LMFDB - Embedded newform 201.3.n.b.115.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(7,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 23]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("201.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.n (of order $66$, degree $20$, 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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			115.4
Character	$\chi$	$=$	201.115
Dual form			201.3.n.b.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.738773 + 1.43302i) q^{2} +(-0.487975 - 1.66189i) q^{3} +(0.812467 + 1.14095i) q^{4} +(1.60508 - 1.39081i) q^{5} +(2.74203 + 0.528482i) q^{6} +(-7.37536 + 0.351332i) q^{7} +(-8.61857 + 1.23916i) q^{8} +(-2.52376 + 1.62192i) q^{9} +O(q^{10})$	\(q+(-0.738773 + 1.43302i) q^{2} +(-0.487975 - 1.66189i) q^{3} +(0.812467 + 1.14095i) q^{4} +(1.60508 - 1.39081i) q^{5} +(2.74203 + 0.528482i) q^{6} +(-7.37536 + 0.351332i) q^{7} +(-8.61857 + 1.23916i) q^{8} +(-2.52376 + 1.62192i) q^{9} +(0.807267 + 3.32760i) q^{10} +(1.99724 + 10.3627i) q^{11} +(1.49967 - 1.90699i) q^{12} +(7.40353 + 18.4931i) q^{13} +(4.94525 - 10.8286i) q^{14} +(-3.09461 - 1.98878i) q^{15} +(2.75897 - 7.97152i) q^{16} +(-3.05265 + 4.28685i) q^{17} +(-0.459761 - 4.81483i) q^{18} +(-0.273139 + 5.73390i) q^{19} +(2.89091 + 0.701328i) q^{20} +(4.18287 + 12.0856i) q^{21} +(-16.3254 - 4.79358i) q^{22} +(-26.0180 - 24.8081i) q^{23} +(6.26500 + 13.7184i) q^{24} +(-2.91594 + 20.2808i) q^{25} +(-31.9705 - 3.05282i) q^{26} +(3.92699 + 3.40276i) q^{27} +(-6.39309 - 8.12947i) q^{28} +(-11.0141 + 19.0770i) q^{29} +(5.13618 - 2.96538i) q^{30} +(-19.6360 + 49.0485i) q^{31} +(-14.6495 - 15.3640i) q^{32} +(16.2470 - 8.37593i) q^{33} +(-3.88792 - 7.54152i) q^{34} +(-11.3494 + 10.8216i) q^{35} +(-3.90100 - 1.56173i) q^{36} +(7.48861 + 12.9706i) q^{37} +(-8.01501 - 4.62747i) q^{38} +(27.1208 - 21.3280i) q^{39} +(-12.1100 + 13.9757i) q^{40} +(5.91850 - 61.9813i) q^{41} +(-20.4091 - 2.93439i) q^{42} +(50.6616 - 23.1364i) q^{43} +(-10.2006 + 10.6981i) q^{44} +(-1.79505 + 6.11338i) q^{45} +(54.7719 - 18.9567i) q^{46} +(20.3814 - 84.0134i) q^{47} +(-14.5941 - 0.695203i) q^{48} +(5.49441 - 0.524653i) q^{49} +(-26.9086 - 19.1615i) q^{50} +(8.61389 + 2.98130i) q^{51} +(-15.0846 + 23.4721i) q^{52} +(47.4847 + 21.6855i) q^{53} +(-7.77737 + 3.11359i) q^{54} +(17.6182 + 13.8551i) q^{55} +(63.1297 - 12.1673i) q^{56} +(9.66240 - 2.34407i) q^{57} +(-19.2008 - 29.8770i) q^{58} +(9.45290 + 65.7464i) q^{59} +(-0.245163 - 5.14661i) q^{60} +(-13.9635 + 72.4495i) q^{61} +(-55.7809 - 64.3745i) q^{62} +(18.0438 - 12.8489i) q^{63} +(65.2146 - 19.1487i) q^{64} +(37.6036 + 19.3860i) q^{65} +29.4702i q^{66} +(-2.07268 - 66.9679i) q^{67} -7.37126 q^{68} +(-28.5322 + 55.3447i) q^{69} +(-7.12298 - 24.2586i) q^{70} +(9.72801 + 13.6611i) q^{71} +(19.7414 - 17.1060i) q^{72} +(39.5902 + 7.63039i) q^{73} +(-24.1196 + 1.14896i) q^{74} +(35.1274 - 5.05056i) q^{75} +(-6.76401 + 4.34697i) q^{76} +(-18.3711 - 75.7268i) q^{77} +(10.5274 + 54.6212i) q^{78} +(57.4231 - 73.0194i) q^{79} +(-6.65849 - 16.6321i) q^{80} +(3.73874 - 8.18669i) q^{81} +(84.4480 + 54.2714i) q^{82} +(-33.9098 + 97.9759i) q^{83} +(-10.3906 + 14.5916i) q^{84} +(1.06244 + 11.1264i) q^{85} +(-4.27254 + 89.6916i) q^{86} +(37.0785 + 8.99515i) q^{87} +(-30.0544 - 86.8365i) q^{88} +(43.6490 + 12.8165i) q^{89} +(-7.43446 - 7.08874i) q^{90} +(-61.1009 - 133.792i) q^{91} +(7.16605 - 49.8409i) q^{92} +(91.0951 + 8.69853i) q^{93} +(105.336 + 91.2739i) q^{94} +(7.53635 + 9.58324i) q^{95} +(-18.3846 + 31.8431i) q^{96} +(39.5366 - 22.8265i) q^{97} +(-3.30729 + 8.26121i) q^{98} +(-21.8480 - 22.9135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 34 q^{4} - 33 q^{6} - 21 q^{7} - 33 q^{8} + 72 q^{9}+O(q^{10}) $ 240 * q - 34 * q^4 - 33 * q^6 - 21 * q^7 - 33 * q^8 + 72 * q^9	\( 240 q - 34 q^{4} - 33 q^{6} - 21 q^{7} - 33 q^{8} + 72 q^{9} + 69 q^{10} - 111 q^{11} - 3 q^{12} - 30 q^{13} - 6 q^{14} - 27 q^{15} + 98 q^{16} - 4 q^{17} + 16 q^{19} - 108 q^{20} + 21 q^{21} + 27 q^{22} + 178 q^{23} + 36 q^{24} + 222 q^{25} - 29 q^{26} - 112 q^{28} - 77 q^{29} + 90 q^{30} + 137 q^{31} + 44 q^{32} + 12 q^{33} - 72 q^{34} - 237 q^{35} + 3 q^{36} + 132 q^{37} + 210 q^{38} - 30 q^{39} + 749 q^{40} - 150 q^{41} - 132 q^{42} - 385 q^{43} + 9 q^{44} - 443 q^{46} - 166 q^{47} - 294 q^{48} - 295 q^{49} - 6 q^{50} + 276 q^{51} - 1804 q^{52} + 176 q^{53} + 199 q^{55} - 1361 q^{56} - 114 q^{57} + 968 q^{58} - 214 q^{59} - 420 q^{60} - 274 q^{61} + 334 q^{62} - 102 q^{63} + 683 q^{64} - 224 q^{65} + 47 q^{67} + 870 q^{68} + 27 q^{69} - 44 q^{70} + 271 q^{71} + 264 q^{72} + 594 q^{73} - 1289 q^{74} + 396 q^{75} + 494 q^{76} + 1360 q^{77} + 441 q^{78} + 1023 q^{79} + 15 q^{80} - 216 q^{81} - 316 q^{82} - 225 q^{83} + 1527 q^{84} - 153 q^{85} - 91 q^{86} - 1676 q^{88} + 871 q^{89} - 207 q^{90} - 692 q^{91} - 488 q^{92} - 390 q^{93} + 440 q^{94} - 531 q^{95} - 33 q^{96} + 84 q^{97} + 85 q^{98} + 36 q^{99}+O(q^{100}) \) 240 * q - 34 * q^4 - 33 * q^6 - 21 * q^7 - 33 * q^8 + 72 * q^9 + 69 * q^10 - 111 * q^11 - 3 * q^12 - 30 * q^13 - 6 * q^14 - 27 * q^15 + 98 * q^16 - 4 * q^17 + 16 * q^19 - 108 * q^20 + 21 * q^21 + 27 * q^22 + 178 * q^23 + 36 * q^24 + 222 * q^25 - 29 * q^26 - 112 * q^28 - 77 * q^29 + 90 * q^30 + 137 * q^31 + 44 * q^32 + 12 * q^33 - 72 * q^34 - 237 * q^35 + 3 * q^36 + 132 * q^37 + 210 * q^38 - 30 * q^39 + 749 * q^40 - 150 * q^41 - 132 * q^42 - 385 * q^43 + 9 * q^44 - 443 * q^46 - 166 * q^47 - 294 * q^48 - 295 * q^49 - 6 * q^50 + 276 * q^51 - 1804 * q^52 + 176 * q^53 + 199 * q^55 - 1361 * q^56 - 114 * q^57 + 968 * q^58 - 214 * q^59 - 420 * q^60 - 274 * q^61 + 334 * q^62 - 102 * q^63 + 683 * q^64 - 224 * q^65 + 47 * q^67 + 870 * q^68 + 27 * q^69 - 44 * q^70 + 271 * q^71 + 264 * q^72 + 594 * q^73 - 1289 * q^74 + 396 * q^75 + 494 * q^76 + 1360 * q^77 + 441 * q^78 + 1023 * q^79 + 15 * q^80 - 216 * q^81 - 316 * q^82 - 225 * q^83 + 1527 * q^84 - 153 * q^85 - 91 * q^86 - 1676 * q^88 + 871 * q^89 - 207 * q^90 - 692 * q^91 - 488 * q^92 - 390 * q^93 + 440 * q^94 - 531 * q^95 - 33 * q^96 + 84 * q^97 + 85 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{43}{66}\right)$

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 $

$2$	−0.738773	+	1.43302i	−0.369387	+	0.716510i	−0.998132	−	0.0611015i	$-0.980539\pi$
$2$	−0.738773	+	1.43302i	−0.369387	+	0.716510i	0.628745	+	0.777612i	$0.283569\pi$
$3$	−0.487975	−	1.66189i	−0.162658	−	0.553964i
$3$	−0.487975	−	1.66189i	−0.162658	−	0.553964i
$4$	0.812467	+	1.14095i	0.203117	+	0.285237i
$5$	1.60508	−	1.39081i	0.321016	−	0.278162i	−0.479413	−	0.877589i	$-0.659151\pi$
$5$	1.60508	−	1.39081i	0.321016	−	0.278162i	0.800429	+	0.599428i	$0.204605\pi$
$6$	2.74203	+	0.528482i	0.457004	+	0.0880804i
$7$	−7.37536	+	0.351332i	−1.05362	+	0.0501903i	−0.567238	−	0.823554i	$-0.691988\pi$
$7$	−7.37536	+	0.351332i	−1.05362	+	0.0501903i	−0.486385	+	0.873744i	$0.661685\pi$
$8$	−8.61857	+	1.23916i	−1.07732	+	0.154895i
$9$	−2.52376	+	1.62192i	−0.280418	+	0.180214i
$10$	0.807267	+	3.32760i	0.0807267	+	0.332760i
$11$	1.99724	+	10.3627i	0.181567	+	0.942061i	0.952360	+	0.304975i	$0.0986483\pi$
$11$	1.99724	+	10.3627i	0.181567	+	0.942061i	−0.770793	+	0.637086i	$0.780140\pi$
$12$	1.49967	−	1.90699i	0.124973	−	0.158915i
$13$	7.40353	+	18.4931i	0.569502	+	1.42255i	0.881372	+	0.472423i	$0.156620\pi$
$13$	7.40353	+	18.4931i	0.569502	+	1.42255i	−0.311870	+	0.950125i	$0.600955\pi$
$14$	4.94525	−	10.8286i	0.353232	−	0.773471i
$15$	−3.09461	−	1.98878i	−0.206307	−	0.132586i
$16$	2.75897	−	7.97152i	0.172436	−	0.498220i
$17$	−3.05265	+	4.28685i	−0.179568	+	0.252168i	−0.894543	−	0.446982i	$-0.852499\pi$
$17$	−3.05265	+	4.28685i	−0.179568	+	0.252168i	0.714975	+	0.699150i	$0.246438\pi$
$18$	−0.459761	−	4.81483i	−0.0255423	−	0.267491i
$19$	−0.273139	+	5.73390i	−0.0143758	+	0.301784i	0.980217	+	0.197928i	$0.0634212\pi$
$19$	−0.273139	+	5.73390i	−0.0143758	+	0.301784i	−0.994592	+	0.103856i	$0.966882\pi$
$20$	2.89091	+	0.701328i	0.144546	+	0.0350664i
$21$	4.18287	+	12.0856i	0.199184	+	0.575505i
$22$	−16.3254	−	4.79358i	−0.742065	−	0.217890i
$23$	−26.0180	−	24.8081i	−1.13122	−	1.07861i	−0.996140	−	0.0877770i	$-0.972024\pi$
$23$	−26.0180	−	24.8081i	−1.13122	−	1.07861i	−0.135076	−	0.990835i	$-0.543128\pi$
$24$	6.26500	+	13.7184i	0.261042	+	0.571602i
$25$	−2.91594	+	20.2808i	−0.116638	+	0.811233i
$26$	−31.9705	−	3.05282i	−1.22964	−	0.117416i
$27$	3.92699	+	3.40276i	0.145444	+	0.126028i
$28$	−6.39309	−	8.12947i	−0.228325	−	0.290338i
$29$	−11.0141	+	19.0770i	−0.379797	+	0.657828i	−0.991033	−	0.133621i	$-0.957340\pi$
$29$	−11.0141	+	19.0770i	−0.379797	+	0.657828i	0.611235	+	0.791449i	$0.290673\pi$
$30$	5.13618	−	2.96538i	0.171206	−	0.0988459i
$31$	−19.6360	+	49.0485i	−0.633421	+	1.58221i	0.169110	+	0.985597i	$0.445911\pi$
$31$	−19.6360	+	49.0485i	−0.633421	+	1.58221i	−0.802530	+	0.596611i	$0.796513\pi$
$32$	−14.6495	−	15.3640i	−0.457798	−	0.480124i
$33$	16.2470	−	8.37593i	0.492334	−	0.253816i
$34$	−3.88792	−	7.54152i	−0.114351	−	0.221809i
$35$	−11.3494	+	10.8216i	−0.324268	+	0.309189i
$36$	−3.90100	−	1.56173i	−0.108361	−	0.0433813i
$37$	7.48861	+	12.9706i	0.202395	+	0.350558i	0.949300	−	0.314373i	$-0.101794\pi$
$37$	7.48861	+	12.9706i	0.202395	+	0.350558i	−0.746905	+	0.664931i	$0.768461\pi$
$38$	−8.01501	−	4.62747i	−0.210921	−	0.121775i
$39$	27.1208	−	21.3280i	0.695405	−	0.546873i
$40$	−12.1100	+	13.9757i	−0.302751	+	0.349393i
$41$	5.91850	−	61.9813i	0.144354	−	1.51174i	−0.575609	−	0.817725i	$-0.695235\pi$
$41$	5.91850	−	61.9813i	0.144354	−	1.51174i	0.719962	−	0.694013i	$-0.244159\pi$
$42$	−20.4091	−	2.93439i	−0.485931	−	0.0698663i
$43$	50.6616	−	23.1364i	1.17818	−	0.538055i	0.272554	−	0.962141i	$-0.412132\pi$
$43$	50.6616	−	23.1364i	1.17818	−	0.538055i	0.905622	+	0.424086i	$0.139404\pi$
$44$	−10.2006	+	10.6981i	−0.231832	+	0.243138i
$45$	−1.79505	+	6.11338i	−0.0398900	+	0.135853i
$46$	54.7719	−	18.9567i	1.19069	−	0.412103i
$47$	20.3814	−	84.0134i	0.433648	−	1.78752i	−0.164766	−	0.986333i	$-0.552687\pi$
$47$	20.3814	−	84.0134i	0.433648	−	1.78752i	0.598413	−	0.801187i	$-0.295798\pi$
$48$	−14.5941	−	0.695203i	−0.304044	−	0.0144834i
$49$	5.49441	−	0.524653i	0.112131	−	0.0107072i
$50$	−26.9086	−	19.1615i	−0.538172	−	0.383231i
$51$	8.61389	+	2.98130i	0.168900	+	0.0584568i
$52$	−15.0846	+	23.4721i	−0.290089	+	0.451387i
$53$	47.4847	+	21.6855i	0.895938	+	0.409161i	0.809516	−	0.587097i	$-0.199729\pi$
$53$	47.4847	+	21.6855i	0.895938	+	0.409161i	0.0864218	+	0.996259i	$0.472457\pi$
$54$	−7.77737	+	3.11359i	−0.144025	+	0.0576591i
$55$	17.6182	+	13.8551i	0.320331	+	0.251911i
$56$	63.1297	−	12.1673i	1.12732	−	0.217272i
$57$	9.66240	−	2.34407i	0.169516	−	0.0411241i
$58$	−19.2008	−	29.8770i	−0.331048	−	0.515121i
$59$	9.45290	+	65.7464i	0.160219	+	1.11435i	0.898220	+	0.439546i	$0.144861\pi$
$59$	9.45290	+	65.7464i	0.160219	+	1.11435i	−0.738001	+	0.674799i	$0.764230\pi$
$60$	−0.245163	−	5.14661i	−0.00408606	−	0.0857769i
$61$	−13.9635	+	72.4495i	−0.228910	+	1.18770i	0.667548	+	0.744567i	$0.267344\pi$
$61$	−13.9635	+	72.4495i	−0.228910	+	1.18770i	−0.896458	+	0.443129i	$0.853868\pi$
$62$	−55.7809	−	64.3745i	−0.899691	−	1.03830i
$63$	18.0438	−	12.8489i	0.286410	−	0.203951i
$64$	65.2146	−	19.1487i	1.01898	−	0.299199i
$65$	37.6036	+	19.3860i	0.578517	+	0.298246i
$66$			29.4702i			0.446519i
$67$	−2.07268	−	66.9679i	−0.0309355	−	0.999521i
$67$	−2.07268	−	66.9679i	−0.0309355	−	0.999521i
$68$	−7.37126			−0.108401
$69$	−28.5322	+	55.3447i	−0.413510	+	0.802098i
$70$	−7.12298	−	24.2586i	−0.101757	−	0.346552i
$71$	9.72801	+	13.6611i	0.137014	+	0.192409i	0.877382	−	0.479792i	$-0.159288\pi$
$71$	9.72801	+	13.6611i	0.137014	+	0.192409i	−0.740368	+	0.672202i	$0.765349\pi$
$72$	19.7414	−	17.1060i	0.274186	−	0.237583i
$73$	39.5902	+	7.63039i	0.542332	+	0.104526i	0.453058	−	0.891481i	$-0.350333\pi$
$73$	39.5902	+	7.63039i	0.542332	+	0.104526i	0.0892741	+	0.996007i	$0.471545\pi$
$74$	−24.1196	+	1.14896i	−0.325940	+	0.0155264i
$75$	35.1274	−	5.05056i	0.468366	−	0.0673408i
$76$	−6.76401	+	4.34697i	−0.0890002	+	0.0571969i
$77$	−18.3711	−	75.7268i	−0.238586	−	0.983465i
$78$	10.5274	+	54.6212i	0.134966	+	0.700272i
$79$	57.4231	−	73.0194i	0.726874	−	0.924296i	−0.272408	−	0.962182i	$-0.587820\pi$
$79$	57.4231	−	73.0194i	0.726874	−	0.924296i	0.999282	+	0.0378862i	$0.0120624\pi$
$80$	−6.65849	−	16.6321i	−0.0832311	−	0.207901i
$81$	3.73874	−	8.18669i	0.0461572	−	0.101070i
$82$	84.4480	+	54.2714i	1.02985	+	0.661847i
$83$	−33.9098	+	97.9759i	−0.408552	+	1.18043i	0.533742	+	0.845647i	$0.320785\pi$
$83$	−33.9098	+	97.9759i	−0.408552	+	1.18043i	−0.942294	+	0.334786i	$0.891336\pi$
$84$	−10.3906	+	14.5916i	−0.123698	+	0.173709i
$85$	1.06244	+	11.1264i	0.0124993	+	0.130899i
$86$	−4.27254	+	89.6916i	−0.0496807	+	1.04293i
$87$	37.0785	+	8.99515i	0.426190	+	0.103393i
$88$	−30.0544	−	86.8365i	−0.341527	−	0.986779i
$89$	43.6490	+	12.8165i	0.490438	+	0.144006i	0.517595	−	0.855626i	$-0.326827\pi$
$89$	43.6490	+	12.8165i	0.490438	+	0.144006i	−0.0271571	+	0.999631i	$0.508645\pi$
$90$	−7.43446	−	7.08874i	−0.0826051	−	0.0787638i
$91$	−61.1009	−	133.792i	−0.671439	−	1.47025i
$92$	7.16605	−	49.8409i	0.0778918	−	0.541749i
$93$	91.0951	+	8.69853i	0.979517	+	0.0935325i
$94$	105.336	+	91.2739i	1.12059	+	0.970999i
$95$	7.53635	+	9.58324i	0.0793300	+	0.100876i
$96$	−18.3846	+	31.8431i	−0.191507	+	0.331699i
$97$	39.5366	−	22.8265i	0.407594	−	0.235324i	−0.282162	−	0.959367i	$-0.591051\pi$
$97$	39.5366	−	22.8265i	0.407594	−	0.235324i	0.689755	+	0.724043i	$0.257718\pi$
$98$	−3.30729	+	8.26121i	−0.0337478	+	0.0842980i
$99$	−21.8480	−	22.9135i	−0.220687	−	0.231450i
$100$	−25.5085	+	13.1506i	−0.255085	+	0.131506i
$101$	11.0925	+	21.5164i	0.109827	+	0.213034i	0.937343	−	0.348407i	$-0.113277\pi$
$101$	11.0925	+	21.5164i	0.109827	+	0.213034i	−0.827517	+	0.561441i	$0.810247\pi$
$102$	−10.6360	+	10.1414i	−0.104274	+	0.0994253i
$103$	−154.741	−	61.9490i	−1.50234	−	0.601446i	−0.532770	−	0.846260i	$-0.678849\pi$
$103$	−154.741	−	61.9490i	−1.50234	−	0.601446i	−0.969570	+	0.244814i	$0.921273\pi$
$104$	−86.7238	−	150.210i	−0.833883	−	1.44433i
$105$	23.5226	+	13.5808i	0.224025	+	0.129341i
$106$	−66.1563	+	52.0259i	−0.624116	+	0.490810i
$107$	−38.5022	+	44.4339i	−0.359834	+	0.415270i	−0.906584	−	0.422026i	$-0.861319\pi$
$107$	−38.5022	+	44.4339i	−0.359834	+	0.415270i	0.546750	+	0.837296i	$0.315865\pi$
$108$	−0.691826	+	7.24513i	−0.00640579	+	0.0670845i
$109$	90.3311	+	12.9877i	0.828726	+	0.119153i	0.543608	−	0.839339i	$-0.317058\pi$
$109$	90.3311	+	12.9877i	0.828726	+	0.119153i	0.285118	+	0.958492i	$0.407967\pi$
$110$	−32.8705	+	15.0115i	−0.298823	+	0.136468i
$111$	17.9015	−	18.7746i	0.161275	−	0.169141i
$112$	−17.5478	+	59.7622i	−0.156676	+	0.533591i
$113$	−67.5131	+	23.3665i	−0.597461	+	0.206783i	−0.609027	−	0.793150i	$-0.708440\pi$
$113$	−67.5131	+	23.3665i	−0.597461	+	0.206783i	0.0115653	+	0.999933i	$0.496319\pi$
$114$	−3.77922	+	15.5782i	−0.0331511	+	0.136651i
$115$	−76.2641	−	3.63291i	−0.663166	−	0.0315905i
$116$	−30.7145	+	2.93288i	−0.264780	+	0.0252835i
$117$	−48.6791	−	34.6643i	−0.416061	−	0.296276i
$118$	−101.199	−	35.0255i	−0.857622	−	0.296826i
$119$	21.0083	−	32.6896i	0.176540	−	0.274702i
$120$	29.1355	+	13.3057i	0.242796	+	0.110881i
$121$	8.93645	−	3.57761i	0.0738549	−	0.0295671i
$122$	−93.5057	−	73.5337i	−0.766440	−	0.602735i
$123$	−105.894	+	20.4094i	−0.860928	+	0.165930i
$124$	−71.9155	+	17.4465i	−0.579963	+	0.140698i
$125$	52.2320	+	81.2746i	0.417856	+	0.650197i
$126$	5.08251	+	35.3496i	0.0403374	+	0.280552i
$127$	5.28692	+	110.986i	0.0416293	+	0.873906i	0.919039	+	0.394165i	$0.128966\pi$
$127$	5.28692	+	110.986i	0.0416293	+	0.873906i	−0.877410	+	0.479741i	$0.840731\pi$
$128$	−4.66801	+	24.2199i	−0.0364688	+	0.189218i
$129$	−63.1717	−	72.9040i	−0.489703	−	0.565147i
$130$	−55.5611	+	39.5649i	−0.427393	+	0.304345i
$131$	−14.5043	+	4.25883i	−0.110720	+	0.0325102i	−0.336623	−	0.941640i	$-0.609285\pi$
$131$	−14.5043	+	4.25883i	−0.110720	+	0.0325102i	0.225903	+	0.974150i	$0.427467\pi$
$132$	22.7567	+	11.7319i	0.172399	+	0.0888779i
$133$		−	42.3856i		−	0.318689i
$134$	97.4976	+	46.5039i	0.727594	+	0.347044i
$135$	11.0357			0.0817460
$136$	20.9974	−	40.7292i	0.154393	−	0.299480i
$137$	−46.4176	−	158.084i	−0.338814	−	1.15390i	−0.936061	−	0.351838i	$-0.885557\pi$
$137$	−46.4176	−	158.084i	−0.338814	−	1.15390i	0.597246	−	0.802058i	$-0.296261\pi$
$138$	−58.2313	−	81.7744i	−0.421966	−	0.592568i
$139$	192.685	−	166.963i	1.38622	−	1.20117i	0.432076	−	0.901837i	$-0.357781\pi$
$139$	192.685	−	166.963i	1.38622	−	1.20117i	0.954149	−	0.299333i	$-0.0967642\pi$
$140$	−21.5679	−	4.15688i	−0.154057	−	0.0296920i
$141$	−149.567	+	7.12474i	−1.06076	+	0.0505301i
$142$	−26.7634	+	3.84799i	−0.188475	+	0.0270985i
$143$	−176.852	+	113.656i	−1.23672	+	0.794794i
$144$	5.96621	+	24.5930i	0.0414320	+	0.170785i
$145$	8.85394	+	45.9386i	0.0610617	+	0.316818i
$146$	−40.1827	+	51.0965i	−0.275224	+	0.349976i
$147$	−3.55305	−	8.87510i	−0.0241704	−	0.0603748i
$148$	−8.71461	+	19.0823i	−0.0588825	+	0.128935i
$149$	171.790	+	110.403i	1.15295	+	0.740956i	0.970225	−	0.242207i	$-0.0778714\pi$
$149$	171.790	+	110.403i	1.15295	+	0.740956i	0.182726	+	0.983164i	$0.441508\pi$
$150$	−18.7136	+	54.0695i	−0.124758	+	0.360463i
$151$	−17.2130	+	24.1723i	−0.113993	+	0.160081i	−0.867631	−	0.497209i	$-0.834358\pi$
$151$	−17.2130	+	24.1723i	−0.113993	+	0.160081i	0.753637	+	0.657291i	$0.228298\pi$
$152$	−4.75117	−	49.7565i	−0.0312577	−	0.327345i
$153$	0.751225	−	15.7701i	0.00490997	−	0.103073i
$154$	122.090	+	29.6187i	0.792793	+	0.192329i
$155$	36.6996	+	106.037i	0.236772	+	0.684107i
$156$	46.3690	+	13.6152i	0.297237	+	0.0872767i
$157$	−101.352	−	96.6387i	−0.645553	−	0.615533i	0.294871	−	0.955537i	$-0.404723\pi$
$157$	−101.352	−	96.6387i	−0.645553	−	0.615533i	−0.940424	+	0.340004i	$0.889572\pi$
$158$	62.2156	+	136.233i	0.393770	+	0.862235i
$159$	12.8676	−	89.4964i	0.0809286	−	0.562871i
$160$	−44.8820	−	4.28571i	−0.280512	−	0.0267857i
$161$	200.608	+	173.828i	1.24601	+	1.07967i
$162$	8.96961	+	11.4058i	0.0553680	+	0.0704061i
$163$	−90.0021	+	155.888i	−0.552160	+	0.956370i	0.445958	+	0.895054i	$0.352863\pi$
$163$	−90.0021	+	155.888i	−0.552160	+	0.956370i	−0.998118	+	0.0613159i	$0.980470\pi$
$164$	75.5261	−	43.6050i	0.460525	−	0.265884i
$165$	14.4284	−	36.0405i	0.0874451	−	0.218427i
$166$	−115.350	−	120.975i	−0.694879	−	0.728768i
$167$	93.9738	−	48.4469i	0.562718	−	0.290101i	−0.153304	−	0.988179i	$-0.548991\pi$
$167$	93.9738	−	48.4469i	0.562718	−	0.290101i	0.716022	+	0.698078i	$0.245961\pi$
$168$	−51.0264	−	98.9774i	−0.303728	−	0.589151i
$169$	−164.872	+	157.205i	−0.975575	+	0.930209i
$170$	−16.7292	−	6.69737i	−0.0984072	−	0.0393963i
$171$	−8.61061	−	14.9140i	−0.0503544	−	0.0872164i
$172$	67.5583	+	39.0048i	0.392781	+	0.226772i
$173$	−128.962	+	101.417i	−0.745446	+	0.586225i	−0.916971	−	0.398954i	$-0.869373\pi$
$173$	−128.962	+	101.417i	−0.745446	+	0.586225i	0.171524	+	0.985180i	$0.445131\pi$
$174$	−40.2828	+	46.4889i	−0.231511	+	0.267177i
$175$	14.3808	−	150.603i	0.0821762	−	0.860588i
$176$	88.1166	+	12.6693i	0.500662	+	0.0719844i
$177$	104.650	−	47.7923i	0.591246	−	0.270013i
$178$	−50.6130	+	53.0814i	−0.284343	+	0.298210i
$179$	−20.9158	+	71.2326i	−0.116848	+	0.397947i	−0.997059	−	0.0766345i	$-0.975583\pi$
$179$	−20.9158	+	71.2326i	−0.116848	+	0.397947i	0.880211	+	0.474582i	$0.157401\pi$
$180$	−8.43348	+	2.91885i	−0.0468526	+	0.0162159i
$181$	−57.4317	+	236.737i	−0.317302	+	1.30794i	0.560197	+	0.828359i	$0.310725\pi$
$181$	−57.4317	+	236.737i	−0.317302	+	1.30794i	−0.877499	+	0.479578i	$0.840790\pi$
$182$	236.867	+	11.2834i	1.30147	+	0.0619965i
$183$	127.217	−	12.1477i	0.695174	−	0.0663811i
$184$	254.979	+	181.570i	1.38576	+	0.986792i
$185$	30.0595	+	10.4037i	0.162484	+	0.0562361i
$186$	−79.7638	+	124.115i	−0.428837	+	0.667284i
$187$	−50.5201	−	23.0718i	−0.270161	−	0.123378i
$188$	112.414	−	45.0039i	0.597949	−	0.239383i
$189$	−30.1585	−	23.7169i	−0.159569	−	0.125486i
$190$	−19.3006	+	3.71989i	−0.101582	+	0.0195784i
$191$	−99.0117	+	24.0200i	−0.518386	+	0.125759i	−0.486412	−	0.873730i	$-0.661695\pi$
$191$	−99.0117	+	24.0200i	−0.518386	+	0.125759i	−0.0319740	+	0.999489i	$0.510179\pi$
$192$	−63.6462	−	99.0355i	−0.331491	−	0.515810i
$193$	11.6586	+	81.0874i	0.0604073	+	0.420142i	0.997476	+	0.0709981i	$0.0226184\pi$
$193$	11.6586	+	81.0874i	0.0604073	+	0.420142i	−0.937069	+	0.349144i	$0.886472\pi$
$194$	3.50220	+	73.5203i	0.0180526	+	0.378971i
$195$	13.8678	−	71.9530i	0.0711169	−	0.368990i
$196$	5.06263	+	5.84259i	0.0258298	+	0.0298091i
$197$	158.392	−	112.791i	0.804021	−	0.572541i	−0.102485	−	0.994735i	$-0.532679\pi$
$197$	158.392	−	112.791i	0.804021	−	0.572541i	0.906506	+	0.422194i	$0.138740\pi$
$198$	48.9763	−	14.3807i	0.247355	−	0.0726300i
$199$	−273.664	−	141.084i	−1.37520	−	0.708962i	−0.397228	−	0.917720i	$-0.630028\pi$
$199$	−273.664	−	141.084i	−1.37520	−	0.708962i	−0.977967	+	0.208758i	$0.933058\pi$
$200$		−	178.405i		−	0.892025i
$201$	−110.282	+	36.1232i	−0.548666	+	0.179718i
$202$	−39.0283			−0.193209
$203$	74.5307	−	144.569i	0.367147	−	0.712165i
$204$	3.59699	+	12.2502i	0.0176323	+	0.0600501i
$205$	−76.7044	−	107.716i	−0.374168	−	0.525445i
$206$	203.093	−	175.981i	0.985887	−	0.854276i
$207$	105.900	+	20.4105i	0.511594	+	0.0986016i
$208$	167.844	−	7.99541i	0.806944	−	0.0384395i
$209$	−59.9641	+	8.62154i	−0.286910	+	0.0412514i
$210$	−36.8394	+	23.6752i	−0.175426	+	0.112739i
$211$	16.7192	+	68.9174i	0.0792379	+	0.326623i	0.997610	−	0.0690947i	$-0.0220111\pi$
$211$	16.7192	+	68.9174i	0.0792379	+	0.326623i	−0.918372	+	0.395718i	$0.870496\pi$
$212$	13.8376	+	71.7965i	0.0652719	+	0.338663i
$213$	17.9562	−	22.8331i	0.0843013	−	0.107198i
$214$	−35.2303	−	88.0010i	−0.164628	−	0.411220i
$215$	49.1375	−	107.596i	0.228547	−	0.500447i
$216$	−38.0616	−	24.4607i	−0.176211	−	0.113244i
$217$	127.591	−	368.649i	0.587975	−	1.69884i
$218$	−85.3458	+	119.851i	−0.391495	+	0.549777i
$219$	−6.63817	−	69.5181i	−0.0303113	−	0.317434i
$220$	−1.49378	+	31.3583i	−0.00678992	+	0.142538i
$221$	−101.878	−	24.7152i	−0.460985	−	0.111834i
$222$	13.6792	+	39.5234i	0.0616180	+	0.178034i
$223$	211.924	+	62.2265i	0.950332	+	0.279043i	0.719925	−	0.694052i	$-0.244176\pi$
$223$	211.924	+	62.2265i	0.950332	+	0.279043i	0.230407	+	0.973094i	$0.425994\pi$
$224$	113.443	+	108.168i	0.506444	+	0.482893i
$225$	−25.5348	−	55.9134i	−0.113488	−	0.248504i
$226$	16.3922	−	114.010i	0.0725319	−	0.504470i
$227$	22.1641	+	2.11642i	0.0976393	+	0.00932342i	0.143761	−	0.989612i	$-0.454080\pi$
$227$	22.1641	+	2.11642i	0.0976393	+	0.00932342i	−0.0461220	+	0.998936i	$0.514686\pi$
$228$	10.5249	+	9.11984i	0.0461616	+	0.0399993i
$229$	61.3768	+	78.0470i	0.268021	+	0.340816i	0.901370	−	0.433050i	$-0.142563\pi$
$229$	61.3768	+	78.0470i	0.268021	+	0.340816i	−0.633349	+	0.773866i	$0.718320\pi$
$230$	61.5479	−	106.604i	0.267600	−	0.463496i
$231$	−116.885	+	67.4836i	−0.505996	+	0.292137i
$232$	71.2864	−	178.065i	0.307269	−	0.767521i
$233$	214.309	+	224.760i	0.919780	+	0.964637i	0.999482	−	0.0321815i	$-0.0102455\pi$
$233$	214.309	+	224.760i	0.919780	+	0.964637i	−0.0797023	+	0.996819i	$0.525397\pi$
$234$	85.6374	−	44.1492i	0.365972	−	0.188672i
$235$	−84.1328	−	163.195i	−0.358012	−	0.694446i
$236$	−67.3331	+	64.2020i	−0.285310	+	0.272042i
$237$	−149.371	−	59.7992i	−0.630258	−	0.252317i
$238$	31.3244	+	54.2555i	0.131615	+	0.227964i
$239$	−226.475	−	130.755i	−0.947593	−	0.547093i	−0.0552605	−	0.998472i	$-0.517599\pi$
$239$	−226.475	−	130.755i	−0.947593	−	0.547093i	−0.892332	+	0.451379i	$0.850932\pi$
$240$	−24.3916	+	19.1817i	−0.101631	+	0.0799239i
$241$	−101.202	+	116.793i	−0.419923	+	0.484617i	−0.925814	−	0.377981i	$-0.876619\pi$
$241$	−101.202	+	116.793i	−0.419923	+	0.484617i	0.505890	+	0.862598i	$0.331164\pi$
$242$	−1.47522	+	15.4492i	−0.00609593	+	0.0638395i
$243$	−15.4298	−	2.21847i	−0.0634971	−	0.00912950i
$244$	−94.0061	+	42.9311i	−0.385271	+	0.175947i
$245$	8.08927	−	8.48378i	0.0330174	−	0.0346277i
$246$	48.9847	−	166.826i	0.199125	−	0.678156i
$247$	−108.060	+	37.3999i	−0.437490	+	0.151417i
$248$	108.456	−	447.060i	0.437321	−	1.80266i
$249$	179.372	+	8.54456i	0.720371	+	0.0343155i
$250$	−155.056	+	14.8060i	−0.620223	+	0.0592242i
$251$	−143.455	−	102.154i	−0.571533	−	0.406987i	0.257424	−	0.966298i	$-0.417126\pi$
$251$	−143.455	−	102.154i	−0.571533	−	0.406987i	−0.828958	+	0.559311i	$0.811066\pi$
$252$	29.3200	+	10.1478i	0.116349	+	0.0402689i
$253$	205.114	−	319.164i	0.810727	−	1.26152i
$254$	−162.951	−	74.4173i	−0.641540	−	0.292982i
$255$	17.9724	−	7.19506i	0.0704799	−	0.0282159i
$256$	182.446	+	143.477i	0.712680	+	0.560458i
$257$	−81.9524	+	15.7950i	−0.318881	+	0.0614592i	−0.346180	−	0.938168i	$-0.612521\pi$
$257$	−81.9524	+	15.7950i	−0.318881	+	0.0614592i	0.0272993	+	0.999627i	$0.491309\pi$
$258$	151.142	−	36.6668i	0.585824	−	0.142119i
$259$	−59.7882	−	93.0322i	−0.230842	−	0.359198i
$260$	8.43322	+	58.6543i	0.0324355	+	0.225594i
$261$	−3.14444	−	66.0098i	−0.0120476	−	0.252911i
$262$	4.61236	−	23.9312i	0.0176044	−	0.0913405i
$263$	19.2344	+	22.1977i	0.0731347	+	0.0844019i	0.791138	−	0.611638i	$-0.209489\pi$
$263$	19.2344	+	22.1977i	0.0731347	+	0.0844019i	−0.718003	+	0.696040i	$0.754944\pi$
$264$	−129.647	+	92.3212i	−0.491087	+	0.349702i
$265$	106.377	−	31.2351i	0.401423	−	0.117868i
$266$	60.7394	+	31.3133i	0.228344	+	0.117719i
$267$		−	78.7940i		−	0.295109i
$268$	74.7231	−	56.7740i	0.278817	−	0.211843i
$269$	25.8478			0.0960885			0.0480442	−	0.998845i	$-0.484701\pi$
$269$	25.8478			0.0960885			0.0480442	+	0.998845i	$0.484701\pi$
$270$	−8.15288	+	15.8144i	−0.0301959	+	0.0585718i
$271$	95.2240	+	324.303i	0.351380	+	1.19669i	0.925763	+	0.378104i	$0.123424\pi$
$271$	95.2240	+	324.303i	0.351380	+	1.19669i	−0.574383	+	0.818587i	$0.694758\pi$
$272$	25.7505	+	36.1616i	0.0946711	+	0.132947i
$273$	−192.533	+	166.830i	−0.705247	+	0.611100i
$274$	260.829	+	50.2707i	0.951932	+	0.183470i
$275$	−215.987	+	10.2888i	−0.785409	+	0.0374136i
$276$	−86.3270	+	12.4120i	−0.312779	+	0.0449709i
$277$	−394.786	+	253.713i	−1.42522	+	0.915932i	−0.425278	+	0.905063i	$0.639824\pi$
$277$	−394.786	+	253.713i	−1.42522	+	0.915932i	−0.999941	+	0.0108694i	$0.996540\pi$
$278$	96.9102	+	399.469i	0.348598	+	1.43694i
$279$	−29.9961	−	155.635i	−0.107513	−	0.557831i
$280$	84.4058	−	107.331i	0.301449	−	0.383324i
$281$	115.546	+	288.620i	0.411196	+	1.02712i	0.978983	+	0.203942i	$0.0653753\pi$
$281$	115.546	+	288.620i	0.411196	+	1.02712i	−0.567787	+	0.823175i	$0.692200\pi$
$282$	100.286	−	219.596i	0.355624	−	0.778709i
$283$	35.2258	+	22.6382i	0.124473	+	0.0799938i	0.601396	−	0.798951i	$-0.294612\pi$
$283$	35.2258	+	22.6382i	0.124473	+	0.0799938i	−0.476923	+	0.878945i	$0.658248\pi$
$284$	−7.68292	+	22.1983i	−0.0270525	+	0.0781632i
$285$	12.2488	−	17.2010i	0.0429781	−	0.0603543i
$286$	−32.2176	−	337.398i	−0.112649	−	1.17971i
$287$	−21.8751	+	459.214i	−0.0762197	+	1.60005i
$288$	61.8911	+	15.0146i	0.214900	+	0.0521341i
$289$	85.4642	+	246.933i	0.295724	+	0.854438i
$290$	−72.3720	−	21.2503i	−0.249559	−	0.0732770i
$291$	−57.2279	−	54.5667i	−0.196660	−	0.187515i
$292$	23.4598	+	51.3699i	0.0803419	+	0.175924i
$293$	−4.11368	+	28.6113i	−0.0140399	+	0.0976495i	−0.995636	−	0.0933168i	$-0.970253\pi$
$293$	−4.11368	+	28.6113i	−0.0140399	+	0.0976495i	0.981597	+	0.190966i	$0.0611621\pi$
$294$	15.3431	+	1.46509i	0.0521874	+	0.00498329i
$295$	106.613	+	92.3809i	0.361401	+	0.313155i
$296$	−80.6138	−	102.509i	−0.272344	−	0.346314i
$297$	−27.4185	+	47.4903i	−0.0923182	+	0.159900i
$298$	−285.123	+	164.616i	−0.956787	+	0.552401i
$299$	266.154	−	664.821i	0.890147	−	2.22348i
$300$	34.3023	+	35.9752i	0.114341	+	0.119917i
$301$	−365.519	+	188.438i	−1.21435	+	0.626040i
$302$	−21.9229	−	42.5244i	−0.0725923	−	0.140809i
$303$	30.3451	−	28.9340i	0.100149	−	0.0954916i
$304$	44.9543	+	17.9970i	0.147876	+	0.0592007i
$305$	78.3508	+	135.708i	0.256888	+	0.444943i
$306$	22.0440	+	12.7271i	0.0720391	+	0.0415918i
$307$	273.316	−	214.938i	0.890281	−	0.700125i	−0.0643462	−	0.997928i	$-0.520496\pi$
$307$	273.316	−	214.938i	0.890281	−	0.700125i	0.954627	+	0.297803i	$0.0962538\pi$
$308$	71.4746	−	82.4860i	0.232060	−	0.267812i
$309$	−27.4426	+	287.392i	−0.0888111	+	0.930072i
$310$	−179.065	−	25.7457i	−0.577630	−	0.0830506i
$311$	180.739	−	82.5408i	0.581155	−	0.265405i	−0.103072	−	0.994674i	$-0.532867\pi$
$311$	180.739	−	82.5408i	0.581155	−	0.265405i	0.684227	+	0.729269i	$0.260140\pi$
$312$	−207.314	+	217.424i	−0.664467	+	0.696873i
$313$	127.970	−	435.826i	0.408850	−	1.39242i	−0.455818	−	0.890073i	$-0.650653\pi$
$313$	127.970	−	435.826i	0.408850	−	1.39242i	0.864668	−	0.502343i	$-0.167529\pi$
$314$	213.361	−	73.8450i	0.679494	−	0.235175i
$315$	11.0913	−	45.7190i	0.0352105	−	0.145140i
$316$	129.966	+	6.19103i	0.411284	+	0.0195919i
$317$	236.362	−	22.5698i	0.745620	−	0.0711981i	0.284672	−	0.958625i	$-0.408115\pi$
$317$	236.362	−	22.5698i	0.745620	−	0.0711981i	0.460948	+	0.887427i	$0.347509\pi$
$318$	118.744	+	84.5571i	0.373408	+	0.265903i
$319$	−219.687	−	76.0343i	−0.688673	−	0.238352i
$320$	78.0423	−	121.436i	0.243882	−	0.379488i
$321$	92.6324	+	42.3038i	0.288575	+	0.131788i
$322$	−397.302	+	159.056i	−1.23386	+	0.493962i
$323$	−23.7466	−	18.6745i	−0.0735188	−	0.0578158i
$324$	12.3782	−	2.38570i	0.0382043	−	0.00736328i
$325$	−396.644	+	96.2248i	−1.22044	+	0.296076i
$326$	−156.900	−	244.141i	−0.481288	−	0.748899i
$327$	−22.4953	−	156.458i	−0.0687929	−	0.478465i
$328$	25.7960	+	541.524i	0.0786463	+	1.65099i
$329$	−120.804	+	626.790i	−0.367185	+	1.90514i
$330$	40.9874	+	47.3020i	0.124204	+	0.143339i
$331$	191.055	−	136.050i	0.577207	−	0.411027i	−0.253826	−	0.967250i	$-0.581689\pi$
$331$	191.055	−	136.050i	0.577207	−	0.411027i	0.831033	+	0.556223i	$0.187750\pi$
$332$	−139.336	+	40.9128i	−0.419687	+	0.123231i
$333$	−39.9368	−	20.5889i	−0.119930	−	0.0618284i
$334$			170.458i			0.510352i
$335$	−96.4663	−	104.606i	−0.287959	−	0.312257i
$336$	107.881			0.321074
$337$	160.488	−	311.304i	0.476227	−	0.923751i	−0.521294	−	0.853377i	$-0.674550\pi$
$337$	160.488	−	311.304i	0.476227	−	0.923751i	0.997521	−	0.0703738i	$-0.0224192\pi$
$338$	−103.475	−	352.404i	−0.306140	−	1.04262i
$339$	71.7773	+	100.797i	0.211733	+	0.297337i
$340$	−11.8314	+	10.2520i	−0.0347984	+	0.0301530i
$341$	−547.491	−	105.520i	−1.60555	−	0.309444i
$342$	27.7334	−	1.32110i	0.0810917	−	0.00386287i
$343$	317.781	−	45.6900i	0.926475	−	0.133207i
$344$	−407.961	+	262.180i	−1.18593	+	0.762152i
$345$	31.1775	+	128.515i	0.0903696	+	0.372508i
$346$	−50.0588	−	259.730i	−0.144679	−	0.750664i
$347$	−18.5829	+	23.6300i	−0.0535529	+	0.0680981i	−0.812092	−	0.583530i	$-0.801671\pi$
$347$	−18.5829	+	23.6300i	−0.0535529	+	0.0680981i	0.758539	+	0.651628i	$0.225914\pi$
$348$	19.8620	+	49.6130i	0.0570748	+	0.142566i
$349$	92.1139	−	201.701i	0.263937	−	0.577940i	−0.730544	−	0.682866i	$-0.760733\pi$
$349$	92.1139	−	201.701i	0.263937	−	0.577940i	0.994480	+	0.104926i	$0.0334605\pi$
$350$	205.193	+	131.869i	0.586265	+	0.376770i
$351$	−33.8540	+	97.8147i	−0.0964501	+	0.278674i
$352$	129.953	−	182.494i	0.369185	−	0.518448i
$353$	55.5491	+	581.737i	0.157363	+	1.64798i	0.637255	+	0.770653i	$0.280070\pi$
$353$	55.5491	+	581.737i	0.157363	+	1.64798i	−0.479892	+	0.877327i	$0.659324\pi$
$354$	−8.82568	+	185.274i	−0.0249313	+	0.523373i
$355$	34.6141	+	8.39730i	0.0975046	+	0.0236544i
$356$	20.8404	+	60.2143i	0.0585404	+	0.169141i
$357$	−64.5780	−	18.9618i	−0.180891	−	0.0531143i
$358$	−86.6257	−	82.5974i	−0.241971	−	0.230719i
$359$	220.969	+	483.855i	0.615513	+	1.34778i	0.918739	+	0.394866i	$0.129209\pi$
$359$	220.969	+	483.855i	0.615513	+	1.34778i	−0.303226	+	0.952919i	$0.598064\pi$
$360$	7.89529	−	54.9129i	0.0219314	−	0.152536i
$361$	326.562	+	31.1829i	0.904605	+	0.0863793i
$362$	−296.819	−	257.195i	−0.819943	−	0.710485i
$363$	−10.3064	−	13.1056i	−0.0283922	−	0.0361036i
$364$	103.008	−	178.415i	0.282989	−	0.490151i
$365$	74.1578	−	42.8150i	0.203172	−	0.117301i
$366$	−76.5765	+	191.279i	−0.209225	+	0.522620i
$367$	−323.522	−	339.300i	−0.881531	−	0.924523i	0.116105	−	0.993237i	$-0.462959\pi$
$367$	−323.522	−	339.300i	−0.881531	−	0.924523i	−0.997636	+	0.0687136i	$0.978111\pi$
$368$	−269.541	+	138.958i	−0.732448	+	0.377603i
$369$	85.5920	+	166.025i	0.231957	+	0.449933i
$370$	−37.1158	+	35.3899i	−0.100313	+	0.0956483i
$371$	−357.836	−	143.256i	−0.964517	−	0.386134i
$372$	64.0871	+	111.002i	0.172277	+	0.298393i
$373$	250.517	+	144.636i	0.671627	+	0.387764i	0.796693	−	0.604385i	$-0.206581\pi$
$373$	250.517	+	144.636i	0.671627	+	0.387764i	−0.125066	+	0.992148i	$0.539914\pi$
$374$	70.3852	−	55.3515i	0.188196	−	0.147999i
$375$	109.582	−	126.464i	0.292218	−	0.337237i
$376$	−71.5525	+	749.332i	−0.190299	+	1.99290i
$377$	−434.337	−	62.4482i	−1.15209	−	0.165645i
$378$	56.2670	−	25.6963i	0.148855	−	0.0679796i
$379$	167.316	−	175.476i	0.441468	−	0.462999i	−0.464977	−	0.885323i	$-0.653937\pi$
$379$	167.316	−	175.476i	0.441468	−	0.462999i	0.906445	+	0.422324i	$0.138786\pi$
$380$	−4.81097	+	16.3847i	−0.0126604	+	0.0431175i
$381$	181.867	−	62.9447i	0.477341	−	0.165209i
$382$	38.7261	−	159.631i	0.101377	−	0.417882i
$383$	−609.652	−	29.0413i	−1.59178	−	0.0758258i	−0.767138	−	0.641482i	$-0.778320\pi$
$383$	−609.652	−	29.0413i	−1.59178	−	0.0758258i	−0.824641	+	0.565656i	$0.808623\pi$
$384$	42.5288	−	4.06100i	0.110752	−	0.0105755i
$385$	−134.808	−	95.9967i	−0.350152	−	0.249342i
$386$	−124.813	−	43.1982i	−0.323350	−	0.111912i
$387$	−90.3323	+	140.560i	−0.233417	+	0.363204i
$388$	58.1660	+	26.5635i	0.149912	+	0.0684627i
$389$	−214.894	+	86.0308i	−0.552428	+	0.221159i	−0.631045	−	0.775746i	$-0.717374\pi$
$389$	−214.894	+	86.0308i	−0.552428	+	0.221159i	0.0786172	+	0.996905i	$0.474950\pi$
$390$	92.8649	+	73.0298i	0.238115	+	0.187256i
$391$	185.772	−	35.8047i	0.475121	−	0.0915721i
$392$	−46.7039	+	11.3302i	−0.119143	+	0.0289037i
$393$	14.1554	+	22.0263i	0.0360189	+	0.0560465i
$394$	44.6152	+	310.306i	0.113237	+	0.787578i
$395$	−9.38742	−	197.066i	−0.0237656	−	0.498902i
$396$	8.39241	−	43.5440i	0.0211930	−	0.109960i
$397$	338.047	+	390.127i	0.851503	+	0.982687i	0.999981	−	0.00622922i	$-0.00198284\pi$
$397$	338.047	+	390.127i	0.851503	+	0.982687i	−0.148478	+	0.988916i	$0.547437\pi$
$398$	404.351	−	287.937i	1.01596	−	0.723460i
$399$	−70.4402	+	20.6831i	−0.176542	+	0.0518374i
$400$	153.624	+	79.1987i	0.384060	+	0.197997i
$401$		−	343.652i		−	0.856988i	−0.903545	−	0.428494i	$-0.859044\pi$
$401$		−	343.652i		−	0.856988i	0.903545	−	0.428494i	$-0.140956\pi$
$402$	29.7080	−	184.723i	0.0739005	−	0.459510i
$403$	−1052.44			−2.61150
$404$	−15.5369	+	30.1373i	−0.0384576	+	0.0745974i
$405$	−5.38515	−	18.3401i	−0.0132967	−	0.0452843i
$406$	152.110	+	213.608i	0.374654	+	0.526128i
$407$	−119.454	+	103.508i	−0.293499	+	0.254318i
$408$	−77.9338	−	15.0205i	−0.191014	−	0.0368150i
$409$	−41.6684	+	1.98491i	−0.101879	+	0.00485308i	−0.0984593	−	0.995141i	$-0.531391\pi$
$409$	−41.6684	+	1.98491i	−0.101879	+	0.00485308i	−0.00341932	+	0.999994i	$0.501088\pi$
$410$	211.027	−	30.3411i	0.514699	−	0.0740026i
$411$	−240.067	+	154.282i	−0.584105	+	0.375382i
$412$	−55.0413	−	226.883i	−0.133595	−	0.550687i
$413$	−92.8174	−	481.582i	−0.224739	−	1.16606i
$414$	−107.485	+	136.678i	−0.259625	+	0.330140i
$415$	81.8378	+	204.421i	0.197200	+	0.492581i
$416$	175.670	−	384.663i	0.422283	−	0.924671i
$417$	−371.499	−	238.748i	−0.890886	−	0.572537i
$418$	31.9450	−	92.2991i	0.0764235	−	0.220811i
$419$	314.534	−	441.701i	0.750677	−	1.05418i	−0.245718	−	0.969341i	$-0.579024\pi$
$419$	314.534	−	441.701i	0.750677	−	1.05418i	0.996395	−	0.0848371i	$-0.0270370\pi$
$420$	3.61634	+	37.8720i	0.00861033	+	0.0901715i
$421$	−9.97386	+	209.377i	−0.0236909	+	0.497333i	0.955574	+	0.294750i	$0.0952364\pi$
$421$	−9.97386	+	209.377i	−0.0236909	+	0.497333i	−0.979265	+	0.202582i	$0.935067\pi$
$422$	−111.112	−	26.9554i	−0.263298	−	0.0638754i
$423$	84.8254	+	245.087i	0.200533	+	0.579402i
$424$	−436.122	−	128.057i	−1.02859	−	0.302021i
$425$	−78.0395	−	74.4105i	−0.183622	−	0.175084i
$426$	19.4548	+	42.6001i	0.0456686	+	0.100000i
$427$	77.5320	−	539.247i	0.181574	−	1.26287i
$428$	−81.9786	−	7.82801i	−0.191539	−	0.0182897i
$429$	275.182	+	238.447i	0.641451	+	0.555820i
$430$	117.886	+	149.904i	0.274153	+	0.348615i
$431$	−60.4697	+	104.737i	−0.140301	+	0.243008i	−0.927610	−	0.373550i	$-0.878140\pi$
$431$	−60.4697	+	104.737i	−0.140301	+	0.243008i	0.787309	+	0.616559i	$0.211474\pi$
$432$	37.9596	−	21.9160i	0.0878694	−	0.0507314i
$433$	−89.4668	+	223.477i	−0.206621	+	0.516114i	−0.995092	−	0.0989584i	$-0.968449\pi$
$433$	−89.4668	+	223.477i	−0.206621	+	0.516114i	0.788471	+	0.615072i	$0.210873\pi$
$434$	434.021	+	455.188i	1.00005	+	1.04882i
$435$	72.0244	−	37.1312i	0.165573	−	0.0853590i
$436$	58.5728	+	113.615i	0.134341	+	0.260586i
$437$	149.354	−	142.408i	0.341770	−	0.325877i
$438$	104.525	+	41.8454i	0.238641	+	0.0955375i
$439$	285.007	+	493.647i	0.649219	+	1.12448i	0.983310	+	0.181939i	$0.0582373\pi$
$439$	285.007	+	493.647i	0.649219	+	1.12448i	−0.334091	+	0.942541i	$0.608429\pi$
$440$	−169.013	−	97.5795i	−0.384120	−	0.221772i
$441$	−13.0156	+	10.2356i	−0.0295139	+	0.0232100i
$442$	110.682	−	127.734i	0.250412	−	0.288990i
$443$	−69.0445	+	723.066i	−0.155857	+	1.63220i	0.492108	+	0.870534i	$0.336226\pi$
$443$	−69.0445	+	723.066i	−0.155857	+	1.63220i	−0.647965	+	0.761670i	$0.724380\pi$
$444$	35.9653	+	5.17103i	0.0810029	+	0.0116465i
$445$	87.8853	−	40.1359i	0.197495	−	0.0901930i
$446$	−245.736	+	257.720i	−0.550977	+	0.577848i
$447$	99.6478	−	339.369i	0.222926	−	0.759215i
$448$	−474.254	+	164.141i	−1.05860	+	0.366386i
$449$	44.8653	−	184.937i	0.0999227	−	0.411887i	−0.899778	−	0.436348i	$-0.856272\pi$
$449$	44.8653	−	184.937i	0.0999227	−	0.411887i	0.999701	+	0.0244609i	$0.00778692\pi$
$450$	98.9894	+	4.71545i	0.219976	+	0.0104788i
$451$	654.113	−	62.4602i	1.45036	−	0.138493i
$452$	−81.5122	−	58.0446i	−0.180337	−	0.128417i
$453$	48.5712	+	16.8107i	0.107221	+	0.0371096i
$454$	−19.4071	+	30.1981i	−0.0427470	+	0.0665156i
$455$	−284.151	−	129.768i	−0.624508	−	0.285203i
$456$	−80.3714	+	32.1759i	−0.176253	+	0.0705611i
$457$	−32.8372	−	25.8234i	−0.0718537	−	0.0565064i	0.581586	−	0.813485i	$-0.302432\pi$
$457$	−32.8372	−	25.8234i	−0.0718537	−	0.0565064i	−0.653440	+	0.756978i	$0.726675\pi$
$458$	−157.186	+	30.2952i	−0.343202	+	0.0661467i
$459$	−26.5748	+	6.44699i	−0.0578972	+	0.0140457i
$460$	−57.8171	−	89.9652i	−0.125689	−	0.195576i
$461$	−51.1760	−	355.937i	−0.111011	−	0.772097i	−0.966940	−	0.255004i	$-0.917923\pi$
$461$	−51.1760	−	355.937i	−0.111011	−	0.772097i	0.855929	−	0.517093i	$-0.172986\pi$
$462$	−10.3538	−	217.354i	−0.0224109	−	0.470462i
$463$	134.068	−	695.612i	0.289564	−	1.50240i	−0.487579	−	0.873079i	$-0.662120\pi$
$463$	134.068	−	695.612i	0.289564	−	1.50240i	0.777143	−	0.629323i	$-0.216668\pi$
$464$	121.685	+	140.432i	0.262252	+	0.302655i
$465$	158.313	−	112.734i	0.340457	−	0.242439i
$466$	−480.412	+	141.062i	−1.03093	+	0.302707i
$467$	−202.018	−	104.147i	−0.432586	−	0.223014i	0.228159	−	0.973624i	$-0.426729\pi$
$467$	−202.018	−	104.147i	−0.432586	−	0.223014i	−0.660745	+	0.750610i	$0.729760\pi$
$468$		−	83.7040i		−	0.178855i
$469$	38.8147	+	493.185i	0.0827606	+	1.05157i
$470$	296.016			0.629822
$471$	−111.146	+	215.593i	−0.235978	+	0.457734i
$472$	−162.941	−	554.926i	−0.345214	−	1.17569i
$473$	340.938	+	478.781i	0.720799	+	1.01222i
$474$	196.045	−	169.874i	0.413597	−	0.358384i
$475$	−115.492	−	22.2592i	−0.243141	−	0.0468615i
$476$	54.3657	−	2.58976i	0.114214	−	0.00544067i
$477$	−155.012	+	22.2874i	−0.324973	+	0.0467241i
$478$	354.688	−	227.944i	0.742026	−	0.476871i
$479$	−157.644	−	649.816i	−0.329110	−	1.35661i	−0.860487	−	0.509473i	$-0.829840\pi$
$479$	−157.644	−	649.816i	−0.329110	−	1.35661i	0.531377	−	0.847136i	$-0.321675\pi$
$480$	14.7789	+	76.6802i	0.0307894	+	0.159750i
$481$	−184.426	+	234.516i	−0.383421	+	0.487560i
$482$	−92.6014	−	231.307i	−0.192119	−	0.479890i
$483$	190.991	−	418.212i	0.395426	−	0.865863i
$484$	11.3424	+	7.28935i	0.0234348	+	0.0150606i
$485$	31.7121	−	91.6260i	0.0653857	−	0.188920i
$486$	14.5782	−	20.4723i	0.0299963	−	0.0421240i
$487$	−27.3527	−	286.451i	−0.0561657	−	0.588194i	−0.979120	−	0.203284i	$-0.934838\pi$
$487$	−27.3527	−	286.451i	−0.0561657	−	0.588194i	0.922954	−	0.384910i	$-0.125768\pi$
$488$	30.5686	−	641.714i	0.0626406	−	1.31499i
$489$	302.988	+	73.5041i	0.619607	+	0.150315i
$490$	6.18130	+	17.8597i	0.0126149	+	0.0364483i
$491$	203.318	+	59.6997i	0.414090	+	0.121588i	0.482140	−	0.876094i	$-0.339860\pi$
$491$	203.318	+	59.6997i	0.414090	+	0.121588i	−0.0680499	+	0.997682i	$0.521678\pi$
$492$	−109.322	−	104.238i	−0.222198	−	0.211866i
$493$	−48.1580	−	105.451i	−0.0976836	−	0.213897i
$494$	26.2370	−	182.482i	0.0531113	−	0.369397i
$495$	−66.9361	−	6.39162i	−0.135224	−	0.0129124i
$496$	336.815	+	291.852i	0.679063	+	0.588412i
$497$	−76.5471	−	97.3376i	−0.154018	−	0.195850i
$498$	−144.760	+	250.732i	−0.290683	+	0.503478i
$499$	149.578	−	86.3586i	0.299755	−	0.173063i	−0.342578	−	0.939489i	$-0.611300\pi$
$499$	149.578	−	86.3586i	0.299755	−	0.173063i	0.642333	+	0.766426i	$0.277967\pi$
$500$	−50.2935	+	125.627i	−0.100587	+	0.251254i
$501$	−126.370	−	132.533i	−0.252236	−	0.264538i
$502$	252.369	−	130.105i	0.502727	−	0.259174i
$503$	220.874	+	428.436i	0.439114	+	0.851762i	0.999720	+	0.0236791i	$0.00753798\pi$
$503$	220.874	+	428.436i	0.439114	+	0.851762i	−0.560606	+	0.828083i	$0.689432\pi$
$504$	−139.590	+	133.099i	−0.276964	+	0.264085i
$505$	47.7295	+	19.1080i	0.0945138	+	0.0378376i
$506$	305.835	+	529.722i	0.604417	+	1.04688i
$507$	341.712	+	197.287i	0.673987	+	0.389127i
$508$	−122.334	+	96.2046i	−0.240815	+	0.189379i
$509$	−402.432	+	464.432i	−0.790633	+	0.912439i	−0.997829	−	0.0658601i	$-0.979021\pi$
$509$	−402.432	+	464.432i	−0.790633	+	0.912439i	0.207196	+	0.978300i	$0.433566\pi$
$510$	−2.96685	+	31.0703i	−0.00581736	+	0.0609222i
$511$	−294.673	−	42.3676i	−0.576660	−	0.0829111i
$512$	−430.139	+	196.438i	−0.840115	+	0.383668i
$513$	−20.5837	+	21.5876i	−0.0401241	+	0.0420810i
$514$	37.9096	−	129.108i	0.0737541	−	0.251184i
$515$	−334.531	+	115.782i	−0.649574	+	0.224820i
$516$	31.8549	−	131.308i	0.0617344	−	0.254473i
$517$	911.311	+	43.4111i	1.76269	+	0.0839673i
$518$	177.487	−	16.9480i	0.342639	−	0.0327181i
$519$	231.474	+	164.832i	0.446001	+	0.317596i
$520$	−348.112	−	120.483i	−0.669446	−	0.231697i
$521$	528.090	−	821.724i	1.01361	−	1.57721i	0.213866	−	0.976863i	$-0.431394\pi$
$521$	528.090	−	821.724i	1.01361	−	1.57721i	0.799743	−	0.600343i	$-0.204969\pi$
$522$	96.9165	+	44.2603i	0.185664	+	0.0847898i
$523$	666.645	−	266.884i	1.27466	−	0.510295i	0.367082	−	0.930189i	$-0.380357\pi$
$523$	666.645	−	266.884i	1.27466	−	0.510295i	0.907573	+	0.419894i	$0.137933\pi$
$524$	−16.6433	−	13.0885i	−0.0317621	−	0.0249780i
$525$	−257.303	+	49.5911i	−0.490101	+	0.0944592i
$526$	−46.0196	+	11.1642i	−0.0874898	+	0.0212248i
$527$	−150.321	−	233.905i	−0.285240	−	0.443842i
$528$	−21.9438	−	152.622i	−0.0415602	−	0.289058i
$529$	36.3229	+	762.511i	0.0686633	+	1.44142i
$530$	−33.8280	+	175.516i	−0.0638264	+	0.331163i
$531$	−130.492	−	150.596i	−0.245748	−	0.283609i
$532$	48.3598	−	34.4369i	0.0909019	−	0.0647310i
$533$	1190.05	−	349.429i	2.23273	−	0.655589i
$534$	112.913	+	58.2109i	0.211448	+	0.109009i
$535$			124.869i			0.233400i
$536$	100.848	+	574.599i	0.188149	+	1.07201i
$537$	128.587			0.239455
$538$	−19.0957	+	37.0404i	−0.0354938	+	0.0688484i
$539$	16.4105	+	55.8890i	0.0304462	+	0.103690i
$540$	8.96614	+	12.5912i	0.0166040	+	0.0233170i
$541$	313.088	−	271.293i	0.578722	−	0.501465i	−0.315598	−	0.948893i	$-0.602205\pi$
$541$	313.088	−	271.293i	0.578722	−	0.501465i	0.894320	+	0.447428i	$0.147660\pi$
$542$	−535.082	−	103.129i	−0.987236	−	0.190274i
$543$	421.456	−	20.0764i	0.776161	−	0.0369731i
$544$	110.583	−	15.8994i	0.203277	−	0.0292269i
$545$	163.052	−	104.787i	0.299178	−	0.192270i
$546$	−96.8334	−	399.153i	−0.177351	−	0.731049i
$547$	12.7628	+	66.2197i	0.0233324	+	0.121060i	0.991727	−	0.128361i	$-0.0409717\pi$
$547$	12.7628	+	66.2197i	0.0233324	+	0.121060i	−0.968395	+	0.249421i	$0.919760\pi$
$548$	142.653	−	181.398i	0.260316	−	0.331018i
$549$	−82.2669	−	205.493i	−0.149849	−	0.374304i
$550$	144.822	−	317.115i	0.263312	−	0.576574i
$551$	−106.377	−	68.3646i	−0.193062	−	0.124074i
$552$	177.326	−	512.349i	0.321242	−	0.928168i
$553$	−397.862	+	558.719i	−0.719461	+	1.01034i
$554$	−71.9192	−	753.172i	−0.129818	−	1.35952i
$555$	2.62151	−	55.0323i	0.00472344	−	0.0991573i
$556$	347.046	+	84.1925i	0.624184	+	0.151425i
$557$	−166.805	−	481.952i	−0.299471	−	0.865263i	−0.989888	−	0.141852i	$-0.954694\pi$
$557$	−166.805	−	481.952i	−0.299471	−	0.865263i	0.690417	−	0.723411i	$-0.257427\pi$
$558$	245.188	+	71.9937i	0.439405	+	0.129021i
$559$	802.938	+	765.600i	1.43638	+	1.36959i
$560$	54.9522	+	120.328i	0.0981289	+	0.214872i
$561$	−13.6902	+	95.2174i	−0.0244032	+	0.169728i
$562$	−498.960	−	47.6449i	−0.887830	−	0.0847775i
$563$	643.234	+	557.365i	1.14251	+	0.989992i	1.00000		0.000198699i	$6.32478e-5\pi$
$563$	643.234	+	557.365i	1.14251	+	0.989992i	0.142512	+	0.989793i	$0.454482\pi$
$564$	−129.647	−	164.860i	−0.229871	−	0.292304i
$565$	−75.8655	+	131.403i	−0.134275	+	0.232571i
$566$	−58.4649	+	33.7548i	−0.103295	+	0.0596374i
$567$	−24.6983	+	61.6933i	−0.0435596	+	0.108807i
$568$	−100.770	−	105.684i	−0.177412	−	0.186064i
$569$	−157.887	+	81.3966i	−0.277482	+	0.143052i	−0.591351	−	0.806414i	$-0.701405\pi$
$569$	−157.887	+	81.3966i	−0.277482	+	0.143052i	0.313869	+	0.949466i	$0.398375\pi$
$570$	15.6003	+	30.2603i	0.0273689	+	0.0530883i
$571$	108.300	−	103.264i	0.189668	−	0.180848i	−0.589295	−	0.807918i	$-0.700594\pi$
$571$	108.300	−	103.264i	0.189668	−	0.180848i	0.778963	+	0.627070i	$0.215746\pi$
$572$	−273.361	−	109.437i	−0.477904	−	0.191324i
$573$	88.2338	+	152.825i	0.153986	+	0.266711i
$574$	−641.902	−	370.602i	−1.11830	−	0.645649i
$575$	578.995	−	455.327i	1.00695	−	0.791873i
$576$	−133.528	+	154.100i	−0.231820	+	0.267535i
$577$	−17.5273	+	183.554i	−0.0303766	+	0.318118i	0.967494	+	0.252894i	$0.0813823\pi$
$577$	−17.5273	+	183.554i	−0.0303766	+	0.318118i	−0.997871	+	0.0652241i	$0.979224\pi$
$578$	−416.998	−	59.9553i	−0.721450	−	0.103729i
$579$	129.069	−	58.9440i	0.222918	−	0.101803i
$580$	−45.2201	+	47.4255i	−0.0779657	+	0.0817681i
$581$	215.675	−	734.522i	0.371213	−	1.26424i
$582$	120.474	−	41.6964i	0.207000	−	0.0716432i
$583$	−129.882	+	535.380i	−0.222782	+	0.918319i
$584$	−350.666	−	16.7043i	−0.600456	−	0.0286033i
$585$	−126.345	+	12.0645i	−0.215975	+	0.0206231i
$586$	−37.9615	−	27.0323i	−0.0647807	−	0.0461301i
$587$	662.822	+	229.405i	1.12917	+	0.390809i	0.826864	−	0.562402i	$-0.190123\pi$
$587$	662.822	+	229.405i	1.12917	+	0.390809i	0.302305	+	0.953211i	$0.402244\pi$
$588$	7.23931	−	11.2646i	0.0123117	−	0.0191574i
$589$	−275.876	−	125.988i	−0.468380	−	0.213902i
$590$	−211.147	+	84.5304i	−0.357876	+	0.143272i
$591$	−264.737	−	208.191i	−0.447947	−	0.352270i
$592$	124.057	−	23.9099i	0.209555	−	0.0403884i
$593$	−438.772	+	106.445i	−0.739920	+	0.179503i	−0.587967	−	0.808885i	$-0.700071\pi$
$593$	−438.772	+	106.445i	−0.739920	+	0.179503i	−0.151953	+	0.988388i	$0.548556\pi$
$594$	−47.7984	−	74.3758i	−0.0804687	−	0.125212i
$595$	−11.7449	−	81.6878i	−0.0197394	−	0.137290i
$596$	13.6097	+	285.702i	0.0228350	+	0.479365i
$597$	−100.924	+	523.645i	−0.169052	+	0.877127i
$598$	756.074	+	872.556i	1.26434	+	1.45912i
$599$	−876.616	+	624.236i	−1.46347	+	1.04213i	−0.476866	+	0.878976i	$0.658227\pi$
$599$	−876.616	+	624.236i	−1.46347	+	1.04213i	−0.986601	+	0.163154i	$0.947833\pi$
$600$	−296.490	+	87.0572i	−0.494149	+	0.145095i
$601$	−814.327	−	419.815i	−1.35495	−	0.698527i	−0.380852	−	0.924636i	$-0.624369\pi$
$601$	−814.327	−	419.815i	−1.35495	−	0.698527i	−0.974102	+	0.226109i	$0.927399\pi$
$602$		−	663.009i		−	1.10134i
$603$	113.848	+	165.649i	0.188802	+	0.274709i
$604$	−41.5644			−0.0688152
$605$	9.36792	−	18.1712i	0.0154842	−	0.0300351i
$606$	19.0448	+	64.8607i	0.0314271	+	0.107031i
$607$	−348.144	−	488.899i	−0.573548	−	0.805435i	0.421289	−	0.906927i	$-0.361578\pi$
$607$	−348.144	−	488.899i	−0.573548	−	0.805435i	−0.994836	+	0.101491i	$0.967639\pi$
$608$	92.0969	−	79.8024i	0.151475	−	0.131254i
$609$	−276.628	−	53.3156i	−0.454233	−	0.0875462i
$610$	−252.355	+	12.0212i	−0.413697	+	0.0197068i
$611$	1704.57	−	245.079i	2.78980	−	0.401112i
$612$	18.6033	−	11.9556i	0.0303975	−	0.0195353i
$613$	−97.4417	−	401.660i	−0.158959	−	0.655237i	−0.994402	−	0.105661i	$-0.966304\pi$
$613$	−97.4417	−	401.660i	−0.158959	−	0.655237i	0.835443	−	0.549576i	$-0.185211\pi$
$614$	106.092	+	550.459i	0.172789	+	0.896512i
$615$	−141.583	+	180.037i	−0.230216	+	0.292743i
$616$	252.171	+	629.892i	0.409368	+	1.02255i
$617$	26.7741	−	58.6271i	0.0433940	−	0.0950195i	−0.886693	−	0.462358i	$-0.847004\pi$
$617$	26.7741	−	58.6271i	0.0433940	−	0.0950195i	0.930087	+	0.367338i	$0.119731\pi$
$618$	−391.565	−	251.644i	−0.633600	−	0.407190i
$619$	52.1853	−	150.780i	0.0843059	−	0.243586i	−0.894967	−	0.446133i	$-0.852801\pi$
$619$	52.1853	−	150.780i	0.0843059	−	0.243586i	0.979272	+	0.202547i	$0.0649220\pi$
$620$	−91.1652	+	128.024i	−0.147041	+	0.206490i
$621$	−17.7564	−	185.954i	−0.0285933	−	0.299443i
$622$	−15.2426	+	319.982i	−0.0245058	+	0.514440i
$623$	−326.430	−	79.1911i	−0.523965	−	0.127112i
$624$	−95.1914	−	275.037i	−0.152550	−	0.440765i
$625$	−294.611	−	86.5057i	−0.471378	−	0.138409i
$626$	530.007	+	505.361i	0.846657	+	0.807285i
$627$	43.5890	+	95.4467i	0.0695200	+	0.152228i
$628$	27.9150	−	194.153i	0.0444506	−	0.309161i
$629$	−78.4633	−	7.49234i	−0.124743	−	0.0119115i
$630$	57.3223	+	49.6701i	0.0909878	+	0.0788414i
$631$	636.409	+	809.259i	1.00857	+	1.28250i	0.958902	+	0.283737i	$0.0915744\pi$
$631$	636.409	+	809.259i	1.00857	+	1.28250i	0.0496696	+	0.998766i	$0.484183\pi$
$632$	−404.422	+	700.479i	−0.639908	+	1.10835i
$633$	106.375	−	61.4155i	0.168048	−	0.0970228i
$634$	−142.275	+	355.385i	−0.224408	+	0.560544i
$635$	162.846	+	170.788i	0.256451	+	0.268958i
$636$	112.565	−	58.0315i	0.176990	−	0.0912445i
$637$	50.3805	+	97.7246i	0.0790903	+	0.153414i
$638$	271.257	−	258.643i	0.425168	−	0.405397i
$639$	−46.7084	−	18.6992i	−0.0730960	−	0.0292632i
$640$	26.1928	+	45.3672i	0.0409262	+	0.0708862i
$641$	725.671	+	418.967i	1.13209	+	0.653614i	0.944460	−	0.328625i	$-0.106585\pi$
$641$	725.671	+	418.967i	1.13209	+	0.653614i	0.187632	+	0.982239i	$0.439919\pi$
$642$	−129.057	+	101.491i	−0.201023	+	0.158086i
$643$	−592.957	+	684.309i	−0.922173	+	1.06424i	0.0755728	+	0.997140i	$0.475921\pi$
$643$	−592.957	+	684.309i	−0.922173	+	1.06424i	−0.997746	+	0.0671043i	$0.978624\pi$
$644$	−35.3415	+	370.113i	−0.0548781	+	0.574709i
$645$	−202.791	−	29.1569i	−0.314405	−	0.0452046i
$646$	44.3043	−	20.2331i	0.0685825	−	0.0313206i
$647$	−754.589	+	791.391i	−1.16629	+	1.22317i	−0.196163	+	0.980571i	$0.562848\pi$
$647$	−754.589	+	791.391i	−1.16629	+	1.22317i	−0.970127	+	0.242598i	$0.922000\pi$
$648$	−22.0779	+	75.1904i	−0.0340708	+	0.116035i
$649$	−662.429	+	229.269i	−1.02069	+	0.353265i
$650$	155.138	−	639.487i	0.238674	−	0.983826i
$651$	−674.915	−	32.1502i	−1.03674	−	0.0493858i
$652$	−250.984	+	23.9661i	−0.384945	+	0.0367578i
$653$	−215.810	−	153.677i	−0.330490	−	0.235341i	0.402751	−	0.915309i	$-0.368054\pi$
$653$	−215.810	−	153.677i	−0.330490	−	0.235341i	−0.733241	+	0.679969i	$0.761993\pi$
$654$	240.827	+	83.3509i	0.368236	+	0.127448i
$655$	−17.3572	+	27.0084i	−0.0264996	+	0.0412342i
$656$	−477.756	−	218.184i	−0.728287	−	0.332597i
$657$	−112.292	+	44.9550i	−0.170916	+	0.0684246i
$658$	−808.956	−	636.170i	−1.22942	−	0.966824i
$659$	−651.482	+	125.563i	−0.988592	+	0.190535i	−0.657820	−	0.753175i	$-0.728521\pi$
$659$	−651.482	+	125.563i	−0.988592	+	0.190535i	−0.330772	+	0.943711i	$0.607309\pi$
$660$	52.8430	−	12.8196i	0.0800652	−	0.0194236i
$661$	−378.350	−	588.724i	−0.572390	−	0.890656i	0.427521	−	0.904006i	$-0.359387\pi$
$661$	−378.350	−	588.724i	−0.572390	−	0.890656i	−0.999911	+	0.0133492i	$0.995751\pi$
$662$	53.8157	+	374.296i	0.0812926	+	0.565402i
$663$	8.63971	+	181.370i	0.0130312	+	0.273559i
$664$	170.846	−	886.432i	0.257298	−	1.33499i
$665$	−58.9502	−	68.0321i	−0.0886469	−	0.102304i
$666$	59.0085	−	42.0198i	0.0886014	−	0.0630928i
$667$	759.829	−	223.106i	1.13917	−	0.334492i
$668$	131.626	+	67.8580i	0.197045	+	0.101584i
$669$		−	382.560i		−	0.571838i
$670$	221.169	−	60.9581i	0.330103	−	0.0909822i
$671$	−778.659			−1.16045
$672$	124.406	−	241.314i	0.185128	−	0.359098i
$673$	−232.504	−	791.834i	−0.345473	−	1.17657i	−0.930724	−	0.365722i	$-0.880822\pi$
$673$	−232.504	−	791.834i	−0.345473	−	1.17657i	0.585251	−	0.810852i	$-0.300996\pi$
$674$	327.540	+	459.966i	0.485965	+	0.682443i
$675$	−80.4616	+	69.7204i	−0.119202	+	0.103289i
$676$	−313.317	−	60.3868i	−0.463486	−	0.0893296i
$677$	524.693	−	24.9942i	0.775027	−	0.0369191i	0.343658	−	0.939095i	$-0.388334\pi$
$677$	524.693	−	24.9942i	0.775027	−	0.0369191i	0.431369	+	0.902176i	$0.358031\pi$
$678$	−197.472	+	28.3921i	−0.291256	+	0.0418763i
$679$	−283.577	+	182.244i	−0.417639	+	0.268400i
$680$	−22.9441	−	94.5769i	−0.0337413	−	0.139084i
$681$	−7.29829	−	37.8671i	−0.0107170	−	0.0556052i
$682$	555.685	−	706.610i	0.814787	−	1.03609i
$683$	80.3822	+	200.785i	0.117690	+	0.293975i	0.975503	−	0.219987i	$-0.0706014\pi$
$683$	80.3822	+	200.785i	0.117690	+	0.293975i	−0.857813	+	0.513962i	$0.828177\pi$
$684$	10.0203	−	21.9414i	0.0146496	−	0.0320781i
$685$	−294.368	−	189.179i	−0.429734	−	0.276173i
$686$	−169.293	+	489.141i	−0.246783	+	0.713034i
$687$	99.7552	−	140.087i	0.145204	−	0.203911i
$688$	−44.6582	−	467.682i	−0.0649102	−	0.679771i
$689$	−49.4789	+	1038.69i	−0.0718126	+	1.50753i
$690$	−207.198	−	50.2658i	−0.300287	−	0.0728489i
$691$	−235.348	−	679.992i	−0.340590	−	0.984069i	−0.977096	−	0.212798i	$-0.931742\pi$
$691$	−235.348	−	679.992i	−0.340590	−	0.984069i	0.636506	−	0.771271i	$-0.280379\pi$
$692$	−220.489	−	64.7415i	−0.318626	−	0.0935571i
$693$	169.187	+	161.320i	0.244138	+	0.232785i
$694$	−20.1338	−	44.0869i	−0.0290112	−	0.0635257i
$695$	77.0617	−	535.976i	0.110880	−	0.771189i
$696$	−330.710	−	31.5790i	−0.475158	−	0.0453721i
$697$	247.637	+	214.579i	0.355290	+	0.307861i
$698$	220.991	+	281.012i	0.316606	+	0.402597i
$699$	268.950	−	465.835i	0.384764	−	0.666431i
$700$	183.514	−	105.952i	0.262163	−	0.151360i
$701$	−34.8187	+	86.9729i	−0.0496700	+	0.124070i	−0.951128	−	0.308797i	$-0.900074\pi$
$701$	−34.8187	+	86.9729i	−0.0496700	+	0.124070i	0.901458	+	0.432867i	$0.142498\pi$
$702$	−115.160	−	120.776i	−0.164046	−	0.172046i
$703$	−76.4179	+	39.3961i	−0.108703	+	0.0560400i
$704$	328.682	+	637.553i	0.466877	+	0.905616i
$705$	−230.157	+	219.454i	−0.326464	+	0.311283i
$706$	−874.679	−	350.169i	−1.23892	−	0.495990i
$707$	−89.3705	−	154.794i	−0.126408	−	0.218945i
$708$	139.554	+	80.5713i	0.197110	+	0.113801i
$709$	−225.310	+	177.186i	−0.317786	+	0.249909i	−0.764291	−	0.644872i	$-0.776911\pi$
$709$	−225.310	+	177.186i	−0.317786	+	0.249909i	0.446505	+	0.894781i	$0.352668\pi$
$710$	−37.6055	+	43.3991i	−0.0529655	+	0.0611254i
$711$	−26.4903	+	277.419i	−0.0372578	+	0.390182i
$712$	−392.074	−	56.3717i	−0.550665	−	0.0791737i
$713$	1727.69	−	789.009i	2.42313	−	1.10660i
$714$	74.8812	−	78.5331i	0.104876	−	0.109990i
$715$	−125.787	+	428.393i	−0.175926	+	0.599150i
$716$	−98.2662	+	34.0103i	−0.137243	+	0.0475004i
$717$	−106.787	+	440.181i	−0.148936	+	0.613921i
$718$	−856.620	−	40.8058i	−1.19306	−	0.0568326i
$719$	−883.922	+	84.4043i	−1.22938	+	0.117391i	−0.689458	−	0.724326i	$-0.742151\pi$
$719$	−883.922	+	84.4043i	−1.22938	+	0.117391i	−0.539919	+	0.841717i	$0.681545\pi$
$720$	43.7804	+	31.1759i	0.0608061	+	0.0432999i
$721$	1163.04	+	402.531i	1.61309	+	0.558295i
$722$	−285.941	+	444.933i	−0.396041	+	0.616251i
$723$	243.481	+	111.194i	0.336764	+	0.153795i
$724$	−316.766	+	126.814i	−0.437522	+	0.175157i
$725$	−354.781	−	279.003i	−0.489353	−	0.384832i
$726$	26.3947	−	5.08716i	0.0363563	−	0.00700710i
$727$	−1168.38	+	283.446i	−1.60712	+	0.389884i	−0.936151	−	0.351598i	$-0.885638\pi$
$727$	−1168.38	+	283.446i	−1.60712	+	0.389884i	−0.670973	+	0.741482i	$0.734123\pi$
$728$	692.393	+	1077.38i	0.951090	+	1.47992i
$729$	3.84250	+	26.7252i	0.00527092	+	0.0366601i
$730$	6.56900	+	137.900i	0.00899862	+	0.188904i
$731$	−55.4700	+	287.806i	−0.0758824	+	0.393715i
$732$	117.219	+	135.278i	0.160136	+	0.184807i
$733$	304.591	−	216.898i	0.415540	−	0.295905i	−0.353101	−	0.935585i	$-0.614873\pi$
$733$	304.591	−	216.898i	0.415540	−	0.295905i	0.768641	+	0.639680i	$0.220933\pi$
$734$	725.233	−	212.948i	0.988056	−	0.290119i
$735$	−18.0465	−	9.30361i	−0.0245530	−	0.0126580i
$736$			763.166i			1.03691i
$737$	689.827	−	155.230i	0.935994	−	0.210624i
$738$	−301.151			−0.408063
$739$	−256.722	+	497.970i	−0.347391	+	0.673844i	−0.996199	−	0.0871083i	$-0.972237\pi$
$739$	−256.722	+	497.970i	−0.347391	+	0.673844i	0.648808	+	0.760952i	$0.275268\pi$
$740$	12.5522	+	42.7490i	0.0169625	+	0.0577689i
$741$	114.885	+	161.334i	0.155041	+	0.217724i
$742$	469.648	−	406.952i	0.632949	−	0.548453i
$743$	551.167	+	106.229i	0.741813	+	0.142973i	0.546137	−	0.837696i	$-0.316098\pi$
$743$	551.167	+	106.229i	0.741813	+	0.142973i	0.195676	+	0.980669i	$0.437310\pi$
$744$	−795.888	+	37.9128i	−1.06974	+	0.0509581i
$745$	429.284	−	61.7218i	0.576221	−	0.0828480i
$746$	−392.341	+	252.142i	−0.525927	+	0.337992i
$747$	−73.3292	−	302.267i	−0.0981649	−	0.404641i
$748$	−14.7222	−	76.3860i	−0.0196821	−	0.102120i
$749$	268.357	−	341.243i	0.358287	−	0.455598i
$750$	100.269	+	250.461i	0.133693	+	0.333948i
$751$	417.332	−	913.830i	0.555702	−	1.21682i	−0.398366	−	0.917227i	$-0.630422\pi$
$751$	417.332	−	913.830i	0.555702	−	1.21682i	0.954068	−	0.299591i	$-0.0968502\pi$
$752$	−613.483	−	394.262i	−0.815802	−	0.524284i
$753$	−99.7660	+	288.255i	−0.132491	+	0.382809i
$754$	410.366	−	576.278i	0.544252	−	0.764295i
$755$	5.99079	+	62.7384i	0.00793482	+	0.0830972i
$756$	2.55702	−	53.6785i	0.00338230	−	0.0710033i
$757$	−48.9532	−	11.8759i	−0.0646674	−	0.0156881i	0.203295	−	0.979118i	$-0.434835\pi$
$757$	−48.9532	−	11.8759i	−0.0646674	−	0.0156881i	−0.267962	+	0.963429i	$0.586350\pi$
$758$	127.852	+	369.405i	0.168671	+	0.487342i
$759$	−630.505	−	185.133i	−0.830705	−	0.243917i
$760$	−76.8277	−	73.2551i	−0.101089	−	0.0963883i
$761$	−274.447	−	600.955i	−0.360640	−	0.789691i	−0.999788	−	0.0206073i	$-0.993440\pi$
$761$	−274.447	−	600.955i	−0.360640	−	0.789691i	0.639148	−	0.769084i	$-0.279287\pi$
$762$	−44.1573	+	307.121i	−0.0579492	+	0.403046i
$763$	−670.788	−	64.0525i	−0.879145	−	0.0839482i
$764$	−107.849	−	93.4519i	−0.141164	−	0.122319i
$765$	−20.7275	−	26.3571i	−0.0270947	−	0.0344538i
$766$	492.011	−	852.188i	0.642312	−	1.11252i
$767$	−1145.87	+	661.569i	−1.49396	+	0.862541i
$768$	149.414	−	373.219i	0.194550	−	0.485962i
$769$	594.047	+	623.019i	0.772493	+	0.810167i	0.985995	−	0.166775i	$-0.0533355\pi$
$769$	594.047	+	623.019i	0.772493	+	0.810167i	−0.213502	+	0.976943i	$0.568487\pi$
$770$	237.158	−	122.264i	0.307998	−	0.158784i
$771$	66.2403	+	128.488i	0.0859148	+	0.166651i
$772$	−83.0444	+	79.1827i	−0.107570	+	0.102568i
$773$	6.71317	+	2.68755i	0.00868457	+	0.00347678i	0.376001	−	0.926619i	$-0.377299\pi$
$773$	6.71317	+	2.68755i	0.00868457	+	0.00347678i	−0.367316	+	0.930096i	$0.619723\pi$
$774$	−134.690	−	233.290i	−0.174018	−	0.301408i
$775$	−937.486	−	541.258i	−1.20966	−	0.698397i
$776$	−312.463	+	245.724i	−0.402659	+	0.316654i
$777$	−125.434	+	144.759i	−0.161434	+	0.186305i
$778$	35.4745	−	371.505i	0.0455970	−	0.477513i
$779$	353.778	+	50.8656i	0.454144	+	0.0652960i
$780$	93.3619	−	42.6369i	0.119695	−	0.0546627i
$781$	−122.136	+	128.093i	−0.156384	+	0.164011i
$782$	−85.9348	+	292.667i	−0.109891	+	0.374254i
$783$	−108.167	+	37.4369i	−0.138144	+	0.0478121i
$784$	10.9766	−	45.2463i	0.0140008	−	0.0577122i
$785$	−297.083	−	14.1518i	−0.378450	−	0.0180278i
$786$	−42.0218	+	4.01259i	−0.0534628	+	0.00510508i
$787$	−459.568	−	327.257i	−0.583949	−	0.415828i	0.249540	−	0.968365i	$-0.419721\pi$
$787$	−459.568	−	327.257i	−0.583949	−	0.415828i	−0.833489	+	0.552536i	$0.813660\pi$
$788$	257.377	+	89.0789i	0.326620	+	0.113044i
$789$	27.5042	−	42.7974i	0.0348596	−	0.0542426i
$790$	289.335	+	132.135i	0.366247	+	0.167259i
$791$	489.724	−	196.056i	0.619121	−	0.247859i
$792$	216.692	+	170.409i	0.273601	+	0.215162i
$793$	−1443.20	+	278.153i	−1.81992	+	0.350761i
$794$	−808.799	+	196.213i	−1.01864	+	0.247119i
$795$	−103.819	−	161.545i	−0.130590	−	0.203201i
$796$	−61.3735	−	426.862i	−0.0771024	−	0.536259i
$797$	32.0333	+	672.463i	0.0401924	+	0.843742i	0.925503	+	0.378741i	$0.123643\pi$
$797$	32.0333	+	672.463i	0.0401924	+	0.843742i	−0.885310	+	0.465001i	$0.846054\pi$
$798$	22.4000	−	116.222i	0.0280702	−	0.145642i
$799$	297.936	+	343.836i	0.372886	+	0.430333i
$800$	354.311	−	252.304i	0.442889	−	0.315380i
$801$	−130.947	+	38.4495i	−0.163479	+	0.0480019i
$802$	492.460	+	253.881i	0.614041	+	0.316560i
$803$			425.500i			0.529888i
$804$	−130.815	−	96.4773i	−0.162706	−	0.119997i
$805$	563.752			0.700313
$806$	777.511	−	1508.16i	0.964654	−	1.87117i
$807$	−12.6131	−	42.9562i	−0.0156296	−	0.0532295i
$808$	−122.264	−	171.695i	−0.151316	−	0.212494i
$809$	800.267	−	693.435i	0.989205	−	0.857151i	−0.000539579	−	1.00000i	$-0.500172\pi$
$809$	800.267	−	693.435i	0.989205	−	0.857151i	0.989745	+	0.142849i	$0.0456263\pi$
$810$	30.2602	+	5.83217i	0.0373583	+	0.00720021i
$811$	1147.36	−	54.6555i	1.41475	−	0.0673927i	0.673779	−	0.738933i	$-0.264670\pi$
$811$	1147.36	−	54.6555i	1.41475	−	0.0673927i	0.740968	+	0.671540i	$0.234367\pi$
$812$	225.500	−	32.4220i	0.277710	−	0.0399286i
$813$	492.490	−	316.504i	0.605768	−	0.389304i
$814$	−60.0789	−	247.649i	−0.0738070	−	0.304237i
$815$	72.3502	+	375.388i	0.0887732	+	0.460599i
$816$	47.5309	−	60.4405i	0.0582487	−	0.0740692i
$817$	118.824	+	296.808i	0.145439	+	0.363290i
$818$	27.9391	−	61.1780i	0.0341553	−	0.0747897i
$819$	371.205	+	238.559i	0.453242	+	0.291281i
$820$	60.5791	−	175.032i	0.0738769	−	0.213453i
$821$	4.13102	−	5.80121i	0.00503169	−	0.00706602i	−0.812052	−	0.583584i	$-0.801650\pi$
$821$	4.13102	−	5.80121i	0.00503169	−	0.00706602i	0.817084	+	0.576518i	$0.195589\pi$
$822$	−43.7338	−	458.001i	−0.0532041	−	0.557178i
$823$	−56.2976	+	1181.83i	−0.0684054	+	1.43601i	0.660209	+	0.751082i	$0.270468\pi$
$823$	−56.2976	+	1181.83i	−0.0684054	+	1.43601i	−0.728615	+	0.684924i	$0.759835\pi$
$824$	1410.41	+	342.162i	1.71166	+	0.415245i
$825$	122.495	+	353.927i	0.148479	+	0.429002i
$826$	758.688	+	222.771i	0.918508	+	0.269698i
$827$	−29.5925	−	28.2164i	−0.0357830	−	0.0341190i	0.671977	−	0.740572i	$-0.265446\pi$
$827$	−29.5925	−	28.2164i	−0.0357830	−	0.0341190i	−0.707760	+	0.706453i	$0.750294\pi$
$828$	62.7528	+	137.409i	0.0757884	+	0.165953i
$829$	105.407	−	733.121i	0.127149	−	0.884344i	−0.821993	−	0.569497i	$-0.807138\pi$
$829$	105.407	−	733.121i	0.127149	−	0.884344i	0.949143	−	0.314847i	$-0.101953\pi$
$830$	−353.399	−	33.7455i	−0.425782	−	0.0406573i
$831$	614.289	+	532.285i	0.739217	+	0.640535i
$832$	836.938	+	1064.25i	1.00594	+	1.27915i
$833$	−14.5234	+	25.1553i	−0.0174351	+	0.0301985i
$834$	616.585	−	355.985i	0.739310	−	0.426841i
$835$	83.4550	−	208.461i	0.0999461	−	0.249653i
$836$	−58.5556	−	61.4113i	−0.0700426	−	0.0734585i
$837$	−244.010	+	125.796i	−0.291530	+	0.150294i
$838$	400.597	+	777.050i	0.478039	+	0.927267i
$839$	88.3908	−	84.2805i	0.105353	−	0.100454i	−0.635572	−	0.772041i	$-0.719236\pi$
$839$	88.3908	−	84.2805i	0.105353	−	0.100454i	0.740925	+	0.671588i	$0.234387\pi$
$840$	−219.560	−	87.8985i	−0.261381	−	0.104641i
$841$	177.878	+	308.095i	0.211508	+	0.366343i
$842$	−292.673	−	168.975i	−0.347593	−	0.200683i
$843$	423.271	−	332.864i	0.502101	−	0.394857i
$844$	−65.0476	+	75.0689i	−0.0770706	+	0.0889442i
$845$	−45.9903	+	481.632i	−0.0544264	+	0.569979i
$846$	−413.881	−	59.5071i	−0.489221	−	0.0703394i
$847$	−64.6526	+	29.5259i	−0.0763313	+	0.0348593i
$848$	303.876	−	318.696i	0.358344	−	0.375820i
$849$	20.4330	−	69.5883i	0.0240671	−	0.0819651i
$850$	164.285	−	56.8597i	0.193277	−	0.0668937i
$851$	126.939	−	523.248i	0.149164	−	0.614862i
$852$	40.6403	+	1.93593i	0.0476999	+	0.00227222i
$853$	595.469	−	56.8604i	0.698088	−	0.0666593i	0.260022	−	0.965603i	$-0.416270\pi$
$853$	595.469	−	56.8604i	0.698088	−	0.0666593i	0.438065	+	0.898943i	$0.355664\pi$
$854$	715.473	+	509.486i	0.837790	+	0.596588i
$855$	−34.5632	−	11.9624i	−0.0404248	−	0.0139912i
$856$	276.773	−	430.667i	0.323333	−	0.503116i
$857$	−507.170	−	231.617i	−0.591797	−	0.270265i	0.0969232	−	0.995292i	$-0.469100\pi$
$857$	−507.170	−	231.617i	−0.591797	−	0.270265i	−0.688720	+	0.725027i	$0.741827\pi$
$858$	−544.996	+	218.184i	−0.635194	+	0.254293i
$859$	−137.150	−	107.856i	−0.159663	−	0.125560i	0.535131	−	0.844769i	$-0.320262\pi$
$859$	−137.150	−	107.856i	−0.159663	−	0.125560i	−0.694794	+	0.719209i	$0.744505\pi$
$860$	162.684	−	31.3549i	0.189168	−	0.0364591i
$861$	773.838	−	187.731i	0.898766	−	0.218038i
$862$	−105.416	−	164.031i	−0.122293	−	0.190291i
$863$	−164.436	−	1143.68i	−0.190540	−	1.32523i	−0.830583	−	0.556894i	$-0.811993\pi$
$863$	−164.436	−	1143.68i	−0.190540	−	1.32523i	0.640044	−	0.768339i	$-0.278916\pi$
$864$	−5.24866	−	110.183i	−0.00607484	−	0.127527i
$865$	−65.9428	+	342.144i	−0.0762345	+	0.395542i
$866$	−254.152	−	293.307i	−0.293478	−	0.338691i
$867$	368.671	−	262.529i	0.425226	−	0.302802i
$868$	524.273	−	153.940i	0.604001	−	0.177351i
$869$	871.364	+	449.219i	1.00272	+	0.516938i
$870$			130.644i			0.150165i
$871$	1223.10	−	534.129i	1.40425	−	0.613237i
$872$	−794.619			−0.911260
$873$	−62.7581	+	121.734i	−0.0718879	+	0.139443i
$874$	93.7357	+	319.234i	0.107249	+	0.365257i
$875$	−413.785	−	581.079i	−0.472897	−	0.664091i
$876$	73.9233	−	64.0549i	0.0843874	−	0.0731221i
$877$	−225.241	−	43.4116i	−0.256831	−	0.0495001i	0.0592105	−	0.998246i	$-0.481142\pi$
$877$	−225.241	−	43.4116i	−0.256831	−	0.0495001i	−0.316041	+	0.948745i	$0.602354\pi$
$878$	−917.961	+	43.7279i	−1.04551	+	0.0498040i
$879$	49.5562	−	7.12511i	0.0563780	−	0.00810593i
$880$	159.054	−	102.218i	0.180744	−	0.116157i
$881$	−244.619	−	1008.33i	−0.277661	−	1.14453i	−0.924279	−	0.381718i	$-0.875332\pi$
$881$	−244.619	−	1008.33i	−0.277661	−	1.14453i	0.646618	−	0.762814i	$-0.276183\pi$
$882$	−5.05223	−	26.2135i	−0.00572816	−	0.0297205i
$883$	358.092	−	455.351i	0.405540	−	0.515686i	−0.539791	−	0.841799i	$-0.681497\pi$
$883$	358.092	−	455.351i	0.405540	−	0.515686i	0.945331	+	0.326113i	$0.105739\pi$
$884$	−54.5733	−	136.318i	−0.0617345	−	0.154205i
$885$	101.502	−	222.259i	0.114692	−	0.251140i
$886$	−985.161	−	633.124i	−1.11192	−	0.714587i
$887$	−404.952	+	1170.03i	−0.456541	+	1.31909i	0.448506	+	0.893780i	$0.351956\pi$
$887$	−404.952	+	1170.03i	−0.456541	+	1.31909i	−0.905048	+	0.425310i	$0.860165\pi$
$888$	−131.021	+	183.993i	−0.147546	+	0.207199i
$889$	−77.9859	−	816.705i	−0.0877232	−	0.918679i
$890$	−7.41180	+	155.593i	−0.00832786	+	0.174823i
$891$	92.3032	+	22.3925i	0.103595	+	0.0251319i
$892$	101.184	+	292.352i	0.113435	+	0.327749i
$893$	476.158	+	139.813i	0.533212	+	0.156565i
$894$	412.706	+	393.514i	0.461640	+	0.440173i
$895$	65.4994	+	143.424i	0.0731837	+	0.160250i
$896$	25.9190	−	180.271i	0.0289275	−	0.201195i
$897$	−1234.74	−	117.903i	−1.37652	−	0.131441i
$898$	231.873	+	200.919i	0.258211	+	0.223741i
$899$	−719.424	−	914.822i	−0.800250	−	1.01760i
$900$	43.0482	−	74.5617i	0.0478313	−	0.0828463i
$901$	−237.917	+	137.361i	−0.264059	+	0.152454i
$902$	−393.734	+	983.501i	−0.436512	+	1.09036i
$903$	491.528	+	515.499i	0.544327	+	0.570874i
$904$	552.912	−	285.046i	0.611628	−	0.315316i
$905$	237.073	+	459.857i	0.261959	+	0.508129i
$906$	−59.9731	+	57.1843i	−0.0661955	+	0.0631173i
$907$	−141.532	−	56.6608i	−0.156044	−	0.0624706i	0.292326	−	0.956319i	$-0.405571\pi$
$907$	−141.532	−	56.6608i	−0.156044	−	0.0624706i	−0.448370	+	0.893848i	$0.647995\pi$
$908$	15.5929	+	27.0077i	0.0171728	+	0.0297441i
$909$	−62.8927	−	36.3111i	−0.0691889	−	0.0399462i
$910$	395.883	−	311.326i	0.435036	−	0.342116i
$911$	−102.511	+	118.304i	−0.112526	+	0.129862i	−0.809218	−	0.587508i	$-0.800109\pi$
$911$	−102.511	+	118.304i	−0.112526	+	0.129862i	0.696692	+	0.717370i	$0.254654\pi$
$912$	7.97245	−	83.4913i	0.00874172	−	0.0915474i
$913$	−1083.02	−	155.715i	−1.18622	−	0.170553i
$914$	61.2647	−	27.9787i	0.0670292	−	0.0306112i
$915$	187.298	−	196.432i	0.204697	−	0.214680i
$916$	−39.1811	+	133.438i	−0.0427741	+	0.145675i
$917$	105.478	−	36.5062i	0.115025	−	0.0398105i
$918$	10.3941	−	42.8451i	0.0113226	−	0.0466723i
$919$	517.950	+	24.6730i	0.563602	+	0.0268477i	0.327450	−	0.944868i	$-0.393811\pi$
$919$	517.950	+	24.6730i	0.563602	+	0.0268477i	0.236152	+	0.971716i	$0.424114\pi$
$920$	661.790	−	63.1932i	0.719337	−	0.0686883i
$921$	−490.576	−	349.337i	−0.532655	−	0.379302i
$922$	547.872	+	189.620i	0.594222	+	0.205662i
$923$	−180.614	+	281.041i	−0.195682	+	0.304487i
$924$	−171.961	−	78.5318i	−0.186105	−	0.0849911i
$925$	−284.892	+	114.053i	−0.307991	+	0.123301i
$926$	897.780	+	706.022i	0.969525	+	0.762443i
$927$	491.006	−	94.6336i	0.529672	−	0.102086i
$928$	454.450	−	110.248i	0.489709	−	0.118802i
$929$	−782.681	−	1217.88i	−0.842498	−	1.31095i	−0.948561	−	0.316593i	$-0.897461\pi$
$929$	−782.681	−	1217.88i	−0.842498	−	1.31095i	0.106063	−	0.994359i	$-0.466175\pi$
$930$	44.5928	+	310.150i	0.0479493	+	0.333495i
$931$	1.50757	+	31.6477i	0.00161930	+	0.0339933i
$932$	−82.3218	+	427.126i	−0.0883281	+	0.458290i
$933$	−225.370	−	260.091i	−0.241554	−	0.278768i
$934$	298.490	−	212.554i	0.319583	−	0.227574i
$935$	−113.177	+	33.2318i	−0.121045	+	0.0355420i
$936$	462.499	+	238.435i	0.494123	+	0.254738i
$937$		−	1131.92i		−	1.20803i	−0.796974	−	0.604013i	$-0.793567\pi$
$937$		−	1131.92i		−	1.20803i	0.796974	−	0.604013i	$-0.206433\pi$
$938$	−735.419	−	308.729i	−0.784028	−	0.329136i
$939$	−786.742			−0.837851
$940$	117.842	−	228.582i	0.125364	−	0.243172i
$941$	−105.543	−	359.446i	−0.112160	−	0.381983i	0.884212	−	0.467086i	$-0.154696\pi$
$941$	−105.543	−	359.446i	−0.112160	−	0.381983i	−0.996372	+	0.0851030i	$0.972878\pi$
$942$	−226.837	−	318.548i	−0.240804	−	0.338162i
$943$	−1691.62	+	1465.80i	−1.79388	+	1.55440i
$944$	550.179	+	106.038i	0.582816	+	0.112329i
$945$	−81.3923	+	3.87719i	−0.0861294	+	0.00410285i
$946$	−937.978	+	134.861i	−0.991520	+	0.142559i
$947$	−740.819	+	476.096i	−0.782280	+	0.502741i	−0.869790	−	0.493423i	$-0.835746\pi$
$947$	−740.819	+	476.096i	−0.782280	+	0.502741i	0.0875093	+	0.996164i	$0.472109\pi$
$948$	−53.1312	−	219.010i	−0.0560456	−	0.231023i
$949$	151.998	+	788.638i	0.160166	+	0.831020i
$950$	117.220	−	149.058i	0.123390	−	0.156903i
$951$	−152.847	−	381.794i	−0.160722	−	0.401465i
$952$	−140.554	+	307.770i	−0.147641	+	0.323288i
$953$	−25.3933	−	16.3193i	−0.0266456	−	0.0171241i	0.527250	−	0.849710i	$-0.323223\pi$
$953$	−25.3933	−	16.3193i	−0.0266456	−	0.0171241i	−0.553896	+	0.832586i	$0.686859\pi$
$954$	82.5807	−	238.601i	0.0865625	−	0.250106i
$955$	−125.514	+	176.260i	−0.131429	+	0.184566i
$956$	−34.8180	−	364.631i	−0.0364205	−	0.381413i
$957$	−19.1591	+	402.198i	−0.0200199	+	0.420270i
$958$	1047.66	+	254.160i	1.09359	+	0.265303i
$959$	397.886	+	1149.62i	0.414897	+	1.19877i
$960$	−239.896	−	70.4400i	−0.249892	−	0.0733749i
$961$	−1324.67	−	1263.07i	−1.37843	−	1.31433i
$962$	−199.818	−	437.540i	−0.207711	−	0.454823i
$963$	25.1020	−	174.588i	0.0260664	−	0.181296i
$964$	−215.478	−	20.5756i	−0.223524	−	0.0213440i
$965$	131.490	+	113.937i	0.136259	+	0.118069i
$966$	458.207	+	582.658i	0.474334	+	0.603165i
$967$	−24.7691	+	42.9013i	−0.0256143	+	0.0443653i	−0.878548	−	0.477653i	$-0.841488\pi$
$967$	−24.7691	+	42.9013i	−0.0256143	+	0.0443653i	0.852934	+	0.522019i	$0.174821\pi$
$968$	−72.5861	+	41.9076i	−0.0749857	+	0.0432930i
$969$	−19.4473	+	48.5769i	−0.0200694	+	0.0501310i
$970$	107.874	+	113.135i	0.111210	+	0.116634i
$971$	310.004	−	159.818i	0.319263	−	0.164591i	−0.291145	−	0.956679i	$-0.594036\pi$
$971$	310.004	−	159.818i	0.319263	−	0.164591i	0.610407	+	0.792088i	$0.291006\pi$
$972$	−10.0050	−	19.4070i	−0.0102932	−	0.0199661i
$973$	−1362.46	+	1299.11i	−1.40027	+	1.33516i
$974$	430.697	+	172.425i	0.442194	+	0.177028i
$975$	353.467	+	612.224i	0.362531	+	0.627922i
$976$	539.007	+	311.196i	0.552262	+	0.318848i
$977$	1371.30	−	1078.40i	1.40359	−	1.10379i	0.423348	−	0.905967i	$-0.360855\pi$
$977$	1371.30	−	1078.40i	1.40359	−	1.10379i	0.980237	−	0.197824i	$-0.0633875\pi$
$978$	−329.172	+	379.885i	−0.336577	+	0.388431i
$979$	−45.6357	+	477.918i	−0.0466146	+	0.488170i
$980$	16.2518	+	2.33666i	0.0165835	+	0.00238435i
$981$	−249.039	+	113.732i	−0.253863	+	0.115935i
$982$	−235.757	+	247.255i	−0.240078	+	0.251787i
$983$	377.599	−	1285.99i	0.384130	−	1.30823i	−0.509906	−	0.860230i	$-0.670320\pi$
$983$	377.599	−	1285.99i	0.384130	−	1.30823i	0.894036	−	0.447996i	$-0.147862\pi$
$984$	887.366	−	307.120i	0.901795	−	0.312114i
$985$	97.3617	−	401.331i	0.0988444	−	0.407442i
$986$	186.692	+	8.89322i	0.189343	+	0.00901950i
$987$	1100.61	−	105.095i	1.11510	−	0.106479i
$988$	−130.467	−	92.9048i	−0.132051	−	0.0940332i
$989$	−1892.08	−	654.855i	−1.91312	−	0.662139i
$990$	58.6099	−	91.1988i	0.0592019	−	0.0921200i
$991$	−896.991	−	409.642i	−0.905137	−	0.413362i	−0.0922178	−	0.995739i	$-0.529396\pi$
$991$	−896.991	−	409.642i	−0.905137	−	0.413362i	−0.812919	+	0.582377i	$0.802123\pi$
$992$	1041.24	−	416.849i	1.04964	−	0.420210i
$993$	−319.331	−	251.124i	−0.321582	−	0.252895i
$994$	196.038	−	37.7832i	0.197221	−	0.0380112i
$995$	−635.472	+	154.164i	−0.638665	+	0.154938i
$996$	135.985	+	211.597i	0.136531	+	0.212447i
$997$	−9.58587	−	66.6712i	−0.00961472	−	0.0668718i	0.984449	−	0.175670i	$-0.0562090\pi$
$997$	−9.58587	−	66.6712i	−0.00961472	−	0.0668718i	−0.994064	+	0.108798i	$0.965300\pi$
$998$	13.2498	+	278.147i	0.0132763	+	0.278705i
$999$	−14.7283	+	76.4175i	−0.0147430	+	0.0764940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.n.b.115.4	yes	240
67.7	odd	66	inner	201.3.n.b.7.4	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.n.b.7.4	✓	240	67.7	odd	66	inner
201.3.n.b.115.4	yes	240	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.n (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.738773 + 1.43302i) q^{2} +(-0.487975 - 1.66189i) q^{3} +(0.812467 + 1.14095i) q^{4} +(1.60508 - 1.39081i) q^{5} +(2.74203 + 0.528482i) q^{6} +(-7.37536 + 0.351332i) q^{7} +(-8.61857 + 1.23916i) q^{8} +(-2.52376 + 1.62192i) q^{9} +O(q^{10})\)	\(q+(-0.738773 + 1.43302i) q^{2} +(-0.487975 - 1.66189i) q^{3} +(0.812467 + 1.14095i) q^{4} +(1.60508 - 1.39081i) q^{5} +(2.74203 + 0.528482i) q^{6} +(-7.37536 + 0.351332i) q^{7} +(-8.61857 + 1.23916i) q^{8} +(-2.52376 + 1.62192i) q^{9} +(0.807267 + 3.32760i) q^{10} +(1.99724 + 10.3627i) q^{11} +(1.49967 - 1.90699i) q^{12} +(7.40353 + 18.4931i) q^{13} +(4.94525 - 10.8286i) q^{14} +(-3.09461 - 1.98878i) q^{15} +(2.75897 - 7.97152i) q^{16} +(-3.05265 + 4.28685i) q^{17} +(-0.459761 - 4.81483i) q^{18} +(-0.273139 + 5.73390i) q^{19} +(2.89091 + 0.701328i) q^{20} +(4.18287 + 12.0856i) q^{21} +(-16.3254 - 4.79358i) q^{22} +(-26.0180 - 24.8081i) q^{23} +(6.26500 + 13.7184i) q^{24} +(-2.91594 + 20.2808i) q^{25} +(-31.9705 - 3.05282i) q^{26} +(3.92699 + 3.40276i) q^{27} +(-6.39309 - 8.12947i) q^{28} +(-11.0141 + 19.0770i) q^{29} +(5.13618 - 2.96538i) q^{30} +(-19.6360 + 49.0485i) q^{31} +(-14.6495 - 15.3640i) q^{32} +(16.2470 - 8.37593i) q^{33} +(-3.88792 - 7.54152i) q^{34} +(-11.3494 + 10.8216i) q^{35} +(-3.90100 - 1.56173i) q^{36} +(7.48861 + 12.9706i) q^{37} +(-8.01501 - 4.62747i) q^{38} +(27.1208 - 21.3280i) q^{39} +(-12.1100 + 13.9757i) q^{40} +(5.91850 - 61.9813i) q^{41} +(-20.4091 - 2.93439i) q^{42} +(50.6616 - 23.1364i) q^{43} +(-10.2006 + 10.6981i) q^{44} +(-1.79505 + 6.11338i) q^{45} +(54.7719 - 18.9567i) q^{46} +(20.3814 - 84.0134i) q^{47} +(-14.5941 - 0.695203i) q^{48} +(5.49441 - 0.524653i) q^{49} +(-26.9086 - 19.1615i) q^{50} +(8.61389 + 2.98130i) q^{51} +(-15.0846 + 23.4721i) q^{52} +(47.4847 + 21.6855i) q^{53} +(-7.77737 + 3.11359i) q^{54} +(17.6182 + 13.8551i) q^{55} +(63.1297 - 12.1673i) q^{56} +(9.66240 - 2.34407i) q^{57} +(-19.2008 - 29.8770i) q^{58} +(9.45290 + 65.7464i) q^{59} +(-0.245163 - 5.14661i) q^{60} +(-13.9635 + 72.4495i) q^{61} +(-55.7809 - 64.3745i) q^{62} +(18.0438 - 12.8489i) q^{63} +(65.2146 - 19.1487i) q^{64} +(37.6036 + 19.3860i) q^{65} +29.4702i q^{66} +(-2.07268 - 66.9679i) q^{67} -7.37126 q^{68} +(-28.5322 + 55.3447i) q^{69} +(-7.12298 - 24.2586i) q^{70} +(9.72801 + 13.6611i) q^{71} +(19.7414 - 17.1060i) q^{72} +(39.5902 + 7.63039i) q^{73} +(-24.1196 + 1.14896i) q^{74} +(35.1274 - 5.05056i) q^{75} +(-6.76401 + 4.34697i) q^{76} +(-18.3711 - 75.7268i) q^{77} +(10.5274 + 54.6212i) q^{78} +(57.4231 - 73.0194i) q^{79} +(-6.65849 - 16.6321i) q^{80} +(3.73874 - 8.18669i) q^{81} +(84.4480 + 54.2714i) q^{82} +(-33.9098 + 97.9759i) q^{83} +(-10.3906 + 14.5916i) q^{84} +(1.06244 + 11.1264i) q^{85} +(-4.27254 + 89.6916i) q^{86} +(37.0785 + 8.99515i) q^{87} +(-30.0544 - 86.8365i) q^{88} +(43.6490 + 12.8165i) q^{89} +(-7.43446 - 7.08874i) q^{90} +(-61.1009 - 133.792i) q^{91} +(7.16605 - 49.8409i) q^{92} +(91.0951 + 8.69853i) q^{93} +(105.336 + 91.2739i) q^{94} +(7.53635 + 9.58324i) q^{95} +(-18.3846 + 31.8431i) q^{96} +(39.5366 - 22.8265i) q^{97} +(-3.30729 + 8.26121i) q^{98} +(-21.8480 - 22.9135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 34 q^{4} - 33 q^{6} - 21 q^{7} - 33 q^{8} + 72 q^{9}+O(q^{10}) \) 240 * q - 34 * q^4 - 33 * q^6 - 21 * q^7 - 33 * q^8 + 72 * q^9	\( 240 q - 34 q^{4} - 33 q^{6} - 21 q^{7} - 33 q^{8} + 72 q^{9} + 69 q^{10} - 111 q^{11} - 3 q^{12} - 30 q^{13} - 6 q^{14} - 27 q^{15} + 98 q^{16} - 4 q^{17} + 16 q^{19} - 108 q^{20} + 21 q^{21} + 27 q^{22} + 178 q^{23} + 36 q^{24} + 222 q^{25} - 29 q^{26} - 112 q^{28} - 77 q^{29} + 90 q^{30} + 137 q^{31} + 44 q^{32} + 12 q^{33} - 72 q^{34} - 237 q^{35} + 3 q^{36} + 132 q^{37} + 210 q^{38} - 30 q^{39} + 749 q^{40} - 150 q^{41} - 132 q^{42} - 385 q^{43} + 9 q^{44} - 443 q^{46} - 166 q^{47} - 294 q^{48} - 295 q^{49} - 6 q^{50} + 276 q^{51} - 1804 q^{52} + 176 q^{53} + 199 q^{55} - 1361 q^{56} - 114 q^{57} + 968 q^{58} - 214 q^{59} - 420 q^{60} - 274 q^{61} + 334 q^{62} - 102 q^{63} + 683 q^{64} - 224 q^{65} + 47 q^{67} + 870 q^{68} + 27 q^{69} - 44 q^{70} + 271 q^{71} + 264 q^{72} + 594 q^{73} - 1289 q^{74} + 396 q^{75} + 494 q^{76} + 1360 q^{77} + 441 q^{78} + 1023 q^{79} + 15 q^{80} - 216 q^{81} - 316 q^{82} - 225 q^{83} + 1527 q^{84} - 153 q^{85} - 91 q^{86} - 1676 q^{88} + 871 q^{89} - 207 q^{90} - 692 q^{91} - 488 q^{92} - 390 q^{93} + 440 q^{94} - 531 q^{95} - 33 q^{96} + 84 q^{97} + 85 q^{98} + 36 q^{99}+O(q^{100}) \) 240 * q - 34 * q^4 - 33 * q^6 - 21 * q^7 - 33 * q^8 + 72 * q^9 + 69 * q^10 - 111 * q^11 - 3 * q^12 - 30 * q^13 - 6 * q^14 - 27 * q^15 + 98 * q^16 - 4 * q^17 + 16 * q^19 - 108 * q^20 + 21 * q^21 + 27 * q^22 + 178 * q^23 + 36 * q^24 + 222 * q^25 - 29 * q^26 - 112 * q^28 - 77 * q^29 + 90 * q^30 + 137 * q^31 + 44 * q^32 + 12 * q^33 - 72 * q^34 - 237 * q^35 + 3 * q^36 + 132 * q^37 + 210 * q^38 - 30 * q^39 + 749 * q^40 - 150 * q^41 - 132 * q^42 - 385 * q^43 + 9 * q^44 - 443 * q^46 - 166 * q^47 - 294 * q^48 - 295 * q^49 - 6 * q^50 + 276 * q^51 - 1804 * q^52 + 176 * q^53 + 199 * q^55 - 1361 * q^56 - 114 * q^57 + 968 * q^58 - 214 * q^59 - 420 * q^60 - 274 * q^61 + 334 * q^62 - 102 * q^63 + 683 * q^64 - 224 * q^65 + 47 * q^67 + 870 * q^68 + 27 * q^69 - 44 * q^70 + 271 * q^71 + 264 * q^72 + 594 * q^73 - 1289 * q^74 + 396 * q^75 + 494 * q^76 + 1360 * q^77 + 441 * q^78 + 1023 * q^79 + 15 * q^80 - 216 * q^81 - 316 * q^82 - 225 * q^83 + 1527 * q^84 - 153 * q^85 - 91 * q^86 - 1676 * q^88 + 871 * q^89 - 207 * q^90 - 692 * q^91 - 488 * q^92 - 390 * q^93 + 440 * q^94 - 531 * q^95 - 33 * q^96 + 84 * q^97 + 85 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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