
$277$	−2518.92			−0.546381			−0.273190	+	0.961960i	$0.588079\pi$
$278$	4010.97			0.865332
$279$	3797.62	+	3974.06i	0.814901	+	0.852762i
$280$		−	4416.49i		−	0.942627i
$281$			506.498i			0.107527i	0.998554	+	0.0537636i	$0.0171218\pi$
$281$			506.498i			0.107527i	−0.998554	+	0.0537636i	$0.982878\pi$
$282$	1210.24	+	3018.22i	0.255563	+	0.637348i
$283$		−	599.808i		−	0.125989i	−0.998014	−	0.0629945i	$-0.979935\pi$
$283$		−	599.808i		−	0.125989i	0.998014	−	0.0629945i	$-0.0200651\pi$
$284$			19082.0i			3.98700i
$285$	4185.72	−	1678.39i	0.869968	−	0.348838i
$286$			2445.24i			0.505559i
$287$			187.886i			0.0386431i
$288$	17415.9	−	16642.7i	3.56335	−	3.40514i
$289$	−3748.60			−0.762995
$290$	−14318.2			−2.89929
$291$	2118.10	−	849.313i	0.426685	−	0.171091i
$292$		−	2540.05i		−	0.509058i
$293$			2503.29i			0.499126i	0.968359	+	0.249563i	$0.0802870\pi$
$293$			2503.29i			0.499126i	−0.968359	+	0.249563i	$0.919713\pi$
$294$	−3408.04	−	8499.30i	−0.676057	−	1.68602i
$295$	106.240	−	4675.13i	0.0209679	−	0.922699i
$296$			5037.11i			0.989108i
$297$	1051.65	+	478.175i	0.205464	+	0.0934226i
$298$	−10910.9			−2.12099
$299$			7368.77i			1.42524i
$300$	−823.063	−	2052.64i	−0.158399	−	0.395030i
$301$		−	1893.51i		−	0.362592i
$302$		−	16363.1i		−	3.11785i
$303$	2512.34	+	6265.52i	0.476337	+	1.18794i
$304$	−23560.1			−4.44495
$305$	2209.08			0.414727
$306$	−9662.30	−	10111.2i	−1.80509	−	1.88895i
$307$	760.651			0.141409			0.0707046	−	0.997497i	$-0.477475\pi$
$307$	760.651			0.141409			0.0707046	+	0.997497i	$0.477475\pi$
$308$	−971.483			−0.179725
$309$	7493.60	−	3004.77i	1.37960	−	0.553190i
$310$	11692.1			2.14215
$311$		−	1585.14i		−	0.289020i	−0.989503	−	0.144510i	$-0.953839\pi$
$311$		−	1585.14i		−	0.289020i	0.989503	−	0.144510i	$-0.0461606\pi$
$312$	21449.3	−	8600.69i	3.89207	−	1.56064i
$313$		−	9851.30i		−	1.77901i	−0.456930	−	0.889503i	$-0.651051\pi$
$313$		−	9851.30i		−	1.77901i	0.456930	−	0.889503i	$-0.348949\pi$
$314$			16180.1i			2.90794i
$315$	−988.336	−	1034.25i	−0.176782	−	0.184996i
$316$	−4147.79			−0.738391
$317$			8857.22i			1.56931i	0.619933	+	0.784655i	$0.287160\pi$
$317$			8857.22i			1.56931i	−0.619933	+	0.784655i	$0.712840\pi$
$318$	−8551.38	+	3428.92i	−1.50798	+	0.604668i
$319$			2052.94i			0.360321i
$320$		−	28115.9i		−	4.91165i
$321$	−6239.16	+	2501.77i	−1.08485	+	0.435001i
$322$	−3946.90			−0.683082
$323$			7827.73i			1.34844i
$324$	760.159	−	16732.8i	0.130343	−	2.86914i
$325$		−	988.297i		−	0.168680i
$326$	9016.25			1.53179
$327$	−8059.25	+	3231.58i	−1.36293	+	0.546505i
$328$			3050.12i			0.513460i
$329$	−577.351			−0.0967489
$330$	2280.79	−	914.546i	0.380464	−	0.152558i
$331$	6102.28			1.01333			0.506664	−	0.862144i	$-0.330879\pi$
$331$	6102.28			1.01333			0.506664	+	0.862144i	$0.330879\pi$
$332$	7794.11			1.28843
$333$	1127.22	+	1179.59i	0.185499	+	0.194118i
$334$			8429.62i			1.38098i
$335$	3191.60			0.520525
$336$	2781.51	+	6936.81i	0.451619	+	1.12629i
$337$		−	461.351i		−	0.0745738i	−0.999305	−	0.0372869i	$-0.988128\pi$
$337$		−	461.351i		−	0.0745738i	0.999305	−	0.0372869i	$-0.0118715\pi$
$338$	3615.98			0.581904
$339$	234.445	+	584.681i	0.0375613	+	0.0936741i
$340$	−22065.6			−3.51963
$341$		−	1676.41i		−	0.266225i
$342$	−9137.79	+	8732.10i	−1.44478	+	1.38064i
$343$	3387.02			0.533183
$344$		−	30739.0i		−	4.81784i
$345$	6873.19	−	2756.00i	1.07258	−	0.430081i
$346$	9776.69			1.51907
$347$	−11976.1			−1.85277			−0.926383	−	0.376583i	$-0.877099\pi$
$347$	−11976.1			−1.85277			−0.926383	+	0.376583i	$0.877099\pi$
$348$	27627.3	−	11077.9i	4.25568	−	1.70644i
$349$		−	4647.83i		−	0.712873i	−0.934320	−	0.356437i	$-0.883992\pi$
$349$		−	4647.83i		−	0.712873i	0.934320	−	0.356437i	$-0.116008\pi$
$350$	529.357			0.0808438
$351$	3098.31	−	6814.10i	0.471155	−	1.03621i
$352$	−7346.72			−1.11245
$353$	3004.19			0.452966			0.226483	−	0.974015i	$-0.427277\pi$
$353$	3004.19			0.452966			0.226483	+	0.974015i	$0.427277\pi$
$354$	4600.17	+	12272.4i	0.690667	+	1.84257i
$355$	8569.63			1.28121
$356$	17075.6			2.54215
$357$	2304.72	−	924.145i	0.341678	−	0.137005i
$358$	15767.7			2.32779
$359$		−	3839.91i		−	0.564520i	−0.959338	−	0.282260i	$-0.908916\pi$
$359$		−	3839.91i		−	0.564520i	0.959338	−	0.282260i	$-0.0910841\pi$
$360$	−16044.5	−	16790.0i	−2.34895	−	2.45808i
$361$	215.146			0.0313670
$362$	−1919.91			−0.278752
$363$	2442.85	+	6092.23i	0.353214	+	0.880879i
$364$			6294.67i			0.906402i
$365$	−1140.72			−0.163584
$366$	−5746.57	+	2304.25i	−0.820705	+	0.329085i
$367$			3094.76i			0.440178i	0.975480	+	0.220089i	$0.0706348\pi$
$367$			3094.76i			0.440178i	−0.975480	+	0.220089i	$0.929365\pi$
$368$	−38687.0			−5.48016
$369$	682.566	+	714.279i	0.0962953	+	0.100769i
$370$	3470.49			0.487627
$371$		−	1635.78i		−	0.228910i
$372$	−22560.2	+	9046.15i	−3.14433	+	1.26081i
$373$	−4.21229			−0.000584729			−0.000292365	−	1.00000i	$-0.500093\pi$
$373$	−4.21229			−0.000584729			−0.000292365		1.00000i	$0.500093\pi$
$374$			4265.30i			0.589715i
$375$	−7142.59	+	2864.03i	−0.983578	+	0.394394i
$376$	−9372.64			−1.28552
$377$	13301.9			1.81719
$378$	3649.81	+	1659.53i	0.496629	+	0.225812i
$379$	6414.25			0.869335			0.434667	−	0.900591i	$-0.356866\pi$
$379$	6414.25			0.869335			0.434667	+	0.900591i	$0.356866\pi$
$380$			19941.3i			2.69202i
$381$	2352.82	+	5867.69i	0.316374	+	0.789005i
$382$	−23873.3			−3.19755
$383$		−	5181.02i		−	0.691221i	−0.938378	−	0.345611i	$-0.887672\pi$
$383$		−	5181.02i		−	0.691221i	0.938378	−	0.345611i	$-0.112328\pi$
$384$	15524.0	+	38715.4i	2.06304	+	5.14501i
$385$			436.289i			0.0577541i
$386$	11004.4			1.45106
$387$	−6878.88	−	7198.48i	−0.903548	−	0.945527i
$388$			10090.9i			1.32033i
$389$			459.528i			0.0598946i	0.999551	+	0.0299473i	$0.00953395\pi$
$389$			459.528i			0.0598946i	−0.999551	+	0.0299473i	$0.990466\pi$
$390$	−5925.75	−	14778.2i	−0.769389	−	1.91878i
$391$			12853.6i			1.66249i
$392$	26393.4			3.40068
$393$	3412.66	+	8510.84i	0.438031	+	1.09240i
$394$		−	73.6233i		−	0.00941393i
$395$			1862.75i			0.237279i
$396$	−3693.24	+	3529.27i	−0.468668	+	0.447860i
$397$			107.728i			0.0136189i	0.999977	+	0.00680946i	$0.00216754\pi$
$397$			107.728i			0.0136189i	−0.999977	+	0.00680946i	$0.997832\pi$
$398$	−23580.6			−2.96982
$399$	−835.176	−	2082.84i	−0.104790	−	0.261335i
$400$	5188.68			0.648586
$401$	588.735			0.0733168			0.0366584	−	0.999328i	$-0.488329\pi$
$401$	588.735			0.0733168			0.0366584	+	0.999328i	$0.488329\pi$
$402$	−8302.43	+	3329.10i	−1.03007	+	0.413035i
$403$	−10862.2			−1.34264
$404$	−29849.7			−3.67593
$405$	−7514.62	−	341.384i	−0.921987	−	0.0418852i
$406$			7124.83i			0.870934i
$407$		−	497.597i		−	0.0606019i
$408$	37414.6	−	15002.4i	4.53995	−	1.82042i
$409$		−	2665.79i		−	0.322286i	−0.986931	−	0.161143i	$-0.948482\pi$
$409$		−	2665.79i		−	0.322286i	0.986931	−	0.161143i	$-0.0515181\pi$
$410$	2101.49			0.253134
$411$	−8324.33	+	3337.88i	−0.999049	+	0.400597i
$412$			35700.4i			4.26901i
$413$	−2326.37	−	52.8656i	−0.277175	−	0.00629866i
$414$	−15004.8	+	14338.6i	−1.78127	+	1.70218i
$415$		−	3500.30i		−	0.414031i
$416$			47602.6i			5.61036i
$417$	1393.67	+	3475.67i	0.163665	+	0.408163i
$418$	3854.68			0.451049
$419$	8979.23			1.04693			0.523466	−	0.852047i	$-0.324639\pi$
$419$	8979.23			1.04693			0.523466	+	0.852047i	$0.324639\pi$
$420$	5871.32	−	2354.27i	0.682122	−	0.273516i
$421$		−	10132.1i		−	1.17294i	−0.809972	−	0.586468i	$-0.800518\pi$
$421$		−	10132.1i		−	1.17294i	0.809972	−	0.586468i	$-0.199482\pi$
$422$		−	14831.8i		−	1.71090i
$423$	−2194.89	+	2097.44i	−0.252291	+	0.241090i
$424$		−	26555.1i		−	3.04158i
$425$		−	1723.92i		−	0.196758i
$426$	−22292.5	+	8938.81i	−2.53539	+	1.01664i
$427$		−	1099.25i		−	0.124582i
$428$		−	29724.1i		−	3.35694i
$429$	−2118.89	+	849.631i	−0.238464	+	0.0956191i
$430$	−21178.7			−2.37518
$431$	−8993.68			−1.00513			−0.502564	−	0.864540i	$-0.667610\pi$
$431$	−8993.68			−1.00513			−0.502564	+	0.864540i	$0.667610\pi$
$432$	35774.9	+	16266.5i	3.98431	+	1.81163i
$433$	8835.09			0.980571			0.490286	−	0.871562i	$-0.336892\pi$
$433$	8835.09			0.980571			0.490286	+	0.871562i	$0.336892\pi$
$434$		−	5818.08i		−	0.643494i
$435$	−4975.05	−	12407.3i	−0.548357	−	1.36755i
$436$		−	38395.2i		−	4.21742i
$437$	11616.1			1.27157
$438$	2967.41	−	1189.87i	0.323717	−	0.129804i
$439$	−8504.84			−0.924633			−0.462317	−	0.886715i	$-0.652982\pi$
$439$	−8504.84			−0.924633			−0.462317	+	0.886715i	$0.652982\pi$
$440$			7082.65i			0.767392i
$441$	6180.81	−	5906.39i	0.667402	−	0.637771i
$442$	27636.8			2.97409
$443$	−10992.3			−1.17892			−0.589460	−	0.807798i	$-0.700659\pi$
$443$	−10992.3			−1.17892			−0.589460	+	0.807798i	$0.700659\pi$
$444$	−6696.38	+	2685.11i	−0.715757	+	0.287003i
$445$		−	7668.57i		−	0.816911i
$446$	26916.2			2.85767
$447$	−3791.16	−	9454.76i	−0.401153	−	1.00044i
$448$	−13990.7			−1.47544
$449$		−	14359.3i		−	1.50926i	−0.656150	−	0.754630i	$-0.727816\pi$
$449$		−	14359.3i		−	1.50926i	0.656150	−	0.754630i	$-0.272184\pi$
$450$	2012.43	−	1923.09i	0.210816	−	0.201456i
$451$		−	301.310i		−	0.0314593i
$452$	−2785.49			−0.289864
$453$	14179.3	−	5685.58i	1.47064	−	0.589695i
$454$	12962.7			1.34002
$455$	2826.91			0.291269
$456$	−13558.1	−	33812.6i	−1.39236	−	3.47242i
$457$		−	4257.86i		−	0.435830i	−0.975968	−	0.217915i	$-0.930075\pi$
$457$		−	4257.86i		−	0.435830i	0.975968	−	0.217915i	$-0.0699255\pi$
$458$			26350.4i			2.68837i
$459$	5404.47	−	11886.0i	0.549584	−	1.20870i
$460$			32744.7i			3.31898i
$461$		−	18982.3i		−	1.91778i	−0.283785	−	0.958888i	$-0.591590\pi$
$461$		−	18982.3i		−	1.91778i	0.283785	−	0.958888i	$-0.408410\pi$
$462$	−455.084	−	1134.93i	−0.0458278	−	0.114290i
$463$			10943.5i			1.09846i	0.835670	+	0.549232i	$0.185080\pi$
$463$			10943.5i			1.09846i	−0.835670	+	0.549232i	$0.814920\pi$
$464$			69836.6i			6.98724i
$465$	4062.58	+	10131.7i	0.405157	+	1.01042i
$466$	15736.3			1.56431
$467$	−8060.59			−0.798714			−0.399357	−	0.916795i	$-0.630767\pi$
$467$	−8060.59			−0.798714			−0.399357	+	0.916795i	$0.630767\pi$
$468$	22867.7	+	23930.2i	2.25868	+	2.36361i
$469$		−	1588.16i		−	0.156364i
$470$			6457.61i			0.633760i
$471$	−14020.7	+	5621.98i	−1.37163	+	0.549994i
$472$	−37766.1	−	858.214i	−3.68289	−	0.0836917i
$473$			3036.60i			0.295186i
$474$	−1943.00	−	4845.66i	−0.188281	−	0.469553i
$475$	−1557.95			−0.150492
$476$			10980.0i			1.05728i
$477$	−5942.59	−	6218.69i	−0.570424	−	0.596927i
$478$		−	3566.49i		−	0.341271i
$479$			7956.38i			0.758948i	0.925202	+	0.379474i	$0.123895\pi$
$479$			7956.38i			0.758948i	−0.925202	+	0.379474i	$0.876105\pi$
$480$	44401.1	−	17803.9i	4.22214	−	1.69299i
$481$	−3224.15			−0.305631
$482$	6250.94			0.590710
$483$	−1371.40	−	3420.15i	−0.129195	−	0.322199i
$484$	−29024.1			−2.72578
$485$	4531.77			0.424283
$486$	19904.2	−	6950.30i	1.85776	−	0.648708i
$487$	5472.03			0.509161			0.254580	−	0.967052i	$-0.418063\pi$
$487$	5472.03			0.509161			0.254580	+	0.967052i	$0.418063\pi$
$488$		−	17845.2i		−	1.65535i
$489$	3132.82	+	7812.93i	0.289716	+	0.722522i
$490$		−	18184.6i		−	1.67653i
$491$		−	7832.96i		−	0.719952i	−0.932962	−	0.359976i	$-0.882785\pi$
$491$		−	7832.96i		−	0.719952i	0.932962	−	0.359976i	$-0.117215\pi$
$492$	−4054.86	+	1625.91i	−0.371560	+	0.148987i
$493$	23202.9			2.11969
$494$		−	24976.1i		−	2.27476i
$495$	1584.98	+	1658.62i	0.143918	+	0.150605i
$496$		−	57028.0i		−	5.16256i
$497$		−	4264.30i		−	0.384870i
$498$	3651.10	+	9105.47i	0.328533	+	0.819329i
$499$	7091.23			0.636166			0.318083	−	0.948063i	$-0.396961\pi$
$499$	7091.23			0.636166			0.318083	+	0.948063i	$0.396961\pi$
$500$		−	34028.2i		−	3.04357i
$501$	−7304.60	+	2928.99i	−0.651388	+	0.261193i
$502$			26706.4i			2.37443i
$503$	−10710.6			−0.949427			−0.474714	−	0.880140i	$-0.657448\pi$
$503$	−10710.6			−0.949427			−0.474714	+	0.880140i	$0.657448\pi$
$504$	−8354.80	+	7983.86i	−0.738397	+	0.705614i
$505$			13405.3i			1.18125i
$506$	6329.59			0.556096
$507$	1256.42	+	3133.39i	0.110059	+	0.274475i
$508$	−27954.4			−2.44148
$509$	−15860.7			−1.38116			−0.690581	−	0.723255i	$-0.742645\pi$
$509$	−15860.7			−1.38116			−0.690581	+	0.723255i	$0.742645\pi$
$510$	−10336.5	−	25778.1i	−0.897463	−	2.23818i
$511$			567.631i			0.0491400i
$512$	−63124.5			−5.44870
$513$	−10741.8	−	4884.17i	−0.924483	−	0.420354i
$514$		−	4005.31i		−	0.343710i
$515$	16032.9			1.37183
$516$	40864.8	−	16385.9i	3.48638	−	1.39796i
$517$	925.889			0.0787632
$518$		−	1726.94i		−	0.146481i
$519$	3397.04	+	8471.88i	0.287310	+	0.716521i
$520$	45891.6			3.87016
$521$			4684.28i			0.393901i	0.980413	+	0.196950i	$0.0631038\pi$
$521$			4684.28i			0.393901i	−0.980413	+	0.196950i	$0.936896\pi$
$522$	25883.6	+	27086.1i	2.17029	+	2.27113i
$523$	1065.36			0.0890727			0.0445363	−	0.999008i	$-0.485819\pi$
$523$	1065.36			0.0890727			0.0445363	+	0.999008i	$0.485819\pi$
$524$	−40546.6			−3.38032
$525$	183.932	+	458.709i	0.0152904	+	0.0381328i
$526$		−	9817.48i		−	0.813807i
$527$	−18947.3			−1.56614
$528$	−4460.67	−	11124.5i	−0.367662	−	0.916913i
$529$	6907.34			0.567711
$530$	−18296.1			−1.49949
$531$	−9036.13	+	8250.44i	−0.738483	+	0.674272i
$532$	9922.92			0.808671
$533$	−1952.32			−0.158658
$534$	7998.94	+	19948.6i	0.648217	+	1.61659i
$535$	−13349.0			−1.07874
$536$		−	25782.0i		−	2.07764i
$537$	5478.70	+	13663.3i	0.440267	+	1.09798i
$538$	22881.5			1.83363
$539$	−2607.30			−0.208357
$540$	13768.0	−	30279.9i	1.09718	−	2.41304i
$541$		−	11849.6i		−	0.941688i	−0.882216	−	0.470844i	$-0.843949\pi$
$541$		−	11849.6i		−	0.941688i	0.882216	−	0.470844i	$-0.156051\pi$
$542$	24105.3			1.91035
$543$	−667.098	−	1663.67i	−0.0527217	−	0.131483i
$544$			83034.7i			6.54427i
$545$	−17243.1			−1.35525
$546$	−7353.74	+	2948.69i	−0.576394	+	0.231121i
$547$	15106.1			1.18079			0.590395	−	0.807114i	$-0.298972\pi$
$547$	15106.1			1.18079			0.590395	+	0.807114i	$0.298972\pi$
$548$		−	39658.1i		−	3.09144i
$549$	−3993.45	−	4178.99i	−0.310448	−	0.324872i
$550$	−848.922			−0.0658149
$551$		−	20969.1i		−	1.62126i
$552$	−22263.2	−	55522.2i	−1.71664	−	4.28113i
$553$	926.919			0.0712778
$554$	14019.5			1.07515
$555$	1205.87	+	3007.31i	0.0922275	+	0.230006i
$556$	−16558.5			−1.26301
$557$			15577.1i			1.18496i	0.805585	+	0.592480i	$0.201851\pi$
$557$			15577.1i			1.18496i	−0.805585	+	0.592480i	$0.798149\pi$
$558$	−21136.3	−	22118.3i	−1.60353	−	1.67803i
$559$	19675.4			1.48870
$560$			14841.6i			1.11995i
$561$	−3696.05	+	1482.04i	−0.278159	+	0.111536i
$562$		−	2819.01i		−	0.211588i
$563$	−184.983			−0.0138474			−0.00692370	−	0.999976i	$-0.502204\pi$
$563$	−184.983			−0.0138474			−0.00692370	+	0.999976i	$0.502204\pi$
$564$	−4996.23	−	12460.1i	−0.373013	−	0.930256i
$565$			1250.95i			0.0931467i
$566$			3338.34i			0.247917i
$567$	−169.875	+	3739.33i	−0.0125821	+	0.276961i
$568$		−	69226.2i		−	5.11385i
$569$	22124.0			1.63003			0.815014	−	0.579441i	$-0.196729\pi$
$569$	22124.0			1.63003			0.815014	+	0.579441i	$0.196729\pi$
$570$	−23296.4	+	9341.35i	−1.71189	+	0.686432i
$571$			9518.89i			0.697641i	0.937190	+	0.348820i	$0.113418\pi$
$571$			9518.89i			0.697641i	−0.937190	+	0.348820i	$0.886582\pi$
$572$		−	10094.7i		−	0.737901i
$573$	−8295.09	−	20687.1i	−0.604768	−	1.50823i
$574$		−	1045.71i		−	0.0760405i
$575$	−2558.24			−0.185541
$576$	−53187.7	+	50826.3i	−3.84749	+	3.67667i
$577$	7109.80			0.512972			0.256486	−	0.966548i	$-0.417435\pi$
$577$	7109.80			0.512972			0.256486	+	0.966548i	$0.417435\pi$
$578$	20863.5			1.50139
$579$	3823.63	+	9535.74i	0.274446	+	0.684442i
$580$	59109.7			4.23172
$581$	−1741.77			−0.124373
$582$	−11788.7	+	4727.00i	−0.839615	+	0.336668i
$583$			2623.28i			0.186355i
$584$			9214.86i			0.652934i
$585$	10746.9	−	10269.8i	0.759539	−	0.725817i
$586$		−	13932.5i		−	0.982162i
$587$	15101.6			1.06185			0.530927	−	0.847418i	$-0.321844\pi$
$587$	15101.6			1.06185			0.530927	+	0.847418i	$0.321844\pi$
$588$	14069.4	+	35087.6i	0.986754	+	2.46087i
$589$			17123.2i			1.19788i
$590$	−591.296	+	26020.2i	−0.0412598	+	1.81565i
$591$	63.7975	−	25.5814i	0.00444040	−	0.00178051i
$592$		−	16927.2i		−	1.17518i
$593$			6719.14i			0.465299i	0.972561	+	0.232649i	$0.0747395\pi$
$593$			6719.14i			0.465299i	−0.972561	+	0.232649i	$0.925261\pi$
$594$	−5853.14	−	2661.37i	−0.404305	−	0.183834i
$595$	4931.06			0.339754
$596$	45043.6			3.09574
$597$	−8193.40	−	20433.5i	−0.561698	−	1.40082i
$598$		−	41012.2i		−	2.80454i
$599$			1436.88i			0.0980125i	0.998798	+	0.0490063i	$0.0156054\pi$
$599$			1436.88i			0.0980125i	−0.998798	+	0.0490063i	$0.984395\pi$
$600$	2985.93	+	7446.62i	0.203167	+	0.506678i
$601$			6652.88i			0.451542i	0.974180	+	0.225771i	$0.0724901\pi$
$601$			6652.88i			0.451542i	−0.974180	+	0.225771i	$0.927510\pi$
$602$			10538.7i			0.713495i
$603$	−5769.58	−	6037.64i	−0.389645	−	0.407748i
$604$			67551.7i			4.55072i
$605$			13034.6i			0.875920i
$606$	−13982.9	−	34871.8i	−0.937318	−	2.33758i
$607$	25508.3			1.70568			0.852842	−	0.522170i	$-0.174877\pi$
$607$	25508.3			1.70568			0.852842	+	0.522170i	$0.174877\pi$
$608$	75040.8			5.00544
$609$	−6173.94	+	2475.62i	−0.410806	+	0.164724i
$610$	−12295.0			−0.816085
$611$		−	5999.24i		−	0.397223i
$612$	39888.8	+	41742.1i	2.63466	+	2.75706i
$613$			12332.0i			0.812539i	0.913753	+	0.406270i	$0.133171\pi$
$613$			12332.0i			0.812539i	−0.913753	+	0.406270i	$0.866829\pi$
$614$	−4233.54			−0.278260
$615$	730.190	+	1821.02i	0.0478766	+	0.119399i
$616$	3524.38			0.230521
$617$		−	1837.26i		−	0.119879i	−0.998202	−	0.0599394i	$-0.980909\pi$
$617$		−	1837.26i		−	0.119879i	0.998202	−	0.0599394i	$-0.0190908\pi$
$618$	−41707.0	+	16723.6i	−2.71473	+	1.08855i
$619$	−23555.3			−1.52951			−0.764754	−	0.644322i	$-0.777140\pi$
$619$	−23555.3			−1.52951			−0.764754	+	0.644322i	$0.777140\pi$
$620$	−48268.5			−3.12663
$621$	−17638.6	−	8020.08i	−1.13979	−	0.518252i
$622$			8822.39i			0.568723i
$623$	−3815.93			−0.245397
$624$	−72080.3	+	28902.7i	−4.62423	+	1.85422i
$625$	−12966.5			−0.829855
$626$			54829.2i			3.50066i
$627$	1339.36	+	3340.23i	0.0853092	+	0.212753i
$628$		−	66796.1i		−	4.24435i
$629$	−5623.99			−0.356507
$630$	5500.76	+	5756.33i	0.347866	+	0.364028i
$631$	1509.61			0.0952405			0.0476203	−	0.998866i	$-0.484836\pi$
$631$	1509.61			0.0952405			0.0476203	+	0.998866i	$0.484836\pi$
$632$	15047.5			0.947084
$633$	12852.4	−	5153.52i	0.807007	−	0.323592i
$634$		−	49296.4i		−	3.08803i
$635$			12554.2i			0.784563i
$636$	35302.6	−	14155.6i	2.20101	−	0.882557i
$637$			16893.9i			1.05080i
$638$		−	11426.0i		−	0.709027i
$639$	−15491.7	−	16211.4i	−0.959062	−	1.00362i
$640$			82833.2i			5.11605i
$641$		−	8463.28i		−	0.521497i	−0.965407	−	0.260748i	$-0.916031\pi$
$641$		−	8463.28i		−	0.521497i	0.965407	−	0.260748i	$-0.0839693\pi$
$642$	34725.2	−	13924.0i	2.13472	−	0.855979i
$643$	−18771.3			−1.15127			−0.575637	−	0.817706i	$-0.695246\pi$
$643$	−18771.3			−1.15127			−0.575637	+	0.817706i	$0.695246\pi$
$644$	16294.0			0.997007
$645$	−7358.83	−	18352.2i	−0.449231	−	1.12034i
$646$		−	43566.6i		−	2.65342i
$647$			21564.6i			1.31034i	0.755481	+	0.655171i	$0.227403\pi$
$647$			21564.6i			1.31034i	−0.755481	+	0.655171i	$0.772597\pi$
$648$	−2757.73	+	60703.8i	−0.167182	+	3.68005i
$649$	3730.77	+	84.7798i	0.225648	+	0.00512773i
$650$			5500.54i			0.331922i
$651$	5041.59	−	2021.57i	0.303526	−	0.121707i
$652$	−37221.7			−2.23576
$653$		−	26279.9i		−	1.57490i	−0.616376	−	0.787452i	$-0.711400\pi$
$653$		−	26279.9i		−	1.57490i	0.616376	−	0.787452i	$-0.288600\pi$
$654$	44855.2	−	17986.0i	2.68192	−	1.07539i
$655$			18209.3i			1.08625i
$656$		−	10249.9i		−	0.610050i
$657$	2062.13	+	2157.94i	0.122453	+	0.128142i
$658$	3213.35			0.190379
$659$	3824.67			0.226082			0.113041	−	0.993590i	$-0.463941\pi$
$659$	3824.67			0.226082			0.113041	+	0.993590i	$0.463941\pi$
$660$	−9415.76	+	3775.52i	−0.555315	+	0.222669i
$661$	7544.32			0.443934			0.221967	−	0.975054i	$-0.428752\pi$
$661$	7544.32			0.443934			0.221967	+	0.975054i	$0.428752\pi$
$662$	−33963.3			−1.99399
$663$	9602.77	+	23948.3i	0.562505	+	1.40283i
$664$	−28275.7			−1.65258
$665$		−	4456.34i		−	0.259864i
$666$	−6273.74	−	6565.23i	−0.365019	−	0.381978i
$667$		−	34432.4i		−	1.99884i
$668$		−	34800.0i		−	2.01565i
$669$	9352.40	+	23324.0i	0.540486	+	1.34792i
$670$	−17763.4			−1.02427
$671$			1762.86i			0.101422i
$672$	−8859.34	−	22094.3i	−0.508566	−	1.26831i
$673$			27395.9i			1.56914i	0.620037	+	0.784572i	$0.287117\pi$
$673$			27395.9i			1.56914i	−0.620037	+	0.784572i	$0.712883\pi$
$674$			2567.73i			0.146744i
$675$	2365.68	+	1075.65i	0.134896	+	0.0613360i
$676$	−14927.8			−0.849331
$677$			5385.78i			0.305749i	0.988246	+	0.152875i	$0.0488531\pi$
$677$			5385.78i			0.305749i	−0.988246	+	0.152875i	$0.951147\pi$
$678$	−1304.84	−	3254.15i	−0.0739118	−	0.184329i
$679$		−	2255.04i		−	0.127453i
$680$	80050.2			4.51439
$681$	4504.06	+	11232.7i	0.253445	+	0.632066i
$682$			9330.36i			0.523868i
$683$	1944.56			0.108941			0.0544703	−	0.998515i	$-0.482653\pi$
$683$	1944.56			0.108941			0.0544703	+	0.998515i	$0.482653\pi$
$684$	37723.5	−	36048.7i	2.10876	−	2.01514i
$685$	−17810.3			−0.993424
$686$	−18851.0			−1.04918
$687$	−22833.6	+	9155.80i	−1.26806	+	0.508465i
$688$			103299.i			5.72416i
$689$	16997.4			0.939840
$690$	−38254.0	+	15339.0i	−2.11058	+	0.846299i
$691$		−	8078.30i		−	0.444737i	−0.974963	−	0.222368i	$-0.928621\pi$
$691$		−	8078.30i		−	0.444737i	0.974963	−	0.222368i	$-0.0713787\pi$
$692$	−40361.1			−2.21719
$693$	825.340	−	788.697i	0.0452411	−	0.0432325i
$694$	66655.0			3.64580
$695$			7436.34i			0.405865i
$696$	−100227.	+	40188.9i	−5.45847	+	2.18873i
$697$	−3405.50			−0.185068
$698$			25868.3i			1.40277i
$699$	5467.79	+	13636.1i	0.295867	+	0.737862i
$700$	−2185.34			−0.117997
$701$	3543.67			0.190931			0.0954655	−	0.995433i	$-0.469566\pi$
$701$	3543.67			0.190931			0.0954655	+	0.995433i	$0.469566\pi$
$702$	−17244.2	+	37925.1i	−0.927121	+	2.03902i
$703$			5082.56i			0.272677i
$704$	22436.6			1.20115
$705$	−5595.77	+	2243.78i	−0.298935	+	0.119866i
$706$	−16720.4			−0.891330
$707$	6670.59			0.354842
$708$	−18990.9	−	50664.1i	−1.00808	−	2.68937i
$709$	−35599.1			−1.88569			−0.942844	−	0.333234i	$-0.891860\pi$
$709$	−35599.1			−1.88569			−0.942844	+	0.333234i	$0.891860\pi$
$710$	−47695.8			−2.52111
$711$	3523.83	−	3367.38i	0.185870	−	0.177618i
$712$	−61947.4			−3.26064
$713$			28117.2i			1.47686i
$714$	−12827.3	+	5143.49i	−0.672341	+	0.269594i
$715$	−4533.47			−0.237122
$716$	−65093.7			−3.39758
$717$	3090.50	−	1239.22i	0.160972	−	0.0645463i
$718$			21371.7i			1.11084i
$719$	10953.5			0.568145			0.284072	−	0.958803i	$-0.408314\pi$
$719$	10953.5			0.568145			0.284072	+	0.958803i	$0.408314\pi$
$720$	53917.6	+	56422.7i	2.79082	+	2.92049i
$721$		−	7978.08i		−	0.412093i
$722$	−1197.43			−0.0617229
$723$	2171.97	+	5416.68i	0.111724	+	0.278629i
$724$	7925.94			0.406858
$725$			4618.06i			0.236566i
$726$	−13596.1	−	33907.4i	−0.695041	−	1.73336i
$727$	−18093.5			−0.923040			−0.461520	−	0.887130i	$-0.652696\pi$
$727$	−18093.5			−0.923040			−0.461520	+	0.887130i	$0.652696\pi$
$728$		−	22836.0i		−	1.16258i
$729$	12938.7	+	14832.8i	0.657353	+	0.753583i
$730$	6348.90			0.321895
$731$	34320.5			1.73651
$732$	23723.5	−	9512.63i	1.19788	−	0.480324i
$733$	−7730.58			−0.389543			−0.194772	−	0.980849i	$-0.562397\pi$
$733$	−7730.58			−0.389543			−0.194772	+	0.980849i	$0.562397\pi$
$734$		−	17224.4i		−	0.866166i
$735$	15757.7	−	6318.49i	0.790791	−	0.317090i
$736$	123221.			6.17118
$737$			2546.91i			0.127295i
$738$	−3798.94	−	3975.44i	−0.189486	−	0.198290i
$739$			1695.25i			0.0843853i	0.999109	+	0.0421926i	$0.0134343\pi$
$739$			1695.25i			0.0843853i	−0.999109	+	0.0421926i	$0.986566\pi$
$740$	−14327.2			−0.711728
$741$	21642.8	−	8678.30i	1.07297	−	0.430237i
$742$			9104.24i			0.450441i
$743$			29123.9i			1.43803i	0.694997	+	0.719013i	$0.255406\pi$
$743$			29123.9i			1.43803i	−0.694997	+	0.719013i	$0.744594\pi$
$744$	81844.6	−	32817.9i	4.03302	−	1.61715i
$745$		−	20228.9i		−	0.994804i
$746$	23.4442			0.00115061
$747$	−6621.62	+	6327.64i	−0.324327	+	0.309928i
$748$		−	17608.4i		−	0.860732i
$749$			6642.54i			0.324049i
$750$	39753.4	−	15940.2i	1.93545	−	0.776074i
$751$			28450.7i			1.38240i	0.722663	+	0.691200i	$0.242918\pi$
$751$			28450.7i			1.38240i	−0.722663	+	0.691200i	$0.757082\pi$
$752$	31496.8			1.52735
$753$	−23142.2	+	9279.51i	−1.11998	+	0.449089i
$754$	−74034.0			−3.57581
$755$	30337.1			1.46236
$756$	−15067.5	−	6851.04i	−0.724866	−	0.329590i
$757$	32205.6			1.54628			0.773138	−	0.634238i	$-0.218686\pi$
$757$	32205.6			1.54628			0.773138	+	0.634238i	$0.218686\pi$
$758$	−35699.6			−1.71065
$759$	2199.30	+	5484.84i	0.105177	+	0.262302i
$760$		−	72343.6i		−	3.45287i
$761$		−	34842.8i		−	1.65972i	−0.557969	−	0.829861i	$-0.688419\pi$
$761$		−	34842.8i		−	1.65972i	0.557969	−	0.829861i	$-0.311581\pi$
$762$	−13095.0	−	32657.7i	−0.622549	−	1.55257i
$763$			8580.29i			0.407113i
$764$	98555.9			4.66705
$765$	18746.2	−	17913.9i	0.885973	−	0.846638i
$766$			28835.9i			1.36016i
$767$	549.326	−	24173.3i	0.0258605	−	1.13800i
$768$	−44247.4	−	110349.i	−2.07896	−	5.18471i
$769$		−	27342.3i		−	1.28217i	−0.767470	−	0.641085i	$-0.778485\pi$
$769$		−	27342.3i		−	1.28217i	0.767470	−	0.641085i	$-0.221515\pi$
$770$		−	2428.24i		−	0.113646i
$771$	3470.76	−	1391.70i	0.162123	−	0.0650076i
$772$	−45429.4			−2.11793
$773$	−23177.9			−1.07846			−0.539231	−	0.842158i	$-0.681285\pi$
$773$	−23177.9			−1.07846			−0.539231	+	0.842158i	$0.681285\pi$
$774$	38285.6	+	40064.4i	1.77797	+	1.86057i
$775$		−	3771.07i		−	0.174788i
$776$		−	36608.0i		−	1.69349i
$777$	1496.46	−	600.048i	0.0690929	−	0.0277048i
$778$		−	2557.59i		−	0.117858i
$779$			3077.64i			0.141551i
$780$	24463.2	+	61008.8i	1.12298	+	2.80060i
$781$			6838.60i			0.313322i
$782$		−	71538.8i		−	3.27138i
$783$	−14477.6	+	31840.6i	−0.660776	+	1.45324i
$784$	−88695.0			−4.04041
$785$	−29997.8			−1.36391
$786$	−18993.8	−	47368.6i	−0.861941	−	2.14959i
$787$	−2712.93			−0.122879			−0.0614394	−	0.998111i	$-0.519569\pi$
$787$	−2712.93			−0.122879			−0.0614394	+	0.998111i	$0.519569\pi$
$788$			303.939i			0.0137403i
$789$	8507.23	−	3411.22i	0.383860	−	0.153920i
$790$		−	10367.5i		−	0.466910i
$791$	622.482			0.0279809
$792$	13398.5	−	12803.6i	0.601128	−	0.574440i
$793$	11422.3			0.511499
$794$		−	599.579i		−	0.0267988i
$795$	−6357.21	−	15854.3i	−0.283606	−	0.707286i
$796$	97347.7			4.33467
$797$	−37934.9			−1.68598			−0.842989	−	0.537930i	$-0.819206\pi$
$797$	−37934.9			−1.68598			−0.842989	+	0.537930i	$0.819206\pi$
$798$	4648.32	+	11592.4i	0.206201	+	0.514246i
$799$		−	10464.7i		−	0.463346i
$800$	−16526.4			−0.730370
$801$	−14506.9	+	13862.8i	−0.639919	+	0.611508i
$802$	−3276.71			−0.144270
$803$		−	910.302i		−	0.0400048i
$804$	34274.9	−	13743.5i	1.50346	−	0.602855i
$805$		−	7317.55i		−	0.320385i
$806$	60455.5			2.64200
$807$	7950.50	+	19827.7i	0.346804	+	0.864894i
$808$	108290.			4.71487
$809$	−28671.2			−1.24601			−0.623007	−	0.782216i	$-0.714089\pi$
$809$	−28671.2			−1.24601			−0.623007	+	0.782216i	$0.714089\pi$
$810$	41824.0	+	1900.03i	1.81425	+	0.0824201i
$811$			12335.6i			0.534108i	0.963682	+	0.267054i	$0.0860501\pi$
$811$			12335.6i			0.534108i	−0.963682	+	0.267054i	$0.913950\pi$
$812$		−	29413.4i		−	1.27119i
$813$	8375.71	+	20888.2i	0.361315	+	0.901083i
$814$			2769.47i			0.119250i
$815$			16716.1i			0.718454i
$816$	−125732.	+	50415.8i	−5.39399	+	2.16287i
$817$		−	31016.4i		−	1.32818i
$818$			14836.9i			0.634183i
$819$	−5110.31	−	5347.74i	−0.218033	−	0.228163i
$820$	−8675.56			−0.369468
$821$	−21096.3			−0.896792			−0.448396	−	0.893835i	$-0.648005\pi$
$821$	−21096.3			−0.896792			−0.448396	+	0.893835i	$0.648005\pi$
$822$	46330.5	−	18577.5i	1.96589	−	0.788280i
$823$			7066.19i			0.299286i	0.988740	+	0.149643i	$0.0478124\pi$
$823$			7066.19i			0.299286i	−0.988740	+	0.149643i	$0.952188\pi$
$824$		−	129515.i		−	5.47557i
$825$	−294.970	−	735.625i	−0.0124479	−	0.0310438i
$826$	12947.8	+	294.233i	0.545416	+	0.0123943i
$827$		−	13668.3i		−	0.574720i	−0.957823	−	0.287360i	$-0.907222\pi$
$827$		−	13668.3i		−	0.574720i	0.957823	−	0.287360i	$-0.0927776\pi$
$828$	61944.1	−	59193.9i	2.59989	−	2.48446i
$829$	962.671			0.0403317			0.0201658	−	0.999797i	$-0.493581\pi$
$829$	962.671			0.0403317			0.0201658	+	0.999797i	$0.493581\pi$
$830$			19481.5i			0.814716i
$831$	4871.27	+	12148.5i	0.203348	+	0.507131i
$832$		−	145377.i		−	6.05773i
$833$			29468.5i			1.22572i
$834$	−7756.70	−	19344.4i	−0.322054	−	0.803169i
$835$	−15628.5			−0.647721
$836$	−15913.2			−0.658338
$837$	11822.3	−	26000.8i	0.488218	−	1.07374i
$838$	−49975.5			−2.06011
$839$	−19977.9			−0.822065			−0.411032	−	0.911621i	$-0.634832\pi$
$839$	−19977.9			−0.822065			−0.411032	+	0.911621i	$0.634832\pi$
$840$	−21300.2	+	8540.91i	−0.874912	+	0.350821i
$841$	−37767.4			−1.54854
$842$			56391.7i			2.30806i
$843$	2442.78	−	979.502i	0.0998029	−	0.0400188i
$844$			61230.1i			2.49719i
$845$			6704.03i			0.272930i
$846$	12216.0	−	11673.7i	0.496449	−	0.474408i
$847$	6486.10			0.263123
$848$			89238.5i			3.61375i
$849$	−2892.80	+	1159.95i	−0.116938	+	0.0468898i
$850$			9594.76i			0.387174i
$851$			8345.84i			0.336183i
$852$	92030.0	−	36902.0i	3.70058	−	1.48385i
$853$	−25908.6			−1.03997			−0.519984	−	0.854176i	$-0.674062\pi$
$853$	−25908.6			−1.03997			−0.519984	+	0.854176i	$0.674062\pi$
$854$			6118.10i			0.245149i
$855$	−16189.3	−	16941.5i	−0.647558	−	0.677644i
$856$			107834.i			4.30572i
$857$	−10456.0			−0.416767			−0.208383	−	0.978047i	$-0.566820\pi$
$857$	−10456.0			−0.416767			−0.208383	+	0.978047i	$0.566820\pi$
$858$	11793.1	−	4728.77i	0.469242	−	0.188156i
$859$		−	11050.4i		−	0.438921i	−0.975621	−	0.219461i	$-0.929570\pi$
$859$		−	11050.4i		−	0.438921i	0.975621	−	0.219461i	$-0.0704298\pi$
$860$	87432.0			3.46675
$861$	906.152	−	363.348i	0.0358671	−	0.0143819i
$862$	50055.9			1.97785
$863$	14261.5			0.562535			0.281268	−	0.959629i	$-0.409245\pi$
$863$	14261.5			0.562535			0.281268	+	0.959629i	$0.409245\pi$
$864$	−113946.	−	51810.1i	−4.48671	−	2.04006i
$865$			18126.0i			0.712487i
$866$	−49173.3			−1.92953
$867$	7249.30	+	18079.0i	0.283967	+	0.708184i
$868$			24018.7i			0.939227i
$869$	−1486.49			−0.0580272
$870$	27689.5	+	69054.9i	1.07904	+	2.69101i
$871$	16502.6			0.641984
$872$			139291.i			5.40940i
$873$	−8192.26	−	8572.88i	−0.317602	−	0.332357i
$874$	−64651.7			−2.50215
$875$			7604.37i			0.293800i
$876$	−12250.3	+	4912.12i	−0.472489	+	0.189458i
$877$	−4121.85			−0.158706			−0.0793529	−	0.996847i	$-0.525285\pi$
$877$	−4121.85			−0.158706			−0.0793529	+	0.996847i	$0.525285\pi$
$878$	47335.2			1.81946
$879$	12073.1	−	4841.04i	0.463270	−	0.185761i
$880$		−	23801.3i		−	0.911751i
$881$	38078.4			1.45618			0.728089	−	0.685482i	$-0.240409\pi$
$881$	38078.4			1.45618			0.728089	+	0.685482i	$0.240409\pi$
$882$	−34400.4	+	32873.1i	−1.31329	+	1.25498i
$883$	−30255.1			−1.15308			−0.576538	−	0.817071i	$-0.695597\pi$
$883$	−30255.1			−1.15308			−0.576538	+	0.817071i	$0.695597\pi$
$884$	−114093.			−4.34090
$885$	−22753.0	+	8528.70i	−0.864219	+	0.323943i
$886$	61179.7			2.31983
$887$	7645.34			0.289408			0.144704	−	0.989475i	$-0.453777\pi$
$887$	7645.34			0.289408			0.144704	+	0.989475i	$0.453777\pi$
$888$	24293.3	−	9741.11i	0.918053	−	0.368120i
$889$	6247.04			0.235680
$890$			42680.8i			1.60749i
$891$	272.426	−	5996.70i	0.0102431	−	0.225474i
$892$	−111118.			−4.17097
$893$	−9457.22			−0.354394
$894$	21100.4	+	52622.2i	0.789375	+	1.96862i
$895$			29233.3i			1.09180i
$896$	41218.4			1.53684
$897$	35538.7	−	14250.2i	1.32286	−	0.530437i
$898$			79919.3i			2.96987i
$899$	50756.4			1.88300
$900$	−8307.92	+	7939.07i	−0.307701	+	0.294039i
$901$	29649.1			1.09629
$902$			1677.00i			0.0619045i
$903$	−9132.17	+	3661.80i	−0.336544	+	0.134947i
$904$	10105.3			0.371789
$905$		−	3559.50i		−	0.130742i
$906$	−78917.2	+	31644.1i	−2.89387	+	1.16038i
$907$	−25965.1			−0.950561			−0.475280	−	0.879834i	$-0.657653\pi$
$907$	−25965.1			−0.950561			−0.475280	+	0.879834i	$0.657653\pi$
$908$	−53513.8			−1.95586
$909$	25359.3	−	24233.4i	0.925318	−	0.884236i
$910$	−15733.6			−0.573149
$911$		−	39400.1i		−	1.43291i	−0.697632	−	0.716456i	$-0.745763\pi$
$911$		−	39400.1i		−	1.43291i	0.697632	−	0.716456i	$-0.254237\pi$
$912$	45562.2	+	113627.i	1.65429	+	4.12564i
$913$	2793.26			0.101252
$914$			23697.9i			0.857610i
$915$	−4272.08	−	10654.1i	−0.154350	−	0.384934i
$916$		−	108782.i		−	3.92387i
$917$	9061.08			0.326307
$918$	−30079.5	+	66153.9i	−1.08145	+	2.37843i
$919$		−	16028.2i		−	0.575321i	−0.957732	−	0.287660i	$-0.907123\pi$
$919$		−	16028.2i		−	0.575321i	0.957732	−	0.287660i	$-0.0928775\pi$
$920$		−	118792.i		−	4.25703i
$921$	−1471.00	−	3668.53i	−0.0526288	−	0.131251i
$922$			105649.i			3.77373i
$923$	44310.3			1.58016
$924$	1878.72	+	4685.34i	0.0668890	+	0.166814i
$925$		−	1119.34i		−	0.0397878i
$926$		−	60908.1i		−	2.16152i
$927$	−28983.3	−	30329.9i	−1.02690	−	1.07461i
$928$		−	222435.i		−	7.86831i
$929$	676.412			0.0238884			0.0119442	−	0.999929i	$-0.496198\pi$
$929$	676.412			0.0238884			0.0119442	+	0.999929i	$0.496198\pi$
$930$	−22611.0	−	56389.6i	−0.797253	−	1.98827i
$931$	26631.5			0.937500
$932$	−64964.1			−2.28323
$933$	−7644.95	+	3065.46i	−0.268258	+	0.107565i
$934$	44862.6			1.57168
$935$	−7907.86			−0.276593
$936$	−82960.2	−	86814.6i	−2.89705	−	3.03165i
$937$		−	17451.4i		−	0.608445i	−0.952601	−	0.304222i	$-0.901603\pi$
$937$		−	17451.4i		−	0.608445i	0.952601	−	0.304222i	$-0.0983966\pi$
$938$			8839.20i			0.307687i
$939$	−47511.6	+	19051.1i	−1.65121	+	0.662099i
$940$		−	26658.9i		−	0.925019i
$941$	−38216.4			−1.32393			−0.661966	−	0.749534i	$-0.730278\pi$
$941$	−38216.4			−1.32393			−0.661966	+	0.749534i	$0.730278\pi$
$942$	78034.5	−	31290.1i	2.69904	−	1.08226i
$943$			5053.66i			0.174517i
$944$	126913.	+	2884.03i	4.37570	+	0.0994355i
$945$	−3076.77	+	6766.74i	−0.105913	+	0.232933i
$946$		−	16900.7i		−	0.580856i
$947$		−	35474.4i		−	1.21728i	−0.793447	−	0.608639i	$-0.791716\pi$
$947$		−	35474.4i		−	1.21728i	0.793447	−	0.608639i	$-0.208284\pi$
$948$	8021.29	+	20004.3i	0.274810	+	0.685347i
$949$	−5898.25			−0.201755
$950$	8671.06			0.296133
$951$	42717.3	−	17128.7i	1.45658	−	0.584055i
$952$		−	39833.5i		−	1.35610i
$953$			25998.2i			0.883699i	0.897089	+	0.441850i	$0.145678\pi$
$953$			25998.2i			0.883699i	−0.897089	+	0.441850i	$0.854322\pi$
$954$	33074.5	+	34611.2i	1.12246	+	1.17461i
$955$		−	44261.0i		−	1.49974i
$956$			14723.5i			0.498109i
$957$	9901.06	−	3970.11i	0.334437	−	0.134102i
$958$		−	44282.6i		−	1.49343i
$959$			8862.51i			0.298421i
$960$	−135600.	+	54372.5i	−4.55881	+	1.82798i
$961$	−11656.2			−0.391267
$962$	17944.6			0.601410
$963$	24131.5	+	25252.6i	0.807503	+	0.845020i
$964$	−25805.7			−0.862185
$965$			20402.1i			0.680588i
$966$	7632.80	+	19035.4i	0.254225	+	0.634011i
$967$		−	48478.6i		−	1.61217i	−0.591801	−	0.806084i	$-0.701583\pi$
$967$		−	48478.6i		−	1.61217i	0.591801	−	0.806084i	$-0.298417\pi$
$968$	105295.			3.49617
$969$	37752.2	−	15137.8i	1.25157	−	0.501854i
$970$	−25222.4			−0.834888
$971$			5719.15i			0.189018i	0.995524	+	0.0945088i	$0.0301281\pi$
$971$			5719.15i			0.189018i	−0.995524	+	0.0945088i	$0.969872\pi$
$972$	−82170.3	+	28692.9i	−2.71154	+	0.946837i
$973$	3700.37			0.121920
$974$	−30455.5			−1.00191
$975$	−4766.44	+	1911.24i	−0.156562	+	0.0627781i
$976$			59968.7i			1.96675i
$977$	28909.4			0.946667			0.473333	−	0.880883i	$-0.343051\pi$
$977$	28909.4			0.946667			0.473333	+	0.880883i	$0.343051\pi$
$978$	−17436.3	−	43484.3i	−0.570092	−	1.42175i
$979$	6119.56			0.199777
$980$			75071.5i			2.44701i
$981$	31171.1	+	32619.3i	1.01449	+	1.06162i
$982$			43595.7i			1.41670i
$983$	34652.4			1.12435			0.562177	−	0.827017i	$-0.309964\pi$
$983$	34652.4			1.12435			0.562177	+	0.827017i	$0.309964\pi$
$984$	14710.4	−	5898.54i	0.476574	−	0.191096i
$985$	136.498			0.00441540
$986$	−129140.			−4.17104
$987$	1116.52	+	2784.49i	0.0360074	+	0.0897988i
$988$			103109.i			3.32017i
$989$		−	50930.6i		−	1.63751i
$990$	−8821.48	−	9231.34i	−0.283197	−	0.296355i
$991$			2035.45i			0.0652454i	0.999468	+	0.0326227i	$0.0103860\pi$
$991$			2035.45i			0.0652454i	−0.999468	+	0.0326227i	$0.989614\pi$
$992$			181639.i			5.81354i
$993$	−11801.0	−	29430.5i	−0.377134	−	0.940533i
$994$			23733.7i			0.757332i
$995$		−	43718.4i		−	1.39293i
$996$	−15072.8	−	37590.1i	−0.479518	−	1.19587i
$997$	4884.56			0.155161			0.0775805	−	0.996986i	$-0.475281\pi$
$997$	4884.56			0.155161			0.0775805	+	0.996986i	$0.475281\pi$
$998$	−39467.5			−1.25183
$999$	3509.13	−	7717.62i	0.111135	−	0.244419i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.d.c.176.1	✓	52
3.2	odd	2	inner	177.4.d.c.176.52	yes	52
59.58	odd	2	inner	177.4.d.c.176.51	yes	52
177.176	even	2	inner	177.4.d.c.176.2	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.d.c.176.1	✓	52	1.1	even	1	trivial
177.4.d.c.176.2	yes	52	177.176	even	2	inner
177.4.d.c.176.51	yes	52	59.58	odd	2	inner
177.4.d.c.176.52	yes	52	3.2	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.56568 q^{2} +(-1.93387 - 4.82288i) q^{3} +22.9768 q^{4} -10.3188i q^{5} +(10.7633 + 26.8426i) q^{6} -5.13468 q^{7} -83.3558 q^{8} +(-19.5203 + 18.6536i) q^{9} +O(q^{10})\)	\(q-5.56568 q^{2} +(-1.93387 - 4.82288i) q^{3} +22.9768 q^{4} -10.3188i q^{5} +(10.7633 + 26.8426i) q^{6} -5.13468 q^{7} -83.3558 q^{8} +(-19.5203 + 18.6536i) q^{9} +57.4309i q^{10} +8.23442 q^{11} +(-44.4341 - 110.814i) q^{12} -53.3544i q^{13} +28.5780 q^{14} +(-49.7661 + 19.9551i) q^{15} +280.117 q^{16} -93.0677i q^{17} +(108.644 - 103.820i) q^{18} -84.1079 q^{19} -237.092i q^{20} +(9.92981 + 24.7639i) q^{21} -45.8301 q^{22} -138.110 q^{23} +(161.199 + 402.015i) q^{24} +18.5232 q^{25} +296.953i q^{26} +(127.714 + 58.0703i) q^{27} -117.978 q^{28} +249.312i q^{29} +(276.982 - 111.064i) q^{30} -203.586i q^{31} -892.196 q^{32} +(-15.9243 - 39.7136i) q^{33} +517.985i q^{34} +52.9836i q^{35} +(-448.513 + 428.600i) q^{36} -60.4290i q^{37} +468.118 q^{38} +(-257.322 + 103.180i) q^{39} +860.128i q^{40} -36.5916i q^{41} +(-55.2661 - 137.828i) q^{42} +368.769i q^{43} +189.200 q^{44} +(192.482 + 201.425i) q^{45} +768.675 q^{46} +112.441 q^{47} +(-541.711 - 1350.97i) q^{48} -316.635 q^{49} -103.094 q^{50} +(-448.854 + 179.981i) q^{51} -1225.91i q^{52} +318.575i q^{53} +(-710.814 - 323.200i) q^{54} -84.9689i q^{55} +428.006 q^{56} +(162.654 + 405.642i) q^{57} -1387.59i q^{58} +(453.071 + 10.2958i) q^{59} +(-1143.46 + 458.504i) q^{60} +214.084i q^{61} +1133.09i q^{62} +(100.231 - 95.7805i) q^{63} +2724.74 q^{64} -550.551 q^{65} +(88.6295 + 221.033i) q^{66} +309.301i q^{67} -2138.39i q^{68} +(267.087 + 666.087i) q^{69} -294.889i q^{70} +830.490i q^{71} +(1627.13 - 1554.89i) q^{72} -110.548i q^{73} +336.328i q^{74} +(-35.8216 - 89.3354i) q^{75} -1932.53 q^{76} -42.2811 q^{77} +(1432.17 - 574.269i) q^{78} -180.521 q^{79} -2890.46i q^{80} +(33.0838 - 728.249i) q^{81} +203.657i q^{82} +339.217 q^{83} +(228.155 + 568.995i) q^{84} -960.343 q^{85} -2052.45i q^{86} +(1202.40 - 482.137i) q^{87} -686.386 q^{88} +743.168 q^{89} +(-1071.29 - 1121.07i) q^{90} +273.958i q^{91} -3173.32 q^{92} +(-981.870 + 393.709i) q^{93} -625.813 q^{94} +867.889i q^{95} +(1725.39 + 4302.95i) q^{96} +439.178i q^{97} +1762.29 q^{98} +(-160.738 + 153.602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9	\( 52 q - 8 q^{3} + 268 q^{4} - 16 q^{7} - 4 q^{9} + 28 q^{12} + 114 q^{15} + 484 q^{16} - 184 q^{19} - 758 q^{21} - 60 q^{22} + 36 q^{25} + 742 q^{27} - 4 q^{28} - 888 q^{36} + 1402 q^{45} - 660 q^{46} - 488 q^{48} - 924 q^{49} - 1772 q^{51} - 630 q^{57} - 1880 q^{60} - 212 q^{63} + 7648 q^{64} + 1316 q^{66} - 1556 q^{75} - 5680 q^{76} + 3224 q^{78} - 1504 q^{79} - 276 q^{81} + 1228 q^{84} - 848 q^{85} + 3598 q^{87} + 5760 q^{88} + 888 q^{94}+O(q^{100}) \) 52 * q - 8 * q^3 + 268 * q^4 - 16 * q^7 - 4 * q^9 + 28 * q^12 + 114 * q^15 + 484 * q^16 - 184 * q^19 - 758 * q^21 - 60 * q^22 + 36 * q^25 + 742 * q^27 - 4 * q^28 - 888 * q^36 + 1402 * q^45 - 660 * q^46 - 488 * q^48 - 924 * q^49 - 1772 * q^51 - 630 * q^57 - 1880 * q^60 - 212 * q^63 + 7648 * q^64 + 1316 * q^66 - 1556 * q^75 - 5680 * q^76 + 3224 * q^78 - 1504 * q^79 - 276 * q^81 + 1228 * q^84 - 848 * q^85 + 3598 * q^87 + 5760 * q^88 + 888 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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