LMFDB - Embedded newform 325.3.g.e.174.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(99,325)] 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([2, 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("325.99"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.g (of order $4$, degree $2$, not 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			174.8
Root			$-1.88633 + 1.88633i$ of defining polynomial
Character	$\chi$	$=$	325.174
Dual form			325.3.g.e.99.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.88633 + 1.88633i) q^{2} +0.793970i q^{3} +3.11650i q^{4} +(-1.49769 + 1.49769i) q^{6} +(8.42514 - 8.42514i) q^{7} +(1.66658 - 1.66658i) q^{8} +8.36961 q^{9} +(-1.45602 - 1.45602i) q^{11} -2.47441 q^{12} +(-5.73623 + 11.6660i) q^{13} +31.7852 q^{14} +18.7534 q^{16} +2.73950 q^{17} +(15.7879 + 15.7879i) q^{18} +(2.87005 - 2.87005i) q^{19} +(6.68931 + 6.68931i) q^{21} -5.49308i q^{22} -41.2582 q^{23} +(1.32321 + 1.32321i) q^{24} +(-32.8264 + 11.1855i) q^{26} +13.7909i q^{27} +(26.2569 + 26.2569i) q^{28} +22.4912 q^{29} +(-25.5438 + 25.5438i) q^{31} +(28.7089 + 28.7089i) q^{32} +(1.15604 - 1.15604i) q^{33} +(5.16762 + 5.16762i) q^{34} +26.0839i q^{36} +(-22.4179 + 22.4179i) q^{37} +10.8277 q^{38} +(-9.26246 - 4.55439i) q^{39} +(35.3618 - 35.3618i) q^{41} +25.2365i q^{42} -4.97904 q^{43} +(4.53769 - 4.53769i) q^{44} +(-77.8267 - 77.8267i) q^{46} +(-16.0871 + 16.0871i) q^{47} +14.8897i q^{48} -92.9659i q^{49} +2.17508i q^{51} +(-36.3571 - 17.8770i) q^{52} -55.8281i q^{53} +(-26.0143 + 26.0143i) q^{54} -28.0823i q^{56} +(2.27873 + 2.27873i) q^{57} +(42.4259 + 42.4259i) q^{58} +(30.7740 + 30.7740i) q^{59} -4.68989 q^{61} -96.3681 q^{62} +(70.5151 - 70.5151i) q^{63} +33.2953i q^{64} +4.36134 q^{66} +(64.9102 + 64.9102i) q^{67} +8.53766i q^{68} -32.7578i q^{69} +(2.47898 - 2.47898i) q^{71} +(13.9486 - 13.9486i) q^{72} +(-75.2167 + 75.2167i) q^{73} -84.5750 q^{74} +(8.94451 + 8.94451i) q^{76} -24.5344 q^{77} +(-8.88097 - 26.0632i) q^{78} -67.8838 q^{79} +64.3769 q^{81} +133.408 q^{82} +(-91.5991 - 91.5991i) q^{83} +(-20.8472 + 20.8472i) q^{84} +(-9.39212 - 9.39212i) q^{86} +17.8573i q^{87} -4.85314 q^{88} +(45.9488 + 45.9488i) q^{89} +(49.9592 + 146.616i) q^{91} -128.581i q^{92} +(-20.2810 - 20.2810i) q^{93} -60.6913 q^{94} +(-22.7940 + 22.7940i) q^{96} +(-111.655 - 111.655i) q^{97} +(175.365 - 175.365i) q^{98} +(-12.1863 - 12.1863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{6} - 20 q^{7} - 18 q^{8} - 72 q^{9} + 6 q^{11} + 120 q^{12} + 18 q^{13} + 24 q^{14} - 128 q^{16} + 16 q^{17} + 58 q^{18} + 20 q^{19} + 90 q^{21} - 28 q^{23} + 28 q^{24} - 278 q^{28} + 40 q^{29}+ \cdots + 410 q^{99}+O(q^{100}) $ 20 * q - 6 * q^6 - 20 * q^7 - 18 * q^8 - 72 * q^9 + 6 * q^11 + 120 * q^12 + 18 * q^13 + 24 * q^14 - 128 * q^16 + 16 * q^17 + 58 * q^18 + 20 * q^19 + 90 * q^21 - 28 * q^23 + 28 * q^24 - 278 * q^28 + 40 * q^29 - 32 * q^31 - 162 * q^32 + 124 * q^33 + 14 * q^34 - 158 * q^37 - 124 * q^38 + 26 * q^39 + 70 * q^41 + 32 * q^43 - 366 * q^44 + 58 * q^46 + 130 * q^47 - 244 * q^52 + 350 * q^54 + 168 * q^57 + 180 * q^58 - 132 * q^59 - 152 * q^61 - 212 * q^62 + 442 * q^63 + 720 * q^66 + 178 * q^67 - 258 * q^71 - 390 * q^72 - 262 * q^73 - 220 * q^74 + 68 * q^76 - 184 * q^77 + 918 * q^78 + 544 * q^79 + 204 * q^81 + 920 * q^82 - 88 * q^83 - 352 * q^84 - 174 * q^86 - 424 * q^88 + 282 * q^89 - 440 * q^91 - 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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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	$0.517613\pi$
$3$			0.793970i			0.264657i	0.991206	+	0.132328i	$0.0422453\pi$
$3$			0.793970i			0.264657i	−0.991206	+	0.132328i	$0.957755\pi$
$4$			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	$-0.425956\pi$
$7$	8.42514	−	8.42514i	1.20359	−	1.20359i	0.973066	−	0.230525i	$-0.0740442\pi$
$8$	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	0.637820	−	0.770186i	$-0.279836\pi$
$11$	−1.45602	−	1.45602i	−0.132366	−	0.132366i	−0.770186	+	0.637820i	$0.779836\pi$
$12$	−2.47441			−0.206201
$13$	−5.73623	+	11.6660i	−0.441249	+	0.897385i
$13$	−5.73623	+	11.6660i	−0.441249	+	0.897385i
$14$	31.7852			2.27037
$15$		0			0
$16$	18.7534			1.17209
$17$	2.73950			0.161147			0.0805737	−	0.996749i	$-0.474325\pi$
$17$	2.73950			0.161147			0.0805737	+	0.996749i	$0.474325\pi$
$18$	15.7879	+	15.7879i	0.877104	+	0.877104i
$19$	2.87005	−	2.87005i	0.151055	−	0.151055i	−0.627534	−	0.778589i	$-0.715936\pi$
$19$	2.87005	−	2.87005i	0.151055	−	0.151055i	0.778589	+	0.627534i	$0.215936\pi$
$20$		0			0
$21$	6.68931	+	6.68931i	0.318538	+	0.318538i
$22$		−	5.49308i		−	0.249685i
$23$	−41.2582			−1.79384			−0.896918	−	0.442197i	$-0.854199\pi$
$23$	−41.2582			−1.79384			−0.896918	+	0.442197i	$0.854199\pi$
$24$	1.32321	+	1.32321i	0.0551338	+	0.0551338i
$25$		0			0
$26$	−32.8264	+	11.1855i	−1.26255	+	0.430212i
$27$			13.7909i			0.510776i
$28$	26.2569	+	26.2569i	0.937748	+	0.937748i
$29$	22.4912			0.775559			0.387780	−	0.921752i	$-0.373242\pi$
$29$	22.4912			0.775559			0.387780	+	0.921752i	$0.373242\pi$
$30$		0			0
$31$	−25.5438	+	25.5438i	−0.823993	+	0.823993i	−0.986678	−	0.162685i	$-0.947984\pi$
$31$	−25.5438	+	25.5438i	−0.823993	+	0.823993i	0.162685	+	0.986678i	$0.447984\pi$
$32$	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	−0.941869	−	0.335981i	$-0.890932\pi$
$37$	−22.4179	+	22.4179i	−0.605888	+	0.605888i	0.335981	+	0.941869i	$0.390932\pi$
$38$	10.8277			0.284940
$39$	−9.26246	−	4.55439i	−0.237499	−	0.116779i
$40$		0			0
$41$	35.3618	−	35.3618i	0.862483	−	0.862483i	−0.129143	−	0.991626i	$-0.541223\pi$
$41$	35.3618	−	35.3618i	0.862483	−	0.862483i	0.991626	+	0.129143i	$0.0412225\pi$
$42$			25.2365i			0.600869i
$43$	−4.97904			−0.115792			−0.0578958	−	0.998323i	$-0.518439\pi$
$43$	−4.97904			−0.115792			−0.0578958	+	0.998323i	$0.518439\pi$
$44$	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	−0.857223	−	0.514945i	$-0.827812\pi$
$47$	−16.0871	+	16.0871i	−0.342279	+	0.342279i	0.514945	+	0.857223i	$0.327812\pi$
$48$			14.8897i			0.310201i
$49$		−	92.9659i		−	1.89726i
$50$		0			0
$51$			2.17508i			0.0426487i
$52$	−36.3571	−	17.8770i	−0.699175	−	0.343788i
$53$		−	55.8281i		−	1.05336i	−0.850063	−	0.526680i	$-0.823436\pi$
$53$		−	55.8281i		−	1.05336i	0.850063	−	0.526680i	$-0.176564\pi$
$54$	−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	$-0.129761\pi$
$59$	30.7740	+	30.7740i	0.521592	+	0.521592i	−0.396460	+	0.918052i	$0.629761\pi$
$60$		0			0
$61$	−4.68989			−0.0768835			−0.0384417	−	0.999261i	$-0.512239\pi$
$61$	−4.68989			−0.0768835			−0.0384417	+	0.999261i	$0.512239\pi$
$62$	−96.3681			−1.55432
$63$	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	$0.509780\pi$
$68$			8.53766i			0.125554i
$69$		−	32.7578i		−	0.474751i
$70$		0			0
$71$	2.47898	−	2.47898i	0.0349153	−	0.0349153i	−0.689434	−	0.724349i	$-0.742141\pi$
$71$	2.47898	−	2.47898i	0.0349153	−	0.0349153i	0.724349	+	0.689434i	$0.242141\pi$
$72$	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
$77$	−24.5344			−0.318628
$78$	−8.88097	−	26.0632i	−0.113859	−	0.334143i
$79$	−67.8838			−0.859289			−0.429644	−	0.902998i	$-0.641361\pi$
$79$	−67.8838			−0.859289			−0.429644	+	0.902998i	$0.641361\pi$
$80$		0			0
$81$	64.3769			0.794777
$82$	133.408			1.62693
$83$	−91.5991	−	91.5991i	−1.10360	−	1.10360i	−0.993972	−	0.109631i	$-0.965033\pi$
$83$	−91.5991	−	91.5991i	−1.10360	−	1.10360i	−0.109631	−	0.993972i	$-0.534967\pi$
$84$	−20.8472	+	20.8472i	−0.248181	+	0.248181i
$85$		0			0
$86$	−9.39212	−	9.39212i	−0.109211	−	0.109211i
$87$			17.8573i			0.205257i
$88$	−4.85314			−0.0551493
$89$	45.9488	+	45.9488i	0.516278	+	0.516278i	0.916443	−	0.400165i	$-0.131047\pi$
$89$	45.9488	+	45.9488i	0.516278	+	0.516278i	−0.400165	+	0.916443i	$0.631047\pi$
$90$		0			0
$91$	49.9592	+	146.616i	0.549002	+	1.61117i
$92$		−	128.581i		−	1.39762i
$93$	−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	$0.141596\pi$
$101$			86.9229i			0.860622i	−0.902681	+	0.430311i	$0.858404\pi$
$102$	−4.10293	+	4.10293i	−0.0402248	+	0.0402248i
$103$	−170.779			−1.65805			−0.829026	−	0.559210i	$-0.811105\pi$
$103$	−170.779			−1.65805			−0.829026	+	0.559210i	$0.811105\pi$
$104$	9.88242	+	29.0021i	0.0950232	+	0.278867i
$105$		0			0
$106$	105.310	−	105.310i	0.993494	−	0.993494i
$107$		−	186.534i		−	1.74331i	−0.490124	−	0.871653i	$-0.663049\pi$
$107$		−	186.534i		−	1.74331i	0.490124	−	0.871653i	$-0.336951\pi$
$108$	−42.9795			−0.397958
$109$	−15.2852	+	15.2852i	−0.140231	+	0.140231i	−0.773737	−	0.633506i	$-0.781615\pi$
$109$	−15.2852	+	15.2852i	−0.140231	+	0.140231i	0.633506	+	0.773737i	$0.281615\pi$
$110$		0			0
$111$	−17.7991	−	17.7991i	−0.160352	−	0.160352i
$112$	158.000	−	158.000i	1.41072	−	1.41072i
$113$			192.529i			1.70379i	0.523709	+	0.851897i	$0.324548\pi$
$113$			192.529i			1.70379i	−0.523709	+	0.851897i	$0.675452\pi$
$114$			8.59689i			0.0754114i
$115$		0			0
$116$			70.0938i			0.604257i
$117$	−48.0100	+	97.6399i	−0.410342	+	0.834529i
$118$			116.100i			0.983897i
$119$	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
$127$	−71.8541			−0.565780			−0.282890	−	0.959152i	$-0.591293\pi$
$127$	−71.8541			−0.565780			−0.282890	+	0.959152i	$0.591293\pi$
$128$	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
$133$		−	48.3611i		−	0.363617i
$134$			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	−0.315191	−	0.949028i	$-0.602069\pi$
$137$	86.8356	−	86.8356i	0.633837	−	0.633837i	0.949028	+	0.315191i	$0.102069\pi$
$138$	61.7921	−	61.7921i	0.447769	−	0.447769i
$139$	−171.504			−1.23384			−0.616922	−	0.787024i	$-0.711621\pi$
$139$	−171.504			−1.23384			−0.616922	+	0.787024i	$0.711621\pi$
$140$		0			0
$141$	−12.7727	−	12.7727i	−0.0905864	−	0.0905864i
$142$	9.35237			0.0658618
$143$	25.3380	−	8.63388i	0.177189	−	0.0603768i
$144$	156.959			1.08999
$145$		0			0
$146$	−283.767			−1.94361
$147$	73.8121			0.502123
$148$	−69.8652	−	69.8652i	−0.472062	−	0.472062i
$149$	−6.63306	+	6.63306i	−0.0445172	+	0.0445172i	−0.729015	−	0.684498i	$-0.760022\pi$
$149$	−6.63306	+	6.63306i	−0.0445172	+	0.0445172i	0.684498	+	0.729015i	$0.260022\pi$
$150$		0			0
$151$	−51.6100	−	51.6100i	−0.341788	−	0.341788i	0.515251	−	0.857039i	$-0.327699\pi$
$151$	−51.6100	−	51.6100i	−0.341788	−	0.341788i	−0.857039	+	0.515251i	$0.827699\pi$
$152$		−	9.56631i		−	0.0629363i
$153$	22.9286			0.149860
$154$	−46.2800	−	46.2800i	−0.300519	−	0.300519i
$155$		0			0
$156$	14.1938	−	28.8664i	0.0909857	−	0.185041i
$157$			62.2106i			0.396246i	0.980177	+	0.198123i	$0.0634845\pi$
$157$			62.2106i			0.396246i	−0.980177	+	0.198123i	$0.936516\pi$
$158$	−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	−0.947123	−	0.320871i	$-0.896024\pi$
$167$	−104.584	+	104.584i	−0.626251	+	0.626251i	0.320871	+	0.947123i	$0.396024\pi$
$168$	22.2965			0.132717
$169$	−103.191	−	133.838i	−0.610599	−	0.791940i
$170$		0			0
$171$	24.0212	−	24.0212i	0.140475	−	0.140475i
$172$		−	15.5172i		−	0.0902161i
$173$	280.273			1.62008			0.810038	−	0.586377i	$-0.199446\pi$
$173$	280.273			1.62008			0.810038	+	0.586377i	$0.199446\pi$
$174$	−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
$178$			173.349i			0.973873i
$179$		−	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	$0.155848\pi$
$181$			170.242i			0.940564i	−0.882516	+	0.470282i	$0.844152\pi$
$182$	−182.327	+	370.806i	−1.00180	+	2.03740i
$183$		−	3.72363i		−	0.0203477i
$184$	−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	$0.222929\pi$
$192$	−26.4355			−0.137685
$193$	−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	$0.767129\pi$
$198$		−	45.9749i		−	0.232197i
$199$			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
$207$	−345.315			−1.66819
$208$	−107.574	+	218.778i	−0.517183	+	1.05182i
$209$	−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	$0.581743\pi$
$212$	173.988			0.820699
$213$	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
$217$			430.420i			1.98350i
$218$	−57.6658			−0.264522
$219$	−59.7198	−	59.7198i	−0.272693	−	0.272693i
$220$		0			0
$221$	−15.7144	+	31.9591i	−0.0711060	+	0.144611i
$222$		−	67.1500i		−	0.302478i
$223$	155.987	+	155.987i	0.699491	+	0.699491i	0.964301	−	0.264809i	$-0.0853090\pi$
$223$	155.987	+	155.987i	0.699491	+	0.699491i	−0.264809	+	0.964301i	$0.585309\pi$
$224$	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	0.981535	+	0.191284i	$0.0612652\pi$
$229$	268.576	+	268.576i	1.17282	+	1.17282i	0.191284	+	0.981535i	$0.438735\pi$
$230$		0			0
$231$		−	19.4795i		−	0.0843270i
$232$	37.4833	−	37.4833i	0.161566	−	0.161566i
$233$	−144.819			−0.621542			−0.310771	−	0.950485i	$-0.600587\pi$
$233$	−144.819			−0.621542			−0.310771	+	0.950485i	$0.600587\pi$
$234$	−274.744	+	93.6185i	−1.17412	+	0.400079i
$235$		0			0
$236$	−95.9070	+	95.9070i	−0.406386	+	0.406386i
$237$		−	53.8977i		−	0.227416i
$238$	87.0758			0.365865
$239$	−164.817	+	164.817i	−0.689612	+	0.689612i	−0.962146	−	0.272534i	$-0.912138\pi$
$239$	−164.817	+	164.817i	−0.689612	+	0.689612i	0.272534	+	0.962146i	$0.412138\pi$
$240$		0			0
$241$	−254.475	−	254.475i	−1.05591	−	1.05591i	−0.998341	−	0.0575708i	$-0.981664\pi$
$241$	−254.475	−	254.475i	−1.05591	−	1.05591i	−0.0575708	−	0.998341i	$-0.518336\pi$
$242$	220.248	−	220.248i	0.910116	−	0.910116i
$243$			175.232i			0.721119i
$244$		−	14.6160i		−	0.0599018i
$245$		0			0
$246$			105.922i			0.430578i
$247$	17.0187	+	49.9453i	0.0689018	+	0.202208i
$248$			85.1413i			0.343312i
$249$	72.7269	−	72.7269i	0.292076	−	0.292076i
$250$		0			0
$251$			111.483i			0.444157i	0.975029	+	0.222078i	$0.0712841\pi$
$251$			111.483i			0.444157i	−0.975029	+	0.222078i	$0.928716\pi$
$252$	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
$257$	102.707			0.399636			0.199818	−	0.979833i	$-0.435965\pi$
$257$	102.707			0.399636			0.199818	+	0.979833i	$0.435965\pi$
$258$	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
$263$		−	60.7931i		−	0.231153i	−0.993299	−	0.115576i	$-0.963129\pi$
$263$		−	60.7931i		−	0.231153i	0.993299	−	0.115576i	$-0.0368715\pi$
$264$		−	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	$-0.221088\pi$
$269$	413.362			1.53666			0.768330	+	0.640053i	$0.221088\pi$
$270$		0			0
$271$	33.0802	+	33.0802i	0.122067	+	0.122067i	0.765501	−	0.643434i	$-0.222491\pi$
$271$	33.0802	+	33.0802i	0.122067	+	0.122067i	−0.643434	+	0.765501i	$0.722491\pi$
$272$	51.3751			0.188879
$273$	−116.409	+	39.6661i	−0.426406	+	0.145297i
$274$	327.602			1.19563
$275$		0			0
$276$	102.090			0.369890
$277$	395.394			1.42742			0.713708	−	0.700444i	$-0.247015\pi$
$277$	395.394			1.42742			0.713708	+	0.700444i	$0.247015\pi$
$278$	−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	0.446149	−	0.894959i	$-0.352795\pi$
$281$	−126.116	−	126.116i	−0.448810	−	0.448810i	−0.894959	+	0.446149i	$0.852795\pi$
$282$		−	48.1870i		−	0.170876i
$283$	426.703			1.50779			0.753893	−	0.656998i	$-0.228174\pi$
$283$	426.703			1.50779			0.753893	+	0.656998i	$0.228174\pi$
$284$	7.72575	+	7.72575i	0.0272033	+	0.0272033i
$285$		0			0
$286$	64.0823	+	31.5096i	0.224064	+	0.110173i
$287$		−	595.856i		−	2.07615i
$288$	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
$298$	−25.0243			−0.0839743
$299$	236.667	−	481.319i	0.791528	−	1.60976i
$300$		0			0
$301$	−41.9491	+	41.9491i	−0.139366	+	0.139366i
$302$		−	194.707i		−	0.644725i
$303$	−69.0141			−0.227769
$304$	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	$-0.438654\pi$
$307$	360.117	−	360.117i	1.17302	−	1.17302i	0.981486	−	0.191534i	$-0.0613463\pi$
$308$		−	76.4613i		−	0.248251i
$309$		−	135.594i		−	0.438815i
$310$		0			0
$311$			209.072i			0.672257i	0.941816	+	0.336128i	$0.109118\pi$
$311$			209.072i			0.672257i	−0.941816	+	0.336128i	$0.890882\pi$
$312$	−23.0268	+	7.84634i	−0.0738039	+	0.0251485i
$313$			333.747i			1.06628i	0.846026	+	0.533142i	$0.178989\pi$
$313$			333.747i			1.06628i	−0.846026	+	0.533142i	$0.821011\pi$
$314$	−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
$322$	−1311.40			−4.07268
$323$	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
$328$		−	117.866i		−	0.359349i
$329$			271.072i			0.823928i
$330$		0			0
$331$	328.694	−	328.694i	0.993032	−	0.993032i	−0.00694351	−	0.999976i	$-0.502210\pi$
$331$	328.694	−	328.694i	0.993032	−	0.993032i	0.999976	+	0.00694351i	$0.00221021\pi$
$332$	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
$337$	239.044			0.709329			0.354664	−	0.934994i	$-0.384595\pi$
$337$	239.044			0.709329			0.354664	+	0.934994i	$0.384595\pi$
$338$	57.8095	−	447.116i	0.171034	−	1.32283i
$339$	−152.862			−0.450921
$340$		0			0
$341$	74.3846			0.218137
$342$	90.6239			0.264982
$343$	−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
$347$			5.90128i			0.0170066i	0.999964	+	0.00850329i	$0.00270671\pi$
$347$			5.90128i			0.0170066i	−0.999964	+	0.00850329i	$0.997293\pi$
$348$	−55.6524			−0.159921
$349$	−11.5942	−	11.5942i	−0.0332212	−	0.0332212i	0.690301	−	0.723522i	$-0.257478\pi$
$349$	−11.5942	−	11.5942i	−0.0332212	−	0.0332212i	−0.723522	+	0.690301i	$0.757478\pi$
$350$		0			0
$351$	−160.885	−	79.1081i	−0.458363	−	0.225379i
$352$		−	83.6015i		−	0.237504i
$353$	129.927	+	129.927i	0.368066	+	0.368066i	0.866772	−	0.498705i	$-0.166191\pi$
$353$	129.927	+	129.927i	0.368066	+	0.368066i	−0.498705	+	0.866772i	$0.666191\pi$
$354$	−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	$-0.431403\pi$
$359$	−273.927	−	273.927i	−0.763027	−	0.763027i	−0.976868	+	0.213841i	$0.931403\pi$
$360$		0			0
$361$			344.526i			0.954365i
$362$	−321.133	+	321.133i	−0.887108	+	0.887108i
$363$	92.7039			0.255383
$364$	−456.929	+	155.698i	−1.25530	+	0.427741i
$365$		0			0
$366$	7.02401	−	7.02401i	0.0191913	−	0.0191913i
$367$		−	125.394i		−	0.341673i	−0.985299	−	0.170836i	$-0.945353\pi$
$367$		−	125.394i		−	0.341673i	0.985299	−	0.170836i	$-0.0546470\pi$
$368$	−773.733			−2.10254
$369$	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
$373$		−	503.396i		−	1.34959i	−0.738007	−	0.674793i	$-0.764233\pi$
$373$		−	503.396i		−	1.34959i	0.738007	−	0.674793i	$-0.235767\pi$
$374$		−	15.0483i		−	0.0402361i
$375$		0			0
$376$			53.6208i			0.142608i
$377$	−129.015	+	262.383i	−0.342214	+	0.695975i
$378$			438.348i			1.15965i
$379$	−464.950	+	464.950i	−1.22678	+	1.22678i	−0.261606	+	0.965175i	$0.584252\pi$
$379$	−464.950	+	464.950i	−1.22678	+	1.22678i	−0.965175	+	0.261606i	$0.915748\pi$
$380$		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	0.159362	−	0.987220i	$-0.449056\pi$
$383$	−317.070	−	317.070i	−0.827858	−	0.827858i	−0.987220	+	0.159362i	$0.949056\pi$
$384$	41.3099	+	41.3099i	0.107578	+	0.107578i
$385$		0			0
$386$	−330.487			−0.856184
$387$	−41.6726			−0.107681
$388$	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
$393$			87.4222i			0.222448i
$394$		−	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	$0.550297\pi$
$397$	−454.524	+	454.524i	−1.14490	+	1.14490i	−0.987542	+	0.157356i	$0.949703\pi$
$398$	−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	0.246520	−	0.969138i	$-0.420713\pi$
$401$	−289.770	−	289.770i	−0.722618	−	0.722618i	−0.969138	+	0.246520i	$0.920713\pi$
$402$	−194.431			−0.483659
$403$	−151.469	−	444.519i	−0.375853	−	1.10302i
$404$	−270.895			−0.670532
$405$		0			0
$406$	714.888			1.76081
$407$	65.2817			0.160397
$408$	3.62494	+	3.62494i	0.00888466	+	0.00888466i
$409$	13.9909	−	13.9909i	0.0342075	−	0.0342075i	−0.689796	−	0.724004i	$-0.742300\pi$
$409$	13.9909	−	13.9909i	0.0342075	−	0.0342075i	0.724004	+	0.689796i	$0.242300\pi$
$410$		0			0
$411$	68.9449	+	68.9449i	0.167749	+	0.167749i
$412$		−	532.234i		−	1.29183i
$413$	518.550			1.25557
$414$	−651.379	−	651.379i	−1.57338	−	1.57338i
$415$		0			0
$416$	−499.599	+	170.237i	−1.20096	+	0.409224i
$417$		−	136.169i		−	0.326545i
$418$	−15.7654	−	15.7654i	−0.0377163	−	0.0377163i
$419$	−151.917			−0.362569			−0.181285	−	0.983431i	$-0.558026\pi$
$419$	−151.917			−0.362569			−0.181285	+	0.983431i	$0.558026\pi$
$420$		0			0
$421$	364.648	−	364.648i	0.866147	−	0.866147i	−0.125897	−	0.992043i	$-0.540181\pi$
$421$	364.648	−	364.648i	0.866147	−	0.866147i	0.992043	+	0.125897i	$0.0401807\pi$
$422$	−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
$428$	581.332			1.35825
$429$	6.85504	+	20.1176i	0.0159791	+	0.0468942i
$430$		0			0
$431$	488.245	−	488.245i	1.13282	−	1.13282i	0.143112	−	0.989707i	$-0.454289\pi$
$431$	488.245	−	488.245i	1.13282	−	1.13282i	0.989707	−	0.143112i	$-0.0457109\pi$
$432$			258.628i			0.598675i
$433$	295.143			0.681624			0.340812	−	0.940132i	$-0.389298\pi$
$433$	295.143			0.681624			0.340812	+	0.940132i	$0.389298\pi$
$434$	−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
$438$		−	225.303i		−	0.514390i
$439$		−	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
$442$	−89.9281	+	30.6428i	−0.203457	+	0.0693276i
$443$		−	414.826i		−	0.936403i	−0.883622	−	0.468201i	$-0.844902\pi$
$443$		−	414.826i		−	0.936403i	0.883622	−	0.468201i	$-0.155098\pi$
$444$	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	$-0.282565\pi$
$449$	−64.8500	−	64.8500i	−0.144432	−	0.144432i	−0.775625	+	0.631193i	$0.782565\pi$
$450$		0			0
$451$	−102.975			−0.228326
$452$	−600.016			−1.32747
$453$	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	$0.698410\pi$
$458$			1013.25i			2.21233i
$459$			37.7804i			0.0823102i
$460$		0			0
$461$	−175.305	+	175.305i	−0.380271	+	0.380271i	−0.871200	−	0.490929i	$-0.836658\pi$
$461$	−175.305	+	175.305i	−0.380271	+	0.380271i	0.490929	+	0.871200i	$0.336658\pi$
$462$	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
$467$	411.919			0.882054			0.441027	−	0.897494i	$-0.354614\pi$
$467$	411.919			0.882054			0.441027	+	0.897494i	$0.354614\pi$
$468$	−304.295	−	149.623i	−0.650202	−	0.319708i
$469$	1093.75			2.33210
$470$		0			0
$471$	−49.3933			−0.104869
$472$	102.574			0.217318
$473$	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
$477$		−	467.260i		−	0.979580i
$478$	−621.801			−1.30084
$479$	−121.114	−	121.114i	−0.252848	−	0.252848i	0.569289	−	0.822137i	$-0.307219\pi$
$479$	−121.114	−	121.114i	−0.252848	−	0.252848i	−0.822137	+	0.569289i	$0.807219\pi$
$480$		0			0
$481$	−132.933	−	390.121i	−0.276367	−	0.811062i
$482$		−	960.048i		−	1.99180i
$483$	−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	$-0.814139\pi$
$491$		−	541.358i		−	1.10256i	0.834320	−	0.551281i	$-0.185861\pi$
$492$	−87.4995	+	87.4995i	−0.177845	+	0.177845i
$493$	61.6148			0.124979
$494$	−62.1104	+	126.316i	−0.125730	+	0.255701i
$495$		0			0
$496$	−479.033	+	479.033i	−0.965793	+	0.965793i
$497$		−	41.7715i		−	0.0840474i
$498$	274.374			0.550952
$499$	−406.898	+	406.898i	−0.815427	+	0.815427i	−0.985442	−	0.170015i	$-0.945618\pi$
$499$	−406.898	+	406.898i	−0.815427	+	0.815427i	0.170015	+	0.985442i	$0.445618\pi$
$500$		0			0
$501$	−83.0365	−	83.0365i	−0.165742	−	0.165742i
$502$	−210.295	+	210.295i	−0.418914	+	0.418914i
$503$			295.334i			0.587146i	0.955937	+	0.293573i	$0.0948443\pi$
$503$			295.334i			0.587146i	−0.955937	+	0.293573i	$0.905156\pi$
$504$		−	235.038i		−	0.466345i
$505$		0			0
$506$			226.635i			0.447895i
$507$	106.263	−	81.9308i	0.209592	−	0.161599i
$508$		−	223.933i		−	0.440814i
$509$	6.08665	−	6.08665i	0.0119581	−	0.0119581i	−0.701102	−	0.713061i	$-0.747308\pi$
$509$	6.08665	−	6.08665i	0.0119581	−	0.0119581i	0.713061	+	0.701102i	$0.247308\pi$
$510$		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
$517$	46.8463			0.0906119
$518$	−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
$523$		−	531.245i		−	1.01577i	−0.861426	−	0.507883i	$-0.830428\pi$
$523$		−	531.245i		−	1.01577i	0.861426	−	0.507883i	$-0.169572\pi$
$524$			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
$532$	150.717			0.283303
$533$	209.688	+	615.375i	0.393410	+	1.15455i
$534$	−137.634			−0.257742
$535$		0			0
$536$	216.356			0.403648
$537$	181.144			0.337326
$538$	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	0.939757	+	0.341844i	$0.111051\pi$
$541$	693.346	+	693.346i	1.28160	+	1.28160i	0.341844	+	0.939757i	$0.388949\pi$
$542$			124.801i			0.230259i
$543$	−135.167			−0.248926
$544$	78.6482	+	78.6482i	0.144574	+	0.144574i
$545$		0			0
$546$	−294.409	−	144.762i	−0.539211	−	0.265133i
$547$			372.319i			0.680657i	0.940307	+	0.340328i	$0.110538\pi$
$547$			372.319i			0.680657i	−0.940307	+	0.340328i	$0.889462\pi$
$548$	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	−0.733692	−	0.679483i	$-0.762204\pi$
$557$	−30.1943	+	30.1943i	−0.0542088	+	0.0542088i	0.679483	+	0.733692i	$0.262204\pi$
$558$	−806.564			−1.44545
$559$	28.5609	−	58.0855i	0.0510928	−	0.103910i
$560$		0			0
$561$	3.16697	−	3.16697i	0.00564522	−	0.00564522i
$562$		−	475.792i		−	0.846606i
$563$	−254.215			−0.451536			−0.225768	−	0.974181i	$-0.572489\pi$
$563$	−254.215			−0.451536			−0.225768	+	0.974181i	$0.572489\pi$
$564$	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
$568$		−	8.26283i		−	0.0145472i
$569$		−	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	$-0.830140\pi$
$571$		−	580.894i		−	1.01733i	0.860965	−	0.508664i	$-0.169860\pi$
$572$	26.9075	+	78.9659i	0.0470410	+	0.138052i
$573$			231.905i			0.404721i
$574$	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
$582$	334.449			0.574655
$583$	−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	$0.886422\pi$
$588$			230.035i			0.391217i
$589$			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
$597$	−62.3041			−0.104362
$598$	1354.36	−	461.495i	2.26481	−	0.771730i
$599$	477.029			0.796376			0.398188	−	0.917304i	$-0.369639\pi$
$599$	477.029			0.796376			0.398188	+	0.917304i	$0.369639\pi$
$600$		0			0
$601$	230.164			0.382968			0.191484	−	0.981496i	$-0.438670\pi$
$601$	230.164			0.382968			0.191484	+	0.981496i	$0.438670\pi$
$602$	−158.260			−0.262890
$603$	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
$607$		−	532.535i		−	0.877323i	−0.898652	−	0.438661i	$-0.855453\pi$
$607$		−	532.535i		−	0.877323i	0.898652	−	0.438661i	$-0.144547\pi$
$608$	164.792			0.271039
$609$	150.451	+	150.451i	0.247045	+	0.247045i
$610$		0			0
$611$	−95.3929	−	279.952i	−0.156126	−	0.458186i
$612$			71.4569i			0.116760i
$613$	−769.790	−	769.790i	−1.25577	−	1.25577i	−0.953091	−	0.302683i	$-0.902117\pi$
$613$	−769.790	−	769.790i	−1.25577	−	1.25577i	−0.302683	−	0.953091i	$-0.597883\pi$
$614$	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	$-0.139681\pi$
$619$	297.357	+	297.357i	0.480383	+	0.480383i	−0.424871	+	0.905254i	$0.639681\pi$
$620$		0			0
$621$		−	568.990i		−	0.916248i
$622$	−394.379	+	394.379i	−0.634050	+	0.634050i
$623$	774.250			1.24278
$624$	−173.703	−	85.4105i	−0.278370	−	0.136876i
$625$		0			0
$626$	−629.557	+	629.557i	−1.00568	+	1.00568i
$627$		−	6.63577i		−	0.0105834i
$628$	−193.879			−0.308725
$629$	−61.4138	+	61.4138i	−0.0976372	+	0.0976372i
$630$		0			0
$631$	440.375	+	440.375i	0.697900	+	0.697900i	0.963957	−	0.266057i	$-0.0857210\pi$
$631$	440.375	+	440.375i	0.697900	+	0.697900i	−0.266057	+	0.963957i	$0.585721\pi$
$632$	−113.134	+	113.134i	−0.179009	+	0.179009i
$633$		−	85.1006i		−	0.134440i
$634$			599.166i			0.945057i
$635$		0			0
$636$			138.141i			0.217204i
$637$	1084.54	+	533.274i	1.70258	+	0.837165i
$638$		−	123.546i		−	0.193646i
$639$	20.7481	−	20.7481i	0.0324697	−	0.0324697i
$640$		0			0
$641$		−	576.939i		−	0.900060i	−0.893013	−	0.450030i	$-0.851413\pi$
$641$		−	576.939i		−	0.900060i	0.893013	−	0.450030i	$-0.148587\pi$
$642$	279.370	+	279.370i	0.435155	+	0.435155i
$643$	459.481	+	459.481i	0.714589	+	0.714589i	0.967492	−	0.252903i	$-0.0813852\pi$
$643$	459.481	+	459.481i	0.714589	+	0.714589i	−0.252903	+	0.967492i	$0.581385\pi$
$644$	−1083.31	−	1083.31i	−1.68217	−	1.68217i
$645$		0			0
$646$	29.6626			0.0459174
$647$	543.648			0.840260			0.420130	−	0.907464i	$-0.361984\pi$
$647$	543.648			0.840260			0.420130	+	0.907464i	$0.361984\pi$
$648$	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
$653$			762.917i			1.16833i	0.811636	+	0.584163i	$0.198577\pi$
$653$			762.917i			1.16833i	−0.811636	+	0.584163i	$0.801423\pi$
$654$		−	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	$-0.710780\pi$
$659$	−810.362			−1.22968			−0.614842	+	0.788650i	$0.710780\pi$
$660$		0			0
$661$	−220.504	−	220.504i	−0.333591	−	0.333591i	0.520357	−	0.853949i	$-0.325799\pi$
$661$	−220.504	−	220.504i	−0.333591	−	0.333591i	−0.853949	+	0.520357i	$0.825799\pi$
$662$	1240.05			1.87319
$663$	−25.3745	−	12.4768i	−0.0382723	−	0.0188187i
$664$	−305.314			−0.459810
$665$		0			0
$666$	−707.860			−1.06285
$667$	−927.947			−1.39123
$668$	−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
$672$			384.085i			0.571555i
$673$	710.668			1.05597			0.527985	−	0.849254i	$-0.322948\pi$
$673$	710.668			1.05597			0.527985	+	0.849254i	$0.322948\pi$
$674$	450.916	+	450.916i	0.669015	+	0.669015i
$675$		0			0
$676$	417.105	−	321.596i	0.617020	−	0.475733i
$677$			1048.84i			1.54925i	0.632421	+	0.774625i	$0.282061\pi$
$677$			1048.84i			1.54925i	−0.632421	+	0.774625i	$0.717939\pi$
$678$	−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
$688$	−93.3740			−0.135718
$689$	651.291	+	320.243i	0.945270	+	0.464794i
$690$		0			0
$691$	−374.671	+	374.671i	−0.542216	+	0.542216i	−0.924178	−	0.381962i	$-0.875249\pi$
$691$	−374.671	+	374.671i	−0.542216	+	0.542216i	0.381962	+	0.924178i	$0.375249\pi$
$692$			873.471i			1.26224i
$693$	−205.343			−0.296310
$694$	−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
$698$		−	43.7410i		−	0.0626662i
$699$		−	114.982i		−	0.164495i
$700$		0			0
$701$			559.394i			0.797994i	0.916952	+	0.398997i	$0.130642\pi$
$701$			559.394i			0.797994i	−0.916952	+	0.398997i	$0.869358\pi$
$702$	−154.259	−	452.707i	−0.219742	−	0.644882i
$703$			128.681i			0.183045i
$704$	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	$-0.126441\pi$
$709$	379.510	+	379.510i	0.535276	+	0.535276i	−0.386862	+	0.922138i	$0.626441\pi$
$710$		0			0
$711$	−568.161			−0.799101
$712$	153.154			0.215104
$713$	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
$718$		−	1033.43i		−	1.43932i
$719$		−	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
$727$	−952.075			−1.30959			−0.654797	−	0.755804i	$-0.727246\pi$
$727$	−952.075			−1.30959			−0.654797	+	0.755804i	$0.727246\pi$
$728$	327.608	+	161.086i	0.450011	+	0.221272i
$729$	440.263			0.603928
$730$		0			0
$731$	−13.6401			−0.0186595
$732$	11.6047			0.0158534
$733$	−492.664	−	492.664i	−0.672119	−	0.672119i	0.286085	−	0.958204i	$-0.407646\pi$
$733$	−492.664	−	492.664i	−0.672119	−	0.672119i	−0.958204	+	0.286085i	$0.907646\pi$
$734$	236.535	−	236.535i	0.322254	−	0.322254i
$735$		0			0
$736$	−1184.48	−	1184.48i	−1.60935	−	1.60935i
$737$		−	189.021i		−	0.256474i
$738$	1116.58			1.51298
$739$	−94.0595	−	94.0595i	−0.127279	−	0.127279i	0.640597	−	0.767877i	$-0.278687\pi$
$739$	−94.0595	−	94.0595i	−0.127279	−	0.127279i	−0.767877	+	0.640597i	$0.778687\pi$
$740$		0			0
$741$	−39.6550	+	13.5124i	−0.0535156	+	0.0182353i
$742$		−	1774.51i		−	2.39152i
$743$	−750.112	−	750.112i	−1.00957	−	1.00957i	−0.999954	−	0.00961857i	$-0.996938\pi$
$743$	−750.112	−	750.112i	−1.00957	−	1.00957i	−0.00961857	−	0.999954i	$-0.503062\pi$
$744$	−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	$-0.928970\pi$
$751$		−	332.394i		−	0.442602i	0.975206	−	0.221301i	$-0.0710304\pi$
$752$	−301.688	+	301.688i	−0.401181	+	0.401181i
$753$	−88.5144			−0.117549
$754$	−738.305	+	251.576i	−0.979185	+	0.333655i
$755$		0			0
$756$	−362.108	+	362.108i	−0.478979	+	0.478979i
$757$		−	354.304i		−	0.468037i	−0.972232	−	0.234018i	$-0.924812\pi$
$757$		−	354.304i		−	0.468037i	0.972232	−	0.234018i	$-0.0751876\pi$
$758$	−1754.10			−2.31412
$759$	−47.6960	+	47.6960i	−0.0628406	+	0.0628406i
$760$		0			0
$761$	800.356	+	800.356i	1.05172	+	1.05172i	0.998588	+	0.0531281i	$0.0169192\pi$
$761$	800.356	+	800.356i	1.05172	+	1.05172i	0.0531281	+	0.998588i	$0.483081\pi$
$762$	107.615	−	107.615i	0.141227	−	0.141227i
$763$			257.559i			0.337561i
$764$			910.277i			1.19146i
$765$		0			0
$766$		−	1196.20i		−	1.56162i
$767$	−535.536	+	182.483i	−0.698221	+	0.237917i
$768$			261.590i			0.340612i
$769$	−628.880	+	628.880i	−0.817790	+	0.817790i	−0.985787	−	0.167998i	$-0.946270\pi$
$769$	−628.880	+	628.880i	−0.817790	+	0.817790i	0.167998	+	0.985787i	$0.446270\pi$
$770$		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	$0.0111707\pi$
$773$	799.646	+	799.646i	1.03447	+	1.03447i	0.0350866	+	0.999384i	$0.488829\pi$
$774$	−78.6084	−	78.6084i	−0.101561	−	0.101561i
$775$		0			0
$776$	−372.163			−0.479592
$777$	−299.920			−0.385997
$778$	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
$783$			310.175i			0.396137i
$784$		−	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	−0.567213	−	0.823571i	$-0.691978\pi$
$787$	201.754	−	201.754i	0.256358	−	0.256358i	0.823571	+	0.567213i	$0.191978\pi$
$788$	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
$792$	−40.6189			−0.0512865
$793$	26.9023	−	54.7123i	0.0339247	−	0.0689941i
$794$	−1714.77			−2.15966
$795$		0			0
$796$	−244.557			−0.307232
$797$	−303.914			−0.381323			−0.190661	−	0.981656i	$-0.561063\pi$
$797$	−303.914			−0.381323			−0.190661	+	0.981656i	$0.561063\pi$
$798$	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
$802$		−	1093.20i		−	1.36310i
$803$	219.034			0.272770
$804$	−160.614	−	160.614i	−0.199769	−	0.199769i
$805$		0			0
$806$	552.790	−	1124.23i	0.685843	−	1.39483i
$807$			328.197i			0.406687i
$808$	144.864	+	144.864i	0.179287	+	0.179287i
$809$	944.687			1.16772			0.583861	−	0.811854i	$-0.301541\pi$
$809$	944.687			1.16772			0.583861	+	0.811854i	$0.301541\pi$
$810$		0			0
$811$	553.234	−	553.234i	0.682163	−	0.682163i	−0.278324	−	0.960487i	$-0.589779\pi$
$811$	553.234	−	553.234i	0.682163	−	0.682163i	0.960487	+	0.278324i	$0.0897790\pi$
$812$	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
$818$	52.7829			0.0645267
$819$	418.139	+	1227.12i	0.510548	+	1.49832i
$820$		0			0
$821$	−251.178	+	251.178i	−0.305942	+	0.305942i	−0.843333	−	0.537391i	$-0.819410\pi$
$821$	−251.178	+	251.178i	−0.305942	+	0.305942i	0.537391	+	0.843333i	$0.319410\pi$
$822$			260.106i			0.316431i
$823$	13.4655			0.0163615			0.00818073	−	0.999967i	$-0.497396\pi$
$823$	13.4655			0.0163615			0.00818073	+	0.999967i	$0.497396\pi$
$824$	−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	−0.361511	−	0.932368i	$-0.617739\pi$
$827$	472.099	−	472.099i	0.570857	−	0.570857i	0.932368	+	0.361511i	$0.117739\pi$
$828$		−	1076.18i		−	1.29973i
$829$			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
$832$	−388.423	−	190.990i	−0.466855	−	0.229555i
$833$		−	254.680i		−	0.305739i
$834$	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	$-0.351955\pi$
$839$	−373.582	−	373.582i	−0.445270	−	0.445270i	−0.893779	+	0.448508i	$0.851955\pi$
$840$		0			0
$841$	−335.145			−0.398508
$842$	1375.69			1.63384
$843$	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
$848$		−	1046.97i		−	1.23463i
$849$			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
$857$	410.502			0.478999			0.239500	−	0.970896i	$-0.423017\pi$
$857$	410.502			0.478999			0.239500	+	0.970896i	$0.423017\pi$
$858$	−25.0177	+	50.8794i	−0.0291581	+	0.0593000i
$859$	847.774			0.986932			0.493466	−	0.869765i	$-0.335730\pi$
$859$	847.774			0.986932			0.493466	+	0.869765i	$0.335730\pi$
$860$		0			0
$861$	473.092			0.549468
$862$	1841.98			2.13687
$863$	−102.685	−	102.685i	−0.118986	−	0.118986i	0.645107	−	0.764093i	$-0.276813\pi$
$863$	−102.685	−	102.685i	−0.118986	−	0.118986i	−0.764093	+	0.645107i	$0.776813\pi$
$864$	−395.923	+	395.923i	−0.458244	+	0.458244i
$865$		0			0
$866$	556.738	+	556.738i	0.642884	+	0.642884i
$867$		−	223.499i		−	0.257784i
$868$	−1341.40			−1.54539
$869$	98.8403	+	98.8403i	0.113740	+	0.113740i
$870$		0			0
$871$	−1129.58	+	384.903i	−1.29688	+	0.441909i
$872$			50.9478i			0.0584264i
$873$	−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	$0.289194\pi$
$881$			1389.52i			1.57720i	−0.614905	+	0.788601i	$0.710806\pi$
$882$	1467.73	−	1467.73i	1.66410	−	1.66410i
$883$	763.229			0.864359			0.432179	−	0.901788i	$-0.357745\pi$
$883$	763.229			0.864359			0.432179	+	0.901788i	$0.357745\pi$
$884$	−99.6004	−	48.9740i	−0.112670	−	0.0554005i
$885$		0			0
$886$	782.500	−	782.500i	0.883183	−	0.883183i
$887$		−	921.219i		−	1.03858i	−0.854599	−	0.519289i	$-0.826197\pi$
$887$		−	921.219i		−	1.03858i	0.854599	−	0.519289i	$-0.173803\pi$
$888$	−59.3271			−0.0668098
$889$	−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
$893$			92.3416i			0.103406i
$894$		−	19.8686i		−	0.0222243i
$895$		0			0
$896$		−	876.712i		−	0.978473i
$897$	382.152	+	187.906i	0.426034	+	0.209483i
$898$		−	244.657i		−	0.272447i
$899$	−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
$907$	952.357			1.05001			0.525004	−	0.851100i	$-0.324064\pi$
$907$	952.357			1.05001			0.525004	+	0.851100i	$0.324064\pi$
$908$	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
$913$			266.740i			0.292158i
$914$			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	$-0.356707\pi$
$919$	799.748			0.870237			0.435118	+	0.900373i	$0.356707\pi$
$920$		0			0
$921$	285.922	+	285.922i	0.310448	+	0.310448i
$922$	−661.367			−0.717317
$923$	14.6998	+	43.1398i	0.0159261	+	0.0467387i
$924$	60.7080			0.0657013
$925$		0			0
$926$	890.580			0.961749
$927$	−1429.36			−1.54192
$928$	645.698	+	645.698i	0.695795	+	0.695795i
$929$	78.6741	−	78.6741i	0.0846869	−	0.0846869i	−0.663494	−	0.748181i	$-0.730927\pi$
$929$	78.6741	−	78.6741i	0.0846869	−	0.0846869i	0.748181	+	0.663494i	$0.230927\pi$
$930$		0			0
$931$	−266.817	−	266.817i	−0.286592	−	0.286592i
$932$		−	451.329i		−	0.484259i
$933$	−165.997			−0.177917
$934$	777.016	+	777.016i	0.831923	+	0.831923i
$935$		0			0
$936$	82.7120	+	242.737i	0.0883675	+	0.259334i
$937$			1466.28i			1.56486i	0.622737	+	0.782431i	$0.286020\pi$
$937$			1466.28i			1.56486i	−0.622737	+	0.782431i	$0.713980\pi$
$938$	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	−0.742804	−	0.669509i	$-0.766504\pi$
$941$	−68.9700	+	68.9700i	−0.0732944	+	0.0732944i	0.669509	+	0.742804i	$0.266504\pi$
$942$	−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	−0.944168	−	0.329464i	$-0.893132\pi$
$947$	−582.125	+	582.125i	−0.614705	+	0.614705i	0.329464	+	0.944168i	$0.393132\pi$
$948$	167.972			0.177186
$949$	−446.018	−	1308.94i	−0.469987	−	1.37928i
$950$		0			0
$951$	−126.096	+	126.096i	−0.132594	+	0.132594i
$952$		−	76.9315i		−	0.0808104i
$953$	1341.06			1.40720			0.703602	−	0.710595i	$-0.251574\pi$
$953$	1341.06			1.40720			0.703602	+	0.710595i	$0.251574\pi$
$954$	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
$958$		−	456.924i		−	0.476956i
$959$		−	1463.20i		−	1.52576i
$960$		0			0
$961$		−	343.969i		−	0.357928i
$962$	485.142	−	986.653i	0.504306	−	1.02563i
$963$		−	1561.21i		−	1.62120i
$964$	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	$0.367562\pi$
$972$	−546.110			−0.561842
$973$	−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	$0.694612\pi$
$978$		−	159.333i		−	0.162918i
$979$		−	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
$987$	−215.223			−0.218058
$988$	−155.654	+	53.0389i	−0.157545	+	0.0536831i
$989$	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	$0.506512\pi$
$992$	−1466.67			−1.47850
$993$	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
$997$		−	966.616i		−	0.969525i	−0.874646	−	0.484762i	$-0.838906\pi$
$997$		−	966.616i		−	0.969525i	0.874646	−	0.484762i	$-0.161094\pi$
$998$	−1535.09			−1.53817
$999$	−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.g.e.174.8		20
5.2	odd	4		325.3.j.c.226.3	yes	20
5.3	odd	4		325.3.j.d.226.8	yes	20
5.4	even	2		325.3.g.f.174.3		20
13.8	odd	4		325.3.g.f.99.3		20
65.8	even	4		325.3.j.d.151.8	yes	20
65.34	odd	4	inner	325.3.g.e.99.8		20
65.47	even	4		325.3.j.c.151.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.3.g.e.99.8		20	65.34	odd	4	inner
325.3.g.e.174.8		20	1.1	even	1	trivial
325.3.g.f.99.3		20	13.8	odd	4
325.3.g.f.174.3		20	5.4	even	2
325.3.j.c.151.3	✓	20	65.47	even	4
325.3.j.c.226.3	yes	20	5.2	odd	4
325.3.j.d.151.8	yes	20	65.8	even	4
325.3.j.d.226.8	yes	20	5.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.g (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.88633 + 1.88633i) q^{2} +0.793970i q^{3} +3.11650i q^{4} +(-1.49769 + 1.49769i) q^{6} +(8.42514 - 8.42514i) q^{7} +(1.66658 - 1.66658i) q^{8} +8.36961 q^{9} +(-1.45602 - 1.45602i) q^{11} -2.47441 q^{12} +(-5.73623 + 11.6660i) q^{13} +31.7852 q^{14} +18.7534 q^{16} +2.73950 q^{17} +(15.7879 + 15.7879i) q^{18} +(2.87005 - 2.87005i) q^{19} +(6.68931 + 6.68931i) q^{21} -5.49308i q^{22} -41.2582 q^{23} +(1.32321 + 1.32321i) q^{24} +(-32.8264 + 11.1855i) q^{26} +13.7909i q^{27} +(26.2569 + 26.2569i) q^{28} +22.4912 q^{29} +(-25.5438 + 25.5438i) q^{31} +(28.7089 + 28.7089i) q^{32} +(1.15604 - 1.15604i) q^{33} +(5.16762 + 5.16762i) q^{34} +26.0839i q^{36} +(-22.4179 + 22.4179i) q^{37} +10.8277 q^{38} +(-9.26246 - 4.55439i) q^{39} +(35.3618 - 35.3618i) q^{41} +25.2365i q^{42} -4.97904 q^{43} +(4.53769 - 4.53769i) q^{44} +(-77.8267 - 77.8267i) q^{46} +(-16.0871 + 16.0871i) q^{47} +14.8897i q^{48} -92.9659i q^{49} +2.17508i q^{51} +(-36.3571 - 17.8770i) q^{52} -55.8281i q^{53} +(-26.0143 + 26.0143i) q^{54} -28.0823i q^{56} +(2.27873 + 2.27873i) q^{57} +(42.4259 + 42.4259i) q^{58} +(30.7740 + 30.7740i) q^{59} -4.68989 q^{61} -96.3681 q^{62} +(70.5151 - 70.5151i) q^{63} +33.2953i q^{64} +4.36134 q^{66} +(64.9102 + 64.9102i) q^{67} +8.53766i q^{68} -32.7578i q^{69} +(2.47898 - 2.47898i) q^{71} +(13.9486 - 13.9486i) q^{72} +(-75.2167 + 75.2167i) q^{73} -84.5750 q^{74} +(8.94451 + 8.94451i) q^{76} -24.5344 q^{77} +(-8.88097 - 26.0632i) q^{78} -67.8838 q^{79} +64.3769 q^{81} +133.408 q^{82} +(-91.5991 - 91.5991i) q^{83} +(-20.8472 + 20.8472i) q^{84} +(-9.39212 - 9.39212i) q^{86} +17.8573i q^{87} -4.85314 q^{88} +(45.9488 + 45.9488i) q^{89} +(49.9592 + 146.616i) q^{91} -128.581i q^{92} +(-20.2810 - 20.2810i) q^{93} -60.6913 q^{94} +(-22.7940 + 22.7940i) q^{96} +(-111.655 - 111.655i) q^{97} +(175.365 - 175.365i) q^{98} +(-12.1863 - 12.1863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{6} - 20 q^{7} - 18 q^{8} - 72 q^{9} + 6 q^{11} + 120 q^{12} + 18 q^{13} + 24 q^{14} - 128 q^{16} + 16 q^{17} + 58 q^{18} + 20 q^{19} + 90 q^{21} - 28 q^{23} + 28 q^{24} - 278 q^{28} + 40 q^{29}+ \cdots + 410 q^{99}+O(q^{100}) \) 20 * q - 6 * q^6 - 20 * q^7 - 18 * q^8 - 72 * q^9 + 6 * q^11 + 120 * q^12 + 18 * q^13 + 24 * q^14 - 128 * q^16 + 16 * q^17 + 58 * q^18 + 20 * q^19 + 90 * q^21 - 28 * q^23 + 28 * q^24 - 278 * q^28 + 40 * q^29 - 32 * q^31 - 162 * q^32 + 124 * q^33 + 14 * q^34 - 158 * q^37 - 124 * q^38 + 26 * q^39 + 70 * q^41 + 32 * q^43 - 366 * q^44 + 58 * q^46 + 130 * q^47 - 244 * q^52 + 350 * q^54 + 168 * q^57 + 180 * q^58 - 132 * q^59 - 152 * q^61 - 212 * q^62 + 442 * q^63 + 720 * q^66 + 178 * q^67 - 258 * q^71 - 390 * q^72 - 262 * q^73 - 220 * q^74 + 68 * q^76 - 184 * q^77 + 918 * q^78 + 544 * q^79 + 204 * q^81 + 920 * q^82 - 88 * q^83 - 352 * q^84 - 174 * q^86 - 424 * q^88 + 282 * q^89 - 440 * q^91 - 522 * q^93 + 544 * q^94 - 1216 * q^96 + 6 * q^97 + 78 * q^98 + 410 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more