LMFDB - Embedded newform 177.5.b.a.119.78

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,5,Mod(119,177)]

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, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("177.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	177.b (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:	$18.2964834658$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.78
Character	$\chi$	$=$	177.119
Dual form			177.5.b.a.119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.85862i q^{2} +(1.36439 - 8.89598i) q^{3} -45.7580 q^{4} -33.8616i q^{5} +(69.9102 + 10.7222i) q^{6} +13.8137 q^{7} -233.857i q^{8} +(-77.2769 - 24.2751i) q^{9} +O(q^{10})$	\(q+7.85862i q^{2} +(1.36439 - 8.89598i) q^{3} -45.7580 q^{4} -33.8616i q^{5} +(69.9102 + 10.7222i) q^{6} +13.8137 q^{7} -233.857i q^{8} +(-77.2769 - 24.2751i) q^{9} +266.105 q^{10} +192.320i q^{11} +(-62.4316 + 407.062i) q^{12} -170.965 q^{13} +108.557i q^{14} +(-301.232 - 46.2003i) q^{15} +1105.66 q^{16} +492.040i q^{17} +(190.769 - 607.290i) q^{18} +210.495 q^{19} +1549.44i q^{20} +(18.8472 - 122.886i) q^{21} -1511.37 q^{22} +115.548i q^{23} +(-2080.38 - 319.071i) q^{24} -521.606 q^{25} -1343.55i q^{26} +(-321.387 + 654.333i) q^{27} -632.087 q^{28} +439.260i q^{29} +(363.071 - 2367.27i) q^{30} +175.455 q^{31} +4947.30i q^{32} +(1710.88 + 262.400i) q^{33} -3866.76 q^{34} -467.753i q^{35} +(3536.03 + 1110.78i) q^{36} +1951.00 q^{37} +1654.20i q^{38} +(-233.263 + 1520.90i) q^{39} -7918.76 q^{40} +1818.50i q^{41} +(965.717 + 148.113i) q^{42} +1528.80 q^{43} -8800.20i q^{44} +(-821.994 + 2616.72i) q^{45} -908.046 q^{46} -1691.29i q^{47} +(1508.56 - 9835.97i) q^{48} -2210.18 q^{49} -4099.10i q^{50} +(4377.18 + 671.334i) q^{51} +7823.03 q^{52} +873.418i q^{53} +(-5142.16 - 2525.66i) q^{54} +6512.27 q^{55} -3230.43i q^{56} +(287.197 - 1872.56i) q^{57} -3451.98 q^{58} -453.188i q^{59} +(13783.8 + 2114.03i) q^{60} -4977.77 q^{61} +1378.83i q^{62} +(-1067.48 - 335.329i) q^{63} -21188.3 q^{64} +5789.15i q^{65} +(-2062.10 + 13445.2i) q^{66} -4017.43 q^{67} -22514.8i q^{68} +(1027.91 + 157.652i) q^{69} +3675.90 q^{70} +233.784i q^{71} +(-5676.91 + 18071.7i) q^{72} -2072.57 q^{73} +15332.1i q^{74} +(-711.672 + 4640.19i) q^{75} -9631.84 q^{76} +2656.66i q^{77} +(-11952.2 - 1833.13i) q^{78} +336.550 q^{79} -37439.5i q^{80} +(5382.44 + 3751.81i) q^{81} -14290.9 q^{82} -687.683i q^{83} +(-862.412 + 5623.03i) q^{84} +16661.3 q^{85} +12014.3i q^{86} +(3907.65 + 599.322i) q^{87} +44975.4 q^{88} +5666.49i q^{89} +(-20563.8 - 6459.74i) q^{90} -2361.66 q^{91} -5287.23i q^{92} +(239.388 - 1560.84i) q^{93} +13291.2 q^{94} -7127.70i q^{95} +(44011.0 + 6750.03i) q^{96} -3420.98 q^{97} -17369.0i q^{98} +(4668.61 - 14861.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	$ 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) $ 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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 $

$2$			7.85862i			1.96466i	0.187167	+	0.982328i	$0.440069\pi$
$2$			7.85862i			1.96466i	−0.187167	+	0.982328i	$0.559931\pi$
$3$	1.36439	−	8.89598i	0.151599	−	0.988442i
$3$	1.36439	−	8.89598i	0.151599	−	0.988442i
$4$	−45.7580			−2.85987
$5$		−	33.8616i		−	1.35446i	−0.735770	−	0.677231i	$-0.763180\pi$
$5$		−	33.8616i		−	1.35446i	0.735770	−	0.677231i	$-0.236820\pi$
$6$	69.9102	+	10.7222i	1.94195	+	0.297839i
$7$	13.8137			0.281912			0.140956	−	0.990016i	$-0.454982\pi$
$7$	13.8137			0.281912			0.140956	+	0.990016i	$0.454982\pi$
$8$		−	233.857i		−	3.65401i
$9$	−77.2769	−	24.2751i	−0.954036	−	0.299693i
$10$	266.105			2.66105
$11$			192.320i			1.58943i	0.606986	+	0.794713i	$0.292379\pi$
$11$			192.320i			1.58943i	−0.606986	+	0.794713i	$0.707621\pi$
$12$	−62.4316	+	407.062i	−0.433553	+	2.82682i
$13$	−170.965			−1.01163			−0.505815	−	0.862642i	$-0.668808\pi$
$13$	−170.965			−1.01163			−0.505815	+	0.862642i	$0.668808\pi$
$14$			108.557i			0.553860i
$15$	−301.232	−	46.2003i	−1.33881	−	0.205335i
$16$	1105.66			4.31900
$17$			492.040i			1.70256i	0.524711	+	0.851281i	$0.324174\pi$
$17$			492.040i			1.70256i	−0.524711	+	0.851281i	$0.675826\pi$
$18$	190.769	−	607.290i	0.588794	−	1.87435i
$19$	210.495			0.583089			0.291545	−	0.956557i	$-0.405831\pi$
$19$	210.495			0.583089			0.291545	+	0.956557i	$0.405831\pi$
$20$			1549.44i			3.87359i
$21$	18.8472	−	122.886i	0.0427375	−	0.278654i
$22$	−1511.37			−3.12267
$23$			115.548i			0.218427i	0.994018	+	0.109213i	$0.0348332\pi$
$23$			115.548i			0.218427i	−0.994018	+	0.109213i	$0.965167\pi$
$24$	−2080.38	−	319.071i	−3.61178	−	0.553943i
$25$	−521.606			−0.834569
$26$		−	1343.55i		−	1.98750i
$27$	−321.387	+	654.333i	−0.440860	+	0.897576i
$28$	−632.087			−0.806233
$29$			439.260i			0.522307i	0.965297	+	0.261154i	$0.0841029\pi$
$29$			439.260i			0.522307i	−0.965297	+	0.261154i	$0.915897\pi$
$30$	363.071	−	2367.27i	0.403412	−	2.63030i
$31$	175.455			0.182575			0.0912876	−	0.995825i	$-0.470902\pi$
$31$	175.455			0.182575			0.0912876	+	0.995825i	$0.470902\pi$
$32$			4947.30i			4.83134i
$33$	1710.88	+	262.400i	1.57106	+	0.240955i
$34$	−3866.76			−3.34495
$35$		−	467.753i		−	0.381839i
$36$	3536.03	+	1110.78i	2.72842	+	0.857084i
$37$	1951.00			1.42512			0.712562	−	0.701609i	$-0.247534\pi$
$37$	1951.00			1.42512			0.712562	+	0.701609i	$0.247534\pi$
$38$			1654.20i			1.14557i
$39$	−233.263	+	1520.90i	−0.153362	+	0.999937i
$40$	−7918.76			−4.94922
$41$			1818.50i			1.08179i	0.841089	+	0.540897i	$0.181915\pi$
$41$			1818.50i			1.08179i	−0.841089	+	0.540897i	$0.818085\pi$
$42$	965.717	+	148.113i	0.547459	+	0.0839645i
$43$	1528.80			0.826825			0.413413	−	0.910544i	$-0.364337\pi$
$43$	1528.80			0.826825			0.413413	+	0.910544i	$0.364337\pi$
$44$		−	8800.20i		−	4.54556i
$45$	−821.994	+	2616.72i	−0.405923	+	1.29221i
$46$	−908.046			−0.429133
$47$		−	1691.29i		−	0.765637i	−0.923824	−	0.382819i	$-0.874953\pi$
$47$		−	1691.29i		−	0.765637i	0.923824	−	0.382819i	$-0.125047\pi$
$48$	1508.56	−	9835.97i	0.654755	−	4.26908i
$49$	−2210.18			−0.920526
$50$		−	4099.10i		−	1.63964i
$51$	4377.18	+	671.334i	1.68288	+	0.258106i
$52$	7823.03			2.89313
$53$			873.418i			0.310936i	0.987841	+	0.155468i	$0.0496885\pi$
$53$			873.418i			0.310936i	−0.987841	+	0.155468i	$0.950312\pi$
$54$	−5142.16	−	2525.66i	−1.76343	−	0.866138i
$55$	6512.27			2.15282
$56$		−	3230.43i		−	1.03011i
$57$	287.197	−	1872.56i	0.0883956	−	0.576350i
$58$	−3451.98			−1.02615
$59$		−	453.188i		−	0.130189i
$59$		−	453.188i		−	0.130189i
$60$	13783.8	+	2114.03i	3.82882	+	0.587231i
$61$	−4977.77			−1.33775			−0.668876	−	0.743374i	$-0.733224\pi$
$61$	−4977.77			−1.33775			−0.668876	+	0.743374i	$0.733224\pi$
$62$			1378.83i			0.358697i
$63$	−1067.48	−	335.329i	−0.268954	−	0.0844871i
$64$	−21188.3			−5.17293
$65$			5789.15i			1.37021i
$66$	−2062.10	+	13445.2i	−0.473393	+	3.08658i
$67$	−4017.43			−0.894951			−0.447475	−	0.894296i	$-0.647677\pi$
$67$	−4017.43			−0.894951			−0.447475	+	0.894296i	$0.647677\pi$
$68$		−	22514.8i		−	4.86911i
$69$	1027.91	+	157.652i	0.215902	+	0.0331132i
$70$	3675.90			0.750183
$71$			233.784i			0.0463765i	0.999731	+	0.0231883i	$0.00738172\pi$
$71$			233.784i			0.0463765i	−0.999731	+	0.0231883i	$0.992618\pi$
$72$	−5676.91	+	18071.7i	−1.09508	+	3.48606i
$73$	−2072.57			−0.388924			−0.194462	−	0.980910i	$-0.562296\pi$
$73$	−2072.57			−0.388924			−0.194462	+	0.980910i	$0.562296\pi$
$74$			15332.1i			2.79988i
$75$	−711.672	+	4640.19i	−0.126520	+	0.824923i
$76$	−9631.84			−1.66756
$77$			2656.66i			0.448078i
$78$	−11952.2	−	1833.13i	−1.96453	−	0.301303i
$79$	336.550			0.0539257			0.0269628	−	0.999636i	$-0.491416\pi$
$79$	336.550			0.0539257			0.0269628	+	0.999636i	$0.491416\pi$
$80$		−	37439.5i		−	5.84993i
$81$	5382.44	+	3751.81i	0.820368	+	0.571836i
$82$	−14290.9			−2.12535
$83$		−	687.683i		−	0.0998234i	−0.998754	−	0.0499117i	$-0.984106\pi$
$83$		−	687.683i		−	0.0998234i	0.998754	−	0.0499117i	$-0.0158940\pi$
$84$	−862.412	+	5623.03i	−0.122224	+	0.796915i
$85$	16661.3			2.30606
$86$			12014.3i			1.62443i
$87$	3907.65	+	599.322i	0.516270	+	0.0791811i
$88$	44975.4			5.80778
$89$			5666.49i			0.715376i	0.933841	+	0.357688i	$0.116435\pi$
$89$			5666.49i			0.715376i	−0.933841	+	0.357688i	$0.883565\pi$
$90$	−20563.8	−	6459.74i	−2.53874	−	0.797499i
$91$	−2361.66			−0.285191
$92$		−	5287.23i		−	0.624673i
$93$	239.388	−	1560.84i	0.0276782	−	0.180465i
$94$	13291.2			1.50421
$95$		−	7127.70i		−	0.789773i
$96$	44011.0	+	6750.03i	4.77550	+	0.732425i
$97$	−3420.98			−0.363586			−0.181793	−	0.983337i	$-0.558190\pi$
$97$	−3420.98			−0.363586			−0.181793	+	0.983337i	$0.558190\pi$
$98$		−	17369.0i		−	1.80852i
$99$	4668.61	−	14861.9i	0.476340	−	1.51637i
$100$	23867.6			2.38676
$101$			584.413i			0.0572898i	0.999590	+	0.0286449i	$0.00911920\pi$
$101$			584.413i			0.0572898i	−0.999590	+	0.0286449i	$0.990881\pi$
$102$	−5275.76	+	34398.6i	−0.507090	+	3.30629i
$103$	−19980.2			−1.88332			−0.941662	−	0.336560i	$-0.890737\pi$
$103$	−19980.2			−1.88332			−0.941662	+	0.336560i	$0.890737\pi$
$104$			39981.4i			3.69651i
$105$	−4161.12	−	638.197i	−0.377426	−	0.0578864i
$106$	−6863.87			−0.610882
$107$			10860.0i			0.948556i	0.880375	+	0.474278i	$0.157291\pi$
$107$			10860.0i			0.948556i	−0.880375	+	0.474278i	$0.842709\pi$
$108$	14706.0	−	29940.9i	1.26080	−	2.56695i
$109$	−5033.51			−0.423660			−0.211830	−	0.977306i	$-0.567942\pi$
$109$	−5033.51			−0.423660			−0.211830	+	0.977306i	$0.567942\pi$
$110$			51177.5i			4.22955i
$111$	2661.92	−	17356.0i	0.216047	−	1.40865i
$112$	15273.3			1.21758
$113$			16750.8i			1.31183i	0.754833	+	0.655917i	$0.227718\pi$
$113$			16750.8i			1.31183i	−0.754833	+	0.655917i	$0.772282\pi$
$114$	14715.8	+	2256.98i	1.13233	+	0.173667i
$115$	3912.63			0.295851
$116$		−	20099.7i		−	1.49373i
$117$	13211.7	+	4150.21i	0.965130	+	0.303178i
$118$	3561.43			0.255776
$119$			6796.89i			0.479973i
$120$	−10804.3	+	70445.1i	−0.750296	+	4.89202i
$121$	−22346.2			−1.52627
$122$		−	39118.5i		−	2.62822i
$123$	16177.3	+	2481.13i	1.06929	+	0.163999i
$124$	−8028.45			−0.522142
$125$		−	3501.10i		−	0.224070i
$126$	2635.23	−	8388.92i	0.165988	−	0.528402i
$127$	8026.58			0.497649			0.248825	−	0.968549i	$-0.419956\pi$
$127$	8026.58			0.497649			0.248825	+	0.968549i	$0.419956\pi$
$128$		−	87354.2i		−	5.33168i
$129$	2085.88	−	13600.2i	0.125346	−	0.817269i
$130$	−45494.8			−2.69200
$131$			21267.7i			1.23931i	0.784876	+	0.619653i	$0.212727\pi$
$131$			21267.7i			1.23931i	−0.784876	+	0.619653i	$0.787273\pi$
$132$	−78286.4	−	12006.9i	−4.49302	−	0.689100i
$133$	2907.72			0.164380
$134$		−	31571.5i		−	1.75827i
$135$	22156.7	+	10882.7i	1.21573	+	0.597128i
$136$	115067.			6.22118
$137$			32442.8i			1.72853i	0.503034	+	0.864266i	$0.332217\pi$
$137$			32442.8i			1.72853i	−0.503034	+	0.864266i	$0.667783\pi$
$138$	−1238.93	+	8077.96i	−0.0650561	+	0.424173i
$139$	18614.4			0.963428			0.481714	−	0.876329i	$-0.340014\pi$
$139$	18614.4			0.963428			0.481714	+	0.876329i	$0.340014\pi$
$140$			21403.4i			1.09201i
$141$	−15045.7	−	2307.58i	−0.756788	−	0.116070i
$142$	−1837.22			−0.0911139
$143$		−	32880.1i		−	1.60791i
$144$	−85442.3	−	26840.2i	−4.12048	−	1.29438i
$145$	14874.0			0.707446
$146$		−	16287.6i		−	0.764101i
$147$	−3015.55	+	19661.7i	−0.139550	+	0.909886i
$148$	−89273.6			−4.07568
$149$		−	4095.47i		−	0.184472i	−0.995737	−	0.0922362i	$-0.970599\pi$
$149$		−	4095.47i		−	0.184472i	0.995737	−	0.0922362i	$-0.0294015\pi$
$150$	−36465.5	−	5592.77i	−1.62069	−	0.248567i
$151$	−25391.9			−1.11363			−0.556816	−	0.830636i	$-0.687977\pi$
$151$	−25391.9			−1.11363			−0.556816	+	0.830636i	$0.687977\pi$
$152$		−	49225.7i		−	2.13062i
$153$	11944.3	−	38023.3i	0.510246	−	1.62430i
$154$	−20877.7			−0.880320
$155$		−	5941.17i		−	0.247291i
$156$	10673.6	−	69593.5i	0.438595	−	2.85969i
$157$	−11978.8			−0.485975			−0.242988	−	0.970029i	$-0.578127\pi$
$157$	−11978.8			−0.485975			−0.242988	+	0.970029i	$0.578127\pi$
$158$			2644.82i			0.105945i
$159$	7769.91	+	1191.68i	0.307342	+	0.0471374i
$160$	167523.			6.54387
$161$			1596.14i			0.0615771i
$162$	−29484.1	+	42298.5i	−1.12346	+	1.61174i
$163$	−5885.26			−0.221509			−0.110754	−	0.993848i	$-0.535327\pi$
$163$	−5885.26			−0.221509			−0.110754	+	0.993848i	$0.535327\pi$
$164$		−	83210.7i		−	3.09379i
$165$	8885.27	−	57933.0i	0.326364	−	2.12794i
$166$	5404.24			0.196119
$167$		−	16035.8i		−	0.574987i	−0.957783	−	0.287493i	$-0.907178\pi$
$167$		−	16035.8i		−	0.574987i	0.957783	−	0.287493i	$-0.0928219\pi$
$168$	−28737.8	−	4407.55i	−1.01820	−	0.156163i
$169$	668.154			0.0233939
$170$			130935.i			4.53061i
$171$	−16266.4	−	5109.80i	−0.556288	−	0.174748i
$172$	−69954.8			−2.36462
$173$		−	26851.9i		−	0.897187i	−0.893736	−	0.448593i	$-0.851925\pi$
$173$		−	26851.9i		−	0.897187i	0.893736	−	0.448593i	$-0.148075\pi$
$174$	−4709.84	+	30708.8i	−0.155564	+	1.01429i
$175$	−7205.30			−0.235275
$176$			212642.i			6.86473i
$177$	−4031.55	−	618.324i	−0.128684	−	0.0197365i
$178$	−44530.8			−1.40547
$179$			36640.6i			1.14355i	0.820410	+	0.571776i	$0.193745\pi$
$179$			36640.6i			1.14355i	−0.820410	+	0.571776i	$0.806255\pi$
$180$	37612.8	−	119736.i	1.16089	−	3.69554i
$181$	40626.2			1.24008			0.620039	−	0.784571i	$-0.287117\pi$
$181$	40626.2			1.24008			0.620039	+	0.784571i	$0.287117\pi$
$182$		−	18559.4i		−	0.560301i
$183$	−6791.62	+	44282.2i	−0.202801	+	1.32229i
$184$	27021.6			0.798134
$185$		−	66063.8i		−	1.93028i
$186$	12266.1	+	1881.26i	0.354552	+	0.0543781i
$187$	−94629.4			−2.70609
$188$			77390.1i			2.18963i
$189$	−4439.54	+	9038.75i	−0.124284	+	0.253038i
$190$	56013.9			1.55163
$191$		−	14680.3i		−	0.402409i	−0.979549	−	0.201204i	$-0.935514\pi$
$191$		−	14680.3i		−	0.402409i	0.979549	−	0.201204i	$-0.0644855\pi$
$192$	−28909.1	+	188491.i	−0.784209	+	5.11314i
$193$	70347.1			1.88856			0.944282	−	0.329137i	$-0.106758\pi$
$193$	70347.1			1.88856			0.944282	+	0.329137i	$0.106758\pi$
$194$		−	26884.2i		−	0.714321i
$195$	51500.2	+	7898.65i	1.35438	+	0.207723i
$196$	101133.			2.63259
$197$		−	63492.6i		−	1.63603i	−0.575198	−	0.818014i	$-0.695075\pi$
$197$		−	63492.6i		−	1.63603i	0.575198	−	0.818014i	$-0.304925\pi$
$198$	116794.	+	36688.8i	2.97914	+	0.935844i
$199$	20815.5			0.525630			0.262815	−	0.964846i	$-0.415349\pi$
$199$	20815.5			0.525630			0.262815	+	0.964846i	$0.415349\pi$
$200$			121981.i			3.04952i
$201$	−5481.34	+	35739.0i	−0.135673	+	0.884607i
$202$	−4592.68			−0.112555
$203$			6067.81i			0.147245i
$204$	−200291.	−	30718.9i	−4.81283	−	0.738151i
$205$	61577.1			1.46525
$206$		−	157017.i		−	3.70008i
$207$	2804.94	−	8929.17i	0.0654610	−	0.208387i
$208$	−189030.			−4.36923
$209$			40482.5i			0.926777i
$210$	5015.35	−	32700.7i	0.113727	−	0.741513i
$211$	49115.2			1.10319			0.551596	−	0.834112i	$-0.314019\pi$
$211$	49115.2			1.10319			0.551596	+	0.834112i	$0.314019\pi$
$212$		−	39965.8i		−	0.889237i
$213$	2079.74	+	318.972i	0.0458405	+	0.00703062i
$214$	−85344.8			−1.86359
$215$		−	51767.6i		−	1.11990i
$216$	153020.	+	75158.5i	3.27975	+	1.61091i
$217$	2423.68			0.0514701
$218$		−	39556.4i		−	0.832347i
$219$	−2827.80	+	18437.6i	−0.0589603	+	0.384429i
$220$	−297988.			−6.15679
$221$		−	84121.8i		−	1.72236i
$222$	136394.	+	20919.0i	2.76752	+	0.424458i
$223$	6583.44			0.132386			0.0661932	−	0.997807i	$-0.478915\pi$
$223$	6583.44			0.132386			0.0661932	+	0.997807i	$0.478915\pi$
$224$			68340.4i			1.36201i
$225$	40308.1	+	12662.0i	0.796208	+	0.250115i
$226$	−131638.			−2.57730
$227$			627.937i			0.0121861i	0.999981	+	0.00609305i	$0.00193949\pi$
$227$			627.937i			0.0121861i	−0.999981	+	0.00609305i	$0.998061\pi$
$228$	−13141.6	+	85684.6i	−0.252800	+	1.64829i
$229$	28854.0			0.550219			0.275110	−	0.961413i	$-0.411286\pi$
$229$	28854.0			0.550219			0.275110	+	0.961413i	$0.411286\pi$
$230$			30747.9i			0.581245i
$231$	23633.6	+	3624.71i	0.442899	+	0.0679281i
$232$	102724.			1.90852
$233$		−	22896.0i		−	0.421742i	−0.977514	−	0.210871i	$-0.932370\pi$
$233$		−	22896.0i		−	0.421742i	0.977514	−	0.210871i	$-0.0676300\pi$
$234$	−32614.9	+	103826.i	−0.595641	+	1.89615i
$235$	−57269.8			−1.03703
$236$			20736.9i			0.372324i
$237$	459.185	−	2993.94i	0.00817506	−	0.0533024i
$238$	−53414.2			−0.942981
$239$			106275.i			1.86053i	0.366887	+	0.930266i	$0.380424\pi$
$239$			106275.i			1.86053i	−0.366887	+	0.930266i	$0.619576\pi$
$240$	−333061.	−	51082.1i	−5.78231	−	0.886841i
$241$	−88624.7			−1.52588			−0.762941	−	0.646468i	$-0.776245\pi$
$241$	−88624.7			−1.52588			−0.762941	+	0.646468i	$0.776245\pi$
$242$		−	175610.i		−	2.99860i
$243$	40719.8	−	42763.1i	0.689593	−	0.724197i
$244$	227773.			3.82580
$245$			74840.2i			1.24682i
$246$	−19498.3	+	127131.i	−0.322201	+	2.10079i
$247$	−35987.4			−0.589870
$248$		−	41031.3i		−	0.667132i
$249$	−6117.61	−	938.267i	−0.0986696	−	0.0151331i
$250$	27513.8			0.440221
$251$			39392.8i			0.625273i	0.949873	+	0.312636i	$0.101212\pi$
$251$			39392.8i			0.625273i	−0.949873	+	0.312636i	$0.898788\pi$
$252$	48845.7	+	15344.0i	0.769175	+	0.241622i
$253$	−22222.2			−0.347173
$254$			63077.9i			0.977709i
$255$	22732.4	−	148218.i	0.349595	−	2.27940i
$256$	347471.			5.30198
$257$		−	47148.3i		−	0.713838i	−0.934135	−	0.356919i	$-0.883827\pi$
$257$		−	47148.3i		−	0.713838i	0.934135	−	0.356919i	$-0.116173\pi$
$258$	106879.	+	16392.1i	1.60565	+	0.246261i
$259$	26950.5			0.401760
$260$		−	264900.i		−	3.91864i
$261$	10663.1	−	33944.7i	0.156532	−	0.498300i
$262$	−167135.			−2.43481
$263$			11954.9i			0.172836i	0.996259	+	0.0864181i	$0.0275421\pi$
$263$			11954.9i			0.172836i	−0.996259	+	0.0864181i	$0.972458\pi$
$264$	61364.0	−	400101.i	0.880452	−	5.74065i
$265$	29575.3			0.421151
$266$			22850.7i			0.322950i
$267$	50409.0	+	7731.29i	0.707107	+	0.108450i
$268$	183830.			2.55945
$269$		−	31888.6i		−	0.440688i	−0.975422	−	0.220344i	$-0.929282\pi$
$269$		−	31888.6i		−	0.440688i	0.975422	−	0.220344i	$-0.0707180\pi$
$270$	−85522.7	+	174121.i	−1.17315	+	2.38850i
$271$	−76590.4			−1.04288			−0.521441	−	0.853287i	$-0.674606\pi$
$271$	−76590.4			−1.04288			−0.521441	+	0.853287i	$0.674606\pi$
$272$			544032.i			7.35337i
$273$	−3222.23	+	21009.3i	−0.0432345	+	0.281894i
$274$	−254956.			−3.39597
$275$		−	100315.i		−	1.32649i
$276$	−47035.1	−	7213.83i	−0.617453	−	0.0946996i
$277$	50328.2			0.655922			0.327961	−	0.944691i	$-0.393639\pi$
$277$	50328.2			0.655922			0.327961	+	0.944691i	$0.393639\pi$
$278$			146284.i			1.89280i
$279$	−13558.6	−	4259.19i	−0.174183	−	0.0547165i
$280$	−109387.			−1.39525
$281$		−	22681.3i		−	0.287247i	−0.989632	−	0.143624i	$-0.954124\pi$
$281$		−	22681.3i		−	0.287247i	0.989632	−	0.143624i	$-0.0458755\pi$
$282$	18134.4	−	118239.i	0.228037	−	1.48683i
$283$	20552.3			0.256619			0.128309	−	0.991734i	$-0.459045\pi$
$283$	20552.3			0.256619			0.128309	+	0.991734i	$0.459045\pi$
$284$		−	10697.5i		−	0.132631i
$285$	−63407.9	−	9724.95i	−0.780645	−	0.119729i
$286$	258393.			3.15899
$287$			25120.1i			0.304971i
$288$	120096.	−	382312.i	1.44792	−	4.60927i
$289$	−158583.			−1.89872
$290$			116890.i			1.38989i
$291$	−4667.54	+	30433.0i	−0.0551191	+	0.359384i
$292$	94836.8			1.11227
$293$		−	78542.5i		−	0.914891i	−0.889238	−	0.457446i	$-0.848764\pi$
$293$		−	78542.5i		−	0.914891i	0.889238	−	0.457446i	$-0.151236\pi$
$294$	−154514.	−	23698.0i	−1.78761	−	0.274169i
$295$	−15345.6			−0.176336
$296$		−	456254.i		−	5.20742i
$297$	−125842.	−	61809.3i	−1.42663	−	0.700714i
$298$	32184.8			0.362425
$299$		−	19754.7i		−	0.220967i
$300$	32564.7	−	212326.i	0.361830	−	2.35918i
$301$	21118.4			0.233092
$302$		−	199546.i		−	2.18790i
$303$	5198.93	+	797.366i	0.0566276	+	0.00868505i
$304$	232737.			2.51836
$305$			168555.i			1.81193i
$306$	298811.	+	93866.1i	3.19120	+	1.00246i
$307$	−143095.			−1.51827			−0.759135	−	0.650934i	$-0.774378\pi$
$307$	−143095.			−1.51827			−0.759135	+	0.650934i	$0.774378\pi$
$308$		−	121563.i		−	1.28145i
$309$	−27260.7	+	177743.i	−0.285510	+	1.86156i
$310$	46689.4			0.485842
$311$			63503.8i			0.656567i	0.944579	+	0.328283i	$0.106470\pi$
$311$			63503.8i			0.656567i	−0.944579	+	0.328283i	$0.893530\pi$
$312$	355674.	+	54550.2i	3.65378	+	0.560385i
$313$	119628.			1.22108			0.610542	−	0.791984i	$-0.290952\pi$
$313$	119628.			1.22108			0.610542	+	0.791984i	$0.290952\pi$
$314$		−	94136.9i		−	0.954774i
$315$	−11354.8	+	36146.5i	−0.114435	+	0.364288i
$316$	−15399.9			−0.154221
$317$			137237.i			1.36569i	0.730561	+	0.682847i	$0.239259\pi$
$317$			137237.i			1.36569i	−0.730561	+	0.682847i	$0.760741\pi$
$318$	−9364.98	+	61060.8i	−0.0926088	+	0.603821i
$319$	−84478.8			−0.830168
$320$			717469.i			7.00653i
$321$	96610.5	+	14817.3i	0.937593	+	0.143800i
$322$	−12543.5			−0.120978
$323$			103572.i			0.992745i
$324$	−246289.	−	171675.i	−2.34615	−	1.63538i
$325$	89176.5			0.844274
$326$		−	46250.1i		−	0.435188i
$327$	−6867.66	+	44778.0i	−0.0642263	+	0.418764i
$328$	425267.			3.95289
$329$		−	23363.0i		−	0.215842i
$330$	455274.	+	69826.0i	4.18066	+	0.641194i
$331$	−118240.			−1.07921			−0.539607	−	0.841917i	$-0.681427\pi$
$331$	−118240.			−1.07921			−0.539607	+	0.841917i	$0.681427\pi$
$332$			31467.0i			0.285482i
$333$	−150767.	−	47360.7i	−1.35962	−	0.427100i
$334$	126019.			1.12965
$335$			136037.i			1.21218i
$336$	20838.7	−	135871.i	0.184583	−	1.20351i
$337$	47426.4			0.417600			0.208800	−	0.977958i	$-0.433044\pi$
$337$	47426.4			0.417600			0.208800	+	0.977958i	$0.433044\pi$
$338$			5250.77i			0.0459610i
$339$	149015.	+	22854.6i	1.29667	+	0.198872i
$340$	−762385.			−6.59503
$341$			33743.5i			0.290190i
$342$	40156.0	−	127832.i	0.343319	−	1.09291i
$343$	−63697.5			−0.541419
$344$		−	357520.i		−	3.02123i
$345$	5338.34	−	34806.6i	0.0448506	−	0.292431i
$346$	211019.			1.76266
$347$			38766.0i			0.321953i	0.986958	+	0.160976i	$0.0514643\pi$
$347$			38766.0i			0.321953i	−0.986958	+	0.160976i	$0.948536\pi$
$348$	−178806.	−	27423.7i	−1.47647	−	0.226448i
$349$	−174398.			−1.43183			−0.715914	−	0.698189i	$-0.753990\pi$
$349$	−174398.			−1.43183			−0.715914	+	0.698189i	$0.753990\pi$
$350$		−	56623.7i		−	0.462235i
$351$	54946.0	−	111868.i	0.445987	−	0.908014i
$352$	−951466.			−7.67906
$353$			122807.i			0.985536i	0.870161	+	0.492768i	$0.164015\pi$
$353$			122807.i			0.985536i	−0.870161	+	0.492768i	$0.835985\pi$
$354$	4859.17	−	31682.4i	0.0387754	−	0.252820i
$355$	7916.29			0.0628153
$356$		−	259287.i		−	2.04588i
$357$	60465.0	+	9273.60i	0.474425	+	0.0727632i
$358$	−287944.			−2.24669
$359$		−	19827.2i		−	0.153841i	−0.997037	−	0.0769204i	$-0.975491\pi$
$359$		−	19827.2i		−	0.153841i	0.997037	−	0.0769204i	$-0.0245087\pi$
$360$	611937.	+	192229.i	4.72173	+	1.48325i
$361$	−86012.8			−0.660007
$362$			319266.i			2.43633i
$363$	−30488.9	+	198791.i	−0.231381	+	1.50863i
$364$	108065.			0.815609
$365$			70180.6i			0.526783i
$366$	−347997.	−	53372.8i	−2.59784	−	0.398435i
$367$	3598.99			0.0267207			0.0133604	−	0.999911i	$-0.495747\pi$
$367$	3598.99			0.0267207			0.0133604	+	0.999911i	$0.495747\pi$
$368$			127757.i			0.943386i
$369$	44144.2	−	140528.i	0.324206	−	1.03207i
$370$	519170.			3.79233
$371$			12065.1i			0.0876565i
$372$	−10953.9	+	71421.0i	−0.0791560	+	0.516107i
$373$	−51310.8			−0.368800			−0.184400	−	0.982851i	$-0.559034\pi$
$373$	−51310.8			−0.368800			−0.184400	+	0.982851i	$0.559034\pi$
$374$		−	743657.i		−	5.31655i
$375$	−31145.7	−	4776.86i	−0.221481	−	0.0339688i
$376$	−395520.			−2.79765
$377$		−	75098.3i		−	0.528381i
$378$	−71032.2	−	34888.7i	−0.497132	−	0.244175i
$379$	134311.			0.935046			0.467523	−	0.883981i	$-0.345147\pi$
$379$	134311.			0.935046			0.467523	+	0.883981i	$0.345147\pi$
$380$			326149.i			2.25865i
$381$	10951.4	−	71404.3i	0.0754429	−	0.491897i
$382$	115367.			0.790595
$383$			19879.1i			0.135518i	0.997702	+	0.0677592i	$0.0215850\pi$
$383$			19879.1i			0.135518i	−0.997702	+	0.0677592i	$0.978415\pi$
$384$	−777101.	−	119185.i	−5.27005	−	0.808275i
$385$	89958.5			0.606905
$386$			552832.i			3.71038i
$387$	−118141.	−	37111.8i	−0.788821	−	0.247794i
$388$	156537.			1.03981
$389$		−	63588.9i		−	0.420225i	−0.977677	−	0.210113i	$-0.932617\pi$
$389$		−	63588.9i		−	0.420225i	0.977677	−	0.210113i	$-0.0673831\pi$
$390$	−62072.6	+	404721.i	−0.408104	+	2.66089i
$391$	−56854.1			−0.371885
$392$			516866.i			3.36361i
$393$	189197.	+	29017.4i	1.22498	+	0.187877i
$394$	498965.			3.21423
$395$		−	11396.1i		−	0.0730403i
$396$	−213626.	+	680052.i	−1.36227	+	4.33662i
$397$	88252.9			0.559948			0.279974	−	0.960008i	$-0.409674\pi$
$397$	88252.9			0.559948			0.279974	+	0.960008i	$0.409674\pi$
$398$			163581.i			1.03268i
$399$	3967.25	−	25867.0i	0.0249198	−	0.162480i
$400$	−576721.			−3.60451
$401$		−	129776.i		−	0.807062i	−0.914966	−	0.403531i	$-0.867783\pi$
$401$		−	129776.i		−	0.807062i	0.914966	−	0.403531i	$-0.132217\pi$
$402$	−280859.	−	43075.8i	−1.73795	−	0.266551i
$403$	−29996.7			−0.184698
$404$		−	26741.6i		−	0.163841i
$405$	127042.	−	182258.i	0.774530	−	1.11116i
$406$	−47684.6			−0.289285
$407$			375217.i			2.26513i
$408$	156996.	−	1.02363e6i	0.943123	−	6.14928i
$409$	226902.			1.35641			0.678207	−	0.734871i	$-0.262757\pi$
$409$	226902.			1.35641			0.678207	+	0.734871i	$0.262757\pi$
$410$			483911.i			2.87871i
$411$	288611.	+	44264.6i	1.70855	+	0.262043i
$412$	914253.			5.38607
$413$		−	6260.19i		−	0.0367018i
$414$	70171.0	+	22042.9i	0.409409	+	0.128608i
$415$	−23286.0			−0.135207
$416$		−	845816.i		−	4.88753i
$417$	25397.3	−	165593.i	0.146054	−	0.952293i
$418$	−318137.			−1.82080
$419$			333074.i			1.89720i	0.316477	+	0.948600i	$0.397500\pi$
$419$			333074.i			1.89720i	−0.316477	+	0.948600i	$0.602500\pi$
$420$	190405.	+	29202.6i	1.07939	+	0.165548i
$421$	−109937.			−0.620267			−0.310133	−	0.950693i	$-0.600374\pi$
$421$	−109937.			−0.620267			−0.310133	+	0.950693i	$0.600374\pi$
$422$			385978.i			2.16739i
$423$	−41056.4	+	130698.i	−0.229456	+	0.730445i
$424$	204255.			1.13616
$425$		−	256651.i		−	1.42090i
$426$	−2506.68	+	16343.9i	−0.0138128	+	0.0900608i
$427$	−68761.4			−0.377128
$428$		−	496933.i		−	2.71275i
$429$	−292501.	−	44861.3i	−1.58933	−	0.243757i
$430$	406822.			2.20023
$431$		−	216245.i		−	1.16410i	−0.813153	−	0.582050i	$-0.802251\pi$
$431$		−	216245.i		−	1.16410i	0.813153	−	0.582050i	$-0.197749\pi$
$432$	−355346.	+	723473.i	−1.90407	+	3.87663i
$433$	107632.			0.574071			0.287035	−	0.957920i	$-0.407330\pi$
$433$	107632.			0.574071			0.287035	+	0.957920i	$0.407330\pi$
$434$			19046.8i			0.101121i
$435$	20294.0	−	132319.i	0.107248	−	0.699269i
$436$	230323.			1.21161
$437$			24322.2i			0.127362i
$438$	−144894.	−	22222.6i	−0.755270	−	0.115837i
$439$	148945.			0.772853			0.386427	−	0.922320i	$-0.373709\pi$
$439$	148945.			0.772853			0.386427	+	0.922320i	$0.373709\pi$
$440$		−	1.52294e6i		−	7.86642i
$441$	170796.	+	53652.5i	0.878214	+	0.275875i
$442$	661082.			3.38385
$443$			9322.46i			0.0475032i	0.999718	+	0.0237516i	$0.00756108\pi$
$443$			9322.46i			0.0475032i	−0.999718	+	0.0237516i	$0.992439\pi$
$444$	−121804.	+	794176.i	−0.617867	+	4.02857i
$445$	191876.			0.968949
$446$			51736.8i			0.260094i
$447$	−36433.2	−	5587.81i	−0.182340	−	0.0279658i
$448$	−292689.			−1.45831
$449$		−	153270.i		−	0.760266i	−0.924932	−	0.380133i	$-0.875878\pi$
$449$		−	153270.i		−	0.760266i	0.924932	−	0.380133i	$-0.124122\pi$
$450$	−99506.3	+	316766.i	−0.491389	+	1.56428i
$451$	−349734.			−1.71943
$452$		−	766483.i		−	3.75168i
$453$	−34644.5	+	225886.i	−0.168825	+	1.10076i
$454$	−4934.72			−0.0239415
$455$			79969.6i			0.386280i
$456$	−437911.	−	67163.0i	−2.10599	−	0.322998i
$457$	27315.8			0.130792			0.0653961	−	0.997859i	$-0.479169\pi$
$457$	27315.8			0.130792			0.0653961	+	0.997859i	$0.479169\pi$
$458$			226753.i			1.08099i
$459$	−321958.	−	158135.i	−1.52818	−	0.750591i
$460$	−179034.			−0.846096
$461$			175848.i			0.827436i	0.910405	+	0.413718i	$0.135770\pi$
$461$			175848.i			0.827436i	−0.910405	+	0.413718i	$0.864230\pi$
$462$	−28485.2	+	185727.i	−0.133455	+	0.870145i
$463$	−189562.			−0.884278			−0.442139	−	0.896946i	$-0.645780\pi$
$463$	−189562.			−0.884278			−0.442139	+	0.896946i	$0.645780\pi$
$464$			485675.i			2.25585i
$465$	−52852.5	−	8106.07i	−0.244433	−	0.0374890i
$466$	179931.			0.828578
$467$			121958.i			0.559213i	0.960115	+	0.279607i	$0.0902041\pi$
$467$			121958.i			0.559213i	−0.960115	+	0.279607i	$0.909796\pi$
$468$	−604539.	−	189905.i	−2.76015	−	0.867052i
$469$	−55495.6			−0.252297
$470$		−	450062.i		−	2.03740i
$471$	−16343.7	+	106563.i	−0.0736732	+	0.480358i
$472$	−105981.			−0.475712
$473$			294020.i			1.31418i
$474$	23528.3	+	3608.56i	0.104721	+	0.0160612i
$475$	−109795.			−0.486628
$476$		−	311012.i		−	1.37266i
$477$	21202.3	−	67495.0i	0.0931853	−	0.296644i
$478$	−835178.			−3.65530
$479$		−	304764.i		−	1.32829i	−0.747604	−	0.664145i	$-0.768796\pi$
$479$		−	304764.i		−	1.32829i	0.747604	−	0.664145i	$-0.231204\pi$
$480$	228567.	−	1.49028e6i	0.992043	−	6.46824i
$481$	−333553.			−1.44170
$482$		−	696469.i		−	2.99783i
$483$	14199.2	+	2177.76i	0.0608654	+	0.00933501i
$484$	1.02252e6			4.36495
$485$			115840.i			0.492463i
$486$	336059.	+	320002.i	1.42280	+	1.35481i
$487$	−187435.			−0.790302			−0.395151	−	0.918616i	$-0.629308\pi$
$487$	−187435.			−0.790302			−0.395151	+	0.918616i	$0.629308\pi$
$488$			1.16409e6i			4.88816i
$489$	−8029.78	+	52355.2i	−0.0335804	+	0.218948i
$490$	−588141.			−2.44957
$491$		−	463302.i		−	1.92177i	−0.276950	−	0.960884i	$-0.589324\pi$
$491$		−	463302.i		−	1.92177i	0.276950	−	0.960884i	$-0.410676\pi$
$492$	−740240.	−	113532.i	−3.05804	−	0.469015i
$493$	−216134.			−0.889260
$494$		−	282811.i		−	1.15889i
$495$	−503248.	−	158086.i	−2.05386	−	0.645184i
$496$	193994.			0.788543
$497$			3229.42i			0.0130741i
$498$	7373.49	−	48076.0i	0.0297313	−	0.193852i
$499$	92062.3			0.369727			0.184863	−	0.982764i	$-0.440816\pi$
$499$	92062.3			0.369727			0.184863	+	0.982764i	$0.440816\pi$
$500$			160203.i			0.640813i
$501$	−142654.	−	21879.1i	−0.568341	−	0.0871672i
$502$	−309573.			−1.22845
$503$		−	325821.i		−	1.28778i	−0.765116	−	0.643892i	$-0.777319\pi$
$503$		−	325821.i		−	1.28778i	0.765116	−	0.643892i	$-0.222681\pi$
$504$	−78419.0	+	249637.i	−0.308717	+	0.982762i
$505$	19789.1			0.0775968
$506$		−	174636.i		−	0.682076i
$507$	911.621	−	5943.88i	0.00354649	−	0.0231235i
$508$	−367280.			−1.42321
$509$			392471.i			1.51486i	0.652917	+	0.757429i	$0.273545\pi$
$509$			392471.i			1.51486i	−0.652917	+	0.757429i	$0.726455\pi$
$510$	1.16479e6	+	178646.i	4.47824	+	0.686834i
$511$	−28629.9			−0.109642
$512$			1.33298e6i			5.08490i
$513$	−67650.4	+	137734.i	−0.257061	+	0.523367i
$514$	370521.			1.40245
$515$			676560.i			2.55089i
$516$	−95445.5	+	622316.i	−0.358473	+	2.33729i
$517$	325270.			1.21692
$518$			211794.i			0.789320i
$519$	−238874.	−	36636.4i	−0.886817	−	0.136012i
$520$	1.35383e6			5.00678
$521$		−	513011.i		−	1.88995i	−0.327137	−	0.944977i	$-0.606084\pi$
$521$		−	513011.i		−	1.88995i	0.327137	−	0.944977i	$-0.393916\pi$
$522$	266758.	+	83797.3i	0.978988	+	0.307531i
$523$	−290306.			−1.06133			−0.530667	−	0.847580i	$-0.678059\pi$
$523$	−290306.			−1.06133			−0.530667	+	0.847580i	$0.678059\pi$
$524$		−	973168.i		−	3.54426i
$525$	−9830.83	+	64098.2i	−0.0356674	+	0.232556i
$526$	−93949.1			−0.339564
$527$			86330.8i			0.310845i
$528$	1.89166e6	+	290126.i	6.78539	+	1.04068i
$529$	266490.			0.952290
$530$			232421.i			0.827416i
$531$	−11001.2	+	35020.9i	−0.0390167	+	0.124205i
$532$	−133051.			−0.470106
$533$		−	310900.i		−	1.09437i
$534$	−60757.3	+	396145.i	−0.213067	+	1.38922i
$535$	367737.			1.28478
$536$			939504.i			3.27016i
$537$	325954.	+	49992.0i	1.13034	+	0.173361i
$538$	250601.			0.865800
$539$		−	425063.i		−	1.46311i
$540$	−1.01385e6	−	497968.i	−3.47684	−	1.70771i
$541$	−42782.2			−0.146173			−0.0730867	−	0.997326i	$-0.523285\pi$
$541$	−42782.2			−0.146173			−0.0730867	+	0.997326i	$0.523285\pi$
$542$		−	601895.i		−	2.04891i
$543$	55429.9	−	361410.i	0.187994	−	1.22575i
$544$	−2.43427e6			−8.22566
$545$			170442.i			0.573832i
$546$	−165104.	−	25322.3i	−0.553825	−	0.0849410i
$547$	348295.			1.16405			0.582026	−	0.813170i	$-0.302260\pi$
$547$	348295.			1.16405			0.582026	+	0.813170i	$0.302260\pi$
$548$		−	1.48452e6i		−	4.94339i
$549$	384667.	+	120836.i	1.27626	+	0.400915i
$550$	788341.			2.60609
$551$			92462.2i			0.304552i
$552$	36868.0	−	240384.i	0.120996	−	0.788909i
$553$	4649.00			0.0152023
$554$			395511.i			1.28866i
$555$	−587702.	−	90136.6i	−1.90797	−	0.292628i
$556$	−851757.			−2.75528
$557$			570919.i			1.84020i	0.391689	+	0.920098i	$0.371891\pi$
$557$			570919.i			1.84020i	−0.391689	+	0.920098i	$0.628109\pi$
$558$	33471.4	−	106552.i	0.107499	−	0.342210i
$559$	−261372.			−0.836441
$560$		−	517178.i		−	1.64917i
$561$	−129111.	+	841821.i	−0.410240	+	2.67482i
$562$	178244.			0.564343
$563$		−	65361.5i		−	0.206208i	−0.994671	−	0.103104i	$-0.967123\pi$
$563$		−	65361.5i		−	0.206208i	0.994671	−	0.103104i	$-0.0328774\pi$
$564$	688461.	+	105590.i	2.16432	+	0.331944i
$565$	567208.			1.77683
$566$			161513.i			0.504168i
$567$	74351.3	+	51826.4i	0.231272	+	0.161207i
$568$	54672.0			0.169460
$569$		−	384477.i		−	1.18753i	−0.804637	−	0.593767i	$-0.797640\pi$
$569$		−	384477.i		−	1.18753i	0.804637	−	0.593767i	$-0.202360\pi$
$570$	76424.7	−	498298.i	0.235225	−	1.53370i
$571$	−54990.0			−0.168660			−0.0843298	−	0.996438i	$-0.526875\pi$
$571$	−54990.0			−0.168660			−0.0843298	+	0.996438i	$0.526875\pi$
$572$			1.50453e6i			4.59842i
$573$	−130595.	−	20029.6i	−0.397758	−	0.0610046i
$574$	−197410.			−0.599163
$575$		−	60270.3i		−	0.182292i
$576$	1.63737e6	+	514349.i	4.93516	+	1.55029i
$577$	421721.			1.26670			0.633350	−	0.773866i	$-0.281680\pi$
$577$	421721.			1.26670			0.633350	+	0.773866i	$0.281680\pi$
$578$		−	1.24624e6i		−	3.73032i
$579$	95980.8	−	625807.i	0.286304	−	1.86674i
$580$	−680606.			−2.02320
$581$		−	9499.44i		−	0.0281414i
$582$	−239161.	−	36680.5i	−0.706065	−	0.108290i
$583$	−167976.			−0.494209
$584$			484686.i			1.42113i
$585$	140533.	−	447368.i	0.410644	−	1.30723i
$586$	617236.			1.79745
$587$			228158.i			0.662156i	0.943603	+	0.331078i	$0.107412\pi$
$587$			228158.i			0.662156i	−0.943603	+	0.331078i	$0.892588\pi$
$588$	137985.	−	899681.i	0.399097	−	2.60216i
$589$	36932.4			0.106458
$590$		−	120596.i		−	0.346440i
$591$	−564829.	−	86628.6i	−1.61712	−	0.248020i
$592$	2.15715e6			6.15512
$593$		−	205389.i		−	0.584073i	−0.956407	−	0.292037i	$-0.905667\pi$
$593$		−	205389.i		−	0.584073i	0.956407	−	0.292037i	$-0.0943329\pi$
$594$	485736.	−	988942.i	1.37666	−	2.80284i
$595$	230153.			0.650105
$596$			187401.i			0.527568i
$597$	28400.4	−	185174.i	0.0796848	−	0.519554i
$598$	155244.			0.434124
$599$		−	88620.3i		−	0.246990i	−0.992345	−	0.123495i	$-0.960590\pi$
$599$		−	88620.3i		−	0.246990i	0.992345	−	0.123495i	$-0.0394103\pi$
$600$	1.08514e6	+	166429.i	3.01428	+	0.462304i
$601$	−363771.			−1.00711			−0.503557	−	0.863962i	$-0.667976\pi$
$601$	−363771.			−1.00711			−0.503557	+	0.863962i	$0.667976\pi$
$602$			165961.i			0.457946i
$603$	310455.	+	97523.7i	0.853815	+	0.268210i
$604$	1.16188e6			3.18485
$605$			756676.i			2.06728i
$606$	−6266.20	+	40856.4i	−0.0170631	+	0.111254i
$607$	−150200.			−0.407653			−0.203827	−	0.979007i	$-0.565338\pi$
$607$	−150200.			−0.407653			−0.203827	+	0.979007i	$0.565338\pi$
$608$			1.04138e6i			2.81710i
$609$	53979.1	+	8278.85i	0.145543	+	0.0223221i
$610$	−1.32461e6			−3.55983
$611$			289152.i			0.774541i
$612$	−546549.	+	1.73987e6i	−1.45924	+	4.64530i
$613$	90472.5			0.240766			0.120383	−	0.992728i	$-0.461588\pi$
$613$	90472.5			0.240766			0.120383	+	0.992728i	$0.461588\pi$
$614$		−	1.12453e6i		−	2.98288i
$615$	84015.1	−	547789.i	0.222130	−	1.44831i
$616$	621277.			1.63728
$617$			42407.5i			0.111397i	0.998448	+	0.0556984i	$0.0177385\pi$
$617$			42407.5i			0.111397i	−0.998448	+	0.0556984i	$0.982261\pi$
$618$	−1.39682e6	−	214232.i	−3.65732	−	0.560928i
$619$	57960.9			0.151270			0.0756352	−	0.997136i	$-0.475902\pi$
$619$	57960.9			0.151270			0.0756352	+	0.997136i	$0.475902\pi$
$620$			271856.i			0.707222i
$621$	−75606.7	−	37135.5i	−0.196055	−	0.0962956i
$622$	−499052.			−1.28993
$623$			78275.2i			0.201673i
$624$	−257911.	+	1.68161e6i	−0.662370	+	4.31873i
$625$	−444556.			−1.13806
$626$			940114.i			2.39901i
$627$	360132.	+	55233.9i	0.916065	+	0.140498i
$628$	548126.			1.38983
$629$			959969.i			2.42636i
$630$	−284062.	−	89232.9i	−0.715701	−	0.224825i
$631$	−214265.			−0.538136			−0.269068	−	0.963121i	$-0.586716\pi$
$631$	−214265.			−0.538136			−0.269068	+	0.963121i	$0.586716\pi$
$632$		−	78704.5i		−	0.197045i
$633$	67012.2	−	436928.i	0.167242	−	1.09044i
$634$	−1.07850e6			−2.68312
$635$		−	271793.i		−	0.674047i
$636$	−355535.	−	54528.9i	−0.878959	−	0.134807i
$637$	377865.			0.931231
$638$		−	663887.i		−	1.63100i
$639$	5675.14	−	18066.1i	0.0138987	−	0.0442449i
$640$	−2.95795e6			−7.22156
$641$			55617.2i			0.135361i	0.997707	+	0.0676804i	$0.0215598\pi$
$641$			55617.2i			0.135361i	−0.997707	+	0.0676804i	$0.978440\pi$
$642$	−116443.	+	759226.i	−0.282517	+	1.84205i
$643$	173926.			0.420672			0.210336	−	0.977629i	$-0.432544\pi$
$643$	173926.			0.420672			0.210336	+	0.977629i	$0.432544\pi$
$644$		−	73036.2i		−	0.176103i
$645$	−460523.	−	70631.0i	−1.10696	−	0.169776i
$646$	−813934.			−1.95040
$647$		−	698038.i		−	1.66752i	−0.552128	−	0.833759i	$-0.686184\pi$
$647$		−	698038.i		−	1.66752i	0.552128	−	0.833759i	$-0.313816\pi$
$648$	877387.	−	1.25872e6i	2.08949	−	2.99763i
$649$	87157.3			0.206926
$650$			700804.i			1.65871i
$651$	3306.84	−	21561.0i	0.00780281	−	0.0508753i
$652$	269298.			0.633487
$653$		−	13267.9i		−	0.0311154i	−0.999879	−	0.0155577i	$-0.995048\pi$
$653$		−	13267.9i		−	0.0311154i	0.999879	−	0.0155577i	$-0.00495237\pi$
$654$	−351893.	−	53970.4i	−0.822727	−	0.126183i
$655$	720159.			1.67859
$656$			2.01065e6i			4.67227i
$657$	160162.	+	50312.0i	0.371047	+	0.116558i
$658$	183601.			0.424056
$659$			481694.i			1.10917i	0.832125	+	0.554587i	$0.187124\pi$
$659$			481694.i			1.10917i	−0.832125	+	0.554587i	$0.812876\pi$
$660$	−406572.	+	2.65090e6i	−0.933361	+	6.08563i
$661$	586120.			1.34148			0.670739	−	0.741693i	$-0.265977\pi$
$661$	586120.			1.34148			0.670739	+	0.741693i	$0.265977\pi$
$662$		−	929201.i		−	2.12028i
$663$	−748346.	−	114775.i	−1.70245	−	0.261108i
$664$	−160819.			−0.364756
$665$		−	98459.8i		−	0.222646i
$666$	372190.	−	1.18482e6i	0.839105	−	2.67119i
$667$	−50755.5			−0.114086
$668$			733766.i			1.64439i
$669$	8982.37	−	58566.2i	0.0200696	−	0.130856i
$670$	−1.06906e6			−2.38151
$671$		−	957328.i		−	2.12626i
$672$	607955.	+	93242.9i	1.34627	+	0.206480i
$673$	148675.			0.328251			0.164126	−	0.986439i	$-0.447520\pi$
$673$	148675.			0.328251			0.164126	+	0.986439i	$0.447520\pi$
$674$			372706.i			0.820440i
$675$	167637.	−	341304.i	0.367928	−	0.749089i
$676$	−30573.4			−0.0669037
$677$		−	315103.i		−	0.687504i	−0.939060	−	0.343752i	$-0.888302\pi$
$677$		−	315103.i		−	0.687504i	0.939060	−	0.343752i	$-0.111698\pi$
$678$	−179606.	+	1.17105e6i	−0.390716	+	2.54751i
$679$	−47256.4			−0.102499
$680$		−	3.89635e6i		−	8.42635i
$681$	5586.12	+	856.750i	0.0120452	+	0.00184740i
$682$	−265178.			−0.570123
$683$			71563.2i			0.153408i	0.997054	+	0.0767040i	$0.0244397\pi$
$683$			71563.2i			0.153408i	−0.997054	+	0.0767040i	$0.975560\pi$
$684$	744318.	+	233814.i	1.59091	+	0.499757i
$685$	1.09857e6			2.34123
$686$		−	500574.i		−	1.06370i
$687$	39368.1	−	256685.i	0.0834125	−	0.543860i
$688$	1.69034e6			3.57106
$689$		−	149324.i		−	0.314552i
$690$	273532.	+	41952.0i	0.574527	+	0.0881160i
$691$	−600494.			−1.25763			−0.628814	−	0.777556i	$-0.716459\pi$
$691$	−600494.			−1.25763			−0.628814	+	0.777556i	$0.716459\pi$
$692$			1.22869e6i			2.56584i
$693$	64490.7	−	205298.i	0.134286	−	0.427483i
$694$	−304648.			−0.632527
$695$		−	630312.i		−	1.30493i
$696$	140155.	−	913831.i	0.289329	−	1.88646i
$697$	−894773.			−1.84182
$698$		−	1.37053e6i		−	2.81305i
$699$	−203682.	−	31239.0i	−0.416868	−	0.0639355i
$700$	329700.			0.672857
$701$			743521.i			1.51306i	0.653957	+	0.756531i	$0.273108\pi$
$701$			743521.i			1.51306i	−0.653957	+	0.756531i	$0.726892\pi$
$702$	879131.	+	431800.i	1.78394	+	0.876211i
$703$	410675.			0.830975
$704$		−	4.07494e6i		−	8.22198i
$705$	−78138.3	+	509471.i	−0.157212	+	1.02504i
$706$	−965091.			−1.93624
$707$			8072.90i			0.0161507i
$708$	184475.	+	28293.2i	0.368021	+	0.0564438i
$709$	578585.			1.15100			0.575499	−	0.817802i	$-0.304808\pi$
$709$	578585.			1.15100			0.575499	+	0.817802i	$0.304808\pi$
$710$			62211.2i			0.123410i
$711$	−26007.5	−	8169.80i	−0.0514470	−	0.0161612i
$712$	1.32515e6			2.61399
$713$			20273.4i			0.0398793i
$714$	−72877.7	+	475172.i	−0.142955	+	0.932082i
$715$	−1.11337e6			−2.17785
$716$		−	1.67660e6i		−	3.27042i
$717$	945424.	+	145001.i	1.83903	+	0.282054i
$718$	155814.			0.302244
$719$		−	754589.i		−	1.45966i	−0.683627	−	0.729832i	$-0.739598\pi$
$719$		−	754589.i		−	1.45966i	0.683627	−	0.729832i	$-0.260402\pi$
$720$	−908850.	+	2.89321e6i	−1.75318	+	5.58104i
$721$	−276000.			−0.530932
$722$		−	675942.i		−	1.29669i
$723$	−120919.	+	788404.i	−0.231322	+	1.50825i
$724$	−1.85897e6			−3.54647
$725$		−	229121.i		−	0.435901i
$726$	−1.56222e6	−	239600.i	−2.96395	−	0.454584i
$727$	−239352.			−0.452864			−0.226432	−	0.974027i	$-0.572706\pi$
$727$	−239352.			−0.452864			−0.226432	+	0.974027i	$0.572706\pi$
$728$			552291.i			1.04209i
$729$	−324862.	−	420588.i	−0.611285	−	0.791410i
$730$	−551523.			−1.03495
$731$			752231.i			1.40772i
$732$	310771.	−	2.02626e6i	0.579986	−	3.78158i
$733$	231674.			0.431191			0.215595	−	0.976483i	$-0.430831\pi$
$733$	231674.			0.431191			0.215595	+	0.976483i	$0.430831\pi$
$734$			28283.1i			0.0524970i
$735$	665777.	+	102111.i	1.23241	+	0.189016i
$736$	−571649.			−1.05529
$737$		−	772635.i		−	1.42246i
$738$	1.10435e6	+	346913.i	2.02766	+	0.636954i
$739$	−731305.			−1.33909			−0.669545	−	0.742772i	$-0.733511\pi$
$739$	−731305.			−1.33909			−0.669545	+	0.742772i	$0.733511\pi$
$740$			3.02294e6i			5.52035i
$741$	−49100.8	+	320143.i	−0.0894236	+	0.583053i
$742$	−94815.3			−0.172215
$743$			797019.i			1.44375i	0.692025	+	0.721873i	$0.256719\pi$
$743$			797019.i			1.44375i	−0.692025	+	0.721873i	$0.743281\pi$
$744$	−365013.	−	55982.6i	−0.659421	−	0.101136i
$745$	−138679.			−0.249861
$746$		−	403232.i		−	0.724565i
$747$	−16693.6	+	53142.0i	−0.0299164	+	0.0952350i
$748$	4.33005e6			7.73909
$749$			150017.i			0.267410i
$750$	37539.5	−	244762.i	0.0667369	−	0.435133i
$751$	1.02196e6			1.81198			0.905991	−	0.423296i	$-0.139127\pi$
$751$	1.02196e6			1.81198			0.905991	+	0.423296i	$0.139127\pi$
$752$		−	1.87000e6i		−	3.30679i
$753$	350438.	+	53747.1i	0.618046	+	0.0947906i
$754$	590169.			1.03809
$755$			859811.i			1.50837i
$756$	203144.	−	413595.i	0.355436	−	0.723655i
$757$	711548.			1.24169			0.620844	−	0.783934i	$-0.286790\pi$
$757$	711548.			1.24169			0.620844	+	0.783934i	$0.286790\pi$
$758$			1.05550e6i			1.83704i
$759$	−30319.7	+	197688.i	−0.0526310	+	0.343160i
$760$	−1.66686e6			−2.88584
$761$		−	1.11176e6i		−	1.91973i	−0.280459	−	0.959866i	$-0.590487\pi$
$761$		−	1.11176e6i		−	1.91973i	0.280459	−	0.959866i	$-0.409513\pi$
$762$	561140.	+	86062.7i	0.966409	+	0.148219i
$763$	−69531.3			−0.119435
$764$			671740.i			1.15084i
$765$	−1.28753e6	−	404454.i	−2.20006	−	0.691109i
$766$	−156222.			−0.266247
$767$			77479.4i			0.131703i
$768$	474085.	−	3.09109e6i	0.803774	−	5.24070i
$769$	864703.			1.46223			0.731113	−	0.682257i	$-0.239001\pi$
$769$	864703.			1.46223			0.731113	+	0.682257i	$0.239001\pi$
$770$			706950.i			1.19236i
$771$	−419430.	−	64328.6i	−0.705588	−	0.108217i
$772$	−3.21894e6			−5.40105
$773$			770578.i			1.28961i	0.764348	+	0.644804i	$0.223061\pi$
$773$			770578.i			1.28961i	−0.764348	+	0.644804i	$0.776939\pi$
$774$	291648.	−	928425.i	0.486830	−	1.54976i
$775$	−91518.2			−0.152372
$776$			800019.i			1.32855i
$777$	36770.9	−	239751.i	0.0609063	−	0.397116i
$778$	499721.			0.825598
$779$			382785.i			0.630782i
$780$	−2.35654e6	−	361426.i	−3.87335	−	0.594061i
$781$	−44961.5			−0.0737120
$782$		−	446795.i		−	0.730626i
$783$	−287422.	−	141172.i	−0.468810	−	0.230264i
$784$	−2.44372e6			−3.97575
$785$			405621.i			0.658235i
$786$	−228037.	+	1.48683e6i	−0.369114	+	2.40667i
$787$	584038.			0.942956			0.471478	−	0.881878i	$-0.343721\pi$
$787$	584038.			0.942956			0.471478	+	0.881878i	$0.343721\pi$
$788$			2.90529e6i			4.67883i
$789$	106351.	+	16311.1i	0.170839	+	0.0262017i
$790$	89557.8			0.143499
$791$			231390.i			0.369822i
$792$	−3.47556e6	−	1.09179e6i	−5.54083	−	1.74055i
$793$	851027.			1.35331
$794$			693546.i			1.10011i
$795$	40352.2	−	263101.i	0.0638459	−	0.416283i
$796$	−952473.			−1.50323
$797$			325582.i			0.512559i	0.966603	+	0.256280i	$0.0824968\pi$
$797$			325582.i			0.512559i	−0.966603	+	0.256280i	$0.917503\pi$
$798$	203279.	+	31177.2i	0.319217	+	0.0489588i
$799$	832184.			1.30354
$800$		−	2.58054e6i		−	4.03209i
$801$	137555.	−	437889.i	0.214393	−	0.682494i
$802$	1.01986e6			1.58560
$803$		−	398599.i		−	0.618165i
$804$	250815.	−	1.63534e6i	0.388009	−	2.52986i
$805$	54047.8			0.0834039
$806$		−	235733.i		−	0.362869i
$807$	−283681.	−	43508.5i	−0.435595	−	0.0668077i
$808$	136669.			0.209337
$809$		−	373051.i		−	0.569995i	−0.958528	−	0.284998i	$-0.908007\pi$
$809$		−	373051.i		−	0.569995i	0.958528	−	0.284998i	$-0.0919928\pi$
$810$	1.43229e6	+	998378.i	2.18304	+	1.52169i
$811$	−574638.			−0.873681			−0.436840	−	0.899539i	$-0.643903\pi$
$811$	−574638.			−0.873681			−0.436840	+	0.899539i	$0.643903\pi$
$812$		−	277651.i		−	0.421101i
$813$	−104499.	+	681346.i	−0.158100	+	1.03083i
$814$	−2.94869e6			−4.45020
$815$			199284.i			0.300025i
$816$	4.83969e6	+	742270.i	7.26838	+	1.11476i
$817$	321805.			0.482113
$818$			1.78314e6i			2.66489i
$819$	182502.	+	57329.7i	0.272082	+	0.0854696i
$820$	−2.81764e6			−4.19043
$821$		−	1.12175e6i		−	1.66422i	−0.554612	−	0.832109i	$-0.687133\pi$
$821$		−	1.12175e6i		−	1.66422i	0.554612	−	0.832109i	$-0.312867\pi$
$822$	−347859.	+	2.26808e6i	−0.514825	+	3.35672i
$823$	475262.			0.701671			0.350836	−	0.936437i	$-0.385898\pi$
$823$	475262.			0.701671			0.350836	+	0.936437i	$0.385898\pi$
$824$			4.67250e6i			6.88169i
$825$	−892404.	−	136869.i	−1.31115	−	0.201093i
$826$	49196.5			0.0721065
$827$			433546.i			0.633905i	0.948441	+	0.316953i	$0.102660\pi$
$827$			433546.i			0.633905i	−0.948441	+	0.316953i	$0.897340\pi$
$828$	−128348.	+	408581.i	−0.187210	+	0.595960i
$829$	894946.			1.30223			0.651115	−	0.758979i	$-0.274302\pi$
$829$	894946.			1.30223			0.651115	+	0.758979i	$0.274302\pi$
$830$		−	182996.i		−	0.265635i
$831$	68667.2	−	447719.i	0.0994369	−	0.648341i
$832$	3.62247e6			5.23308
$833$		−	1.08750e6i		−	1.56725i
$834$	1.30133e6	+	199587.i	1.87093	+	0.286947i
$835$	−542997.			−0.778798
$836$		−	1.85240e6i		−	2.65047i
$837$	−56388.8	+	114806.i	−0.0804901	+	0.163875i
$838$	−2.61751e6			−3.72735
$839$		−	1.03179e6i		−	1.46578i	−0.680346	−	0.732891i	$-0.738171\pi$
$839$		−	1.03179e6i		−	1.46578i	0.680346	−	0.732891i	$-0.261829\pi$
$840$	−149247.	+	973107.i	−0.211517	+	1.37912i
$841$	514331.			0.727195
$842$		−	863951.i		−	1.21861i
$843$	−201773.	−	30946.2i	−0.283928	−	0.0435463i
$844$	−2.24741e6			−3.15499
$845$		−	22624.7i		−	0.0316862i
$846$	−1.02711e6	−	322647.i	−1.43507	−	0.450802i
$847$	−308683.			−0.430275
$848$			965708.i			1.34293i
$849$	28041.4	−	182833.i	0.0389031	−	0.253653i
$850$	2.01692e6			2.79159
$851$			225433.i			0.311285i
$852$	−95164.6	−	14595.5i	−0.131098	−	0.0201067i
$853$	−545690.			−0.749977			−0.374989	−	0.927029i	$-0.622353\pi$
$853$	−545690.			−0.749977			−0.374989	+	0.927029i	$0.622353\pi$
$854$		−	540370.i		−	0.740927i
$855$	−173026.	+	550806.i	−0.236689	+	0.753471i
$856$	2.53969e6			3.46604
$857$			517563.i			0.704696i	0.935869	+	0.352348i	$0.114617\pi$
$857$			517563.i			0.704696i	−0.935869	+	0.352348i	$0.885383\pi$
$858$	352548.	−	2.29866e6i	0.478899	−	3.12248i
$859$	−91381.3			−0.123843			−0.0619214	−	0.998081i	$-0.519723\pi$
$859$	−91381.3			−0.123843			−0.0619214	+	0.998081i	$0.519723\pi$
$860$			2.36878e6i			3.20278i
$861$	223468.	+	34273.6i	0.301446	+	0.0462332i
$862$	1.69938e6			2.28706
$863$			1.00141e6i			1.34458i	0.740286	+	0.672292i	$0.234690\pi$
$863$			1.00141e6i			1.34458i	−0.740286	+	0.672292i	$0.765310\pi$
$864$	−3.23718e6	−	1.59000e6i	−4.33650	−	2.12995i
$865$	−909248.			−1.21521
$866$			845839.i			1.12785i
$867$	−216368.	+	1.41075e6i	−0.287843	+	1.87677i
$868$	−110903.			−0.147198
$869$			64725.5i			0.0857108i
$870$	1.03985e6	+	159483.i	1.37382	+	0.210705i
$871$	686842.			0.905358
$872$			1.17712e6i			1.54806i
$873$	264363.	+	83044.8i	0.346874	+	0.108964i
$874$	−191139.			−0.250223
$875$		−	48363.1i		−	0.0631681i
$876$	129394.	−	843666.i	0.168619	−	1.09942i
$877$	561064.			0.729480			0.364740	−	0.931109i	$-0.381158\pi$
$877$	561064.			0.729480			0.364740	+	0.931109i	$0.381158\pi$
$878$			1.17050e6i			1.51839i
$879$	−698712.	−	107162.i	−0.904317	−	0.138696i
$880$	7.20039e6			9.29802
$881$		−	43779.4i		−	0.0564051i	−0.999602	−	0.0282025i	$-0.991022\pi$
$881$		−	43779.4i		−	0.0564051i	0.999602	−	0.0282025i	$-0.00897833\pi$
$882$	−421635.	+	1.34222e6i	−0.542000	+	1.72539i
$883$	915410.			1.17407			0.587035	−	0.809561i	$-0.300295\pi$
$883$	915410.			1.17407			0.587035	+	0.809561i	$0.300295\pi$
$884$			3.84924e6i			4.92573i
$885$	−20937.4	+	136515.i	−0.0267323	+	0.174298i
$886$	−73261.7			−0.0933275
$887$		−	697550.i		−	0.886600i	−0.896373	−	0.443300i	$-0.853808\pi$
$887$		−	697550.i		−	0.886600i	0.896373	−	0.443300i	$-0.146192\pi$
$888$	−4.05882e6	−	622507.i	−5.14724	−	0.789439i
$889$	110877.			0.140293
$890$			1.50788e6i			1.90365i
$891$	−721551.	+	1.03515e6i	−0.908890	+	1.30391i
$892$	−301245.			−0.378608
$893$		−	356009.i		−	0.446435i
$894$	43912.5	−	286315.i	0.0549431	−	0.358236i
$895$	1.24071e6			1.54890
$896$		−	1.20668e6i		−	1.50306i
$897$	−175737.	−	26953.0i	−0.218413	−	0.0334983i
$898$	1.20449e6			1.49366
$899$			77070.3i			0.0953603i
$900$	−1.84441e6	−	579390.i	−2.27706	−	0.715296i
$901$	−429757.			−0.529387
$902$		−	2.74843e6i		−	3.37809i
$903$	28813.7	−	187869.i	0.0353364	−	0.230398i
$904$	3.91729e6			4.79345
$905$		−	1.37567e6i		−	1.67964i
$906$	−1.77515e6	−	272258.i	−2.16262	−	0.331684i
$907$	−1.26560e6			−1.53844			−0.769222	−	0.638981i	$-0.779356\pi$
$907$	−1.26560e6			−1.53844			−0.769222	+	0.638981i	$0.779356\pi$
$908$		−	28733.1i		−	0.0348507i
$909$	14186.7	−	45161.6i	0.0171693	−	0.0546565i
$910$	−628451.			−0.758907
$911$			1.09092e6i			1.31449i	0.753679	+	0.657243i	$0.228278\pi$
$911$			1.09092e6i			1.31449i	−0.753679	+	0.657243i	$0.771722\pi$
$912$	317544.	−	2.07042e6i	0.381781	−	2.48926i
$913$	132256.			0.158662
$914$			214665.i			0.256962i
$915$	1.49946e6	+	229975.i	1.79099	+	0.274687i
$916$	−1.32030e6			−1.57356
$917$			293786.i			0.349375i
$918$	1.24273e6	−	2.53015e6i	1.47465	−	3.00234i
$919$	−1.08170e6			−1.28079			−0.640394	−	0.768047i	$-0.721229\pi$
$919$	−1.08170e6			−1.28079			−0.640394	+	0.768047i	$0.721229\pi$
$920$		−	914994.i		−	1.08104i
$921$	−195238.	+	1.27297e6i	−0.230168	+	1.50072i
$922$	−1.38192e6			−1.62563
$923$		−	39969.0i		−	0.0469159i
$924$	−1.08142e6	−	165859.i	−1.26664	−	0.194266i
$925$	−1.01765e6			−1.18936
$926$		−	1.48970e6i		−	1.73730i
$927$	1.54401e6	+	485022.i	1.79676	+	0.564419i
$928$	−2.17315e6			−2.52345
$929$			1.05414e6i			1.22143i	0.791851	+	0.610715i	$0.209118\pi$
$929$			1.05414e6i			1.22143i	−0.791851	+	0.610715i	$0.790882\pi$
$930$	63702.5	−	415348.i	0.0736530	−	0.480227i
$931$	−465233.			−0.536749
$932$			1.04767e6i			1.20613i
$933$	564928.	+	86643.8i	0.648978	+	0.0995347i
$934$	−958424.			−1.09866
$935$			3.20430e6i			3.66530i
$936$	970554.	−	3.08964e6i	1.10782	−	3.52660i
$937$	568699.			0.647744			0.323872	−	0.946101i	$-0.395015\pi$
$937$	568699.			0.647744			0.323872	+	0.946101i	$0.395015\pi$
$938$		−	436119.i		−	0.495678i
$939$	163219.	−	1.06421e6i	0.185115	−	1.20697i
$940$	2.62055e6			2.96577
$941$		−	664710.i		−	0.750676i	−0.926888	−	0.375338i	$-0.877527\pi$
$941$		−	664710.i		−	0.750676i	0.926888	−	0.375338i	$-0.122473\pi$
$942$	−837440.	−	128439.i	−0.943739	−	0.144742i
$943$	−210123.			−0.236293
$944$		−	501074.i		−	0.562286i
$945$	306066.	+	150330.i	0.342730	+	0.168338i
$946$	−2.31059e6			−2.58191
$947$		−	465871.i		−	0.519476i	−0.965679	−	0.259738i	$-0.916364\pi$
$947$		−	465871.i		−	0.519476i	0.965679	−	0.259738i	$-0.0836362\pi$
$948$	−21011.4	+	136997.i	−0.0233796	+	0.152438i
$949$	354339.			0.393447
$950$		−	862841.i		−	0.956057i
$951$	1.22086e6	+	187245.i	1.34991	+	0.207038i
$952$	1.58950e6			1.75383
$953$			1.57070e6i			1.72945i	0.502245	+	0.864725i	$0.332508\pi$
$953$			1.57070e6i			1.72945i	−0.502245	+	0.864725i	$0.667492\pi$
$954$	530418.	+	166621.i	0.582803	+	0.183077i
$955$	−497097.			−0.545048
$956$		−	4.86295e6i		−	5.32088i
$957$	−115262.	+	751521.i	−0.125852	+	0.820573i
$958$	2.39503e6			2.60963
$959$			448155.i			0.487294i
$960$	6.38259e6	+	978906.i	6.92555	+	1.06218i
$961$	−892737.			−0.966666
$962$		−	2.62127e6i		−	2.83244i
$963$	263629.	−	839229.i	0.284276	−	0.904957i
$964$	4.05529e6			4.36383
$965$		−	2.38206e6i		−	2.55799i
$966$	−17114.2	+	111586.i	−0.0183401	+	0.119580i
$967$	867458.			0.927675			0.463837	−	0.885920i	$-0.346472\pi$
$967$	867458.			0.927675			0.463837	+	0.885920i	$0.346472\pi$
$968$			5.22580e6i			5.57702i
$969$	921375.	+	141313.i	0.981271	+	0.150499i
$970$	−910341.			−0.967521
$971$			901029.i			0.955653i	0.878454	+	0.477826i	$0.158575\pi$
$971$			901029.i			0.955653i	−0.878454	+	0.477826i	$0.841425\pi$
$972$	−1.86326e6	+	1.95675e6i	−1.97215	+	2.07111i
$973$	257133.			0.271602
$974$		−	1.47298e6i		−	1.55267i
$975$	121671.	−	793312.i	0.127991	−	0.834516i
$976$	−5.50375e6			−5.77775
$977$			950985.i			0.996288i	0.867094	+	0.498144i	$0.165985\pi$
$977$			950985.i			0.996288i	−0.867094	+	0.498144i	$0.834015\pi$
$978$	−411440.	−	63103.0i	−0.430158	−	0.0659740i
$979$	−1.08978e6			−1.13704
$980$		−	3.42454e6i		−	3.56574i
$981$	388974.	+	122189.i	0.404187	+	0.126968i
$982$	3.64092e6			3.77561
$983$			301730.i			0.312256i	0.987737	+	0.156128i	$0.0499012\pi$
$983$			301730.i			0.312256i	−0.987737	+	0.156128i	$0.950099\pi$
$984$	580230.	−	3.78317e6i	0.599253	−	3.90720i
$985$	−2.14996e6			−2.21594
$986$		−	1.69851e6i		−	1.74709i
$987$	−207837.	−	31876.2i	−0.213348	−	0.0327214i
$988$	1.64671e6			1.68695
$989$			176649.i			0.180601i
$990$	1.24234e6	−	3.95484e6i	1.26757	−	4.03514i
$991$	620066.			0.631379			0.315690	−	0.948863i	$-0.397764\pi$
$991$	620066.			0.631379			0.315690	+	0.948863i	$0.397764\pi$
$992$			868026.i			0.882083i
$993$	−161325.	+	1.05186e6i	−0.163607	+	1.06674i
$994$	−25378.8			−0.0256861
$995$		−	704844.i		−	0.711946i
$996$	279930.	+	42933.2i	0.282183	+	0.0432787i
$997$	−884593.			−0.889924			−0.444962	−	0.895549i	$-0.646783\pi$
$997$	−884593.			−0.889924			−0.444962	+	0.895549i	$0.646783\pi$
$998$			723483.i			0.726386i
$999$	−627024.	+	1.27660e6i	−0.628280	+	1.27916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.5.b.a.119.78	yes	78
3.2	odd	2	inner	177.5.b.a.119.1	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.5.b.a.119.1	✓	78	3.2	odd	2	inner
177.5.b.a.119.78	yes	78	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+7.85862i q^{2} +(1.36439 - 8.89598i) q^{3} -45.7580 q^{4} -33.8616i q^{5} +(69.9102 + 10.7222i) q^{6} +13.8137 q^{7} -233.857i q^{8} +(-77.2769 - 24.2751i) q^{9} +O(q^{10})\)	\(q+7.85862i q^{2} +(1.36439 - 8.89598i) q^{3} -45.7580 q^{4} -33.8616i q^{5} +(69.9102 + 10.7222i) q^{6} +13.8137 q^{7} -233.857i q^{8} +(-77.2769 - 24.2751i) q^{9} +266.105 q^{10} +192.320i q^{11} +(-62.4316 + 407.062i) q^{12} -170.965 q^{13} +108.557i q^{14} +(-301.232 - 46.2003i) q^{15} +1105.66 q^{16} +492.040i q^{17} +(190.769 - 607.290i) q^{18} +210.495 q^{19} +1549.44i q^{20} +(18.8472 - 122.886i) q^{21} -1511.37 q^{22} +115.548i q^{23} +(-2080.38 - 319.071i) q^{24} -521.606 q^{25} -1343.55i q^{26} +(-321.387 + 654.333i) q^{27} -632.087 q^{28} +439.260i q^{29} +(363.071 - 2367.27i) q^{30} +175.455 q^{31} +4947.30i q^{32} +(1710.88 + 262.400i) q^{33} -3866.76 q^{34} -467.753i q^{35} +(3536.03 + 1110.78i) q^{36} +1951.00 q^{37} +1654.20i q^{38} +(-233.263 + 1520.90i) q^{39} -7918.76 q^{40} +1818.50i q^{41} +(965.717 + 148.113i) q^{42} +1528.80 q^{43} -8800.20i q^{44} +(-821.994 + 2616.72i) q^{45} -908.046 q^{46} -1691.29i q^{47} +(1508.56 - 9835.97i) q^{48} -2210.18 q^{49} -4099.10i q^{50} +(4377.18 + 671.334i) q^{51} +7823.03 q^{52} +873.418i q^{53} +(-5142.16 - 2525.66i) q^{54} +6512.27 q^{55} -3230.43i q^{56} +(287.197 - 1872.56i) q^{57} -3451.98 q^{58} -453.188i q^{59} +(13783.8 + 2114.03i) q^{60} -4977.77 q^{61} +1378.83i q^{62} +(-1067.48 - 335.329i) q^{63} -21188.3 q^{64} +5789.15i q^{65} +(-2062.10 + 13445.2i) q^{66} -4017.43 q^{67} -22514.8i q^{68} +(1027.91 + 157.652i) q^{69} +3675.90 q^{70} +233.784i q^{71} +(-5676.91 + 18071.7i) q^{72} -2072.57 q^{73} +15332.1i q^{74} +(-711.672 + 4640.19i) q^{75} -9631.84 q^{76} +2656.66i q^{77} +(-11952.2 - 1833.13i) q^{78} +336.550 q^{79} -37439.5i q^{80} +(5382.44 + 3751.81i) q^{81} -14290.9 q^{82} -687.683i q^{83} +(-862.412 + 5623.03i) q^{84} +16661.3 q^{85} +12014.3i q^{86} +(3907.65 + 599.322i) q^{87} +44975.4 q^{88} +5666.49i q^{89} +(-20563.8 - 6459.74i) q^{90} -2361.66 q^{91} -5287.23i q^{92} +(239.388 - 1560.84i) q^{93} +13291.2 q^{94} -7127.70i q^{95} +(44011.0 + 6750.03i) q^{96} -3420.98 q^{97} -17369.0i q^{98} +(4668.61 - 14861.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9	\( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) 78 * q - 612 * q^4 + 64 * q^6 + 76 * q^7 - 100 * q^9 - 156 * q^10 - 4 * q^13 + 13 * q^15 + 4948 * q^16 + 22 * q^18 + 812 * q^19 - 173 * q^21 - 1644 * q^22 - 678 * q^24 - 8238 * q^25 + 777 * q^27 - 3764 * q^28 + 1374 * q^30 + 4664 * q^31 - 1042 * q^33 + 3244 * q^34 + 3648 * q^36 - 3960 * q^37 - 7078 * q^39 - 1576 * q^40 + 4934 * q^42 - 1492 * q^43 - 2063 * q^45 - 2036 * q^46 - 2620 * q^48 + 24274 * q^49 + 7300 * q^51 + 8408 * q^52 - 14766 * q^54 + 9780 * q^55 + 6939 * q^57 - 3856 * q^58 + 4712 * q^60 - 212 * q^61 - 7438 * q^63 - 45760 * q^64 + 3048 * q^66 - 12972 * q^67 + 21672 * q^69 + 5828 * q^70 - 866 * q^72 - 5240 * q^73 - 20922 * q^75 + 12368 * q^76 - 16508 * q^78 - 14976 * q^79 + 25524 * q^81 - 14484 * q^82 + 9540 * q^84 + 11572 * q^85 + 5695 * q^87 + 62160 * q^88 - 31672 * q^90 + 8284 * q^91 - 9590 * q^93 - 10992 * q^94 + 34102 * q^96 - 55000 * q^97 - 14254 * q^99

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