LMFDB - Embedded newform 690.2.w.b.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	690.7
Dual form			690.2.w.b.493.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 - 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.40926 - 1.73608i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.26240 - 2.31192i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 - 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.40926 - 1.73608i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.26240 - 2.31192i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-1.52952 - 1.63113i) q^{10} +(-3.41960 + 2.96310i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(4.05636 - 2.21494i) q^{13} +(1.09425 - 2.39608i) q^{14} +(-1.99597 + 1.00802i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.81116 - 3.75527i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(0.166109 + 1.15532i) q^{19} +(-1.64199 - 1.51786i) q^{20} +(-1.99074 - 1.72498i) q^{21} +(-3.19951 + 3.19951i) q^{22} +(-0.0981907 - 4.79483i) q^{23} -1.00000i q^{24} +(-1.02798 + 4.89319i) q^{25} +(3.88801 - 2.49867i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(0.920532 - 2.46804i) q^{28} +(-1.94866 - 0.280175i) q^{29} +(-1.91897 + 1.14784i) q^{30} +(1.55826 + 1.00144i) q^{31} +(0.936950 - 0.349464i) q^{32} +(2.16850 + 3.97131i) q^{33} +(-3.07189 - 3.54515i) q^{34} +(-5.79273 + 1.06645i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-4.10060 - 10.9941i) q^{37} +(0.248105 + 1.14052i) q^{38} +(-1.30208 - 4.43448i) q^{39} +(-1.74608 - 1.39685i) q^{40} +(4.03813 + 8.84228i) q^{41} +(-2.10872 - 1.57857i) q^{42} +(0.304775 + 0.0662997i) q^{43} +(-2.96310 + 3.41960i) q^{44} +(0.560711 + 2.16463i) q^{45} +(-0.439999 - 4.77560i) q^{46} +(3.83051 + 3.83051i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(0.0331903 + 0.0516451i) q^{49} +(-0.676284 + 4.95405i) q^{50} +(-4.26700 + 1.94867i) q^{51} +(3.69985 - 2.76968i) q^{52} +(7.71569 + 4.21309i) q^{53} +(-0.540641 + 0.841254i) q^{54} +(9.96330 + 1.76094i) q^{55} +(0.742118 - 2.52742i) q^{56} +(1.16422 + 0.0832668i) q^{57} +(-1.96369 - 0.140446i) q^{58} +(0.914088 - 3.11310i) q^{59} +(-1.83220 + 1.28182i) q^{60} +(7.55752 - 11.7597i) q^{61} +(1.62574 + 0.887719i) q^{62} +(-2.10872 + 1.57857i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-9.56178 - 3.92076i) q^{65} +(2.44628 + 3.80649i) q^{66} +(0.841611 + 11.7673i) q^{67} +(-3.31697 - 3.31697i) q^{68} +(-4.70612 - 0.923267i) q^{69} +(-5.70189 + 1.47698i) q^{70} +(7.31113 - 8.43750i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(-0.684298 - 0.512259i) q^{73} +(-4.87447 - 10.6736i) q^{74} +(4.56285 + 2.04461i) q^{75} +(0.328837 + 1.11992i) q^{76} +(2.53353 + 11.6465i) q^{77} +(-1.61511 - 4.33029i) q^{78} +(6.01121 + 1.76505i) q^{79} +(-1.84129 - 1.26873i) q^{80} +(0.654861 + 0.755750i) q^{81} +(4.65865 + 8.53167i) q^{82} +(9.32162 - 3.47678i) q^{83} +(-2.21597 - 1.42411i) q^{84} +(-2.55781 + 10.1726i) q^{85} +(0.308728 + 0.0443884i) q^{86} +(-0.687991 + 1.84457i) q^{87} +(-2.71160 + 3.62228i) q^{88} +(-11.9217 + 7.66163i) q^{89} +(0.713705 + 2.11911i) q^{90} -12.1741i q^{91} +(-0.779566 - 4.73205i) q^{92} +(1.30978 - 1.30978i) q^{93} +(4.09402 + 3.54749i) q^{94} +(1.77163 - 1.91652i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(9.37574 + 3.49697i) q^{97} +(0.0367900 + 0.0491457i) q^{98} +(4.34150 - 1.27478i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−1.40926	−	1.73608i	−0.630240	−	0.776401i
$5$	−1.40926	−	1.73608i	−0.630240	−	0.776401i
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	1.26240	−	2.31192i	0.477143	−	0.873822i	−0.522631	−	0.852559i	$-0.675049\pi$
$7$	1.26240	−	2.31192i	0.477143	−	0.873822i	0.999774	−	0.0212629i	$-0.00676871\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	−1.52952	−	1.63113i	−0.483676	−	0.515807i
$11$	−3.41960	+	2.96310i	−1.03105	+	0.893409i	−0.994375	−	0.105918i	$-0.966222\pi$
$11$	−3.41960	+	2.96310i	−1.03105	+	0.893409i	−0.0366743	+	0.999327i	$0.511676\pi$
$12$	0.0713392	−	0.997452i	0.0205938	−	0.287940i
$13$	4.05636	−	2.21494i	1.12503	−	0.614314i	0.194638	−	0.980875i	$-0.437647\pi$
$13$	4.05636	−	2.21494i	1.12503	−	0.614314i	0.930394	+	0.366561i	$0.119465\pi$
$14$	1.09425	−	2.39608i	0.292452	−	0.640380i
$15$	−1.99597	+	1.00802i	−0.515357	+	0.260270i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−2.81116	−	3.75527i	−0.681806	−	0.910786i	0.317492	−	0.948261i	$-0.397159\pi$
$17$	−2.81116	−	3.75527i	−0.681806	−	0.910786i	−0.999298	+	0.0374749i	$0.988069\pi$
$18$	−0.936950	−	0.349464i	−0.220841	−	0.0823695i
$19$	0.166109	+	1.15532i	0.0381081	+	0.265047i	0.999964	−	0.00850979i	$-0.00270878\pi$
$19$	0.166109	+	1.15532i	0.0381081	+	0.265047i	−0.961856	+	0.273557i	$0.911800\pi$
$20$	−1.64199	−	1.51786i	−0.367159	−	0.339403i
$21$	−1.99074	−	1.72498i	−0.434415	−	0.376422i
$22$	−3.19951	+	3.19951i	−0.682137	+	0.682137i
$23$	−0.0981907	−	4.79483i	−0.0204742	−	0.999790i
$23$	−0.0981907	−	4.79483i	−0.0204742	−	0.999790i
$24$		−	1.00000i		−	0.204124i
$25$	−1.02798	+	4.89319i	−0.205596	+	0.978637i
$26$	3.88801	−	2.49867i	0.762502	−	0.490030i
$27$	−0.599278	+	0.800541i	−0.115331	+	0.154064i
$28$	0.920532	−	2.46804i	0.173964	−	0.466416i
$29$	−1.94866	−	0.280175i	−0.361858	−	0.0520273i	−0.0410116	−	0.999159i	$-0.513058\pi$
$29$	−1.94866	−	0.280175i	−0.361858	−	0.0520273i	−0.320846	+	0.947131i	$0.603967\pi$
$30$	−1.91897	+	1.14784i	−0.350355	+	0.209567i
$31$	1.55826	+	1.00144i	0.279872	+	0.179863i	0.673045	−	0.739602i	$-0.264986\pi$
$31$	1.55826	+	1.00144i	0.279872	+	0.179863i	−0.393172	+	0.919465i	$0.628622\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	2.16850	+	3.97131i	0.377487	+	0.691316i
$34$	−3.07189	−	3.54515i	−0.526825	−	0.607989i
$35$	−5.79273	+	1.06645i	−0.979150	+	0.180263i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	−4.10060	−	10.9941i	−0.674135	−	1.80743i	−0.584408	−	0.811460i	$-0.698673\pi$
$37$	−4.10060	−	10.9941i	−0.674135	−	1.80743i	−0.0897272	−	0.995966i	$-0.528600\pi$
$38$	0.248105	+	1.14052i	0.0402480	+	0.185017i
$39$	−1.30208	−	4.43448i	−0.208500	−	0.710085i
$40$	−1.74608	−	1.39685i	−0.276080	−	0.220861i
$41$	4.03813	+	8.84228i	0.630651	+	1.38093i	0.907514	+	0.420023i	$0.137978\pi$
$41$	4.03813	+	8.84228i	0.630651	+	1.38093i	−0.276863	+	0.960909i	$0.589295\pi$
$42$	−2.10872	−	1.57857i	−0.325383	−	0.243579i
$43$	0.304775	+	0.0662997i	0.0464777	+	0.0101106i	0.235744	−	0.971815i	$-0.424247\pi$
$43$	0.304775	+	0.0662997i	0.0464777	+	0.0101106i	−0.189266	+	0.981926i	$0.560611\pi$
$44$	−2.96310	+	3.41960i	−0.446705	+	0.515525i
$45$	0.560711	+	2.16463i	0.0835859	+	0.322683i
$46$	−0.439999	−	4.77560i	−0.0648744	−	0.704125i
$47$	3.83051	+	3.83051i	0.558737	+	0.558737i	0.928948	−	0.370210i	$-0.120714\pi$
$47$	3.83051	+	3.83051i	0.558737	+	0.558737i	−0.370210	+	0.928948i	$0.620714\pi$
$48$	−0.0713392	−	0.997452i	−0.0102969	−	0.143970i
$49$	0.0331903	+	0.0516451i	0.00474147	+	0.00737787i
$50$	−0.676284	+	4.95405i	−0.0956409	+	0.700609i
$51$	−4.26700	+	1.94867i	−0.597500	+	0.272869i
$52$	3.69985	−	2.76968i	0.513077	−	0.384085i
$53$	7.71569	+	4.21309i	1.05983	+	0.578712i	0.911953	−	0.410294i	$-0.134574\pi$
$53$	7.71569	+	4.21309i	1.05983	+	0.578712i	0.147878	+	0.989006i	$0.452756\pi$
$54$	−0.540641	+	0.841254i	−0.0735719	+	0.114480i
$55$	9.96330	+	1.76094i	1.34345	+	0.237445i
$56$	0.742118	−	2.52742i	0.0991698	−	0.337741i
$57$	1.16422	+	0.0832668i	0.154205	+	0.0110290i
$58$	−1.96369	−	0.140446i	−0.257844	−	0.0184414i
$59$	0.914088	−	3.11310i	0.119004	−	0.405291i	−0.878347	−	0.478023i	$-0.841354\pi$
$59$	0.914088	−	3.11310i	0.119004	−	0.405291i	0.997352	+	0.0727321i	$0.0231718\pi$
$60$	−1.83220	+	1.28182i	−0.236536	+	0.165482i
$61$	7.55752	−	11.7597i	0.967641	−	1.50568i	0.108400	−	0.994107i	$-0.465427\pi$
$61$	7.55752	−	11.7597i	0.967641	−	1.50568i	0.859241	−	0.511571i	$-0.170936\pi$
$62$	1.62574	+	0.887719i	0.206469	+	0.112740i
$63$	−2.10872	+	1.57857i	−0.265674	+	0.198881i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−9.56178	−	3.92076i	−1.18599	−	0.486310i
$66$	2.44628	+	3.80649i	0.301117	+	0.468547i
$67$	0.841611	+	11.7673i	0.102819	+	1.43760i	0.742956	+	0.669340i	$0.233423\pi$
$67$	0.841611	+	11.7673i	0.102819	+	1.43760i	−0.640137	+	0.768261i	$0.721123\pi$
$68$	−3.31697	−	3.31697i	−0.402242	−	0.402242i
$69$	−4.70612	−	0.923267i	−0.566550	−	0.111148i
$70$	−5.70189	+	1.47698i	−0.681506	+	0.176533i
$71$	7.31113	−	8.43750i	0.867672	−	1.00135i	−0.132277	−	0.991213i	$-0.542229\pi$
$71$	7.31113	−	8.43750i	0.867672	−	1.00135i	0.999949	−	0.0101341i	$-0.00322583\pi$
$72$	−0.977147	−	0.212565i	−0.115158	−	0.0250511i
$73$	−0.684298	−	0.512259i	−0.0800910	−	0.0599554i	0.558482	−	0.829517i	$-0.311384\pi$
$73$	−0.684298	−	0.512259i	−0.0800910	−	0.0599554i	−0.638573	+	0.769561i	$0.720475\pi$
$74$	−4.87447	−	10.6736i	−0.566646	−	1.24078i
$75$	4.56285	+	2.04461i	0.526872	+	0.236091i
$76$	0.328837	+	1.11992i	0.0377202	+	0.128463i
$77$	2.53353	+	11.6465i	0.288723	+	1.32724i
$78$	−1.61511	−	4.33029i	−0.182876	−	0.490309i
$79$	6.01121	+	1.76505i	0.676313	+	0.198584i	0.601813	−	0.798637i	$-0.294445\pi$
$79$	6.01121	+	1.76505i	0.676313	+	0.198584i	0.0745010	+	0.997221i	$0.476264\pi$
$80$	−1.84129	−	1.26873i	−0.205862	−	0.141848i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	4.65865	+	8.53167i	0.514461	+	0.942166i
$83$	9.32162	−	3.47678i	1.02318	−	0.381627i	0.218818	−	0.975766i	$-0.429780\pi$
$83$	9.32162	−	3.47678i	1.02318	−	0.381627i	0.804362	+	0.594139i	$0.202507\pi$
$84$	−2.21597	−	1.42411i	−0.241782	−	0.155384i
$85$	−2.55781	+	10.1726i	−0.277434	+	1.10337i
$86$	0.308728	+	0.0443884i	0.0332910	+	0.00478652i
$87$	−0.687991	+	1.84457i	−0.0737603	+	0.197759i
$88$	−2.71160	+	3.62228i	−0.289058	+	0.386136i
$89$	−11.9217	+	7.66163i	−1.26370	+	0.812131i	−0.988786	−	0.149338i	$-0.952286\pi$
$89$	−11.9217	+	7.66163i	−1.26370	+	0.812131i	−0.274914	+	0.961469i	$0.588649\pi$
$90$	0.713705	+	2.11911i	0.0752312	+	0.223374i
$91$		−	12.1741i		−	1.27619i
$92$	−0.779566	−	4.73205i	−0.0812754	−	0.493350i
$93$	1.30978	−	1.30978i	0.135818	−	0.135818i
$94$	4.09402	+	3.54749i	0.422266	+	0.365895i
$95$	1.77163	−	1.91652i	0.181766	−	0.196631i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	9.37574	+	3.49697i	0.951962	+	0.355063i	0.776992	−	0.629510i	$-0.216744\pi$
$97$	9.37574	+	3.49697i	0.951962	+	0.355063i	0.174970	+	0.984574i	$0.444017\pi$
$98$	0.0367900	+	0.0491457i	0.00371635	+	0.00496447i
$99$	4.34150	−	1.27478i	0.436337	−	0.128120i
$100$	−0.321142	+	4.98968i	−0.0321142	+	0.498968i
$101$	−7.10678	+	15.5617i	−0.707151	+	1.54844i	0.123929	+	0.992291i	$0.460451\pi$
$101$	−7.10678	+	15.5617i	−0.707151	+	1.54844i	−0.831080	+	0.556154i	$0.812277\pi$
$102$	−4.11711	+	2.24811i	−0.407655	+	0.222596i
$103$	−1.01142	+	14.1415i	−0.0996579	+	1.39340i	0.663978	+	0.747752i	$0.268867\pi$
$103$	−1.01142	+	14.1415i	−0.0996579	+	1.39340i	−0.763636	+	0.645647i	$0.776588\pi$
$104$	3.49284	−	3.02656i	0.342501	−	0.296779i
$105$	−0.189253	+	5.88704i	−0.0184692	+	0.574516i
$106$	7.99659	+	3.65192i	0.776697	+	0.354706i
$107$	0.444094	−	0.0966067i	0.0429322	−	0.00933932i	−0.191048	−	0.981581i	$-0.561189\pi$
$107$	0.444094	−	0.0966067i	0.0429322	−	0.00933932i	0.233980	+	0.972241i	$0.424825\pi$
$108$	−0.479249	+	0.877679i	−0.0461158	+	0.0844547i
$109$	−0.469544	+	3.26575i	−0.0449742	+	0.312802i	0.954900	+	0.296928i	$0.0959622\pi$
$109$	−0.469544	+	3.26575i	−0.0449742	+	0.312802i	−0.999874	+	0.0158740i	$0.994947\pi$
$110$	10.0635	+	1.04568i	0.959521	+	0.0997017i
$111$	−11.6145	+	1.66992i	−1.10240	+	0.158502i
$112$	0.559923	−	2.57393i	0.0529078	−	0.243213i
$113$	−6.24707	+	0.446800i	−0.587675	+	0.0420314i	−0.362011	−	0.932174i	$-0.617910\pi$
$113$	−6.24707	+	0.446800i	−0.587675	+	0.0420314i	−0.225664	+	0.974205i	$0.572455\pi$
$114$	1.16720			0.109318
$115$	−8.18585	+	6.92762i	−0.763334	+	0.646004i
$116$	−1.96870			−0.182789
$117$	−4.60991	+	0.329708i	−0.426187	+	0.0304815i
$118$	0.689673	−	3.17037i	0.0634895	−	0.291857i
$119$	−12.2307	+	1.75850i	−1.12118	+	0.161202i
$120$	−1.73608	+	1.40926i	−0.158482	+	0.128647i
$121$	1.34824	−	9.37724i	0.122568	−	0.852476i
$122$	6.69933	−	12.2689i	0.606529	−	1.11077i
$123$	9.49857	−	2.06629i	0.856457	−	0.186311i
$124$	1.68492	+	0.769478i	0.151310	+	0.0691012i
$125$	9.94367	−	5.11111i	0.889389	−	0.457151i
$126$	−1.99074	+	1.72498i	−0.177349	+	0.153674i
$127$	0.503228	−	7.03605i	0.0446543	−	0.624349i	−0.925015	−	0.379930i	$-0.875948\pi$
$127$	0.503228	−	7.03605i	0.0446543	−	0.624349i	0.969670	−	0.244419i	$-0.0785972\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	0.129569	−	0.283717i	0.0114079	−	0.0249799i
$130$	−9.81713	−	3.22864i	−0.861019	−	0.283170i
$131$	12.0699	−	3.54404i	1.05455	−	0.309644i	0.291896	−	0.956450i	$-0.405714\pi$
$131$	12.0699	−	3.54404i	1.05455	−	0.309644i	0.762655	+	0.646806i	$0.223896\pi$
$132$	2.71160	+	3.62228i	0.236015	+	0.315279i
$133$	2.88069	+	1.07444i	0.249787	+	0.0931658i
$134$	1.67893	+	11.6772i	0.145038	+	1.00876i
$135$	2.23434	−	0.0877732i	0.192302	−	0.00755432i
$136$	−3.54515	−	3.07189i	−0.303994	−	0.263413i
$137$	10.5237	−	10.5237i	0.899102	−	0.899102i	−0.0962547	−	0.995357i	$-0.530686\pi$
$137$	10.5237	−	10.5237i	0.899102	−	0.899102i	0.995357	+	0.0962547i	$0.0306863\pi$
$138$	−4.76000	−	0.585184i	−0.405198	−	0.0498141i
$139$		−	0.618374i		−	0.0524498i	−0.999656	−	0.0262249i	$-0.991651\pi$
$139$		−	0.618374i		−	0.0524498i	0.999656	−	0.0262249i	$-0.00834860\pi$
$140$	−5.58200	+	1.87999i	−0.471765	+	0.158888i
$141$	4.55721	−	2.92874i	0.383786	−	0.246644i
$142$	6.69058	−	8.93757i	0.561461	−	0.750024i
$143$	−7.30805	+	19.5936i	−0.611129	+	1.63850i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	2.25976	+	3.77788i	0.187663	+	0.313736i
$146$	−0.719098	−	0.462136i	−0.0595130	−	0.0382467i
$147$	0.0575199	−	0.0214538i	0.00474416	−	0.00176948i
$148$	−5.62350	−	10.2987i	−0.462249	−	0.846545i
$149$	−11.4446	−	13.2078i	−0.937581	−	1.08203i	−0.996486	−	0.0837626i	$-0.973306\pi$
$149$	−11.4446	−	13.2078i	−0.937581	−	1.08203i	0.0589047	−	0.998264i	$-0.481239\pi$
$150$	4.69708	+	1.71389i	0.383515	+	0.139938i
$151$	9.34558	+	2.74411i	0.760532	+	0.223312i	0.638928	−	0.769266i	$-0.279378\pi$
$151$	9.34558	+	2.74411i	0.760532	+	0.223312i	0.121604	+	0.992579i	$0.461196\pi$
$152$	0.407893	+	1.09360i	0.0330845	+	0.0887030i
$153$	0.997125	+	4.58371i	0.0806128	+	0.370571i
$154$	3.35793	+	11.4360i	0.270589	+	0.921543i
$155$	−0.457421	−	4.11656i	−0.0367409	−	0.330650i
$156$	−1.91992	−	4.20404i	−0.153717	−	0.336592i
$157$	−11.0467	−	8.26943i	−0.881620	−	0.659973i	0.0594327	−	0.998232i	$-0.481071\pi$
$157$	−11.0467	−	8.26943i	−0.881620	−	0.659973i	−0.941053	+	0.338260i	$0.890162\pi$
$158$	6.12181	+	1.33172i	0.487025	+	0.105946i
$159$	5.75689	−	6.64381i	0.456551	−	0.526888i
$160$	−1.92710	−	1.13414i	−0.152351	−	0.0896615i
$161$	−11.2092	−	5.82599i	−0.883408	−	0.459152i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	1.03593	+	14.4841i	0.0811400	+	1.13448i	0.861025	+	0.508562i	$0.169823\pi$
$163$	1.03593	+	14.4841i	0.0811400	+	1.13448i	−0.779885	+	0.625923i	$0.784723\pi$
$164$	5.25542	+	8.17759i	0.410379	+	0.638563i
$165$	3.83855	−	9.36130i	0.298831	−	0.728776i
$166$	9.04984	−	4.13292i	0.702404	−	0.320777i
$167$	0.106099	−	0.0794245i	0.00821017	−	0.00614605i	−0.595165	−	0.803604i	$-0.702913\pi$
$167$	0.106099	−	0.0794245i	0.00821017	−	0.00614605i	0.603375	+	0.797458i	$0.293822\pi$
$168$	−2.31192	−	1.26240i	−0.178368	−	0.0973964i
$169$	4.51976	−	7.03289i	0.347674	−	0.540992i
$170$	−1.82559	+	10.3291i	−0.140017	+	0.792206i
$171$	0.328837	−	1.11992i	0.0251468	−	0.0856421i
$172$	0.311108	+	0.0222509i	0.0237218	+	0.00169661i
$173$	2.00177	+	0.143169i	0.152192	+	0.0108850i	0.147227	−	0.989103i	$-0.452965\pi$
$173$	2.00177	+	0.143169i	0.152192	+	0.0108850i	0.00496464	+	0.999988i	$0.498420\pi$
$174$	−0.554647	+	1.88895i	−0.0420477	+	0.143201i
$175$	10.0149	+	8.55376i	0.757056	+	0.646604i
$176$	−2.44628	+	3.80649i	−0.184396	+	0.286925i
$177$	−2.84765	−	1.55493i	−0.214042	−	0.116876i
$178$	−11.3448	+	8.49259i	−0.850327	+	0.636547i
$179$	−14.8957	+	6.80265i	−1.11336	+	0.508454i	−0.885219	−	0.465174i	$-0.845992\pi$
$179$	−14.8957	+	6.80265i	−1.11336	+	0.508454i	−0.228140	+	0.973628i	$0.573264\pi$
$180$	0.863063	+	2.06279i	0.0643289	+	0.153752i
$181$	4.84436	+	7.53796i	0.360078	+	0.560293i	0.973276	−	0.229636i	$-0.0737537\pi$
$181$	4.84436	+	7.53796i	0.360078	+	0.560293i	−0.613198	+	0.789929i	$0.710117\pi$
$182$	−0.868491	−	12.1431i	−0.0643768	−	0.900105i
$183$	−9.88451	−	9.88451i	−0.730684	−	0.730684i
$184$	−1.11516	−	4.66438i	−0.0822107	−	0.343862i
$185$	−13.3080	+	22.6126i	−0.978420	+	1.66251i
$186$	1.21301	−	1.39988i	0.0889419	−	0.102644i
$187$	20.7403	+	4.51177i	1.51668	+	0.329934i
$188$	4.33666	+	3.24638i	0.316283	+	0.236767i
$189$	1.09425	+	2.39608i	0.0795953	+	0.174289i
$190$	1.63040	−	2.03802i	0.118281	−	0.147854i
$191$	2.19534	+	7.47664i	0.158849	+	0.540990i	1.00000		0.000189880i	$6.04406e-5\pi$
$191$	2.19534	+	7.47664i	0.158849	+	0.540990i	−0.841151	+	0.540801i	$0.818121\pi$
$192$	−0.212565	−	0.977147i	−0.0153406	−	0.0705195i
$193$	−1.64454	−	4.40917i	−0.118376	−	0.317379i	0.864225	−	0.503105i	$-0.167809\pi$
$193$	−1.64454	−	4.40917i	−0.118376	−	0.317379i	−0.982602	+	0.185726i	$0.940536\pi$
$194$	9.60132	+	2.81920i	0.689335	+	0.202407i
$195$	−5.86366	+	8.50985i	−0.419905	+	0.609403i
$196$	0.0402023	+	0.0463959i	0.00287159	+	0.00331399i
$197$	−3.78409	−	6.93004i	−0.269605	−	0.493745i	0.707441	−	0.706772i	$-0.249849\pi$
$197$	−3.78409	−	6.93004i	−0.269605	−	0.493745i	−0.977046	+	0.213027i	$0.931668\pi$
$198$	4.23949	−	1.58125i	0.301288	−	0.112375i
$199$	13.4732	+	8.65867i	0.955087	+	0.613797i	0.922634	−	0.385676i	$-0.126032\pi$
$199$	13.4732	+	8.65867i	0.955087	+	0.613797i	0.0324527	+	0.999473i	$0.489668\pi$
$200$	0.0356353	+	4.99987i	0.00251979	+	0.353544i
$201$	11.6772	+	1.67893i	0.823649	+	0.118423i
$202$	−5.97851	+	16.0290i	−0.420647	+	1.12780i
$203$	−3.10774	+	4.15145i	−0.218120	+	0.291375i
$204$	−3.94625	+	2.53610i	−0.276292	+	0.177562i
$205$	9.66017	−	19.4716i	0.674695	−	1.35996i
$206$			14.1776i			0.987799i
$207$	−1.90253	+	4.40232i	−0.132235	+	0.305982i
$208$	3.26803	−	3.26803i	0.226597	−	0.226597i
$209$	−3.99135	−	3.45852i	−0.276087	−	0.239231i
$210$	0.231206	+	5.88554i	0.0159547	+	0.406141i
$211$	0.301358	+	2.09599i	0.0207464	+	0.144294i	0.997562	−	0.0697893i	$-0.0222327\pi$
$211$	0.301358	+	2.09599i	0.0207464	+	0.144294i	−0.976815	+	0.214083i	$0.931324\pi$
$212$	8.23674	+	3.07215i	0.565702	+	0.210996i
$213$	−6.69058	−	8.93757i	−0.458431	−	0.612392i
$214$	0.436071	−	0.128042i	0.0298092	−	0.00875276i
$215$	−0.314405	−	0.622548i	−0.0214422	−	0.0424574i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	4.28239	−	2.33836i	0.290707	−	0.158738i
$218$	−0.235372	+	3.29093i	−0.0159414	+	0.222890i
$219$	−0.646010	+	0.559771i	−0.0436533	+	0.0378258i
$220$	10.1125	+	0.325091i	0.681785	+	0.0219176i
$221$	−19.7208	−	9.00617i	−1.32656	−	0.605821i
$222$	−11.4658	+	2.49424i	−0.769535	+	0.167402i
$223$	−3.76562	+	6.89622i	−0.252165	+	0.461805i	−0.972843	−	0.231464i	$-0.925648\pi$
$223$	−3.76562	+	6.89622i	−0.252165	+	0.461805i	0.720679	+	0.693269i	$0.243830\pi$
$224$	0.374875	−	2.60731i	0.0250474	−	0.174208i
$225$	2.96778	−	4.02396i	0.197852	−	0.268264i
$226$	−6.19928	+	0.891322i	−0.412370	+	0.0592899i
$227$	−6.07540	+	27.9282i	−0.403239	+	1.85366i	0.107902	+	0.994162i	$0.465587\pi$
$227$	−6.07540	+	27.9282i	−0.403239	+	1.85366i	−0.511141	+	0.859497i	$0.670777\pi$
$228$	1.16422	−	0.0832668i	0.0771025	−	0.00551448i
$229$	−25.4851			−1.68410			−0.842052	−	0.539396i	$-0.818653\pi$
$229$	−25.4851			−1.68410			−0.842052	+	0.539396i	$0.818653\pi$
$230$	−7.67078	+	7.49394i	−0.505796	+	0.494136i
$231$	11.9188			0.784202
$232$	−1.96369	+	0.140446i	−0.128922	+	0.00922070i
$233$	2.13183	−	9.79988i	0.139661	−	0.642012i	−0.853084	−	0.521774i	$-0.825271\pi$
$233$	2.13183	−	9.79988i	0.139661	−	0.642012i	0.992745	−	0.120238i	$-0.0383658\pi$
$234$	−4.57465	+	0.657735i	−0.299054	+	0.0429975i
$235$	1.25191	−	12.0483i	0.0816655	−	0.785943i
$236$	0.461744	−	3.21150i	0.0300570	−	0.209051i
$237$	3.00249	−	5.49864i	0.195032	−	0.357175i
$238$	−12.0741	+	2.62655i	−0.782645	+	0.170254i
$239$	−5.35058	−	2.44353i	−0.346100	−	0.158059i	0.234778	−	0.972049i	$-0.424564\pi$
$239$	−5.35058	−	2.44353i	−0.346100	−	0.158059i	−0.580879	+	0.813990i	$0.697291\pi$
$240$	−1.63113	+	1.52952i	−0.105289	+	0.0987300i
$241$	13.4756	−	11.6767i	0.868038	−	0.752160i	−0.102084	−	0.994776i	$-0.532551\pi$
$241$	13.4756	−	11.6767i	0.868038	−	0.752160i	0.970122	+	0.242616i	$0.0780056\pi$
$242$	0.675844	−	9.44953i	0.0434449	−	0.607439i
$243$	0.877679	−	0.479249i	0.0563031	−	0.0307438i
$244$	5.80701	−	12.7156i	0.371756	−	0.814031i
$245$	0.0428865	−	0.130402i	0.00273992	−	0.00833110i
$246$	9.32696	−	2.73864i	0.594665	−	0.174610i
$247$	3.23275	+	4.31845i	0.205695	+	0.274777i
$248$	1.73552	+	0.647317i	0.110206	+	0.0411047i
$249$	−1.41588	−	9.84764i	−0.0897275	−	0.624069i
$250$	9.55371	−	5.80746i	0.604230	−	0.367296i
$251$	−11.3900	−	9.86949i	−0.718930	−	0.622957i	0.216576	−	0.976266i	$-0.430511\pi$
$251$	−11.3900	−	9.86949i	−0.718930	−	0.622957i	−0.935507	+	0.353309i	$0.885056\pi$
$252$	−1.86261	+	1.86261i	−0.117333	+	0.117333i
$253$	14.5433	+	16.1055i	0.914332	+	1.01254i
$254$		−	7.05402i		−	0.442609i
$255$	9.39638	+	4.66169i	0.588424	+	0.291926i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	12.6644	−	16.9176i	0.789983	−	1.05529i	−0.207051	−	0.978330i	$-0.566387\pi$
$257$	12.6644	−	16.9176i	0.789983	−	1.05529i	0.997034	−	0.0769631i	$-0.0245224\pi$
$258$	0.108999	−	0.292237i	0.00678597	−	0.0181939i
$259$	−30.5941	−	4.39877i	−1.90103	−	0.273326i
$260$	−10.0224	−	2.52007i	−0.621565	−	0.156288i
$261$	1.65618	+	1.06436i	0.102515	+	0.0658822i
$262$	11.7863	−	4.39606i	0.728160	−	0.271590i
$263$	10.8711	+	19.9089i	0.670339	+	1.22763i	0.962504	+	0.271266i	$0.0874422\pi$
$263$	10.8711	+	19.9089i	0.670339	+	1.22763i	−0.292166	+	0.956368i	$0.594376\pi$
$264$	2.96310	+	3.41960i	0.182366	+	0.210462i
$265$	−3.55913	−	19.3324i	−0.218636	−	1.18758i
$266$	2.95000	+	0.866197i	0.180876	+	0.0531100i
$267$	4.95239	+	13.2779i	0.303081	+	0.812593i
$268$	2.50770	+	11.5277i	0.153182	+	0.704167i
$269$	−6.02633	−	20.5238i	−0.367432	−	1.25136i	−0.911145	−	0.412086i	$-0.864800\pi$
$269$	−6.02633	−	20.5238i	−0.367432	−	1.25136i	0.543713	−	0.839271i	$-0.317018\pi$
$270$	2.22239	−	0.246946i	0.135250	−	0.0150287i
$271$	1.22330	+	2.67865i	0.0743101	+	0.162716i	0.943141	−	0.332392i	$-0.107856\pi$
$271$	1.22330	+	2.67865i	0.0743101	+	0.162716i	−0.868831	+	0.495108i	$0.835128\pi$
$272$	−3.75527	−	2.81116i	−0.227697	−	0.170452i
$273$	−11.8959	−	2.58779i	−0.719972	−	0.156620i
$274$	9.74615	−	11.2477i	0.588787	−	0.679496i
$275$	−10.9837	−	19.7788i	−0.662344	−	1.19270i
$276$	−4.78961	−	0.244118i	−0.288301	−	0.0146942i
$277$	−18.6413	−	18.6413i	−1.12004	−	1.12004i	−0.991734	−	0.128311i	$-0.959045\pi$
$277$	−18.6413	−	18.6413i	−1.12004	−	1.12004i	−0.128311	−	0.991734i	$-0.540955\pi$
$278$	−0.0441143	−	0.616798i	−0.00264580	−	0.0369931i
$279$	−1.00144	−	1.55826i	−0.0599544	−	0.0932908i
$280$	−5.43366	+	2.27341i	−0.324723	+	0.135862i
$281$	−5.88889	+	2.68937i	−0.351302	+	0.160434i	−0.583247	−	0.812295i	$-0.698218\pi$
$281$	−5.88889	+	2.68937i	−0.351302	+	0.160434i	0.231945	+	0.972729i	$0.425491\pi$
$282$	4.33666	−	3.24638i	0.258244	−	0.193319i
$283$	−22.6027	−	12.3420i	−1.34359	−	0.733657i	−0.363387	−	0.931638i	$-0.618380\pi$
$283$	−22.6027	−	12.3420i	−1.34359	−	0.733657i	−0.980206	+	0.197981i	$0.936562\pi$
$284$	6.03594	−	9.39210i	0.358167	−	0.557319i
$285$	−1.49613	−	2.13853i	−0.0886232	−	0.126676i
$286$	−5.89163	+	20.0651i	−0.348380	+	1.18647i
$287$	25.5403	+	1.82668i	1.50760	+	0.107826i
$288$	−0.997452	−	0.0713392i	−0.0587754	−	0.00420370i
$289$	−1.40997	+	4.80192i	−0.0829395	+	0.282466i
$290$	2.52352	+	3.60705i	0.148186	+	0.211813i
$291$	5.41001	−	8.41814i	0.317140	−	0.493480i
$292$	−0.750234	−	0.409659i	−0.0439042	−	0.0239735i
$293$	−18.1982	+	13.6230i	−1.06315	+	0.795864i	−0.979664	−	0.200645i	$-0.935696\pi$
$293$	−18.1982	+	13.6230i	−1.06315	+	0.795864i	−0.0834858	+	0.996509i	$0.526605\pi$
$294$	0.0558429	−	0.0255026i	0.00325682	−	0.00148734i
$295$	−6.69278	+	2.80023i	−0.389669	+	0.163035i
$296$	−6.34387	−	9.87125i	−0.368730	−	0.573755i
$297$	−0.322794	−	4.51326i	−0.0187304	−	0.261886i
$298$	−12.3577	−	12.3577i	−0.715863	−	0.715863i
$299$	−11.0185	−	19.2321i	−0.637219	−	1.11222i
$300$	4.80738	+	1.37444i	0.277554	+	0.0793531i
$301$	0.538028	−	0.620917i	0.0310114	−	0.0357891i
$302$	9.51753	+	2.07041i	0.547672	+	0.119139i
$303$	13.6954	+	10.2522i	0.786780	+	0.588976i
$304$	0.484871	+	1.06172i	0.0278092	+	0.0608937i
$305$	−31.0664	+	3.45201i	−1.77886	+	0.197662i
$306$	1.32158	+	4.50090i	0.0755498	+	0.257299i
$307$	3.89832	+	17.9203i	0.222489	+	1.02277i	0.943893	+	0.330251i	$0.107133\pi$
$307$	3.89832	+	17.9203i	0.222489	+	1.02277i	−0.721404	+	0.692514i	$0.756503\pi$
$308$	4.16521	+	11.1674i	0.237335	+	0.636319i
$309$	13.6033	+	3.99429i	0.773864	+	0.227227i
$310$	−0.749927	−	4.07344i	−0.0425930	−	0.231356i
$311$	14.3057	+	16.5097i	0.811203	+	0.936179i	0.998940	−	0.0460408i	$-0.0146604\pi$
$311$	14.3057	+	16.5097i	0.811203	+	0.936179i	−0.187736	+	0.982220i	$0.560115\pi$
$312$	−2.21494	−	4.05636i	−0.125396	−	0.229646i
$313$	2.68796	−	1.00256i	0.151933	−	0.0566680i	−0.272347	−	0.962199i	$-0.587800\pi$
$313$	2.68796	−	1.00256i	0.151933	−	0.0566680i	0.424280	+	0.905531i	$0.360527\pi$
$314$	−11.6085	−	7.46030i	−0.655103	−	0.421009i
$315$	5.71227	+	1.43631i	0.321850	+	0.0809268i
$316$	6.20121	+	0.891600i	0.348845	+	0.0501564i
$317$	−1.35566	+	3.63466i	−0.0761412	+	0.204143i	−0.969444	−	0.245313i	$-0.921109\pi$
$317$	−1.35566	+	3.63466i	−0.0761412	+	0.204143i	0.893303	+	0.449456i	$0.148382\pi$
$318$	5.26826	−	7.03757i	0.295429	−	0.394647i
$319$	7.49384	−	4.81600i	0.419575	−	0.269644i
$320$	−2.00310	−	0.993771i	−0.111977	−	0.0555535i
$321$		−	0.454480i		−	0.0253666i
$322$	−11.5962	−	5.01149i	−0.646234	−	0.279279i
$323$	3.87156	−	3.87156i	0.215419	−	0.215419i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	6.66826	+	22.1254i	0.369889	+	1.22730i
$326$	2.06657	+	14.3733i	0.114457	+	0.796065i
$327$	3.09131	+	1.15300i	0.170950	+	0.0637610i
$328$	5.82541	+	7.78184i	0.321655	+	0.429680i
$329$	13.6915	−	4.02018i	0.754835	−	0.221639i
$330$	3.16094	−	9.61128i	0.174004	−	0.529084i
$331$	8.04460	−	17.6152i	0.442171	−	0.968220i	−0.549023	−	0.835807i	$-0.685000\pi$
$331$	8.04460	−	17.6152i	0.442171	−	0.968220i	0.991195	−	0.132413i	$-0.0422726\pi$
$332$	8.73194	−	4.76800i	0.479228	−	0.261678i
$333$	−0.837092	+	11.7041i	−0.0458724	+	0.641380i
$334$	0.100162	−	0.0867912i	0.00548064	−	0.00474900i
$335$	19.2429	−	18.0442i	1.05135	−	0.985862i
$336$	−2.39608	−	1.09425i	−0.130717	−	0.0596965i
$337$	−27.7597	+	6.03875i	−1.51217	+	0.328952i	−0.890738	−	0.454518i	$-0.849812\pi$
$337$	−27.7597	+	6.03875i	−1.51217	+	0.328952i	−0.621430	+	0.783470i	$0.713448\pi$
$338$	4.00653	−	7.33741i	0.217926	−	0.399102i
$339$	−0.891322	+	6.19928i	−0.0484100	+	0.336699i
$340$	−1.08407	+	10.4330i	−0.0587921	+	0.565810i
$341$	−8.29600	+	1.19278i	−0.449254	+	0.0645929i
$342$	0.248105	−	1.14052i	0.0134160	−	0.0616723i
$343$	18.5532	−	1.32695i	1.00178	−	0.0716486i
$344$	0.311903			0.0168167
$345$	5.02927	+	9.47135i	0.270767	+	0.509920i
$346$	2.00688			0.107891
$347$	−10.8188	+	0.773779i	−0.580786	+	0.0415387i	−0.358642	−	0.933475i	$-0.616760\pi$
$347$	−10.8188	+	0.773779i	−0.580786	+	0.0415387i	−0.222144	+	0.975014i	$0.571306\pi$
$348$	−0.418478	+	1.92371i	−0.0224327	+	0.103122i
$349$	−10.7522	+	1.54593i	−0.575552	+	0.0827518i	−0.423943	−	0.905689i	$-0.639354\pi$
$349$	−10.7522	+	1.54593i	−0.575552	+	0.0827518i	−0.151608	+	0.988441i	$0.548445\pi$
$350$	10.5996	+	7.81751i	0.566573	+	0.417864i
$351$	−0.657735	+	4.57465i	−0.0351073	+	0.244177i
$352$	−2.16850	+	3.97131i	−0.115581	+	0.211671i
$353$	15.8844	−	3.45543i	0.845440	−	0.183914i	0.231075	−	0.972936i	$-0.425776\pi$
$353$	15.8844	−	3.45543i	0.845440	−	0.183914i	0.614365	+	0.789022i	$0.289412\pi$
$354$	−2.95132	−	1.34782i	−0.156861	−	0.0716360i
$355$	−24.9515	−	0.802126i	−1.32429	−	0.0425724i
$356$	−10.7100	+	9.28028i	−0.567630	+	0.491854i
$357$	−0.881498	+	12.3250i	−0.0466538	+	0.652306i
$358$	−14.3725	+	7.84797i	−0.759609	+	0.414778i
$359$	4.16390	−	9.11768i	0.219762	−	0.481213i	−0.767352	−	0.641226i	$-0.778426\pi$
$359$	4.16390	−	9.11768i	0.219762	−	0.481213i	0.987115	+	0.160013i	$0.0511536\pi$
$360$	1.00802	+	1.99597i	0.0531274	+	0.105197i
$361$	16.9232	−	4.96910i	0.890695	−	0.261532i
$362$	5.36977	+	7.17317i	0.282229	+	0.377013i
$363$	−8.87635	−	3.31071i	−0.465888	−	0.173767i
$364$	−1.73256	−	12.0502i	−0.0908106	−	0.631601i
$365$	0.0750280	+	1.90990i	0.00392715	+	0.0999689i
$366$	−10.5645	−	9.15417i	−0.552214	−	0.478496i
$367$	0.654177	−	0.654177i	0.0341478	−	0.0341478i	−0.689827	−	0.723974i	$-0.742313\pi$
$367$	0.654177	−	0.654177i	0.0341478	−	0.0341478i	0.723974	+	0.689827i	$0.242313\pi$
$368$	−1.44507	−	4.57294i	−0.0753296	−	0.238381i
$369$		−	9.72072i		−	0.506041i
$370$	−11.6609	+	23.5044i	−0.606220	+	1.22193i
$371$	19.4806	−	12.5194i	1.01138	−	0.649976i
$372$	1.11005	−	1.48285i	0.0575534	−	0.0768823i
$373$	11.3662	−	30.4739i	0.588518	−	1.57788i	−0.211161	−	0.977451i	$-0.567724\pi$
$373$	11.3662	−	30.4739i	0.588518	−	1.57788i	0.799679	−	0.600427i	$-0.205003\pi$
$374$	21.0093	+	3.02068i	1.08637	+	0.156196i
$375$	−2.88062	−	10.8029i	−0.148755	−	0.557858i
$376$	4.55721	+	2.92874i	0.235020	+	0.151038i
$377$	−8.52505	+	3.17968i	−0.439062	+	0.163762i
$378$	1.26240	+	2.31192i	0.0649309	+	0.118912i
$379$	−18.0203	−	20.7966i	−0.925642	−	1.06825i	−0.997488	−	0.0708316i	$-0.977435\pi$
$379$	−18.0203	−	20.7966i	−0.925642	−	1.06825i	0.0718468	−	0.997416i	$-0.477111\pi$
$380$	1.48085	−	2.14914i	0.0759661	−	0.110249i
$381$	−6.76829	−	1.98735i	−0.346750	−	0.101815i
$382$	2.72312	+	7.30097i	0.139327	+	0.373550i
$383$	−7.19431	−	33.0717i	−0.367612	−	1.68989i	−0.674608	−	0.738176i	$-0.735688\pi$
$383$	−7.19431	−	33.0717i	−0.367612	−	1.68989i	0.306996	−	0.951711i	$-0.400676\pi$
$384$	−0.281733	−	0.959493i	−0.0143771	−	0.0489639i
$385$	16.6488	−	20.8113i	0.848503	−	1.06064i
$386$	−1.95489	−	4.28062i	−0.0995014	−	0.217878i
$387$	−0.249691	−	0.186916i	−0.0126925	−	0.00950149i
$388$	9.77798	+	2.12707i	0.496402	+	0.107986i
$389$	6.61191	−	7.63055i	0.335237	−	0.386884i	−0.562955	−	0.826488i	$-0.690335\pi$
$389$	6.61191	−	7.63055i	0.335237	−	0.386884i	0.898192	+	0.439603i	$0.144881\pi$
$390$	−5.24164	+	8.90648i	−0.265421	+	0.450997i
$391$	−17.7298	+	13.8477i	−0.896636	+	0.700311i
$392$	0.0434097	+	0.0434097i	0.00219252	+	0.00219252i
$393$	−0.897407	−	12.5474i	−0.0452682	−	0.632932i
$394$	−4.26883	−	6.64243i	−0.215061	−	0.334641i
$395$	−5.40707	−	12.9234i	−0.272059	−	0.650245i
$396$	4.11589	−	1.87966i	0.206831	−	0.0944566i
$397$	−25.5806	+	19.1494i	−1.28385	+	0.961081i	−0.283856	+	0.958867i	$0.591614\pi$
$397$	−25.5806	+	19.1494i	−1.28385	+	0.961081i	−0.999998	+	0.00221370i	$0.999295\pi$
$398$	14.0565	+	7.67545i	0.704590	+	0.384735i
$399$	1.66222	−	2.58647i	0.0832151	−	0.129485i
$400$	0.392231	+	4.98459i	0.0196116	+	0.249230i
$401$	−1.37408	+	4.67969i	−0.0686183	+	0.233693i	−0.986661	−	0.162789i	$-0.947951\pi$
$401$	−1.37408	+	4.67969i	−0.0686183	+	0.233693i	0.918043	+	0.396482i	$0.129769\pi$
$402$	11.7673	+	0.841611i	0.586898	+	0.0419758i
$403$	8.53900	+	0.610721i	0.425358	+	0.0304222i
$404$	−4.81979	+	16.4147i	−0.239793	+	0.816661i
$405$	0.389177	−	2.20194i	0.0193383	−	0.109415i
$406$	−2.80366	+	4.36258i	−0.139143	+	0.216511i
$407$	46.5992	+	25.4451i	2.30984	+	1.26127i
$408$	−3.75527	+	2.81116i	−0.185913	+	0.139173i
$409$	−11.4633	+	5.23509i	−0.566822	+	0.258859i	−0.678148	−	0.734925i	$-0.737217\pi$
$409$	−11.4633	+	5.23509i	−0.566822	+	0.258859i	0.111327	+	0.993784i	$0.464490\pi$
$410$	8.24647	−	20.1111i	0.407264	−	0.993218i
$411$	−8.04624	−	12.5202i	−0.396892	−	0.617576i
$412$	1.01142	+	14.1415i	0.0498289	+	0.696700i
$413$	−6.04327	−	6.04327i	−0.297370	−	0.297370i
$414$	−1.58362	+	4.52683i	−0.0778307	+	0.222481i
$415$	−19.1726	−	11.2834i	−0.941144	−	0.553882i
$416$	3.02656	−	3.49284i	0.148389	−	0.171251i
$417$	−0.604242	−	0.131445i	−0.0295899	−	0.00643688i
$418$	−4.22790	−	3.16497i	−0.206794	−	0.154804i
$419$	0.511535	+	1.12011i	0.0249901	+	0.0547208i	0.921715	−	0.387867i	$-0.126788\pi$
$419$	0.511535	+	1.12011i	0.0249901	+	0.0547208i	−0.896725	+	0.442587i	$0.854061\pi$
$420$	0.650486	+	5.85405i	0.0317405	+	0.285648i
$421$	−2.89748	−	9.86790i	−0.141214	−	0.480932i	0.858265	−	0.513207i	$-0.171543\pi$
$421$	−2.89748	−	9.86790i	−0.141214	−	0.480932i	−0.999479	+	0.0322753i	$0.989725\pi$
$422$	0.450117	+	2.06915i	0.0219113	+	0.100725i
$423$	−1.89310	−	5.07561i	−0.0920459	−	0.246784i
$424$	8.43492	+	2.47672i	0.409636	+	0.120280i
$425$	21.2650	−	9.89518i	1.03151	−	0.479987i
$426$	−7.31113	−	8.43750i	−0.354226	−	0.408798i
$427$	−17.6469	−	32.3178i	−0.853992	−	1.56397i
$428$	0.425825	−	0.158825i	0.0205830	−	0.00767708i
$429$	17.5924	+	11.3060i	0.849370	+	0.545857i
$430$	−0.358016	−	0.598533i	−0.0172651	−	0.0288638i
$431$	20.5071	+	2.94848i	0.987794	+	0.142023i	0.617229	−	0.786783i	$-0.288255\pi$
$431$	20.5071	+	2.94848i	0.987794	+	0.142023i	0.370565	+	0.928807i	$0.379164\pi$
$432$	−0.349464	+	0.936950i	−0.0168136	+	0.0450790i
$433$	2.47490	−	3.30608i	0.118936	−	0.158880i	−0.737122	−	0.675760i	$-0.763816\pi$
$433$	2.47490	−	3.30608i	0.118936	−	0.158880i	0.856058	+	0.516880i	$0.172907\pi$
$434$	4.10466	−	2.63791i	0.197030	−	0.126624i
$435$	4.17189	−	1.40507i	0.200027	−	0.0673681i
$436$			3.29933i			0.158009i
$437$	5.52323	−	0.909906i	0.264212	−	0.0435267i
$438$	−0.604430	+	0.604430i	−0.0288808	+	0.0288808i
$439$	7.81634	+	6.77289i	0.373053	+	0.323253i	0.821129	−	0.570743i	$-0.193345\pi$
$439$	7.81634	+	6.77289i	0.373053	+	0.323253i	−0.448075	+	0.893996i	$0.647890\pi$
$440$	10.1099	−	0.397155i	0.481972	−	0.0189336i
$441$	−0.00873679	−	0.0607657i	−0.000416038	−	0.00289361i
$442$	−20.3130	−	7.57636i	−0.966191	−	0.360371i
$443$	12.2820	+	16.4068i	0.583534	+	0.779510i	0.991022	−	0.133701i	$-0.0426860\pi$
$443$	12.2820	+	16.4068i	0.583534	+	0.779510i	−0.407488	+	0.913211i	$0.633595\pi$
$444$	−11.2587	+	3.30584i	−0.534313	+	0.156888i
$445$	30.1020	+	9.89991i	1.42697	+	0.469301i
$446$	−3.26406	+	7.14729i	−0.154558	+	0.338434i
$447$	−15.3387	+	8.37557i	−0.725496	+	0.396151i
$448$	0.187916	−	2.62741i	0.00887821	−	0.124134i
$449$	−2.94267	+	2.54984i	−0.138873	+	0.120334i	−0.721527	−	0.692386i	$-0.756560\pi$
$449$	−2.94267	+	2.54984i	−0.138873	+	0.120334i	0.582654	+	0.812720i	$0.302014\pi$
$450$	2.67316	−	4.22543i	0.126014	−	0.199189i
$451$	−40.0094	−	18.2717i	−1.88397	−	0.860380i
$452$	−6.11990	+	1.33130i	−0.287856	+	0.0626192i
$453$	4.66794	−	8.54870i	0.219319	−	0.401653i
$454$	−4.06755	+	28.2904i	−0.190900	+	1.32774i
$455$	−21.1353	+	17.1565i	−0.990837	+	0.804307i
$456$	1.15532	−	0.166109i	0.0541026	−	0.00777878i
$457$	−6.84106	+	31.4478i	−0.320011	+	1.47107i	0.483272	+	0.875470i	$0.339448\pi$
$457$	−6.84106	+	31.4478i	−0.320011	+	1.47107i	−0.803283	+	0.595597i	$0.796915\pi$
$458$	−25.4202	+	1.81809i	−1.18781	+	0.0849537i
$459$	4.69091			0.218953
$460$	−7.11662	+	8.02207i	−0.331814	+	0.374031i
$461$	−23.9834			−1.11702			−0.558508	−	0.829499i	$-0.688626\pi$
$461$	−23.9834			−1.11702			−0.558508	+	0.829499i	$0.688626\pi$
$462$	11.8885	−	0.850280i	0.553102	−	0.0395586i
$463$	−1.35808	+	6.24301i	−0.0631155	+	0.290137i	−0.997876	−	0.0651410i	$-0.979250\pi$
$463$	−1.35808	+	6.24301i	−0.0631155	+	0.290137i	0.934761	+	0.355278i	$0.115614\pi$
$464$	−1.94866	+	0.280175i	−0.0904644	+	0.0130068i
$465$	−4.11972	−	0.428070i	−0.191047	−	0.0198513i
$466$	1.42729	−	9.92700i	0.0661178	−	0.459859i
$467$	6.87683	−	12.5940i	0.318222	−	0.582780i	−0.668785	−	0.743455i	$-0.733186\pi$
$467$	6.87683	−	12.5940i	0.318222	−	0.582780i	0.987007	+	0.160676i	$0.0513673\pi$
$468$	−4.51607	+	0.982411i	−0.208755	+	0.0454120i
$469$	28.2674	+	12.9093i	1.30527	+	0.596095i
$470$	0.389205	−	12.1069i	0.0179527	−	0.558449i
$471$	−10.4286	+	9.03642i	−0.480524	+	0.416376i
$472$	0.231462	−	3.23626i	0.0106539	−	0.148961i
$473$	−1.23866	+	0.676361i	−0.0569537	+	0.0310991i
$474$	2.60257	−	5.69883i	0.119540	−	0.261756i
$475$	−5.82393	−	0.374836i	−0.267220	−	0.0171987i
$476$	−11.8559	+	3.48121i	−0.543415	+	0.159561i
$477$	−5.26826	−	7.03757i	−0.241217	−	0.322228i
$478$	−5.51127	−	2.05560i	−0.252080	−	0.0940208i
$479$	0.385202	+	2.67914i	0.0176003	+	0.122413i	0.996727	−	0.0808360i	$-0.0257590\pi$
$479$	0.385202	+	2.67914i	0.0176003	+	0.122413i	−0.979127	+	0.203249i	$0.934850\pi$
$480$	−1.51786	+	1.64199i	−0.0692803	+	0.0749460i
$481$	−40.9849	−	35.5136i	−1.86875	−	1.61928i
$482$	12.6082	−	12.6082i	0.574290	−	0.574290i
$483$	−8.07553	+	9.71462i	−0.367449	+	0.442031i
$484$		−	9.47367i		−	0.430621i
$485$	−7.14181	−	21.2052i	−0.324293	−	0.962879i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	−7.14348	+	9.54258i	−0.323702	+	0.432415i	−0.932643	−	0.360800i	$-0.882504\pi$
$487$	−7.14348	+	9.54258i	−0.323702	+	0.432415i	0.608941	+	0.793215i	$0.291595\pi$
$488$	4.88509	−	13.0974i	0.221138	−	0.592893i
$489$	14.3733	+	2.06657i	0.649984	+	0.0934536i
$490$	0.0334744	−	0.133130i	0.00151222	−	0.00601418i
$491$	−10.3173	−	6.63055i	−0.465615	−	0.299232i	0.286719	−	0.958015i	$-0.407435\pi$
$491$	−10.3173	−	6.63055i	−0.465615	−	0.299232i	−0.752334	+	0.658782i	$0.771072\pi$
$492$	9.10783	−	3.39704i	0.410613	−	0.153151i
$493$	4.42587	+	8.10537i	0.199331	+	0.365047i
$494$	3.53259	+	4.07683i	0.158939	+	0.183425i
$495$	−8.33142	−	5.74071i	−0.374469	−	0.258026i
$496$	1.77728	+	0.521857i	0.0798022	+	0.0234321i
$497$	−10.2772	−	27.5542i	−0.460995	−	1.23598i
$498$	−2.11479	−	9.72154i	−0.0947661	−	0.435633i
$499$	8.40131	+	28.6122i	0.376094	+	1.28086i	0.902523	+	0.430641i	$0.141712\pi$
$499$	8.40131	+	28.6122i	0.376094	+	1.28086i	−0.526429	+	0.850219i	$0.676469\pi$
$500$	9.11507	−	6.47422i	0.407638	−	0.289536i
$501$	−0.0550565	−	0.120557i	−0.00245974	−	0.00538609i
$502$	−12.0651	−	9.03179i	−0.538490	−	0.403108i
$503$	−12.6183	−	2.74495i	−0.562623	−	0.122391i	−0.0777457	−	0.996973i	$-0.524772\pi$
$503$	−12.6183	−	2.74495i	−0.562623	−	0.122391i	−0.484878	+	0.874582i	$0.661136\pi$
$504$	−1.72498	+	1.99074i	−0.0768369	+	0.0886745i
$505$	37.0317	−	9.59246i	1.64789	−	0.426859i
$506$	15.6552	+	15.0269i	0.695960	+	0.668028i
$507$	−5.91142	−	5.91142i	−0.262535	−	0.262535i
$508$	−0.503228	−	7.03605i	−0.0223271	−	0.312174i
$509$	19.9307	+	31.0127i	0.883412	+	1.37462i	0.926799	+	0.375557i	$0.122549\pi$
$509$	19.9307	+	31.0127i	0.883412	+	1.37462i	−0.0433878	+	0.999058i	$0.513815\pi$
$510$	9.70500	+	3.97948i	0.429744	+	0.176214i
$511$	−2.04816	+	0.935362i	−0.0906051	+	0.0413780i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	−1.02442	−	0.559377i	−0.0452294	−	0.0246971i
$514$	11.4252	−	17.7780i	0.503945	−	0.784154i
$515$	25.9761	−	18.1731i	1.14464	−	0.800801i
$516$	0.0878732	−	0.299269i	0.00386840	−	0.0131746i
$517$	−24.4490	−	1.74863i	−1.07527	−	0.0769046i
$518$	−30.8300	−	2.20500i	−1.35459	−	0.0968824i
$519$	0.565405	−	1.92559i	0.0248185	−	0.0845241i
$520$	−10.1767	−	1.79865i	−0.446277	−	0.0788762i
$521$	−15.8799	+	24.7096i	−0.695711	+	1.08255i	0.296140	+	0.955144i	$0.404300\pi$
$521$	−15.8799	+	24.7096i	−0.695711	+	1.08255i	−0.991851	+	0.127403i	$0.959336\pi$
$522$	1.72789	+	0.943498i	0.0756276	+	0.0412958i
$523$	−7.85071	+	5.87697i	−0.343288	+	0.256982i	−0.756985	−	0.653433i	$-0.773328\pi$
$523$	−7.85071	+	5.87697i	−0.343288	+	0.256982i	0.413697	+	0.910415i	$0.364237\pi$
$524$	11.4427	−	5.22569i	0.499875	−	0.228285i
$525$	10.4871	−	7.96780i	0.457695	−	0.347743i
$526$	12.2636	+	19.0826i	0.534720	+	0.832041i
$527$	−0.619868	−	8.66689i	−0.0270019	−	0.377536i
$528$	3.19951	+	3.19951i	0.139241	+	0.139241i
$529$	−22.9807	+	0.941614i	−0.999162	+	0.0409398i
$530$	−4.92922	−	19.0293i	−0.214112	−	0.826578i
$531$	−2.12471	+	2.45205i	−0.0922046	+	0.106410i
$532$	3.00427	+	0.653540i	0.130252	+	0.0283346i
$533$	35.9652	+	26.9232i	1.55783	+	1.16618i
$534$	5.88701	+	12.8907i	0.254756	+	0.557837i
$535$	−0.793561	−	0.634841i	−0.0343086	−	0.0274466i
$536$	3.32369	+	11.3194i	0.143562	+	0.488926i
$537$	3.48087	+	16.0013i	0.150211	+	0.690508i
$538$	−7.47512	−	20.0416i	−0.322275	−	0.864054i
$539$	−0.266527	−	0.0782594i	−0.0114801	−	0.00337087i
$540$	2.19911	−	0.404860i	0.0946347	−	0.0174224i
$541$	3.54518	+	4.09135i	0.152419	+	0.175901i	0.826824	−	0.562461i	$-0.190145\pi$
$541$	3.54518	+	4.09135i	0.152419	+	0.175901i	−0.674405	+	0.738362i	$0.735600\pi$
$542$	1.41127	+	2.58456i	0.0606194	+	0.111016i
$543$	8.39544	−	3.13134i	0.360283	−	0.134379i
$544$	−3.94625	−	2.53610i	−0.169194	−	0.108734i
$545$	6.33133	−	3.78712i	0.271204	−	0.162222i
$546$	−12.0502	−	1.73256i	−0.515700	−	0.0741465i
$547$	−2.78435	+	7.46514i	−0.119050	+	0.319186i	−0.982783	−	0.184764i	$-0.940848\pi$
$547$	−2.78435	+	7.46514i	−0.119050	+	0.319186i	0.863733	+	0.503951i	$0.168121\pi$
$548$	8.91892	−	11.9143i	0.380997	−	0.508953i
$549$	−11.7597	+	7.55752i	−0.501893	+	0.322547i
$550$	−12.3667	−	18.9448i	−0.527320	−	0.807809i
$551$		−	2.29786i		−	0.0978921i
$552$	−4.79483	+	0.0981907i	−0.204081	+	0.00417927i
$553$	11.6692	−	11.6692i	0.496225	−	0.496225i
$554$	−19.9236	−	17.2639i	−0.846473	−	0.733473i
$555$	19.2670	+	17.8105i	0.817839	+	0.756013i
$556$	−0.0880038	−	0.612080i	−0.00373219	−	0.0259580i
$557$	−19.4621	−	7.25898i	−0.824634	−	0.307573i	−0.0985100	−	0.995136i	$-0.531408\pi$
$557$	−19.4621	−	7.25898i	−0.824634	−	0.307573i	−0.726124	+	0.687563i	$0.758680\pi$
$558$	−1.11005	−	1.48285i	−0.0469921	−	0.0627741i
$559$	1.38313	−	0.406123i	0.0585000	−	0.0171772i
$560$	−5.25763	+	2.65525i	−0.222175	+	0.112205i
$561$	8.81733	−	19.3073i	0.372268	−	0.815153i
$562$	−5.68203	+	3.10262i	−0.239682	+	0.130876i
$563$	−0.851538	+	11.9061i	−0.0358881	+	0.501781i	0.947439	+	0.319936i	$0.103661\pi$
$563$	−0.851538	+	11.9061i	−0.0358881	+	0.501781i	−0.983327	+	0.181845i	$0.941793\pi$
$564$	4.09402	−	3.54749i	0.172389	−	0.149376i
$565$	9.57943	+	10.2158i	0.403009	+	0.429782i
$566$	−23.4256	−	10.6981i	−0.984652	−	0.449675i
$567$	2.57393	−	0.559923i	0.108095	−	0.0235146i
$568$	5.35053	−	9.79877i	0.224503	−	0.411147i
$569$	3.17428	−	22.0776i	0.133073	−	0.925541i	−0.808444	−	0.588574i	$-0.799690\pi$
$569$	3.17428	−	22.0776i	0.133073	−	0.925541i	0.941516	−	0.336967i	$-0.109401\pi$
$570$	−1.64488	−	2.02635i	−0.0688965	−	0.0848745i
$571$	9.69085	−	1.39333i	0.405549	−	0.0583092i	0.0634781	−	0.997983i	$-0.479781\pi$
$571$	9.69085	−	1.39333i	0.405549	−	0.0583092i	0.342071	+	0.939674i	$0.388872\pi$
$572$	−4.44520	+	20.4342i	−0.185863	+	0.854398i
$573$	7.77242	−	0.555895i	0.324698	−	0.0232228i
$574$	25.6056			1.06876
$575$	23.5629	+	4.44851i	0.982641	+	0.185516i
$576$	−1.00000			−0.0416667
$577$	25.3476	−	1.81290i	1.05524	−	0.0754719i	0.467076	−	0.884217i	$-0.345307\pi$
$577$	25.3476	−	1.81290i	1.05524	−	0.0754719i	0.588159	+	0.808745i	$0.299853\pi$
$578$	−1.06381	+	4.89027i	−0.0442488	+	0.203409i
$579$	−4.65798	+	0.669716i	−0.193579	+	0.0278324i
$580$	2.77441	+	3.41783i	0.115201	+	0.141918i
$581$	3.72959	−	25.9399i	0.154730	−	1.07617i
$582$	4.79568	−	8.78263i	0.198787	−	0.364052i
$583$	−38.8684	+	8.45530i	−1.60976	+	0.350183i
$584$	−0.777548	−	0.355094i	−0.0321752	−	0.0146939i
$585$	7.06896	+	7.53856i	0.292266	+	0.311681i
$586$	−17.1800	+	14.8865i	−0.709698	+	0.614957i
$587$	1.14757	−	16.0452i	0.0473654	−	0.662255i	−0.917203	−	0.398421i	$-0.869558\pi$
$587$	1.14757	−	16.0452i	0.0473654	−	0.662255i	0.964568	−	0.263834i	$-0.0849871\pi$
$588$	0.0538812	−	0.0294214i	0.00222202	−	0.00121332i
$589$	−0.898132	+	1.96663i	−0.0370069	+	0.0810337i
$590$	−6.47597	+	3.27055i	−0.266611	+	0.134646i
$591$	−7.57603	+	2.22452i	−0.311636	+	0.0915047i
$592$	−7.03191	−	9.39353i	−0.289010	−	0.386072i
$593$	8.78672	+	3.27728i	0.360828	+	0.134582i	0.523338	−	0.852125i	$-0.324686\pi$
$593$	8.78672	+	3.27728i	0.360828	+	0.134582i	−0.162511	+	0.986707i	$0.551959\pi$
$594$	−0.643944	−	4.47873i	−0.0264213	−	0.183764i
$595$	20.2891	+	18.7553i	0.831772	+	0.768892i
$596$	−13.2078	−	11.4446i	−0.541013	−	0.468791i
$597$	11.3247	−	11.3247i	0.463490	−	0.463490i
$598$	−12.3625	−	18.3970i	−0.505539	−	0.752309i
$599$			31.6731i			1.29413i	0.762436	+	0.647064i	$0.224003\pi$
$599$			31.6731i			1.29413i	−0.762436	+	0.647064i	$0.775997\pi$
$600$	4.89319	+	1.02798i	0.199763	+	0.0419670i
$601$	−27.5536	+	17.7076i	−1.12393	+	0.722309i	−0.964285	−	0.264865i	$-0.914673\pi$
$601$	−27.5536	+	17.7076i	−1.12393	+	0.722309i	−0.159649	+	0.987174i	$0.551036\pi$
$602$	0.492361	−	0.657717i	0.0200671	−	0.0268066i
$603$	4.12274	−	11.0535i	0.167891	−	0.450133i
$604$	9.64098	+	1.38616i	0.392286	+	0.0564022i
$605$	−18.1797	+	10.8743i	−0.739110	+	0.442103i
$606$	14.3919	+	9.24910i	0.584630	+	0.375719i
$607$	−17.2095	+	6.41880i	−0.698511	+	0.260531i	−0.673533	−	0.739157i	$-0.735224\pi$
$607$	−17.2095	+	6.41880i	−0.698511	+	0.260531i	−0.0249775	+	0.999688i	$0.507951\pi$
$608$	0.559377	+	1.02442i	0.0226857	+	0.0415458i
$609$	3.39598	+	3.91917i	0.137612	+	0.158813i
$610$	−30.7410	+	5.65946i	−1.24466	+	0.229145i
$611$	24.0223	+	7.05358i	0.971838	+	0.285357i
$612$	1.63931	+	4.39515i	0.0662650	+	0.177663i
$613$	7.75578	+	35.6527i	0.313253	+	1.44000i	0.817244	+	0.576292i	$0.195501\pi$
$613$	7.75578	+	35.6527i	0.313253	+	1.44000i	−0.503991	+	0.863709i	$0.668135\pi$
$614$	5.16681	+	17.5965i	0.208515	+	0.710138i
$615$	−16.9732	−	13.5784i	−0.684425	−	0.547534i
$616$	4.95127	+	10.8418i	0.199492	+	0.436827i
$617$	11.5395	+	8.63835i	0.464562	+	0.347767i	0.805778	−	0.592218i	$-0.201748\pi$
$617$	11.5395	+	8.63835i	0.464562	+	0.347767i	−0.341215	+	0.939985i	$0.610839\pi$
$618$	13.8536	+	3.01366i	0.557273	+	0.121227i
$619$	−6.05581	+	6.98877i	−0.243403	+	0.280903i	−0.864286	−	0.503001i	$-0.832229\pi$
$619$	−6.05581	+	6.98877i	−0.243403	+	0.280903i	0.620882	+	0.783904i	$0.286775\pi$
$620$	−1.03861	−	4.00956i	−0.0417117	−	0.161028i
$621$	3.89730	+	2.79483i	0.156393	+	0.112153i
$622$	15.4471	+	15.4471i	0.619371	+	0.619371i
$623$	2.66303	+	37.2341i	0.106692	+	1.49175i
$624$	−2.49867	−	3.88801i	−0.100027	−	0.155645i
$625$	−22.8865	−	10.0602i	−0.915461	−	0.402407i
$626$	2.60959	−	1.19176i	0.104300	−	0.0476324i
$627$	−4.22790	+	3.16497i	−0.168846	+	0.126397i
$628$	−12.1111	−	6.61316i	−0.483285	−	0.263894i
$629$	−29.7585	+	46.3051i	−1.18655	+	1.84631i
$630$	5.80018	+	1.02514i	0.231085	+	0.0408425i
$631$	4.92393	−	16.7694i	0.196018	−	0.667577i	−0.801553	−	0.597924i	$-0.795992\pi$
$631$	4.92393	−	16.7694i	0.196018	−	0.667577i	0.997571	−	0.0696534i	$-0.0221893\pi$
$632$	6.24902	+	0.446939i	0.248573	+	0.0177783i
$633$	2.11215	+	0.151064i	0.0839505	+	0.00600425i
$634$	−1.09291	+	3.72211i	−0.0434050	+	0.147824i
$635$	−12.9244	+	9.04197i	−0.512888	+	0.358820i
$636$	4.75278	−	7.39547i	0.188460	−	0.293250i
$637$	0.249022	+	0.135976i	0.00986662	+	0.00538758i
$638$	7.13118	−	5.33833i	0.282326	−	0.211347i
$639$	−10.1555	+	4.63786i	−0.401746	+	0.183471i
$640$	−2.06889	−	0.848339i	−0.0817802	−	0.0335335i
$641$	17.3208	+	26.9518i	0.684132	+	1.06453i	0.993527	+	0.113597i	$0.0362372\pi$
$641$	17.3208	+	26.9518i	0.684132	+	1.06453i	−0.309395	+	0.950934i	$0.600126\pi$
$642$	−0.0324222	−	0.453322i	−0.00127960	−	0.0178912i
$643$	14.6215	+	14.6215i	0.576617	+	0.576617i	0.933970	−	0.357352i	$-0.116320\pi$
$643$	14.6215	+	14.6215i	0.576617	+	0.576617i	−0.357352	+	0.933970i	$0.616320\pi$
$644$	−11.9242	−	4.17145i	−0.469880	−	0.164378i
$645$	−0.675153	+	0.174887i	−0.0265841	+	0.00688619i
$646$	3.58550	−	4.13789i	0.141070	−	0.162803i
$647$	31.3444	+	6.81856i	1.23228	+	0.268065i	0.781120	−	0.624381i	$-0.214649\pi$
$647$	31.3444	+	6.81856i	1.23228	+	0.268065i	0.451155	+	0.892446i	$0.351012\pi$
$648$	0.800541	+	0.599278i	0.0314482	+	0.0235419i
$649$	6.09861	+	13.3541i	0.239391	+	0.524194i
$650$	8.22968	+	21.5933i	0.322795	+	0.846961i
$651$	−1.37464	−	4.68158i	−0.0538762	−	0.183485i
$652$	3.08669	+	14.1893i	0.120884	+	0.555695i
$653$	2.01249	+	5.39568i	0.0787546	+	0.211149i	0.970360	−	0.241664i	$-0.0776931\pi$
$653$	2.01249	+	5.39568i	0.0787546	+	0.211149i	−0.891605	+	0.452813i	$0.850420\pi$
$654$	3.16569	+	0.929529i	0.123788	+	0.0363475i
$655$	−23.1623	−	15.9599i	−0.905028	−	0.623604i
$656$	6.36572	+	7.34643i	0.248540	+	0.286830i
$657$	0.409659	+	0.750234i	0.0159823	+	0.0292694i
$658$	13.3698	−	4.98667i	0.521208	−	0.194401i
$659$	3.98564	+	2.56142i	0.155258	+	0.0997786i	0.615963	−	0.787775i	$-0.288767\pi$
$659$	3.98564	+	2.56142i	0.155258	+	0.0997786i	−0.460705	+	0.887553i	$0.652403\pi$
$660$	2.46723	−	9.81229i	0.0960367	−	0.381943i
$661$	−8.65317	−	1.24414i	−0.336569	−	0.0483913i	−0.0280417	−	0.999607i	$-0.508927\pi$
$661$	−8.65317	−	1.24414i	−0.336569	−	0.0483913i	−0.308528	+	0.951215i	$0.599836\pi$
$662$	6.76745	−	18.1442i	0.263024	−	0.705196i
$663$	−12.9923	+	17.3557i	−0.504579	+	0.674039i
$664$	8.36955	−	5.37878i	0.324801	−	0.208737i
$665$	−2.19431	−	6.51528i	−0.0850919	−	0.252652i
$666$			11.7340i			0.454682i
$667$	−1.15205	+	9.37101i	−0.0446076	+	0.362847i
$668$	0.0937155	−	0.0937155i	0.00362596	−	0.00362596i
$669$	5.93818	+	5.14546i	0.229583	+	0.198935i
$670$	17.9066	−	19.3710i	0.691793	−	0.748368i
$671$	9.00157	+	62.6073i	0.347502	+	2.41693i
$672$	−2.46804	−	0.920532i	−0.0952068	−	0.0355103i
$673$	−13.9490	−	18.6337i	−0.537696	−	0.718278i	0.446614	−	0.894727i	$-0.352630\pi$
$673$	−13.9490	−	18.6337i	−0.537696	−	0.718278i	−0.984310	+	0.176449i	$0.943539\pi$
$674$	−27.2582	+	8.00372i	−1.04995	+	0.308292i
$675$	−3.30115	−	3.75532i	−0.127061	−	0.144542i
$676$	3.47287	−	7.60454i	0.133572	−	0.292482i
$677$	5.02226	−	2.74236i	0.193021	−	0.105398i	−0.379832	−	0.925055i	$-0.624018\pi$
$677$	5.02226	−	2.74236i	0.193021	−	0.105398i	0.572853	+	0.819658i	$0.305836\pi$
$678$	−0.446800	+	6.24707i	−0.0171592	+	0.239917i
$679$	19.9206	−	17.2613i	0.764484	−	0.662429i
$680$	−0.337027	+	10.4838i	−0.0129244	+	0.402035i
$681$	25.9985	+	11.8731i	0.996265	+	0.454979i
$682$	−8.18977	+	1.78158i	−0.313603	+	0.0682201i
$683$	8.50666	−	15.5788i	0.325498	−	0.596105i	−0.662772	−	0.748821i	$-0.730620\pi$
$683$	8.50666	−	15.5788i	0.325498	−	0.596105i	0.988270	+	0.152716i	$0.0488020\pi$
$684$	0.166109	−	1.15532i	0.00635135	−	0.0441746i
$685$	−33.1007	−	3.43942i	−1.26471	−	0.131413i
$686$	18.4113	−	2.64714i	0.702945	−	0.101068i
$687$	−5.41725	+	24.9027i	−0.206681	+	0.950098i
$688$	0.311108	−	0.0222509i	0.0118609	−	0.000848307i
$689$	40.6293			1.54785
$690$	5.69214	+	9.08843i	0.216696	+	0.345991i
$691$	3.65274			0.138957			0.0694783	−	0.997583i	$-0.477867\pi$
$691$	3.65274			0.138957			0.0694783	+	0.997583i	$0.477867\pi$
$692$	2.00177	−	0.143169i	0.0760959	−	0.00544249i
$693$	2.53353	−	11.6465i	0.0962409	−	0.442412i
$694$	−10.7361	+	1.54362i	−0.407536	+	0.0585949i
$695$	−1.07355	+	0.871449i	−0.0407221	+	0.0330559i
$696$	−0.280175	+	1.94866i	−0.0106200	+	0.0738639i
$697$	21.8533	−	40.0213i	0.827752	−	1.51592i
$698$	−10.6145	+	2.30905i	−0.401765	+	0.0873986i
$699$	−9.12277	−	4.16623i	−0.345055	−	0.157581i
$700$	11.1303	+	7.04143i	0.420686	+	0.266141i
$701$	11.5419	−	10.0011i	0.435931	−	0.377736i	−0.409069	−	0.912504i	$-0.634146\pi$
$701$	11.5419	−	10.0011i	0.435931	−	0.377736i	0.844999	+	0.534768i	$0.179601\pi$
$702$	−0.329708	+	4.60991i	−0.0124440	+	0.173990i
$703$	12.0206	−	6.56372i	0.453364	−	0.247555i
$704$	−1.87966	+	4.11589i	−0.0708425	+	0.155123i
$705$	−11.5068	−	3.78434i	−0.433372	−	0.142527i
$706$	15.5974	−	4.57981i	0.587016	−	0.172363i
$707$	27.0057	+	36.0754i	1.01565	+	1.35675i
$708$	−3.03995	−	1.13384i	−0.114248	−	0.0426125i
$709$	5.57636	+	38.7844i	0.209425	+	1.45658i	0.775040	+	0.631912i	$0.217729\pi$
$709$	5.57636	+	38.7844i	0.209425	+	1.45658i	−0.565616	+	0.824669i	$0.691361\pi$
$710$	−24.9451	+	0.979937i	−0.936175	+	0.0367764i
$711$	−4.73476	−	4.10269i	−0.177567	−	0.153863i
$712$	−10.0207	+	10.0207i	−0.375541	+	0.375541i
$713$	4.64870	−	7.56994i	0.174095	−	0.283496i
$714$			12.3564i			0.462428i
$715$	44.3151	−	14.9251i	1.65729	−	0.558168i
$716$	−13.7760	+	8.85329i	−0.514833	+	0.330863i
$717$	−3.52504	+	4.70890i	−0.131645	+	0.175857i
$718$	3.50285	−	9.39150i	0.130725	−	0.350488i
$719$	49.4765	+	7.11365i	1.84516	+	0.265294i	0.974139	−	0.225949i	$-0.0725483\pi$
$719$	49.4765	+	7.11365i	1.84516	+	0.265294i	0.871022	+	0.491243i	$0.163457\pi$
$720$	1.14784	+	1.91897i	0.0427776	+	0.0715159i
$721$	31.4170	+	20.1905i	1.17003	+	0.751934i
$722$	16.5256	−	6.16373i	0.615019	−	0.229390i
$723$	−8.54537	−	15.6497i	−0.317806	−	0.582018i
$724$	5.86781	+	6.77182i	0.218076	+	0.251673i
$725$	3.37413	−	9.24715i	0.125312	−	0.343431i
$726$	−9.08992	−	2.66904i	−0.337358	−	0.0990574i
$727$	3.35725	+	9.00113i	0.124513	+	0.333833i	0.984219	−	0.176957i	$-0.0566254\pi$
$727$	3.35725	+	9.00113i	0.124513	+	0.333833i	−0.859705	+	0.510791i	$0.829353\pi$
$728$	−2.58779	−	11.8959i	−0.0959099	−	0.440891i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	0.211088	+	1.89969i	0.00781271	+	0.0703105i
$731$	−0.607797	−	1.33089i	−0.0224802	−	0.0492248i
$732$	−11.1906	−	8.37719i	−0.413617	−	0.309630i
$733$	8.82527	+	1.91982i	0.325969	+	0.0709102i	0.372572	−	0.928003i	$-0.378476\pi$
$733$	8.82527	+	1.91982i	0.325969	+	0.0709102i	−0.0466032	+	0.998913i	$0.514840\pi$
$734$	0.605842	−	0.699179i	0.0223620	−	0.0258072i
$735$	−0.118306	−	0.0696254i	−0.00436379	−	0.00256817i
$736$	−1.76762	−	4.45820i	−0.0651553	−	0.164331i
$737$	−37.7456	−	37.7456i	−1.39038	−	1.39038i
$738$	−0.693468	−	9.69595i	−0.0255269	−	0.356913i
$739$	10.2985	+	16.0248i	0.378836	+	0.589480i	0.977349	−	0.211633i	$-0.0678780\pi$
$739$	10.2985	+	16.0248i	0.378836	+	0.589480i	−0.598513	+	0.801113i	$0.704242\pi$
$740$	−9.95439	+	24.2763i	−0.365931	+	0.892416i
$741$	4.90693	−	2.24092i	0.180261	−	0.0823223i
$742$	18.5378	−	13.8772i	0.680545	−	0.509450i
$743$	25.1199	+	13.7165i	0.921560	+	0.503210i	0.868670	−	0.495390i	$-0.164975\pi$
$743$	25.1199	+	13.7165i	0.921560	+	0.503210i	0.0528899	+	0.998600i	$0.483157\pi$
$744$	1.00144	−	1.55826i	0.0367144	−	0.0571287i
$745$	−6.80142	+	38.4821i	−0.249185	+	1.40987i
$746$	9.16323	−	31.2071i	0.335490	−	1.14257i
$747$	−9.92355	−	0.709747i	−0.363084	−	0.0259683i
$748$	21.1713	+	1.51420i	0.774099	+	0.0553646i
$749$	0.337278	−	1.14866i	0.0123239	−	0.0419713i
$750$	−3.64395	−	10.5698i	−0.133058	−	0.385956i
$751$	−25.7265	+	40.0312i	−0.938773	+	1.46076i	−0.0519508	+	0.998650i	$0.516544\pi$
$751$	−25.7265	+	40.0312i	−0.938773	+	1.46076i	−0.886823	+	0.462110i	$0.847092\pi$
$752$	4.75453	+	2.59617i	0.173380	+	0.0946725i
$753$	−12.0651	+	9.03179i	−0.439675	+	0.329137i
$754$	−8.27649	+	3.77975i	−0.301412	+	0.137650i
$755$	−8.40633	−	20.0919i	−0.305938	−	0.731218i
$756$	1.42411	+	2.21597i	0.0517946	+	0.0805939i
$757$	0.501993	+	7.01877i	0.0182452	+	0.255102i	0.998386	+	0.0567973i	$0.0180889\pi$
$757$	0.501993	+	7.01877i	0.0182452	+	0.255102i	−0.980140	+	0.198304i	$0.936457\pi$
$758$	−19.4580	−	19.4580i	−0.706747	−	0.706747i
$759$	18.8288	−	10.7875i	0.683442	−	0.391562i
$760$	1.32376	−	2.24931i	0.0480179	−	0.0815910i
$761$	14.7426	−	17.0139i	0.534419	−	0.616752i	−0.422763	−	0.906240i	$-0.638940\pi$
$761$	14.7426	−	17.0139i	0.534419	−	0.616752i	0.957182	+	0.289488i	$0.0934850\pi$
$762$	−6.89282	−	1.49944i	−0.249700	−	0.0543190i
$763$	6.95739	+	5.20823i	0.251874	+	0.188551i
$764$	3.23703	+	7.08811i	0.117112	+	0.256439i
$765$	6.55250	−	8.19073i	0.236906	−	0.296136i
$766$	−9.53529	−	32.4742i	−0.344524	−	1.17334i
$767$	−3.18745	−	14.6525i	−0.115092	−	0.529071i
$768$	−0.349464	−	0.936950i	−0.0126102	−	0.0338093i
$769$	32.2977	+	9.48346i	1.16468	+	0.341982i	0.806252	−	0.591573i	$-0.201493\pi$
$769$	32.2977	+	9.48346i	1.16468	+	0.341982i	0.358433	+	0.933555i	$0.383311\pi$
$770$	15.1218	−	21.9460i	0.544950	−	0.790879i
$771$	−13.8390	−	15.9711i	−0.498400	−	0.575184i
$772$	−2.25529	−	4.13025i	−0.0811695	−	0.148651i
$773$	−21.8282	+	8.14149i	−0.785105	+	0.292829i	−0.709866	−	0.704336i	$-0.751245\pi$
$773$	−21.8282	+	8.14149i	−0.785105	+	0.292829i	−0.0752390	+	0.997166i	$0.523972\pi$
$774$	−0.262389	−	0.168627i	−0.00943139	−	0.00606119i
$775$	−6.50207	+	6.59542i	−0.233561	+	0.236914i
$776$	9.90481	+	1.42410i	0.355562	+	0.0511221i
$777$	−10.8015	+	28.9599i	−0.387502	+	1.03893i
$778$	6.05071	−	8.08280i	0.216928	−	0.289782i
$779$	−9.54485	+	6.13410i	−0.341980	+	0.219777i
$780$	−4.59290	+	9.25772i	−0.164452	+	0.331479i
$781$			50.5165i			1.80762i
$782$	−16.6968	+	15.0773i	−0.597075	+	0.539163i
$783$	1.39208	−	1.39208i	0.0497489	−	0.0497489i
$784$	0.0463959	+	0.0402023i	0.00165700	+	0.00143580i
$785$	1.21118	+	30.8317i	0.0432290	+	1.10043i
$786$	−1.79024	−	12.4514i	−0.0638558	−	0.444127i
$787$	−31.1472	−	11.6173i	−1.11028	−	0.414113i	−0.273620	−	0.961838i	$-0.588221\pi$
$787$	−31.1472	−	11.6173i	−1.11028	−	0.414113i	−0.836658	+	0.547725i	$0.815494\pi$
$788$	−4.73182	−	6.32097i	−0.168564	−	0.225175i
$789$	21.7647	−	6.39069i	0.774844	−	0.227515i
$790$	−6.31524	−	12.5047i	−0.224686	−	0.444898i
$791$	−6.85335	+	15.0067i	−0.243677	+	0.533578i
$792$	3.97131	−	2.16850i	0.141114	−	0.0770542i
$793$	4.60892	−	64.4411i	0.163668	−	2.28837i
$794$	−24.1493	+	20.9255i	−0.857027	+	0.742618i
$795$	−19.6472	−	0.631606i	−0.696813	−	0.0224007i
$796$	14.5683	+	6.65311i	0.516359	+	0.235813i
$797$	−20.0501	+	4.36164i	−0.710212	+	0.154497i	−0.553138	−	0.833090i	$-0.686570\pi$
$797$	−20.0501	+	4.36164i	−0.710212	+	0.154497i	−0.157074	+	0.987587i	$0.550206\pi$
$798$	1.47347	−	2.69846i	0.0521602	−	0.0955244i
$799$	3.61642	−	25.1528i	0.127940	−	0.889841i
$800$	0.746829	+	4.94391i	0.0264044	+	0.174794i
$801$	14.0271	−	2.01680i	0.495625	−	0.0712601i
$802$	−1.03673	+	4.76579i	−0.0366084	+	0.168286i
$803$	3.85790	−	0.275923i	0.136142	−	0.00973710i
$804$	11.7973			0.416060
$805$	5.68224	+	27.6704i	0.200273	+	0.975254i
$806$	8.56081			0.301542
$807$	−21.3357	+	1.52596i	−0.751053	+	0.0537164i
$808$	−3.63650	+	16.7167i	−0.127931	+	0.588091i
$809$	−0.623326	+	0.0896208i	−0.0219150	+	0.00315090i	−0.153264	−	0.988185i	$-0.548978\pi$
$809$	−0.623326	+	0.0896208i	−0.0219150	+	0.00315090i	0.131349	+	0.991336i	$0.458069\pi$
$810$	0.231101	−	2.22409i	0.00812005	−	0.0781467i
$811$	−2.94368	+	20.4737i	−0.103366	+	0.718930i	0.870559	+	0.492063i	$0.163757\pi$
$811$	−2.94368	+	20.4737i	−0.103366	+	0.718930i	−0.973926	+	0.226866i	$0.927152\pi$
$812$	−2.48529	+	4.55147i	−0.0872166	+	0.159725i
$813$	2.87746	−	0.625954i	0.100917	−	0.0219532i
$814$	48.2957	+	22.0559i	1.69276	+	0.773060i
$815$	23.6858	−	22.2103i	0.829677	−	0.777995i
$816$	−3.54515	+	3.07189i	−0.124105	+	0.107538i
$817$	−0.0259711	+	0.363124i	−0.000908615	+	0.0127041i
$818$	−11.0606	+	6.03954i	−0.386724	+	0.211167i
$819$	−5.05731	+	11.0740i	−0.176717	+	0.386955i
$820$	6.79074	−	20.6482i	0.237143	−	0.721066i
$821$	7.44469	−	2.18596i	0.259822	−	0.0762905i	−0.149228	−	0.988803i	$-0.547679\pi$
$821$	7.44469	−	2.18596i	0.259822	−	0.0762905i	0.409049	+	0.912512i	$0.365860\pi$
$822$	−8.91892	−	11.9143i	−0.311083	−	0.415558i
$823$	−10.0788	−	3.75920i	−0.351325	−	0.131037i	0.167605	−	0.985854i	$-0.446397\pi$
$823$	−10.0788	−	3.75920i	−0.351325	−	0.131037i	−0.518930	+	0.854817i	$0.673669\pi$
$824$	2.01768	+	14.0333i	0.0702892	+	0.488872i
$825$	−21.6615	+	6.52844i	−0.754157	+	0.227291i
$826$	−6.45899	−	5.59675i	−0.224737	−	0.194736i
$827$	6.88175	−	6.88175i	0.239302	−	0.239302i	−0.577259	−	0.816561i	$-0.695878\pi$
$827$	6.88175	−	6.88175i	0.239302	−	0.239302i	0.816561	+	0.577259i	$0.195878\pi$
$828$	−1.25665	+	4.62827i	−0.0436714	+	0.160843i
$829$			7.95502i			0.276289i	0.990412	+	0.138145i	$0.0441139\pi$
$829$			7.95502i			0.276289i	−0.990412	+	0.138145i	$0.955886\pi$
$830$	−19.9287	−	9.88693i	−0.691734	−	0.343180i
$831$	−22.1777	+	14.2528i	−0.769337	+	0.494423i
$832$	2.76968	−	3.69985i	0.0960212	−	0.128269i
$833$	0.100638	−	0.269821i	0.00348690	−	0.00934873i
$834$	−0.612080	−	0.0880038i	−0.0211946	−	0.00304732i
$835$	−0.287408	−	0.0722667i	−0.00994617	−	0.00250089i
$836$	−4.44292	−	2.85529i	−0.153662	−	0.0987523i
$837$	−1.73552	+	0.647317i	−0.0599885	+	0.0223745i
$838$	0.590139	+	1.08076i	0.0203860	+	0.0373342i
$839$	−10.8689	−	12.5434i	−0.375238	−	0.433047i	0.536449	−	0.843932i	$-0.319765\pi$
$839$	−10.8689	−	12.5434i	−0.375238	−	0.433047i	−0.911687	+	0.410885i	$0.865220\pi$
$840$	1.06645	+	5.79273i	0.0367961	+	0.199868i
$841$	−24.1065	−	7.07831i	−0.831259	−	0.244080i
$842$	−3.59406	−	9.63606i	−0.123860	−	0.332080i
$843$	1.37613	+	6.32598i	0.0473965	+	0.217878i
$844$	0.596582	+	2.03177i	0.0205352	+	0.0699364i
$845$	−18.5792	+	2.06447i	−0.639144	+	0.0710200i
$846$	−2.25037	−	4.92762i	−0.0773693	−	0.169415i
$847$	−19.9774	−	14.9549i	−0.686430	−	0.513855i
$848$	8.59011	+	1.86866i	0.294986	+	0.0641702i
$849$	−16.8645	+	19.4627i	−0.578789	+	0.667958i
$850$	20.5049	−	11.3870i	0.703313	−	0.390571i
$851$	−52.3124	+	20.7412i	−1.79325	+	0.710999i
$852$	−7.89443	−	7.89443i	−0.270459	−	0.270459i
$853$	−0.983874	−	13.7564i	−0.0336872	−	0.471009i	−0.986095	−	0.166182i	$-0.946856\pi$
$853$	−0.983874	−	13.7564i	−0.0336872	−	0.471009i	0.952408	−	0.304827i	$-0.0985985\pi$
$854$	−19.9074	−	30.9766i	−0.681218	−	1.06000i
$855$	−2.40769	+	1.00736i	−0.0823411	+	0.0344511i
$856$	0.413410	−	0.188798i	0.0141301	−	0.00645298i
$857$	−4.80764	+	3.59895i	−0.164226	+	0.122938i	−0.678230	−	0.734850i	$-0.737253\pi$
$857$	−4.80764	+	3.59895i	−0.164226	+	0.122938i	0.514004	+	0.857788i	$0.328162\pi$
$858$	18.3542	+	10.0221i	0.626600	+	0.342150i
$859$	−7.86063	+	12.2314i	−0.268201	+	0.417329i	−0.949065	−	0.315081i	$-0.897968\pi$
$859$	−7.86063	+	12.2314i	−0.268201	+	0.417329i	0.680864	+	0.732410i	$0.261605\pi$
$860$	−0.399803	−	0.571467i	−0.0136332	−	0.0194869i
$861$	7.21393	−	24.5684i	0.245850	−	0.837288i
$862$	20.6652	+	1.47801i	0.703861	+	0.0503411i
$863$	−54.4301	−	3.89292i	−1.85282	−	0.132516i	−0.899970	−	0.435952i	$-0.856412\pi$
$863$	−54.4301	−	3.89292i	−1.85282	−	0.132516i	−0.952852	+	0.303435i	$0.901866\pi$
$864$	−0.281733	+	0.959493i	−0.00958474	+	0.0326426i
$865$	−2.57246	−	3.67701i	−0.0874662	−	0.125022i
$866$	2.23274	−	3.47422i	0.0758717	−	0.118059i
$867$	4.39247	+	2.39847i	0.149176	+	0.0814564i
$868$	3.90602	−	2.92401i	0.132579	−	0.0992473i
$869$	−25.7860	+	11.7761i	−0.874729	+	0.399475i
$870$	4.06103	−	1.69911i	0.137682	−	0.0576053i
$871$	29.4777	+	45.8681i	0.998813	+	1.55418i
$872$	0.235372	+	3.29093i	0.00797069	+	0.111445i
$873$	−7.07578	−	7.07578i	−0.239479	−	0.239479i
$874$	5.44424	−	1.30161i	0.184154	−	0.0440276i
$875$	0.736455	−	29.4412i	0.0248967	−	0.995294i
$876$	−0.559771	+	0.646010i	−0.0189129	+	0.0218267i
$877$	18.9530	+	4.12297i	0.639998	+	0.139223i	0.520843	−	0.853653i	$-0.325618\pi$
$877$	18.9530	+	4.12297i	0.639998	+	0.139223i	0.119155	+	0.992876i	$0.461981\pi$
$878$	8.27959	+	6.19803i	0.279423	+	0.209173i
$879$	9.44336	+	20.6781i	0.318517	+	0.697454i
$880$	10.0558	−	1.11738i	0.338982	−	0.0376668i
$881$	8.25269	+	28.1061i	0.278040	+	0.946918i	0.973564	+	0.228415i	$0.0733543\pi$
$881$	8.25269	+	28.1061i	0.278040	+	0.946918i	−0.695524	+	0.718503i	$0.744828\pi$
$882$	−0.0130495	−	0.0599876i	−0.000439400	−	0.00201989i
$883$	−15.3883	−	41.2576i	−0.517857	−	1.38843i	−0.888167	−	0.459520i	$-0.848021\pi$
$883$	−15.3883	−	41.2576i	−0.517857	−	1.38843i	0.370310	−	0.928908i	$-0.379251\pi$
$884$	−20.8017	−	6.10794i	−0.699638	−	0.205432i
$885$	1.31358	+	7.13506i	0.0441554	+	0.239843i
$886$	13.4211	+	15.4888i	0.450891	+	0.520356i
$887$	−25.8897	−	47.4135i	−0.869292	−	1.59199i	−0.804393	−	0.594098i	$-0.797509\pi$
$887$	−25.8897	−	47.4135i	−0.869292	−	1.59199i	−0.0648990	−	0.997892i	$-0.520673\pi$
$888$	−10.9941	+	4.10060i	−0.368939	+	0.137607i
$889$	−15.6315	−	10.0457i	−0.524263	−	0.336923i
$890$	30.7316	+	7.72723i	1.03013	+	0.259017i
$891$	−4.47873	−	0.643944i	−0.150043	−	0.0215729i
$892$	−2.74586	+	7.36193i	−0.0919381	+	0.246496i
$893$	−3.78916	+	5.06173i	−0.126800	+	0.169384i
$894$	−14.7021	+	9.44848i	−0.491712	+	0.316004i
$895$	32.8019	+	16.2735i	1.09645	+	0.543965i
$896$		−	2.63412i		−	0.0879999i
$897$	−21.1347	+	6.67867i	−0.705667	+	0.222994i
$898$	−2.75327	+	2.75327i	−0.0918777	+	0.0918777i
$899$	−2.75595	−	2.38805i	−0.0919162	−	0.0796458i
$900$	2.36491	−	4.40536i	0.0788303	−	0.146845i
$901$	−5.86876	−	40.8181i	−0.195517	−	1.35985i
$902$	−41.2109	−	15.3709i	−1.37217	−	0.511795i
$903$	−0.492361	−	0.657717i	−0.0163847	−	0.0218875i
$904$	−6.00933	+	1.76450i	−0.199867	+	0.0586864i
$905$	6.25959	−	19.0332i	0.208076	−	0.632683i
$906$	4.04619	−	8.85993i	0.134426	−	0.294351i
$907$	33.9292	−	18.5267i	1.12660	−	0.615171i	0.195781	−	0.980648i	$-0.437276\pi$
$907$	33.9292	−	18.5267i	1.12660	−	0.615171i	0.930820	+	0.365477i	$0.119094\pi$
$908$	−2.03897	+	28.5085i	−0.0676656	+	0.946089i
$909$	12.9291	−	11.2031i	0.428831	−	0.371585i
$910$	−19.8575	+	18.6205i	−0.658269	+	0.617264i
$911$	−41.8377	−	19.1066i	−1.38614	−	0.633031i	−0.424023	−	0.905651i	$-0.639382\pi$
$911$	−41.8377	−	19.1066i	−1.38614	−	0.633031i	−0.962122	+	0.272620i	$0.912110\pi$
$912$	1.14052	−	0.248105i	0.0377664	−	0.00821559i
$913$	−21.5742	+	39.5101i	−0.714001	+	1.30760i
$914$	−4.58016	+	31.8557i	−0.151498	+	1.05369i
$915$	−3.23051	+	31.0902i	−0.106797	+	1.02781i
$916$	−25.2257	+	3.62691i	−0.833481	+	0.119837i
$917$	7.04352	−	32.3786i	0.232598	−	1.06923i
$918$	4.67896	−	0.334646i	0.154429	−	0.0110450i
$919$	−39.7867			−1.31244			−0.656221	−	0.754569i	$-0.727846\pi$
$919$	−39.7867			−1.31244			−0.656221	+	0.754569i	$0.727846\pi$
$920$	−6.52620	+	8.50933i	−0.215163	+	0.280544i
$921$	18.3394			0.604304
$922$	−23.9222	+	1.71095i	−0.787837	+	0.0563472i
$923$	10.9680	−	50.4193i	0.361017	−	1.65957i
$924$	11.7975	−	1.69623i	0.388110	−	0.0558018i
$925$	58.0117	−	8.76327i	1.90741	−	0.288135i
$926$	−0.909253	+	6.32399i	−0.0298799	+	0.207819i
$927$	6.79459	−	12.4434i	0.223164	−	0.408694i
$928$	−1.92371	+	0.418478i	−0.0631489	+	0.0137372i
$929$	54.2608	+	24.7801i	1.78024	+	0.813008i	0.975700	+	0.219109i	$0.0703149\pi$
$929$	54.2608	+	24.7801i	1.78024	+	0.813008i	0.804539	+	0.593900i	$0.202412\pi$
$930$	−4.13976	−	0.133083i	−0.135748	−	0.00436395i
$931$	−0.0541531	+	0.0469239i	−0.00177480	+	0.00153787i
$932$	0.715466	−	10.0035i	0.0234359	−	0.327676i
$933$	19.1733	−	10.4694i	0.627705	−	0.342753i
$934$	5.96087	−	13.0525i	0.195045	−	0.427090i
$935$	−21.3956	−	42.3652i	−0.699712	−	1.38549i
$936$	−4.43448	+	1.30208i	−0.144945	+	0.0425598i
$937$	17.4937	+	23.3689i	0.571495	+	0.763428i	0.989424	−	0.145052i	$-0.0463348\pi$
$937$	17.4937	+	23.3689i	0.571495	+	0.763428i	−0.417929	+	0.908480i	$0.637244\pi$
$938$	29.1163	+	10.8598i	0.950681	+	0.354586i
$939$	−0.408279	−	2.83964i	−0.0133237	−	0.0926683i
$940$	−0.475482	−	12.1038i	−0.0155085	−	0.394783i
$941$	13.6511	+	11.8287i	0.445013	+	0.385606i	0.848341	−	0.529449i	$-0.177601\pi$
$941$	13.6511	+	11.8287i	0.445013	+	0.385606i	−0.403329	+	0.915055i	$0.632147\pi$
$942$	−9.75737	+	9.75737i	−0.317912	+	0.317912i
$943$	42.0007	−	20.2304i	1.36773	−	0.658792i
$944$		−	3.24452i		−	0.105600i
$945$	2.61772	−	5.27642i	0.0851543	−	0.171642i
$946$	−1.18726	+	0.763003i	−0.0386010	+	0.0248074i
$947$	13.9021	−	18.5710i	0.451758	−	0.603478i	−0.515619	−	0.856818i	$-0.672438\pi$
$947$	13.9021	−	18.5710i	0.451758	−	0.603478i	0.967377	+	0.253340i	$0.0815291\pi$
$948$	2.18939	−	5.86997i	0.0711080	−	0.190648i
$949$	−3.91038	−	0.562228i	−0.126936	−	0.0182507i
$950$	−5.83583	+	0.0415933i	−0.189339	+	0.00134947i
$951$	3.26343	+	2.09728i	0.105824	+	0.0680089i
$952$	−11.5774	+	4.31813i	−0.375225	+	0.139952i
$953$	−4.28144	−	7.84087i	−0.138689	−	0.253991i	0.799098	−	0.601201i	$-0.205311\pi$
$953$	−4.28144	−	7.84087i	−0.138689	−	0.253991i	−0.937787	+	0.347210i	$0.887129\pi$
$954$	−5.75689	−	6.64381i	−0.186386	−	0.215101i
$955$	9.88627	−	14.3478i	0.319912	−	0.464284i
$956$	−5.64387	−	1.65719i	−0.182536	−	0.0535974i
$957$	−3.11301	−	8.34630i	−0.100629	−	0.269798i
$958$	0.575348	+	2.64483i	0.0185887	+	0.0854507i
$959$	−11.0448	−	37.6151i	−0.356655	−	1.21466i
$960$	−1.39685	+	1.74608i	−0.0450831	+	0.0563546i
$961$	−11.4526	−	25.0776i	−0.369437	−	0.808955i
$962$	−43.4140	−	32.4993i	−1.39972	−	1.04782i
$963$	−0.444094	−	0.0966067i	−0.0143107	−	0.00311311i
$964$	11.6767	−	13.4756i	0.376080	−	0.434019i
$965$	−5.33711	+	9.06871i	−0.171808	+	0.291932i
$966$	−7.36192	+	10.2660i	−0.236866	+	0.330302i
$967$	−5.44163	−	5.44163i	−0.174991	−	0.174991i	0.614177	−	0.789168i	$-0.289488\pi$
$967$	−5.44163	−	5.44163i	−0.174991	−	0.174991i	−0.789168	+	0.614177i	$0.789488\pi$
$968$	−0.675844	−	9.44953i	−0.0217224	−	0.303719i
$969$	−2.96012	−	4.60604i	−0.0950928	−	0.147967i
$970$	−8.63637	−	20.6417i	−0.277297	−	0.662765i
$971$	8.98520	−	4.10341i	0.288349	−	0.131685i	−0.265989	−	0.963976i	$-0.585699\pi$
$971$	8.98520	−	4.10341i	0.288349	−	0.131685i	0.554338	+	0.832291i	$0.312971\pi$
$972$	0.800541	−	0.599278i	0.0256774	−	0.0192218i
$973$	−1.42963	−	0.780636i	−0.0458318	−	0.0250260i
$974$	−6.44452	+	10.0279i	−0.206496	+	0.321314i
$975$	23.0372	−	1.81277i	0.737782	−	0.0580551i
$976$	3.93829	−	13.4126i	0.126061	−	0.429326i
$977$	−57.1379	−	4.08658i	−1.82800	−	0.130741i	−0.885437	−	0.464760i	$-0.846141\pi$
$977$	−57.1379	−	4.08658i	−1.82800	−	0.130741i	−0.942567	+	0.334018i	$0.891595\pi$
$978$	14.4841	+	1.03593i	0.463152	+	0.0331252i
$979$	18.0654	−	61.5250i	0.577372	−	1.96635i
$980$	0.0238918	−	0.135178i	0.000763195	−	0.00431812i
$981$	1.78375	−	2.77558i	0.0569509	−	0.0886173i
$982$	−10.7641	−	5.87762i	−0.343495	−	0.187562i
$983$	42.1329	−	31.5403i	1.34383	−	1.00598i	0.346132	−	0.938186i	$-0.387495\pi$
$983$	42.1329	−	31.5403i	1.34383	−	1.00598i	0.997699	−	0.0677942i	$-0.0215961\pi$
$984$	8.84228	−	4.03813i	0.281882	−	0.128731i
$985$	−6.69838	+	16.3357i	−0.213428	+	0.520499i
$986$	4.99282	+	7.76898i	0.159004	+	0.247415i
$987$	−1.01797	−	14.2331i	−0.0324024	−	0.453045i
$988$	3.81443	+	3.81443i	0.121353	+	0.121353i
$989$	0.287970	−	1.46785i	0.00915690	−	0.0466750i
$990$	−8.71973	−	5.13173i	−0.277131	−	0.163097i
$991$	14.3127	−	16.5178i	0.454659	−	0.524705i	−0.481422	−	0.876489i	$-0.659879\pi$
$991$	14.3127	−	16.5178i	0.454659	−	0.524705i	0.936081	+	0.351784i	$0.114425\pi$
$992$	1.80998	+	0.393737i	0.0574670	+	0.0125012i
$993$	−15.5027	−	11.6051i	−0.491962	−	0.368278i
$994$	−12.2167	−	26.7509i	−0.387490	−	0.848486i
$995$	−3.95498	−	35.5929i	−0.125381	−	1.12837i
$996$	−2.80293	−	9.54590i	−0.0888142	−	0.302473i
$997$	7.89723	+	36.3030i	0.250108	+	1.14973i	0.915211	+	0.402975i	$0.132024\pi$
$997$	7.89723	+	36.3030i	0.250108	+	1.14973i	−0.665103	+	0.746752i	$0.731612\pi$
$998$	10.4211	+	27.9400i	0.329873	+	0.884425i
$999$	11.2587	+	3.30584i	0.356208	+	0.104592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.7.8	✓	240
5.3	odd	4	inner	690.2.w.b.283.4	yes	240
23.10	odd	22	inner	690.2.w.b.217.4	yes	240
115.33	even	44	inner	690.2.w.b.493.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.8	✓	240	1.1	even	1	trivial
690.2.w.b.217.4	yes	240	23.10	odd	22	inner
690.2.w.b.283.4	yes	240	5.3	odd	4	inner
690.2.w.b.493.8	yes	240	115.33	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.40926 - 1.73608i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.26240 - 2.31192i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 - 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.40926 - 1.73608i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.26240 - 2.31192i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(-1.52952 - 1.63113i) q^{10} +(-3.41960 + 2.96310i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(4.05636 - 2.21494i) q^{13} +(1.09425 - 2.39608i) q^{14} +(-1.99597 + 1.00802i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.81116 - 3.75527i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(0.166109 + 1.15532i) q^{19} +(-1.64199 - 1.51786i) q^{20} +(-1.99074 - 1.72498i) q^{21} +(-3.19951 + 3.19951i) q^{22} +(-0.0981907 - 4.79483i) q^{23} -1.00000i q^{24} +(-1.02798 + 4.89319i) q^{25} +(3.88801 - 2.49867i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(0.920532 - 2.46804i) q^{28} +(-1.94866 - 0.280175i) q^{29} +(-1.91897 + 1.14784i) q^{30} +(1.55826 + 1.00144i) q^{31} +(0.936950 - 0.349464i) q^{32} +(2.16850 + 3.97131i) q^{33} +(-3.07189 - 3.54515i) q^{34} +(-5.79273 + 1.06645i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-4.10060 - 10.9941i) q^{37} +(0.248105 + 1.14052i) q^{38} +(-1.30208 - 4.43448i) q^{39} +(-1.74608 - 1.39685i) q^{40} +(4.03813 + 8.84228i) q^{41} +(-2.10872 - 1.57857i) q^{42} +(0.304775 + 0.0662997i) q^{43} +(-2.96310 + 3.41960i) q^{44} +(0.560711 + 2.16463i) q^{45} +(-0.439999 - 4.77560i) q^{46} +(3.83051 + 3.83051i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(0.0331903 + 0.0516451i) q^{49} +(-0.676284 + 4.95405i) q^{50} +(-4.26700 + 1.94867i) q^{51} +(3.69985 - 2.76968i) q^{52} +(7.71569 + 4.21309i) q^{53} +(-0.540641 + 0.841254i) q^{54} +(9.96330 + 1.76094i) q^{55} +(0.742118 - 2.52742i) q^{56} +(1.16422 + 0.0832668i) q^{57} +(-1.96369 - 0.140446i) q^{58} +(0.914088 - 3.11310i) q^{59} +(-1.83220 + 1.28182i) q^{60} +(7.55752 - 11.7597i) q^{61} +(1.62574 + 0.887719i) q^{62} +(-2.10872 + 1.57857i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-9.56178 - 3.92076i) q^{65} +(2.44628 + 3.80649i) q^{66} +(0.841611 + 11.7673i) q^{67} +(-3.31697 - 3.31697i) q^{68} +(-4.70612 - 0.923267i) q^{69} +(-5.70189 + 1.47698i) q^{70} +(7.31113 - 8.43750i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(-0.684298 - 0.512259i) q^{73} +(-4.87447 - 10.6736i) q^{74} +(4.56285 + 2.04461i) q^{75} +(0.328837 + 1.11992i) q^{76} +(2.53353 + 11.6465i) q^{77} +(-1.61511 - 4.33029i) q^{78} +(6.01121 + 1.76505i) q^{79} +(-1.84129 - 1.26873i) q^{80} +(0.654861 + 0.755750i) q^{81} +(4.65865 + 8.53167i) q^{82} +(9.32162 - 3.47678i) q^{83} +(-2.21597 - 1.42411i) q^{84} +(-2.55781 + 10.1726i) q^{85} +(0.308728 + 0.0443884i) q^{86} +(-0.687991 + 1.84457i) q^{87} +(-2.71160 + 3.62228i) q^{88} +(-11.9217 + 7.66163i) q^{89} +(0.713705 + 2.11911i) q^{90} -12.1741i q^{91} +(-0.779566 - 4.73205i) q^{92} +(1.30978 - 1.30978i) q^{93} +(4.09402 + 3.54749i) q^{94} +(1.77163 - 1.91652i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(9.37574 + 3.49697i) q^{97} +(0.0367900 + 0.0491457i) q^{98} +(4.34150 - 1.27478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more