LMFDB - Embedded newform 825.2.m.d.361.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(16,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("825.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.m (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.18
Character	$\chi$	$=$	825.361
Dual form			825.2.m.d.16.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.300458 + 0.924714i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.853212 - 0.619895i) q^{4} +(1.61330 + 1.54831i) q^{5} +(0.786609 - 0.571505i) q^{6} +(-2.89935 - 2.10650i) q^{7} +(2.40280 + 1.74574i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.947013 + 1.95704i) q^{10} +(-1.16824 - 3.10407i) q^{11} +(-0.853212 - 0.619895i) q^{12} +(2.19607 - 1.59554i) q^{13} +(1.07678 - 3.31399i) q^{14} +(0.973990 - 2.01279i) q^{15} +(-0.240570 + 0.740400i) q^{16} +(5.22816 - 3.79848i) q^{17} +(-0.786609 - 0.571505i) q^{18} +(0.752879 + 0.546998i) q^{19} +(2.33628 + 0.320957i) q^{20} +(-1.10745 + 3.40839i) q^{21} +(2.51937 - 2.01293i) q^{22} +(-0.526966 + 0.382863i) q^{23} +(0.917787 - 2.82466i) q^{24} +(0.205486 + 4.99578i) q^{25} +(2.13525 + 1.55135i) q^{26} +(0.809017 + 0.587785i) q^{27} -3.77957 q^{28} +(-0.207522 + 0.150773i) q^{29} +(2.15390 + 0.295903i) q^{30} -0.516104 q^{31} +5.18310 q^{32} +(-2.59114 + 2.07027i) q^{33} +(5.08335 + 3.69327i) q^{34} +(-1.41602 - 7.88751i) q^{35} +(-0.325898 + 1.00301i) q^{36} +(-1.80024 - 5.54056i) q^{37} +(-0.279609 + 0.860548i) q^{38} +(-2.19607 - 1.59554i) q^{39} +(1.17350 + 6.53667i) q^{40} +12.2196 q^{41} -3.48453 q^{42} -7.15991 q^{43} +(-2.92095 - 1.92424i) q^{44} +(-2.21526 - 0.304332i) q^{45} +(-0.512370 - 0.372259i) q^{46} +(-1.14821 - 3.53383i) q^{47} +0.778502 q^{48} +(1.80577 + 5.55759i) q^{49} +(-4.55793 + 1.69104i) q^{50} +(-5.22816 - 3.79848i) q^{51} +(0.884649 - 2.72267i) q^{52} +(-6.46806 - 4.69932i) q^{53} +(-0.300458 + 0.924714i) q^{54} +(2.92133 - 6.81658i) q^{55} +(-3.28916 - 10.1230i) q^{56} +(0.287574 - 0.885062i) q^{57} +(-0.201774 - 0.146597i) q^{58} +(1.77683 + 5.46852i) q^{59} +(-0.416701 - 2.32111i) q^{60} +(12.3692 + 8.98678i) q^{61} +(-0.155068 - 0.477249i) q^{62} +3.58380 q^{63} +(2.03845 + 6.27369i) q^{64} +(6.01332 + 0.826109i) q^{65} +(-2.69293 - 1.77403i) q^{66} +(-0.133617 - 0.411231i) q^{67} +(2.10607 - 6.48182i) q^{68} +(0.526966 + 0.382863i) q^{69} +(6.86825 - 3.67928i) q^{70} -2.17575 q^{71} -2.97002 q^{72} -8.20795 q^{73} +(4.58254 - 3.32941i) q^{74} +(4.68777 - 1.73921i) q^{75} +0.981447 q^{76} +(-3.15160 + 11.4607i) q^{77} +(0.815592 - 2.51013i) q^{78} +(12.1595 + 8.83441i) q^{79} +(-1.53448 + 0.822011i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.67148 + 11.2996i) q^{82} +(-2.82602 + 2.05322i) q^{83} +(1.16795 + 3.59459i) q^{84} +(14.3158 + 1.96670i) q^{85} +(-2.15125 - 6.62087i) q^{86} +(0.207522 + 0.150773i) q^{87} +(2.61184 - 9.49787i) q^{88} +(-13.0138 + 9.45511i) q^{89} +(-0.384172 - 2.13992i) q^{90} -9.72820 q^{91} +(-0.212279 + 0.653327i) q^{92} +(0.159485 + 0.490844i) q^{93} +(2.92279 - 2.12353i) q^{94} +(0.367699 + 2.04816i) q^{95} +(-1.60167 - 4.92943i) q^{96} +(2.73984 + 1.99061i) q^{97} +(-4.59663 + 3.33965i) q^{98} +(2.76965 + 1.82457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q + 4 q^{2} + 29 q^{3} - 30 q^{4} - 3 q^{5} + q^{6} - 2 q^{7} + 11 q^{8} - 29 q^{9} + 2 q^{10} + 2 q^{11} + 30 q^{12} + 20 q^{13} - 2 q^{14} + 3 q^{15} - 26 q^{16} + 11 q^{17} - q^{18} - q^{19} + 17 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) $ 116 * q + 4 * q^2 + 29 * q^3 - 30 * q^4 - 3 * q^5 + q^6 - 2 * q^7 + 11 * q^8 - 29 * q^9 + 2 * q^10 + 2 * q^11 + 30 * q^12 + 20 * q^13 - 2 * q^14 + 3 * q^15 - 26 * q^16 + 11 * q^17 - q^18 - q^19 + 17 * q^20 + 2 * q^21 - 14 * q^22 + 14 * q^23 - q^24 - 13 * q^25 - 16 * q^26 + 29 * q^27 - 12 * q^28 + 5 * q^29 - 12 * q^30 + 62 * q^31 - 94 * q^32 + 13 * q^33 + 20 * q^34 + 19 * q^35 - 35 * q^36 - 10 * q^37 - 21 * q^38 - 20 * q^39 - 8 * q^40 + 4 * q^41 + 12 * q^42 - 46 * q^43 - 25 * q^44 + 2 * q^45 - 15 * q^46 - 15 * q^47 - 134 * q^48 - 5 * q^49 + 100 * q^50 - 11 * q^51 + 4 * q^52 - 6 * q^53 - 4 * q^54 - 21 * q^55 + 28 * q^56 + 21 * q^57 - 9 * q^58 - 29 * q^59 - 7 * q^60 - 10 * q^61 + 22 * q^62 + 8 * q^63 + 3 * q^64 + 10 * q^65 - 6 * q^66 - 35 * q^67 + 60 * q^68 - 14 * q^69 + 94 * q^70 + 50 * q^71 - 24 * q^72 - 60 * q^73 - 12 * q^74 - 17 * q^75 + 126 * q^76 + 76 * q^77 - 19 * q^78 + 11 * q^79 + q^80 - 29 * q^81 - 21 * q^82 - 13 * q^83 - 13 * q^84 - 21 * q^85 + 6 * q^86 - 5 * q^87 - 61 * q^88 + 13 * q^89 - 8 * q^90 + 20 * q^91 + 97 * q^92 + 43 * q^93 + 39 * q^94 - 36 * q^95 - 26 * q^96 - 20 * q^97 - 34 * q^98 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.300458	+	0.924714i	0.212456	+	0.653872i	0.999324	+	0.0367512i	$0.0117009\pi$
$2$	0.300458	+	0.924714i	0.212456	+	0.653872i	−0.786869	+	0.617121i	$0.788299\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.853212	−	0.619895i	0.426606	−	0.309948i
$5$	1.61330	+	1.54831i	0.721491	+	0.692424i
$5$	1.61330	+	1.54831i	0.721491	+	0.692424i
$6$	0.786609	−	0.571505i	0.321132	−	0.233316i
$7$	−2.89935	−	2.10650i	−1.09585	−	0.796183i	−0.115474	−	0.993310i	$-0.536839\pi$
$7$	−2.89935	−	2.10650i	−1.09585	−	0.796183i	−0.980378	+	0.197127i	$0.936839\pi$
$8$	2.40280	+	1.74574i	0.849517	+	0.617211i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.947013	+	1.95704i	−0.299472	+	0.618872i
$11$	−1.16824	−	3.10407i	−0.352236	−	0.935911i
$11$	−1.16824	−	3.10407i	−0.352236	−	0.935911i
$12$	−0.853212	−	0.619895i	−0.246301	−	0.178948i
$13$	2.19607	−	1.59554i	0.609081	−	0.442523i	−0.240009	−	0.970771i	$-0.577151\pi$
$13$	2.19607	−	1.59554i	0.609081	−	0.442523i	0.849091	+	0.528247i	$0.177151\pi$
$14$	1.07678	−	3.31399i	0.287782	−	0.885701i
$15$	0.973990	−	2.01279i	0.251483	−	0.519701i
$16$	−0.240570	+	0.740400i	−0.0601426	+	0.185100i
$17$	5.22816	−	3.79848i	1.26801	−	0.921266i	0.268892	−	0.963170i	$-0.413342\pi$
$17$	5.22816	−	3.79848i	1.26801	−	0.921266i	0.999122	+	0.0419040i	$0.0133424\pi$
$18$	−0.786609	−	0.571505i	−0.185406	−	0.134705i
$19$	0.752879	+	0.546998i	0.172722	+	0.125490i	0.670788	−	0.741649i	$-0.265956\pi$
$19$	0.752879	+	0.546998i	0.172722	+	0.125490i	−0.498066	+	0.867139i	$0.665956\pi$
$20$	2.33628	+	0.320957i	0.522407	+	0.0717682i
$21$	−1.10745	+	3.40839i	−0.241666	+	0.743772i
$22$	2.51937	−	2.01293i	0.537131	−	0.429157i
$23$	−0.526966	+	0.382863i	−0.109880	+	0.0798325i	−0.641368	−	0.767233i	$-0.721633\pi$
$23$	−0.526966	+	0.382863i	−0.109880	+	0.0798325i	0.531488	+	0.847066i	$0.321633\pi$
$24$	0.917787	−	2.82466i	0.187343	−	0.576581i
$25$	0.205486	+	4.99578i	0.0410973	+	0.999155i
$26$	2.13525	+	1.55135i	0.418756	+	0.304244i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−3.77957			−0.714272
$29$	−0.207522	+	0.150773i	−0.0385358	+	0.0279979i	−0.606886	−	0.794789i	$-0.707582\pi$
$29$	−0.207522	+	0.150773i	−0.0385358	+	0.0279979i	0.568351	+	0.822786i	$0.307582\pi$
$30$	2.15390	+	0.295903i	0.393247	+	0.0540242i
$31$	−0.516104			−0.0926951			−0.0463475	−	0.998925i	$-0.514758\pi$
$31$	−0.516104			−0.0926951			−0.0463475	+	0.998925i	$0.514758\pi$
$32$	5.18310			0.916252
$33$	−2.59114	+	2.07027i	−0.451059	+	0.360387i
$34$	5.08335	+	3.69327i	0.871787	+	0.633390i
$35$	−1.41602	−	7.88751i	−0.239350	−	1.33323i
$36$	−0.325898	+	1.00301i	−0.0543163	+	0.167169i
$37$	−1.80024	−	5.54056i	−0.295957	−	0.910863i	−0.982898	−	0.184150i	$-0.941047\pi$
$37$	−1.80024	−	5.54056i	−0.295957	−	0.910863i	0.686941	−	0.726713i	$-0.258953\pi$
$38$	−0.279609	+	0.860548i	−0.0453586	+	0.139599i
$39$	−2.19607	−	1.59554i	−0.351653	−	0.255491i
$40$	1.17350	+	6.53667i	0.185547	+	1.03354i
$41$	12.2196			1.90838			0.954191	−	0.299198i	$-0.0967190\pi$
$41$	12.2196			1.90838			0.954191	+	0.299198i	$0.0967190\pi$
$42$	−3.48453			−0.537675
$43$	−7.15991			−1.09188			−0.545938	−	0.837825i	$-0.683827\pi$
$43$	−7.15991			−1.09188			−0.545938	+	0.837825i	$0.683827\pi$
$44$	−2.92095	−	1.92424i	−0.440350	−	0.290091i
$45$	−2.21526	−	0.304332i	−0.330232	−	0.0453672i
$46$	−0.512370	−	0.372259i	−0.0755448	−	0.0548865i
$47$	−1.14821	−	3.53383i	−0.167484	−	0.515462i	0.831727	−	0.555185i	$-0.187353\pi$
$47$	−1.14821	−	3.53383i	−0.167484	−	0.515462i	−0.999211	+	0.0397228i	$0.987353\pi$
$48$	0.778502			0.112367
$49$	1.80577	+	5.55759i	0.257967	+	0.793942i
$50$	−4.55793	+	1.69104i	−0.644588	+	0.239149i
$51$	−5.22816	−	3.79848i	−0.732088	−	0.531893i
$52$	0.884649	−	2.72267i	0.122679	−	0.377566i
$53$	−6.46806	−	4.69932i	−0.888456	−	0.645501i	0.0470187	−	0.998894i	$-0.485028\pi$
$53$	−6.46806	−	4.69932i	−0.888456	−	0.645501i	−0.935475	+	0.353393i	$0.885028\pi$
$54$	−0.300458	+	0.924714i	−0.0408871	+	0.125838i
$55$	2.92133	−	6.81658i	0.393912	−	0.919148i
$56$	−3.28916	−	10.1230i	−0.439533	−	1.35274i
$57$	0.287574	−	0.885062i	0.0380901	−	0.117229i
$58$	−0.201774	−	0.146597i	−0.0264942	−	0.0192492i
$59$	1.77683	+	5.46852i	0.231323	+	0.711940i	0.997588	+	0.0694149i	$0.0221132\pi$
$59$	1.77683	+	5.46852i	0.231323	+	0.711940i	−0.766264	+	0.642525i	$0.777887\pi$
$60$	−0.416701	−	2.32111i	−0.0537958	−	0.299654i
$61$	12.3692	+	8.98678i	1.58372	+	1.15064i	0.912270	+	0.409589i	$0.134328\pi$
$61$	12.3692	+	8.98678i	1.58372	+	1.15064i	0.671449	+	0.741051i	$0.265672\pi$
$62$	−0.155068	−	0.477249i	−0.0196936	−	0.0606107i
$63$	3.58380			0.451516
$64$	2.03845	+	6.27369i	0.254806	+	0.784211i
$65$	6.01332	+	0.826109i	0.745860	+	0.102466i
$66$	−2.69293	−	1.77403i	−0.331477	−	0.218368i
$67$	−0.133617	−	0.411231i	−0.0163239	−	0.0502399i	0.942563	−	0.334029i	$-0.108408\pi$
$67$	−0.133617	−	0.411231i	−0.0163239	−	0.0502399i	−0.958887	+	0.283789i	$0.908408\pi$
$68$	2.10607	−	6.48182i	0.255398	−	0.786036i
$69$	0.526966	+	0.382863i	0.0634392	+	0.0460913i
$70$	6.86825	−	3.67928i	0.820912	−	0.439758i
$71$	−2.17575			−0.258214			−0.129107	−	0.991631i	$-0.541211\pi$
$71$	−2.17575			−0.258214			−0.129107	+	0.991631i	$0.541211\pi$
$72$	−2.97002			−0.350020
$73$	−8.20795			−0.960668			−0.480334	−	0.877086i	$-0.659484\pi$
$73$	−8.20795			−0.960668			−0.480334	+	0.877086i	$0.659484\pi$
$74$	4.58254	−	3.32941i	0.532710	−	0.387036i
$75$	4.68777	−	1.73921i	0.541297	−	0.200827i
$76$	0.981447			0.112580
$77$	−3.15160	+	11.4607i	−0.359158	+	1.30606i
$78$	0.815592	−	2.51013i	0.0923476	−	0.284217i
$79$	12.1595	+	8.83441i	1.36805	+	0.993949i	0.997886	+	0.0649839i	$0.0206996\pi$
$79$	12.1595	+	8.83441i	1.36805	+	0.993949i	0.370167	+	0.928965i	$0.379300\pi$
$80$	−1.53448	+	0.822011i	−0.171560	+	0.0919036i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	3.67148	+	11.2996i	0.405447	+	1.24784i
$83$	−2.82602	+	2.05322i	−0.310196	+	0.225371i	−0.731981	−	0.681325i	$-0.761404\pi$
$83$	−2.82602	+	2.05322i	−0.310196	+	0.225371i	0.421785	+	0.906696i	$0.361404\pi$
$84$	1.16795	+	3.59459i	0.127434	+	0.392202i
$85$	14.3158	+	1.96670i	1.55277	+	0.213319i
$86$	−2.15125	−	6.62087i	−0.231976	−	0.713947i
$87$	0.207522	+	0.150773i	0.0222487	+	0.0161646i
$88$	2.61184	−	9.49787i	0.278423	−	1.01248i
$89$	−13.0138	+	9.45511i	−1.37947	+	1.00224i	−0.382535	+	0.923941i	$0.624949\pi$
$89$	−13.0138	+	9.45511i	−1.37947	+	1.00224i	−0.996930	+	0.0782991i	$0.975051\pi$
$90$	−0.384172	−	2.13992i	−0.0404953	−	0.225568i
$91$	−9.72820			−1.01979
$92$	−0.212279	+	0.653327i	−0.0221316	+	0.0681141i
$93$	0.159485	+	0.490844i	0.0165378	+	0.0508982i
$94$	2.92279	−	2.12353i	0.301463	−	0.219026i
$95$	0.367699	+	2.04816i	0.0377251	+	0.210137i
$96$	−1.60167	−	4.92943i	−0.163469	−	0.503107i
$97$	2.73984	+	1.99061i	0.278188	+	0.202116i	0.718127	−	0.695912i	$-0.245000\pi$
$97$	2.73984	+	1.99061i	0.278188	+	0.202116i	−0.439938	+	0.898028i	$0.645000\pi$
$98$	−4.59663	+	3.33965i	−0.464329	+	0.337355i
$99$	2.76965	+	1.82457i	0.278360	+	0.183376i
$100$	3.27218	+	4.13508i	0.327218	+	0.413508i
$101$	2.65112	−	8.15931i	0.263796	−	0.811881i	−0.728172	−	0.685394i	$-0.759630\pi$
$101$	2.65112	−	8.15931i	0.263796	−	0.811881i	0.991968	−	0.126487i	$-0.0403702\pi$
$102$	1.94167	−	5.97583i	0.192254	−	0.591696i
$103$	−3.15177	+	2.28989i	−0.310553	+	0.225630i	−0.732134	−	0.681161i	$-0.761475\pi$
$103$	−3.15177	+	2.28989i	−0.310553	+	0.225630i	0.421581	+	0.906791i	$0.361475\pi$
$104$	8.06211			0.790555
$105$	−7.06390	+	3.78409i	−0.689366	+	0.369289i
$106$	2.40215	−	7.39306i	0.233317	−	0.718077i
$107$	−9.82131	+	7.13560i	−0.949462	+	0.689825i	−0.950680	−	0.310175i	$-0.899613\pi$
$107$	−9.82131	+	7.13560i	−0.949462	+	0.689825i	0.00121733	+	0.999999i	$0.499613\pi$
$108$	1.05463			0.101482
$109$	5.27702	+	3.83398i	0.505447	+	0.367228i	0.811094	−	0.584916i	$-0.198873\pi$
$109$	5.27702	+	3.83398i	0.505447	+	0.367228i	−0.305647	+	0.952145i	$0.598873\pi$
$110$	7.18113	+	0.653301i	0.684694	+	0.0622898i
$111$	−4.71308	+	3.42426i	−0.447346	+	0.325016i
$112$	2.25715	−	1.63992i	0.213281	−	0.154958i
$113$	4.51819			0.425036			0.212518	−	0.977157i	$-0.431834\pi$
$113$	4.51819			0.425036			0.212518	+	0.977157i	$0.431834\pi$
$114$	0.904834			0.0847454
$115$	−1.44294	−	0.198232i	−0.134555	−	0.0184852i
$116$	−0.0835965	+	0.257283i	−0.00776174	+	0.0238882i
$117$	−0.838826	+	2.58164i	−0.0775494	+	0.238673i
$118$	−4.52295	+	3.28612i	−0.416372	+	0.302512i
$119$	−23.1598			−2.12305
$120$	5.85411	−	3.13601i	0.534405	−	0.286277i
$121$	−8.27045	+	7.25256i	−0.751859	+	0.659324i
$122$	−4.59377	+	14.1382i	−0.415900	+	1.28001i
$123$	−3.77607	−	11.6215i	−0.340476	−	1.04788i
$124$	−0.440346	+	0.319930i	−0.0395443	+	0.0287306i
$125$	−7.40349	+	8.37785i	−0.662188	+	0.749338i
$126$	1.07678	+	3.31399i	0.0959272	+	0.295234i
$127$	−1.11130	−	0.807407i	−0.0986120	−	0.0716458i	0.537387	−	0.843336i	$-0.319412\pi$
$127$	−1.11130	−	0.807407i	−0.0986120	−	0.0716458i	−0.635999	+	0.771690i	$0.719412\pi$
$128$	3.19753	−	2.32315i	0.282625	−	0.205339i
$129$	2.21253	+	6.80948i	0.194803	+	0.599541i
$130$	1.04283	+	5.80881i	0.0914626	+	0.509467i
$131$	−6.93483	−	21.3432i	−0.605899	−	1.86476i	−0.490491	−	0.871446i	$-0.663183\pi$
$131$	−6.93483	−	21.3432i	−0.605899	−	1.86476i	−0.115408	−	0.993318i	$-0.536817\pi$
$132$	−0.927442	+	3.37261i	−0.0807234	+	0.293548i
$133$	−1.03061	−	3.17188i	−0.0893650	−	0.275037i
$134$	0.340125	−	0.247115i	0.0293823	−	0.0213475i
$135$	0.395116	+	2.20088i	0.0340062	+	0.189422i
$136$	19.1933			1.64582
$137$	5.50792	−	16.9516i	0.470573	−	1.44827i	−0.381263	−	0.924467i	$-0.624511\pi$
$137$	5.50792	−	16.9516i	0.470573	−	1.44827i	0.851836	−	0.523808i	$-0.175489\pi$
$138$	−0.195708	+	0.602327i	−0.0166598	+	0.0512735i
$139$	−7.78187			−0.660049			−0.330025	−	0.943972i	$-0.607057\pi$
$139$	−7.78187			−0.660049			−0.330025	+	0.943972i	$0.607057\pi$
$140$	−6.09759	−	5.85194i	−0.515341	−	0.494579i
$141$	−3.00606	+	2.18403i	−0.253156	+	0.183928i
$142$	−0.653721	−	2.01195i	−0.0548590	−	0.168839i
$143$	−7.51820	−	4.95279i	−0.628703	−	0.414173i
$144$	−0.240570	−	0.740400i	−0.0200475	−	0.0617000i
$145$	−0.568239	−	0.0780646i	−0.0471897	−	0.00648291i
$146$	−2.46614	−	7.59001i	−0.204099	−	0.628153i
$147$	4.72757	−	3.43478i	0.389923	−	0.283296i
$148$	−4.97055	−	3.61132i	−0.408577	−	0.296848i
$149$	4.80944	+	14.8019i	0.394005	+	1.21262i	0.929734	+	0.368232i	$0.120037\pi$
$149$	4.80944	+	14.8019i	0.394005	+	1.21262i	−0.535730	+	0.844390i	$0.679963\pi$
$150$	3.01675	+	3.81229i	0.246316	+	0.311272i
$151$	−11.2598	+	8.18073i	−0.916310	+	0.665738i	−0.942603	−	0.333916i	$-0.891630\pi$
$151$	−11.2598	+	8.18073i	−0.916310	+	0.665738i	0.0262926	+	0.999654i	$0.491630\pi$
$152$	0.854101	+	2.62865i	0.0692768	+	0.213212i
$153$	−1.99698	+	6.14607i	−0.161446	+	0.496880i
$154$	−11.5448	+	0.529124i	−0.930304	+	0.0426380i
$155$	−0.832632	−	0.799088i	−0.0668786	−	0.0641843i
$156$	−2.86278			−0.229206
$157$	−8.49225	+	6.16998i	−0.677755	+	0.492418i	−0.872612	−	0.488414i	$-0.837576\pi$
$157$	−8.49225	+	6.16998i	−0.677755	+	0.492418i	0.194857	+	0.980832i	$0.437576\pi$
$158$	−4.51588	+	13.8985i	−0.359264	+	1.10570i
$159$	−2.47058	+	7.60366i	−0.195930	+	0.603010i
$160$	8.36191	+	8.02504i	0.661067	+	0.634435i
$161$	2.33436			0.183973
$162$	0.972302			0.0763913
$163$	3.13057	−	2.27449i	0.245205	−	0.178152i	−0.458394	−	0.888749i	$-0.651575\pi$
$163$	3.13057	−	2.27449i	0.245205	−	0.178152i	0.703599	+	0.710597i	$0.251575\pi$
$164$	10.4259	−	7.57487i	0.814128	−	0.591498i
$165$	−7.38570	−	0.671911i	−0.574976	−	0.0523082i
$166$	−2.74775	−	1.99635i	−0.213266	−	0.154947i
$167$	8.29591			0.641957			0.320978	−	0.947087i	$-0.395988\pi$
$167$	8.29591			0.641957			0.320978	+	0.947087i	$0.395988\pi$
$168$	−8.61114	+	6.25636i	−0.664364	+	0.482689i
$169$	−1.74023	+	5.35588i	−0.133864	+	0.411991i
$170$	2.48266	+	13.8289i	0.190411	+	1.06063i
$171$	−0.930609			−0.0711655
$172$	−6.10893	+	4.43839i	−0.465801	+	0.338424i
$173$	−4.60060	+	14.1592i	−0.349777	+	1.07650i	0.609199	+	0.793017i	$0.291491\pi$
$173$	−4.60060	+	14.1592i	−0.349777	+	1.07650i	−0.958976	+	0.283486i	$0.908509\pi$
$174$	−0.0770708	+	0.237199i	−0.00584272	+	0.0179820i
$175$	9.92784	−	14.9174i	0.750474	−	1.12765i
$176$	2.57929	−	0.118215i	0.194421	−	0.00891079i
$177$	4.65180	−	3.37973i	0.349651	−	0.254036i
$178$	−12.6534	−	9.19323i	−0.948412	−	0.689062i
$179$	3.81925	+	11.7544i	0.285464	+	0.878568i	0.986259	+	0.165205i	$0.0528286\pi$
$179$	3.81925	+	11.7544i	0.285464	+	0.878568i	−0.700795	+	0.713362i	$0.747171\pi$
$180$	−2.07874	+	1.11357i	−0.154940	+	0.0830006i
$181$	−4.73095	+	3.43723i	−0.351649	+	0.255488i	−0.749560	−	0.661936i	$-0.769735\pi$
$181$	−4.73095	+	3.43723i	−0.351649	+	0.255488i	0.397912	+	0.917424i	$0.369735\pi$
$182$	−2.92292	−	8.99581i	−0.216661	−	0.666814i
$183$	4.72463	−	14.5409i	0.349255	−	1.07490i
$184$	−1.93457			−0.142618
$185$	5.67417	−	11.7259i	0.417173	−	0.862107i
$186$	−0.405972	+	0.294956i	−0.0297673	+	0.0216272i
$187$	−17.8984	−	11.7910i	−1.30886	−	0.862245i
$188$	−3.17027	−	2.30334i	−0.231216	−	0.167988i
$189$	−1.10745	−	3.40839i	−0.0805554	−	0.247924i
$190$	−1.78349	+	0.955403i	−0.129388	+	0.0693122i
$191$	5.48641	+	16.8854i	0.396983	+	1.22179i	0.927407	+	0.374055i	$0.122033\pi$
$191$	5.48641	+	16.8854i	0.396983	+	1.22179i	−0.530424	+	0.847733i	$0.677967\pi$
$192$	5.33672	−	3.87735i	0.385145	−	0.279824i
$193$	2.84124	+	8.74443i	0.204517	+	0.629438i	0.999733	+	0.0231116i	$0.00735732\pi$
$193$	2.84124	+	8.74443i	0.204517	+	0.629438i	−0.795216	+	0.606326i	$0.792643\pi$
$194$	−1.01754	+	3.13166i	−0.0730550	+	0.224840i
$195$	−1.07254	−	5.97429i	−0.0768063	−	0.427828i
$196$	4.98583	+	3.62242i	0.356131	+	0.258744i
$197$	0.228584	−	0.703511i	0.0162860	−	0.0501231i	−0.942583	−	0.333971i	$-0.891611\pi$
$197$	0.228584	−	0.703511i	0.0162860	−	0.0501231i	0.958869	+	0.283848i	$0.0916112\pi$
$198$	−0.855044	+	3.10934i	−0.0607653	+	0.220971i
$199$	−25.6888			−1.82103			−0.910517	−	0.413472i	$-0.864316\pi$
$199$	−25.6888			−1.82103			−0.910517	+	0.413472i	$0.864316\pi$
$200$	−8.22756	+	12.3626i	−0.581776	+	0.874165i
$201$	−0.349814	+	0.254155i	−0.0246740	+	0.0179267i
$202$	8.34158			0.586911
$203$	0.919284			0.0645211
$204$	−6.81538			−0.477172
$205$	19.7139	+	18.9197i	1.37688	+	1.32141i
$206$	−3.06447	−	2.22647i	−0.213512	−	0.155125i
$207$	0.201283	−	0.619486i	0.0139901	−	0.0430572i
$208$	0.653027	+	2.00981i	0.0452793	+	0.139355i
$209$	0.818379	−	2.97601i	0.0566085	−	0.205855i
$210$	−5.62160	−	5.39513i	−0.387928	−	0.372299i
$211$	−0.616030	−	1.89594i	−0.0424092	−	0.130522i	0.927610	−	0.373550i	$-0.121859\pi$
$211$	−0.616030	−	1.89594i	−0.0424092	−	0.130522i	−0.970019	+	0.243028i	$0.921859\pi$
$212$	−8.43171			−0.579092
$213$	0.672343	+	2.06926i	0.0460682	+	0.141783i
$214$	−9.54929	−	6.93796i	−0.652776	−	0.474269i
$215$	−11.5511	−	11.0857i	−0.787779	−	0.756042i
$216$	0.917787	+	2.82466i	0.0624475	+	0.192194i
$217$	1.49637	+	1.08718i	0.101580	+	0.0738023i
$218$	−1.95981	+	6.03168i	−0.132735	+	0.408517i
$219$	2.53640	+	7.80622i	0.171394	+	0.527496i
$220$	−1.73305	−	7.62691i	−0.116842	−	0.514206i
$221$	5.42079	−	16.6835i	0.364642	−	1.12225i
$222$	−4.58254	−	3.32941i	−0.307560	−	0.223455i
$223$	−3.55532	+	10.9421i	−0.238082	+	0.732740i	0.758616	+	0.651538i	$0.225876\pi$
$223$	−3.55532	+	10.9421i	−0.238082	+	0.732740i	−0.996698	+	0.0812018i	$0.974124\pi$
$224$	−15.0276	−	10.9182i	−1.00408	−	0.729505i
$225$	−3.10269	−	3.92089i	−0.206846	−	0.261392i
$226$	1.35753	+	4.17804i	0.0903013	+	0.277919i
$227$	22.0937			1.46641			0.733205	−	0.680007i	$-0.238023\pi$
$227$	22.0937			1.46641			0.733205	+	0.680007i	$0.238023\pi$
$228$	−0.303284	−	0.933412i	−0.0200855	−	0.0618167i
$229$	−3.37663	−	2.45326i	−0.223134	−	0.162116i	0.470602	−	0.882345i	$-0.344037\pi$
$229$	−3.37663	−	2.45326i	−0.223134	−	0.162116i	−0.693736	+	0.720229i	$0.744037\pi$
$230$	−0.250237	−	1.39387i	−0.0165001	−	0.0919092i
$231$	11.8736	−	0.544197i	0.781228	−	0.0358055i
$232$	−0.761844			−0.0500175
$233$	−6.39305			−0.418823			−0.209411	−	0.977828i	$-0.567155\pi$
$233$	−6.39305			−0.418823			−0.209411	+	0.977828i	$0.567155\pi$
$234$	−2.63931			−0.172537
$235$	3.61905	−	7.47892i	0.236081	−	0.487871i
$236$	4.90592	+	3.56436i	0.319348	+	0.232020i
$237$	4.64453	−	14.2944i	0.301694	−	0.928520i
$238$	−6.95854	−	21.4162i	−0.451055	−	1.38820i
$239$	2.59439	−	7.98470i	0.167817	−	0.516487i	−0.831416	−	0.555650i	$-0.812469\pi$
$239$	2.59439	−	7.98470i	0.167817	−	0.516487i	0.999233	+	0.0391634i	$0.0124693\pi$
$240$	1.25596	+	1.20536i	0.0810718	+	0.0778057i
$241$	−15.6423	−	11.3648i	−1.00761	−	0.732069i	−0.0439007	−	0.999036i	$-0.513979\pi$
$241$	−15.6423	−	11.3648i	−1.00761	−	0.732069i	−0.963706	+	0.266967i	$0.913979\pi$
$242$	−9.19147	−	5.46871i	−0.590850	−	0.351542i
$243$	−1.00000			−0.0641500
$244$	16.1245			1.03226
$245$	−5.69161	+	11.7620i	−0.363624	+	0.751444i
$246$	9.61205	−	6.98357i	0.612842	−	0.445256i
$247$	2.52614			0.160734
$248$	−1.24009	−	0.900981i	−0.0787461	−	0.0572124i
$249$	2.82602	+	2.05322i	0.179092	+	0.130118i
$250$	−9.97156	−	4.32892i	−0.630657	−	0.273785i
$251$	−2.81111	+	8.65171i	−0.177436	+	0.546091i	−0.999736	−	0.0229624i	$-0.992690\pi$
$251$	−2.81111	+	8.65171i	−0.177436	+	0.546091i	0.822301	+	0.569053i	$0.192690\pi$
$252$	3.05774	−	2.22158i	0.192619	−	0.139946i
$253$	1.80405	+	1.18846i	0.113420	+	0.0747180i
$254$	0.412722	−	1.27023i	0.0258965	−	0.0797012i
$255$	−2.55338	−	14.2229i	−0.159899	−	0.890672i
$256$	13.7824	+	10.0135i	0.861401	+	0.625844i
$257$	−19.4514	−	14.1323i	−1.21335	−	0.881548i	−0.217817	−	0.975990i	$-0.569893\pi$
$257$	−19.4514	−	14.1323i	−1.21335	−	0.881548i	−0.995530	+	0.0944416i	$0.969893\pi$
$258$	−5.63205	+	4.09193i	−0.350636	+	0.254752i
$259$	−6.45169	+	19.8562i	−0.400888	+	1.23381i
$260$	5.64274	−	3.02278i	0.349948	−	0.187465i
$261$	0.0792663	−	0.243957i	0.00490646	−	0.0151005i
$262$	17.6527	−	12.8255i	1.09059	−	0.792360i
$263$	17.7293	+	12.8811i	1.09324	+	0.794282i	0.979943	−	0.199280i	$-0.0638602\pi$
$263$	17.7293	+	12.8811i	1.09324	+	0.794282i	0.113293	+	0.993562i	$0.463860\pi$
$264$	−9.84012	+	0.450996i	−0.605617	+	0.0277569i
$265$	−3.15894	−	17.5960i	−0.194052	−	1.08091i
$266$	2.62343	−	1.90603i	0.160853	−	0.116866i
$267$	13.0138	+	9.45511i	0.796435	+	0.578644i
$268$	−0.368924	−	0.268039i	−0.0225356	−	0.0163731i
$269$	−2.59057	+	1.88216i	−0.157950	+	0.114757i	−0.663953	−	0.747775i	$-0.731122\pi$
$269$	−2.59057	+	1.88216i	−0.157950	+	0.114757i	0.506003	+	0.862532i	$0.331122\pi$
$270$	−1.91647	+	1.02664i	−0.116633	+	0.0624795i
$271$	−17.5291	+	12.7356i	−1.06482	+	0.773634i	−0.974973	−	0.222322i	$-0.928636\pi$
$271$	−17.5291	+	12.7356i	−1.06482	+	0.773634i	−0.0898423	+	0.995956i	$0.528636\pi$
$272$	1.55465	+	4.78473i	0.0942646	+	0.290117i
$273$	3.00618	+	9.25207i	0.181942	+	0.559961i
$274$	17.3303			1.04696
$275$	15.2672	−	6.47409i	0.920644	−	0.390402i
$276$	0.686949			0.0413495
$277$	−7.32441	−	22.5422i	−0.440081	−	1.35443i	−0.887789	−	0.460251i	$-0.847759\pi$
$277$	−7.32441	−	22.5422i	−0.440081	−	1.35443i	0.447707	−	0.894180i	$-0.352241\pi$
$278$	−2.33812	−	7.19600i	−0.140231	−	0.431588i
$279$	0.417537	−	0.303358i	0.0249973	−	0.0181616i
$280$	10.3671	−	21.4241i	0.619553	−	1.28033i
$281$	18.8960	−	13.7287i	1.12724	−	0.818988i	0.141949	−	0.989874i	$-0.454663\pi$
$281$	18.8960	−	13.7287i	1.12724	−	0.818988i	0.985291	+	0.170886i	$0.0546630\pi$
$282$	−2.92279	−	2.12353i	−0.174050	−	0.126455i
$283$	10.0803	+	7.32374i	0.599209	+	0.435351i	0.845598	−	0.533820i	$-0.179244\pi$
$283$	10.0803	+	7.32374i	0.599209	+	0.435351i	−0.246389	+	0.969171i	$0.579244\pi$
$284$	−1.85638	+	1.34874i	−0.110156	+	0.0800327i
$285$	1.83429	−	0.982619i	0.108654	−	0.0582053i
$286$	2.32101	−	8.44029i	0.137244	−	0.499085i
$287$	−35.4290	−	25.7406i	−2.09130	−	1.51942i
$288$	−4.19322	+	3.04655i	−0.247088	+	0.179520i
$289$	7.65189	−	23.5501i	0.450111	−	1.38530i
$290$	−0.0985445	−	0.548914i	−0.00578673	−	0.0322333i
$291$	1.04652	−	3.22087i	0.0613484	−	0.188811i
$292$	−7.00312	+	5.08807i	−0.409827	+	0.297757i
$293$	13.0893	+	9.50992i	0.764684	+	0.555575i	0.900343	−	0.435180i	$-0.143315\pi$
$293$	13.0893	+	9.50992i	0.764684	+	0.555575i	−0.135659	+	0.990756i	$0.543315\pi$
$294$	4.59663	+	3.33965i	0.268081	+	0.194772i
$295$	−5.60039	+	11.5734i	−0.326067	+	0.673832i
$296$	5.34674	−	16.4556i	0.310773	−	0.956462i
$297$	0.879401	−	3.19791i	0.0510280	−	0.185562i
$298$	−12.2425	+	8.89471i	−0.709190	+	0.515257i
$299$	−0.546382	+	1.68159i	−0.0315981	+	0.0972489i
$300$	2.92153	−	4.38984i	0.168675	−	0.253447i
$301$	20.7591	+	15.0824i	1.19654	+	0.869334i
$302$	−10.9479	−	7.95414i	−0.629983	−	0.457709i
$303$	−8.57920			−0.492862
$304$	−0.586118	+	0.425839i	−0.0336162	+	0.0244236i
$305$	6.04102	+	33.6498i	0.345908	+	1.92678i
$306$	−6.28336			−0.359196
$307$	7.85750			0.448451			0.224226	−	0.974537i	$-0.428015\pi$
$307$	7.85750			0.448451			0.224226	+	0.974537i	$0.428015\pi$
$308$	4.41543	+	11.7320i	0.251593	+	0.668495i
$309$	3.15177	+	2.28989i	0.179298	+	0.130267i
$310$	0.488757	−	1.01004i	0.0277596	−	0.0573664i
$311$	7.48162	−	23.0261i	0.424244	−	1.30569i	−0.479472	−	0.877557i	$-0.659172\pi$
$311$	7.48162	−	23.0261i	0.424244	−	1.30569i	0.903716	−	0.428132i	$-0.140828\pi$
$312$	−2.49133	−	7.66753i	−0.141044	−	0.434088i
$313$	−2.44458	+	7.52365i	−0.138176	+	0.425262i	−0.996070	−	0.0885639i	$-0.971772\pi$
$313$	−2.44458	+	7.52365i	−0.138176	+	0.425262i	0.857895	+	0.513826i	$0.171772\pi$
$314$	−8.25703	−	5.99908i	−0.465971	−	0.338548i
$315$	5.78175	+	5.54882i	0.325764	+	0.312641i
$316$	15.8511			0.891692
$317$	−33.4303			−1.87763			−0.938815	−	0.344421i	$-0.888075\pi$
$317$	−33.4303			−1.87763			−0.938815	+	0.344421i	$0.888075\pi$
$318$	−7.77352			−0.435917
$319$	0.710445	+	0.468022i	0.0397773	+	0.0262042i
$320$	−6.42498	+	13.2775i	−0.359167	+	0.742235i
$321$	9.82131	+	7.13560i	0.548172	+	0.398271i
$322$	0.701378	+	2.15862i	0.0390862	+	0.120295i
$323$	6.01393			0.334624
$324$	−0.325898	−	1.00301i	−0.0181054	−	0.0557228i
$325$	8.42223	+	10.6432i	0.467181	+	0.590380i
$326$	3.04386	+	2.21149i	0.168584	+	0.122483i
$327$	2.01564	−	6.20351i	0.111465	−	0.343055i
$328$	29.3613	+	21.3322i	1.62120	+	1.17787i
$329$	−4.11496	+	12.6645i	−0.226865	+	0.698218i
$330$	−1.59777	−	7.03154i	−0.0879541	−	0.387074i
$331$	0.868363	+	2.67255i	0.0477296	+	0.146896i	0.972081	−	0.234646i	$-0.0753931\pi$
$331$	0.868363	+	2.67255i	0.0477296	+	0.146896i	−0.924351	+	0.381542i	$0.875393\pi$
$332$	−1.13841	+	3.50367i	−0.0624785	+	0.192289i
$333$	4.71308	+	3.42426i	0.258275	+	0.187648i
$334$	2.49257	+	7.67135i	0.136387	+	0.419757i
$335$	0.421147	−	0.870320i	0.0230097	−	0.0475507i
$336$	−2.25715	−	1.63992i	−0.123138	−	0.0894648i
$337$	9.80719	+	30.1834i	0.534232	+	1.64420i	0.745303	+	0.666725i	$0.232305\pi$
$337$	9.80719	+	30.1834i	0.534232	+	1.64420i	−0.211072	+	0.977471i	$0.567695\pi$
$338$	−5.47553			−0.297830
$339$	−1.39620	−	4.29705i	−0.0758310	−	0.233384i
$340$	13.4336	−	7.19628i	0.728538	−	0.390273i
$341$	0.602932	+	1.60202i	0.0326506	+	0.0867543i
$342$	−0.279609	−	0.860548i	−0.0151195	−	0.0465331i
$343$	−1.28066	+	3.94147i	−0.0691492	+	0.212819i
$344$	−17.2038	−	12.4993i	−0.927568	−	0.673918i
$345$	0.257365	+	1.43358i	0.0138561	+	0.0771813i
$346$	−14.4755			−0.778207
$347$	14.2551			0.765253			0.382626	−	0.923903i	$-0.375020\pi$
$347$	14.2551			0.765253			0.382626	+	0.923903i	$0.375020\pi$
$348$	0.270524			0.0145016
$349$	−4.72955	+	3.43622i	−0.253167	+	0.183937i	−0.707129	−	0.707084i	$-0.750010\pi$
$349$	−4.72955	+	3.43622i	−0.253167	+	0.183937i	0.453962	+	0.891021i	$0.350010\pi$
$350$	16.7772	+	4.69837i	0.896779	+	0.251139i
$351$	2.71450			0.144889
$352$	−6.05509	−	16.0887i	−0.322737	−	0.857530i
$353$	−2.74069	+	8.43498i	−0.145872	+	0.448949i	−0.997122	−	0.0758120i	$-0.975845\pi$
$353$	−2.74069	+	8.43498i	−0.145872	+	0.448949i	0.851250	+	0.524761i	$0.175845\pi$
$354$	4.52295	+	3.28612i	0.240392	+	0.174655i
$355$	−3.51014	−	3.36873i	−0.186299	−	0.178794i
$356$	−5.24240	+	16.1344i	−0.277846	+	0.855123i
$357$	7.15676	+	22.0263i	0.378776	+	1.16575i
$358$	−9.72197	+	7.06342i	−0.513822	+	0.373314i
$359$	1.06663	+	3.28275i	0.0562946	+	0.173257i	0.975250	−	0.221104i	$-0.0709660\pi$
$359$	1.06663	+	3.28275i	0.0562946	+	0.173257i	−0.918956	+	0.394361i	$0.870966\pi$
$360$	−4.79154	−	4.59851i	−0.252536	−	0.242363i
$361$	−5.60370	−	17.2464i	−0.294932	−	0.907707i
$362$	−4.59991	−	3.34203i	−0.241766	−	0.175653i
$363$	9.45331	+	5.62450i	0.496170	+	0.295210i
$364$	−8.30022	+	6.03046i	−0.435050	+	0.316082i
$365$	−13.2419	−	12.7084i	−0.693113	−	0.665190i
$366$	14.8657			0.777045
$367$	−4.56990	+	14.0647i	−0.238547	+	0.734171i	0.758084	+	0.652156i	$0.226136\pi$
$367$	−4.56990	+	14.0647i	−0.238547	+	0.734171i	−0.996631	+	0.0820149i	$0.973864\pi$
$368$	−0.156699	−	0.482271i	−0.00816852	−	0.0251401i
$369$	−9.88587	+	7.18251i	−0.514638	+	0.373906i
$370$	12.5480	+	1.72384i	0.652338	+	0.0896181i
$371$	8.85405	+	27.2500i	0.459680	+	1.41475i
$372$	0.440346	+	0.319930i	0.0228309	+	0.0165876i
$373$	11.7320	−	8.52377i	0.607458	−	0.441344i	−0.241060	−	0.970510i	$-0.577495\pi$
$373$	11.7320	−	8.52377i	0.607458	−	0.441344i	0.848518	+	0.529166i	$0.177495\pi$
$374$	5.52560	−	20.0937i	0.285722	−	1.03902i
$375$	10.2556	+	4.45224i	0.529598	+	0.229912i
$376$	3.41021	−	10.4956i	0.175868	−	0.541267i
$377$	−0.215168	+	0.662219i	−0.0110817	+	0.0341060i
$378$	2.81905	−	2.04816i	0.144996	−	0.105346i
$379$	35.6994			1.83376			0.916878	−	0.399167i	$-0.130701\pi$
$379$	35.6994			1.83376			0.916878	+	0.399167i	$0.130701\pi$
$380$	1.58337	+	1.51958i	0.0812252	+	0.0779529i
$381$	−0.424479	+	1.30641i	−0.0217467	+	0.0669295i
$382$	−13.9658	+	10.1467i	−0.714551	+	0.519152i
$383$	14.7224			0.752278			0.376139	−	0.926563i	$-0.377252\pi$
$383$	14.7224			0.752278			0.376139	+	0.926563i	$0.377252\pi$
$384$	−3.19753	−	2.32315i	−0.163174	−	0.118553i
$385$	−22.8291	+	13.6099i	−1.16348	+	0.693624i
$386$	−7.23242	+	5.25466i	−0.368121	+	0.267455i
$387$	5.79249	−	4.20849i	0.294449	−	0.213930i
$388$	3.57163			0.181322
$389$	1.14906			0.0582595			0.0291298	−	0.999576i	$-0.490726\pi$
$389$	1.14906			0.0582595			0.0291298	+	0.999576i	$0.490726\pi$
$390$	5.20226	−	2.78682i	0.263426	−	0.141116i
$391$	−1.30076	+	4.00334i	−0.0657824	+	0.202457i
$392$	−5.36318	+	16.5062i	−0.270882	+	0.833688i
$393$	−18.1556	+	13.1908i	−0.915830	+	0.665389i
$394$	0.719226			0.0362341
$395$	5.93860	+	33.0793i	0.298803	+	1.66440i
$396$	3.49414	−	0.160145i	0.175587	−	0.00804757i
$397$	−2.26085	+	6.95817i	−0.113469	+	0.349221i	−0.991625	−	0.129154i	$-0.958774\pi$
$397$	−2.26085	+	6.95817i	−0.113469	+	0.349221i	0.878156	+	0.478375i	$0.158774\pi$
$398$	−7.71842	−	23.7548i	−0.386889	−	1.19072i
$399$	−2.69816	+	1.96033i	−0.135077	+	0.0981393i
$400$	−3.74830	−	1.04969i	−0.187415	−	0.0524847i
$401$	7.21973	+	22.2200i	0.360536	+	1.10962i	0.952730	+	0.303820i	$0.0982621\pi$
$401$	7.21973	+	22.2200i	0.360536	+	1.10962i	−0.592194	+	0.805796i	$0.701738\pi$
$402$	−0.340125	−	0.247115i	−0.0169639	−	0.0123250i
$403$	−1.13340	+	0.823465i	−0.0564588	+	0.0410197i
$404$	−2.79595	−	8.60504i	−0.139103	−	0.428117i
$405$	1.97107	−	1.05589i	0.0979431	−	0.0524675i
$406$	0.276206	+	0.850075i	0.0137079	+	0.0421885i
$407$	−15.0952	+	12.0607i	−0.748240	+	0.597829i
$408$	−5.93107	−	18.2540i	−0.293632	−	0.903705i
$409$	6.53162	−	4.74550i	0.322968	−	0.234650i	−0.414473	−	0.910062i	$-0.636034\pi$
$409$	6.53162	−	4.74550i	0.322968	−	0.234650i	0.737441	+	0.675412i	$0.236034\pi$
$410$	−11.5721	+	23.9143i	−0.571507	+	1.18104i
$411$	−17.8240			−0.879193
$412$	−1.26963	+	3.90753i	−0.0625503	+	0.192510i
$413$	6.36779	−	19.5981i	0.313339	−	0.964357i
$414$	0.633324			0.0311262
$415$	−7.73825	−	1.06308i	−0.379856	−	0.0521845i
$416$	11.3825	−	8.26986i	0.558072	−	0.405463i
$417$	2.40473	+	7.40099i	0.117760	+	0.362428i
$418$	2.99785	−	0.137398i	0.146629	−	0.00672037i
$419$	9.88478	+	30.4222i	0.482903	+	1.48622i	0.834995	+	0.550258i	$0.185470\pi$
$419$	9.88478	+	30.4222i	0.482903	+	1.48622i	−0.352092	+	0.935965i	$0.614530\pi$
$420$	−3.68127	+	7.60751i	−0.179628	+	0.371208i
$421$	3.51034	+	10.8037i	0.171083	+	0.526541i	0.999433	−	0.0336709i	$-0.0107198\pi$
$421$	3.51034	+	10.8037i	0.171083	+	0.526541i	−0.828350	+	0.560212i	$0.810720\pi$
$422$	1.56812	−	1.13930i	0.0763347	−	0.0554604i
$423$	3.00606	+	2.18403i	0.146159	+	0.106191i
$424$	−7.33767	−	22.5830i	−0.356349	−	1.09673i
$425$	20.0507	+	25.3382i	0.972600	+	1.22908i
$426$	−1.71146	+	1.24345i	−0.0829207	+	0.0602454i
$427$	−16.9321	−	52.1117i	−0.819403	−	2.52186i
$428$	−3.95634	+	12.1764i	−0.191237	+	0.588567i
$429$	−2.38713	+	8.68073i	−0.115252	+	0.419109i
$430$	6.78053	−	14.0123i	0.326986	−	0.675732i
$431$	14.7688			0.711386			0.355693	−	0.934603i	$-0.384245\pi$
$431$	14.7688			0.711386			0.355693	+	0.934603i	$0.384245\pi$
$432$	−0.629821	+	0.457592i	−0.0303023	+	0.0220159i
$433$	3.10888	−	9.56815i	0.149403	−	0.459816i	−0.848148	−	0.529760i	$-0.822282\pi$
$433$	3.10888	−	9.56815i	0.149403	−	0.459816i	0.997551	+	0.0699438i	$0.0222820\pi$
$434$	−0.555731	+	1.71036i	−0.0266759	+	0.0821001i
$435$	0.101352	+	0.564551i	0.00485944	+	0.0270681i
$436$	6.87908			0.329448
$437$	−0.606167			−0.0289969
$438$	−6.45645	+	4.69088i	−0.308501	+	0.224139i
$439$	17.8347	−	12.9577i	0.851204	−	0.618436i	−0.0742739	−	0.997238i	$-0.523664\pi$
$439$	17.8347	−	12.9577i	0.851204	−	0.618436i	0.925478	+	0.378802i	$0.123664\pi$
$440$	18.9193	−	11.2790i	0.901943	−	0.537705i
$441$	−4.72757	−	3.43478i	−0.225122	−	0.163561i
$442$	17.0562			0.811279
$443$	27.0453	−	19.6496i	1.28496	−	0.933578i	0.285270	−	0.958447i	$-0.407917\pi$
$443$	27.0453	−	19.6496i	1.28496	−	0.933578i	0.999691	+	0.0248689i	$0.00791685\pi$
$444$	−1.89858	+	5.84323i	−0.0901027	+	0.277308i
$445$	−35.6347	−	4.89549i	−1.68925	−	0.232068i
$446$	−11.1866			−0.529700
$447$	12.5913	−	9.14809i	0.595547	−	0.432690i
$448$	7.30537	−	22.4836i	0.345147	−	1.06225i
$449$	10.5201	−	32.3777i	0.496476	−	1.52800i	−0.318167	−	0.948035i	$-0.603067\pi$
$449$	10.5201	−	32.3777i	0.496476	−	1.52800i	0.814643	−	0.579963i	$-0.196933\pi$
$450$	2.69347	−	4.04716i	0.126972	−	0.190785i
$451$	−14.2754	−	37.9305i	−0.672202	−	1.78608i
$452$	3.85498	−	2.80080i	0.181323	−	0.131739i
$453$	11.2598	+	8.18073i	0.529032	+	0.384364i
$454$	6.63823	+	20.4304i	0.311548	+	0.958845i
$455$	−15.6945	−	15.0623i	−0.735771	−	0.706129i
$456$	2.23607	−	1.62460i	0.104713	−	0.0760787i
$457$	−6.71954	−	20.6806i	−0.314327	−	0.967399i	−0.976031	−	0.217633i	$-0.930166\pi$
$457$	−6.71954	−	20.6806i	−0.314327	−	0.967399i	0.661704	−	0.749765i	$-0.269834\pi$
$458$	1.25403	−	3.85952i	0.0585971	−	0.180343i
$459$	6.46236			0.301637
$460$	−1.35402	+	0.725341i	−0.0631316	+	0.0338192i
$461$	22.8087	−	16.5715i	1.06231	−	0.771810i	0.0877918	−	0.996139i	$-0.472019\pi$
$461$	22.8087	−	16.5715i	1.06231	−	0.771810i	0.974513	+	0.224329i	$0.0720190\pi$
$462$	4.07076	+	10.8162i	0.189389	+	0.503216i
$463$	−30.3913	−	22.0806i	−1.41241	−	1.02617i	−0.992967	−	0.118388i	$-0.962227\pi$
$463$	−30.3913	−	22.0806i	−1.41241	−	1.02617i	−0.419438	−	0.907784i	$-0.637773\pi$
$464$	−0.0617090	−	0.189921i	−0.00286477	−	0.00881685i
$465$	−0.502681	+	1.03881i	−0.0233113	+	0.0481737i
$466$	−1.92084	−	5.91175i	−0.0889814	−	0.273856i
$467$	26.1576	−	19.0046i	1.21043	−	0.879429i	0.215161	−	0.976579i	$-0.430972\pi$
$467$	26.1576	−	19.0046i	1.21043	−	0.879429i	0.995270	+	0.0971491i	$0.0309724\pi$
$468$	0.884649	+	2.72267i	0.0408929	+	0.125855i
$469$	−0.478856	+	1.47377i	−0.0221115	+	0.0680523i
$470$	8.00324	+	1.09948i	0.369162	+	0.0507154i
$471$	8.49225	+	6.16998i	0.391302	+	0.284298i
$472$	−5.27722	+	16.2416i	−0.242904	+	0.747581i
$473$	8.36447	+	22.2248i	0.384599	+	1.02190i
$474$	14.6137			0.671230
$475$	−2.57798	+	3.87361i	−0.118286	+	0.177734i
$476$	−19.7602	+	14.3566i	−0.905707	+	0.658035i
$477$	7.99496			0.366064
$478$	8.16307			0.373370
$479$	39.2261			1.79229			0.896144	−	0.443764i	$-0.146357\pi$
$479$	39.2261			1.79229			0.896144	+	0.443764i	$0.146357\pi$
$480$	5.04829	−	10.4325i	0.230422	−	0.476177i
$481$	−12.7936	−	9.29513i	−0.583340	−	0.423821i
$482$	5.80932	−	17.8793i	0.264607	−	0.814378i
$483$	−0.721358	−	2.22011i	−0.0328229	−	0.101019i
$484$	−2.56062	+	11.3148i	−0.116392	+	0.514308i
$485$	1.33811	+	7.45356i	0.0607605	+	0.338449i
$486$	−0.300458	−	0.924714i	−0.0136290	−	0.0419459i
$487$	19.0886			0.864988			0.432494	−	0.901637i	$-0.357634\pi$
$487$	19.0886			0.864988			0.432494	+	0.901637i	$0.357634\pi$
$488$	14.0323	+	43.1868i	0.635210	+	1.95498i
$489$	−3.13057	−	2.27449i	−0.141569	−	0.102856i
$490$	−12.5865	−	1.72914i	−0.568602	−	0.0781145i
$491$	−10.2834	−	31.6490i	−0.464083	−	1.42830i	−0.860132	−	0.510072i	$-0.829619\pi$
$491$	−10.2834	−	31.6490i	−0.464083	−	1.42830i	0.396049	−	0.918230i	$-0.370381\pi$
$492$	−10.4259	−	7.57487i	−0.470037	−	0.341502i
$493$	−0.512247	+	1.57653i	−0.0230704	+	0.0710035i
$494$	0.758997	+	2.33595i	0.0341489	+	0.105100i
$495$	1.64328	+	7.23185i	0.0738600	+	0.325047i
$496$	0.124159	−	0.382123i	0.00557492	−	0.0171578i
$497$	6.30826	+	4.58322i	0.282964	+	0.205586i
$498$	−1.04955	+	3.23017i	−0.0470313	+	0.144747i
$499$	4.54963	+	3.30550i	0.203670	+	0.147975i	0.684945	−	0.728595i	$-0.259826\pi$
$499$	4.54963	+	3.30550i	0.203670	+	0.147975i	−0.481275	+	0.876570i	$0.659826\pi$
$500$	−1.12336	+	11.7375i	−0.0502381	+	0.524916i
$501$	−2.56358	−	7.88988i	−0.114532	−	0.352494i
$502$	−8.84498			−0.394771
$503$	−2.82880	−	8.70615i	−0.126130	−	0.388188i	0.867975	−	0.496607i	$-0.165421\pi$
$503$	−2.82880	−	8.70615i	−0.126130	−	0.388188i	−0.994105	+	0.108419i	$0.965421\pi$
$504$	8.61114	+	6.25636i	0.383571	+	0.278680i
$505$	16.9102	−	9.05868i	0.752493	−	0.403106i
$506$	−0.556946	+	2.02532i	−0.0247593	+	0.0900363i
$507$	5.63151			0.250104
$508$	−1.44868			−0.0642749
$509$	−26.7648			−1.18633			−0.593163	−	0.805082i	$-0.702121\pi$
$509$	−26.7648			−1.18633			−0.593163	+	0.805082i	$0.702121\pi$
$510$	12.3849	−	6.63453i	0.548414	−	0.293782i
$511$	23.7977	+	17.2901i	1.05275	+	0.764867i
$512$	−2.67590	+	8.23557i	−0.118259	+	0.363964i
$513$	0.287574	+	0.885062i	0.0126967	+	0.0390764i
$514$	7.22400	−	22.2332i	0.318637	−	0.980663i
$515$	−8.63021	−	1.18562i	−0.380292	−	0.0522445i
$516$	6.10893	+	4.43839i	0.268930	+	0.195389i
$517$	−9.62786	+	7.69247i	−0.423433	+	0.338314i
$518$	−20.2998			−0.891923
$519$	14.8878			0.653504
$520$	13.0066	+	12.4826i	0.570378	+	0.547400i
$521$	8.68716	−	6.31159i	0.380591	−	0.276516i	−0.380998	−	0.924576i	$-0.624419\pi$
$521$	8.68716	−	6.31159i	0.380591	−	0.276516i	0.761589	+	0.648060i	$0.224419\pi$
$522$	0.249406			0.0109162
$523$	−27.9379	−	20.2981i	−1.22164	−	0.887573i	−0.225404	−	0.974265i	$-0.572370\pi$
$523$	−27.9379	−	20.2981i	−1.22164	−	0.887573i	−0.996235	+	0.0866925i	$0.972370\pi$
$524$	−19.1474	−	13.9114i	−0.836459	−	0.607723i
$525$	−17.2551	−	4.83221i	−0.753076	−	0.210895i
$526$	−6.58442	+	20.2648i	−0.287094	+	0.883586i
$527$	−2.69827	+	1.96041i	−0.117539	+	0.0853968i
$528$	−0.909474	−	2.41652i	−0.0395798	−	0.105166i
$529$	−6.97628	+	21.4708i	−0.303317	+	0.933513i
$530$	15.3221	−	8.20797i	0.665550	−	0.356531i
$531$	−4.65180	−	3.37973i	−0.201871	−	0.146668i
$532$	−2.84556	−	2.06742i	−0.123371	−	0.0896341i
$533$	26.8352	−	19.4969i	1.16236	−	0.844504i
$534$	−4.83317	+	14.8750i	−0.209152	+	0.643702i
$535$	−26.8929	−	3.69454i	−1.16268	−	0.159729i
$536$	0.396846	−	1.22136i	0.0171411	−	0.0527549i
$537$	9.99892	−	7.26464i	0.431485	−	0.313492i
$538$	−2.51881	−	1.83002i	−0.108594	−	0.0788980i
$539$	15.1416	−	12.0978i	0.652193	−	0.521090i
$540$	1.70143	+	1.63289i	0.0732181	+	0.0702684i
$541$	8.34929	−	6.06612i	0.358964	−	0.260803i	−0.393656	−	0.919258i	$-0.628790\pi$
$541$	8.34929	−	6.06612i	0.358964	−	0.260803i	0.752620	+	0.658455i	$0.228790\pi$
$542$	−17.0436	−	12.3829i	−0.732084	−	0.531890i
$543$	4.73095	+	3.43723i	0.203024	+	0.147506i
$544$	27.0981	−	19.6879i	1.16182	−	0.844112i
$545$	2.57725	+	14.3558i	0.110397	+	0.614935i
$546$	−7.65229	+	5.55972i	−0.327488	+	0.237934i
$547$	−5.03851	−	15.5069i	−0.215431	−	0.663029i	−0.999123	−	0.0418788i	$-0.986666\pi$
$547$	−5.03851	−	15.5069i	−0.215431	−	0.663029i	0.783692	−	0.621150i	$-0.213334\pi$
$548$	−5.80880	−	17.8777i	−0.248140	−	0.763696i
$549$	−15.2892			−0.652528
$550$	10.5738	+	12.1726i	0.450869	+	0.519040i
$551$	−0.238712			−0.0101695
$552$	0.597815	+	1.83989i	0.0254447	+	0.0783107i
$553$	−16.6450	−	51.2282i	−0.707819	−	2.17844i
$554$	18.6444	−	13.5460i	0.792127	−	0.575514i
$555$	−12.9054	−	1.77295i	−0.547805	−	0.0752573i
$556$	−6.63958	+	4.82394i	−0.281581	+	0.204581i
$557$	5.01346	+	3.64249i	0.212427	+	0.154337i	0.688911	−	0.724846i	$-0.258089\pi$
$557$	5.01346	+	3.64249i	0.212427	+	0.154337i	−0.476484	+	0.879183i	$0.658089\pi$
$558$	0.405972	+	0.294956i	0.0171862	+	0.0124865i
$559$	−15.7237	+	11.4239i	−0.665041	+	0.483181i
$560$	6.18056	+	0.849085i	0.261177	+	0.0358804i
$561$	−5.68301	+	20.6661i	−0.239937	+	0.872522i
$562$	18.3726	+	13.3485i	0.775002	+	0.563072i
$563$	5.97217	−	4.33903i	0.251697	−	0.182869i	−0.454782	−	0.890603i	$-0.650283\pi$
$563$	5.97217	−	4.33903i	0.251697	−	0.182869i	0.706479	+	0.707734i	$0.250283\pi$
$564$	−1.21094	+	3.72688i	−0.0509896	+	0.156930i
$565$	7.28920	+	6.99555i	0.306659	+	0.294305i
$566$	−3.74367	+	11.5218i	−0.157358	+	0.484299i
$567$	−2.89935	+	2.10650i	−0.121761	+	0.0884648i
$568$	−5.22788	−	3.79828i	−0.219357	−	0.159372i
$569$	−25.0468	−	18.1976i	−1.05002	−	0.762883i	−0.0778023	−	0.996969i	$-0.524790\pi$
$569$	−25.0468	−	18.1976i	−1.05002	−	0.762883i	−0.972216	+	0.234086i	$0.924790\pi$
$570$	1.45977	+	1.40096i	0.0611430	+	0.0586798i
$571$	−4.26493	+	13.1261i	−0.178482	+	0.549310i	−0.999775	−	0.0211955i	$-0.993253\pi$
$571$	−4.26493	+	13.1261i	−0.178482	+	0.549310i	0.821294	+	0.570506i	$0.193253\pi$
$572$	−9.48483	+	0.434712i	−0.396581	+	0.0181762i
$573$	14.3636	−	10.4358i	0.600048	−	0.435961i
$574$	13.1578	−	40.4956i	0.549197	−	1.69026i
$575$	−2.02098	−	2.55393i	−0.0842808	−	0.106506i
$576$	−5.33672	−	3.87735i	−0.222363	−	0.161556i
$577$	−2.48913	−	1.80846i	−0.103624	−	0.0752870i	0.534767	−	0.845000i	$-0.320399\pi$
$577$	−2.48913	−	1.80846i	−0.103624	−	0.0752870i	−0.638390	+	0.769713i	$0.720399\pi$
$578$	24.0762			1.00144
$579$	7.43845	−	5.40435i	0.309132	−	0.224597i
$580$	−0.533220	+	0.285643i	−0.0221408	+	0.0118607i
$581$	12.5188			0.519365
$582$	3.29282			0.136492
$583$	−7.03078	+	25.5672i	−0.291185	+	1.05889i
$584$	−19.7220	−	14.3289i	−0.816104	−	0.592934i
$585$	−5.35045	+	2.86620i	−0.221214	+	0.118503i
$586$	−4.86118	+	14.9612i	−0.200814	+	0.618040i
$587$	8.56403	+	26.3574i	0.353475	+	1.08789i	0.956888	+	0.290457i	$0.0938072\pi$
$587$	8.56403	+	26.3574i	0.353475	+	1.08789i	−0.603413	+	0.797429i	$0.706193\pi$
$588$	1.90442	−	5.86120i	0.0785369	−	0.241712i
$589$	−0.388564	−	0.282308i	−0.0160105	−	0.0116323i
$590$	−12.3848	−	1.70142i	−0.509875	−	0.0700465i
$591$	−0.739715			−0.0304278
$592$	4.53531			0.186400
$593$	6.15688			0.252833			0.126416	−	0.991977i	$-0.459652\pi$
$593$	6.15688			0.252833			0.126416	+	0.991977i	$0.459652\pi$
$594$	3.22138	−	0.147643i	0.132175	−	0.00605788i
$595$	−37.3637	−	35.8585i	−1.53176	−	1.47005i
$596$	13.2791	+	9.64784i	0.543934	+	0.395191i
$597$	7.93829	+	24.4315i	0.324893	+	0.999917i
$598$	−1.71916			−0.0703015
$599$	4.89942	+	15.0789i	0.200185	+	0.616106i	0.999877	+	0.0156954i	$0.00499621\pi$
$599$	4.89942	+	15.0789i	0.200185	+	0.616106i	−0.799692	+	0.600411i	$0.795004\pi$
$600$	14.3000	+	4.00463i	0.583793	+	0.163488i
$601$	−30.9273	−	22.4700i	−1.26155	−	0.916571i	−0.262719	−	0.964873i	$-0.584619\pi$
$601$	−30.9273	−	22.4700i	−1.26155	−	0.916571i	−0.998833	+	0.0483018i	$0.984619\pi$
$602$	−7.70965	+	23.7279i	−0.314222	+	0.967076i
$603$	0.349814	+	0.254155i	0.0142455	+	0.0103500i
$604$	−4.53581	+	13.9598i	−0.184560	+	0.568016i
$605$	−24.5719	−	1.10463i	−0.998991	−	0.0449095i
$606$	−2.57769	−	7.93331i	−0.104711	−	0.322269i
$607$	−11.9797	+	36.8696i	−0.486239	+	1.49649i	0.343938	+	0.938992i	$0.388239\pi$
$607$	−11.9797	+	36.8696i	−0.486239	+	1.49649i	−0.830178	+	0.557499i	$0.811761\pi$
$608$	3.90225	+	2.83515i	0.158257	+	0.114981i
$609$	−0.284074	−	0.874291i	−0.0115113	−	0.0354280i
$610$	−29.3014	+	15.6966i	−1.18638	+	0.635535i
$611$	−8.15993	−	5.92853i	−0.330115	−	0.239843i
$612$	2.10607	+	6.48182i	0.0851328	+	0.262012i
$613$	−11.1667			−0.451018			−0.225509	−	0.974241i	$-0.572404\pi$
$613$	−11.1667			−0.451018			−0.225509	+	0.974241i	$0.572404\pi$
$614$	2.36085	+	7.26594i	0.0952760	+	0.293229i
$615$	11.9018	−	24.5956i	0.479926	−	0.991789i
$616$	−27.5799	+	22.0358i	−1.11123	+	0.887849i
$617$	4.35213	+	13.3945i	0.175210	+	0.539241i	0.999643	−	0.0267185i	$-0.00850577\pi$
$617$	4.35213	+	13.3945i	0.175210	+	0.539241i	−0.824433	+	0.565960i	$0.808506\pi$
$618$	−1.17052	+	3.60250i	−0.0470853	+	0.144914i
$619$	−15.6337	−	11.3585i	−0.628371	−	0.456538i	0.227464	−	0.973786i	$-0.426956\pi$
$619$	−15.6337	−	11.3585i	−0.628371	−	0.456538i	−0.855835	+	0.517248i	$0.826956\pi$
$620$	−1.20576	−	0.165647i	−0.0484246	−	0.00665256i
$621$	−0.651366			−0.0261384
$622$	23.5404			0.943886
$623$	57.6490			2.30966
$624$	1.70965	−	1.24213i	0.0684407	−	0.0497251i
$625$	−24.9156	+	2.05313i	−0.996622	+	0.0821251i
$626$	−7.69172			−0.307423
$627$	−3.08325	+	0.141312i	−0.123133	+	0.00564347i
$628$	−3.42095	+	10.5286i	−0.136511	+	0.420137i
$629$	−30.4576	−	22.1288i	−1.21442	−	0.882331i
$630$	−3.39390	+	7.01365i	−0.135216	+	0.279431i
$631$	3.98362	−	12.2603i	0.158585	−	0.488076i	−0.839921	−	0.542708i	$-0.817399\pi$
$631$	3.98362	−	12.2603i	0.158585	−	0.488076i	0.998507	+	0.0546329i	$0.0173989\pi$
$632$	13.7943	+	42.4546i	0.548709	+	1.68875i
$633$	−1.61279	+	1.17176i	−0.0641025	+	0.0465732i
$634$	−10.0444	−	30.9134i	−0.398914	−	1.22773i
$635$	−0.542749	−	3.02323i	−0.0215383	−	0.119973i
$636$	2.60554	+	8.01904i	0.103316	+	0.317975i
$637$	12.8330	+	9.32370i	0.508461	+	0.369418i
$638$	−0.219328	+	0.797580i	−0.00868329	+	0.0315765i
$639$	1.76022	−	1.27887i	0.0696331	−	0.0505914i
$640$	8.75553	+	1.20283i	0.346093	+	0.0475462i
$641$	22.7947			0.900338			0.450169	−	0.892943i	$-0.351364\pi$
$641$	22.7947			0.900338			0.450169	+	0.892943i	$0.351364\pi$
$642$	−3.64750	+	11.2259i	−0.143955	+	0.443049i
$643$	6.32645	+	19.4708i	0.249491	+	0.767854i	0.994865	+	0.101208i	$0.0322707\pi$
$643$	6.32645	+	19.4708i	0.249491	+	0.767854i	−0.745374	+	0.666646i	$0.767729\pi$
$644$	1.99171	−	1.44706i	0.0784842	−	0.0570221i
$645$	−6.97369	+	14.4114i	−0.274589	+	0.567450i
$646$	1.80693	+	5.56117i	0.0710928	+	0.218801i
$647$	−14.6950	−	10.6765i	−0.577719	−	0.419738i	0.260182	−	0.965560i	$-0.416217\pi$
$647$	−14.6950	−	10.6765i	−0.577719	−	0.419738i	−0.837901	+	0.545822i	$0.816217\pi$
$648$	2.40280	−	1.74574i	0.0943908	−	0.0685790i
$649$	14.8989	−	11.9039i	0.584832	−	0.467269i
$650$	−7.31142	+	10.9860i	−0.286778	+	0.430906i
$651$	0.571562	−	1.75909i	0.0224013	−	0.0689440i
$652$	1.26109	−	3.88124i	0.0493882	−	0.152001i
$653$	5.12919	−	3.72658i	0.200721	−	0.145832i	−0.482885	−	0.875684i	$-0.660411\pi$
$653$	5.12919	−	3.72658i	0.200721	−	0.145832i	0.683605	+	0.729852i	$0.260411\pi$
$654$	6.34209			0.247995
$655$	21.8579	−	45.1703i	0.854058	−	1.76495i
$656$	−2.93968	+	9.04739i	−0.114775	+	0.353241i
$657$	6.64037	−	4.82451i	0.259065	−	0.188222i
$658$	−12.9474			−0.504744
$659$	−2.89285	−	2.10178i	−0.112689	−	0.0818736i	0.530013	−	0.847989i	$-0.322187\pi$
$659$	−2.89285	−	2.10178i	−0.112689	−	0.0818736i	−0.642703	+	0.766116i	$0.722187\pi$
$660$	−6.71808	+	4.00507i	−0.261501	+	0.155897i
$661$	−26.7112	+	19.4068i	−1.03895	+	0.754839i	−0.970080	−	0.242787i	$-0.921938\pi$
$661$	−26.7112	+	19.4068i	−1.03895	+	0.754839i	−0.0688670	+	0.997626i	$0.521938\pi$
$662$	−2.21044	+	1.60598i	−0.0859110	+	0.0624180i
$663$	−17.5420			−0.681277
$664$	−10.3747			−0.402618
$665$	3.24837	−	6.71290i	0.125966	−	0.260315i
$666$	−1.75037	+	5.38710i	−0.0678257	+	0.208746i
$667$	0.0516313	−	0.158905i	0.00199917	−	0.00615282i
$668$	7.07817	−	5.14259i	0.273863	−	0.198973i
$669$	11.5052			0.444818
$670$	0.931334	+	0.127947i	0.0359806	+	0.00494301i
$671$	13.4454	−	48.8936i	0.519053	−	1.88752i
$672$	−5.74005	+	17.6661i	−0.221427	+	0.681483i
$673$	2.21402	+	6.81405i	0.0853442	+	0.262663i	0.984617	−	0.174725i	$-0.0559037\pi$
$673$	2.21402	+	6.81405i	0.0853442	+	0.262663i	−0.899273	+	0.437388i	$0.855904\pi$
$674$	−24.9644	+	18.1377i	−0.961593	+	0.698638i
$675$	−2.77020	+	4.16245i	−0.106625	+	0.160213i
$676$	1.83530	+	5.64847i	0.0705884	+	0.217249i
$677$	−19.1621	−	13.9221i	−0.736460	−	0.535070i	0.155140	−	0.987892i	$-0.450417\pi$
$677$	−19.1621	−	13.9221i	−0.736460	−	0.535070i	−0.891601	+	0.452823i	$0.850417\pi$
$678$	3.55405	−	2.58217i	0.136492	−	0.0991676i
$679$	−3.75053	−	11.5429i	−0.143932	−	0.442978i
$680$	30.9647	+	29.7172i	1.18744	+	1.13960i
$681$	−6.82733	−	21.0124i	−0.261624	−	0.805196i
$682$	−1.30026	+	1.03888i	−0.0497894	+	0.0397808i
$683$	0.166488	+	0.512397i	0.00637048	+	0.0196063i	0.954191	−	0.299197i	$-0.0967189\pi$
$683$	0.166488	+	0.512397i	0.00637048	+	0.0196063i	−0.947821	+	0.318804i	$0.896719\pi$
$684$	−0.794007	+	0.576880i	−0.0303596	+	0.0220576i
$685$	35.1323	−	18.8201i	1.34233	−	0.719080i
$686$	−4.02952			−0.153848
$687$	−1.28976	+	3.96946i	−0.0492073	+	0.151444i
$688$	1.72246	−	5.30120i	0.0656683	−	0.202106i
$689$	−21.7023			−0.826792
$690$	−1.24832	+	0.668719i	−0.0475229	+	0.0254577i
$691$	34.2789	−	24.9051i	1.30403	−	0.947433i	0.304043	−	0.952658i	$-0.401663\pi$
$691$	34.2789	−	24.9051i	1.30403	−	0.947433i	0.999986	+	0.00522524i	$0.00166325\pi$
$692$	4.85192	+	14.9327i	0.184442	+	0.567655i
$693$	−4.18672	−	11.1243i	−0.159040	−	0.422579i
$694$	4.28305	+	13.1819i	0.162582	+	0.500377i
$695$	−12.5545	−	12.0487i	−0.476219	−	0.457034i
$696$	0.235423	+	0.724556i	0.00892367	+	0.0274642i
$697$	63.8860	−	46.4159i	2.41986	−	1.75813i
$698$	−4.59856	−	3.34105i	−0.174058	−	0.126460i
$699$	1.97556	+	6.08016i	0.0747226	+	0.229973i
$700$	−0.776651	−	18.8819i	−0.0293546	−	0.713669i
$701$	−9.96420	+	7.23941i	−0.376343	+	0.273429i	−0.759836	−	0.650115i	$-0.774721\pi$
$701$	−9.96420	+	7.23941i	−0.376343	+	0.273429i	0.383494	+	0.923544i	$0.374721\pi$
$702$	0.815592	+	2.51013i	0.0307825	+	0.0947389i
$703$	1.67532	−	5.15610i	0.0631858	−	0.194466i
$704$	17.0926	−	13.6566i	0.644200	−	0.514703i
$705$	−8.23122	−	1.13080i	−0.310006	−	0.0425885i
$706$	−8.62341			−0.324546
$707$	−24.8741	+	18.0721i	−0.935488	+	0.679672i
$708$	1.87389	−	5.76725i	0.0704252	−	0.216747i
$709$	−8.97073	+	27.6091i	−0.336903	+	1.03688i	0.628874	+	0.777507i	$0.283516\pi$
$709$	−8.97073	+	27.6091i	−0.336903	+	1.03688i	−0.965777	+	0.259373i	$0.916484\pi$
$710$	2.06046	−	4.25804i	0.0773278	−	0.159801i
$711$	−15.0300			−0.563669
$712$	−47.7758			−1.79047
$713$	0.271969	−	0.197597i	0.0101853	−	0.00740008i
$714$	−18.2177	+	13.2359i	−0.681780	+	0.495342i
$715$	−4.46068	−	19.6308i	−0.166820	−	0.734151i
$716$	10.5451	+	7.66149i	0.394090	+	0.286324i
$717$	−8.39561			−0.313540
$718$	−2.71513	+	1.97266i	−0.101328	+	0.0736190i
$719$	8.12062	−	24.9927i	0.302848	−	0.932071i	−0.677623	−	0.735409i	$-0.736990\pi$
$719$	8.12062	−	24.9927i	0.302848	−	0.932071i	0.980471	−	0.196662i	$-0.0630100\pi$
$720$	0.758254	−	1.56697i	0.0282584	−	0.0583973i
$721$	13.9617			0.519963
$722$	14.2643	−	10.3637i	0.530864	−	0.385695i
$723$	−5.97481	+	18.3886i	−0.222206	+	0.683878i
$724$	−1.90578	+	5.86538i	−0.0708277	+	0.217985i
$725$	−0.795873	−	1.00575i	−0.0295580	−	0.0373526i
$726$	−2.36073	+	10.4315i	−0.0876151	+	0.387151i
$727$	−5.59717	+	4.06658i	−0.207588	+	0.150821i	−0.686721	−	0.726921i	$-0.740951\pi$
$727$	−5.59717	+	4.06658i	−0.207588	+	0.150821i	0.479134	+	0.877742i	$0.340951\pi$
$728$	−23.3749	−	16.9829i	−0.866332	−	0.629427i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	7.77303	−	16.0633i	0.287693	−	0.594530i
$731$	−37.4331	+	27.1968i	−1.38451	+	1.00591i
$732$	−4.98273	−	15.3353i	−0.184167	−	0.566808i
$733$	2.54229	−	7.82437i	0.0939017	−	0.289000i	−0.893064	−	0.449929i	$-0.851449\pi$
$733$	2.54229	−	7.82437i	0.0939017	−	0.289000i	0.986966	+	0.160930i	$0.0514492\pi$
$734$	−14.3789			−0.530735
$735$	12.9451	+	1.77840i	0.477487	+	0.0655971i
$736$	−2.73132	+	1.98442i	−0.100678	+	0.0731467i
$737$	−1.12039	+	0.895171i	−0.0412702	+	0.0329740i
$738$	−9.61205	−	6.98357i	−0.353825	−	0.257069i
$739$	3.12959	+	9.63188i	0.115124	+	0.354314i	0.991973	−	0.126451i	$-0.0403587\pi$
$739$	3.12959	+	9.63188i	0.115124	+	0.354314i	−0.876849	+	0.480766i	$0.840359\pi$
$740$	−2.42757	−	13.5221i	−0.0892392	−	0.497082i
$741$	−0.780619	−	2.40250i	−0.0286768	−	0.0882580i
$742$	−22.5382	+	16.3749i	−0.827402	+	0.601143i
$743$	10.3747	+	31.9301i	0.380612	+	1.17140i	0.939614	+	0.342236i	$0.111184\pi$
$743$	10.3747	+	31.9301i	0.380612	+	1.17140i	−0.559002	+	0.829166i	$0.688816\pi$
$744$	−0.473674	+	1.45782i	−0.0173657	+	0.0534462i
$745$	−15.1589	+	31.3265i	−0.555378	+	1.14771i
$746$	11.4070	+	8.28768i	0.417641	+	0.303434i
$747$	1.07944	−	3.32219i	0.0394948	−	0.121552i
$748$	−22.5804	+	1.03491i	−0.825620	+	0.0378401i
$749$	43.5066			1.58970
$750$	−1.03567	+	10.8212i	−0.0378172	+	0.395135i
$751$	18.7124	−	13.5953i	0.682825	−	0.496101i	−0.191469	−	0.981499i	$-0.561325\pi$
$751$	18.7124	−	13.5953i	0.682825	−	0.496101i	0.874294	+	0.485398i	$0.161325\pi$
$752$	2.89267			0.105485
$753$	9.09694			0.331511
$754$	−0.677012			−0.0246553
$755$	−30.8318	−	4.23566i	−1.12208	−	0.154152i
$756$	−3.05774	−	2.22158i	−0.111209	−	0.0807980i
$757$	12.0656	−	37.1342i	0.438533	−	1.34966i	−0.450890	−	0.892579i	$-0.648893\pi$
$757$	12.0656	−	37.1342i	0.438533	−	1.34966i	0.889423	−	0.457085i	$-0.151107\pi$
$758$	10.7262	+	33.0118i	0.389592	+	1.19904i
$759$	0.572812	−	2.08301i	0.0207918	−	0.0756085i
$760$	−2.69204	+	5.56322i	−0.0976506	+	0.201799i
$761$	−13.7924	−	42.4486i	−0.499974	−	1.53876i	−0.809059	−	0.587728i	$-0.800023\pi$
$761$	−13.7924	−	42.4486i	−0.499974	−	1.53876i	0.309085	−	0.951034i	$-0.399977\pi$
$762$	−1.33560			−0.0483835
$763$	−7.22365	−	22.2321i	−0.261514	−	0.804856i
$764$	15.1483	+	11.0059i	0.548045	+	0.398178i
$765$	−12.7377	+	6.82352i	−0.460534	+	0.246705i
$766$	4.42345	+	13.6140i	0.159826	+	0.491893i
$767$	12.6273	+	9.17426i	0.455945	+	0.331263i
$768$	5.26441	−	16.2022i	0.189963	−	0.584646i
$769$	2.81057	+	8.65005i	0.101352	+	0.311929i	0.988857	−	0.148869i	$-0.0475633\pi$
$769$	2.81057	+	8.65005i	0.101352	+	0.311929i	−0.887505	+	0.460798i	$0.847563\pi$
$770$	−19.4444	−	17.0212i	−0.700729	−	0.613402i
$771$	−7.42979	+	22.8665i	−0.267577	+	0.823518i
$772$	7.84480	+	5.69958i	0.282341	+	0.205133i
$773$	2.30082	−	7.08121i	0.0827549	−	0.254693i	−0.901115	−	0.433581i	$-0.857250\pi$
$773$	2.30082	−	7.08121i	0.0827549	−	0.254693i	0.983870	+	0.178888i	$0.0572498\pi$
$774$	5.63205	+	4.09193i	0.202440	+	0.147081i
$775$	−0.106052	−	2.57834i	−0.00380951	−	0.0926167i
$776$	3.10820	+	9.56606i	0.111578	+	0.343402i
$777$	20.8781			0.748997
$778$	0.345243	+	1.06255i	0.0123776	+	0.0380943i
$779$	9.19988	+	6.68411i	0.329620	+	0.239483i
$780$	−4.61854	−	4.43247i	−0.165370	−	0.158708i
$781$	2.54179	+	6.75367i	0.0909523	+	0.241665i
$782$	−4.09277			−0.146357
$783$	−0.256511			−0.00916696
$784$	−4.54925			−0.162473
$785$	−23.2536	−	3.19457i	−0.829956	−	0.114019i
$786$	−17.6527	−	12.8255i	−0.629653	−	0.457469i
$787$	−11.2281	+	34.5566i	−0.400239	+	1.23181i	0.524567	+	0.851369i	$0.324227\pi$
$787$	−11.2281	+	34.5566i	−0.400239	+	1.23181i	−0.924806	+	0.380440i	$0.875773\pi$
$788$	−0.241072	−	0.741942i	−0.00858782	−	0.0264306i
$789$	6.77199	−	20.8420i	0.241089	−	0.741996i
$790$	−28.8046	+	15.4304i	−1.02482	+	0.548990i
$791$	−13.0998	−	9.51758i	−0.465776	−	0.338406i
$792$	3.46969	+	9.21914i	0.123290	+	0.327588i
$793$	41.5025			1.47380
$794$	−7.11361			−0.252453
$795$	−15.7586	+	8.44178i	−0.558900	+	0.299399i
$796$	−21.9180	+	15.9244i	−0.776864	+	0.564425i
$797$	11.8329			0.419143			0.209572	−	0.977793i	$-0.432793\pi$
$797$	11.8329			0.419143			0.209572	+	0.977793i	$0.432793\pi$
$798$	−2.62343	−	1.90603i	−0.0928685	−	0.0674729i
$799$	−19.4262	−	14.1140i	−0.687250	−	0.499316i
$800$	1.06506	+	25.8936i	0.0376554	+	0.915478i
$801$	4.97085	−	15.2987i	0.175636	−	0.540553i
$802$	−18.3780	+	13.3524i	−0.648948	+	0.471489i
$803$	9.58882	+	25.4780i	0.338382	+	0.899099i
$804$	−0.140916	+	0.433696i	−0.00496974	+	0.0152953i
$805$	3.76603	+	3.61431i	0.132735	+	0.127388i
$806$	−1.10201	−	0.800657i	−0.0388167	−	0.0282019i
$807$	2.59057	+	1.88216i	0.0911922	+	0.0662550i
$808$	20.6141	−	14.9770i	0.725201	−	0.526889i
$809$	−7.01515	+	21.5904i	−0.246639	+	0.759078i	0.748723	+	0.662883i	$0.230667\pi$
$809$	−7.01515	+	21.5904i	−0.246639	+	0.759078i	−0.995362	+	0.0961953i	$0.969333\pi$
$810$	1.56862	+	1.50542i	0.0551156	+	0.0528952i
$811$	9.55699	−	29.4134i	0.335591	−	1.03284i	−0.630839	−	0.775914i	$-0.717289\pi$
$811$	9.55699	−	29.4134i	0.335591	−	1.03284i	0.966430	−	0.256930i	$-0.0827109\pi$
$812$	0.784344	−	0.569859i	0.0275251	−	0.0199981i
$813$	17.5291	+	12.7356i	0.614772	+	0.446658i
$814$	−15.6882	−	10.3350i	−0.549871	−	0.362241i
$815$	8.57216	+	1.17764i	0.300270	+	0.0412510i
$816$	4.07013	−	2.95712i	0.142483	−	0.103520i
$817$	−5.39055	−	3.91646i	−0.188591	−	0.137020i
$818$	6.35071	+	4.61406i	0.222047	+	0.161327i
$819$	7.87028	−	5.71809i	0.275010	−	0.199806i
$820$	28.5484	+	3.92197i	0.996953	+	0.136961i
$821$	−32.6423	+	23.7160i	−1.13923	+	0.827696i	−0.987011	−	0.160652i	$-0.948640\pi$
$821$	−32.6423	+	23.7160i	−1.13923	+	0.827696i	−0.152214	+	0.988348i	$0.548640\pi$
$822$	−5.35536	−	16.4821i	−0.186790	−	0.574879i
$823$	13.7293	+	42.2545i	0.478574	+	1.47290i	0.841076	+	0.540916i	$0.181922\pi$
$823$	13.7293	+	42.2545i	0.478574	+	1.47290i	−0.362503	+	0.931983i	$0.618078\pi$
$824$	−11.5706			−0.403081
$825$	−10.8750	−	12.5193i	−0.378620	−	0.435867i
$826$	20.0359			0.697136
$827$	−14.3087	−	44.0376i	−0.497562	−	1.53134i	−0.812926	−	0.582368i	$-0.802126\pi$
$827$	−14.3087	−	44.0376i	−0.497562	−	1.53134i	0.315364	−	0.948971i	$-0.397874\pi$
$828$	−0.212279	−	0.653327i	−0.00737720	−	0.0227047i
$829$	13.6088	−	9.88740i	0.472654	−	0.343404i	−0.325820	−	0.945432i	$-0.605640\pi$
$829$	13.6088	−	9.88740i	0.472654	−	0.343404i	0.798475	+	0.602028i	$0.205640\pi$
$830$	−1.34197	−	7.47508i	−0.0465806	−	0.259464i
$831$	−19.1756	+	13.9319i	−0.665193	+	0.483291i
$832$	14.4865	+	10.5251i	0.502229	+	0.364891i
$833$	30.5512	+	22.1968i	1.05854	+	0.769073i
$834$	−6.12129	+	4.44737i	−0.211963	+	0.154000i
$835$	13.3838	+	12.8446i	0.463166	+	0.444506i
$836$	−1.14656	−	3.04648i	−0.0396547	−	0.105365i
$837$	−0.417537	−	0.303358i	−0.0144322	−	0.0104856i
$838$	−25.1619	+	18.2812i	−0.869204	+	0.631513i
$839$	−6.67308	+	20.5376i	−0.230380	+	0.709038i	0.767320	+	0.641264i	$0.221590\pi$
$839$	−6.67308	+	20.5376i	−0.230380	+	0.709038i	−0.997701	+	0.0677740i	$0.978410\pi$
$840$	−23.5791	−	3.23930i	−0.813558	−	0.111766i
$841$	−8.94116	+	27.5181i	−0.308316	+	0.948899i
$842$	−8.93564	+	6.49212i	−0.307942	+	0.223733i
$843$	−18.8960	−	13.7287i	−0.650812	−	0.472843i
$844$	−1.70089	−	1.23577i	−0.0585471	−	0.0425369i
$845$	−11.1001	+	5.94624i	−0.381854	+	0.204557i
$846$	−1.11641	+	3.43595i	−0.0383829	+	0.118130i
$847$	39.2565	−	3.60601i	1.34887	−	0.123904i
$848$	5.03540	−	3.65843i	0.172916	−	0.125631i
$849$	3.85032	−	11.8501i	0.132143	−	0.406693i
$850$	−17.4062	+	26.1542i	−0.597027	+	0.897081i
$851$	3.06994	+	2.23044i	0.105236	+	0.0764586i
$852$	1.85638	+	1.34874i	0.0635984	+	0.0462069i
$853$	−50.6897			−1.73558			−0.867792	−	0.496928i	$-0.834461\pi$
$853$	−50.6897			−1.73558			−0.867792	+	0.496928i	$0.834461\pi$
$854$	43.1010	−	31.3147i	1.47489	−	1.07157i
$855$	−1.50135	−	1.44087i	−0.0513452	−	0.0492767i
$856$	−36.0555			−1.23235
$857$	−8.21047			−0.280464			−0.140232	−	0.990119i	$-0.544785\pi$
$857$	−8.21047			−0.280464			−0.140232	+	0.990119i	$0.544785\pi$
$858$	−8.74442	+	0.400778i	−0.298530	+	0.0136823i
$859$	−44.8410	−	32.5789i	−1.52995	−	1.11158i	−0.956264	−	0.292504i	$-0.905512\pi$
$859$	−44.8410	−	32.5789i	−1.52995	−	1.11158i	−0.573690	−	0.819073i	$-0.694488\pi$
$860$	−16.7275	−	2.29803i	−0.570404	−	0.0783621i
$861$	−13.5327	+	41.6492i	−0.461192	+	1.41940i
$862$	4.43739	+	13.6569i	0.151138	+	0.465155i
$863$	−14.4685	+	44.5296i	−0.492515	+	1.51580i	0.328280	+	0.944581i	$0.393531\pi$
$863$	−14.4685	+	44.5296i	−0.492515	+	1.51580i	−0.820794	+	0.571224i	$0.806469\pi$
$864$	4.19322	+	3.04655i	0.142656	+	0.103646i
$865$	−29.3449	+	15.7199i	−0.997758	+	0.534493i
$866$	9.78190			0.332402
$867$	−24.7621			−0.840963
$868$	1.95065			0.0662095
$869$	13.2174	−	48.0646i	0.448370	−	1.63048i
$870$	−0.491596	+	0.263345i	−0.0166667	+	0.00892823i
$871$	−0.949569	−	0.689902i	−0.0321749	−	0.0233764i
$872$	5.98650	+	18.4246i	0.202728	+	0.623934i
$873$	−3.38663			−0.114620
$874$	−0.182128	−	0.560531i	−0.00616056	−	0.0189603i
$875$	39.1133	−	8.69488i	1.32227	−	0.293940i
$876$	7.00312	+	5.08807i	0.236614	+	0.171910i
$877$	−3.68731	+	11.3484i	−0.124512	+	0.383207i	−0.993812	−	0.111077i	$-0.964570\pi$
$877$	−3.68731	+	11.3484i	−0.124512	+	0.383207i	0.869300	+	0.494284i	$0.164570\pi$
$878$	17.3407	+	12.5988i	0.585221	+	0.425188i
$879$	4.99966	−	15.3874i	0.168634	−	0.519003i
$880$	4.34421	+	3.80282i	0.146443	+	0.128193i
$881$	14.2507	+	43.8592i	0.480118	+	1.47765i	0.838928	+	0.544242i	$0.183183\pi$
$881$	14.2507	+	43.8592i	0.480118	+	1.47765i	−0.358810	+	0.933411i	$0.616817\pi$
$882$	1.75576	−	5.40366i	0.0591194	−	0.181951i
$883$	−28.9653	−	21.0445i	−0.974760	−	0.708205i	−0.0182289	−	0.999834i	$-0.505803\pi$
$883$	−28.9653	−	21.0445i	−0.974760	−	0.708205i	−0.956532	+	0.291629i	$0.905803\pi$
$884$	−5.71692	−	17.5949i	−0.192281	−	0.591779i
$885$	12.7376	+	1.74989i	0.428170	+	0.0588220i
$886$	26.2962	+	19.1053i	0.883438	+	0.641855i
$887$	−11.5690	−	35.6056i	−0.388448	−	1.19552i	−0.933948	−	0.357409i	$-0.883660\pi$
$887$	−11.5690	−	35.6056i	−0.388448	−	1.19552i	0.545500	−	0.838111i	$-0.316340\pi$
$888$	−17.3024			−0.580632
$889$	1.52125	+	4.68192i	0.0510210	+	0.157026i
$890$	−6.17980	−	34.4228i	−0.207147	−	1.15385i
$891$	−3.31315	+	0.151849i	−0.110995	+	0.00508714i
$892$	3.74954	+	11.5399i	0.125544	+	0.386384i
$893$	1.06854	−	3.28862i	0.0357572	−	0.110049i
$894$	12.2425	+	8.89471i	0.409451	+	0.297484i
$895$	−12.0379	+	24.8768i	−0.402382	+	0.831540i
$896$	−14.1645			−0.473202
$897$	1.76813			0.0590361
$898$	33.1010			1.10459
$899$	0.107103	−	0.0778148i	0.00357208	−	0.00259527i
$900$	−5.07779	−	1.42201i	−0.169260	−	0.0474003i
$901$	−51.6663			−1.72125
$902$	30.7857	−	24.5972i	1.02505	−	0.818996i
$903$	7.92927	−	24.4038i	0.263870	−	0.812108i
$904$	10.8563	+	7.88756i	0.361075	+	0.262336i
$905$	−12.9543	−	1.77967i	−0.430617	−	0.0591581i
$906$	−4.18174	+	12.8701i	−0.138929	+	0.427580i
$907$	8.89677	+	27.3814i	0.295412	+	0.909185i	0.983083	+	0.183162i	$0.0586334\pi$
$907$	8.89677	+	27.3814i	0.295412	+	0.909185i	−0.687670	+	0.726023i	$0.741367\pi$
$908$	18.8506	−	13.6958i	0.625580	−	0.454510i
$909$	2.65112	+	8.15931i	0.0879321	+	0.270627i
$910$	9.21274	−	19.0385i	0.305399	−	0.631121i
$911$	−3.34010	−	10.2798i	−0.110662	−	0.340584i	0.880355	−	0.474315i	$-0.157304\pi$
$911$	−3.34010	−	10.2798i	−0.110662	−	0.340584i	−0.991018	+	0.133731i	$0.957304\pi$
$912$	0.586118	+	0.425839i	0.0194083	+	0.0141010i
$913$	9.67480	+	6.37350i	0.320189	+	0.210932i
$914$	17.1047	−	12.4273i	0.565774	−	0.411059i
$915$	30.1361	−	16.1437i	0.996268	−	0.533695i
$916$	−4.40174			−0.145438
$917$	−24.8530	+	76.4897i	−0.820719	+	2.52591i
$918$	1.94167	+	5.97583i	0.0640845	+	0.197232i
$919$	−21.7877	+	15.8297i	−0.718710	+	0.522173i	−0.885972	−	0.463739i	$-0.846507\pi$
$919$	−21.7877	+	15.8297i	−0.718710	+	0.522173i	0.167262	+	0.985913i	$0.446507\pi$
$920$	−3.12105	−	2.99531i	−0.102898	−	0.0987524i
$921$	−2.42810	−	7.47292i	−0.0800086	−	0.246241i
$922$	22.1769	+	16.1125i	0.730358	+	0.530636i
$923$	−4.77810	+	3.47150i	−0.157273	+	0.114266i
$924$	9.79339	−	7.82473i	0.322179	−	0.257415i
$925$	27.3095	−	10.1321i	0.897930	−	0.333141i
$926$	11.2869	−	34.7376i	0.370912	−	1.14155i
$927$	1.20387	−	3.70512i	0.0395402	−	0.121692i
$928$	−1.07561	+	0.781474i	−0.0353085	+	0.0256532i
$929$	−13.5940			−0.446003			−0.223002	−	0.974818i	$-0.571586\pi$
$929$	−13.5940			−0.446003			−0.223002	+	0.974818i	$0.571586\pi$
$930$	−1.11164	−	0.152717i	−0.0364521	−	0.00500778i
$931$	−1.68047	+	5.17195i	−0.0550751	+	0.169504i
$932$	−5.45463	+	3.96302i	−0.178672	+	0.129813i
$933$	−24.2110			−0.792634
$934$	25.4331	+	18.4782i	0.832197	+	0.604627i
$935$	−10.6195	−	46.7348i	−0.347294	−	1.52839i
$936$	−6.52239	+	4.73879i	−0.213191	+	0.154892i
$937$	13.7696	−	10.0042i	0.449835	−	0.326824i	−0.339696	−	0.940535i	$-0.610324\pi$
$937$	13.7696	−	10.0042i	0.449835	−	0.326824i	0.789531	+	0.613711i	$0.210324\pi$
$938$	−1.50669			−0.0491952
$939$	7.91084			0.258160
$940$	−1.54833	−	8.62453i	−0.0505010	−	0.281301i
$941$	−0.0107749	+	0.0331616i	−0.000351251	+	0.00108104i	−0.951232	−	0.308476i	$-0.900181\pi$
$941$	−0.0107749	+	0.0331616i	−0.000351251	+	0.00108104i	0.950881	+	0.309557i	$0.100181\pi$
$942$	−3.15390	+	9.70672i	−0.102760	+	0.316262i
$943$	−6.43932	+	4.67844i	−0.209693	+	0.152351i
$944$	−4.47634			−0.145692
$945$	3.49058	−	7.21345i	0.113549	−	0.234653i
$946$	−18.0385	+	14.4124i	−0.586481	+	0.468587i
$947$	−3.63566	+	11.1894i	−0.118143	+	0.363607i	−0.992590	−	0.121515i	$-0.961225\pi$
$947$	−3.63566	+	11.1894i	−0.118143	+	0.363607i	0.874447	+	0.485122i	$0.161225\pi$
$948$	−4.89825	−	15.0753i	−0.159088	−	0.489622i
$949$	−18.0253	+	13.0961i	−0.585125	+	0.425118i
$950$	−4.35656	−	1.22003i	−0.141345	−	0.0395831i
$951$	10.3305	+	31.7941i	0.334990	+	1.03099i
$952$	−55.6483	−	40.4308i	−1.80357	−	1.31037i
$953$	−13.9284	+	10.1196i	−0.451186	+	0.327806i	−0.790064	−	0.613024i	$-0.789953\pi$
$953$	−13.9284	+	10.1196i	−0.451186	+	0.327806i	0.338878	+	0.940830i	$0.389953\pi$
$954$	2.40215	+	7.39306i	0.0777725	+	0.239359i
$955$	−17.2926	+	35.7360i	−0.559576	+	1.15639i
$956$	−2.73611	−	8.42089i	−0.0884922	−	0.272351i
$957$	0.225576	−	0.820300i	0.00729184	−	0.0265165i
$958$	11.7858	+	36.2730i	0.380782	+	1.17193i
$959$	−51.6780	+	37.5463i	−1.66877	+	1.21243i
$960$	14.6131	+	2.00754i	0.471635	+	0.0647931i
$961$	−30.7336			−0.991408
$962$	4.75139	−	14.6233i	0.153191	−	0.471473i
$963$	3.75141	−	11.5456i	0.120887	−	0.372053i
$964$	−20.3911			−0.656754
$965$	−8.95529	+	18.5065i	−0.288281	+	0.595746i
$966$	1.83623	−	1.33410i	0.0590797	−	0.0429239i
$967$	−12.8835	−	39.6512i	−0.414304	−	1.27510i	−0.912872	−	0.408246i	$-0.866141\pi$
$967$	−12.8835	−	39.6512i	−0.414304	−	1.27510i	0.498568	−	0.866851i	$-0.333859\pi$
$968$	−32.5333	+	2.98843i	−1.04566	+	0.0960518i
$969$	−1.85841	−	5.71959i	−0.0597006	−	0.183740i
$970$	−6.49037	+	3.47685i	−0.208393	+	0.111635i
$971$	−3.15405	−	9.70717i	−0.101218	−	0.311518i	0.887606	−	0.460604i	$-0.152367\pi$
$971$	−3.15405	−	9.70717i	−0.101218	−	0.311518i	−0.988824	+	0.149086i	$0.952367\pi$
$972$	−0.853212	+	0.619895i	−0.0273668	+	0.0198831i
$973$	22.5624	+	16.3925i	0.723316	+	0.525520i
$974$	5.73533	+	17.6515i	0.183772	+	0.565591i
$975$	7.51970	−	11.2990i	0.240823	−	0.361856i
$976$	−9.62948	+	6.99623i	−0.308232	+	0.223944i
$977$	12.2377	+	37.6638i	0.391519	+	1.20497i	0.931639	+	0.363385i	$0.118379\pi$
$977$	12.2377	+	37.6638i	0.391519	+	1.20497i	−0.540120	+	0.841588i	$0.681621\pi$
$978$	1.16265	−	3.57827i	0.0371774	−	0.114420i
$979$	44.5525	+	29.3500i	1.42391	+	0.938031i
$980$	2.43503	+	13.5637i	0.0777843	+	0.433275i
$981$	−6.52275			−0.208255
$982$	26.1766	−	19.0184i	0.835329	−	0.606902i
$983$	6.36356	−	19.5850i	0.202966	−	0.624665i	−0.796825	−	0.604210i	$-0.793489\pi$
$983$	6.36356	−	19.5850i	0.202966	−	0.624665i	0.999791	−	0.0204547i	$-0.00651138\pi$
$984$	11.2150	−	34.5162i	0.357521	−	1.10034i
$985$	1.45803	−	0.781056i	0.0464566	−	0.0248865i
$986$	−1.61175			−0.0513287
$987$	13.3163			0.423862
$988$	2.15533	−	1.56594i	0.0685702	−	0.0498192i
$989$	3.77303	−	2.74127i	0.119975	−	0.0871672i
$990$	−6.19366	+	3.69243i	−0.196847	+	0.117353i
$991$	28.4658	+	20.6816i	0.904247	+	0.656974i	0.939553	−	0.342402i	$-0.111241\pi$
$991$	28.4658	+	20.6816i	0.904247	+	0.656974i	−0.0353062	+	0.999377i	$0.511241\pi$
$992$	−2.67502			−0.0849320
$993$	2.27340	−	1.65172i	0.0721443	−	0.0524159i
$994$	−2.34280	+	7.21040i	−0.0743092	+	0.228700i
$995$	−41.4439	−	39.7742i	−1.31386	−	1.26093i
$996$	3.68398			0.116731
$997$	−6.70012	+	4.86792i	−0.212195	+	0.154169i	−0.688806	−	0.724946i	$-0.741865\pi$
$997$	−6.70012	+	4.86792i	−0.212195	+	0.154169i	0.476611	+	0.879114i	$0.341865\pi$
$998$	−1.68967	+	5.20028i	−0.0534856	+	0.164612i
$999$	1.80024	−	5.54056i	0.0569570	−	0.175296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.m.d.361.18	yes	116
11.5	even	5		825.2.o.d.511.12	yes	116
25.16	even	5		825.2.o.d.691.12	yes	116
275.16	even	5	inner	825.2.m.d.16.18	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.m.d.16.18	✓	116	275.16	even	5	inner
825.2.m.d.361.18	yes	116	1.1	even	1	trivial
825.2.o.d.511.12	yes	116	11.5	even	5
825.2.o.d.691.12	yes	116	25.16	even	5

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.300458 + 0.924714i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.853212 - 0.619895i) q^{4} +(1.61330 + 1.54831i) q^{5} +(0.786609 - 0.571505i) q^{6} +(-2.89935 - 2.10650i) q^{7} +(2.40280 + 1.74574i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.947013 + 1.95704i) q^{10} +(-1.16824 - 3.10407i) q^{11} +(-0.853212 - 0.619895i) q^{12} +(2.19607 - 1.59554i) q^{13} +(1.07678 - 3.31399i) q^{14} +(0.973990 - 2.01279i) q^{15} +(-0.240570 + 0.740400i) q^{16} +(5.22816 - 3.79848i) q^{17} +(-0.786609 - 0.571505i) q^{18} +(0.752879 + 0.546998i) q^{19} +(2.33628 + 0.320957i) q^{20} +(-1.10745 + 3.40839i) q^{21} +(2.51937 - 2.01293i) q^{22} +(-0.526966 + 0.382863i) q^{23} +(0.917787 - 2.82466i) q^{24} +(0.205486 + 4.99578i) q^{25} +(2.13525 + 1.55135i) q^{26} +(0.809017 + 0.587785i) q^{27} -3.77957 q^{28} +(-0.207522 + 0.150773i) q^{29} +(2.15390 + 0.295903i) q^{30} -0.516104 q^{31} +5.18310 q^{32} +(-2.59114 + 2.07027i) q^{33} +(5.08335 + 3.69327i) q^{34} +(-1.41602 - 7.88751i) q^{35} +(-0.325898 + 1.00301i) q^{36} +(-1.80024 - 5.54056i) q^{37} +(-0.279609 + 0.860548i) q^{38} +(-2.19607 - 1.59554i) q^{39} +(1.17350 + 6.53667i) q^{40} +12.2196 q^{41} -3.48453 q^{42} -7.15991 q^{43} +(-2.92095 - 1.92424i) q^{44} +(-2.21526 - 0.304332i) q^{45} +(-0.512370 - 0.372259i) q^{46} +(-1.14821 - 3.53383i) q^{47} +0.778502 q^{48} +(1.80577 + 5.55759i) q^{49} +(-4.55793 + 1.69104i) q^{50} +(-5.22816 - 3.79848i) q^{51} +(0.884649 - 2.72267i) q^{52} +(-6.46806 - 4.69932i) q^{53} +(-0.300458 + 0.924714i) q^{54} +(2.92133 - 6.81658i) q^{55} +(-3.28916 - 10.1230i) q^{56} +(0.287574 - 0.885062i) q^{57} +(-0.201774 - 0.146597i) q^{58} +(1.77683 + 5.46852i) q^{59} +(-0.416701 - 2.32111i) q^{60} +(12.3692 + 8.98678i) q^{61} +(-0.155068 - 0.477249i) q^{62} +3.58380 q^{63} +(2.03845 + 6.27369i) q^{64} +(6.01332 + 0.826109i) q^{65} +(-2.69293 - 1.77403i) q^{66} +(-0.133617 - 0.411231i) q^{67} +(2.10607 - 6.48182i) q^{68} +(0.526966 + 0.382863i) q^{69} +(6.86825 - 3.67928i) q^{70} -2.17575 q^{71} -2.97002 q^{72} -8.20795 q^{73} +(4.58254 - 3.32941i) q^{74} +(4.68777 - 1.73921i) q^{75} +0.981447 q^{76} +(-3.15160 + 11.4607i) q^{77} +(0.815592 - 2.51013i) q^{78} +(12.1595 + 8.83441i) q^{79} +(-1.53448 + 0.822011i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.67148 + 11.2996i) q^{82} +(-2.82602 + 2.05322i) q^{83} +(1.16795 + 3.59459i) q^{84} +(14.3158 + 1.96670i) q^{85} +(-2.15125 - 6.62087i) q^{86} +(0.207522 + 0.150773i) q^{87} +(2.61184 - 9.49787i) q^{88} +(-13.0138 + 9.45511i) q^{89} +(-0.384172 - 2.13992i) q^{90} -9.72820 q^{91} +(-0.212279 + 0.653327i) q^{92} +(0.159485 + 0.490844i) q^{93} +(2.92279 - 2.12353i) q^{94} +(0.367699 + 2.04816i) q^{95} +(-1.60167 - 4.92943i) q^{96} +(2.73984 + 1.99061i) q^{97} +(-4.59663 + 3.33965i) q^{98} +(2.76965 + 1.82457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q + 4 q^{2} + 29 q^{3} - 30 q^{4} - 3 q^{5} + q^{6} - 2 q^{7} + 11 q^{8} - 29 q^{9} + 2 q^{10} + 2 q^{11} + 30 q^{12} + 20 q^{13} - 2 q^{14} + 3 q^{15} - 26 q^{16} + 11 q^{17} - q^{18} - q^{19} + 17 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) \) 116 * q + 4 * q^2 + 29 * q^3 - 30 * q^4 - 3 * q^5 + q^6 - 2 * q^7 + 11 * q^8 - 29 * q^9 + 2 * q^10 + 2 * q^11 + 30 * q^12 + 20 * q^13 - 2 * q^14 + 3 * q^15 - 26 * q^16 + 11 * q^17 - q^18 - q^19 + 17 * q^20 + 2 * q^21 - 14 * q^22 + 14 * q^23 - q^24 - 13 * q^25 - 16 * q^26 + 29 * q^27 - 12 * q^28 + 5 * q^29 - 12 * q^30 + 62 * q^31 - 94 * q^32 + 13 * q^33 + 20 * q^34 + 19 * q^35 - 35 * q^36 - 10 * q^37 - 21 * q^38 - 20 * q^39 - 8 * q^40 + 4 * q^41 + 12 * q^42 - 46 * q^43 - 25 * q^44 + 2 * q^45 - 15 * q^46 - 15 * q^47 - 134 * q^48 - 5 * q^49 + 100 * q^50 - 11 * q^51 + 4 * q^52 - 6 * q^53 - 4 * q^54 - 21 * q^55 + 28 * q^56 + 21 * q^57 - 9 * q^58 - 29 * q^59 - 7 * q^60 - 10 * q^61 + 22 * q^62 + 8 * q^63 + 3 * q^64 + 10 * q^65 - 6 * q^66 - 35 * q^67 + 60 * q^68 - 14 * q^69 + 94 * q^70 + 50 * q^71 - 24 * q^72 - 60 * q^73 - 12 * q^74 - 17 * q^75 + 126 * q^76 + 76 * q^77 - 19 * q^78 + 11 * q^79 + q^80 - 29 * q^81 - 21 * q^82 - 13 * q^83 - 13 * q^84 - 21 * q^85 + 6 * q^86 - 5 * q^87 - 61 * q^88 + 13 * q^89 - 8 * q^90 + 20 * q^91 + 97 * q^92 + 43 * q^93 + 39 * q^94 - 36 * q^95 - 26 * q^96 - 20 * q^97 - 34 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more