LMFDB - Embedded newform 177.4.f.a.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(2,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([29, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("177.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.f (of order $58$, degree $28$, 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:	$1624$
Relative dimension:	$58$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			89.4
Character	$\chi$	$=$	177.89
Dual form			177.4.f.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281900 - 5.19934i) q^{2} +(-5.12170 - 0.876440i) q^{3} +(-19.0005 + 2.06643i) q^{4} +(2.67889 + 7.95067i) q^{5} +(-3.11310 + 26.8765i) q^{6} +(1.88189 - 2.77557i) q^{7} +(9.36119 + 57.1007i) q^{8} +(25.4637 + 8.97773i) q^{9} +O(q^{10})$	\(q+(-0.281900 - 5.19934i) q^{2} +(-5.12170 - 0.876440i) q^{3} +(-19.0005 + 2.06643i) q^{4} +(2.67889 + 7.95067i) q^{5} +(-3.11310 + 26.8765i) q^{6} +(1.88189 - 2.77557i) q^{7} +(9.36119 + 57.1007i) q^{8} +(25.4637 + 8.97773i) q^{9} +(40.5830 - 16.1698i) q^{10} +(-16.4146 - 3.61312i) q^{11} +(99.1263 + 6.06917i) q^{12} +(17.9772 + 15.2700i) q^{13} +(-14.9617 - 9.00213i) q^{14} +(-6.75221 - 43.0689i) q^{15} +(144.921 - 31.8995i) q^{16} +(-10.8155 + 7.33310i) q^{17} +(39.5000 - 134.925i) q^{18} +(13.4617 + 25.3916i) q^{19} +(-67.3300 - 145.531i) q^{20} +(-12.0711 + 12.5663i) q^{21} +(-14.1586 + 86.3633i) q^{22} +(15.5017 + 14.6840i) q^{23} +(2.10012 - 300.657i) q^{24} +(43.4750 - 33.0488i) q^{25} +(74.3261 - 97.7743i) q^{26} +(-122.549 - 68.2987i) q^{27} +(-30.0213 + 56.6262i) q^{28} +(-137.368 - 7.44789i) q^{29} +(-222.026 + 47.2481i) q^{30} +(291.813 + 154.709i) q^{31} +(-82.8698 - 298.470i) q^{32} +(80.9038 + 32.8917i) q^{33} +(41.1762 + 54.1663i) q^{34} +(27.1090 + 7.52679i) q^{35} +(-502.376 - 117.963i) q^{36} +(124.838 + 20.4662i) q^{37} +(128.224 - 77.1501i) q^{38} +(-78.6908 - 93.9644i) q^{39} +(-428.911 + 227.394i) q^{40} +(292.349 + 308.629i) q^{41} +(68.7393 + 59.2192i) q^{42} +(-68.4907 - 311.156i) q^{43} +(319.352 + 34.7316i) q^{44} +(-3.16445 + 226.504i) q^{45} +(71.9770 - 84.7379i) q^{46} +(-415.052 - 139.847i) q^{47} +(-770.201 + 36.3654i) q^{48} +(122.795 + 308.192i) q^{49} +(-184.088 - 216.725i) q^{50} +(61.8209 - 28.0788i) q^{51} +(-373.132 - 252.990i) q^{52} +(341.047 + 135.886i) q^{53} +(-320.561 + 656.428i) q^{54} +(-15.2461 - 140.186i) q^{55} +(176.104 + 81.4743i) q^{56} +(-46.6929 - 141.846i) q^{57} +716.324i q^{58} +(178.691 - 416.472i) q^{59} +(217.295 + 804.379i) q^{60} +(685.953 - 37.1913i) q^{61} +(722.124 - 1560.85i) q^{62} +(72.8381 - 53.7813i) q^{63} +(-403.505 + 135.957i) q^{64} +(-73.2476 + 183.838i) q^{65} +(148.208 - 429.918i) q^{66} +(862.884 - 141.463i) q^{67} +(190.347 - 161.682i) q^{68} +(-66.5254 - 88.7933i) q^{69} +(31.4923 - 143.071i) q^{70} +(-135.678 + 402.678i) q^{71} +(-274.264 + 1538.04i) q^{72} +(-308.947 + 513.473i) q^{73} +(71.2188 - 654.846i) q^{74} +(-251.631 + 131.163i) q^{75} +(-308.251 - 454.636i) q^{76} +(-40.9188 + 38.7603i) q^{77} +(-466.370 + 435.629i) q^{78} +(-231.427 + 107.070i) q^{79} +(641.850 + 1066.76i) q^{80} +(567.801 + 457.213i) q^{81} +(1522.25 - 1607.02i) q^{82} +(-185.083 + 666.609i) q^{83} +(203.390 - 263.711i) q^{84} +(-87.2766 - 66.3460i) q^{85} +(-1598.50 + 443.821i) q^{86} +(697.032 + 158.541i) q^{87} +(52.6518 - 971.106i) q^{88} +(-55.8604 + 1030.29i) q^{89} +(1178.56 - 47.3984i) q^{90} +(76.2141 - 21.1607i) q^{91} +(-324.884 - 246.970i) q^{92} +(-1358.99 - 1048.13i) q^{93} +(-610.110 + 2197.42i) q^{94} +(-165.817 + 175.051i) q^{95} +(162.844 + 1601.31i) q^{96} +(162.774 + 270.533i) q^{97} +(1567.78 - 725.333i) q^{98} +(-385.538 - 239.369i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1624 q - 21 q^{3} - 278 q^{4} - 29 q^{6} - 42 q^{7} - 25 q^{9}+O(q^{10}) $ 1624 * q - 21 * q^3 - 278 * q^4 - 29 * q^6 - 42 * q^7 - 25 * q^9	$ 1624 q - 21 q^{3} - 278 q^{4} - 29 q^{6} - 42 q^{7} - 25 q^{9} - 58 q^{10} - 57 q^{12} - 58 q^{13} - 11 q^{15} - 926 q^{16} - 29 q^{18} + 126 q^{19} + 159 q^{21} + 2 q^{22} - 29 q^{24} + 656 q^{25} - 99 q^{27} - 54 q^{28} - 29 q^{30} - 58 q^{31} - 29 q^{33} - 58 q^{34} + 859 q^{36} - 58 q^{37} - 29 q^{39} - 58 q^{40} - 29 q^{42} - 58 q^{43} + 1703 q^{45} + 602 q^{46} + 9507 q^{48} - 1192 q^{49} + 1511 q^{51} - 58 q^{52} - 7743 q^{54} - 58 q^{55} - 7441 q^{57} - 18722 q^{60} - 58 q^{61} - 3251 q^{63} - 4634 q^{64} - 1751 q^{66} - 58 q^{67} + 6003 q^{69} - 58 q^{70} + 21547 q^{72} - 58 q^{73} + 3869 q^{75} + 5622 q^{76} - 3253 q^{78} + 1446 q^{79} + 247 q^{81} - 58 q^{82} + 3303 q^{84} + 790 q^{85} - 2199 q^{87} - 5818 q^{88} - 29 q^{90} - 58 q^{91} - 29 q^{93} - 946 q^{94} - 29 q^{96} - 58 q^{97} - 29 q^{99}+O(q^{100}) $ 1624 * q - 21 * q^3 - 278 * q^4 - 29 * q^6 - 42 * q^7 - 25 * q^9 - 58 * q^10 - 57 * q^12 - 58 * q^13 - 11 * q^15 - 926 * q^16 - 29 * q^18 + 126 * q^19 + 159 * q^21 + 2 * q^22 - 29 * q^24 + 656 * q^25 - 99 * q^27 - 54 * q^28 - 29 * q^30 - 58 * q^31 - 29 * q^33 - 58 * q^34 + 859 * q^36 - 58 * q^37 - 29 * q^39 - 58 * q^40 - 29 * q^42 - 58 * q^43 + 1703 * q^45 + 602 * q^46 + 9507 * q^48 - 1192 * q^49 + 1511 * q^51 - 58 * q^52 - 7743 * q^54 - 58 * q^55 - 7441 * q^57 - 18722 * q^60 - 58 * q^61 - 3251 * q^63 - 4634 * q^64 - 1751 * q^66 - 58 * q^67 + 6003 * q^69 - 58 * q^70 + 21547 * q^72 - 58 * q^73 + 3869 * q^75 + 5622 * q^76 - 3253 * q^78 + 1446 * q^79 + 247 * q^81 - 58 * q^82 + 3303 * q^84 + 790 * q^85 - 2199 * q^87 - 5818 * q^88 - 29 * q^90 - 58 * q^91 - 29 * q^93 - 946 * q^94 - 29 * q^96 - 58 * q^97 - 29 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{57}{58}\right)$	$-1$

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 $

$2$	−0.281900	−	5.19934i	−0.0996667	−	1.83824i	−0.440069	−	0.897964i	$-0.645046\pi$
$2$	−0.281900	−	5.19934i	−0.0996667	−	1.83824i	0.340402	−	0.940280i	$-0.389437\pi$
$3$	−5.12170	−	0.876440i	−0.985672	−	0.168671i
$3$	−5.12170	−	0.876440i	−0.985672	−	0.168671i
$4$	−19.0005	+	2.06643i	−2.37507	+	0.258304i
$5$	2.67889	+	7.95067i	0.239607	+	0.711129i	0.998223	+	0.0595908i	$0.0189796\pi$
$5$	2.67889	+	7.95067i	0.239607	+	0.711129i	−0.758615	+	0.651539i	$0.774124\pi$
$6$	−3.11310	+	26.8765i	−0.211820	+	1.82872i
$7$	1.88189	−	2.77557i	0.101612	−	0.149867i	−0.773484	−	0.633816i	$-0.781488\pi$
$7$	1.88189	−	2.77557i	0.101612	−	0.149867i	0.875096	+	0.483949i	$0.160798\pi$
$8$	9.36119	+	57.1007i	0.413710	+	2.52352i
$9$	25.4637	+	8.97773i	0.943100	+	0.332509i
$10$	40.5830	−	16.1698i	1.28335	−	0.511333i
$11$	−16.4146	−	3.61312i	−0.449925	−	0.0990359i	−0.0157729	−	0.999876i	$-0.505021\pi$
$11$	−16.4146	−	3.61312i	−0.449925	−	0.0990359i	−0.434152	+	0.900840i	$0.642952\pi$
$12$	99.1263	+	6.06917i	2.38461	+	0.146002i
$13$	17.9772	+	15.2700i	0.383537	+	0.325780i	0.818328	−	0.574752i	$-0.194902\pi$
$13$	17.9772	+	15.2700i	0.383537	+	0.325780i	−0.434790	+	0.900532i	$0.643177\pi$
$14$	−14.9617	−	9.00213i	−0.285619	−	0.171851i
$15$	−6.75221	−	43.0689i	−0.116228	−	0.741355i
$16$	144.921	−	31.8995i	2.26439	−	0.498430i
$17$	−10.8155	+	7.33310i	−0.154303	+	0.104620i	−0.635895	−	0.771775i	$-0.719369\pi$
$17$	−10.8155	+	7.33310i	−0.154303	+	0.104620i	0.481592	+	0.876395i	$0.340059\pi$
$18$	39.5000	−	134.925i	0.517236	−	1.76679i
$19$	13.4617	+	25.3916i	0.162544	+	0.306591i	0.951384	−	0.308009i	$-0.0996626\pi$
$19$	13.4617	+	25.3916i	0.162544	+	0.306591i	−0.788840	+	0.614599i	$0.789318\pi$
$20$	−67.3300	−	145.531i	−0.752772	−	1.62709i
$21$	−12.0711	+	12.5663i	−0.125435	+	0.130581i
$22$	−14.1586	+	86.3633i	−0.137210	+	0.836942i
$23$	15.5017	+	14.6840i	0.140536	+	0.133123i	0.754739	−	0.656026i	$-0.227764\pi$
$23$	15.5017	+	14.6840i	0.140536	+	0.133123i	−0.614203	+	0.789148i	$0.710522\pi$
$24$	2.10012	−	300.657i	0.0178618	−	2.55714i
$25$	43.4750	−	33.0488i	0.347800	−	0.264390i
$26$	74.3261	−	97.7743i	0.560636	−	0.737505i
$27$	−122.549	−	68.2987i	−0.873503	−	0.486818i
$28$	−30.0213	+	56.6262i	−0.202625	+	0.382191i
$29$	−137.368	−	7.44789i	−0.879609	−	0.0476910i	−0.391200	−	0.920306i	$-0.627940\pi$
$29$	−137.368	−	7.44789i	−0.879609	−	0.0476910i	−0.488409	+	0.872615i	$0.662423\pi$
$30$	−222.026	+	47.2481i	−1.35121	+	0.287543i
$31$	291.813	+	154.709i	1.69068	+	0.896343i	0.981535	+	0.191281i	$0.0612642\pi$
$31$	291.813	+	154.709i	1.69068	+	0.896343i	0.709146	+	0.705061i	$0.249081\pi$
$32$	−82.8698	−	298.470i	−0.457795	−	1.64883i
$33$	80.9038	+	32.8917i	0.426774	+	0.173506i
$34$	41.1762	+	54.1663i	0.207696	+	0.273219i
$35$	27.1090	+	7.52679i	0.130922	+	0.0363503i
$36$	−502.376	−	117.963i	−2.32582	−	0.546124i
$37$	124.838	+	20.4662i	0.554683	+	0.0909357i	0.432603	−	0.901585i	$-0.357595\pi$
$37$	124.838	+	20.4662i	0.554683	+	0.0909357i	0.122080	+	0.992520i	$0.461043\pi$
$38$	128.224	−	77.1501i	0.547388	−	0.329352i
$39$	−78.6908	−	93.9644i	−0.323093	−	0.385804i
$40$	−428.911	+	227.394i	−1.69542	+	0.898855i
$41$	292.349	+	308.629i	1.11359	+	1.17560i	0.982892	+	0.184181i	$0.0589631\pi$
$41$	292.349	+	308.629i	1.11359	+	1.17560i	0.130698	+	0.991422i	$0.458278\pi$
$42$	68.7393	+	59.2192i	0.252541	+	0.217565i
$43$	−68.4907	−	311.156i	−0.242901	−	1.10351i	−0.927276	−	0.374379i	$-0.877856\pi$
$43$	−68.4907	−	311.156i	−0.242901	−	1.10351i	0.684375	−	0.729130i	$-0.260075\pi$
$44$	319.352	+	34.7316i	1.09418	+	0.119000i
$45$	−3.16445	+	226.504i	−0.0104828	+	0.750338i
$46$	71.9770	−	84.7379i	0.230705	−	0.271607i
$47$	−415.052	−	139.847i	−1.28812	−	0.434018i	−0.409836	−	0.912159i	$-0.634414\pi$
$47$	−415.052	−	139.847i	−1.28812	−	0.434018i	−0.878283	+	0.478142i	$0.841311\pi$
$48$	−770.201	+	36.3654i	−2.31602	+	0.109352i
$49$	122.795	+	308.192i	0.358003	+	0.898520i
$50$	−184.088	−	216.725i	−0.520678	−	0.612990i
$51$	61.8209	−	28.0788i	0.169738	−	0.0770945i
$52$	−373.132	−	252.990i	−0.995078	−	0.674680i
$53$	341.047	+	135.886i	0.883895	+	0.352176i	0.767517	−	0.641029i	$-0.221492\pi$
$53$	341.047	+	135.886i	0.883895	+	0.352176i	0.116379	+	0.993205i	$0.462871\pi$
$54$	−320.561	+	656.428i	−0.807831	+	1.65423i
$55$	−15.2461	−	140.186i	−0.0373779	−	0.343685i
$56$	176.104	+	81.4743i	0.420230	+	0.194419i
$57$	−46.6929	−	141.846i	−0.108502	−	0.329614i
$58$			716.324i			1.62169i
$59$	178.691	−	416.472i	0.394298	−	0.918983i
$59$	178.691	−	416.472i	0.394298	−	0.918983i
$60$	217.295	+	804.379i	0.467544	+	1.73075i
$61$	685.953	−	37.1913i	1.43979	−	0.0780632i	0.682378	−	0.730999i	$-0.260946\pi$
$61$	685.953	−	37.1913i	1.43979	−	0.0780632i	0.757413	+	0.652936i	$0.226463\pi$
$62$	722.124	−	1560.85i	1.47919	−	3.19722i
$63$	72.8381	−	53.7813i	0.145663	−	0.107553i
$64$	−403.505	+	135.957i	−0.788097	+	0.265541i
$65$	−73.2476	+	183.838i	−0.139773	+	0.350804i
$66$	148.208	−	429.918i	0.276412	−	0.801807i
$67$	862.884	−	141.463i	1.57340	−	0.257946i	0.689032	−	0.724731i	$-0.258036\pi$
$67$	862.884	−	141.463i	1.57340	−	0.257946i	0.884371	+	0.466784i	$0.154588\pi$
$68$	190.347	−	161.682i	0.339456	−	0.288336i
$69$	−66.5254	−	88.7933i	−0.116068	−	0.154920i
$70$	31.4923	−	143.071i	0.0537721	−	0.244289i
$71$	−135.678	+	402.678i	−0.226789	+	0.673086i	0.772487	+	0.635031i	$0.219013\pi$
$71$	−135.678	+	402.678i	−0.226789	+	0.673086i	−0.999276	+	0.0380548i	$0.987884\pi$
$72$	−274.264	+	1538.04i	−0.448922	+	2.51749i
$73$	−308.947	+	513.473i	−0.495335	+	0.823254i	−0.999178	−	0.0405418i	$-0.987092\pi$
$73$	−308.947	+	513.473i	−0.495335	+	0.823254i	0.503843	+	0.863796i	$0.331919\pi$
$74$	71.2188	−	654.846i	0.111879	−	1.02871i
$75$	−251.631	+	131.163i	−0.387412	+	0.201939i
$76$	−308.251	−	454.636i	−0.465247	−	0.686188i
$77$	−40.9188	+	38.7603i	−0.0605601	+	0.0573656i
$78$	−466.370	+	435.629i	−0.677000	+	0.632375i
$79$	−231.427	+	107.070i	−0.329590	+	0.152485i	−0.577704	−	0.816246i	$-0.696051\pi$
$79$	−231.427	+	107.070i	−0.329590	+	0.152485i	0.248114	+	0.968731i	$0.420189\pi$
$80$	641.850	+	1066.76i	0.897013	+	1.49085i
$81$	567.801	+	457.213i	0.778876	+	0.627178i
$82$	1522.25	−	1607.02i	2.05006	−	2.16422i
$83$	−185.083	+	666.609i	−0.244765	+	0.881565i	0.734437	+	0.678677i	$0.237446\pi$
$83$	−185.083	+	666.609i	−0.244765	+	0.881565i	−0.979202	+	0.202888i	$0.934967\pi$
$84$	203.390	−	263.711i	0.264186	−	0.342538i
$85$	−87.2766	−	66.3460i	−0.111370	−	0.0846615i
$86$	−1598.50	+	443.821i	−2.00431	+	0.556494i
$87$	697.032	+	158.541i	0.858962	+	0.195372i
$88$	52.6518	−	971.106i	0.0637807	−	1.17637i
$89$	−55.8604	+	1030.29i	−0.0665303	+	1.22708i	0.754541	+	0.656253i	$0.227860\pi$
$89$	−55.8604	+	1030.29i	−0.0665303	+	1.22708i	−0.821071	+	0.570826i	$0.806623\pi$
$90$	1178.56	−	47.3984i	1.38035	−	0.0555137i
$91$	76.2141	−	21.1607i	0.0877957	−	0.0243764i
$92$	−324.884	−	246.970i	−0.368168	−	0.279874i
$93$	−1358.99	−	1048.13i	−1.51527	−	1.16867i
$94$	−610.110	+	2197.42i	−0.669448	+	2.41113i
$95$	−165.817	+	175.051i	−0.179079	+	0.189051i
$96$	162.844	+	1601.31i	0.173127	+	1.70242i
$97$	162.774	+	270.533i	0.170384	+	0.283180i	0.930270	−	0.366876i	$-0.119573\pi$
$97$	162.774	+	270.533i	0.170384	+	0.283180i	−0.759886	+	0.650056i	$0.774745\pi$
$98$	1567.78	−	725.333i	1.61602	−	0.747649i
$99$	−385.538	−	239.369i	−0.391394	−	0.243005i
$100$	−757.755	+	717.784i	−0.757755	+	0.717784i
$101$	113.712	+	167.712i	0.112027	+	0.165228i	0.879569	−	0.475771i	$-0.157831\pi$
$101$	113.712	+	167.712i	0.112027	+	0.165228i	−0.767542	+	0.640999i	$0.778520\pi$
$102$	−163.419	−	313.512i	−0.158636	−	0.304337i
$103$	−135.853	+	1249.15i	−0.129961	+	1.19497i	0.729575	+	0.683900i	$0.239718\pi$
$103$	−135.853	+	1249.15i	−0.129961	+	1.19497i	−0.859537	+	0.511074i	$0.829248\pi$
$104$	−703.639	+	1169.46i	−0.663438	+	1.10264i
$105$	−132.248	−	62.3094i	−0.122915	−	0.0579122i
$106$	610.374	−	1811.53i	0.559291	−	1.65992i
$107$	−12.9355	+	58.7666i	−0.0116871	+	0.0530952i	−0.982103	−	0.188343i	$-0.939688\pi$
$107$	−12.9355	+	58.7666i	−0.0116871	+	0.0530952i	0.970416	+	0.241439i	$0.0776192\pi$
$108$	2469.64	+	1044.47i	2.20038	+	0.930597i
$109$	−227.024	+	192.836i	−0.199495	+	0.169453i	−0.741566	−	0.670880i	$-0.765916\pi$
$109$	−227.024	+	192.836i	−0.199495	+	0.169453i	0.542070	+	0.840333i	$0.317641\pi$
$110$	−724.576	+	118.788i	−0.628051	+	0.102964i
$111$	−621.447	−	214.235i	−0.531398	−	0.183192i
$112$	184.185	−	462.270i	0.155392	−	0.390004i
$113$	−1784.62	+	601.307i	−1.48569	+	0.500586i	−0.941103	−	0.338120i	$-0.890209\pi$
$113$	−1784.62	+	601.307i	−1.48569	+	0.500586i	−0.544584	+	0.838706i	$0.683312\pi$
$114$	−724.345	+	282.759i	−0.595097	+	0.232305i
$115$	−75.2201	+	162.586i	−0.0609940	+	0.131836i
$116$	2625.46	−	142.349i	2.10145	−	0.113937i
$117$	320.677	+	550.226i	0.253390	+	0.434772i
$118$	−2215.75	−	811.671i	−1.72861	−	0.633223i
$119$			43.8193i			0.0337555i
$120$	2396.05	−	788.732i	1.82274	−	0.600008i
$121$	−951.600	−	440.257i	−0.714951	−	0.330772i
$122$	−386.740	−	3556.02i	−0.286998	−	2.63891i
$123$	−1226.83	−	1836.93i	−0.899345	−	1.34659i
$124$	−5864.30	−	2336.55i	−4.24701	−	1.69216i
$125$	1247.25	+	845.655i	0.892458	+	0.605102i
$126$	−300.160	−	363.549i	−0.212226	−	0.257044i
$127$	−558.973	−	658.074i	−0.390558	−	0.459800i	0.531382	−	0.847132i	$-0.321673\pi$
$127$	−558.973	−	658.074i	−0.390558	−	0.459800i	−0.921940	+	0.387332i	$0.873397\pi$
$128$	−96.6007	−	242.449i	−0.0667061	−	0.167420i
$129$	78.0792	+	1653.68i	0.0532906	+	1.12867i
$130$	976.483	+	329.015i	0.658794	+	0.221974i
$131$	102.282	−	120.416i	0.0682172	−	0.0803115i	−0.726995	−	0.686643i	$-0.759084\pi$
$131$	102.282	−	120.416i	0.0682172	−	0.0803115i	0.795212	+	0.606331i	$0.207359\pi$
$132$	−1605.18	−	457.778i	−1.05843	−	0.301852i
$133$	95.8096	+	10.4199i	0.0624643	+	0.00679340i
$134$	−978.759	−	4446.55i	−0.630984	−	2.86659i
$135$	214.724	−	1157.31i	0.136893	−	0.737819i
$136$	−519.971	−	548.927i	−0.327847	−	0.346104i
$137$	914.613	−	484.897i	0.570370	−	0.302391i	−0.158151	−	0.987415i	$-0.550553\pi$
$137$	914.613	−	484.897i	0.570370	−	0.302391i	0.728520	+	0.685024i	$0.240208\pi$
$138$	−442.913	+	370.919i	−0.273212	+	0.228802i
$139$	−254.110	+	152.893i	−0.155060	+	0.0932965i	−0.590969	−	0.806694i	$-0.701255\pi$
$139$	−254.110	+	152.893i	−0.155060	+	0.0932965i	0.435909	+	0.899991i	$0.356427\pi$
$140$	−530.640	−	86.9941i	−0.320338	−	0.0525167i
$141$	2003.21	+	1080.02i	1.19646	+	0.645067i
$142$	2131.91	+	591.921i	1.25990	+	0.349809i
$143$	−239.916	−	315.604i	−0.140299	−	0.184560i
$144$	3976.61	+	488.782i	2.30128	+	0.282860i
$145$	−308.779	−	1112.12i	−0.176846	−	0.636943i
$146$	2756.81	+	1461.57i	1.56271	+	0.828496i
$147$	−358.808	−	1686.09i	−0.201320	−	0.946031i
$148$	−2414.29	−	130.899i	−1.34090	−	0.0727015i
$149$	−899.799	+	1697.20i	−0.494728	+	0.933155i	0.502902	+	0.864343i	$0.332266\pi$
$149$	−899.799	+	1697.20i	−0.494728	+	0.933155i	−0.997630	+	0.0688119i	$0.978079\pi$
$150$	752.896	+	1271.34i	0.409825	+	0.692030i
$151$	−623.770	+	820.556i	−0.336170	+	0.442224i	−0.932855	−	0.360251i	$-0.882691\pi$
$151$	−623.770	+	820.556i	−0.336170	+	0.442224i	0.596685	+	0.802475i	$0.296484\pi$
$152$	−1323.86	+	1006.37i	−0.706441	+	0.537022i
$153$	−341.238	+	89.6291i	−0.180310	+	0.0473600i
$154$	213.063	+	201.824i	0.111488	+	0.105607i
$155$	−448.308	+	2734.56i	−0.232316	+	1.41706i
$156$	1689.34	+	1622.77i	0.867022	+	0.832854i
$157$	−389.701	−	842.326i	−0.198099	−	0.428184i	0.782913	−	0.622131i	$-0.213733\pi$
$157$	−389.701	−	842.326i	−0.198099	−	0.428184i	−0.981012	+	0.193947i	$0.937871\pi$
$158$	621.931	+	1173.09i	0.313153	+	0.590669i
$159$	−1627.65	−	994.874i	−0.811829	−	0.496218i
$160$	2151.04	−	1458.44i	1.06284	−	0.720623i
$161$	69.9289	−	15.3925i	0.0342308	−	0.00753478i
$162$	2217.14	−	3081.08i	1.07528	−	1.49427i
$163$	2705.98	+	1628.13i	1.30030	+	0.782363i	0.985965	−	0.166951i	$-0.0533921\pi$
$163$	2705.98	+	1628.13i	1.30030	+	0.782363i	0.314332	+	0.949313i	$0.398220\pi$
$164$	−6192.55	−	5260.00i	−2.94852	−	2.50449i
$165$	−44.7783	+	731.353i	−0.0211272	+	0.345065i
$166$	3518.10	+	774.393i	1.64493	+	0.362075i
$167$	3927.45	−	1564.84i	1.81985	−	0.725096i	0.835353	−	0.549714i	$-0.185263\pi$
$167$	3927.45	−	1564.84i	1.81985	−	0.725096i	0.984501	−	0.175381i	$-0.0561159\pi$
$168$	−830.545	−	571.632i	−0.381416	−	0.262514i
$169$	−265.427	−	1619.03i	−0.120813	−	0.736929i
$170$	−320.352	+	472.484i	−0.144529	+	0.213164i
$171$	114.827	+	767.419i	0.0513513	+	0.343193i
$172$	1944.35	+	5770.61i	0.861947	+	2.55817i
$173$	−122.125	+	13.2819i	−0.0536706	+	0.00583703i	−0.134915	−	0.990857i	$-0.543076\pi$
$173$	−122.125	+	13.2819i	−0.0536706	+	0.00583703i	0.0812443	+	0.996694i	$0.474111\pi$
$174$	627.815	−	3668.80i	0.273532	−	1.59845i
$175$	−9.91449	−	182.862i	−0.00428266	−	0.0789890i
$176$	−2494.07			−1.06817
$177$	−1280.21	+	1976.43i	−0.543654	+	0.839309i
$178$	5372.55			2.26230
$179$	−58.3463	−	1076.13i	−0.0243632	−	0.449352i	−0.985110	−	0.171926i	$-0.945001\pi$
$179$	−58.3463	−	1076.13i	−0.0243632	−	0.449352i	0.960747	−	0.277427i	$-0.0894816\pi$
$180$	−407.929	−	4310.24i	−0.168918	−	1.78481i
$181$	−1051.12	+	114.316i	−0.431651	+	0.0469449i	−0.321366	−	0.946955i	$-0.604142\pi$
$181$	−1051.12	+	114.316i	−0.431651	+	0.0469449i	−0.110285	+	0.993900i	$0.535176\pi$
$182$	−131.507	−	390.298i	−0.0535600	−	0.158960i
$183$	−3545.84	−	410.714i	−1.43233	−	0.165906i
$184$	−693.351	+	1022.62i	−0.277796	+	0.409719i
$185$	171.708	+	1047.37i	0.0682392	+	0.416241i
$186$	−5066.49	+	7361.29i	−1.99728	+	2.90192i
$187$	204.027	−	81.2918i	0.0797858	−	0.0317896i
$188$	8175.20	+	1799.50i	3.17148	+	0.698095i
$189$	−420.192	+	211.614i	−0.161717	+	0.0814425i
$190$	956.894	+	812.793i	0.365370	+	0.310348i
$191$	−4127.20	−	2483.26i	−1.56353	−	0.940744i	−0.992824	−	0.119589i	$-0.961842\pi$
$191$	−4127.20	−	2483.26i	−1.56353	−	0.940744i	−0.570705	−	0.821155i	$-0.693330\pi$
$192$	2185.79	−	342.682i	0.821594	−	0.128807i
$193$	1611.90	−	354.806i	0.601177	−	0.132329i	0.0960537	−	0.995376i	$-0.469378\pi$
$193$	1611.90	−	354.806i	0.601177	−	0.132329i	0.505124	+	0.863047i	$0.331447\pi$
$194$	1360.71	−	922.582i	0.503572	−	0.341431i
$195$	536.275	−	877.365i	0.196941	−	0.322202i
$196$	−2970.03	−	5602.08i	−1.08237	−	2.04157i
$197$	−286.469	−	619.193i	−0.103605	−	0.223937i	0.848840	−	0.528650i	$-0.177302\pi$
$197$	−286.469	−	619.193i	−0.103605	−	0.223937i	−0.952444	+	0.304713i	$0.901440\pi$
$198$	−1135.88	+	2072.02i	−0.407693	+	0.743697i
$199$	−291.810	+	1779.96i	−0.103949	+	0.634062i	0.882540	+	0.470237i	$0.155831\pi$
$199$	−291.810	+	1779.96i	−0.103949	+	0.634062i	−0.986489	+	0.163825i	$0.947617\pi$
$200$	2294.09	+	2173.07i	0.811082	+	0.768298i
$201$	−4543.42	−	31.7361i	−1.59437	−	0.0111368i
$202$	839.938	−	638.505i	0.292564	−	0.222401i
$203$	−279.184	+	367.260i	−0.0965264	+	0.126978i
$204$	−1116.61	+	661.262i	−0.383226	+	0.226949i
$205$	−1670.63	+	3151.15i	−0.569181	+	1.07359i
$206$	6533.05	+	354.212i	2.20961	+	0.119801i
$207$	262.902	+	513.078i	0.0882750	+	0.172277i
$208$	3092.38	+	1639.48i	1.03086	+	0.546526i
$209$	−129.226	−	465.430i	−0.0427691	−	0.154040i
$210$	−286.687	+	705.166i	−0.0942062	+	0.231719i
$211$	1706.50	+	2244.86i	0.556778	+	0.732429i	0.985249	−	0.171127i	$-0.0547408\pi$
$211$	1706.50	+	2244.86i	0.556778	+	0.732429i	−0.428471	+	0.903555i	$0.640948\pi$
$212$	−6760.89	−	1877.15i	−2.19028	−	0.608128i
$213$	1047.83	−	1943.48i	0.337070	−	0.625189i
$214$	309.194	+	50.6898i	0.0987666	+	0.0161920i
$215$	2290.42	−	1378.10i	0.726537	−	0.437143i
$216$	2752.70	−	7637.00i	0.867118	−	2.40570i
$217$	978.566	−	518.803i	0.306126	−	0.162298i
$218$	1066.62	+	1126.02i	0.331378	+	0.349832i
$219$	2032.36	−	2359.09i	0.627097	−	0.727910i
$220$	579.369	+	2632.10i	0.177550	+	0.806619i
$221$	−306.409	−	33.3240i	−0.0932639	−	0.0101431i
$222$	−938.694	+	3291.51i	−0.283788	+	0.995097i
$223$	4287.97	−	5048.18i	1.28764	−	1.51593i	0.563924	−	0.825826i	$-0.309291\pi$
$223$	4287.97	−	5048.18i	1.28764	−	1.51593i	0.723715	−	0.690099i	$-0.242433\pi$
$224$	−984.377	−	331.675i	−0.293623	−	0.0989330i
$225$	1403.74	−	451.239i	0.415922	−	0.133700i
$226$	3629.48	+	9109.32i	1.06827	+	2.68116i
$227$	−3764.47	−	4431.88i	−1.10069	−	1.29583i	−0.951712	−	0.306992i	$-0.900678\pi$
$227$	−3764.47	−	4431.88i	−1.10069	−	1.29583i	−0.148977	−	0.988841i	$-0.547598\pi$
$228$	1180.31	+	2598.67i	0.342841	+	0.754830i
$229$	953.485	+	646.479i	0.275144	+	0.186553i	0.690953	−	0.722900i	$-0.257191\pi$
$229$	953.485	+	646.479i	0.275144	+	0.186553i	−0.415809	+	0.909452i	$0.636501\pi$
$230$	866.542	+	345.262i	0.248426	+	0.0989821i
$231$	243.545	−	162.656i	0.0693683	−	0.0463289i
$232$	−860.650	−	7913.55i	−0.243554	−	2.23944i
$233$	3495.31	+	1617.10i	0.982770	+	0.454678i	0.844406	−	0.535704i	$-0.179954\pi$
$233$	3495.31	+	1617.10i	0.982770	+	0.454678i	0.138364	+	0.990381i	$0.455816\pi$
$234$	2770.41	−	1822.42i	0.773963	−	0.509124i
$235$		−	3674.58i		−	1.02001i
$236$	−2534.61	+	8282.44i	−0.699107	+	2.28450i
$237$	1279.14	−	345.547i	0.350587	−	0.0947076i
$238$	227.831	−	12.3527i	0.0620509	−	0.00336430i
$239$	766.035	−	1655.76i	0.207325	−	0.448126i	−0.775820	−	0.630955i	$-0.782663\pi$
$239$	766.035	−	1655.76i	0.207325	−	0.448126i	0.983145	+	0.182829i	$0.0585255\pi$
$240$	−2352.41	−	6026.19i	−0.632698	−	1.62079i
$241$	−5442.22	+	1833.70i	−1.45462	+	0.490120i	−0.932005	−	0.362446i	$-0.881942\pi$
$241$	−5442.22	+	1833.70i	−1.45462	+	0.490120i	−0.522619	+	0.852566i	$0.675045\pi$
$242$	−2020.79	+	5071.80i	−0.536782	+	1.34722i
$243$	−2507.39	−	2839.35i	−0.661930	−	0.749566i
$244$	−12956.6	+	2124.13i	−3.39944	+	0.557310i
$245$	−2121.38	+	1801.92i	−0.553184	+	0.469879i
$246$	−9204.98	+	6896.53i	−2.38573	+	1.78743i
$247$	−145.724	+	662.031i	−0.0375392	+	0.170543i
$248$	−6102.30	+	18111.0i	−1.56249	+	4.63729i
$249$	1532.18	−	3251.96i	0.389953	−	0.827649i
$250$	4045.25	−	6723.26i	1.02338	−	1.70086i
$251$	148.836	−	1368.52i	0.0374280	−	0.344145i	−0.960419	−	0.278559i	$-0.910143\pi$
$251$	148.836	−	1368.52i	0.0374280	−	0.344145i	0.997847	−	0.0655851i	$-0.0208914\pi$
$252$	−1272.83	+	1172.39i	−0.318177	+	0.293070i
$253$	−201.398	−	297.040i	−0.0500466	−	0.0738133i
$254$	−3263.98	+	3091.80i	−0.806300	+	0.763768i
$255$	388.857	+	416.297i	0.0954947	+	0.102233i
$256$	−4324.87	+	2000.90i	−1.05588	+	0.488500i
$257$	2387.39	+	3967.88i	0.579461	+	0.963072i	0.998481	+	0.0550947i	$0.0175461\pi$
$257$	2387.39	+	3967.88i	0.579461	+	0.963072i	−0.419020	+	0.907977i	$0.637626\pi$
$258$	8576.03	−	872.132i	2.06946	−	0.210452i
$259$	291.737	−	307.983i	0.0699909	−	0.0738885i
$260$	1011.86	−	3644.38i	0.241356	−	0.869288i
$261$	−3431.04	−	1422.91i	−0.813702	−	0.337455i
$262$	−654.917	−	497.855i	−0.154431	−	0.117395i
$263$	−5086.23	+	1412.19i	−1.19251	+	0.331099i	−0.806410	−	0.591357i	$-0.798592\pi$
$263$	−5086.23	+	1412.19i	−1.19251	+	0.331099i	−0.386102	+	0.922456i	$0.626179\pi$
$264$	−1120.78	+	4927.57i	−0.261286	+	1.14875i
$265$	−166.753	+	3075.58i	−0.0386549	+	0.712948i
$266$	27.1680	−	501.084i	0.00626232	−	0.115502i
$267$	1189.08	−	5227.86i	0.272550	−	1.19828i
$268$	−16102.9	+	4470.96i	−3.67031	+	1.01906i
$269$	−1625.57	−	1235.72i	−0.368448	−	0.280087i	0.404523	−	0.914528i	$-0.367437\pi$
$269$	−1625.57	−	1235.72i	−0.368448	−	0.280087i	−0.772972	+	0.634440i	$0.781231\pi$
$270$	−6077.79	−	790.179i	−1.36994	−	0.178106i
$271$	−1230.27	+	4431.04i	−0.275770	+	0.993235i	0.687826	+	0.725875i	$0.258565\pi$
$271$	−1230.27	+	4431.04i	−0.275770	+	0.993235i	−0.963597	+	0.267360i	$0.913849\pi$
$272$	−1333.47	+	1407.73i	−0.297256	+	0.313809i
$273$	−408.892	+	41.5820i	−0.0906494	+	0.00921852i
$274$	−2778.97	−	4618.69i	−0.612715	−	1.01834i
$275$	−833.031	+	385.401i	−0.182668	+	0.0845112i
$276$	1447.50	+	1549.65i	0.315687	+	0.337964i
$277$	3045.19	−	2884.56i	0.660534	−	0.625691i	−0.282153	−	0.959369i	$-0.591049\pi$
$277$	3045.19	−	2884.56i	0.660534	−	0.625691i	0.942687	+	0.333679i	$0.108290\pi$
$278$	866.576	+	1278.10i	0.186956	+	0.275740i
$279$	6041.70	+	6559.29i	1.29644	+	1.40751i
$280$	−176.012	+	1618.40i	−0.0375669	+	0.345422i
$281$	−1436.43	+	2387.37i	−0.304948	+	0.506827i	−0.971000	−	0.239077i	$-0.923155\pi$
$281$	−1436.43	+	2387.37i	−0.304948	+	0.506827i	0.666053	+	0.745905i	$0.267983\pi$
$282$	5050.71	−	10719.8i	1.06654	−	2.26367i
$283$	2367.11	−	7025.34i	0.497209	−	1.47566i	−0.346081	−	0.938205i	$-0.612488\pi$
$283$	2367.11	−	7025.34i	0.497209	−	1.47566i	0.843290	−	0.537459i	$-0.180616\pi$
$284$	1745.85	−	7931.47i	0.364779	−	1.65721i
$285$	1002.69	−	751.231i	0.208401	−	0.156137i
$286$	−1573.30	+	1336.37i	−0.325284	+	0.276299i
$287$	1406.79	−	230.631i	0.289338	−	0.0474346i
$288$	569.412	−	8344.14i	0.116503	−	1.70723i
$289$	−1755.29	+	4405.44i	−0.357274	+	0.896690i
$290$	−5695.25	+	1918.95i	−1.15323	+	0.388569i
$291$	−596.576	−	1528.25i	−0.120178	−	0.307862i
$292$	4809.10	−	10394.7i	0.963805	−	2.08323i
$293$	1899.89	−	103.009i	0.378815	−	0.0205387i	0.136251	−	0.990674i	$-0.456495\pi$
$293$	1899.89	−	103.009i	0.378815	−	0.0205387i	0.242563	+	0.970136i	$0.422012\pi$
$294$	−8665.42	+	2340.87i	−1.71897	+	0.464362i
$295$	3789.92	+	305.029i	0.747992	+	0.0602017i
$296$			7319.94i			1.43737i
$297$	1764.82	+	1563.88i	0.344798	+	0.305540i
$298$	9077.98	+	4199.92i	1.76467	+	0.816425i
$299$	54.4531	+	500.688i	0.0105321	+	0.0968412i
$300$	4510.09	−	3012.15i	0.867967	−	0.579688i
$301$	−992.529	−	395.460i	−0.190061	−	0.0757273i
$302$	4442.19	+	3011.88i	0.846421	+	0.573888i
$303$	−435.409	−	958.635i	−0.0825530	−	0.181756i
$304$	2760.87	+	3250.35i	0.520877	+	0.613224i
$305$	2133.29	+	5354.15i	0.400498	+	1.00517i
$306$	562.207	+	1748.94i	0.105030	+	0.326733i
$307$	8374.85	+	2821.82i	1.55693	+	0.524591i	0.960549	−	0.278110i	$-0.0897078\pi$
$307$	8374.85	+	2821.82i	1.55693	+	0.524591i	0.596382	+	0.802701i	$0.296604\pi$
$308$	697.384	−	821.024i	0.129017	−	0.151890i
$309$	1790.60	−	6278.71i	0.329657	−	1.15593i
$310$	14344.3	+	1560.03i	2.62806	+	0.285819i
$311$	−1075.72	−	4887.02i	−0.196136	−	0.891054i	−0.967144	−	0.254229i	$-0.918178\pi$
$311$	−1075.72	−	4887.02i	−0.196136	−	0.891054i	0.771008	−	0.636825i	$-0.219753\pi$
$312$	4628.79	−	5372.92i	0.839916	−	0.974941i
$313$	2463.48	+	2600.66i	0.444869	+	0.469643i	0.909405	−	0.415911i	$-0.136537\pi$
$313$	2463.48	+	2600.66i	0.444869	+	0.469643i	−0.464536	+	0.885554i	$0.653779\pi$
$314$	−4269.68	+	2263.64i	−0.767363	+	0.406830i
$315$	622.723	+	435.038i	0.111386	+	0.0778146i
$316$	4175.99	−	2512.61i	0.743411	−	0.447296i
$317$	−2016.26	−	330.549i	−0.357238	−	0.0585661i	−0.0195091	−	0.999810i	$-0.506210\pi$
$317$	−2016.26	−	330.549i	−0.357238	−	0.0585661i	−0.337729	+	0.941244i	$0.609659\pi$
$318$	−4713.85	+	8743.15i	−0.831257	+	1.54180i
$319$	2227.93	+	618.581i	0.391035	+	0.108570i
$320$	−2161.90	−	2843.92i	−0.377668	−	0.496813i
$321$	117.757	−	289.648i	0.0204753	−	0.0503631i
$322$	−99.7438	−	359.245i	−0.0172624	−	0.0621737i
$323$	−331.794	−	175.906i	−0.0571565	−	0.0303024i
$324$	−11733.3	−	7513.97i	−2.01189	−	1.28840i
$325$	1286.21	+	69.7365i	0.219527	+	0.0119024i
$326$	7702.39	−	14528.3i	1.30858	−	2.46824i
$327$	1331.76	−	788.676i	0.225219	−	0.133376i
$328$	−14886.2	+	19582.4i	−2.50595	+	3.29652i
$329$	−1169.24	+	888.831i	−0.195934	+	0.148945i
$330$	3815.17	+	26.6493i	0.636419	+	0.00444544i
$331$	5344.41	+	5062.50i	0.887479	+	0.840664i	0.988029	−	0.154268i	$-0.0493018\pi$
$331$	5344.41	+	5062.50i	0.887479	+	0.840664i	−0.100550	+	0.994932i	$0.532060\pi$
$332$	2139.18	−	13048.4i	0.353622	−	2.15700i
$333$	2995.10	+	1641.91i	0.492885	+	0.270198i
$334$	−9243.28	−	19979.0i	−1.51428	−	3.27307i
$335$	3436.29	+	6481.54i	0.560432	+	1.05709i
$336$	−1348.49	+	2206.18i	−0.218948	+	0.358206i
$337$	3223.03	−	2185.27i	0.520979	−	0.353232i	−0.272181	−	0.962246i	$-0.587745\pi$
$337$	3223.03	−	2185.27i	0.520979	−	0.353232i	0.793160	+	0.609014i	$0.208435\pi$
$338$	−8343.08	+	1836.45i	−1.34261	+	0.295532i
$339$	9667.29	−	1515.61i	1.54884	−	0.242822i
$340$	1795.40	+	1080.26i	0.286381	+	0.172310i
$341$	−4230.99	−	3593.84i	−0.671909	−	0.570725i
$342$	3957.70	−	813.362i	0.625754	−	0.128601i
$343$	2209.82	+	486.419i	0.347869	+	0.0765718i
$344$	17126.1	−	6823.66i	2.68424	−	1.06950i
$345$	527.751	−	766.789i	0.0823570	−	0.119660i
$346$	103.484	+	631.227i	0.0160791	+	0.0980780i
$347$	−3911.39	+	5768.87i	−0.605114	+	0.892476i	−0.999651	−	0.0264038i	$-0.991594\pi$
$347$	−3911.39	+	5768.87i	−0.605114	+	0.892476i	0.394538	+	0.918880i	$0.370905\pi$
$348$	−13571.6	−	1571.99i	−2.09056	−	0.242149i
$349$	−44.4027	−	131.782i	−0.00681038	−	0.0202125i	0.944194	−	0.329390i	$-0.106843\pi$
$349$	−44.4027	−	131.782i	−0.00681038	−	0.0202125i	−0.951004	+	0.309177i	$0.899946\pi$
$350$	−947.967	+	103.098i	−0.144774	+	0.0157451i
$351$	−1160.17	−	3099.15i	−0.176426	−	0.471283i
$352$	281.864	+	5198.67i	0.0426801	+	0.787188i
$353$	7803.85			1.17665			0.588324	−	0.808625i	$-0.299788\pi$
$353$	7803.85			1.17665			0.588324	+	0.808625i	$0.299788\pi$
$354$	10637.0	+	6099.11i	1.59704	+	0.915718i
$355$	−3565.03			−0.532992
$356$	−1067.64	−	19691.4i	−0.158946	−	2.93158i
$357$	38.4050	−	224.430i	0.00569358	−	0.0332719i
$358$	−5578.74	+	606.725i	−0.823591	+	0.0895709i
$359$	2795.31	+	8296.18i	0.410949	+	1.21965i	0.930842	+	0.365422i	$0.119075\pi$
$359$	2795.31	+	8296.18i	0.410949	+	1.21965i	−0.519892	+	0.854232i	$0.674028\pi$
$360$	−12963.2	+	1939.65i	−1.89783	+	0.283969i
$361$	3385.67	−	4993.49i	0.493610	−	0.728020i
$362$	890.676	+	5432.88i	0.129317	+	0.788801i
$363$	4487.95	+	3088.89i	0.648916	+	0.446624i
$364$	−1404.38	+	559.557i	−0.202224	+	0.0805735i
$365$	−4910.09	−	1080.79i	−0.704126	−	0.154990i
$366$	−1135.87	+	18551.8i	−0.162221	+	2.64951i
$367$	−8306.74	−	7055.81i	−1.18149	−	1.00357i	−0.999796	−	0.0202165i	$-0.993564\pi$
$367$	−8306.74	−	7055.81i	−1.18149	−	1.00357i	−0.181699	−	0.983354i	$-0.558160\pi$
$368$	2714.93	+	1633.52i	0.384580	+	0.231394i
$369$	4673.50	+	10483.5i	0.659329	+	1.47899i
$370$	5397.25	−	1188.02i	0.758350	−	0.166926i
$371$	1018.97	−	690.881i	0.142594	−	0.0966813i
$372$	27987.4	+	17106.8i	3.90075	+	2.38427i
$373$	−3316.38	−	6255.35i	−0.460363	−	0.868337i	−0.999656	−	0.0262189i	$-0.991653\pi$
$373$	−3316.38	−	6255.35i	−0.460363	−	0.868337i	0.539293	−	0.842118i	$-0.318692\pi$
$374$	−480.179	−	1037.89i	−0.0663889	−	0.143497i
$375$	−5646.87	−	5424.33i	−0.777608	−	0.746964i
$376$	4100.00	−	25008.9i	0.562344	−	3.43015i
$377$	−2355.77	−	2231.51i	−0.321826	−	0.304850i
$378$	1218.70	+	2125.06i	0.165829	+	0.289157i
$379$	−8790.47	+	6682.34i	−1.19139	+	0.905670i	−0.997162	−	0.0752872i	$-0.976013\pi$
$379$	−8790.47	+	6682.34i	−1.19139	+	0.905670i	−0.194226	+	0.980957i	$0.562220\pi$
$380$	2788.89	−	3668.72i	0.376492	−	0.495266i
$381$	2286.13	+	3860.37i	0.307407	+	0.519088i
$382$	−11747.8	+	22158.8i	−1.57348	+	2.96791i
$383$	−575.138	−	31.1831i	−0.0767315	−	0.00416026i	0.0157332	−	0.999876i	$-0.494992\pi$
$383$	−575.138	−	31.1831i	−0.0767315	−	0.00416026i	−0.0924647	+	0.995716i	$0.529475\pi$
$384$	282.268	+	1326.42i	0.0375115	+	0.176272i
$385$	−417.788	−	221.497i	−0.0553050	−	0.0293209i
$386$	−2299.15	−	8280.80i	−0.303171	−	1.09192i
$387$	1049.45	−	8538.09i	0.137847	−	1.12149i
$388$	−3651.84	−	4803.91i	−0.477820	−	0.628561i
$389$	2135.98	+	593.051i	0.278402	+	0.0772979i	0.403923	−	0.914793i	$-0.367646\pi$
$389$	2135.98	+	593.051i	0.278402	+	0.0772979i	−0.125521	+	0.992091i	$0.540060\pi$
$390$	−4712.89	−	2540.95i	−0.611915	−	0.329913i
$391$	−275.338	−	45.1393i	−0.0356123	−	0.00583835i
$392$	−16448.5	+	9896.73i	−2.11932	+	1.27515i
$393$	−629.397	+	527.091i	−0.0807860	+	0.0676545i
$394$	−3138.64	+	1664.00i	−0.401326	+	0.212769i
$395$	−1471.24	−	1553.17i	−0.187408	−	0.197845i
$396$	7820.07	+	3751.45i	0.992357	+	0.476054i
$397$	−1734.97	−	7882.05i	−0.219334	−	0.996445i	−0.949644	−	0.313330i	$-0.898555\pi$
$397$	−1734.97	−	7882.05i	−0.219334	−	0.996445i	0.730310	−	0.683116i	$-0.239376\pi$
$398$	9336.90	+	1015.45i	1.17592	+	0.127889i
$399$	−481.576	−	137.339i	−0.0604234	−	0.0172320i
$400$	5246.19	−	6176.30i	0.655774	−	0.772037i
$401$	2553.20	+	860.274i	0.317957	+	0.107132i	0.473755	−	0.880657i	$-0.342898\pi$
$401$	2553.20	+	860.274i	0.317957	+	0.107132i	−0.155798	+	0.987789i	$0.549795\pi$
$402$	1115.78	+	23631.7i	0.138433	+	2.93195i
$403$	2883.57	+	7237.23i	0.356429	+	0.894571i
$404$	−2507.15	−	2951.65i	−0.308751	−	0.363490i
$405$	−2114.07	+	5739.22i	−0.259380	+	0.704158i
$406$	1988.21	+	1348.04i	0.243037	+	0.164783i
$407$	−1975.22	−	786.998i	−0.240560	−	0.0958478i
$408$	2182.04	+	3267.16i	0.264772	+	0.396443i
$409$	−679.272	−	6245.80i	−0.0821219	−	0.755098i	−0.960717	−	0.277530i	$-0.910484\pi$
$409$	−679.272	−	6245.80i	−0.0821219	−	0.755098i	0.878595	−	0.477568i	$-0.158481\pi$
$410$	16854.9	+	7797.88i	2.03025	+	0.939293i
$411$	−5109.36	+	1681.90i	−0.613202	+	0.201854i
$412$		−	24015.3i		−	2.87172i
$413$	−819.672	−	1279.72i	−0.0976596	−	0.152472i
$414$	2593.56	−	1511.55i	0.307890	−	0.179441i
$415$	−5795.81	+	314.239i	−0.685554	+	0.0371697i
$416$	3067.87	−	6631.09i	0.361573	−	0.781528i
$417$	1435.48	−	560.361i	0.168575	−	0.0658057i
$418$	−2383.50	+	803.094i	−0.278901	+	0.0939728i
$419$	5530.49	−	13880.5i	0.644826	−	1.61839i	−0.133878	−	0.990998i	$-0.542743\pi$
$419$	5530.49	−	13880.5i	0.644826	−	1.61839i	0.778703	−	0.627392i	$-0.215878\pi$
$420$	2641.54	+	910.632i	0.306890	+	0.105796i
$421$	1715.03	−	281.165i	0.198540	−	0.0325490i	−0.0616913	−	0.998095i	$-0.519649\pi$
$421$	1715.03	−	281.165i	0.198540	−	0.0325490i	0.260231	+	0.965546i	$0.416201\pi$
$422$	11190.7	−	9505.48i	1.29089	−	1.09649i
$423$	−9313.25	−	7287.26i	−1.07051	−	0.837633i
$424$	−4566.56	+	20746.1i	−0.523047	+	2.37623i
$425$	−227.854	+	676.246i	−0.0260060	+	0.0771829i
$426$	−10400.2	−	4900.13i	−1.18285	−	0.557306i
$427$	1187.66	−	1973.90i	0.134601	−	0.223709i
$428$	124.344	−	1143.33i	0.0140430	−	0.129123i
$429$	952.170	+	1826.70i	0.107159	+	0.205580i
$430$	−7810.89	−	11520.2i	−0.875987	−	1.29198i
$431$	155.195	−	147.008i	0.0173445	−	0.0164296i	−0.678978	−	0.734158i	$-0.737577\pi$
$431$	155.195	−	147.008i	0.0173445	−	0.0164296i	0.696323	+	0.717729i	$0.254818\pi$
$432$	−19938.6	−	5988.66i	−2.22060	−	0.666966i
$433$	−11050.5	+	5112.52i	−1.22645	+	0.567418i	−0.922769	−	0.385354i	$-0.874079\pi$
$433$	−11050.5	+	5112.52i	−1.22645	+	0.567418i	−0.303686	+	0.952772i	$0.598217\pi$
$434$	−2973.29	−	4941.64i	−0.328853	−	0.546559i
$435$	606.767	+	5966.59i	0.0668788	+	0.657646i
$436$	3915.10	−	4133.12i	0.430044	−	0.453992i
$437$	−164.169	+	591.284i	−0.0179709	+	0.0647253i
$438$	−12838.6	−	9901.91i	−1.40058	−	1.08021i
$439$	−11141.5	−	8469.54i	−1.21129	−	0.920795i	−0.212871	−	0.977080i	$-0.568281\pi$
$439$	−11141.5	−	8469.54i	−1.21129	−	0.920795i	−0.998415	+	0.0562853i	$0.982074\pi$
$440$	7861.99	−	2182.87i	0.851831	−	0.236510i
$441$	359.949	+	8950.14i	0.0388672	+	0.966434i
$442$	−86.8861	+	1602.52i	−0.00935011	+	0.172453i
$443$	863.961	−	15934.8i	0.0926592	−	1.70900i	−0.470294	−	0.882510i	$-0.655852\pi$
$443$	863.961	−	15934.8i	0.0926592	−	1.70900i	0.562953	−	0.826489i	$-0.309665\pi$
$444$	12250.5	+	2786.40i	1.30943	+	0.297831i
$445$	−8341.10	+	2315.89i	−0.888553	+	0.246705i
$446$	−27456.0	−	20871.5i	−2.91498	−	2.21591i
$447$	6096.00	−	7903.94i	0.645036	−	0.836339i
$448$	−381.993	+	1375.81i	−0.0402845	+	0.145092i
$449$	−5739.06	+	6058.65i	−0.603213	+	0.636805i	−0.954055	−	0.299630i	$-0.903137\pi$
$449$	−5739.06	+	6058.65i	−0.603213	+	0.636805i	0.350842	+	0.936435i	$0.385895\pi$
$450$	−2741.86	−	7171.30i	−0.287227	−	0.751241i
$451$	−3683.66	−	6122.29i	−0.384605	−	0.639218i
$452$	32666.1	−	15113.0i	3.39930	−	1.57269i
$453$	3913.93	−	3655.95i	0.405944	−	0.379186i
$454$	−21981.6	+	20822.1i	−2.27235	+	2.15249i
$455$	372.411	+	549.266i	0.0383712	+	0.0565934i
$456$	7662.43	−	3994.05i	0.786899	−	0.410172i
$457$	−822.856	+	7566.04i	−0.0842267	+	0.774452i	0.873510	+	0.486806i	$0.161838\pi$
$457$	−822.856	+	7566.04i	−0.0842267	+	0.774452i	−0.957737	+	0.287646i	$0.907127\pi$
$458$	3092.48	−	5139.73i	0.315506	−	0.524376i
$459$	1826.27	−	159.980i	0.185715	−	0.0162684i
$460$	1093.25	−	3244.65i	0.110811	−	0.328875i
$461$	1508.14	−	6851.53i	0.152366	−	0.692207i	−0.837053	−	0.547122i	$-0.815723\pi$
$461$	1508.14	−	6851.53i	0.152366	−	0.692207i	0.989419	−	0.145085i	$-0.0463457\pi$
$462$	−914.359	−	1220.42i	−0.0920776	−	0.122898i
$463$	−4917.27	+	4176.76i	−0.493574	+	0.419246i	−0.859296	−	0.511479i	$-0.829098\pi$
$463$	−4917.27	+	4176.76i	−0.493574	+	0.419246i	0.365722	+	0.930724i	$0.380822\pi$
$464$	−20145.1	+	3302.63i	−2.01555	+	0.330432i
$465$	4692.77	−	13612.7i	0.468005	−	1.35758i
$466$	7422.54	−	18629.2i	0.737859	−	1.85189i
$467$	−7645.45	+	2576.05i	−0.757578	+	0.255258i	−0.671474	−	0.741028i	$-0.734338\pi$
$467$	−7645.45	+	2576.05i	−0.757578	+	0.255258i	−0.0861045	+	0.996286i	$0.527442\pi$
$468$	−7230.04	−	9791.93i	−0.714122	−	0.967163i
$469$	1231.21	−	2661.21i	0.121219	−	0.262012i
$470$	−19105.4	+	1035.86i	−1.87503	+	0.101661i
$471$	1257.69	+	4655.69i	0.123039	+	0.455463i
$472$	25453.6	+	6304.71i	2.48219	+	0.614826i
$473$			5354.96i			0.520552i
$474$	−2157.21	−	6553.28i	−0.209037	−	0.635026i
$475$	1424.41	+	659.002i	0.137592	+	0.0636570i
$476$	−90.5497	−	832.591i	−0.00871920	−	0.0801717i
$477$	7464.38	+	6521.98i	0.716500	+	0.626040i
$478$	−8824.79	−	3516.12i	−0.844428	−	0.336451i
$479$	13515.3	+	9163.61i	1.28921	+	0.874105i	0.996621	−	0.0821342i	$-0.0261736\pi$
$479$	13515.3	+	9163.61i	1.28921	+	0.874105i	0.292587	+	0.956239i	$0.405484\pi$
$480$	−12295.2	+	5584.44i	−1.16916	+	0.531028i
$481$	1931.73	+	2274.21i	0.183117	+	0.215582i
$482$	11068.2	+	27779.0i	1.04594	+	2.62511i
$483$	−371.646	+	17.5474i	−0.0350113	+	0.00165307i
$484$	18990.7	+	6398.71i	1.78350	+	0.600930i
$485$	−1714.86	+	2018.89i	−0.160552	+	0.189017i
$486$	−14055.9	+	13837.2i	−1.31191	+	1.29150i
$487$	−6329.00	−	688.320i	−0.588900	−	0.0640468i	−0.191182	−	0.981555i	$-0.561232\pi$
$487$	−6329.00	−	688.320i	−0.588900	−	0.0640468i	−0.397718	+	0.917508i	$0.630198\pi$
$488$	8544.98	+	38820.2i	0.792650	+	3.60104i
$489$	−12432.2	−	10710.4i	−1.14970	−	0.990476i
$490$	9966.79	+	10521.8i	0.918885	+	0.970056i
$491$	2302.26	−	1220.58i	0.211608	−	0.112187i	−0.359234	−	0.933248i	$-0.616962\pi$
$491$	2302.26	−	1220.58i	0.211608	−	0.112187i	0.570842	+	0.821060i	$0.306617\pi$
$492$	27106.3	+	32367.5i	2.48384	+	2.96594i
$493$	1540.32	−	926.783i	0.140715	−	0.0846657i
$494$	3483.20	+	571.042i	0.317240	+	0.0520089i
$495$	870.328	−	3706.53i	0.0790269	−	0.336557i
$496$	47225.0	+	13111.9i	4.27513	+	1.18698i
$497$	862.332	+	1134.38i	0.0778288	+	0.102382i
$498$	−17340.0	−	7049.61i	−1.56029	−	0.634339i
$499$	3186.54	+	11476.9i	0.285870	+	1.02961i	0.957431	+	0.288661i	$0.0932100\pi$
$499$	3186.54	+	11476.9i	0.285870	+	1.02961i	−0.671562	+	0.740949i	$0.734376\pi$
$500$	−25445.9	−	13490.6i	−2.27595	−	1.20663i
$501$	−21486.7	+	4572.47i	−1.91608	+	0.407751i
$502$	−7157.36	−	388.061i	−0.636352	−	0.0345020i
$503$	−4521.39	+	8528.24i	−0.400793	+	0.755975i	−0.998969	−	0.0453889i	$-0.985547\pi$
$503$	−4521.39	+	8528.24i	−0.400793	+	0.755975i	0.598177	+	0.801364i	$0.295892\pi$
$504$	3752.80	+	3655.65i	0.331673	+	0.323087i
$505$	−1028.80	+	1353.37i	−0.0906558	+	0.119256i
$506$	−1487.64	+	1130.87i	−0.130699	+	0.0993546i
$507$	−59.5467	+	8524.84i	−0.00521610	+	0.746748i
$508$	11980.7	+	11348.7i	1.04637	+	0.991175i
$509$	2123.64	−	12953.7i	0.184929	−	1.12802i	−0.717301	−	0.696763i	$-0.754623\pi$
$509$	2123.64	−	12953.7i	0.184929	−	1.12802i	0.902230	−	0.431254i	$-0.141929\pi$
$510$	2054.85	−	2139.15i	0.178412	−	0.185732i
$511$	843.781	+	1823.80i	0.0730463	+	0.157887i
$512$	10644.5	+	20077.7i	0.918802	+	1.73304i
$513$	84.4843	−	4031.13i	0.00727110	−	0.346937i
$514$	19957.3	−	13531.4i	1.71261	−	1.16118i
$515$	−10295.5	+	2266.21i	−0.880921	+	0.193905i
$516$	−4900.77	−	31259.5i	−0.418109	−	2.66690i
$517$	6307.61	+	3795.16i	0.536573	+	0.322845i
$518$	−1683.55	−	1430.02i	−0.142801	−	0.121296i
$519$	637.131	+	39.0094i	0.0538862	+	0.00329927i
$520$	−11182.9	−	2461.55i	−0.943086	−	0.207589i
$521$	122.721	−	48.8964i	0.0103196	−	0.00411169i	−0.364973	−	0.931018i	$-0.618922\pi$
$521$	122.721	−	48.8964i	0.0103196	−	0.00411169i	0.375292	+	0.926907i	$0.377542\pi$
$522$	−6430.96	+	18240.3i	−0.539225	+	1.52941i
$523$	−3007.14	−	18342.7i	−0.251421	−	1.53360i	−0.746876	−	0.664964i	$-0.768447\pi$
$523$	−3007.14	−	18342.7i	−0.251421	−	1.53360i	0.495455	−	0.868634i	$-0.335001\pi$
$524$	−1694.59	+	2499.33i	−0.141276	+	0.208366i
$525$	−109.489	+	945.255i	−0.00910185	+	0.0785796i
$526$	8776.24	+	26047.0i	0.727495	+	2.15913i
$527$	−4290.60	+	466.631i	−0.354652	+	0.0385707i
$528$	12773.9	+	2185.90i	1.05286	+	0.180169i
$529$	−634.025	−	11693.9i	−0.0521102	−	0.961116i
$530$	16038.0			1.31442
$531$	8289.10	−	9000.67i	0.677432	−	0.735585i
$532$	−1841.97			−0.150112
$533$	542.860	+	10012.5i	0.0441161	+	0.813673i
$534$	−27516.6	−	4708.72i	−2.22989	−	0.381584i
$535$	−501.887	+	54.5835i	−0.0405578	+	0.00441093i
$536$	16155.2	+	47947.0i	1.30186	+	3.86380i
$537$	−644.335	+	5562.78i	−0.0517786	+	0.447024i
$538$	−5966.70	+	8800.23i	−0.478147	+	0.705213i
$539$	−902.091	−	5502.51i	−0.0720887	−	0.439722i
$540$	−1688.37	+	22433.3i	−0.134548	+	1.78773i
$541$	−7370.61	+	2936.72i	−0.585744	+	0.233382i	−0.644135	−	0.764912i	$-0.722782\pi$
$541$	−7370.61	+	2936.72i	−0.585744	+	0.233382i	0.0583910	+	0.998294i	$0.481403\pi$
$542$	23385.3	+	5147.50i	1.85329	+	0.407941i
$543$	5483.70	+	335.749i	0.433385	+	0.0265347i
$544$	3084.99	+	2620.41i	0.243139	+	0.206524i
$545$	−2141.35	−	1288.41i	−0.168303	−	0.101265i
$546$	331.465	+	2114.25i	0.0259806	+	0.165717i
$547$	5619.17	−	1236.87i	0.439229	−	0.0966816i	0.0101498	−	0.999948i	$-0.496769\pi$
$547$	5619.17	−	1236.87i	0.439229	−	0.0966816i	0.429079	+	0.903267i	$0.358838\pi$
$548$	−16376.1	+	11103.3i	−1.27656	+	0.865528i
$549$	17800.8	+	5211.27i	1.38382	+	0.405122i
$550$	2238.66	+	4222.57i	0.173558	+	0.327365i
$551$	−1660.10	−	3588.26i	−0.128354	−	0.277432i
$552$	4447.40	−	4629.86i	0.342924	−	0.356992i
$553$	−138.340	+	843.837i	−0.0106380	+	0.0648889i
$554$	−15856.2	−	15019.8i	−1.21600	−	1.15186i
$555$	38.5215	−	5514.83i	0.00294621	−	0.421787i
$556$	4512.29	−	3430.15i	0.344179	−	0.261638i
$557$	−4468.46	+	5878.16i	−0.339919	+	0.447155i	−0.934012	−	0.357240i	$-0.883718\pi$
$557$	−4468.46	+	5878.16i	−0.339919	+	0.447155i	0.594094	+	0.804396i	$0.297511\pi$
$558$	32400.8	−	33261.9i	2.45813	−	2.52346i
$559$	3520.08	−	6639.58i	0.266339	−	0.502369i
$560$	4168.77	+	226.024i	0.314576	+	0.0170558i
$561$	−1116.21	+	237.535i	−0.0840046	+	0.0178765i
$562$	12817.7	+	6795.50i	0.962065	+	0.510055i
$563$	5909.49	+	21284.0i	0.442371	+	1.59328i	0.763214	+	0.646145i	$0.223620\pi$
$563$	5909.49	+	21284.0i	0.442371	+	1.59328i	−0.320843	+	0.947132i	$0.603966\pi$
$564$	−40293.8	−	16381.6i	−3.00829	−	1.22303i
$565$	−9561.59	−	12578.1i	−0.711963	−	0.936572i
$566$	−37194.4	−	10327.0i	−2.76219	−	0.766917i
$567$	2337.56	−	715.551i	0.173137	−	0.0529988i
$568$	−24263.3	−	3977.77i	−1.79237	−	0.293844i
$569$	−13529.6	+	8140.50i	−0.996821	+	0.599767i	−0.917774	−	0.397104i	$-0.870015\pi$
$569$	−13529.6	+	8140.50i	−0.996821	+	0.599767i	−0.0790469	+	0.996871i	$0.525188\pi$
$570$	−4188.56	−	5001.55i	−0.307789	−	0.367529i
$571$	−16601.7	+	8801.67i	−1.21674	+	0.645076i	−0.948041	−	0.318148i	$-0.896939\pi$
$571$	−16601.7	+	8801.67i	−1.21674	+	0.645076i	−0.268701	+	0.963224i	$0.586594\pi$
$572$	5210.71	+	5500.88i	0.380893	+	0.402104i
$573$	18961.9	+	16335.7i	1.38245	+	1.19099i
$574$	−1595.70	−	7249.36i	−0.116034	−	0.527147i
$575$	1159.22	+	126.073i	0.0840747	+	0.00914367i
$576$	−11495.3	−	160.599i	−0.831549	−	0.0116174i
$577$	913.604	−	1075.58i	0.0659166	−	0.0776030i	−0.728215	−	0.685348i	$-0.759650\pi$
$577$	913.604	−	1075.58i	0.0659166	−	0.0776030i	0.794132	+	0.607745i	$0.207926\pi$
$578$	23400.2	+	7884.44i	1.68394	+	0.567387i
$579$	−8566.65	+	404.478i	−0.614884	+	0.0290320i
$580$	8165.10	+	20492.9i	0.584547	+	1.46710i
$581$	1501.92	+	1768.19i	0.107246	+	0.126260i
$582$	−7777.72	+	3532.61i	−0.553947	+	0.251601i
$583$	−5107.17	−	3462.75i	−0.362808	−	0.245990i
$584$	−32211.8	−	12834.4i	−2.28242	−	0.909400i
$585$	−3515.60	+	4023.59i	−0.248465	+	0.284368i
$586$	−1071.16	−	9849.12i	−0.0755104	−	0.694306i
$587$	−2065.08	−	955.409i	−0.145205	−	0.0671788i	0.345941	−	0.938256i	$-0.387560\pi$
$587$	−2065.08	−	955.409i	−0.145205	−	0.0671788i	−0.491146	+	0.871077i	$0.663422\pi$
$588$	10301.7	+	31295.2i	0.722512	+	2.19489i
$589$			9492.24i			0.664042i
$590$	517.572	−	19791.1i	0.0361155	−	1.38099i
$591$	924.525	+	3422.40i	0.0643484	+	0.238204i
$592$	18744.5	−	1016.30i	1.30134	−	0.0705569i
$593$	−2794.44	+	6040.09i	−0.193514	+	0.418275i	−0.979908	−	0.199452i	$-0.936084\pi$
$593$	−2794.44	+	6040.09i	−0.193514	+	0.418275i	0.786393	+	0.617726i	$0.211946\pi$
$594$	7633.62	−	9616.74i	0.527292	−	0.664276i
$595$	−348.393	+	117.387i	−0.0240046	+	0.00808808i
$596$	13589.5	−	34107.1i	0.933974	−	2.34410i
$597$	3054.60	−	8860.69i	0.209408	−	0.607444i
$598$	2587.90	−	424.264i	0.176968	−	0.0290124i
$599$	1271.68	−	1080.18i	0.0867437	−	0.0736808i	−0.602965	−	0.797767i	$-0.706014\pi$
$599$	1271.68	−	1080.18i	0.0867437	−	0.0736808i	0.689709	+	0.724087i	$0.257738\pi$
$600$	−9845.07	−	13140.5i	−0.669872	−	0.894096i
$601$	−3702.90	+	16822.4i	−0.251322	+	1.14177i	0.666728	+	0.745301i	$0.267694\pi$
$601$	−3702.90	+	16822.4i	−0.251322	+	1.14177i	−0.918050	+	0.396465i	$0.870237\pi$
$602$	−1776.34	+	5271.98i	−0.120263	+	0.356926i
$603$	23242.2	+	4144.58i	1.56965	+	0.279901i
$604$	10156.4	−	16880.0i	0.684199	−	1.13715i
$605$	951.104	−	8745.26i	0.0639139	−	0.587678i
$606$	−4861.53	+	2534.08i	−0.325885	+	0.169868i
$607$	−2557.91	−	3772.63i	−0.171042	−	0.252267i	0.732501	−	0.680766i	$-0.238353\pi$
$607$	−2557.91	−	3772.63i	−0.171042	−	0.252267i	−0.903542	+	0.428499i	$0.859043\pi$
$608$	6463.04	−	6122.12i	0.431104	−	0.408363i
$609$	1751.78	−	1636.31i	0.116561	−	0.108878i
$610$	27236.7	−	12601.0i	1.80784	−	0.836395i
$611$	−5326.02	−	8851.91i	−0.352648	−	0.586105i
$612$	6298.49	−	2408.15i	0.416015	−	0.159058i
$613$	14309.0	−	15105.8i	0.942795	−	0.995296i	−0.0572005	−	0.998363i	$-0.518217\pi$
$613$	14309.0	−	15105.8i	0.942795	−	0.995296i	0.999995	+	0.00306631i	$0.000976040\pi$
$614$	12310.7	−	44339.1i	0.809152	−	2.91430i
$615$	11318.3	−	14675.1i	0.742110	−	0.962204i
$616$	−2596.29	−	1973.65i	−0.169817	−	0.129092i
$617$	22350.8	−	6205.66i	1.45836	−	0.404911i	0.554299	−	0.832317i	$-0.312986\pi$
$617$	22350.8	−	6205.66i	1.45836	−	0.404911i	0.904060	+	0.427406i	$0.140573\pi$
$618$	−33149.9	−	7539.99i	−2.15774	−	0.490782i
$619$	−184.435	+	3401.70i	−0.0119759	+	0.220882i	0.986419	+	0.164248i	$0.0525196\pi$
$619$	−184.435	+	3401.70i	−0.0119759	+	0.220882i	−0.998395	+	0.0566341i	$0.981963\pi$
$620$	2867.31	−	52884.5i	0.185732	−	3.42563i
$621$	−896.821	−	2858.25i	−0.0579520	−	0.184698i
$622$	−25106.0	+	6970.66i	−1.61843	+	0.449354i
$623$	2754.51	+	2093.92i	0.177138	+	0.134657i
$624$	−14401.4	−	11107.2i	−0.923904	−	0.712571i
$625$	−1556.05	+	5604.40i	−0.0995874	+	0.358681i
$626$	12827.3	−	13541.6i	0.818980	−	0.864586i
$627$	253.936	+	2497.05i	0.0161742	+	0.159047i
$628$	9145.15	+	15199.4i	0.581101	+	0.965797i
$629$	−1500.27	+	694.099i	−0.0951028	+	0.0439993i
$630$	2086.36	−	3360.39i	0.131941	−	0.212509i
$631$	7832.11	−	7418.97i	0.494123	−	0.468058i	−0.399592	−	0.916693i	$-0.630848\pi$
$631$	7832.11	−	7418.97i	0.494123	−	0.468058i	0.893715	+	0.448635i	$0.148090\pi$
$632$	−8280.19	−	12212.4i	−0.521152	−	0.768642i
$633$	−6772.69	−	12993.1i	−0.425261	−	0.815847i
$634$	−1150.25	+	10576.4i	−0.0720542	+	0.662527i
$635$	3734.70	−	6207.12i	0.233397	−	0.387909i
$636$	32982.0	+	15539.7i	2.05633	+	0.968852i
$637$	−2498.58	+	7415.53i	−0.155412	+	0.461246i
$638$	2588.16	−	11758.1i	0.160605	−	0.729638i
$639$	−7070.00	+	9035.60i	−0.437692	+	0.559378i
$640$	1668.85	−	1417.54i	0.103074	−	0.0875516i
$641$	19564.8	−	3207.49i	1.20556	−	0.197641i	0.474686	−	0.880155i	$-0.342562\pi$
$641$	19564.8	−	3207.49i	1.20556	−	0.197641i	0.730872	+	0.682514i	$0.239113\pi$
$642$	−1539.17	−	530.608i	−0.0946204	−	0.0326190i
$643$	3952.46	−	9919.94i	0.242411	−	0.608405i	−0.756553	−	0.653933i	$-0.773118\pi$
$643$	3952.46	−	9919.94i	0.242411	−	0.608405i	0.998963	+	0.0455284i	$0.0144971\pi$
$644$	−1296.88	+	436.969i	−0.0793543	+	0.0267376i
$645$	−12938.7	+	5050.81i	−0.789861	+	0.308334i
$646$	−821.063	+	1774.70i	−0.0500067	+	0.108088i
$647$	−16056.8	+	870.573i	−0.975667	+	0.0528991i	−0.535072	−	0.844807i	$-0.679715\pi$
$647$	−16056.8	+	870.573i	−0.975667	+	0.0528991i	−0.440596	+	0.897706i	$0.645233\pi$
$648$	−20791.9	+	36701.9i	−1.26047	+	2.22498i
$649$	−4437.89	+	6190.56i	−0.268417	+	0.374424i
$650$		−	6707.12i		−	0.404731i
$651$	−5466.62	+	1799.50i	−0.329115	+	0.108338i
$652$	−54779.4	−	25343.7i	−3.29038	−	1.52229i
$653$	3151.75	+	28979.8i	0.188878	+	1.73670i	0.578458	+	0.815712i	$0.303655\pi$
$653$	3151.75	+	28979.8i	0.188878	+	1.73670i	−0.389580	+	0.920993i	$0.627380\pi$
$654$	−4476.02	−	6701.94i	−0.267624	−	0.400714i
$655$	1231.39	+	490.631i	0.0734572	+	0.0292680i
$656$	52212.6	+	35401.0i	3.10756	+	2.10698i
$657$	−12476.8	+	10301.3i	−0.740890	+	0.611708i
$658$	4950.94	+	5828.70i	0.293325	+	0.345329i
$659$	8332.84	+	20913.8i	0.492566	+	1.23625i	0.939767	+	0.341815i	$0.111042\pi$
$659$	8332.84	+	20913.8i	0.492566	+	1.23625i	−0.447201	+	0.894434i	$0.647579\pi$
$660$	−660.480	−	13988.6i	−0.0389532	−	0.825010i
$661$	−4037.15	−	1360.28i	−0.237560	−	0.0800432i	0.198003	−	0.980201i	$-0.436554\pi$
$661$	−4037.15	−	1360.28i	−0.237560	−	0.0800432i	−0.435563	+	0.900158i	$0.643451\pi$
$662$	24815.0	−	29214.5i	1.45689	−	1.71519i
$663$	1540.13	+	439.225i	0.0902168	+	0.0257286i
$664$	−39796.4	−	4328.12i	−2.32591	−	0.252958i
$665$	173.818	+	789.664i	0.0101359	+	0.0460479i
$666$	7692.52	−	16035.4i	0.447566	−	0.932973i
$667$	−2020.08	−	2132.57i	−0.117268	−	0.123798i
$668$	−71390.1	+	37848.7i	−4.13498	+	2.19223i
$669$	−26386.1	+	22097.2i	−1.52488	+	1.27702i
$670$	32731.0	−	19693.6i	1.88733	−	1.13557i
$671$	−11394.0	−	1867.95i	−0.655529	−	0.107469i
$672$	4751.00	+	2561.49i	0.272729	+	0.147041i
$673$	−9239.55	−	2565.35i	−0.529210	−	0.146935i	−0.00736210	−	0.999973i	$-0.502343\pi$
$673$	−9239.55	−	2565.35i	−0.529210	−	0.146935i	−0.521848	+	0.853038i	$0.674757\pi$
$674$	−12270.5	−	16141.6i	−0.701251	−	0.922480i
$675$	−7585.01	+	1080.82i	−0.432514	+	0.0616307i
$676$	8388.88	+	30214.0i	0.477292	+	1.71905i
$677$	−406.226	−	215.367i	−0.0230613	−	0.0122263i	0.456838	−	0.889550i	$-0.348982\pi$
$677$	−406.226	−	215.367i	−0.0230613	−	0.0122263i	−0.479899	+	0.877324i	$0.659327\pi$
$678$	−10605.4	−	49836.3i	−0.600733	−	2.82294i
$679$	1057.21	+	57.3201i	0.0597524	+	0.00323968i
$680$	2971.39	−	5604.63i	0.167570	−	0.316070i
$681$	15396.2	+	25998.1i	0.866350	+	1.46292i
$682$	−17492.9	+	23011.5i	−0.982165	+	1.29202i
$683$	10026.6	−	7622.03i	0.561724	−	0.427012i	−0.285399	−	0.958409i	$-0.592126\pi$
$683$	10026.6	−	7622.03i	0.561724	−	0.427012i	0.847123	+	0.531397i	$0.178333\pi$
$684$	−3767.61	−	14344.1i	−0.210611	−	0.801843i
$685$	6305.40	+	5972.80i	0.351704	+	0.333152i
$686$	1906.11	−	11626.7i	0.106087	−	0.647100i
$687$	−4316.87	−	4146.75i	−0.239736	−	0.230289i
$688$	−19851.5	−	42908.3i	−1.10004	−	2.37771i
$689$	4056.11	+	7650.64i	0.224275	+	0.423028i
$690$	−4135.57	−	2527.80i	−0.228172	−	0.139466i
$691$	−6548.78	+	4440.19i	−0.360532	+	0.244447i	−0.727981	−	0.685597i	$-0.759541\pi$
$691$	−6548.78	+	4440.19i	−0.360532	+	0.244447i	0.367450	+	0.930043i	$0.380231\pi$
$692$	2293.00	−	504.728i	0.125964	−	0.0277267i
$693$	−1389.92	+	619.624i	−0.0761888	+	0.0339647i
$694$	31096.9	+	18710.4i	1.70090	+	1.02340i
$695$	−1896.34	−	1610.76i	−0.103499	−	0.0879132i
$696$	−2527.75	+	41285.2i	−0.137664	+	2.24843i
$697$	−5425.11	−	1194.16i	−0.294821	−	0.0648951i
$698$	−672.665	+	268.014i	−0.0364767	+	0.0145336i
$699$	−16484.7	−	11345.8i	−0.891998	−	0.613928i
$700$	566.253	+	3453.99i	0.0305748	+	0.186498i
$701$	886.320	−	1307.22i	0.0477544	−	0.0704325i	−0.803062	−	0.595895i	$-0.796797\pi$
$701$	886.320	−	1307.22i	0.0477544	−	0.0704325i	0.850817	+	0.525463i	$0.176108\pi$
$702$	−15786.5	+	6905.78i	−0.848749	+	0.371285i
$703$	1160.87	+	3445.35i	0.0622804	+	0.184842i
$704$	7114.59	−	773.758i	0.380882	−	0.0414234i
$705$	−3220.55	+	18820.1i	−0.172047	+	1.00540i
$706$	−2199.90	−	40574.8i	−0.117273	−	2.16297i
$707$	679.491			0.0361455
$708$	20240.6	−	40198.8i	1.07442	−	2.13385i
$709$	14285.7			0.756716			0.378358	−	0.925659i	$-0.376489\pi$
$709$	14285.7			0.756716			0.378358	+	0.925659i	$0.376489\pi$
$710$	1004.98	+	18535.8i	0.0531215	+	0.979768i
$711$	−6854.24	+	648.698i	−0.361539	+	0.0342167i
$712$	−59352.9	+	6455.02i	−3.12408	+	0.339764i
$713$	2251.84	+	6683.23i	0.118278	+	0.351036i
$714$	−1177.71	−	136.414i	−0.0617293	−	0.00715008i
$715$	1866.55	−	2752.96i	0.0976296	−	0.143993i
$716$	3332.37	+	20326.6i	0.173934	+	1.06095i
$717$	−5374.58	+	7808.92i	−0.279940	+	0.406735i
$718$	42346.7	−	16872.5i	2.20106	−	0.876984i
$719$	17089.9	+	3761.76i	0.886432	+	0.195118i	0.634774	−	0.772698i	$-0.281093\pi$
$719$	17089.9	+	3761.76i	0.886432	+	0.195118i	0.251658	+	0.967816i	$0.419024\pi$
$720$	6766.77	+	32926.1i	0.350254	+	1.70428i
$721$	3211.45	+	2727.83i	0.165881	+	0.140901i
$722$	−26917.3	−	16195.6i	−1.38747	−	0.834816i
$723$	29480.6	−	4621.88i	1.51645	−	0.237745i
$724$	19735.6	−	4344.13i	1.01308	−	0.222995i
$725$	−6218.23	+	4216.06i	−0.318537	+	0.215973i
$726$	14795.0	−	24205.2i	0.756328	−	1.23738i
$727$	8563.61	+	16152.7i	0.436873	+	0.824030i	0.999997	−	0.00234235i	$-0.000745595\pi$
$727$	8563.61	+	16152.7i	0.436873	+	0.824030i	−0.563124	+	0.826372i	$0.690401\pi$
$728$	1921.75	+	4153.79i	0.0978361	+	0.211469i
$729$	10353.6	+	16739.9i	0.526016	+	0.850475i
$730$	−4235.25	+	25833.9i	−0.214731	+	1.30980i
$731$	3022.50	+	2863.07i	0.152929	+	0.144862i
$732$	68221.7	+	476.534i	3.44474	+	0.0240617i
$733$	−3497.59	+	2658.80i	−0.176244	+	0.133977i	−0.689577	−	0.724212i	$-0.742204\pi$
$733$	−3497.59	+	2658.80i	−0.176244	+	0.133977i	0.513333	+	0.858189i	$0.328410\pi$
$734$	−34343.9	+	45178.6i	−1.72705	+	2.27190i
$735$	12444.4	−	7369.62i	0.624513	−	0.369840i
$736$	3098.10	−	5843.65i	0.155160	−	0.292663i
$737$	−14675.0	−	795.654i	−0.733459	−	0.0397670i
$738$	53189.6	−	27254.4i	2.65303	−	1.35941i
$739$	−12109.1	−	6419.86i	−0.602763	−	0.319565i	0.138932	−	0.990302i	$-0.455633\pi$
$739$	−12109.1	−	6419.86i	−0.602763	−	0.319565i	−0.741695	+	0.670737i	$0.765978\pi$
$740$	−5426.88	−	19545.9i	−0.269589	−	0.970973i
$741$	1326.59	−	3263.01i	0.0657670	−	0.161767i
$742$	−3879.37	−	5103.23i	−0.191936	−	0.252487i
$743$	−26784.6	−	7436.70i	−1.32252	−	0.367195i	−0.466674	−	0.884429i	$-0.654548\pi$
$743$	−26784.6	−	7436.70i	−1.32252	−	0.367195i	−0.855844	+	0.517234i	$0.826962\pi$
$744$	47127.4	−	87410.8i	2.32228	−	4.30730i
$745$	−15904.3	−	2607.39i	−0.782135	−	0.128224i
$746$	−31588.8	+	19006.3i	−1.55033	+	0.932804i
$747$	−10697.5	+	15312.7i	−0.523966	+	0.750017i
$748$	−3708.64	+	1966.20i	−0.181285	+	0.0961114i
$749$	138.768	+	146.495i	0.00676965	+	0.00714663i
$750$	−26611.1	+	30889.1i	−1.29560	+	1.50388i
$751$	3070.83	+	13950.9i	0.149209	+	0.677865i	0.990526	+	0.137323i	$0.0438498\pi$
$751$	3070.83	+	13950.9i	0.149209	+	0.677865i	−0.841317	+	0.540542i	$0.818219\pi$
$752$	−64610.8	−	7026.85i	−3.13313	−	0.340748i
$753$	−1961.72	+	6878.71i	−0.0949389	+	0.332901i
$754$	−10938.3	+	12877.5i	−0.528313	+	0.621978i
$755$	−8194.98	−	2761.21i	−0.395028	−	0.133100i
$756$	7546.58	−	4889.08i	0.363051	−	0.235204i
$757$	−12442.9	−	31229.3i	−0.597417	−	1.49940i	−0.847293	−	0.531126i	$-0.821769\pi$
$757$	−12442.9	−	31229.3i	−0.597417	−	1.49940i	0.249876	−	0.968278i	$-0.419610\pi$
$758$	37221.8	+	43820.9i	1.78358	+	2.09980i
$759$	771.164	+	1697.87i	0.0368794	+	0.0811971i
$760$	−11547.8	−	7829.60i	−0.551161	−	0.373696i
$761$	8840.86	+	3522.52i	0.421131	+	0.167794i	0.571070	−	0.820901i	$-0.306528\pi$
$761$	8840.86	+	3522.52i	0.421131	+	0.167794i	−0.149939	+	0.988695i	$0.547908\pi$
$762$	19426.9	−	12974.6i	0.923573	−	0.616825i
$763$	107.997	+	993.018i	0.00512420	+	0.0471162i
$764$	83550.6	+	38654.6i	3.95649	+	1.83047i
$765$	−1626.75	−	2472.96i	−0.0768827	−	0.116876i
$766$			2999.13i			0.141466i
$767$	9571.89	−	4758.40i	0.450614	−	0.224010i
$768$	23904.4	−	6457.52i	1.12314	−	0.303406i
$769$	26723.4	−	1448.90i	1.25315	−	0.0679438i	0.584421	−	0.811451i	$-0.301322\pi$
$769$	26723.4	−	1448.90i	1.25315	−	0.0679438i	0.668728	+	0.743507i	$0.266839\pi$
$770$	−1033.86	+	2234.66i	−0.0483868	+	0.104586i
$771$	−8749.91	−	22414.7i	−0.408717	−	1.04701i
$772$	−29893.8	+	10072.4i	−1.39366	+	0.469577i
$773$	12474.7	−	31309.2i	0.580445	−	1.45681i	−0.286341	−	0.958128i	$-0.592439\pi$
$773$	12474.7	−	31309.2i	0.580445	−	1.45681i	0.866786	−	0.498680i	$-0.166182\pi$
$774$	−44688.2	−	3049.57i	−2.07530	−	0.141621i
$775$	17799.5	−	2918.08i	0.825003	−	0.135252i
$776$	−13923.9	+	11827.0i	−0.644121	+	0.547121i
$777$	−1764.12	+	1321.71i	−0.0814509	+	0.0610244i
$778$	2481.34	−	11272.8i	0.114345	−	0.519474i
$779$	−3901.04	+	11577.9i	−0.179421	+	0.532504i
$780$	−8376.51	+	17778.6i	−0.384522	+	0.816123i
$781$	3682.02	−	6119.56i	0.168698	−	0.280378i
$782$	−157.077	+	1444.30i	−0.00718294	+	0.0660460i
$783$	16325.7	+	10294.8i	0.745124	+	0.469868i
$784$	27626.8	+	40746.4i	1.25851	+	1.85616i
$785$	5653.08	−	5354.89i	0.257028	−	0.243470i
$786$	2917.95	+	3123.86i	0.132417	+	0.141761i
$787$	12889.3	−	5963.24i	0.583806	−	0.270097i	−0.105676	−	0.994401i	$-0.533701\pi$
$787$	12889.3	−	5963.24i	0.583806	−	0.270097i	0.689481	+	0.724303i	$0.257839\pi$
$788$	6722.59	+	11173.0i	0.303912	+	0.505105i
$789$	27287.9	−	2775.02i	1.23127	−	0.125213i
$790$	−7660.73	+	8087.34i	−0.345008	+	0.364221i
$791$	−1689.47	+	6084.93i	−0.0759427	+	0.273521i
$792$	10059.0	−	24255.3i	0.451303	−	1.08822i
$793$	12899.4	+	9805.90i	0.577645	+	0.439115i
$794$	−40492.4	+	11242.6i	−1.80985	+	0.502502i
$795$	3549.62	−	15606.0i	0.158355	−	0.696213i
$796$	1866.38	−	34423.3i	0.0831055	−	1.53279i
$797$	1945.38	−	35880.4i	0.0864604	−	1.59467i	−0.557875	−	0.829925i	$-0.688383\pi$
$797$	1945.38	−	35880.4i	0.0864604	−	1.59467i	0.644335	−	0.764743i	$-0.277134\pi$
$798$	−578.316	+	2542.59i	−0.0256544	+	0.112790i
$799$	5514.51	−	1531.10i	0.244167	−	0.0677926i
$800$	−13466.8	−	10237.2i	−0.595156	−	0.452426i
$801$	−10672.0	+	25733.4i	−0.470759	+	1.13514i
$802$	3753.11	−	13517.5i	0.165246	−	0.595161i
$803$	6926.46	−	7312.18i	0.304395	−	0.321346i
$804$	86393.0	−	8785.67i	3.78961	−	0.385381i
$805$	309.713	+	514.746i	0.0135602	+	0.0225372i
$806$	36815.9	−	17032.9i	1.60891	−	0.744363i
$807$	7242.64	+	7753.73i	0.315927	+	0.338221i
$808$	−8512.02	+	8063.02i	−0.370609	+	0.351059i
$809$	2222.98	+	3278.65i	0.0966078	+	0.142486i	0.872921	−	0.487861i	$-0.162223\pi$
$809$	2222.98	+	3278.65i	0.0966078	+	0.142486i	−0.776313	+	0.630347i	$0.782913\pi$
$810$	30436.1	+	9373.88i	1.32027	+	0.406623i
$811$	−1979.67	+	18202.8i	−0.0857160	+	0.788145i	0.869840	+	0.493335i	$0.164222\pi$
$811$	−1979.67	+	18202.8i	−0.0857160	+	0.788145i	−0.955556	+	0.294811i	$0.904743\pi$
$812$	4545.72	−	7555.05i	0.196458	−	0.326515i
$813$	10184.6	−	21616.2i	0.439349	−	0.932490i
$814$	−3535.06	+	10491.7i	−0.152216	+	0.451761i
$815$	−5695.72	+	25875.9i	−0.244800	+	1.11214i
$816$	8063.44	−	6041.27i	0.345928	−	0.259175i
$817$	6978.74	−	5927.79i	0.298844	−	0.253840i
$818$	−32282.6	+	5292.46i	−1.37987	+	0.226218i
$819$	2130.67	+	145.399i	0.0909055	+	0.00620348i
$820$	25231.3	−	63325.9i	1.07453	−	2.69687i
$821$	−14545.1	+	4900.80i	−0.618302	+	0.208330i	−0.610984	−	0.791643i	$-0.709226\pi$
$821$	−14545.1	+	4900.80i	−0.618302	+	0.208330i	−0.00731818	+	0.999973i	$0.502329\pi$
$822$	10185.1	+	26091.2i	0.432172	+	1.10710i
$823$	13651.0	−	29506.2i	0.578184	−	1.24972i	−0.369119	−	0.929382i	$-0.620340\pi$
$823$	13651.0	−	29506.2i	0.578184	−	1.24972i	0.947302	−	0.320341i	$-0.103798\pi$
$824$	−72599.1	+	3936.21i	−3.06931	+	0.166413i
$825$	4604.32	−	1243.81i	0.194305	−	0.0524896i
$826$	−6422.64	+	4622.51i	−0.270548	+	0.194719i
$827$			1139.71i			0.0479221i	0.999713	+	0.0239611i	$0.00762777\pi$
$827$			1139.71i			0.0479221i	−0.999713	+	0.0239611i	$0.992372\pi$
$828$	−6055.52	−	9205.50i	−0.254159	−	0.386369i
$829$	22033.0	+	10193.5i	0.923084	+	0.427064i	0.823082	−	0.567923i	$-0.192253\pi$
$829$	22033.0	+	10193.5i	0.923084	+	0.427064i	0.100002	+	0.994987i	$0.468115\pi$
$830$	3267.67	+	30045.8i	0.136654	+	1.25651i
$831$	−18124.7	+	12104.9i	−0.756605	+	0.505313i
$832$	−9329.97	−	3717.40i	−0.388772	−	0.154901i
$833$	−3588.10	−	2432.79i	−0.149244	−	0.101190i
$834$	−3318.17	−	7305.58i	−0.137768	−	0.303323i
$835$	22962.8	+	27033.8i	0.951687	+	1.12041i
$836$	3417.14	+	8576.38i	0.141369	+	0.354809i
$837$	−25195.0	−	38889.9i	−1.04046	−	1.60601i
$838$	−73728.3	−	24842.0i	−3.03926	−	1.02405i
$839$	5559.72	−	6545.40i	0.228776	−	0.269335i	−0.635783	−	0.771868i	$-0.719323\pi$
$839$	5559.72	−	6545.40i	0.228776	−	0.269335i	0.864558	+	0.502533i	$0.167598\pi$
$840$	2319.92	−	8134.73i	0.0952914	−	0.334137i
$841$	−5431.45	−	590.705i	−0.222701	−	0.0242202i
$842$	−1945.34	−	8837.75i	−0.0796208	−	0.361721i
$843$	9449.36	−	10968.4i	0.386066	−	0.448130i
$844$	−37063.2	−	39127.2i	−1.51157	−	1.59575i
$845$	12161.3	−	6447.54i	0.495104	−	0.262488i
$846$	−35263.5	+	50477.0i	−1.43308	+	2.05134i
$847$	−3012.77	+	1812.72i	−0.122220	+	0.0735371i
$848$	53759.6	+	8813.44i	2.17702	+	0.356904i
$849$	−18280.9	+	33907.1i	−0.738987	+	1.37066i
$850$	3580.26	+	994.055i	0.144473	+	0.0401127i
$851$	1634.68	+	2150.38i	0.0658473	+	0.0866206i
$852$	−15893.2	+	39092.5i	−0.639075	+	1.57193i
$853$	9603.27	+	34587.8i	0.385474	+	1.38835i	0.860979	+	0.508640i	$0.169852\pi$
$853$	9603.27	+	34587.8i	0.385474	+	1.38835i	−0.475505	+	0.879713i	$0.657735\pi$
$854$	−10597.8	−	5618.59i	−0.424647	−	0.225134i
$855$	−5793.88	+	2968.79i	−0.231750	+	0.118749i
$856$	−3476.71	−	188.502i	−0.138822	−	0.00752669i
$857$	17416.2	−	32850.5i	0.694197	−	1.30939i	−0.246169	−	0.969227i	$-0.579172\pi$
$857$	17416.2	−	32850.5i	0.694197	−	1.30939i	0.940365	−	0.340167i	$-0.110483\pi$
$858$	9229.23	−	5465.60i	0.367227	−	0.217474i
$859$	21599.7	−	28414.0i	0.857943	−	1.12860i	−0.132568	−	0.991174i	$-0.542322\pi$
$859$	21599.7	−	28414.0i	0.857943	−	1.12860i	0.990511	−	0.137431i	$-0.0438846\pi$
$860$	−40671.5	+	30917.7i	−1.61266	+	1.22591i
$861$	−7407.29	−	51.7405i	−0.293194	−	0.00204798i
$862$	−808.096	−	765.469i	−0.0319302	−	0.0302459i
$863$	−3811.40	+	23248.5i	−0.150338	+	0.917021i	0.798670	+	0.601769i	$0.205537\pi$
$863$	−3811.40	+	23248.5i	−0.150338	+	0.917021i	−0.949008	+	0.315252i	$0.897911\pi$
$864$	−10229.5	+	42237.1i	−0.402794	+	1.66312i
$865$	−432.761	−	935.398i	−0.0170108	−	0.0367682i
$866$	29696.9	+	56014.2i	1.16529	+	2.19797i
$867$	12851.2	−	21025.0i	0.503401	−	0.823581i
$868$	−17521.2	+	11879.7i	−0.685148	+	0.464542i
$869$	4185.63	−	921.327i	0.163392	−	0.0359653i
$870$	30851.3	−	4836.77i	1.20225	−	0.188485i
$871$	17672.4	+	10633.1i	0.687493	+	0.413651i
$872$	−13136.3	−	11158.1i	−0.510150	−	0.433326i
$873$	1716.06	+	8350.12i	0.0665292	+	0.323721i
$874$	3120.56	+	686.888i	0.120772	+	0.0265839i
$875$	4694.36	−	1870.40i	0.181369	−	0.0722642i
$876$	−33741.1	+	49023.7i	−1.30138	+	1.89082i
$877$	−11.6052	−	70.7887i	−0.000446842	−	0.00272561i	0.986602	−	0.163145i	$-0.0521637\pi$
$877$	−11.6052	−	70.7887i	−0.000446842	−	0.00272561i	−0.987049	+	0.160419i	$0.948715\pi$
$878$	−40895.2	+	60315.9i	−1.57192	+	2.31841i
$879$	−9820.95	−	1137.56i	−0.376851	−	0.0436505i
$880$	−6681.34	−	19829.5i	−0.255941	−	0.759606i
$881$	13061.5	−	1420.52i	0.499493	−	0.0543231i	0.145095	−	0.989418i	$-0.453651\pi$
$881$	13061.5	−	1420.52i	0.499493	−	0.0543231i	0.354398	+	0.935095i	$0.384686\pi$
$882$	46433.3	−	4394.54i	1.77267	−	0.167769i
$883$	−157.333	−	2901.83i	−0.00599622	−	0.110594i	−0.999999	−	0.00124107i	$-0.999605\pi$
$883$	−157.333	−	2901.83i	−0.00599622	−	0.110594i	0.994003	−	0.109353i	$-0.0348778\pi$
$884$	5890.81			0.224128
$885$	−19143.5	−	4883.91i	−0.727121	−	0.185504i
$886$	−83094.1			−3.15079
$887$	−631.461	−	11646.6i	−0.0239035	−	0.440874i	−0.985849	−	0.167634i	$-0.946387\pi$
$887$	−631.461	−	11646.6i	−0.0239035	−	0.440874i	0.961946	−	0.273240i	$-0.0880953\pi$
$888$	6415.49	−	37490.6i	0.242443	−	1.41678i
$889$	−2878.46	+	313.051i	−0.108594	+	0.0118103i
$890$	14392.5	+	42715.3i	0.542064	+	1.60879i
$891$	−7668.23	−	9556.47i	−0.288323	−	0.359320i
$892$	−71042.0	+	104779.i	−2.66666	+	3.93303i
$893$	−2036.39	−	12421.4i	−0.0763103	−	0.465472i
$894$	−42813.7	−	29467.0i	−1.60168	−	1.10238i
$895$	8399.69	−	3346.74i	0.313710	−	0.124994i
$896$	−854.728	−	188.140i	−0.0318688	−	0.00701486i
$897$	159.930	−	2612.10i	0.00595308	−	0.0972302i
$898$	33118.8	+	28131.4i	1.23072	+	1.04539i
$899$	−38933.6	−	23425.6i	−1.44439	−	0.869061i
$900$	−25739.3	+	11474.5i	−0.953308	+	0.424982i
$901$	−4685.06	+	1031.26i	−0.173232	+	0.0381313i
$902$	−30793.4	+	20878.5i	−1.13671	+	0.770706i
$903$	4736.84	+	2895.32i	0.174565	+	0.106700i
$904$	−51041.2	−	96273.9i	−1.87788	−	3.54206i
$905$	−3724.71	−	8050.84i	−0.136811	−	0.295712i
$906$	−20111.8	−	19319.3i	−0.737496	−	0.708432i
$907$	−3781.19	+	23064.3i	−0.138426	+	0.844362i	0.822745	+	0.568410i	$0.192441\pi$
$907$	−3781.19	+	23064.3i	−0.138426	+	0.844362i	−0.961171	+	0.275952i	$0.911007\pi$
$908$	80685.1	+	76429.0i	2.94893	+	2.79338i
$909$	1389.85	+	5291.46i	0.0507133	+	0.193076i
$910$	2750.84	−	2091.13i	0.100208	−	0.0761762i
$911$	3454.42	−	4544.21i	0.125631	−	0.165265i	−0.728977	−	0.684538i	$-0.760004\pi$
$911$	3454.42	−	4544.21i	0.125631	−	0.165265i	0.854609	+	0.519273i	$0.173797\pi$
$912$	−11291.6	−	19067.0i	−0.409981	−	0.692295i
$913$	5446.59	−	10273.4i	0.197433	−	0.372397i
$914$	39570.4	+	2145.44i	1.43203	+	0.0776422i
$915$	−6233.48	−	29292.1i	−0.225216	−	1.05832i
$916$	−19452.6	−	10313.1i	−0.701674	−	0.372004i
$917$	−141.740	−	510.501i	−0.00510433	−	0.0183841i
$918$	−1346.61	−	9450.31i	−0.0484149	−	0.339768i
$919$	−3981.46	−	5237.52i	−0.142912	−	0.187998i	0.719068	−	0.694940i	$-0.244569\pi$
$919$	−3981.46	−	5237.52i	−0.142912	−	0.187998i	−0.861980	+	0.506942i	$0.830776\pi$
$920$	−9987.90	−	2773.13i	−0.357925	−	0.0993775i
$921$	−40420.4	−	21792.6i	−1.44614	−	0.779684i
$922$	−36048.6	−	5909.86i	−1.28763	−	0.211097i
$923$	−8588.01	+	5167.23i	−0.306260	+	0.184270i
$924$	−4291.37	+	3593.82i	−0.152788	+	0.127953i
$925$	6103.72	−	3235.99i	0.216961	−	0.115026i
$926$	23102.6	+	24389.1i	0.819869	+	0.865525i
$927$	−14673.9	+	30588.3i	−0.519906	+	1.08377i
$928$	9160.71	+	41617.5i	0.324046	+	1.47216i
$929$	18292.7	+	1989.45i	0.646031	+	0.0702601i	0.425268	−	0.905067i	$-0.360180\pi$
$929$	18292.7	+	1989.45i	0.646031	+	0.0702601i	0.220763	+	0.975327i	$0.429145\pi$
$930$	−72099.8	−	20561.9i	−2.54220	−	0.725002i
$931$	−6172.45	+	7266.77i	−0.217287	+	0.255809i
$932$	−69754.5	−	23503.0i	−2.45159	−	0.826037i
$933$	1226.31	+	25972.7i	0.0430307	+	0.911370i
$934$	15549.0	+	39025.1i	0.544731	+	1.36717i
$935$	1192.89	+	1404.38i	0.0417237	+	0.0491210i
$936$	−28416.3	+	23461.6i	−0.992326	+	0.819303i
$937$	−29929.3	−	20292.6i	−1.04349	−	0.707503i	−0.0860945	−	0.996287i	$-0.527439\pi$
$937$	−29929.3	−	20292.6i	−1.04349	−	0.707503i	−0.957394	+	0.288784i	$0.906749\pi$
$938$	−14183.6	−	5651.27i	−0.493723	−	0.196717i
$939$	−10337.9	−	15478.9i	−0.359280	−	0.537951i
$940$	7593.27	+	69819.0i	0.263474	+	2.42260i
$941$	−35764.5	−	16546.4i	−1.23899	−	0.573218i	−0.312637	−	0.949873i	$-0.601212\pi$
$941$	−35764.5	−	16546.4i	−1.23899	−	0.573218i	−0.926354	+	0.376654i	$0.877074\pi$
$942$	23852.0	−	7851.58i	0.824989	−	0.271569i
$943$			9077.11i			0.313458i
$944$	12610.8	−	66055.6i	0.434796	−	2.27747i
$945$	−2808.12	−	2773.91i	−0.0966647	−	0.0954872i
$946$	27842.2	−	1509.56i	0.956902	−	0.0518817i
$947$	16696.8	−	36089.5i	0.572939	−	1.23839i	−0.377076	−	0.926182i	$-0.623071\pi$
$947$	16696.8	−	36089.5i	0.572939	−	1.23839i	0.950015	−	0.312204i	$-0.101067\pi$
$948$	−23590.4	+	9208.85i	−0.808206	+	0.315495i
$949$	−13394.7	+	4513.22i	−0.458179	+	0.154378i
$950$	3024.83	−	7591.76i	0.103304	−	0.259273i
$951$	10037.0	+	3460.10i	0.342241	+	0.117983i
$952$	−2502.11	+	410.201i	−0.0851827	+	0.0139650i
$953$	37037.2	−	31459.7i	1.25892	−	1.06934i	0.264444	−	0.964401i	$-0.414812\pi$
$953$	37037.2	−	31459.7i	1.25892	−	1.06934i	0.994479	−	0.104937i	$-0.0334642\pi$
$954$	31805.8	−	40648.4i	1.07940	−	1.37950i
$955$	8687.21	−	39466.4i	0.294358	−	1.33728i
$956$	−11133.6	+	33043.3i	−0.376658	+	1.11788i
$957$	−10868.6	−	5120.84i	−0.367120	−	0.172971i
$958$	43834.8	−	72853.9i	1.47833	−	2.45700i
$959$	375.329	−	3451.10i	0.0126382	−	0.116206i
$960$	8580.06	+	16460.5i	0.288459	+	0.553397i
$961$	44501.4	+	65634.7i	1.49379	+	2.20317i
$962$	11279.8	−	10684.8i	0.378041	−	0.358100i
$963$	−856.977	+	1380.28i	−0.0286767	+	0.0461880i
$964$	99616.0	−	46087.3i	3.32823	−	1.53980i
$965$	7139.06	+	11865.2i	0.238150	+	0.395808i
$966$	196.002	+	1927.36i	0.00652821	+	0.0641945i
$967$	−25946.7	+	27391.6i	−0.862863	+	0.910913i	−0.996789	−	0.0800780i	$-0.974483\pi$
$967$	−25946.7	+	27391.6i	−0.862863	+	0.910913i	0.133926	+	0.990991i	$0.457242\pi$
$968$	16230.9	−	58458.4i	0.538926	−	1.94104i
$969$	1545.18	+	1191.74i	0.0512264	+	0.0395089i
$970$	10980.3	+	8347.03i	0.363461	+	0.276296i
$971$	1041.88	−	289.276i	0.0344341	−	0.00956057i	−0.250269	−	0.968176i	$-0.580519\pi$
$971$	1041.88	−	289.276i	0.0344341	−	0.00956057i	0.284703	+	0.958616i	$0.408105\pi$
$972$	53509.1	+	48767.9i	1.76575	+	1.60929i
$973$	−53.8405	+	993.029i	−0.00177394	+	0.0327184i
$974$	−1794.67	+	33100.7i	−0.0590398	+	1.08893i
$975$	−6526.49	−	1484.46i	−0.214374	−	0.0487598i
$976$	98222.6	−	27271.4i	3.22134	−	0.894401i
$977$	−13236.3	−	10061.9i	−0.433435	−	0.329488i	0.365602	−	0.930771i	$-0.380863\pi$
$977$	−13236.3	−	10061.9i	−0.433435	−	0.329488i	−0.799036	+	0.601283i	$0.794656\pi$
$978$	−52182.5	+	67658.7i	−1.70615	+	2.21216i
$979$	4639.46	−	16709.8i	0.151459	−	0.545504i
$980$	36583.9	−	38621.1i	1.19248	−	1.25888i
$981$	−7512.11	+	2872.16i	−0.244488	+	0.0934771i
$982$	−6995.22	−	11626.1i	−0.227318	−	0.377806i
$983$	14206.4	−	6572.58i	0.460950	−	0.213258i	−0.175650	−	0.984453i	$-0.556203\pi$
$983$	14206.4	−	6572.58i	0.460950	−	0.213258i	0.636599	+	0.771195i	$0.280341\pi$
$984$	93405.5	−	87248.7i	3.02608	−	2.82661i
$985$	4155.58	−	3936.37i	0.134424	−	0.127333i
$986$	−5252.87	−	7747.41i	−0.169661	−	0.250231i
$987$	6767.49	−	3527.56i	0.218249	−	0.113762i
$988$	1400.79	−	12880.1i	0.0451064	−	0.414747i
$989$	3507.29	−	5829.16i	0.112766	−	0.187418i
$990$	−19516.8	−	3480.26i	−0.626551	−	0.111727i
$991$	−1391.56	+	4130.00i	−0.0446058	+	0.132385i	−0.967641	−	0.252329i	$-0.918803\pi$
$991$	−1391.56	+	4130.00i	−0.0446058	+	0.132385i	0.923036	+	0.384714i	$0.125700\pi$
$992$	21993.6	−	99918.1i	0.703930	−	3.19799i
$993$	−22935.5	−	30612.7i	−0.732968	−	0.978312i
$994$	5654.93	−	4803.34i	0.180446	−	0.153272i
$995$	−14933.6	+	2448.24i	−0.475807	+	0.0780046i
$996$	−22392.4	+	64955.2i	−0.712379	+	2.06645i
$997$	−11406.2	+	28627.3i	−0.362324	+	0.909364i	0.628938	+	0.777456i	$0.283490\pi$
$997$	−11406.2	+	28627.3i	−0.362324	+	0.909364i	−0.991262	+	0.131909i	$0.957889\pi$
$998$	58773.8	−	19803.2i	1.86418	−	0.628116i
$999$	−13901.0	−	11034.4i	−0.440249	−	0.349463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.f.a.89.4	yes	1624
3.2	odd	2	inner	177.4.f.a.89.55	yes	1624
59.2	odd	58	inner	177.4.f.a.2.55	yes	1624
177.2	even	58	inner	177.4.f.a.2.4	✓	1624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.f.a.2.4	✓	1624	177.2	even	58	inner
177.4.f.a.2.55	yes	1624	59.2	odd	58	inner
177.4.f.a.89.4	yes	1624	1.1	even	1	trivial
177.4.f.a.89.55	yes	1624	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.f (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281900 - 5.19934i) q^{2} +(-5.12170 - 0.876440i) q^{3} +(-19.0005 + 2.06643i) q^{4} +(2.67889 + 7.95067i) q^{5} +(-3.11310 + 26.8765i) q^{6} +(1.88189 - 2.77557i) q^{7} +(9.36119 + 57.1007i) q^{8} +(25.4637 + 8.97773i) q^{9} +O(q^{10})\)	\(q+(-0.281900 - 5.19934i) q^{2} +(-5.12170 - 0.876440i) q^{3} +(-19.0005 + 2.06643i) q^{4} +(2.67889 + 7.95067i) q^{5} +(-3.11310 + 26.8765i) q^{6} +(1.88189 - 2.77557i) q^{7} +(9.36119 + 57.1007i) q^{8} +(25.4637 + 8.97773i) q^{9} +(40.5830 - 16.1698i) q^{10} +(-16.4146 - 3.61312i) q^{11} +(99.1263 + 6.06917i) q^{12} +(17.9772 + 15.2700i) q^{13} +(-14.9617 - 9.00213i) q^{14} +(-6.75221 - 43.0689i) q^{15} +(144.921 - 31.8995i) q^{16} +(-10.8155 + 7.33310i) q^{17} +(39.5000 - 134.925i) q^{18} +(13.4617 + 25.3916i) q^{19} +(-67.3300 - 145.531i) q^{20} +(-12.0711 + 12.5663i) q^{21} +(-14.1586 + 86.3633i) q^{22} +(15.5017 + 14.6840i) q^{23} +(2.10012 - 300.657i) q^{24} +(43.4750 - 33.0488i) q^{25} +(74.3261 - 97.7743i) q^{26} +(-122.549 - 68.2987i) q^{27} +(-30.0213 + 56.6262i) q^{28} +(-137.368 - 7.44789i) q^{29} +(-222.026 + 47.2481i) q^{30} +(291.813 + 154.709i) q^{31} +(-82.8698 - 298.470i) q^{32} +(80.9038 + 32.8917i) q^{33} +(41.1762 + 54.1663i) q^{34} +(27.1090 + 7.52679i) q^{35} +(-502.376 - 117.963i) q^{36} +(124.838 + 20.4662i) q^{37} +(128.224 - 77.1501i) q^{38} +(-78.6908 - 93.9644i) q^{39} +(-428.911 + 227.394i) q^{40} +(292.349 + 308.629i) q^{41} +(68.7393 + 59.2192i) q^{42} +(-68.4907 - 311.156i) q^{43} +(319.352 + 34.7316i) q^{44} +(-3.16445 + 226.504i) q^{45} +(71.9770 - 84.7379i) q^{46} +(-415.052 - 139.847i) q^{47} +(-770.201 + 36.3654i) q^{48} +(122.795 + 308.192i) q^{49} +(-184.088 - 216.725i) q^{50} +(61.8209 - 28.0788i) q^{51} +(-373.132 - 252.990i) q^{52} +(341.047 + 135.886i) q^{53} +(-320.561 + 656.428i) q^{54} +(-15.2461 - 140.186i) q^{55} +(176.104 + 81.4743i) q^{56} +(-46.6929 - 141.846i) q^{57} +716.324i q^{58} +(178.691 - 416.472i) q^{59} +(217.295 + 804.379i) q^{60} +(685.953 - 37.1913i) q^{61} +(722.124 - 1560.85i) q^{62} +(72.8381 - 53.7813i) q^{63} +(-403.505 + 135.957i) q^{64} +(-73.2476 + 183.838i) q^{65} +(148.208 - 429.918i) q^{66} +(862.884 - 141.463i) q^{67} +(190.347 - 161.682i) q^{68} +(-66.5254 - 88.7933i) q^{69} +(31.4923 - 143.071i) q^{70} +(-135.678 + 402.678i) q^{71} +(-274.264 + 1538.04i) q^{72} +(-308.947 + 513.473i) q^{73} +(71.2188 - 654.846i) q^{74} +(-251.631 + 131.163i) q^{75} +(-308.251 - 454.636i) q^{76} +(-40.9188 + 38.7603i) q^{77} +(-466.370 + 435.629i) q^{78} +(-231.427 + 107.070i) q^{79} +(641.850 + 1066.76i) q^{80} +(567.801 + 457.213i) q^{81} +(1522.25 - 1607.02i) q^{82} +(-185.083 + 666.609i) q^{83} +(203.390 - 263.711i) q^{84} +(-87.2766 - 66.3460i) q^{85} +(-1598.50 + 443.821i) q^{86} +(697.032 + 158.541i) q^{87} +(52.6518 - 971.106i) q^{88} +(-55.8604 + 1030.29i) q^{89} +(1178.56 - 47.3984i) q^{90} +(76.2141 - 21.1607i) q^{91} +(-324.884 - 246.970i) q^{92} +(-1358.99 - 1048.13i) q^{93} +(-610.110 + 2197.42i) q^{94} +(-165.817 + 175.051i) q^{95} +(162.844 + 1601.31i) q^{96} +(162.774 + 270.533i) q^{97} +(1567.78 - 725.333i) q^{98} +(-385.538 - 239.369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1624 q - 21 q^{3} - 278 q^{4} - 29 q^{6} - 42 q^{7} - 25 q^{9}+O(q^{10}) \) 1624 * q - 21 * q^3 - 278 * q^4 - 29 * q^6 - 42 * q^7 - 25 * q^9	\( 1624 q - 21 q^{3} - 278 q^{4} - 29 q^{6} - 42 q^{7} - 25 q^{9} - 58 q^{10} - 57 q^{12} - 58 q^{13} - 11 q^{15} - 926 q^{16} - 29 q^{18} + 126 q^{19} + 159 q^{21} + 2 q^{22} - 29 q^{24} + 656 q^{25} - 99 q^{27} - 54 q^{28} - 29 q^{30} - 58 q^{31} - 29 q^{33} - 58 q^{34} + 859 q^{36} - 58 q^{37} - 29 q^{39} - 58 q^{40} - 29 q^{42} - 58 q^{43} + 1703 q^{45} + 602 q^{46} + 9507 q^{48} - 1192 q^{49} + 1511 q^{51} - 58 q^{52} - 7743 q^{54} - 58 q^{55} - 7441 q^{57} - 18722 q^{60} - 58 q^{61} - 3251 q^{63} - 4634 q^{64} - 1751 q^{66} - 58 q^{67} + 6003 q^{69} - 58 q^{70} + 21547 q^{72} - 58 q^{73} + 3869 q^{75} + 5622 q^{76} - 3253 q^{78} + 1446 q^{79} + 247 q^{81} - 58 q^{82} + 3303 q^{84} + 790 q^{85} - 2199 q^{87} - 5818 q^{88} - 29 q^{90} - 58 q^{91} - 29 q^{93} - 946 q^{94} - 29 q^{96} - 58 q^{97} - 29 q^{99}+O(q^{100}) \) 1624 * q - 21 * q^3 - 278 * q^4 - 29 * q^6 - 42 * q^7 - 25 * q^9 - 58 * q^10 - 57 * q^12 - 58 * q^13 - 11 * q^15 - 926 * q^16 - 29 * q^18 + 126 * q^19 + 159 * q^21 + 2 * q^22 - 29 * q^24 + 656 * q^25 - 99 * q^27 - 54 * q^28 - 29 * q^30 - 58 * q^31 - 29 * q^33 - 58 * q^34 + 859 * q^36 - 58 * q^37 - 29 * q^39 - 58 * q^40 - 29 * q^42 - 58 * q^43 + 1703 * q^45 + 602 * q^46 + 9507 * q^48 - 1192 * q^49 + 1511 * q^51 - 58 * q^52 - 7743 * q^54 - 58 * q^55 - 7441 * q^57 - 18722 * q^60 - 58 * q^61 - 3251 * q^63 - 4634 * q^64 - 1751 * q^66 - 58 * q^67 + 6003 * q^69 - 58 * q^70 + 21547 * q^72 - 58 * q^73 + 3869 * q^75 + 5622 * q^76 - 3253 * q^78 + 1446 * q^79 + 247 * q^81 - 58 * q^82 + 3303 * q^84 + 790 * q^85 - 2199 * q^87 - 5818 * q^88 - 29 * q^90 - 58 * q^91 - 29 * q^93 - 946 * q^94 - 29 * q^96 - 58 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more