LMFDB - Embedded newform 23.3.d.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,3,Mod(5,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("23.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	23.d (of order $22$, degree $10$, 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:	$0.626704608029$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	23.19
Dual form			23.3.d.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.282292 - 0.618133i) q^{2} +(0.844537 - 0.247978i) q^{3} +(2.31704 - 2.67401i) q^{4} +(-3.24760 + 5.05336i) q^{5} +(-0.391690 - 0.452034i) q^{6} +(-3.20136 + 0.460286i) q^{7} +(-4.91504 - 1.44319i) q^{8} +(-6.91953 + 4.44691i) q^{9} +O(q^{10})$	\(q+(-0.282292 - 0.618133i) q^{2} +(0.844537 - 0.247978i) q^{3} +(2.31704 - 2.67401i) q^{4} +(-3.24760 + 5.05336i) q^{5} +(-0.391690 - 0.452034i) q^{6} +(-3.20136 + 0.460286i) q^{7} +(-4.91504 - 1.44319i) q^{8} +(-6.91953 + 4.44691i) q^{9} +(4.04042 + 0.580925i) q^{10} +(10.2164 + 4.66569i) q^{11} +(1.29373 - 2.83288i) q^{12} +(2.01084 - 13.9857i) q^{13} +(1.18824 + 1.84893i) q^{14} +(-1.48959 + 5.07308i) q^{15} +(-1.51877 - 10.5633i) q^{16} +(9.44556 - 8.18463i) q^{17} +(4.70212 + 3.02187i) q^{18} +(5.84675 + 5.06623i) q^{19} +(5.98792 + 20.3930i) q^{20} +(-2.58952 + 1.18259i) q^{21} -7.63220i q^{22} +(-22.9998 + 0.0832022i) q^{23} -4.50881 q^{24} +(-4.60420 - 10.0818i) q^{25} +(-9.21266 + 2.70508i) q^{26} +(-9.92868 + 11.4583i) q^{27} +(-6.18687 + 9.62696i) q^{28} +(-20.6546 - 23.8367i) q^{29} +(3.55634 - 0.511325i) q^{30} +(58.8820 + 17.2893i) q^{31} +(-23.3382 + 14.9986i) q^{32} +(9.78514 + 1.40689i) q^{33} +(-7.72560 - 3.52816i) q^{34} +(8.07073 - 17.6724i) q^{35} +(-4.14176 + 28.8066i) q^{36} +(-26.1385 - 40.6723i) q^{37} +(1.48112 - 5.04423i) q^{38} +(-1.76992 - 12.3101i) q^{39} +(23.2550 - 20.1506i) q^{40} +(38.1340 + 24.5073i) q^{41} +(1.46200 + 1.26683i) q^{42} +(16.7324 + 56.9854i) q^{43} +(36.1480 - 16.5082i) q^{44} -49.4087i q^{45} +(6.54411 + 14.1935i) q^{46} +3.02235 q^{47} +(-3.90212 - 8.54445i) q^{48} +(-36.9783 + 10.8578i) q^{49} +(-4.93216 + 5.69202i) q^{50} +(5.94751 - 9.25451i) q^{51} +(-32.7387 - 37.7824i) q^{52} +(-41.9463 + 6.03096i) q^{53} +(9.88555 + 2.90266i) q^{54} +(-56.7563 + 36.4750i) q^{55} +(16.3991 + 2.35783i) q^{56} +(6.19411 + 2.82875i) q^{57} +(-8.90363 + 19.4962i) q^{58} +(4.28281 - 29.7876i) q^{59} +(10.1140 + 15.7377i) q^{60} +(-26.7949 + 91.2550i) q^{61} +(-5.93481 - 41.2775i) q^{62} +(20.1050 - 17.4211i) q^{63} +(-20.0518 - 12.8865i) q^{64} +(64.1443 + 55.5814i) q^{65} +(-1.89262 - 6.44567i) q^{66} +(-30.1105 + 13.7510i) q^{67} -44.2217i q^{68} +(-19.4036 + 5.77373i) q^{69} -13.2022 q^{70} +(-10.9275 - 23.9279i) q^{71} +(40.4275 - 11.8706i) q^{72} +(53.2081 - 61.4055i) q^{73} +(-17.7622 + 27.6385i) q^{74} +(-6.38848 - 7.37270i) q^{75} +(27.0943 - 3.89557i) q^{76} +(-34.8540 - 10.2341i) q^{77} +(-7.10963 + 4.56908i) q^{78} +(86.0607 + 12.3737i) q^{79} +(58.3124 + 26.6304i) q^{80} +(25.2084 - 55.1986i) q^{81} +(4.38382 - 30.4901i) q^{82} +(-0.815582 - 1.26907i) q^{83} +(-2.83776 + 9.66453i) q^{84} +(10.6845 + 74.3122i) q^{85} +(30.5012 - 26.4294i) q^{86} +(-23.3546 - 15.0091i) q^{87} +(-43.4807 - 37.6763i) q^{88} +(-11.3052 - 38.5019i) q^{89} +(-30.5412 + 13.9477i) q^{90} +45.6987i q^{91} +(-53.0692 + 61.6946i) q^{92} +54.0153 q^{93} +(-0.853185 - 1.86821i) q^{94} +(-44.5894 + 13.0926i) q^{95} +(-15.9906 + 18.4542i) q^{96} +(-15.4923 + 24.1065i) q^{97} +(17.1503 + 19.7925i) q^{98} +(-91.4408 + 13.1472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) $ 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.282292	−	0.618133i	−0.141146	−	0.309067i	0.825836	−	0.563910i	$-0.190703\pi$
$2$	−0.282292	−	0.618133i	−0.141146	−	0.309067i	−0.966982	+	0.254843i	$0.917976\pi$
$3$	0.844537	−	0.247978i	0.281512	−	0.0826594i	−0.137928	−	0.990442i	$-0.544044\pi$
$3$	0.844537	−	0.247978i	0.281512	−	0.0826594i	0.419441	+	0.907783i	$0.362226\pi$
$4$	2.31704	−	2.67401i	0.579261	−	0.668502i
$5$	−3.24760	+	5.05336i	−0.649520	+	1.01067i	0.347804	+	0.937567i	$0.386927\pi$
$5$	−3.24760	+	5.05336i	−0.649520	+	1.01067i	−0.997324	+	0.0731054i	$0.976709\pi$
$6$	−0.391690	−	0.452034i	−0.0652816	−	0.0753390i
$7$	−3.20136	+	0.460286i	−0.457337	+	0.0657551i	−0.367133	−	0.930168i	$-0.619661\pi$
$7$	−3.20136	+	0.460286i	−0.457337	+	0.0657551i	−0.0902032	+	0.995923i	$0.528752\pi$
$8$	−4.91504	−	1.44319i	−0.614380	−	0.180398i
$9$	−6.91953	+	4.44691i	−0.768837	+	0.494102i
$10$	4.04042	+	0.580925i	0.404042	+	0.0580925i
$11$	10.2164	+	4.66569i	0.928766	+	0.424153i	0.821585	−	0.570086i	$-0.193090\pi$
$11$	10.2164	+	4.66569i	0.928766	+	0.424153i	0.107181	+	0.994239i	$0.465817\pi$
$12$	1.29373	−	2.83288i	0.107811	−	0.236073i
$13$	2.01084	−	13.9857i	0.154680	−	1.07582i	−0.753562	−	0.657377i	$-0.771666\pi$
$13$	2.01084	−	13.9857i	0.154680	−	1.07582i	0.908242	−	0.418445i	$-0.137425\pi$
$14$	1.18824	+	1.84893i	0.0848740	+	0.132066i
$15$	−1.48959	+	5.07308i	−0.0993061	+	0.338206i
$16$	−1.51877	−	10.5633i	−0.0949232	−	0.660205i
$17$	9.44556	−	8.18463i	0.555621	−	0.481449i	−0.331200	−	0.943560i	$-0.607454\pi$
$17$	9.44556	−	8.18463i	0.555621	−	0.481449i	0.886822	+	0.462112i	$0.152908\pi$
$18$	4.70212	+	3.02187i	0.261229	+	0.167881i
$19$	5.84675	+	5.06623i	0.307723	+	0.266644i	0.795007	−	0.606600i	$-0.207467\pi$
$19$	5.84675	+	5.06623i	0.307723	+	0.266644i	−0.487284	+	0.873244i	$0.662012\pi$
$20$	5.98792	+	20.3930i	0.299396	+	1.01965i
$21$	−2.58952	+	1.18259i	−0.123311	+	0.0563140i
$22$		−	7.63220i		−	0.346918i
$23$	−22.9998	+	0.0832022i	−0.999993	+	0.00361749i
$23$	−22.9998	+	0.0832022i	−0.999993	+	0.00361749i
$24$	−4.50881			−0.187867
$25$	−4.60420	−	10.0818i	−0.184168	−	0.403272i
$26$	−9.21266	+	2.70508i	−0.354333	+	0.104042i
$27$	−9.92868	+	11.4583i	−0.367729	+	0.424382i
$28$	−6.18687	+	9.62696i	−0.220960	+	0.343820i
$29$	−20.6546	−	23.8367i	−0.712229	−	0.821956i	0.278121	−	0.960546i	$-0.410288\pi$
$29$	−20.6546	−	23.8367i	−0.712229	−	0.821956i	−0.990350	+	0.138590i	$0.955743\pi$
$30$	3.55634	−	0.511325i	0.118545	−	0.0170442i
$31$	58.8820	+	17.2893i	1.89942	+	0.557719i	0.989840	+	0.142186i	$0.0454130\pi$
$31$	58.8820	+	17.2893i	1.89942	+	0.557719i	0.909578	+	0.415534i	$0.136405\pi$
$32$	−23.3382	+	14.9986i	−0.729319	+	0.468705i
$33$	9.78514	+	1.40689i	0.296519	+	0.0426330i
$34$	−7.72560	−	3.52816i	−0.227223	−	0.103769i
$35$	8.07073	−	17.6724i	0.230592	−	0.504927i
$36$	−4.14176	+	28.8066i	−0.115049	+	0.800183i
$37$	−26.1385	−	40.6723i	−0.706446	−	1.09925i	−0.990105	−	0.140326i	$-0.955185\pi$
$37$	−26.1385	−	40.6723i	−0.706446	−	1.09925i	0.283660	−	0.958925i	$-0.408451\pi$
$38$	1.48112	−	5.04423i	0.0389768	−	0.132743i
$39$	−1.76992	−	12.3101i	−0.0453826	−	0.315643i
$40$	23.2550	−	20.1506i	0.581376	−	0.503765i
$41$	38.1340	+	24.5073i	0.930098	+	0.597738i	0.915571	−	0.402157i	$-0.131739\pi$
$41$	38.1340	+	24.5073i	0.930098	+	0.597738i	0.0145274	+	0.999894i	$0.495376\pi$
$42$	1.46200	+	1.26683i	0.0348096	+	0.0301627i
$43$	16.7324	+	56.9854i	0.389126	+	1.32524i	0.888508	+	0.458860i	$0.151742\pi$
$43$	16.7324	+	56.9854i	0.389126	+	1.32524i	−0.499382	+	0.866382i	$0.666440\pi$
$44$	36.1480	−	16.5082i	0.821545	−	0.375187i
$45$		−	49.4087i		−	1.09797i
$46$	6.54411	+	14.1935i	0.142263	+	0.308554i
$47$	3.02235			0.0643053			0.0321526	−	0.999483i	$-0.489764\pi$
$47$	3.02235			0.0643053			0.0321526	+	0.999483i	$0.489764\pi$
$48$	−3.90212	−	8.54445i	−0.0812942	−	0.178009i
$49$	−36.9783	+	10.8578i	−0.754660	+	0.221588i
$50$	−4.93216	+	5.69202i	−0.0986432	+	0.113840i
$51$	5.94751	−	9.25451i	0.116618	−	0.181461i
$52$	−32.7387	−	37.7824i	−0.629590	−	0.726585i
$53$	−41.9463	+	6.03096i	−0.791439	+	0.113792i	−0.526166	−	0.850382i	$-0.676371\pi$
$53$	−41.9463	+	6.03096i	−0.791439	+	0.113792i	−0.265273	+	0.964173i	$0.585462\pi$
$54$	9.88555	+	2.90266i	0.183066	+	0.0537530i
$55$	−56.7563	+	36.4750i	−1.03193	+	0.663182i
$56$	16.3991	+	2.35783i	0.292841	+	0.0421041i
$57$	6.19411	+	2.82875i	0.108669	+	0.0496273i
$58$	−8.90363	+	19.4962i	−0.153511	+	0.336142i
$59$	4.28281	−	29.7876i	0.0725900	−	0.504875i	−0.920795	−	0.390046i	$-0.872459\pi$
$59$	4.28281	−	29.7876i	0.0725900	−	0.504875i	0.993385	−	0.114829i	$-0.0366319\pi$
$60$	10.1140	+	15.7377i	0.168567	+	0.262296i
$61$	−26.7949	+	91.2550i	−0.439261	+	1.49598i	0.381314	+	0.924445i	$0.375472\pi$
$61$	−26.7949	+	91.2550i	−0.439261	+	1.49598i	−0.820575	+	0.571539i	$0.806347\pi$
$62$	−5.93481	−	41.2775i	−0.0957228	−	0.665767i
$63$	20.1050	−	17.4211i	0.319128	−	0.276526i
$64$	−20.0518	−	12.8865i	−0.313310	−	0.201352i
$65$	64.1443	+	55.5814i	0.986836	+	0.855098i
$66$	−1.89262	−	6.44567i	−0.0286761	−	0.0976617i
$67$	−30.1105	+	13.7510i	−0.449410	+	0.205239i	−0.627246	−	0.778821i	$-0.715818\pi$
$67$	−30.1105	+	13.7510i	−0.449410	+	0.205239i	0.177835	+	0.984060i	$0.443091\pi$
$68$		−	44.2217i		−	0.650319i
$69$	−19.4036	+	5.77373i	−0.281211	+	0.0836773i
$70$	−13.2022			−0.188603
$71$	−10.9275	−	23.9279i	−0.153909	−	0.337013i	0.816934	−	0.576732i	$-0.195672\pi$
$71$	−10.9275	−	23.9279i	−0.153909	−	0.337013i	−0.970842	+	0.239718i	$0.922945\pi$
$72$	40.4275	−	11.8706i	0.561493	−	0.164869i
$73$	53.2081	−	61.4055i	0.728879	−	0.841171i	−0.263466	−	0.964669i	$-0.584866\pi$
$73$	53.2081	−	61.4055i	0.728879	−	0.841171i	0.992345	+	0.123498i	$0.0394112\pi$
$74$	−17.7622	+	27.6385i	−0.240030	+	0.373494i
$75$	−6.38848	−	7.37270i	−0.0851797	−	0.0983026i
$76$	27.0943	−	3.89557i	0.356504	−	0.0512576i
$77$	−34.8540	−	10.2341i	−0.452649	−	0.132910i
$78$	−7.10963	+	4.56908i	−0.0911491	+	0.0585780i
$79$	86.0607	+	12.3737i	1.08938	+	0.156629i	0.663517	−	0.748161i	$-0.269063\pi$
$79$	86.0607	+	12.3737i	1.08938	+	0.156629i	0.425859	+	0.904790i	$0.359972\pi$
$80$	58.3124	+	26.6304i	0.728906	+	0.332880i
$81$	25.2084	−	55.1986i	0.311214	−	0.681464i
$82$	4.38382	−	30.4901i	0.0534612	−	0.371831i
$83$	−0.815582	−	1.26907i	−0.00982628	−	0.0152900i	0.836306	−	0.548263i	$-0.184711\pi$
$83$	−0.815582	−	1.26907i	−0.00982628	−	0.0152900i	−0.846132	+	0.532973i	$0.821075\pi$
$84$	−2.83776	+	9.66453i	−0.0337829	+	0.115054i
$85$	10.6845	+	74.3122i	0.125700	+	0.874262i
$86$	30.5012	−	26.4294i	0.354665	−	0.307319i
$87$	−23.3546	−	15.0091i	−0.268443	−	0.172518i
$88$	−43.4807	−	37.6763i	−0.494099	−	0.428139i
$89$	−11.3052	−	38.5019i	−0.127025	−	0.432606i	0.871282	−	0.490783i	$-0.163289\pi$
$89$	−11.3052	−	38.5019i	−0.127025	−	0.432606i	−0.998306	+	0.0581774i	$0.981471\pi$
$90$	−30.5412	+	13.9477i	−0.339346	+	0.154974i
$91$			45.6987i			0.502184i
$92$	−53.0692	+	61.6946i	−0.576839	+	0.670594i
$93$	54.0153			0.580810
$94$	−0.853185	−	1.86821i	−0.00907644	−	0.0198746i
$95$	−44.5894	+	13.0926i	−0.469362	+	0.137817i
$96$	−15.9906	+	18.4542i	−0.166569	+	0.192231i
$97$	−15.4923	+	24.1065i	−0.159714	+	0.248520i	−0.911883	−	0.410450i	$-0.865371\pi$
$97$	−15.4923	+	24.1065i	−0.159714	+	0.248520i	0.752169	+	0.658971i	$0.229008\pi$
$98$	17.1503	+	19.7925i	0.175003	+	0.201964i
$99$	−91.4408	+	13.1472i	−0.923645	+	0.132800i
$100$	−37.6269	−	11.0483i	−0.376269	−	0.110483i
$101$	16.0807	−	10.3344i	0.159214	−	0.102321i	−0.458608	−	0.888639i	$-0.651652\pi$
$101$	16.0807	−	10.3344i	0.159214	−	0.102321i	0.617822	+	0.786318i	$0.288015\pi$
$102$	−7.39946	−	1.06388i	−0.0725437	−	0.0104302i
$103$	−65.6925	−	30.0007i	−0.637791	−	0.291269i	0.0701549	−	0.997536i	$-0.477651\pi$
$103$	−65.6925	−	30.0007i	−0.637791	−	0.291269i	−0.707946	+	0.706267i	$0.750378\pi$
$104$	−30.0673	+	65.8382i	−0.289109	+	0.633060i
$105$	2.43365	−	16.9264i	0.0231776	−	0.161204i
$106$	15.5690	+	24.2259i	0.146878	+	0.228546i
$107$	41.4606	−	141.202i	0.387482	−	1.31964i	−0.502867	−	0.864364i	$-0.667722\pi$
$107$	41.4606	−	141.202i	0.387482	−	1.31964i	0.890349	−	0.455278i	$-0.150460\pi$
$108$	7.63445	+	53.0988i	0.0706894	+	0.491655i
$109$	−38.0406	+	32.9623i	−0.348996	+	0.302407i	−0.811664	−	0.584125i	$-0.801438\pi$
$109$	−38.0406	+	32.9623i	−0.348996	+	0.302407i	0.462668	+	0.886532i	$0.346892\pi$
$110$	38.5683	+	24.7863i	0.350621	+	0.225330i
$111$	−32.1608	−	27.8675i	−0.289737	−	0.251058i
$112$	9.72425	+	33.1178i	0.0868237	+	0.295694i
$113$	105.316	−	48.0963i	0.932001	−	0.425631i	0.109238	−	0.994016i	$-0.465159\pi$
$113$	105.316	−	48.0963i	0.932001	−	0.425631i	0.822763	+	0.568385i	$0.192432\pi$
$114$		−	4.62732i		−	0.0405905i
$115$	74.2738	−	116.497i	0.645859	−	1.01302i
$116$	−111.597			−0.962046
$117$	48.2791	+	105.716i	0.412642	+	0.903559i
$118$	−19.6217	+	5.76146i	−0.166286	+	0.0488259i
$119$	−26.4713	+	30.5496i	−0.222448	+	0.256719i
$120$	14.6428	−	22.7847i	0.122023	−	0.189872i
$121$	3.36862	+	3.88759i	0.0278398	+	0.0321289i
$122$	63.9718	−	9.19775i	0.524359	−	0.0753914i
$123$	38.2828	+	11.2409i	0.311243	+	0.0913891i
$124$	182.664	−	117.391i	1.47309	−	0.946701i
$125$	−82.7455	−	11.8970i	−0.661964	−	0.0951761i
$126$	−16.4441	−	7.50975i	−0.130508	−	0.0596012i
$127$	16.6630	−	36.4869i	0.131205	−	0.287298i	−0.832615	−	0.553852i	$-0.813157\pi$
$127$	16.6630	−	36.4869i	0.131205	−	0.287298i	0.963820	+	0.266553i	$0.0858848\pi$
$128$	−18.0976	+	125.872i	−0.141388	+	0.983372i
$129$	28.2623	+	43.9770i	0.219088	+	0.340907i
$130$	16.2493	−	55.3399i	0.124994	−	0.425692i
$131$	−10.4402	−	72.6133i	−0.0796963	−	0.554300i	−0.990077	−	0.140528i	$-0.955120\pi$
$131$	−10.4402	−	72.6133i	−0.0796963	−	0.554300i	0.910380	−	0.413772i	$-0.135789\pi$
$132$	26.4346	−	22.9057i	0.200262	−	0.173528i
$133$	−21.0494	−	13.5276i	−0.158266	−	0.101712i
$134$	16.9999	+	14.7305i	0.126865	+	0.109929i
$135$	−25.6586	−	87.3852i	−0.190064	−	0.647298i
$136$	−58.2373	+	26.5961i	−0.428215	+	0.195559i
$137$			264.626i			1.93157i	0.259335	+	0.965787i	$0.416497\pi$
$137$			264.626i			1.93157i	−0.259335	+	0.965787i	$0.583503\pi$
$138$	9.04641	+	10.3641i	0.0655537	+	0.0751023i
$139$	41.1911			0.296339			0.148169	−	0.988962i	$-0.452662\pi$
$139$	41.1911			0.296339			0.148169	+	0.988962i	$0.452662\pi$
$140$	−28.5560	−	62.5290i	−0.203972	−	0.446636i
$141$	2.55248	−	0.749477i	0.0181027	−	0.00531544i
$142$	−11.7059	+	13.5093i	−0.0824360	+	0.0951362i
$143$	85.7964	−	133.502i	0.599975	−	0.933579i
$144$	57.4832	+	66.3391i	0.399189	+	0.460688i
$145$	187.534	−	26.9633i	1.29333	−	0.185953i
$146$	−52.9770	−	15.5555i	−0.362856	−	0.106544i
$147$	−28.5371	+	18.3396i	−0.194130	+	0.124760i
$148$	−169.322	−	24.3448i	−1.14407	−	0.164492i
$149$	−164.873	−	75.2952i	−1.10653	−	0.505337i	−0.223527	−	0.974698i	$-0.571757\pi$
$149$	−164.873	−	75.2952i	−1.10653	−	0.505337i	−0.883006	+	0.469361i	$0.844484\pi$
$150$	−2.75389	+	6.03019i	−0.0183593	+	0.0402012i
$151$	−3.40068	+	23.6523i	−0.0225211	+	0.156638i	−0.997979	−	0.0635499i	$-0.979758\pi$
$151$	−3.40068	+	23.6523i	−0.0225211	+	0.156638i	0.975458	+	0.220187i	$0.0706669\pi$
$152$	−21.4255	−	33.3387i	−0.140957	−	0.219334i
$153$	−28.9626	+	98.6374i	−0.189298	+	0.644689i
$154$	3.51299	+	24.4334i	0.0228116	+	0.158658i
$155$	−278.594	+	241.403i	−1.79738	+	1.55744i
$156$	−37.0182	−	23.7902i	−0.237296	−	0.152501i
$157$	−38.1039	−	33.0172i	−0.242700	−	0.210301i	0.525014	−	0.851094i	$-0.324060\pi$
$157$	−38.1039	−	33.0172i	−0.242700	−	0.210301i	−0.767714	+	0.640793i	$0.778606\pi$
$158$	−16.6457	−	56.6900i	−0.105352	−	0.358797i
$159$	−33.9296	+	15.4951i	−0.213394	+	0.0974537i
$160$		−	166.646i		−	1.04154i
$161$	73.5924	−	10.8529i	0.457096	−	0.0674091i
$162$	−41.2362			−0.254545
$163$	12.1006	+	26.4966i	0.0742368	+	0.162556i	0.943112	−	0.332475i	$-0.107884\pi$
$163$	12.1006	+	26.4966i	0.0742368	+	0.162556i	−0.868875	+	0.495031i	$0.835157\pi$
$164$	153.891	−	45.1864i	0.938359	−	0.275527i
$165$	−38.8877	+	44.8788i	−0.235683	+	0.271993i
$166$	−0.554222	+	0.862386i	−0.00333869	+	0.00519510i
$167$	178.580	+	206.093i	1.06934	+	1.23409i	0.971036	+	0.238933i	$0.0767976\pi$
$167$	178.580	+	206.093i	1.06934	+	1.23409i	0.0983081	+	0.995156i	$0.468657\pi$
$168$	14.4343	−	2.07534i	0.0859185	−	0.0123532i
$169$	−29.4016	−	8.63309i	−0.173974	−	0.0510834i
$170$	42.9187	−	27.5822i	0.252463	−	0.162248i
$171$	−62.9859	−	9.05600i	−0.368338	−	0.0529591i
$172$	191.149	+	87.2950i	1.11133	+	0.507529i
$173$	−47.1604	+	103.267i	−0.272603	+	0.596918i	−0.995576	−	0.0939583i	$-0.970048\pi$
$173$	−47.1604	+	103.267i	−0.272603	+	0.596918i	0.722973	+	0.690877i	$0.242775\pi$
$174$	−2.68480	+	18.6732i	−0.0154299	+	0.107317i
$175$	19.3802	+	30.1562i	0.110744	+	0.172321i
$176$	33.7685	−	115.005i	0.191867	−	0.653438i
$177$	−3.76969	−	26.2188i	−0.0212977	−	0.148129i
$178$	−20.6080	+	17.8569i	−0.115775	+	0.100320i
$179$	−105.122	−	67.5578i	−0.587274	−	0.377418i	0.213000	−	0.977052i	$-0.431676\pi$
$179$	−105.122	−	67.5578i	−0.587274	−	0.377418i	−0.800274	+	0.599634i	$0.795313\pi$
$180$	−132.119	−	114.482i	−0.733996	−	0.636012i
$181$	−76.3685	−	260.087i	−0.421925	−	1.43695i	−0.846906	−	0.531743i	$-0.821537\pi$
$181$	−76.3685	−	260.087i	−0.421925	−	1.43695i	0.424980	−	0.905203i	$-0.360281\pi$
$182$	28.2479	−	12.9004i	0.155208	−	0.0708812i
$183$			83.7128i			0.457447i
$184$	113.165	+	32.7841i	0.615029	+	0.178175i
$185$	290.419			1.56983
$186$	−15.2481	−	33.3887i	−0.0819790	−	0.179509i
$187$	134.687	−	39.5476i	0.720250	−	0.211485i
$188$	7.00291	−	8.08179i	0.0372495	−	0.0429882i
$189$	26.5111	−	41.2522i	0.140271	−	0.218265i
$190$	20.6802	+	23.8663i	0.108843	+	0.125612i
$191$	−76.8547	+	11.0500i	−0.402381	+	0.0578536i	−0.340534	−	0.940232i	$-0.610608\pi$
$191$	−76.8547	+	11.0500i	−0.402381	+	0.0578536i	−0.0618464	+	0.998086i	$0.519699\pi$
$192$	−20.1301	−	5.91072i	−0.104844	−	0.0307850i
$193$	71.3848	−	45.8762i	0.369870	−	0.237701i	−0.342481	−	0.939525i	$-0.611267\pi$
$193$	71.3848	−	45.8762i	0.369870	−	0.237701i	0.712350	+	0.701824i	$0.247631\pi$
$194$	19.2743	+	2.77123i	0.0993523	+	0.0142847i
$195$	67.9552	+	31.0341i	0.348488	+	0.159149i
$196$	−56.6465	+	124.038i	−0.289013	+	0.632849i
$197$	30.3926	−	211.385i	0.154277	−	1.07302i	−0.754668	−	0.656107i	$-0.772202\pi$
$197$	30.3926	−	211.385i	0.154277	−	1.07302i	0.908945	−	0.416915i	$-0.136889\pi$
$198$	33.9397	+	52.8113i	0.171413	+	0.266724i
$199$	−3.89229	+	13.2559i	−0.0195593	+	0.0666127i	−0.968694	−	0.248256i	$-0.920142\pi$
$199$	−3.89229	+	13.2559i	−0.0195593	+	0.0666127i	0.949135	+	0.314869i	$0.101961\pi$
$200$	8.07993	+	56.1971i	0.0403996	+	0.280986i
$201$	−22.0195	+	19.0800i	−0.109550	+	0.0949253i
$202$	−10.9275	−	7.02267i	−0.0540964	−	0.0347657i
$203$	77.0946	+	66.8028i	0.379776	+	0.329078i
$204$	−10.9660	−	37.3468i	−0.0537550	−	0.183073i
$205$	−247.688	+	113.115i	−1.20823	+	0.551782i
$206$			49.0757i			0.238231i
$207$	158.778	−	102.854i	0.767045	−	0.496880i
$208$	−150.789			−0.724946
$209$	36.0954	+	79.0379i	0.172705	+	0.378172i
$210$	−11.1498	+	3.27387i	−0.0530941	+	0.0155898i
$211$	54.5636	−	62.9698i	0.258595	−	0.298435i	−0.611575	−	0.791187i	$-0.709464\pi$
$211$	54.5636	−	62.9698i	0.258595	−	0.298435i	0.870170	+	0.492752i	$0.164009\pi$
$212$	−81.0645	+	126.139i	−0.382380	+	0.594994i
$213$	−15.1623	−	17.4982i	−0.0711845	−	0.0821513i
$214$	−98.9855	+	14.2320i	−0.462549	+	0.0665045i
$215$	−342.308	−	100.511i	−1.59213	−	0.467492i
$216$	65.3364	−	41.9891i	0.302483	−	0.194394i
$217$	−196.460	−	28.2467i	−0.905346	−	0.130169i
$218$	31.1137	+	14.2091i	0.142723	+	0.0651795i
$219$	29.7090	−	65.0536i	0.135657	−	0.297048i
$220$	−33.9721	+	236.281i	−0.154419	+	1.07400i
$221$	−95.4741	−	148.561i	−0.432010	−	0.672220i
$222$	−8.14708	+	27.7464i	−0.0366986	+	0.124984i
$223$	15.2776	+	106.258i	0.0685094	+	0.476493i	0.994976	+	0.100116i	$0.0319213\pi$
$223$	15.2776	+	106.258i	0.0685094	+	0.476493i	−0.926466	+	0.376378i	$0.877170\pi$
$224$	67.8103	−	58.7579i	0.302724	−	0.262312i
$225$	76.6918	+	49.2868i	0.340852	+	0.219052i
$226$	−59.4598	−	51.5222i	−0.263096	−	0.227974i
$227$	53.0998	+	180.841i	0.233920	+	0.796657i	0.989864	+	0.142021i	$0.0453600\pi$
$227$	53.0998	+	180.841i	0.233920	+	0.796657i	−0.755944	+	0.654636i	$0.772822\pi$
$228$	21.9161	−	10.0088i	0.0961233	−	0.0438981i
$229$			167.091i			0.729653i	0.931076	+	0.364826i	$0.118872\pi$
$229$			167.091i			0.729653i	−0.931076	+	0.364826i	$0.881128\pi$
$230$	−92.9775	−	13.0250i	−0.404250	−	0.0566305i
$231$	−31.9733			−0.138412
$232$	67.1176	+	146.967i	0.289300	+	0.633478i
$233$	143.837	−	42.2344i	0.617326	−	0.181263i	0.0419064	−	0.999122i	$-0.486657\pi$
$233$	143.837	−	42.2344i	0.617326	−	0.181263i	0.575420	+	0.817858i	$0.304839\pi$
$234$	51.7181	−	59.6858i	0.221017	−	0.255068i
$235$	−9.81538	+	15.2730i	−0.0417676	+	0.0649916i
$236$	−69.7289	−	80.4714i	−0.295461	−	0.340981i
$237$	75.7498	−	10.8912i	0.319620	−	0.0459543i
$238$	26.3564	+	7.73892i	0.110741	+	0.0325165i
$239$	64.8270	−	41.6618i	0.271243	−	0.174317i	−0.397948	−	0.917408i	$-0.630277\pi$
$239$	64.8270	−	41.6618i	0.271243	−	0.174317i	0.669190	+	0.743091i	$0.266641\pi$
$240$	55.8508	+	8.03013i	0.232711	+	0.0334589i
$241$	−254.146	−	116.065i	−1.05455	−	0.481596i	−0.188768	−	0.982022i	$-0.560449\pi$
$241$	−254.146	−	116.065i	−1.05455	−	0.481596i	−0.865779	+	0.500426i	$0.833177\pi$
$242$	1.45212	−	3.17969i	0.00600048	−	0.0131392i
$243$	27.0207	−	187.933i	0.111196	−	0.773387i
$244$	181.932	+	283.092i	0.745623	+	1.16021i
$245$	65.2223	−	222.127i	0.266213	−	0.906640i
$246$	−3.85859	−	26.8371i	−0.0156853	−	0.109094i
$247$	82.6116	−	71.5834i	0.334460	−	0.289811i
$248$	−264.456	−	169.955i	−1.06635	−	0.685304i
$249$	−1.00349	−	0.869529i	−0.00403008	−	0.00349208i
$250$	16.0045	+	54.5062i	0.0640179	+	0.218025i
$251$	111.327	−	50.8411i	0.443532	−	0.202554i	−0.181114	−	0.983462i	$-0.557970\pi$
$251$	111.327	−	50.8411i	0.443532	−	0.202554i	0.624646	+	0.780908i	$0.285243\pi$
$252$		−	94.1266i		−	0.373518i
$253$	−235.364	−	106.460i	−0.930294	−	0.420791i
$254$	−27.2576			−0.107313
$255$	27.4513	+	60.1099i	0.107652	+	0.235725i
$256$	−8.56624	+	2.51528i	−0.0334619	+	0.00982530i
$257$	−98.5228	+	113.701i	−0.383357	+	0.442418i	−0.914329	−	0.404971i	$-0.867281\pi$
$257$	−98.5228	+	113.701i	−0.383357	+	0.442418i	0.530972	+	0.847389i	$0.321827\pi$
$258$	19.2054	−	29.8842i	0.0744396	−	0.115830i
$259$	102.400	+	118.175i	0.395365	+	0.456275i
$260$	297.250	−	42.7382i	1.14327	−	0.164378i
$261$	248.920	+	73.0896i	0.953718	+	0.280037i
$262$	−41.9375	+	26.9516i	−0.160067	+	0.102869i
$263$	502.874	+	72.3024i	1.91207	+	0.274914i	0.992900	−	0.118948i	$-0.0379523\pi$
$263$	502.874	+	72.3024i	1.91207	+	0.274914i	0.919169	+	0.393862i	$0.128861\pi$
$264$	−46.0639	−	21.0367i	−0.174485	−	0.0796845i
$265$	105.748	−	231.556i	0.399049	−	0.873796i
$266$	−2.41980	+	16.8301i	−0.00909701	+	0.0632711i
$267$	−19.0953	−	29.7128i	−0.0715179	−	0.111284i
$268$	−32.9970	+	112.377i	−0.123123	+	0.419319i
$269$	13.4539	+	93.5740i	0.0500145	+	0.347859i	0.999428	+	0.0338289i	$0.0107701\pi$
$269$	13.4539	+	93.5740i	0.0500145	+	0.347859i	−0.949413	+	0.314030i	$0.898321\pi$
$270$	−46.7725	+	40.5286i	−0.173231	+	0.150106i
$271$	223.744	+	143.792i	0.825624	+	0.530596i	0.883885	−	0.467705i	$-0.154919\pi$
$271$	223.744	+	143.792i	0.825624	+	0.530596i	−0.0582607	+	0.998301i	$0.518555\pi$
$272$	−100.802	−	87.3456i	−0.370596	−	0.321123i
$273$	11.3323	+	38.5942i	0.0415102	+	0.141371i
$274$	163.574	−	74.7018i	0.596985	−	0.272634i
$275$		−	124.482i		−	0.452660i
$276$	−29.5199	+	65.2634i	−0.106956	+	0.236461i
$277$	−58.0724			−0.209648			−0.104824	−	0.994491i	$-0.533428\pi$
$277$	−58.0724			−0.209648			−0.104824	+	0.994491i	$0.533428\pi$
$278$	−11.6279	−	25.4616i	−0.0418270	−	0.0915884i
$279$	−484.320	+	142.209i	−1.73591	+	0.509710i
$280$	−65.1726	+	75.2132i	−0.232759	+	0.268619i
$281$	13.3378	−	20.7539i	0.0474653	−	0.0738575i	−0.816710	−	0.577048i	$-0.804204\pi$
$281$	13.3378	−	20.7539i	0.0474653	−	0.0738575i	0.864175	+	0.503191i	$0.167841\pi$
$282$	−1.18382	−	1.36620i	−0.00419795	−	0.00484470i
$283$	−395.068	+	56.8022i	−1.39600	+	0.200715i	−0.798906	−	0.601456i	$-0.794588\pi$
$283$	−395.068	+	56.8022i	−1.39600	+	0.200715i	−0.597095	+	0.802171i	$0.703678\pi$
$284$	−89.3031	−	26.2218i	−0.314448	−	0.0923301i
$285$	−34.4107	+	22.1144i	−0.120739	+	0.0775944i
$286$	−106.742	−	15.3471i	−0.373222	−	0.0536613i
$287$	−133.361	−	60.9039i	−0.464672	−	0.212209i
$288$	94.7922	−	207.566i	0.329140	−	0.720715i
$289$	−18.8984	+	131.442i	−0.0653926	+	0.454815i
$290$	−69.6061	−	108.309i	−0.240021	−	0.373480i
$291$	−7.10592	+	24.2005i	−0.0244190	+	0.0831633i
$292$	−40.9133	−	284.558i	−0.140114	−	0.974514i
$293$	55.1994	−	47.8305i	0.188394	−	0.163244i	−0.555557	−	0.831478i	$-0.687495\pi$
$293$	55.1994	−	47.8305i	0.188394	−	0.163244i	0.743951	+	0.668234i	$0.232950\pi$
$294$	19.3921	+	12.4626i	0.0659596	+	0.0423897i
$295$	136.619	+	118.381i	0.463114	+	0.401291i
$296$	69.7741	+	237.629i	0.235723	+	0.802800i
$297$	−154.897	+	70.7389i	−0.521537	+	0.238178i
$298$			123.169i			0.413319i
$299$	−45.0853	+	321.836i	−0.150787	+	1.07637i
$300$	−34.5170			−0.115057
$301$	−79.7960	−	174.729i	−0.265103	−	0.580495i
$302$	15.5802	−	4.57477i	0.0515902	−	0.0151483i
$303$	11.0180	−	12.7154i	0.0363630	−	0.0419651i
$304$	44.6362	−	69.4553i	0.146830	−	0.228471i
$305$	−374.126	−	431.764i	−1.22664	−	1.41562i
$306$	69.1470	−	9.94183i	0.225970	−	0.0324897i
$307$	443.905	+	130.342i	1.44594	+	0.424567i	0.908198	−	0.418540i	$-0.137458\pi$
$307$	443.905	+	130.342i	1.44594	+	0.424567i	0.537745	+	0.843107i	$0.319276\pi$
$308$	−108.124	+	69.4871i	−0.351052	+	0.225608i
$309$	−62.9192	−	9.04642i	−0.203622	−	0.0292764i
$310$	227.864	+	104.062i	0.735046	+	0.335684i
$311$	−228.461	+	500.260i	−0.734601	+	1.60855i	0.0576353	+	0.998338i	$0.481644\pi$
$311$	−228.461	+	500.260i	−0.734601	+	1.60855i	−0.792236	+	0.610214i	$0.791083\pi$
$312$	−9.06649	+	63.0588i	−0.0290593	+	0.202112i
$313$	−68.9126	−	107.230i	−0.220168	−	0.342588i	0.713546	−	0.700609i	$-0.247088\pi$
$313$	−68.9126	−	107.230i	−0.220168	−	0.342588i	−0.933714	+	0.358021i	$0.883452\pi$
$314$	−9.65262	+	32.8738i	−0.0307408	+	0.104694i
$315$	22.7421	+	158.175i	0.0721972	+	0.502142i
$316$	232.494	−	201.457i	0.735740	−	0.637522i
$317$	142.955	+	91.8719i	0.450964	+	0.289817i	0.746341	−	0.665564i	$-0.231809\pi$
$317$	142.955	+	91.8719i	0.450964	+	0.289817i	−0.295377	+	0.955381i	$0.595445\pi$
$318$	19.1561	+	16.5989i	0.0602394	+	0.0521977i
$319$	−99.8019	−	339.894i	−0.312859	−	1.06550i
$320$	130.241	−	59.4789i	0.407002	−	0.185871i
$321$		−	129.531i		−	0.403524i
$322$	−27.4831	−	42.4263i	−0.0853512	−	0.131759i
$323$	96.6910			0.299353
$324$	−89.1928	−	195.305i	−0.275286	−	0.602793i
$325$	−150.259	+	44.1200i	−0.462335	+	0.135754i
$326$	12.9625	−	14.9596i	0.0397624	−	0.0458883i
$327$	−23.9527	+	37.2711i	−0.0732499	+	0.113979i
$328$	−152.062	−	175.489i	−0.463603	−	0.535026i
$329$	−9.67562	+	1.39114i	−0.0294092	+	0.00422840i
$330$	38.7188	+	11.3689i	0.117330	+	0.0344511i
$331$	−374.054	+	240.390i	−1.13007	+	0.726254i	−0.965575	−	0.260124i	$-0.916237\pi$
$331$	−374.054	+	240.390i	−1.13007	+	0.726254i	−0.164498	+	0.986377i	$0.552600\pi$
$332$	−5.28324	−	0.759616i	−0.0159134	−	0.00228800i
$333$	361.732	+	165.198i	1.08628	+	0.496089i
$334$	76.9810	−	168.565i	0.230482	−	0.504685i
$335$	28.2980	−	196.817i	0.0844717	−	0.587514i
$336$	16.4250	+	25.5578i	0.0488838	+	0.0760647i
$337$	−69.9416	+	238.199i	−0.207542	+	0.706823i	0.788264	+	0.615337i	$0.210980\pi$
$337$	−69.9416	+	238.199i	−0.207542	+	0.706823i	−0.995806	+	0.0914863i	$0.970838\pi$
$338$	2.96344	+	20.6112i	0.00876757	+	0.0609798i
$339$	77.0165	−	66.7352i	0.227187	−	0.196859i
$340$	223.468	+	143.614i	0.657259	+	0.422395i
$341$	520.897	+	451.360i	1.52756	+	1.32364i
$342$	12.1826	+	41.4901i	0.0356216	+	0.121316i
$343$	257.541	−	117.615i	0.750849	−	0.342901i
$344$		−	304.234i		−	0.884400i
$345$	33.8383	−	116.804i	0.0980820	−	0.338563i
$346$	77.1457			0.222964
$347$	−118.487	−	259.450i	−0.341461	−	0.747695i	0.658527	−	0.752557i	$-0.271180\pi$
$347$	−118.487	−	259.450i	−0.341461	−	0.747695i	−0.999988	+	0.00486177i	$0.998452\pi$
$348$	−94.2480	+	27.6737i	−0.270828	+	0.0795222i
$349$	297.571	−	343.415i	0.852638	−	0.983997i	−0.147349	−	0.989085i	$-0.547074\pi$
$349$	297.571	−	343.415i	0.852638	−	0.983997i	0.999987	+	0.00508777i	$0.00161950\pi$
$350$	13.1697	−	20.4924i	0.0376276	−	0.0585497i
$351$	140.287	+	161.900i	0.399679	+	0.461254i
$352$	−308.412	+	44.3429i	−0.876169	+	0.125974i
$353$	64.5112	+	18.9422i	0.182751	+	0.0536606i	0.371828	−	0.928302i	$-0.378731\pi$
$353$	64.5112	+	18.9422i	0.182751	+	0.0536606i	−0.189076	+	0.981962i	$0.560549\pi$
$354$	−15.1425	+	9.73152i	−0.0427755	+	0.0274902i
$355$	156.405	+	22.4876i	0.440577	+	0.0633454i
$356$	−129.149	−	58.9804i	−0.362778	−	0.165675i
$357$	−14.7804	+	32.3645i	−0.0414017	+	0.0906570i
$358$	−12.0846	+	84.0505i	−0.0337560	+	0.234778i
$359$	−236.941	−	368.687i	−0.660002	−	1.02698i	−0.996360	−	0.0852490i	$-0.972831\pi$
$359$	−236.941	−	368.687i	−0.660002	−	1.02698i	0.336358	−	0.941734i	$-0.390805\pi$
$360$	−71.3060	+	242.846i	−0.198072	+	0.674572i
$361$	−42.8579	−	298.084i	−0.118720	−	0.825716i
$362$	−139.210	+	120.626i	−0.384559	+	0.333222i
$363$	3.80896	+	2.44787i	0.0104930	+	0.00674344i
$364$	122.199	+	105.886i	0.335711	+	0.290895i
$365$	137.505	+	468.300i	0.376727	+	1.28301i
$366$	51.7457	−	23.6314i	0.141382	−	0.0645668i
$367$		−	548.797i		−	1.49536i	−0.664060	−	0.747679i	$-0.731168\pi$
$367$		−	548.797i		−	1.49536i	0.664060	−	0.747679i	$-0.268832\pi$
$368$	35.8104	+	242.828i	0.0973108	+	0.659857i
$369$	−372.851			−1.01044
$370$	−81.9830	−	179.518i	−0.221576	−	0.485183i
$371$	131.509	−	38.6145i	0.354472	−	0.104082i
$372$	125.156	−	144.438i	0.336440	−	0.388273i
$373$	−157.464	+	245.019i	−0.422156	+	0.656887i	−0.985566	−	0.169290i	$-0.945853\pi$
$373$	−157.464	+	245.019i	−0.422156	+	0.656887i	0.563410	+	0.826177i	$0.309489\pi$
$374$	−62.4667	−	72.0904i	−0.167023	−	0.192755i
$375$	−72.8318	+	10.4716i	−0.194218	+	0.0279244i
$376$	−14.8550	−	4.36181i	−0.0395079	−	0.0116006i
$377$	−374.906	+	240.937i	−0.994446	+	0.639091i
$378$	−32.9832	−	4.74227i	−0.0872572	−	0.0125457i
$379$	84.1521	+	38.4310i	0.222037	+	0.101401i	0.523328	−	0.852131i	$-0.324690\pi$
$379$	84.1521	+	38.4310i	0.222037	+	0.101401i	−0.301291	+	0.953532i	$0.597418\pi$
$380$	−68.3057	+	149.569i	−0.179752	+	0.393602i
$381$	5.02456	−	34.9466i	0.0131878	−	0.0917233i
$382$	28.5259	+	44.3871i	0.0746751	+	0.116197i
$383$	−101.803	+	346.708i	−0.265803	+	0.905243i	0.713125	+	0.701037i	$0.247279\pi$
$383$	−101.803	+	346.708i	−0.265803	+	0.905243i	−0.978928	+	0.204206i	$0.934539\pi$
$384$	15.9293	+	110.791i	0.0414827	+	0.288518i
$385$	164.908	−	142.894i	0.428333	−	0.371152i
$386$	−48.5090	−	31.1748i	−0.125671	−	0.0807638i
$387$	−369.190	−	319.905i	−0.953979	−	0.826627i
$388$	28.5646	+	97.2822i	0.0736202	+	0.250727i
$389$	−104.351	+	47.6557i	−0.268255	+	0.122508i	−0.545002	−	0.838435i	$-0.683471\pi$
$389$	−104.351	+	47.6557i	−0.268255	+	0.122508i	0.276746	+	0.960943i	$0.410744\pi$
$390$		−	50.7661i		−	0.130169i
$391$	−216.566	+	189.031i	−0.553876	+	0.483455i
$392$	197.420			0.503622
$393$	−26.8237	−	58.7356i	−0.0682536	−	0.149455i
$394$	−139.244	+	40.8857i	−0.353411	+	0.103771i
$395$	−342.019	+	394.711i	−0.865872	+	0.999269i
$396$	−176.717	+	274.976i	−0.446254	+	0.694385i
$397$	−18.0591	−	20.8414i	−0.0454890	−	0.0524971i	0.732549	−	0.680714i	$-0.238330\pi$
$397$	−18.0591	−	20.8414i	−0.0454890	−	0.0524971i	−0.778038	+	0.628217i	$0.783785\pi$
$398$	9.29270	−	1.33609i	0.0233485	−	0.00335701i
$399$	−21.1316	−	6.20479i	−0.0529613	−	0.0155509i
$400$	−99.5041	+	63.9474i	−0.248760	+	0.159868i
$401$	431.208	+	61.9983i	1.07533	+	0.154609i	0.657154	−	0.753756i	$-0.271760\pi$
$401$	431.208	+	61.9983i	1.07533	+	0.154609i	0.418177	+	0.908366i	$0.362669\pi$
$402$	18.0099	+	8.22484i	0.0448007	+	0.0204598i
$403$	360.205	−	788.738i	0.893808	−	1.95717i
$404$	9.62525	−	66.9451i	0.0238249	−	0.165706i
$405$	197.072	+	306.650i	0.486597	+	0.757160i
$406$	19.5299	−	66.5126i	0.0481031	−	0.163824i
$407$	−77.2779	−	537.480i	−0.189872	−	1.32059i
$408$	−42.5883	+	36.9029i	−0.104383	+	0.0904484i
$409$	−25.3687	−	16.3035i	−0.0620262	−	0.0398618i	0.509260	−	0.860613i	$-0.329919\pi$
$409$	−25.3687	−	16.3035i	−0.0620262	−	0.0398618i	−0.571286	+	0.820751i	$0.693555\pi$
$410$	139.841	+	121.173i	0.341075	+	0.295543i
$411$	65.6214	+	223.486i	0.159663	+	0.543762i
$412$	−232.435	+	106.149i	−0.564161	+	0.257644i
$413$			97.3321i			0.235671i
$414$	−108.399	−	69.1112i	−0.261834	−	0.166935i
$415$	9.06175			0.0218355
$416$	162.836	+	356.560i	0.391432	+	0.857116i
$417$	34.7874	−	10.2145i	0.0834230	−	0.0244952i
$418$	38.6665	−	44.6235i	0.0925036	−	0.106755i
$419$	175.582	−	273.212i	0.419051	−	0.652057i	−0.565983	−	0.824417i	$-0.691503\pi$
$419$	175.582	−	273.212i	0.419051	−	0.652057i	0.985034	+	0.172361i	$0.0551394\pi$
$420$	−39.6225	−	45.7268i	−0.0943392	−	0.108873i
$421$	329.228	−	47.3358i	0.782014	−	0.112437i	0.260267	−	0.965537i	$-0.416189\pi$
$421$	329.228	−	47.3358i	0.782014	−	0.112437i	0.521747	+	0.853100i	$0.325280\pi$
$422$	−54.3266	−	15.9517i	−0.128736	−	0.0378003i
$423$	−20.9132	+	13.4401i	−0.0494403	+	0.0317733i
$424$	214.872	+	30.8939i	0.506772	+	0.0728629i
$425$	−126.005	−	57.5445i	−0.296482	−	0.135399i
$426$	−6.53604	+	14.3119i	−0.0153428	+	0.0335961i
$427$	43.7766	−	304.473i	0.102521	−	0.713052i
$428$	−281.509	−	438.036i	−0.657731	−	1.02345i
$429$	39.3526	−	134.023i	0.0917311	−	0.312407i
$430$	34.5018	+	239.966i	0.0802368	+	0.558059i
$431$	404.427	−	350.438i	0.938346	−	0.813081i	−0.0442152	−	0.999022i	$-0.514079\pi$
$431$	404.427	−	350.438i	0.938346	−	0.813081i	0.982561	+	0.185941i	$0.0595333\pi$
$432$	136.117	+	87.4769i	0.315085	+	0.202493i
$433$	−43.6959	−	37.8627i	−0.100914	−	0.0874428i	0.602942	−	0.797785i	$-0.293995\pi$
$433$	−43.6959	−	37.8627i	−0.100914	−	0.0874428i	−0.703857	+	0.710342i	$0.748540\pi$
$434$	37.9989	+	129.412i	0.0875551	+	0.298185i
$435$	151.693	−	69.2757i	0.348719	−	0.159255i
$436$			178.096i			0.408477i
$437$	−134.896	−	116.036i	−0.308686	−	0.265529i
$438$	−48.5984			−0.110955
$439$	203.717	+	446.078i	0.464048	+	1.01612i	0.986546	+	0.163483i	$0.0522728\pi$
$439$	203.717	+	446.078i	0.464048	+	1.01612i	−0.522498	+	0.852640i	$0.675000\pi$
$440$	331.600	−	97.3665i	0.753636	−	0.221287i
$441$	207.589	−	239.571i	0.470723	−	0.543244i
$442$	−64.8787	+	100.953i	−0.146784	+	0.228401i
$443$	−419.263	−	483.855i	−0.946417	−	1.09222i	−0.995625	−	0.0934353i	$-0.970215\pi$
$443$	−419.263	−	483.855i	−0.946417	−	1.09222i	0.0492080	−	0.998789i	$-0.484330\pi$
$444$	−149.036	+	21.4281i	−0.335666	+	0.0482615i
$445$	231.279	+	67.9096i	0.519728	+	0.152606i
$446$	61.3689	−	39.4394i	0.137598	−	0.0884291i
$447$	−157.913	−	22.7045i	−0.353273	−	0.0507931i
$448$	70.1245	+	32.0248i	0.156528	+	0.0714839i
$449$	−237.091	+	519.157i	−0.528043	+	1.15625i	0.438261	+	0.898848i	$0.355594\pi$
$449$	−237.091	+	519.157i	−0.528043	+	1.15625i	−0.966304	+	0.257404i	$0.917133\pi$
$450$	8.81634	−	61.3190i	0.0195919	−	0.136264i
$451$	275.250	+	428.298i	0.610311	+	0.949663i
$452$	115.412	−	393.057i	0.255336	−	0.869596i
$453$	2.99325	+	20.8185i	0.00660761	+	0.0459570i
$454$	96.7943	−	83.8728i	0.213203	−	0.184742i
$455$	−230.932	−	148.411i	−0.507543	−	0.326178i
$456$	−26.3619	−	22.8427i	−0.0578111	−	0.0500936i
$457$	43.3209	+	147.538i	0.0947942	+	0.322839i	0.993214	−	0.116297i	$-0.0371026\pi$
$457$	43.3209	+	147.538i	0.0947942	+	0.322839i	−0.898420	+	0.439137i	$0.855284\pi$
$458$	103.284	−	47.1683i	0.225511	−	0.102988i
$459$			189.493i			0.412838i
$460$	−139.418	−	468.537i	−0.303082	−	1.01856i
$461$	292.976			0.635523			0.317762	−	0.948171i	$-0.397069\pi$
$461$	292.976			0.635523			0.317762	+	0.948171i	$0.397069\pi$
$462$	9.02580	+	19.7638i	0.0195364	+	0.0427787i
$463$	−302.097	+	88.7036i	−0.652477	+	0.191584i	−0.591186	−	0.806535i	$-0.701340\pi$
$463$	−302.097	+	88.7036i	−0.652477	+	0.191584i	−0.0612911	+	0.998120i	$0.519522\pi$
$464$	−220.424	+	254.383i	−0.475052	+	0.548240i
$465$	−175.420	+	272.959i	−0.377248	+	0.587009i
$466$	−66.7105	−	76.9880i	−0.143156	−	0.165210i
$467$	−57.1037	+	8.21027i	−0.122278	+	0.0175809i	−0.203182	−	0.979141i	$-0.565128\pi$
$467$	−57.1037	+	8.21027i	−0.122278	+	0.0175809i	0.0809043	+	0.996722i	$0.474219\pi$
$468$	394.551	+	115.851i	0.843059	+	0.247544i
$469$	90.0651	−	57.8813i	0.192036	−	0.123414i
$470$	12.2116	+	1.75576i	0.0259821	+	0.00373566i
$471$	−40.3677	−	18.4353i	−0.0857064	−	0.0391408i
$472$	−64.0393	+	140.226i	−0.135676	+	0.297090i
$473$	−94.9304	+	660.256i	−0.200699	+	1.39589i
$474$	−28.1158	−	43.7490i	−0.0593160	−	0.0922975i
$475$	24.1571	−	82.2716i	0.0508571	−	0.173203i
$476$	20.3546	+	141.569i	0.0427617	+	0.297414i
$477$	263.429	−	228.263i	0.552263	−	0.478539i
$478$	−44.0527	−	28.3110i	−0.0921605	−	0.0592279i
$479$	−390.803	−	338.632i	−0.815872	−	0.706957i	0.143331	−	0.989675i	$-0.454219\pi$
$479$	−390.803	−	338.632i	−0.815872	−	0.706957i	−0.959203	+	0.282718i	$0.908764\pi$
$480$	−41.3245	−	140.738i	−0.0860927	−	0.293205i
$481$	−621.390	+	283.779i	−1.29187	+	0.589978i
$482$			189.860i			0.393901i
$483$	59.4602	−	27.4150i	0.123106	−	0.0567597i
$484$	18.2007			0.0376047
$485$	−71.5059	−	156.576i	−0.147435	−	0.322837i
$486$	−123.795	+	36.3496i	−0.254723	+	0.0747935i
$487$	−511.316	+	590.090i	−1.04993	+	1.21168i	−0.0731759	+	0.997319i	$0.523313\pi$
$487$	−511.316	+	590.090i	−1.04993	+	1.21168i	−0.976754	+	0.214364i	$0.931232\pi$
$488$	263.396	−	409.852i	0.539746	−	0.839861i
$489$	16.7900	+	19.3767i	0.0343354	+	0.0396251i
$490$	−155.716	+	22.3885i	−0.317787	+	0.0456909i
$491$	−510.415	−	149.871i	−1.03954	−	0.305237i	−0.282957	−	0.959133i	$-0.591315\pi$
$491$	−510.415	−	149.871i	−1.03954	−	0.305237i	−0.756585	+	0.653895i	$0.773134\pi$
$492$	118.761	−	76.3232i	0.241384	−	0.155128i
$493$	−390.189	−	56.1008i	−0.791459	−	0.113795i
$494$	−67.5687	−	30.8576i	−0.136779	−	0.0624647i
$495$	230.525	−	504.780i	0.465708	−	1.01976i
$496$	93.2036	−	648.245i	0.187910	−	1.30695i
$497$	45.9966	+	71.5721i	0.0925485	+	0.144008i
$498$	−0.254208	+	0.865752i	−0.000510457	+	0.00173846i
$499$	61.1025	+	424.977i	0.122450	+	0.851658i	0.954766	+	0.297357i	$0.0961052\pi$
$499$	61.1025	+	424.977i	0.122450	+	0.851658i	−0.832316	+	0.554301i	$0.812986\pi$
$500$	−223.538	+	193.696i	−0.447075	+	0.387393i
$501$	201.924	+	129.769i	0.403042	+	0.259020i
$502$	−62.8532	−	54.4626i	−0.125206	−	0.108491i
$503$	127.873	+	435.494i	0.254220	+	0.865794i	0.983397	+	0.181469i	$0.0580851\pi$
$503$	127.873	+	435.494i	0.254220	+	0.865794i	−0.729177	+	0.684326i	$0.760097\pi$
$504$	−123.959	+	56.6102i	−0.245950	+	0.112322i
$505$			114.823i			0.227373i
$506$	0.635016	+	175.539i	0.00125497	+	0.346916i
$507$	−26.9715			−0.0531983
$508$	−58.9574	−	129.099i	−0.116058	−	0.254131i
$509$	605.538	−	177.802i	1.18966	−	0.349316i	0.373770	−	0.927521i	$-0.378065\pi$
$509$	605.538	−	177.802i	1.18966	−	0.349316i	0.815892	+	0.578205i	$0.196247\pi$
$510$	29.4066	−	33.9371i	0.0576601	−	0.0665433i
$511$	−142.074	+	221.072i	−0.278032	+	0.432626i
$512$	337.077	+	389.008i	0.658354	+	0.759781i
$513$	−116.101	+	16.6928i	−0.226318	+	0.0325396i
$514$	98.0948	+	28.8032i	0.190846	+	0.0560374i
$515$	364.947	−	234.537i	0.708636	−	0.455412i
$516$	183.080	+	26.3229i	0.354806	+	0.0510134i
$517$	30.8776	+	14.1013i	0.0597246	+	0.0272753i
$518$	44.1415	−	96.6565i	0.0852153	−	0.186596i
$519$	−14.2207	+	98.9074i	−0.0274003	+	0.190573i
$520$	−235.058	−	365.757i	−0.452034	−	0.703379i
$521$	115.915	−	394.771i	0.222486	−	0.757719i	−0.770285	−	0.637699i	$-0.779886\pi$
$521$	115.915	−	394.771i	0.222486	−	0.757719i	0.992772	−	0.120019i	$-0.0382956\pi$
$522$	−25.0891	−	174.499i	−0.0480634	−	0.334288i
$523$	−673.174	+	583.308i	−1.28714	+	1.11531i	−0.300259	+	0.953858i	$0.597073\pi$
$523$	−673.174	+	583.308i	−1.28714	+	1.11531i	−0.986880	+	0.161454i	$0.948382\pi$
$524$	−218.359	−	140.331i	−0.416716	−	0.267807i
$525$	23.8453	+	20.6621i	0.0454197	+	0.0393564i
$526$	−97.2649	−	331.254i	−0.184914	−	0.629760i
$527$	697.680	−	318.620i	1.32387	−	0.604591i
$528$		−	105.500i		−	0.199810i
$529$	528.986	−	3.82728i	0.999974	−	0.00723493i
$530$	−172.984			−0.326385
$531$	102.828	+	225.162i	0.193649	+	0.424033i
$532$	−84.9455	+	24.9422i	−0.159672	+	0.0468839i
$533$	419.432	−	484.050i	0.786927	−	0.908162i
$534$	−12.9760	+	20.1911i	−0.0242997	+	0.0378111i
$535$	578.896	+	668.082i	1.08205	+	1.24875i
$536$	167.840	−	24.1317i	0.313134	−	0.0450218i
$537$	−105.532	−	30.9871i	−0.196522	−	0.0577040i
$538$	54.0433	−	34.7315i	0.100452	−	0.0645567i
$539$	−428.446	−	61.6012i	−0.794890	−	0.114288i
$540$	−293.121	−	133.864i	−0.542817	−	0.247896i
$541$	−141.709	+	310.300i	−0.261939	+	0.573567i	−0.994211	−	0.107446i	$-0.965733\pi$
$541$	−141.709	+	310.300i	−0.261939	+	0.573567i	0.732272	+	0.681012i	$0.238460\pi$
$542$	25.7212	−	178.895i	0.0474561	−	0.330064i
$543$	−128.992	−	200.715i	−0.237554	−	0.369642i
$544$	−97.6849	+	332.684i	−0.179568	+	0.611552i
$545$	−43.0301	−	299.281i	−0.0789544	−	0.549140i
$546$	20.6574	−	17.8997i	0.0378340	−	0.0327834i
$547$	167.953	+	107.937i	0.307043	+	0.197325i	0.685084	−	0.728464i	$-0.259766\pi$
$547$	167.953	+	107.937i	0.307043	+	0.197325i	−0.378040	+	0.925789i	$0.623402\pi$
$548$	707.612	+	613.149i	1.29126	+	1.11889i
$549$	−220.395	−	750.597i	−0.401448	−	1.36721i
$550$	−76.9462	+	35.1402i	−0.139902	+	0.0638912i
$551$		−	244.008i		−	0.442847i
$552$	103.702	−	0.375143i	0.187866	−	0.000679607i
$553$	−281.206			−0.508511
$554$	16.3934	+	35.8965i	0.0295909	+	0.0647951i
$555$	245.270	−	72.0177i	0.441927	−	0.129762i
$556$	95.4415	−	110.145i	0.171657	−	0.198103i
$557$	9.50422	−	14.7889i	0.0170632	−	0.0265509i	−0.832617	−	0.553849i	$-0.813159\pi$
$557$	9.50422	−	14.7889i	0.0170632	−	0.0265509i	0.849680	+	0.527298i	$0.176795\pi$
$558$	224.624	+	259.230i	0.402552	+	0.464569i
$559$	830.626	−	119.426i	1.48591	−	0.213642i
$560$	−198.937	−	58.4130i	−0.355244	−	0.104309i
$561$	103.941	−	66.7988i	0.185278	−	0.119071i
$562$	−16.5938	−	2.38584i	−0.0295264	−	0.00424526i
$563$	387.481	+	176.957i	0.688243	+	0.314310i	0.728663	−	0.684873i	$-0.240142\pi$
$563$	387.481	+	176.957i	0.688243	+	0.314310i	−0.0404196	+	0.999183i	$0.512869\pi$
$564$	3.91011	−	8.56194i	0.00693281	−	0.0151807i
$565$	−98.9767	+	688.398i	−0.175180	+	1.21840i
$566$	146.636	+	228.170i	0.259074	+	0.403127i
$567$	−55.2938	+	188.314i	−0.0975200	+	0.332123i
$568$	19.1768	+	133.377i	0.0337619	+	0.234819i
$569$	−424.544	+	367.870i	−0.746123	+	0.646520i	−0.942575	−	0.333994i	$-0.891604\pi$
$569$	−424.544	+	367.870i	−0.746123	+	0.646520i	0.196452	+	0.980513i	$0.437058\pi$
$570$	23.3835	+	15.0277i	0.0410237	+	0.0263643i
$571$	−742.583	−	643.452i	−1.30050	−	1.12689i	−0.983976	−	0.178300i	$-0.942940\pi$
$571$	−742.583	−	643.452i	−1.30050	−	1.12689i	−0.316519	−	0.948586i	$-0.602514\pi$
$572$	−158.191	−	538.750i	−0.276558	−	0.941870i
$573$	−62.1665	+	28.3905i	−0.108493	+	0.0495471i
$574$			99.6275i			0.173567i
$575$	106.735	+	231.497i	0.185626	+	0.402603i
$576$	196.054			0.340372
$577$	−223.966	−	490.418i	−0.388156	−	0.849944i	−0.998335	−	0.0576803i	$-0.981630\pi$
$577$	−223.966	−	490.418i	−0.388156	−	0.849944i	0.610179	−	0.792264i	$-0.291098\pi$
$578$	86.5833	−	25.4232i	0.149798	−	0.0439847i
$579$	48.9108	−	56.4460i	0.0844746	−	0.0974889i
$580$	362.423	−	563.942i	0.624868	−	0.972313i
$581$	3.19510	+	3.68734i	0.00549931	+	0.00634655i
$582$	16.9651	−	2.43921i	0.0291497	−	0.00419109i
$583$	−456.680	−	134.093i	−0.783327	−	0.230006i
$584$	−350.140	+	225.021i	−0.599554	+	0.385310i
$585$	−691.015	−	99.3529i	−1.18122	−	0.169834i
$586$	−45.1480	−	20.6184i	−0.0770444	−	0.0351850i
$587$	−299.450	+	655.705i	−0.510137	+	1.11704i	0.462903	+	0.886409i	$0.346808\pi$
$587$	−299.450	+	655.705i	−0.510137	+	1.11704i	−0.973040	+	0.230635i	$0.925920\pi$
$588$	−17.0812	+	118.802i	−0.0290496	+	0.202044i
$589$	256.676	+	399.396i	0.435783	+	0.678091i
$590$	34.6087	−	117.867i	0.0586589	−	0.199774i
$591$	−26.7513	−	186.059i	−0.0452645	−	0.314821i
$592$	−389.934	+	337.880i	−0.658673	+	0.570743i
$593$	−664.843	−	427.269i	−1.12115	−	0.720521i	−0.157457	−	0.987526i	$-0.550330\pi$
$593$	−664.843	−	427.269i	−1.12115	−	0.720521i	−0.963695	+	0.267005i	$0.913966\pi$
$594$	87.4521	+	75.7777i	0.147226	+	0.127572i
$595$	−68.4097	−	232.982i	−0.114974	−	0.391566i
$596$	−583.359	+	266.411i	−0.978790	+	0.446999i
$597$			12.1603i			0.0203691i
$598$	211.665	−	62.9830i	0.353954	−	0.105323i
$599$	46.3546			0.0773867			0.0386933	−	0.999251i	$-0.487680\pi$
$599$	46.3546			0.0773867			0.0386933	+	0.999251i	$0.487680\pi$
$600$	20.7595	+	45.4569i	0.0345991	+	0.0757615i
$601$	−231.629	+	68.0123i	−0.385405	+	0.113165i	−0.468695	−	0.883360i	$-0.655276\pi$
$601$	−231.629	+	68.0123i	−0.385405	+	0.113165i	0.0832894	+	0.996525i	$0.473457\pi$
$602$	−85.4800	+	98.6492i	−0.141993	+	0.163869i
$603$	147.201	−	229.049i	0.244115	−	0.379850i
$604$	55.3669	+	63.8968i	0.0916670	+	0.105789i
$605$	−30.5853	+	4.39751i	−0.0505543	+	0.00726861i
$606$	−10.9701	−	3.22112i	−0.0181025	−	0.00531538i
$607$	587.143	−	377.334i	0.967287	−	0.621637i	0.0412812	−	0.999148i	$-0.486856\pi$
$607$	587.143	−	377.334i	0.967287	−	0.621637i	0.926005	+	0.377510i	$0.123220\pi$
$608$	−212.439	−	30.5441i	−0.349406	−	0.0502370i
$609$	81.6748	+	37.2996i	0.134113	+	0.0612474i
$610$	−161.275	+	353.143i	−0.264385	+	0.578923i
$611$	6.07745	−	42.2696i	0.00994673	−	0.0691810i
$612$	196.650	+	305.993i	0.321323	+	0.499989i
$613$	−71.2188	+	242.549i	−0.116181	+	0.395675i	−0.996966	−	0.0778412i	$-0.975197\pi$
$613$	−71.2188	+	242.549i	−0.116181	+	0.395675i	0.880785	+	0.473516i	$0.157015\pi$
$614$	−44.7419	−	311.187i	−0.0728696	−	0.506819i
$615$	−181.131	+	156.951i	−0.294523	+	0.255205i
$616$	156.539	+	100.602i	0.254122	+	0.163314i
$617$	412.293	+	357.254i	0.668221	+	0.579017i	0.921501	−	0.388376i	$-0.126964\pi$
$617$	412.293	+	357.254i	0.668221	+	0.579017i	−0.253280	+	0.967393i	$0.581509\pi$
$618$	12.1697	+	41.4462i	0.0196921	+	0.0670650i
$619$	547.790	−	250.167i	0.884960	−	0.404148i	0.0795257	−	0.996833i	$-0.474659\pi$
$619$	547.790	−	250.167i	0.884960	−	0.404148i	0.805434	+	0.592685i	$0.201932\pi$
$620$			1304.30i			2.10372i
$621$	227.405	−	264.365i	0.366191	−	0.425709i
$622$	373.720			0.600836
$623$	53.9138	+	118.055i	0.0865390	+	0.189494i
$624$	−127.347	+	37.3923i	−0.204081	+	0.0599236i
$625$	510.296	−	588.913i	0.816473	−	0.942260i
$626$	−46.8290	+	72.8673i	−0.0748067	+	0.116401i
$627$	50.0836	+	57.7995i	0.0798781	+	0.0921842i
$628$	−176.577	+	25.3879i	−0.281173	+	0.0404266i
$629$	−579.780	−	170.239i	−0.921749	−	0.270650i
$630$	91.3533	−	58.7092i	0.145005	−	0.0931892i
$631$	−179.220	−	25.7679i	−0.284025	−	0.0408366i	−0.00117005	−	0.999999i	$-0.500372\pi$
$631$	−179.220	−	25.7679i	−0.284025	−	0.0408366i	−0.282855	+	0.959163i	$0.591282\pi$
$632$	−405.135	−	185.019i	−0.641036	−	0.292751i
$633$	30.4658	−	66.7108i	0.0481293	−	0.105388i
$634$	16.4339	−	114.300i	0.0259210	−	0.180284i
$635$	130.267	+	202.699i	0.205145	+	0.319211i
$636$	−37.1822	+	126.631i	−0.0584626	+	0.199105i
$637$	77.4966	+	539.001i	0.121659	+	0.846155i
$638$	−181.927	+	157.640i	−0.285151	+	0.247085i
$639$	182.019	+	116.976i	0.284850	+	0.183062i
$640$	−577.301	−	500.234i	−0.902033	−	0.781616i
$641$	−321.888	−	1096.25i	−0.502165	−	1.71022i	−0.686303	−	0.727316i	$-0.740768\pi$
$641$	−321.888	−	1096.25i	−0.502165	−	1.71022i	0.184138	−	0.982900i	$-0.441051\pi$
$642$	−80.0676	+	36.5657i	−0.124716	+	0.0569559i
$643$		−	131.647i		−	0.204739i	−0.994746	−	0.102370i	$-0.967358\pi$
$643$		−	131.647i		−	0.204739i	0.994746	−	0.102370i	$-0.0326424\pi$
$644$	141.496	−	221.933i	0.219714	−	0.344617i
$645$	−314.016			−0.486847
$646$	−27.2951	−	59.7680i	−0.0422525	−	0.0925201i
$647$	206.303	−	60.5760i	0.318861	−	0.0936259i	−0.118386	−	0.992968i	$-0.537772\pi$
$647$	206.303	−	60.5760i	0.318861	−	0.0936259i	0.437246	+	0.899342i	$0.355954\pi$
$648$	−203.562	+	234.923i	−0.314139	+	0.362536i
$649$	182.735	−	284.341i	0.281563	−	0.438121i
$650$	69.6890	+	80.4254i	0.107214	+	0.123731i
$651$	−172.922	+	24.8625i	−0.265626	+	0.0381912i
$652$	98.8899	+	29.0367i	0.151672	+	0.0445348i
$653$	893.050	−	573.929i	1.36761	−	0.878911i	0.368891	−	0.929473i	$-0.379738\pi$
$653$	893.050	−	573.929i	1.36761	−	0.878911i	0.998721	+	0.0505622i	$0.0161013\pi$
$654$	29.8002	+	4.28462i	0.0455660	+	0.00655141i
$655$	400.847	+	183.061i	0.611980	+	0.279482i
$656$	200.960	−	440.041i	0.306342	−	0.670795i
$657$	−95.1107	+	661.509i	−0.144765	+	1.00686i
$658$	3.59126	+	5.58811i	0.00545784	+	0.00849257i
$659$	304.903	−	1038.41i	0.462676	−	1.57573i	−0.316290	−	0.948663i	$-0.602437\pi$
$659$	304.903	−	1038.41i	0.462676	−	1.57573i	0.778966	−	0.627067i	$-0.215745\pi$
$660$	29.9019	+	207.972i	0.0453059	+	0.315110i
$661$	475.684	−	412.183i	0.719644	−	0.623575i	−0.216053	−	0.976382i	$-0.569318\pi$
$661$	475.684	−	412.183i	0.719644	−	0.623575i	0.935696	+	0.352807i	$0.114773\pi$
$662$	254.186	+	163.355i	0.383966	+	0.246760i
$663$	−117.471	−	101.789i	−0.177181	−	0.153528i
$664$	2.17711	+	7.41457i	0.00327878	+	0.0111665i
$665$	136.720	−	62.4380i	0.205594	−	0.0938918i
$666$		−	270.233i		−	0.405755i
$667$	477.037	+	546.522i	0.715198	+	0.819374i
$668$	964.873			1.44442
$669$	39.2522	+	85.9503i	0.0586729	+	0.128476i
$670$	−129.647	+	38.0679i	−0.193504	+	0.0568178i
$671$	−699.515	+	807.284i	−1.04250	+	1.20311i
$672$	42.6976	−	66.4387i	0.0635380	−	0.0988671i
$673$	−90.5587	−	104.510i	−0.134560	−	0.155290i	0.684471	−	0.729041i	$-0.260033\pi$
$673$	−90.5587	−	104.510i	−0.134560	−	0.155290i	−0.819030	+	0.573750i	$0.805488\pi$
$674$	166.983	−	24.0085i	0.247749	−	0.0356210i
$675$	161.234	+	47.3425i	0.238865	+	0.0701371i
$676$	−91.2097	+	58.6169i	−0.134926	+	0.0867114i
$677$	616.883	+	88.6944i	0.911201	+	0.131011i	0.581944	−	0.813229i	$-0.302292\pi$
$677$	616.883	+	88.6944i	0.911201	+	0.131011i	0.329258	+	0.944240i	$0.393202\pi$
$678$	−62.9924	−	28.7677i	−0.0929091	−	0.0424302i
$679$	38.5004	−	84.3042i	0.0567017	−	0.124159i
$680$	54.7317	−	380.667i	0.0804878	−	0.559805i
$681$	89.6894	+	139.559i	0.131702	+	0.204933i
$682$	131.955	−	449.399i	0.193483	−	0.658943i
$683$	160.700	+	1117.70i	0.235286	+	1.63645i	0.674647	+	0.738141i	$0.264296\pi$
$683$	160.700	+	1117.70i	0.235286	+	1.63645i	−0.439361	+	0.898311i	$0.644795\pi$
$684$	−170.157	+	147.442i	−0.248767	+	0.215558i
$685$	−1337.25	−	859.398i	−1.95219	−	1.25460i
$686$	−145.404	−	125.993i	−0.211959	−	0.183663i
$687$	41.4348	+	141.114i	0.0603127	+	0.205406i
$688$	576.540	−	263.297i	0.837995	−	0.382699i
$689$			598.775i			0.869049i
$690$	−81.7528	+	12.0563i	−0.118482	+	0.0174729i
$691$	−1216.59			−1.76062			−0.880312	−	0.474395i	$-0.842667\pi$
$691$	−1216.59			−1.76062			−0.880312	+	0.474395i	$0.842667\pi$
$692$	166.864	+	365.381i	0.241133	+	0.528007i
$693$	286.683	−	84.1778i	0.413684	−	0.121469i
$694$	−126.927	+	146.481i	−0.182892	+	0.211068i
$695$	−133.772	+	208.153i	−0.192478	+	0.299501i
$696$	93.1279	+	107.475i	0.133804	+	0.154418i
$697$	560.780	−	80.6280i	0.804562	−	0.115679i
$698$	−296.278	−	86.9951i	−0.424467	−	0.124635i
$699$	111.002	−	71.3369i	0.158802	−	0.102056i
$700$	125.543	+	18.0503i	0.179347	+	0.0257861i
$701$	−740.635	−	338.237i	−1.05654	−	0.482506i	−0.190089	−	0.981767i	$-0.560878\pi$
$701$	−740.635	−	338.237i	−1.05654	−	0.482506i	−0.866452	+	0.499261i	$0.833605\pi$
$702$	60.4739	−	132.419i	0.0861452	−	0.188632i
$703$	53.2302	−	370.224i	0.0757186	−	0.526635i
$704$	−144.733	−	225.210i	−0.205587	−	0.319900i
$705$	−4.50207	+	15.3326i	−0.00638591	+	0.0217484i
$706$	−6.50220	−	45.2238i	−0.00920991	−	0.0640563i
$707$	−46.7231	+	40.4858i	−0.0660864	+	0.0572642i
$708$	−78.8438	−	50.6698i	−0.111361	−	0.0715675i
$709$	−213.119	−	184.669i	−0.300591	−	0.260463i	0.491485	−	0.870886i	$-0.336454\pi$
$709$	−213.119	−	184.669i	−0.300591	−	0.260463i	−0.792076	+	0.610423i	$0.791000\pi$
$710$	−30.2515	−	103.027i	−0.0426077	−	0.145109i
$711$	−650.525	+	297.085i	−0.914943	+	0.417841i
$712$			205.554i			0.288699i
$713$	−1355.71	−	392.752i	−1.90142	−	0.550845i
$714$	24.1780			0.0338627
$715$	396.001	+	867.121i	0.553847	+	1.21276i
$716$	−424.222	+	124.563i	−0.592489	+	0.173971i
$717$	44.4176	−	51.2606i	0.0619492	−	0.0714932i
$718$	−161.011	+	250.538i	−0.224250	+	0.348939i
$719$	691.121	+	797.596i	0.961225	+	1.10931i	0.993948	+	0.109849i	$0.0350367\pi$
$719$	691.121	+	797.596i	0.961225	+	1.10931i	−0.0327229	+	0.999464i	$0.510418\pi$
$720$	−521.918	+	75.0405i	−0.724886	+	0.104223i
$721$	224.114	+	65.8058i	0.310838	+	0.0912701i
$722$	−172.157	+	110.639i	−0.238445	+	0.153239i
$723$	−243.417	−	34.9981i	−0.336676	−	0.0484067i
$724$	−872.425	−	398.423i	−1.20501	−	0.550308i
$725$	−145.219	+	317.985i	−0.200302	+	0.438600i
$726$	0.437871	−	3.04546i	0.000603128	−	0.00419485i
$727$	−137.632	−	214.159i	−0.189314	−	0.294579i	0.733602	−	0.679579i	$-0.237838\pi$
$727$	−137.632	−	214.159i	−0.189314	−	0.294579i	−0.922916	+	0.385000i	$0.874201\pi$
$728$	65.9518	−	224.611i	0.0905931	−	0.308532i
$729$	53.9406	+	375.165i	0.0739927	+	0.514630i
$730$	250.655	−	217.194i	0.343364	−	0.297526i
$731$	624.452	+	401.311i	0.854243	+	0.548989i
$732$	223.849	+	193.966i	0.305804	+	0.264981i
$733$	286.471	+	975.629i	0.390819	+	1.33101i	0.886590	+	0.462555i	$0.153067\pi$
$733$	286.471	+	975.629i	0.390819	+	1.33101i	−0.495771	+	0.868453i	$0.665115\pi$
$734$	−339.230	+	154.921i	−0.462166	+	0.211064i
$735$		−	203.768i		−	0.277235i
$736$	535.527	−	346.906i	0.727619	−	0.471340i
$737$	−371.780			−0.504450
$738$	105.253	+	230.472i	0.142619	+	0.312292i
$739$	401.231	−	117.812i	0.542937	−	0.159421i	0.00124741	−	0.999999i	$-0.499603\pi$
$739$	401.231	−	117.812i	0.542937	−	0.159421i	0.541690	+	0.840578i	$0.317785\pi$
$740$	672.914	−	776.584i	0.909343	−	1.04944i
$741$	52.0174	−	80.9406i	0.0701989	−	0.109232i
$742$	−60.9929	−	70.3895i	−0.0822007	−	0.0948646i
$743$	−379.794	+	54.6062i	−0.511163	+	0.0734942i	−0.393070	−	0.919508i	$-0.628587\pi$
$743$	−379.794	+	54.6062i	−0.511163	+	0.0734942i	−0.118093	+	0.993003i	$0.537678\pi$
$744$	−265.488	−	77.9542i	−0.356838	−	0.104777i
$745$	915.937	−	588.637i	1.22945	−	0.790117i
$746$	195.905	+	28.1669i	0.262608	+	0.0377573i
$747$	11.2869	+	5.15455i	0.0151096	+	0.00690033i
$748$	206.324	−	451.787i	0.275835	−	0.603994i
$749$	−67.7369	+	471.121i	−0.0904365	+	0.628999i
$750$	27.0327	+	42.0637i	0.0360436	+	0.0560850i
$751$	2.27775	−	7.75731i	0.00303296	−	0.0103293i	−0.957963	−	0.286893i	$-0.907378\pi$
$751$	2.27775	−	7.75731i	0.00303296	−	0.0103293i	0.960996	+	0.276564i	$0.0891957\pi$
$752$	−4.59025	−	31.9259i	−0.00610406	−	0.0424547i
$753$	81.4118	−	70.5438i	0.108117	−	0.0936836i
$754$	254.764	+	163.727i	0.337884	+	0.217145i
$755$	−108.479	−	93.9980i	−0.143681	−	0.124501i
$756$	−48.8812	−	166.474i	−0.0646577	−	0.220204i
$757$	−907.788	+	414.573i	−1.19919	+	0.547653i	−0.911988	−	0.410217i	$-0.865453\pi$
$757$	−907.788	+	414.573i	−1.19919	+	0.547653i	−0.287204	+	0.957869i	$0.592726\pi$
$758$		−	62.8659i		−	0.0829366i
$759$	−225.174	−	31.5441i	−0.296672	−	0.0415601i
$760$	238.054			0.313229
$761$	−354.156	−	775.494i	−0.465383	−	1.01905i	−0.986227	−	0.165395i	$-0.947110\pi$
$761$	−354.156	−	775.494i	−0.465383	−	1.01905i	0.520845	−	0.853652i	$-0.325617\pi$
$762$	−23.0200	+	6.75930i	−0.0302100	+	0.00887047i
$763$	106.609	−	123.034i	0.139724	−	0.161250i
$764$	−148.528	+	231.114i	−0.194408	+	0.302505i
$765$	−404.392	−	466.693i	−0.528617	−	0.610056i
$766$	243.050	−	34.9453i	0.317297	−	0.0456205i
$767$	−407.988	−	119.796i	−0.531927	−	0.156188i
$768$	−6.61077	+	4.24848i	−0.00860777	+	0.00553188i
$769$	191.624	+	27.5513i	0.249185	+	0.0358275i	0.265776	−	0.964035i	$-0.414372\pi$
$769$	191.624	+	27.5513i	0.249185	+	0.0358275i	−0.0165902	+	0.999862i	$0.505281\pi$
$770$	−134.880	−	61.5975i	−0.175168	−	0.0799967i
$771$	−55.0106	+	120.456i	−0.0713497	+	0.156234i
$772$	42.7282	−	297.181i	0.0553474	−	0.384949i
$773$	260.031	+	404.617i	0.336392	+	0.523437i	0.967703	−	0.252093i	$-0.0811190\pi$
$773$	260.031	+	404.617i	0.336392	+	0.523437i	−0.631311	+	0.775530i	$0.717483\pi$
$774$	−93.5245	+	318.515i	−0.120833	+	0.411518i
$775$	−96.7971	−	673.239i	−0.124900	−	0.868695i
$776$	110.935	−	96.1260i	0.142958	−	0.123874i
$777$	115.785	+	74.4105i	0.149015	+	0.0957664i
$778$	58.9151	+	51.0502i	0.0757264	+	0.0656173i
$779$	98.8005	+	336.484i	0.126830	+	0.431943i
$780$	240.441	−	109.806i	0.308257	−	0.140776i
$781$		−	295.443i		−	0.378287i
$782$	177.981	+	80.5044i	0.227597	+	0.102947i
$783$	478.202			0.610730
$784$	170.856	+	374.122i	0.217928	+	0.477196i
$785$	290.594	−	85.3262i	0.370184	−	0.108696i
$786$	−28.7343	+	33.1612i	−0.0365577	+	0.0421898i
$787$	280.746	−	436.849i	0.356730	−	0.555082i	−0.615788	−	0.787912i	$-0.711162\pi$
$787$	280.746	−	436.849i	0.356730	−	0.555082i	0.972517	+	0.232830i	$0.0747986\pi$
$788$	−494.826	−	571.059i	−0.627951	−	0.724694i
$789$	442.625	−	63.6399i	0.560995	−	0.0806589i
$790$	340.534	+	99.9897i	0.431055	+	0.126569i
$791$	−315.016	+	202.449i	−0.398251	+	0.255940i
$792$	468.409	+	67.3471i	0.591426	+	0.0850342i
$793$	1222.38	+	558.244i	1.54147	+	0.703965i
$794$	−7.78479	+	17.0463i	−0.00980452	+	0.0214689i
$795$	31.8872	−	221.781i	0.0401097	−	0.278969i
$796$	26.4279	+	41.1226i	0.0332009	+	0.0516616i
$797$	−111.392	+	379.367i	−0.139764	+	0.475993i	−0.999390	−	0.0349314i	$-0.988879\pi$
$797$	−111.392	+	379.367i	−0.139764	+	0.475993i	0.859625	+	0.510925i	$0.170697\pi$
$798$	2.12989	+	14.8137i	0.00266903	+	0.0185635i
$799$	28.5478	−	24.7368i	0.0357294	−	0.0309597i
$800$	258.666	+	166.235i	0.323332	+	0.207793i
$801$	249.441	+	216.142i	0.311412	+	0.269840i
$802$	−83.4033	−	284.045i	−0.103994	−	0.354171i
$803$	830.096	−	379.092i	1.03374	−	0.472095i
$804$			103.089i			0.128221i
$805$	−184.155	+	407.135i	−0.228764	+	0.505758i
$806$	−589.229			−0.731053
$807$	34.5666	+	75.6904i	0.0428335	+	0.0937923i
$808$	−93.9516	+	27.5867i	−0.116277	+	0.0341419i
$809$	−332.291	+	383.485i	−0.410743	+	0.474023i	−0.922995	−	0.384812i	$-0.874266\pi$
$809$	−332.291	+	383.485i	−0.410743	+	0.474023i	0.512251	+	0.858836i	$0.328812\pi$
$810$	133.919	−	208.382i	0.165332	−	0.257261i
$811$	−120.437	−	138.991i	−0.148504	−	0.171382i	0.676624	−	0.736329i	$-0.263442\pi$
$811$	−120.437	−	138.991i	−0.148504	−	0.171382i	−0.825128	+	0.564946i	$0.808897\pi$
$812$	357.263	−	51.3666i	0.439979	−	0.0632594i
$813$	224.617	+	65.9536i	0.276282	+	0.0811237i
$814$	−310.419	+	199.494i	−0.381350	+	0.245079i
$815$	−173.195	−	24.9017i	−0.212509	−	0.0305542i
$816$	−106.791	−	48.7698i	−0.130871	−	0.0597669i
$817$	−190.871	+	417.950i	−0.233624	+	0.511566i
$818$	−2.91634	+	20.2836i	−0.00356521	+	0.0247966i
$819$	−203.218	−	316.214i	−0.248130	−	0.386097i
$820$	−271.432	+	924.413i	−0.331015	+	1.12733i
$821$	−128.915	−	896.625i	−0.157022	−	1.09211i	−0.904083	−	0.427357i	$-0.859445\pi$
$821$	−128.915	−	896.625i	−0.157022	−	1.09211i	0.747061	−	0.664756i	$-0.231464\pi$
$822$	119.620	−	103.651i	0.145523	−	0.126096i
$823$	−961.796	−	618.109i	−1.16865	−	0.751043i	−0.195381	−	0.980727i	$-0.562594\pi$
$823$	−961.796	−	618.109i	−1.16865	−	0.751043i	−0.973265	+	0.229684i	$0.926231\pi$
$824$	279.585	+	242.261i	0.339302	+	0.294006i
$825$	−30.8687	−	105.129i	−0.0374167	−	0.127429i
$826$	60.1642	−	27.4761i	0.0728380	−	0.0332640i
$827$		−	986.987i		−	1.19345i	−0.802444	−	0.596727i	$-0.796467\pi$
$827$		−	986.987i		−	1.19345i	0.802444	−	0.596727i	$-0.203533\pi$
$828$	92.8631	−	662.892i	0.112154	−	0.800594i
$829$	703.717			0.848875			0.424437	−	0.905457i	$-0.360472\pi$
$829$	703.717			0.848875			0.424437	+	0.905457i	$0.360472\pi$
$830$	−2.55806	−	5.60137i	−0.00308200	−	0.00674864i
$831$	−49.0443	+	14.4007i	−0.0590184	+	0.0173294i
$832$	−220.548	+	254.526i	−0.265081	+	0.305920i
$833$	−260.414	+	405.212i	−0.312622	+	0.486449i
$834$	−16.1341	−	18.6198i	−0.0193455	−	0.0223259i
$835$	−1621.42	+	233.125i	−1.94182	+	0.279192i
$836$	294.983	+	86.6147i	0.352850	+	0.103606i
$837$	−782.726	+	503.028i	−0.935157	+	0.600989i
$838$	−218.447	−	31.4079i	−0.260676	−	0.0374796i
$839$	1176.27	+	537.183i	1.40199	+	0.640266i	0.965728	−	0.259555i	$-0.0835760\pi$
$839$	1176.27	+	537.183i	1.40199	+	0.640266i	0.436259	+	0.899821i	$0.356303\pi$
$840$	−36.3894	+	79.6817i	−0.0433207	+	0.0948592i
$841$	−21.8885	+	152.238i	−0.0260267	+	0.181020i
$842$	−122.198	−	190.144i	−0.145129	−	0.225825i
$843$	6.11769	−	20.8349i	0.00725705	−	0.0247152i
$844$	−41.9555	−	291.807i	−0.0497104	−	0.345743i
$845$	139.111	−	120.540i	0.164628	−	0.142651i
$846$	14.2114	+	9.13313i	0.0167984	+	0.0107957i
$847$	−12.5735	−	10.8950i	−0.0148448	−	0.0128631i
$848$	127.414	+	433.931i	0.150252	+	0.511711i
$849$	−319.564	+	145.940i	−0.376400	+	0.171896i
$850$			94.1322i			0.110744i
$851$	604.565	+	933.282i	0.710418	+	1.09669i
$852$	−81.9222			−0.0961528
$853$	−293.079	−	641.754i	−0.343586	−	0.752349i	0.656412	−	0.754403i	$-0.272073\pi$
$853$	−293.079	−	641.754i	−0.343586	−	0.752349i	−0.999998	+	0.00205404i	$0.999346\pi$
$854$	−200.563	+	58.8906i	−0.234851	+	0.0689585i
$855$	250.316	−	288.880i	0.292767	−	0.337871i
$856$	−407.561	+	634.177i	−0.476122	+	0.740861i
$857$	−527.115	−	608.323i	−0.615070	−	0.709828i	0.359693	−	0.933071i	$-0.382881\pi$
$857$	−527.115	−	608.323i	−0.615070	−	0.709828i	−0.974763	+	0.223242i	$0.928336\pi$
$858$	−93.9529	+	13.5084i	−0.109502	+	0.0157440i
$859$	−40.3200	−	11.8390i	−0.0469383	−	0.0137823i	0.258179	−	0.966097i	$-0.416878\pi$
$859$	−40.3200	−	11.8390i	−0.0469383	−	0.0137823i	−0.305117	+	0.952315i	$0.598696\pi$
$860$	−1061.91	+	682.448i	−1.23478	+	0.793544i
$861$	−127.731	−	18.3650i	−0.148352	−	0.0213298i
$862$	−330.784	−	151.064i	−0.383740	−	0.175248i
$863$	352.113	−	771.020i	0.408010	−	0.893418i	−0.588384	−	0.808581i	$-0.700236\pi$
$863$	352.113	−	771.020i	0.408010	−	0.893418i	0.996395	−	0.0848368i	$-0.0270369\pi$
$864$	59.8595	−	416.332i	0.0692819	−	0.481866i
$865$	−368.687	−	573.688i	−0.426228	−	0.663223i
$866$	−11.0692	+	37.6983i	−0.0127820	+	0.0435315i
$867$	16.6342	+	115.694i	0.0191860	+	0.133441i
$868$	−530.738	+	459.888i	−0.611450	+	0.529824i
$869$	821.502	+	527.947i	0.945341	+	0.607534i
$870$	−85.6433	−	74.2103i	−0.0984405	−	0.0852992i
$871$	131.770	+	448.767i	0.151286	+	0.515232i
$872$	234.542	−	107.112i	0.268970	−	0.122834i
$873$		−	235.698i		−	0.269986i
$874$	−33.6458	+	116.140i	−0.0384963	+	0.132883i
$875$	270.374			0.308999
$876$	−105.117	−	230.174i	−0.119997	−	0.262756i
$877$	−359.435	+	105.540i	−0.409846	+	0.120342i	−0.480155	−	0.877184i	$-0.659420\pi$
$877$	−359.435	+	105.540i	−0.409846	+	0.120342i	0.0703091	+	0.997525i	$0.477601\pi$
$878$	218.228	−	251.849i	0.248551	−	0.286843i
$879$	34.7570	−	54.0829i	0.0395415	−	0.0615277i
$880$	471.496	+	544.135i	0.535791	+	0.618335i
$881$	896.921	−	128.958i	1.01807	−	0.146377i	0.386982	−	0.922087i	$-0.373517\pi$
$881$	896.921	−	128.958i	1.01807	−	0.146377i	0.631089	+	0.775711i	$0.282608\pi$
$882$	−206.687	−	60.6889i	−0.234339	−	0.0688082i
$883$	−1453.42	+	934.059i	−1.64601	+	1.05782i	−0.711001	+	0.703191i	$0.751758\pi$
$883$	−1453.42	+	934.059i	−1.64601	+	1.05782i	−0.935006	+	0.354633i	$0.884606\pi$
$884$	−618.470	−	88.9226i	−0.699627	−	0.100591i
$885$	144.735	+	66.0984i	0.163543	+	0.0746875i
$886$	−180.732	+	395.749i	−0.203987	+	0.446669i
$887$	−0.250172	+	1.73998i	−0.000282043	+	0.00196165i	−0.989962	−	0.141334i	$-0.954861\pi$
$887$	−0.250172	+	1.73998i	−0.000282043	+	0.00196165i	0.989680	+	0.143296i	$0.0457700\pi$
$888$	117.854	+	183.384i	0.132718	+	0.206513i
$889$	−36.5498	+	124.477i	−0.0411134	+	0.140019i
$890$	−23.3110	−	162.132i	−0.0261921	−	0.182170i
$891$	515.079	−	446.318i	0.578091	−	0.500919i
$892$	319.534	+	205.352i	0.358222	+	0.230215i
$893$	17.6709	+	15.3119i	0.0197882	+	0.0171466i
$894$	30.5432	+	104.021i	0.0341647	+	0.116354i
$895$	682.788	−	311.819i	0.762892	−	0.348401i
$896$		−	411.290i		−	0.459029i
$897$	41.7321	+	282.982i	0.0465241	+	0.315476i
$898$	387.837			0.431890
$899$	−804.065	−	1760.66i	−0.894399	−	1.95846i
$900$	309.491	−	90.8749i	0.343879	−	0.100972i
$901$	−346.845	+	400.280i	−0.384956	+	0.444262i
$902$	187.044	−	291.047i	0.207366	−	0.322668i
$903$	−110.720	−	127.777i	−0.122613	−	0.141503i
$904$	−587.045	+	84.4043i	−0.649386	+	0.0933676i
$905$	1562.33	+	458.741i	1.72633	+	0.506896i
$906$	12.0236	−	7.72712i	0.0132711	−	0.00852884i
$907$	691.604	+	99.4377i	0.762518	+	0.109634i	0.512593	−	0.858632i	$-0.328685\pi$
$907$	691.604	+	99.4377i	0.762518	+	0.109634i	0.249925	+	0.968265i	$0.419594\pi$
$908$	606.606	+	277.028i	0.668068	+	0.305096i
$909$	−65.3144	+	143.019i	−0.0718530	+	0.157336i
$910$	−26.5475	+	184.642i	−0.0291731	+	0.202904i
$911$	−189.064	−	294.189i	−0.207534	−	0.322930i	0.721846	−	0.692054i	$-0.243294\pi$
$911$	−189.064	−	294.189i	−0.207534	−	0.322930i	−0.929380	+	0.369124i	$0.879658\pi$
$912$	20.4735	−	69.7263i	0.0224490	−	0.0764543i
$913$	−2.41125	−	16.7706i	−0.00264102	−	0.0183687i
$914$	78.9687	−	68.4268i	0.0863990	−	0.0748652i
$915$	−423.031	−	271.865i	−0.462329	−	0.297121i
$916$	446.802	+	387.156i	0.487775	+	0.422659i
$917$	66.8457	+	227.656i	0.0728961	+	0.248261i
$918$	117.132	−	53.4923i	0.127595	−	0.0582705i
$919$		−	966.448i		−	1.05163i	−0.850599	−	0.525815i	$-0.823760\pi$
$919$		−	966.448i		−	1.05163i	0.850599	−	0.525815i	$-0.176240\pi$
$920$	−533.186	+	465.396i	−0.579550	+	0.505865i
$921$	407.216			0.442145
$922$	−82.7049	−	181.098i	−0.0897016	−	0.196419i
$923$	−356.622	+	104.714i	−0.386373	+	0.113449i
$924$	−74.0835	+	85.4969i	−0.0801769	+	0.0925291i
$925$	−289.703	+	450.786i	−0.313192	+	0.487336i
$926$	140.110	+	161.696i	0.151307	+	0.174617i
$927$	587.972	−	84.5376i	0.634274	−	0.0911948i
$928$	839.558	+	246.517i	0.904697	+	0.265643i
$929$	451.608	−	290.231i	0.486122	−	0.312412i	−0.274522	−	0.961581i	$-0.588520\pi$
$929$	451.608	−	290.231i	0.486122	−	0.312412i	0.760644	+	0.649169i	$0.224883\pi$
$930$	218.245	+	31.3789i	0.234672	+	0.0337407i
$931$	−271.211	−	123.858i	−0.291312	−	0.133038i
$932$	220.341	−	482.480i	0.236418	−	0.517683i
$933$	−68.8901	+	479.141i	−0.0738372	+	0.513549i
$934$	21.1950	+	32.9800i	0.0226927	+	0.0353105i
$935$	−237.560	+	809.056i	−0.254075	+	0.865301i
$936$	−84.7252	−	589.276i	−0.0905183	−	0.629569i
$937$	927.995	−	804.112i	0.990390	−	0.858178i	0.000497552	−	1.00000i	$-0.499842\pi$
$937$	927.995	−	804.112i	0.990390	−	0.858178i	0.989892	+	0.141822i	$0.0452962\pi$
$938$	−61.2030	−	39.3328i	−0.0652484	−	0.0419326i
$939$	−84.7899	−	73.4709i	−0.0902981	−	0.0782437i
$940$	18.0976	+	61.6347i	0.0192527	+	0.0655688i
$941$	169.343	−	77.3363i	0.179961	−	0.0821852i	−0.323397	−	0.946263i	$-0.604825\pi$
$941$	169.343	−	77.3363i	0.179961	−	0.0821852i	0.503358	+	0.864078i	$0.332098\pi$
$942$			30.1568i			0.0320136i
$943$	−879.116	−	560.490i	−0.932254	−	0.594369i
$944$	−321.159			−0.340211
$945$	122.365	+	267.941i	0.129486	+	0.283535i
$946$	434.924	−	127.705i	0.459751	−	0.134995i
$947$	450.639	−	520.065i	0.475860	−	0.549171i	−0.466173	−	0.884694i	$-0.654367\pi$
$947$	450.639	−	520.065i	0.475860	−	0.549171i	0.942032	+	0.335523i	$0.108913\pi$
$948$	146.392	−	227.791i	0.154422	−	0.240286i
$949$	−751.804	−	867.629i	−0.792207	−	0.914256i
$950$	−57.6742	+	8.29230i	−0.0607097	+	0.00872873i
$951$	143.513	+	42.1393i	0.150908	+	0.0443105i
$952$	174.196	−	111.949i	0.182980	−	0.117594i
$953$	−684.106	−	98.3596i	−0.717845	−	0.103211i	−0.226294	−	0.974059i	$-0.572661\pi$
$953$	−684.106	−	98.3596i	−0.717845	−	0.103211i	−0.491551	+	0.870849i	$0.663570\pi$
$954$	−215.461	−	98.3977i	−0.225850	−	0.103142i
$955$	193.753	−	424.261i	0.202883	−	0.444252i
$956$	38.8029	−	269.880i	0.0405888	−	0.282302i
$957$	−168.573	−	262.304i	−0.176147	−	0.274090i
$958$	−98.9995	+	337.161i	−0.103340	+	0.351943i
$959$	−121.803	−	847.161i	−0.127011	−	0.883380i
$960$	95.2434	−	82.5289i	0.0992119	−	0.0859676i
$961$	2359.72	+	1516.50i	2.45548	+	1.57804i
$962$	350.827	+	303.993i	0.364685	+	0.316001i
$963$	341.024	+	1161.42i	0.354127	+	1.20604i
$964$	−899.225	+	410.662i	−0.932806	+	0.425998i
$965$			509.721i			0.528208i
$966$	−33.7312	−	29.0153i	−0.0349185	−	0.0300366i
$967$	−1523.80			−1.57580			−0.787900	−	0.615803i	$-0.788832\pi$
$967$	−1523.80			−1.57580			−0.787900	+	0.615803i	$0.788832\pi$
$968$	−10.9464	−	23.9692i	−0.0113082	−	0.0247616i
$969$	81.6591	−	23.9773i	0.0842715	−	0.0247444i
$970$	−76.5994	+	88.4004i	−0.0789685	+	0.0911345i
$971$	−472.031	+	734.495i	−0.486129	+	0.756431i	−0.994503	−	0.104705i	$-0.966610\pi$
$971$	−472.031	+	734.495i	−0.486129	+	0.756431i	0.508375	+	0.861136i	$0.330247\pi$
$972$	−439.927	−	507.703i	−0.452600	−	0.522328i
$973$	−131.867	+	18.9597i	−0.135527	+	0.0194858i
$974$	509.095	+	149.484i	0.522684	+	0.153474i
$975$	−115.958	+	74.5220i	−0.118932	+	0.0764328i
$976$	1004.65	+	144.447i	1.02935	+	0.147999i
$977$	−847.493	−	387.037i	−0.867444	−	0.396148i	−0.0685698	−	0.997646i	$-0.521844\pi$
$977$	−847.493	−	387.037i	−0.867444	−	0.396148i	−0.798874	+	0.601498i	$0.794571\pi$
$978$	7.23769	−	15.8483i	0.00740050	−	0.0162048i
$979$	64.1393	−	446.098i	0.0655151	−	0.455668i
$980$	−442.846	−	689.082i	−0.451884	−	0.703145i
$981$	116.642	−	397.247i	0.118901	−	0.404941i
$982$	51.4456	+	357.812i	0.0523886	+	0.364371i
$983$	−733.929	+	635.953i	−0.746622	+	0.646951i	−0.942702	−	0.333636i	$-0.891724\pi$
$983$	−733.929	+	635.953i	−0.746622	+	0.646951i	0.196080	+	0.980588i	$0.437179\pi$
$984$	−171.939	−	110.499i	−0.174735	−	0.112295i
$985$	969.504	+	840.080i	0.984268	+	0.852873i
$986$	75.4696	+	257.026i	0.0765412	+	0.260675i
$987$	−7.82644	+	3.57421i	−0.00792952	+	0.00362129i
$988$		−	386.766i		−	0.391464i
$989$	−389.585	−	1309.26i	−0.393918	−	1.32383i
$990$	−377.097			−0.380906
$991$	526.748	+	1153.42i	0.531532	+	1.16389i	0.964886	+	0.262669i	$0.0846027\pi$
$991$	526.748	+	1153.42i	0.531532	+	1.16389i	−0.433354	+	0.901224i	$0.642670\pi$
$992$	−1633.51	+	479.643i	−1.64669	+	0.483511i
$993$	−256.291	+	295.775i	−0.258098	+	0.297860i
$994$	31.2566	−	48.6363i	0.0314453	−	0.0489298i
$995$	−54.3464	−	62.7191i	−0.0546195	−	0.0630343i
$996$	−4.65026	+	0.668606i	−0.00466893	+	0.000671291i
$997$	−883.309	−	259.363i	−0.885967	−	0.260143i	−0.193074	−	0.981184i	$-0.561846\pi$
$997$	−883.309	−	259.363i	−0.885967	−	0.260143i	−0.692892	+	0.721041i	$0.743664\pi$
$998$	245.444	−	157.737i	0.245936	−	0.158053i
$999$	725.556	+	104.319i	0.726283	+	0.104424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.19.2	yes	30
3.2	odd	2		207.3.j.a.19.2		30
4.3	odd	2		368.3.p.a.65.1		30
23.11	odd	22		529.3.b.b.528.13		30
23.12	even	11		529.3.b.b.528.14		30
23.17	odd	22	inner	23.3.d.a.17.2	✓	30
69.17	even	22		207.3.j.a.109.2		30
92.63	even	22		368.3.p.a.17.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.17.2	✓	30	23.17	odd	22	inner
23.3.d.a.19.2	yes	30	1.1	even	1	trivial
207.3.j.a.19.2		30	3.2	odd	2
207.3.j.a.109.2		30	69.17	even	22
368.3.p.a.17.1		30	92.63	even	22
368.3.p.a.65.1		30	4.3	odd	2
529.3.b.b.528.13		30	23.11	odd	22
529.3.b.b.528.14		30	23.12	even	11

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.282292 - 0.618133i) q^{2} +(0.844537 - 0.247978i) q^{3} +(2.31704 - 2.67401i) q^{4} +(-3.24760 + 5.05336i) q^{5} +(-0.391690 - 0.452034i) q^{6} +(-3.20136 + 0.460286i) q^{7} +(-4.91504 - 1.44319i) q^{8} +(-6.91953 + 4.44691i) q^{9} +O(q^{10})\)	\(q+(-0.282292 - 0.618133i) q^{2} +(0.844537 - 0.247978i) q^{3} +(2.31704 - 2.67401i) q^{4} +(-3.24760 + 5.05336i) q^{5} +(-0.391690 - 0.452034i) q^{6} +(-3.20136 + 0.460286i) q^{7} +(-4.91504 - 1.44319i) q^{8} +(-6.91953 + 4.44691i) q^{9} +(4.04042 + 0.580925i) q^{10} +(10.2164 + 4.66569i) q^{11} +(1.29373 - 2.83288i) q^{12} +(2.01084 - 13.9857i) q^{13} +(1.18824 + 1.84893i) q^{14} +(-1.48959 + 5.07308i) q^{15} +(-1.51877 - 10.5633i) q^{16} +(9.44556 - 8.18463i) q^{17} +(4.70212 + 3.02187i) q^{18} +(5.84675 + 5.06623i) q^{19} +(5.98792 + 20.3930i) q^{20} +(-2.58952 + 1.18259i) q^{21} -7.63220i q^{22} +(-22.9998 + 0.0832022i) q^{23} -4.50881 q^{24} +(-4.60420 - 10.0818i) q^{25} +(-9.21266 + 2.70508i) q^{26} +(-9.92868 + 11.4583i) q^{27} +(-6.18687 + 9.62696i) q^{28} +(-20.6546 - 23.8367i) q^{29} +(3.55634 - 0.511325i) q^{30} +(58.8820 + 17.2893i) q^{31} +(-23.3382 + 14.9986i) q^{32} +(9.78514 + 1.40689i) q^{33} +(-7.72560 - 3.52816i) q^{34} +(8.07073 - 17.6724i) q^{35} +(-4.14176 + 28.8066i) q^{36} +(-26.1385 - 40.6723i) q^{37} +(1.48112 - 5.04423i) q^{38} +(-1.76992 - 12.3101i) q^{39} +(23.2550 - 20.1506i) q^{40} +(38.1340 + 24.5073i) q^{41} +(1.46200 + 1.26683i) q^{42} +(16.7324 + 56.9854i) q^{43} +(36.1480 - 16.5082i) q^{44} -49.4087i q^{45} +(6.54411 + 14.1935i) q^{46} +3.02235 q^{47} +(-3.90212 - 8.54445i) q^{48} +(-36.9783 + 10.8578i) q^{49} +(-4.93216 + 5.69202i) q^{50} +(5.94751 - 9.25451i) q^{51} +(-32.7387 - 37.7824i) q^{52} +(-41.9463 + 6.03096i) q^{53} +(9.88555 + 2.90266i) q^{54} +(-56.7563 + 36.4750i) q^{55} +(16.3991 + 2.35783i) q^{56} +(6.19411 + 2.82875i) q^{57} +(-8.90363 + 19.4962i) q^{58} +(4.28281 - 29.7876i) q^{59} +(10.1140 + 15.7377i) q^{60} +(-26.7949 + 91.2550i) q^{61} +(-5.93481 - 41.2775i) q^{62} +(20.1050 - 17.4211i) q^{63} +(-20.0518 - 12.8865i) q^{64} +(64.1443 + 55.5814i) q^{65} +(-1.89262 - 6.44567i) q^{66} +(-30.1105 + 13.7510i) q^{67} -44.2217i q^{68} +(-19.4036 + 5.77373i) q^{69} -13.2022 q^{70} +(-10.9275 - 23.9279i) q^{71} +(40.4275 - 11.8706i) q^{72} +(53.2081 - 61.4055i) q^{73} +(-17.7622 + 27.6385i) q^{74} +(-6.38848 - 7.37270i) q^{75} +(27.0943 - 3.89557i) q^{76} +(-34.8540 - 10.2341i) q^{77} +(-7.10963 + 4.56908i) q^{78} +(86.0607 + 12.3737i) q^{79} +(58.3124 + 26.6304i) q^{80} +(25.2084 - 55.1986i) q^{81} +(4.38382 - 30.4901i) q^{82} +(-0.815582 - 1.26907i) q^{83} +(-2.83776 + 9.66453i) q^{84} +(10.6845 + 74.3122i) q^{85} +(30.5012 - 26.4294i) q^{86} +(-23.3546 - 15.0091i) q^{87} +(-43.4807 - 37.6763i) q^{88} +(-11.3052 - 38.5019i) q^{89} +(-30.5412 + 13.9477i) q^{90} +45.6987i q^{91} +(-53.0692 + 61.6946i) q^{92} +54.0153 q^{93} +(-0.853185 - 1.86821i) q^{94} +(-44.5894 + 13.0926i) q^{95} +(-15.9906 + 18.4542i) q^{96} +(-15.4923 + 24.1065i) q^{97} +(17.1503 + 19.7925i) q^{98} +(-91.4408 + 13.1472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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