LMFDB - Embedded newform 507.2.p.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	507.25
Dual form			507.2.p.b.142.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.42142 - 0.918325i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(3.52295 + 3.12106i) q^{4} +(-2.78849 - 0.338584i) q^{5} +(0.619759 + 2.51446i) q^{6} +(0.357250 + 0.680683i) q^{7} +(-3.25740 - 6.20646i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(-2.42142 - 0.918325i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(3.52295 + 3.12106i) q^{4} +(-2.78849 - 0.338584i) q^{5} +(0.619759 + 2.51446i) q^{6} +(0.357250 + 0.680683i) q^{7} +(-3.25740 - 6.20646i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(6.44118 + 3.38059i) q^{10} +(4.55001 - 1.72559i) q^{11} +(0.567319 - 4.67229i) q^{12} +(0.426821 + 3.58020i) q^{13} +(-0.239965 - 1.97629i) q^{14} +(1.30539 + 2.48722i) q^{15} +(1.05336 + 8.67523i) q^{16} +(-4.26999 + 2.24106i) q^{17} +(1.71730 - 1.93843i) q^{18} -8.27012i q^{19} +(-8.76695 - 9.89585i) q^{20} +(0.357250 - 0.680683i) q^{21} -12.6022 q^{22} +7.93022 q^{23} +(-3.25740 + 6.20646i) q^{24} +(2.80631 + 0.691694i) q^{25} +(2.25427 - 9.06114i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.865879 + 3.51301i) q^{28} +(0.487944 - 1.28660i) q^{29} +(-0.876834 - 7.22138i) q^{30} +(0.182989 + 0.742415i) q^{31} +(2.06115 - 8.36241i) q^{32} +(-4.00484 - 2.76434i) q^{33} +(12.3975 - 1.50533i) q^{34} +(-0.765719 - 2.01903i) q^{35} +(-4.16749 + 2.18727i) q^{36} +(-1.62657 - 6.59927i) q^{37} +(-7.59465 + 20.0255i) q^{38} +(2.70398 - 2.38505i) q^{39} +(6.98182 + 18.4095i) q^{40} +(-3.69768 + 2.55233i) q^{41} +(-1.49014 + 1.32015i) q^{42} +(-3.71907 - 0.916669i) q^{43} +(21.4151 + 8.12169i) q^{44} +(1.30539 - 2.48722i) q^{45} +(-19.2024 - 7.28252i) q^{46} +(-6.53082 - 7.37177i) q^{47} +(6.54119 - 5.79499i) q^{48} +(3.64075 - 5.27454i) q^{49} +(-6.16007 - 4.25199i) q^{50} +(4.26999 + 2.24106i) q^{51} +(-9.67034 + 13.9450i) q^{52} +(-9.82440 + 5.15625i) q^{53} +(-2.57083 - 0.312155i) q^{54} +(-13.2719 + 3.27123i) q^{55} +(3.06092 - 4.43451i) q^{56} +(-6.80617 + 4.69796i) q^{57} +(-2.36304 + 2.66732i) q^{58} +(-8.22987 - 0.999287i) q^{59} +(-3.16392 + 12.8365i) q^{60} +(-4.46187 - 2.34177i) q^{61} +(0.238684 - 1.96574i) q^{62} +(-0.763132 + 0.0926610i) q^{63} +(-2.74174 + 3.97210i) q^{64} +(0.0220109 - 10.1279i) q^{65} +(7.15884 + 10.3714i) q^{66} +(-0.939647 - 1.06064i) q^{67} +(-22.0374 - 5.43174i) q^{68} +(-4.50488 - 6.52645i) q^{69} +5.59212i q^{70} +(12.2981 - 8.48880i) q^{71} +(6.95823 - 0.844882i) q^{72} +(1.03109 - 0.391040i) q^{73} +(-2.12165 + 17.4734i) q^{74} +(-1.02492 - 2.70248i) q^{75} +(25.8115 - 29.1352i) q^{76} +(2.80007 + 2.48065i) q^{77} +(-8.73774 + 3.29208i) q^{78} +(-1.36177 + 1.20643i) q^{79} -24.5474i q^{80} +(-0.748511 - 0.663123i) q^{81} +(11.2975 - 2.78459i) q^{82} +(-5.58437 - 3.85461i) q^{83} +(3.38302 - 1.28301i) q^{84} +(12.6656 - 4.80343i) q^{85} +(8.16364 + 5.63496i) q^{86} +(-1.33604 + 0.329304i) q^{87} +(-25.5310 - 22.6185i) q^{88} +3.92147i q^{89} +(-5.44498 + 4.82383i) q^{90} +(-2.28450 + 1.56956i) q^{91} +(27.9378 + 24.7507i) q^{92} +(0.507046 - 0.572336i) q^{93} +(9.04419 + 23.8476i) q^{94} +(-2.80013 + 23.0611i) q^{95} +(-8.05299 + 3.05410i) q^{96} +(-2.17329 + 0.263885i) q^{97} +(-13.6595 + 9.42850i) q^{98} +4.86624i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	−2.42142	−	0.918325i	−1.71220	−	0.649353i	−0.713520	−	0.700635i	$-0.752900\pi$
$2$	−2.42142	−	0.918325i	−1.71220	−	0.649353i	−0.998684	+	0.0512812i	$0.983670\pi$
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$4$	3.52295	+	3.12106i	1.76147	+	1.56053i
$5$	−2.78849	−	0.338584i	−1.24705	−	0.151419i	−0.529732	−	0.848165i	$-0.677707\pi$
$5$	−2.78849	−	0.338584i	−1.24705	−	0.151419i	−0.717318	+	0.696746i	$0.754630\pi$
$6$	0.619759	+	2.51446i	0.253015	+	1.02652i
$7$	0.357250	+	0.680683i	0.135028	+	0.257274i	0.943576	−	0.331156i	$-0.107439\pi$
$7$	0.357250	+	0.680683i	0.135028	+	0.257274i	−0.808548	+	0.588430i	$0.799746\pi$
$8$	−3.25740	−	6.20646i	−1.15167	−	2.19431i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	6.44118	+	3.38059i	2.03688	+	1.06904i
$11$	4.55001	−	1.72559i	1.37188	−	0.520286i	0.444963	−	0.895549i	$-0.353217\pi$
$11$	4.55001	−	1.72559i	1.37188	−	0.520286i	0.926918	+	0.375263i	$0.122448\pi$
$12$	0.567319	−	4.67229i	0.163771	−	1.34877i
$13$	0.426821	+	3.58020i	0.118379	+	0.992968i
$13$	0.426821	+	3.58020i	0.118379	+	0.992968i
$14$	−0.239965	−	1.97629i	−0.0641334	−	0.528186i
$15$	1.30539	+	2.48722i	0.337051	+	0.642197i
$16$	1.05336	+	8.67523i	0.263341	+	2.16881i
$17$	−4.26999	+	2.24106i	−1.03562	+	0.543538i	−0.894786	−	0.446495i	$-0.852672\pi$
$17$	−4.26999	+	2.24106i	−1.03562	+	0.543538i	−0.140838	+	0.990033i	$0.544980\pi$
$18$	1.71730	−	1.93843i	0.404771	−	0.456892i
$19$		−	8.27012i		−	1.89730i	−0.316334	−	0.948648i	$-0.602452\pi$
$19$		−	8.27012i		−	1.89730i	0.316334	−	0.948648i	$-0.397548\pi$
$20$	−8.76695	−	9.89585i	−1.96035	−	2.21278i
$21$	0.357250	−	0.680683i	0.0779583	−	0.148537i
$22$	−12.6022			−2.68679
$23$	7.93022			1.65357			0.826783	−	0.562521i	$-0.190169\pi$
$23$	7.93022			1.65357			0.826783	+	0.562521i	$0.190169\pi$
$24$	−3.25740	+	6.20646i	−0.664914	+	1.26689i
$25$	2.80631	+	0.691694i	0.561263	+	0.138339i
$26$	2.25427	−	9.06114i	0.442099	−	1.77703i
$27$	0.970942	−	0.239316i	0.186858	−	0.0460563i
$28$	−0.865879	+	3.51301i	−0.163636	+	0.663896i
$29$	0.487944	−	1.28660i	0.0906090	−	0.238916i	−0.882049	−	0.471157i	$-0.843836\pi$
$29$	0.487944	−	1.28660i	0.0906090	−	0.238916i	0.972658	+	0.232241i	$0.0746057\pi$
$30$	−0.876834	−	7.22138i	−0.160087	−	1.31844i
$31$	0.182989	+	0.742415i	0.0328657	+	0.133342i	0.985083	−	0.172080i	$-0.0550488\pi$
$31$	0.182989	+	0.742415i	0.0328657	+	0.133342i	−0.952217	+	0.305422i	$0.901203\pi$
$32$	2.06115	−	8.36241i	0.364363	−	1.47828i
$33$	−4.00484	−	2.76434i	−0.697153	−	0.481210i
$34$	12.3975	−	1.50533i	2.12615	−	0.258161i
$35$	−0.765719	−	2.01903i	−0.129430	−	0.341279i
$36$	−4.16749	+	2.18727i	−0.694582	+	0.364545i
$37$	−1.62657	−	6.59927i	−0.267407	−	1.08491i	−0.938979	−	0.343974i	$-0.888227\pi$
$37$	−1.62657	−	6.59927i	−0.267407	−	1.08491i	0.671572	−	0.740940i	$-0.265620\pi$
$38$	−7.59465	+	20.0255i	−1.23202	+	3.24856i
$39$	2.70398	−	2.38505i	0.432984	−	0.381914i
$40$	6.98182	+	18.4095i	1.10392	+	2.91080i
$41$	−3.69768	+	2.55233i	−0.577481	+	0.398607i	−0.820695	−	0.571366i	$-0.806414\pi$
$41$	−3.69768	+	2.55233i	−0.577481	+	0.398607i	0.243214	+	0.969973i	$0.421798\pi$
$42$	−1.49014	+	1.32015i	−0.229934	+	0.203704i
$43$	−3.71907	−	0.916669i	−0.567153	−	0.139791i	−0.0546953	−	0.998503i	$-0.517419\pi$
$43$	−3.71907	−	0.916669i	−0.567153	−	0.139791i	−0.512458	+	0.858712i	$0.671265\pi$
$44$	21.4151	+	8.12169i	3.22845	+	1.22439i
$45$	1.30539	−	2.48722i	0.194596	−	0.370773i
$46$	−19.2024	−	7.28252i	−2.83124	−	1.07375i
$47$	−6.53082	−	7.37177i	−0.952618	−	1.07528i	−0.997087	−	0.0762722i	$-0.975698\pi$
$47$	−6.53082	−	7.37177i	−0.952618	−	1.07528i	0.0444694	−	0.999011i	$-0.485840\pi$
$48$	6.54119	−	5.79499i	0.944140	−	0.836435i
$49$	3.64075	−	5.27454i	0.520107	−	0.753506i
$50$	−6.16007	−	4.25199i	−0.871166	−	0.601323i
$51$	4.26999	+	2.24106i	0.597918	+	0.313812i
$52$	−9.67034	+	13.9450i	−1.34104	+	1.93382i
$53$	−9.82440	+	5.15625i	−1.34949	+	0.708265i	−0.975671	−	0.219239i	$-0.929643\pi$
$53$	−9.82440	+	5.15625i	−1.34949	+	0.708265i	−0.373815	+	0.927503i	$0.621950\pi$
$54$	−2.57083	−	0.312155i	−0.349846	−	0.0424790i
$55$	−13.2719	+	3.27123i	−1.78958	+	0.441093i
$56$	3.06092	−	4.43451i	0.409033	−	0.592587i
$57$	−6.80617	+	4.69796i	−0.901500	+	0.622260i
$58$	−2.36304	+	2.66732i	−0.310282	+	0.350236i
$59$	−8.22987	−	0.999287i	−1.07144	−	0.130096i	−0.434240	−	0.900797i	$-0.642983\pi$
$59$	−8.22987	−	0.999287i	−1.07144	−	0.130096i	−0.637197	+	0.770701i	$0.719906\pi$
$60$	−3.16392	+	12.8365i	−0.408461	+	1.65719i
$61$	−4.46187	−	2.34177i	−0.571284	−	0.299833i	0.154236	−	0.988034i	$-0.450708\pi$
$61$	−4.46187	−	2.34177i	−0.571284	−	0.299833i	−0.725520	+	0.688201i	$0.758401\pi$
$62$	0.238684	−	1.96574i	0.0303129	−	0.249650i
$63$	−0.763132	+	0.0926610i	−0.0961456	+	0.0116742i
$64$	−2.74174	+	3.97210i	−0.342718	+	0.496513i
$65$	0.0220109	−	10.1279i	0.00273012	−	1.25621i
$66$	7.15884	+	10.3714i	0.881193	+	1.27663i
$67$	−0.939647	−	1.06064i	−0.114796	−	0.129578i	0.688303	−	0.725423i	$-0.258356\pi$
$67$	−0.939647	−	1.06064i	−0.114796	−	0.129578i	−0.803100	+	0.595845i	$0.796817\pi$
$68$	−22.0374	−	5.43174i	−2.67243	−	0.658695i
$69$	−4.50488	−	6.52645i	−0.542324	−	0.785692i
$70$			5.59212i			0.668386i
$71$	12.2981	−	8.48880i	1.45952	−	1.00744i	0.467147	−	0.884180i	$-0.345282\pi$
$71$	12.2981	−	8.48880i	1.45952	−	1.00744i	0.992375	−	0.123255i	$-0.0393334\pi$
$72$	6.95823	−	0.844882i	0.820035	−	0.0995703i
$73$	1.03109	−	0.391040i	0.120680	−	0.0457678i	−0.293526	−	0.955951i	$-0.594829\pi$
$73$	1.03109	−	0.391040i	0.120680	−	0.0457678i	0.414206	+	0.910183i	$0.364059\pi$
$74$	−2.12165	+	17.4734i	−0.246637	+	2.03124i
$75$	−1.02492	−	2.70248i	−0.118347	−	0.312055i
$76$	25.8115	−	29.1352i	2.96079	−	3.34204i
$77$	2.80007	+	2.48065i	0.319098	+	0.282696i
$78$	−8.73774	+	3.29208i	−0.989354	+	0.372755i
$79$	−1.36177	+	1.20643i	−0.153211	+	0.135733i	−0.736246	−	0.676714i	$-0.763404\pi$
$79$	−1.36177	+	1.20643i	−0.153211	+	0.135733i	0.583035	+	0.812447i	$0.301865\pi$
$80$		−	24.5474i		−	2.74448i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	11.2975	−	2.78459i	1.24760	−	0.307506i
$83$	−5.58437	−	3.85461i	−0.612965	−	0.423099i	0.220722	−	0.975337i	$-0.429159\pi$
$83$	−5.58437	−	3.85461i	−0.612965	−	0.423099i	−0.833687	+	0.552238i	$0.813774\pi$
$84$	3.38302	−	1.28301i	0.369118	−	0.139988i
$85$	12.6656	−	4.80343i	1.37378	−	0.521005i
$86$	8.16364	+	5.63496i	0.880308	+	0.607633i
$87$	−1.33604	+	0.329304i	−0.143238	+	0.0353051i
$88$	−25.5310	−	22.6185i	−2.72162	−	2.41114i
$89$			3.92147i			0.415675i	0.978163	+	0.207837i	$0.0666425\pi$
$89$			3.92147i			0.415675i	−0.978163	+	0.207837i	$0.933358\pi$
$90$	−5.44498	+	4.82383i	−0.573951	+	0.508476i
$91$	−2.28450	+	1.56956i	−0.239480	+	0.164534i
$92$	27.9378	+	24.7507i	2.91271	+	2.58044i
$93$	0.507046	−	0.572336i	0.0525782	−	0.0593485i
$94$	9.04419	+	23.8476i	0.932837	+	2.45969i
$95$	−2.80013	+	23.0611i	−0.287287	+	2.36602i
$96$	−8.05299	+	3.05410i	−0.821905	+	0.311707i
$97$	−2.17329	+	0.263885i	−0.220664	+	0.0267935i	−0.230122	−	0.973162i	$-0.573912\pi$
$97$	−2.17329	+	0.263885i	−0.220664	+	0.0267935i	0.00945793	+	0.999955i	$0.496989\pi$
$98$	−13.6595	+	9.42850i	−1.37982	+	0.952422i
$99$			4.86624i			0.489076i
$100$	7.72768	+	11.1955i	0.772768	+	1.11955i
$101$	2.52267	+	0.621781i	0.251015	+	0.0618695i	0.362815	−	0.931861i	$-0.381816\pi$
$101$	2.52267	+	0.621781i	0.251015	+	0.0618695i	−0.111801	+	0.993731i	$0.535662\pi$
$102$	−8.28143	−	9.34780i	−0.819983	−	0.925570i
$103$	2.53510	+	3.67272i	0.249791	+	0.361884i	0.927742	−	0.373223i	$-0.121747\pi$
$103$	2.53510	+	3.67272i	0.249791	+	0.361884i	−0.677951	+	0.735107i	$0.737132\pi$
$104$	20.8300	−	14.3112i	2.04255	−	1.40333i
$105$	−1.22666	+	1.77712i	−0.119709	+	0.173429i
$106$	28.5241	−	3.46346i	2.77051	−	0.336401i
$107$	2.09903	−	17.2871i	0.202921	−	1.67121i	−0.434486	−	0.900679i	$-0.643070\pi$
$107$	2.09903	−	17.2871i	0.202921	−	1.67121i	0.637407	−	0.770527i	$-0.280007\pi$
$108$	4.16749	+	2.18727i	0.401017	+	0.210470i
$109$	3.22359	−	13.0786i	0.308764	−	1.25270i	−0.587516	−	0.809213i	$-0.699894\pi$
$109$	3.22359	−	13.0786i	0.308764	−	1.25270i	0.896279	−	0.443490i	$-0.146260\pi$
$110$	35.1410	+	4.26689i	3.35056	+	0.406832i
$111$	−4.50710	+	5.08746i	−0.427795	+	0.482880i
$112$	−5.52876	+	3.81623i	−0.522419	+	0.360600i
$113$	2.92601	−	4.23905i	0.275255	−	0.398776i	−0.660838	−	0.750529i	$-0.729799\pi$
$113$	2.92601	−	4.23905i	0.275255	−	0.398776i	0.936093	+	0.351753i	$0.114414\pi$
$114$	20.7949	−	5.12548i	1.94762	−	0.480045i
$115$	−22.1133	−	2.68504i	−2.06208	−	0.250382i
$116$	5.73457	−	3.00973i	0.532441	−	0.279447i
$117$	−3.49890	−	0.870471i	−0.323473	−	0.0804751i
$118$	19.0103	+	9.97739i	1.75004	+	0.918493i
$119$	−3.05091	−	2.10589i	−0.279676	−	0.193047i
$120$	11.1846	−	16.2037i	1.02101	−	1.47919i
$121$	9.49134	−	8.40859i	0.862849	−	0.764418i
$122$	8.65357	+	9.76787i	0.783458	+	0.884341i
$123$	4.20105	+	1.59325i	0.378796	+	0.143658i
$124$	−1.67246	+	3.18661i	−0.150191	+	0.286166i
$125$	5.54098	+	2.10142i	0.495600	+	0.187956i
$126$	1.93296	+	0.476431i	0.172202	+	0.0424439i
$127$	2.72861	−	2.41733i	0.242125	−	0.214504i	−0.533330	−	0.845908i	$-0.679059\pi$
$127$	2.72861	−	2.41733i	0.242125	−	0.214504i	0.775454	+	0.631404i	$0.217521\pi$
$128$	−3.88959	+	2.68479i	−0.343794	+	0.237304i
$129$	1.35827	+	3.58146i	0.119589	+	0.315330i
$130$	−9.35395	+	24.5036i	−0.820396	+	2.14911i
$131$	5.57670	−	14.7045i	0.487238	−	1.28474i	−0.435803	−	0.900042i	$-0.643536\pi$
$131$	5.57670	−	14.7045i	0.487238	−	1.28474i	0.923042	−	0.384700i	$-0.125695\pi$
$132$	−5.48116	−	22.2380i	−0.477074	−	1.93557i
$133$	5.62933	−	2.95450i	0.488125	−	0.256188i
$134$	1.30127	+	3.43116i	0.112412	+	0.296407i
$135$	−2.78849	+	0.338584i	−0.239995	+	0.0291406i
$136$	27.8181	+	19.2015i	2.38538	+	1.64651i
$137$	4.58736	−	18.6117i	0.391925	−	1.59010i	−0.361372	−	0.932422i	$-0.617692\pi$
$137$	4.58736	−	18.6117i	0.391925	−	1.59010i	0.753297	−	0.657680i	$-0.228462\pi$
$138$	4.91482	+	19.9402i	0.418378	+	1.69742i
$139$	−0.0516411	−	0.425303i	−0.00438014	−	0.0360737i	0.990355	−	0.138554i	$-0.0442453\pi$
$139$	−0.0516411	−	0.425303i	−0.00438014	−	0.0360737i	−0.994735	+	0.102480i	$0.967322\pi$
$140$	3.60394	−	9.50281i	0.304588	−	0.803134i
$141$	−2.35692	+	9.56240i	−0.198488	+	0.805299i
$142$	−37.5745	+	9.26128i	−3.15318	+	0.777189i
$143$	8.12001	+	15.5534i	0.679029	+	1.30064i
$144$	−8.48501	−	2.09137i	−0.707084	−	0.174281i
$145$	−1.79625	+	3.42247i	−0.149170	+	0.284221i
$146$	−2.85580			−0.236348
$147$	−6.40904			−0.528609
$148$	14.8664	−	28.3255i	1.22201	−	2.32834i
$149$	−1.39934	−	1.57952i	−0.114638	−	0.129400i	0.688390	−	0.725341i	$-0.258318\pi$
$149$	−1.39934	−	1.57952i	−0.114638	−	0.129400i	−0.803028	+	0.595941i	$0.796779\pi$
$150$			7.48505i			0.611152i
$151$	−4.20328	+	4.74452i	−0.342058	+	0.386104i	−0.894216	−	0.447636i	$-0.852266\pi$
$151$	−4.20328	+	4.74452i	−0.342058	+	0.386104i	0.552158	+	0.833740i	$0.313805\pi$
$152$	−51.3282	+	26.9391i	−4.16326	+	2.18505i
$153$	−0.581271	−	4.78720i	−0.0469930	−	0.387022i
$154$	−4.50212	−	8.57808i	−0.362791	−	0.691241i
$155$	−0.258892	−	2.13217i	−0.0207947	−	0.171260i
$156$	16.9699	+	0.0368808i	1.35868	+	0.00295282i
$157$	1.93726	−	15.9548i	0.154610	−	1.27333i	−0.684356	−	0.729148i	$-0.739917\pi$
$157$	1.93726	−	15.9548i	0.154610	−	1.27333i	0.838967	−	0.544183i	$-0.183160\pi$
$158$	4.40532	−	1.67072i	0.350468	−	0.132915i
$159$	9.82440	+	5.15625i	0.779126	+	0.408917i
$160$	−8.57886	+	22.6206i	−0.678219	+	1.78832i
$161$	2.83307	+	5.39797i	0.223277	+	0.425419i
$162$	1.20350	+	2.29308i	0.0945558	+	0.180161i
$163$	−0.836592	−	3.39419i	−0.0655269	−	0.265853i	0.929036	−	0.369989i	$-0.120639\pi$
$163$	−0.836592	−	3.39419i	−0.0655269	−	0.265853i	−0.994563	+	0.104136i	$0.966792\pi$
$164$	−20.9927	−	2.54898i	−1.63926	−	0.199042i
$165$	10.2315	+	9.06430i	0.796520	+	0.705655i
$166$	9.98234	+	14.4619i	0.774780	+	1.12246i
$167$	11.4094	+	4.32701i	0.882885	+	0.334834i	0.754038	−	0.656830i	$-0.228103\pi$
$167$	11.4094	+	4.32701i	0.882885	+	0.334834i	0.128847	+	0.991665i	$0.458873\pi$
$168$	−5.38834			−0.415719
$169$	−12.6356	+	3.05621i	−0.971973	+	0.235093i
$170$	−35.0799			−2.69050
$171$	7.73270	+	2.93262i	0.591334	+	0.224263i
$172$	−10.2411	−	14.8368i	−0.780878	−	1.13130i
$173$	11.1403	+	9.86944i	0.846981	+	0.750359i	0.970274	−	0.242011i	$-0.0778070\pi$
$173$	11.1403	+	9.86944i	0.846981	+	0.750359i	−0.123293	+	0.992370i	$0.539345\pi$
$174$	3.53752	+	0.429533i	0.268179	+	0.0325628i
$175$	0.531731	+	2.15732i	0.0401951	+	0.163078i
$176$	19.7627	+	37.6547i	1.48967	+	2.83833i
$177$	3.85270	+	7.34071i	0.289587	+	0.551761i
$178$	3.60118	−	9.49553i	0.269920	−	0.711720i
$179$	10.8313	+	5.68469i	0.809567	+	0.424893i	0.818104	−	0.575070i	$-0.195025\pi$
$179$	10.8313	+	5.68469i	0.809567	+	0.424893i	−0.00853737	+	0.999964i	$0.502718\pi$
$180$	12.3616	−	4.68813i	0.921378	−	0.349433i
$181$	0.270541	−	2.22811i	0.0201092	−	0.165614i	−0.979195	−	0.202924i	$-0.934956\pi$
$181$	0.270541	−	2.22811i	0.0201092	−	0.165614i	0.999304	+	0.0373096i	$0.0118788\pi$
$182$	6.97310	−	1.70265i	0.516880	−	0.126209i
$183$	0.607392	+	5.00233i	0.0448997	+	0.369783i
$184$	−25.8319	−	49.2186i	−1.90435	−	3.62844i
$185$	2.30128	+	18.9527i	0.169193	+	1.39343i
$186$	−1.75336	+	0.920236i	−0.128563	+	0.0674750i
$187$	−15.5613	+	17.5651i	−1.13796	+	1.28449i
$188$		−	46.3534i		−	3.38067i
$189$	0.509767	+	0.575408i	0.0370801	+	0.0418548i
$190$	27.9579	−	53.2693i	2.02828	−	3.86456i
$191$	−5.63891			−0.408018			−0.204009	−	0.978969i	$-0.565397\pi$
$191$	−5.63891			−0.408018			−0.204009	+	0.978969i	$0.565397\pi$
$192$	4.82646			0.348320
$193$	−6.11067	+	11.6429i	−0.439855	+	0.838075i	0.560098	+	0.828426i	$0.310763\pi$
$193$	−6.11067	+	11.6429i	−0.439855	+	0.838075i	−0.999953	+	0.00964824i	$0.996929\pi$
$194$	5.50478	+	1.35681i	0.395220	+	0.0974130i
$195$	−8.34756	+	5.73516i	−0.597782	+	0.410704i
$196$	29.2883	−	7.21892i	2.09202	−	0.515637i
$197$	2.43916	−	9.89607i	0.173783	−	0.705066i	−0.817790	−	0.575517i	$-0.804801\pi$
$197$	2.43916	−	9.89607i	0.173783	−	0.705066i	0.991573	−	0.129549i	$-0.0413530\pi$
$198$	4.46879	−	11.7832i	0.317583	−	0.837397i
$199$	−0.00631563	−	0.0520139i	−0.000447703	−	0.00368717i	0.992483	−	0.122380i	$-0.0390527\pi$
$199$	−0.00631563	−	0.0520139i	−0.000447703	−	0.00368717i	−0.992931	+	0.118693i	$0.962130\pi$
$200$	−4.84832	−	19.6704i	−0.342828	−	1.39091i
$201$	−0.339111	+	1.37583i	−0.0239190	+	0.0970434i
$202$	−5.53744	−	3.82222i	−0.389613	−	0.268930i
$203$	1.05009	−	0.127504i	0.0737017	−	0.00894900i
$204$	8.04845	+	21.2220i	0.563505	+	1.48584i
$205$	11.1751	−	5.86516i	0.780504	−	0.409640i
$206$	−2.76579	−	11.2213i	−0.192702	−	0.781822i
$207$	−2.81210	+	7.41489i	−0.195454	+	0.515370i
$208$	−30.6094	+	7.47402i	−2.12238	+	0.518230i
$209$	−14.2709	−	37.6292i	−0.987136	−	2.60286i
$210$	4.60222	−	3.17668i	0.317583	−	0.219212i
$211$	8.16226	−	7.23113i	0.561913	−	0.497812i	−0.333680	−	0.942687i	$-0.608290\pi$
$211$	8.16226	−	7.23113i	0.561913	−	0.497812i	0.895593	+	0.444875i	$0.146752\pi$
$212$	−50.7038	−	12.4974i	−3.48235	−	0.858322i
$213$	−13.9723	−	5.29899i	−0.957365	−	0.363081i
$214$	−20.9578	+	39.9318i	−1.43265	+	2.72968i
$215$	10.0602	+	3.81534i	0.686101	+	0.260204i
$216$	−4.64805	−	5.24656i	−0.316260	−	0.356983i
$217$	−0.439976	+	0.389785i	−0.0298675	+	0.0264603i
$218$	−19.8161	+	28.7085i	−1.34211	+	1.94439i
$219$	−0.907545	−	0.626433i	−0.0613262	−	0.0423304i
$220$	−56.9660	−	29.8980i	−3.84064	−	2.01573i
$221$	−9.84597	−	14.3309i	−0.662312	−	0.963999i
$222$	15.5855	−	8.17991i	1.04603	−	0.549000i
$223$	−13.6473	−	1.65708i	−0.913891	−	0.110966i	−0.349937	−	0.936773i	$-0.613797\pi$
$223$	−13.6473	−	1.65708i	−0.913891	−	0.110966i	−0.563953	+	0.825807i	$0.690720\pi$
$224$	6.42849	−	1.58448i	0.429522	−	0.105868i
$225$	−1.64188	+	2.37867i	−0.109459	+	0.158578i
$226$	−10.9779	+	7.57751i	−0.730240	+	0.504049i
$227$	−15.7579	+	17.7869i	−1.04589	+	1.18056i	−0.0626846	+	0.998033i	$0.519966\pi$
$227$	−15.7579	+	17.7869i	−1.04589	+	1.18056i	−0.983201	+	0.182527i	$0.941572\pi$
$228$	−38.6404	−	4.69180i	−2.55902	−	0.310722i
$229$	−3.12803	+	12.6909i	−0.206706	+	0.838640i	0.772375	+	0.635167i	$0.219069\pi$
$229$	−3.12803	+	12.6909i	−0.206706	+	0.838640i	−0.979081	+	0.203472i	$0.934777\pi$
$230$	51.0800	+	26.8088i	3.36811	+	1.76772i
$231$	0.450911	−	3.71358i	0.0296678	−	0.244336i
$232$	−9.57468	+	1.16258i	−0.628609	+	0.0763269i
$233$	−0.892843	+	1.29351i	−0.0584921	+	0.0847404i	−0.851138	−	0.524941i	$-0.824087\pi$
$233$	−0.892843	+	1.29351i	−0.0584921	+	0.0847404i	0.792646	+	0.609682i	$0.208703\pi$
$234$	7.67293	+	5.32090i	0.501595	+	0.347838i
$235$	15.7151	+	22.7673i	1.02514	+	1.48518i
$236$	−25.8746	−	29.2063i	−1.68429	−	1.90117i
$237$	1.76644	+	0.435389i	0.114743	+	0.0282816i
$238$	5.45365	+	7.90097i	0.353507	+	0.512144i
$239$			27.6529i			1.78872i	0.447352	+	0.894358i	$0.352367\pi$
$239$			27.6529i			1.78872i	−0.447352	+	0.894358i	$0.647633\pi$
$240$	−20.2021	+	13.9445i	−1.30404	+	0.900115i
$241$	−13.2499	+	1.60883i	−0.853499	+	0.103634i	−0.535580	−	0.844484i	$-0.679907\pi$
$241$	−13.2499	+	1.60883i	−0.853499	+	0.103634i	−0.317919	+	0.948118i	$0.602984\pi$
$242$	−30.7044	+	11.6446i	−1.97375	+	0.748545i
$243$	−0.120537	+	0.992709i	−0.00773243	+	0.0636823i
$244$	−8.41013	−	22.1757i	−0.538404	−	1.41965i
$245$	−11.9381	+	13.4753i	−0.762695	+	0.860905i
$246$	−8.70940	−	7.71585i	−0.555291	−	0.491945i
$247$	29.6087	−	3.52986i	1.88395	−	0.224600i
$248$	4.01170	−	3.55405i	0.254743	−	0.225683i
$249$			6.78552i			0.430015i
$250$	−11.4873	−	10.1768i	−0.726518	−	0.643639i
$251$	−12.1788	+	3.00180i	−0.768718	+	0.189472i	−0.604125	−	0.796889i	$-0.706477\pi$
$251$	−12.1788	+	3.00180i	−0.768718	+	0.189472i	−0.164593	+	0.986362i	$0.552631\pi$
$252$	−2.97767	−	2.05534i	−0.187576	−	0.129474i
$253$	36.0826	−	13.6843i	2.26850	−	0.860327i
$254$	−8.82701	+	3.34764i	−0.553856	+	0.210050i
$255$	−11.1480	−	7.69493i	−0.698116	−	0.481875i
$256$	21.2563	−	5.23920i	1.32852	−	0.327450i
$257$	−13.1594	−	11.6582i	−0.820863	−	0.727222i	0.144112	−	0.989561i	$-0.453967\pi$
$257$	−13.1594	−	11.6582i	−0.820863	−	0.727222i	−0.964976	+	0.262340i	$0.915506\pi$
$258$		−	9.91957i		−	0.617565i
$259$	3.91092	−	3.46477i	0.243013	−	0.215290i
$260$	31.6872	−	35.6112i	1.96515	−	2.20851i
$261$	1.02997	+	0.912472i	0.0637534	+	0.0564806i
$262$	−27.0071	+	30.4847i	−1.66850	+	1.88335i
$263$	0.695405	+	1.83363i	0.0428805	+	0.113067i	0.954746	−	0.297423i	$-0.0961271\pi$
$263$	0.695405	+	1.83363i	0.0428805	+	0.113067i	−0.911865	+	0.410489i	$0.865358\pi$
$264$	−4.11140	+	33.8604i	−0.253039	+	2.08396i
$265$	29.1411	−	11.0517i	1.79012	−	0.678903i
$266$	−16.3442	+	1.98454i	−1.00213	+	0.121680i
$267$	3.22730	−	2.22765i	0.197508	−	0.136330i
$268$		−	6.66928i		−	0.407391i
$269$	2.67381	+	3.87369i	0.163025	+	0.236183i	0.895980	−	0.444095i	$-0.146475\pi$
$269$	2.67381	+	3.87369i	0.163025	+	0.236183i	−0.732955	+	0.680278i	$0.761859\pi$
$270$	7.06304	+	1.74088i	0.429843	+	0.105947i
$271$	−14.2078	−	16.0372i	−0.863060	−	0.974193i	0.136806	−	0.990598i	$-0.456316\pi$
$271$	−14.2078	−	16.0372i	−0.863060	−	0.974193i	−0.999865	+	0.0164047i	$0.994778\pi$
$272$	−23.9396	−	34.6825i	−1.45155	−	2.10293i
$273$	2.58946	+	0.988496i	0.156721	+	0.0598265i
$274$	−28.1995	+	40.8540i	−1.70359	+	2.46808i
$275$	13.9624	−	1.69534i	0.841962	−	0.102233i
$276$	4.49897	−	37.0523i	0.270806	−	2.23029i
$277$	0.252669	+	0.132611i	0.0151814	+	0.00796781i	0.472297	−	0.881440i	$-0.343425\pi$
$277$	0.252669	+	0.132611i	0.0151814	+	0.00796781i	−0.457115	+	0.889407i	$0.651117\pi$
$278$	−0.265521	+	1.07726i	−0.0159249	+	0.0646099i
$279$	−0.759058	−	0.0921664i	−0.0454436	−	0.00551786i
$280$	−10.0368	+	11.3292i	−0.599814	+	0.677050i
$281$	−23.7558	+	16.3974i	−1.41715	+	0.978190i	−0.419640	+	0.907690i	$0.637844\pi$
$281$	−23.7558	+	16.3974i	−1.41715	+	0.978190i	−0.997512	+	0.0704991i	$0.977541\pi$
$282$	14.4885	−	20.9902i	0.862777	−	1.24995i
$283$	9.64866	−	2.37818i	0.573553	−	0.141368i	0.0581377	−	0.998309i	$-0.481484\pi$
$283$	9.64866	−	2.37818i	0.573553	−	0.141368i	0.515415	+	0.856940i	$0.327638\pi$
$284$	69.8198	+	8.47765i	4.14304	+	0.503056i
$285$	20.5696	−	10.7958i	1.21844	−	0.639485i
$286$	−5.37887	−	45.1182i	−0.318059	−	2.66790i
$287$	−3.05832	−	1.60513i	−0.180527	−	0.0947479i
$288$	7.08809	+	4.89256i	0.417670	+	0.288297i
$289$	3.55334	−	5.14790i	0.209020	−	0.302818i
$290$	7.49242	−	6.63770i	0.439970	−	0.389779i
$291$	1.45174	+	1.63868i	0.0851026	+	0.0960609i
$292$	4.85293	+	1.84047i	0.283996	+	0.107706i
$293$	15.5110	−	29.5538i	0.906165	−	1.72655i	0.256139	−	0.966640i	$-0.417550\pi$
$293$	15.5110	−	29.5538i	0.906165	−	1.72655i	0.650026	−	0.759912i	$-0.274758\pi$
$294$	15.5190	+	5.88558i	0.905087	+	0.343254i
$295$	22.6105	+	5.57300i	1.31644	+	0.324472i
$296$	−35.6597	+	31.5917i	−2.07268	+	1.83623i
$297$	4.00484	−	2.76434i	0.232384	−	0.160403i
$298$	1.93787	+	5.10974i	0.112258	+	0.295999i
$299$	3.38479	+	28.3918i	0.195747	+	1.64194i
$300$	4.82387	−	12.7195i	0.278506	−	0.734361i
$301$	−0.704677	−	2.85899i	−0.0406169	−	0.164789i
$302$	14.5349	−	7.62852i	0.836391	−	0.438972i
$303$	−0.921321	−	2.42932i	−0.0529285	−	0.139561i
$304$	71.7452	−	8.71144i	4.11487	−	0.499635i
$305$	11.6490	+	8.04072i	0.667019	+	0.460410i
$306$	−2.98870	+	12.1256i	−0.170853	+	0.693176i
$307$	4.29035	+	17.4066i	0.244863	+	0.993449i	0.956693	+	0.291097i	$0.0940203\pi$
$307$	4.29035	+	17.4066i	0.244863	+	0.993449i	−0.711830	+	0.702351i	$0.752134\pi$
$308$	2.12226	+	17.4784i	0.120927	+	0.995924i
$309$	1.58249	−	4.17269i	0.0900248	−	0.237376i
$310$	−1.33114	+	5.40063i	−0.0756035	+	0.306735i
$311$	17.8917	−	4.40990i	1.01454	−	0.250062i	0.303215	−	0.952922i	$-0.401940\pi$
$311$	17.8917	−	4.40990i	1.01454	−	0.250062i	0.711328	+	0.702860i	$0.248094\pi$
$312$	−23.6107	−	9.01309i	−1.33669	−	0.510266i
$313$	−7.36217	−	1.81461i	−0.416135	−	0.102568i	0.0256888	−	0.999670i	$-0.491822\pi$
$313$	−7.36217	−	1.81461i	−0.416135	−	0.102568i	−0.441823	+	0.897102i	$0.645668\pi$
$314$	−19.3426	+	36.8543i	−1.09157	+	2.07981i
$315$	2.15936			0.121666
$316$	−8.56278			−0.481694
$317$	4.61630	−	8.79563i	0.259277	−	0.494012i	−0.720667	−	0.693281i	$-0.756164\pi$
$317$	4.61630	−	8.79563i	0.259277	−	0.494012i	0.979945	+	0.199269i	$0.0638568\pi$
$318$	−19.0539	−	21.5074i	−1.06849	−	1.20608i
$319$		−	6.69606i		−	0.374907i
$320$	8.99021	−	10.1478i	0.502568	−	0.567282i
$321$	−15.4194	+	8.09272i	−0.860626	+	0.451691i
$322$	−1.90298	−	15.6724i	−0.106049	−	0.873391i
$323$	18.5339	+	35.3133i	1.03125	+	1.96489i
$324$	−0.567319	−	4.67229i	−0.0315177	−	0.259572i
$325$	−1.27861	+	10.3424i	−0.0709244	+	0.573693i
$326$	−1.09122	+	8.98702i	−0.0604372	+	0.497745i
$327$	−12.5947	+	4.77653i	−0.696488	+	0.264143i
$328$	27.8858	+	14.6356i	1.53973	+	0.808114i
$329$	2.68470	−	7.07898i	0.148012	−	0.390277i
$330$	−16.4508	−	31.3443i	−0.905585	−	1.72545i
$331$	−0.668855	−	1.27440i	−0.0367636	−	0.0700472i	0.866381	−	0.499383i	$-0.166440\pi$
$331$	−0.668855	−	1.27440i	−0.0367636	−	0.0700472i	−0.903145	+	0.429336i	$0.858748\pi$
$332$	−7.64297	−	31.0088i	−0.419463	−	1.70183i
$333$	6.74722	+	0.819261i	0.369745	+	0.0448952i
$334$	−23.6533	−	20.9550i	−1.29425	−	1.14661i
$335$	2.26108	+	3.27574i	0.123536	+	0.178973i
$336$	6.28139	+	2.38222i	0.342678	+	0.129961i
$337$	−9.28686			−0.505887			−0.252944	−	0.967481i	$-0.581399\pi$
$337$	−9.28686			−0.505887			−0.252944	+	0.967481i	$0.581399\pi$
$338$	33.4028	+	4.20325i	1.81687	+	0.228626i
$339$	−5.15083			−0.279755
$340$	59.6120	+	22.6079i	3.23292	+	1.22608i
$341$	2.11371	+	3.06223i	0.114464	+	0.165829i
$342$	−16.0310	−	14.2022i	−0.866859	−	0.767970i
$343$	10.2329	+	1.24250i	0.552523	+	0.0670885i
$344$	6.42524	+	26.0682i	0.346426	+	1.40550i
$345$	10.3521	+	19.7242i	0.557336	+	1.06191i
$346$	−17.9120	−	34.1285i	−0.962955	−	1.83476i
$347$	5.53699	−	14.5999i	0.297241	−	0.783761i	−0.700311	−	0.713838i	$-0.746955\pi$
$347$	5.53699	−	14.5999i	0.297241	−	0.783761i	0.997552	−	0.0699232i	$-0.0222754\pi$
$348$	−5.73457	−	3.00973i	−0.307405	−	0.161339i
$349$	18.0074	−	6.82929i	0.963912	−	0.365564i	0.178088	−	0.984014i	$-0.443009\pi$
$349$	18.0074	−	6.82929i	0.963912	−	0.365564i	0.785823	+	0.618451i	$0.212239\pi$
$350$	0.693572	−	5.71208i	0.0370730	−	0.305324i
$351$	1.27122	+	3.37402i	0.0678525	+	0.180092i
$352$	−5.05186	−	41.6058i	−0.269265	−	2.21760i
$353$	4.82454	+	9.19239i	0.256784	+	0.489262i	0.979385	−	0.202004i	$-0.0647456\pi$
$353$	4.82454	+	9.19239i	0.256784	+	0.489262i	−0.722600	+	0.691266i	$0.757053\pi$
$354$	−2.58787	−	21.3130i	−0.137543	−	1.13277i
$355$	−37.1674	+	19.5070i	−1.97264	+	1.03532i
$356$	−12.2391	+	13.8151i	−0.648673	+	0.732200i
$357$			3.70713i			0.196202i
$358$	−21.0067	−	23.7116i	−1.11024	−	1.25320i
$359$	−5.45121	+	10.3864i	−0.287704	+	0.548174i	−0.985819	−	0.167812i	$-0.946330\pi$
$359$	−5.45121	+	10.3864i	−0.287704	+	0.548174i	0.698115	+	0.715985i	$0.254022\pi$
$360$	−19.6890			−1.03770
$361$	−49.3949			−2.59973
$362$	−2.70122	+	5.14675i	−0.141973	+	0.270507i
$363$	−12.3118	−	3.03459i	−0.646204	−	0.159275i
$364$	−12.9468	−	1.60059i	−0.678599	−	0.0838938i
$365$	−3.00758	+	0.741301i	−0.157424	+	0.0388015i
$366$	3.12301	−	12.6705i	0.163242	−	0.662299i
$367$	6.59311	−	17.3846i	0.344158	−	0.907469i	−0.645466	−	0.763789i	$-0.723337\pi$
$367$	6.59311	−	17.3846i	0.344158	−	0.907469i	0.989624	−	0.143681i	$-0.0458938\pi$
$368$	8.35341	+	68.7965i	0.435451	+	3.58626i
$369$	−1.07525	−	4.36246i	−0.0559753	−	0.227101i
$370$	11.8324	−	48.0059i	0.615136	−	2.49571i
$371$	−7.01954	−	4.84524i	−0.364436	−	0.251552i
$372$	3.57259	−	0.433791i	0.185230	−	0.0224910i
$373$	11.7236	+	30.9126i	0.607026	+	1.60059i	0.787020	+	0.616927i	$0.211623\pi$
$373$	11.7236	+	30.9126i	0.607026	+	1.60059i	−0.179995	+	0.983668i	$0.557608\pi$
$374$	53.8111	−	28.2422i	2.78251	−	1.46037i
$375$	−1.41820	−	5.75387i	−0.0732357	−	0.297129i
$376$	−24.4791	+	64.5460i	−1.26241	+	3.32871i
$377$	4.81456	+	1.19779i	0.247963	+	0.0616892i
$378$	−0.705950	−	1.86144i	−0.0363102	−	0.0957420i
$379$	−6.58609	+	4.54605i	−0.338305	+	0.233515i	−0.725089	−	0.688655i	$-0.758201\pi$
$379$	−6.58609	+	4.54605i	−0.338305	+	0.233515i	0.386784	+	0.922170i	$0.373586\pi$
$380$	−81.8398	+	72.5038i	−4.19829	+	3.71936i
$381$	−3.53945	−	0.872397i	−0.181332	−	0.0446942i
$382$	13.6542	+	5.17835i	0.698609	+	0.264948i
$383$	0.519168	−	0.989192i	0.0265283	−	0.0505454i	−0.871831	−	0.489807i	$-0.837067\pi$
$383$	0.519168	−	0.989192i	0.0265283	−	0.0505454i	0.898359	+	0.439261i	$0.144760\pi$
$384$	4.41907	+	1.67593i	0.225510	+	0.0855247i
$385$	−6.96806	−	7.86532i	−0.355125	−	0.400854i
$386$	25.4885	−	22.5808i	1.29733	−	1.14933i
$387$	2.17590	−	3.15234i	0.110607	−	0.160242i
$388$	−8.47998	−	5.85331i	−0.430506	−	0.297157i
$389$	1.61708	+	0.848708i	0.0819891	+	0.0430312i	0.505219	−	0.862991i	$-0.331412\pi$
$389$	1.61708	+	0.848708i	0.0819891	+	0.0430312i	−0.423230	+	0.906022i	$0.639104\pi$
$390$	25.4797	−	6.22148i	1.29022	−	0.315037i
$391$	−33.8620	+	17.7721i	−1.71247	+	0.898775i
$392$	−44.5956	−	5.41489i	−2.25242	−	0.273493i
$393$	−15.2695	+	3.76360i	−0.770246	+	0.189848i
$394$	−14.9941	+	21.7226i	−0.755390	+	1.09437i
$395$	4.20576	−	2.90303i	0.211615	−	0.146067i
$396$	−15.1878	+	17.1435i	−0.763217	+	0.861494i
$397$	21.4537	+	2.60496i	1.07673	+	0.130739i	0.639638	−	0.768677i	$-0.279084\pi$
$397$	21.4537	+	2.60496i	1.07673	+	0.130739i	0.437095	+	0.899416i	$0.356007\pi$
$398$	−0.0324728	+	0.131748i	−0.00162772	+	0.00660391i
$399$	−5.62933	−	2.95450i	−0.281819	−	0.147910i
$400$	−3.04454	+	25.0740i	−0.152227	+	1.25370i
$401$	32.5923	−	3.95742i	1.62758	−	0.197624i	0.744760	−	0.667332i	$-0.232564\pi$
$401$	32.5923	−	3.95742i	1.62758	−	0.197624i	0.882822	+	0.469708i	$0.155641\pi$
$402$	2.08459	−	3.02005i	0.103970	−	0.150626i
$403$	−2.57989	+	0.972014i	−0.128513	+	0.0484195i
$404$	6.94660	+	10.0639i	0.345606	+	0.500697i
$405$	1.86269	+	2.10254i	0.0925578	+	0.104476i
$406$	−2.65979	−	0.655581i	−0.132003	−	0.0325359i
$407$	−18.7886	−	27.2200i	−0.931316	−	1.34924i
$408$		−	33.8015i		−	1.67343i
$409$	−8.75266	+	6.04153i	−0.432791	+	0.298734i	−0.764471	−	0.644658i	$-0.777000\pi$
$409$	−8.75266	+	6.04153i	−0.432791	+	0.298734i	0.331680	+	0.943392i	$0.392385\pi$
$410$	−32.4458	+	3.93964i	−1.60238	+	0.194565i
$411$	−17.9230	+	6.79730i	−0.884077	+	0.335286i
$412$	−2.53177	+	20.8510i	−0.124731	+	1.02725i
$413$	−2.25992	−	5.95893i	−0.111204	−	0.293220i
$414$	13.6185	−	15.3722i	0.669315	−	0.755500i
$415$	14.2668	+	12.6393i	0.700332	+	0.620440i
$416$	30.8188	+	3.81007i	1.51102	+	0.186804i
$417$	−0.320682	+	0.284100i	−0.0157039	+	0.0139124i
$418$			104.221i			5.09763i
$419$	−9.90912	−	8.77872i	−0.484092	−	0.428868i	0.385449	−	0.922729i	$-0.374047\pi$
$419$	−9.90912	−	8.77872i	−0.484092	−	0.428868i	−0.869541	+	0.493861i	$0.835585\pi$
$420$	−9.86793	+	2.43223i	−0.481505	+	0.118680i
$421$	2.76667	+	1.90969i	0.134839	+	0.0930727i	0.633575	−	0.773681i	$-0.281587\pi$
$421$	2.76667	+	1.90969i	0.134839	+	0.0930727i	−0.498736	+	0.866754i	$0.666202\pi$
$422$	−26.4048	+	10.0140i	−1.28537	+	0.487475i
$423$	9.20858	−	3.49235i	0.447737	−	0.169804i
$424$	64.0040	+	44.1788i	3.10831	+	2.14551i
$425$	−13.5331	+	3.33560i	−0.656450	+	0.161800i
$426$	28.9666	+	25.6622i	1.40344	+	1.24334i
$427$		−	3.87372i		−	0.187462i
$428$	61.3488	−	54.3503i	2.96541	−	2.62712i
$429$	8.18754	−	15.5180i	0.395298	−	0.749216i
$430$	−20.8563	−	18.4771i	−1.00578	−	0.891044i
$431$	−19.6653	+	22.1975i	−0.947244	+	1.06922i	0.0502694	+	0.998736i	$0.483992\pi$
$431$	−19.6653	+	22.1975i	−0.947244	+	1.06922i	−0.997513	+	0.0704814i	$0.977546\pi$
$432$	3.09887	+	8.17105i	0.149095	+	0.393130i
$433$	0.922182	−	7.59485i	0.0443172	−	0.364985i	−0.953632	−	0.300975i	$-0.902688\pi$
$433$	0.922182	−	7.59485i	0.0443172	−	0.364985i	0.997949	−	0.0640102i	$-0.0203890\pi$
$434$	1.42332	−	0.539793i	0.0683214	−	0.0259109i
$435$	3.83702	−	0.465899i	0.183971	−	0.0223381i
$436$	52.1756	−	36.0142i	2.49876	−	1.72477i
$437$		−	65.5839i		−	3.13730i
$438$	1.62228	+	2.35028i	0.0775156	+	0.112301i
$439$	−8.70864	−	2.14649i	−0.415641	−	0.102446i	0.0259491	−	0.999663i	$-0.491739\pi$
$439$	−8.70864	−	2.14649i	−0.415641	−	0.102446i	−0.441590	+	0.897217i	$0.645585\pi$
$440$	63.5347	+	71.7159i	3.02890	+	3.41892i
$441$	3.64075	+	5.27454i	0.173369	+	0.251169i
$442$	10.6809	+	43.7429i	0.508037	+	2.08064i
$443$	22.7750	−	32.9953i	1.08207	−	1.56766i	0.290205	−	0.956964i	$-0.406276\pi$
$443$	22.7750	−	32.9953i	1.08207	−	1.56766i	0.791869	−	0.610691i	$-0.209108\pi$
$444$	−31.7565	+	3.85594i	−1.50710	+	0.182995i
$445$	1.32774	−	10.9350i	0.0629411	−	0.518367i
$446$	31.5241	+	16.5451i	1.49271	+	0.783435i
$447$	−0.505009	+	2.04890i	−0.0238861	+	0.0969097i
$448$	−3.68323	−	0.447225i	−0.174016	−	0.0211294i
$449$	1.93497	−	2.18413i	0.0913169	−	0.103075i	−0.701076	−	0.713087i	$-0.747297\pi$
$449$	1.93497	−	2.18413i	0.0913169	−	0.103075i	0.792393	+	0.610011i	$0.208835\pi$
$450$	6.16007	−	4.25199i	0.290389	−	0.200441i
$451$	−12.4202	+	17.9938i	−0.584846	+	0.847296i
$452$	23.5385	−	5.80172i	1.10716	−	0.272890i
$453$	6.29240	+	0.764036i	0.295643	+	0.0358975i
$454$	54.4906	−	28.5989i	2.55737	−	1.34221i
$455$	6.90172	−	3.60319i	0.323558	−	0.168920i
$456$	51.3282	+	26.9391i	2.40366	+	1.26154i
$457$	−15.2865	−	10.5515i	−0.715071	−	0.493578i	0.154121	−	0.988052i	$-0.450745\pi$
$457$	−15.2865	−	10.5515i	−0.715071	−	0.493578i	−0.869192	+	0.494474i	$0.835361\pi$
$458$	19.2287	−	27.8575i	0.898497	−	1.30170i
$459$	−3.60959	+	3.19782i	−0.168481	+	0.149261i
$460$	−69.5239	−	78.4763i	−3.24157	−	3.65897i
$461$	−6.91866	−	2.62390i	−0.322234	−	0.122207i	0.188184	−	0.982134i	$-0.439740\pi$
$461$	−6.91866	−	2.62390i	−0.322234	−	0.122207i	−0.510418	+	0.859927i	$0.670509\pi$
$462$	−4.50212	+	8.57808i	−0.209458	+	0.399088i
$463$	−27.6968	−	10.5040i	−1.28718	−	0.488163i	−0.386357	−	0.922349i	$-0.626267\pi$
$463$	−27.6968	−	10.5040i	−1.28718	−	0.488163i	−0.900823	+	0.434186i	$0.857036\pi$
$464$	11.6756	+	2.87777i	0.542024	+	0.133597i
$465$	−1.60767	+	1.42428i	−0.0745541	+	0.0660492i
$466$	3.34981	−	2.31220i	0.155177	−	0.107111i
$467$	10.8735	+	28.6710i	0.503164	+	1.32673i	0.910520	+	0.413465i	$0.135682\pi$
$467$	10.8735	+	28.6710i	0.503164	+	1.32673i	−0.407356	+	0.913269i	$0.633549\pi$
$468$	−9.60964	−	13.9869i	−0.444206	−	0.646544i
$469$	0.386272	−	1.01852i	0.0178364	−	0.0470307i
$470$	−17.1452	−	69.5609i	−0.790850	−	3.20860i
$471$	−14.2310	+	7.46902i	−0.655731	+	0.344154i
$472$	20.6059	+	54.3334i	0.948465	+	2.50090i
$473$	−18.5036	+	2.24675i	−0.850798	+	0.103306i
$474$	−3.87748	−	2.67643i	−0.178098	−	0.122932i
$475$	5.72040	−	23.2086i	0.262470	−	1.06488i
$476$	−4.17558	−	16.9410i	−0.191387	−	0.776489i
$477$	−1.33739	−	11.0144i	−0.0612349	−	0.504315i
$478$	25.3943	−	66.9593i	1.16151	−	3.06265i
$479$	2.91494	−	11.8264i	0.133187	−	0.540361i	−0.866000	−	0.500044i	$-0.833317\pi$
$479$	2.91494	−	11.8264i	0.133187	−	0.540361i	0.999187	−	0.0403169i	$-0.0128367\pi$
$480$	23.4897	−	5.78970i	1.07215	−	0.264262i
$481$	22.9325	−	8.64017i	1.04563	−	0.393958i
$482$	33.5610	+	8.27203i	1.52866	+	0.376781i
$483$	2.83307	−	5.39797i	0.128909	−	0.245616i
$484$	59.6812			2.71278
$485$	6.14953			0.279236
$486$	1.20350	−	2.29308i	0.0545918	−	0.104016i
$487$	23.3457	+	26.3518i	1.05789	+	1.19411i	0.980379	+	0.197123i	$0.0631597\pi$
$487$	23.3457	+	26.3518i	1.05789	+	1.19411i	0.0775139	+	0.996991i	$0.475302\pi$
$488$			35.3205i			1.59888i
$489$	−2.31812	+	2.61662i	−0.104829	+	0.118328i
$490$	41.2818	−	21.6664i	1.86492	−	0.978786i
$491$	−0.0536323	−	0.441701i	−0.00242039	−	0.0199337i	0.991449	−	0.130497i	$-0.0416574\pi$
$491$	−0.0536323	−	0.441701i	−0.00242039	−	0.0199337i	−0.993869	+	0.110564i	$0.964734\pi$
$492$	9.82745	+	18.7246i	0.443056	+	0.844172i
$493$	0.799843	+	6.58730i	0.0360231	+	0.296677i
$494$	−74.9367	−	18.6431i	−3.37156	−	0.838792i
$495$	1.64763	−	13.5695i	0.0740554	−	0.609901i
$496$	−6.24786	+	2.36950i	−0.280537	+	0.106394i
$497$	10.1717	+	5.33852i	0.456263	+	0.239465i
$498$	6.23131	−	16.4306i	0.279232	−	0.736273i
$499$	11.8637	+	22.6043i	0.531091	+	1.01191i	0.992211	+	0.124572i	$0.0397556\pi$
$499$	11.8637	+	22.6043i	0.531091	+	1.01191i	−0.461119	+	0.887338i	$0.652552\pi$
$500$	12.9619	+	24.6969i	0.579675	+	1.10448i
$501$	−2.92021	−	11.8478i	−0.130465	−	0.529319i
$502$	32.2466	+	3.91545i	1.43924	+	0.174755i
$503$	−5.36026	−	4.74877i	−0.239002	−	0.211737i	0.535116	−	0.844779i	$-0.320268\pi$
$503$	−5.36026	−	4.74877i	−0.239002	−	0.211737i	−0.774118	+	0.633041i	$0.781806\pi$
$504$	3.06092	+	4.43451i	0.136344	+	0.197529i
$505$	−6.82390	−	2.58796i	−0.303659	−	0.115163i
$506$	−99.9379			−4.44278
$507$	9.69308	+	8.66281i	0.430485	+	0.384729i
$508$	17.1574			0.761235
$509$	24.6337	+	9.34234i	1.09187	+	0.414092i	0.833818	−	0.552039i	$-0.186150\pi$
$509$	24.6337	+	9.34234i	1.09187	+	0.414092i	0.258052	+	0.966131i	$0.416919\pi$
$510$	19.9276	+	28.8702i	0.882411	+	1.27839i
$511$	0.634530	+	0.562145i	0.0280700	+	0.0248678i
$512$	−46.8982	−	5.69448i	−2.07263	−	0.251663i
$513$	−1.97917	−	8.02980i	−0.0873824	−	0.354525i
$514$	21.1585	+	40.3142i	0.933262	+	1.77818i
$515$	−5.82556	−	11.0997i	−0.256705	−	0.489111i
$516$	−6.39284	+	16.8565i	−0.281429	+	0.742068i
$517$	−42.4360	−	22.2721i	−1.86633	−	0.979527i
$518$	−12.6518	+	4.79818i	−0.555887	+	0.210820i
$519$	1.79398	−	14.7748i	0.0787470	−	0.648540i
$520$	−62.9298	+	32.8539i	−2.75965	+	1.44074i
$521$	0.572819	+	4.71759i	0.0250957	+	0.206681i	0.999863	−	0.0165411i	$-0.00526544\pi$
$521$	0.572819	+	4.71759i	0.0250957	+	0.206681i	−0.974768	+	0.223222i	$0.928342\pi$
$522$	−1.65604	−	3.15532i	−0.0724830	−	0.138105i
$523$	2.53734	+	20.8968i	0.110950	+	0.913755i	0.936800	+	0.349865i	$0.113773\pi$
$523$	2.53734	+	20.8968i	0.110950	+	0.913755i	−0.825850	+	0.563890i	$0.809304\pi$
$524$	65.5401	−	34.3981i	2.86313	−	1.50269i
$525$	1.47338	−	1.66310i	0.0643036	−	0.0725838i
$526$		−	5.07860i		−	0.221438i
$527$	−2.44516	−	2.76001i	−0.106513	−	0.120228i
$528$	19.7627	−	37.6547i	0.860062	−	1.63871i
$529$	39.8884			1.73428
$530$	−80.7119			−3.50590
$531$	3.85270	−	7.34071i	0.167193	−	0.318560i
$532$	29.0530	+	7.16092i	1.25961	+	0.310465i
$533$	−10.7161	−	12.1491i	−0.464165	−	0.526234i
$534$	−9.86037	+	2.43036i	−0.426700	+	0.105172i
$535$	−11.7063	+	47.4941i	−0.506105	+	2.05335i
$536$	−3.52202	+	9.28681i	−0.152128	+	0.401129i
$537$	−1.47445	−	12.1432i	−0.0636274	−	0.524019i
$538$	−2.91713	−	11.8353i	−0.125766	−	0.510255i
$539$	7.46376	−	30.2817i	0.321487	−	1.30432i
$540$	−10.8804	−	7.51022i	−0.468219	−	0.323188i
$541$	1.73006	−	0.210068i	0.0743812	−	0.00903151i	−0.0832615	−	0.996528i	$-0.526534\pi$
$541$	1.73006	−	0.210068i	0.0743812	−	0.00903151i	0.157643	+	0.987496i	$0.449611\pi$
$542$	19.6756	+	51.8803i	0.845139	+	2.22845i
$543$	−1.98738	+	1.04306i	−0.0852867	+	0.0447619i
$544$	9.93960	+	40.3266i	0.426157	+	1.72899i
$545$	−13.4171	+	35.3781i	−0.574727	+	1.51543i
$546$	−5.36242	−	4.77153i	−0.229490	−	0.204203i
$547$	0.954009	+	2.51552i	0.0407905	+	0.107556i	0.953864	−	0.300240i	$-0.0970668\pi$
$547$	0.954009	+	2.51552i	0.0407905	+	0.107556i	−0.913073	+	0.407796i	$0.866298\pi$
$548$	74.2491	−	51.2505i	3.17177	−	2.18931i
$549$	3.77180	−	3.34152i	0.160976	−	0.142613i
$550$	−35.3656	−	8.71685i	−1.50800	−	0.371688i
$551$	−10.6404	−	4.03536i	−0.453295	−	0.171912i
$552$	−25.8319	+	49.2186i	−1.09948	+	2.09488i
$553$	−1.30769	−	0.495940i	−0.0556085	−	0.0210895i
$554$	−0.490038	−	0.553139i	−0.0208197	−	0.0235006i
$555$	14.2905	−	12.6603i	0.606598	−	0.537399i
$556$	1.14547	−	1.65950i	0.0485786	−	0.0703783i
$557$	−23.6706	−	16.3387i	−1.00296	−	0.692292i	−0.0510560	−	0.998696i	$-0.516259\pi$
$557$	−23.6706	−	16.3387i	−1.00296	−	0.692292i	−0.951901	+	0.306404i	$0.900874\pi$
$558$	1.75336	+	0.920236i	0.0742258	+	0.0389567i
$559$	1.69448	−	13.7063i	0.0716688	−	0.579713i
$560$	16.7090	−	8.76956i	0.706084	−	0.370582i
$561$	23.2957	+	2.82861i	0.983544	+	0.119424i
$562$	72.5810	−	17.8896i	3.06165	−	0.754628i
$563$	−3.36105	+	4.86932i	−0.141651	+	0.205217i	−0.887388	−	0.461024i	$-0.847482\pi$
$563$	−3.36105	+	4.86932i	−0.141651	+	0.205217i	0.745737	+	0.666241i	$0.232098\pi$
$564$	−38.1481	+	26.3317i	−1.60633	+	1.10877i
$565$	−9.59440	+	10.8298i	−0.403640	+	0.455615i
$566$	−25.5474	−	3.10202i	−1.07384	−	0.130388i
$567$	0.183971	−	0.746399i	0.00772605	−	0.0313458i
$568$	−92.7454	−	48.6765i	−3.89151	−	2.04242i
$569$	0.0539948	−	0.444687i	0.00226358	−	0.0186423i	−0.991533	−	0.129852i	$-0.958550\pi$
$569$	0.0539948	−	0.444687i	0.00226358	−	0.0186423i	0.993797	+	0.111210i	$0.0354727\pi$
$570$	−59.7217	+	7.25152i	−2.50147	+	0.303733i
$571$	−19.0550	+	27.6060i	−0.797429	+	1.15527i	0.187492	+	0.982266i	$0.439964\pi$
$571$	−19.0550	+	27.6060i	−0.797429	+	1.15527i	−0.984920	+	0.173009i	$0.944651\pi$
$572$	−19.9368	+	80.1369i	−0.833601	+	3.35069i
$573$	3.20327	+	4.64074i	0.133818	+	0.193870i
$574$	5.93146	+	6.69524i	0.247574	+	0.279454i
$575$	22.2547	+	5.48529i	0.928085	+	0.228752i
$576$	−2.74174	−	3.97210i	−0.114239	−	0.165504i
$577$			38.6390i			1.60856i	0.594249	+	0.804281i	$0.297449\pi$
$577$			38.6390i			1.60856i	−0.594249	+	0.804281i	$0.702551\pi$
$578$	−13.3316	+	9.20213i	−0.554521	+	0.382758i
$579$	13.0532	−	1.58494i	0.542472	−	0.0658680i
$580$	−17.0098	+	6.45097i	−0.706294	+	0.267862i
$581$	0.628753	−	5.17825i	0.0260851	−	0.214830i
$582$	−2.01044	−	5.30110i	−0.0833355	−	0.219738i
$583$	−35.8036	+	40.4139i	−1.48283	+	1.67377i
$584$	−5.78564	−	5.12563i	−0.239412	−	0.212100i
$585$	9.46190	+	3.61197i	0.391202	+	0.149336i
$586$	−64.6988	+	57.3181i	−2.67268	+	2.36779i
$587$		−	40.2141i		−	1.65981i	−0.557902	−	0.829907i	$-0.688394\pi$
$587$		−	40.2141i		−	1.65981i	0.557902	−	0.829907i	$-0.311606\pi$
$588$	−22.5787	−	20.0030i	−0.931131	−	0.824910i
$589$	6.13986	−	1.51334i	0.252988	−	0.0623560i
$590$	−49.6319	−	34.2584i	−2.04331	−	1.41040i
$591$	−9.52991	+	3.61422i	−0.392008	+	0.148669i
$592$	55.5368	−	21.0623i	2.28255	−	0.865657i
$593$	25.5159	+	17.6123i	1.04781	+	0.723252i	0.961997	−	0.273059i	$-0.0880353\pi$
$593$	25.5159	+	17.6123i	1.04781	+	0.723252i	0.0858146	+	0.996311i	$0.472651\pi$
$594$	−12.2360	+	3.01589i	−0.502048	+	0.123744i
$595$	7.79440	+	6.90523i	0.319539	+	0.283087i
$596$		−	9.93198i		−	0.406830i
$597$	−0.0392189	+	0.0347449i	−0.00160512	+	0.00142202i
$598$	17.8769	−	71.8568i	0.731039	−	2.93844i
$599$	−5.39475	−	4.77933i	−0.220424	−	0.195278i	0.545683	−	0.837992i	$-0.316270\pi$
$599$	−5.39475	−	4.77933i	−0.220424	−	0.195278i	−0.766107	+	0.642713i	$0.777809\pi$
$600$	−13.4343	+	15.1641i	−0.548452	+	0.619074i
$601$	11.3120	+	29.8272i	0.461425	+	1.21668i	0.940769	+	0.339049i	$0.110105\pi$
$601$	11.3120	+	29.8272i	0.461425	+	1.21668i	−0.479344	+	0.877627i	$0.659125\pi$
$602$	−0.919157	+	7.56994i	−0.0374621	+	0.308528i
$603$	1.32492	−	0.502476i	0.0539549	−	0.0204624i
$604$	−29.6159	+	3.59602i	−1.20505	+	0.146320i
$605$	−29.3135	+	20.2336i	−1.19176	+	0.822615i
$606$			6.72849i			0.273326i
$607$	−9.22256	−	13.3612i	−0.374332	−	0.542313i	0.589865	−	0.807502i	$-0.299181\pi$
$607$	−9.22256	−	13.3612i	−0.374332	−	0.542313i	−0.964197	+	0.265189i	$0.914566\pi$
$608$	−69.1581	−	17.0459i	−2.80473	−	0.691304i
$609$	−0.701451	−	0.791774i	−0.0284242	−	0.0320843i
$610$	−20.8231	−	30.1675i	−0.843104	−	1.22145i
$611$	23.6049	−	26.5281i	0.954952	−	1.07321i
$612$	12.8933	−	18.6792i	0.521183	−	0.755063i
$613$	25.0246	−	3.03853i	1.01073	−	0.122725i	0.401618	−	0.915807i	$-0.368448\pi$
$613$	25.0246	−	3.03853i	1.01073	−	0.122725i	0.609115	+	0.793082i	$0.291525\pi$
$614$	5.59618	−	46.0887i	0.225844	−	1.85999i
$615$	−11.1751	−	5.86516i	−0.450624	−	0.236506i
$616$	6.27508	−	25.4590i	0.252830	−	1.02577i
$617$	−34.3746	−	4.17384i	−1.38387	−	0.168032i	−0.605504	−	0.795842i	$-0.707028\pi$
$617$	−34.3746	−	4.17384i	−1.38387	−	0.168032i	−0.778367	+	0.627810i	$0.783952\pi$
$618$	−7.66377	+	8.65060i	−0.308282	+	0.347978i
$619$	25.6383	−	17.6968i	1.03049	−	0.711295i	0.0722860	−	0.997384i	$-0.476971\pi$
$619$	25.6383	−	17.6968i	1.03049	−	0.711295i	0.958203	+	0.286089i	$0.0923552\pi$
$620$	5.74257	−	8.31954i	0.230627	−	0.334121i
$621$	7.69978	−	1.89783i	0.308982	−	0.0761572i
$622$	−47.3730	−	5.75212i	−1.89948	−	0.230639i
$623$	−2.66928	+	1.40094i	−0.106942	+	0.0561276i
$624$	23.5391	+	20.9453i	0.942320	+	0.838485i
$625$	−27.5356	−	14.4518i	−1.10142	−	0.578072i
$626$	16.1605	+	11.1548i	0.645905	+	0.445836i
$627$	−22.8614	+	33.1205i	−0.912997	+	1.32270i
$628$	56.6207	−	50.1616i	2.25941	−	2.00166i
$629$	21.7348	+	24.5336i	0.866625	+	0.978218i
$630$	−5.22872	−	1.98299i	−0.208317	−	0.0790043i
$631$	16.7745	−	31.9611i	0.667781	−	1.27235i	−0.281994	−	0.959416i	$-0.590996\pi$
$631$	16.7745	−	31.9611i	0.667781	−	1.27235i	0.949775	−	0.312934i	$-0.101312\pi$
$632$	11.9235	+	4.52197i	0.474290	+	0.179874i
$633$	−10.5878	−	2.60966i	−0.420827	−	0.103725i
$634$	−19.2553	+	17.0587i	−0.764724	+	0.677487i
$635$	−8.42715	+	5.81684i	−0.334421	+	0.230834i
$636$	18.5179	+	48.8277i	0.734283	+	1.93615i
$637$	20.4378	+	10.7833i	0.809777	+	0.427251i
$638$	−6.14915	+	16.2140i	−0.243447	+	0.641918i
$639$	3.57618	+	14.5091i	0.141472	+	0.573973i
$640$	11.7551	−	6.16955i	0.464661	−	0.243873i
$641$	−10.4726	−	27.6140i	−0.413644	−	1.09069i	−0.966331	−	0.257301i	$-0.917167\pi$
$641$	−10.4726	−	27.6140i	−0.413644	−	1.09069i	0.552688	−	0.833389i	$-0.313602\pi$
$642$	44.7686	−	5.43589i	1.76687	−	0.214537i
$643$	−31.6412	−	21.8404i	−1.24781	−	0.861300i	−0.253448	−	0.967349i	$-0.581565\pi$
$643$	−31.6412	−	21.8404i	−1.24781	−	0.861300i	−0.994361	+	0.106049i	$0.966180\pi$
$644$	−6.86661	+	27.8589i	−0.270582	+	1.09780i
$645$	−2.57489	−	10.4468i	−0.101386	−	0.411340i
$646$	−12.4492	−	102.529i	−0.489808	−	4.03393i
$647$	−3.69210	+	9.73528i	−0.145152	+	0.382733i	−0.987799	−	0.155732i	$-0.950226\pi$
$647$	−3.69210	+	9.73528i	−0.145152	+	0.382733i	0.842648	+	0.538465i	$0.180996\pi$
$648$	−1.67744	+	6.80566i	−0.0658962	+	0.267351i
$649$	−39.1704	+	9.65463i	−1.53757	+	0.378977i
$650$	12.5937	−	23.8691i	0.493967	−	0.936224i
$651$	0.570722	+	0.140670i	0.0223683	+	0.00551330i
$652$	7.64618	−	14.5686i	0.299448	−	0.570550i
$653$	34.9950			1.36946			0.684731	−	0.728796i	$-0.259920\pi$
$653$	34.9950			1.36946			0.684731	+	0.728796i	$0.259920\pi$
$654$	34.8835			1.36405
$655$	−20.5293	+	39.1153i	−0.802145	+	1.52836i
$656$	−26.0370	−	29.3897i	−1.01657	−	1.14748i
$657$			1.10275i			0.0430223i
$658$	−13.0016	+	14.6758i	−0.506855	+	0.572121i
$659$	38.5840	−	20.2505i	1.50302	−	0.788846i	0.505750	−	0.862680i	$-0.331216\pi$
$659$	38.5840	−	20.2505i	1.50302	−	0.788846i	0.997271	+	0.0738338i	$0.0235234\pi$
$660$	7.75475	+	63.8661i	0.301853	+	2.48598i
$661$	1.31300	+	2.50171i	0.0510698	+	0.0973053i	0.909653	−	0.415368i	$-0.136347\pi$
$661$	1.31300	+	2.50171i	0.0510698	+	0.0973053i	−0.858583	+	0.512674i	$0.828655\pi$
$662$	0.449271	+	3.70008i	0.0174614	+	0.143808i
$663$	−6.20093	+	16.2439i	−0.240824	+	0.630862i
$664$	−5.73296	+	47.2152i	−0.222482	+	1.83231i
$665$	−16.6977	+	6.33259i	−0.647507	+	0.245567i
$666$	−15.5855	−	8.17991i	−0.603927	−	0.316965i
$667$	3.86951	−	10.2031i	0.149828	−	0.395064i
$668$	26.6898	+	50.8532i	1.03266	+	1.96757i
$669$	6.38880	+	12.1728i	0.247005	+	0.470629i
$670$	−2.46684	−	10.0083i	−0.0953022	−	0.386656i
$671$	−24.3425	−	2.95572i	−0.939733	−	0.114104i
$672$	−4.95580	−	4.39046i	−0.191174	−	0.169366i
$673$	1.79655	+	2.60275i	0.0692520	+	0.100329i	0.856080	−	0.516844i	$-0.172893\pi$
$673$	1.79655	+	2.60275i	0.0692520	+	0.100329i	−0.786828	+	0.617173i	$0.788278\pi$
$674$	22.4874	+	8.52835i	0.866183	+	0.328500i
$675$	2.89030			0.111248
$676$	−54.0533	−	28.6697i	−2.07897	−	1.10268i
$677$	−25.3056			−0.972574			−0.486287	−	0.873799i	$-0.661649\pi$
$677$	−25.3056			−0.972574			−0.486287	+	0.873799i	$0.661649\pi$
$678$	12.4723	+	4.73013i	0.478997	+	0.181660i
$679$	−0.956029	−	1.38505i	−0.0366890	−	0.0531532i
$680$	−71.0692	−	62.9618i	−2.72538	−	2.41448i
$681$	23.5898	+	2.86433i	0.903965	+	0.109761i
$682$	−2.30605	−	9.35603i	−0.0883034	−	0.358261i
$683$	7.65058	+	14.5770i	0.292741	+	0.557772i	0.986760	−	0.162185i	$-0.0518540\pi$
$683$	7.65058	+	14.5770i	0.292741	+	0.557772i	−0.694019	+	0.719957i	$0.744162\pi$
$684$	18.0890	+	34.4657i	0.691650	+	1.31783i
$685$	−19.0934	+	50.3452i	−0.729522	+	1.92359i
$686$	−23.6371	−	12.4057i	−0.902468	−	0.473652i
$687$	12.2214	−	4.63495i	0.466274	−	0.176834i
$688$	4.03478	−	33.2294i	0.153824	−	1.26686i
$689$	−22.6536	−	32.9725i	−0.863035	−	1.25615i
$690$	−6.95349	−	57.2671i	−0.264715	−	2.18012i
$691$	−3.96356	−	7.55193i	−0.150781	−	0.287289i	0.798336	−	0.602212i	$-0.205714\pi$
$691$	−3.96356	−	7.55193i	−0.150781	−	0.287289i	−0.949117	+	0.314923i	$0.898021\pi$
$692$	8.44356	+	69.5390i	0.320976	+	2.64348i
$693$	−3.31237	+	1.73846i	−0.125826	+	0.0660388i
$694$	−26.8148	+	30.2677i	−1.01788	+	1.14894i
$695$			1.20344i			0.0456490i
$696$	6.39582	+	7.21939i	0.242433	+	0.273650i
$697$	10.0691	−	19.1852i	0.381396	−	0.726689i
$698$	−49.8749			−1.88779
$699$	1.57173			0.0594482
$700$	−4.85986	+	9.25968i	−0.183685	+	0.349983i
$701$	9.49969	+	2.34146i	0.358798	+	0.0884358i	0.414594	−	0.910006i	$-0.363924\pi$
$701$	9.49969	+	2.34146i	0.358798	+	0.0884358i	−0.0557960	+	0.998442i	$0.517770\pi$
$702$	0.0202929	−	9.33732i	0.000765904	−	0.352414i
$703$	−54.5768	+	13.4520i	−2.05840	+	0.507351i
$704$	−5.62074	+	22.8043i	−0.211840	+	0.859468i
$705$	9.80991	−	25.8666i	0.369463	−	0.974193i
$706$	−3.24065	−	26.6892i	−0.121963	−	1.00446i
$707$	0.477986	+	1.93927i	0.0179765	+	0.0729336i
$708$	−9.33792	+	37.8854i	−0.350940	+	1.42382i
$709$	7.57609	+	5.22940i	0.284526	+	0.196394i	0.701776	−	0.712398i	$-0.252391\pi$
$709$	7.57609	+	5.22940i	0.284526	+	0.196394i	−0.417250	+	0.908792i	$0.637006\pi$
$710$	107.912	−	13.1029i	4.04985	−	0.491741i
$711$	−0.645136	−	1.70108i	−0.0241945	−	0.0637956i
$712$	24.3384	−	12.7738i	0.912121	−	0.478718i
$713$	1.45114	+	5.88751i	0.0543457	+	0.220489i
$714$	3.40435	−	8.97652i	0.127404	−	0.335938i
$715$	−17.3764	−	46.1199i	−0.649841	−	1.72479i
$716$	20.4157	+	53.8319i	0.762972	+	2.01179i
$717$	22.7579	−	15.7086i	0.849908	−	0.586649i
$718$	22.7378	−	20.1439i	0.848566	−	0.751764i
$719$	−28.1603	−	6.94090i	−1.05020	−	0.258852i	−0.323803	−	0.946124i	$-0.604962\pi$
$719$	−28.1603	−	6.94090i	−1.05020	−	0.258852i	−0.726400	+	0.687273i	$0.758808\pi$
$720$	22.9522	+	8.70463i	0.855379	+	0.324403i
$721$	−1.59430	+	3.03768i	−0.0593747	+	0.113129i
$722$	119.606	+	45.3605i	4.45127	+	1.68814i
$723$	8.85082	+	9.99051i	0.329166	+	0.371551i
$724$	7.90716	−	7.00513i	0.293867	−	0.260344i
$725$	2.25926	−	3.27311i	0.0839069	−	0.121560i
$726$	27.0254	+	18.6543i	1.00301	+	0.692326i
$727$	30.9294	+	16.2330i	1.14711	+	0.602049i	0.927605	−	0.373563i	$-0.121864\pi$
$727$	30.9294	+	16.2330i	1.14711	+	0.602049i	0.219503	+	0.975612i	$0.429556\pi$
$728$	17.1829	+	9.06597i	0.636841	+	0.336007i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	7.96337	+	0.966928i	0.294737	+	0.0357876i
$731$	17.9347	−	4.42051i	0.663339	−	0.163498i
$732$	−13.4727	+	19.5186i	−0.497967	+	0.721430i
$733$	22.7161	−	15.6798i	0.839040	−	0.579147i	−0.0691976	−	0.997603i	$-0.522044\pi$
$733$	22.7161	−	15.6798i	0.839040	−	0.579147i	0.908237	+	0.418456i	$0.137429\pi$
$734$	−31.9294	+	36.0409i	−1.17854	+	1.33029i
$735$	17.8715	+	2.17000i	0.659202	+	0.0800416i
$736$	16.3454	−	66.3158i	0.602498	−	2.44443i
$737$	−6.10564	−	3.20449i	−0.224904	−	0.118039i
$738$	−1.40252	+	11.5508i	−0.0516275	+	0.425191i
$739$	−24.1139	+	2.92795i	−0.887043	+	0.107707i	−0.551359	−	0.834268i	$-0.685891\pi$
$739$	−24.1139	+	2.92795i	−0.887043	+	0.107707i	−0.335684	+	0.941975i	$0.608968\pi$
$740$	−51.0453	+	73.9519i	−1.87646	+	2.71852i
$741$	−19.7247	−	22.3623i	−0.724604	−	0.821498i
$742$	12.5478	+	18.1786i	0.460643	+	0.667357i
$743$	−9.69338	−	10.9416i	−0.355616	−	0.401407i	0.543293	−	0.839543i	$-0.317177\pi$
$743$	−9.69338	−	10.9416i	−0.355616	−	0.401407i	−0.898909	+	0.438136i	$0.855639\pi$
$744$	−5.20383	−	1.28263i	−0.190782	−	0.0470235i
$745$	3.36723	+	4.87827i	0.123366	+	0.178726i
$746$		−	85.6186i		−	3.13472i
$747$	5.58437	−	3.85461i	0.204322	−	0.141033i
$748$	−109.644	+	13.3131i	−4.00897	+	0.486777i
$749$	12.5169	−	4.74704i	0.457358	−	0.173453i
$750$	−1.84986	+	15.2349i	−0.0675472	+	0.556301i
$751$	0.544592	+	1.43597i	0.0198724	+	0.0523993i	0.944585	−	0.328266i	$-0.106464\pi$
$751$	0.544592	+	1.43597i	0.0198724	+	0.0523993i	−0.924713	+	0.380665i	$0.875695\pi$
$752$	57.0724	−	64.4215i	2.08122	−	2.34921i
$753$	9.38878	+	8.31773i	0.342146	+	0.303115i
$754$	−10.5581	−	7.32168i	−0.384504	−	0.266640i
$755$	13.3272	−	11.8069i	0.485027	−	0.429696i
$756$			3.61814i			0.131591i
$757$	−25.8077	−	22.8637i	−0.937999	−	0.830994i	0.0478119	−	0.998856i	$-0.484775\pi$
$757$	−25.8077	−	22.8637i	−0.937999	−	0.830994i	−0.985810	+	0.167862i	$0.946314\pi$
$758$	20.1225	−	4.95974i	0.730881	−	0.180146i
$759$	−31.7593	−	21.9218i	−1.15279	−	0.795712i
$760$	152.249	−	57.7404i	5.52265	−	2.09447i
$761$	−16.6244	+	6.30479i	−0.602633	+	0.228549i	−0.637004	−	0.770861i	$-0.719826\pi$
$761$	−16.6244	+	6.30479i	−0.602633	+	0.228549i	0.0343708	+	0.999409i	$0.489057\pi$
$762$	7.76937	+	5.36281i	0.281454	+	0.194274i
$763$	10.0540	−	2.47809i	0.363980	−	0.0897129i
$764$	−19.8656	−	17.5994i	−0.718712	−	0.636723i
$765$			13.5459i			0.489752i
$766$	−2.16553	+	1.91849i	−0.0782436	+	0.0693178i
$767$	0.0649625	−	29.8911i	0.00234566	−	1.07930i
$768$	−16.3867	−	14.5174i	−0.591305	−	0.523850i
$769$	−15.7363	+	17.7626i	−0.567464	+	0.640534i	−0.960265	−	0.279089i	$-0.909968\pi$
$769$	−15.7363	+	17.7626i	−0.567464	+	0.640534i	0.392801	+	0.919623i	$0.371506\pi$
$770$	9.64971	+	25.4442i	0.347752	+	0.916945i
$771$	−2.11914	+	17.4526i	−0.0763188	+	0.628542i
$772$	−57.8657	+	21.9456i	−2.08263	+	0.789839i
$773$	48.2699	−	5.86103i	1.73615	−	0.210807i	0.809600	−	0.586981i	$-0.199684\pi$
$773$	48.2699	−	5.86103i	1.73615	−	0.210807i	0.926549	+	0.376175i	$0.122761\pi$
$774$	−8.16364	+	5.63496i	−0.293436	+	0.202544i
$775$			2.21002i			0.0793863i
$776$	8.71706	+	12.6288i	0.312924	+	0.453349i
$777$	−5.07311	−	1.25041i	−0.181997	−	0.0448582i
$778$	−3.13624	−	3.54008i	−0.112440	−	0.126918i
$779$	21.1081	+	30.5803i	0.756274	+	1.09565i
$780$	−47.3078	−	5.84857i	−1.69389	−	0.209412i
$781$	41.3085	−	59.8457i	1.47814	−	2.14145i
$782$	98.3147	−	11.9376i	3.51573	−	0.426887i
$783$	0.165861	−	1.36599i	0.00592740	−	0.0488165i
$784$	49.5929	+	26.0283i	1.77117	+	0.929584i
$785$	−10.8041	+	43.8338i	−0.385614	+	1.56450i
$786$	40.4302	+	4.90911i	1.44210	+	0.175102i
$787$	−9.46351	+	10.6821i	−0.337338	+	0.380776i	−0.892562	−	0.450925i	$-0.851094\pi$
$787$	−9.46351	+	10.6821i	−0.337338	+	0.380776i	0.555224	+	0.831701i	$0.312633\pi$
$788$	39.4793	−	27.2506i	1.40639	−	0.970761i
$789$	1.11401	−	1.61393i	0.0396600	−	0.0574574i
$790$	−12.8498	+	3.16720i	−0.457177	+	0.112684i
$791$	3.93076	+	0.477281i	0.139762	+	0.0169702i
$792$	30.2021	−	15.8513i	1.07319	−	0.563251i
$793$	6.47958	−	16.9739i	0.230097	−	0.602761i
$794$	−49.5564	−	26.0092i	−1.75869	−	0.923032i
$795$	−25.6494	−	17.7045i	−0.909691	−	0.627914i
$796$	0.140089	−	0.202954i	0.00496532	−	0.00719351i
$797$	4.18970	−	3.71175i	0.148407	−	0.131477i	−0.585653	−	0.810562i	$-0.699162\pi$
$797$	4.18970	−	3.71175i	0.148407	−	0.131477i	0.734060	+	0.679085i	$0.237623\pi$
$798$	10.9178	+	12.3236i	0.386486	+	0.436252i
$799$	44.4071	+	16.8414i	1.57101	+	0.595806i
$800$	11.5685	−	22.0419i	0.409007	−	0.779298i
$801$	−3.66664	−	1.39057i	−0.129554	−	0.0491334i
$802$	−82.5540	−	20.3477i	−2.91508	−	0.718503i
$803$	4.01669	−	3.55848i	0.141746	−	0.125576i
$804$	−5.48871	+	3.78858i	−0.193572	+	0.133613i
$805$	−6.07232	−	16.0114i	−0.214021	−	0.564328i
$806$	7.13962	+	0.0155166i	0.251483	+	0.000546549i
$807$	1.66908	−	4.40101i	0.0587545	−	0.154923i
$808$	−4.35827	−	17.6822i	−0.153323	−	0.622058i
$809$	−12.7353	+	6.68400i	−0.447749	+	0.234997i	−0.673499	−	0.739189i	$-0.735209\pi$
$809$	−12.7353	+	6.68400i	−0.447749	+	0.234997i	0.225749	+	0.974185i	$0.427517\pi$
$810$	−2.57954	−	6.80170i	−0.0906359	−	0.238987i
$811$	30.0438	−	3.64798i	1.05498	−	0.128098i	0.425378	−	0.905016i	$-0.360141\pi$
$811$	30.0438	−	3.64798i	1.05498	−	0.128098i	0.629602	+	0.776918i	$0.283218\pi$
$812$	4.09735	+	2.82819i	0.143789	+	0.0992502i
$813$	−5.12747	+	20.8030i	−0.179828	+	0.729591i
$814$	20.4984	+	83.1651i	0.718467	+	2.91494i
$815$	1.18361	+	9.74790i	0.0414600	+	0.341454i
$816$	−14.9439	+	39.4038i	−0.523141	+	1.37941i
$817$	−7.58096	+	30.7572i	−0.265224	+	1.07606i
$818$	26.7420	−	6.59131i	0.935012	−	0.230460i
$819$	−0.657466	−	2.69262i	−0.0229737	−	0.0940876i
$820$	57.6749	+	14.2156i	2.01409	+	0.496429i
$821$	−19.9956	+	38.0985i	−0.697853	+	1.32965i	0.235917	+	0.971773i	$0.424191\pi$
$821$	−19.9956	+	38.0985i	−0.697853	+	1.32965i	−0.933770	+	0.357875i	$0.883502\pi$
$822$	49.6413			1.73144
$823$	47.5654			1.65803			0.829013	−	0.559229i	$-0.188903\pi$
$823$	47.5654			1.65803			0.829013	+	0.559229i	$0.188903\pi$
$824$	14.5368	−	27.6975i	0.506413	−	0.964889i
$825$	−9.32676	−	10.5277i	−0.324716	−	0.366529i
$826$			16.5044i			0.574262i
$827$	−35.3512	+	39.9033i	−1.22928	+	1.38757i	−0.333699	+	0.942680i	$0.608297\pi$
$827$	−35.3512	+	39.9033i	−1.22928	+	1.38757i	−0.895583	+	0.444894i	$0.853241\pi$
$828$	−33.0492	+	17.3455i	−1.14854	+	0.602799i
$829$	3.92038	+	32.2872i	0.136160	+	1.12138i	0.887285	+	0.461221i	$0.152588\pi$
$829$	3.92038	+	32.2872i	0.136160	+	1.12138i	−0.751125	+	0.660160i	$0.770488\pi$
$830$	−22.9391	−	43.7067i	−0.796227	−	1.51708i
$831$	−0.0343957	−	0.283274i	−0.00119317	−	0.00982666i
$832$	−15.3912	−	8.12061i	−0.533592	−	0.281532i
$833$	−3.72539	+	30.6814i	−0.129077	+	1.06305i
$834$	1.03740	−	0.393435i	0.0359223	−	0.0136235i
$835$	−30.3499	−	15.9288i	−1.05030	−	0.551240i
$836$	67.1673	−	177.106i	2.32303	−	6.12533i
$837$	0.355343	+	0.677049i	0.0122824	+	0.0234022i
$838$	15.9325	+	30.3568i	0.550378	+	1.04866i
$839$	6.28931	+	25.5167i	0.217131	+	0.880936i	0.973849	+	0.227195i	$0.0729554\pi$
$839$	6.28931	+	25.5167i	0.217131	+	0.880936i	−0.756718	+	0.653741i	$0.773198\pi$
$840$	15.0253	+	1.82440i	0.518422	+	0.0629479i
$841$	20.2896	+	17.9750i	0.699640	+	0.619827i
$842$	−4.94555	−	7.16487i	−0.170435	−	0.246918i
$843$	26.9897	+	10.2358i	0.929573	+	0.352541i
$844$	51.3240			1.76664
$845$	36.2691	−	4.24398i	1.24770	−	0.145997i
$846$	−25.5050			−0.876880
$847$	9.11437	+	3.45662i	0.313173	+	0.118771i
$848$	−55.0803	−	79.7975i	−1.89146	−	2.74026i
$849$	−7.43827	−	6.58973i	−0.255281	−	0.226159i
$850$	35.8324	+	4.35085i	1.22904	+	0.149233i
$851$	−12.8991	−	52.3337i	−0.442175	−	1.79398i
$852$	−32.6852	−	62.2764i	−1.11978	−	2.13355i
$853$	17.2237	+	32.8170i	0.589729	+	1.12363i	0.979258	+	0.202620i	$0.0649455\pi$
$853$	17.2237	+	32.8170i	0.589729	+	1.12363i	−0.389529	+	0.921014i	$0.627362\pi$
$854$	−3.55733	+	9.37991i	−0.121729	+	0.320974i
$855$	−20.5696	−	10.7958i	−0.703465	−	0.369207i
$856$	−114.129	+	43.2834i	−3.90085	+	1.47940i
$857$	−1.78626	+	14.7112i	−0.0610176	+	0.502525i	0.929876	+	0.367874i	$0.119914\pi$
$857$	−1.78626	+	14.7112i	−0.0610176	+	0.502525i	−0.990893	+	0.134651i	$0.957009\pi$
$858$	−34.0760	+	30.0568i	−1.16334	+	1.02612i
$859$	−2.99807	−	24.6914i	−0.102293	−	0.842459i	−0.950055	−	0.312082i	$-0.898974\pi$
$859$	−2.99807	−	24.6914i	−0.102293	−	0.842459i	0.847762	−	0.530377i	$-0.177949\pi$
$860$	23.5337	+	44.8397i	0.802493	+	1.52902i
$861$	0.416328	+	3.42877i	0.0141884	+	0.116852i
$862$	68.0025	−	35.6905i	2.31617	−	1.21562i
$863$	−0.137119	+	0.154776i	−0.00466760	+	0.00526863i	−0.750840	−	0.660484i	$-0.770351\pi$
$863$	−0.137119	+	0.154776i	−0.00466760	+	0.00526863i	0.746172	+	0.665753i	$0.231889\pi$
$864$		−	8.61268i		−	0.293009i
$865$	−27.7229	−	31.2927i	−0.942608	−	1.06398i
$866$	−9.20753	+	17.5435i	−0.312885	+	0.596152i
$867$	−6.25517			−0.212437
$868$	−2.76655			−0.0939030
$869$	−4.11429	+	7.83912i	−0.139568	+	0.265924i
$870$	−9.71890	−	2.39549i	−0.329502	−	0.0812148i
$871$	3.39625	−	3.81683i	0.115077	−	0.129328i
$872$	−91.6723	+	22.5952i	−3.10442	+	0.765170i
$873$	0.523922	−	2.12563i	0.0177321	−	0.0719418i
$874$	−60.2273	+	158.806i	−2.03722	+	5.37170i
$875$	0.549116	+	4.52238i	0.0185635	+	0.152884i
$876$	−1.24210	−	5.03939i	−0.0419666	−	0.170265i
$877$	−0.123727	+	0.501979i	−0.00417796	+	0.0169506i	−0.972994	−	0.230831i	$-0.925855\pi$
$877$	−0.123727	+	0.501979i	−0.00417796	+	0.0169506i	0.968816	+	0.247782i	$0.0797016\pi$
$878$	19.1161	+	13.1949i	0.645138	+	0.445307i
$879$	−33.1336	+	4.02315i	−1.11757	+	0.135697i
$880$	−42.3588	−	111.691i	−1.42792	−	3.76511i
$881$	16.0080	−	8.40165i	0.539323	−	0.283059i	−0.172986	−	0.984924i	$-0.555342\pi$
$881$	16.0080	−	8.40165i	0.539323	−	0.283059i	0.712310	+	0.701865i	$0.247649\pi$
$882$	−3.97206	−	16.1153i	−0.133746	−	0.542630i
$883$	11.8905	−	31.3527i	0.400148	−	1.05510i	−0.571900	−	0.820323i	$-0.693794\pi$
$883$	11.8905	−	31.3527i	0.400148	−	1.05510i	0.972048	−	0.234781i	$-0.0754372\pi$
$884$	10.0407	−	81.2168i	0.337704	−	2.73162i
$885$	−8.25776	−	21.7739i	−0.277582	−	0.731923i
$886$	−85.4484	+	58.9808i	−2.87069	+	1.98150i
$887$	3.90344	−	3.45815i	0.131065	−	0.116113i	−0.595044	−	0.803693i	$-0.702865\pi$
$887$	3.90344	−	3.45815i	0.131065	−	0.116113i	0.726109	+	0.687580i	$0.241327\pi$
$888$	46.2565	+	11.4012i	1.55227	+	0.382600i
$889$	2.62023	+	0.993723i	0.0878798	+	0.0333284i
$890$	−13.2569	+	25.2589i	−0.444371	+	0.846679i
$891$	−4.55001	−	1.72559i	−0.152431	−	0.0578095i
$892$	−42.9069	−	48.4318i	−1.43663	−	1.62162i
$893$	−60.9654	+	54.0106i	−2.04013	+	1.80740i
$894$	3.10440	−	4.49750i	0.103827	−	0.150419i
$895$	−28.2781	−	19.5190i	−0.945233	−	0.652447i
$896$	−3.21704	−	1.68844i	−0.107474	−	0.0564067i
$897$	21.4432	−	18.9140i	0.715967	−	0.631520i
$898$	−6.69112	+	3.51177i	−0.223286	+	0.117189i
$899$	1.04448	+	0.126823i	0.0348354	+	0.00422978i
$900$	−13.2082	+	3.25553i	−0.440274	+	0.108518i
$901$	30.3946	−	44.0342i	1.01259	−	1.46699i
$902$	46.5988	−	32.1648i	1.55157	−	1.07097i
$903$	−1.95260	+	2.20403i	−0.0649784	+	0.0733455i
$904$	−35.8407	−	4.35184i	−1.19204	−	0.144740i
$905$	−1.50880	+	6.12145i	−0.0501543	+	0.203484i
$906$	−14.5349	−	7.62852i	−0.482891	−	0.253441i
$907$	−1.80771	+	14.8878i	−0.0600239	+	0.494341i	0.931434	+	0.363911i	$0.118559\pi$
$907$	−1.80771	+	14.8878i	−0.0600239	+	0.494341i	−0.991458	+	0.130430i	$0.958364\pi$
$908$	−111.028	+	13.4813i	−3.68460	+	0.447391i
$909$	−1.47592	+	2.13825i	−0.0489533	+	0.0709212i
$910$	−20.0209	+	2.38683i	−0.663686	+	0.0791228i
$911$	16.1526	+	23.4010i	0.535158	+	0.775310i	0.993545	−	0.113443i	$-0.0361878\pi$
$911$	16.1526	+	23.4010i	0.535158	+	0.775310i	−0.458386	+	0.888753i	$0.651572\pi$
$912$	−47.9253	−	54.0964i	−1.58696	−	1.79131i
$913$	−32.0605	−	7.90220i	−1.06105	−	0.261525i
$914$	27.3253	+	39.5876i	0.903841	+	1.30944i
$915$		−	14.1546i		−	0.467936i
$916$	−50.6290	+	34.9467i	−1.67283	+	1.15467i
$917$	12.0014	−	1.45723i	0.396321	−	0.0481221i
$918$	11.6770	−	4.42849i	0.385398	−	0.146162i
$919$	4.29762	−	35.3941i	0.141765	−	1.16754i	−0.732038	−	0.681264i	$-0.761431\pi$
$919$	4.29762	−	35.3941i	0.141765	−	1.16754i	0.873803	−	0.486279i	$-0.161646\pi$
$920$	55.3673	+	145.992i	1.82541	+	4.81320i
$921$	11.8882	−	13.4190i	0.391729	−	0.442170i
$922$	14.3434	+	12.7072i	0.472375	+	0.418488i
$923$	35.6407	+	40.4066i	1.17313	+	1.33000i
$924$	13.1788	−	11.6754i	0.433552	−	0.384094i
$925$		−	19.6447i		−	0.645915i
$926$	57.4196	+	50.8693i	1.88693	+	1.67167i
$927$	−4.33301	+	1.06799i	−0.142315	+	0.0350775i
$928$	−9.75338	−	6.73227i	−0.320170	−	0.220998i
$929$	54.8285	−	20.7937i	1.79887	−	0.682220i	0.802537	−	0.596602i	$-0.203483\pi$
$929$	54.8285	−	20.7937i	1.79887	−	0.682220i	0.996328	−	0.0856178i	$-0.0272864\pi$
$930$	5.20081	−	1.97241i	0.170541	−	0.0646777i
$931$	−43.6211	−	30.1094i	−1.42962	−	0.986797i
$932$	−7.18254	+	1.77034i	−0.235272	+	0.0579893i
$933$	−13.7929	−	12.2194i	−0.451559	−	0.400046i
$934$		−	79.4099i		−	2.59837i
$935$	49.3399	−	43.7113i	1.61359	−	1.42951i
$936$	5.99477	+	24.5512i	0.195945	+	0.802482i
$937$	27.3396	+	24.2208i	0.893147	+	0.791259i	0.978747	−	0.205071i	$-0.0657424\pi$
$937$	27.3396	+	24.2208i	0.893147	+	0.791259i	−0.0856006	+	0.996330i	$0.527281\pi$
$938$	−1.87066	+	2.11153i	−0.0610791	+	0.0689440i
$939$	2.68879	+	7.08977i	0.0877455	+	0.231366i
$940$	−15.6945	+	129.256i	−0.511898	+	4.21586i
$941$	−9.44266	+	3.58113i	−0.307822	+	0.116741i	−0.503679	−	0.863891i	$-0.668020\pi$
$941$	−9.44266	+	3.58113i	−0.307822	+	0.116741i	0.195857	+	0.980633i	$0.437251\pi$
$942$	41.3183	−	5.01695i	1.34622	−	0.163461i
$943$	−29.3235	+	20.2405i	−0.954903	+	0.659122i
$944$		−	72.4486i		−	2.35800i
$945$	−1.22666	−	1.77712i	−0.0399031	−	0.0578096i
$946$	46.8683	+	11.5520i	1.52382	+	0.375588i
$947$	−39.7384	−	44.8553i	−1.29132	−	1.45760i	−0.816299	−	0.577630i	$-0.803978\pi$
$947$	−39.7384	−	44.8553i	−1.29132	−	1.45760i	−0.475024	−	0.879973i	$-0.657561\pi$
$948$	4.86421	+	7.04703i	0.157982	+	0.228877i
$949$	1.84009	+	3.52460i	0.0597319	+	0.114413i
$950$	−35.1645	+	50.9446i	−1.14089	+	1.65286i
$951$	−9.86102	+	1.19734i	−0.319766	+	0.0388266i
$952$	−3.13209	+	25.7950i	−0.101511	+	0.836022i
$953$	−36.8569	−	19.3440i	−1.19391	−	0.626614i	−0.253728	−	0.967276i	$-0.581657\pi$
$953$	−36.8569	−	19.3440i	−1.19391	−	0.626614i	−0.940186	+	0.340662i	$0.889349\pi$
$954$	−6.87641	+	27.8987i	−0.222632	+	0.903254i
$955$	15.7240	+	1.90924i	0.508818	+	0.0617817i
$956$	−86.3062	+	97.4196i	−2.79134	+	3.15078i
$957$	−5.51075	+	3.80379i	−0.178137	+	0.122959i
$958$	−17.9188	+	25.9598i	−0.578929	+	0.838723i
$959$	14.3075	−	3.52648i	0.462013	−	0.113876i
$960$	−13.4585	−	1.63416i	−0.434372	−	0.0527424i
$961$	26.9314	−	14.1347i	0.868756	−	0.455958i
$962$	−63.4637	−	0.137926i	−2.04615	−	0.00444691i
$963$	15.4194	+	8.09272i	0.496883	+	0.260784i
$964$	−51.6998	−	35.6858i	−1.66514	−	1.14936i
$965$	20.9816	−	30.3971i	0.675422	−	0.978518i
$966$	−11.8171	+	10.4691i	−0.380211	+	0.336837i
$967$	−20.3930	−	23.0190i	−0.655796	−	0.740241i	0.322701	−	0.946501i	$-0.395409\pi$
$967$	−20.3930	−	23.0190i	−0.655796	−	0.740241i	−0.978497	+	0.206260i	$0.933871\pi$
$968$	−83.1047	−	31.5174i	−2.67109	−	1.01301i
$969$	18.5339	−	35.3133i	0.595393	−	1.13443i
$970$	−14.8906	−	5.64727i	−0.478109	−	0.181323i
$971$	−31.7449	−	7.82440i	−1.01874	−	0.251097i	−0.305631	−	0.952150i	$-0.598868\pi$
$971$	−31.7449	−	7.82440i	−1.01874	−	0.251097i	−0.713109	+	0.701053i	$0.752714\pi$
$972$	−3.52295	+	3.12106i	−0.112999	+	0.100108i
$973$	0.271048	−	0.187091i	0.00868939	−	0.00599785i
$974$	−32.3302	−	85.2477i	−1.03593	−	2.73151i
$975$	9.23796	−	4.82288i	0.295851	−	0.154456i
$976$	15.6154	−	41.1745i	0.499838	−	1.31796i
$977$	3.87045	+	15.7030i	0.123827	+	0.502384i	0.999800	+	0.0200238i	$0.00637421\pi$
$977$	3.87045	+	15.7030i	0.123827	+	0.502384i	−0.875973	+	0.482360i	$0.839780\pi$
$978$	8.01606	−	4.20715i	0.256325	−	0.134530i
$979$	6.76686	+	17.8427i	0.216270	+	0.570256i
$980$	−84.1143	+	10.2133i	−2.68693	+	0.326253i
$981$	11.0856	+	7.65184i	0.353936	+	0.244305i
$982$	−0.275759	+	1.11880i	−0.00879982	+	0.0357023i
$983$	5.64194	+	22.8903i	0.179950	+	0.730086i	0.989681	+	0.143285i	$0.0457666\pi$
$983$	5.64194	+	22.8903i	0.179950	+	0.730086i	−0.809731	+	0.586801i	$0.800387\pi$
$984$	−3.79607	−	31.2635i	−0.121014	−	0.996643i
$985$	−10.1522	+	26.7692i	−0.323477	+	0.852938i
$986$	4.11252	−	16.6851i	0.130969	−	0.531363i
$987$	−7.35097	+	1.81185i	−0.233984	+	0.0576719i
$988$	115.327	+	79.9749i	3.66903	+	2.54434i
$989$	−29.4931	−	7.26939i	−0.937825	−	0.231153i
$990$	−16.4508	+	31.3443i	−0.522840	+	0.996188i
$991$	44.7001			1.41994			0.709972	−	0.704230i	$-0.248708\pi$
$991$	44.7001			1.41994			0.709972	+	0.704230i	$0.248708\pi$
$992$	6.58554			0.209091
$993$	−0.668855	+	1.27440i	−0.0212255	+	0.0404418i
$994$	−19.7275	−	22.2677i	−0.625718	−	0.706289i
$995$			0.147179i			0.00466587i
$996$	−21.1780	+	23.9050i	−0.671051	+	0.757460i
$997$	11.9583	−	6.27617i	0.378722	−	0.198768i	−0.264611	−	0.964355i	$-0.585244\pi$
$997$	11.9583	−	6.27617i	0.378722	−	0.198768i	0.643333	+	0.765587i	$0.277551\pi$
$998$	−7.96885	−	65.6294i	−0.252250	−	2.07746i
$999$	−3.15862	−	6.01825i	−0.0999343	−	0.190409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.25.2	✓	192
169.142	even	26	inner	507.2.p.b.142.2	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.25.2	✓	192	1.1	even	1	trivial
507.2.p.b.142.2	yes	192	169.142	even	26	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42142 - 0.918325i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(3.52295 + 3.12106i) q^{4} +(-2.78849 - 0.338584i) q^{5} +(0.619759 + 2.51446i) q^{6} +(0.357250 + 0.680683i) q^{7} +(-3.25740 - 6.20646i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(-2.42142 - 0.918325i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(3.52295 + 3.12106i) q^{4} +(-2.78849 - 0.338584i) q^{5} +(0.619759 + 2.51446i) q^{6} +(0.357250 + 0.680683i) q^{7} +(-3.25740 - 6.20646i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(6.44118 + 3.38059i) q^{10} +(4.55001 - 1.72559i) q^{11} +(0.567319 - 4.67229i) q^{12} +(0.426821 + 3.58020i) q^{13} +(-0.239965 - 1.97629i) q^{14} +(1.30539 + 2.48722i) q^{15} +(1.05336 + 8.67523i) q^{16} +(-4.26999 + 2.24106i) q^{17} +(1.71730 - 1.93843i) q^{18} -8.27012i q^{19} +(-8.76695 - 9.89585i) q^{20} +(0.357250 - 0.680683i) q^{21} -12.6022 q^{22} +7.93022 q^{23} +(-3.25740 + 6.20646i) q^{24} +(2.80631 + 0.691694i) q^{25} +(2.25427 - 9.06114i) q^{26} +(0.970942 - 0.239316i) q^{27} +(-0.865879 + 3.51301i) q^{28} +(0.487944 - 1.28660i) q^{29} +(-0.876834 - 7.22138i) q^{30} +(0.182989 + 0.742415i) q^{31} +(2.06115 - 8.36241i) q^{32} +(-4.00484 - 2.76434i) q^{33} +(12.3975 - 1.50533i) q^{34} +(-0.765719 - 2.01903i) q^{35} +(-4.16749 + 2.18727i) q^{36} +(-1.62657 - 6.59927i) q^{37} +(-7.59465 + 20.0255i) q^{38} +(2.70398 - 2.38505i) q^{39} +(6.98182 + 18.4095i) q^{40} +(-3.69768 + 2.55233i) q^{41} +(-1.49014 + 1.32015i) q^{42} +(-3.71907 - 0.916669i) q^{43} +(21.4151 + 8.12169i) q^{44} +(1.30539 - 2.48722i) q^{45} +(-19.2024 - 7.28252i) q^{46} +(-6.53082 - 7.37177i) q^{47} +(6.54119 - 5.79499i) q^{48} +(3.64075 - 5.27454i) q^{49} +(-6.16007 - 4.25199i) q^{50} +(4.26999 + 2.24106i) q^{51} +(-9.67034 + 13.9450i) q^{52} +(-9.82440 + 5.15625i) q^{53} +(-2.57083 - 0.312155i) q^{54} +(-13.2719 + 3.27123i) q^{55} +(3.06092 - 4.43451i) q^{56} +(-6.80617 + 4.69796i) q^{57} +(-2.36304 + 2.66732i) q^{58} +(-8.22987 - 0.999287i) q^{59} +(-3.16392 + 12.8365i) q^{60} +(-4.46187 - 2.34177i) q^{61} +(0.238684 - 1.96574i) q^{62} +(-0.763132 + 0.0926610i) q^{63} +(-2.74174 + 3.97210i) q^{64} +(0.0220109 - 10.1279i) q^{65} +(7.15884 + 10.3714i) q^{66} +(-0.939647 - 1.06064i) q^{67} +(-22.0374 - 5.43174i) q^{68} +(-4.50488 - 6.52645i) q^{69} +5.59212i q^{70} +(12.2981 - 8.48880i) q^{71} +(6.95823 - 0.844882i) q^{72} +(1.03109 - 0.391040i) q^{73} +(-2.12165 + 17.4734i) q^{74} +(-1.02492 - 2.70248i) q^{75} +(25.8115 - 29.1352i) q^{76} +(2.80007 + 2.48065i) q^{77} +(-8.73774 + 3.29208i) q^{78} +(-1.36177 + 1.20643i) q^{79} -24.5474i q^{80} +(-0.748511 - 0.663123i) q^{81} +(11.2975 - 2.78459i) q^{82} +(-5.58437 - 3.85461i) q^{83} +(3.38302 - 1.28301i) q^{84} +(12.6656 - 4.80343i) q^{85} +(8.16364 + 5.63496i) q^{86} +(-1.33604 + 0.329304i) q^{87} +(-25.5310 - 22.6185i) q^{88} +3.92147i q^{89} +(-5.44498 + 4.82383i) q^{90} +(-2.28450 + 1.56956i) q^{91} +(27.9378 + 24.7507i) q^{92} +(0.507046 - 0.572336i) q^{93} +(9.04419 + 23.8476i) q^{94} +(-2.80013 + 23.0611i) q^{95} +(-8.05299 + 3.05410i) q^{96} +(-2.17329 + 0.263885i) q^{97} +(-13.6595 + 9.42850i) q^{98} +4.86624i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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