LMFDB - Embedded newform 140.2.m.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(13,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("140.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.11574317056.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 45x^{4} + 4 $ x^8 + 45*x^4 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.4
Root			$1.83051 - 1.83051i$ of defining polynomial
Character	$\chi$	$=$	140.13
Dual form			140.2.m.a.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.83051 - 1.83051i) q^{3} +(1.83051 + 1.28422i) q^{5} +(-2.12393 + 1.57763i) q^{7} -3.70156i q^{9} +O(q^{10})$	\(q+(1.83051 - 1.83051i) q^{3} +(1.83051 + 1.28422i) q^{5} +(-2.12393 + 1.57763i) q^{7} -3.70156i q^{9} -4.70156 q^{11} +(1.83051 - 1.83051i) q^{13} +(5.70156 - 1.00000i) q^{15} +(-0.737925 - 0.737925i) q^{17} -4.75362 q^{19} +(-1.00000 + 6.77576i) q^{21} +(3.70156 + 3.70156i) q^{23} +(1.70156 + 4.70156i) q^{25} +(-1.28422 - 1.28422i) q^{27} -0.701562i q^{29} -8.79790i q^{31} +(-8.60627 + 8.60627i) q^{33} +(-5.91391 + 0.160291i) q^{35} +(-3.70156 + 3.70156i) q^{37} -6.70156i q^{39} +4.75362i q^{41} +(-5.00000 - 5.00000i) q^{43} +(4.75362 - 6.77576i) q^{45} +(8.05998 + 8.05998i) q^{47} +(2.02214 - 6.70156i) q^{49} -2.70156 q^{51} +(5.00000 + 5.00000i) q^{53} +(-8.60627 - 6.03784i) q^{55} +(-8.70156 + 8.70156i) q^{57} +4.75362 q^{59} -9.50723i q^{61} +(5.83971 + 7.86185i) q^{63} +(5.70156 - 1.00000i) q^{65} +(5.00000 - 5.00000i) q^{67} +13.5515 q^{69} -5.40312 q^{71} +(3.11473 - 3.11473i) q^{73} +(11.7210 + 5.49154i) q^{75} +(9.98578 - 7.41734i) q^{77} +6.70156i q^{79} +6.40312 q^{81} +(7.86835 - 7.86835i) q^{83} +(-0.403124 - 2.29844i) q^{85} +(-1.28422 - 1.28422i) q^{87} -13.5515 q^{89} +(-1.00000 + 6.77576i) q^{91} +(-16.1047 - 16.1047i) q^{93} +(-8.70156 - 6.10469i) q^{95} +(-5.49154 - 5.49154i) q^{97} +17.4031i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{7}+O(q^{10}) $ 8 * q - 2 * q^7	$ 8 q - 2 q^{7} - 12 q^{11} + 20 q^{15} - 8 q^{21} + 4 q^{23} - 12 q^{25} - 14 q^{35} - 4 q^{37} - 40 q^{43} + 4 q^{51} + 40 q^{53} - 44 q^{57} + 42 q^{63} + 20 q^{65} + 40 q^{67} + 8 q^{71} + 44 q^{77} + 48 q^{85} - 8 q^{91} - 52 q^{93} - 44 q^{95}+O(q^{100}) $ 8 * q - 2 * q^7 - 12 * q^11 + 20 * q^15 - 8 * q^21 + 4 * q^23 - 12 * q^25 - 14 * q^35 - 4 * q^37 - 40 * q^43 + 4 * q^51 + 40 * q^53 - 44 * q^57 + 42 * q^63 + 20 * q^65 + 40 * q^67 + 8 * q^71 + 44 * q^77 + 48 * q^85 - 8 * q^91 - 52 * q^93 - 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.83051	−	1.83051i	1.05685	−	1.05685i	0.0585640	−	0.998284i	$-0.481348\pi$
$3$	1.83051	−	1.83051i	1.05685	−	1.05685i	0.998284	−	0.0585640i	$-0.0186522\pi$
$4$		0			0
$5$	1.83051	+	1.28422i	0.818631	+	0.574320i
$5$	1.83051	+	1.28422i	0.818631	+	0.574320i
$6$		0			0
$7$	−2.12393	+	1.57763i	−0.802769	+	0.596289i
$7$	−2.12393	+	1.57763i	−0.802769	+	0.596289i
$8$		0			0
$9$		−	3.70156i		−	1.23385i
$10$		0			0
$11$	−4.70156			−1.41757			−0.708787	−	0.705422i	$-0.750757\pi$
$11$	−4.70156			−1.41757			−0.708787	+	0.705422i	$0.750757\pi$
$12$		0			0
$13$	1.83051	−	1.83051i	0.507693	−	0.507693i	−0.406125	−	0.913818i	$-0.633120\pi$
$13$	1.83051	−	1.83051i	0.507693	−	0.507693i	0.913818	+	0.406125i	$0.133120\pi$
$14$		0			0
$15$	5.70156	−	1.00000i	1.47214	−	0.258199i
$16$		0			0
$17$	−0.737925	−	0.737925i	−0.178973	−	0.178973i	0.611935	−	0.790908i	$-0.290391\pi$
$17$	−0.737925	−	0.737925i	−0.178973	−	0.178973i	−0.790908	+	0.611935i	$0.790391\pi$
$18$		0			0
$19$	−4.75362			−1.09055			−0.545277	−	0.838256i	$-0.683576\pi$
$19$	−4.75362			−1.09055			−0.545277	+	0.838256i	$0.683576\pi$
$20$		0			0
$21$	−1.00000	+	6.77576i	−0.218218	+	1.47859i
$22$		0			0
$23$	3.70156	+	3.70156i	0.771829	+	0.771829i	0.978426	−	0.206597i	$-0.0662389\pi$
$23$	3.70156	+	3.70156i	0.771829	+	0.771829i	−0.206597	+	0.978426i	$0.566239\pi$
$24$		0			0
$25$	1.70156	+	4.70156i	0.340312	+	0.940312i
$26$		0			0
$27$	−1.28422	−	1.28422i	−0.247148	−	0.247148i
$28$		0			0
$29$		−	0.701562i		−	0.130277i	−0.997876	−	0.0651384i	$-0.979251\pi$
$29$		−	0.701562i		−	0.130277i	0.997876	−	0.0651384i	$-0.0207489\pi$
$30$		0			0
$31$		−	8.79790i		−	1.58015i	−0.613010	−	0.790075i	$-0.710041\pi$
$31$		−	8.79790i		−	1.58015i	0.613010	−	0.790075i	$-0.289959\pi$
$32$		0			0
$33$	−8.60627	+	8.60627i	−1.49816	+	1.49816i
$34$		0			0
$35$	−5.91391	+	0.160291i	−0.999633	+	0.0270941i
$36$		0			0
$37$	−3.70156	+	3.70156i	−0.608533	+	0.608533i	−0.942563	−	0.334030i	$-0.891591\pi$
$37$	−3.70156	+	3.70156i	−0.608533	+	0.608533i	0.334030	+	0.942563i	$0.391591\pi$
$38$		0			0
$39$		−	6.70156i		−	1.07311i
$40$		0			0
$41$			4.75362i			0.742390i	0.928555	+	0.371195i	$0.121052\pi$
$41$			4.75362i			0.742390i	−0.928555	+	0.371195i	$0.878948\pi$
$42$		0			0
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	0.214280	−	0.976772i	$-0.431260\pi$
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	−0.976772	+	0.214280i	$0.931260\pi$
$44$		0			0
$45$	4.75362	−	6.77576i	0.708627	−	1.01007i
$46$		0			0
$47$	8.05998	+	8.05998i	1.17567	+	1.17567i	0.980837	+	0.194832i	$0.0624163\pi$
$47$	8.05998	+	8.05998i	1.17567	+	1.17567i	0.194832	+	0.980837i	$0.437584\pi$
$48$		0			0
$49$	2.02214	−	6.70156i	0.288878	−	0.957366i
$50$		0			0
$51$	−2.70156			−0.378294
$52$		0			0
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	−8.60627	−	6.03784i	−1.16047	−	0.814142i
$56$		0			0
$57$	−8.70156	+	8.70156i	−1.15255	+	1.15255i
$58$		0			0
$59$	4.75362			0.618868			0.309434	−	0.950921i	$-0.399860\pi$
$59$	4.75362			0.618868			0.309434	+	0.950921i	$0.399860\pi$
$60$		0			0
$61$		−	9.50723i		−	1.21728i	−0.793448	−	0.608638i	$-0.791716\pi$
$61$		−	9.50723i		−	1.21728i	0.793448	−	0.608638i	$-0.208284\pi$
$62$		0			0
$63$	5.83971	+	7.86185i	0.735734	+	0.990500i
$64$		0			0
$65$	5.70156	−	1.00000i	0.707192	−	0.124035i
$66$		0			0
$67$	5.00000	−	5.00000i	0.610847	−	0.610847i	−0.332320	−	0.943167i	$-0.607831\pi$
$67$	5.00000	−	5.00000i	0.610847	−	0.610847i	0.943167	+	0.332320i	$0.107831\pi$
$68$		0			0
$69$	13.5515			1.63141
$70$		0			0
$71$	−5.40312			−0.641233			−0.320616	−	0.947209i	$-0.603890\pi$
$71$	−5.40312			−0.641233			−0.320616	+	0.947209i	$0.603890\pi$
$72$		0			0
$73$	3.11473	−	3.11473i	0.364552	−	0.364552i	−0.500934	−	0.865486i	$-0.667010\pi$
$73$	3.11473	−	3.11473i	0.364552	−	0.364552i	0.865486	+	0.500934i	$0.167010\pi$
$74$		0			0
$75$	11.7210	+	5.49154i	1.35343	+	0.634109i
$76$		0			0
$77$	9.98578	−	7.41734i	1.13799	−	0.845285i
$78$		0			0
$79$			6.70156i			0.753985i	0.926216	+	0.376992i	$0.123042\pi$
$79$			6.70156i			0.753985i	−0.926216	+	0.376992i	$0.876958\pi$
$80$		0			0
$81$	6.40312			0.711458
$82$		0			0
$83$	7.86835	−	7.86835i	0.863664	−	0.863664i	−0.128098	−	0.991762i	$-0.540887\pi$
$83$	7.86835	−	7.86835i	0.863664	−	0.863664i	0.991762	+	0.128098i	$0.0408872\pi$
$84$		0			0
$85$	−0.403124	−	2.29844i	−0.0437250	−	0.249301i
$86$		0			0
$87$	−1.28422	−	1.28422i	−0.137683	−	0.137683i
$88$		0			0
$89$	−13.5515			−1.43646			−0.718229	−	0.695807i	$-0.755047\pi$
$89$	−13.5515			−1.43646			−0.718229	+	0.695807i	$0.755047\pi$
$90$		0			0
$91$	−1.00000	+	6.77576i	−0.104828	+	0.710293i
$92$		0			0
$93$	−16.1047	−	16.1047i	−1.66998	−	1.66998i
$94$		0			0
$95$	−8.70156	−	6.10469i	−0.892761	−	0.626328i
$96$		0			0
$97$	−5.49154	−	5.49154i	−0.557582	−	0.557582i	0.371037	−	0.928618i	$-0.379002\pi$
$97$	−5.49154	−	5.49154i	−0.557582	−	0.557582i	−0.928618	+	0.371037i	$0.879002\pi$
$98$		0			0
$99$			17.4031i			1.74908i
$100$		0			0
$101$		−	4.75362i		−	0.473003i	−0.971631	−	0.236501i	$-0.923999\pi$
$101$		−	4.75362i		−	0.473003i	0.971631	−	0.236501i	$-0.0760008\pi$
$102$		0			0
$103$	−2.92310	+	2.92310i	−0.288022	+	0.288022i	−0.836298	−	0.548276i	$-0.815284\pi$
$103$	−2.92310	+	2.92310i	−0.288022	+	0.288022i	0.548276	+	0.836298i	$0.315284\pi$
$104$		0			0
$105$	−10.5321	+	11.1189i	−1.02783	+	1.08509i
$106$		0			0
$107$	2.40312	−	2.40312i	0.232319	−	0.232319i	−0.581341	−	0.813660i	$-0.697472\pi$
$107$	2.40312	−	2.40312i	0.232319	−	0.232319i	0.813660	+	0.581341i	$0.197472\pi$
$108$		0			0
$109$		−	3.29844i		−	0.315933i	−0.987444	−	0.157967i	$-0.949506\pi$
$109$		−	3.29844i		−	0.315933i	0.987444	−	0.157967i	$-0.0504938\pi$
$110$		0			0
$111$			13.5515i			1.28625i
$112$		0			0
$113$	−6.29844	−	6.29844i	−0.592507	−	0.592507i	0.345801	−	0.938308i	$-0.387607\pi$
$113$	−6.29844	−	6.29844i	−0.592507	−	0.592507i	−0.938308	+	0.345801i	$0.887607\pi$
$114$		0			0
$115$	2.02214	+	11.5294i	0.188566	+	1.07512i
$116$		0			0
$117$	−6.77576	−	6.77576i	−0.626419	−	0.626419i
$118$		0			0
$119$	2.73147	+	0.403124i	0.250394	+	0.0369543i
$120$		0			0
$121$	11.1047			1.00952
$122$		0			0
$123$	8.70156	+	8.70156i	0.784593	+	0.784593i
$124$		0			0
$125$	−2.92310	+	10.7915i	−0.261450	+	0.965217i
$126$		0			0
$127$	2.40312	−	2.40312i	0.213243	−	0.213243i	−0.592401	−	0.805643i	$-0.701820\pi$
$127$	2.40312	−	2.40312i	0.213243	−	0.213243i	0.805643	+	0.592401i	$0.201820\pi$
$128$		0			0
$129$	−18.3051			−1.61168
$130$		0			0
$131$		−	4.04429i		−	0.353351i	−0.984269	−	0.176676i	$-0.943466\pi$
$131$		−	4.04429i		−	0.353351i	0.984269	−	0.176676i	$-0.0565343\pi$
$132$		0			0
$133$	10.0963	−	7.49947i	0.875464	−	0.650286i
$134$		0			0
$135$	−0.701562	−	4.00000i	−0.0603809	−	0.344265i
$136$		0			0
$137$	−3.70156	+	3.70156i	−0.316246	+	0.316246i	−0.847323	−	0.531077i	$-0.821787\pi$
$137$	−3.70156	+	3.70156i	−0.316246	+	0.316246i	0.531077	+	0.847323i	$0.321787\pi$
$138$		0			0
$139$	−17.5958			−1.49246			−0.746229	−	0.665690i	$-0.768137\pi$
$139$	−17.5958			−1.49246			−0.746229	+	0.665690i	$0.768137\pi$
$140$		0			0
$141$	29.5078			2.48501
$142$		0			0
$143$	−8.60627	+	8.60627i	−0.719693	+	0.719693i
$144$		0			0
$145$	0.900960	−	1.28422i	0.0748206	−	0.106649i
$146$		0			0
$147$	−8.56574	−	15.9689i	−0.706490	−	1.31709i
$148$		0			0
$149$			18.8062i			1.54067i	0.637641	+	0.770334i	$0.279910\pi$
$149$			18.8062i			1.54067i	−0.637641	+	0.770334i	$0.720090\pi$
$150$		0			0
$151$	−7.29844			−0.593938			−0.296969	−	0.954887i	$-0.595976\pi$
$151$	−7.29844			−0.593938			−0.296969	+	0.954887i	$0.595976\pi$
$152$		0			0
$153$	−2.73147	+	2.73147i	−0.220827	+	0.220827i
$154$		0			0
$155$	11.2984	−	16.1047i	0.907512	−	1.29356i
$156$		0			0
$157$	8.25161	+	8.25161i	0.658550	+	0.658550i	0.955037	−	0.296487i	$-0.0958151\pi$
$157$	8.25161	+	8.25161i	0.658550	+	0.658550i	−0.296487	+	0.955037i	$0.595815\pi$
$158$		0			0
$159$	18.3051			1.45169
$160$		0			0
$161$	−13.7016	−	2.02214i	−1.07983	−	0.159367i
$162$		0			0
$163$	3.70156	+	3.70156i	0.289929	+	0.289929i	0.837052	−	0.547123i	$-0.184277\pi$
$163$	3.70156	+	3.70156i	0.289929	+	0.289929i	−0.547123	+	0.837052i	$0.684277\pi$
$164$		0			0
$165$	−26.8062	+	4.70156i	−2.08686	+	0.366016i
$166$		0			0
$167$	3.30636	+	3.30636i	0.255854	+	0.255854i	0.823365	−	0.567511i	$-0.192094\pi$
$167$	3.30636	+	3.30636i	0.255854	+	0.255854i	−0.567511	+	0.823365i	$0.692094\pi$
$168$		0			0
$169$			6.29844i			0.484495i
$170$		0			0
$171$			17.5958i			1.34559i
$172$		0			0
$173$	6.58413	−	6.58413i	0.500582	−	0.500582i	−0.411037	−	0.911619i	$-0.634833\pi$
$173$	6.58413	−	6.58413i	0.500582	−	0.500582i	0.911619	+	0.411037i	$0.134833\pi$
$174$		0			0
$175$	−11.0313	−	7.30134i	−0.833891	−	0.551929i
$176$		0			0
$177$	8.70156	−	8.70156i	0.654049	−	0.654049i
$178$		0			0
$179$			8.80625i			0.658210i	0.944293	+	0.329105i	$0.106747\pi$
$179$			8.80625i			0.658210i	−0.944293	+	0.329105i	$0.893253\pi$
$180$		0			0
$181$		−	14.2609i		−	1.06000i	−0.847997	−	0.530000i	$-0.822192\pi$
$181$		−	14.2609i		−	1.06000i	0.847997	−	0.530000i	$-0.177808\pi$
$182$		0			0
$183$	−17.4031	−	17.4031i	−1.28648	−	1.28648i
$184$		0			0
$185$	−11.5294	+	2.02214i	−0.847657	+	0.148671i
$186$		0			0
$187$	3.46940	+	3.46940i	0.253708	+	0.253708i
$188$		0			0
$189$	4.75362	+	0.701562i	0.345775	+	0.0510311i
$190$		0			0
$191$	−2.10469			−0.152290			−0.0761449	−	0.997097i	$-0.524261\pi$
$191$	−2.10469			−0.152290			−0.0761449	+	0.997097i	$0.524261\pi$
$192$		0			0
$193$	−1.10469	−	1.10469i	−0.0795171	−	0.0795171i	0.666230	−	0.745747i	$-0.267907\pi$
$193$	−1.10469	−	1.10469i	−0.0795171	−	0.0795171i	−0.745747	+	0.666230i	$0.767907\pi$
$194$		0			0
$195$	8.60627	−	12.2673i	0.616308	−	0.878480i
$196$		0			0
$197$	2.40312	−	2.40312i	0.171216	−	0.171216i	−0.616298	−	0.787513i	$-0.711368\pi$
$197$	2.40312	−	2.40312i	0.171216	−	0.171216i	0.787513	+	0.616298i	$0.211368\pi$
$198$		0			0
$199$	22.3494			1.58431			0.792154	−	0.610321i	$-0.208959\pi$
$199$	22.3494			1.58431			0.792154	+	0.610321i	$0.208959\pi$
$200$		0			0
$201$		−	18.3051i		−	1.29114i
$202$		0			0
$203$	1.10681	+	1.49007i	0.0776827	+	0.104582i
$204$		0			0
$205$	−6.10469	+	8.70156i	−0.426370	+	0.607743i
$206$		0			0
$207$	13.7016	−	13.7016i	0.952324	−	0.952324i
$208$		0			0
$209$	22.3494			1.54594
$210$		0			0
$211$	12.7016			0.874412			0.437206	−	0.899361i	$-0.355968\pi$
$211$	12.7016			0.874412			0.437206	+	0.899361i	$0.355968\pi$
$212$		0			0
$213$	−9.89049	+	9.89049i	−0.677685	+	0.677685i
$214$		0			0
$215$	−2.73147	−	15.5737i	−0.186285	−	1.06212i
$216$		0			0
$217$	13.8799	+	18.6861i	0.942227	+	1.26850i
$218$		0			0
$219$		−	11.4031i		−	0.770552i
$220$		0			0
$221$	−2.70156			−0.181727
$222$		0			0
$223$	−15.7653	+	15.7653i	−1.05572	+	1.05572i	−0.0573692	+	0.998353i	$0.518271\pi$
$223$	−15.7653	+	15.7653i	−1.05572	+	1.05572i	−0.998353	+	0.0573692i	$0.981729\pi$
$224$		0			0
$225$	17.4031	−	6.29844i	1.16021	−	0.419896i
$226$		0			0
$227$	−6.20087	−	6.20087i	−0.411566	−	0.411566i	0.470718	−	0.882284i	$-0.343995\pi$
$227$	−6.20087	−	6.20087i	−0.411566	−	0.411566i	−0.882284	+	0.470718i	$0.843995\pi$
$228$		0			0
$229$	0.709330			0.0468738			0.0234369	−	0.999725i	$-0.492539\pi$
$229$	0.709330			0.0468738			0.0234369	+	0.999725i	$0.492539\pi$
$230$		0			0
$231$	4.70156	−	31.8567i	0.309340	−	2.09601i
$232$		0			0
$233$	11.1047	+	11.1047i	0.727492	+	0.727492i	0.970120	−	0.242627i	$-0.0780092\pi$
$233$	11.1047	+	11.1047i	0.727492	+	0.727492i	−0.242627	+	0.970120i	$0.578009\pi$
$234$		0			0
$235$	4.40312	+	25.1047i	0.287228	+	1.63765i
$236$		0			0
$237$	12.2673	+	12.2673i	0.796847	+	0.796847i
$238$		0			0
$239$			24.1047i			1.55920i	0.626276	+	0.779601i	$0.284578\pi$
$239$			24.1047i			1.55920i	−0.626276	+	0.779601i	$0.715422\pi$
$240$		0			0
$241$			27.1030i			1.74586i	0.487845	+	0.872930i	$0.337783\pi$
$241$			27.1030i			1.74586i	−0.487845	+	0.872930i	$0.662217\pi$
$242$		0			0
$243$	15.5737	−	15.5737i	0.999051	−	0.999051i
$244$		0			0
$245$	12.3078	−	9.67043i	0.786319	−	0.617821i
$246$		0			0
$247$	−8.70156	+	8.70156i	−0.553667	+	0.553667i
$248$		0			0
$249$		−	28.8062i		−	1.82552i
$250$		0			0
$251$		−	4.04429i		−	0.255273i	−0.991821	−	0.127637i	$-0.959261\pi$
$251$		−	4.04429i		−	0.255273i	0.991821	−	0.127637i	$-0.0407391\pi$
$252$		0			0
$253$	−17.4031	−	17.4031i	−1.09413	−	1.09413i
$254$		0			0
$255$	−4.94525	−	3.46940i	−0.309683	−	0.217262i
$256$		0			0
$257$	−9.34420	−	9.34420i	−0.582875	−	0.582875i	0.352817	−	0.935692i	$-0.385224\pi$
$257$	−9.34420	−	9.34420i	−0.582875	−	0.582875i	−0.935692	+	0.352817i	$0.885224\pi$
$258$		0			0
$259$	2.02214	−	13.7016i	0.125650	−	0.851374i
$260$		0			0
$261$	−2.59688			−0.160743
$262$		0			0
$263$	12.4031	+	12.4031i	0.764809	+	0.764809i	0.977188	−	0.212378i	$-0.0681209\pi$
$263$	12.4031	+	12.4031i	0.764809	+	0.764809i	−0.212378	+	0.977188i	$0.568121\pi$
$264$		0			0
$265$	2.73147	+	15.5737i	0.167793	+	0.956683i
$266$		0			0
$267$	−24.8062	+	24.8062i	−1.51812	+	1.51812i
$268$		0			0
$269$	−13.5515			−0.826251			−0.413125	−	0.910674i	$-0.635563\pi$
$269$	−13.5515			−0.826251			−0.413125	+	0.910674i	$0.635563\pi$
$270$		0			0
$271$			23.0588i			1.40072i	0.713790	+	0.700360i	$0.246977\pi$
$271$			23.0588i			1.40072i	−0.713790	+	0.700360i	$0.753023\pi$
$272$		0			0
$273$	10.5726	+	14.2336i	0.639883	+	0.861459i
$274$		0			0
$275$	−8.00000	−	22.1047i	−0.482418	−	1.33296i
$276$		0			0
$277$	11.1047	−	11.1047i	0.667216	−	0.667216i	−0.289855	−	0.957071i	$-0.593607\pi$
$277$	11.1047	−	11.1047i	0.667216	−	0.667216i	0.957071	+	0.289855i	$0.0936070\pi$
$278$		0			0
$279$	−32.5660			−1.94967
$280$		0			0
$281$	−26.9109			−1.60537			−0.802686	−	0.596402i	$-0.796596\pi$
$281$	−26.9109			−1.60537			−0.802686	+	0.596402i	$0.796596\pi$
$282$		0			0
$283$	−7.67672	+	7.67672i	−0.456334	+	0.456334i	−0.897450	−	0.441116i	$-0.854583\pi$
$283$	−7.67672	+	7.67672i	−0.456334	+	0.456334i	0.441116	+	0.897450i	$0.354583\pi$
$284$		0			0
$285$	−27.1030	+	4.75362i	−1.60545	+	0.281580i
$286$		0			0
$287$	−7.49947	−	10.0963i	−0.442680	−	0.595968i
$288$		0			0
$289$		−	15.9109i		−	0.935937i
$290$		0			0
$291$	−20.1047			−1.17856
$292$		0			0
$293$	−7.67672	+	7.67672i	−0.448479	+	0.448479i	−0.894849	−	0.446370i	$-0.852717\pi$
$293$	−7.67672	+	7.67672i	−0.448479	+	0.448479i	0.446370	+	0.894849i	$0.352717\pi$
$294$		0			0
$295$	8.70156	+	6.10469i	0.506625	+	0.355429i
$296$		0			0
$297$	6.03784	+	6.03784i	0.350351	+	0.350351i
$298$		0			0
$299$	13.5515			0.783705
$300$		0			0
$301$	18.5078	+	2.73147i	1.06677	+	0.157440i
$302$		0			0
$303$	−8.70156	−	8.70156i	−0.499892	−	0.499892i
$304$		0			0
$305$	12.2094	−	17.4031i	0.699107	−	0.996500i
$306$		0			0
$307$	−9.53583	−	9.53583i	−0.544239	−	0.544239i	0.380530	−	0.924769i	$-0.375742\pi$
$307$	−9.53583	−	9.53583i	−0.544239	−	0.544239i	−0.924769	+	0.380530i	$0.875742\pi$
$308$		0			0
$309$			10.7016i			0.608791i
$310$		0			0
$311$		−	8.79790i		−	0.498883i	−0.968390	−	0.249442i	$-0.919753\pi$
$311$		−	8.79790i		−	0.498883i	0.968390	−	0.249442i	$-0.0802471\pi$
$312$		0			0
$313$	11.3377	−	11.3377i	0.640847	−	0.640847i	−0.309916	−	0.950764i	$-0.600301\pi$
$313$	11.3377	−	11.3377i	0.640847	−	0.640847i	0.950764	+	0.309916i	$0.100301\pi$
$314$		0			0
$315$	0.593326	+	21.8907i	0.0334302	+	1.23340i
$316$		0			0
$317$	−12.4031	+	12.4031i	−0.696629	+	0.696629i	−0.963682	−	0.267053i	$-0.913950\pi$
$317$	−12.4031	+	12.4031i	−0.696629	+	0.696629i	0.267053	+	0.963682i	$0.413950\pi$
$318$		0			0
$319$			3.29844i			0.184677i
$320$		0			0
$321$		−	8.79790i		−	0.491051i
$322$		0			0
$323$	3.50781	+	3.50781i	0.195180	+	0.195180i
$324$		0			0
$325$	11.7210	+	5.49154i	0.650165	+	0.304616i
$326$		0			0
$327$	−6.03784	−	6.03784i	−0.333893	−	0.333893i
$328$		0			0
$329$	−29.8345	−	4.40312i	−1.64483	−	0.242752i
$330$		0			0
$331$	9.40312			0.516842			0.258421	−	0.966032i	$-0.416798\pi$
$331$	9.40312			0.516842			0.258421	+	0.966032i	$0.416798\pi$
$332$		0			0
$333$	13.7016	+	13.7016i	0.750841	+	0.750841i
$334$		0			0
$335$	15.5737	−	2.73147i	0.850880	−	0.149236i
$336$		0			0
$337$	−21.1047	+	21.1047i	−1.14965	+	1.14965i	−0.163023	+	0.986622i	$0.552125\pi$
$337$	−21.1047	+	21.1047i	−1.14965	+	1.14965i	−0.986622	+	0.163023i	$0.947875\pi$
$338$		0			0
$339$	−23.0588			−1.25238
$340$		0			0
$341$			41.3639i			2.23998i
$342$		0			0
$343$	6.27772	+	17.4238i	0.338965	+	0.940799i
$344$		0			0
$345$	24.8062	+	17.4031i	1.33552	+	0.936953i
$346$		0			0
$347$	13.7016	−	13.7016i	0.735538	−	0.735538i	−0.236173	−	0.971711i	$-0.575893\pi$
$347$	13.7016	−	13.7016i	0.735538	−	0.735538i	0.971711	+	0.236173i	$0.0758931\pi$
$348$		0			0
$349$	−8.79790			−0.470941			−0.235471	−	0.971881i	$-0.575663\pi$
$349$	−8.79790			−0.470941			−0.235471	+	0.971881i	$0.575663\pi$
$350$		0			0
$351$	−4.70156			−0.250951
$352$		0			0
$353$	16.0914	−	16.0914i	0.856457	−	0.856457i	−0.134462	−	0.990919i	$-0.542931\pi$
$353$	16.0914	−	16.0914i	0.856457	−	0.856457i	0.990919	+	0.134462i	$0.0429306\pi$
$354$		0			0
$355$	−9.89049	−	6.93880i	−0.524933	−	0.368273i
$356$		0			0
$357$	5.73792	−	4.26208i	0.303683	−	0.225573i
$358$		0			0
$359$		−	6.00000i		−	0.316668i	−0.987386	−	0.158334i	$-0.949388\pi$
$359$		−	6.00000i		−	0.316668i	0.987386	−	0.158334i	$-0.0506123\pi$
$360$		0			0
$361$	3.59688			0.189309
$362$		0			0
$363$	20.3273	−	20.3273i	1.06691	−	1.06691i
$364$		0			0
$365$	9.70156	−	1.70156i	0.507803	−	0.0890638i
$366$		0			0
$367$	−0.0285948	−	0.0285948i	−0.00149264	−	0.00149264i	0.706360	−	0.707853i	$-0.250336\pi$
$367$	−0.0285948	−	0.0285948i	−0.00149264	−	0.00149264i	−0.707853	+	0.706360i	$0.750336\pi$
$368$		0			0
$369$	17.5958			0.916001
$370$		0			0
$371$	−18.5078	−	2.73147i	−0.960878	−	0.141811i
$372$		0			0
$373$	−6.29844	−	6.29844i	−0.326121	−	0.326121i	0.524989	−	0.851109i	$-0.324070\pi$
$373$	−6.29844	−	6.29844i	−0.326121	−	0.326121i	−0.851109	+	0.524989i	$0.824070\pi$
$374$		0			0
$375$	14.4031	+	25.1047i	0.743774	+	1.29640i
$376$		0			0
$377$	−1.28422	−	1.28422i	−0.0661407	−	0.0661407i
$378$		0			0
$379$		−	33.0156i		−	1.69590i	−0.530077	−	0.847949i	$-0.677837\pi$
$379$		−	33.0156i		−	1.69590i	0.530077	−	0.847949i	$-0.322163\pi$
$380$		0			0
$381$		−	8.79790i		−	0.450730i
$382$		0			0
$383$	7.86835	−	7.86835i	0.402054	−	0.402054i	−0.476902	−	0.878956i	$-0.658240\pi$
$383$	7.86835	−	7.86835i	0.402054	−	0.402054i	0.878956	+	0.476902i	$0.158240\pi$
$384$		0			0
$385$	27.8046	−	0.753617i	1.41705	−	0.0384079i
$386$		0			0
$387$	−18.5078	+	18.5078i	−0.940805	+	0.940805i
$388$		0			0
$389$		−	20.7016i		−	1.04961i	−0.851222	−	0.524805i	$-0.824138\pi$
$389$		−	20.7016i		−	1.04961i	0.851222	−	0.524805i	$-0.175862\pi$
$390$		0			0
$391$		−	5.46295i		−	0.276273i
$392$		0			0
$393$	−7.40312	−	7.40312i	−0.373438	−	0.373438i
$394$		0			0
$395$	−8.60627	+	12.2673i	−0.433029	+	0.617235i
$396$		0			0
$397$	−10.2452	−	10.2452i	−0.514190	−	0.514190i	0.401618	−	0.915807i	$-0.368448\pi$
$397$	−10.2452	−	10.2452i	−0.514190	−	0.514190i	−0.915807	+	0.401618i	$0.868448\pi$
$398$		0			0
$399$	4.75362	−	32.2094i	0.237979	−	1.61249i
$400$		0			0
$401$	−24.3141			−1.21419			−0.607093	−	0.794631i	$-0.707664\pi$
$401$	−24.3141			−1.21419			−0.607093	+	0.794631i	$0.707664\pi$
$402$		0			0
$403$	−16.1047	−	16.1047i	−0.802232	−	0.802232i
$404$		0			0
$405$	11.7210	+	8.22302i	0.582422	+	0.408605i
$406$		0			0
$407$	17.4031	−	17.4031i	0.862641	−	0.862641i
$408$		0			0
$409$	35.9009			1.77519			0.887594	−	0.460627i	$-0.152375\pi$
$409$	35.9009			1.77519			0.887594	+	0.460627i	$0.152375\pi$
$410$		0			0
$411$			13.5515i			0.668447i
$412$		0			0
$413$	−10.0963	+	7.49947i	−0.496809	+	0.369025i
$414$		0			0
$415$	24.5078	−	4.29844i	1.20304	−	0.211002i
$416$		0			0
$417$	−32.2094	+	32.2094i	−1.57730	+	1.57730i
$418$		0			0
$419$	4.75362			0.232229			0.116115	−	0.993236i	$-0.462956\pi$
$419$	4.75362			0.232229			0.116115	+	0.993236i	$0.462956\pi$
$420$		0			0
$421$	5.29844			0.258230			0.129115	−	0.991630i	$-0.458786\pi$
$421$	5.29844			0.258230			0.129115	+	0.991630i	$0.458786\pi$
$422$		0			0
$423$	29.8345	−	29.8345i	1.45060	−	1.45060i
$424$		0			0
$425$	2.21377	−	4.72502i	0.107384	−	0.229197i
$426$		0			0
$427$	14.9989	+	20.1927i	0.725849	+	0.977193i
$428$		0			0
$429$			31.5078i			1.52121i
$430$		0			0
$431$	−7.29844			−0.351553			−0.175777	−	0.984430i	$-0.556244\pi$
$431$	−7.29844			−0.351553			−0.175777	+	0.984430i	$0.556244\pi$
$432$		0			0
$433$	−9.72746	+	9.72746i	−0.467472	+	0.467472i	−0.901095	−	0.433623i	$-0.857235\pi$
$433$	−9.72746	+	9.72746i	−0.467472	+	0.467472i	0.433623	+	0.901095i	$0.357235\pi$
$434$		0			0
$435$	−0.701562	−	4.00000i	−0.0336373	−	0.191785i
$436$		0			0
$437$	−17.5958	−	17.5958i	−0.841722	−	0.841722i
$438$		0			0
$439$	−19.0145			−0.907511			−0.453756	−	0.891126i	$-0.649916\pi$
$439$	−19.0145			−0.907511			−0.453756	+	0.891126i	$0.649916\pi$
$440$		0			0
$441$	−24.8062	−	7.48509i	−1.18125	−	0.356433i
$442$		0			0
$443$	0.193752	+	0.193752i	0.00920541	+	0.00920541i	0.711695	−	0.702489i	$-0.247928\pi$
$443$	0.193752	+	0.193752i	0.00920541	+	0.00920541i	−0.702489	+	0.711695i	$0.747928\pi$
$444$		0			0
$445$	−24.8062	−	17.4031i	−1.17593	−	0.824987i
$446$		0			0
$447$	34.4251	+	34.4251i	1.62825	+	1.62825i
$448$		0			0
$449$		−	0.701562i		−	0.0331088i	−0.999863	−	0.0165544i	$-0.994730\pi$
$449$		−	0.701562i		−	0.0331088i	0.999863	−	0.0165544i	$-0.00526966\pi$
$450$		0			0
$451$		−	22.3494i		−	1.05239i
$452$		0			0
$453$	−13.3599	+	13.3599i	−0.627702	+	0.627702i
$454$		0			0
$455$	−10.5321	+	11.1189i	−0.493751	+	0.521262i
$456$		0			0
$457$	22.4031	−	22.4031i	1.04797	−	1.04797i	0.0491842	−	0.998790i	$-0.484338\pi$
$457$	22.4031	−	22.4031i	1.04797	−	1.04797i	0.998790	−	0.0491842i	$-0.0156621\pi$
$458$		0			0
$459$			1.89531i			0.0884657i
$460$		0			0
$461$		−	17.5958i		−	0.819519i	−0.912194	−	0.409759i	$-0.865613\pi$
$461$		−	17.5958i		−	0.819519i	0.912194	−	0.409759i	$-0.134387\pi$
$462$		0			0
$463$	21.1047	+	21.1047i	0.980818	+	0.980818i	0.999819	−	0.0190015i	$-0.00604873\pi$
$463$	21.1047	+	21.1047i	0.980818	+	0.980818i	−0.0190015	+	0.999819i	$0.506049\pi$
$464$		0			0
$465$	−8.79790	−	50.1618i	−0.407993	−	2.32620i
$466$		0			0
$467$	8.05998	+	8.05998i	0.372971	+	0.372971i	0.868558	−	0.495587i	$-0.165047\pi$
$467$	8.05998	+	8.05998i	0.372971	+	0.372971i	−0.495587	+	0.868558i	$0.665047\pi$
$468$		0			0
$469$	−2.73147	+	18.5078i	−0.126128	+	0.854611i
$470$		0			0
$471$	30.2094			1.39197
$472$		0			0
$473$	23.5078	+	23.5078i	1.08089	+	1.08089i
$474$		0			0
$475$	−8.08857	−	22.3494i	−0.371129	−	1.02546i
$476$		0			0
$477$	18.5078	−	18.5078i	0.847414	−	0.847414i
$478$		0			0
$479$	28.5217			1.30319			0.651595	−	0.758567i	$-0.274100\pi$
$479$	28.5217			1.30319			0.651595	+	0.758567i	$0.274100\pi$
$480$		0			0
$481$			13.5515i			0.617896i
$482$		0			0
$483$	−28.7825	+	21.3793i	−1.30965	+	0.972794i
$484$		0			0
$485$	−3.00000	−	17.1047i	−0.136223	−	0.776684i
$486$		0			0
$487$	−15.9109	+	15.9109i	−0.720993	+	0.720993i	−0.968808	−	0.247814i	$-0.920288\pi$
$487$	−15.9109	+	15.9109i	−0.720993	+	0.720993i	0.247814	+	0.968808i	$0.420288\pi$
$488$		0			0
$489$	13.5515			0.612821
$490$		0			0
$491$	24.9109			1.12421			0.562107	−	0.827064i	$-0.309991\pi$
$491$	24.9109			1.12421			0.562107	+	0.827064i	$0.309991\pi$
$492$		0			0
$493$	−0.517700	+	0.517700i	−0.0233160	+	0.0233160i
$494$		0			0
$495$	−22.3494	+	31.8567i	−1.00453	+	1.43185i
$496$		0			0
$497$	11.4758	−	8.52415i	0.514762	−	0.382360i
$498$		0			0
$499$			4.10469i			0.183751i	0.995771	+	0.0918755i	$0.0292862\pi$
$499$			4.10469i			0.183751i	−0.995771	+	0.0918755i	$0.970714\pi$
$500$		0			0
$501$	12.1047			0.540798
$502$		0			0
$503$	−17.1840	+	17.1840i	−0.766195	+	0.766195i	−0.977434	−	0.211240i	$-0.932250\pi$
$503$	−17.1840	+	17.1840i	−0.766195	+	0.766195i	0.211240	+	0.977434i	$0.432250\pi$
$504$		0			0
$505$	6.10469	−	8.70156i	0.271655	−	0.387214i
$506$		0			0
$507$	11.5294	+	11.5294i	0.512038	+	0.512038i
$508$		0			0
$509$	13.5515			0.600661			0.300330	−	0.953835i	$-0.402903\pi$
$509$	13.5515			0.600661			0.300330	+	0.953835i	$0.402903\pi$
$510$		0			0
$511$	−1.70156	+	11.5294i	−0.0752727	+	0.510030i
$512$		0			0
$513$	6.10469	+	6.10469i	0.269528	+	0.269528i
$514$		0			0
$515$	−9.10469	+	1.59688i	−0.401200	+	0.0703668i
$516$		0			0
$517$	−37.8945	−	37.8945i	−1.66660	−	1.66660i
$518$		0			0
$519$		−	24.1047i		−	1.05808i
$520$		0			0
$521$		−	3.33496i		−	0.146107i	−0.997328	−	0.0730536i	$-0.976726\pi$
$521$		−	3.33496i		−	0.146107i	0.997328	−	0.0730536i	$-0.0232744\pi$
$522$		0			0
$523$	−14.4811	+	14.4811i	−0.633213	+	0.633213i	−0.948873	−	0.315659i	$-0.897774\pi$
$523$	−14.4811	+	14.4811i	−0.633213	+	0.633213i	0.315659	+	0.948873i	$0.397774\pi$
$524$		0			0
$525$	−33.5582	+	6.82782i	−1.46460	+	0.297990i
$526$		0			0
$527$	−6.49219	+	6.49219i	−0.282804	+	0.282804i
$528$		0			0
$529$			4.40312i			0.191440i
$530$		0			0
$531$		−	17.5958i		−	0.763593i
$532$		0			0
$533$	8.70156	+	8.70156i	0.376906	+	0.376906i
$534$		0			0
$535$	7.48509	−	1.31281i	0.323609	−	0.0567579i
$536$		0			0
$537$	16.1200	+	16.1200i	0.695628	+	0.695628i
$538$		0			0
$539$	−9.50723	+	31.5078i	−0.409506	+	1.35714i
$540$		0			0
$541$	−32.1047			−1.38029			−0.690144	−	0.723672i	$-0.742453\pi$
$541$	−32.1047			−1.38029			−0.690144	+	0.723672i	$0.742453\pi$
$542$		0			0
$543$	−26.1047	−	26.1047i	−1.12026	−	1.12026i
$544$		0			0
$545$	4.23592	−	6.03784i	0.181447	−	0.258632i
$546$		0			0
$547$	−3.70156	+	3.70156i	−0.158267	+	0.158267i	−0.781799	−	0.623531i	$-0.785697\pi$
$547$	−3.70156	+	3.70156i	−0.158267	+	0.158267i	0.623531	+	0.781799i	$0.285697\pi$
$548$		0			0
$549$	−35.1916			−1.50194
$550$		0			0
$551$			3.33496i			0.142074i
$552$		0			0
$553$	−10.5726	−	14.2336i	−0.449593	−	0.605276i
$554$		0			0
$555$	−17.4031	+	24.8062i	−0.738721	+	1.05297i
$556$		0			0
$557$	−8.89531	+	8.89531i	−0.376907	+	0.376907i	−0.869985	−	0.493078i	$-0.835872\pi$
$557$	−8.89531	+	8.89531i	−0.376907	+	0.376907i	0.493078	+	0.869985i	$0.335872\pi$
$558$		0			0
$559$	−18.3051			−0.774225
$560$		0			0
$561$	12.7016			0.536260
$562$		0			0
$563$	−19.2347	+	19.2347i	−0.810646	+	0.810646i	−0.984731	−	0.174085i	$-0.944303\pi$
$563$	−19.2347	+	19.2347i	−0.810646	+	0.810646i	0.174085	+	0.984731i	$0.444303\pi$
$564$		0			0
$565$	−3.44080	−	19.6180i	−0.144756	−	0.825333i
$566$		0			0
$567$	−13.5998	+	10.1018i	−0.571137	+	0.424235i
$568$		0			0
$569$		−	30.8062i		−	1.29147i	−0.763564	−	0.645733i	$-0.776552\pi$
$569$		−	30.8062i		−	1.29147i	0.763564	−	0.645733i	$-0.223448\pi$
$570$		0			0
$571$	4.20937			0.176157			0.0880784	−	0.996114i	$-0.471927\pi$
$571$	4.20937			0.176157			0.0880784	+	0.996114i	$0.471927\pi$
$572$		0			0
$573$	−3.85266	+	3.85266i	−0.160947	+	0.160947i
$574$		0			0
$575$	−11.1047	+	23.7016i	−0.463097	+	0.988423i
$576$		0			0
$577$	−10.2452	−	10.2452i	−0.426512	−	0.426512i	0.460927	−	0.887438i	$-0.347517\pi$
$577$	−10.2452	−	10.2452i	−0.426512	−	0.426512i	−0.887438	+	0.460927i	$0.847517\pi$
$578$		0			0
$579$	−4.04429			−0.168075
$580$		0			0
$581$	−4.29844	+	29.1252i	−0.178329	+	1.20832i
$582$		0			0
$583$	−23.5078	−	23.5078i	−0.973594	−	0.973594i
$584$		0			0
$585$	−3.70156	−	21.1047i	−0.153041	−	0.872571i
$586$		0			0
$587$	18.4682	+	18.4682i	0.762263	+	0.762263i	0.976731	−	0.214468i	$-0.0688017\pi$
$587$	18.4682	+	18.4682i	0.762263	+	0.762263i	−0.214468	+	0.976731i	$0.568802\pi$
$588$		0			0
$589$			41.8219i			1.72324i
$590$		0			0
$591$		−	8.79790i		−	0.361897i
$592$		0			0
$593$	−12.4303	+	12.4303i	−0.510453	+	0.510453i	−0.914665	−	0.404212i	$-0.867546\pi$
$593$	−12.4303	+	12.4303i	−0.510453	+	0.510453i	0.404212	+	0.914665i	$0.367546\pi$
$594$		0			0
$595$	4.48230	+	4.24574i	0.183756	+	0.174058i
$596$		0			0
$597$	40.9109	−	40.9109i	1.67437	−	1.67437i
$598$		0			0
$599$			6.70156i			0.273818i	0.990584	+	0.136909i	$0.0437169\pi$
$599$			6.70156i			0.273818i	−0.990584	+	0.136909i	$0.956283\pi$
$600$		0			0
$601$		−	4.75362i		−	0.193904i	−0.995289	−	0.0969520i	$-0.969091\pi$
$601$		−	4.75362i		−	0.193904i	0.995289	−	0.0969520i	$-0.0309093\pi$
$602$		0			0
$603$	−18.5078	−	18.5078i	−0.753696	−	0.753696i
$604$		0			0
$605$	20.3273	+	14.2609i	0.826422	+	0.579786i
$606$		0			0
$607$	−1.44725	−	1.44725i	−0.0587422	−	0.0587422i	0.677125	−	0.735868i	$-0.263225\pi$
$607$	−1.44725	−	1.44725i	−0.0587422	−	0.0587422i	−0.735868	+	0.677125i	$0.763225\pi$
$608$		0			0
$609$	4.75362	+	0.701562i	0.192626	+	0.0284287i
$610$		0			0
$611$	29.5078			1.19376
$612$		0			0
$613$	19.8062	+	19.8062i	0.799967	+	0.799967i	0.983090	−	0.183123i	$-0.0586207\pi$
$613$	19.8062	+	19.8062i	0.799967	+	0.799967i	−0.183123	+	0.983090i	$0.558621\pi$
$614$		0			0
$615$	4.75362	+	27.1030i	0.191684	+	1.09290i
$616$		0			0
$617$	−1.10469	+	1.10469i	−0.0444730	+	0.0444730i	−0.728994	−	0.684521i	$-0.760012\pi$
$617$	−1.10469	+	1.10469i	−0.0444730	+	0.0444730i	0.684521	+	0.728994i	$0.260012\pi$
$618$		0			0
$619$	27.1030			1.08936			0.544682	−	0.838643i	$-0.316650\pi$
$619$	27.1030			1.08936			0.544682	+	0.838643i	$0.316650\pi$
$620$		0			0
$621$		−	9.50723i		−	0.381512i
$622$		0			0
$623$	28.7825	−	21.3793i	1.15314	−	0.856545i
$624$		0			0
$625$	−19.2094	+	16.0000i	−0.768375	+	0.640000i
$626$		0			0
$627$	40.9109	−	40.9109i	1.63383	−	1.63383i
$628$		0			0
$629$	5.46295			0.217822
$630$		0			0
$631$	−7.29844			−0.290546			−0.145273	−	0.989392i	$-0.546406\pi$
$631$	−7.29844			−0.290546			−0.145273	+	0.989392i	$0.546406\pi$
$632$		0			0
$633$	23.2504	−	23.2504i	0.924120	−	0.924120i
$634$		0			0
$635$	7.48509	−	1.31281i	0.297037	−	0.0520974i
$636$		0			0
$637$	−8.56574	−	15.9689i	−0.339387	−	0.632709i
$638$		0			0
$639$			20.0000i			0.791188i
$640$		0			0
$641$	9.79063			0.386707			0.193353	−	0.981129i	$-0.438064\pi$
$641$	9.79063			0.386707			0.193353	+	0.981129i	$0.438064\pi$
$642$		0			0
$643$	24.1799	−	24.1799i	0.953564	−	0.953564i	−0.0454049	−	0.998969i	$-0.514458\pi$
$643$	24.1799	−	24.1799i	0.953564	−	0.953564i	0.998969	+	0.0454049i	$0.0144578\pi$
$644$		0			0
$645$	−33.5078	−	23.5078i	−1.31937	−	0.925619i
$646$		0			0
$647$	−32.4030	−	32.4030i	−1.27389	−	1.27389i	−0.944029	−	0.329863i	$-0.892998\pi$
$647$	−32.4030	−	32.4030i	−1.27389	−	1.27389i	−0.329863	−	0.944029i	$-0.607002\pi$
$648$		0			0
$649$	−22.3494			−0.877292
$650$		0			0
$651$	59.6125	+	8.79790i	2.33640	+	0.344817i
$652$		0			0
$653$	5.00000	+	5.00000i	0.195665	+	0.195665i	0.798139	−	0.602474i	$-0.205818\pi$
$653$	5.00000	+	5.00000i	0.195665	+	0.195665i	−0.602474	+	0.798139i	$0.705818\pi$
$654$		0			0
$655$	5.19375	−	7.40312i	0.202937	−	0.289264i
$656$		0			0
$657$	−11.5294	−	11.5294i	−0.449804	−	0.449804i
$658$		0			0
$659$			38.9109i			1.51575i	0.652397	+	0.757877i	$0.273764\pi$
$659$			38.9109i			1.51575i	−0.652397	+	0.757877i	$0.726236\pi$
$660$		0			0
$661$		−	19.0145i		−	0.739577i	−0.929116	−	0.369789i	$-0.879430\pi$
$661$		−	19.0145i		−	0.739577i	0.929116	−	0.369789i	$-0.120570\pi$
$662$		0			0
$663$	−4.94525	+	4.94525i	−0.192057	+	0.192057i
$664$		0			0
$665$	28.1125	−	0.761961i	1.09015	−	0.0295476i
$666$		0			0
$667$	2.59688	−	2.59688i	0.100551	−	0.100551i
$668$		0			0
$669$			57.7172i			2.23148i
$670$		0			0
$671$			44.6989i			1.72558i
$672$		0			0
$673$	13.7016	+	13.7016i	0.528156	+	0.528156i	0.920022	−	0.391866i	$-0.128170\pi$
$673$	13.7016	+	13.7016i	0.528156	+	0.528156i	−0.391866	+	0.920022i	$0.628170\pi$
$674$		0			0
$675$	3.85266	−	8.22302i	0.148289	−	0.316504i
$676$		0			0
$677$	12.1043	+	12.1043i	0.465205	+	0.465205i	0.900357	−	0.435152i	$-0.143305\pi$
$677$	12.1043	+	12.1043i	0.465205	+	0.465205i	−0.435152	+	0.900357i	$0.643305\pi$
$678$		0			0
$679$	20.3273	+	3.00000i	0.780090	+	0.115129i
$680$		0			0
$681$	−22.7016			−0.869926
$682$		0			0
$683$	−28.5078	−	28.5078i	−1.09082	−	1.09082i	−0.995441	−	0.0953801i	$-0.969593\pi$
$683$	−28.5078	−	28.5078i	−1.09082	−	1.09082i	−0.0953801	−	0.995441i	$-0.530407\pi$
$684$		0			0
$685$	−11.5294	+	2.02214i	−0.440515	+	0.0772621i
$686$		0			0
$687$	1.29844	−	1.29844i	0.0495385	−	0.0495385i
$688$		0			0
$689$	18.3051			0.697370
$690$		0			0
$691$		−	32.5660i		−	1.23887i	−0.785048	−	0.619434i	$-0.787362\pi$
$691$		−	32.5660i		−	1.23887i	0.785048	−	0.619434i	$-0.212638\pi$
$692$		0			0
$693$	−27.4558	−	36.9630i	−1.04296	−	1.40411i
$694$		0			0
$695$	−32.2094	−	22.5969i	−1.22177	−	0.857148i
$696$		0			0
$697$	3.50781	−	3.50781i	0.132868	−	0.132868i
$698$		0			0
$699$	40.6546			1.53770
$700$		0			0
$701$	−34.7016			−1.31066			−0.655330	−	0.755343i	$-0.727470\pi$
$701$	−34.7016			−1.31066			−0.655330	+	0.755343i	$0.727470\pi$
$702$		0			0
$703$	17.5958	−	17.5958i	0.663639	−	0.663639i
$704$		0			0
$705$	54.0145	+	37.8945i	2.03430	+	1.42719i
$706$		0			0
$707$	7.49947	+	10.0963i	0.282046	+	0.379712i
$708$		0			0
$709$			11.5078i			0.432185i	0.976373	+	0.216092i	$0.0693313\pi$
$709$			11.5078i			0.432185i	−0.976373	+	0.216092i	$0.930669\pi$
$710$		0			0
$711$	24.8062			0.930307
$712$		0			0
$713$	32.5660	−	32.5660i	1.21961	−	1.21961i
$714$		0			0
$715$	−26.8062	+	4.70156i	−1.00250	+	0.175828i
$716$		0			0
$717$	44.1240	+	44.1240i	1.64784	+	1.64784i
$718$		0			0
$719$	−44.6989			−1.66699			−0.833493	−	0.552530i	$-0.813662\pi$
$719$	−44.6989			−1.66699			−0.833493	+	0.552530i	$0.813662\pi$
$720$		0			0
$721$	1.59688	−	10.8200i	0.0594708	−	0.402960i
$722$		0			0
$723$	49.6125	+	49.6125i	1.84511	+	1.84511i
$724$		0			0
$725$	3.29844	−	1.19375i	0.122501	−	0.0443348i
$726$		0			0
$727$	−19.5608	−	19.5608i	−0.725469	−	0.725469i	0.244245	−	0.969714i	$-0.421460\pi$
$727$	−19.5608	−	19.5608i	−0.725469	−	0.725469i	−0.969714	+	0.244245i	$0.921460\pi$
$728$		0			0
$729$		−	37.8062i		−	1.40023i
$730$		0			0
$731$			7.37925i			0.272931i
$732$		0			0
$733$	19.4263	−	19.4263i	0.717528	−	0.717528i	−0.250571	−	0.968098i	$-0.580618\pi$
$733$	19.4263	−	19.4263i	0.717528	−	0.717528i	0.968098	+	0.250571i	$0.0806183\pi$
$734$		0			0
$735$	4.82782	−	40.2315i	0.178077	−	1.48396i
$736$		0			0
$737$	−23.5078	+	23.5078i	−0.865921	+	0.865921i
$738$		0			0
$739$		−	25.5078i		−	0.938320i	−0.883113	−	0.469160i	$-0.844557\pi$
$739$		−	25.5078i		−	0.938320i	0.883113	−	0.469160i	$-0.155443\pi$
$740$		0			0
$741$			31.8567i			1.17028i
$742$		0			0
$743$	−32.0156	−	32.0156i	−1.17454	−	1.17454i	−0.981115	−	0.193424i	$-0.938041\pi$
$743$	−32.0156	−	32.0156i	−1.17454	−	1.17454i	−0.193424	−	0.981115i	$-0.561959\pi$
$744$		0			0
$745$	−24.1513	+	34.4251i	−0.884837	+	1.26124i
$746$		0			0
$747$	−29.1252	−	29.1252i	−1.06563	−	1.06563i
$748$		0			0
$749$	−1.31281	+	8.89531i	−0.0479692	+	0.325028i
$750$		0			0
$751$	−2.10469			−0.0768011			−0.0384005	−	0.999262i	$-0.512226\pi$
$751$	−2.10469			−0.0768011			−0.0384005	+	0.999262i	$0.512226\pi$
$752$		0			0
$753$	−7.40312	−	7.40312i	−0.269785	−	0.269785i
$754$		0			0
$755$	−13.3599	−	9.37279i	−0.486216	−	0.341111i
$756$		0			0
$757$	−6.29844	+	6.29844i	−0.228921	+	0.228921i	−0.812242	−	0.583321i	$-0.801753\pi$
$757$	−6.29844	+	6.29844i	−0.228921	+	0.228921i	0.583321	+	0.812242i	$0.301753\pi$
$758$		0			0
$759$	−63.7133			−2.31265
$760$		0			0
$761$		−	35.1916i		−	1.27570i	−0.770163	−	0.637848i	$-0.779825\pi$
$761$		−	35.1916i		−	1.27570i	0.770163	−	0.637848i	$-0.220175\pi$
$762$		0			0
$763$	5.20373	+	7.00565i	0.188388	+	0.253621i
$764$		0			0
$765$	−8.50781	+	1.49219i	−0.307601	+	0.0539502i
$766$		0			0
$767$	8.70156	−	8.70156i	0.314195	−	0.314195i
$768$		0			0
$769$	−26.3937			−0.951782			−0.475891	−	0.879504i	$-0.657874\pi$
$769$	−26.3937			−0.951782			−0.475891	+	0.879504i	$0.657874\pi$
$770$		0			0
$771$	−34.2094			−1.23202
$772$		0			0
$773$	−20.5189	+	20.5189i	−0.738014	+	0.738014i	−0.972193	−	0.234179i	$-0.924760\pi$
$773$	−20.5189	+	20.5189i	−0.738014	+	0.738014i	0.234179	+	0.972193i	$0.424760\pi$
$774$		0			0
$775$	41.3639	−	14.9702i	1.48583	−	0.537745i
$776$		0			0
$777$	−21.3793	−	28.7825i	−0.766979	−	1.03257i
$778$		0			0
$779$		−	22.5969i		−	0.809617i
$780$		0			0
$781$	25.4031			0.908995
$782$		0			0
$783$	−0.900960	+	0.900960i	−0.0321977	+	0.0321977i
$784$		0			0
$785$	4.50781	+	25.7016i	0.160891	+	0.917328i
$786$		0			0
$787$	3.30636	+	3.30636i	0.117859	+	0.117859i	0.763576	−	0.645717i	$-0.223442\pi$
$787$	3.30636	+	3.30636i	0.117859	+	0.117859i	−0.645717	+	0.763576i	$0.723442\pi$
$788$		0			0
$789$	45.4082			1.61657
$790$		0			0
$791$	23.3141	+	3.44080i	0.828953	+	0.122341i
$792$		0			0
$793$	−17.4031	−	17.4031i	−0.618003	−	0.618003i
$794$		0			0
$795$	33.5078	+	23.5078i	1.18840	+	0.833736i
$796$		0			0
$797$	16.8579	+	16.8579i	0.597137	+	0.597137i	0.939550	−	0.342413i	$-0.111244\pi$
$797$	16.8579	+	16.8579i	0.597137	+	0.597137i	−0.342413	+	0.939550i	$0.611244\pi$
$798$		0			0
$799$		−	11.8953i		−	0.420826i
$800$		0			0
$801$			50.1618i			1.77238i
$802$		0			0
$803$	−14.6441	+	14.6441i	−0.516779	+	0.516779i
$804$		0			0
$805$	−22.4840	−	21.2974i	−0.792458	−	0.750634i
$806$		0			0
$807$	−24.8062	+	24.8062i	−0.873221	+	0.873221i
$808$		0			0
$809$			19.2984i			0.678497i	0.940697	+	0.339248i	$0.110173\pi$
$809$			19.2984i			0.678497i	−0.940697	+	0.339248i	$0.889827\pi$
$810$		0			0
$811$		−	4.04429i		−	0.142014i	−0.997476	−	0.0710071i	$-0.977379\pi$
$811$		−	4.04429i		−	0.142014i	0.997476	−	0.0710071i	$-0.0226213\pi$
$812$		0			0
$813$	42.2094	+	42.2094i	1.48035	+	1.48035i
$814$		0			0
$815$	2.02214	+	11.5294i	0.0708326	+	0.403856i
$816$		0			0
$817$	23.7681	+	23.7681i	0.831540	+	0.831540i
$818$		0			0
$819$	25.0809	+	3.70156i	0.876398	+	0.129343i
$820$		0			0
$821$	52.3141			1.82577			0.912887	−	0.408213i	$-0.133848\pi$
$821$	52.3141			1.82577			0.912887	+	0.408213i	$0.133848\pi$
$822$		0			0
$823$	−10.1938	−	10.1938i	−0.355332	−	0.355332i	0.506757	−	0.862089i	$-0.330844\pi$
$823$	−10.1938	−	10.1938i	−0.355332	−	0.355332i	−0.862089	+	0.506757i	$0.830844\pi$
$824$		0			0
$825$	−55.1070	−	25.8188i	−1.91858	−	0.898896i
$826$		0			0
$827$	31.1047	−	31.1047i	1.08162	−	1.08162i	0.0852569	−	0.996359i	$-0.472829\pi$
$827$	31.1047	−	31.1047i	1.08162	−	1.08162i	0.996359	−	0.0852569i	$-0.0271711\pi$
$828$		0			0
$829$	−10.2166			−0.354836			−0.177418	−	0.984136i	$-0.556774\pi$
$829$	−10.2166			−0.354836			−0.177418	+	0.984136i	$0.556774\pi$
$830$		0			0
$831$		−	40.6546i		−	1.41029i
$832$		0			0
$833$	−6.43744	+	3.45306i	−0.223044	+	0.119641i
$834$		0			0
$835$	1.80625	+	10.2984i	0.0625078	+	0.356392i
$836$		0			0
$837$	−11.2984	+	11.2984i	−0.390531	+	0.390531i
$838$		0			0
$839$	35.1916			1.21495			0.607475	−	0.794339i	$-0.292183\pi$
$839$	35.1916			1.21495			0.607475	+	0.794339i	$0.292183\pi$
$840$		0			0
$841$	28.5078			0.983028
$842$		0			0
$843$	−49.2608	+	49.2608i	−1.69663	+	1.69663i
$844$		0			0
$845$	−8.08857	+	11.5294i	−0.278255	+	0.396623i
$846$		0			0
$847$	−23.5856	+	17.5191i	−0.810409	+	0.601964i
$848$		0			0
$849$			28.1047i			0.964550i
$850$		0			0
$851$	−27.4031			−0.939367
$852$		0			0
$853$	−23.9883	+	23.9883i	−0.821344	+	0.821344i	−0.986301	−	0.164957i	$-0.947252\pi$
$853$	−23.9883	+	23.9883i	−0.821344	+	0.821344i	0.164957	+	0.986301i	$0.447252\pi$
$854$		0			0
$855$	−22.5969	+	32.2094i	−0.772797	+	1.10154i
$856$		0			0
$857$	8.25161	+	8.25161i	0.281870	+	0.281870i	0.833854	−	0.551985i	$-0.186129\pi$
$857$	8.25161	+	8.25161i	0.281870	+	0.281870i	−0.551985	+	0.833854i	$0.686129\pi$
$858$		0			0
$859$	−27.1030			−0.924744			−0.462372	−	0.886686i	$-0.653002\pi$
$859$	−27.1030			−0.924744			−0.462372	+	0.886686i	$0.653002\pi$
$860$		0			0
$861$	−32.2094	−	4.75362i	−1.09769	−	0.162003i
$862$		0			0
$863$	12.4031	+	12.4031i	0.422207	+	0.422207i	0.885963	−	0.463756i	$-0.153498\pi$
$863$	12.4031	+	12.4031i	0.422207	+	0.422207i	−0.463756	+	0.885963i	$0.653498\pi$
$864$		0			0
$865$	20.5078	−	3.59688i	0.697286	−	0.122297i
$866$		0			0
$867$	−29.1252	−	29.1252i	−0.989143	−	0.989143i
$868$		0			0
$869$		−	31.5078i		−	1.06883i
$870$		0			0
$871$		−	18.3051i		−	0.620246i
$872$		0			0
$873$	−20.3273	+	20.3273i	−0.687974	+	0.687974i
$874$		0			0
$875$	−10.8165	−	27.5319i	−0.365664	−	0.930747i
$876$		0			0
$877$	39.8062	−	39.8062i	1.34416	−	1.34416i	0.452291	−	0.891870i	$-0.350607\pi$
$877$	39.8062	−	39.8062i	1.34416	−	1.34416i	0.891870	−	0.452291i	$-0.149393\pi$
$878$		0			0
$879$			28.1047i			0.947948i
$880$		0			0
$881$			27.1030i			0.913125i	0.889691	+	0.456562i	$0.150919\pi$
$881$			27.1030i			0.913125i	−0.889691	+	0.456562i	$0.849081\pi$
$882$		0			0
$883$	23.7016	+	23.7016i	0.797621	+	0.797621i	0.982720	−	0.185099i	$-0.0592605\pi$
$883$	23.7016	+	23.7016i	0.797621	+	0.797621i	−0.185099	+	0.982720i	$0.559261\pi$
$884$		0			0
$885$	27.1030	−	4.75362i	0.911059	−	0.159791i
$886$		0			0
$887$	0.872365	+	0.872365i	0.0292911	+	0.0292911i	0.721601	−	0.692310i	$-0.243407\pi$
$887$	0.872365	+	0.872365i	0.0292911	+	0.0292911i	−0.692310	+	0.721601i	$0.743407\pi$
$888$		0			0
$889$	−1.31281	+	8.89531i	−0.0440304	+	0.298339i
$890$		0			0
$891$	−30.1047			−1.00854
$892$		0			0
$893$	−38.3141	−	38.3141i	−1.28213	−	1.28213i
$894$		0			0
$895$	−11.3092	+	16.1200i	−0.378023	+	0.538831i
$896$		0			0
$897$	24.8062	−	24.8062i	0.828257	−	0.828257i
$898$		0			0
$899$	−6.17228			−0.205857
$900$		0			0
$901$		−	7.37925i		−	0.245838i
$902$		0			0
$903$	38.8788	−	28.8788i	1.29381	−	0.961026i
$904$		0			0
$905$	18.3141	−	26.1047i	0.608780	−	0.867749i
$906$		0			0
$907$	−18.5078	+	18.5078i	−0.614542	+	0.614542i	−0.944126	−	0.329584i	$-0.893091\pi$
$907$	−18.5078	+	18.5078i	−0.614542	+	0.614542i	0.329584	+	0.944126i	$0.393091\pi$
$908$		0			0
$909$	−17.5958			−0.583616
$910$		0			0
$911$	−10.5969			−0.351090			−0.175545	−	0.984471i	$-0.556169\pi$
$911$	−10.5969			−0.351090			−0.175545	+	0.984471i	$0.556169\pi$
$912$		0			0
$913$	−36.9935	+	36.9935i	−1.22431	+	1.22431i
$914$		0			0
$915$	−9.50723	−	54.2061i	−0.314299	−	1.79200i
$916$		0			0
$917$	6.38040	+	8.58978i	0.210700	+	0.283659i
$918$		0			0
$919$		−	22.9109i		−	0.755762i	−0.925854	−	0.377881i	$-0.876653\pi$
$919$		−	22.9109i		−	0.755762i	0.925854	−	0.377881i	$-0.123347\pi$
$920$		0			0
$921$	−34.9109			−1.15035
$922$		0			0
$923$	−9.89049	+	9.89049i	−0.325550	+	0.325550i
$924$		0			0
$925$	−23.7016	−	11.1047i	−0.779303	−	0.365120i
$926$		0			0
$927$	10.8200	+	10.8200i	0.355377	+	0.355377i
$928$		0			0
$929$	−2.12799			−0.0698171			−0.0349085	−	0.999391i	$-0.511114\pi$
$929$	−2.12799			−0.0698171			−0.0349085	+	0.999391i	$0.511114\pi$
$930$		0			0
$931$	−9.61250	+	31.8567i	−0.315037	+	1.04406i
$932$		0			0
$933$	−16.1047	−	16.1047i	−0.527244	−	0.527244i
$934$		0			0
$935$	1.89531	+	10.8062i	0.0619834	+	0.353402i
$936$		0			0
$937$	40.6260	+	40.6260i	1.32719	+	1.32719i	0.907809	+	0.419383i	$0.137754\pi$
$937$	40.6260	+	40.6260i	1.32719	+	1.32719i	0.419383	+	0.907809i	$0.362246\pi$
$938$		0			0
$939$		−	41.5078i		−	1.35456i
$940$		0			0
$941$		−	46.1175i		−	1.50339i	−0.659512	−	0.751694i	$-0.729237\pi$
$941$		−	46.1175i		−	1.50339i	0.659512	−	0.751694i	$-0.270763\pi$
$942$		0			0
$943$	−17.5958	+	17.5958i	−0.572998	+	0.572998i
$944$		0			0
$945$	7.80060	+	7.38891i	0.253754	+	0.240361i
$946$		0			0
$947$	−15.0000	+	15.0000i	−0.487435	+	0.487435i	−0.907496	−	0.420061i	$-0.862009\pi$
$947$	−15.0000	+	15.0000i	−0.487435	+	0.487435i	0.420061	+	0.907496i	$0.362009\pi$
$948$		0			0
$949$		−	11.4031i		−	0.370161i
$950$		0			0
$951$			45.4082i			1.47246i
$952$		0			0
$953$	39.8062	+	39.8062i	1.28945	+	1.28945i	0.935120	+	0.354331i	$0.115291\pi$
$953$	39.8062	+	39.8062i	1.28945	+	1.28945i	0.354331	+	0.935120i	$0.384709\pi$
$954$		0			0
$955$	−3.85266	−	2.70288i	−0.124669	−	0.0874631i
$956$		0			0
$957$	6.03784	+	6.03784i	0.195176	+	0.195176i
$958$		0			0
$959$	2.02214	−	13.7016i	0.0652984	−	0.442447i
$960$		0			0
$961$	−46.4031			−1.49687
$962$		0			0
$963$	−8.89531	−	8.89531i	−0.286647	−	0.286647i
$964$		0			0
$965$	−0.603484	−	3.44080i	−0.0194268	−	0.110763i
$966$		0			0
$967$	25.0000	−	25.0000i	0.803946	−	0.803946i	−0.179764	−	0.983710i	$-0.557533\pi$
$967$	25.0000	−	25.0000i	0.803946	−	0.803946i	0.983710	+	0.179764i	$0.0575334\pi$
$968$		0			0
$969$	12.8422			0.412551
$970$		0			0
$971$		−	54.9154i		−	1.76232i	−0.472819	−	0.881160i	$-0.656763\pi$
$971$		−	54.9154i		−	1.76232i	0.472819	−	0.881160i	$-0.343237\pi$
$972$		0			0
$973$	37.3722	−	27.7597i	1.19810	−	0.889936i
$974$		0			0
$975$	31.5078	−	11.4031i	1.00906	−	0.365192i
$976$		0			0
$977$	−32.4031	+	32.4031i	−1.03667	+	1.03667i	−0.0373661	+	0.999302i	$0.511897\pi$
$977$	−32.4031	+	32.4031i	−1.03667	+	1.03667i	−0.999302	+	0.0373661i	$0.988103\pi$
$978$		0			0
$979$	63.7133			2.03629
$980$		0			0
$981$	−12.2094			−0.389815
$982$		0			0
$983$	−12.4303	+	12.4303i	−0.396466	+	0.396466i	−0.876985	−	0.480518i	$-0.840449\pi$
$983$	−12.4303	+	12.4303i	−0.396466	+	0.396466i	0.480518	+	0.876985i	$0.340449\pi$
$984$		0			0
$985$	7.48509	−	1.31281i	0.238495	−	0.0418297i
$986$		0			0
$987$	−62.6725	+	46.5525i	−1.99489	+	1.48178i
$988$		0			0
$989$		−	37.0156i		−	1.17703i
$990$		0			0
$991$	−17.6125			−0.559479			−0.279740	−	0.960076i	$-0.590248\pi$
$991$	−17.6125			−0.559479			−0.279740	+	0.960076i	$0.590248\pi$
$992$		0			0
$993$	17.2125	−	17.2125i	0.546224	−	0.546224i
$994$		0			0
$995$	40.9109	+	28.7016i	1.29696	+	0.909901i
$996$		0			0
$997$	−2.15658	−	2.15658i	−0.0682997	−	0.0682997i	0.672132	−	0.740432i	$-0.265379\pi$
$997$	−2.15658	−	2.15658i	−0.0682997	−	0.0682997i	−0.740432	+	0.672132i	$0.765379\pi$
$998$		0			0
$999$	9.50723			0.300796

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.m.a.13.4	yes	8
3.2	odd	2		1260.2.ba.a.433.1		8
4.3	odd	2		560.2.bj.b.433.1		8
5.2	odd	4	inner	140.2.m.a.97.1	yes	8
5.3	odd	4		700.2.m.c.657.4		8
5.4	even	2		700.2.m.c.293.1		8
7.2	even	3		980.2.v.b.913.4		16
7.3	odd	6		980.2.v.b.313.4		16
7.4	even	3		980.2.v.b.313.1		16
7.5	odd	6		980.2.v.b.913.1		16
7.6	odd	2	inner	140.2.m.a.13.1	✓	8
15.2	even	4		1260.2.ba.a.937.4		8
20.7	even	4		560.2.bj.b.97.4		8
21.20	even	2		1260.2.ba.a.433.4		8
28.27	even	2		560.2.bj.b.433.4		8
35.2	odd	12		980.2.v.b.717.4		16
35.12	even	12		980.2.v.b.717.1		16
35.13	even	4		700.2.m.c.657.1		8
35.17	even	12		980.2.v.b.117.4		16
35.27	even	4	inner	140.2.m.a.97.4	yes	8
35.32	odd	12		980.2.v.b.117.1		16
35.34	odd	2		700.2.m.c.293.4		8
105.62	odd	4		1260.2.ba.a.937.1		8
140.27	odd	4		560.2.bj.b.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.m.a.13.1	✓	8	7.6	odd	2	inner
140.2.m.a.13.4	yes	8	1.1	even	1	trivial
140.2.m.a.97.1	yes	8	5.2	odd	4	inner
140.2.m.a.97.4	yes	8	35.27	even	4	inner
560.2.bj.b.97.1		8	140.27	odd	4
560.2.bj.b.97.4		8	20.7	even	4
560.2.bj.b.433.1		8	4.3	odd	2
560.2.bj.b.433.4		8	28.27	even	2
700.2.m.c.293.1		8	5.4	even	2
700.2.m.c.293.4		8	35.34	odd	2
700.2.m.c.657.1		8	35.13	even	4
700.2.m.c.657.4		8	5.3	odd	4
980.2.v.b.117.1		16	35.32	odd	12
980.2.v.b.117.4		16	35.17	even	12
980.2.v.b.313.1		16	7.4	even	3
980.2.v.b.313.4		16	7.3	odd	6
980.2.v.b.717.1		16	35.12	even	12
980.2.v.b.717.4		16	35.2	odd	12
980.2.v.b.913.1		16	7.5	odd	6
980.2.v.b.913.4		16	7.2	even	3
1260.2.ba.a.433.1		8	3.2	odd	2
1260.2.ba.a.433.4		8	21.20	even	2
1260.2.ba.a.937.1		8	105.62	odd	4
1260.2.ba.a.937.4		8	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.83051 - 1.83051i) q^{3} +(1.83051 + 1.28422i) q^{5} +(-2.12393 + 1.57763i) q^{7} -3.70156i q^{9} +O(q^{10})\)	\(q+(1.83051 - 1.83051i) q^{3} +(1.83051 + 1.28422i) q^{5} +(-2.12393 + 1.57763i) q^{7} -3.70156i q^{9} -4.70156 q^{11} +(1.83051 - 1.83051i) q^{13} +(5.70156 - 1.00000i) q^{15} +(-0.737925 - 0.737925i) q^{17} -4.75362 q^{19} +(-1.00000 + 6.77576i) q^{21} +(3.70156 + 3.70156i) q^{23} +(1.70156 + 4.70156i) q^{25} +(-1.28422 - 1.28422i) q^{27} -0.701562i q^{29} -8.79790i q^{31} +(-8.60627 + 8.60627i) q^{33} +(-5.91391 + 0.160291i) q^{35} +(-3.70156 + 3.70156i) q^{37} -6.70156i q^{39} +4.75362i q^{41} +(-5.00000 - 5.00000i) q^{43} +(4.75362 - 6.77576i) q^{45} +(8.05998 + 8.05998i) q^{47} +(2.02214 - 6.70156i) q^{49} -2.70156 q^{51} +(5.00000 + 5.00000i) q^{53} +(-8.60627 - 6.03784i) q^{55} +(-8.70156 + 8.70156i) q^{57} +4.75362 q^{59} -9.50723i q^{61} +(5.83971 + 7.86185i) q^{63} +(5.70156 - 1.00000i) q^{65} +(5.00000 - 5.00000i) q^{67} +13.5515 q^{69} -5.40312 q^{71} +(3.11473 - 3.11473i) q^{73} +(11.7210 + 5.49154i) q^{75} +(9.98578 - 7.41734i) q^{77} +6.70156i q^{79} +6.40312 q^{81} +(7.86835 - 7.86835i) q^{83} +(-0.403124 - 2.29844i) q^{85} +(-1.28422 - 1.28422i) q^{87} -13.5515 q^{89} +(-1.00000 + 6.77576i) q^{91} +(-16.1047 - 16.1047i) q^{93} +(-8.70156 - 6.10469i) q^{95} +(-5.49154 - 5.49154i) q^{97} +17.4031i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{7}+O(q^{10}) \) 8 * q - 2 * q^7	\( 8 q - 2 q^{7} - 12 q^{11} + 20 q^{15} - 8 q^{21} + 4 q^{23} - 12 q^{25} - 14 q^{35} - 4 q^{37} - 40 q^{43} + 4 q^{51} + 40 q^{53} - 44 q^{57} + 42 q^{63} + 20 q^{65} + 40 q^{67} + 8 q^{71} + 44 q^{77} + 48 q^{85} - 8 q^{91} - 52 q^{93} - 44 q^{95}+O(q^{100}) \) 8 * q - 2 * q^7 - 12 * q^11 + 20 * q^15 - 8 * q^21 + 4 * q^23 - 12 * q^25 - 14 * q^35 - 4 * q^37 - 40 * q^43 + 4 * q^51 + 40 * q^53 - 44 * q^57 + 42 * q^63 + 20 * q^65 + 40 * q^67 + 8 * q^71 + 44 * q^77 + 48 * q^85 - 8 * q^91 - 52 * q^93 - 44 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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