LMFDB - Embedded newform 185.2.f.c.142.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(43,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("185.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.f (of order $4$, 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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			142.3
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	185.142
Dual form			185.2.f.c.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.48119i q^{2} +(-2.07816 - 2.07816i) q^{3} -0.193937 q^{4} +(-1.48119 + 1.67513i) q^{5} +(3.07816 - 3.07816i) q^{6} +(1.07816 + 1.07816i) q^{7} +2.67513i q^{8} +5.63752i q^{9} +O(q^{10})$	\(q+1.48119i q^{2} +(-2.07816 - 2.07816i) q^{3} -0.193937 q^{4} +(-1.48119 + 1.67513i) q^{5} +(3.07816 - 3.07816i) q^{6} +(1.07816 + 1.07816i) q^{7} +2.67513i q^{8} +5.63752i q^{9} +(-2.48119 - 2.19394i) q^{10} +5.76845i q^{11} +(0.403032 + 0.403032i) q^{12} -2.63752i q^{13} +(-1.59697 + 1.59697i) q^{14} +(6.55936 - 0.403032i) q^{15} -4.35026 q^{16} -3.28726 q^{17} -8.35026 q^{18} +(4.07816 + 4.07816i) q^{19} +(0.287258 - 0.324869i) q^{20} -4.48119i q^{21} -8.54420 q^{22} -1.76845i q^{23} +(5.55936 - 5.55936i) q^{24} +(-0.612127 - 4.96239i) q^{25} +3.90668 q^{26} +(5.48119 - 5.48119i) q^{27} +(-0.209095 - 0.209095i) q^{28} +(2.35026 - 2.35026i) q^{29} +(0.596968 + 9.71568i) q^{30} +(-1.46604 - 1.46604i) q^{31} -1.09332i q^{32} +(11.9878 - 11.9878i) q^{33} -4.86907i q^{34} +(-3.40303 + 0.209095i) q^{35} -1.09332i q^{36} +(-1.00000 + 6.00000i) q^{37} +(-6.04055 + 6.04055i) q^{38} +(-5.48119 + 5.48119i) q^{39} +(-4.48119 - 3.96239i) q^{40} -9.38058i q^{41} +6.63752 q^{42} +8.73084i q^{43} -1.11871i q^{44} +(-9.44358 - 8.35026i) q^{45} +2.61942 q^{46} +(1.94723 + 1.94723i) q^{47} +(9.04055 + 9.04055i) q^{48} -4.67513i q^{49} +(7.35026 - 0.906679i) q^{50} +(6.83146 + 6.83146i) q^{51} +0.511511i q^{52} +(-0.518806 + 0.518806i) q^{53} +(8.11871 + 8.11871i) q^{54} +(-9.66291 - 8.54420i) q^{55} +(-2.88423 + 2.88423i) q^{56} -16.9502i q^{57} +(3.48119 + 3.48119i) q^{58} +(5.46604 + 5.46604i) q^{59} +(-1.27210 + 0.0781626i) q^{60} +(4.19394 + 4.19394i) q^{61} +(2.17148 - 2.17148i) q^{62} +(-6.07816 + 6.07816i) q^{63} -7.08110 q^{64} +(4.41819 + 3.90668i) q^{65} +(17.7562 + 17.7562i) q^{66} +(10.7157 - 10.7157i) q^{67} +0.637519 q^{68} +(-3.67513 + 3.67513i) q^{69} +(-0.309711 - 5.04055i) q^{70} +4.57452 q^{71} -15.0811 q^{72} +(-1.16854 - 1.16854i) q^{73} +(-8.88717 - 1.48119i) q^{74} +(-9.04055 + 11.5847i) q^{75} +(-0.790905 - 0.790905i) q^{76} +(-6.21933 + 6.21933i) q^{77} +(-8.11871 - 8.11871i) q^{78} +(-7.55936 - 7.55936i) q^{79} +(6.44358 - 7.28726i) q^{80} -5.86907 q^{81} +13.8945 q^{82} +(-0.559357 + 0.559357i) q^{83} +0.869067i q^{84} +(4.86907 - 5.50659i) q^{85} -12.9321 q^{86} -9.76845 q^{87} -15.4314 q^{88} +(-6.02539 + 6.02539i) q^{89} +(12.3684 - 13.9878i) q^{90} +(2.84367 - 2.84367i) q^{91} +0.342968i q^{92} +6.09332i q^{93} +(-2.88423 + 2.88423i) q^{94} +(-12.8720 + 0.790905i) q^{95} +(-2.27210 + 2.27210i) q^{96} -4.15633 q^{97} +6.92478 q^{98} -32.5198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{7}+O(q^{10}) $ 6 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^7	$ 6 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{7} - 4 q^{10} + 2 q^{12} - 10 q^{14} + 18 q^{15} - 6 q^{16} - 8 q^{17} - 30 q^{18} + 14 q^{19} - 10 q^{20} - 32 q^{22} + 12 q^{24} - 2 q^{25} + 36 q^{26} + 22 q^{27} - 6 q^{29} + 4 q^{30} + 20 q^{33} - 20 q^{35} - 6 q^{37} - 4 q^{38} - 22 q^{39} - 16 q^{40} + 8 q^{42} - 24 q^{45} + 40 q^{46} - 8 q^{47} + 22 q^{48} + 24 q^{50} + 10 q^{51} - 14 q^{53} + 6 q^{54} + 4 q^{55} - 6 q^{56} + 10 q^{58} + 24 q^{59} + 2 q^{60} + 26 q^{61} - 10 q^{62} - 26 q^{63} + 22 q^{64} + 24 q^{65} + 32 q^{66} + 22 q^{67} - 28 q^{68} - 12 q^{69} - 14 q^{70} + 4 q^{71} - 26 q^{72} - 38 q^{73} + 12 q^{74} - 22 q^{75} - 6 q^{76} - 8 q^{77} - 6 q^{78} - 24 q^{79} + 6 q^{80} - 26 q^{81} + 44 q^{82} + 18 q^{83} + 20 q^{85} - 60 q^{86} - 36 q^{87} - 8 q^{88} - 6 q^{89} - 2 q^{90} + 38 q^{91} - 6 q^{94} - 14 q^{95} - 4 q^{96} - 4 q^{97} - 2 q^{98} - 72 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^7 - 4 * q^10 + 2 * q^12 - 10 * q^14 + 18 * q^15 - 6 * q^16 - 8 * q^17 - 30 * q^18 + 14 * q^19 - 10 * q^20 - 32 * q^22 + 12 * q^24 - 2 * q^25 + 36 * q^26 + 22 * q^27 - 6 * q^29 + 4 * q^30 + 20 * q^33 - 20 * q^35 - 6 * q^37 - 4 * q^38 - 22 * q^39 - 16 * q^40 + 8 * q^42 - 24 * q^45 + 40 * q^46 - 8 * q^47 + 22 * q^48 + 24 * q^50 + 10 * q^51 - 14 * q^53 + 6 * q^54 + 4 * q^55 - 6 * q^56 + 10 * q^58 + 24 * q^59 + 2 * q^60 + 26 * q^61 - 10 * q^62 - 26 * q^63 + 22 * q^64 + 24 * q^65 + 32 * q^66 + 22 * q^67 - 28 * q^68 - 12 * q^69 - 14 * q^70 + 4 * q^71 - 26 * q^72 - 38 * q^73 + 12 * q^74 - 22 * q^75 - 6 * q^76 - 8 * q^77 - 6 * q^78 - 24 * q^79 + 6 * q^80 - 26 * q^81 + 44 * q^82 + 18 * q^83 + 20 * q^85 - 60 * q^86 - 36 * q^87 - 8 * q^88 - 6 * q^89 - 2 * q^90 + 38 * q^91 - 6 * q^94 - 14 * q^95 - 4 * q^96 - 4 * q^97 - 2 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.48119i			1.04736i	0.851914	+	0.523681i	$0.175442\pi$
$2$			1.48119i			1.04736i	−0.851914	+	0.523681i	$0.824558\pi$
$3$	−2.07816	−	2.07816i	−1.19983	−	1.19983i	−0.974218	−	0.225610i	$-0.927562\pi$
$3$	−2.07816	−	2.07816i	−1.19983	−	1.19983i	−0.225610	−	0.974218i	$-0.572438\pi$
$4$	−0.193937			−0.0969683
$5$	−1.48119	+	1.67513i	−0.662410	+	0.749141i
$5$	−1.48119	+	1.67513i	−0.662410	+	0.749141i
$6$	3.07816	−	3.07816i	1.25665	−	1.25665i
$7$	1.07816	+	1.07816i	0.407507	+	0.407507i	0.880868	−	0.473361i	$-0.156959\pi$
$7$	1.07816	+	1.07816i	0.407507	+	0.407507i	−0.473361	+	0.880868i	$0.656959\pi$
$8$			2.67513i			0.945802i
$9$			5.63752i			1.87917i
$10$	−2.48119	−	2.19394i	−0.784623	−	0.693784i
$11$			5.76845i			1.73925i	0.493710	+	0.869627i	$0.335641\pi$
$11$			5.76845i			1.73925i	−0.493710	+	0.869627i	$0.664359\pi$
$12$	0.403032	+	0.403032i	0.116345	+	0.116345i
$13$		−	2.63752i		−	0.731516i	−0.930710	−	0.365758i	$-0.880810\pi$
$13$		−	2.63752i		−	0.731516i	0.930710	−	0.365758i	$-0.119190\pi$
$14$	−1.59697	+	1.59697i	−0.426808	+	0.426808i
$15$	6.55936	−	0.403032i	1.69362	−	0.104062i
$16$	−4.35026			−1.08757
$17$	−3.28726			−0.797277			−0.398639	−	0.917108i	$-0.630517\pi$
$17$	−3.28726			−0.797277			−0.398639	+	0.917108i	$0.630517\pi$
$18$	−8.35026			−1.96818
$19$	4.07816	+	4.07816i	0.935595	+	0.935595i	0.998048	−	0.0624532i	$-0.0198924\pi$
$19$	4.07816	+	4.07816i	0.935595	+	0.935595i	−0.0624532	+	0.998048i	$0.519892\pi$
$20$	0.287258	−	0.324869i	0.0642328	−	0.0726429i
$21$		−	4.48119i		−	0.977877i
$22$	−8.54420			−1.82163
$23$		−	1.76845i		−	0.368748i	−0.982856	−	0.184374i	$-0.940974\pi$
$23$		−	1.76845i		−	0.368748i	0.982856	−	0.184374i	$-0.0590257\pi$
$24$	5.55936	−	5.55936i	1.13480	−	1.13480i
$25$	−0.612127	−	4.96239i	−0.122425	−	0.992478i
$26$	3.90668			0.766163
$27$	5.48119	−	5.48119i	1.05486	−	1.05486i
$28$	−0.209095	−	0.209095i	−0.0395153	−	0.0395153i
$29$	2.35026	−	2.35026i	0.436433	−	0.436433i	−0.454377	−	0.890810i	$-0.650138\pi$
$29$	2.35026	−	2.35026i	0.436433	−	0.436433i	0.890810	+	0.454377i	$0.150138\pi$
$30$	0.596968	+	9.71568i	0.108991	+	1.77383i
$31$	−1.46604	−	1.46604i	−0.263308	−	0.263308i	0.563089	−	0.826396i	$-0.309613\pi$
$31$	−1.46604	−	1.46604i	−0.263308	−	0.263308i	−0.826396	+	0.563089i	$0.809613\pi$
$32$		−	1.09332i		−	0.193274i
$33$	11.9878	−	11.9878i	2.08680	−	2.08680i
$34$		−	4.86907i		−	0.835038i
$35$	−3.40303	+	0.209095i	−0.575217	+	0.0353435i
$36$		−	1.09332i		−	0.182220i
$37$	−1.00000	+	6.00000i	−0.164399	+	0.986394i
$37$	−1.00000	+	6.00000i	−0.164399	+	0.986394i
$38$	−6.04055	+	6.04055i	−0.979907	+	0.979907i
$39$	−5.48119	+	5.48119i	−0.877694	+	0.877694i
$40$	−4.48119	−	3.96239i	−0.708539	−	0.626509i
$41$		−	9.38058i		−	1.46500i	−0.680767	−	0.732500i	$-0.738353\pi$
$41$		−	9.38058i		−	1.46500i	0.680767	−	0.732500i	$-0.261647\pi$
$42$	6.63752			1.02419
$43$			8.73084i			1.33144i	0.746201	+	0.665720i	$0.231876\pi$
$43$			8.73084i			1.33144i	−0.746201	+	0.665720i	$0.768124\pi$
$44$		−	1.11871i		−	0.168652i
$45$	−9.44358	−	8.35026i	−1.40777	−	1.24478i
$46$	2.61942			0.386213
$47$	1.94723	+	1.94723i	0.284033	+	0.284033i	0.834715	−	0.550682i	$-0.185632\pi$
$47$	1.94723	+	1.94723i	0.284033	+	0.284033i	−0.550682	+	0.834715i	$0.685632\pi$
$48$	9.04055	+	9.04055i	1.30489	+	1.30489i
$49$		−	4.67513i		−	0.667876i
$50$	7.35026	−	0.906679i	1.03948	−	0.128224i
$51$	6.83146	+	6.83146i	0.956595	+	0.956595i
$52$			0.511511i			0.0709339i
$53$	−0.518806	+	0.518806i	−0.0712634	+	0.0712634i	−0.741840	−	0.670577i	$-0.766047\pi$
$53$	−0.518806	+	0.518806i	−0.0712634	+	0.0712634i	0.670577	+	0.741840i	$0.266047\pi$
$54$	8.11871	+	8.11871i	1.10482	+	1.10482i
$55$	−9.66291	−	8.54420i	−1.30295	−	1.15210i
$56$	−2.88423	+	2.88423i	−0.385421	+	0.385421i
$57$		−	16.9502i		−	2.24510i
$58$	3.48119	+	3.48119i	0.457103	+	0.457103i
$59$	5.46604	+	5.46604i	0.711617	+	0.711617i	0.966873	−	0.255256i	$-0.0821598\pi$
$59$	5.46604	+	5.46604i	0.711617	+	0.711617i	−0.255256	+	0.966873i	$0.582160\pi$
$60$	−1.27210	+	0.0781626i	−0.164227	+	0.0100907i
$61$	4.19394	+	4.19394i	0.536979	+	0.536979i	0.922640	−	0.385662i	$-0.126027\pi$
$61$	4.19394	+	4.19394i	0.536979	+	0.536979i	−0.385662	+	0.922640i	$0.626027\pi$
$62$	2.17148	−	2.17148i	0.275779	−	0.275779i
$63$	−6.07816	+	6.07816i	−0.765777	+	0.765777i
$64$	−7.08110			−0.885138
$65$	4.41819	+	3.90668i	0.548009	+	0.484564i
$66$	17.7562	+	17.7562i	2.18564	+	2.18564i
$67$	10.7157	−	10.7157i	1.30913	−	1.30913i	0.387085	−	0.922044i	$-0.373482\pi$
$67$	10.7157	−	10.7157i	1.30913	−	1.30913i	0.922044	−	0.387085i	$-0.126518\pi$
$68$	0.637519			0.0773106
$69$	−3.67513	+	3.67513i	−0.442434	+	0.442434i
$70$	−0.309711	−	5.04055i	−0.0370175	−	0.602461i
$71$	4.57452			0.542895			0.271448	−	0.962453i	$-0.412498\pi$
$71$	4.57452			0.542895			0.271448	+	0.962453i	$0.412498\pi$
$72$	−15.0811			−1.77732
$73$	−1.16854	−	1.16854i	−0.136768	−	0.136768i	0.635408	−	0.772176i	$-0.280832\pi$
$73$	−1.16854	−	1.16854i	−0.136768	−	0.136768i	−0.772176	+	0.635408i	$0.780832\pi$
$74$	−8.88717	−	1.48119i	−1.03311	−	0.172185i
$75$	−9.04055	+	11.5847i	−1.04391	+	1.33769i
$76$	−0.790905	−	0.790905i	−0.0907230	−	0.0907230i
$77$	−6.21933	+	6.21933i	−0.708758	+	0.708758i
$78$	−8.11871	−	8.11871i	−0.919263	−	0.919263i
$79$	−7.55936	−	7.55936i	−0.850494	−	0.850494i	0.139700	−	0.990194i	$-0.455386\pi$
$79$	−7.55936	−	7.55936i	−0.850494	−	0.850494i	−0.990194	+	0.139700i	$0.955386\pi$
$80$	6.44358	−	7.28726i	0.720414	−	0.814740i
$81$	−5.86907			−0.652119
$82$	13.8945			1.53439
$83$	−0.559357	+	0.559357i	−0.0613974	+	0.0613974i	−0.737139	−	0.675741i	$-0.763824\pi$
$83$	−0.559357	+	0.559357i	−0.0613974	+	0.0613974i	0.675741	+	0.737139i	$0.263824\pi$
$84$			0.869067i			0.0948230i
$85$	4.86907	−	5.50659i	0.528125	−	0.597273i
$86$	−12.9321			−1.39450
$87$	−9.76845			−1.04729
$88$	−15.4314			−1.64499
$89$	−6.02539	+	6.02539i	−0.638690	+	0.638690i	−0.950232	−	0.311542i	$-0.899155\pi$
$89$	−6.02539	+	6.02539i	−0.638690	+	0.638690i	0.311542	+	0.950232i	$0.399155\pi$
$90$	12.3684	−	13.9878i	1.30374	−	1.47444i
$91$	2.84367	−	2.84367i	0.298098	−	0.298098i
$92$			0.342968i			0.0357568i
$93$			6.09332i			0.631848i
$94$	−2.88423	+	2.88423i	−0.297485	+	0.297485i
$95$	−12.8720	+	0.790905i	−1.32064	+	0.0811451i
$96$	−2.27210	+	2.27210i	−0.231895	+	0.231895i
$97$	−4.15633			−0.422011			−0.211005	−	0.977485i	$-0.567674\pi$
$97$	−4.15633			−0.422011			−0.211005	+	0.977485i	$0.567674\pi$
$98$	6.92478			0.699508
$99$	−32.5198			−3.26836
$100$	0.118714	+	0.962389i	0.0118714	+	0.0962389i
$101$		−	5.80114i		−	0.577235i	−0.957444	−	0.288617i	$-0.906804\pi$
$101$		−	5.80114i		−	0.577235i	0.957444	−	0.288617i	$-0.0931956\pi$
$102$	−10.1187	+	10.1187i	−1.00190	+	1.00190i
$103$	14.4993			1.42866			0.714329	−	0.699810i	$-0.246732\pi$
$103$	14.4993			1.42866			0.714329	+	0.699810i	$0.246732\pi$
$104$	7.05571			0.691869
$105$	7.50659	+	6.63752i	0.732568	+	0.647756i
$106$	−0.768452	−	0.768452i	−0.0746387	−	0.0746387i
$107$	−1.07816	−	1.07816i	−0.104230	−	0.104230i	0.653069	−	0.757299i	$-0.273481\pi$
$107$	−1.07816	−	1.07816i	−0.104230	−	0.104230i	−0.757299	+	0.653069i	$0.773481\pi$
$108$	−1.06300	+	1.06300i	−0.102288	+	0.102288i
$109$	4.98778	+	4.98778i	0.477743	+	0.477743i	0.904409	−	0.426666i	$-0.140312\pi$
$109$	4.98778	+	4.98778i	0.477743	+	0.477743i	−0.426666	+	0.904409i	$0.640312\pi$
$110$	12.6556	−	14.3127i	1.20667	−	1.36466i
$111$	14.5471	−	10.3908i	1.38075	−	0.986252i
$112$	−4.69029	−	4.69029i	−0.443191	−	0.443191i
$113$	14.2496			1.34049			0.670247	−	0.742138i	$-0.266188\pi$
$113$	14.2496			1.34049			0.670247	+	0.742138i	$0.266188\pi$
$114$	25.1065			2.35144
$115$	2.96239	+	2.61942i	0.276244	+	0.244262i
$116$	−0.455802	+	0.455802i	−0.0423201	+	0.0423201i
$117$	14.8691			1.37465
$118$	−8.09626	+	8.09626i	−0.745321	+	0.745321i
$119$	−3.54420	−	3.54420i	−0.324896	−	0.324896i
$120$	1.07816	+	17.5471i	0.0984223	+	1.60183i
$121$	−22.2750			−2.02500
$122$	−6.21203	+	6.21203i	−0.562411	+	0.562411i
$123$	−19.4944	+	19.4944i	−1.75775	+	1.75775i
$124$	0.284318	+	0.284318i	0.0255325	+	0.0255325i
$125$	9.21933	+	6.32487i	0.824602	+	0.565713i
$126$	−9.00294	−	9.00294i	−0.802046	−	0.802046i
$127$	13.5521	+	13.5521i	1.20255	+	1.20255i	0.973388	+	0.229163i	$0.0735989\pi$
$127$	13.5521	+	13.5521i	1.20255	+	1.20255i	0.229163	+	0.973388i	$0.426401\pi$
$128$		−	12.6751i		−	1.12033i
$129$	18.1441	−	18.1441i	1.59750	−	1.59750i
$130$	−5.78655	+	6.54420i	−0.507514	+	0.573964i
$131$	7.67807	+	7.67807i	0.670836	+	0.670836i	0.957909	−	0.287073i	$-0.0926821\pi$
$131$	7.67807	+	7.67807i	0.670836	+	0.670836i	−0.287073	+	0.957909i	$0.592682\pi$
$132$	−2.32487	+	2.32487i	−0.202354	+	0.202354i
$133$			8.79384i			0.762523i
$134$	15.8720	+	15.8720i	1.37113	+	1.37113i
$135$	1.06300	+	17.3004i	0.0914888	+	1.48898i
$136$		−	8.79384i		−	0.754066i
$137$	0.100615	+	0.100615i	0.00859615	+	0.00859615i	0.711392	−	0.702796i	$-0.248065\pi$
$137$	0.100615	+	0.100615i	0.00859615	+	0.00859615i	−0.702796	+	0.711392i	$0.748065\pi$
$138$	−5.44358	−	5.44358i	−0.463389	−	0.463389i
$139$	−13.2750			−1.12597			−0.562987	−	0.826466i	$-0.690348\pi$
$139$	−13.2750			−1.12597			−0.562987	+	0.826466i	$0.690348\pi$
$140$	0.659972	−	0.0405512i	0.0557778	−	0.00342720i
$141$		−	8.09332i		−	0.681581i
$142$			6.77575i			0.568608i
$143$	15.2144			1.27229
$144$		−	24.5247i		−	2.04372i
$145$	0.455802	+	7.41819i	0.0378523	+	0.616047i
$146$	1.73084	−	1.73084i	0.143245	−	0.143245i
$147$	−9.71568	+	9.71568i	−0.801336	+	0.801336i
$148$	0.193937	−	1.16362i	0.0159415	−	0.0956489i
$149$		−	4.45088i		−	0.364630i	−0.983240	−	0.182315i	$-0.941641\pi$
$149$		−	4.45088i		−	0.364630i	0.983240	−	0.182315i	$-0.0583591\pi$
$150$	−17.1593	−	13.3908i	−1.40105	−	1.09336i
$151$		−	4.03032i		−	0.327983i	−0.986462	−	0.163991i	$-0.947563\pi$
$151$		−	4.03032i		−	0.327983i	0.986462	−	0.163991i	$-0.0524369\pi$
$152$	−10.9096	+	10.9096i	−0.884887	+	0.884887i
$153$		−	18.5320i		−	1.49822i
$154$	−9.21203	−	9.21203i	−0.742327	−	0.742327i
$155$	4.62729	−	0.284318i	0.371673	−	0.0228370i
$156$	1.06300	−	1.06300i	0.0851084	−	0.0851084i
$157$	6.28726	+	6.28726i	0.501778	+	0.501778i	0.911990	−	0.410212i	$-0.134545\pi$
$157$	6.28726	+	6.28726i	0.501778	+	0.501778i	−0.410212	+	0.911990i	$0.634545\pi$
$158$	11.1969	−	11.1969i	0.890776	−	0.890776i
$159$	2.15633			0.171008
$160$	1.83146	+	1.61942i	0.144789	+	0.128026i
$161$	1.90668	−	1.90668i	0.150267	−	0.150267i
$162$		−	8.69323i		−	0.683005i
$163$	6.57452			0.514956			0.257478	−	0.966284i	$-0.417109\pi$
$163$	6.57452			0.514956			0.257478	+	0.966284i	$0.417109\pi$
$164$			1.81924i			0.142059i
$165$	2.32487	+	37.8373i	0.180991	+	2.94563i
$166$	−0.828516	−	0.828516i	−0.0643053	−	0.0643053i
$167$	−2.00000			−0.154765			−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000			−0.154765			−0.0773823	+	0.997001i	$0.524656\pi$
$168$	11.9878			0.924877
$169$	6.04349			0.464884
$170$	8.15633	+	7.21203i	0.625562	+	0.553138i
$171$	−22.9907	+	22.9907i	−1.75814	+	1.75814i
$172$		−	1.69323i		−	0.129108i
$173$	1.77575	+	1.77575i	0.135007	+	0.135007i	0.771381	−	0.636374i	$-0.219566\pi$
$173$	1.77575	+	1.77575i	0.135007	+	0.135007i	−0.636374	+	0.771381i	$0.719566\pi$
$174$		−	14.4690i		−	1.09689i
$175$	4.69029	−	6.01023i	0.354553	−	0.454331i
$176$		−	25.0943i		−	1.89155i
$177$		−	22.7186i		−	1.70764i
$178$	−8.92478	−	8.92478i	−0.668940	−	0.668940i
$179$	5.58475	−	5.58475i	0.417424	−	0.417424i	−0.466891	−	0.884315i	$-0.654626\pi$
$179$	5.58475	−	5.58475i	0.417424	−	0.417424i	0.884315	+	0.466891i	$0.154626\pi$
$180$	1.83146	+	1.61942i	0.136509	+	0.120705i
$181$	13.6507			1.01465			0.507324	−	0.861755i	$-0.330635\pi$
$181$	13.6507			1.01465			0.507324	+	0.861755i	$0.330635\pi$
$182$	4.21203	+	4.21203i	0.312217	+	0.312217i
$183$		−	17.4314i		−	1.28856i
$184$	4.73084			0.348762
$185$	−8.56959	−	10.5623i	−0.630049	−	0.776555i
$186$	−9.02539			−0.661774
$187$		−	18.9624i		−	1.38667i
$188$	−0.377639	−	0.377639i	−0.0275422	−	0.0275422i
$189$	11.8192			0.859723
$190$	−1.17148	−	19.0659i	−0.0849884	−	1.38319i
$191$	4.33510	−	4.33510i	0.313677	−	0.313677i	−0.532655	−	0.846332i	$-0.678806\pi$
$191$	4.33510	−	4.33510i	0.313677	−	0.313677i	0.846332	+	0.532655i	$0.178806\pi$
$192$	14.7157	+	14.7157i	1.06201	+	1.06201i
$193$			17.2750i			1.24348i	0.783222	+	0.621742i	$0.213575\pi$
$193$			17.2750i			1.24348i	−0.783222	+	0.621742i	$0.786425\pi$
$194$		−	6.15633i		−	0.441998i
$195$	−1.06300	−	17.3004i	−0.0761233	−	1.23891i
$196$			0.906679i			0.0647628i
$197$	−17.8568	−	17.8568i	−1.27225	−	1.27225i	−0.944906	−	0.327342i	$-0.893847\pi$
$197$	−17.8568	−	17.8568i	−1.27225	−	1.27225i	−0.327342	−	0.944906i	$-0.606153\pi$
$198$		−	48.1681i		−	3.42316i
$199$	−1.13387	+	1.13387i	−0.0803781	+	0.0803781i	−0.746153	−	0.665775i	$-0.768101\pi$
$199$	−1.13387	+	1.13387i	−0.0803781	+	0.0803781i	0.665775	+	0.746153i	$0.268101\pi$
$200$	13.2750	−	1.63752i	0.938687	−	0.115790i
$201$	−44.5379			−3.14146
$202$	8.59261			0.604574
$203$	5.06793			0.355699
$204$	−1.32487	−	1.32487i	−0.0927594	−	0.0927594i
$205$	15.7137	+	13.8945i	1.09749	+	0.970431i
$206$			21.4763i			1.49632i
$207$	9.96968			0.692941
$208$			11.4739i			0.795572i
$209$	−23.5247	+	23.5247i	−1.62724	+	1.62724i
$210$	−9.83146	+	11.1187i	−0.678435	+	0.767264i
$211$	−27.3258			−1.88119			−0.940594	−	0.339534i	$-0.889731\pi$
$211$	−27.3258			−1.88119			−0.940594	+	0.339534i	$0.889731\pi$
$212$	0.100615	−	0.100615i	0.00691029	−	0.00691029i
$213$	−9.50659	−	9.50659i	−0.651381	−	0.651381i
$214$	1.59697	−	1.59697i	0.109167	−	0.109167i
$215$	−14.6253	−	12.9321i	−0.997437	−	0.881960i
$216$	14.6629	+	14.6629i	0.997685	+	0.997685i
$217$		−	3.16125i		−	0.214600i
$218$	−7.38787	+	7.38787i	−0.500370	+	0.500370i
$219$			4.85685i			0.328195i
$220$	1.87399	+	1.65703i	0.126345	+	0.111717i
$221$			8.67021i			0.583221i
$222$	15.3908	+	21.5471i	1.03296	+	1.44615i
$223$	−8.26717	+	8.26717i	−0.553611	+	0.553611i	−0.927481	−	0.373870i	$-0.878031\pi$
$223$	−8.26717	+	8.26717i	−0.553611	+	0.553611i	0.373870	+	0.927481i	$0.378031\pi$
$224$	1.17878	−	1.17878i	0.0787604	−	0.0787604i
$225$	27.9756	−	3.45088i	1.86504	−	0.230058i
$226$			21.1065i			1.40398i
$227$	−22.3634			−1.48431			−0.742157	−	0.670226i	$-0.766197\pi$
$227$	−22.3634			−1.48431			−0.742157	+	0.670226i	$0.766197\pi$
$228$			3.28726i			0.217704i
$229$		−	22.8423i		−	1.50946i	−0.656036	−	0.754730i	$-0.727768\pi$
$229$		−	22.8423i		−	1.50946i	0.656036	−	0.754730i	$-0.272232\pi$
$230$	−3.87987	+	4.38787i	−0.255831	+	0.289328i
$231$	25.8496			1.70078
$232$	6.28726	+	6.28726i	0.412779	+	0.412779i
$233$	−6.59991	−	6.59991i	−0.432374	−	0.432374i	0.457061	−	0.889435i	$-0.348902\pi$
$233$	−6.59991	−	6.59991i	−0.432374	−	0.432374i	−0.889435	+	0.457061i	$0.848902\pi$
$234$			22.0240i			1.43975i
$235$	−6.14609	+	0.377639i	−0.400927	+	0.0246345i
$236$	−1.06006	−	1.06006i	−0.0690043	−	0.0690043i
$237$			31.4191i			2.04089i
$238$	5.24965	−	5.24965i	0.340284	−	0.340284i
$239$	19.2599	+	19.2599i	1.24582	+	1.24582i	0.957550	+	0.288268i	$0.0930796\pi$
$239$	19.2599	+	19.2599i	1.24582	+	1.24582i	0.288268	+	0.957550i	$0.406920\pi$
$240$	−28.5349	+	1.75329i	−1.84192	+	0.113175i
$241$	8.95746	−	8.95746i	0.577001	−	0.577001i	−0.357075	−	0.934076i	$-0.616226\pi$
$241$	8.95746	−	8.95746i	0.577001	−	0.577001i	0.934076	+	0.357075i	$0.116226\pi$
$242$		−	32.9937i		−	2.12091i
$243$	−4.24671	−	4.24671i	−0.272426	−	0.272426i
$244$	−0.813358	−	0.813358i	−0.0520699	−	0.0520699i
$245$	7.83146	+	6.92478i	0.500333	+	0.442408i
$246$	−28.8749	−	28.8749i	−1.84100	−	1.84100i
$247$	10.7562	−	10.7562i	0.684403	−	0.684403i
$248$	3.92184	−	3.92184i	0.249037	−	0.249037i
$249$	2.32487			0.147333
$250$	−9.36836	+	13.6556i	−0.592507	+	0.863657i
$251$	0.453817	+	0.453817i	0.0286447	+	0.0286447i	0.721284	−	0.692639i	$-0.243552\pi$
$251$	0.453817	+	0.453817i	0.0286447	+	0.0286447i	−0.692639	+	0.721284i	$0.743552\pi$
$252$	1.17878	−	1.17878i	0.0742560	−	0.0742560i
$253$	10.2012			0.641346
$254$	−20.0732	+	20.0732i	−1.25951	+	1.25951i
$255$	−21.5623	+	1.32487i	−1.35028	+	0.0829665i
$256$	4.61213			0.288258
$257$	−16.7635			−1.04568			−0.522840	−	0.852431i	$-0.675128\pi$
$257$	−16.7635			−1.04568			−0.522840	+	0.852431i	$0.675128\pi$
$258$	26.8749	+	26.8749i	1.67316	+	1.67316i
$259$	−7.54714	+	5.39081i	−0.468956	+	0.334969i
$260$	−0.856849	−	0.757648i	−0.0531395	−	0.0469873i
$261$	13.2496	+	13.2496i	0.820133	+	0.820133i
$262$	−11.3727	+	11.3727i	−0.702609	+	0.702609i
$263$	−3.39811	−	3.39811i	−0.209536	−	0.209536i	0.594534	−	0.804070i	$-0.297337\pi$
$263$	−3.39811	−	3.39811i	−0.209536	−	0.209536i	−0.804070	+	0.594534i	$0.797337\pi$
$264$	32.0689	+	32.0689i	1.97370	+	1.97370i
$265$	−0.100615	−	1.63752i	−0.00618075	−	0.100592i
$266$	−13.0254			−0.798638
$267$	25.0435			1.53264
$268$	−2.07816	+	2.07816i	−0.126944	+	0.126944i
$269$		−	25.6507i		−	1.56395i	−0.623310	−	0.781975i	$-0.714212\pi$
$269$		−	25.6507i		−	1.56395i	0.623310	−	0.781975i	$-0.285788\pi$
$270$	−25.6253	+	1.57452i	−1.55951	+	0.0958220i
$271$	20.1260			1.22257			0.611284	−	0.791411i	$-0.290653\pi$
$271$	20.1260			1.22257			0.611284	+	0.791411i	$0.290653\pi$
$272$	14.3004			0.867091
$273$	−11.8192			−0.715333
$274$	−0.149031	+	0.149031i	−0.00900329	+	0.00900329i
$275$	28.6253	−	3.53102i	1.72617	−	0.212929i
$276$	0.712742	−	0.712742i	0.0429020	−	0.0429020i
$277$			4.82416i			0.289856i	0.989442	+	0.144928i	$0.0462950\pi$
$277$			4.82416i			0.289856i	−0.989442	+	0.144928i	$0.953705\pi$
$278$		−	19.6629i		−	1.17930i
$279$	8.26480	−	8.26480i	0.494801	−	0.494801i
$280$	−0.559357	−	9.10356i	−0.0334280	−	0.544041i
$281$	−2.36248	+	2.36248i	−0.140934	+	0.140934i	−0.774054	−	0.633120i	$-0.781774\pi$
$281$	−2.36248	+	2.36248i	−0.140934	+	0.140934i	0.633120	+	0.774054i	$0.281774\pi$
$282$	11.9878			0.713862
$283$	−2.72496			−0.161982			−0.0809911	−	0.996715i	$-0.525809\pi$
$283$	−2.72496			−0.161982			−0.0809911	+	0.996715i	$0.525809\pi$
$284$	−0.887166			−0.0526436
$285$	28.3938	+	25.1065i	1.68190	+	1.48718i
$286$			22.5355i			1.33255i
$287$	10.1138	−	10.1138i	0.596998	−	0.596998i
$288$	6.16362			0.363195
$289$	−6.19394			−0.364349
$290$	−10.9878	+	0.675131i	−0.645225	+	0.0396450i
$291$	8.63752	+	8.63752i	0.506340	+	0.506340i
$292$	0.226623	+	0.226623i	0.0132621	+	0.0132621i
$293$	−1.88717	+	1.88717i	−0.110249	+	0.110249i	−0.760080	−	0.649830i	$-0.774840\pi$
$293$	−1.88717	+	1.88717i	−0.110249	+	0.110249i	0.649830	+	0.760080i	$0.274840\pi$
$294$	−14.3908	−	14.3908i	−0.839289	−	0.839289i
$295$	−17.2526	+	1.06006i	−1.00448	+	0.0617193i
$296$	−16.0508	−	2.67513i	−0.932933	−	0.155489i
$297$	31.6180	+	31.6180i	1.83466	+	1.83466i
$298$	6.59261			0.381900
$299$	−4.66433			−0.269745
$300$	1.75329	−	2.24671i	0.101226	−	0.129714i
$301$	−9.41327	+	9.41327i	−0.542572	+	0.542572i
$302$	5.96968			0.343517
$303$	−12.0557	+	12.0557i	−0.692582	+	0.692582i
$304$	−17.7411	−	17.7411i	−1.01752	−	1.01752i
$305$	−13.2374	+	0.813358i	−0.757973	+	0.0465727i
$306$	27.4495			1.56918
$307$	7.17148	−	7.17148i	0.409298	−	0.409298i	−0.472196	−	0.881494i	$-0.656538\pi$
$307$	7.17148	−	7.17148i	0.409298	−	0.409298i	0.881494	+	0.472196i	$0.156538\pi$
$308$	1.20616	−	1.20616i	0.0687271	−	0.0687271i
$309$	−30.1319	−	30.1319i	−1.71414	−	1.71414i
$310$	0.421130	+	6.85391i	0.0239186	+	0.389276i
$311$	−20.2599	−	20.2599i	−1.14883	−	1.14883i	−0.986783	−	0.162050i	$-0.948189\pi$
$311$	−20.2599	−	20.2599i	−1.14883	−	1.14883i	−0.162050	−	0.986783i	$-0.551811\pi$
$312$	−14.6629	−	14.6629i	−0.830124	−	0.830124i
$313$		−	1.90431i		−	0.107638i	−0.998551	−	0.0538190i	$-0.982861\pi$
$313$		−	1.90431i		−	0.107638i	0.998551	−	0.0538190i	$-0.0171394\pi$
$314$	−9.31265	+	9.31265i	−0.525543	+	0.525543i
$315$	−1.17878	−	19.1847i	−0.0664166	−	1.08093i
$316$	1.46604	+	1.46604i	0.0824710	+	0.0824710i
$317$	−1.56230	+	1.56230i	−0.0877473	+	0.0877473i	−0.749618	−	0.661871i	$-0.769763\pi$
$317$	−1.56230	+	1.56230i	−0.0877473	+	0.0877473i	0.661871	+	0.749618i	$0.269763\pi$
$318$			3.19394i			0.179107i
$319$	13.5574	+	13.5574i	0.759067	+	0.759067i
$320$	10.4885	−	11.8618i	0.586324	−	0.663093i
$321$			4.48119i			0.250116i
$322$	2.82416	+	2.82416i	0.157384	+	0.157384i
$323$	−13.4060	−	13.4060i	−0.745928	−	0.745928i
$324$	1.13823			0.0632348
$325$	−13.0884	+	1.61450i	−0.726014	+	0.0895562i
$326$			9.73813i			0.539345i
$327$		−	20.7308i		−	1.14642i
$328$	25.0943			1.38560
$329$			4.19886i			0.231491i
$330$	−56.0444	+	3.44358i	−3.08515	+	0.189563i
$331$	10.1715	−	10.1715i	0.559075	−	0.559075i	−0.369969	−	0.929044i	$-0.620632\pi$
$331$	10.1715	−	10.1715i	0.559075	−	0.559075i	0.929044	+	0.369969i	$0.120632\pi$
$332$	0.108480	−	0.108480i	0.00595360	−	0.00595360i
$333$	−33.8251	−	5.63752i	−1.85360	−	0.308934i
$334$		−	2.96239i		−	0.162095i
$335$	2.07816	+	33.8222i	0.113542	+	1.84790i
$336$			19.4944i			1.06350i
$337$	0.876362	−	0.876362i	0.0477385	−	0.0477385i	−0.682835	−	0.730573i	$-0.739253\pi$
$337$	0.876362	−	0.876362i	0.0477385	−	0.0477385i	0.730573	+	0.682835i	$0.239253\pi$
$338$			8.95158i			0.486902i
$339$	−29.6131	−	29.6131i	−1.60836	−	1.60836i
$340$	−0.944290	+	1.06793i	−0.0512113	+	0.0579166i
$341$	8.45676	−	8.45676i	0.457959	−	0.457959i
$342$	−34.0537	−	34.0537i	−1.84141	−	1.84141i
$343$	12.5877	−	12.5877i	0.679671	−	0.679671i
$344$	−23.3561			−1.25928
$345$	−0.712742	−	11.5999i	−0.0383728	−	0.624518i
$346$	−2.63023	+	2.63023i	−0.141402	+	0.141402i
$347$		−	5.16950i		−	0.277513i	−0.990327	−	0.138757i	$-0.955689\pi$
$347$		−	5.16950i		−	0.277513i	0.990327	−	0.138757i	$-0.0443106\pi$
$348$	1.89446			0.101554
$349$			3.87636i			0.207497i	0.994604	+	0.103748i	$0.0330837\pi$
$349$			3.87636i			0.207497i	−0.994604	+	0.103748i	$0.966916\pi$
$350$	8.90232	+	6.94723i	0.475849	+	0.371345i
$351$	−14.4568	−	14.4568i	−0.771645	−	0.771645i
$352$	6.30677			0.336152
$353$	−1.35026			−0.0718672			−0.0359336	−	0.999354i	$-0.511440\pi$
$353$	−1.35026			−0.0718672			−0.0359336	+	0.999354i	$0.511440\pi$
$354$	33.6507			1.78851
$355$	−6.77575	+	7.66291i	−0.359619	+	0.406705i
$356$	1.16854	−	1.16854i	0.0619327	−	0.0619327i
$357$			14.7308i			0.779639i
$358$	8.27210	+	8.27210i	0.437194	+	0.437194i
$359$			7.65703i			0.404123i	0.979373	+	0.202061i	$0.0647640\pi$
$359$			7.65703i			0.404123i	−0.979373	+	0.202061i	$0.935236\pi$
$360$	22.3380	−	25.2628i	1.17732	−	1.33147i
$361$			14.2628i			0.750675i
$362$			20.2193i			1.06270i
$363$	46.2912	+	46.2912i	2.42966	+	2.42966i
$364$	−0.551493	+	0.551493i	−0.0289061	+	0.0289061i
$365$	3.68830	−	0.226623i	0.193055	−	0.0118620i
$366$	25.8192			1.34959
$367$	−2.18370	−	2.18370i	−0.113988	−	0.113988i	0.647812	−	0.761800i	$-0.275684\pi$
$367$	−2.18370	−	2.18370i	−0.113988	−	0.113988i	−0.761800	+	0.647812i	$0.775684\pi$
$368$			7.69323i			0.401037i
$369$	52.8832			2.75299
$370$	15.6448	−	12.6932i	0.813335	−	0.659890i
$371$	−1.11871			−0.0580807
$372$		−	1.18172i		−	0.0612692i
$373$	12.1065	+	12.1065i	0.626851	+	0.626851i	0.947274	−	0.320424i	$-0.103825\pi$
$373$	12.1065	+	12.1065i	0.626851	+	0.626851i	−0.320424	+	0.947274i	$0.603825\pi$
$374$	28.0870			1.45234
$375$	−6.01516	−	32.3034i	−0.310621	−	1.66814i
$376$	−5.20910	+	5.20910i	−0.268639	+	0.268639i
$377$	−6.19886	−	6.19886i	−0.319258	−	0.319258i
$378$			17.5066i			0.900442i
$379$			30.5296i			1.56820i	0.620634	+	0.784100i	$0.286875\pi$
$379$			30.5296i			1.56820i	−0.620634	+	0.784100i	$0.713125\pi$
$380$	2.49635	−	0.153385i	0.128060	−	0.00786850i
$381$		−	56.3268i		−	2.88571i
$382$	6.42113	+	6.42113i	0.328534	+	0.328534i
$383$			3.21837i			0.164451i	0.996614	+	0.0822256i	$0.0262028\pi$
$383$			3.21837i			0.164451i	−0.996614	+	0.0822256i	$0.973797\pi$
$384$	−26.3410	+	26.3410i	−1.34421	+	1.34421i
$385$	−1.20616	−	19.6302i	−0.0614714	−	1.00045i
$386$	−25.5877			−1.30238
$387$	−49.2203			−2.50201
$388$	0.806063			0.0409217
$389$	9.63752	+	9.63752i	0.488642	+	0.488642i	0.907877	−	0.419236i	$-0.137702\pi$
$389$	9.63752	+	9.63752i	0.488642	+	0.488642i	−0.419236	+	0.907877i	$0.637702\pi$
$390$	25.6253	−	1.57452i	1.29759	−	0.0797287i
$391$			5.81336i			0.293994i
$392$	12.5066			0.631678
$393$		−	31.9126i		−	1.60978i
$394$	26.4495	−	26.4495i	1.33250	−	1.33250i
$395$	23.8598	−	1.46604i	1.20052	−	0.0737643i
$396$	6.30677			0.316927
$397$	−25.3757	+	25.3757i	−1.27357	+	1.27357i	−0.329365	+	0.944203i	$0.606835\pi$
$397$	−25.3757	+	25.3757i	−1.27357	+	1.27357i	−0.944203	+	0.329365i	$0.893165\pi$
$398$	−1.67949	−	1.67949i	−0.0841850	−	0.0841850i
$399$	18.2750	−	18.2750i	0.914896	−	0.914896i
$400$	2.66291	+	21.5877i	0.133146	+	1.07938i
$401$	−17.4241	−	17.4241i	−0.870117	−	0.870117i	0.122368	−	0.992485i	$-0.460951\pi$
$401$	−17.4241	−	17.4241i	−0.870117	−	0.870117i	−0.992485	+	0.122368i	$0.960951\pi$
$402$		−	65.9692i		−	3.29025i
$403$	−3.86670	+	3.86670i	−0.192614	+	0.192614i
$404$			1.12505i			0.0559735i
$405$	8.69323	−	9.83146i	0.431970	−	0.488529i
$406$			7.50659i			0.372546i
$407$	−34.6107	−	5.76845i	−1.71559	−	0.285932i
$408$	−18.2750	+	18.2750i	−0.904749	+	0.904749i
$409$	0.531024	−	0.531024i	0.0262575	−	0.0262575i	−0.693856	−	0.720114i	$-0.744090\pi$
$409$	0.531024	−	0.531024i	0.0262575	−	0.0262575i	0.720114	+	0.693856i	$0.244090\pi$
$410$	−20.5804	+	23.2750i	−1.01639	+	1.14947i
$411$		−	0.418190i		−	0.0206278i
$412$	−2.81194			−0.138534
$413$			11.7866i			0.579978i
$414$			14.7670i			0.725760i
$415$	−0.108480	−	1.76551i	−0.00532506	−	0.0866656i
$416$	−2.88366			−0.141383
$417$	27.5877	+	27.5877i	1.35097	+	1.35097i
$418$	−34.8446	−	34.8446i	−1.70431	−	1.70431i
$419$			24.3430i			1.18923i	0.804010	+	0.594616i	$0.202696\pi$
$419$			24.3430i			1.18923i	−0.804010	+	0.594616i	$0.797304\pi$
$420$	−1.45580	−	1.28726i	−0.0710358	−	0.0628117i
$421$	−0.488489	−	0.488489i	−0.0238075	−	0.0238075i	0.695103	−	0.718910i	$-0.255359\pi$
$421$	−0.488489	−	0.488489i	−0.0238075	−	0.0238075i	−0.718910	+	0.695103i	$0.755359\pi$
$422$		−	40.4749i		−	1.97029i
$423$	−10.9775	+	10.9775i	−0.533747	+	0.533747i
$424$	−1.38787	−	1.38787i	−0.0674011	−	0.0674011i
$425$	2.01222	+	16.3127i	0.0976069	+	0.791280i
$426$	14.0811	−	14.0811i	0.682232	−	0.682232i
$427$			9.04349i			0.437645i
$428$	0.209095	+	0.209095i	0.0101070	+	0.0101070i
$429$	−31.6180	−	31.6180i	−1.52653	−	1.52653i
$430$	19.1549	−	21.6629i	0.923732	−	1.04468i
$431$	8.39811	+	8.39811i	0.404523	+	0.404523i	0.879823	−	0.475301i	$-0.157661\pi$
$431$	8.39811	+	8.39811i	0.404523	+	0.404523i	−0.475301	+	0.879823i	$0.657661\pi$
$432$	−23.8446	+	23.8446i	−1.14723	+	1.14723i
$433$	13.2071	−	13.2071i	0.634693	−	0.634693i	−0.314548	−	0.949241i	$-0.601853\pi$
$433$	13.2071	−	13.2071i	0.634693	−	0.634693i	0.949241	+	0.314548i	$0.101853\pi$
$434$	4.68243			0.224764
$435$	14.4690	−	16.3634i	0.693734	−	0.784567i
$436$	−0.967313	−	0.967313i	−0.0463259	−	0.0463259i
$437$	7.21203	−	7.21203i	0.344998	−	0.344998i
$438$	−7.19394			−0.343740
$439$	−12.6224	+	12.6224i	−0.602432	+	0.602432i	−0.940957	−	0.338525i	$-0.890072\pi$
$439$	−12.6224	+	12.6224i	−0.602432	+	0.602432i	0.338525	+	0.940957i	$0.390072\pi$
$440$	22.8568	−	25.8496i	1.08966	−	1.23233i
$441$	26.3561			1.25505
$442$	−12.8423			−0.610844
$443$	4.82852	+	4.82852i	0.229410	+	0.229410i	0.812446	−	0.583036i	$-0.198135\pi$
$443$	4.82852	+	4.82852i	0.229410	+	0.229410i	−0.583036	+	0.812446i	$0.698135\pi$
$444$	−2.82122	+	2.01516i	−0.133889	+	0.0956352i
$445$	−1.16854	−	19.0181i	−0.0553943	−	0.901544i
$446$	−12.2453	−	12.2453i	−0.579831	−	0.579831i
$447$	−9.24965	+	9.24965i	−0.437493	+	0.437493i
$448$	−7.63458	−	7.63458i	−0.360700	−	0.360700i
$449$	−6.38058	−	6.38058i	−0.301118	−	0.301118i	0.540333	−	0.841451i	$-0.318298\pi$
$449$	−6.38058	−	6.38058i	−0.301118	−	0.301118i	−0.841451	+	0.540333i	$0.818298\pi$
$450$	5.11142	+	41.4372i	0.240955	+	1.95337i
$451$	54.1114			2.54801
$452$	−2.76353			−0.129985
$453$	−8.37565	+	8.37565i	−0.393523	+	0.393523i
$454$		−	33.1246i		−	1.55461i
$455$	0.551493	+	8.97556i	0.0258544	+	0.420781i
$456$	45.3439			2.12342
$457$	11.1939			0.523630			0.261815	−	0.965118i	$-0.415679\pi$
$457$	11.1939			0.523630			0.261815	+	0.965118i	$0.415679\pi$
$458$	33.8338			1.58095
$459$	−18.0181	+	18.0181i	−0.841013	+	0.841013i
$460$	−0.574515	−	0.508002i	−0.0267869	−	0.0236857i
$461$	−10.6507	+	10.6507i	−0.496052	+	0.496052i	−0.910207	−	0.414154i	$-0.864077\pi$
$461$	−10.6507	+	10.6507i	−0.496052	+	0.496052i	0.414154	+	0.910207i	$0.364077\pi$
$462$			38.2882i			1.78133i
$463$		−	11.5672i		−	0.537574i	−0.963200	−	0.268787i	$-0.913377\pi$
$463$		−	11.5672i		−	0.537574i	0.963200	−	0.268787i	$-0.0866228\pi$
$464$	−10.2243	+	10.2243i	−0.474649	+	0.474649i
$465$	−10.2071	−	9.02539i	−0.473343	−	0.418543i
$466$	9.77575	−	9.77575i	0.452853	−	0.452853i
$467$	−5.97556			−0.276516			−0.138258	−	0.990396i	$-0.544150\pi$
$467$	−5.97556			−0.276516			−0.138258	+	0.990396i	$0.544150\pi$
$468$	−2.88366			−0.133297
$469$	23.1065			1.06696
$470$	−0.559357	−	9.10356i	−0.0258012	−	0.419916i
$471$		−	26.1319i		−	1.20409i
$472$	−14.6224	+	14.6224i	−0.673049	+	0.673049i
$473$	−50.3634			−2.31571
$474$	−46.5379			−2.13755
$475$	17.7411	−	22.7338i	0.814016	−	1.04310i
$476$	0.687350	+	0.687350i	0.0315046	+	0.0315046i
$477$	−2.92478	−	2.92478i	−0.133916	−	0.133916i
$478$	−28.5276	+	28.5276i	−1.30482	+	1.30482i
$479$	24.9472	+	24.9472i	1.13987	+	1.13987i	0.988473	+	0.151395i	$0.0483764\pi$
$479$	24.9472	+	24.9472i	1.13987	+	1.13987i	0.151395	+	0.988473i	$0.451624\pi$
$480$	−0.440643	−	7.17148i	−0.0201125	−	0.327332i
$481$	15.8251	+	2.63752i	0.721563	+	0.120261i
$482$	13.2677	+	13.2677i	0.604329	+	0.604329i
$483$	−7.92478			−0.360590
$484$	4.31994			0.196361
$485$	6.15633	−	6.96239i	0.279544	−	0.316146i
$486$	6.29020	−	6.29020i	0.285329	−	0.285329i
$487$	37.4880			1.69874			0.849372	−	0.527794i	$-0.176981\pi$
$487$	37.4880			1.69874			0.849372	+	0.527794i	$0.176981\pi$
$488$	−11.2193	+	11.2193i	−0.507875	+	0.507875i
$489$	−13.6629	−	13.6629i	−0.617858	−	0.617858i
$490$	−10.2569	+	11.5999i	−0.463361	+	0.524030i
$491$	4.07522			0.183912			0.0919561	−	0.995763i	$-0.470688\pi$
$491$	4.07522			0.183912			0.0919561	+	0.995763i	$0.470688\pi$
$492$	3.78067	−	3.78067i	0.170446	−	0.170446i
$493$	−7.72592	+	7.72592i	−0.347958	+	0.347958i
$494$	15.9321	+	15.9321i	0.716818	+	0.716818i
$495$	48.1681	−	54.4749i	2.16499	−	2.44846i
$496$	6.37764	+	6.37764i	0.286364	+	0.286364i
$497$	4.93207	+	4.93207i	0.221234	+	0.221234i
$498$			3.44358i			0.154311i
$499$	0.954524	−	0.954524i	0.0427304	−	0.0427304i	−0.685419	−	0.728149i	$-0.740381\pi$
$499$	0.954524	−	0.954524i	0.0427304	−	0.0427304i	0.728149	+	0.685419i	$0.240381\pi$
$500$	−1.78797	−	1.22662i	−0.0799602	−	0.0548563i
$501$	4.15633	+	4.15633i	0.185691	+	0.185691i
$502$	−0.672191	+	0.672191i	−0.0300014	+	0.0300014i
$503$			23.0435i			1.02746i	0.857952	+	0.513729i	$0.171736\pi$
$503$			23.0435i			1.02746i	−0.857952	+	0.513729i	$0.828264\pi$
$504$	−16.2599	−	16.2599i	−0.724273	−	0.724273i
$505$	9.71767	+	8.59261i	0.432430	+	0.382366i
$506$			15.1100i			0.671722i
$507$	−12.5594	−	12.5594i	−0.557781	−	0.557781i
$508$	−2.62824	−	2.62824i	−0.116609	−	0.116609i
$509$	1.87399			0.0830632			0.0415316	−	0.999137i	$-0.486776\pi$
$509$	1.87399			0.0830632			0.0415316	+	0.999137i	$0.486776\pi$
$510$	−1.96239	−	31.9380i	−0.0868960	−	1.41424i
$511$		−	2.51976i		−	0.111468i
$512$		−	18.5188i		−	0.818423i
$513$	44.7064			1.97384
$514$		−	24.8300i		−	1.09521i
$515$	−21.4763	+	24.2882i	−0.946358	+	1.07027i
$516$	−3.51881	+	3.51881i	−0.154907	+	0.154907i
$517$	−11.2325	+	11.2325i	−0.494005	+	0.494005i
$518$	−7.98484	−	11.1788i	−0.350834	−	0.491167i
$519$		−	7.38058i		−	0.323971i
$520$	−10.4509	+	11.8192i	−0.458301	+	0.518308i
$521$		−	29.0762i		−	1.27385i	−0.770926	−	0.636925i	$-0.780206\pi$
$521$		−	29.0762i		−	1.27385i	0.770926	−	0.636925i	$-0.219794\pi$
$522$	−19.6253	+	19.6253i	−0.858976	+	0.858976i
$523$			5.25457i			0.229766i	0.993379	+	0.114883i	$0.0366494\pi$
$523$			5.25457i			0.229766i	−0.993379	+	0.114883i	$0.963351\pi$
$524$	−1.48906	−	1.48906i	−0.0650498	−	0.0650498i
$525$	−22.2374	+	2.74306i	−0.970521	+	0.119717i
$526$	5.03326	−	5.03326i	0.219460	−	0.219460i
$527$	4.81924	+	4.81924i	0.209929	+	0.209929i
$528$	−52.1500	+	52.1500i	−2.26954	+	2.26954i
$529$	19.8726			0.864025
$530$	2.42548	−	0.149031i	0.105356	−	0.00647349i
$531$	−30.8149	+	30.8149i	−1.33725	+	1.33725i
$532$		−	1.70545i		−	0.0739405i
$533$	−24.7415			−1.07167
$534$			37.0943i			1.60523i
$535$	3.40303	−	0.209095i	0.147126	−	0.00903997i
$536$	28.6659	+	28.6659i	1.23818	+	1.23818i
$537$	−23.2120			−1.00167
$538$	37.9937			1.63802
$539$	26.9683			1.16161
$540$	−0.206155	−	3.35519i	−0.00887151	−	0.144384i
$541$	17.2677	−	17.2677i	0.742398	−	0.742398i	−0.230641	−	0.973039i	$-0.574082\pi$
$541$	17.2677	−	17.2677i	0.742398	−	0.742398i	0.973039	+	0.230641i	$0.0740822\pi$
$542$			29.8105i			1.28047i
$543$	−28.3684	−	28.3684i	−1.21740	−	1.21740i
$544$			3.59403i			0.154093i
$545$	−15.7431	+	0.967313i	−0.674359	+	0.0414351i
$546$		−	17.5066i		−	0.749213i
$547$			8.80606i			0.376520i	0.982119	+	0.188260i	$0.0602848\pi$
$547$			8.80606i			0.376520i	−0.982119	+	0.188260i	$0.939715\pi$
$548$	−0.0195130	−	0.0195130i	−0.000833554	−	0.000833554i
$549$	−23.6434	+	23.6434i	−1.00908	+	1.00908i
$550$	5.23013	+	42.3996i	0.223014	+	1.80793i
$551$	19.1695			0.816648
$552$	−9.83146	−	9.83146i	−0.418455	−	0.418455i
$553$		−	16.3004i		−	0.693165i
$554$	−7.14552			−0.303584
$555$	−4.14117	+	39.7592i	−0.175783	+	1.68768i
$556$	2.57452			0.109184
$557$		−	33.3282i		−	1.41216i	−0.708132	−	0.706080i	$-0.750462\pi$
$557$		−	33.3282i		−	1.41216i	0.708132	−	0.706080i	$-0.249538\pi$
$558$	12.2418	+	12.2418i	0.518236	+	0.518236i
$559$	23.0278			0.973971
$560$	14.8041	−	0.909619i	0.625587	−	0.0384384i
$561$	−39.4069	+	39.4069i	−1.66376	+	1.66376i
$562$	−3.49929	−	3.49929i	−0.147609	−	0.147609i
$563$		−	25.0435i		−	1.05546i	−0.849413	−	0.527729i	$-0.823044\pi$
$563$		−	25.0435i		−	1.05546i	0.849413	−	0.527729i	$-0.176956\pi$
$564$			1.56959i			0.0660917i
$565$	−21.1065	+	23.8700i	−0.887957	+	1.00422i
$566$		−	4.03620i		−	0.169654i
$567$	−6.32781	−	6.32781i	−0.265743	−	0.265743i
$568$			12.2374i			0.513471i
$569$	−32.6566	+	32.6566i	−1.36903	+	1.36903i	−0.507215	+	0.861819i	$0.669325\pi$
$569$	−32.6566	+	32.6566i	−1.36903	+	1.36903i	−0.861819	+	0.507215i	$0.830675\pi$
$570$	−37.1876	+	42.0567i	−1.55762	+	1.76156i
$571$	−17.1246			−0.716642			−0.358321	−	0.933598i	$-0.616651\pi$
$571$	−17.1246			−0.716642			−0.358321	+	0.933598i	$0.616651\pi$
$572$	−2.95063			−0.123372
$573$	−18.0181			−0.752717
$574$	14.9805	+	14.9805i	0.625273	+	0.625273i
$575$	−8.77575	+	1.08252i	−0.365974	+	0.0451441i
$576$		−	39.9199i		−	1.66333i
$577$	13.5345			0.563450			0.281725	−	0.959495i	$-0.409093\pi$
$577$	13.5345			0.563450			0.281725	+	0.959495i	$0.409093\pi$
$578$		−	9.17442i		−	0.381606i
$579$	35.9003	−	35.9003i	1.49197	−	1.49197i
$580$	−0.0883966	−	1.43866i	−0.00367047	−	0.0597370i
$581$	−1.20616			−0.0500398
$582$	−12.7938	+	12.7938i	−0.530322	+	0.530322i
$583$	−2.99271	−	2.99271i	−0.123945	−	0.123945i
$584$	3.12601	−	3.12601i	0.129355	−	0.129355i
$585$	−22.0240	+	24.9076i	−0.910579	+	1.02980i
$586$	−2.79526	−	2.79526i	−0.115471	−	0.115471i
$587$			6.39375i			0.263898i	0.991256	+	0.131949i	$0.0421236\pi$
$587$			6.39375i			0.263898i	−0.991256	+	0.131949i	$0.957876\pi$
$588$	1.88423	−	1.88423i	0.0777042	−	0.0777042i
$589$		−	11.9575i		−	0.492699i
$590$	−1.57016	−	25.5544i	−0.0646425	−	1.05206i
$591$			74.2189i			3.05296i
$592$	4.35026	−	26.1016i	0.178795	−	1.07277i
$593$	26.6507	−	26.6507i	1.09441	−	1.09441i	0.0993614	−	0.995051i	$-0.468320\pi$
$593$	26.6507	−	26.6507i	1.09441	−	1.09441i	0.995051	−	0.0993614i	$-0.0316800\pi$
$594$	−46.8324	+	46.8324i	−1.92156	+	1.92156i
$595$	11.1866	−	0.687350i	0.458608	−	0.0281786i
$596$			0.863188i			0.0353576i
$597$	4.71274			0.192880
$598$		−	6.90877i		−	0.282521i
$599$		−	19.4314i		−	0.793944i	−0.917831	−	0.396972i	$-0.870061\pi$
$599$		−	19.4314i		−	0.793944i	0.917831	−	0.396972i	$-0.129939\pi$
$600$	−30.9907	−	24.1847i	−1.26519	−	0.987335i
$601$	−36.8749			−1.50416			−0.752080	−	0.659072i	$-0.770949\pi$
$601$	−36.8749			−1.50416			−0.752080	+	0.659072i	$0.770949\pi$
$602$	−13.9429	−	13.9429i	−0.568269	−	0.568269i
$603$	60.4099	+	60.4099i	2.46008	+	2.46008i
$604$			0.781626i			0.0318039i
$605$	32.9937	−	37.3136i	1.34138	−	1.51701i
$606$	−17.8568	−	17.8568i	−0.725385	−	0.725385i
$607$		−	12.2315i		−	0.496463i	−0.968701	−	0.248232i	$-0.920151\pi$
$607$		−	12.2315i		−	0.496463i	0.968701	−	0.248232i	$-0.0798494\pi$
$608$	4.45874	−	4.45874i	0.180826	−	0.180826i
$609$	−10.5320	−	10.5320i	−0.426777	−	0.426777i
$610$	−1.20474	−	19.6072i	−0.0487785	−	0.793872i
$611$	5.13586	−	5.13586i	0.207775	−	0.207775i
$612$			3.59403i			0.145280i
$613$	−14.0581	−	14.0581i	−0.567800	−	0.567800i	0.363711	−	0.931512i	$-0.381509\pi$
$613$	−14.0581	−	14.0581i	−0.567800	−	0.567800i	−0.931512	+	0.363711i	$0.881509\pi$
$614$	10.6224	+	10.6224i	0.428684	+	0.428684i
$615$	−3.78067	−	61.5306i	−0.152451	−	2.48115i
$616$	−16.6375	−	16.6375i	−0.670345	−	0.670345i
$617$	−8.87399	+	8.87399i	−0.357253	+	0.357253i	−0.862800	−	0.505546i	$-0.831291\pi$
$617$	−8.87399	+	8.87399i	−0.357253	+	0.357253i	0.505546	+	0.862800i	$0.331291\pi$
$618$	44.6312	−	44.6312i	1.79533	−	1.79533i
$619$	−38.4894			−1.54702			−0.773511	−	0.633783i	$-0.781501\pi$
$619$	−38.4894			−1.54702			−0.773511	+	0.633783i	$0.781501\pi$
$620$	−0.897400	+	0.0551396i	−0.0360404	+	0.00221446i
$621$	−9.69323	−	9.69323i	−0.388976	−	0.388976i
$622$	30.0088	−	30.0088i	1.20324	−	1.20324i
$623$	−12.9927			−0.520542
$624$	23.8446	−	23.8446i	0.954549	−	0.954549i
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$	2.82065			0.112736
$627$	97.7762			3.90481
$628$	−1.21933	−	1.21933i	−0.0486565	−	0.0486565i
$629$	3.28726	−	19.7235i	0.131072	−	0.786429i
$630$	28.4162	−	1.74600i	1.13213	−	0.0695623i
$631$	−27.4646	−	27.4646i	−1.09335	−	1.09335i	−0.995169	−	0.0981807i	$-0.968698\pi$
$631$	−27.4646	−	27.4646i	−1.09335	−	1.09335i	−0.0981807	−	0.995169i	$-0.531302\pi$
$632$	20.2223	−	20.2223i	0.804399	−	0.804399i
$633$	56.7875	+	56.7875i	2.25710	+	2.25710i
$634$	−2.31406	−	2.31406i	−0.0919033	−	0.0919033i
$635$	−42.7747	+	2.62824i	−1.69746	+	0.104299i
$636$	−0.418190			−0.0165823
$637$	−12.3307			−0.488562
$638$	−20.0811	+	20.0811i	−0.795018	+	0.795018i
$639$			25.7889i			1.02019i
$640$	21.2325	+	18.7743i	0.839288	+	0.742121i
$641$	2.18427			0.0862736			0.0431368	−	0.999069i	$-0.486265\pi$
$641$	2.18427			0.0862736			0.0431368	+	0.999069i	$0.486265\pi$
$642$	−6.63752			−0.261962
$643$	−43.7235			−1.72429			−0.862144	−	0.506663i	$-0.830879\pi$
$643$	−43.7235			−1.72429			−0.862144	+	0.506663i	$0.830879\pi$
$644$	−0.369775	+	0.369775i	−0.0145712	+	0.0145712i
$645$	3.51881	+	57.2687i	0.138553	+	2.25495i
$646$	19.8568	−	19.8568i	0.781257	−	0.781257i
$647$			10.8813i			0.427788i	0.976857	+	0.213894i	$0.0686146\pi$
$647$			10.8813i			0.427788i	−0.976857	+	0.213894i	$0.931385\pi$
$648$		−	15.7005i		−	0.616775i
$649$	−31.5306	+	31.5306i	−1.23768	+	1.23768i
$650$	−2.39138	−	19.3865i	−0.0937978	−	0.760399i
$651$	−6.56959	+	6.56959i	−0.257483	+	0.257483i
$652$	−1.27504			−0.0499344
$653$	44.5256			1.74242			0.871211	−	0.490908i	$-0.163335\pi$
$653$	44.5256			1.74242			0.871211	+	0.490908i	$0.163335\pi$
$654$	30.7064			1.20072
$655$	−24.2345	+	1.48906i	−0.946920	+	0.0581823i
$656$			40.8080i			1.59328i
$657$	6.58769	−	6.58769i	0.257010	−	0.257010i
$658$	−6.21933			−0.242455
$659$	17.2243			0.670962			0.335481	−	0.942047i	$-0.391101\pi$
$659$	17.2243			0.670962			0.335481	+	0.942047i	$0.391101\pi$
$660$	−0.450877	−	7.33804i	−0.0175504	−	0.285633i
$661$	21.5804	+	21.5804i	0.839380	+	0.839380i	0.988777	−	0.149397i	$-0.0477333\pi$
$661$	21.5804	+	21.5804i	0.839380	+	0.839380i	−0.149397	+	0.988777i	$0.547733\pi$
$662$	15.0659	+	15.0659i	0.585555	+	0.585555i
$663$	18.0181	−	18.0181i	0.699765	−	0.699765i
$664$	−1.49635	−	1.49635i	−0.0580698	−	0.0580698i
$665$	−14.7308	−	13.0254i	−0.571237	−	0.505103i
$666$	8.35026	−	50.1016i	0.323566	−	1.94140i
$667$	−4.15633	−	4.15633i	−0.160934	−	0.160934i
$668$	0.387873			0.0150073
$669$	34.3611			1.32848
$670$	−50.0972	+	3.07816i	−1.93542	+	0.118920i
$671$	−24.1925	+	24.1925i	−0.933942	+	0.933942i
$672$	−4.89938			−0.188998
$673$	24.6629	−	24.6629i	0.950685	−	0.950685i	−0.0481545	−	0.998840i	$-0.515334\pi$
$673$	24.6629	−	24.6629i	0.950685	−	0.950685i	0.998840	+	0.0481545i	$0.0153340\pi$
$674$	1.29806	+	1.29806i	0.0499995	+	0.0499995i
$675$	−30.5550	−	23.8446i	−1.17606	−	0.917780i
$676$	−1.17205			−0.0450790
$677$	22.4944	−	22.4944i	0.864529	−	0.864529i	−0.127331	−	0.991860i	$-0.540641\pi$
$677$	22.4944	−	22.4944i	0.864529	−	0.864529i	0.991860	+	0.127331i	$0.0406412\pi$
$678$	43.8627	−	43.8627i	1.68454	−	1.68454i
$679$	−4.48119	−	4.48119i	−0.171972	−	0.171972i
$680$	14.7308	+	13.0254i	0.564902	+	0.499501i
$681$	46.4749	+	46.4749i	1.78092	+	1.78092i
$682$	12.5261	+	12.5261i	0.479649	+	0.479649i
$683$		−	18.3185i		−	0.700939i	−0.936574	−	0.350470i	$-0.886022\pi$
$683$		−	18.3185i		−	0.700939i	0.936574	−	0.350470i	$-0.113978\pi$
$684$	4.45874	−	4.45874i	0.170484	−	0.170484i
$685$	−0.317575	+	0.0195130i	−0.0121339	+	0.000745554i
$686$	18.6448	+	18.6448i	0.711862	+	0.711862i
$687$	−47.4699	+	47.4699i	−1.81109	+	1.81109i
$688$		−	37.9814i		−	1.44803i
$689$	1.36836	+	1.36836i	0.0521304	+	0.0521304i
$690$	17.1817	−	1.05571i	0.654097	−	0.0401902i
$691$		−	3.89446i		−	0.148152i	−0.997253	−	0.0740761i	$-0.976399\pi$
$691$		−	3.89446i		−	0.148152i	0.997253	−	0.0740761i	$-0.0236008\pi$
$692$	−0.344382	−	0.344382i	−0.0130914	−	0.0130914i
$693$	−35.0616	−	35.0616i	−1.33188	−	1.33188i
$694$	7.65703			0.290657
$695$	19.6629	−	22.2374i	0.745857	−	0.843514i
$696$		−	26.1319i		−	0.990527i
$697$			30.8364i			1.16801i
$698$	−5.74164			−0.217324
$699$			27.4314i			1.03755i
$700$	−0.909619	+	1.16560i	−0.0343804	+	0.0440557i
$701$	−19.0484	+	19.0484i	−0.719449	+	0.719449i	−0.968492	−	0.249044i	$-0.919884\pi$
$701$	−19.0484	+	19.0484i	−0.719449	+	0.719449i	0.249044	+	0.968492i	$0.419884\pi$
$702$	21.4133	−	21.4133i	0.808192	−	0.808192i
$703$	−28.5471	+	20.3908i	−1.07668	+	0.769054i
$704$		−	40.8470i		−	1.53948i
$705$	13.5574	+	11.9878i	0.510600	+	0.451486i
$706$		−	2.00000i		−	0.0752710i
$707$	6.25457	−	6.25457i	0.235227	−	0.235227i
$708$			4.40597i			0.165587i
$709$	9.71862	+	9.71862i	0.364991	+	0.364991i	0.865646	−	0.500656i	$-0.166908\pi$
$709$	9.71862	+	9.71862i	0.364991	+	0.364991i	−0.500656	+	0.865646i	$0.666908\pi$
$710$	−11.3503	−	10.0362i	−0.425968	−	0.376652i
$711$	42.6160	−	42.6160i	1.59823	−	1.59823i
$712$	−16.1187	−	16.1187i	−0.604074	−	0.604074i
$713$	−2.59261	+	2.59261i	−0.0970942	+	0.0970942i
$714$	−21.8192			−0.816564
$715$	−22.5355	+	25.4861i	−0.842780	+	0.953127i
$716$	−1.08309	+	1.08309i	−0.0404769	+	0.0404769i
$717$		−	80.0503i		−	2.98953i
$718$	−11.3416			−0.423263
$719$		−	18.2579i		−	0.680905i	−0.940262	−	0.340452i	$-0.889420\pi$
$719$		−	18.2579i		−	0.680905i	0.940262	−	0.340452i	$-0.110580\pi$
$720$	41.0821	+	36.3258i	1.53104	+	1.35378i
$721$	15.6326	+	15.6326i	0.582188	+	0.582188i
$722$	−21.1260			−0.786229
$723$	−37.2301			−1.38460
$724$	−2.64737			−0.0983887
$725$	−13.1016	−	10.2243i	−0.486580	−	0.379719i
$726$	−68.5662	+	68.5662i	−2.54473	+	2.54473i
$727$		−	18.4445i		−	0.684070i	−0.939687	−	0.342035i	$-0.888884\pi$
$727$		−	18.4445i		−	0.684070i	0.939687	−	0.342035i	$-0.111116\pi$
$728$	7.60720	+	7.60720i	0.281942	+	0.281942i
$729$			35.2579i			1.30585i
$730$	0.335673	+	5.46310i	0.0124238	+	0.202198i
$731$		−	28.7005i		−	1.06153i
$732$			3.38058i			0.124950i
$733$	25.1319	+	25.1319i	0.928267	+	0.928267i	0.997594	−	0.0693266i	$-0.0220850\pi$
$733$	25.1319	+	25.1319i	0.928267	+	0.928267i	−0.0693266	+	0.997594i	$0.522085\pi$
$734$	3.23449	−	3.23449i	0.119387	−	0.119387i
$735$	−1.88423	−	30.6659i	−0.0695007	−	1.13113i
$736$	−1.93349			−0.0712692
$737$	61.8129	+	61.8129i	2.27691	+	2.27691i
$738$			78.3303i			2.88338i
$739$	29.1509			1.07233			0.536167	−	0.844112i	$-0.319872\pi$
$739$	29.1509			1.07233			0.536167	+	0.844112i	$0.319872\pi$
$740$	1.66196	+	2.04842i	0.0610948	+	0.0753013i
$741$	−44.7064			−1.64233
$742$		−	1.65703i		−	0.0608316i
$743$	−10.4406	−	10.4406i	−0.383030	−	0.383030i	0.489163	−	0.872193i	$-0.337302\pi$
$743$	−10.4406	−	10.4406i	−0.383030	−	0.383030i	−0.872193	+	0.489163i	$0.837302\pi$
$744$	−16.3004			−0.597603
$745$	7.45580	+	6.59261i	0.273159	+	0.241535i
$746$	−17.9321	+	17.9321i	−0.656540	+	0.656540i
$747$	−3.15339	−	3.15339i	−0.115376	−	0.115376i
$748$			3.67750i			0.134463i
$749$		−	2.32487i		−	0.0849489i
$750$	47.8476	−	8.90962i	1.74715	−	0.325333i
$751$			6.64386i			0.242438i	0.992626	+	0.121219i	$0.0386803\pi$
$751$			6.64386i			0.242438i	−0.992626	+	0.121219i	$0.961320\pi$
$752$	−8.47096	−	8.47096i	−0.308904	−	0.308904i
$753$		−	1.88621i		−	0.0687373i
$754$	9.18172	−	9.18172i	0.334378	−	0.334378i
$755$	6.75131	+	5.96968i	0.245705	+	0.217259i
$756$	−2.29218			−0.0833659
$757$	−12.1359			−0.441085			−0.220543	−	0.975377i	$-0.570783\pi$
$757$	−12.1359			−0.441085			−0.220543	+	0.975377i	$0.570783\pi$
$758$	−45.2203			−1.64247
$759$	−21.1998	−	21.1998i	−0.769505	−	0.769505i
$760$	−2.11577	−	34.4343i	−0.0767472	−	1.24906i
$761$			20.6615i			0.748979i	0.927231	+	0.374489i	$0.122182\pi$
$761$			20.6615i			0.748979i	−0.927231	+	0.374489i	$0.877818\pi$
$762$	83.4309			3.02238
$763$			10.7553i			0.389367i
$764$	−0.840735	+	0.840735i	−0.0304167	+	0.0304167i
$765$	31.0435	+	27.4495i	1.12238	+	0.992437i
$766$	−4.76704			−0.172240
$767$	14.4168	−	14.4168i	0.520560	−	0.520560i
$768$	−9.58475	−	9.58475i	−0.345860	−	0.345860i
$769$	−12.2447	+	12.2447i	−0.441556	+	0.441556i	−0.892535	−	0.450979i	$-0.851075\pi$
$769$	−12.2447	+	12.2447i	−0.441556	+	0.441556i	0.450979	+	0.892535i	$0.351075\pi$
$770$	29.0762	−	1.78655i	1.04783	−	0.0643828i
$771$	34.8373	+	34.8373i	1.25464	+	1.25464i
$772$		−	3.35026i		−	0.120579i
$773$	20.7685	−	20.7685i	0.746989	−	0.746989i	−0.226923	−	0.973913i	$-0.572867\pi$
$773$	20.7685	−	20.7685i	0.746989	−	0.746989i	0.973913	+	0.226923i	$0.0728667\pi$
$774$		−	72.9048i		−	2.62051i
$775$	−6.37764	+	8.17244i	−0.229092	+	0.293563i
$776$		−	11.1187i		−	0.399139i
$777$	26.8872	+	4.48119i	0.964572	+	0.160762i
$778$	−14.2750	+	14.2750i	−0.511785	+	0.511785i
$779$	38.2555	−	38.2555i	1.37065	−	1.37065i
$780$	0.206155	+	3.35519i	0.00738155	+	0.120135i
$781$			26.3879i			0.944232i
$782$	−8.61071			−0.307918
$783$		−	25.7645i		−	0.920747i
$784$			20.3380i			0.726359i
$785$	−19.8446	+	1.21933i	−0.708285	+	0.0435197i
$786$	47.2687			1.68602
$787$	−6.25988	−	6.25988i	−0.223141	−	0.223141i	0.586679	−	0.809820i	$-0.300435\pi$
$787$	−6.25988	−	6.25988i	−0.223141	−	0.223141i	−0.809820	+	0.586679i	$0.800435\pi$
$788$	3.46310	+	3.46310i	0.123368	+	0.123368i
$789$			14.1236i			0.502815i
$790$	2.17148	+	35.3410i	0.0772579	+	1.25738i
$791$	15.3634	+	15.3634i	0.546261	+	0.546261i
$792$		−	86.9946i		−	3.09122i
$793$	11.0616	−	11.0616i	0.392809	−	0.392809i
$794$	−37.5863	−	37.5863i	−1.33389	−	1.33389i
$795$	−3.19394	+	3.61213i	−0.113277	+	0.128109i
$796$	0.219899	−	0.219899i	0.00779412	−	0.00779412i
$797$			29.2022i			1.03439i	0.855866	+	0.517197i	$0.173025\pi$
$797$			29.2022i			1.03439i	−0.855866	+	0.517197i	$0.826975\pi$
$798$	27.0689	+	27.0689i	0.958228	+	0.958228i
$799$	−6.40105	−	6.40105i	−0.226453	−	0.226453i
$800$	−5.42548	+	0.669251i	−0.191820	+	0.0236616i
$801$	−33.9683	−	33.9683i	−1.20021	−	1.20021i
$802$	25.8084	−	25.8084i	0.911327	−	0.911327i
$803$	6.74069	−	6.74069i	0.237874	−	0.237874i
$804$	8.63752			0.304622
$805$	0.369775	+	6.01810i	0.0130328	+	0.212110i
$806$	−5.72733	−	5.72733i	−0.201737	−	0.201737i
$807$	−53.3063	+	53.3063i	−1.87647	+	1.87647i
$808$	15.5188			0.545950
$809$	12.6873	−	12.6873i	0.446063	−	0.446063i	−0.447980	−	0.894044i	$-0.647856\pi$
$809$	12.6873	−	12.6873i	0.446063	−	0.446063i	0.894044	+	0.447980i	$0.147856\pi$
$810$	14.5623	+	12.8764i	0.511667	+	0.452429i
$811$	−6.62530			−0.232646			−0.116323	−	0.993211i	$-0.537111\pi$
$811$	−6.62530			−0.232646			−0.116323	+	0.993211i	$0.537111\pi$
$812$	−0.982857			−0.0344915
$813$	−41.8251	−	41.8251i	−1.46687	−	1.46687i
$814$	8.54420	−	51.2652i	0.299474	−	1.79684i
$815$	−9.73813	+	11.0132i	−0.341112	+	0.385775i
$816$	−29.7186	−	29.7186i	−1.04036	−	1.04036i
$817$	−35.6058	+	35.6058i	−1.24569	+	1.24569i
$818$	0.786550	+	0.786550i	0.0275011	+	0.0275011i
$819$	16.0313	+	16.0313i	0.560178	+	0.560178i
$820$	−3.04746	−	2.69464i	−0.106422	−	0.0941010i
$821$	−22.1504			−0.773056			−0.386528	−	0.922278i	$-0.626326\pi$
$821$	−22.1504			−0.773056			−0.386528	+	0.922278i	$0.626326\pi$
$822$	0.619421			0.0216048
$823$	28.0528	−	28.0528i	0.977858	−	0.977858i	−0.0219020	−	0.999760i	$-0.506972\pi$
$823$	28.0528	−	28.0528i	0.977858	−	0.977858i	0.999760	+	0.0219020i	$0.00697219\pi$
$824$			38.7875i			1.35123i
$825$	−66.8261	−	52.1500i	−2.32659	−	1.81563i
$826$	−17.4582			−0.607447
$827$	−17.2144			−0.598604			−0.299302	−	0.954159i	$-0.596754\pi$
$827$	−17.2144			−0.598604			−0.299302	+	0.954159i	$0.596754\pi$
$828$	−1.93349			−0.0671933
$829$	−20.7235	+	20.7235i	−0.719759	+	0.719759i	−0.968556	−	0.248797i	$-0.919965\pi$
$829$	−20.7235	+	20.7235i	−0.719759	+	0.719759i	0.248797	+	0.968556i	$0.419965\pi$
$830$	2.61507	−	0.160680i	0.0907703	−	0.00557727i
$831$	10.0254	−	10.0254i	0.347777	−	0.347777i
$832$			18.6765i			0.647493i
$833$			15.3684i			0.532482i
$834$	−40.8627	+	40.8627i	−1.41496	+	1.41496i
$835$	2.96239	−	3.35026i	0.102518	−	0.115941i
$836$	4.56230	−	4.56230i	0.157790	−	0.157790i
$837$	−16.0713			−0.555504
$838$	−36.0567			−1.24556
$839$	−24.1378			−0.833328			−0.416664	−	0.909061i	$-0.636801\pi$
$839$	−24.1378			−0.833328			−0.416664	+	0.909061i	$0.636801\pi$
$840$	−17.7562	+	20.0811i	−0.612648	+	0.692864i
$841$			17.9525i			0.619053i
$842$	0.723546	−	0.723546i	0.0249351	−	0.0249351i
$843$	9.81924			0.338192
$844$	5.29948			0.182416
$845$	−8.95158	+	10.1236i	−0.307944	+	0.348264i
$846$	−16.2599	−	16.2599i	−0.559026	−	0.559026i
$847$	−24.0161	−	24.0161i	−0.825203	−	0.825203i
$848$	2.25694	−	2.25694i	0.0775037	−	0.0775037i
$849$	5.66291	+	5.66291i	0.194351	+	0.194351i
$850$	−24.1622	+	2.98049i	−0.828757	+	0.102230i
$851$	10.6107	+	1.76845i	0.363731	+	0.0606218i
$852$	1.84367	+	1.84367i	0.0631633	+	0.0631633i
$853$	5.95509			0.203899			0.101949	−	0.994790i	$-0.467492\pi$
$853$	5.95509			0.203899			0.101949	+	0.994790i	$0.467492\pi$
$854$	−13.3952			−0.458373
$855$	−4.45874	−	72.5662i	−0.152486	−	2.48171i
$856$	2.88423	−	2.88423i	0.0985808	−	0.0985808i
$857$	−29.0336			−0.991770			−0.495885	−	0.868388i	$-0.665156\pi$
$857$	−29.0336			−0.991770			−0.495885	+	0.868388i	$0.665156\pi$
$858$	46.8324	−	46.8324i	1.59883	−	1.59883i
$859$	−6.23941	−	6.23941i	−0.212886	−	0.212886i	0.592606	−	0.805492i	$-0.298099\pi$
$859$	−6.23941	−	6.23941i	−0.212886	−	0.212886i	−0.805492	+	0.592606i	$0.798099\pi$
$860$	2.83638	+	2.50800i	0.0967198	+	0.0855221i
$861$	−42.0362			−1.43259
$862$	−12.4392	+	12.4392i	−0.423682	+	0.423682i
$863$	21.7108	−	21.7108i	0.739043	−	0.739043i	−0.233350	−	0.972393i	$-0.574969\pi$
$863$	21.7108	−	21.7108i	0.739043	−	0.739043i	0.972393	+	0.233350i	$0.0749688\pi$
$864$	−5.99271	−	5.99271i	−0.203876	−	0.203876i
$865$	−5.60483	+	0.344382i	−0.190570	+	0.0117093i
$866$	19.5623	+	19.5623i	0.664754	+	0.664754i
$867$	12.8720	+	12.8720i	0.437156	+	0.437156i
$868$			0.613082i			0.0208094i
$869$	43.6058	−	43.6058i	1.47923	−	1.47923i
$870$	24.2374	+	21.4314i	0.821726	+	0.726591i
$871$	−28.2628	−	28.2628i	−0.957649	−	0.957649i
$872$	−13.3430	+	13.3430i	−0.451850	+	0.451850i
$873$		−	23.4314i		−	0.793032i
$874$	10.6824	+	10.6824i	0.361338	+	0.361338i
$875$	3.12070	+	16.7592i	0.105499	+	0.566563i
$876$		−	0.941921i		−	0.0318245i
$877$	−20.3987	−	20.3987i	−0.688814	−	0.688814i	0.273156	−	0.961970i	$-0.411933\pi$
$877$	−20.3987	−	20.3987i	−0.688814	−	0.688814i	−0.961970	+	0.273156i	$0.911933\pi$
$878$	−18.6962	−	18.6962i	−0.630965	−	0.630965i
$879$	7.84367			0.264561
$880$	42.0362	+	37.1695i	1.41704	+	1.25298i
$881$		−	48.3366i		−	1.62850i	−0.580513	−	0.814251i	$-0.697148\pi$
$881$		−	48.3366i		−	1.62850i	0.580513	−	0.814251i	$-0.302852\pi$
$882$			39.0386i			1.31450i
$883$	−53.4782			−1.79968			−0.899842	−	0.436216i	$-0.856318\pi$
$883$	−53.4782			−1.79968			−0.899842	+	0.436216i	$0.856318\pi$
$884$		−	1.68147i		−	0.0565540i
$885$	38.0567	+	33.6507i	1.27926	+	1.13116i
$886$	−7.15197	+	7.15197i	−0.240275	+	0.240275i
$887$	37.6487	−	37.6487i	1.26412	−	1.26412i	0.315042	−	0.949078i	$-0.397981\pi$
$887$	37.6487	−	37.6487i	1.26412	−	1.26412i	0.949078	−	0.315042i	$-0.102019\pi$
$888$	27.7968	+	38.9155i	0.932799	+	1.30592i
$889$			29.2227i			0.980096i
$890$	28.1695	−	1.73084i	0.944244	−	0.0580179i
$891$		−	33.8554i		−	1.13420i
$892$	1.60331	−	1.60331i	0.0536827	−	0.0536827i
$893$			15.8822i			0.531479i
$894$	−13.7005	−	13.7005i	−0.458214	−	0.458214i
$895$	1.08309	+	17.6273i	0.0362036	+	0.589215i
$896$	13.6659	−	13.6659i	0.456544	−	0.456544i
$897$	9.69323	+	9.69323i	0.323648	+	0.323648i
$898$	9.45088	−	9.45088i	0.315380	−	0.315380i
$899$	−6.89114			−0.229832
$900$	−5.42548	+	0.669251i	−0.180849	+	0.0223084i
$901$	1.70545	−	1.70545i	0.0568167	−	0.0568167i
$902$			80.1495i			2.66869i
$903$	39.1246			1.30198
$904$			38.1197i			1.26784i
$905$	−20.2193	+	22.8667i	−0.672113	+	0.760115i
$906$	−12.4060	−	12.4060i	−0.412161	−	0.412161i
$907$	−54.6009			−1.81299			−0.906496	−	0.422215i	$-0.861253\pi$
$907$	−54.6009			−1.81299			−0.906496	+	0.422215i	$0.861253\pi$
$908$	4.33709			0.143931
$909$	32.7040			1.08472
$910$	−13.2946	+	0.816868i	−0.440710	+	0.0270789i
$911$	3.82947	−	3.82947i	0.126876	−	0.126876i	−0.640817	−	0.767693i	$-0.721404\pi$
$911$	3.82947	−	3.82947i	0.126876	−	0.126876i	0.767693	+	0.640817i	$0.221404\pi$
$912$			73.7377i			2.44170i
$913$	−3.22662	−	3.22662i	−0.106786	−	0.106786i
$914$			16.5804i			0.548431i
$915$	29.1998	+	25.8192i	0.965316	+	0.853558i
$916$			4.42995i			0.146370i
$917$			16.5564i			0.546741i
$918$	−26.6883	−	26.6883i	−0.880845	−	0.880845i
$919$	37.9555	−	37.9555i	1.25204	−	1.25204i	0.297230	−	0.954806i	$-0.403937\pi$
$919$	37.9555	−	37.9555i	1.25204	−	1.25204i	0.954806	−	0.297230i	$-0.0960627\pi$
$920$	−7.00729	+	7.92478i	−0.231024	+	0.261272i
$921$	−29.8070			−0.982175
$922$	−15.7757	−	15.7757i	−0.519547	−	0.519547i
$923$		−	12.0654i		−	0.397137i
$924$	−5.01317			−0.164921
$925$	30.3865	+	1.28963i	0.999101	+	0.0424027i
$926$	17.1333			0.563035
$927$			81.7400i			2.68470i
$928$	−2.56959	−	2.56959i	−0.0843510	−	0.0843510i
$929$	6.33312			0.207783			0.103891	−	0.994589i	$-0.466871\pi$
$929$	6.33312			0.207783			0.103891	+	0.994589i	$0.466871\pi$
$930$	13.3684	−	15.1187i	0.438366	−	0.495762i
$931$	19.0659	−	19.0659i	0.624861	−	0.624861i
$932$	1.27996	+	1.27996i	0.0419266	+	0.0419266i
$933$			84.2067i			2.75680i
$934$		−	8.85097i		−	0.289613i
$935$	31.7645	+	28.0870i	1.03881	+	0.918543i
$936$			39.7767i			1.30014i
$937$	−21.4690	−	21.4690i	−0.701361	−	0.701361i	0.263342	−	0.964703i	$-0.415175\pi$
$937$	−21.4690	−	21.4690i	−0.701361	−	0.701361i	−0.964703	+	0.263342i	$0.915175\pi$
$938$			34.2252i			1.11749i
$939$	−3.95746	+	3.95746i	−0.129147	+	0.129147i
$940$	1.19195	−	0.0732380i	0.0388772	−	0.00238876i
$941$	−19.4495			−0.634034			−0.317017	−	0.948420i	$-0.602681\pi$
$941$	−19.4495			−0.634034			−0.317017	+	0.948420i	$0.602681\pi$
$942$	38.7064			1.26112
$943$	−16.5891			−0.540216
$944$	−23.7787	−	23.7787i	−0.773930	−	0.773930i
$945$	−17.5066	+	19.7988i	−0.569489	+	0.644054i
$946$		−	74.5980i		−	2.42539i
$947$	−30.9234			−1.00487			−0.502437	−	0.864614i	$-0.667563\pi$
$947$	−30.9234			−1.00487			−0.502437	+	0.864614i	$0.667563\pi$
$948$		−	6.09332i		−	0.197902i
$949$	−3.08206	+	3.08206i	−0.100048	+	0.100048i
$950$	33.6731	+	26.2780i	1.09250	+	0.852570i
$951$	6.49341			0.210563
$952$	9.48119	−	9.48119i	0.307287	−	0.307287i
$953$	26.7889	+	26.7889i	0.867778	+	0.867778i	0.992226	−	0.124448i	$-0.0397160\pi$
$953$	26.7889	+	26.7889i	0.867778	+	0.867778i	−0.124448	+	0.992226i	$0.539716\pi$
$954$	4.33216	−	4.33216i	0.140259	−	0.140259i
$955$	0.840735	+	13.6830i	0.0272055	+	0.442771i
$956$	−3.73520	−	3.73520i	−0.120805	−	0.120805i
$957$		−	56.3488i		−	1.82150i
$958$	−36.9517	+	36.9517i	−1.19386	+	1.19386i
$959$			0.216960i			0.00700599i
$960$	−46.4475	+	2.85391i	−1.49909	+	0.0921095i
$961$		−	26.7015i		−	0.861338i
$962$	−3.90668	+	23.4401i	−0.125956	+	0.755738i
$963$	6.07816	−	6.07816i	0.195866	−	0.195866i
$964$	−1.73718	+	1.73718i	−0.0559508	+	0.0559508i
$965$	−28.9380	−	25.5877i	−0.931546	−	0.823697i
$966$		−	11.7381i		−	0.377668i
$967$	7.13727			0.229519			0.114760	−	0.993393i	$-0.463390\pi$
$967$	7.13727			0.229519			0.114760	+	0.993393i	$0.463390\pi$
$968$		−	59.5886i		−	1.91525i
$969$			55.7196i			1.78997i
$970$	10.3127	+	9.11871i	0.331119	+	0.292784i
$971$	14.1016			0.452541			0.226270	−	0.974065i	$-0.427347\pi$
$971$	14.1016			0.452541			0.226270	+	0.974065i	$0.427347\pi$
$972$	0.823592	+	0.823592i	0.0264167	+	0.0264167i
$973$	−14.3127	−	14.3127i	−0.458843	−	0.458843i
$974$			55.5271i			1.77920i
$975$	30.5550	+	23.8446i	0.978543	+	0.763639i
$976$	−18.2447	−	18.2447i	−0.583999	−	0.583999i
$977$		−	36.1417i		−	1.15628i	−0.815939	−	0.578138i	$-0.803779\pi$
$977$		−	36.1417i		−	1.15628i	0.815939	−	0.578138i	$-0.196221\pi$
$978$	20.2374	−	20.2374i	0.647122	−	0.647122i
$979$	−34.7572	−	34.7572i	−1.11084	−	1.11084i
$980$	−1.51881	−	1.34297i	−0.0485165	−	0.0428995i
$981$	−28.1187	+	28.1187i	−0.897761	+	0.897761i
$982$			6.03620i			0.192623i
$983$	32.4778	+	32.4778i	1.03588	+	1.03588i	0.999332	+	0.0365489i	$0.0116365\pi$
$983$	32.4778	+	32.4778i	1.03588	+	1.03588i	0.0365489	+	0.999332i	$0.488364\pi$
$984$	−52.1500	−	52.1500i	−1.66248	−	1.66248i
$985$	56.3620	−	3.46310i	1.79584	−	0.110343i
$986$	−11.4436	−	11.4436i	−0.364438	−	0.364438i
$987$	8.72592	−	8.72592i	0.277749	−	0.277749i
$988$	−2.08603	+	2.08603i	−0.0663654	+	0.0663654i
$989$	15.4401			0.490966
$990$	80.6878	+	71.3463i	2.56443	+	2.26753i
$991$	17.1945	+	17.1945i	0.546202	+	0.546202i	0.925340	−	0.379138i	$-0.123780\pi$
$991$	17.1945	+	17.1945i	0.546202	+	0.546202i	−0.379138	+	0.925340i	$0.623780\pi$
$992$	−1.60285	+	1.60285i	−0.0508905	+	0.0508905i
$993$	−42.2760			−1.34159
$994$	−7.30536	+	7.30536i	−0.231712	+	0.231712i
$995$	−0.219899	−	3.57887i	−0.00697128	−	0.113458i
$996$	−0.450877			−0.0142866
$997$	51.0033			1.61529			0.807646	−	0.589668i	$-0.200741\pi$
$997$	51.0033			1.61529			0.807646	+	0.589668i	$0.200741\pi$
$998$	1.41384	+	1.41384i	0.0447542	+	0.0447542i
$999$	27.4060	+	38.3684i	0.867087	+	1.21392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.f.c.142.3	yes	6
5.2	odd	4		925.2.k.c.68.1		6
5.3	odd	4		185.2.k.c.68.3	yes	6
5.4	even	2		925.2.f.c.882.1		6
37.6	odd	4		185.2.k.c.117.3	yes	6
185.43	even	4	inner	185.2.f.c.43.1	✓	6
185.117	even	4		925.2.f.c.43.3		6
185.154	odd	4		925.2.k.c.857.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.f.c.43.1	✓	6	185.43	even	4	inner
185.2.f.c.142.3	yes	6	1.1	even	1	trivial
185.2.k.c.68.3	yes	6	5.3	odd	4
185.2.k.c.117.3	yes	6	37.6	odd	4
925.2.f.c.43.3		6	185.117	even	4
925.2.f.c.882.1		6	5.4	even	2
925.2.k.c.68.1		6	5.2	odd	4
925.2.k.c.857.1		6	185.154	odd	4

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.48119i q^{2} +(-2.07816 - 2.07816i) q^{3} -0.193937 q^{4} +(-1.48119 + 1.67513i) q^{5} +(3.07816 - 3.07816i) q^{6} +(1.07816 + 1.07816i) q^{7} +2.67513i q^{8} +5.63752i q^{9} +O(q^{10})\)	\(q+1.48119i q^{2} +(-2.07816 - 2.07816i) q^{3} -0.193937 q^{4} +(-1.48119 + 1.67513i) q^{5} +(3.07816 - 3.07816i) q^{6} +(1.07816 + 1.07816i) q^{7} +2.67513i q^{8} +5.63752i q^{9} +(-2.48119 - 2.19394i) q^{10} +5.76845i q^{11} +(0.403032 + 0.403032i) q^{12} -2.63752i q^{13} +(-1.59697 + 1.59697i) q^{14} +(6.55936 - 0.403032i) q^{15} -4.35026 q^{16} -3.28726 q^{17} -8.35026 q^{18} +(4.07816 + 4.07816i) q^{19} +(0.287258 - 0.324869i) q^{20} -4.48119i q^{21} -8.54420 q^{22} -1.76845i q^{23} +(5.55936 - 5.55936i) q^{24} +(-0.612127 - 4.96239i) q^{25} +3.90668 q^{26} +(5.48119 - 5.48119i) q^{27} +(-0.209095 - 0.209095i) q^{28} +(2.35026 - 2.35026i) q^{29} +(0.596968 + 9.71568i) q^{30} +(-1.46604 - 1.46604i) q^{31} -1.09332i q^{32} +(11.9878 - 11.9878i) q^{33} -4.86907i q^{34} +(-3.40303 + 0.209095i) q^{35} -1.09332i q^{36} +(-1.00000 + 6.00000i) q^{37} +(-6.04055 + 6.04055i) q^{38} +(-5.48119 + 5.48119i) q^{39} +(-4.48119 - 3.96239i) q^{40} -9.38058i q^{41} +6.63752 q^{42} +8.73084i q^{43} -1.11871i q^{44} +(-9.44358 - 8.35026i) q^{45} +2.61942 q^{46} +(1.94723 + 1.94723i) q^{47} +(9.04055 + 9.04055i) q^{48} -4.67513i q^{49} +(7.35026 - 0.906679i) q^{50} +(6.83146 + 6.83146i) q^{51} +0.511511i q^{52} +(-0.518806 + 0.518806i) q^{53} +(8.11871 + 8.11871i) q^{54} +(-9.66291 - 8.54420i) q^{55} +(-2.88423 + 2.88423i) q^{56} -16.9502i q^{57} +(3.48119 + 3.48119i) q^{58} +(5.46604 + 5.46604i) q^{59} +(-1.27210 + 0.0781626i) q^{60} +(4.19394 + 4.19394i) q^{61} +(2.17148 - 2.17148i) q^{62} +(-6.07816 + 6.07816i) q^{63} -7.08110 q^{64} +(4.41819 + 3.90668i) q^{65} +(17.7562 + 17.7562i) q^{66} +(10.7157 - 10.7157i) q^{67} +0.637519 q^{68} +(-3.67513 + 3.67513i) q^{69} +(-0.309711 - 5.04055i) q^{70} +4.57452 q^{71} -15.0811 q^{72} +(-1.16854 - 1.16854i) q^{73} +(-8.88717 - 1.48119i) q^{74} +(-9.04055 + 11.5847i) q^{75} +(-0.790905 - 0.790905i) q^{76} +(-6.21933 + 6.21933i) q^{77} +(-8.11871 - 8.11871i) q^{78} +(-7.55936 - 7.55936i) q^{79} +(6.44358 - 7.28726i) q^{80} -5.86907 q^{81} +13.8945 q^{82} +(-0.559357 + 0.559357i) q^{83} +0.869067i q^{84} +(4.86907 - 5.50659i) q^{85} -12.9321 q^{86} -9.76845 q^{87} -15.4314 q^{88} +(-6.02539 + 6.02539i) q^{89} +(12.3684 - 13.9878i) q^{90} +(2.84367 - 2.84367i) q^{91} +0.342968i q^{92} +6.09332i q^{93} +(-2.88423 + 2.88423i) q^{94} +(-12.8720 + 0.790905i) q^{95} +(-2.27210 + 2.27210i) q^{96} -4.15633 q^{97} +6.92478 q^{98} -32.5198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{7}+O(q^{10}) \) 6 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^7	\( 6 q - 2 q^{3} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 4 q^{7} - 4 q^{10} + 2 q^{12} - 10 q^{14} + 18 q^{15} - 6 q^{16} - 8 q^{17} - 30 q^{18} + 14 q^{19} - 10 q^{20} - 32 q^{22} + 12 q^{24} - 2 q^{25} + 36 q^{26} + 22 q^{27} - 6 q^{29} + 4 q^{30} + 20 q^{33} - 20 q^{35} - 6 q^{37} - 4 q^{38} - 22 q^{39} - 16 q^{40} + 8 q^{42} - 24 q^{45} + 40 q^{46} - 8 q^{47} + 22 q^{48} + 24 q^{50} + 10 q^{51} - 14 q^{53} + 6 q^{54} + 4 q^{55} - 6 q^{56} + 10 q^{58} + 24 q^{59} + 2 q^{60} + 26 q^{61} - 10 q^{62} - 26 q^{63} + 22 q^{64} + 24 q^{65} + 32 q^{66} + 22 q^{67} - 28 q^{68} - 12 q^{69} - 14 q^{70} + 4 q^{71} - 26 q^{72} - 38 q^{73} + 12 q^{74} - 22 q^{75} - 6 q^{76} - 8 q^{77} - 6 q^{78} - 24 q^{79} + 6 q^{80} - 26 q^{81} + 44 q^{82} + 18 q^{83} + 20 q^{85} - 60 q^{86} - 36 q^{87} - 8 q^{88} - 6 q^{89} - 2 q^{90} + 38 q^{91} - 6 q^{94} - 14 q^{95} - 4 q^{96} - 4 q^{97} - 2 q^{98} - 72 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 4 * q^7 - 4 * q^10 + 2 * q^12 - 10 * q^14 + 18 * q^15 - 6 * q^16 - 8 * q^17 - 30 * q^18 + 14 * q^19 - 10 * q^20 - 32 * q^22 + 12 * q^24 - 2 * q^25 + 36 * q^26 + 22 * q^27 - 6 * q^29 + 4 * q^30 + 20 * q^33 - 20 * q^35 - 6 * q^37 - 4 * q^38 - 22 * q^39 - 16 * q^40 + 8 * q^42 - 24 * q^45 + 40 * q^46 - 8 * q^47 + 22 * q^48 + 24 * q^50 + 10 * q^51 - 14 * q^53 + 6 * q^54 + 4 * q^55 - 6 * q^56 + 10 * q^58 + 24 * q^59 + 2 * q^60 + 26 * q^61 - 10 * q^62 - 26 * q^63 + 22 * q^64 + 24 * q^65 + 32 * q^66 + 22 * q^67 - 28 * q^68 - 12 * q^69 - 14 * q^70 + 4 * q^71 - 26 * q^72 - 38 * q^73 + 12 * q^74 - 22 * q^75 - 6 * q^76 - 8 * q^77 - 6 * q^78 - 24 * q^79 + 6 * q^80 - 26 * q^81 + 44 * q^82 + 18 * q^83 + 20 * q^85 - 60 * q^86 - 36 * q^87 - 8 * q^88 - 6 * q^89 - 2 * q^90 + 38 * q^91 - 6 * q^94 - 14 * q^95 - 4 * q^96 - 4 * q^97 - 2 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more