LMFDB - Embedded newform 177.4.d.c.176.17

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			176.17
Character	$\chi$	$=$	177.176
Dual form			177.4.d.c.176.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62059 q^{2} +(5.14935 - 0.695815i) q^{3} -1.13250 q^{4} -14.1294i q^{5} +(-13.4944 + 1.82345i) q^{6} +10.3672 q^{7} +23.9326 q^{8} +(26.0317 - 7.16599i) q^{9} +O(q^{10})$	\(q-2.62059 q^{2} +(5.14935 - 0.695815i) q^{3} -1.13250 q^{4} -14.1294i q^{5} +(-13.4944 + 1.82345i) q^{6} +10.3672 q^{7} +23.9326 q^{8} +(26.0317 - 7.16599i) q^{9} +37.0275i q^{10} -30.0340 q^{11} +(-5.83163 + 0.788009i) q^{12} +8.23644i q^{13} -27.1683 q^{14} +(-9.83148 - 72.7575i) q^{15} -53.6575 q^{16} -83.4833i q^{17} +(-68.2184 + 18.7791i) q^{18} -30.5066 q^{19} +16.0016i q^{20} +(53.3845 - 7.21367i) q^{21} +78.7068 q^{22} -41.7480 q^{23} +(123.237 - 16.6526i) q^{24} -74.6412 q^{25} -21.5844i q^{26} +(129.060 - 55.0135i) q^{27} -11.7409 q^{28} +73.8768i q^{29} +(25.7643 + 190.668i) q^{30} -289.520i q^{31} -50.8461 q^{32} +(-154.656 + 20.8981i) q^{33} +218.776i q^{34} -146.483i q^{35} +(-29.4808 + 8.11548i) q^{36} -191.214i q^{37} +79.9454 q^{38} +(5.73104 + 42.4124i) q^{39} -338.154i q^{40} +36.3424i q^{41} +(-139.899 + 18.9041i) q^{42} -491.069i q^{43} +34.0134 q^{44} +(-101.252 - 367.813i) q^{45} +109.405 q^{46} +26.4171 q^{47} +(-276.301 + 37.3357i) q^{48} -235.521 q^{49} +195.604 q^{50} +(-58.0889 - 429.885i) q^{51} -9.32776i q^{52} -181.825i q^{53} +(-338.214 + 144.168i) q^{54} +424.363i q^{55} +248.114 q^{56} +(-157.089 + 21.2270i) q^{57} -193.601i q^{58} +(-187.180 + 412.726i) q^{59} +(11.1341 + 82.3977i) q^{60} +775.225i q^{61} +758.713i q^{62} +(269.876 - 74.2915i) q^{63} +562.507 q^{64} +116.376 q^{65} +(405.289 - 54.7654i) q^{66} +176.188i q^{67} +94.5447i q^{68} +(-214.975 + 29.0489i) q^{69} +383.873i q^{70} +447.258i q^{71} +(623.005 - 171.501i) q^{72} -417.573i q^{73} +501.095i q^{74} +(-384.354 + 51.9364i) q^{75} +34.5487 q^{76} -311.369 q^{77} +(-15.0187 - 111.145i) q^{78} +574.434 q^{79} +758.150i q^{80} +(626.297 - 373.086i) q^{81} -95.2385i q^{82} +998.011 q^{83} +(-60.4579 + 8.16947i) q^{84} -1179.57 q^{85} +1286.89i q^{86} +(51.4046 + 380.418i) q^{87} -718.790 q^{88} +1179.83 q^{89} +(265.339 + 963.888i) q^{90} +85.3891i q^{91} +47.2796 q^{92} +(-201.452 - 1490.84i) q^{93} -69.2284 q^{94} +431.041i q^{95} +(-261.825 + 35.3795i) q^{96} +806.397i q^{97} +617.203 q^{98} +(-781.835 + 215.223i) 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 $

$2$	−2.62059			−0.926519			−0.463260	−	0.886223i	$-0.653320\pi$
$2$	−2.62059			−0.926519			−0.463260	+	0.886223i	$0.653320\pi$
$3$	5.14935	−	0.695815i	0.990994	−	0.133910i
$3$	5.14935	−	0.695815i	0.990994	−	0.133910i
$4$	−1.13250			−0.141562
$5$		−	14.1294i		−	1.26378i	−0.775060	−	0.631888i	$-0.782280\pi$
$5$		−	14.1294i		−	1.26378i	0.775060	−	0.631888i	$-0.217720\pi$
$6$	−13.4944	+	1.82345i	−0.918174	+	0.124070i
$7$	10.3672			0.559778			0.279889	−	0.960032i	$-0.409702\pi$
$7$	10.3672			0.559778			0.279889	+	0.960032i	$0.409702\pi$
$8$	23.9326			1.05768
$9$	26.0317	−	7.16599i	0.964136	−	0.265407i
$10$			37.0275i			1.17091i
$11$	−30.0340			−0.823235			−0.411617	−	0.911357i	$-0.635036\pi$
$11$	−30.0340			−0.823235			−0.411617	+	0.911357i	$0.635036\pi$
$12$	−5.83163	+	0.788009i	−0.140287	+	0.0189566i
$13$			8.23644i			0.175721i	0.996133	+	0.0878607i	$0.0280030\pi$
$13$			8.23644i			0.175721i	−0.996133	+	0.0878607i	$0.971997\pi$
$14$	−27.1683			−0.518645
$15$	−9.83148	−	72.7575i	−0.169232	−	1.25239i
$16$	−53.6575			−0.838398
$17$		−	83.4833i		−	1.19104i	−0.803341	−	0.595520i	$-0.796946\pi$
$17$		−	83.4833i		−	1.19104i	0.803341	−	0.595520i	$-0.203054\pi$
$18$	−68.2184	+	18.7791i	−0.893291	+	0.245905i
$19$	−30.5066			−0.368352			−0.184176	−	0.982893i	$-0.558962\pi$
$19$	−30.5066			−0.368352			−0.184176	+	0.982893i	$0.558962\pi$
$20$			16.0016i			0.178903i
$21$	53.3845	−	7.21367i	0.554736	−	0.0749597i
$22$	78.7068			0.762743
$23$	−41.7480			−0.378481			−0.189241	−	0.981931i	$-0.560603\pi$
$23$	−41.7480			−0.378481			−0.189241	+	0.981931i	$0.560603\pi$
$24$	123.237	−	16.6526i	1.04815	−	0.141633i
$25$	−74.6412			−0.597129
$26$		−	21.5844i		−	0.162809i
$27$	129.060	−	55.0135i	0.919912	−	0.392124i
$28$	−11.7409			−0.0792434
$29$			73.8768i			0.473054i	0.971625	+	0.236527i	$0.0760092\pi$
$29$			73.8768i			0.473054i	−0.971625	+	0.236527i	$0.923991\pi$
$30$	25.7643	+	190.668i	0.156796	+	1.16037i
$31$		−	289.520i		−	1.67740i	−0.544597	−	0.838698i	$-0.683317\pi$
$31$		−	289.520i		−	1.67740i	0.544597	−	0.838698i	$-0.316683\pi$
$32$	−50.8461			−0.280888
$33$	−154.656	+	20.8981i	−0.815821	+	0.110239i
$34$			218.776i			1.10352i
$35$		−	146.483i		−	0.707434i
$36$	−29.4808	+	8.11548i	−0.136485	+	0.0375716i
$37$		−	191.214i		−	0.849607i	−0.905286	−	0.424803i	$-0.860343\pi$
$37$		−	191.214i		−	0.849607i	0.905286	−	0.424803i	$-0.139657\pi$
$38$	79.9454			0.341286
$39$	5.73104	+	42.4124i	0.0235308	+	0.174139i
$40$		−	338.154i		−	1.33667i
$41$			36.3424i			0.138432i	0.997602	+	0.0692162i	$0.0220498\pi$
$41$			36.3424i			0.138432i	−0.997602	+	0.0692162i	$0.977950\pi$
$42$	−139.899	+	18.9041i	−0.513974	+	0.0694516i
$43$		−	491.069i		−	1.74156i	−0.491669	−	0.870782i	$-0.663613\pi$
$43$		−	491.069i		−	1.74156i	0.491669	−	0.870782i	$-0.336387\pi$
$44$	34.0134			0.116539
$45$	−101.252	−	367.813i	−0.335415	−	1.21845i
$46$	109.405			0.350670
$47$	26.4171			0.0819857			0.0409929	−	0.999159i	$-0.486948\pi$
$47$	26.4171			0.0819857			0.0409929	+	0.999159i	$0.486948\pi$
$48$	−276.301	+	37.3357i	−0.830847	+	0.112270i
$49$	−235.521			−0.686649
$50$	195.604			0.553252
$51$	−58.0889	−	429.885i	−0.159492	−	1.18031i
$52$		−	9.32776i		−	0.0248755i
$53$		−	181.825i		−	0.471238i	−0.971846	−	0.235619i	$-0.924288\pi$
$53$		−	181.825i		−	0.471238i	0.971846	−	0.235619i	$-0.0757117\pi$
$54$	−338.214	+	144.168i	−0.852316	+	0.363310i
$55$			424.363i			1.04038i
$56$	248.114			0.592065
$57$	−157.089	+	21.2270i	−0.365035	+	0.0493260i
$58$		−	193.601i		−	0.438294i
$59$	−187.180	+	412.726i	−0.413029	+	0.910718i
$59$	−187.180	+	412.726i	−0.413029	+	0.910718i
$60$	11.1341	+	82.3977i	0.0239568	+	0.177292i
$61$			775.225i			1.62717i	0.581446	+	0.813585i	$0.302487\pi$
$61$			775.225i			1.62717i	−0.581446	+	0.813585i	$0.697513\pi$
$62$			758.713i			1.55414i
$63$	269.876	−	74.2915i	0.539702	−	0.148569i
$64$	562.507			1.09865
$65$	116.376			0.222072
$66$	405.289	−	54.7654i	0.755873	−	0.102139i
$67$			176.188i			0.321265i	0.987014	+	0.160632i	$0.0513533\pi$
$67$			176.188i			0.321265i	−0.987014	+	0.160632i	$0.948647\pi$
$68$			94.5447i			0.168606i
$69$	−214.975	+	29.0489i	−0.375072	+	0.0506823i
$70$			383.873i			0.655451i
$71$			447.258i			0.747602i	0.927509	+	0.373801i	$0.121946\pi$
$71$			447.258i			0.747602i	−0.927509	+	0.373801i	$0.878054\pi$
$72$	623.005	−	171.501i	1.01975	−	0.280716i
$73$		−	417.573i		−	0.669496i	−0.942308	−	0.334748i	$-0.891349\pi$
$73$		−	417.573i		−	0.669496i	0.942308	−	0.334748i	$-0.108651\pi$
$74$			501.095i			0.787177i
$75$	−384.354	+	51.9364i	−0.591751	+	0.0799614i
$76$	34.5487			0.0521448
$77$	−311.369			−0.460829
$78$	−15.0187	−	111.145i	−0.0218017	−	0.161343i
$79$	574.434			0.818086			0.409043	−	0.912515i	$-0.365863\pi$
$79$	574.434			0.818086			0.409043	+	0.912515i	$0.365863\pi$
$80$			758.150i			1.05955i
$81$	626.297	−	373.086i	0.859118	−	0.511777i
$82$		−	95.2385i		−	0.128260i
$83$	998.011			1.31983			0.659916	−	0.751340i	$-0.270592\pi$
$83$	998.011			1.31983			0.659916	+	0.751340i	$0.270592\pi$
$84$	−60.4579	+	8.16947i	−0.0785297	+	0.0106115i
$85$	−1179.57			−1.50521
$86$			1286.89i			1.61359i
$87$	51.4046	+	380.418i	0.0633466	+	0.468794i
$88$	−718.790			−0.870719
$89$	1179.83			1.40518			0.702592	−	0.711593i	$-0.252026\pi$
$89$	1179.83			1.40518			0.702592	+	0.711593i	$0.252026\pi$
$90$	265.339	+	963.888i	0.310769	+	1.12892i
$91$			85.3891i			0.0983649i
$92$	47.2796			0.0535786
$93$	−201.452	−	1490.84i	−0.224619	−	1.66229i
$94$	−69.2284			−0.0759613
$95$			431.041i			0.465515i
$96$	−261.825	+	35.3795i	−0.278358	+	0.0376136i
$97$			806.397i			0.844095i	0.906574	+	0.422048i	$0.138688\pi$
$97$			806.397i			0.844095i	−0.906574	+	0.422048i	$0.861312\pi$
$98$	617.203			0.636193
$99$	−781.835	+	215.223i	−0.793711	+	0.218492i
$100$	84.5310			0.0845310
$101$	−891.133			−0.877931			−0.438966	−	0.898504i	$-0.644655\pi$
$101$	−891.133			−0.877931			−0.438966	+	0.898504i	$0.644655\pi$
$102$	152.227	+	1126.55i	0.147772	+	1.09358i
$103$		−	950.143i		−	0.908936i	−0.890763	−	0.454468i	$-0.849829\pi$
$103$		−	950.143i		−	0.908936i	0.890763	−	0.454468i	$-0.150171\pi$
$104$			197.119i			0.185857i
$105$	−101.925	−	754.294i	−0.0947322	−	0.701062i
$106$			476.489i			0.436611i
$107$			1066.57i			0.963637i	0.876271	+	0.481818i	$0.160024\pi$
$107$			1066.57i			0.963637i	−0.876271	+	0.481818i	$0.839976\pi$
$108$	−146.160	+	62.3027i	−0.130225	+	0.0555100i
$109$			1354.53i			1.19028i	0.803622	+	0.595140i	$0.202903\pi$
$109$			1354.53i			1.19028i	−0.803622	+	0.595140i	$0.797097\pi$
$110$		−	1112.08i		−	0.963936i
$111$	−133.050	−	984.630i	−0.113771	−	0.841955i
$112$	−556.279			−0.469317
$113$	−1014.43			−0.844506			−0.422253	−	0.906478i	$-0.638761\pi$
$113$	−1014.43			−0.844506			−0.422253	+	0.906478i	$0.638761\pi$
$114$	411.667	−	55.6272i	0.338212	−	0.0457014i
$115$			589.876i			0.478315i
$116$		−	83.6654i		−	0.0669667i
$117$	59.0223	+	214.408i	0.0466377	+	0.169419i
$118$	490.522	−	1081.59i	0.382680	−	0.843797i
$119$		−	865.491i		−	0.666718i
$120$	−235.292	−	1741.27i	−0.178993	−	1.32463i
$121$	−428.960			−0.322284
$122$		−	2031.55i		−	1.50760i
$123$	25.2876	+	187.140i	0.0185374	+	0.137186i
$124$			327.881i			0.237456i
$125$		−	711.542i		−	0.509138i
$126$	−707.236	+	194.688i	−0.500044	+	0.137652i
$127$	2012.85			1.40639			0.703195	−	0.710997i	$-0.251756\pi$
$127$	2012.85			1.40639			0.703195	+	0.710997i	$0.251756\pi$
$128$	−1067.33			−0.737029
$129$	−341.693	−	2528.69i	−0.233212	−	1.72588i
$130$	−304.975			−0.205754
$131$	2285.52			1.52433			0.762164	−	0.647384i	$-0.224137\pi$
$131$	2285.52			1.52433			0.762164	+	0.647384i	$0.224137\pi$
$132$	175.147	−	23.6671i	0.115489	−	0.0156057i
$133$	−316.269			−0.206196
$134$		−	461.716i		−	0.297658i
$135$	−777.310	−	1823.55i	−0.495557	−	1.16256i
$136$		−	1997.97i		−	1.25974i
$137$		−	187.297i		−	0.116802i	−0.998293	−	0.0584009i	$-0.981400\pi$
$137$		−	187.297i		−	0.116802i	0.998293	−	0.0584009i	$-0.0186002\pi$
$138$	563.363	−	76.1253i	0.347512	−	0.0469581i
$139$	1350.81			0.824274			0.412137	−	0.911122i	$-0.364782\pi$
$139$	1350.81			0.824274			0.412137	+	0.911122i	$0.364782\pi$
$140$			165.892i			0.100146i
$141$	136.031	−	18.3814i	0.0812473	−	0.0109787i
$142$		−	1172.08i		−	0.692667i
$143$		−	247.373i		−	0.144660i
$144$	−1396.79	+	384.509i	−0.808330	+	0.222517i
$145$	1043.84			0.597835
$146$			1094.29i			0.620301i
$147$	−1212.78	+	163.879i	−0.680464	+	0.0919489i
$148$			216.550i			0.120272i
$149$	412.444			0.226770			0.113385	−	0.993551i	$-0.463831\pi$
$149$	412.444			0.226770			0.113385	+	0.993551i	$0.463831\pi$
$150$	1007.23	−	136.104i	0.548269	−	0.0740857i
$151$			1168.07i			0.629509i	0.949173	+	0.314755i	$0.101922\pi$
$151$			1168.07i			0.629509i	−0.949173	+	0.314755i	$0.898078\pi$
$152$	−730.101			−0.389599
$153$	−598.241	−	2173.21i	−0.316111	−	1.14832i
$154$	815.972			0.426967
$155$	−4090.75			−2.11985
$156$	−6.49039	−	48.0319i	−0.00333107	−	0.0246515i
$157$			1079.86i			0.548932i	0.961597	+	0.274466i	$0.0885010\pi$
$157$			1079.86i			0.548932i	−0.961597	+	0.274466i	$0.911499\pi$
$158$	−1505.36			−0.757973
$159$	−126.517	−	936.281i	−0.0631033	−	0.466993i
$160$			718.427i			0.354979i
$161$	−432.811			−0.211865
$162$	−1641.27	+	977.706i	−0.795989	+	0.474172i
$163$	2225.21			1.06928			0.534638	−	0.845081i	$-0.320448\pi$
$163$	2225.21			1.06928			0.534638	+	0.845081i	$0.320448\pi$
$164$		−	41.1577i		−	0.0195968i
$165$	295.278	+	2185.20i	0.139318	+	1.03101i
$166$	−2615.38			−1.22285
$167$		−	1986.92i		−	0.920675i	−0.887744	−	0.460337i	$-0.847728\pi$
$167$		−	1986.92i		−	0.920675i	0.887744	−	0.460337i	$-0.152272\pi$
$168$	1277.63	−	172.642i	0.586733	−	0.0792833i
$169$	2129.16			0.969122
$170$	3091.18			1.39460
$171$	−794.139	+	218.610i	−0.355142	+	0.0977634i
$172$			556.134i			0.246540i
$173$	1605.80			0.705702			0.352851	−	0.935679i	$-0.385212\pi$
$173$	1605.80			0.705702			0.352851	+	0.935679i	$0.385212\pi$
$174$	−134.710	−	996.920i	−0.0586918	−	0.434347i
$175$	−773.822			−0.334260
$176$	1611.55			0.690198
$177$	−676.674	+	2255.51i	−0.287356	+	0.957824i
$178$	−3091.84			−1.30193
$179$	−2114.17			−0.882795			−0.441397	−	0.897312i	$-0.645517\pi$
$179$	−2114.17			−0.882795			−0.441397	+	0.897312i	$0.645517\pi$
$180$	114.667	+	416.548i	0.0474821	+	0.172487i
$181$	43.0123			0.0176634			0.00883172	−	0.999961i	$-0.497189\pi$
$181$	43.0123			0.0176634			0.00883172	+	0.999961i	$0.497189\pi$
$182$		−	223.770i		−	0.0911370i
$183$	539.413	+	3991.91i	0.217894	+	1.61252i
$184$	−999.137			−0.400312
$185$	−2701.75			−1.07371
$186$	527.924	+	3906.88i	0.208114	+	1.54014i
$187$			2507.34i			0.980506i
$188$	−29.9173			−0.0116061
$189$	1338.00	−	570.337i	0.514947	−	0.219502i
$190$		−	1129.58i		−	0.431309i
$191$	3484.72			1.32013			0.660066	−	0.751207i	$-0.270528\pi$
$191$	3484.72			1.32013			0.660066	+	0.751207i	$0.270528\pi$
$192$	2896.55	−	391.400i	1.08875	−	0.147119i
$193$	2185.66			0.815166			0.407583	−	0.913168i	$-0.366372\pi$
$193$	2185.66			0.815166			0.407583	+	0.913168i	$0.366372\pi$
$194$		−	2113.24i		−	0.782070i
$195$	599.263	−	80.9764i	0.220072	−	0.0297376i
$196$	266.727			0.0972036
$197$		−	2739.35i		−	0.990713i	−0.868690	−	0.495357i	$-0.835037\pi$
$197$		−	2739.35i		−	0.990713i	0.868690	−	0.495357i	$-0.164963\pi$
$198$	2048.87	−	564.012i	0.735388	−	0.202437i
$199$	−5466.83			−1.94740			−0.973701	−	0.227829i	$-0.926837\pi$
$199$	−5466.83			−1.94740			−0.973701	+	0.227829i	$0.926837\pi$
$200$	−1786.35			−0.631571
$201$	122.594	+	907.252i	0.0430204	+	0.318371i
$202$	2335.30			0.813420
$203$			765.898i			0.264805i
$204$	65.7856	+	486.844i	0.0225780	+	0.167088i
$205$	513.498			0.174947
$206$			2489.94i			0.842147i
$207$	−1086.77	+	299.166i	−0.364907	+	0.100452i
$208$		−	441.947i		−	0.147324i
$209$	916.235			0.303241
$210$	267.104	+	1976.70i	0.0877712	+	0.649548i
$211$		−	2434.64i		−	0.794349i	−0.917743	−	0.397174i	$-0.869991\pi$
$211$		−	2434.64i		−	0.794349i	0.917743	−	0.397174i	$-0.130009\pi$
$212$			205.917i			0.0667095i
$213$	311.209	+	2303.09i	0.100111	+	0.740868i
$214$		−	2795.04i		−	0.892828i
$215$	−6938.52			−2.20095
$216$	3088.74	−	1316.61i	0.972972	−	0.414741i
$217$		−	3001.52i		−	0.938969i
$218$		−	3549.67i		−	1.10282i
$219$	−290.554	−	2150.23i	−0.0896520	−	0.663466i
$220$		−	480.591i		−	0.147279i
$221$	687.605			0.209291
$222$	348.669	+	2580.31i	0.105411	+	0.780087i
$223$	−1839.93			−0.552516			−0.276258	−	0.961084i	$-0.589094\pi$
$223$	−1839.93			−0.552516			−0.276258	+	0.961084i	$0.589094\pi$
$224$	−527.133			−0.157235
$225$	−1943.03	+	534.878i	−0.575714	+	0.158482i
$226$	2658.40			0.782451
$227$	5447.94			1.59292			0.796459	−	0.604693i	$-0.206704\pi$
$227$	5447.94			1.59292			0.796459	+	0.604693i	$0.206704\pi$
$228$	177.903	−	24.0395i	0.0516752	−	0.00698269i
$229$			514.199i			0.148381i	0.997244	+	0.0741904i	$0.0236373\pi$
$229$			514.199i			0.148381i	−0.997244	+	0.0741904i	$0.976363\pi$
$230$		−	1545.83i		−	0.443168i
$231$	−1603.35	+	216.655i	−0.456678	+	0.0617094i
$232$			1768.06i			0.500340i
$233$	168.140			0.0472756			0.0236378	−	0.999721i	$-0.492475\pi$
$233$	168.140			0.0472756			0.0236378	+	0.999721i	$0.492475\pi$
$234$	−154.673	−	561.877i	−0.0432107	−	0.156970i
$235$		−	373.259i		−	0.103612i
$236$	211.981	−	467.411i	0.0584694	−	0.128923i
$237$	2957.96	−	399.700i	0.810718	−	0.109550i
$238$			2268.10i			0.617727i
$239$		−	4028.24i		−	1.09023i	−0.838361	−	0.545116i	$-0.816486\pi$
$239$		−	4028.24i		−	1.09023i	0.838361	−	0.545116i	$-0.183514\pi$
$240$	527.532	+	3903.98i	0.141884	+	1.05000i
$241$	−3105.01			−0.829922			−0.414961	−	0.909839i	$-0.636205\pi$
$241$	−3105.01			−0.829922			−0.414961	+	0.909839i	$0.636205\pi$
$242$	1124.13			0.298602
$243$	2965.43	−	2356.94i	0.782848	−	0.622212i
$244$		−	877.941i		−	0.230346i
$245$			3327.77i			0.867770i
$246$	−66.2684	−	490.417i	−0.0171753	−	0.127105i
$247$		−	251.266i		−	0.0647274i
$248$		−	6928.94i		−	1.77415i
$249$	5139.11	−	694.431i	1.30794	−	0.176738i
$250$			1864.66i			0.471726i
$251$			6148.67i			1.54622i	0.634274	+	0.773108i	$0.281299\pi$
$251$			6148.67i			1.54622i	−0.634274	+	0.773108i	$0.718701\pi$
$252$	−305.635	+	84.1350i	−0.0764015	+	0.0210318i
$253$	1253.86			0.311579
$254$	−5274.86			−1.30305
$255$	−6074.04	+	820.764i	−1.49165	+	0.201562i
$256$	−1703.01			−0.415775
$257$			5810.82i			1.41038i	0.709016	+	0.705192i	$0.249139\pi$
$257$			5810.82i			1.41038i	−0.709016	+	0.705192i	$0.750861\pi$
$258$	895.437	+	6626.65i	0.216076	+	1.59906i
$259$		−	1982.36i		−	0.475591i
$260$	−131.796			−0.0314371
$261$	529.401	+	1923.14i	0.125552	+	0.456089i
$262$	−5989.42			−1.41232
$263$		−	1977.98i		−	0.463756i	−0.972745	−	0.231878i	$-0.925513\pi$
$263$		−	1977.98i		−	0.463756i	0.972745	−	0.231878i	$-0.0744870\pi$
$264$	−3701.30	+	500.145i	−0.862877	+	0.116598i
$265$	−2569.09			−0.595539
$266$	828.812			0.191044
$267$	6075.34	−	820.941i	1.39253	−	0.188168i
$268$		−	199.532i		−	0.0454790i
$269$	3386.28			0.767529			0.383765	−	0.923431i	$-0.374627\pi$
$269$	3386.28			0.767529			0.383765	+	0.923431i	$0.374627\pi$
$270$	2037.01	+	4778.77i	0.459143	+	1.07714i
$271$	−1085.64			−0.243351			−0.121676	−	0.992570i	$-0.538827\pi$
$271$	−1085.64			−0.243351			−0.121676	+	0.992570i	$0.538827\pi$
$272$			4479.50i			0.998565i
$273$	59.4150	+	439.699i	0.0131720	+	0.0974790i
$274$			490.828i			0.108219i
$275$	2241.77			0.491578
$276$	243.459	−	32.8978i	0.0530961	−	0.00717470i
$277$	482.947			0.104756			0.0523781	−	0.998627i	$-0.483320\pi$
$277$	482.947			0.104756			0.0523781	+	0.998627i	$0.483320\pi$
$278$	−3539.92			−0.763706
$279$	−2074.70	−	7536.68i	−0.445193	−	1.61724i
$280$		−	3505.72i		−	0.748238i
$281$			8460.57i			1.79614i	0.439853	+	0.898070i	$0.355031\pi$
$281$			8460.57i			1.79614i	−0.439853	+	0.898070i	$0.644969\pi$
$282$	−356.482	+	48.1702i	−0.0752772	+	0.0101720i
$283$		−	3950.67i		−	0.829834i	−0.909859	−	0.414917i	$-0.863811\pi$
$283$		−	3950.67i		−	0.829834i	0.909859	−	0.414917i	$-0.136189\pi$
$284$		−	506.518i		−	0.105832i
$285$	299.925	+	2219.58i	0.0623369	+	0.461322i
$286$			648.264i			0.134030i
$287$			376.770i			0.0774914i
$288$	−1323.61	+	364.363i	−0.270814	+	0.0745496i
$289$	−2056.46			−0.418576
$290$	−2735.47			−0.553905
$291$	561.103	+	4152.42i	0.113032	+	0.836493i
$292$			472.901i			0.0947754i
$293$			3996.29i			0.796812i	0.917209	+	0.398406i	$0.130437\pi$
$293$			3996.29i			0.796812i	−0.917209	+	0.398406i	$0.869563\pi$
$294$	3178.20	−	429.459i	0.630463	−	0.0851924i
$295$	5831.59	+	2644.75i	1.15094	+	0.521977i
$296$		−	4576.25i		−	0.898611i
$297$	−3876.19	+	1652.27i	−0.757304	+	0.322810i
$298$	−1080.85			−0.210107
$299$		−	343.855i		−	0.0665072i
$300$	435.280	−	58.8179i	0.0837697	−	0.0113195i
$301$		−	5091.02i		−	0.974889i
$302$		−	3061.03i		−	0.583252i
$303$	−4588.76	+	620.064i	−0.870024	+	0.117563i
$304$	1636.91			0.308826
$305$	10953.5			2.05638
$306$	1567.75	+	5695.10i	0.292882	+	1.06394i
$307$	3399.89			0.632058			0.316029	−	0.948750i	$-0.397650\pi$
$307$	3399.89			0.632058			0.316029	+	0.948750i	$0.397650\pi$
$308$	352.625			0.0652360
$309$	−661.124	−	4892.62i	−0.121715	−	0.900750i
$310$	10720.2			1.96408
$311$		−	9897.44i		−	1.80460i	−0.431104	−	0.902302i	$-0.641876\pi$
$311$		−	9897.44i		−	1.80460i	0.431104	−	0.902302i	$-0.358124\pi$
$312$	137.158	+	1015.04i	0.0248880	+	0.184183i
$313$			2022.75i			0.365280i	0.983180	+	0.182640i	$0.0584643\pi$
$313$			2022.75i			0.365280i	−0.983180	+	0.182640i	$0.941536\pi$
$314$		−	2829.87i		−	0.508596i
$315$	−1049.70	−	3813.20i	−0.187758	−	0.682063i
$316$	−650.545			−0.115810
$317$			4543.64i			0.805036i	0.915412	+	0.402518i	$0.131865\pi$
$317$			4543.64i			0.805036i	−0.915412	+	0.402518i	$0.868135\pi$
$318$	331.548	+	2453.61i	0.0584664	+	0.432678i
$319$		−	2218.81i		−	0.389435i
$320$		−	7947.90i		−	1.38844i
$321$	742.135	+	5492.14i	0.129040	+	0.954958i
$322$	1134.22			0.196297
$323$			2546.79i			0.438722i
$324$	−709.280	+	422.519i	−0.121619	+	0.0724484i
$325$		−	614.778i		−	0.104928i
$326$	−5831.37			−0.990705
$327$	942.502	+	6974.96i	0.159390	+	1.17956i
$328$			869.766i			0.146417i
$329$	273.872			0.0458938
$330$	−773.804	−	5726.51i	−0.129080	−	0.955254i
$331$	3902.76			0.648082			0.324041	−	0.946043i	$-0.394958\pi$
$331$	3902.76			0.648082			0.324041	+	0.946043i	$0.394958\pi$
$332$	−1130.25			−0.186838
$333$	−1370.24	−	4977.63i	−0.225492	−	0.819137i
$334$			5206.91i			0.853023i
$335$	2489.43			0.406007
$336$	−2864.48	+	387.067i	−0.465090	+	0.0628460i
$337$			4345.21i			0.702369i	0.936306	+	0.351185i	$0.114221\pi$
$337$			4345.21i			0.702369i	−0.936306	+	0.351185i	$0.885779\pi$
$338$	−5579.66			−0.897910
$339$	−5223.64	+	705.852i	−0.836900	+	0.113087i
$340$	1335.86			0.213081
$341$			8695.43i			1.38089i
$342$	2081.11	−	572.888i	0.329046	−	0.0905797i
$343$	−5997.66			−0.944149
$344$		−	11752.5i		−	1.84202i
$345$	410.445	+	3037.48i	0.0640510	+	0.474007i
$346$	−4208.14			−0.653847
$347$	−8675.42			−1.34213			−0.671067	−	0.741396i	$-0.734164\pi$
$347$	−8675.42			−1.34213			−0.671067	+	0.741396i	$0.734164\pi$
$348$	−58.2156	−	430.822i	−0.00896748	−	0.0663635i
$349$			1901.71i			0.291679i	0.989308	+	0.145840i	$0.0465883\pi$
$349$			1901.71i			0.291679i	−0.989308	+	0.145840i	$0.953412\pi$
$350$	2027.87			0.309698
$351$	453.115	+	1063.00i	0.0689046	+	0.161648i
$352$	1527.11			0.231237
$353$	3640.14			0.548853			0.274427	−	0.961608i	$-0.411512\pi$
$353$	3640.14			0.548853			0.274427	+	0.961608i	$0.411512\pi$
$354$	1773.29	−	5910.78i	0.266241	−	0.887442i
$355$	6319.50			0.944801
$356$	−1336.15			−0.198921
$357$	−602.221	−	4456.72i	−0.0892799	−	0.660713i
$358$	5540.37			0.817926
$359$		−	3116.66i		−	0.458193i	−0.973404	−	0.229096i	$-0.926423\pi$
$359$		−	3116.66i		−	0.458193i	0.973404	−	0.229096i	$-0.0735771\pi$
$360$	−2423.21	−	8802.71i	−0.354762	−	1.28873i
$361$	−5928.35			−0.864316
$362$	−112.718			−0.0163655
$363$	−2208.87	+	298.477i	−0.319382	+	0.0431570i
$364$		−	96.7030i		−	0.0139248i
$365$	−5900.07			−0.846093
$366$	−1413.58	−	10461.2i	−0.201883	−	1.49403i
$367$			12568.8i			1.78770i	0.448363	+	0.893852i	$0.352007\pi$
$367$			12568.8i			1.78770i	−0.448363	+	0.893852i	$0.647993\pi$
$368$	2240.09			0.317318
$369$	260.429	+	946.053i	0.0367409	+	0.133468i
$370$	7080.19			0.994815
$371$		−	1885.02i		−	0.263788i
$372$	228.144	+	1688.37i	0.0317976	+	0.235317i
$373$	−7837.46			−1.08796			−0.543979	−	0.839099i	$-0.683083\pi$
$373$	−7837.46			−1.08796			−0.543979	+	0.839099i	$0.683083\pi$
$374$		−	6570.70i		−	0.908457i
$375$	−495.102	−	3663.98i	−0.0681785	−	0.504553i
$376$	632.228			0.0867146
$377$	−608.482			−0.0831258
$378$	−3506.34	+	1494.62i	−0.477108	+	0.203373i
$379$	−958.789			−0.129946			−0.0649732	−	0.997887i	$-0.520696\pi$
$379$	−958.789			−0.129946			−0.0649732	+	0.997887i	$0.520696\pi$
$380$		−	488.154i		−	0.0658994i
$381$	10364.9	−	1400.57i	1.39372	−	0.188329i
$382$	−9132.02			−1.22313
$383$			4651.79i			0.620615i	0.950636	+	0.310307i	$0.100432\pi$
$383$			4651.79i			0.620615i	−0.950636	+	0.310307i	$0.899568\pi$
$384$	−5496.07	+	742.665i	−0.730391	+	0.0986952i
$385$			4399.47i			0.582384i
$386$	−5727.72			−0.755267
$387$	−3518.99	−	12783.3i	−0.462224	−	1.67911i
$388$		−	913.243i		−	0.119492i
$389$		−	4534.02i		−	0.590961i	−0.955349	−	0.295481i	$-0.904520\pi$
$389$		−	4534.02i		−	0.590961i	0.955349	−	0.295481i	$-0.0954797\pi$
$390$	−1570.42	+	212.206i	−0.203901	+	0.0275525i
$391$			3485.26i			0.450786i
$392$	−5636.61			−0.726254
$393$	11769.0	−	1590.30i	1.51060	−	0.204122i
$394$			7178.72i			0.917915i
$395$		−	8116.43i		−	1.03388i
$396$	885.427	−	243.740i	0.112360	−	0.0309303i
$397$			12116.2i			1.53172i	0.643006	+	0.765861i	$0.277687\pi$
$397$			12116.2i			1.53172i	−0.643006	+	0.765861i	$0.722313\pi$
$398$	14326.3			1.80431
$399$	−1628.58	+	220.065i	−0.204338	+	0.0276116i
$400$	4005.06			0.500632
$401$	6566.79			0.817780			0.408890	−	0.912584i	$-0.365916\pi$
$401$	6566.79			0.817780			0.408890	+	0.912584i	$0.365916\pi$
$402$	−321.269	−	2377.54i	−0.0398593	−	0.294977i
$403$	2384.61			0.294754
$404$	1009.21			0.124282
$405$	−5271.49	−	8849.23i	−0.646772	−	1.08573i
$406$		−	2007.11i		−	0.245347i
$407$			5742.93i			0.699426i
$408$	−1390.22	−	10288.2i	−0.168691	−	1.24839i
$409$		−	13854.7i		−	1.67498i	−0.546449	−	0.837492i	$-0.684021\pi$
$409$		−	13854.7i		−	1.67498i	0.546449	−	0.837492i	$-0.315979\pi$
$410$	−1345.67			−0.162092
$411$	−130.324	−	964.457i	−0.0156409	−	0.115750i
$412$			1076.04i			0.128671i
$413$	−1940.54	+	4278.83i	−0.231205	+	0.509800i
$414$	2847.98	−	783.992i	0.338094	−	0.0930703i
$415$		−	14101.3i		−	1.66797i
$416$		−	418.791i		−	0.0493580i
$417$	6955.79	−	939.913i	0.816850	−	0.110378i
$418$	−2401.08			−0.280958
$419$	−13610.4			−1.58690			−0.793452	−	0.608633i	$-0.791718\pi$
$419$	−13610.4			−1.58690			−0.793452	+	0.608633i	$0.791718\pi$
$420$	115.430	+	854.236i	0.0134105	+	0.0992440i
$421$		−	6670.28i		−	0.772185i	−0.922460	−	0.386092i	$-0.873825\pi$
$421$		−	6670.28i		−	0.772185i	0.922460	−	0.386092i	$-0.126175\pi$
$422$			6380.20i			0.735979i
$423$	687.681	−	189.305i	0.0790454	−	0.0217596i
$424$		−	4351.54i		−	0.498418i
$425$			6231.29i			0.711205i
$426$	−815.551	−	6035.45i	−0.0927548	−	0.686429i
$427$			8036.94i			0.910854i
$428$		−	1207.89i		−	0.136415i
$429$	−172.126	−	1273.81i	−0.0193714	−	0.143357i
$430$	18183.0			2.03922
$431$	3357.81			0.375266			0.187633	−	0.982239i	$-0.439918\pi$
$431$	3357.81			0.375266			0.187633	+	0.982239i	$0.439918\pi$
$432$	−6925.04	+	2951.88i	−0.771253	+	0.328756i
$433$	−13001.8			−1.44301			−0.721507	−	0.692408i	$-0.756550\pi$
$433$	−13001.8			−1.44301			−0.721507	+	0.692408i	$0.756550\pi$
$434$			7865.75i			0.869973i
$435$	5375.09	−	726.318i	0.592450	−	0.0800558i
$436$		−	1534.00i		−	0.168499i
$437$	1273.59			0.139414
$438$	761.422	+	5634.88i	0.0830643	+	0.614714i
$439$	−6978.94			−0.758740			−0.379370	−	0.925245i	$-0.623859\pi$
$439$	−6978.94			−0.758740			−0.379370	+	0.925245i	$0.623859\pi$
$440$			10156.1i			1.10039i
$441$	−6131.00	+	1687.74i	−0.662023	+	0.182242i
$442$	−1801.93			−0.193912
$443$	12822.4			1.37519			0.687595	−	0.726094i	$-0.258666\pi$
$443$	12822.4			1.37519			0.687595	+	0.726094i	$0.258666\pi$
$444$	150.679	+	1115.09i	0.0161056	+	0.119189i
$445$		−	16670.3i		−	1.77584i
$446$	4821.72			0.511917
$447$	2123.82	−	286.985i	0.224728	−	0.0303667i
$448$	5831.64			0.614998
$449$			11068.9i			1.16342i	0.813397	+	0.581709i	$0.197616\pi$
$449$			11068.9i			1.16342i	−0.813397	+	0.581709i	$0.802384\pi$
$450$	5091.90	−	1401.70i	0.533410	−	0.146837i
$451$		−	1091.51i		−	0.113962i
$452$	1148.84			0.119550
$453$	812.758	+	6014.79i	0.0842974	+	0.623840i
$454$	−14276.8			−1.47587
$455$	1206.50			0.124311
$456$	−3759.55	+	508.015i	−0.386090	+	0.0521710i
$457$			14195.7i			1.45306i	0.687135	+	0.726530i	$0.258868\pi$
$457$			14195.7i			1.45306i	−0.687135	+	0.726530i	$0.741132\pi$
$458$		−	1347.50i		−	0.137478i
$459$	−4592.71	−	10774.4i	−0.467035	−	1.09565i
$460$		−	668.034i		−	0.0677114i
$461$			12340.2i			1.24672i	0.781934	+	0.623361i	$0.214233\pi$
$461$			12340.2i			1.24672i	−0.781934	+	0.623361i	$0.785767\pi$
$462$	4201.73	−	567.765i	0.423121	−	0.0571750i
$463$		−	12455.4i		−	1.25022i	−0.780536	−	0.625111i	$-0.785054\pi$
$463$		−	12455.4i		−	1.25022i	0.780536	−	0.625111i	$-0.214946\pi$
$464$		−	3964.04i		−	0.396608i
$465$	−21064.7	+	2846.41i	−2.10076	+	0.283869i
$466$	−440.626			−0.0438018
$467$	14655.7			1.45221			0.726106	−	0.687583i	$-0.241328\pi$
$467$	14655.7			1.45221			0.726106	+	0.687583i	$0.241328\pi$
$468$	−66.8426	−	242.817i	−0.00660214	−	0.0239834i
$469$			1826.58i			0.179837i
$470$			978.159i			0.0959981i
$471$	751.383	+	5560.58i	0.0735072	+	0.543988i
$472$	−4479.69	+	9877.58i	−0.436853	+	0.963247i
$473$			14748.7i			1.43372i
$474$	−7751.61	+	1047.45i	−0.751146	+	0.101500i
$475$	2277.05			0.219954
$476$			980.167i			0.0943821i
$477$	−1302.96	−	4733.21i	−0.125070	−	0.454337i
$478$			10556.4i			1.01012i
$479$		−	19253.9i		−	1.83660i	−0.395883	−	0.918301i	$-0.629561\pi$
$479$		−	19253.9i		−	1.83660i	0.395883	−	0.918301i	$-0.370439\pi$
$480$	499.892	+	3699.43i	0.0475351	+	0.351782i
$481$	1574.93			0.149294
$482$	8136.96			0.768939
$483$	−2228.70	+	301.157i	−0.209957	+	0.0283708i
$484$	485.797			0.0456233
$485$	11393.9			1.06675
$486$	−7771.17	+	6176.57i	−0.725324	+	0.576492i
$487$	−6730.13			−0.626225			−0.313112	−	0.949716i	$-0.601372\pi$
$487$	−6730.13			−0.626225			−0.313112	+	0.949716i	$0.601372\pi$
$488$			18553.1i			1.72102i
$489$	11458.4	−	1548.34i	1.05965	−	0.143186i
$490$		−	8720.74i		−	0.804006i
$491$		−	13349.0i		−	1.22695i	−0.789715	−	0.613473i	$-0.789772\pi$
$491$		−	13349.0i		−	1.22695i	0.789715	−	0.613473i	$-0.210228\pi$
$492$	−28.6381	−	211.935i	−0.00262420	−	0.0194203i
$493$	6167.48			0.563427
$494$			658.466i			0.0599712i
$495$	3040.99	+	11046.9i	0.276126	+	1.00307i
$496$			15534.9i			1.40633i
$497$			4636.82i			0.418491i
$498$	−13467.5	+	1819.82i	−1.21184	+	0.163751i
$499$	13091.9			1.17449			0.587247	−	0.809408i	$-0.300212\pi$
$499$	13091.9			1.17449			0.587247	+	0.809408i	$0.300212\pi$
$500$			805.820i			0.0720748i
$501$	−1382.53	−	10231.4i	−0.123287	−	0.912383i
$502$		−	16113.1i		−	1.43260i
$503$	−22274.5			−1.97449			−0.987246	−	0.159205i	$-0.949107\pi$
$503$	−22274.5			−1.97449			−0.987246	+	0.159205i	$0.949107\pi$
$504$	6458.83	−	1777.99i	0.570832	−	0.157138i
$505$			12591.2i			1.10951i
$506$	−3285.85			−0.288684
$507$	10963.8	−	1481.50i	0.960394	−	0.129775i
$508$	−2279.55			−0.199092
$509$	2733.09			0.238000			0.119000	−	0.992894i	$-0.462031\pi$
$509$	2733.09			0.238000			0.119000	+	0.992894i	$0.462031\pi$
$510$	15917.6	−	2150.89i	1.38204	−	0.186751i
$511$		−	4329.08i		−	0.374769i
$512$	13001.6			1.12225
$513$	−3937.19	+	1678.27i	−0.338852	+	0.144440i
$514$		−	15227.8i		−	1.30675i
$515$	−13425.0			−1.14869
$516$	386.966	+	2863.73i	0.0330141	+	0.244319i
$517$	−793.410			−0.0674935
$518$			5194.96i			0.440644i
$519$	8268.82	−	1117.34i	0.699346	−	0.0945003i
$520$	2785.18			0.234881
$521$			9376.92i			0.788504i	0.919002	+	0.394252i	$0.128996\pi$
$521$			9376.92i			0.788504i	−0.919002	+	0.394252i	$0.871004\pi$
$522$	−1387.34	−	5039.76i	−0.116326	−	0.422575i
$523$	−5235.01			−0.437688			−0.218844	−	0.975760i	$-0.570229\pi$
$523$	−5235.01			−0.437688			−0.218844	+	0.975760i	$0.570229\pi$
$524$	−2588.35			−0.215787
$525$	−3984.68	+	538.437i	−0.331249	+	0.0447606i
$526$			5183.49i			0.429679i
$527$	−24170.1			−1.99784
$528$	8298.43	−	1121.34i	0.683982	−	0.0924242i
$529$	−10424.1			−0.856752
$530$	6732.53			0.551778
$531$	−1915.01	+	12085.3i	−0.156506	+	0.987677i
$532$	358.174			0.0291895
$533$	−299.332			−0.0243255
$534$	−15921.0	+	2151.35i	−1.29020	+	0.174341i
$535$	15070.0			1.21782
$536$			4216.62i			0.339795i
$537$	−10886.6	+	1471.07i	−0.874844	+	0.118215i
$538$	−8874.07			−0.711131
$539$	7073.62			0.565273
$540$	880.302	+	2065.16i	0.0701522	+	0.164575i
$541$		−	11705.8i		−	0.930261i	−0.885242	−	0.465131i	$-0.846007\pi$
$541$		−	11705.8i		−	0.930261i	0.885242	−	0.465131i	$-0.153993\pi$
$542$	2845.03			0.225469
$543$	221.486	−	29.9286i	0.0175043	−	0.00236530i
$544$			4244.80i			0.334548i
$545$	19138.8			1.50425
$546$	−155.702	−	1152.27i	−0.0122041	−	0.0903162i
$547$	24163.1			1.88874			0.944369	−	0.328889i	$-0.106674\pi$
$547$	24163.1			1.88874			0.944369	+	0.328889i	$0.106674\pi$
$548$			212.113i			0.0165347i
$549$	5555.26	+	20180.4i	0.431863	+	1.56881i
$550$	−5874.77			−0.455456
$551$		−	2253.73i		−	0.174251i
$552$	−5144.91	+	695.214i	−0.396706	+	0.0536056i
$553$	5955.29			0.457947
$554$	−1265.61			−0.0970586
$555$	−13912.3	+	1879.92i	−1.06404	+	0.143780i
$556$	−1529.79			−0.116686
$557$		−	1473.30i		−	0.112075i	−0.998429	−	0.0560374i	$-0.982153\pi$
$557$		−	1473.30i		−	0.112075i	0.998429	−	0.0560374i	$-0.0178466\pi$
$558$	5436.93	+	19750.6i	0.412480	+	1.49840i
$559$	4044.66			0.306030
$560$			7859.92i			0.593111i
$561$	1744.64	+	12911.2i	0.131299	+	0.971675i
$562$		−	22171.7i		−	1.66416i
$563$	2473.95			0.185194			0.0925971	−	0.995704i	$-0.470483\pi$
$563$	2473.95			0.185194			0.0925971	+	0.995704i	$0.470483\pi$
$564$	−154.055	+	20.8169i	−0.0115016	+	0.00155417i
$565$			14333.3i			1.06727i
$566$			10353.1i			0.768857i
$567$	6492.97	−	3867.87i	0.480915	−	0.286482i
$568$			10704.0i			0.790723i
$569$	−5358.46			−0.394795			−0.197398	−	0.980324i	$-0.563249\pi$
$569$	−5358.46			−0.394795			−0.197398	+	0.980324i	$0.563249\pi$
$570$	−785.981	−	5816.63i	−0.0577564	−	0.427424i
$571$		−	14870.4i		−	1.08985i	−0.838483	−	0.544927i	$-0.816557\pi$
$571$		−	14870.4i		−	1.08985i	0.838483	−	0.544927i	$-0.183443\pi$
$572$			280.150i			0.0204784i
$573$	17944.0	−	2424.72i	1.30824	−	0.176779i
$574$		−	987.360i		−	0.0717972i
$575$	3116.12			0.226002
$576$	14643.0	−	4030.92i	1.05924	−	0.291588i
$577$	13682.7			0.987206			0.493603	−	0.869687i	$-0.335680\pi$
$577$	13682.7			0.987206			0.493603	+	0.869687i	$0.335680\pi$
$578$	5389.15			0.387818
$579$	11254.7	−	1520.81i	0.807824	−	0.109159i
$580$	−1182.14			−0.0846309
$581$	10346.6			0.738812
$582$	−1470.42	−	10881.8i	−0.104727	−	0.775027i
$583$			5460.93i			0.387939i
$584$		−	9993.59i		−	0.708112i
$585$	3029.47	−	833.952i	0.214108	−	0.0589396i
$586$		−	10472.7i		−	0.738262i
$587$	−9648.79			−0.678446			−0.339223	−	0.940706i	$-0.610164\pi$
$587$	−9648.79			−0.678446			−0.339223	+	0.940706i	$0.610164\pi$
$588$	1373.47	−	185.592i	0.0963281	−	0.0130165i
$589$			8832.27i			0.617873i
$590$	−15282.2	−	6930.80i	−1.06637	−	0.483621i
$591$	−1906.08	−	14105.9i	−0.132666	−	0.981791i
$592$			10260.1i			0.712308i
$593$			18246.6i			1.26357i	0.775143	+	0.631786i	$0.217678\pi$
$593$			18246.6i			1.26357i	−0.775143	+	0.631786i	$0.782322\pi$
$594$	10157.9	−	4329.93i	0.701657	−	0.299090i
$595$	−12228.9			−0.842582
$596$	−467.092			−0.0321021
$597$	−28150.6	+	3803.90i	−1.92986	+	0.260776i
$598$			901.104i			0.0616202i
$599$		−	10841.3i		−	0.739506i	−0.929130	−	0.369753i	$-0.879442\pi$
$599$		−	10841.3i		−	0.739506i	0.929130	−	0.369753i	$-0.120558\pi$
$600$	−9198.56	+	1242.97i	−0.625883	+	0.0845735i
$601$			12538.7i			0.851022i	0.904953	+	0.425511i	$0.139906\pi$
$601$			12538.7i			0.851022i	−0.904953	+	0.425511i	$0.860094\pi$
$602$			13341.5i			0.903253i
$603$	1262.56	+	4586.46i	0.0852660	+	0.309743i
$604$		−	1322.83i		−	0.0891148i
$605$			6060.97i			0.407295i
$606$	12025.3	−	1624.93i	0.806094	−	0.108925i
$607$	17732.8			1.18575			0.592876	−	0.805294i	$-0.297993\pi$
$607$	17732.8			1.18575			0.592876	+	0.805294i	$0.297993\pi$
$608$	1551.14			0.103466
$609$	532.923	+	3943.88i	0.0354600	+	0.262420i
$610$	−28704.6			−1.90527
$611$			217.583i			0.0144066i
$612$	677.507	+	2461.16i	0.0447493	+	0.162559i
$613$		−	20181.4i		−	1.32972i	−0.746967	−	0.664861i	$-0.768491\pi$
$613$		−	20181.4i		−	1.32972i	0.746967	−	0.664861i	$-0.231509\pi$
$614$	−8909.72			−0.585614
$615$	2644.18	−	357.299i	0.173372	−	0.0234272i
$616$	−7451.86			−0.487409
$617$		−	12638.9i		−	0.824672i	−0.911032	−	0.412336i	$-0.864713\pi$
$617$		−	12638.9i		−	0.824672i	0.911032	−	0.412336i	$-0.135287\pi$
$618$	1732.54	+	12821.6i	0.112772	+	0.834562i
$619$	−20291.8			−1.31760			−0.658802	−	0.752316i	$-0.728937\pi$
$619$	−20291.8			−1.31760			−0.658802	+	0.752316i	$0.728937\pi$
$620$	4632.77			0.300091
$621$	−5388.01	+	2296.70i	−0.348169	+	0.148412i
$622$			25937.1i			1.67200i
$623$	12231.5			0.786591
$624$	−307.513	−	2275.74i	−0.0197282	−	0.145998i
$625$	−19383.8			−1.24057
$626$		−	5300.80i		−	0.338439i
$627$	4718.02	−	637.530i	0.300510	−	0.0406069i
$628$		−	1222.94i		−	0.0777080i
$629$	−15963.2			−1.01192
$630$	2750.83	+	9992.85i	0.173961	+	0.631944i
$631$	−16311.4			−1.02907			−0.514537	−	0.857468i	$-0.672036\pi$
$631$	−16311.4			−1.02907			−0.514537	+	0.857468i	$0.672036\pi$
$632$	13747.7			0.865273
$633$	−1694.06	−	12536.8i	−0.106371	−	0.787194i
$634$		−	11907.0i		−	0.745882i
$635$		−	28440.5i		−	1.77736i
$636$	143.280	+	1060.34i	0.00893304	+	0.0661086i
$637$		−	1939.85i		−	0.120659i
$638$			5814.61i			0.360819i
$639$	3205.05	+	11642.9i	0.198419	+	0.720790i
$640$			15080.8i			0.931439i
$641$			39.0296i			0.00240496i	0.999999	+	0.00120248i	$0.000382761\pi$
$641$			39.0296i			0.00240496i	−0.999999	+	0.00120248i	$0.999617\pi$
$642$	−1944.83	−	14392.7i	−0.119558	−	0.884787i
$643$	−16730.8			−1.02612			−0.513062	−	0.858352i	$-0.671489\pi$
$643$	−16730.8			−1.02612			−0.513062	+	0.858352i	$0.671489\pi$
$644$	490.158			0.0299921
$645$	−35728.9	+	4827.93i	−2.18112	+	0.294728i
$646$		−	6674.10i		−	0.406485i
$647$		−	1223.42i		−	0.0743392i	−0.999309	−	0.0371696i	$-0.988166\pi$
$647$		−	1223.42i		−	0.0743392i	0.999309	−	0.0371696i	$-0.0118342\pi$
$648$	14988.9	−	8928.89i	0.908671	−	0.541296i
$649$	5621.75	−	12395.8i	0.340020	−	0.749735i
$650$			1611.08i			0.0972182i
$651$	−2088.50	−	15455.9i	−0.125737	−	0.930512i
$652$	−2520.05			−0.151369
$653$		−	17337.5i		−	1.03900i	−0.854470	−	0.519501i	$-0.826118\pi$
$653$		−	17337.5i		−	1.03900i	0.854470	−	0.519501i	$-0.173882\pi$
$654$	−2469.91	−	18278.5i	−0.147678	−	1.09288i
$655$		−	32293.1i		−	1.92641i
$656$		−	1950.04i		−	0.116061i
$657$	−2992.33	−	10870.1i	−0.177689	−	0.645486i
$658$	−717.707			−0.0425215
$659$	2323.76			0.137361			0.0686805	−	0.997639i	$-0.478121\pi$
$659$	2323.76			0.137361			0.0686805	+	0.997639i	$0.478121\pi$
$660$	−334.402	−	2474.73i	−0.0197221	−	0.145953i
$661$	12976.1			0.763556			0.381778	−	0.924254i	$-0.375312\pi$
$661$	12976.1			0.763556			0.381778	+	0.924254i	$0.375312\pi$
$662$	−10227.5			−0.600460
$663$	3540.72	−	478.446i	0.207406	−	0.0280261i
$664$	23885.0			1.39596
$665$			4468.71i			0.260585i
$666$	3590.84	+	13044.3i	0.208922	+	0.758946i
$667$		−	3084.21i		−	0.179042i
$668$			2250.19i			0.130333i
$669$	−9474.47	+	1280.25i	−0.547540	+	0.0739872i
$670$	−6523.78			−0.376173
$671$		−	23283.1i		−	1.33954i
$672$	−2714.40	+	366.787i	−0.155819	+	0.0210552i
$673$		−	25426.3i		−	1.45633i	−0.685400	−	0.728166i	$-0.740373\pi$
$673$		−	25426.3i		−	1.45633i	0.685400	−	0.728166i	$-0.259627\pi$
$674$		−	11387.0i		−	0.650759i
$675$	−9633.20	+	4106.27i	−0.549307	+	0.234149i
$676$	−2411.27			−0.137191
$677$		−	28904.4i		−	1.64090i	−0.571721	−	0.820448i	$-0.693724\pi$
$677$		−	28904.4i		−	1.64090i	0.571721	−	0.820448i	$-0.306276\pi$
$678$	13689.0	−	1849.75i	0.775403	−	0.104778i
$679$			8360.11i			0.472506i
$680$	−28230.2			−1.59203
$681$	28053.3	−	3790.76i	1.57857	−	0.213307i
$682$		−	22787.2i		−	1.27942i
$683$	30973.2			1.73522			0.867611	−	0.497244i	$-0.165655\pi$
$683$	30973.2			1.73522			0.867611	+	0.497244i	$0.165655\pi$
$684$	899.360	−	247.576i	0.0502747	−	0.0138396i
$685$	−2646.40			−0.147611
$686$	15717.4			0.874772
$687$	357.787	+	2647.79i	0.0198696	+	0.147044i
$688$			26349.5i			1.46012i
$689$	1497.59			0.0828065
$690$	−1075.61	−	7960.00i	−0.0593445	−	0.439177i
$691$			29027.7i			1.59807i	0.601286	+	0.799034i	$0.294655\pi$
$691$			29027.7i			1.59807i	−0.601286	+	0.799034i	$0.705345\pi$
$692$	−1818.56			−0.0999008
$693$	−8105.46	+	2231.27i	−0.444302	+	0.122307i
$694$	22734.7			1.24351
$695$		−	19086.2i		−	1.04170i
$696$	1230.24	+	9104.37i	0.0670003	+	0.495834i
$697$	3033.98			0.164878
$698$		−	4983.59i		−	0.270246i
$699$	865.812	−	116.994i	0.0468498	−	0.00633066i
$700$	876.352			0.0473186
$701$	−14844.2			−0.799800			−0.399900	−	0.916559i	$-0.630955\pi$
$701$	−14844.2			−0.799800			−0.399900	+	0.916559i	$0.630955\pi$
$702$	−1187.43	−	2785.68i	−0.0638414	−	0.149770i
$703$			5833.30i			0.312955i
$704$	−16894.3			−0.904444
$705$	−259.719	−	1922.04i	−0.0138746	−	0.102678i
$706$	−9539.33			−0.508523
$707$	−9238.58			−0.491446
$708$	766.332	−	2554.37i	0.0406787	−	0.135592i
$709$	6585.05			0.348811			0.174405	−	0.984674i	$-0.444200\pi$
$709$	6585.05			0.348811			0.174405	+	0.984674i	$0.444200\pi$
$710$	−16560.8			−0.875376
$711$	14953.5	−	4116.39i	0.788747	−	0.217126i
$712$	28236.3			1.48623
$713$			12086.9i			0.634863i
$714$	1578.18	+	11679.2i	0.0827196	+	0.612163i
$715$	−3495.24			−0.182818
$716$	2394.29			0.124970
$717$	−2802.91	−	20742.8i	−0.145992	−	1.08041i
$718$			8167.51i			0.424525i
$719$	−37101.0			−1.92439			−0.962193	−	0.272368i	$-0.912193\pi$
$719$	−37101.0			−1.92439			−0.962193	+	0.272368i	$0.912193\pi$
$720$	5432.90	+	19735.9i	0.281211	+	1.02155i
$721$		−	9850.36i		−	0.508802i
$722$	15535.8			0.800806
$723$	−15988.8	+	2160.51i	−0.822448	+	0.111135i
$724$	−48.7114			−0.00250048
$725$		−	5514.25i		−	0.282475i
$726$	5788.54	−	782.186i	0.295913	−	0.0399857i
$727$	−25067.3			−1.27881			−0.639404	−	0.768871i	$-0.720819\pi$
$727$	−25067.3			−1.27881			−0.639404	+	0.768871i	$0.720819\pi$
$728$			2043.58i			0.104039i
$729$	13630.0	−	14200.1i	0.692478	−	0.721439i
$730$	15461.7			0.783921
$731$	−40996.0			−2.07427
$732$	−610.884	−	4520.83i	−0.0308455	−	0.228271i
$733$	30886.1			1.55635			0.778176	−	0.628047i	$-0.216145\pi$
$733$	30886.1			1.55635			0.778176	+	0.628047i	$0.216145\pi$
$734$		−	32937.8i		−	1.65634i
$735$	2315.51	+	17135.9i	0.116203	+	0.859955i
$736$	2122.72			0.106311
$737$		−	5291.61i		−	0.264476i
$738$	−682.479	−	2479.22i	−0.0340412	−	0.123660i
$739$			13226.2i			0.658368i	0.944266	+	0.329184i	$0.106774\pi$
$739$			13226.2i			0.658368i	−0.944266	+	0.329184i	$0.893226\pi$
$740$	3059.73			0.151997
$741$	−174.835	−	1293.86i	−0.00866762	−	0.0641444i
$742$			4939.87i			0.244405i
$743$			13180.4i			0.650797i	0.945577	+	0.325399i	$0.105498\pi$
$743$			13180.4i			0.650797i	−0.945577	+	0.325399i	$0.894502\pi$
$744$	−4821.26	−	35679.6i	−0.237575	−	1.75817i
$745$		−	5827.60i		−	0.286586i
$746$	20538.8			1.00801
$747$	25979.9	−	7151.74i	1.27250	−	0.350293i
$748$		−	2839.55i		−	0.138803i
$749$			11057.4i			0.539423i
$750$	1297.46	+	9601.80i	0.0631687	+	0.467478i
$751$		−	11157.1i		−	0.542117i	−0.962563	−	0.271058i	$-0.912626\pi$
$751$		−	11157.1i		−	0.542117i	0.962563	−	0.271058i	$-0.0873737\pi$
$752$	−1417.47			−0.0687366
$753$	4278.33	+	31661.7i	0.207053	+	1.53229i
$754$	1594.58			0.0770176
$755$	16504.1			0.795558
$756$	−1515.28	+	645.906i	−0.0728970	+	0.0310732i
$757$	6916.46			0.332078			0.166039	−	0.986119i	$-0.446902\pi$
$757$	6916.46			0.332078			0.166039	+	0.986119i	$0.446902\pi$
$758$	2512.60			0.120398
$759$	6456.56	−	872.454i	0.308773	−	0.0417234i
$760$			10315.9i			0.492366i
$761$		−	16380.6i		−	0.780283i	−0.920755	−	0.390141i	$-0.872426\pi$
$761$		−	16380.6i		−	0.780283i	0.920755	−	0.390141i	$-0.127574\pi$
$762$	−27162.1	+	3670.33i	−1.29131	+	0.174491i
$763$			14042.7i			0.666292i
$764$	−3946.44			−0.186881
$765$	−30706.3	+	8452.81i	−1.45122	+	0.399493i
$766$		−	12190.5i		−	0.575012i
$767$	−3399.39	−	1541.70i	−0.160033	−	0.0725781i
$768$	−8769.41	+	1184.98i	−0.412030	+	0.0556762i
$769$			39727.7i			1.86296i	0.363792	+	0.931480i	$0.381482\pi$
$769$			39727.7i			1.86296i	−0.363792	+	0.931480i	$0.618518\pi$
$770$		−	11529.2i		−	0.539590i
$771$	4043.25	+	29922.0i	0.188864	+	1.39768i
$772$	−2475.25			−0.115397
$773$	−21849.0			−1.01663			−0.508315	−	0.861171i	$-0.669732\pi$
$773$	−21849.0			−1.01663			−0.508315	+	0.861171i	$0.669732\pi$
$774$	9221.85	+	33499.9i	0.428259	+	1.55572i
$775$			21610.1i			1.00162i
$776$			19299.1i			0.892782i
$777$	−1379.36	−	10207.9i	−0.0636862	−	0.471308i
$778$			11881.8i			0.547537i
$779$		−	1108.68i		−	0.0509919i
$780$	−678.664	+	91.7056i	−0.0311539	+	0.00420973i
$781$		−	13432.9i		−	0.615452i
$782$		−	9133.45i		−	0.417662i
$783$	4064.22	+	9534.55i	0.185496	+	0.435169i
$784$	12637.4			0.575685
$785$	15257.8			0.693726
$786$	−30841.6	+	4167.53i	−1.39960	+	0.189123i
$787$	−15147.8			−0.686102			−0.343051	−	0.939317i	$-0.611460\pi$
$787$	−15147.8			−0.686102			−0.343051	+	0.939317i	$0.611460\pi$
$788$			3102.31i			0.140248i
$789$	−1376.31	−	10185.3i	−0.0621014	−	0.459579i
$790$			21269.8i			0.957908i
$791$	−10516.8			−0.472736
$792$	−18711.3	+	5150.84i	−0.839492	+	0.231095i
$793$	−6385.10			−0.285929
$794$		−	31751.6i		−	1.41917i
$795$	−13229.1	+	1787.61i	−0.590175	+	0.0797484i
$796$	6191.17			0.275679
$797$	37662.9			1.67389			0.836943	−	0.547290i	$-0.184340\pi$
$797$	37662.9			1.67389			0.836943	+	0.547290i	$0.184340\pi$
$798$	4267.85	−	576.700i	0.189324	−	0.0255827i
$799$		−	2205.39i		−	0.0976482i
$800$	3795.21			0.167726
$801$	30712.9	−	8454.63i	1.35479	−	0.372946i
$802$	−17208.9			−0.757689
$803$			12541.4i			0.551153i
$804$	−138.837	−	1027.46i	−0.00609007	−	0.0450694i
$805$			6115.38i			0.267750i
$806$	−6249.09			−0.273096
$807$	17437.2	−	2356.23i	0.760617	−	0.102780i
$808$	−21327.1			−0.928570
$809$	5200.95			0.226027			0.113013	−	0.993593i	$-0.463950\pi$
$809$	5200.95			0.226027			0.113013	+	0.993593i	$0.463950\pi$
$810$	13814.4	+	23190.2i	0.599247	+	1.00595i
$811$		−	24302.4i		−	1.05225i	−0.850408	−	0.526124i	$-0.823645\pi$
$811$		−	24302.4i		−	1.05225i	0.850408	−	0.526124i	$-0.176355\pi$
$812$		−	867.378i		−	0.0374865i
$813$	−5590.36	+	755.407i	−0.241159	+	0.0325871i
$814$		−	15049.9i		−	0.648031i
$815$		−	31441.0i		−	1.35133i
$816$	3116.90	+	23066.5i	0.133718	+	0.989572i
$817$			14980.8i			0.641509i
$818$			36307.4i			1.55191i
$819$	611.898	+	2222.82i	0.0261068	+	0.0948372i
$820$	−581.535			−0.0247660
$821$	−4074.71			−0.173214			−0.0866068	−	0.996243i	$-0.527602\pi$
$821$	−4074.71			−0.173214			−0.0866068	+	0.996243i	$0.527602\pi$
$822$	341.526	+	2527.45i	0.0144916	+	0.107244i
$823$			16731.6i			0.708660i	0.935120	+	0.354330i	$0.115291\pi$
$823$			16731.6i			0.708660i	−0.935120	+	0.354330i	$0.884709\pi$
$824$		−	22739.4i		−	0.961363i
$825$	11543.7	−	1559.86i	0.487150	−	0.0658270i
$826$	5085.35	−	11213.1i	0.214216	−	0.472339i
$827$			35981.6i			1.51294i	0.654028	+	0.756470i	$0.273078\pi$
$827$			35981.6i			1.51294i	−0.654028	+	0.756470i	$0.726922\pi$
$828$	1230.77	−	338.805i	0.0516571	−	0.0142202i
$829$	38433.4			1.61019			0.805095	−	0.593145i	$-0.202114\pi$
$829$	38433.4			1.61019			0.805095	+	0.593145i	$0.202114\pi$
$830$			36953.9i			1.54541i
$831$	2486.86	−	336.042i	0.103813	−	0.0140279i
$832$			4633.05i			0.193056i
$833$			19662.0i			0.817826i
$834$	−18228.3	+	2463.13i	−0.756827	+	0.102268i
$835$	−28074.1			−1.16353
$836$	−1037.63			−0.0429274
$837$	−15927.5	−	37365.4i	−0.657747	−	1.54306i
$838$	35667.4			1.47030
$839$	21518.9			0.885478			0.442739	−	0.896651i	$-0.354007\pi$
$839$	21518.9			0.885478			0.442739	+	0.896651i	$0.354007\pi$
$840$	−2439.33	−	18052.2i	−0.100196	−	0.741499i
$841$	18931.2			0.776219
$842$			17480.1i			0.715444i
$843$	5886.99	+	43566.5i	0.240520	+	1.77996i
$844$			2757.23i			0.112450i
$845$		−	30083.9i		−	1.22475i
$846$	−1802.13	+	496.090i	−0.0732371	+	0.0201607i
$847$	−4447.13			−0.180408
$848$			9756.27i			0.395085i
$849$	−2748.94	−	20343.4i	−0.111123	−	0.822361i
$850$		−	16329.7i		−	0.658945i
$851$			7982.82i			0.321560i
$852$	−352.443	−	2608.24i	−0.0141720	−	0.104879i
$853$	23549.8			0.945287			0.472643	−	0.881254i	$-0.343300\pi$
$853$	23549.8			0.945287			0.472643	+	0.881254i	$0.343300\pi$
$854$		−	21061.5i		−	0.843924i
$855$	3088.84	+	11220.7i	0.123551	+	0.448820i
$856$			25525.7i			1.01922i
$857$	−33967.7			−1.35393			−0.676963	−	0.736017i	$-0.736704\pi$
$857$	−33967.7			−1.35393			−0.676963	+	0.736017i	$0.736704\pi$
$858$	451.072	+	3338.14i	0.0179479	+	0.132823i
$859$			30060.4i			1.19400i	0.802240	+	0.597001i	$0.203641\pi$
$859$			30060.4i			1.19400i	−0.802240	+	0.597001i	$0.796359\pi$
$860$	7857.87			0.311571
$861$	262.162	+	1940.12i	0.0103768	+	0.0767934i
$862$	−8799.44			−0.347692
$863$	19376.6			0.764296			0.382148	−	0.924101i	$-0.375184\pi$
$863$	19376.6			0.764296			0.382148	+	0.924101i	$0.375184\pi$
$864$	−6562.20	+	2797.22i	−0.258392	+	0.110143i
$865$		−	22689.0i		−	0.891849i
$866$	34072.3			1.33698
$867$	−10589.4	+	1430.92i	−0.414806	+	0.0560513i
$868$			3399.21i			0.132923i
$869$	−17252.5			−0.673477
$870$	−14085.9	+	1903.38i	−0.548917	+	0.0741733i
$871$	−1451.16			−0.0564531
$872$			32417.4i			1.25893i
$873$	5778.64	+	20991.9i	0.224029	+	0.813823i
$874$	−3337.56			−0.129170
$875$		−	7376.72i		−	0.285004i
$876$	329.051	+	2435.13i	0.0126913	+	0.0939218i
$877$	14147.0			0.544709			0.272354	−	0.962197i	$-0.412198\pi$
$877$	14147.0			0.544709			0.272354	+	0.962197i	$0.412198\pi$
$878$	18289.0			0.702987
$879$	2780.68	+	20578.3i	0.106701	+	0.789636i
$880$		−	22770.3i		−	0.872256i
$881$	2549.18			0.0974849			0.0487424	−	0.998811i	$-0.484479\pi$
$881$	2549.18			0.0974849			0.0487424	+	0.998811i	$0.484479\pi$
$882$	16066.8	−	4422.87i	0.613377	−	0.168850i
$883$	−13536.1			−0.515883			−0.257942	−	0.966160i	$-0.583044\pi$
$883$	−13536.1			−0.515883			−0.257942	+	0.966160i	$0.583044\pi$
$884$	−778.712			−0.0296277
$885$	31869.2	+	9561.03i	1.21047	+	0.363153i
$886$	−33602.2			−1.27414
$887$	−16602.7			−0.628483			−0.314242	−	0.949343i	$-0.601750\pi$
$887$	−16602.7			−0.628483			−0.314242	+	0.949343i	$0.601750\pi$
$888$	−3184.22	−	23564.7i	−0.120333	−	0.890518i
$889$	20867.7			0.787266
$890$			43686.0i			1.64535i
$891$	−18810.2	+	11205.3i	−0.707256	+	0.421313i
$892$	2083.72			0.0782154
$893$	−805.896			−0.0301996
$894$	−5565.66	+	752.070i	−0.208214	+	0.0281353i
$895$			29872.0i			1.11565i
$896$	−11065.3			−0.412572
$897$	−239.260	−	1770.63i	−0.00890596	−	0.0659082i
$898$		−	29007.1i		−	1.07793i
$899$	21388.8			0.793500
$900$	2200.48	−	605.749i	0.0814994	−	0.0224351i
$901$	−15179.4			−0.561263
$902$			2860.39i			0.105588i
$903$	−3542.41	−	26215.5i	−0.130547	−	0.966109i
$904$	−24277.8			−0.893216
$905$		−	607.740i		−	0.0223226i
$906$	−2129.91	−	15762.3i	−0.0781031	−	0.577999i
$907$	5440.27			0.199164			0.0995818	−	0.995029i	$-0.468250\pi$
$907$	5440.27			0.199164			0.0995818	+	0.995029i	$0.468250\pi$
$908$	−6169.78			−0.225497
$909$	−23197.7	+	6385.85i	−0.846445	+	0.233009i
$910$	−3161.75			−0.115177
$911$		−	14392.2i		−	0.523418i	−0.965147	−	0.261709i	$-0.915714\pi$
$911$		−	14392.2i		−	0.523418i	0.965147	−	0.261709i	$-0.0842861\pi$
$912$	8429.02	−	1138.98i	0.306045	−	0.0413548i
$913$	−29974.3			−1.08653
$914$		−	37201.2i		−	1.34629i
$915$	56403.4	−	7621.61i	2.03786	−	0.275369i
$916$		−	582.329i		−	0.0210051i
$917$	23694.5			0.853285
$918$	12035.6	+	28235.2i	0.432717	+	1.01514i
$919$		−	26438.6i		−	0.948998i	−0.880256	−	0.474499i	$-0.842629\pi$
$919$		−	26438.6i		−	0.948998i	0.880256	−	0.474499i	$-0.157371\pi$
$920$			14117.2i			0.505904i
$921$	17507.2	−	2365.69i	0.626365	−	0.0846387i
$922$		−	32338.5i		−	1.15511i
$923$	−3683.81			−0.131370
$924$	1815.79	−	245.362i	0.0646484	−	0.00873573i
$925$			14272.5i			0.507325i
$926$			32640.6i			1.15835i
$927$	−6808.72	−	24733.8i	−0.241238	−	0.876338i
$928$		−	3756.35i		−	0.132875i
$929$	−26072.7			−0.920792			−0.460396	−	0.887714i	$-0.652293\pi$
$929$	−26072.7			−0.920792			−0.460396	+	0.887714i	$0.652293\pi$
$930$	55202.1	−	7459.27i	1.94639	−	0.263010i
$931$	7184.93			0.252929
$932$	−190.418			−0.00669244
$933$	−6886.78	−	50965.4i	−0.241654	−	1.78835i
$934$	−38406.5			−1.34550
$935$	35427.3			1.23914
$936$	1412.55	+	5131.34i	0.0493278	+	0.179191i
$937$		−	37249.1i		−	1.29869i	−0.760492	−	0.649347i	$-0.775042\pi$
$937$		−	37249.1i		−	1.29869i	0.760492	−	0.649347i	$-0.224958\pi$
$938$		−	4786.71i		−	0.166622i
$939$	1407.46	+	10415.9i	0.0489145	+	0.361990i
$940$			422.715i			0.0146675i
$941$	−52166.0			−1.80719			−0.903593	−	0.428392i	$-0.859080\pi$
$941$	−52166.0			−1.80719			−0.903593	+	0.428392i	$0.859080\pi$
$942$	−1969.07	−	14572.0i	−0.0681059	−	0.504015i
$943$		−	1517.22i		−	0.0523940i
$944$	10043.6	−	22145.8i	0.346283	−	0.763544i
$945$	−8058.55	−	18905.1i	−0.277402	−	0.650777i
$946$		−	38650.4i		−	1.32837i
$947$			33444.5i			1.14762i	0.818987	+	0.573812i	$0.194536\pi$
$947$			33444.5i			1.14762i	−0.818987	+	0.573812i	$0.805464\pi$
$948$	−3349.89	+	452.659i	−0.114767	+	0.0155081i
$949$	3439.32			0.117645
$950$	−5967.22			−0.203792
$951$	3161.54	+	23396.8i	0.107802	+	0.797786i
$952$		−	20713.4i		−	0.705173i
$953$		−	28659.1i		−	0.974142i	−0.873362	−	0.487071i	$-0.838065\pi$
$953$		−	28659.1i		−	0.974142i	0.873362	−	0.487071i	$-0.161935\pi$
$954$	3414.52	+	12403.8i	0.115880	+	0.420952i
$955$		−	49237.1i		−	1.66835i
$956$			4561.98i			0.154336i
$957$	−1543.88	−	11425.5i	−0.0521491	−	0.385928i
$958$			50456.6i			1.70165i
$959$		−	1941.75i		−	0.0653830i
$960$	−5530.27	−	40926.6i	−0.185926	−	1.37594i
$961$	−54030.6			−1.81366
$962$	−4127.24			−0.138324
$963$	7643.03	+	27764.6i	0.255756	+	0.929077i
$964$	3516.42			0.117486
$965$		−	30882.1i		−	1.03019i
$966$	5840.51	−	789.209i	0.194529	−	0.0262861i
$967$		−	6588.23i		−	0.219093i	−0.993982	−	0.109547i	$-0.965060\pi$
$967$		−	6588.23i		−	0.219093i	0.993982	−	0.109547i	$-0.0349399\pi$
$968$	−10266.1			−0.340873
$969$	1772.10	+	13114.3i	0.0587492	+	0.434771i
$970$	−29858.9			−0.988362
$971$		−	31219.5i		−	1.03180i	−0.856647	−	0.515902i	$-0.827457\pi$
$971$		−	31219.5i		−	1.03180i	0.856647	−	0.515902i	$-0.172543\pi$
$972$	−3358.34	+	2669.23i	−0.110822	+	0.0880818i
$973$	14004.1			0.461410
$974$	17636.9			0.580209
$975$	−427.771	−	3165.71i	−0.0140509	−	0.103983i
$976$		−	41596.6i		−	1.36422i
$977$	−957.564			−0.0313564			−0.0156782	−	0.999877i	$-0.504991\pi$
$977$	−957.564			−0.0313564			−0.0156782	+	0.999877i	$0.504991\pi$
$978$	−30027.8	+	4057.55i	−0.981782	+	0.132665i
$979$	−35434.9			−1.15680
$980$		−	3768.70i		−	0.122844i
$981$	9706.56	+	35260.7i	0.315909	+	1.14759i
$982$			34982.2i			1.13679i
$983$	7934.27			0.257441			0.128720	−	0.991681i	$-0.458913\pi$
$983$	7934.27			0.257441			0.128720	+	0.991681i	$0.458913\pi$
$984$	605.196	+	4478.73i	0.0196067	+	0.145098i
$985$	−38705.5			−1.25204
$986$	−16162.4			−0.522026
$987$	1410.26	−	190.564i	0.0454804	−	0.00614562i
$988$			284.558i			0.00916296i
$989$			20501.1i			0.659149i
$990$	−7969.18	−	28949.4i	−0.255836	−	0.929366i
$991$			48895.2i			1.56731i	0.621194	+	0.783657i	$0.286648\pi$
$991$			48895.2i			1.56731i	−0.621194	+	0.783657i	$0.713352\pi$
$992$			14720.9i			0.471160i
$993$	20096.7	−	2715.60i	0.642245	−	0.0867844i
$994$		−	12151.2i		−	0.387740i
$995$			77243.2i			2.46108i
$996$	−5820.04	+	786.442i	−0.185156	+	0.0250195i
$997$	9073.83			0.288236			0.144118	−	0.989561i	$-0.453966\pi$
$997$	9073.83			0.288236			0.144118	+	0.989561i	$0.453966\pi$
$998$	−34308.4			−1.08819
$999$	−10519.4	−	24678.1i	−0.333151	−	0.781564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.d.c.176.17	✓	52
3.2	odd	2	inner	177.4.d.c.176.36	yes	52
59.58	odd	2	inner	177.4.d.c.176.35	yes	52
177.176	even	2	inner	177.4.d.c.176.18	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.d.c.176.17	✓	52	1.1	even	1	trivial
177.4.d.c.176.18	yes	52	177.176	even	2	inner
177.4.d.c.176.35	yes	52	59.58	odd	2	inner
177.4.d.c.176.36	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)

\(f(q)\)	\(=\)	\(q-2.62059 q^{2} +(5.14935 - 0.695815i) q^{3} -1.13250 q^{4} -14.1294i q^{5} +(-13.4944 + 1.82345i) q^{6} +10.3672 q^{7} +23.9326 q^{8} +(26.0317 - 7.16599i) q^{9} +O(q^{10})\)	\(q-2.62059 q^{2} +(5.14935 - 0.695815i) q^{3} -1.13250 q^{4} -14.1294i q^{5} +(-13.4944 + 1.82345i) q^{6} +10.3672 q^{7} +23.9326 q^{8} +(26.0317 - 7.16599i) q^{9} +37.0275i q^{10} -30.0340 q^{11} +(-5.83163 + 0.788009i) q^{12} +8.23644i q^{13} -27.1683 q^{14} +(-9.83148 - 72.7575i) q^{15} -53.6575 q^{16} -83.4833i q^{17} +(-68.2184 + 18.7791i) q^{18} -30.5066 q^{19} +16.0016i q^{20} +(53.3845 - 7.21367i) q^{21} +78.7068 q^{22} -41.7480 q^{23} +(123.237 - 16.6526i) q^{24} -74.6412 q^{25} -21.5844i q^{26} +(129.060 - 55.0135i) q^{27} -11.7409 q^{28} +73.8768i q^{29} +(25.7643 + 190.668i) q^{30} -289.520i q^{31} -50.8461 q^{32} +(-154.656 + 20.8981i) q^{33} +218.776i q^{34} -146.483i q^{35} +(-29.4808 + 8.11548i) q^{36} -191.214i q^{37} +79.9454 q^{38} +(5.73104 + 42.4124i) q^{39} -338.154i q^{40} +36.3424i q^{41} +(-139.899 + 18.9041i) q^{42} -491.069i q^{43} +34.0134 q^{44} +(-101.252 - 367.813i) q^{45} +109.405 q^{46} +26.4171 q^{47} +(-276.301 + 37.3357i) q^{48} -235.521 q^{49} +195.604 q^{50} +(-58.0889 - 429.885i) q^{51} -9.32776i q^{52} -181.825i q^{53} +(-338.214 + 144.168i) q^{54} +424.363i q^{55} +248.114 q^{56} +(-157.089 + 21.2270i) q^{57} -193.601i q^{58} +(-187.180 + 412.726i) q^{59} +(11.1341 + 82.3977i) q^{60} +775.225i q^{61} +758.713i q^{62} +(269.876 - 74.2915i) q^{63} +562.507 q^{64} +116.376 q^{65} +(405.289 - 54.7654i) q^{66} +176.188i q^{67} +94.5447i q^{68} +(-214.975 + 29.0489i) q^{69} +383.873i q^{70} +447.258i q^{71} +(623.005 - 171.501i) q^{72} -417.573i q^{73} +501.095i q^{74} +(-384.354 + 51.9364i) q^{75} +34.5487 q^{76} -311.369 q^{77} +(-15.0187 - 111.145i) q^{78} +574.434 q^{79} +758.150i q^{80} +(626.297 - 373.086i) q^{81} -95.2385i q^{82} +998.011 q^{83} +(-60.4579 + 8.16947i) q^{84} -1179.57 q^{85} +1286.89i q^{86} +(51.4046 + 380.418i) q^{87} -718.790 q^{88} +1179.83 q^{89} +(265.339 + 963.888i) q^{90} +85.3891i q^{91} +47.2796 q^{92} +(-201.452 - 1490.84i) q^{93} -69.2284 q^{94} +431.041i q^{95} +(-261.825 + 35.3795i) q^{96} +806.397i q^{97} +617.203 q^{98} +(-781.835 + 215.223i) 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

Related objects

Downloads

Learn more