LMFDB - Embedded newform 315.2.r.b.184.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(184,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("315.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.r (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			184.7
Character	$\chi$	$=$	315.184
Dual form			315.2.r.b.214.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12646i q^{2} +(-1.54581 - 0.781334i) q^{3} -2.52185 q^{4} +(-2.23351 + 0.106887i) q^{5} +(-1.66148 + 3.28710i) q^{6} +(-2.47990 - 0.921996i) q^{7} +1.10970i q^{8} +(1.77903 + 2.41558i) q^{9} +O(q^{10})$	\(q-2.12646i q^{2} +(-1.54581 - 0.781334i) q^{3} -2.52185 q^{4} +(-2.23351 + 0.106887i) q^{5} +(-1.66148 + 3.28710i) q^{6} +(-2.47990 - 0.921996i) q^{7} +1.10970i q^{8} +(1.77903 + 2.41558i) q^{9} +(0.227292 + 4.74948i) q^{10} +(1.15902 - 2.00747i) q^{11} +(3.89830 + 1.97041i) q^{12} +(4.60600 + 2.65927i) q^{13} +(-1.96059 + 5.27343i) q^{14} +(3.53609 + 1.57989i) q^{15} -2.68397 q^{16} +(-1.44402 + 0.833705i) q^{17} +(5.13665 - 3.78305i) q^{18} +(-3.46071 + 5.99412i) q^{19} +(5.63259 - 0.269554i) q^{20} +(3.11306 + 3.36286i) q^{21} +(-4.26882 - 2.46461i) q^{22} +(-2.41231 + 1.39275i) q^{23} +(0.867047 - 1.71538i) q^{24} +(4.97715 - 0.477467i) q^{25} +(5.65485 - 9.79449i) q^{26} +(-0.862667 - 5.12404i) q^{27} +(6.25395 + 2.32514i) q^{28} +(-4.12420 - 7.14332i) q^{29} +(3.35958 - 7.51937i) q^{30} -9.92832 q^{31} +7.92676i q^{32} +(-3.36012 + 2.19759i) q^{33} +(1.77284 + 3.07066i) q^{34} +(5.63744 + 1.79422i) q^{35} +(-4.48646 - 6.09174i) q^{36} +(-1.03864 - 0.599659i) q^{37} +(12.7463 + 7.35908i) q^{38} +(-5.04220 - 7.70954i) q^{39} +(-0.118613 - 2.47853i) q^{40} +(0.796182 - 1.37903i) q^{41} +(7.15100 - 6.61982i) q^{42} +(-6.33616 + 3.65818i) q^{43} +(-2.92287 + 5.06256i) q^{44} +(-4.23169 - 5.20507i) q^{45} +(2.96163 + 5.12970i) q^{46} -6.86244i q^{47} +(4.14889 + 2.09707i) q^{48} +(5.29985 + 4.57292i) q^{49} +(-1.01532 - 10.5837i) q^{50} +(2.88358 - 0.160485i) q^{51} +(-11.6156 - 6.70629i) q^{52} +(-1.06364 + 0.614094i) q^{53} +(-10.8961 + 1.83443i) q^{54} +(-2.37410 + 4.60760i) q^{55} +(1.02314 - 2.75195i) q^{56} +(10.0330 - 6.56179i) q^{57} +(-15.1900 + 8.76997i) q^{58} -0.325713 q^{59} +(-8.91750 - 3.98425i) q^{60} -5.03554 q^{61} +21.1122i q^{62} +(-2.18468 - 7.63067i) q^{63} +11.4880 q^{64} +(-10.5718 - 5.44720i) q^{65} +(4.67310 + 7.14518i) q^{66} -8.35343i q^{67} +(3.64160 - 2.10248i) q^{68} +(4.81717 - 0.268099i) q^{69} +(3.81534 - 11.9878i) q^{70} +0.982974 q^{71} +(-2.68057 + 1.97420i) q^{72} +(-0.166572 + 0.0961705i) q^{73} +(-1.27515 + 2.20863i) q^{74} +(-8.06677 - 3.15074i) q^{75} +(8.72740 - 15.1163i) q^{76} +(-4.72513 + 3.90974i) q^{77} +(-16.3941 + 10.7221i) q^{78} +9.68269 q^{79} +(5.99467 - 0.286881i) q^{80} +(-2.67007 + 8.59481i) q^{81} +(-2.93245 - 1.69305i) q^{82} +(-11.4921 + 6.63499i) q^{83} +(-7.85069 - 8.48064i) q^{84} +(3.13612 - 2.01644i) q^{85} +(7.77900 + 13.4736i) q^{86} +(0.793894 + 14.2646i) q^{87} +(2.22770 + 1.28616i) q^{88} +(-3.37915 + 5.85286i) q^{89} +(-11.0684 + 8.99854i) q^{90} +(-8.97059 - 10.8415i) q^{91} +(6.08350 - 3.51231i) q^{92} +(15.3473 + 7.75733i) q^{93} -14.5927 q^{94} +(7.08884 - 13.7579i) q^{95} +(6.19345 - 12.2532i) q^{96} +(-2.79359 + 1.61288i) q^{97} +(9.72416 - 11.2699i) q^{98} +(6.91115 - 0.771669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.12646i		−	1.50364i	−0.659370	−	0.751819i	$-0.729177\pi$
$2$		−	2.12646i		−	1.50364i	0.659370	−	0.751819i	$-0.270823\pi$
$3$	−1.54581	−	0.781334i	−0.892472	−	0.451103i
$3$	−1.54581	−	0.781334i	−0.892472	−	0.451103i
$4$	−2.52185			−1.26093
$5$	−2.23351	+	0.106887i	−0.998857	+	0.0478014i
$5$	−2.23351	+	0.106887i	−0.998857	+	0.0478014i
$6$	−1.66148	+	3.28710i	−0.678296	+	1.34195i
$7$	−2.47990	−	0.921996i	−0.937316	−	0.348482i
$7$	−2.47990	−	0.921996i	−0.937316	−	0.348482i
$8$			1.10970i			0.392338i
$9$	1.77903	+	2.41558i	0.593012	+	0.805194i
$10$	0.227292	+	4.74948i	0.0718759	+	1.50192i
$11$	1.15902	−	2.00747i	0.349457	−	0.605276i	−0.636696	−	0.771115i	$-0.719700\pi$
$11$	1.15902	−	2.00747i	0.349457	−	0.605276i	0.986153	+	0.165838i	$0.0530329\pi$
$12$	3.89830	+	1.97041i	1.12534	+	0.568808i
$13$	4.60600	+	2.65927i	1.27747	+	0.737550i	0.976383	−	0.216046i	$-0.0693161\pi$
$13$	4.60600	+	2.65927i	1.27747	+	0.737550i	0.301090	+	0.953596i	$0.402649\pi$
$14$	−1.96059	+	5.27343i	−0.523990	+	1.40938i
$15$	3.53609	+	1.57989i	0.913015	+	0.407926i
$16$	−2.68397			−0.670991
$17$	−1.44402	+	0.833705i	−0.350226	+	0.202203i	−0.664785	−	0.747035i	$-0.731477\pi$
$17$	−1.44402	+	0.833705i	−0.350226	+	0.202203i	0.314559	+	0.949238i	$0.398143\pi$
$18$	5.13665	−	3.78305i	1.21072	−	0.891675i
$19$	−3.46071	+	5.99412i	−0.793941	+	1.37515i	0.129568	+	0.991570i	$0.458641\pi$
$19$	−3.46071	+	5.99412i	−0.793941	+	1.37515i	−0.923509	+	0.383576i	$0.874692\pi$
$20$	5.63259	−	0.269554i	1.25948	−	0.0602740i
$21$	3.11306	+	3.36286i	0.679326	+	0.733836i
$22$	−4.26882	−	2.46461i	−0.910116	−	0.525456i
$23$	−2.41231	+	1.39275i	−0.503002	+	0.290408i	−0.729952	−	0.683498i	$-0.760458\pi$
$23$	−2.41231	+	1.39275i	−0.503002	+	0.290408i	0.226950	+	0.973906i	$0.427125\pi$
$24$	0.867047	−	1.71538i	0.176985	−	0.350151i
$25$	4.97715	−	0.477467i	0.995430	−	0.0954935i
$26$	5.65485	−	9.79449i	1.10901	−	1.92086i
$27$	−0.862667	−	5.12404i	−0.166020	−	0.986122i
$28$	6.25395	+	2.32514i	1.18189	+	0.439410i
$29$	−4.12420	−	7.14332i	−0.765845	−	1.32648i	−0.939799	−	0.341728i	$-0.888988\pi$
$29$	−4.12420	−	7.14332i	−0.765845	−	1.32648i	0.173954	−	0.984754i	$-0.444346\pi$
$30$	3.35958	−	7.51937i	0.613373	−	1.37284i
$31$	−9.92832			−1.78318			−0.891589	−	0.452845i	$-0.850409\pi$
$31$	−9.92832			−1.78318			−0.891589	+	0.452845i	$0.850409\pi$
$32$			7.92676i			1.40127i
$33$	−3.36012	+	2.19759i	−0.584922	+	0.382551i
$34$	1.77284	+	3.07066i	0.304040	+	0.526613i
$35$	5.63744	+	1.79422i	0.952902	+	0.303278i
$36$	−4.48646	−	6.09174i	−0.747744	−	1.01529i
$37$	−1.03864	−	0.599659i	−0.170751	−	0.0985833i	0.412189	−	0.911098i	$-0.364764\pi$
$37$	−1.03864	−	0.599659i	−0.170751	−	0.0985833i	−0.582940	+	0.812515i	$0.698098\pi$
$38$	12.7463	+	7.35908i	2.06772	+	1.19380i
$39$	−5.04220	−	7.70954i	−0.807398	−	1.23451i
$40$	−0.118613	−	2.47853i	−0.0187543	−	0.391890i
$41$	0.796182	−	1.37903i	0.124343	−	0.215368i	−0.797133	−	0.603804i	$-0.793651\pi$
$41$	0.796182	−	1.37903i	0.124343	−	0.215368i	0.921476	+	0.388436i	$0.126984\pi$
$42$	7.15100	−	6.61982i	1.10342	−	1.02146i
$43$	−6.33616	+	3.65818i	−0.966255	+	0.557868i	−0.898093	−	0.439806i	$-0.855047\pi$
$43$	−6.33616	+	3.65818i	−0.966255	+	0.557868i	−0.0681629	+	0.997674i	$0.521714\pi$
$44$	−2.92287	+	5.06256i	−0.440639	+	0.763209i
$45$	−4.23169	−	5.20507i	−0.630823	−	0.775927i
$46$	2.96163	+	5.12970i	0.436669	+	0.756333i
$47$		−	6.86244i		−	1.00099i	−0.865740	−	0.500495i	$-0.833152\pi$
$47$		−	6.86244i		−	1.00099i	0.865740	−	0.500495i	$-0.166848\pi$
$48$	4.14889	+	2.09707i	0.598841	+	0.302686i
$49$	5.29985	+	4.57292i	0.757121	+	0.653275i
$50$	−1.01532	−	10.5837i	−0.143588	−	1.49677i
$51$	2.88358	−	0.160485i	0.403781	−	0.0224724i
$52$	−11.6156	−	6.70629i	−1.61080	−	0.929996i
$53$	−1.06364	+	0.614094i	−0.146103	+	0.0843523i	−0.571269	−	0.820763i	$-0.693549\pi$
$53$	−1.06364	+	0.614094i	−0.146103	+	0.0843523i	0.425167	+	0.905115i	$0.360215\pi$
$54$	−10.8961	+	1.83443i	−1.48277	+	0.249635i
$55$	−2.37410	+	4.60760i	−0.320124	+	0.621289i
$56$	1.02314	−	2.75195i	0.136723	−	0.367745i
$57$	10.0330	−	6.56179i	1.32890	−	0.869130i
$58$	−15.1900	+	8.76997i	−1.99455	+	1.15155i
$59$	−0.325713			−0.0424042			−0.0212021	−	0.999775i	$-0.506749\pi$
$59$	−0.325713			−0.0424042			−0.0212021	+	0.999775i	$0.506749\pi$
$60$	−8.91750	−	3.98425i	−1.15124	−	0.514365i
$61$	−5.03554			−0.644734			−0.322367	−	0.946615i	$-0.604479\pi$
$61$	−5.03554			−0.644734			−0.322367	+	0.946615i	$0.604479\pi$
$62$			21.1122i			2.68125i
$63$	−2.18468	−	7.63067i	−0.275244	−	0.961375i
$64$	11.4880			1.43601
$65$	−10.5718	−	5.44720i	−1.31127	−	0.675642i
$66$	4.67310	+	7.14518i	0.575218	+	0.879511i
$67$		−	8.35343i		−	1.02053i	−0.860016	−	0.510267i	$-0.829547\pi$
$67$		−	8.35343i		−	1.02053i	0.860016	−	0.510267i	$-0.170453\pi$
$68$	3.64160	−	2.10248i	0.441609	−	0.254963i
$69$	4.81717	−	0.268099i	0.579919	−	0.0322754i
$70$	3.81534	−	11.9878i	0.456021	−	1.43282i
$71$	0.982974			0.116658			0.0583288	−	0.998297i	$-0.481423\pi$
$71$	0.982974			0.116658			0.0583288	+	0.998297i	$0.481423\pi$
$72$	−2.68057	+	1.97420i	−0.315908	+	0.232661i
$73$	−0.166572	+	0.0961705i	−0.0194958	+	0.0112559i	−0.509716	−	0.860343i	$-0.670250\pi$
$73$	−0.166572	+	0.0961705i	−0.0194958	+	0.0112559i	0.490220	+	0.871598i	$0.336916\pi$
$74$	−1.27515	+	2.20863i	−0.148233	+	0.256748i
$75$	−8.06677	−	3.15074i	−0.931471	−	0.363817i
$76$	8.72740	−	15.1163i	1.00110	−	1.73396i
$77$	−4.72513	+	3.90974i	−0.538479	+	0.445556i
$78$	−16.3941	+	10.7221i	−1.85626	+	1.21403i
$79$	9.68269			1.08939			0.544694	−	0.838635i	$-0.316646\pi$
$79$	9.68269			1.08939			0.544694	+	0.838635i	$0.316646\pi$
$80$	5.99467	−	0.286881i	0.670224	−	0.0320743i
$81$	−2.67007	+	8.59481i	−0.296675	+	0.954979i
$82$	−2.93245	−	1.69305i	−0.323835	−	0.186966i
$83$	−11.4921	+	6.63499i	−1.26143	+	0.728284i	−0.973350	−	0.229324i	$-0.926349\pi$
$83$	−11.4921	+	6.63499i	−1.26143	+	0.728284i	−0.288075	+	0.957608i	$0.593015\pi$
$84$	−7.85069	−	8.48064i	−0.856580	−	0.925313i
$85$	3.13612	−	2.01644i	0.340160	−	0.218713i
$86$	7.77900	+	13.4736i	0.838831	+	1.45290i
$87$	0.793894	+	14.2646i	0.0851143	+	1.52932i
$88$	2.22770	+	1.28616i	0.237473	+	0.137105i
$89$	−3.37915	+	5.85286i	−0.358189	+	0.620402i	−0.987658	−	0.156624i	$-0.949939\pi$
$89$	−3.37915	+	5.85286i	−0.358189	+	0.620402i	0.629469	+	0.777025i	$0.283272\pi$
$90$	−11.0684	+	8.99854i	−1.16671	+	0.948529i
$91$	−8.97059	−	10.8415i	−0.940373	−	1.13649i
$92$	6.08350	−	3.51231i	0.634249	−	0.366184i
$93$	15.3473	+	7.75733i	1.59144	+	0.804398i
$94$	−14.5927			−1.50512
$95$	7.08884	−	13.7579i	0.727300	−	1.41153i
$96$	6.19345	−	12.2532i	0.632116	−	1.25059i
$97$	−2.79359	+	1.61288i	−0.283646	+	0.163763i	−0.635073	−	0.772452i	$-0.719030\pi$
$97$	−2.79359	+	1.61288i	−0.283646	+	0.163763i	0.351427	+	0.936215i	$0.385697\pi$
$98$	9.72416	−	11.2699i	0.982288	−	1.13844i
$99$	6.91115	−	0.771669i	0.694597	−	0.0775557i
$100$	−12.5516	+	1.20410i	−1.25516	+	0.120410i
$101$	0.886755	−	1.53590i	0.0882354	−	0.152828i	−0.818530	−	0.574464i	$-0.805211\pi$
$101$	0.886755	−	1.53590i	0.0882354	−	0.152828i	0.906765	+	0.421636i	$0.138544\pi$
$102$	−0.341266	−	6.13182i	−0.0337904	−	0.607141i
$103$	7.14434	−	4.12479i	0.703953	−	0.406427i	−0.104865	−	0.994486i	$-0.533441\pi$
$103$	7.14434	−	4.12479i	0.703953	−	0.406427i	0.808818	+	0.588059i	$0.200108\pi$
$104$	−2.95100	+	5.11128i	−0.289369	+	0.501202i
$105$	−7.31251	−	7.17824i	−0.713628	−	0.700525i
$106$	1.30585	+	2.26180i	0.126835	+	0.219685i
$107$	−5.37786	−	3.10491i	−0.519897	−	0.300163i	0.216995	−	0.976173i	$-0.430374\pi$
$107$	−5.37786	−	3.10491i	−0.519897	−	0.300163i	−0.736893	+	0.676010i	$0.763708\pi$
$108$	2.17552	+	12.9221i	0.209339	+	1.24343i
$109$	−4.73603	−	8.20304i	−0.453629	−	0.785709i	0.544979	−	0.838450i	$-0.316538\pi$
$109$	−4.73603	−	8.20304i	−0.453629	−	0.785709i	−0.998608	+	0.0527407i	$0.983204\pi$
$110$	9.79790	+	5.04845i	0.934194	+	0.481350i
$111$	1.13700	+	1.73848i	0.107919	+	0.165009i
$112$	6.65598	+	2.47461i	0.628931	+	0.233828i
$113$	1.64209	+	0.948059i	0.154474	+	0.0891859i	0.575245	−	0.817981i	$-0.304907\pi$
$113$	1.64209	+	0.948059i	0.154474	+	0.0891859i	−0.420770	+	0.907167i	$0.638240\pi$
$114$	−13.9534	−	21.3348i	−1.30686	−	1.99819i
$115$	5.23906	−	3.36857i	0.488545	−	0.314121i
$116$	10.4006	+	18.0144i	0.965674	+	1.67260i
$117$	1.77054	+	15.8571i	0.163686	+	1.46599i
$118$			0.692616i			0.0637605i
$119$	4.34970	−	0.736128i	0.398736	−	0.0674808i
$120$	−1.75321	+	3.92400i	−0.160045	+	0.358211i
$121$	2.81336	+	4.87289i	0.255760	+	0.442990i
$122$			10.7079i			0.969447i
$123$	−2.30822	+	1.50963i	−0.208126	+	0.136118i
$124$	25.0377			2.24846
$125$	−11.0655	+	1.59842i	−0.989727	+	0.142967i
$126$	−16.2264	+	4.64564i	−1.44556	+	0.413867i
$127$		−	0.263637i		−	0.0233940i	−0.999932	−	0.0116970i	$-0.996277\pi$
$127$		−	0.263637i		−	0.0233940i	0.999932	−	0.0116970i	$-0.00372336\pi$
$128$		−	8.57540i		−	0.757965i
$129$	12.6527	−	0.704187i	1.11401	−	0.0620002i
$130$	−11.5833	+	22.4805i	−1.01592	+	1.97167i
$131$	−6.21341	−	10.7619i	−0.542868	−	0.940275i	−0.998738	−	0.0502282i	$-0.984005\pi$
$131$	−6.21341	−	10.7619i	−0.542868	−	0.940275i	0.455870	−	0.890046i	$-0.349328\pi$
$132$	8.47373	−	5.54199i	0.737544	−	0.482369i
$133$	14.1088	−	11.6741i	1.22339	−	1.01227i
$134$	−17.7633			−1.53451
$135$	2.47447	+	11.3524i	0.212969	+	0.977059i
$136$	−0.925163	−	1.60243i	−0.0793320	−	0.137407i
$137$	−3.63121	−	2.09648i	−0.310235	−	0.179115i	0.336796	−	0.941577i	$-0.390657\pi$
$137$	−3.63121	−	2.09648i	−0.310235	−	0.179115i	−0.647032	+	0.762463i	$0.723990\pi$
$138$	−0.570104	−	10.2435i	−0.0485305	−	0.871989i
$139$	8.65296	−	14.9874i	0.733934	−	1.27121i	−0.221255	−	0.975216i	$-0.571015\pi$
$139$	8.65296	−	14.9874i	0.733934	−	1.27121i	0.955189	−	0.295995i	$-0.0956513\pi$
$140$	−14.2168	−	4.52476i	−1.20154	−	0.382412i
$141$	−5.36185	+	10.6080i	−0.451550	+	0.893354i
$142$		−	2.09026i		−	0.175411i
$143$	10.6768	−	6.16428i	0.892843	−	0.515483i
$144$	−4.77487	−	6.48334i	−0.397906	−	0.540278i
$145$	9.97498	+	15.5139i	0.828377	+	1.28836i
$146$	0.204503	+	0.354210i	0.0169248	+	0.0293146i
$147$	−4.61956	−	11.2098i	−0.381015	−	0.924569i
$148$	2.61929	+	1.51225i	0.215305	+	0.124306i
$149$	0.598175	+	1.03607i	0.0490044	+	0.0848782i	0.889487	−	0.456960i	$-0.151062\pi$
$149$	0.598175	+	1.03607i	0.0490044	+	0.0848782i	−0.840483	+	0.541838i	$0.817728\pi$
$150$	−6.69995	+	17.1537i	−0.547048	+	1.40059i
$151$	1.30221	−	2.25550i	0.105973	−	0.183550i	−0.808162	−	0.588960i	$-0.799538\pi$
$151$	1.30221	−	2.25550i	0.105973	−	0.183550i	0.914135	+	0.405409i	$0.132871\pi$
$152$	−6.65168	−	3.84035i	−0.539523	−	0.311494i
$153$	−4.58284	−	2.00496i	−0.370501	−	0.162091i
$154$	8.31392	+	10.0478i	0.669955	+	0.809677i
$155$	22.1750	−	1.06121i	1.78114	−	0.0852384i
$156$	12.7157	+	19.4423i	1.01807	+	1.55663i
$157$		−	21.7189i		−	1.73336i	−0.498865	−	0.866679i	$-0.666250\pi$
$157$		−	21.7189i		−	1.73336i	0.498865	−	0.866679i	$-0.333750\pi$
$158$		−	20.5899i		−	1.63804i
$159$	2.12400	−	0.118211i	0.168444	−	0.00937474i
$160$	−0.847268	−	17.7045i	−0.0669825	−	1.39966i
$161$	7.26642	−	1.22974i	0.572674	−	0.0969173i
$162$	18.2766	+	5.67781i	1.43594	+	0.446091i
$163$	5.97677	+	3.45069i	0.468137	+	0.270279i	0.715459	−	0.698654i	$-0.246217\pi$
$163$	5.97677	+	3.45069i	0.468137	+	0.270279i	−0.247323	+	0.968933i	$0.579551\pi$
$164$	−2.00785	+	3.47770i	−0.156787	+	0.271563i
$165$	7.26998	−	5.26749i	0.565967	−	0.410074i
$166$	14.1091	+	24.4376i	1.09508	+	1.89673i
$167$	2.60216	+	1.50236i	0.201361	+	0.116256i	0.597290	−	0.802025i	$-0.296244\pi$
$167$	2.60216	+	1.50236i	0.201361	+	0.116256i	−0.395929	+	0.918281i	$0.629577\pi$
$168$	−3.73177	+	3.45457i	−0.287912	+	0.266526i
$169$	7.64347	+	13.2389i	0.587959	+	1.01838i
$170$	−4.28788	−	6.66885i	−0.328866	−	0.511478i
$171$	−20.6360	+	2.30413i	−1.57808	+	0.176201i
$172$	15.9789	−	9.22540i	1.21838	−	0.703430i
$173$			3.40831i			0.259129i	0.991571	+	0.129564i	$0.0413579\pi$
$173$			3.40831i			0.259129i	−0.991571	+	0.129564i	$0.958642\pi$
$174$	30.3331	−	1.68819i	2.29955	−	0.127981i
$175$	−12.7831	−	3.40484i	−0.966310	−	0.257382i
$176$	−3.11076	+	5.38799i	−0.234482	+	0.406135i
$177$	0.503489	+	0.254490i	0.0378445	+	0.0191287i
$178$	12.4459	+	7.18564i	0.932859	+	0.538587i
$179$	−2.04514	−	3.54229i	−0.152861	−	0.264763i	0.779417	−	0.626505i	$-0.215515\pi$
$179$	−2.04514	−	3.54229i	−0.152861	−	0.264763i	−0.932278	+	0.361742i	$0.882182\pi$
$180$	10.6717	+	13.1264i	0.795421	+	0.978386i
$181$	0.767210			0.0570262			0.0285131	−	0.999593i	$-0.490923\pi$
$181$	0.767210			0.0570262			0.0285131	+	0.999593i	$0.490923\pi$
$182$	−23.0540	+	19.0756i	−1.70887	+	1.41398i
$183$	7.78396	+	3.93443i	0.575407	+	0.290842i
$184$	−1.54554	−	2.67695i	−0.113938	−	0.197347i
$185$	2.38391	+	1.22833i	0.175268	+	0.0903084i
$186$	16.4957	−	32.6354i	1.20952	−	2.39294i
$187$			3.86511i			0.282645i
$188$			17.3060i			1.26217i
$189$	−2.58501	+	13.5025i	−0.188032	+	0.982163i
$190$	−29.2556	−	15.0742i	−2.12242	−	1.09360i
$191$	−19.4320			−1.40605			−0.703024	−	0.711166i	$-0.748167\pi$
$191$	−19.4320			−1.40605			−0.703024	+	0.711166i	$0.748167\pi$
$192$	−17.7583	−	8.97600i	−1.28159	−	0.647787i
$193$			10.9716i			0.789753i	0.918734	+	0.394876i	$0.129213\pi$
$193$			10.9716i			0.789753i	−0.918734	+	0.394876i	$0.870787\pi$
$194$	3.42973	+	5.94047i	0.246241	+	0.426501i
$195$	12.0859	+	16.6804i	0.865487	+	1.19451i
$196$	−13.3654	−	11.5322i	−0.954674	−	0.823731i
$197$		−	9.06563i		−	0.645900i	−0.946416	−	0.322950i	$-0.895326\pi$
$197$		−	9.06563i		−	0.645900i	0.946416	−	0.322950i	$-0.104674\pi$
$198$	−1.64093	−	14.6963i	−0.116616	−	1.04442i
$199$	0.796301	+	1.37923i	0.0564483	+	0.0977713i	0.892869	−	0.450317i	$-0.148689\pi$
$199$	0.796301	+	1.37923i	0.0564483	+	0.0977713i	−0.836420	+	0.548088i	$0.815356\pi$
$200$	0.529846	+	5.52315i	0.0374657	+	0.390545i
$201$	−6.52682	+	12.9128i	−0.460366	+	0.910797i
$202$	−3.26605	−	1.88565i	−0.229798	−	0.132674i
$203$	3.64151	+	21.5173i	0.255584	+	1.51022i
$204$	−7.27195	+	0.404720i	−0.509139	+	0.0283361i
$205$	−1.63088	+	3.16518i	−0.113906	+	0.221066i
$206$	−8.77121	−	15.1922i	−0.611119	−	1.05849i
$207$	−7.65589	−	3.34939i	−0.532121	−	0.232799i
$208$	−12.3623	−	7.13740i	−0.857174	−	0.494890i
$209$	8.02203	+	13.8946i	0.554896	+	0.961108i
$210$	−15.2643	+	15.5498i	−1.05334	+	1.07304i
$211$	−6.77020	+	11.7263i	−0.466080	+	0.807274i	−0.999250	−	0.0387341i	$-0.987667\pi$
$211$	−6.77020	+	11.7263i	−0.466080	+	0.807274i	0.533169	+	0.846008i	$0.321001\pi$
$212$	2.68235	−	1.54866i	0.184225	−	0.106362i
$213$	−1.51949	−	0.768031i	−0.104114	−	0.0526246i
$214$	−6.60248	+	11.4358i	−0.451336	+	0.781737i
$215$	13.7609	−	8.84785i	0.938484	−	0.603418i
$216$	5.68615	−	0.957302i	0.386894	−	0.0651362i
$217$	24.6213	+	9.15387i	1.67140	+	0.621405i
$218$	−17.4435	+	10.0710i	−1.18142	+	0.682094i
$219$	0.332630	−	0.0185125i	0.0224770	−	0.00125096i
$220$	5.98714	−	11.6197i	0.403653	−	0.783400i
$221$	−8.86820			−0.596539
$222$	3.69682	−	2.41779i	0.248114	−	0.162272i
$223$	−0.744234	+	0.429683i	−0.0498376	+	0.0287737i	−0.524712	−	0.851280i	$-0.675827\pi$
$223$	−0.744234	+	0.429683i	−0.0498376	+	0.0287737i	0.474874	+	0.880054i	$0.342494\pi$
$224$	7.30844	−	19.6576i	0.488316	−	1.31343i
$225$	10.0079	+	11.1733i	0.667192	+	0.744886i
$226$	2.01601	−	3.49184i	0.134103	−	0.232274i
$227$	−17.4323	−	10.0645i	−1.15702	−	0.668006i	−0.206432	−	0.978461i	$-0.566185\pi$
$227$	−17.4323	−	10.0645i	−1.15702	−	0.668006i	−0.950588	+	0.310455i	$0.899519\pi$
$228$	−25.3017	+	16.5479i	−1.67565	+	1.09591i
$229$	−11.7038	−	20.2716i	−0.773409	−	1.33958i	−0.935684	−	0.352838i	$-0.885217\pi$
$229$	−11.7038	−	20.2716i	−0.773409	−	1.33958i	0.162276	−	0.986745i	$-0.448117\pi$
$230$	−7.16314	−	11.1407i	−0.472324	−	0.734595i
$231$	10.3589	−	2.35179i	0.681569	−	0.154736i
$232$	7.92695	−	4.57663i	0.520430	−	0.300470i
$233$	−17.4973	−	10.1020i	−1.14628	−	0.661807i	−0.198305	−	0.980140i	$-0.563544\pi$
$233$	−17.4973	−	10.1020i	−1.14628	−	0.661807i	−0.947979	+	0.318333i	$0.896877\pi$
$234$	33.7196	−	3.76498i	2.20432	−	0.246125i
$235$	0.733506	+	15.3273i	0.0478487	+	0.999845i
$236$	0.821399			0.0534685
$237$	−14.9676	−	7.56541i	−0.972248	−	0.491426i
$238$	−1.56535	−	9.24949i	−0.101467	−	0.599555i
$239$	3.36926	−	5.83574i	0.217940	−	0.377482i	−0.736238	−	0.676722i	$-0.763400\pi$
$239$	3.36926	−	5.83574i	0.217940	−	0.377482i	0.954178	+	0.299240i	$0.0967331\pi$
$240$	−9.49075	−	4.24038i	−0.612625	−	0.273715i
$241$	−8.28748	+	14.3543i	−0.533844	+	0.924645i	0.465375	+	0.885114i	$0.345920\pi$
$241$	−8.28748	+	14.3543i	−0.533844	+	0.924645i	−0.999218	+	0.0395308i	$0.987414\pi$
$242$	10.3620	−	5.98252i	0.666096	−	0.384571i
$243$	10.8428	−	11.1997i	0.695568	−	0.718461i
$244$	12.6989			0.812962
$245$	−12.3261	−	9.64719i	−0.787483	−	0.616336i
$246$	3.21017	+	4.90836i	0.204673	+	0.312945i
$247$	−31.8800	+	18.4059i	−2.02848	+	1.17114i
$248$		−	11.0175i		−	0.699609i
$249$	22.9487	−	1.27721i	1.45432	−	0.0809399i
$250$	3.39899	+	23.5304i	0.214971	+	1.48819i
$251$	−12.8791			−0.812925			−0.406462	−	0.913668i	$-0.633238\pi$
$251$	−12.8791			−0.812925			−0.406462	+	0.913668i	$0.633238\pi$
$252$	5.50944	+	19.2434i	0.347062	+	1.21222i
$253$			6.45688i			0.405941i
$254$	−0.560615			−0.0351761
$255$	−6.42335	+	0.666663i	−0.402246	+	0.0417480i
$256$	4.74080			0.296300
$257$	15.3731	−	8.87564i	0.958945	−	0.553647i	0.0630970	−	0.998007i	$-0.479902\pi$
$257$	15.3731	−	8.87564i	0.958945	−	0.553647i	0.895848	+	0.444360i	$0.146569\pi$
$258$	−1.49743	−	26.9056i	−0.0932259	−	1.67507i
$259$	2.02284	+	2.44472i	0.125693	+	0.151907i
$260$	26.6605	+	13.7370i	1.65341	+	0.851934i
$261$	9.91819	−	22.6706i	0.613921	−	1.40327i
$262$	−22.8849	+	13.2126i	−1.41383	+	0.816276i
$263$	−8.64716	−	4.99244i	−0.533207	−	0.307847i	0.209115	−	0.977891i	$-0.432942\pi$
$263$	−8.64716	−	4.99244i	−0.533207	−	0.307847i	−0.742321	+	0.670044i	$0.766275\pi$
$264$	−2.43867	−	3.72873i	−0.150089	−	0.229487i
$265$	2.31002	−	1.48528i	0.141903	−	0.0912398i
$266$	−24.8245	−	30.0018i	−1.52209	−	1.83953i
$267$	9.79655	−	6.40714i	0.599539	−	0.392111i
$268$			21.0661i			1.28682i
$269$	6.52402	+	11.2999i	0.397776	+	0.688969i	0.993451	−	0.114257i	$-0.0364487\pi$
$269$	6.52402	+	11.2999i	0.397776	+	0.688969i	−0.595675	+	0.803226i	$0.703115\pi$
$270$	24.1405	−	5.26188i	1.46914	−	0.320228i
$271$	1.99814	−	3.46087i	0.121378	−	0.210233i	−0.798933	−	0.601420i	$-0.794602\pi$
$271$	1.99814	−	3.46087i	0.121378	−	0.210233i	0.920311	+	0.391187i	$0.127935\pi$
$272$	3.87570	−	2.23764i	0.234999	−	0.135677i
$273$	5.39600	+	23.7678i	0.326581	+	1.43849i
$274$	−4.45809	+	7.72165i	−0.269323	+	0.466482i
$275$	4.81009	−	10.5449i	0.290060	−	0.635881i
$276$	−12.1482	+	0.676107i	−0.731236	+	0.0406969i
$277$	5.89300	+	3.40233i	0.354076	+	0.204426i	0.666479	−	0.745524i	$-0.267801\pi$
$277$	5.89300	+	3.40233i	0.354076	+	0.204426i	−0.312403	+	0.949950i	$0.601134\pi$
$278$	−31.8701	−	18.4002i	−1.91144	−	1.10357i
$279$	−17.6628	−	23.9827i	−1.05745	−	1.43580i
$280$	−1.99105	+	6.25587i	−0.118988	+	0.373860i
$281$	13.2100	+	22.8803i	0.788041	+	1.36493i	0.927166	+	0.374652i	$0.122238\pi$
$281$	13.2100	+	22.8803i	0.788041	+	1.36493i	−0.139125	+	0.990275i	$0.544429\pi$
$282$	22.5575	+	11.4018i	1.34328	+	0.678967i
$283$		−	9.90172i		−	0.588596i	−0.955714	−	0.294298i	$-0.904914\pi$
$283$		−	9.90172i		−	0.588596i	0.955714	−	0.294298i	$-0.0950858\pi$
$284$	−2.47892			−0.147097
$285$	−21.7074	+	15.7282i	−1.28584	+	0.931660i
$286$	−13.1081	−	22.7039i	−0.775100	−	1.34251i
$287$	−3.24591	+	2.68578i	−0.191600	+	0.158537i
$288$	−19.1477	+	14.1020i	−1.12829	+	0.830967i
$289$	−7.10987	+	12.3147i	−0.418228	+	0.724392i
$290$	32.9897	−	21.2114i	1.93722	−	1.24558i
$291$	5.57855	−	0.310474i	0.327020	−	0.0182003i
$292$	0.420070	−	0.242528i	0.0245828	−	0.0141929i
$293$	−1.19028	−	0.687210i	−0.0695370	−	0.0401472i	0.464828	−	0.885401i	$-0.346116\pi$
$293$	−1.19028	−	0.687210i	−0.0695370	−	0.0401472i	−0.534365	+	0.845254i	$0.679449\pi$
$294$	−23.8373	+	9.82333i	−1.39022	+	0.572908i
$295$	0.727483	−	0.0348145i	0.0423557	−	0.00202698i
$296$	0.665441	−	1.15258i	0.0386780	−	0.0669922i
$297$	−11.2862	−	4.20706i	−0.654894	−	0.244119i
$298$	2.20317	−	1.27200i	0.127626	−	0.0736849i
$299$	−14.8148			−0.856763
$300$	20.3432	+	7.94571i	1.17452	+	0.458746i
$301$	19.0859	−	3.23003i	1.10009	−	0.186176i
$302$	−4.79624	−	2.76911i	−0.275993	−	0.159345i
$303$	−2.57081	+	1.68136i	−0.147689	+	0.0965916i
$304$	9.28842	−	16.0880i	0.532728	−	0.922711i
$305$	11.2469	−	0.538234i	0.643997	−	0.0308192i
$306$	−4.26347	+	9.74525i	−0.243726	+	0.557099i
$307$		−	17.5144i		−	0.999597i	−0.866142	−	0.499799i	$-0.833407\pi$
$307$		−	17.5144i		−	0.999597i	0.866142	−	0.499799i	$-0.166593\pi$
$308$	11.9161	−	9.85978i	0.678982	−	0.561813i
$309$	−14.2666	+	0.794006i	−0.811598	+	0.0451694i
$310$	−2.25662	−	47.1544i	−0.128168	−	2.67819i
$311$	22.0262			1.24899			0.624494	−	0.781029i	$-0.285305\pi$
$311$	22.0262			1.24899			0.624494	+	0.781029i	$0.285305\pi$
$312$	8.55528	−	5.59533i	0.484348	−	0.316773i
$313$		−	27.2669i		−	1.54122i	−0.637308	−	0.770609i	$-0.719952\pi$
$313$		−	27.2669i		−	1.54122i	0.637308	−	0.770609i	$-0.280048\pi$
$314$	−46.1845			−2.60634
$315$	5.69513	+	16.8097i	0.320884	+	0.947118i
$316$	−24.4183			−1.37364
$317$			6.29492i			0.353558i	0.984251	+	0.176779i	$0.0565677\pi$
$317$			6.29492i			0.353558i	−0.984251	+	0.176779i	$0.943432\pi$
$318$	−0.251371	−	4.51661i	−0.0140962	−	0.253279i
$319$	−19.1201			−1.07052
$320$	−25.6587	+	1.22792i	−1.43436	+	0.0686430i
$321$	5.88716	+	9.00149i	0.328589	+	0.502414i
$322$	−2.61500	−	15.4518i	−0.145729	−	0.861094i
$323$		−	11.5408i		−	0.642149i
$324$	6.73352	−	21.6748i	0.374085	−	1.20416i
$325$	24.1945	+	11.0364i	1.34207	+	0.612189i
$326$	7.33777	−	12.7094i	0.406401	−	0.703908i
$327$	0.911669	+	16.3807i	0.0504154	+	0.905857i
$328$	1.53031	+	0.883524i	0.0844971	+	0.0487844i
$329$	−6.32714	+	17.0182i	−0.348826	+	0.938243i
$330$	−11.2011	−	15.4594i	−0.616603	−	0.851010i
$331$	−3.25676			−0.179008			−0.0895038	−	0.995986i	$-0.528528\pi$
$331$	−3.25676			−0.179008			−0.0895038	+	0.995986i	$0.528528\pi$
$332$	28.9815	−	16.7325i	1.59056	−	0.918313i
$333$	−0.399251	−	3.57573i	−0.0218788	−	0.195949i
$334$	3.19471	−	5.53340i	0.174807	−	0.302774i
$335$	0.892874	+	18.6575i	0.0487829	+	1.01937i
$336$	−8.35536	−	9.02580i	−0.455822	−	0.492398i
$337$	23.4709	+	13.5509i	1.27854	+	0.738165i	0.976580	−	0.215155i	$-0.0690258\pi$
$337$	23.4709	+	13.5509i	1.27854	+	0.738165i	0.301960	+	0.953321i	$0.402359\pi$
$338$	28.1520	−	16.2536i	1.53127	−	0.884078i
$339$	−1.79760	−	2.74853i	−0.0976320	−	0.149280i
$340$	−7.90884	+	5.08516i	−0.428917	+	0.275781i
$341$	−11.5071	+	19.9308i	−0.623143	+	1.07932i
$342$	4.89965	+	43.8818i	0.264943	+	2.37285i
$343$	−8.92690	−	16.2268i	−0.482007	−	0.876167i
$344$	−4.05949	−	7.03124i	−0.218873	−	0.379099i
$345$	−10.7306	+	1.11370i	−0.577714	+	0.0599594i
$346$	7.24765			0.389636
$347$			32.9831i			1.77062i	0.464997	+	0.885312i	$0.346055\pi$
$347$			32.9831i			1.77062i	−0.464997	+	0.885312i	$0.653945\pi$
$348$	−2.00208	−	35.9732i	−0.107323	−	1.92836i
$349$	−1.64149	−	2.84314i	−0.0878669	−	0.152190i	0.818742	−	0.574161i	$-0.194672\pi$
$349$	−1.64149	−	2.84314i	−0.0878669	−	0.152190i	−0.906609	+	0.421971i	$0.861338\pi$
$350$	−7.24027	+	27.1828i	−0.387009	+	1.45298i
$351$	9.65279	−	25.8954i	0.515228	−	1.38219i
$352$	15.9128	+	9.18724i	0.848153	+	0.489682i
$353$	5.53569	+	3.19603i	0.294635	+	0.170108i	0.640030	−	0.768350i	$-0.278922\pi$
$353$	5.53569	+	3.19603i	0.294635	+	0.170108i	−0.345395	+	0.938457i	$0.612255\pi$
$354$	0.541165	−	1.07065i	0.0287626	−	0.0569045i
$355$	−2.19548	+	0.105067i	−0.116524	+	0.00557639i
$356$	8.52172	−	14.7600i	0.451650	−	0.782281i
$357$	−7.29896	−	2.26066i	−0.386302	−	0.119647i
$358$	−7.53255	+	4.34892i	−0.398108	+	0.229848i
$359$	3.59845	−	6.23269i	0.189919	−	0.328949i	−0.755304	−	0.655374i	$-0.772511\pi$
$359$	3.59845	−	6.23269i	0.189919	−	0.328949i	0.945223	+	0.326425i	$0.105844\pi$
$360$	5.77607	−	4.69591i	0.304426	−	0.247496i
$361$	−14.4530	−	25.0334i	−0.760685	−	1.31754i
$362$		−	1.63144i		−	0.0857468i
$363$	−0.541562	−	9.73072i	−0.0284246	−	0.510730i
$364$	22.6225	+	27.3405i	1.18574	+	1.43303i
$365$	0.361762	−	0.232602i	0.0189355	−	0.0121750i
$366$	8.36644	−	16.5523i	0.437321	−	0.865204i
$367$	28.5244	+	16.4686i	1.48896	+	0.859652i	0.999921	−	0.0126087i	$-0.00401358\pi$
$367$	28.5244	+	16.4686i	1.48896	+	0.859652i	0.489041	+	0.872261i	$0.337347\pi$
$368$	6.47457	−	3.73809i	0.337510	−	0.194862i
$369$	4.74759	−	0.530095i	0.247150	−	0.0275957i
$370$	2.61199	−	5.06930i	0.135791	−	0.263540i
$371$	3.20392	−	0.542221i	0.166339	−	0.0281507i
$372$	−38.7035	−	19.5628i	−2.00668	−	1.01429i
$373$	−3.02764	+	1.74801i	−0.156765	+	0.0905083i	−0.576330	−	0.817217i	$-0.695516\pi$
$373$	−3.02764	+	1.74801i	−0.156765	+	0.0905083i	0.419565	+	0.907725i	$0.362183\pi$
$374$	8.21902			0.424995
$375$	18.3540	+	6.17499i	0.947797	+	0.318875i
$376$	7.61525			0.392726
$377$		−	43.8695i		−	2.25939i
$378$	28.7126	+	5.49694i	1.47682	+	0.282732i
$379$	26.7447			1.37378			0.686891	−	0.726761i	$-0.258975\pi$
$379$	26.7447			1.37378			0.686891	+	0.726761i	$0.258975\pi$
$380$	−17.8770	+	34.6953i	−0.917071	+	1.77983i
$381$	−0.205989	+	0.407532i	−0.0105531	+	0.0208785i
$382$			41.3214i			2.11419i
$383$	−5.72643	+	3.30616i	−0.292607	+	0.168937i	−0.639117	−	0.769110i	$-0.720700\pi$
$383$	−5.72643	+	3.30616i	−0.292607	+	0.168937i	0.346510	+	0.938046i	$0.387367\pi$
$384$	−6.70025	+	13.2559i	−0.341921	+	0.676463i
$385$	10.1357	−	9.23750i	0.516565	−	0.470787i
$386$	23.3307			1.18750
$387$	−20.1089	−	8.79748i	−1.02219	−	0.447201i
$388$	7.04503	−	4.06745i	0.357657	−	0.206493i
$389$	−0.253671	+	0.439372i	−0.0128616	+	0.0222770i	−0.872385	−	0.488820i	$-0.837427\pi$
$389$	−0.253671	+	0.439372i	−0.0128616	+	0.0222770i	0.859523	+	0.511097i	$0.170761\pi$
$390$	35.4703	−	25.7002i	1.79611	−	1.30138i
$391$	2.32228	−	4.02232i	0.117443	−	0.203417i
$392$	−5.07457	+	5.88124i	−0.256305	+	0.297048i
$393$	1.19606	+	21.4906i	0.0603332	+	1.08406i
$394$	−19.2777			−0.971199
$395$	−21.6264	+	1.03495i	−1.08814	+	0.0520742i
$396$	−17.4289	+	1.94604i	−0.875835	+	0.0977920i
$397$	−29.7582	−	17.1809i	−1.49352	−	0.862285i	−0.493550	−	0.869718i	$-0.664301\pi$
$397$	−29.7582	−	17.1809i	−1.49352	−	0.862285i	−0.999972	+	0.00743204i	$0.997634\pi$
$398$	2.93289	−	1.69331i	0.147013	−	0.0848778i
$399$	−30.9308	+	7.02222i	−1.54848	+	0.351550i
$400$	−13.3585	+	1.28151i	−0.667925	+	0.0640753i
$401$	16.1697	+	28.0067i	0.807475	+	1.39859i	0.914608	+	0.404343i	$0.132500\pi$
$401$	16.1697	+	28.0067i	0.807475	+	1.39859i	−0.107133	+	0.994245i	$0.534167\pi$
$402$	27.4586	+	13.8790i	1.36951	+	0.692224i
$403$	−45.7298	−	26.4021i	−2.27796	−	1.31518i
$404$	−2.23626	+	3.87332i	−0.111258	+	0.192705i
$405$	5.04496	−	19.4820i	0.250686	−	0.968068i
$406$	45.7557	−	7.74353i	2.27082	−	0.384305i
$407$	−2.40760	+	1.39003i	−0.119340	+	0.0689011i
$408$	0.178090	+	3.19991i	0.00881679	+	0.158419i
$409$	−5.44369			−0.269173			−0.134587	−	0.990902i	$-0.542971\pi$
$409$	−5.44369			−0.269173			−0.134587	+	0.990902i	$0.542971\pi$
$410$	6.73064	+	3.46801i	0.332402	+	0.171273i
$411$	3.97510	+	6.07794i	0.196077	+	0.299803i
$412$	−18.0170	+	10.4021i	−0.887632	+	0.512475i
$413$	0.807736	+	0.300306i	0.0397461	+	0.0147771i
$414$	−7.12236	+	16.2800i	−0.350045	+	0.800118i
$415$	24.9586	−	16.0477i	1.22517	−	0.787750i
$416$	−21.0794	+	36.5106i	−1.03350	+	1.79008i
$417$	−25.0859	+	16.4067i	−1.22846	+	0.803440i
$418$	29.5463	−	17.0586i	1.44516	−	0.834362i
$419$	−10.3024	+	17.8443i	−0.503307	+	0.871753i	0.496686	+	0.867930i	$0.334550\pi$
$419$	−10.3024	+	17.8443i	−0.503307	+	0.871753i	−0.999993	+	0.00382263i	$0.998783\pi$
$420$	18.4411	+	18.1025i	0.899832	+	0.883310i
$421$	2.17301	+	3.76376i	0.105906	+	0.183434i	0.914108	−	0.405471i	$-0.132892\pi$
$421$	2.17301	+	3.76376i	0.105906	+	0.183434i	−0.808202	+	0.588905i	$0.799559\pi$
$422$	24.9356	+	14.3966i	1.21385	+	0.700816i
$423$	16.5768	−	12.2085i	0.805990	−	0.593598i
$424$	−0.681461	−	1.18032i	−0.0330947	−	0.0573216i
$425$	−6.78903	+	4.83895i	−0.329317	+	0.234723i
$426$	−1.63319	+	3.23114i	−0.0791284	+	0.156549i
$427$	12.4876	+	4.64274i	0.604319	+	0.224678i
$428$	13.5622	+	7.83012i	0.655552	+	0.378483i
$429$	−21.3207	+	1.18660i	−1.02937	+	0.0572897i
$430$	−18.8146	−	29.2620i	−0.907323	−	1.41114i
$431$	4.34107	+	7.51895i	0.209102	+	0.362175i	0.951432	−	0.307859i	$-0.0996127\pi$
$431$	4.34107	+	7.51895i	0.209102	+	0.362175i	−0.742330	+	0.670034i	$0.766279\pi$
$432$	2.31537	+	13.7528i	0.111398	+	0.661680i
$433$			22.4727i			1.07997i	0.841675	+	0.539985i	$0.181570\pi$
$433$			22.4727i			1.07997i	−0.841675	+	0.539985i	$0.818430\pi$
$434$	19.4654	−	52.3563i	0.934368	−	2.51318i
$435$	−3.29787	−	31.7752i	−0.158121	−	1.52351i
$436$	11.9436	+	20.6869i	0.571993	+	0.990721i
$437$		−	19.2796i		−	0.922269i
$438$	−0.0393661	−	0.707325i	−0.00188099	−	0.0337973i
$439$	41.6673			1.98867			0.994336	−	0.106286i	$-0.0338961\pi$
$439$	41.6673			1.98867			0.994336	+	0.106286i	$0.0338961\pi$
$440$	−5.11306	−	2.63454i	−0.243756	−	0.125597i
$441$	−1.61766	+	20.9376i	−0.0770312	+	0.997029i
$442$			18.8579i			0.896979i
$443$			13.3970i			0.636513i	0.948005	+	0.318257i	$0.103097\pi$
$443$			13.3970i			0.636513i	−0.948005	+	0.318257i	$0.896903\pi$
$444$	−2.86735	−	4.38419i	−0.136078	−	0.208064i
$445$	6.92178	−	13.4336i	0.328124	−	0.636815i
$446$	0.913707	+	1.58259i	0.0432653	+	0.0749376i
$447$	−0.115147	−	2.06894i	−0.00544625	−	0.0978574i
$448$	−28.4892	−	10.5919i	−1.34599	−	0.500422i
$449$	−36.2695			−1.71166			−0.855832	−	0.517253i	$-0.826955\pi$
$449$	−36.2695			−1.71166			−0.855832	+	0.517253i	$0.826955\pi$
$450$	23.7596	−	21.2814i	1.12004	−	1.00322i
$451$	−1.84558	−	3.19663i	−0.0869048	−	0.150523i
$452$	−4.14110	−	2.39086i	−0.194781	−	0.112457i
$453$	−3.77527	+	2.46910i	−0.177378	+	0.116009i
$454$	−21.4019	+	37.0691i	−1.00444	+	1.73974i
$455$	21.1947	+	23.2557i	0.993624	+	1.09024i
$456$	7.28162	+	11.1336i	0.340993	+	0.521380i
$457$		−	20.0627i		−	0.938494i	−0.883067	−	0.469247i	$-0.844525\pi$
$457$		−	20.0627i		−	0.938494i	0.883067	−	0.469247i	$-0.155475\pi$
$458$	−43.1068	+	24.8877i	−2.01425	+	1.16293i
$459$	5.51765	+	6.68000i	0.257542	+	0.311796i
$460$	−13.2121	+	8.49503i	−0.616020	+	0.396083i
$461$	−10.7895	−	18.6880i	−0.502518	−	0.870387i	−0.999996	−	0.00291020i	$-0.999074\pi$
$461$	−10.7895	−	18.6880i	−0.502518	−	0.870387i	0.497478	−	0.867477i	$-0.334260\pi$
$462$	−5.00100	−	22.0279i	−0.232668	−	1.02483i
$463$	−11.5858	−	6.68906i	−0.538438	−	0.310867i	0.206008	−	0.978550i	$-0.433953\pi$
$463$	−11.5858	−	6.68906i	−0.538438	−	0.310867i	−0.744445	+	0.667683i	$0.767286\pi$
$464$	11.0692	+	19.1724i	0.513875	+	0.890058i
$465$	−35.1074	−	15.6857i	−1.62807	−	0.727405i
$466$	−21.4816	+	37.2073i	−0.995118	+	1.72359i
$467$	27.9477	+	16.1356i	1.29327	+	0.746668i	0.979232	−	0.202744i	$-0.0649859\pi$
$467$	27.9477	+	16.1356i	1.29327	+	0.746668i	0.314035	+	0.949412i	$0.398319\pi$
$468$	−4.46503	−	39.9893i	−0.206396	−	1.84850i
$469$	−7.70183	+	20.7157i	−0.355637	+	0.956562i
$470$	32.5930	−	1.55977i	1.50340	−	0.0719470i
$471$	−16.9697	+	33.5733i	−0.781924	+	1.54697i
$472$		−	0.361443i		−	0.0166368i
$473$			16.9596i			0.779802i
$474$	−16.0876	+	31.8280i	−0.738927	+	1.46191i
$475$	−14.3625	+	31.4860i	−0.658995	+	1.44468i
$476$	−10.9693	+	1.85641i	−0.502777	+	0.0850883i
$477$	−3.37565	−	1.47682i	−0.154561	−	0.0676190i
$478$	−12.4095	−	7.16462i	−0.567597	−	0.327702i
$479$	−11.5053	+	19.9278i	−0.525692	+	0.910525i	0.473860	+	0.880600i	$0.342860\pi$
$479$	−11.5053	+	19.9278i	−0.525692	+	0.910525i	−0.999552	+	0.0299248i	$0.990473\pi$
$480$	−12.5234	+	28.0297i	−0.571613	+	1.27938i
$481$	−3.18931	−	5.52405i	−0.145420	−	0.251875i
$482$	30.5240	+	17.6230i	1.39033	+	0.802708i
$483$	−12.1933	−	3.77655i	−0.554815	−	0.171839i
$484$	−7.09489	−	12.2887i	−0.322495	−	0.558577i
$485$	6.06712	−	3.90099i	0.275494	−	0.177135i
$486$	−23.8158	−	23.0569i	−1.08030	−	1.04588i
$487$	6.38630	−	3.68713i	0.289391	−	0.167080i	−0.348276	−	0.937392i	$-0.613233\pi$
$487$	6.38630	−	3.68713i	0.289391	−	0.167080i	0.637667	+	0.770312i	$0.279900\pi$
$488$		−	5.58794i		−	0.252954i
$489$	−6.54279	−	10.0039i	−0.295875	−	0.452394i
$490$	−20.5144	+	26.2109i	−0.926747	+	1.18409i
$491$	16.9639	−	29.3823i	0.765570	−	1.32601i	−0.174374	−	0.984679i	$-0.555790\pi$
$491$	16.9639	−	29.3823i	0.765570	−	1.32601i	0.939945	−	0.341327i	$-0.110876\pi$
$492$	5.82100	−	3.80705i	0.262431	−	0.171635i
$493$	11.9108	+	6.87673i	0.536438	+	0.309712i
$494$	39.1396	+	67.7918i	1.76097	+	3.05010i
$495$	−15.3537	+	2.46225i	−0.690095	+	0.110670i
$496$	26.6473			1.19650
$497$	−2.43768	−	0.906298i	−0.109345	−	0.0406530i
$498$	−2.71594	−	48.7997i	−0.121704	−	2.18677i
$499$	7.64494	+	13.2414i	0.342235	+	0.592768i	0.984847	−	0.173423i	$-0.0554829\pi$
$499$	7.64494	+	13.2414i	0.342235	+	0.592768i	−0.642613	+	0.766191i	$0.722150\pi$
$500$	27.9055	−	4.03098i	1.24797	−	0.180271i
$501$	−2.84859	−	4.35551i	−0.127266	−	0.194590i
$502$			27.3871i			1.22234i
$503$			37.1071i			1.65452i	0.561817	+	0.827261i	$0.310102\pi$
$503$			37.1071i			1.65452i	−0.561817	+	0.827261i	$0.689898\pi$
$504$	8.46776	−	2.42434i	0.377184	−	0.107989i
$505$	−1.81641	+	3.52524i	−0.0808291	+	0.156871i
$506$	13.7303			0.610387
$507$	−1.47134	−	26.4368i	−0.0653445	−	1.17410i
$508$			0.664854i			0.0294981i
$509$	−13.4011	−	23.2114i	−0.593994	−	1.02883i	−0.993688	−	0.112179i	$-0.964217\pi$
$509$	−13.4011	−	23.2114i	−0.593994	−	1.02883i	0.399694	−	0.916648i	$-0.369116\pi$
$510$	1.41763	+	13.6590i	0.0627739	+	0.604832i
$511$	0.501752	−	0.0849147i	0.0221962	−	0.00375641i
$512$		−	27.2319i		−	1.20349i
$513$	33.6996	+	12.5619i	1.48787	+	0.554621i
$514$	−18.8737	−	32.6903i	−0.832485	−	1.44191i
$515$	−15.5161	+	9.97640i	−0.683720	+	0.439612i
$516$	−31.9083	+	1.77586i	−1.40469	+	0.0781777i
$517$	−13.7762	−	7.95367i	−0.605875	−	0.349802i
$518$	5.19860	−	4.30150i	0.228414	−	0.188997i
$519$	2.66303	−	5.26859i	0.116894	−	0.231265i
$520$	6.04476	−	11.7315i	0.265080	−	0.514461i
$521$	−8.92581	−	15.4600i	−0.391047	−	0.677313i	0.601541	−	0.798842i	$-0.294554\pi$
$521$	−8.92581	−	15.4600i	−0.391047	−	0.677313i	−0.992588	+	0.121529i	$0.961220\pi$
$522$	−48.2082	−	21.0907i	−2.11001	−	0.923114i
$523$	−17.0345	−	9.83486i	−0.744865	−	0.430048i	0.0789702	−	0.996877i	$-0.474837\pi$
$523$	−17.0345	−	9.83486i	−0.744865	−	0.430048i	−0.823836	+	0.566829i	$0.808170\pi$
$524$	15.6693	+	27.1400i	0.684516	+	1.18562i
$525$	17.0998	+	15.2511i	0.746298	+	0.665611i
$526$	−10.6162	+	18.3879i	−0.462890	+	0.801749i
$527$	14.3367	−	8.27729i	0.624516	−	0.360564i
$528$	9.01845	−	5.89825i	0.392478	−	0.256689i
$529$	−7.62049	+	13.1991i	−0.331326	+	0.573873i
$530$	−3.15839	−	4.91218i	−0.137192	−	0.213371i
$531$	−0.579454	−	0.786786i	−0.0251462	−	0.0341436i
$532$	−35.5803	+	29.4403i	−1.54260	+	1.27640i
$533$	7.33442	−	4.23453i	0.317689	−	0.183418i
$534$	−13.6246	−	20.8320i	−0.589592	−	0.901489i
$535$	12.3434	+	6.36003i	0.533651	+	0.274968i
$536$	9.26980			0.400395
$537$	0.393682	+	7.07363i	0.0169886	+	0.305250i
$538$	24.0289	−	13.8731i	1.03596	−	0.598111i
$539$	15.3226	−	5.33922i	0.659993	−	0.229976i
$540$	−6.24025	−	28.6291i	−0.268538	−	1.23200i
$541$	14.0625	−	24.3569i	0.604593	−	1.04719i	−0.387522	−	0.921860i	$-0.626669\pi$
$541$	14.0625	−	24.3569i	0.604593	−	1.04719i	0.992116	−	0.125326i	$-0.0399977\pi$
$542$	−7.35943	−	4.24897i	−0.316114	−	0.182509i
$543$	−1.18596	−	0.599447i	−0.0508943	−	0.0257247i
$544$	−6.60858	−	11.4464i	−0.283340	−	0.490760i
$545$	11.4548	+	17.8154i	0.490669	+	0.763127i
$546$	50.5414	−	11.4744i	2.16297	−	0.491059i
$547$	10.3490	−	5.97497i	0.442490	−	0.255471i	−0.262164	−	0.965023i	$-0.584436\pi$
$547$	10.3490	−	5.97497i	0.442490	−	0.255471i	0.704653	+	0.709552i	$0.251103\pi$
$548$	9.15738	+	5.28702i	0.391184	+	0.225850i
$549$	−8.95839	−	12.1637i	−0.382335	−	0.519136i
$550$	−22.4234	−	10.2285i	−0.956135	−	0.436144i
$551$	57.0906			2.43214
$552$	0.297510	+	5.34562i	0.0126629	+	0.227525i
$553$	−24.0121	−	8.92740i	−1.02110	−	0.379632i
$554$	7.23493	−	12.5313i	0.307383	−	0.532402i
$555$	−2.72533	−	3.76138i	−0.115684	−	0.159662i
$556$	−21.8215	+	37.7959i	−0.925437	+	1.60290i
$557$	22.5457	−	13.0167i	0.955291	−	0.551537i	0.0605702	−	0.998164i	$-0.480708\pi$
$557$	22.5457	−	13.0167i	0.955291	−	0.551537i	0.894720	+	0.446627i	$0.147375\pi$
$558$	−50.9983	+	37.5594i	−2.15893	+	1.59001i
$559$	−38.9125			−1.64582
$560$	−15.1307	−	4.81562i	−0.639389	−	0.203497i
$561$	3.01994	−	5.97471i	0.127502	−	0.252253i
$562$	48.6542	−	28.0905i	2.05235	−	1.18493i
$563$			15.2899i			0.644393i	0.946673	+	0.322197i	$0.104421\pi$
$563$			15.2899i			0.644393i	−0.946673	+	0.322197i	$0.895579\pi$
$564$	13.5218	−	26.7518i	0.569371	−	1.12645i
$565$	−3.76895	−	1.94198i	−0.158561	−	0.0816998i
$566$	−21.0557			−0.885035
$567$	14.5459	−	18.8525i	0.610870	−	0.791731i
$568$			1.09081i			0.0457692i
$569$	19.6027			0.821787			0.410894	−	0.911683i	$-0.365217\pi$
$569$	19.6027			0.821787			0.410894	+	0.911683i	$0.365217\pi$
$570$	33.4455	+	46.1601i	1.40088	+	1.93343i
$571$	19.0706			0.798078			0.399039	−	0.916934i	$-0.369344\pi$
$571$	19.0706			0.798078			0.399039	+	0.916934i	$0.369344\pi$
$572$	−26.9254	+	15.5454i	−1.12581	+	0.649986i
$573$	30.0381	+	15.1829i	1.25486	+	0.634273i
$574$	5.71122	+	6.90232i	0.238382	+	0.288097i
$575$	−11.3415	+	8.08373i	−0.472971	+	0.337115i
$576$	20.4376	+	27.7503i	0.851568	+	1.15626i
$577$	−25.1403	+	14.5147i	−1.04660	+	0.604256i	−0.921696	−	0.387912i	$-0.873196\pi$
$577$	−25.1403	+	14.5147i	−1.04660	+	0.604256i	−0.124906	+	0.992169i	$0.539863\pi$
$578$	26.1867	+	15.1189i	1.08922	+	0.628863i
$579$	8.57248	−	16.9600i	0.356260	−	0.704832i
$580$	−25.1554	−	39.1237i	−1.04452	−	1.62452i
$581$	34.6168	−	5.85843i	1.43615	−	0.243049i
$582$	−0.660212	−	11.8626i	−0.0273666	−	0.491720i
$583$			2.84698i			0.117910i
$584$	−0.106720	−	0.184845i	−0.00441612	−	0.00764895i
$585$	−5.64943	−	35.2278i	−0.233575	−	1.45649i
$586$	−1.46133	+	2.53109i	−0.0603669	+	0.104558i
$587$	15.6684	−	9.04613i	0.646702	−	0.373374i	−0.140489	−	0.990082i	$-0.544868\pi$
$587$	15.6684	−	9.04613i	0.646702	−	0.373374i	0.787192	+	0.616708i	$0.211534\pi$
$588$	11.6498	+	28.2695i	0.480431	+	1.16581i
$589$	34.3590	−	59.5116i	1.41574	−	2.45213i
$590$	−0.0740318	−	1.54697i	−0.00304784	−	0.0636876i
$591$	−7.08329	+	14.0137i	−0.291367	+	0.576447i
$592$	2.78767	+	1.60946i	0.114573	+	0.0661485i
$593$	25.1013	+	14.4922i	1.03079	+	0.595125i	0.917210	−	0.398404i	$-0.130436\pi$
$593$	25.1013	+	14.4922i	1.03079	+	0.595125i	0.113577	+	0.993529i	$0.463769\pi$
$594$	−8.94617	+	23.9998i	−0.367066	+	0.984723i
$595$	−9.63643	+	2.10908i	−0.395055	+	0.0864638i
$596$	−1.50851	−	2.61282i	−0.0617910	−	0.107025i
$597$	−0.153285	−	2.75421i	−0.00627354	−	0.112722i
$598$			31.5032i			1.28826i
$599$	−9.70851			−0.396679			−0.198340	−	0.980133i	$-0.563555\pi$
$599$	−9.70851			−0.396679			−0.198340	+	0.980133i	$0.563555\pi$
$600$	3.49638	−	8.95170i	0.142739	−	0.365452i
$601$	−9.00931	−	15.6046i	−0.367498	−	0.636524i	0.621676	−	0.783274i	$-0.286452\pi$
$601$	−9.00931	−	15.6046i	−0.367498	−	0.636524i	−0.989174	+	0.146750i	$0.953119\pi$
$602$	−6.86855	−	40.5855i	−0.279941	−	1.65414i
$603$	20.1784	−	14.8610i	0.821728	−	0.605188i
$604$	−3.28399	+	5.68804i	−0.133624	+	0.231443i
$605$	−6.80453	−	10.5829i	−0.276643	−	0.430258i
$606$	3.57535	+	5.46673i	0.145239	+	0.222071i
$607$	3.02303	−	1.74535i	0.122701	−	0.0708415i	−0.437393	−	0.899270i	$-0.644098\pi$
$607$	3.02303	−	1.74535i	0.122701	−	0.0708415i	0.560094	+	0.828429i	$0.310765\pi$
$608$	−47.5140	−	27.4322i	−1.92695	−	1.11252i
$609$	11.1831	−	36.1067i	0.453162	−	1.46312i
$610$	−1.14454	−	23.9162i	−0.0463409	−	0.968338i
$611$	18.2491	−	31.6084i	0.738279	−	1.27874i
$612$	11.5573	+	5.05620i	0.467174	+	0.204385i
$613$	−8.32733	+	4.80779i	−0.336338	+	0.194185i	−0.658651	−	0.752448i	$-0.728873\pi$
$613$	−8.32733	+	4.80779i	−0.336338	+	0.194185i	0.322314	+	0.946633i	$0.395539\pi$
$614$	−37.2437			−1.50303
$615$	4.99409	−	3.61849i	0.201381	−	0.145911i
$616$	−4.33864	−	5.24348i	−0.174809	−	0.211266i
$617$	−27.4106	−	15.8255i	−1.10351	−	0.637112i	−0.166369	−	0.986064i	$-0.553204\pi$
$617$	−27.4106	−	15.8255i	−1.10351	−	0.637112i	−0.937141	+	0.348952i	$0.886538\pi$
$618$	1.68843	+	30.3374i	0.0679185	+	1.22035i
$619$	−10.0769	+	17.4537i	−0.405025	+	0.701524i	−0.994324	−	0.106391i	$-0.966070\pi$
$619$	−10.0769	+	17.4537i	−0.405025	+	0.701524i	0.589299	+	0.807915i	$0.299404\pi$
$620$	−55.9221	+	2.67621i	−2.24589	+	0.107479i
$621$	9.21753	+	11.1593i	0.369887	+	0.447808i
$622$		−	46.8379i		−	1.87803i
$623$	13.7763	−	11.3990i	0.551935	−	0.456690i
$624$	13.5331	+	20.6921i	0.541757	+	0.828349i
$625$	24.5440	−	4.75285i	0.981762	−	0.190114i
$626$	−57.9822			−2.31743
$627$	−1.54421	−	27.7462i	−0.0616699	−	1.10808i
$628$			54.7719i			2.18564i
$629$	1.99975			0.0797354
$630$	35.7452	−	12.1105i	1.42412	−	0.482493i
$631$	−8.91410			−0.354865			−0.177432	−	0.984133i	$-0.556779\pi$
$631$	−8.91410			−0.354865			−0.177432	+	0.984133i	$0.556779\pi$
$632$			10.7449i			0.427409i
$633$	19.6276	−	12.8369i	0.780127	−	0.510219i
$634$	13.3859			0.531623
$635$	0.0281794	+	0.588836i	0.00111827	+	0.0233673i
$636$	−5.35641	+	0.298111i	−0.212395	+	0.0118209i
$637$	12.2504	+	35.1566i	0.485380	+	1.39296i
$638$			40.6581i			1.60967i
$639$	1.74875	+	2.37445i	0.0691793	+	0.0939320i
$640$	0.916600	+	19.1533i	0.0362318	+	0.757099i
$641$	20.1407	−	34.8847i	0.795509	−	1.37786i	−0.127006	−	0.991902i	$-0.540537\pi$
$641$	20.1407	−	34.8847i	0.795509	−	1.37786i	0.922515	−	0.385960i	$-0.126130\pi$
$642$	19.1414	−	12.5188i	0.755449	−	0.494079i
$643$	−15.8671	−	9.16086i	−0.625736	−	0.361269i	0.153363	−	0.988170i	$-0.450990\pi$
$643$	−15.8671	−	9.16086i	−0.625736	−	0.361269i	−0.779099	+	0.626901i	$0.784323\pi$
$644$	−18.3248	+	3.10123i	−0.722099	+	0.122206i
$645$	−28.1848	+	2.92523i	−1.10977	+	0.115181i
$646$	−24.5412			−0.965560
$647$	4.60456	−	2.65844i	0.181024	−	0.104514i	−0.406750	−	0.913540i	$-0.633338\pi$
$647$	4.60456	−	2.65844i	0.181024	−	0.104514i	0.587774	+	0.809025i	$0.300005\pi$
$648$	−9.53766	−	2.96298i	−0.374675	−	0.116397i
$649$	−0.377506	+	0.653860i	−0.0148184	+	0.0256662i
$650$	23.4685	−	51.4487i	0.920510	−	2.01798i
$651$	−30.9075	−	33.3875i	−1.21136	−	1.30856i
$652$	−15.0725	−	8.70213i	−0.590286	−	0.340802i
$653$	−30.1884	+	17.4293i	−1.18136	+	0.682060i	−0.956329	−	0.292291i	$-0.905582\pi$
$653$	−30.1884	+	17.4293i	−1.18136	+	0.682060i	−0.225033	+	0.974351i	$0.572249\pi$
$654$	34.8331	−	1.93863i	1.36208	−	0.0758065i
$655$	15.0280	+	23.3728i	0.587194	+	0.913250i
$656$	−2.13693	+	3.70126i	−0.0834329	+	0.144510i
$657$	−0.528645	−	0.231278i	−0.0206244	−	0.00902302i
$658$	36.1886	+	13.4544i	1.41078	+	0.524508i
$659$	−23.9549	−	41.4911i	−0.933149	−	1.61626i	−0.777901	−	0.628387i	$-0.783716\pi$
$659$	−23.9549	−	41.4911i	−0.933149	−	1.61626i	−0.155248	−	0.987875i	$-0.549618\pi$
$660$	−18.3338	+	13.2838i	−0.713643	+	0.517073i
$661$	−1.90076			−0.0739308			−0.0369654	−	0.999317i	$-0.511769\pi$
$661$	−1.90076			−0.0739308			−0.0369654	+	0.999317i	$0.511769\pi$
$662$			6.92538i			0.269163i
$663$	13.7085	+	6.92902i	0.532395	+	0.269101i
$664$	−7.36285	−	12.7528i	−0.285734	−	0.494906i
$665$	−30.2643	+	27.5823i	−1.17360	+	1.06959i
$666$	−7.60367	+	0.848992i	−0.294636	+	0.0328978i
$667$	19.8977	+	11.4880i	0.770443	+	0.444816i
$668$	−6.56226	−	3.78872i	−0.253902	−	0.146590i
$669$	1.48617	−	0.0827125i	0.0574585	−	0.00319785i
$670$	39.6745	−	1.89866i	1.53276	−	0.0733518i
$671$	−5.83627	+	10.1087i	−0.225307	+	0.390242i
$672$	−26.6566	+	24.6765i	−1.02830	+	0.951917i
$673$	13.1692	−	7.60322i	0.507634	−	0.293083i	−0.224226	−	0.974537i	$-0.571986\pi$
$673$	13.1692	−	7.60322i	0.507634	−	0.293083i	0.731861	+	0.681454i	$0.238652\pi$
$674$	28.8155	−	49.9100i	1.10993	−	1.92246i
$675$	−6.74019	−	25.0912i	−0.259430	−	0.965762i
$676$	−19.2757	−	33.3865i	−0.741373	−	1.28410i
$677$		−	7.37190i		−	0.283325i	−0.989915	−	0.141662i	$-0.954755\pi$
$677$		−	7.37190i		−	0.283325i	0.989915	−	0.141662i	$-0.0452448\pi$
$678$	−5.84466	+	3.82252i	−0.224463	+	0.146803i
$679$	8.41491	−	1.42411i	0.322935	−	0.0546523i
$680$	2.23764	+	3.48016i	0.0858096	+	0.133458i
$681$	19.0832	+	29.1782i	0.731268	+	1.11811i
$682$	42.3822	+	24.4694i	1.62290	+	0.936982i
$683$	12.6407	−	7.29813i	0.483684	−	0.279255i	−0.238266	−	0.971200i	$-0.576579\pi$
$683$	12.6407	−	7.29813i	0.483684	−	0.279255i	0.721951	+	0.691945i	$0.243246\pi$
$684$	52.0410	−	5.81067i	1.98984	−	0.222177i
$685$	8.33444	+	4.29439i	0.318443	+	0.164080i
$686$	−34.5058	+	18.9827i	−1.31744	+	0.724764i
$687$	2.25294	+	40.4805i	0.0859550	+	1.54443i
$688$	17.0060	−	9.81844i	0.648349	−	0.374325i
$689$	−6.53218			−0.248856
$690$	2.36824	+	22.8181i	0.0901572	+	0.868672i
$691$	−31.9777			−1.21649			−0.608244	−	0.793750i	$-0.708126\pi$
$691$	−31.9777			−1.21649			−0.608244	+	0.793750i	$0.708126\pi$
$692$		−	8.59525i		−	0.326742i
$693$	−17.8505	−	4.45839i	−0.678083	−	0.169360i
$694$	70.1374			2.66238
$695$	−17.7245	+	34.3993i	−0.672330	+	1.30484i
$696$	−15.8294	+	0.880984i	−0.600012	+	0.0333936i
$697$			2.65512i			0.100570i
$698$	−6.04584	+	3.49057i	−0.228839	+	0.132120i
$699$	19.1543	+	29.2870i	0.724482	+	1.10774i
$700$	32.2370	+	8.58650i	1.21845	+	0.324539i
$701$	10.2924			0.388739			0.194369	−	0.980928i	$-0.437734\pi$
$701$	10.2924			0.388739			0.194369	+	0.980928i	$0.437734\pi$
$702$	−55.0656	−	20.5263i	−2.07832	−	0.774716i
$703$	7.18885	−	4.15049i	0.271133	−	0.156539i
$704$	13.3148	−	23.0620i	0.501821	−	0.869180i
$705$	10.8419	−	24.2662i	0.408330	−	0.913918i
$706$	6.79625	−	11.7715i	0.255780	−	0.443024i
$707$	−3.61516	+	2.99131i	−0.135962	+	0.112500i
$708$	−1.26972	−	0.641787i	−0.0477192	−	0.0241198i
$709$	−13.4400			−0.504750			−0.252375	−	0.967630i	$-0.581212\pi$
$709$	−13.4400			−0.504750			−0.252375	+	0.967630i	$0.581212\pi$
$710$	0.223422	+	4.66862i	0.00838487	+	0.175210i
$711$	17.2258	+	23.3893i	0.646019	+	0.877168i
$712$	−6.49492	−	3.74984i	−0.243407	−	0.140531i
$713$	23.9502	−	13.8277i	0.896943	−	0.517850i
$714$	−4.80721	+	15.5210i	−0.179905	+	0.580858i
$715$	−23.1880	+	14.9092i	−0.867182	+	0.557573i
$716$	5.15754	+	8.93313i	0.192746	+	0.333847i
$717$	−9.76789	+	6.38840i	−0.364788	+	0.238579i
$718$	−13.2536	−	7.65197i	−0.494620	−	0.285569i
$719$	22.6128	−	39.1665i	0.843314	−	1.46066i	−0.0437630	−	0.999042i	$-0.513935\pi$
$719$	22.6128	−	39.1665i	0.843314	−	1.46066i	0.887077	−	0.461621i	$-0.152732\pi$
$720$	11.3577	+	13.9702i	0.423277	+	0.520640i
$721$	−21.5203	+	3.64202i	−0.801458	+	0.135636i
$722$	−53.2325	+	30.7338i	−1.98111	+	1.14379i
$723$	24.0264	−	15.7137i	0.893551	−	0.584400i
$724$	−1.93479			−0.0719059
$725$	−23.9375	−	33.5842i	−0.889015	−	1.24729i
$726$	−20.6920	+	1.15161i	−0.767953	+	0.0427404i
$727$	−25.0004	+	14.4340i	−0.927212	+	0.535326i	−0.885929	−	0.463821i	$-0.846478\pi$
$727$	−25.0004	+	14.4340i	−0.927212	+	0.535326i	−0.0412831	+	0.999147i	$0.513145\pi$
$728$	12.0308	−	9.95467i	0.445890	−	0.368945i
$729$	−25.5116	+	8.84069i	−0.944874	+	0.327433i
$730$	−0.494621	−	0.769273i	−0.0183067	−	0.0284721i
$731$	6.09969	−	10.5650i	0.225605	−	0.390760i
$732$	−19.6300	−	9.92206i	−0.725546	−	0.366730i
$733$	24.9858	−	14.4256i	0.922872	−	0.532821i	0.0383220	−	0.999265i	$-0.487799\pi$
$733$	24.9858	−	14.4256i	0.922872	−	0.532821i	0.884550	+	0.466445i	$0.154465\pi$
$734$	35.0198	−	60.6561i	1.29261	−	2.23886i
$735$	11.5160	+	24.5435i	0.424775	+	0.905299i
$736$	−11.0400	−	19.1218i	−0.406940	−	0.704840i
$737$	−16.7693	−	9.68176i	−0.617705	−	0.356632i
$738$	−1.12723	−	10.0956i	−0.0414939	−	0.371624i
$739$	9.92303	+	17.1872i	0.365025	+	0.632241i	0.988780	−	0.149378i	$-0.0477273\pi$
$739$	9.92303	+	17.1872i	0.365025	+	0.632241i	−0.623756	+	0.781619i	$0.714394\pi$
$740$	−6.01186	−	3.09766i	−0.221001	−	0.113872i
$741$	63.6615	−	3.54308i	2.33867	−	0.130158i
$742$	−1.15301	−	6.81303i	−0.0423285	−	0.250114i
$743$	−39.6207	−	22.8750i	−1.45354	−	0.839202i	−0.454861	−	0.890563i	$-0.650311\pi$
$743$	−39.6207	−	22.8750i	−1.45354	−	0.839202i	−0.998680	+	0.0513604i	$0.983644\pi$
$744$	−8.60831	+	17.0309i	−0.315596	+	0.624382i
$745$	−1.44677	−	2.25014i	−0.0530057	−	0.0824386i
$746$	3.71707	+	6.43816i	0.136092	+	0.235718i
$747$	−36.4723	−	15.9563i	−1.33445	−	0.583811i
$748$		−	9.74724i		−	0.356394i
$749$	10.4739	+	12.6582i	0.382707	+	0.462522i
$750$	13.1309	−	39.0291i	0.479473	−	1.42514i
$751$	−5.98885	−	10.3730i	−0.218536	−	0.378516i	0.735824	−	0.677172i	$-0.236795\pi$
$751$	−5.98885	−	10.3730i	−0.218536	−	0.378516i	−0.954361	+	0.298657i	$0.903461\pi$
$752$			18.4185i			0.671655i
$753$	19.9087	+	10.0629i	0.725512	+	0.366713i
$754$	−93.2870			−3.39731
$755$	−2.66743	+	5.17688i	−0.0970776	+	0.188406i
$756$	6.51902	−	34.0513i	0.237095	−	1.23843i
$757$			47.6984i			1.73363i	0.498630	+	0.866815i	$0.333836\pi$
$757$			47.6984i			1.73363i	−0.498630	+	0.866815i	$0.666164\pi$
$758$		−	56.8716i		−	2.06567i
$759$	5.04498	−	9.98108i	0.183121	−	0.362290i
$760$	15.2671	+	7.86649i	0.553796	+	0.285348i
$761$	−9.68257	−	16.7707i	−0.350993	−	0.607938i	0.635431	−	0.772158i	$-0.280823\pi$
$761$	−9.68257	−	16.7707i	−0.350993	−	0.607938i	−0.986424	+	0.164220i	$0.947489\pi$
$762$	0.866602	+	0.438027i	0.0313937	+	0.0158681i
$763$	4.18173	+	24.7094i	0.151389	+	0.894539i
$764$	49.0046			1.77292
$765$	10.4501	+	3.98825i	0.377826	+	0.144195i
$766$	7.03043	+	12.1771i	0.254020	+	0.439975i
$767$	−1.50023	−	0.866159i	−0.0541702	−	0.0312752i
$768$	−7.32836	−	3.70415i	−0.264439	−	0.133662i
$769$	5.83789	−	10.1115i	0.210520	−	0.364631i	−0.741358	−	0.671110i	$-0.765818\pi$
$769$	5.83789	−	10.1115i	0.210520	−	0.364631i	0.951877	+	0.306480i	$0.0991511\pi$
$770$	−19.6432	−	21.5533i	−0.707892	−	0.776727i
$771$	−30.6986	+	1.70853i	−1.10558	+	0.0615312i
$772$		−	27.6687i		−	0.995820i
$773$	−24.8851	+	14.3674i	−0.895054	+	0.516760i	−0.875592	−	0.483051i	$-0.839529\pi$
$773$	−24.8851	+	14.3674i	−0.895054	+	0.516760i	−0.0194616	+	0.999811i	$0.506195\pi$
$774$	−18.7075	+	42.7609i	−0.672428	+	1.53701i
$775$	−49.4147	+	4.74045i	−1.77503	+	0.170282i
$776$	−1.78981	−	3.10005i	−0.0642506	−	0.111285i
$777$	−1.21678	−	5.35957i	−0.0436518	−	0.192274i
$778$	0.934308	+	0.539423i	0.0334966	+	0.0193393i
$779$	5.51071	+	9.54483i	0.197442	+	0.341979i
$780$	−30.4788	−	42.0655i	−1.09131	−	1.50619i
$781$	1.13928	−	1.97330i	0.0407667	−	0.0706101i
$782$	−8.55331	−	4.93826i	−0.305866	−	0.176592i
$783$	−33.0449	+	27.2949i	−1.18093	+	0.975440i
$784$	−14.2246	−	12.2736i	−0.508022	−	0.438342i
$785$	2.32147	+	48.5095i	0.0828569	+	1.73138i
$786$	45.6990	−	2.54338i	1.63003	−	0.0907192i
$787$			42.7495i			1.52386i	0.647662	+	0.761928i	$0.275747\pi$
$787$			42.7495i			1.52386i	−0.647662	+	0.761928i	$0.724253\pi$
$788$			22.8622i			0.814432i
$789$	9.46607	+	14.4737i	0.337001	+	0.515276i
$790$	2.20079	+	45.9878i	0.0783008	+	1.63617i
$791$	−3.19811	−	3.86509i	−0.113712	−	0.137427i
$792$	0.856322	+	7.66931i	0.0304281	+	0.272517i
$793$	−23.1937	−	13.3909i	−0.823631	−	0.475524i
$794$	−36.5346	+	63.2798i	−1.29656	+	2.24572i
$795$	−4.73134	+	0.491054i	−0.167803	+	0.0174159i
$796$	−2.00815	−	3.47822i	−0.0711771	−	0.123282i
$797$	−15.5282	−	8.96519i	−0.550036	−	0.317563i	0.199101	−	0.979979i	$-0.436198\pi$
$797$	−15.5282	−	8.96519i	−0.550036	−	0.317563i	−0.749137	+	0.662416i	$0.769531\pi$
$798$	14.9325	+	65.7733i	0.528605	+	2.32835i
$799$	5.72125	+	9.90949i	0.202403	+	0.350573i
$800$	3.78477	+	39.4527i	0.133812	+	1.39486i
$801$	−20.1497	+	2.24983i	−0.711954	+	0.0794937i
$802$	59.5552	−	34.3842i	2.10297	−	1.21415i
$803$			0.445853i			0.0157338i
$804$	16.4597	−	32.5641i	0.580488	−	1.14845i
$805$	−16.0982	+	3.52333i	−0.567386	+	0.124181i
$806$	−56.1432	+	97.2428i	−1.97756	+	3.42523i
$807$	−1.25585	−	22.5649i	−0.0442080	−	0.794323i
$808$	1.70439	+	0.984032i	0.0599604	+	0.0346181i
$809$	−7.34812	−	12.7273i	−0.258346	−	0.447469i	0.707453	−	0.706761i	$-0.249844\pi$
$809$	−7.34812	−	12.7273i	−0.258346	−	0.447469i	−0.965799	+	0.259292i	$0.916511\pi$
$810$	−41.4278	−	10.7279i	−1.45562	−	0.376941i
$811$	−24.3237			−0.854121			−0.427060	−	0.904223i	$-0.640451\pi$
$811$	−24.3237			−0.854121			−0.427060	+	0.904223i	$0.640451\pi$
$812$	−9.18334	−	54.2633i	−0.322272	−	1.90427i
$813$	−5.79283	+	3.78863i	−0.203163	+	0.132873i
$814$	2.95585	+	5.11967i	0.103602	+	0.179444i
$815$	−13.7180	−	7.06831i	−0.480521	−	0.247592i
$816$	−7.73942	+	0.430737i	−0.270934	+	0.0150788i
$817$		−	50.6396i		−	1.77166i
$818$			11.5758i			0.404739i
$819$	10.2294	−	40.9565i	0.357445	−	1.43114i
$820$	4.11284	−	7.98211i	0.143627	−	0.278747i
$821$	−57.0366			−1.99059			−0.995296	−	0.0968819i	$-0.969113\pi$
$821$	−57.0366			−1.99059			−0.995296	+	0.0968819i	$0.969113\pi$
$822$	12.9245	−	8.45291i	0.450795	−	0.294829i
$823$			1.78145i			0.0620975i	0.999518	+	0.0310488i	$0.00988472\pi$
$823$			1.78145i			0.0620975i	−0.999518	+	0.0310488i	$0.990115\pi$
$824$	4.57728	+	7.92808i	0.159457	+	0.276188i
$825$	−15.6746	+	12.5421i	−0.545718	+	0.436659i
$826$	0.638590	−	1.71762i	0.0222194	−	0.0597637i
$827$			35.3529i			1.22934i	0.788784	+	0.614671i	$0.210711\pi$
$827$			35.3529i			1.22934i	−0.788784	+	0.614671i	$0.789289\pi$
$828$	19.3070	+	8.44667i	0.670966	+	0.293542i
$829$	−20.7864	−	36.0032i	−0.721943	−	1.25044i	−0.960220	−	0.279245i	$-0.909916\pi$
$829$	−20.7864	−	36.0032i	−0.721943	−	1.25044i	0.238277	−	0.971197i	$-0.423417\pi$
$830$	−34.1248	−	53.0736i	−1.18449	−	1.84221i
$831$	−6.45109	−	9.86374i	−0.223786	−	0.342169i
$832$	52.9139	+	30.5498i	1.83446	+	1.05913i
$833$	−11.4655	−	2.18488i	−0.397258	−	0.0757016i
$834$	34.8883	+	53.3443i	1.20808	+	1.84716i
$835$	−5.97254	−	3.07740i	−0.206688	−	0.106498i
$836$	−20.2304	−	35.0401i	−0.699683	−	1.21189i
$837$	8.56484	+	50.8731i	0.296044	+	1.75843i
$838$	37.9454	+	21.9078i	1.31080	+	0.756791i
$839$	4.54196	+	7.86691i	0.156806	+	0.271596i	0.933715	−	0.358017i	$-0.116547\pi$
$839$	4.54196	+	7.86691i	0.156806	+	0.271596i	−0.776909	+	0.629613i	$0.783214\pi$
$840$	7.96570	−	8.11470i	0.274843	−	0.279984i
$841$	−19.5181	+	33.8063i	−0.673037	+	1.16573i
$842$	8.00350	−	4.62082i	0.275819	−	0.159244i
$843$	−2.54287	−	45.6900i	−0.0875811	−	1.57365i
$844$	17.0735	−	29.5721i	0.587693	−	1.01791i
$845$	−18.4868	−	28.7522i	−0.635967	−	0.989106i
$846$	−25.9610	−	35.2499i	−0.892557	−	1.21192i
$847$	−2.48409	−	14.6782i	−0.0853543	−	0.504349i
$848$	2.85478	−	1.64821i	0.0980336	−	0.0565997i
$849$	−7.73655	+	15.3061i	−0.265518	+	0.525305i
$850$	10.2898	+	14.4366i	0.352939	+	0.495173i
$851$	3.34070			0.114518
$852$	3.83192	+	1.93686i	0.131280	+	0.0663558i
$853$	6.85295	−	3.95655i	0.234641	−	0.135470i	−0.378070	−	0.925777i	$-0.623412\pi$
$853$	6.85295	−	3.95655i	0.234641	−	0.135470i	0.612711	+	0.790307i	$0.290079\pi$
$854$	9.87263	−	26.5545i	0.337834	−	0.908677i
$855$	45.8445	−	7.35202i	1.56785	−	0.251434i
$856$	3.44552	−	5.96781i	0.117765	−	0.203976i
$857$	8.71857	+	5.03367i	0.297821	+	0.171947i	0.641463	−	0.767154i	$-0.278328\pi$
$857$	8.71857	+	5.03367i	0.297821	+	0.171947i	−0.343643	+	0.939100i	$0.611661\pi$
$858$	2.52327	+	45.3377i	0.0861429	+	1.54780i
$859$	16.7987	+	29.0963i	0.573166	+	0.992753i	0.996238	+	0.0866566i	$0.0276183\pi$
$859$	16.7987	+	29.0963i	0.573166	+	0.992753i	−0.423072	+	0.906096i	$0.639048\pi$
$860$	−34.7029	+	22.3130i	−1.18336	+	0.760866i
$861$	7.11604	−	1.61555i	0.242514	−	0.0550579i
$862$	15.9888	−	9.23113i	0.544580	−	0.314413i
$863$	24.1849	+	13.9632i	0.823263	+	0.475311i	0.851541	−	0.524289i	$-0.175669\pi$
$863$	24.1849	+	13.9632i	0.823263	+	0.475311i	−0.0282771	+	0.999600i	$0.509002\pi$
$864$	40.6170	−	6.83816i	1.38182	−	0.232639i
$865$	−0.364304	−	7.61250i	−0.0123867	−	0.258833i
$866$	47.7875			1.62388
$867$	20.6123	−	13.4809i	0.700032	−	0.457835i
$868$	−62.0912	−	23.0847i	−2.10751	−	0.783546i
$869$	11.2224	−	19.4378i	0.380694	−	0.659381i
$870$	−67.5689	+	7.01281i	−2.29080	+	0.237756i
$871$	22.2140	−	38.4759i	0.752694	−	1.30370i
$872$	9.10292	−	5.25557i	0.308264	−	0.177976i
$873$	−8.86594	−	3.87878i	−0.300067	−	0.131277i
$874$	−40.9974			−1.38676
$875$	28.9151	+	6.23840i	0.977508	+	0.210896i
$876$	−0.838843	+	0.0466857i	−0.0283419	+	0.00157736i
$877$	−4.23012	+	2.44226i	−0.142841	+	0.0824694i	−0.569717	−	0.821841i	$-0.692947\pi$
$877$	−4.23012	+	2.44226i	−0.142841	+	0.0824694i	0.426876	+	0.904310i	$0.359614\pi$
$878$		−	88.6040i		−	2.99024i
$879$	1.30301	+	1.99230i	0.0439493	+	0.0671986i
$880$	6.37201	−	12.3666i	0.214800	−	0.416880i
$881$	29.6470			0.998833			0.499417	−	0.866362i	$-0.333548\pi$
$881$	29.6470			0.998833			0.499417	+	0.866362i	$0.333548\pi$
$882$	44.5231	+	3.43989i	1.49917	+	0.115827i
$883$		−	14.3897i		−	0.484251i	−0.970245	−	0.242125i	$-0.922155\pi$
$883$		−	14.3897i		−	0.484251i	0.970245	−	0.242125i	$-0.0778445\pi$
$884$	22.3643			0.752192
$885$	−1.15175	−	0.514591i	−0.0387156	−	0.0172978i
$886$	28.4884			0.957085
$887$	24.5378	−	14.1669i	0.823898	−	0.475678i	−0.0278610	−	0.999612i	$-0.508870\pi$
$887$	24.5378	−	14.1669i	0.823898	−	0.475678i	0.851759	+	0.523934i	$0.175536\pi$
$888$	−1.92919	+	1.26173i	−0.0647394	+	0.0423409i
$889$	−0.243072	+	0.653795i	−0.00815238	+	0.0219276i
$890$	−28.5661	−	14.7189i	−0.957538	−	0.493379i
$891$	14.1592	+	15.3216i	0.474351	+	0.513294i
$892$	1.87685	−	1.08360i	0.0628415	−	0.0362815i
$893$	41.1343	+	23.7489i	1.37651	+	0.794726i
$894$	−4.39952	+	0.244855i	−0.147142	+	0.00818918i
$895$	4.94647	+	7.69314i	0.165342	+	0.257153i
$896$	−7.90648	+	21.2662i	−0.264137	+	0.710453i
$897$	22.9008	+	11.5753i	0.764637	+	0.386489i
$898$			77.1259i			2.57372i
$899$	40.9464	+	70.9212i	1.36564	+	2.36535i
$900$	−25.2384	−	28.1774i	−0.841280	−	0.939246i
$901$	1.02395	−	1.77353i	0.0341126	−	0.0590848i
$902$	−6.79752	+	3.92455i	−0.226333	+	0.130673i
$903$	−32.0268	−	9.91946i	−1.06579	−	0.330099i
$904$	−1.05206	+	1.82222i	−0.0349910	+	0.0606062i
$905$	−1.71357	+	0.0820048i	−0.0569611	+	0.00272593i
$906$	5.25046	+	8.02798i	0.174435	+	0.266712i
$907$	−36.5106	−	21.0794i	−1.21232	−	0.699931i	−0.249053	−	0.968490i	$-0.580119\pi$
$907$	−36.5106	−	21.0794i	−1.21232	−	0.699931i	−0.963263	+	0.268559i	$0.913453\pi$
$908$	43.9616	+	25.3812i	1.45892	+	0.842306i
$909$	5.28767	−	0.590398i	0.175381	−	0.0195823i
$910$	49.4524	−	45.0698i	1.63933	−	1.49405i
$911$	−21.5225	−	37.2780i	−0.713072	−	1.23508i	−0.963699	−	0.266992i	$-0.913970\pi$
$911$	−21.5225	−	37.2780i	−0.713072	−	1.23508i	0.250627	−	0.968084i	$-0.419363\pi$
$912$	−26.9282	+	17.6116i	−0.891683	+	0.583179i
$913$			30.7602i			1.01801i
$914$	−42.6626			−1.41115
$915$	−17.8061	−	7.95560i	−0.588652	−	0.263004i
$916$	29.5153	+	51.1219i	0.975211	+	1.68912i
$917$	5.48619	+	32.4173i	0.181170	+	1.07051i
$918$	14.2048	−	11.7331i	0.468828	−	0.387249i
$919$	−10.3064	+	17.8512i	−0.339976	+	0.588856i	−0.984428	−	0.175789i	$-0.943752\pi$
$919$	−10.3064	+	17.8512i	−0.339976	+	0.588856i	0.644452	+	0.764645i	$0.277086\pi$
$920$	3.73810	+	5.81379i	0.123242	+	0.191675i
$921$	−13.6846	+	27.0738i	−0.450922	+	0.892112i
$922$	−39.7394	+	22.9435i	−1.30875	+	0.755605i
$923$	4.52758	+	2.61400i	0.149027	+	0.0860408i
$924$	−26.1237	+	5.93087i	−0.859408	+	0.195111i
$925$	−5.45578	−	2.48867i	−0.179385	−	0.0818271i
$926$	−14.2241	+	24.6368i	−0.467431	+	0.809615i
$927$	22.6738	+	9.91960i	0.744705	+	0.325802i
$928$	56.6234	−	32.6915i	1.85875	−	1.07315i
$929$	34.9786			1.14761			0.573805	−	0.818992i	$-0.305467\pi$
$929$	34.9786			1.14761			0.573805	+	0.818992i	$0.305467\pi$
$930$	−33.3550	+	74.6547i	−1.09375	+	2.44802i
$931$	−45.7519	+	15.9424i	−1.49946	+	0.522491i
$932$	44.1255	+	25.4759i	1.44538	+	0.834490i
$933$	−34.0482	−	17.2098i	−1.11469	−	0.563423i
$934$	34.3118	−	59.4298i	1.12272	−	1.94460i
$935$	−0.413130	−	8.63277i	−0.0135108	−	0.282322i
$936$	−17.5966	+	1.96476i	−0.575164	+	0.0642203i
$937$		−	38.7498i		−	1.26590i	−0.774193	−	0.632950i	$-0.781844\pi$
$937$		−	38.7498i		−	1.26590i	0.774193	−	0.632950i	$-0.218156\pi$
$938$	44.0512	+	16.3777i	1.43832	+	0.534750i
$939$	−21.3046	+	42.1494i	−0.695249	+	1.37549i
$940$	−1.84979	−	38.6533i	−0.0603336	−	1.26073i
$941$	38.3229			1.24929			0.624645	−	0.780909i	$-0.285244\pi$
$941$	38.3229			1.24929			0.624645	+	0.780909i	$0.285244\pi$
$942$	71.3923	+	36.0855i	2.32609	+	1.17573i
$943$			4.43553i			0.144441i
$944$	0.874202			0.0284528
$945$	4.33041	−	30.4343i	0.140868	−	0.990028i
$946$	36.0639			1.17254
$947$			51.8344i			1.68439i	0.539172	+	0.842196i	$0.318737\pi$
$947$			51.8344i			1.68439i	−0.539172	+	0.842196i	$0.681263\pi$
$948$	37.7460	+	19.0789i	1.22593	+	0.619652i
$949$	−1.02297			−0.0332072
$950$	66.9539	+	30.5413i	2.17227	+	0.990890i
$951$	4.91843	−	9.73072i	0.159491	−	0.315540i
$952$	0.816882	+	4.82687i	0.0264753	+	0.156440i
$953$		−	2.58243i		−	0.0836532i	−0.999125	−	0.0418266i	$-0.986682\pi$
$953$		−	2.58243i		−	0.0836532i	0.999125	−	0.0418266i	$-0.0133177\pi$
$954$	−3.14041	+	7.17821i	−0.101674	+	0.232403i
$955$	43.4015	−	2.07703i	1.40444	−	0.0672110i
$956$	−8.49679	+	14.7169i	−0.274806	+	0.475977i
$957$	29.5559	+	14.9392i	0.955407	+	0.482914i
$958$	42.3758	+	24.4657i	1.36910	+	0.790450i
$959$	7.07211	+	8.54704i	0.228370	+	0.275998i
$960$	40.6228	+	18.1499i	1.31109	+	0.585784i
$961$	67.5715			2.17973
$962$	−11.7467	+	6.78196i	−0.378729	+	0.218659i
$963$	−2.06724	−	18.5144i	−0.0666158	−	0.596618i
$964$	20.8998	−	36.1995i	0.673138	−	1.16591i
$965$	−1.17272	−	24.5052i	−0.0377513	−	0.788850i
$966$	−8.03071	+	25.9286i	−0.258384	+	0.834241i
$967$	−47.5367	−	27.4453i	−1.52868	−	0.882582i	−0.999418	−	0.0341208i	$-0.989137\pi$
$967$	−47.5367	−	27.4453i	−1.52868	−	0.882582i	−0.529258	−	0.848461i	$-0.677530\pi$
$968$	−5.40745	+	3.12199i	−0.173802	+	0.100345i
$969$	−9.01725	+	17.8399i	−0.289676	+	0.573100i
$970$	−8.29531	−	12.9015i	−0.266346	−	0.414243i
$971$	−18.6885	+	32.3694i	−0.599742	+	1.03878i	0.393116	+	0.919489i	$0.371397\pi$
$971$	−18.6885	+	32.3694i	−0.599742	+	1.03878i	−0.992859	+	0.119295i	$0.961936\pi$
$972$	−27.3440	+	28.2440i	−0.877059	+	0.905926i
$973$	−35.2768	+	29.1892i	−1.13092	+	0.935764i
$974$	−7.84056	−	13.5802i	−0.251228	−	0.435139i
$975$	−28.7768	−	35.9641i	−0.921596	−	1.15177i
$976$	13.5152			0.432611
$977$		−	4.05759i		−	0.129814i	−0.997891	−	0.0649070i	$-0.979325\pi$
$977$		−	4.05759i		−	0.129814i	0.997891	−	0.0649070i	$-0.0206751\pi$
$978$	−21.2730	+	13.9130i	−0.680237	+	0.444889i
$979$	7.83298	+	13.5671i	0.250343	+	0.433607i
$980$	31.0845	+	24.3288i	0.992958	+	0.777155i
$981$	11.3896	−	26.0338i	0.363641	−	0.831194i
$982$	−62.4805	−	36.0731i	−1.99383	−	1.15114i
$983$	−50.7014	−	29.2725i	−1.61712	−	0.933647i	−0.987659	−	0.156617i	$-0.949941\pi$
$983$	−50.7014	−	29.2725i	−1.61712	−	0.933647i	−0.629464	−	0.777029i	$-0.716726\pi$
$984$	−1.67523	−	2.56144i	−0.0534045	−	0.0816557i
$985$	0.968999	+	20.2482i	0.0308749	+	0.645161i
$986$	14.6231	−	25.3280i	0.465695	−	0.806608i
$987$	23.0774	−	21.3632i	0.734562	−	0.679998i
$988$	80.3967	−	46.4171i	2.55776	−	1.47672i
$989$	10.1899	−	17.6494i	0.324019	−	0.561218i
$990$	5.23588	+	32.6490i	0.166407	+	1.03765i
$991$	23.7862	+	41.1988i	0.755592	+	1.30872i	0.945079	+	0.326841i	$0.105984\pi$
$991$	23.7862	+	41.1988i	0.755592	+	1.30872i	−0.189487	+	0.981883i	$0.560683\pi$
$992$		−	78.6994i		−	2.49871i
$993$	5.03432	+	2.54461i	0.159759	+	0.0807509i
$994$	−1.92721	+	5.18364i	−0.0611274	+	0.164415i
$995$	−1.92597	−	2.99542i	−0.0610574	−	0.0949612i
$996$	−57.8734	+	3.22094i	−1.83379	+	0.102059i
$997$	2.41372	+	1.39356i	0.0764434	+	0.0441346i	0.537735	−	0.843114i	$-0.319280\pi$
$997$	2.41372	+	1.39356i	0.0764434	+	0.0441346i	−0.461291	+	0.887249i	$0.652614\pi$
$998$	28.1574	−	16.2567i	0.891308	−	0.514597i
$999$	−2.17668	+	5.83934i	−0.0688670	+	0.184748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.r.b.184.7	✓	84
3.2	odd	2		945.2.r.b.604.36		84
5.4	even	2	inner	315.2.r.b.184.36	yes	84
7.4	even	3		315.2.bo.b.4.36	yes	84
9.2	odd	6		945.2.bo.b.289.36		84
9.7	even	3		315.2.bo.b.79.7	yes	84
15.14	odd	2		945.2.r.b.604.7		84
21.11	odd	6		945.2.bo.b.739.7		84
35.4	even	6		315.2.bo.b.4.7	yes	84
45.29	odd	6		945.2.bo.b.289.7		84
45.34	even	6		315.2.bo.b.79.36	yes	84
63.11	odd	6		945.2.r.b.424.36		84
63.25	even	3	inner	315.2.r.b.214.7	yes	84
105.74	odd	6		945.2.bo.b.739.36		84
315.74	odd	6		945.2.r.b.424.7		84
315.214	even	6	inner	315.2.r.b.214.36	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.7	✓	84	1.1	even	1	trivial
315.2.r.b.184.36	yes	84	5.4	even	2	inner
315.2.r.b.214.7	yes	84	63.25	even	3	inner
315.2.r.b.214.36	yes	84	315.214	even	6	inner
315.2.bo.b.4.7	yes	84	35.4	even	6
315.2.bo.b.4.36	yes	84	7.4	even	3
315.2.bo.b.79.7	yes	84	9.7	even	3
315.2.bo.b.79.36	yes	84	45.34	even	6
945.2.r.b.424.7		84	315.74	odd	6
945.2.r.b.424.36		84	63.11	odd	6
945.2.r.b.604.7		84	15.14	odd	2
945.2.r.b.604.36		84	3.2	odd	2
945.2.bo.b.289.7		84	45.29	odd	6
945.2.bo.b.289.36		84	9.2	odd	6
945.2.bo.b.739.7		84	21.11	odd	6
945.2.bo.b.739.36		84	105.74	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.12646i q^{2} +(-1.54581 - 0.781334i) q^{3} -2.52185 q^{4} +(-2.23351 + 0.106887i) q^{5} +(-1.66148 + 3.28710i) q^{6} +(-2.47990 - 0.921996i) q^{7} +1.10970i q^{8} +(1.77903 + 2.41558i) q^{9} +O(q^{10})\)	\(q-2.12646i q^{2} +(-1.54581 - 0.781334i) q^{3} -2.52185 q^{4} +(-2.23351 + 0.106887i) q^{5} +(-1.66148 + 3.28710i) q^{6} +(-2.47990 - 0.921996i) q^{7} +1.10970i q^{8} +(1.77903 + 2.41558i) q^{9} +(0.227292 + 4.74948i) q^{10} +(1.15902 - 2.00747i) q^{11} +(3.89830 + 1.97041i) q^{12} +(4.60600 + 2.65927i) q^{13} +(-1.96059 + 5.27343i) q^{14} +(3.53609 + 1.57989i) q^{15} -2.68397 q^{16} +(-1.44402 + 0.833705i) q^{17} +(5.13665 - 3.78305i) q^{18} +(-3.46071 + 5.99412i) q^{19} +(5.63259 - 0.269554i) q^{20} +(3.11306 + 3.36286i) q^{21} +(-4.26882 - 2.46461i) q^{22} +(-2.41231 + 1.39275i) q^{23} +(0.867047 - 1.71538i) q^{24} +(4.97715 - 0.477467i) q^{25} +(5.65485 - 9.79449i) q^{26} +(-0.862667 - 5.12404i) q^{27} +(6.25395 + 2.32514i) q^{28} +(-4.12420 - 7.14332i) q^{29} +(3.35958 - 7.51937i) q^{30} -9.92832 q^{31} +7.92676i q^{32} +(-3.36012 + 2.19759i) q^{33} +(1.77284 + 3.07066i) q^{34} +(5.63744 + 1.79422i) q^{35} +(-4.48646 - 6.09174i) q^{36} +(-1.03864 - 0.599659i) q^{37} +(12.7463 + 7.35908i) q^{38} +(-5.04220 - 7.70954i) q^{39} +(-0.118613 - 2.47853i) q^{40} +(0.796182 - 1.37903i) q^{41} +(7.15100 - 6.61982i) q^{42} +(-6.33616 + 3.65818i) q^{43} +(-2.92287 + 5.06256i) q^{44} +(-4.23169 - 5.20507i) q^{45} +(2.96163 + 5.12970i) q^{46} -6.86244i q^{47} +(4.14889 + 2.09707i) q^{48} +(5.29985 + 4.57292i) q^{49} +(-1.01532 - 10.5837i) q^{50} +(2.88358 - 0.160485i) q^{51} +(-11.6156 - 6.70629i) q^{52} +(-1.06364 + 0.614094i) q^{53} +(-10.8961 + 1.83443i) q^{54} +(-2.37410 + 4.60760i) q^{55} +(1.02314 - 2.75195i) q^{56} +(10.0330 - 6.56179i) q^{57} +(-15.1900 + 8.76997i) q^{58} -0.325713 q^{59} +(-8.91750 - 3.98425i) q^{60} -5.03554 q^{61} +21.1122i q^{62} +(-2.18468 - 7.63067i) q^{63} +11.4880 q^{64} +(-10.5718 - 5.44720i) q^{65} +(4.67310 + 7.14518i) q^{66} -8.35343i q^{67} +(3.64160 - 2.10248i) q^{68} +(4.81717 - 0.268099i) q^{69} +(3.81534 - 11.9878i) q^{70} +0.982974 q^{71} +(-2.68057 + 1.97420i) q^{72} +(-0.166572 + 0.0961705i) q^{73} +(-1.27515 + 2.20863i) q^{74} +(-8.06677 - 3.15074i) q^{75} +(8.72740 - 15.1163i) q^{76} +(-4.72513 + 3.90974i) q^{77} +(-16.3941 + 10.7221i) q^{78} +9.68269 q^{79} +(5.99467 - 0.286881i) q^{80} +(-2.67007 + 8.59481i) q^{81} +(-2.93245 - 1.69305i) q^{82} +(-11.4921 + 6.63499i) q^{83} +(-7.85069 - 8.48064i) q^{84} +(3.13612 - 2.01644i) q^{85} +(7.77900 + 13.4736i) q^{86} +(0.793894 + 14.2646i) q^{87} +(2.22770 + 1.28616i) q^{88} +(-3.37915 + 5.85286i) q^{89} +(-11.0684 + 8.99854i) q^{90} +(-8.97059 - 10.8415i) q^{91} +(6.08350 - 3.51231i) q^{92} +(15.3473 + 7.75733i) q^{93} -14.5927 q^{94} +(7.08884 - 13.7579i) q^{95} +(6.19345 - 12.2532i) q^{96} +(-2.79359 + 1.61288i) q^{97} +(9.72416 - 11.2699i) q^{98} +(6.91115 - 0.771669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

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