LMFDB - Embedded newform 325.3.j.d.151.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(151,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.151"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,0,-6,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{17} + 336 x^{16} - 90 x^{15} + 18 x^{14} - 654 x^{13} + 30550 x^{12} - 9690 x^{11} + \cdots + 46656 $ x^20 - 6x^17 + 336x^16 - 90x^15 + 18x^14 - 654x^13 + 30550x^12 - 9690x^11 + 1926x^10 - 32442x^9 + 812544x^8 - 376230x^7 + 83574x^6 + 45630x^5 + 2633913x^4 - 1039590x^3 + 206082x^2 + 138672*x + 46656
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			151.8
Root			$-1.88633 + 1.88633i$ of defining polynomial
Character	$\chi$	$=$	325.151
Dual form			325.3.j.d.226.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.88633 + 1.88633i) q^{2} -0.793970 q^{3} +3.11650i q^{4} +(-1.49769 - 1.49769i) q^{6} +(-8.42514 + 8.42514i) q^{7} +(1.66658 - 1.66658i) q^{8} -8.36961 q^{9} +(-1.45602 + 1.45602i) q^{11} -2.47441i q^{12} +(-11.6660 + 5.73623i) q^{13} -31.7852 q^{14} +18.7534 q^{16} +2.73950i q^{17} +(-15.7879 - 15.7879i) q^{18} +(-2.87005 - 2.87005i) q^{19} +(6.68931 - 6.68931i) q^{21} -5.49308 q^{22} +41.2582i q^{23} +(-1.32321 + 1.32321i) q^{24} +(-32.8264 - 11.1855i) q^{26} +13.7909 q^{27} +(-26.2569 - 26.2569i) q^{28} -22.4912 q^{29} +(-25.5438 - 25.5438i) q^{31} +(28.7089 + 28.7089i) q^{32} +(1.15604 - 1.15604i) q^{33} +(-5.16762 + 5.16762i) q^{34} -26.0839i q^{36} +(22.4179 - 22.4179i) q^{37} -10.8277i q^{38} +(9.26246 - 4.55439i) q^{39} +(35.3618 + 35.3618i) q^{41} +25.2365 q^{42} +4.97904i q^{43} +(-4.53769 - 4.53769i) q^{44} +(-77.8267 + 77.8267i) q^{46} +(16.0871 - 16.0871i) q^{47} -14.8897 q^{48} -92.9659i q^{49} -2.17508i q^{51} +(-17.8770 - 36.3571i) q^{52} +55.8281 q^{53} +(26.0143 + 26.0143i) q^{54} +28.0823i q^{56} +(2.27873 + 2.27873i) q^{57} +(-42.4259 - 42.4259i) q^{58} +(-30.7740 + 30.7740i) q^{59} -4.68989 q^{61} -96.3681i q^{62} +(70.5151 - 70.5151i) q^{63} +33.2953i q^{64} +4.36134 q^{66} +(64.9102 + 64.9102i) q^{67} -8.53766 q^{68} -32.7578i q^{69} +(2.47898 + 2.47898i) q^{71} +(-13.9486 + 13.9486i) q^{72} +(-75.2167 + 75.2167i) q^{73} +84.5750 q^{74} +(8.94451 - 8.94451i) q^{76} -24.5344i q^{77} +(26.0632 + 8.88097i) q^{78} +67.8838 q^{79} +64.3769 q^{81} +133.408i q^{82} +(91.5991 + 91.5991i) q^{83} +(20.8472 + 20.8472i) q^{84} +(-9.39212 + 9.39212i) q^{86} +17.8573 q^{87} +4.85314i q^{88} +(-45.9488 + 45.9488i) q^{89} +(49.9592 - 146.616i) q^{91} -128.581 q^{92} +(20.2810 + 20.2810i) q^{93} +60.6913 q^{94} +(-22.7940 - 22.7940i) q^{96} +(-111.655 - 111.655i) q^{97} +(175.365 - 175.365i) q^{98} +(12.1863 - 12.1863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{6} + 20 q^{7} - 18 q^{8} + 72 q^{9} + 6 q^{11} + 6 q^{13} - 24 q^{14} - 128 q^{16} - 58 q^{18} - 20 q^{19} + 90 q^{21} + 24 q^{22} - 28 q^{24} - 12 q^{27} + 278 q^{28} - 40 q^{29} - 32 q^{31}+ \cdots - 410 q^{99}+O(q^{100}) $ 20 * q - 6 * q^6 + 20 * q^7 - 18 * q^8 + 72 * q^9 + 6 * q^11 + 6 * q^13 - 24 * q^14 - 128 * q^16 - 58 * q^18 - 20 * q^19 + 90 * q^21 + 24 * q^22 - 28 * q^24 - 12 * q^27 + 278 * q^28 - 40 * q^29 - 32 * q^31 - 162 * q^32 + 124 * q^33 - 14 * q^34 + 158 * q^37 - 26 * q^39 + 70 * q^41 - 320 * q^42 + 366 * q^44 + 58 * q^46 - 130 * q^47 - 716 * q^48 + 300 * q^52 + 216 * q^53 - 350 * q^54 + 168 * q^57 - 180 * q^58 + 132 * q^59 - 152 * q^61 + 442 * q^63 + 720 * q^66 + 178 * q^67 - 216 * q^68 - 258 * q^71 + 390 * q^72 - 262 * q^73 + 220 * q^74 + 68 * q^76 + 102 * q^78 - 544 * q^79 + 204 * q^81 + 88 * q^83 + 352 * q^84 - 174 * q^86 - 976 * q^87 - 282 * q^89 - 440 * q^91 - 992 * q^92 + 522 * q^93 - 544 * q^94 - 1216 * q^96 + 6 * q^97 + 78 * q^98 - 410 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.88633	+	1.88633i	0.943166	+	0.943166i	0.998470	−	0.0553034i	$-0.0176126\pi$
$2$	1.88633	+	1.88633i	0.943166	+	0.943166i	−0.0553034	+	0.998470i	$0.517613\pi$
$3$	−0.793970			−0.264657			−0.132328	−	0.991206i	$-0.542245\pi$
$3$	−0.793970			−0.264657			−0.132328	+	0.991206i	$0.542245\pi$
$4$			3.11650i			0.779125i
$5$		0			0
$5$		0			0
$6$	−1.49769	−	1.49769i	−0.249615	−	0.249615i
$7$	−8.42514	+	8.42514i	−1.20359	+	1.20359i	−0.230525	+	0.973066i	$0.574044\pi$
$7$	−8.42514	+	8.42514i	−1.20359	+	1.20359i	−0.973066	+	0.230525i	$0.925956\pi$
$8$	1.66658	−	1.66658i	0.208322	−	0.208322i
$9$	−8.36961			−0.929957
$10$		0			0
$11$	−1.45602	+	1.45602i	−0.132366	+	0.132366i	−0.770186	−	0.637820i	$-0.779836\pi$
$11$	−1.45602	+	1.45602i	−0.132366	+	0.132366i	0.637820	+	0.770186i	$0.279836\pi$
$12$		−	2.47441i		−	0.206201i
$13$	−11.6660	+	5.73623i	−0.897385	+	0.441249i
$13$	−11.6660	+	5.73623i	−0.897385	+	0.441249i
$14$	−31.7852			−2.27037
$15$		0			0
$16$	18.7534			1.17209
$17$			2.73950i			0.161147i	0.996749	+	0.0805737i	$0.0256752\pi$
$17$			2.73950i			0.161147i	−0.996749	+	0.0805737i	$0.974325\pi$
$18$	−15.7879	−	15.7879i	−0.877104	−	0.877104i
$19$	−2.87005	−	2.87005i	−0.151055	−	0.151055i	0.627534	−	0.778589i	$-0.284064\pi$
$19$	−2.87005	−	2.87005i	−0.151055	−	0.151055i	−0.778589	+	0.627534i	$0.784064\pi$
$20$		0			0
$21$	6.68931	−	6.68931i	0.318538	−	0.318538i
$22$	−5.49308			−0.249685
$23$			41.2582i			1.79384i	0.442197	+	0.896918i	$0.354199\pi$
$23$			41.2582i			1.79384i	−0.442197	+	0.896918i	$0.645801\pi$
$24$	−1.32321	+	1.32321i	−0.0551338	+	0.0551338i
$25$		0			0
$26$	−32.8264	−	11.1855i	−1.26255	−	0.430212i
$27$	13.7909			0.510776
$28$	−26.2569	−	26.2569i	−0.937748	−	0.937748i
$29$	−22.4912			−0.775559			−0.387780	−	0.921752i	$-0.626758\pi$
$29$	−22.4912			−0.775559			−0.387780	+	0.921752i	$0.626758\pi$
$30$		0			0
$31$	−25.5438	−	25.5438i	−0.823993	−	0.823993i	0.162685	−	0.986678i	$-0.447984\pi$
$31$	−25.5438	−	25.5438i	−0.823993	−	0.823993i	−0.986678	+	0.162685i	$0.947984\pi$
$32$	28.7089	+	28.7089i	0.897153	+	0.897153i
$33$	1.15604	−	1.15604i	0.0350314	−	0.0350314i
$34$	−5.16762	+	5.16762i	−0.151989	+	0.151989i
$35$		0			0
$36$		−	26.0839i		−	0.724552i
$37$	22.4179	−	22.4179i	0.605888	−	0.605888i	−0.335981	−	0.941869i	$-0.609068\pi$
$37$	22.4179	−	22.4179i	0.605888	−	0.605888i	0.941869	+	0.335981i	$0.109068\pi$
$38$		−	10.8277i		−	0.284940i
$39$	9.26246	−	4.55439i	0.237499	−	0.116779i
$40$		0			0
$41$	35.3618	+	35.3618i	0.862483	+	0.862483i	0.991626	−	0.129143i	$-0.0412225\pi$
$41$	35.3618	+	35.3618i	0.862483	+	0.862483i	−0.129143	+	0.991626i	$0.541223\pi$
$42$	25.2365			0.600869
$43$			4.97904i			0.115792i	0.998323	+	0.0578958i	$0.0184391\pi$
$43$			4.97904i			0.115792i	−0.998323	+	0.0578958i	$0.981561\pi$
$44$	−4.53769	−	4.53769i	−0.103129	−	0.103129i
$45$		0			0
$46$	−77.8267	+	77.8267i	−1.69189	+	1.69189i
$47$	16.0871	−	16.0871i	0.342279	−	0.342279i	−0.514945	−	0.857223i	$-0.672188\pi$
$47$	16.0871	−	16.0871i	0.342279	−	0.342279i	0.857223	+	0.514945i	$0.172188\pi$
$48$	−14.8897			−0.310201
$49$		−	92.9659i		−	1.89726i
$50$		0			0
$51$		−	2.17508i		−	0.0426487i
$52$	−17.8770	−	36.3571i	−0.343788	−	0.699175i
$53$	55.8281			1.05336			0.526680	−	0.850063i	$-0.323436\pi$
$53$	55.8281			1.05336			0.526680	+	0.850063i	$0.323436\pi$
$54$	26.0143	+	26.0143i	0.481746	+	0.481746i
$55$		0			0
$56$			28.0823i			0.501469i
$57$	2.27873	+	2.27873i	0.0399778	+	0.0399778i
$58$	−42.4259	−	42.4259i	−0.731481	−	0.731481i
$59$	−30.7740	+	30.7740i	−0.521592	+	0.521592i	−0.918052	−	0.396460i	$-0.870239\pi$
$59$	−30.7740	+	30.7740i	−0.521592	+	0.521592i	0.396460	+	0.918052i	$0.370239\pi$
$60$		0			0
$61$	−4.68989			−0.0768835			−0.0384417	−	0.999261i	$-0.512239\pi$
$61$	−4.68989			−0.0768835			−0.0384417	+	0.999261i	$0.512239\pi$
$62$		−	96.3681i		−	1.55432i
$63$	70.5151	−	70.5151i	1.11929	−	1.11929i
$64$			33.2953i			0.520239i
$65$		0			0
$66$	4.36134			0.0660809
$67$	64.9102	+	64.9102i	0.968809	+	0.968809i	0.999528	−	0.0307193i	$-0.00977980\pi$
$67$	64.9102	+	64.9102i	0.968809	+	0.968809i	−0.0307193	+	0.999528i	$0.509780\pi$
$68$	−8.53766			−0.125554
$69$		−	32.7578i		−	0.474751i
$70$		0			0
$71$	2.47898	+	2.47898i	0.0349153	+	0.0349153i	0.724349	−	0.689434i	$-0.242141\pi$
$71$	2.47898	+	2.47898i	0.0349153	+	0.0349153i	−0.689434	+	0.724349i	$0.742141\pi$
$72$	−13.9486	+	13.9486i	−0.193730	+	0.193730i
$73$	−75.2167	+	75.2167i	−1.03037	+	1.03037i	−0.0308411	+	0.999524i	$0.509819\pi$
$73$	−75.2167	+	75.2167i	−1.03037	+	1.03037i	−0.999524	+	0.0308411i	$0.990181\pi$
$74$	84.5750			1.14291
$75$		0			0
$76$	8.94451	−	8.94451i	0.117691	−	0.117691i
$77$		−	24.5344i		−	0.318628i
$78$	26.0632	+	8.88097i	0.334143	+	0.113859i
$79$	67.8838			0.859289			0.429644	−	0.902998i	$-0.358639\pi$
$79$	67.8838			0.859289			0.429644	+	0.902998i	$0.358639\pi$
$80$		0			0
$81$	64.3769			0.794777
$82$			133.408i			1.62693i
$83$	91.5991	+	91.5991i	1.10360	+	1.10360i	0.993972	+	0.109631i	$0.0349669\pi$
$83$	91.5991	+	91.5991i	1.10360	+	1.10360i	0.109631	+	0.993972i	$0.465033\pi$
$84$	20.8472	+	20.8472i	0.248181	+	0.248181i
$85$		0			0
$86$	−9.39212	+	9.39212i	−0.109211	+	0.109211i
$87$	17.8573			0.205257
$88$			4.85314i			0.0551493i
$89$	−45.9488	+	45.9488i	−0.516278	+	0.516278i	−0.916443	−	0.400165i	$-0.868953\pi$
$89$	−45.9488	+	45.9488i	−0.516278	+	0.516278i	0.400165	+	0.916443i	$0.368953\pi$
$90$		0			0
$91$	49.9592	−	146.616i	0.549002	−	1.61117i
$92$	−128.581			−1.39762
$93$	20.2810	+	20.2810i	0.218075	+	0.218075i
$94$	60.6913			0.645652
$95$		0			0
$96$	−22.7940	−	22.7940i	−0.237437	−	0.237437i
$97$	−111.655	−	111.655i	−1.15108	−	1.15108i	−0.986336	−	0.164747i	$-0.947319\pi$
$97$	−111.655	−	111.655i	−1.15108	−	1.15108i	−0.164747	−	0.986336i	$-0.552681\pi$
$98$	175.365	−	175.365i	1.78943	−	1.78943i
$99$	12.1863	−	12.1863i	0.123094	−	0.123094i
$100$		0			0
$101$		−	86.9229i		−	0.860622i	−0.902681	−	0.430311i	$-0.858404\pi$
$101$		−	86.9229i		−	0.860622i	0.902681	−	0.430311i	$-0.141596\pi$
$102$	4.10293	−	4.10293i	0.0402248	−	0.0402248i
$103$			170.779i			1.65805i	0.559210	+	0.829026i	$0.311105\pi$
$103$			170.779i			1.65805i	−0.559210	+	0.829026i	$0.688895\pi$
$104$	−9.88242	+	29.0021i	−0.0950232	+	0.278867i
$105$		0			0
$106$	105.310	+	105.310i	0.993494	+	0.993494i
$107$	−186.534			−1.74331			−0.871653	−	0.490124i	$-0.836951\pi$
$107$	−186.534			−1.74331			−0.871653	+	0.490124i	$0.836951\pi$
$108$			42.9795i			0.397958i
$109$	15.2852	+	15.2852i	0.140231	+	0.140231i	0.773737	−	0.633506i	$-0.218385\pi$
$109$	15.2852	+	15.2852i	0.140231	+	0.140231i	−0.633506	+	0.773737i	$0.718385\pi$
$110$		0			0
$111$	−17.7991	+	17.7991i	−0.160352	+	0.160352i
$112$	−158.000	+	158.000i	−1.41072	+	1.41072i
$113$	−192.529			−1.70379			−0.851897	−	0.523709i	$-0.824548\pi$
$113$	−192.529			−1.70379			−0.851897	+	0.523709i	$0.824548\pi$
$114$			8.59689i			0.0754114i
$115$		0			0
$116$		−	70.0938i		−	0.604257i
$117$	97.6399	−	48.0100i	0.834529	−	0.410342i
$118$	−116.100			−0.983897
$119$	−23.0807	−	23.0807i	−0.193956	−	0.193956i
$120$		0			0
$121$			116.760i			0.964959i
$122$	−8.84669	−	8.84669i	−0.0725139	−	0.0725139i
$123$	−28.0762	−	28.0762i	−0.228262	−	0.228262i
$124$	79.6072	−	79.6072i	0.641993	−	0.641993i
$125$		0			0
$126$	266.030			2.11135
$127$		−	71.8541i		−	0.565780i	−0.959152	−	0.282890i	$-0.908707\pi$
$127$		−	71.8541i		−	0.565780i	0.959152	−	0.282890i	$-0.0912932\pi$
$128$	52.0295	−	52.0295i	0.406481	−	0.406481i
$129$		−	3.95320i		−	0.0306450i
$130$		0			0
$131$	110.108			0.840517			0.420258	−	0.907405i	$-0.361939\pi$
$131$	110.108			0.840517			0.420258	+	0.907405i	$0.361939\pi$
$132$	3.60279	+	3.60279i	0.0272939	+	0.0272939i
$133$	48.3611			0.363617
$134$			244.884i			1.82750i
$135$		0			0
$136$	4.56559	+	4.56559i	0.0335705	+	0.0335705i
$137$	−86.8356	+	86.8356i	−0.633837	+	0.633837i	−0.949028	−	0.315191i	$-0.897931\pi$
$137$	−86.8356	+	86.8356i	−0.633837	+	0.633837i	0.315191	+	0.949028i	$0.397931\pi$
$138$	61.7921	−	61.7921i	0.447769	−	0.447769i
$139$	171.504			1.23384			0.616922	−	0.787024i	$-0.288379\pi$
$139$	171.504			1.23384			0.616922	+	0.787024i	$0.288379\pi$
$140$		0			0
$141$	−12.7727	+	12.7727i	−0.0905864	+	0.0905864i
$142$			9.35237i			0.0658618i
$143$	8.63388	−	25.3380i	0.0603768	−	0.177189i
$144$	−156.959			−1.08999
$145$		0			0
$146$	−283.767			−1.94361
$147$			73.8121i			0.502123i
$148$	69.8652	+	69.8652i	0.472062	+	0.472062i
$149$	6.63306	+	6.63306i	0.0445172	+	0.0445172i	0.729015	−	0.684498i	$-0.239978\pi$
$149$	6.63306	+	6.63306i	0.0445172	+	0.0445172i	−0.684498	+	0.729015i	$0.739978\pi$
$150$		0			0
$151$	−51.6100	+	51.6100i	−0.341788	+	0.341788i	−0.857039	−	0.515251i	$-0.827699\pi$
$151$	−51.6100	+	51.6100i	−0.341788	+	0.341788i	0.515251	+	0.857039i	$0.327699\pi$
$152$	−9.56631			−0.0629363
$153$		−	22.9286i		−	0.149860i
$154$	46.2800	−	46.2800i	0.300519	−	0.300519i
$155$		0			0
$156$	14.1938	+	28.8664i	0.0909857	+	0.185041i
$157$	62.2106			0.396246			0.198123	−	0.980177i	$-0.436516\pi$
$157$	62.2106			0.396246			0.198123	+	0.980177i	$0.436516\pi$
$158$	128.051	+	128.051i	0.810452	+	0.810452i
$159$	−44.3258			−0.278779
$160$		0			0
$161$	−347.606	−	347.606i	−2.15904	−	2.15904i
$162$	121.436	+	121.436i	0.749606	+	0.749606i
$163$	−53.1930	+	53.1930i	−0.326338	+	0.326338i	−0.851192	−	0.524854i	$-0.824120\pi$
$163$	−53.1930	+	53.1930i	−0.326338	+	0.326338i	0.524854	+	0.851192i	$0.324120\pi$
$164$	−110.205	+	110.205i	−0.671982	+	0.671982i
$165$		0			0
$166$			345.573i			2.08176i
$167$	104.584	−	104.584i	0.626251	−	0.626251i	−0.320871	−	0.947123i	$-0.603976\pi$
$167$	104.584	−	104.584i	0.626251	−	0.626251i	0.947123	+	0.320871i	$0.103976\pi$
$168$		−	22.2965i		−	0.132717i
$169$	103.191	−	133.838i	0.610599	−	0.791940i
$170$		0			0
$171$	24.0212	+	24.0212i	0.140475	+	0.140475i
$172$	−15.5172			−0.0902161
$173$		−	280.273i		−	1.62008i	−0.586377	−	0.810038i	$-0.699446\pi$
$173$		−	280.273i		−	1.62008i	0.586377	−	0.810038i	$-0.300554\pi$
$174$	33.6849	+	33.6849i	0.193591	+	0.193591i
$175$		0			0
$176$	−27.3054	+	27.3054i	−0.155144	+	0.155144i
$177$	24.4336	−	24.4336i	0.138043	−	0.138043i
$178$	−173.349			−0.973873
$179$		−	228.150i		−	1.27458i	−0.770625	−	0.637289i	$-0.780056\pi$
$179$		−	228.150i		−	1.27458i	0.770625	−	0.637289i	$-0.219944\pi$
$180$		0			0
$181$		−	170.242i		−	0.940564i	−0.882516	−	0.470282i	$-0.844152\pi$
$181$		−	170.242i		−	0.940564i	0.882516	−	0.470282i	$-0.155848\pi$
$182$	370.806	−	182.327i	2.03740	−	1.00180i
$183$	3.72363			0.0203477
$184$	68.7600	+	68.7600i	0.373695	+	0.373695i
$185$		0			0
$186$			76.5134i			0.411362i
$187$	−3.98878	−	3.98878i	−0.0213304	−	0.0213304i
$188$	50.1355	+	50.1355i	0.266678	+	0.266678i
$189$	−116.191	+	116.191i	−0.614765	+	0.614765i
$190$		0			0
$191$	292.083			1.52923			0.764616	−	0.644487i	$-0.222929\pi$
$191$	292.083			1.52923			0.764616	+	0.644487i	$0.222929\pi$
$192$		−	26.4355i		−	0.137685i
$193$	−87.6005	+	87.6005i	−0.453888	+	0.453888i	−0.896643	−	0.442754i	$-0.854001\pi$
$193$	−87.6005	+	87.6005i	−0.453888	+	0.453888i	0.442754	+	0.896643i	$0.354001\pi$
$194$		−	421.237i		−	2.17132i
$195$		0			0
$196$	289.728			1.47820
$197$	−14.9848	−	14.9848i	−0.0760648	−	0.0760648i	0.668051	−	0.744116i	$-0.267129\pi$
$197$	−14.9848	−	14.9848i	−0.0760648	−	0.0760648i	−0.744116	+	0.668051i	$0.767129\pi$
$198$	45.9749			0.232197
$199$			78.4716i			0.394330i	0.980370	+	0.197165i	$0.0631734\pi$
$199$			78.4716i			0.394330i	−0.980370	+	0.197165i	$0.936827\pi$
$200$		0			0
$201$	−51.5367	−	51.5367i	−0.256402	−	0.256402i
$202$	163.965	−	163.965i	0.811710	−	0.811710i
$203$	189.492	−	189.492i	0.933456	−	0.933456i
$204$	6.77865			0.0332287
$205$		0			0
$206$	−322.147	+	322.147i	−1.56382	+	1.56382i
$207$		−	345.315i		−	1.66819i
$208$	−218.778	+	107.574i	−1.05182	+	0.517183i
$209$	8.35771			0.0399890
$210$		0			0
$211$	−107.184			−0.507979			−0.253990	−	0.967207i	$-0.581743\pi$
$211$	−107.184			−0.507979			−0.253990	+	0.967207i	$0.581743\pi$
$212$			173.988i			0.820699i
$213$	−1.96824	−	1.96824i	−0.00924055	−	0.00924055i
$214$	−351.864	−	351.864i	−1.64423	−	1.64423i
$215$		0			0
$216$	22.9837	−	22.9837i	0.106406	−	0.106406i
$217$	430.420			1.98350
$218$			57.6658i			0.264522i
$219$	59.7198	−	59.7198i	0.272693	−	0.272693i
$220$		0			0
$221$	−15.7144	−	31.9591i	−0.0711060	−	0.144611i
$222$	−67.1500			−0.302478
$223$	−155.987	−	155.987i	−0.699491	−	0.699491i	0.264809	−	0.964301i	$-0.414691\pi$
$223$	−155.987	−	155.987i	−0.699491	−	0.699491i	−0.964301	+	0.264809i	$0.914691\pi$
$224$	−483.753			−2.15961
$225$		0			0
$226$	−363.173	−	363.173i	−1.60696	−	1.60696i
$227$	−109.822	−	109.822i	−0.483798	−	0.483798i	0.422544	−	0.906342i	$-0.361137\pi$
$227$	−109.822	−	109.822i	−0.483798	−	0.483798i	−0.906342	+	0.422544i	$0.861137\pi$
$228$	−7.10167	+	7.10167i	−0.0311477	+	0.0311477i
$229$	−268.576	+	268.576i	−1.17282	+	1.17282i	−0.191284	+	0.981535i	$0.561265\pi$
$229$	−268.576	+	268.576i	−1.17282	+	1.17282i	−0.981535	+	0.191284i	$0.938735\pi$
$230$		0			0
$231$			19.4795i			0.0843270i
$232$	−37.4833	+	37.4833i	−0.161566	+	0.161566i
$233$			144.819i			0.621542i	0.950485	+	0.310771i	$0.100587\pi$
$233$			144.819i			0.621542i	−0.950485	+	0.310771i	$0.899413\pi$
$234$	274.744	+	93.6185i	1.17412	+	0.400079i
$235$		0			0
$236$	−95.9070	−	95.9070i	−0.406386	−	0.406386i
$237$	−53.8977			−0.227416
$238$		−	87.0758i		−	0.365865i
$239$	164.817	+	164.817i	0.689612	+	0.689612i	0.962146	−	0.272534i	$-0.0878617\pi$
$239$	164.817	+	164.817i	0.689612	+	0.689612i	−0.272534	+	0.962146i	$0.587862\pi$
$240$		0			0
$241$	−254.475	+	254.475i	−1.05591	+	1.05591i	−0.0575708	+	0.998341i	$0.518336\pi$
$241$	−254.475	+	254.475i	−1.05591	+	1.05591i	−0.998341	+	0.0575708i	$0.981664\pi$
$242$	−220.248	+	220.248i	−0.910116	+	0.910116i
$243$	−175.232			−0.721119
$244$		−	14.6160i		−	0.0599018i
$245$		0			0
$246$		−	105.922i		−	0.430578i
$247$	49.9453	+	17.0187i	0.202208	+	0.0689018i
$248$	−85.1413			−0.343312
$249$	−72.7269	−	72.7269i	−0.292076	−	0.292076i
$250$		0			0
$251$		−	111.483i		−	0.444157i	−0.975029	−	0.222078i	$-0.928716\pi$
$251$		−	111.483i		−	0.444157i	0.975029	−	0.222078i	$-0.0712841\pi$
$252$	219.760	+	219.760i	0.872065	+	0.872065i
$253$	−60.0729	−	60.0729i	−0.237442	−	0.237442i
$254$	135.541	−	135.541i	0.533625	−	0.533625i
$255$		0			0
$256$	329.471			1.28700
$257$			102.707i			0.399636i	0.979833	+	0.199818i	$0.0640351\pi$
$257$			102.707i			0.399636i	−0.979833	+	0.199818i	$0.935965\pi$
$258$	7.45706	−	7.45706i	0.0289033	−	0.0289033i
$259$			377.747i			1.45848i
$260$		0			0
$261$	188.243			0.721236
$262$	207.700	+	207.700i	0.792747	+	0.792747i
$263$	60.7931			0.231153			0.115576	−	0.993299i	$-0.463129\pi$
$263$	60.7931			0.231153			0.115576	+	0.993299i	$0.463129\pi$
$264$		−	3.85325i		−	0.0145956i
$265$		0			0
$266$	91.2251	+	91.2251i	0.342952	+	0.342952i
$267$	36.4820	−	36.4820i	0.136637	−	0.136637i
$268$	−202.293	+	202.293i	−0.754823	+	0.754823i
$269$	−413.362			−1.53666			−0.768330	−	0.640053i	$-0.778912\pi$
$269$	−413.362			−1.53666			−0.768330	+	0.640053i	$0.778912\pi$
$270$		0			0
$271$	33.0802	−	33.0802i	0.122067	−	0.122067i	−0.643434	−	0.765501i	$-0.722491\pi$
$271$	33.0802	−	33.0802i	0.122067	−	0.122067i	0.765501	+	0.643434i	$0.222491\pi$
$272$			51.3751i			0.188879i
$273$	−39.6661	+	116.409i	−0.145297	+	0.426406i
$274$	−327.602			−1.19563
$275$		0			0
$276$	102.090			0.369890
$277$			395.394i			1.42742i	0.700444	+	0.713708i	$0.252985\pi$
$277$			395.394i			1.42742i	−0.700444	+	0.713708i	$0.747015\pi$
$278$	323.514	+	323.514i	1.16372	+	1.16372i
$279$	213.791	+	213.791i	0.766278	+	0.766278i
$280$		0			0
$281$	−126.116	+	126.116i	−0.448810	+	0.448810i	−0.894959	−	0.446149i	$-0.852795\pi$
$281$	−126.116	+	126.116i	−0.448810	+	0.448810i	0.446149	+	0.894959i	$0.352795\pi$
$282$	−48.1870			−0.170876
$283$		−	426.703i		−	1.50779i	−0.656998	−	0.753893i	$-0.728174\pi$
$283$		−	426.703i		−	1.50779i	0.656998	−	0.753893i	$-0.271826\pi$
$284$	−7.72575	+	7.72575i	−0.0272033	+	0.0272033i
$285$		0			0
$286$	64.0823	−	31.5096i	0.224064	−	0.110173i
$287$	−595.856			−2.07615
$288$	−240.282	−	240.282i	−0.834314	−	0.834314i
$289$	281.495			0.974032
$290$		0			0
$291$	88.6507	+	88.6507i	0.304642	+	0.304642i
$292$	−234.413	−	234.413i	−0.802783	−	0.802783i
$293$	15.6125	−	15.6125i	0.0532849	−	0.0532849i	−0.679962	−	0.733247i	$-0.738004\pi$
$293$	15.6125	−	15.6125i	0.0532849	−	0.0532849i	0.733247	+	0.679962i	$0.238004\pi$
$294$	−139.234	+	139.234i	−0.473586	+	0.473586i
$295$		0			0
$296$		−	74.7221i		−	0.252440i
$297$	−20.0799	+	20.0799i	−0.0676091	+	0.0676091i
$298$			25.0243i			0.0839743i
$299$	−236.667	−	481.319i	−0.791528	−	1.60976i
$300$		0			0
$301$	−41.9491	−	41.9491i	−0.139366	−	0.139366i
$302$	−194.707			−0.644725
$303$			69.0141i			0.227769i
$304$	−53.8233	−	53.8233i	−0.177050	−	0.177050i
$305$		0			0
$306$	43.2509	−	43.2509i	0.141343	−	0.141343i
$307$	−360.117	+	360.117i	−1.17302	+	1.17302i	−0.191534	+	0.981486i	$0.561346\pi$
$307$	−360.117	+	360.117i	−1.17302	+	1.17302i	−0.981486	+	0.191534i	$0.938654\pi$
$308$	76.4613			0.248251
$309$		−	135.594i		−	0.438815i
$310$		0			0
$311$		−	209.072i		−	0.672257i	−0.941816	−	0.336128i	$-0.890882\pi$
$311$		−	209.072i		−	0.672257i	0.941816	−	0.336128i	$-0.109118\pi$
$312$	7.84634	−	23.0268i	0.0251485	−	0.0738039i
$313$	−333.747			−1.06628			−0.533142	−	0.846026i	$-0.678989\pi$
$313$	−333.747			−1.06628			−0.533142	+	0.846026i	$0.678989\pi$
$314$	117.350	+	117.350i	0.373726	+	0.373726i
$315$		0			0
$316$			211.560i			0.669493i
$317$	158.818	+	158.818i	0.501002	+	0.501002i	0.911749	−	0.410747i	$-0.134732\pi$
$317$	158.818	+	158.818i	0.501002	+	0.501002i	−0.410747	+	0.911749i	$0.634732\pi$
$318$	−83.6133	−	83.6133i	−0.262935	−	0.262935i
$319$	32.7477	−	32.7477i	0.102657	−	0.102657i
$320$		0			0
$321$	148.102			0.461377
$322$		−	1311.40i		−	4.07268i
$323$	7.86251	−	7.86251i	0.0243421	−	0.0243421i
$324$			200.631i			0.619230i
$325$		0			0
$326$	−200.679			−0.615581
$327$	−12.1360	−	12.1360i	−0.0371130	−	0.0371130i
$328$	117.866			0.359349
$329$			271.072i			0.823928i
$330$		0			0
$331$	328.694	+	328.694i	0.993032	+	0.993032i	0.999976	−	0.00694351i	$-0.00221021\pi$
$331$	328.694	+	328.694i	0.993032	+	0.993032i	−0.00694351	+	0.999976i	$0.502210\pi$
$332$	−285.468	+	285.468i	−0.859845	+	0.859845i
$333$	−187.629	+	187.629i	−0.563450	+	0.563450i
$334$	394.560			1.18132
$335$		0			0
$336$	125.447	−	125.447i	0.373355	−	0.373355i
$337$			239.044i			0.709329i	0.934994	+	0.354664i	$0.115405\pi$
$337$			239.044i			0.709329i	−0.934994	+	0.354664i	$0.884595\pi$
$338$	447.116	−	57.8095i	1.32283	−	0.171034i
$339$	152.862			0.450921
$340$		0			0
$341$	74.3846			0.218137
$342$			90.6239i			0.264982i
$343$	370.419	+	370.419i	1.07994	+	1.07994i
$344$	8.29794	+	8.29794i	0.0241219	+	0.0241219i
$345$		0			0
$346$	528.688	−	528.688i	1.52800	−	1.52800i
$347$	5.90128			0.0170066			0.00850329	−	0.999964i	$-0.497293\pi$
$347$	5.90128			0.0170066			0.00850329	+	0.999964i	$0.497293\pi$
$348$			55.6524i			0.159921i
$349$	11.5942	−	11.5942i	0.0332212	−	0.0332212i	−0.690301	−	0.723522i	$-0.742522\pi$
$349$	11.5942	−	11.5942i	0.0332212	−	0.0332212i	0.723522	+	0.690301i	$0.242522\pi$
$350$		0			0
$351$	−160.885	+	79.1081i	−0.458363	+	0.225379i
$352$	−83.6015			−0.237504
$353$	−129.927	−	129.927i	−0.368066	−	0.368066i	0.498705	−	0.866772i	$-0.333809\pi$
$353$	−129.927	−	129.927i	−0.368066	−	0.368066i	−0.866772	+	0.498705i	$0.833809\pi$
$354$	92.1798			0.260395
$355$		0			0
$356$	−143.199	−	143.199i	−0.402245	−	0.402245i
$357$	18.3254	+	18.3254i	0.0513316	+	0.0513316i
$358$	430.366	−	430.366i	1.20214	−	1.20214i
$359$	273.927	−	273.927i	0.763027	−	0.763027i	−0.213841	−	0.976868i	$-0.568597\pi$
$359$	273.927	−	273.927i	0.763027	−	0.763027i	0.976868	+	0.213841i	$0.0685975\pi$
$360$		0			0
$361$		−	344.526i		−	0.954365i
$362$	321.133	−	321.133i	0.887108	−	0.887108i
$363$		−	92.7039i		−	0.255383i
$364$	456.929	+	155.698i	1.25530	+	0.427741i
$365$		0			0
$366$	7.02401	+	7.02401i	0.0191913	+	0.0191913i
$367$	−125.394			−0.341673			−0.170836	−	0.985299i	$-0.554647\pi$
$367$	−125.394			−0.341673			−0.170836	+	0.985299i	$0.554647\pi$
$368$			773.733i			2.10254i
$369$	−295.965	−	295.965i	−0.802072	−	0.802072i
$370$		0			0
$371$	−470.360	+	470.360i	−1.26782	+	1.26782i
$372$	−63.2057	+	63.2057i	−0.169908	+	0.169908i
$373$	503.396			1.34959			0.674793	−	0.738007i	$-0.264233\pi$
$373$	503.396			1.34959			0.674793	+	0.738007i	$0.264233\pi$
$374$		−	15.0483i		−	0.0402361i
$375$		0			0
$376$		−	53.6208i		−	0.142608i
$377$	262.383	−	129.015i	0.695975	−	0.342214i
$378$	−438.348			−1.15965
$379$	464.950	+	464.950i	1.22678	+	1.22678i	0.965175	+	0.261606i	$0.0842522\pi$
$379$	464.950	+	464.950i	1.22678	+	1.22678i	0.261606	+	0.965175i	$0.415748\pi$
$380$		0			0
$381$			57.0500i			0.149738i
$382$	550.966	+	550.966i	1.44232	+	1.44232i
$383$	317.070	+	317.070i	0.827858	+	0.827858i	0.987220	−	0.159362i	$-0.0509437\pi$
$383$	317.070	+	317.070i	0.827858	+	0.827858i	−0.159362	+	0.987220i	$0.550944\pi$
$384$	−41.3099	+	41.3099i	−0.107578	+	0.107578i
$385$		0			0
$386$	−330.487			−0.856184
$387$		−	41.6726i		−	0.107681i
$388$	347.973	−	347.973i	0.896837	−	0.896837i
$389$		−	92.1151i		−	0.236800i	−0.992966	−	0.118400i	$-0.962224\pi$
$389$		−	92.1151i		−	0.236800i	0.992966	−	0.118400i	$-0.0377765\pi$
$390$		0			0
$391$	−113.027			−0.289072
$392$	−154.935	−	154.935i	−0.395242	−	0.395242i
$393$	−87.4222			−0.222448
$394$		−	56.5325i		−	0.143483i
$395$		0			0
$396$	37.9787	+	37.9787i	0.0959058	+	0.0959058i
$397$	454.524	−	454.524i	1.14490	−	1.14490i	0.157356	−	0.987542i	$-0.449703\pi$
$397$	454.524	−	454.524i	1.14490	−	1.14490i	0.987542	−	0.157356i	$-0.0502969\pi$
$398$	−148.023	+	148.023i	−0.371918	+	0.371918i
$399$	−38.3973			−0.0962338
$400$		0			0
$401$	−289.770	+	289.770i	−0.722618	+	0.722618i	−0.969138	−	0.246520i	$-0.920713\pi$
$401$	−289.770	+	289.770i	−0.722618	+	0.722618i	0.246520	+	0.969138i	$0.420713\pi$
$402$		−	194.431i		−	0.483659i
$403$	444.519	+	151.469i	1.10302	+	0.375853i
$404$	270.895			0.670532
$405$		0			0
$406$	714.888			1.76081
$407$			65.2817i			0.160397i
$408$	−3.62494	−	3.62494i	−0.00888466	−	0.00888466i
$409$	−13.9909	−	13.9909i	−0.0342075	−	0.0342075i	0.689796	−	0.724004i	$-0.257700\pi$
$409$	−13.9909	−	13.9909i	−0.0342075	−	0.0342075i	−0.724004	+	0.689796i	$0.757700\pi$
$410$		0			0
$411$	68.9449	−	68.9449i	0.167749	−	0.167749i
$412$	−532.234			−1.29183
$413$		−	518.550i		−	1.25557i
$414$	651.379	−	651.379i	1.57338	−	1.57338i
$415$		0			0
$416$	−499.599	−	170.237i	−1.20096	−	0.409224i
$417$	−136.169			−0.326545
$418$	15.7654	+	15.7654i	0.0377163	+	0.0377163i
$419$	151.917			0.362569			0.181285	−	0.983431i	$-0.441974\pi$
$419$	151.917			0.362569			0.181285	+	0.983431i	$0.441974\pi$
$420$		0			0
$421$	364.648	+	364.648i	0.866147	+	0.866147i	0.992043	−	0.125897i	$-0.0401807\pi$
$421$	364.648	+	364.648i	0.866147	+	0.866147i	−0.125897	+	0.992043i	$0.540181\pi$
$422$	−202.184	−	202.184i	−0.479109	−	0.479109i
$423$	−134.643	+	134.643i	−0.318305	+	0.318305i
$424$	93.0418	−	93.0418i	0.219438	−	0.219438i
$425$		0			0
$426$		−	7.42550i		−	0.0174308i
$427$	39.5130	−	39.5130i	0.0925363	−	0.0925363i
$428$		−	581.332i		−	1.35825i
$429$	−6.85504	+	20.1176i	−0.0159791	+	0.0468942i
$430$		0			0
$431$	488.245	+	488.245i	1.13282	+	1.13282i	0.989707	+	0.143112i	$0.0457109\pi$
$431$	488.245	+	488.245i	1.13282	+	1.13282i	0.143112	+	0.989707i	$0.454289\pi$
$432$	258.628			0.598675
$433$		−	295.143i		−	0.681624i	−0.940132	−	0.340812i	$-0.889298\pi$
$433$		−	295.143i		−	0.681624i	0.940132	−	0.340812i	$-0.110702\pi$
$434$	811.914	+	811.914i	1.87077	+	1.87077i
$435$		0			0
$436$	−47.6362	+	47.6362i	−0.109257	+	0.109257i
$437$	118.413	−	118.413i	0.270968	−	0.270968i
$438$	225.303			0.514390
$439$		−	54.2049i		−	0.123473i	−0.998092	−	0.0617367i	$-0.980336\pi$
$439$		−	54.2049i		−	0.123473i	0.998092	−	0.0617367i	$-0.0196639\pi$
$440$		0			0
$441$			778.088i			1.76437i
$442$	30.6428	−	89.9281i	0.0693276	−	0.203457i
$443$	414.826			0.936403			0.468201	−	0.883622i	$-0.344902\pi$
$443$	414.826			0.936403			0.468201	+	0.883622i	$0.344902\pi$
$444$	−55.4709	−	55.4709i	−0.124934	−	0.124934i
$445$		0			0
$446$		−	588.485i		−	1.31947i
$447$	−5.26645	−	5.26645i	−0.0117818	−	0.0117818i
$448$	−280.518	−	280.518i	−0.626156	−	0.626156i
$449$	64.8500	−	64.8500i	0.144432	−	0.144432i	−0.631193	−	0.775625i	$-0.717435\pi$
$449$	64.8500	−	64.8500i	0.144432	−	0.144432i	0.775625	+	0.631193i	$0.217435\pi$
$450$		0			0
$451$	−102.975			−0.228326
$452$		−	600.016i		−	1.32747i
$453$	40.9768	−	40.9768i	0.0904564	−	0.0904564i
$454$		−	414.322i		−	0.912604i
$455$		0			0
$456$	7.59536			0.0166565
$457$	104.290	+	104.290i	0.228206	+	0.228206i	0.811943	−	0.583737i	$-0.198410\pi$
$457$	104.290	+	104.290i	0.228206	+	0.228206i	−0.583737	+	0.811943i	$0.698410\pi$
$458$	−1013.25			−2.21233
$459$			37.7804i			0.0823102i
$460$		0			0
$461$	−175.305	−	175.305i	−0.380271	−	0.380271i	0.490929	−	0.871200i	$-0.336658\pi$
$461$	−175.305	−	175.305i	−0.380271	−	0.380271i	−0.871200	+	0.490929i	$0.836658\pi$
$462$	−36.7449	+	36.7449i	−0.0795344	+	0.0795344i
$463$	236.061	−	236.061i	0.509851	−	0.509851i	−0.404629	−	0.914481i	$-0.632599\pi$
$463$	236.061	−	236.061i	0.509851	−	0.509851i	0.914481	+	0.404629i	$0.132599\pi$
$464$	−421.787			−0.909024
$465$		0			0
$466$	−273.177	+	273.177i	−0.586217	+	0.586217i
$467$			411.919i			0.882054i	0.897494	+	0.441027i	$0.145386\pi$
$467$			411.919i			0.882054i	−0.897494	+	0.441027i	$0.854614\pi$
$468$	149.623	+	304.295i	0.319708	+	0.650202i
$469$	−1093.75			−2.33210
$470$		0			0
$471$	−49.3933			−0.104869
$472$			102.574i			0.217318i
$473$	−7.24958	−	7.24958i	−0.0153268	−	0.0153268i
$474$	−101.669	−	101.669i	−0.214491	−	0.214491i
$475$		0			0
$476$	71.9310	−	71.9310i	0.151116	−	0.151116i
$477$	−467.260			−0.979580
$478$			621.801i			1.30084i
$479$	121.114	−	121.114i	0.252848	−	0.252848i	−0.569289	−	0.822137i	$-0.692781\pi$
$479$	121.114	−	121.114i	0.252848	−	0.252848i	0.822137	+	0.569289i	$0.192781\pi$
$480$		0			0
$481$	−132.933	+	390.121i	−0.276367	+	0.811062i
$482$	−960.048			−1.99180
$483$	275.989	+	275.989i	0.571406	+	0.571406i
$484$	−363.882			−0.751823
$485$		0			0
$486$	−330.546	−	330.546i	−0.680135	−	0.680135i
$487$	500.824	+	500.824i	1.02839	+	1.02839i	0.999585	+	0.0288012i	$0.00916897\pi$
$487$	500.824	+	500.824i	1.02839	+	1.02839i	0.0288012	+	0.999585i	$0.490831\pi$
$488$	−7.81606	+	7.81606i	−0.0160165	+	0.0160165i
$489$	42.2337	−	42.2337i	0.0863674	−	0.0863674i
$490$		0			0
$491$			541.358i			1.10256i	0.834320	+	0.551281i	$0.185861\pi$
$491$			541.358i			1.10256i	−0.834320	+	0.551281i	$0.814139\pi$
$492$	87.4995	−	87.4995i	0.177845	−	0.177845i
$493$		−	61.6148i		−	0.124979i
$494$	62.1104	+	126.316i	0.125730	+	0.255701i
$495$		0			0
$496$	−479.033	−	479.033i	−0.965793	−	0.965793i
$497$	−41.7715			−0.0840474
$498$		−	274.374i		−	0.550952i
$499$	406.898	+	406.898i	0.815427	+	0.815427i	0.985442	−	0.170015i	$-0.0543815\pi$
$499$	406.898	+	406.898i	0.815427	+	0.815427i	−0.170015	+	0.985442i	$0.554382\pi$
$500$		0			0
$501$	−83.0365	+	83.0365i	−0.165742	+	0.165742i
$502$	210.295	−	210.295i	0.418914	−	0.418914i
$503$	−295.334			−0.587146			−0.293573	−	0.955937i	$-0.594844\pi$
$503$	−295.334			−0.587146			−0.293573	+	0.955937i	$0.594844\pi$
$504$		−	235.038i		−	0.466345i
$505$		0			0
$506$		−	226.635i		−	0.447895i
$507$	−81.9308	+	106.263i	−0.161599	+	0.209592i
$508$	223.933			0.440814
$509$	−6.08665	−	6.08665i	−0.0119581	−	0.0119581i	0.701102	−	0.713061i	$-0.252692\pi$
$509$	−6.08665	−	6.08665i	−0.0119581	−	0.0119581i	−0.713061	+	0.701102i	$0.752692\pi$
$510$		0			0
$511$		−	1267.42i		−	2.48028i
$512$	413.374	+	413.374i	0.807371	+	0.807371i
$513$	−39.5807	−	39.5807i	−0.0771554	−	0.0771554i
$514$	−193.739	+	193.739i	−0.376923	+	0.376923i
$515$		0			0
$516$	12.3202			0.0238763
$517$			46.8463i			0.0906119i
$518$	−712.556	+	712.556i	−1.37559	+	1.37559i
$519$			222.528i			0.428764i
$520$		0			0
$521$	583.890			1.12071			0.560356	−	0.828252i	$-0.310664\pi$
$521$	583.890			1.12071			0.560356	+	0.828252i	$0.310664\pi$
$522$	355.088	+	355.088i	0.680246	+	0.680246i
$523$	531.245			1.01577			0.507883	−	0.861426i	$-0.330428\pi$
$523$	531.245			1.01577			0.507883	+	0.861426i	$0.330428\pi$
$524$			343.150i			0.654867i
$525$		0			0
$526$	114.676	+	114.676i	0.218015	+	0.218015i
$527$	69.9773	−	69.9773i	0.132784	−	0.132784i
$528$	21.6797	−	21.6797i	0.0410600	−	0.0410600i
$529$	−1173.24			−2.21785
$530$		0			0
$531$	257.566	−	257.566i	0.485059	−	0.485059i
$532$			150.717i			0.283303i
$533$	−615.375	−	209.688i	−1.15455	−	0.393410i
$534$	137.634			0.257742
$535$		0			0
$536$	216.356			0.403648
$537$			181.144i			0.337326i
$538$	−779.738	−	779.738i	−1.44933	−	1.44933i
$539$	135.360	+	135.360i	0.251132	+	0.251132i
$540$		0			0
$541$	693.346	−	693.346i	1.28160	−	1.28160i	0.341844	−	0.939757i	$-0.388949\pi$
$541$	693.346	−	693.346i	1.28160	−	1.28160i	0.939757	−	0.341844i	$-0.111051\pi$
$542$	124.801			0.230259
$543$			135.167i			0.248926i
$544$	−78.6482	+	78.6482i	−0.144574	+	0.144574i
$545$		0			0
$546$	−294.409	+	144.762i	−0.539211	+	0.265133i
$547$	372.319			0.680657			0.340328	−	0.940307i	$-0.389462\pi$
$547$	372.319			0.680657			0.340328	+	0.940307i	$0.389462\pi$
$548$	−270.623	−	270.623i	−0.493838	−	0.493838i
$549$	39.2526			0.0714983
$550$		0			0
$551$	64.5509	+	64.5509i	0.117152	+	0.117152i
$552$	−54.5933	−	54.5933i	−0.0989010	−	0.0989010i
$553$	−571.930	+	571.930i	−1.03423	+	1.03423i
$554$	−745.845	+	745.845i	−1.34629	+	1.34629i
$555$		0			0
$556$			534.493i			0.961318i
$557$	30.1943	−	30.1943i	0.0542088	−	0.0542088i	−0.679483	−	0.733692i	$-0.737796\pi$
$557$	30.1943	−	30.1943i	0.0542088	−	0.0542088i	0.733692	+	0.679483i	$0.237796\pi$
$558$			806.564i			1.44545i
$559$	−28.5609	−	58.0855i	−0.0510928	−	0.103910i
$560$		0			0
$561$	3.16697	+	3.16697i	0.00564522	+	0.00564522i
$562$	−475.792			−0.846606
$563$			254.215i			0.451536i	0.974181	+	0.225768i	$0.0724891\pi$
$563$			254.215i			0.451536i	−0.974181	+	0.225768i	$0.927511\pi$
$564$	−39.8060	−	39.8060i	−0.0705781	−	0.0705781i
$565$		0			0
$566$	804.904	−	804.904i	1.42209	−	1.42209i
$567$	−542.384	+	542.384i	−0.956586	+	0.956586i
$568$	8.26283			0.0145472
$569$		−	913.655i		−	1.60572i	−0.596168	−	0.802860i	$-0.703311\pi$
$569$		−	913.655i		−	1.60572i	0.596168	−	0.802860i	$-0.296689\pi$
$570$		0			0
$571$			580.894i			1.01733i	0.860965	+	0.508664i	$0.169860\pi$
$571$			580.894i			1.01733i	−0.860965	+	0.508664i	$0.830140\pi$
$572$	78.9659	+	26.9075i	0.138052	+	0.0470410i
$573$	−231.905			−0.404721
$574$	−1123.98	−	1123.98i	−1.95816	−	1.95816i
$575$		0			0
$576$		−	278.669i		−	0.483800i
$577$	50.8969	+	50.8969i	0.0882095	+	0.0882095i	0.749835	−	0.661625i	$-0.230133\pi$
$577$	50.8969	+	50.8969i	0.0882095	+	0.0882095i	−0.661625	+	0.749835i	$0.730133\pi$
$578$	530.993	+	530.993i	0.918674	+	0.918674i
$579$	69.5521	−	69.5521i	0.120125	−	0.120125i
$580$		0			0
$581$	−1543.47			−2.65657
$582$			334.449i			0.574655i
$583$	−81.2869	+	81.2869i	−0.139429	+	0.139429i
$584$			250.709i			0.429296i
$585$		0			0
$586$	58.9006			0.100513
$587$	−344.992	−	344.992i	−0.587720	−	0.587720i	0.349294	−	0.937013i	$-0.386422\pi$
$587$	−344.992	−	344.992i	−0.587720	−	0.587720i	−0.937013	+	0.349294i	$0.886422\pi$
$588$	−230.035			−0.391217
$589$			146.624i			0.248937i
$590$		0			0
$591$	11.8975	+	11.8975i	0.0201311	+	0.0201311i
$592$	420.412	−	420.412i	0.710155	−	0.710155i
$593$	−103.349	+	103.349i	−0.174282	+	0.174282i	−0.788858	−	0.614576i	$-0.789327\pi$
$593$	−103.349	+	103.349i	−0.174282	+	0.174282i	0.614576	+	0.788858i	$0.289327\pi$
$594$	−75.7548			−0.127533
$595$		0			0
$596$	−20.6719	+	20.6719i	−0.0346845	+	0.0346845i
$597$		−	62.3041i		−	0.104362i
$598$	461.495	−	1354.36i	0.771730	−	2.26481i
$599$	−477.029			−0.796376			−0.398188	−	0.917304i	$-0.630361\pi$
$599$	−477.029			−0.796376			−0.398188	+	0.917304i	$0.630361\pi$
$600$		0			0
$601$	230.164			0.382968			0.191484	−	0.981496i	$-0.438670\pi$
$601$	230.164			0.382968			0.191484	+	0.981496i	$0.438670\pi$
$602$		−	158.260i		−	0.262890i
$603$	−543.273	−	543.273i	−0.900950	−	0.900950i
$604$	−160.842	−	160.842i	−0.266295	−	0.266295i
$605$		0			0
$606$	−130.184	+	130.184i	−0.214824	+	0.214824i
$607$	−532.535			−0.877323			−0.438661	−	0.898652i	$-0.644547\pi$
$607$	−532.535			−0.877323			−0.438661	+	0.898652i	$0.644547\pi$
$608$		−	164.792i		−	0.271039i
$609$	−150.451	+	150.451i	−0.247045	+	0.247045i
$610$		0			0
$611$	−95.3929	+	279.952i	−0.156126	+	0.458186i
$612$	71.4569			0.116760
$613$	769.790	+	769.790i	1.25577	+	1.25577i	0.953091	+	0.302683i	$0.0978825\pi$
$613$	769.790	+	769.790i	1.25577	+	1.25577i	0.302683	+	0.953091i	$0.402117\pi$
$614$	−1358.60			−2.21271
$615$		0			0
$616$	−40.8884	−	40.8884i	−0.0663772	−	0.0663772i
$617$	−730.372	−	730.372i	−1.18375	−	1.18375i	−0.978766	−	0.204981i	$-0.934287\pi$
$617$	−730.372	−	730.372i	−1.18375	−	1.18375i	−0.204981	−	0.978766i	$-0.565713\pi$
$618$	255.775	−	255.775i	0.413875	−	0.413875i
$619$	−297.357	+	297.357i	−0.480383	+	0.480383i	−0.905254	−	0.424871i	$-0.860319\pi$
$619$	−297.357	+	297.357i	−0.480383	+	0.480383i	0.424871	+	0.905254i	$0.360319\pi$
$620$		0			0
$621$			568.990i			0.916248i
$622$	394.379	−	394.379i	0.634050	−	0.634050i
$623$		−	774.250i		−	1.24278i
$624$	173.703	−	85.4105i	0.278370	−	0.136876i
$625$		0			0
$626$	−629.557	−	629.557i	−1.00568	−	1.00568i
$627$	−6.63577			−0.0105834
$628$			193.879i			0.308725i
$629$	61.4138	+	61.4138i	0.0976372	+	0.0976372i
$630$		0			0
$631$	440.375	−	440.375i	0.697900	−	0.697900i	−0.266057	−	0.963957i	$-0.585721\pi$
$631$	440.375	−	440.375i	0.697900	−	0.697900i	0.963957	+	0.266057i	$0.0857210\pi$
$632$	113.134	−	113.134i	0.179009	−	0.179009i
$633$	85.1006			0.134440
$634$			599.166i			0.945057i
$635$		0			0
$636$		−	138.141i		−	0.217204i
$637$	533.274	+	1084.54i	0.837165	+	1.70258i
$638$	123.546			0.193646
$639$	−20.7481	−	20.7481i	−0.0324697	−	0.0324697i
$640$		0			0
$641$			576.939i			0.900060i	0.893013	+	0.450030i	$0.148587\pi$
$641$			576.939i			0.900060i	−0.893013	+	0.450030i	$0.851413\pi$
$642$	279.370	+	279.370i	0.435155	+	0.435155i
$643$	−459.481	−	459.481i	−0.714589	−	0.714589i	0.252903	−	0.967492i	$-0.418615\pi$
$643$	−459.481	−	459.481i	−0.714589	−	0.714589i	−0.967492	+	0.252903i	$0.918615\pi$
$644$	1083.31	−	1083.31i	1.68217	−	1.68217i
$645$		0			0
$646$	29.6626			0.0459174
$647$			543.648i			0.840260i	0.907464	+	0.420130i	$0.138016\pi$
$647$			543.648i			0.840260i	−0.907464	+	0.420130i	$0.861984\pi$
$648$	107.289	−	107.289i	0.165569	−	0.165569i
$649$		−	89.6151i		−	0.138082i
$650$		0			0
$651$	−341.740			−0.524947
$652$	−165.776	−	165.776i	−0.254258	−	0.254258i
$653$	−762.917			−1.16833			−0.584163	−	0.811636i	$-0.698577\pi$
$653$	−762.917			−1.16833			−0.584163	+	0.811636i	$0.698577\pi$
$654$		−	45.7849i		−	0.0700075i
$655$		0			0
$656$	663.155	+	663.155i	1.01091	+	1.01091i
$657$	629.534	−	629.534i	0.958195	−	0.958195i
$658$	−511.332	+	511.332i	−0.777101	+	0.777101i
$659$	810.362			1.22968			0.614842	−	0.788650i	$-0.289220\pi$
$659$	810.362			1.22968			0.614842	+	0.788650i	$0.289220\pi$
$660$		0			0
$661$	−220.504	+	220.504i	−0.333591	+	0.333591i	−0.853949	−	0.520357i	$-0.825799\pi$
$661$	−220.504	+	220.504i	−0.333591	+	0.333591i	0.520357	+	0.853949i	$0.325799\pi$
$662$			1240.05i			1.87319i
$663$	12.4768	+	25.3745i	0.0188187	+	0.0382723i
$664$	305.314			0.459810
$665$		0			0
$666$	−707.860			−1.06285
$667$		−	927.947i		−	1.39123i
$668$	325.936	+	325.936i	0.487928	+	0.487928i
$669$	123.849	+	123.849i	0.185125	+	0.185125i
$670$		0			0
$671$	6.82858	−	6.82858i	0.0101767	−	0.0101767i
$672$	384.085			0.571555
$673$		−	710.668i		−	1.05597i	−0.849254	−	0.527985i	$-0.822948\pi$
$673$		−	710.668i		−	1.05597i	0.849254	−	0.527985i	$-0.177052\pi$
$674$	−450.916	+	450.916i	−0.669015	+	0.669015i
$675$		0			0
$676$	417.105	+	321.596i	0.617020	+	0.475733i
$677$	1048.84			1.54925			0.774625	−	0.632421i	$-0.217939\pi$
$677$	1048.84			1.54925			0.774625	+	0.632421i	$0.217939\pi$
$678$	288.349	+	288.349i	0.425293	+	0.425293i
$679$	1881.42			2.77087
$680$		0			0
$681$	87.1955	+	87.1955i	0.128040	+	0.128040i
$682$	140.314	+	140.314i	0.205739	+	0.205739i
$683$	−607.809	+	607.809i	−0.889910	+	0.889910i	−0.994514	−	0.104604i	$-0.966643\pi$
$683$	−607.809	+	607.809i	−0.889910	+	0.889910i	0.104604	+	0.994514i	$0.466643\pi$
$684$	−74.8621	+	74.8621i	−0.109447	+	0.109447i
$685$		0			0
$686$			1397.47i			2.03712i
$687$	213.241	−	213.241i	0.310394	−	0.310394i
$688$			93.3740i			0.135718i
$689$	−651.291	+	320.243i	−0.945270	+	0.464794i
$690$		0			0
$691$	−374.671	−	374.671i	−0.542216	−	0.542216i	0.381962	−	0.924178i	$-0.375249\pi$
$691$	−374.671	−	374.671i	−0.542216	−	0.542216i	−0.924178	+	0.381962i	$0.875249\pi$
$692$	873.471			1.26224
$693$			205.343i			0.296310i
$694$	11.1318	+	11.1318i	0.0160400	+	0.0160400i
$695$		0			0
$696$	29.7606	−	29.7606i	0.0427595	−	0.0427595i
$697$	−96.8739	+	96.8739i	−0.138987	+	0.138987i
$698$	43.7410			0.0626662
$699$		−	114.982i		−	0.164495i
$700$		0			0
$701$		−	559.394i		−	0.797994i	−0.916952	−	0.398997i	$-0.869358\pi$
$701$		−	559.394i		−	0.797994i	0.916952	−	0.398997i	$-0.130642\pi$
$702$	−452.707	−	154.259i	−0.644882	−	0.219742i
$703$	−128.681			−0.183045
$704$	−48.4787	−	48.4787i	−0.0688618	−	0.0688618i
$705$		0			0
$706$		−	490.172i		−	0.694295i
$707$	732.337	+	732.337i	1.03584	+	1.03584i
$708$	76.1473	+	76.1473i	0.107553	+	0.107553i
$709$	−379.510	+	379.510i	−0.535276	+	0.535276i	−0.922138	−	0.386862i	$-0.873559\pi$
$709$	−379.510	+	379.510i	−0.535276	+	0.535276i	0.386862	+	0.922138i	$0.373559\pi$
$710$		0			0
$711$	−568.161			−0.799101
$712$			153.154i			0.215104i
$713$	1053.89	−	1053.89i	1.47811	−	1.47811i
$714$			69.1355i			0.0968285i
$715$		0			0
$716$	711.028			0.993056
$717$	−130.860	−	130.860i	−0.182510	−	0.182510i
$718$	1033.43			1.43932
$719$		−	427.082i		−	0.593995i	−0.954878	−	0.296997i	$-0.904015\pi$
$719$		−	427.082i		−	0.593995i	0.954878	−	0.296997i	$-0.0959852\pi$
$720$		0			0
$721$	−1438.84	−	1438.84i	−1.99562	−	1.99562i
$722$	649.890	−	649.890i	0.900124	−	0.900124i
$723$	202.045	−	202.045i	0.279454	−	0.279454i
$724$	530.559			0.732816
$725$		0			0
$726$	174.870	−	174.870i	0.240868	−	0.240868i
$727$		−	952.075i		−	1.30959i	−0.755804	−	0.654797i	$-0.772754\pi$
$727$		−	952.075i		−	1.30959i	0.755804	−	0.654797i	$-0.227246\pi$
$728$	−161.086	−	327.608i	−0.221272	−	0.450011i
$729$	−440.263			−0.603928
$730$		0			0
$731$	−13.6401			−0.0186595
$732$			11.6047i			0.0158534i
$733$	492.664	+	492.664i	0.672119	+	0.672119i	0.958204	−	0.286085i	$-0.0923539\pi$
$733$	492.664	+	492.664i	0.672119	+	0.672119i	−0.286085	+	0.958204i	$0.592354\pi$
$734$	−236.535	−	236.535i	−0.322254	−	0.322254i
$735$		0			0
$736$	−1184.48	+	1184.48i	−1.60935	+	1.60935i
$737$	−189.021			−0.256474
$738$		−	1116.58i		−	1.51298i
$739$	94.0595	−	94.0595i	0.127279	−	0.127279i	−0.640597	−	0.767877i	$-0.721313\pi$
$739$	94.0595	−	94.0595i	0.127279	−	0.127279i	0.767877	+	0.640597i	$0.221313\pi$
$740$		0			0
$741$	−39.6550	−	13.5124i	−0.0535156	−	0.0182353i
$742$	−1774.51			−2.39152
$743$	750.112	+	750.112i	1.00957	+	1.00957i	0.999954	+	0.00961857i	$0.00306173\pi$
$743$	750.112	+	750.112i	1.00957	+	1.00957i	0.00961857	+	0.999954i	$0.496938\pi$
$744$	67.5996			0.0908597
$745$		0			0
$746$	949.572	+	949.572i	1.27288	+	1.27288i
$747$	−766.649	−	766.649i	−1.02630	−	1.02630i
$748$	12.4310	−	12.4310i	0.0166190	−	0.0166190i
$749$	1571.57	−	1571.57i	2.09823	−	2.09823i
$750$		0			0
$751$			332.394i			0.442602i	0.975206	+	0.221301i	$0.0710304\pi$
$751$			332.394i			0.442602i	−0.975206	+	0.221301i	$0.928970\pi$
$752$	301.688	−	301.688i	0.401181	−	0.401181i
$753$			88.5144i			0.117549i
$754$	738.305	+	251.576i	0.979185	+	0.333655i
$755$		0			0
$756$	−362.108	−	362.108i	−0.478979	−	0.478979i
$757$	−354.304			−0.468037			−0.234018	−	0.972232i	$-0.575188\pi$
$757$	−354.304			−0.468037			−0.234018	+	0.972232i	$0.575188\pi$
$758$			1754.10i			2.31412i
$759$	47.6960	+	47.6960i	0.0628406	+	0.0628406i
$760$		0			0
$761$	800.356	−	800.356i	1.05172	−	1.05172i	0.0531281	−	0.998588i	$-0.483081\pi$
$761$	800.356	−	800.356i	1.05172	−	1.05172i	0.998588	−	0.0531281i	$-0.0169192\pi$
$762$	−107.615	+	107.615i	−0.141227	+	0.141227i
$763$	−257.559			−0.337561
$764$			910.277i			1.19146i
$765$		0			0
$766$			1196.20i			1.56162i
$767$	182.483	−	535.536i	0.237917	−	0.698221i
$768$	−261.590			−0.340612
$769$	628.880	+	628.880i	0.817790	+	0.817790i	0.985787	−	0.167998i	$-0.0537301\pi$
$769$	628.880	+	628.880i	0.817790	+	0.817790i	−0.167998	+	0.985787i	$0.553730\pi$
$770$		0			0
$771$		−	81.5459i		−	0.105766i
$772$	−273.007	−	273.007i	−0.353636	−	0.353636i
$773$	−799.646	−	799.646i	−1.03447	−	1.03447i	−0.999384	−	0.0350866i	$-0.988829\pi$
$773$	−799.646	−	799.646i	−1.03447	−	1.03447i	−0.0350866	−	0.999384i	$-0.511171\pi$
$774$	78.6084	−	78.6084i	0.101561	−	0.101561i
$775$		0			0
$776$	−372.163			−0.479592
$777$		−	299.920i		−	0.385997i
$778$	173.760	−	173.760i	0.223342	−	0.223342i
$779$		−	202.980i		−	0.260565i
$780$		0			0
$781$	−7.21890			−0.00924316
$782$	−213.207	−	213.207i	−0.272643	−	0.272643i
$783$	−310.175			−0.396137
$784$		−	1743.43i		−	2.22376i
$785$		0			0
$786$	−164.907	−	164.907i	−0.209806	−	0.209806i
$787$	−201.754	+	201.754i	−0.256358	+	0.256358i	−0.823571	−	0.567213i	$-0.808022\pi$
$787$	−201.754	+	201.754i	−0.256358	+	0.256358i	0.567213	+	0.823571i	$0.308022\pi$
$788$	46.7000	−	46.7000i	0.0592640	−	0.0592640i
$789$	−48.2679			−0.0611761
$790$		0			0
$791$	1622.08	−	1622.08i	2.05067	−	2.05067i
$792$		−	40.6189i		−	0.0512865i
$793$	54.7123	−	26.9023i	0.0689941	−	0.0339247i
$794$	1714.77			2.15966
$795$		0			0
$796$	−244.557			−0.307232
$797$		−	303.914i		−	0.381323i	−0.981656	−	0.190661i	$-0.938937\pi$
$797$		−	303.914i		−	0.381323i	0.981656	−	0.190661i	$-0.0610632\pi$
$798$	−72.4300	−	72.4300i	−0.0907644	−	0.0907644i
$799$	44.0707	+	44.0707i	0.0551573	+	0.0551573i
$800$		0			0
$801$	384.574	−	384.574i	0.480117	−	0.480117i
$802$	−1093.20			−1.36310
$803$		−	219.034i		−	0.272770i
$804$	160.614	−	160.614i	0.199769	−	0.199769i
$805$		0			0
$806$	552.790	+	1124.23i	0.685843	+	1.39483i
$807$	328.197			0.406687
$808$	−144.864	−	144.864i	−0.179287	−	0.179287i
$809$	−944.687			−1.16772			−0.583861	−	0.811854i	$-0.698459\pi$
$809$	−944.687			−1.16772			−0.583861	+	0.811854i	$0.698459\pi$
$810$		0			0
$811$	553.234	+	553.234i	0.682163	+	0.682163i	0.960487	−	0.278324i	$-0.0897790\pi$
$811$	553.234	+	553.234i	0.682163	+	0.682163i	−0.278324	+	0.960487i	$0.589779\pi$
$812$	590.550	+	590.550i	0.727279	+	0.727279i
$813$	−26.2647	+	26.2647i	−0.0323059	+	0.0323059i
$814$	−123.143	+	123.143i	−0.151281	+	0.151281i
$815$		0			0
$816$		−	40.7903i		−	0.0499881i
$817$	14.2901	−	14.2901i	0.0174909	−	0.0174909i
$818$		−	52.7829i		−	0.0645267i
$819$	−418.139	+	1227.12i	−0.510548	+	1.49832i
$820$		0			0
$821$	−251.178	−	251.178i	−0.305942	−	0.305942i	0.537391	−	0.843333i	$-0.319410\pi$
$821$	−251.178	−	251.178i	−0.305942	−	0.305942i	−0.843333	+	0.537391i	$0.819410\pi$
$822$	260.106			0.316431
$823$		−	13.4655i		−	0.0163615i	−0.999967	−	0.00818073i	$-0.997396\pi$
$823$		−	13.4655i		−	0.0163615i	0.999967	−	0.00818073i	$-0.00260403\pi$
$824$	284.617	+	284.617i	0.345409	+	0.345409i
$825$		0			0
$826$	978.157	−	978.157i	1.18421	−	1.18421i
$827$	−472.099	+	472.099i	−0.570857	+	0.570857i	−0.932368	−	0.361511i	$-0.882261\pi$
$827$	−472.099	+	472.099i	−0.570857	+	0.570857i	0.361511	+	0.932368i	$0.382261\pi$
$828$	1076.18			1.29973
$829$			922.692i			1.11302i	0.830841	+	0.556509i	$0.187860\pi$
$829$			922.692i			1.11302i	−0.830841	+	0.556509i	$0.812140\pi$
$830$		0			0
$831$		−	313.931i		−	0.377775i
$832$	−190.990	−	388.423i	−0.229555	−	0.466855i
$833$	254.680			0.305739
$834$	−256.860	−	256.860i	−0.307986	−	0.307986i
$835$		0			0
$836$			26.0468i			0.0311564i
$837$	−352.273	−	352.273i	−0.420876	−	0.420876i
$838$	286.565	+	286.565i	0.341963	+	0.341963i
$839$	373.582	−	373.582i	0.445270	−	0.445270i	−0.448508	−	0.893779i	$-0.648045\pi$
$839$	373.582	−	373.582i	0.445270	−	0.445270i	0.893779	+	0.448508i	$0.148045\pi$
$840$		0			0
$841$	−335.145			−0.398508
$842$			1375.69i			1.63384i
$843$	100.132	−	100.132i	0.118781	−	0.118781i
$844$		−	334.038i		−	0.395779i
$845$		0			0
$846$	−507.962			−0.600428
$847$	−983.719	−	983.719i	−1.16142	−	1.16142i
$848$	1046.97			1.23463
$849$			338.790i			0.399045i
$850$		0			0
$851$	924.921	+	924.921i	1.08686	+	1.08686i
$852$	6.13401	−	6.13401i	0.00719954	−	0.00719954i
$853$	−724.580	+	724.580i	−0.849449	+	0.849449i	−0.990064	−	0.140615i	$-0.955092\pi$
$853$	−724.580	+	724.580i	−0.849449	+	0.849449i	0.140615	+	0.990064i	$0.455092\pi$
$854$	149.069			0.174554
$855$		0			0
$856$	−310.872	+	310.872i	−0.363169	+	0.363169i
$857$			410.502i			0.478999i	0.970896	+	0.239500i	$0.0769834\pi$
$857$			410.502i			0.478999i	−0.970896	+	0.239500i	$0.923017\pi$
$858$	−50.8794	+	25.0177i	−0.0593000	+	0.0291581i
$859$	−847.774			−0.986932			−0.493466	−	0.869765i	$-0.664270\pi$
$859$	−847.774			−0.986932			−0.493466	+	0.869765i	$0.664270\pi$
$860$		0			0
$861$	473.092			0.549468
$862$			1841.98i			2.13687i
$863$	102.685	+	102.685i	0.118986	+	0.118986i	0.764093	−	0.645107i	$-0.223187\pi$
$863$	102.685	+	102.685i	0.118986	+	0.118986i	−0.645107	+	0.764093i	$0.723187\pi$
$864$	395.923	+	395.923i	0.458244	+	0.458244i
$865$		0			0
$866$	556.738	−	556.738i	0.642884	−	0.642884i
$867$	−223.499			−0.257784
$868$			1341.40i			1.54539i
$869$	−98.8403	+	98.8403i	−0.113740	+	0.113740i
$870$		0			0
$871$	−1129.58	−	384.903i	−1.29688	−	0.441909i
$872$	50.9478			0.0584264
$873$	934.509	+	934.509i	1.07046	+	1.07046i
$874$	446.733			0.511136
$875$		0			0
$876$	186.117	+	186.117i	0.212462	+	0.212462i
$877$	490.033	+	490.033i	0.558761	+	0.558761i	0.928955	−	0.370194i	$-0.120709\pi$
$877$	490.033	+	490.033i	0.558761	+	0.558761i	−0.370194	+	0.928955i	$0.620709\pi$
$878$	102.248	−	102.248i	0.116456	−	0.116456i
$879$	−12.3958	+	12.3958i	−0.0141022	+	0.0141022i
$880$		0			0
$881$		−	1389.52i		−	1.57720i	−0.614905	−	0.788601i	$-0.710806\pi$
$881$		−	1389.52i		−	1.57720i	0.614905	−	0.788601i	$-0.289194\pi$
$882$	−1467.73	+	1467.73i	−1.66410	+	1.66410i
$883$		−	763.229i		−	0.864359i	−0.901788	−	0.432179i	$-0.857745\pi$
$883$		−	763.229i		−	0.864359i	0.901788	−	0.432179i	$-0.142255\pi$
$884$	99.6004	−	48.9740i	0.112670	−	0.0554005i
$885$		0			0
$886$	782.500	+	782.500i	0.883183	+	0.883183i
$887$	−921.219			−1.03858			−0.519289	−	0.854599i	$-0.673803\pi$
$887$	−921.219			−1.03858			−0.519289	+	0.854599i	$0.673803\pi$
$888$			59.3271i			0.0668098i
$889$	605.381	+	605.381i	0.680968	+	0.680968i
$890$		0			0
$891$	−93.7342	+	93.7342i	−0.105201	+	0.105201i
$892$	486.132	−	486.132i	0.544991	−	0.544991i
$893$	−92.3416			−0.103406
$894$		−	19.8686i		−	0.0222243i
$895$		0			0
$896$			876.712i			0.978473i
$897$	187.906	+	382.152i	0.209483	+	0.426034i
$898$	244.657			0.272447
$899$	574.510	+	574.510i	0.639055	+	0.639055i
$900$		0			0
$901$			152.941i			0.169746i
$902$	−194.245	−	194.245i	−0.215350	−	0.215350i
$903$	33.3063	+	33.3063i	0.0368840	+	0.0368840i
$904$	−320.864	+	320.864i	−0.354938	+	0.354938i
$905$		0			0
$906$	154.592			0.170631
$907$			952.357i			1.05001i	0.851100	+	0.525004i	$0.175936\pi$
$907$			952.357i			1.05001i	−0.851100	+	0.525004i	$0.824064\pi$
$908$	342.261	−	342.261i	0.376939	−	0.376939i
$909$			727.511i			0.800342i
$910$		0			0
$911$	146.413			0.160717			0.0803586	−	0.996766i	$-0.474393\pi$
$911$	146.413			0.160717			0.0803586	+	0.996766i	$0.474393\pi$
$912$	42.7341	+	42.7341i	0.0468575	+	0.0468575i
$913$	−266.740			−0.292158
$914$			393.452i			0.430473i
$915$		0			0
$916$	−837.015	−	837.015i	−0.913772	−	0.913772i
$917$	−927.672	+	927.672i	−1.01164	+	1.01164i
$918$	−71.2663	+	71.2663i	−0.0776322	+	0.0776322i
$919$	−799.748			−0.870237			−0.435118	−	0.900373i	$-0.643293\pi$
$919$	−799.748			−0.870237			−0.435118	+	0.900373i	$0.643293\pi$
$920$		0			0
$921$	285.922	−	285.922i	0.310448	−	0.310448i
$922$		−	661.367i		−	0.717317i
$923$	−43.1398	−	14.6998i	−0.0467387	−	0.0159261i
$924$	−60.7080			−0.0657013
$925$		0			0
$926$	890.580			0.961749
$927$		−	1429.36i		−	1.54192i
$928$	−645.698	−	645.698i	−0.695795	−	0.695795i
$929$	−78.6741	−	78.6741i	−0.0846869	−	0.0846869i	0.663494	−	0.748181i	$-0.269073\pi$
$929$	−78.6741	−	78.6741i	−0.0846869	−	0.0846869i	−0.748181	+	0.663494i	$0.769073\pi$
$930$		0			0
$931$	−266.817	+	266.817i	−0.286592	+	0.286592i
$932$	−451.329			−0.484259
$933$			165.997i			0.177917i
$934$	−777.016	+	777.016i	−0.831923	+	0.831923i
$935$		0			0
$936$	82.7120	−	242.737i	0.0883675	−	0.259334i
$937$	1466.28			1.56486			0.782431	−	0.622737i	$-0.213980\pi$
$937$	1466.28			1.56486			0.782431	+	0.622737i	$0.213980\pi$
$938$	−2063.18	−	2063.18i	−2.19956	−	2.19956i
$939$	264.985			0.282199
$940$		0			0
$941$	−68.9700	−	68.9700i	−0.0732944	−	0.0732944i	0.669509	−	0.742804i	$-0.266504\pi$
$941$	−68.9700	−	68.9700i	−0.0732944	−	0.0732944i	−0.742804	+	0.669509i	$0.766504\pi$
$942$	−93.1722	−	93.1722i	−0.0989089	−	0.0989089i
$943$	−1458.97	+	1458.97i	−1.54715	+	1.54715i
$944$	−577.117	+	577.117i	−0.611353	+	0.611353i
$945$		0			0
$946$		−	27.3502i		−	0.0289115i
$947$	582.125	−	582.125i	0.614705	−	0.614705i	−0.329464	−	0.944168i	$-0.606868\pi$
$947$	582.125	−	582.125i	0.614705	−	0.614705i	0.944168	+	0.329464i	$0.106868\pi$
$948$		−	167.972i		−	0.177186i
$949$	446.018	−	1308.94i	0.469987	−	1.37928i
$950$		0			0
$951$	−126.096	−	126.096i	−0.132594	−	0.132594i
$952$	−76.9315			−0.0808104
$953$		−	1341.06i		−	1.40720i	−0.710595	−	0.703602i	$-0.751574\pi$
$953$		−	1341.06i		−	1.40720i	0.710595	−	0.703602i	$-0.248426\pi$
$954$	−881.407	−	881.407i	−0.923907	−	0.923907i
$955$		0			0
$956$	−513.653	+	513.653i	−0.537294	+	0.537294i
$957$	−26.0007	+	26.0007i	−0.0271689	+	0.0271689i
$958$	456.924			0.476956
$959$		−	1463.20i		−	1.52576i
$960$		0			0
$961$			343.969i			0.357928i
$962$	−986.653	+	485.142i	−1.02563	+	0.504306i
$963$	1561.21			1.62120
$964$	−793.071	−	793.071i	−0.822687	−	0.822687i
$965$		0			0
$966$			1041.21i			1.07786i
$967$	158.077	+	158.077i	0.163471	+	0.163471i	0.784103	−	0.620631i	$-0.213124\pi$
$967$	158.077	+	158.077i	0.163471	+	0.163471i	−0.620631	+	0.784103i	$0.713124\pi$
$968$	194.589	+	194.589i	0.201022	+	0.201022i
$969$	−6.24260	+	6.24260i	−0.00644231	+	0.00644231i
$970$		0			0
$971$	784.890			0.808332			0.404166	−	0.914686i	$-0.367562\pi$
$971$	784.890			0.808332			0.404166	+	0.914686i	$0.367562\pi$
$972$		−	546.110i		−	0.561842i
$973$	−1444.95	+	1444.95i	−1.48504	+	1.48504i
$974$			1889.44i			1.93988i
$975$		0			0
$976$	−87.9515			−0.0901143
$977$	239.209	+	239.209i	0.244840	+	0.244840i	0.818849	−	0.574009i	$-0.194612\pi$
$977$	239.209	+	239.209i	0.244840	+	0.244840i	−0.574009	+	0.818849i	$0.694612\pi$
$978$	159.333			0.162918
$979$		−	133.805i		−	0.136675i
$980$		0			0
$981$	−127.931	−	127.931i	−0.130409	−	0.130409i
$982$	−1021.18	+	1021.18i	−1.03990	+	1.03990i
$983$	821.678	−	821.678i	0.835888	−	0.835888i	−0.152427	−	0.988315i	$-0.548709\pi$
$983$	821.678	−	821.678i	0.835888	−	0.835888i	0.988315	+	0.152427i	$0.0487088\pi$
$984$	−93.5823			−0.0951040
$985$		0			0
$986$	116.226	−	116.226i	0.117876	−	0.117876i
$987$		−	215.223i		−	0.218058i
$988$	−53.0389	+	155.654i	−0.0536831	+	0.157545i
$989$	−205.426			−0.207711
$990$		0			0
$991$	−40.5436			−0.0409119			−0.0204559	−	0.999791i	$-0.506512\pi$
$991$	−40.5436			−0.0409119			−0.0204559	+	0.999791i	$0.506512\pi$
$992$		−	1466.67i		−	1.47850i
$993$	−260.973	−	260.973i	−0.262813	−	0.262813i
$994$	−78.7950	−	78.7950i	−0.0792706	−	0.0792706i
$995$		0			0
$996$	226.653	−	226.653i	0.227564	−	0.227564i
$997$	−966.616			−0.969525			−0.484762	−	0.874646i	$-0.661094\pi$
$997$	−966.616			−0.969525			−0.484762	+	0.874646i	$0.661094\pi$
$998$			1535.09i			1.53817i
$999$	309.163	−	309.163i	0.309473	−	0.309473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.j.d.151.8	yes	20
5.2	odd	4		325.3.g.f.99.3		20
5.3	odd	4		325.3.g.e.99.8		20
5.4	even	2		325.3.j.c.151.3	✓	20
13.5	odd	4	inner	325.3.j.d.226.8	yes	20
65.18	even	4		325.3.g.f.174.3		20
65.44	odd	4		325.3.j.c.226.3	yes	20
65.57	even	4		325.3.g.e.174.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.3.g.e.99.8		20	5.3	odd	4
325.3.g.e.174.8		20	65.57	even	4
325.3.g.f.99.3		20	5.2	odd	4
325.3.g.f.174.3		20	65.18	even	4
325.3.j.c.151.3	✓	20	5.4	even	2
325.3.j.c.226.3	yes	20	65.44	odd	4
325.3.j.d.151.8	yes	20	1.1	even	1	trivial
325.3.j.d.226.8	yes	20	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.88633 + 1.88633i) q^{2} -0.793970 q^{3} +3.11650i q^{4} +(-1.49769 - 1.49769i) q^{6} +(-8.42514 + 8.42514i) q^{7} +(1.66658 - 1.66658i) q^{8} -8.36961 q^{9} +(-1.45602 + 1.45602i) q^{11} -2.47441i q^{12} +(-11.6660 + 5.73623i) q^{13} -31.7852 q^{14} +18.7534 q^{16} +2.73950i q^{17} +(-15.7879 - 15.7879i) q^{18} +(-2.87005 - 2.87005i) q^{19} +(6.68931 - 6.68931i) q^{21} -5.49308 q^{22} +41.2582i q^{23} +(-1.32321 + 1.32321i) q^{24} +(-32.8264 - 11.1855i) q^{26} +13.7909 q^{27} +(-26.2569 - 26.2569i) q^{28} -22.4912 q^{29} +(-25.5438 - 25.5438i) q^{31} +(28.7089 + 28.7089i) q^{32} +(1.15604 - 1.15604i) q^{33} +(-5.16762 + 5.16762i) q^{34} -26.0839i q^{36} +(22.4179 - 22.4179i) q^{37} -10.8277i q^{38} +(9.26246 - 4.55439i) q^{39} +(35.3618 + 35.3618i) q^{41} +25.2365 q^{42} +4.97904i q^{43} +(-4.53769 - 4.53769i) q^{44} +(-77.8267 + 77.8267i) q^{46} +(16.0871 - 16.0871i) q^{47} -14.8897 q^{48} -92.9659i q^{49} -2.17508i q^{51} +(-17.8770 - 36.3571i) q^{52} +55.8281 q^{53} +(26.0143 + 26.0143i) q^{54} +28.0823i q^{56} +(2.27873 + 2.27873i) q^{57} +(-42.4259 - 42.4259i) q^{58} +(-30.7740 + 30.7740i) q^{59} -4.68989 q^{61} -96.3681i q^{62} +(70.5151 - 70.5151i) q^{63} +33.2953i q^{64} +4.36134 q^{66} +(64.9102 + 64.9102i) q^{67} -8.53766 q^{68} -32.7578i q^{69} +(2.47898 + 2.47898i) q^{71} +(-13.9486 + 13.9486i) q^{72} +(-75.2167 + 75.2167i) q^{73} +84.5750 q^{74} +(8.94451 - 8.94451i) q^{76} -24.5344i q^{77} +(26.0632 + 8.88097i) q^{78} +67.8838 q^{79} +64.3769 q^{81} +133.408i q^{82} +(91.5991 + 91.5991i) q^{83} +(20.8472 + 20.8472i) q^{84} +(-9.39212 + 9.39212i) q^{86} +17.8573 q^{87} +4.85314i q^{88} +(-45.9488 + 45.9488i) q^{89} +(49.9592 - 146.616i) q^{91} -128.581 q^{92} +(20.2810 + 20.2810i) q^{93} +60.6913 q^{94} +(-22.7940 - 22.7940i) q^{96} +(-111.655 - 111.655i) q^{97} +(175.365 - 175.365i) q^{98} +(12.1863 - 12.1863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{6} + 20 q^{7} - 18 q^{8} + 72 q^{9} + 6 q^{11} + 6 q^{13} - 24 q^{14} - 128 q^{16} - 58 q^{18} - 20 q^{19} + 90 q^{21} + 24 q^{22} - 28 q^{24} - 12 q^{27} + 278 q^{28} - 40 q^{29} - 32 q^{31}+ \cdots - 410 q^{99}+O(q^{100}) \) 20 * q - 6 * q^6 + 20 * q^7 - 18 * q^8 + 72 * q^9 + 6 * q^11 + 6 * q^13 - 24 * q^14 - 128 * q^16 - 58 * q^18 - 20 * q^19 + 90 * q^21 + 24 * q^22 - 28 * q^24 - 12 * q^27 + 278 * q^28 - 40 * q^29 - 32 * q^31 - 162 * q^32 + 124 * q^33 - 14 * q^34 + 158 * q^37 - 26 * q^39 + 70 * q^41 - 320 * q^42 + 366 * q^44 + 58 * q^46 - 130 * q^47 - 716 * q^48 + 300 * q^52 + 216 * q^53 - 350 * q^54 + 168 * q^57 - 180 * q^58 + 132 * q^59 - 152 * q^61 + 442 * q^63 + 720 * q^66 + 178 * q^67 - 216 * q^68 - 258 * q^71 + 390 * q^72 - 262 * q^73 + 220 * q^74 + 68 * q^76 + 102 * q^78 - 544 * q^79 + 204 * q^81 + 88 * q^83 + 352 * q^84 - 174 * q^86 - 976 * q^87 - 282 * q^89 - 440 * q^91 - 992 * q^92 + 522 * q^93 - 544 * q^94 - 1216 * q^96 + 6 * q^97 + 78 * q^98 - 410 * q^99

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