LMFDB - Embedded newform 690.2.q.a.251.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, 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:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			251.10
Character	$\chi$	$=$	690.251
Dual form			690.2.q.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 - 0.841254i) q^{2} +(-1.25644 - 1.19221i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.68223 + 0.412423i) q^{6} +(3.70222 + 3.20799i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(0.157263 + 2.99588i) q^{9} +O(q^{10})$	\(q+(0.540641 - 0.841254i) q^{2} +(-1.25644 - 1.19221i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.68223 + 0.412423i) q^{6} +(3.70222 + 3.20799i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(0.157263 + 2.99588i) q^{9} +(-0.755750 + 0.654861i) q^{10} +(2.80081 - 1.79997i) q^{11} +(-0.562531 + 1.63816i) q^{12} +(3.81776 + 4.40593i) q^{13} +(4.70031 - 1.38014i) q^{14} +(0.869657 + 1.49790i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.40866 - 5.27422i) q^{17} +(2.60531 + 1.48739i) q^{18} +(-1.05335 + 0.481051i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-0.826998 - 8.44447i) q^{21} -3.32933i q^{22} +(-3.28761 + 3.49165i) q^{23} +(1.07398 + 1.35889i) q^{24} +(0.841254 + 0.540641i) q^{25} +(5.77054 - 0.829678i) q^{26} +(3.37413 - 3.95162i) q^{27} +(1.38014 - 4.70031i) q^{28} +(1.40873 + 0.643347i) q^{29} +(1.73028 + 0.0782228i) q^{30} +(0.0108063 - 0.0751597i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-5.66499 - 1.07761i) q^{33} +(-3.13474 - 4.87775i) q^{34} +(-2.64846 - 4.12108i) q^{35} +(2.65981 - 1.38758i) q^{36} +(-2.82705 - 9.62804i) q^{37} +(-0.164801 + 1.14621i) q^{38} +(0.456029 - 10.0873i) q^{39} +(0.909632 + 0.415415i) q^{40} +(-1.93806 + 6.60042i) q^{41} +(-7.55105 - 3.86971i) q^{42} +(3.74808 - 0.538893i) q^{43} +(-2.80081 - 1.79997i) q^{44} +(0.693143 - 2.91883i) q^{45} +(1.15995 + 4.65344i) q^{46} -6.09793i q^{47} +(1.72380 - 0.168818i) q^{48} +(2.41902 + 16.8247i) q^{49} +(0.909632 - 0.415415i) q^{50} +(-9.31431 + 3.75509i) q^{51} +(2.42182 - 5.30304i) q^{52} +(-2.15669 + 2.48895i) q^{53} +(-1.50012 - 4.97490i) q^{54} +(-3.19447 + 0.937982i) q^{55} +(-3.20799 - 3.70222i) q^{56} +(1.89699 + 0.651412i) q^{57} +(1.30284 - 0.837282i) q^{58} +(1.85353 - 1.60609i) q^{59} +(1.00127 - 1.41332i) q^{60} +(11.3125 + 1.62650i) q^{61} +(-0.0573860 - 0.0497252i) q^{62} +(-9.02853 + 11.5959i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-2.42182 - 5.30304i) q^{65} +(-3.96927 + 4.18310i) q^{66} +(4.35207 - 6.77195i) q^{67} -5.79819 q^{68} +(8.29346 - 0.467509i) q^{69} -4.89874 q^{70} +(-0.0737642 + 0.114779i) q^{71} +(0.270695 - 2.98776i) q^{72} +(-2.95980 - 6.48106i) q^{73} +(-9.62804 - 2.82705i) q^{74} +(-0.412423 - 1.68223i) q^{75} +(0.875159 + 0.758330i) q^{76} +(16.1435 + 2.32109i) q^{77} +(-8.23946 - 5.83726i) q^{78} +(4.93755 - 4.27841i) q^{79} +(0.841254 - 0.540641i) q^{80} +(-8.95054 + 0.942281i) q^{81} +(4.50483 + 5.19886i) q^{82} +(9.78245 - 2.87239i) q^{83} +(-7.33782 + 4.26022i) q^{84} +(-3.79701 + 4.38198i) q^{85} +(1.57302 - 3.44444i) q^{86} +(-1.00298 - 2.48783i) q^{87} +(-3.02847 + 1.38306i) q^{88} +(2.62988 + 18.2912i) q^{89} +(-2.08073 - 2.16115i) q^{90} +28.5591i q^{91} +(4.54184 + 1.54003i) q^{92} +(-0.103184 + 0.0815499i) q^{93} +(-5.12990 - 3.29679i) q^{94} +(1.14621 - 0.164801i) q^{95} +(0.789940 - 1.54143i) q^{96} +(-3.87364 + 13.1924i) q^{97} +(15.4616 + 7.06109i) q^{98} +(5.83296 + 8.10782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$3$	−1.25644	−	1.19221i	−0.725404	−	0.688324i
$3$	−1.25644	−	1.19221i	−0.725404	−	0.688324i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$6$	−1.68223	+	0.412423i	−0.686769	+	0.168371i
$7$	3.70222	+	3.20799i	1.39931	+	1.21251i	0.947240	+	0.320525i	$0.103859\pi$
$7$	3.70222	+	3.20799i	1.39931	+	1.21251i	0.452069	+	0.891983i	$0.350686\pi$
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	0.157263	+	2.99588i	0.0524210	+	0.998625i
$10$	−0.755750	+	0.654861i	−0.238989	+	0.207085i
$11$	2.80081	−	1.79997i	0.844477	−	0.542713i	−0.0453705	−	0.998970i	$-0.514447\pi$
$11$	2.80081	−	1.79997i	0.844477	−	0.542713i	0.889848	+	0.456258i	$0.150810\pi$
$12$	−0.562531	+	1.63816i	−0.162389	+	0.472895i
$13$	3.81776	+	4.40593i	1.05886	+	1.22198i	0.974227	+	0.225572i	$0.0724251\pi$
$13$	3.81776	+	4.40593i	1.05886	+	1.22198i	0.0846290	+	0.996413i	$0.473029\pi$
$14$	4.70031	−	1.38014i	1.25621	−	0.368857i
$15$	0.869657	+	1.49790i	0.224544	+	0.386755i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	2.40866	−	5.27422i	0.584185	−	1.27919i	−0.354708	−	0.934977i	$-0.615420\pi$
$17$	2.40866	−	5.27422i	0.584185	−	1.27919i	0.938893	−	0.344209i	$-0.111853\pi$
$18$	2.60531	+	1.48739i	0.614078	+	0.350582i
$19$	−1.05335	+	0.481051i	−0.241656	+	0.110361i	−0.532562	−	0.846391i	$-0.678771\pi$
$19$	−1.05335	+	0.481051i	−0.241656	+	0.110361i	0.290906	+	0.956752i	$0.406043\pi$
$20$	0.142315	+	0.989821i	0.0318226	+	0.221331i
$21$	−0.826998	−	8.44447i	−0.180466	−	1.84274i
$22$		−	3.32933i		−	0.709816i
$23$	−3.28761	+	3.49165i	−0.685514	+	0.728059i
$23$	−3.28761	+	3.49165i	−0.685514	+	0.728059i
$24$	1.07398	+	1.35889i	0.219225	+	0.277381i
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	5.77054	−	0.829678i	1.13170	−	0.162713i
$27$	3.37413	−	3.95162i	0.649351	−	0.760489i
$28$	1.38014	−	4.70031i	0.260821	−	0.888275i
$29$	1.40873	+	0.643347i	0.261595	+	0.119467i	0.541896	−	0.840446i	$-0.317707\pi$
$29$	1.40873	+	0.643347i	0.261595	+	0.119467i	−0.280300	+	0.959912i	$0.590434\pi$
$30$	1.73028	+	0.0782228i	0.315905	+	0.0142815i
$31$	0.0108063	−	0.0751597i	0.00194087	−	0.0134991i	−0.988828	−	0.149061i	$-0.952375\pi$
$31$	0.0108063	−	0.0751597i	0.00194087	−	0.0134991i	0.990769	+	0.135562i	$0.0432840\pi$
$32$	0.281733	+	0.959493i	0.0498038	+	0.169616i
$33$	−5.66499	−	1.07761i	−0.986149	−	0.187588i
$34$	−3.13474	−	4.87775i	−0.537603	−	0.836527i
$35$	−2.64846	−	4.12108i	−0.447672	−	0.696590i
$36$	2.65981	−	1.38758i	0.443302	−	0.231264i
$37$	−2.82705	−	9.62804i	−0.464764	−	1.58284i	−0.774859	−	0.632134i	$-0.782179\pi$
$37$	−2.82705	−	9.62804i	−0.464764	−	1.58284i	0.310095	−	0.950705i	$-0.399639\pi$
$38$	−0.164801	+	1.14621i	−0.0267342	+	0.185941i
$39$	0.456029	−	10.0873i	0.0730231	−	1.61527i
$40$	0.909632	+	0.415415i	0.143825	+	0.0656829i
$41$	−1.93806	+	6.60042i	−0.302674	+	1.03081i	0.657973	+	0.753041i	$0.271414\pi$
$41$	−1.93806	+	6.60042i	−0.302674	+	1.03081i	−0.960647	+	0.277771i	$0.910404\pi$
$42$	−7.55105	−	3.86971i	−1.16515	−	0.597109i
$43$	3.74808	−	0.538893i	0.571577	−	0.0821804i	0.149535	−	0.988756i	$-0.452222\pi$
$43$	3.74808	−	0.538893i	0.571577	−	0.0821804i	0.422043	+	0.906576i	$0.361313\pi$
$44$	−2.80081	−	1.79997i	−0.422239	−	0.271356i
$45$	0.693143	−	2.91883i	0.103328	−	0.435113i
$46$	1.15995	+	4.65344i	0.171025	+	0.686113i
$47$		−	6.09793i		−	0.889474i	−0.895661	−	0.444737i	$-0.853297\pi$
$47$		−	6.09793i		−	0.889474i	0.895661	−	0.444737i	$-0.146703\pi$
$48$	1.72380	−	0.168818i	0.248810	−	0.0243668i
$49$	2.41902	+	16.8247i	0.345575	+	2.40352i
$50$	0.909632	−	0.415415i	0.128641	−	0.0587486i
$51$	−9.31431	+	3.75509i	−1.30426	+	0.525818i
$52$	2.42182	−	5.30304i	0.335846	−	0.735400i
$53$	−2.15669	+	2.48895i	−0.296244	+	0.341884i	−0.884285	−	0.466947i	$-0.845354\pi$
$53$	−2.15669	+	2.48895i	−0.296244	+	0.341884i	0.588041	+	0.808831i	$0.299899\pi$
$54$	−1.50012	−	4.97490i	−0.204141	−	0.676998i
$55$	−3.19447	+	0.937982i	−0.430743	+	0.126477i
$56$	−3.20799	−	3.70222i	−0.428686	−	0.494730i
$57$	1.89699	+	0.651412i	0.251262	+	0.0862816i
$58$	1.30284	−	0.837282i	0.171071	−	0.109941i
$59$	1.85353	−	1.60609i	0.241309	−	0.209096i	−0.525807	−	0.850604i	$-0.676237\pi$
$59$	1.85353	−	1.60609i	0.241309	−	0.209096i	0.767116	+	0.641508i	$0.221691\pi$
$60$	1.00127	−	1.41332i	0.129263	−	0.182458i
$61$	11.3125	+	1.62650i	1.44842	+	0.208252i	0.821223	−	0.570608i	$-0.193292\pi$
$61$	11.3125	+	1.62650i	1.44842	+	0.208252i	0.627199	+	0.778859i	$0.284201\pi$
$62$	−0.0573860	−	0.0497252i	−0.00728803	−	0.00631511i
$63$	−9.02853	+	11.5959i	−1.13749	+	1.46095i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−2.42182	−	5.30304i	−0.300390	−	0.657762i
$66$	−3.96927	+	4.18310i	−0.488583	+	0.514903i
$67$	4.35207	−	6.77195i	0.531690	−	0.827325i	−0.466679	−	0.884427i	$-0.654550\pi$
$67$	4.35207	−	6.77195i	0.531690	−	0.827325i	0.998368	+	0.0571015i	$0.0181859\pi$
$68$	−5.79819			−0.703134
$69$	8.29346	−	0.467509i	0.998415	−	0.0562814i
$70$	−4.89874			−0.585512
$71$	−0.0737642	+	0.114779i	−0.00875420	+	0.0136218i	−0.845603	−	0.533812i	$-0.820759\pi$
$71$	−0.0737642	+	0.114779i	−0.00875420	+	0.0136218i	0.836849	+	0.547434i	$0.184395\pi$
$72$	0.270695	−	2.98776i	0.0319017	−	0.352111i
$73$	−2.95980	−	6.48106i	−0.346418	−	0.758550i	−0.999999	−	0.00169305i	$-0.999461\pi$
$73$	−2.95980	−	6.48106i	−0.346418	−	0.758550i	0.653580	−	0.756857i	$-0.273266\pi$
$74$	−9.62804	−	2.82705i	−1.11924	−	0.328638i
$75$	−0.412423	−	1.68223i	−0.0476225	−	0.194248i
$76$	0.875159	+	0.758330i	0.100388	+	0.0869864i
$77$	16.1435	+	2.32109i	1.83973	+	0.264513i
$78$	−8.23946	−	5.83726i	−0.932936	−	0.660940i
$79$	4.93755	−	4.27841i	0.555517	−	0.481358i	−0.331270	−	0.943536i	$-0.607477\pi$
$79$	4.93755	−	4.27841i	0.555517	−	0.481358i	0.886787	+	0.462178i	$0.152932\pi$
$80$	0.841254	−	0.540641i	0.0940550	−	0.0604455i
$81$	−8.95054	+	0.942281i	−0.994504	+	0.104698i
$82$	4.50483	+	5.19886i	0.497476	+	0.574117i
$83$	9.78245	−	2.87239i	1.07376	−	0.315285i	0.303382	−	0.952869i	$-0.401884\pi$
$83$	9.78245	−	2.87239i	1.07376	−	0.315285i	0.770381	+	0.637584i	$0.220066\pi$
$84$	−7.33782	+	4.26022i	−0.800621	+	0.464829i
$85$	−3.79701	+	4.38198i	−0.411843	+	0.475293i
$86$	1.57302	−	3.44444i	0.169623	−	0.371423i
$87$	−1.00298	−	2.48783i	−0.107530	−	0.266724i
$88$	−3.02847	+	1.38306i	−0.322836	+	0.147434i
$89$	2.62988	+	18.2912i	0.278767	+	1.93887i	0.339247	+	0.940697i	$0.389828\pi$
$89$	2.62988	+	18.2912i	0.278767	+	1.93887i	−0.0604799	+	0.998169i	$0.519263\pi$
$90$	−2.08073	−	2.16115i	−0.219328	−	0.227805i
$91$			28.5591i			2.99380i
$92$	4.54184	+	1.54003i	0.473519	+	0.160559i
$93$	−0.103184	+	0.0815499i	−0.0106996	+	0.00845633i
$94$	−5.12990	−	3.29679i	−0.529109	−	0.340038i
$95$	1.14621	−	0.164801i	0.117599	−	0.0169082i
$96$	0.789940	−	1.54143i	0.0806229	−	0.157321i
$97$	−3.87364	+	13.1924i	−0.393308	+	1.33949i	0.490421	+	0.871486i	$0.336843\pi$
$97$	−3.87364	+	13.1924i	−0.393308	+	1.33949i	−0.883729	+	0.467999i	$0.844975\pi$
$98$	15.4616	+	7.06109i	1.56186	+	0.713278i
$99$	5.83296	+	8.10782i	0.586235	+	0.814867i
$100$	0.142315	−	0.989821i	0.0142315	−	0.0989821i
$101$	−1.82251	−	6.20689i	−0.181346	−	0.617609i	−0.999115	−	0.0420619i	$-0.986607\pi$
$101$	−1.82251	−	6.20689i	−0.181346	−	0.617609i	0.817769	−	0.575547i	$-0.195211\pi$
$102$	−1.87671	+	9.86585i	−0.185822	+	0.976865i
$103$	−9.69259	−	15.0820i	−0.955039	−	1.48607i	−0.871989	−	0.489525i	$-0.837170\pi$
$103$	−9.69259	−	15.0820i	−0.955039	−	1.48607i	−0.0830500	−	0.996545i	$-0.526466\pi$
$104$	−3.15187	−	4.90441i	−0.309066	−	0.480916i
$105$	−1.58558	+	8.33540i	−0.154737	+	0.813452i
$106$	0.927845	+	3.15995i	0.0901203	+	0.306921i
$107$	−1.46787	+	10.2093i	−0.141904	+	0.986966i	0.787081	+	0.616850i	$0.211591\pi$
$107$	−1.46787	+	10.2093i	−0.141904	+	0.986966i	−0.928985	+	0.370116i	$0.879318\pi$
$108$	−4.99618	−	1.42765i	−0.480758	−	0.137376i
$109$	−1.41677	−	0.647018i	−0.135702	−	0.0619731i	0.346407	−	0.938084i	$-0.387402\pi$
$109$	−1.41677	−	0.647018i	−0.135702	−	0.0619731i	−0.482109	+	0.876111i	$0.660129\pi$
$110$	−0.937982	+	3.19447i	−0.0894331	+	0.304581i
$111$	−7.92665	+	15.4675i	−0.752365	+	1.46811i
$112$	−4.84888	+	0.697164i	−0.458176	+	0.0658758i
$113$	−8.85931	−	5.69354i	−0.833414	−	0.535603i	0.0529469	−	0.998597i	$-0.483139\pi$
$113$	−8.85931	−	5.69354i	−0.833414	−	0.535603i	−0.886361	+	0.462995i	$0.846775\pi$
$114$	1.57359	−	1.24367i	0.147380	−	0.116480i
$115$	4.13815	−	2.42399i	0.385884	−	0.226038i
$116$		−	1.54868i		−	0.143792i
$117$	−12.5992	+	12.1304i	−1.16480	+	1.12146i
$118$	−0.349037	−	2.42761i	−0.0321315	−	0.223479i
$119$	25.8371	−	11.7994i	2.36848	−	1.08165i
$120$	−0.647632	−	1.60642i	−0.0591204	−	0.146645i
$121$	0.0350886	−	0.0768333i	0.00318987	−	0.00698484i
$122$	7.48431	−	8.63736i	0.677598	−	0.781990i
$123$	10.3041	−	5.98243i	0.929093	−	0.539418i
$124$	−0.0728567	+	0.0213927i	−0.00654273	+	0.00192112i
$125$	−0.654861	−	0.755750i	−0.0585725	−	0.0675963i
$126$	4.87390	+	13.8645i	0.434201	+	1.23515i
$127$	10.8270	−	6.95808i	0.960740	−	0.617430i	0.0365372	−	0.999332i	$-0.488367\pi$
$127$	10.8270	−	6.95808i	0.960740	−	0.617430i	0.924203	+	0.381902i	$0.124731\pi$
$128$	0.755750	−	0.654861i	0.0667995	−	0.0578821i
$129$	−5.35170	−	3.79142i	−0.471191	−	0.333816i
$130$	−5.77054	−	0.829678i	−0.506110	−	0.0727676i
$131$	9.65854	+	8.36917i	0.843871	+	0.731218i	0.965233	−	0.261390i	$-0.0841809\pi$
$131$	9.65854	+	8.36917i	0.843871	+	0.731218i	−0.121363	+	0.992608i	$0.538726\pi$
$132$	1.37309	+	5.60072i	0.119512	+	0.487480i
$133$	−5.44296	−	1.59820i	−0.471965	−	0.138581i
$134$	−3.34402	−	7.32239i	−0.288879	−	0.632558i
$135$	−4.35075	+	2.84095i	−0.374453	+	0.244510i
$136$	−3.13474	+	4.87775i	−0.268802	+	0.418264i
$137$	−10.5804			−0.903946			−0.451973	−	0.892032i	$-0.649280\pi$
$137$	−10.5804			−0.903946			−0.451973	+	0.892032i	$0.649280\pi$
$138$	4.09049	−	7.22965i	0.348205	−	0.615429i
$139$	−20.1327			−1.70764			−0.853818	−	0.520572i	$-0.825719\pi$
$139$	−20.1327			−1.70764			−0.853818	+	0.520572i	$0.825719\pi$
$140$	−2.64846	+	4.12108i	−0.223836	+	0.348295i
$141$	−7.27002	+	7.66166i	−0.612246	+	0.645228i
$142$	0.0566786	+	0.124109i	0.00475636	+	0.0104150i
$143$	18.6234	+	5.46832i	1.55737	+	0.457284i
$144$	−2.36712	−	1.84303i	−0.197260	−	0.153586i
$145$	−1.17042	−	1.01417i	−0.0971979	−	0.0842225i
$146$	−7.05240	−	1.01398i	−0.583661	−	0.0839177i
$147$	17.0192	−	24.0231i	1.40372	−	1.98139i
$148$	−7.58357	+	6.57120i	−0.623366	+	0.540150i
$149$	−16.3214	+	10.4891i	−1.33710	+	0.859304i	−0.996716	−	0.0809813i	$-0.974195\pi$
$149$	−16.3214	+	10.4891i	−1.33710	+	0.859304i	−0.340387	+	0.940285i	$0.610558\pi$
$150$	−1.63816	−	0.562531i	−0.133755	−	0.0459305i
$151$	−5.49774	−	6.34473i	−0.447400	−	0.516327i	0.486588	−	0.873632i	$-0.338241\pi$
$151$	−5.49774	−	6.34473i	−0.447400	−	0.516327i	−0.933988	+	0.357304i	$0.883696\pi$
$152$	1.11109	−	0.326247i	0.0901216	−	0.0264621i
$153$	16.1797	+	6.38659i	1.30805	+	0.516325i
$154$	10.6805	−	12.3259i	0.860658	−	0.993252i
$155$	−0.0315435	+	0.0690707i	−0.00253364	+	0.00554789i
$156$	−9.36521	+	3.77561i	−0.749817	+	0.302291i
$157$	9.61878	−	4.39275i	0.767662	−	0.350580i	0.00721050	−	0.999974i	$-0.497705\pi$
$157$	9.61878	−	4.39275i	0.767662	−	0.350580i	0.760452	+	0.649394i	$0.224978\pi$
$158$	−0.929787	−	6.46681i	−0.0739699	−	0.514472i
$159$	5.67710	−	0.555979i	0.450223	−	0.0440920i
$160$		−	1.00000i		−	0.0790569i
$161$	−23.3727	+	2.38023i	−1.84202	+	0.187589i
$162$	−4.04633	+	8.03911i	−0.317910	+	0.631612i
$163$	−10.2795	−	6.60623i	−0.805153	−	0.517440i	0.0721409	−	0.997394i	$-0.477017\pi$
$163$	−10.2795	−	6.60623i	−0.805153	−	0.517440i	−0.877293	+	0.479954i	$0.840653\pi$
$164$	6.80905	−	0.978994i	0.531698	−	0.0764466i
$165$	5.13192	+	2.62997i	0.399520	+	0.204743i
$166$	2.87239	−	9.78245i	0.222940	−	0.759265i
$167$	3.00432	+	1.37203i	0.232481	+	0.106171i	0.528250	−	0.849089i	$-0.322848\pi$
$167$	3.00432	+	1.37203i	0.232481	+	0.106171i	−0.295768	+	0.955260i	$0.595576\pi$
$168$	−0.383193	+	8.47621i	−0.0295640	+	0.653954i
$169$	−2.98683	+	20.7739i	−0.229756	+	1.59799i
$170$	1.63354	+	5.56332i	0.125287	+	0.426687i
$171$	−1.60682	−	3.08007i	−0.122877	−	0.235539i
$172$	−2.04720	−	3.18551i	−0.156098	−	0.242893i
$173$	−0.829595	−	1.29088i	−0.0630729	−	0.0981434i	0.808285	−	0.588792i	$-0.200396\pi$
$173$	−0.829595	−	1.29088i	−0.0630729	−	0.0981434i	−0.871358	+	0.490649i	$0.836760\pi$
$174$	−2.63515	−	0.501265i	−0.199770	−	0.0380008i
$175$	1.38014	+	4.70031i	0.104328	+	0.355310i
$176$	−0.473814	+	3.29545i	−0.0357150	+	0.248404i
$177$	−4.24365	−	0.191847i	−0.318972	−	0.0144201i
$178$	16.8094	+	7.67659i	1.25992	+	0.575385i
$179$	2.50918	−	8.54547i	0.187545	−	0.638719i	−0.811013	−	0.585028i	$-0.801083\pi$
$179$	2.50918	−	8.54547i	0.187545	−	0.638719i	0.998558	−	0.0536904i	$-0.0170984\pi$
$180$	−2.94300	+	0.582020i	−0.219358	+	0.0433812i
$181$	−6.81543	+	0.979911i	−0.506587	+	0.0728362i	−0.390870	−	0.920446i	$-0.627826\pi$
$181$	−6.81543	+	0.979911i	−0.506587	+	0.0728362i	−0.115717	+	0.993282i	$0.536917\pi$
$182$	24.0254	+	15.4402i	1.78088	+	1.14450i
$183$	−12.2743	−	15.5305i	−0.907346	−	1.14805i
$184$	3.75106	−	2.98823i	0.276532	−	0.220296i
$185$			10.0345i			0.737752i
$186$	0.0128188	+	0.130893i	0.000939921	+	0.00959753i
$187$	−2.74726	−	19.1076i	−0.200900	−	1.39729i
$188$	−5.54687	+	2.53317i	−0.404547	+	0.184750i
$189$	25.1685	−	3.80559i	1.83074	−	0.276816i
$190$	0.481051	−	1.05335i	0.0348991	−	0.0764184i
$191$	−1.06729	+	1.23171i	−0.0772261	+	0.0891237i	−0.793048	−	0.609159i	$-0.791507\pi$
$191$	−1.06729	+	1.23171i	−0.0772261	+	0.0891237i	0.715822	+	0.698283i	$0.246052\pi$
$192$	−0.869657	−	1.49790i	−0.0627621	−	0.108101i
$193$	−16.5375	+	4.85585i	−1.19040	+	0.349532i	−0.816173	−	0.577807i	$-0.803909\pi$
$193$	−16.5375	+	4.85585i	−1.19040	+	0.349532i	−0.374222	+	0.927339i	$0.622090\pi$
$194$	9.00391	+	10.3911i	0.646443	+	0.746035i
$195$	−3.27949	+	9.55025i	−0.234849	+	0.683908i
$196$	14.2994	−	9.18964i	1.02138	−	0.656403i
$197$	1.73164	−	1.50047i	0.123374	−	0.106904i	−0.590989	−	0.806680i	$-0.701262\pi$
$197$	1.73164	−	1.50047i	0.123374	−	0.106904i	0.714363	+	0.699776i	$0.246717\pi$
$198$	9.97427	−	0.523581i	0.708840	−	0.0372093i
$199$	2.01184	+	0.289259i	0.142616	+	0.0205050i	0.213253	−	0.976997i	$-0.431594\pi$
$199$	2.01184	+	0.289259i	0.142616	+	0.0205050i	−0.0706372	+	0.997502i	$0.522503\pi$
$200$	−0.755750	−	0.654861i	−0.0534396	−	0.0463056i
$201$	−13.5417	+	3.31994i	−0.955157	+	0.234170i
$202$	−6.20689	−	1.82251i	−0.436715	−	0.128231i
$203$	3.15159	+	6.90102i	0.221198	+	0.484357i
$204$	7.28506	+	6.91267i	0.510056	+	0.483984i
$205$	3.71911	−	5.78704i	0.259754	−	0.404185i
$206$	−17.9280			−1.24910
$207$	−10.9776	−	9.30016i	−0.762994	−	0.646406i
$208$	−5.82988			−0.404229
$209$	−2.08437	+	3.24335i	−0.144179	+	0.224347i
$210$	6.15496	+	5.84034i	0.424732	+	0.403022i
$211$	−4.52663	−	9.91193i	−0.311626	−	0.682366i	0.687410	−	0.726270i	$-0.258748\pi$
$211$	−4.52663	−	9.91193i	−0.311626	−	0.682366i	−0.999036	+	0.0439042i	$0.986020\pi$
$212$	3.15995	+	0.927845i	0.217026	+	0.0637246i
$213$	0.229521	−	0.0562703i	0.0157265	−	0.00385558i
$214$	7.79498	+	6.75439i	0.532854	+	0.461721i
$215$	−3.74808	−	0.538893i	−0.255617	−	0.0367522i
$216$	−3.90216	+	3.43121i	−0.265508	+	0.233464i
$217$	0.281119	−	0.243591i	0.0190836	−	0.0165360i
$218$	−1.31027	+	0.842060i	−0.0887428	+	0.0570315i
$219$	−4.00799	+	11.6717i	−0.270835	+	0.788703i
$220$	2.18025	+	2.51614i	0.146992	+	0.169638i
$221$	32.4335	−	9.52333i	2.18171	−	0.640609i
$222$	8.72657	+	15.0307i	0.585689	+	1.00879i
$223$	−14.0160	+	16.1753i	−0.938579	+	1.08318i	0.0578152	+	0.998327i	$0.481587\pi$
$223$	−14.0160	+	16.1753i	−0.938579	+	1.08318i	−0.996394	+	0.0848500i	$0.972959\pi$
$224$	−2.03501	+	4.45605i	−0.135970	+	0.297733i
$225$	−1.48739	+	2.60531i	−0.0991596	+	0.173688i
$226$	−9.57941	+	4.37477i	−0.637213	+	0.291005i
$227$	0.437069	+	3.03989i	0.0290093	+	0.201764i	0.999172	−	0.0406916i	$-0.0129561\pi$
$227$	0.437069	+	3.03989i	0.0290093	+	0.201764i	−0.970162	+	0.242456i	$0.922047\pi$
$228$	−0.195492	−	1.99617i	−0.0129468	−	0.132199i
$229$			11.8517i			0.783183i	0.920139	+	0.391591i	$0.128075\pi$
$229$			11.8517i			0.783183i	−0.920139	+	0.391591i	$0.871925\pi$
$230$	0.198065	−	4.79174i	0.0130600	−	0.315958i
$231$	−17.5161	−	22.1628i	−1.15247	−	1.45821i
$232$	−1.30284	−	0.837282i	−0.0855354	−	0.0549703i
$233$	−7.79717	+	1.12106i	−0.510809	+	0.0734433i	−0.392900	−	0.919581i	$-0.628528\pi$
$233$	−7.79717	+	1.12106i	−0.510809	+	0.0734433i	−0.117909	+	0.993024i	$0.537619\pi$
$234$	3.39310	+	17.1573i	0.221814	+	1.12161i
$235$	−1.71798	+	5.85092i	−0.112069	+	0.381672i
$236$	−2.23094	−	1.01884i	−0.145222	−	0.0663205i
$237$	−11.3045	−	0.511054i	−0.734305	−	0.0331965i
$238$	4.04229	−	28.1147i	0.262023	−	1.82241i
$239$	−6.51727	−	22.1958i	−0.421567	−	1.43572i	−0.847415	−	0.530930i	$-0.821843\pi$
$239$	−6.51727	−	22.1958i	−0.421567	−	1.43572i	0.425849	−	0.904794i	$-0.359976\pi$
$240$	−1.70154	−	0.323672i	−0.109834	−	0.0208929i
$241$	10.4575	+	16.2722i	0.673626	+	1.04818i	0.994868	+	0.101185i	$0.0322635\pi$
$241$	10.4575	+	16.2722i	0.673626	+	1.04818i	−0.321241	+	0.946997i	$0.604100\pi$
$242$	−0.0456660	−	0.0710576i	−0.00293552	−	0.00456776i
$243$	12.3692	+	9.48702i	0.793483	+	0.608593i
$244$	−3.21988	−	10.9659i	−0.206132	−	0.702021i
$245$	2.41902	−	16.8247i	0.154546	−	1.07489i
$246$	0.538100	−	11.9027i	0.0343080	−	0.758891i
$247$	−6.14093	−	2.80447i	−0.390738	−	0.178444i
$248$	−0.0213927	+	0.0728567i	−0.00135844	+	0.00462641i
$249$	−15.7155	−	8.05378i	−0.995930	−	0.510388i
$250$	−0.989821	+	0.142315i	−0.0626018	+	0.00900078i
$251$	9.61375	+	6.17838i	0.606814	+	0.389976i	0.807661	−	0.589647i	$-0.200733\pi$
$251$	9.61375	+	6.17838i	0.606814	+	0.389976i	−0.200847	+	0.979623i	$0.564369\pi$
$252$	14.2986	+	3.39553i	0.900726	+	0.213898i
$253$	−2.92310	+	15.6971i	−0.183774	+	0.986867i
$254$		−	12.8701i		−	0.807540i
$255$	9.99495	−	0.978842i	0.625908	−	0.0612974i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−3.76268	+	1.71836i	−0.234710	+	0.107188i	−0.529298	−	0.848436i	$-0.677545\pi$
$257$	−3.76268	+	1.71836i	−0.234710	+	0.107188i	0.294589	+	0.955624i	$0.404817\pi$
$258$	−6.08290	+	2.45234i	−0.378705	+	0.152676i
$259$	20.4203	−	44.7143i	1.26886	−	2.77841i
$260$	−3.81776	+	4.40593i	−0.236767	+	0.273244i
$261$	−1.70585	+	4.32156i	−0.105589	+	0.267498i
$262$	12.2624	−	3.60057i	0.757574	−	0.222444i
$263$	4.44615	+	5.13113i	0.274161	+	0.316399i	0.876087	−	0.482153i	$-0.160145\pi$
$263$	4.44615	+	5.13113i	0.274161	+	0.316399i	−0.601926	+	0.798552i	$0.705600\pi$
$264$	5.45397	+	1.87286i	0.335669	+	0.115266i
$265$	2.77055	−	1.78052i	0.170193	−	0.109377i
$266$	−4.28718	+	3.71486i	−0.262864	+	0.227773i
$267$	18.5027	−	26.1171i	1.13235	−	1.59834i
$268$	−7.96790	−	1.14561i	−0.486717	−	0.0699793i
$269$	7.16937	+	6.21229i	0.437124	+	0.378770i	0.845440	−	0.534071i	$-0.179338\pi$
$269$	7.16937	+	6.21229i	0.437124	+	0.378770i	−0.408316	+	0.912841i	$0.633884\pi$
$270$	0.0377638	+	5.19602i	0.00229823	+	0.316219i
$271$	−5.91719	−	1.73744i	−0.359444	−	0.105542i	0.0970242	−	0.995282i	$-0.469068\pi$
$271$	−5.91719	−	1.73744i	−0.359444	−	0.105542i	−0.456468	+	0.889740i	$0.650886\pi$
$272$	2.40866	+	5.27422i	0.146046	+	0.319797i
$273$	34.0485	−	35.8826i	2.06071	−	2.17172i
$274$	−5.72021	+	8.90082i	−0.345570	+	0.537718i
$275$	3.32933			0.200766
$276$	−3.87049	−	7.34978i	−0.232976	−	0.442405i
$277$	−2.47047			−0.148436			−0.0742180	−	0.997242i	$-0.523646\pi$
$277$	−2.47047			−0.148436			−0.0742180	+	0.997242i	$0.523646\pi$
$278$	−10.8846	+	16.9367i	−0.652813	+	1.01580i
$279$	0.226868	+	0.0205546i	0.0135823	+	0.00123057i
$280$	2.03501	+	4.45605i	0.121615	+	0.266300i
$281$	−17.0094	−	4.99442i	−1.01470	−	0.297942i	−0.268224	−	0.963357i	$-0.586437\pi$
$281$	−17.0094	−	4.99442i	−1.01470	−	0.297942i	−0.746474	+	0.665414i	$0.768255\pi$
$282$	2.51493	+	10.2581i	0.149762	+	0.610863i
$283$	−4.41850	−	3.82865i	−0.262652	−	0.227590i	0.513572	−	0.858047i	$-0.328322\pi$
$283$	−4.41850	−	3.82865i	−0.262652	−	0.227590i	−0.776224	+	0.630457i	$0.782867\pi$
$284$	0.135050	+	0.0194172i	0.00801372	+	0.00115220i
$285$	−1.63662	−	1.15947i	−0.0969451	−	0.0686810i
$286$	14.6688	−	12.7106i	0.867385	−	0.751593i
$287$	−28.3492	+	18.2189i	−1.67340	+	1.07543i
$288$	−2.83022	+	0.994928i	−0.166772	+	0.0586267i
$289$	−10.8831	−	12.5598i	−0.640185	−	0.738813i
$290$	−1.48595	+	0.436315i	−0.0872581	+	0.0256213i
$291$	20.5951	−	11.9572i	1.20731	−	0.700944i
$292$	−4.66583	+	5.38466i	−0.273047	+	0.315113i
$293$	2.43967	−	5.34213i	0.142527	−	0.312090i	−0.824884	−	0.565302i	$-0.808760\pi$
$293$	2.43967	−	5.34213i	0.142527	−	0.312090i	0.967411	+	0.253212i	$0.0814869\pi$
$294$	−11.0082	−	27.3054i	−0.642014	−	1.59248i
$295$	−2.23094	+	1.01884i	−0.129890	+	0.0593189i
$296$	1.42806	+	9.93237i	0.0830042	+	0.577307i
$297$	2.33749	−	17.1411i	0.135635	−	0.994626i
$298$			19.4013i			1.12389i
$299$	−27.9353	−	1.15469i	−1.61554	−	0.0667777i
$300$	−1.35889	+	1.07398i	−0.0784553	+	0.0620061i
$301$	15.6050	+	10.0287i	0.899458	+	0.578046i
$302$	−8.30983	+	1.19477i	−0.478177	+	0.0687515i
$303$	−5.11007	+	9.97138i	−0.293566	+	0.572841i
$304$	0.326247	−	1.11109i	0.0187115	−	0.0637256i
$305$	−10.3961	−	4.74772i	−0.595277	−	0.271854i
$306$	14.1201	−	10.1584i	0.807195	−	0.580716i
$307$	2.39718	−	16.6727i	0.136814	−	0.951563i	−0.799567	−	0.600577i	$-0.794938\pi$
$307$	2.39718	−	16.6727i	0.136814	−	0.951563i	0.936381	−	0.350986i	$-0.114153\pi$
$308$	−4.59493	−	15.6489i	−0.261821	−	0.891679i
$309$	−5.80277	+	30.5051i	−0.330108	+	1.73538i
$310$	0.0410522	+	0.0638785i	0.00233161	+	0.00362806i
$311$	−9.12245	−	14.1948i	−0.517287	−	0.804914i	0.480096	−	0.877216i	$-0.340602\pi$
$311$	−9.12245	−	14.1948i	−0.517287	−	0.804914i	−0.997383	+	0.0723019i	$0.976965\pi$
$312$	−1.88697	+	9.91977i	−0.106828	+	0.561596i
$313$	5.38827	+	18.3508i	0.304563	+	1.03725i	0.959534	+	0.281592i	$0.0908625\pi$
$313$	5.38827	+	18.3508i	0.304563	+	1.03725i	−0.654971	+	0.755654i	$0.727319\pi$
$314$	1.50489	−	10.4667i	0.0849258	−	0.590672i
$315$	11.9298	−	8.58255i	0.672165	−	0.483572i
$316$	−5.94291	−	2.71403i	−0.334315	−	0.152676i
$317$	−0.0495520	+	0.168759i	−0.00278312	+	0.00947843i	−0.960873	−	0.276990i	$-0.910663\pi$
$317$	−0.0495520	+	0.168759i	−0.00278312	+	0.00947843i	0.958090	+	0.286468i	$0.0924813\pi$
$318$	2.60155	−	5.07646i	0.145888	−	0.284674i
$319$	5.10361	−	0.733788i	0.285747	−	0.0410842i
$320$	−0.841254	−	0.540641i	−0.0470275	−	0.0302227i
$321$	14.0159	−	11.0773i	0.782290	−	0.618273i
$322$	−10.6338	+	20.9492i	−0.592600	+	1.16745i
$323$			6.71431i			0.373594i
$324$	4.57532	+	7.75026i	0.254184	+	0.430570i
$325$	0.829678	+	5.77054i	0.0460223	+	0.320092i
$326$	−11.1150	+	5.07607i	−0.615605	+	0.281137i
$327$	1.00870	+	2.50203i	0.0557813	+	0.138363i
$328$	2.85767	−	6.25742i	0.157788	−	0.345508i
$329$	19.5621	−	22.5759i	1.07849	−	1.24465i
$330$	4.98700	−	2.89538i	0.274525	−	0.159385i
$331$	11.1122	−	3.26284i	0.610783	−	0.179342i	0.0383101	−	0.999266i	$-0.487803\pi$
$331$	11.1122	−	3.26284i	0.610783	−	0.179342i	0.572472	+	0.819924i	$0.305984\pi$
$332$	−6.67659	−	7.70520i	−0.366425	−	0.422878i
$333$	28.3998	−	9.98361i	1.55630	−	0.547099i
$334$	2.77848	−	1.78562i	0.152032	−	0.0977049i
$335$	−6.08366	+	5.27152i	−0.332386	+	0.288014i
$336$	6.92348	+	4.90495i	0.377707	+	0.267587i
$337$	4.55302	+	0.654626i	0.248019	+	0.0356597i	0.265203	−	0.964193i	$-0.414561\pi$
$337$	4.55302	+	0.654626i	0.248019	+	0.0356597i	−0.0171841	+	0.999852i	$0.505470\pi$
$338$	15.8613	+	13.7439i	0.862740	+	0.747568i
$339$	4.34326	+	17.7157i	0.235894	+	0.962187i
$340$	5.56332	+	1.63354i	0.301714	+	0.0885911i
$341$	−0.105019	−	0.229959i	−0.00568709	−	0.0124530i
$342$	−3.45983	−	0.313465i	−0.187086	−	0.0169503i
$343$	−26.4785	+	41.2013i	−1.42970	+	2.22466i
$344$	−3.78663			−0.204161
$345$	−8.08923	−	1.88797i	−0.435509	−	0.101645i
$346$	−1.53447			−0.0824934
$347$	3.33102	−	5.18318i	0.178819	−	0.278247i	−0.740260	−	0.672320i	$-0.765298\pi$
$347$	3.33102	−	5.18318i	0.178819	−	0.278247i	0.919079	+	0.394073i	$0.128934\pi$
$348$	−1.84636	+	1.94582i	−0.0989753	+	0.104307i
$349$	7.46343	+	16.3426i	0.399508	+	0.874801i	0.997320	+	0.0731645i	$0.0233098\pi$
$349$	7.46343	+	16.3426i	0.399508	+	0.874801i	−0.597812	+	0.801637i	$0.703963\pi$
$350$	4.70031	+	1.38014i	0.251242	+	0.0737713i
$351$	30.2921	−	0.220159i	1.61687	−	0.0117512i
$352$	2.51614	+	2.18025i	0.134111	+	0.116208i
$353$	10.8295	+	1.55704i	0.576394	+	0.0828730i	0.424346	−	0.905500i	$-0.360504\pi$
$353$	10.8295	+	1.55704i	0.576394	+	0.0828730i	0.152048	+	0.988373i	$0.451413\pi$
$354$	−2.45568	+	3.46626i	−0.130518	+	0.184230i
$355$	0.103113	−	0.0893481i	0.00547268	−	0.00474211i
$356$	15.5458	−	9.99068i	0.823926	−	0.529505i
$357$	−46.5300	−	15.9781i	−2.46263	−	0.845649i
$358$	−5.83235	−	6.73089i	−0.308249	−	0.355738i
$359$	−6.42730	+	1.88722i	−0.339220	+	0.0996039i	−0.446906	−	0.894581i	$-0.647474\pi$
$359$	−6.42730	+	1.88722i	−0.339220	+	0.0996039i	0.107686	+	0.994185i	$0.465656\pi$
$360$	−1.10148	+	2.79047i	−0.0580531	+	0.147071i
$361$	−11.5642	+	13.3458i	−0.608642	+	0.702411i
$362$	−2.86035	+	6.26328i	−0.150336	+	0.329191i
$363$	−0.135688	+	0.0547031i	−0.00712178	+	0.00287117i
$364$	25.9782	−	11.8639i	1.36163	−	0.621836i
$365$	1.01398	+	7.05240i	0.0530742	+	0.369139i
$366$	−19.7011	+	1.92940i	−1.02979	+	0.100852i
$367$			3.14108i			0.163963i	0.996634	+	0.0819816i	$0.0261249\pi$
$367$			3.14108i			0.163963i	−0.996634	+	0.0819816i	$0.973875\pi$
$368$	−0.485887	−	4.77115i	−0.0253286	−	0.248714i
$369$	−20.0788	−	4.76818i	−1.04526	−	0.248221i
$370$	8.44156	+	5.42506i	0.438856	+	0.282036i
$371$	−15.9691	+	2.29601i	−0.829073	+	0.119203i
$372$	0.117044	+	0.0599821i	0.00606847	+	0.00310993i
$373$	6.91810	−	23.5609i	0.358206	−	1.21994i	−0.561549	−	0.827443i	$-0.689794\pi$
$373$	6.91810	−	23.5609i	0.358206	−	1.21994i	0.919755	−	0.392493i	$-0.128387\pi$
$374$	−17.5596	−	8.01922i	−0.907987	−	0.414664i
$375$	−0.0782228	+	1.73028i	−0.00403941	+	0.0893515i
$376$	−0.867826	+	6.03586i	−0.0447547	+	0.311276i
$377$	2.54366	+	8.66292i	0.131005	+	0.446163i
$378$	10.4057	−	23.2306i	0.535210	−	1.19485i
$379$	−14.9462	−	23.2568i	−0.767736	−	1.19462i	−0.976260	−	0.216603i	$-0.930502\pi$
$379$	−14.9462	−	23.2568i	−0.767736	−	1.19462i	0.208524	−	0.978017i	$-0.433134\pi$
$380$	−0.626063	−	0.974173i	−0.0321163	−	0.0499740i
$381$	−21.8989	−	4.16568i	−1.12192	−	0.213414i
$382$	0.459165	+	1.56377i	0.0234929	+	0.0800096i
$383$	2.51842	−	17.5160i	0.128685	−	0.895027i	−0.818538	−	0.574453i	$-0.805215\pi$
$383$	2.51842	−	17.5160i	0.128685	−	0.895027i	0.947223	−	0.320574i	$-0.103876\pi$
$384$	−1.73028	−	0.0782228i	−0.0882982	−	0.00399179i
$385$	−14.8357	−	6.77523i	−0.756097	−	0.345298i
$386$	−4.85585	+	16.5375i	−0.247156	+	0.841737i
$387$	2.20389	+	11.1440i	0.112030	+	0.566484i
$388$	13.6094	−	1.95674i	0.690912	−	0.0993382i
$389$	−20.7460	−	13.3327i	−1.05187	−	0.675993i	−0.103972	−	0.994580i	$-0.533155\pi$
$389$	−20.7460	−	13.3327i	−1.05187	−	0.675993i	−0.947894	+	0.318587i	$0.896792\pi$
$390$	6.26116	+	7.92214i	0.317046	+	0.401153i
$391$	10.4970	+	25.7498i	0.530857	+	1.30222i
$392$		−	16.9977i		−	0.858513i
$393$	−2.15751	−	22.0304i	−0.108832	−	1.11128i
$394$	−0.326083	−	2.26796i	−0.0164278	−	0.114258i
$395$	−5.94291	+	2.71403i	−0.299020	+	0.136558i
$396$	4.95203	−	8.67396i	0.248849	−	0.435883i
$397$	9.53510	−	20.8790i	0.478553	−	1.04788i	−0.504306	−	0.863525i	$-0.668252\pi$
$397$	9.53510	−	20.8790i	0.478553	−	1.04788i	0.982859	−	0.184360i	$-0.0590211\pi$
$398$	1.33102	−	1.53608i	0.0667182	−	0.0769969i
$399$	4.93335	+	8.49720i	0.246976	+	0.425392i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	−5.85844	−	6.76100i	−0.292557	−	0.337628i	0.590376	−	0.807128i	$-0.298980\pi$
$401$	−5.85844	−	6.76100i	−0.292557	−	0.337628i	−0.882932	+	0.469500i	$0.844434\pi$
$402$	−4.52828	+	13.1869i	−0.225850	+	0.657702i
$403$	0.372404	−	0.239329i	0.0185508	−	0.0119219i
$404$	−4.88889	+	4.23625i	−0.243231	+	0.210761i
$405$	8.85345	+	1.61755i	0.439931	+	0.0803765i
$406$	7.50939	+	1.07969i	0.372685	+	0.0535840i
$407$	−25.2482	−	21.8777i	−1.25151	−	1.08444i
$408$	9.75391	−	2.39131i	0.482890	−	0.118387i
$409$	−11.1899	−	3.28564i	−0.553303	−	0.162464i	−0.00688382	−	0.999976i	$-0.502191\pi$
$409$	−11.1899	−	3.28564i	−0.553303	−	0.162464i	−0.546419	+	0.837512i	$0.684009\pi$
$410$	−2.85767	−	6.25742i	−0.141130	−	0.309032i
$411$	13.2936	+	12.6141i	0.655726	+	0.622208i
$412$	−9.69259	+	15.0820i	−0.477520	+	0.743035i
$413$	12.0145			0.591196
$414$	−13.7587	+	4.20687i	−0.676204	+	0.206756i
$415$	−10.1954			−0.500474
$416$	−3.15187	+	4.90441i	−0.154533	+	0.240458i
$417$	25.2955	+	24.0025i	1.23873	+	1.17541i
$418$	1.60158	+	3.50697i	0.0783358	+	0.171532i
$419$	23.8529	+	7.00384i	1.16529	+	0.342160i	0.806486	−	0.591253i	$-0.201367\pi$
$419$	23.8529	+	7.00384i	1.16529	+	0.342160i	0.358804	+	0.933413i	$0.383185\pi$
$420$	8.24083	−	2.02035i	0.402111	−	0.0985832i
$421$	−17.5759	−	15.2296i	−0.856599	−	0.742247i	0.111246	−	0.993793i	$-0.464516\pi$
$421$	−17.5759	−	15.2296i	−0.856599	−	0.742247i	−0.967845	+	0.251545i	$0.919061\pi$
$422$	−10.7857	−	1.55075i	−0.525041	−	0.0754895i
$423$	18.2686	−	0.958978i	0.888251	−	0.0466271i
$424$	2.48895	−	2.15669i	0.120874	−	0.104738i
$425$	4.87775	−	3.13474i	0.236606	−	0.152057i
$426$	0.0767509	−	0.223507i	0.00371859	−	0.0108290i
$427$	36.6637	+	42.3122i	1.77428	+	2.04763i
$428$	9.89644	−	2.90586i	0.478363	−	0.140460i
$429$	−16.8797	−	29.0736i	−0.814960	−	1.40369i
$430$	−2.47971	+	2.86174i	−0.119582	+	0.138005i
$431$	1.10799	−	2.42616i	0.0533699	−	0.116864i	−0.881068	−	0.472989i	$-0.843175\pi$
$431$	1.10799	−	2.42616i	0.0533699	−	0.116864i	0.934438	+	0.356125i	$0.115902\pi$
$432$	0.776850	+	5.13775i	0.0373762	+	0.247190i
$433$	−14.0489	+	6.41593i	−0.675148	+	0.308330i	−0.723324	−	0.690509i	$-0.757387\pi$
$433$	−14.0489	+	6.41593i	−0.675148	+	0.308330i	0.0481755	+	0.998839i	$0.484659\pi$
$434$	−0.0529374	−	0.368188i	−0.00254108	−	0.0176736i
$435$	0.261447	+	2.66963i	0.0125354	+	0.127999i
$436$			1.55752i			0.0745918i
$437$	1.78336	−	5.25946i	0.0853096	−	0.251594i
$438$	7.65201	+	9.68196i	0.365627	+	0.462622i
$439$	16.0963	+	10.3444i	0.768233	+	0.493714i	0.865110	−	0.501583i	$-0.167249\pi$
$439$	16.0963	+	10.3444i	0.768233	+	0.493714i	−0.0968763	+	0.995296i	$0.530885\pi$
$440$	3.29545	−	0.473814i	0.157104	−	0.0225882i
$441$	−50.0242	+	9.89299i	−2.38210	+	0.471095i
$442$	9.52333	−	32.4335i	0.452979	−	1.54270i
$443$	24.3091	+	11.1016i	1.15496	+	0.527454i	0.898445	−	0.439086i	$-0.144698\pi$
$443$	24.3091	+	11.1016i	1.15496	+	0.527454i	0.256517	+	0.966540i	$0.417425\pi$
$444$	17.3625	+	0.784927i	0.823990	+	0.0372510i
$445$	2.62988	−	18.2912i	0.124668	−	0.867088i
$446$	6.02991	+	20.5360i	0.285525	+	0.972408i
$447$	33.0121	+	6.27965i	1.56142	+	0.297017i
$448$	2.64846	+	4.12108i	0.125128	+	0.194703i
$449$	−10.5191	−	16.3680i	−0.496426	−	0.772455i	0.499139	−	0.866522i	$-0.333650\pi$
$449$	−10.5191	−	16.3680i	−0.496426	−	0.772455i	−0.995566	+	0.0940671i	$0.970013\pi$
$450$	1.38758	+	2.65981i	0.0654113	+	0.125385i
$451$	6.45244	+	21.9750i	0.303834	+	1.03476i
$452$	−1.49873	+	10.4239i	−0.0704943	+	0.490299i
$453$	−0.656703	+	14.5262i	−0.0308546	+	0.682502i
$454$	2.79361	+	1.27580i	0.131111	+	0.0598762i
$455$	8.04602	−	27.4022i	0.377203	−	1.28464i
$456$	−1.78497	−	0.914751i	−0.0835890	−	0.0428371i
$457$	23.0420	−	3.31294i	1.07786	−	0.154973i	0.419558	−	0.907728i	$-0.362185\pi$
$457$	23.0420	−	3.31294i	1.07786	−	0.154973i	0.658300	+	0.752756i	$0.271276\pi$
$458$	9.97029	+	6.40752i	0.465881	+	0.299404i
$459$	−12.7146	−	27.3140i	−0.593466	−	1.27491i
$460$	−3.92399	−	2.75723i	−0.182957	−	0.128557i
$461$		−	24.4776i		−	1.14003i	−0.821633	−	0.570017i	$-0.806937\pi$
$461$		−	24.4776i		−	1.14003i	0.821633	−	0.570017i	$-0.193063\pi$
$462$	−28.1145	+	2.75335i	−1.30800	+	0.128098i
$463$	−1.85526	−	12.9036i	−0.0862211	−	0.599681i	−0.986425	−	0.164212i	$-0.947492\pi$
$463$	−1.85526	−	12.9036i	−0.0862211	−	0.599681i	0.900204	−	0.435469i	$-0.143417\pi$
$464$	−1.40873	+	0.643347i	−0.0653988	+	0.0298666i
$465$	0.121979	−	0.0491763i	0.00565665	−	0.00228050i
$466$	−3.27237	+	7.16549i	−0.151590	+	0.331935i
$467$	−4.93693	+	5.69752i	−0.228454	+	0.263650i	−0.858391	−	0.512997i	$-0.828535\pi$
$467$	−4.93693	+	5.69752i	−0.228454	+	0.263650i	0.629937	+	0.776646i	$0.283081\pi$
$468$	16.2681	+	6.42149i	0.751994	+	0.296834i
$469$	37.8367	−	11.1099i	1.74714	−	0.513006i
$470$	3.99329	+	4.60851i	0.184197	+	0.212575i
$471$	−17.3225	−	5.94841i	−0.798177	−	0.274088i
$472$	−2.06324	+	1.32596i	−0.0949681	+	0.0610323i
$473$	9.52769	−	8.25579i	0.438084	−	0.379602i
$474$	−6.54159	+	9.23363i	−0.300465	+	0.424115i
$475$	−1.14621	−	0.164801i	−0.0525919	−	0.00756158i
$476$	−21.4662	−	18.6006i	−0.983902	−	0.852556i
$477$	−7.79575	−	6.06975i	−0.356943	−	0.277915i
$478$	−22.1958	−	6.51727i	−1.01521	−	0.298093i
$479$	12.3761	+	27.0998i	0.565477	+	1.23822i	0.949171	+	0.314762i	$0.101925\pi$
$479$	12.3761	+	27.0998i	0.565477	+	1.23822i	−0.383693	+	0.923461i	$0.625348\pi$
$480$	−1.19221	+	1.25644i	−0.0544168	+	0.0573482i
$481$	31.6275	−	49.2133i	1.44209	−	2.24393i
$482$	19.3428			0.881039
$483$	32.2040	+	24.8745i	1.46533	+	1.13183i
$484$	−0.0844663			−0.00383938
$485$	7.43346	−	11.5667i	0.337536	−	0.525216i
$486$	14.6683	−	5.27654i	0.665366	−	0.239349i
$487$	1.92969	+	4.22543i	0.0874427	+	0.191473i	0.948301	−	0.317371i	$-0.102800\pi$
$487$	1.92969	+	4.22543i	0.0874427	+	0.191473i	−0.860859	+	0.508844i	$0.830073\pi$
$488$	−10.9659	−	3.21988i	−0.496404	−	0.145757i
$489$	5.03951	+	20.5556i	0.227894	+	0.929559i
$490$	−12.8460	−	11.1311i	−0.580323	−	0.502853i
$491$	−21.2893	−	3.06093i	−0.960770	−	0.138138i	−0.355955	−	0.934503i	$-0.615844\pi$
$491$	−21.2893	−	3.06093i	−0.960770	−	0.138138i	−0.604816	+	0.796365i	$0.706753\pi$
$492$	−9.72231	−	6.88779i	−0.438315	−	0.310525i
$493$	6.78631	−	5.88037i	0.305640	−	0.264838i
$494$	−5.67931	+	3.64987i	−0.255524	+	0.164215i
$495$	−3.31245	−	9.42273i	−0.148884	−	0.423520i
$496$	0.0497252	+	0.0573860i	0.00223273	+	0.00257671i
$497$	−0.641303	+	0.188303i	−0.0287664	+	0.00844656i
$498$	−15.2717	+	8.86653i	−0.684342	+	0.397319i
$499$	−27.5809	+	31.8300i	−1.23469	+	1.42491i	−0.365220	+	0.930921i	$0.619006\pi$
$499$	−27.5809	+	31.8300i	−1.23469	+	1.42491i	−0.869469	+	0.493987i	$0.835539\pi$
$500$	−0.415415	+	0.909632i	−0.0185779	+	0.0406800i
$501$	−2.13899	−	5.30565i	−0.0955631	−	0.237039i
$502$	10.3952	−	4.74731i	0.463959	−	0.211883i
$503$	−5.45635	−	37.9498i	−0.243287	−	1.69210i	−0.635403	−	0.772181i	$-0.719166\pi$
$503$	−5.45635	−	37.9498i	−0.243287	−	1.69210i	0.392116	−	0.919916i	$-0.371743\pi$
$504$	10.5869	−	10.1930i	0.471578	−	0.454031i
$505$			6.46893i			0.287864i
$506$	11.6249	+	10.9456i	0.516789	+	0.486589i
$507$	28.5196	−	22.5401i	1.26660	−	1.00104i
$508$	−10.8270	−	6.95808i	−0.480370	−	0.308715i
$509$	9.98240	−	1.43525i	0.442462	−	0.0636165i	0.0825165	−	0.996590i	$-0.473704\pi$
$509$	9.98240	−	1.43525i	0.442462	−	0.0636165i	0.359946	+	0.932973i	$0.382795\pi$
$510$	4.58022	−	8.93748i	0.202816	−	0.395758i
$511$	9.83336	−	33.4893i	0.435002	−	1.48148i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	−1.65322	+	5.78558i	−0.0729916	+	0.255440i
$514$	−0.588684	+	4.09438i	−0.0259657	+	0.180596i
$515$	5.05089	+	17.2018i	0.222569	+	0.758000i
$516$	−1.22562	+	6.44309i	−0.0539551	+	0.283641i
$517$	−10.9761	−	17.0792i	−0.482729	−	0.751141i
$518$	−26.5760	−	41.3530i	−1.16768	−	1.81695i
$519$	−0.496663	+	2.61095i	−0.0218011	+	0.114608i
$520$	1.64247	+	5.59373i	0.0720269	+	0.245301i
$521$	−5.46189	+	37.9883i	−0.239290	+	1.66430i	0.416336	+	0.909211i	$0.363314\pi$
$521$	−5.46189	+	37.9883i	−0.239290	+	1.66430i	−0.655626	+	0.755086i	$0.727595\pi$
$522$	2.71328	+	3.77146i	0.118757	+	0.165072i
$523$	−37.8416	−	17.2817i	−1.65470	−	0.755674i	−0.654696	−	0.755892i	$-0.727203\pi$
$523$	−37.8416	−	17.2817i	−1.65470	−	0.755674i	−1.00000		0.000217648i	$0.999931\pi$
$524$	3.60057	−	12.2624i	0.157291	−	0.535685i
$525$	3.86971	−	7.55105i	0.168888	−	0.329555i
$526$	6.72035	−	0.966241i	0.293021	−	0.0421301i
$527$	−0.370380	−	0.238029i	−0.0161340	−	0.0103687i
$528$	4.52419	−	3.57563i	0.196890	−	0.155609i
$529$	−1.38324	−	22.9584i	−0.0601410	−	0.998190i
$530$		−	3.29335i		−	0.143054i
$531$	5.10315	+	5.30037i	0.221458	+	0.230016i
$532$	0.807317	+	5.61501i	0.0350016	+	0.243442i
$533$	−36.4800	+	16.6599i	−1.58012	+	0.721619i
$534$	−11.9678	−	29.6855i	−0.517897	−	1.28462i
$535$	4.28469	−	9.38216i	0.185243	−	0.405626i
$536$	−5.27152	+	6.08366i	−0.227695	+	0.262774i
$537$	−13.3406	+	7.74537i	−0.575691	+	0.334237i
$538$	9.10216	−	2.67264i	0.392422	−	0.115226i
$539$	37.0592	+	42.7686i	1.59625	+	1.84217i
$540$	4.39158	+	2.77741i	0.188984	+	0.119521i
$541$	−4.25568	+	2.73496i	−0.182966	+	0.117585i	−0.628917	−	0.777472i	$-0.716502\pi$
$541$	−4.25568	+	2.73496i	−0.182966	+	0.117585i	0.445952	+	0.895057i	$0.352865\pi$
$542$	−4.66071	+	4.03853i	−0.200195	+	0.173470i
$543$	9.73141	+	6.89424i	0.417615	+	0.295860i
$544$	5.73917	+	0.825169i	0.246065	+	0.0353788i
$545$	1.17710	+	1.01996i	0.0504213	+	0.0436903i
$546$	−11.7784	−	48.0430i	−0.504070	−	2.05605i
$547$	−18.4259	−	5.41033i	−0.787834	−	0.231329i	−0.137022	−	0.990568i	$-0.543753\pi$
$547$	−18.4259	−	5.41033i	−0.787834	−	0.231329i	−0.650812	+	0.759239i	$0.725571\pi$
$548$	4.39527	+	9.62429i	0.187756	+	0.411129i
$549$	−3.09374	+	34.1467i	−0.132038	+	1.45735i
$550$	1.79997	−	2.80081i	0.0767511	−	0.119427i
$551$	−1.79338			−0.0764005
$552$	−8.27558	−	0.717532i	−0.352232	−	0.0305402i
$553$	32.0050			1.36099
$554$	−1.33564	+	2.07829i	−0.0567458	+	0.0882981i
$555$	11.9633	−	12.6077i	0.507812	−	0.535168i
$556$	8.36344	+	18.3134i	0.354689	+	0.776660i
$557$	−15.5246	−	4.55843i	−0.657798	−	0.193147i	−0.0642356	−	0.997935i	$-0.520461\pi$
$557$	−15.5246	−	4.55843i	−0.657798	−	0.193147i	−0.593563	+	0.804788i	$0.702279\pi$
$558$	0.139946	−	0.179741i	0.00592438	−	0.00760905i
$559$	16.6836	+	14.4564i	0.705641	+	0.611441i
$560$	4.84888	+	0.697164i	0.204903	+	0.0294605i
$561$	−19.3286	+	27.2828i	−0.816053	+	1.15188i
$562$	−13.3976	+	11.6091i	−0.565142	+	0.489699i
$563$	−19.9942	+	12.8495i	−0.842656	+	0.541542i	−0.889276	−	0.457370i	$-0.848791\pi$
$563$	−19.9942	+	12.8495i	−0.842656	+	0.541542i	0.0466201	+	0.998913i	$0.485155\pi$
$564$	9.98936	+	3.43028i	0.420628	+	0.144441i
$565$	6.89640	+	7.95886i	0.290134	+	0.334832i
$566$	−5.60968	+	1.64715i	−0.235793	+	0.0692350i
$567$	−36.1597	−	25.2247i	−1.51857	−	1.05934i
$568$	0.0893481	−	0.103113i	0.00374896	−	0.00432654i
$569$	−15.6152	+	34.1925i	−0.654623	+	1.43342i	0.232827	+	0.972518i	$0.425202\pi$
$569$	−15.6152	+	34.1925i	−0.654623	+	1.43342i	−0.887449	+	0.460905i	$0.847525\pi$
$570$	−1.86023	+	0.749958i	−0.0779165	+	0.0314123i
$571$	−7.74485	+	3.53695i	−0.324112	+	0.148017i	−0.570825	−	0.821072i	$-0.693377\pi$
$571$	−7.74485	+	3.53695i	−0.324112	+	0.148017i	0.246713	+	0.969088i	$0.420649\pi$
$572$	−2.76228	−	19.2120i	−0.115497	−	0.803296i
$573$	2.80944	−	0.275139i	0.117366	−	0.0114941i
$574$			33.6988i			1.40656i
$575$	−4.65344	+	1.15995i	−0.194062	+	0.0483731i
$576$	−0.693143	+	2.91883i	−0.0288810	+	0.121618i
$577$	30.4170	+	19.5478i	1.26627	+	0.813785i	0.989130	−	0.147043i	$-0.0469755\pi$
$577$	30.4170	+	19.5478i	1.26627	+	0.813785i	0.277145	+	0.960828i	$0.410612\pi$
$578$	−16.4499	+	2.36513i	−0.684224	+	0.0983766i
$579$	26.5675	+	13.6151i	1.10411	+	0.565826i
$580$	−0.436315	+	1.48595i	−0.0181170	+	0.0617008i
$581$	45.4314	+	20.7478i	1.88481	+	0.860765i
$582$	1.07551	−	23.7903i	0.0445814	−	0.986138i
$583$	−1.56044	+	10.8531i	−0.0646266	+	0.449488i
$584$	2.00732	+	6.83631i	0.0830636	+	0.282889i
$585$	15.5064	−	8.08944i	0.641110	−	0.334457i
$586$	−3.17510	−	4.94055i	−0.131162	−	0.204092i
$587$	7.66289	+	11.9237i	0.316281	+	0.492143i	0.962601	−	0.270924i	$-0.0873291\pi$
$587$	7.66289	+	11.9237i	0.316281	+	0.492143i	−0.646320	+	0.763067i	$0.723693\pi$
$588$	−28.9222	−	5.50167i	−1.19273	−	0.226885i
$589$	0.0247727	+	0.0843682i	0.00102074	+	0.00347633i
$590$	−0.349037	+	2.42761i	−0.0143696	+	0.0999431i
$591$	−3.96457	−	0.179230i	−0.163080	−	0.00737256i
$592$	9.12771	+	4.16848i	0.375146	+	0.171324i
$593$	−4.66749	+	15.8960i	−0.191671	+	0.652771i	0.806439	+	0.591317i	$0.201392\pi$
$593$	−4.66749	+	15.8960i	−0.191671	+	0.652771i	−0.998110	+	0.0614540i	$0.980426\pi$
$594$	−13.1563	−	11.2336i	−0.539808	−	0.460920i
$595$	−28.1147	+	4.04229i	−1.15259	+	0.165718i
$596$	16.3214	+	10.4891i	0.668552	+	0.429652i
$597$	−2.18289	−	2.76198i	−0.0893398	−	0.113040i
$598$	−16.0743	+	22.8764i	−0.657328	+	0.935484i
$599$			0.452727i			0.0184979i	0.999957	+	0.00924896i	$0.00294408\pi$
$599$			0.452727i			0.0184979i	−0.999957	+	0.00924896i	$0.997056\pi$
$600$	0.168818	+	1.72380i	0.00689198	+	0.0703740i
$601$	−1.63673	−	11.3837i	−0.0667638	−	0.464352i	−0.995588	−	0.0938317i	$-0.970088\pi$
$601$	−1.63673	−	11.3837i	−0.0667638	−	0.464352i	0.928824	−	0.370520i	$-0.120821\pi$
$602$	16.8734	−	7.70583i	0.687709	−	0.314066i
$603$	20.9723	+	11.9733i	0.854060	+	0.487590i
$604$	−3.48753	+	7.63662i	−0.141906	+	0.310730i
$605$	−0.0553137	+	0.0638354i	−0.00224882	+	0.00259528i
$606$	5.62575	+	9.68980i	0.228530	+	0.393621i
$607$	−11.6500	+	3.42076i	−0.472861	+	0.138844i	−0.509476	−	0.860485i	$-0.670161\pi$
$607$	−11.6500	+	3.42076i	−0.472861	+	0.138844i	0.0366151	+	0.999329i	$0.488342\pi$
$608$	−0.758330	−	0.875159i	−0.0307543	−	0.0354924i
$609$	4.26771	−	12.4281i	0.172936	−	0.503610i
$610$	−9.61457	+	6.17891i	−0.389283	+	0.250177i
$611$	26.8670	−	23.2804i	1.08692	−	0.941825i
$612$	−0.911841	−	17.3707i	−0.0368590	−	0.702167i
$613$	41.9749	+	6.03508i	1.69535	+	0.243755i	0.921156	−	0.389194i	$-0.127246\pi$
$613$	41.9749	+	6.03508i	1.69535	+	0.243755i	0.774194	+	0.632948i	$0.218155\pi$
$614$	−12.7300	−	11.0306i	−0.513740	−	0.445158i
$615$	−11.5722	+	2.83709i	−0.466636	+	0.114402i
$616$	−15.6489	−	4.59493i	−0.630512	−	0.185135i
$617$	−4.69795	−	10.2871i	−0.189132	−	0.414142i	0.791183	−	0.611579i	$-0.209465\pi$
$617$	−4.69795	−	10.2871i	−0.189132	−	0.414142i	−0.980316	+	0.197437i	$0.936738\pi$
$618$	22.5253	+	21.3739i	0.906102	+	0.859786i
$619$	−2.49418	+	3.88102i	−0.100250	+	0.155991i	−0.887755	−	0.460317i	$-0.847736\pi$
$619$	−2.49418	+	3.88102i	−0.100250	+	0.155991i	0.787505	+	0.616308i	$0.211372\pi$
$620$	0.0759325			0.00304952
$621$	2.70485	+	24.7726i	0.108542	+	0.994092i
$622$	−16.8734			−0.676562
$623$	−48.9418	+	76.1549i	−1.96081	+	3.05108i
$624$	7.32487	+	6.95045i	0.293229	+	0.278241i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	18.3508	+	5.38827i	0.733444	+	0.215358i
$627$	6.48564	−	1.59004i	0.259011	−	0.0635003i
$628$	−7.99157	−	6.92474i	−0.318898	−	0.276327i
$629$	−57.5898	−	8.28016i	−2.29625	−	0.330152i
$630$	−0.770391	−	14.6760i	−0.0306931	−	0.584707i
$631$	2.98801	−	2.58913i	0.118951	−	0.103071i	−0.593354	−	0.804941i	$-0.702197\pi$
$631$	2.98801	−	2.58913i	0.118951	−	0.103071i	0.712305	+	0.701870i	$0.247651\pi$
$632$	−5.49617	+	3.53217i	−0.218626	+	0.140502i
$633$	−6.12970	+	17.8504i	−0.243634	+	0.709490i
$634$	0.115179	+	0.132924i	0.00457434	+	0.00527907i
$635$	−12.3487	+	3.62592i	−0.490045	+	0.143890i
$636$	−2.86409	−	4.93311i	−0.113568	−	0.195610i
$637$	−64.8930	+	74.8906i	−2.57116	+	2.96727i
$638$	2.14192	−	4.69014i	0.0847993	−	0.185685i
$639$	−0.355465	−	0.202938i	−0.0140620	−	0.00802809i
$640$	−0.909632	+	0.415415i	−0.0359564	+	0.0164207i
$641$	4.44630	+	30.9247i	0.175618	+	1.22145i	0.866757	+	0.498731i	$0.166200\pi$
$641$	4.44630	+	30.9247i	0.175618	+	1.22145i	−0.691138	+	0.722722i	$0.742891\pi$
$642$	−1.74123	−	17.7797i	−0.0687210	−	0.701710i
$643$		−	17.6159i		−	0.694703i	−0.937735	−	0.347351i	$-0.887081\pi$
$643$		−	17.6159i		−	0.694703i	0.937735	−	0.347351i	$-0.112919\pi$
$644$	11.8745	+	20.2717i	0.467920	+	0.798818i
$645$	4.06675	+	5.14559i	0.160128	+	0.202608i
$646$	5.64844	+	3.63003i	0.222235	+	0.142822i
$647$	−36.8500	+	5.29823i	−1.44872	+	0.208295i	−0.821350	−	0.570424i	$-0.806779\pi$
$647$	−36.8500	+	5.29823i	−1.44872	+	0.208295i	−0.627373	+	0.778719i	$0.715870\pi$
$648$	8.99353	+	0.341105i	0.353299	+	0.0133999i
$649$	2.30047	−	7.83468i	0.0903013	−	0.307538i
$650$	5.30304	+	2.42182i	0.208002	+	0.0949915i
$651$	−0.643621	−	0.0290968i	−0.0252255	−	0.00114040i
$652$	−1.73898	+	12.0949i	−0.0681038	+	0.473672i
$653$	−2.00598	−	6.83173i	−0.0785000	−	0.267346i	0.910886	−	0.412658i	$-0.135400\pi$
$653$	−2.00598	−	6.83173i	−0.0785000	−	0.267346i	−0.989386	+	0.145312i	$0.953581\pi$
$654$	2.65019	+	0.504126i	0.103630	+	0.0197129i
$655$	−6.90943	−	10.7513i	−0.269974	−	0.420088i
$656$	−3.71911	−	5.78704i	−0.145207	−	0.225946i
$657$	18.9510	−	9.88642i	0.739348	−	0.385706i
$658$	−8.41597	−	28.6621i	−0.328089	−	1.11737i
$659$	−6.06757	+	42.2009i	−0.236359	+	1.64391i	0.433303	+	0.901248i	$0.357348\pi$
$659$	−6.06757	+	42.2009i	−0.236359	+	1.64391i	−0.669662	+	0.742666i	$0.733561\pi$
$660$	0.260430	−	5.76069i	0.0101372	−	0.224235i
$661$	10.2077	+	4.66170i	0.397033	+	0.181319i	0.603918	−	0.797046i	$-0.293605\pi$
$661$	10.2077	+	4.66170i	0.397033	+	0.181319i	−0.206885	+	0.978365i	$0.566333\pi$
$662$	3.26284	−	11.1122i	0.126814	−	0.431889i
$663$	−52.1044	−	26.7021i	−2.02357	−	1.03702i
$664$	−10.0917	+	1.45096i	−0.391632	+	0.0563082i
$665$	4.77222	+	3.06692i	0.185059	+	0.118930i
$666$	6.95535	−	29.2890i	0.269514	−	1.13493i
$667$	−6.87771	+	2.80373i	−0.266306	+	0.108561i
$668$		−	3.30279i		−	0.127789i
$669$	36.8945	−	3.61322i	1.42642	−	0.139695i
$670$	1.14561	+	7.96790i	0.0442588	+	0.307827i
$671$	34.6120	−	15.8068i	1.33618	−	0.610213i
$672$	7.86942	−	3.17258i	0.303569	−	0.122385i
$673$	0.192056	−	0.420545i	0.00740323	−	0.0162108i	−0.905894	−	0.423504i	$-0.860800\pi$
$673$	0.192056	−	0.420545i	0.00740323	−	0.0162108i	0.913297	+	0.407293i	$0.133527\pi$
$674$	3.01225	−	3.47633i	0.116028	−	0.133903i
$675$	4.97490	−	1.50012i	0.191484	−	0.0577397i
$676$	20.1373	−	5.91285i	0.774513	−	0.227417i
$677$	0.961607	+	1.10975i	0.0369575	+	0.0426513i	0.773927	−	0.633274i	$-0.218290\pi$
$677$	0.961607	+	1.10975i	0.0369575	+	0.0426513i	−0.736970	+	0.675926i	$0.763744\pi$
$678$	17.2516	+	5.92407i	0.662543	+	0.227512i
$679$	−56.6622	+	36.4146i	−2.17450	+	1.39746i
$680$	4.38198	−	3.79701i	0.168041	−	0.145609i
$681$	3.07504	−	4.34050i	0.117836	−	0.166328i
$682$	−0.250232	−	0.0359779i	−0.00958186	−	0.00137766i
$683$	−13.5967	−	11.7816i	−0.520265	−	0.450812i	0.354713	−	0.934975i	$-0.384579\pi$
$683$	−13.5967	−	11.7816i	−0.520265	−	0.450812i	−0.874978	+	0.484163i	$0.839124\pi$
$684$	−2.13423	+	2.74112i	−0.0816043	+	0.104809i
$685$	10.1518	+	2.98085i	0.387882	+	0.113892i
$686$	20.3454	+	44.5502i	0.776791	+	1.70093i
$687$	14.1297	−	14.8909i	0.539083	−	0.568124i
$688$	−2.04720	+	3.18551i	−0.0780489	+	0.121447i
$689$	−19.1998			−0.731456
$690$	−5.96162	+	5.78438i	−0.226955	+	0.220208i
$691$	34.0057			1.29364			0.646818	−	0.762644i	$-0.276099\pi$
$691$	34.0057			1.29364			0.646818	+	0.762644i	$0.276099\pi$
$692$	−0.829595	+	1.29088i	−0.0315365	+	0.0490717i
$693$	−4.41492	+	48.7291i	−0.167709	+	1.85106i
$694$	−2.55948	−	5.60447i	−0.0971564	−	0.212743i
$695$	19.3172	+	5.67205i	0.732744	+	0.215153i
$696$	0.638713	+	2.60525i	0.0242104	+	0.0987517i
$697$	30.1440	+	26.1199i	1.14178	+	0.989361i
$698$	17.7833	+	2.55686i	0.673109	+	0.0967785i
$699$	11.1332	+	7.88733i	0.421096	+	0.298326i
$700$	3.70222	−	3.20799i	0.139931	−	0.121251i
$701$	−12.5471	+	8.06352i	−0.473897	+	0.304555i	−0.755701	−	0.654917i	$-0.772704\pi$
$701$	−12.5471	+	8.06352i	−0.473897	+	0.304555i	0.281804	+	0.959472i	$0.409067\pi$
$702$	16.1920	−	25.6024i	0.611126	−	0.966300i
$703$	7.60946	+	8.78179i	0.286996	+	0.331211i
$704$	3.19447	−	0.937982i	0.120396	−	0.0353515i
$705$	9.13407	−	5.30310i	0.344009	−	0.199726i
$706$	7.16472	−	8.26852i	0.269648	−	0.311190i
$707$	13.1643	−	28.8259i	0.495096	−	1.08411i
$708$	1.58836	+	3.93985i	0.0596944	+	0.148069i
$709$	−3.64079	+	1.66269i	−0.136733	+	0.0624438i	−0.482606	−	0.875837i	$-0.660310\pi$
$709$	−3.64079	+	1.66269i	−0.136733	+	0.0624438i	0.345874	+	0.938281i	$0.387583\pi$
$710$	−0.0194172	−	0.135050i	−0.000728715	−	0.00506832i
$711$	13.5941	+	14.1194i	0.509817	+	0.529520i
$712$		−	18.4793i		−	0.692542i
$713$	0.226904	+	0.284828i	0.00849763	+	0.0106669i
$714$	−38.5976	+	30.5051i	−1.44448	+	1.14162i
$715$	−16.3284	−	10.4936i	−0.610648	−	0.392439i
$716$	−8.81559	+	1.26749i	−0.329454	+	0.0473683i
$717$	−18.2735	+	35.6575i	−0.682437	+	1.33165i
$718$	−1.88722	+	6.42730i	−0.0704306	+	0.239865i
$719$	−17.7331	−	8.09845i	−0.661335	−	0.302021i	0.0563280	−	0.998412i	$-0.482061\pi$
$719$	−17.7331	−	8.09845i	−0.661335	−	0.302021i	−0.717663	+	0.696391i	$0.754788\pi$
$720$	1.75199	+	2.43527i	0.0652928	+	0.0907571i
$721$	12.4987	−	86.9306i	0.465477	−	3.23746i
$722$	4.97512	+	16.9437i	0.185155	+	0.630580i
$723$	6.26070	−	32.9125i	0.232838	−	1.22403i
$724$	3.72259	+	5.79246i	0.138349	+	0.215275i
$725$	0.837282	+	1.30284i	0.0310959	+	0.0483861i
$726$	−0.0273394	+	0.143723i	−0.00101466	+	0.00533405i
$727$	−9.65750	−	32.8904i	−0.358177	−	1.21984i	−0.919781	−	0.392432i	$-0.871634\pi$
$727$	−9.65750	−	32.8904i	−0.358177	−	1.21984i	0.561604	−	0.827406i	$-0.310184\pi$
$728$	4.06438	−	28.2684i	0.150636	−	1.04770i
$729$	−4.23054	−	26.6665i	−0.156687	−	0.987648i
$730$	6.48106	+	2.95980i	0.239875	+	0.109547i
$731$	6.18560	−	21.0662i	0.228783	−	0.779163i
$732$	−9.02811	+	17.6168i	−0.333689	+	0.651134i
$733$	−26.5003	+	3.81016i	−0.978810	+	0.140732i	−0.613107	−	0.790000i	$-0.710081\pi$
$733$	−26.5003	+	3.81016i	−0.978810	+	0.140732i	−0.365703	+	0.930732i	$0.619171\pi$
$734$	2.64245	+	1.69820i	0.0975345	+	0.0626816i
$735$	−23.0979	+	18.2551i	−0.851979	+	0.673351i
$736$	−4.27644	−	2.17073i	−0.157632	−	0.0800141i
$737$		−	26.8006i		−	0.987212i
$738$	−14.8667	+	14.3135i	−0.547250	+	0.526887i
$739$	−1.20643	−	8.39090i	−0.0443792	−	0.308664i	−0.999905	−	0.0137578i	$-0.995621\pi$
$739$	−1.20643	−	8.39090i	−0.0443792	−	0.308664i	0.955526	−	0.294906i	$-0.0952885\pi$
$740$	9.12771	−	4.16848i	0.335541	−	0.153237i
$741$	4.37217	+	10.8449i	0.160616	+	0.398398i
$742$	−6.70201	+	14.6754i	−0.246039	+	0.538749i
$743$	−16.7358	+	19.3142i	−0.613978	+	0.708568i	−0.974552	−	0.224163i	$-0.928035\pi$
$743$	−16.7358	+	19.3142i	−0.613978	+	0.708568i	0.360574	+	0.932731i	$0.382581\pi$
$744$	0.113739	−	0.0660352i	0.00416988	−	0.00242097i
$745$	18.6154	−	5.46598i	0.682016	−	0.200258i
$746$	−16.0805	−	18.5579i	−0.588748	−	0.679451i
$747$	10.1437	+	28.8553i	0.371140	+	1.05576i
$748$	−16.2397	+	10.4366i	−0.593781	+	0.381600i
$749$	−38.1856	+	33.0880i	−1.39527	+	1.20901i
$750$	1.41332	+	1.00127i	0.0516070	+	0.0365611i
$751$	−6.69390	−	0.962437i	−0.244264	−	0.0351198i	0.0190955	−	0.999818i	$-0.493921\pi$
$751$	−6.69390	−	0.962437i	−0.244264	−	0.0351198i	−0.263359	+	0.964698i	$0.584830\pi$
$752$	4.60851	+	3.99329i	0.168055	+	0.145620i
$753$	−4.71312	−	19.2244i	−0.171756	−	0.700575i
$754$	8.66292	+	2.54366i	0.315485	+	0.0926347i
$755$	3.48753	+	7.63662i	0.126924	+	0.277925i
$756$	−13.9171	−	21.3132i	−0.506159	−	0.775154i
$757$	4.46861	−	6.95329i	0.162414	−	0.252722i	−0.750502	−	0.660868i	$-0.770188\pi$
$757$	4.46861	−	6.95329i	0.162414	−	0.252722i	0.912917	+	0.408146i	$0.133825\pi$
$758$	−27.6454			−1.00413
$759$	22.3869	−	16.2374i	0.812594	−	0.589381i
$760$	−1.15800			−0.0420051
$761$	26.9587	−	41.9485i	0.977250	−	1.52063i	0.128587	−	0.991698i	$-0.458956\pi$
$761$	26.9587	−	41.9485i	0.977250	−	1.52063i	0.848664	−	0.528933i	$-0.177408\pi$
$762$	−15.3438	+	16.1704i	−0.555849	+	0.585792i
$763$	−3.16958	−	6.94040i	−0.114746	−	0.251260i
$764$	1.56377	+	0.459165i	0.0565753	+	0.0166120i
$765$	−13.7250	−	10.6862i	−0.496228	−	0.386362i
$766$	−13.3739	−	11.5885i	−0.483217	−	0.418710i
$767$	14.1527	+	2.03485i	0.511023	+	0.0734740i
$768$	−1.00127	+	1.41332i	−0.0361301	+	0.0509987i
$769$	−11.0690	+	9.59138i	−0.399160	+	0.345874i	−0.831193	−	0.555984i	$-0.812342\pi$
$769$	−11.0690	+	9.59138i	−0.399160	+	0.345874i	0.432033	+	0.901858i	$0.357796\pi$
$770$	−13.7205	+	8.81761i	−0.494451	+	0.317765i
$771$	6.77622	+	2.32690i	0.244039	+	0.0838014i
$772$	11.2870	+	13.0259i	0.406227	+	0.468811i
$773$	29.4462	−	8.64619i	1.05911	−	0.310982i	0.294616	−	0.955616i	$-0.404808\pi$
$773$	29.4462	−	8.64619i	1.05911	−	0.310982i	0.764491	+	0.644634i	$0.222990\pi$
$774$	10.5665	+	4.17089i	0.379804	+	0.149920i
$775$	0.0497252	−	0.0573860i	0.00178618	−	0.00206137i
$776$	5.71168	−	12.5068i	0.205037	−	0.448969i
$777$	−78.9657	+	31.8353i	−2.83288	+	1.14208i
$778$	−22.4323	+	10.2445i	−0.804237	+	0.367283i
$779$	−1.13368	−	7.88489i	−0.0406182	−	0.282506i
$780$	10.0496	−	0.984191i	0.359832	−	0.0352397i
$781$			0.454249i			0.0162543i
$782$	27.3372	+	5.09072i	0.977576	+	0.182044i
$783$	7.29550	−	3.39604i	0.260720	−	0.121365i
$784$	−14.2994	−	9.18964i	−0.510691	−	0.328201i
$785$	−10.4667	+	1.50489i	−0.373574	+	0.0537118i
$786$	−19.6996	−	10.0955i	−0.702660	−	0.360094i
$787$	−3.32582	+	11.3267i	−0.118553	+	0.403753i	−0.997292	−	0.0735496i	$-0.976567\pi$
$787$	−3.32582	+	11.3267i	−0.118553	+	0.403753i	0.878739	+	0.477303i	$0.158385\pi$
$788$	−2.08422	−	0.951833i	−0.0742474	−	0.0339076i
$789$	0.531090	−	11.7477i	0.0189073	−	0.418229i
$790$	−0.929787	+	6.46681i	−0.0330803	+	0.230079i
$791$	−14.5343	−	49.4994i	−0.516781	−	1.75999i
$792$	−4.61973	−	8.85541i	−0.164155	−	0.314663i
$793$	36.0223	+	56.0518i	1.27919	+	1.99046i
$794$	−12.4094	−	19.3095i	−0.440394	−	0.685267i
$795$	−5.60377	−	1.06596i	−0.198745	−	0.0378059i
$796$	−0.572630	−	1.95020i	−0.0202963	−	0.0691229i
$797$	−4.64416	+	32.3008i	−0.164504	+	1.14415i	0.725507	+	0.688215i	$0.241605\pi$
$797$	−4.64416	+	32.3008i	−0.164504	+	1.14415i	−0.890011	+	0.455939i	$0.849304\pi$
$798$	9.81547	+	0.443738i	0.347464	+	0.0157082i
$799$	−32.1618	−	14.6878i	−1.13780	−	0.519617i
$800$	−0.281733	+	0.959493i	−0.00996075	+	0.0339232i
$801$	−54.3847	+	10.7553i	−1.92159	+	0.380021i
$802$	−8.85503	+	1.27316i	−0.312682	+	0.0449569i
$803$	−19.9556	−	12.8247i	−0.704217	−	0.452573i
$804$	8.64534	+	10.9388i	0.304898	+	0.385782i
$805$	23.0965	+	4.30102i	0.814044	+	0.151591i
$806$		−	0.442677i		−	0.0155926i
$807$	−1.60148	−	16.3527i	−0.0563749	−	0.575644i
$808$	0.920625	+	6.40309i	0.0323875	+	0.225260i
$809$	15.1046	−	6.89804i	0.531050	−	0.242522i	−0.131798	−	0.991277i	$-0.542075\pi$
$809$	15.1046	−	6.89804i	0.531050	−	0.242522i	0.662848	+	0.748754i	$0.269348\pi$
$810$	6.14730	−	6.57348i	0.215994	−	0.230969i
$811$	−18.6114	+	40.7532i	−0.653534	+	1.43104i	0.234893	+	0.972021i	$0.424526\pi$
$811$	−18.6114	+	40.7532i	−0.653534	+	1.43104i	−0.888427	+	0.459019i	$0.848201\pi$
$812$	4.96817	−	5.73358i	0.174349	−	0.201209i
$813$	5.36317	+	9.23753i	0.188095	+	0.323974i
$814$	−32.0550	+	9.41218i	−1.12353	+	0.329897i
$815$	8.00192	+	9.23470i	0.280295	+	0.323478i
$816$	3.26166	−	9.49835i	0.114181	−	0.332509i
$817$	−3.68883	+	2.37067i	−0.129056	+	0.0829391i
$818$	−8.81375	+	7.63716i	−0.308166	+	0.267027i
$819$	−85.5594	+	4.49128i	−2.98969	+	0.156938i
$820$	−6.80905	−	0.978994i	−0.237782	−	0.0341879i
$821$	−7.68658	−	6.66046i	−0.268264	−	0.232452i	0.510332	−	0.859977i	$-0.329522\pi$
$821$	−7.68658	−	6.66046i	−0.268264	−	0.232452i	−0.778596	+	0.627526i	$0.784068\pi$
$822$	17.7987	−	4.36361i	0.620802	−	0.152198i
$823$	−18.2627	−	5.36242i	−0.636599	−	0.186922i	−0.0525209	−	0.998620i	$-0.516726\pi$
$823$	−18.2627	−	5.36242i	−0.636599	−	0.186922i	−0.584078	+	0.811697i	$0.698544\pi$
$824$	7.44755	+	16.3079i	0.259448	+	0.568111i
$825$	−4.18310	−	3.96927i	−0.145637	−	0.138192i
$826$	6.49554	−	10.1073i	0.226009	−	0.351677i
$827$	−16.2099			−0.563673			−0.281837	−	0.959462i	$-0.590944\pi$
$827$	−16.2099			−0.563673			−0.281837	+	0.959462i	$0.590944\pi$
$828$	−3.89948	+	13.8490i	−0.135516	+	0.481285i
$829$	−3.71257			−0.128943			−0.0644714	−	0.997920i	$-0.520536\pi$
$829$	−3.71257			−0.128943			−0.0644714	+	0.997920i	$0.520536\pi$
$830$	−5.51207	+	8.57695i	−0.191327	+	0.297710i
$831$	3.10399	+	2.94532i	0.107676	+	0.102172i
$832$	2.42182	+	5.30304i	0.0839615	+	0.183850i
$833$	94.5636	+	27.7664i	3.27644	+	0.962048i
$834$	33.8679	−	8.30320i	1.17275	−	0.287516i
$835$	−2.49608	−	2.16287i	−0.0863805	−	0.0748491i
$836$	3.81613	+	0.548677i	0.131984	+	0.0189764i
$837$	−0.260540	−	0.296301i	−0.00900559	−	0.0102416i
$838$	18.7878	−	16.2798i	0.649015	−	0.562375i
$839$	36.8906	−	23.7081i	1.27360	−	0.818495i	0.283519	−	0.958967i	$-0.408498\pi$
$839$	36.8906	−	23.7081i	1.27360	−	0.818495i	0.990085	+	0.140472i	$0.0448619\pi$
$840$	2.75570	−	8.02491i	0.0950806	−	0.276886i
$841$	−17.4203	−	20.1041i	−0.600701	−	0.693246i
$842$	−22.3143	+	6.55206i	−0.769000	+	0.225799i
$843$	15.4169	+	26.5540i	0.530985	+	0.914569i
$844$	−7.13578	+	8.23513i	−0.245624	+	0.283465i
$845$	8.71851	−	19.0909i	0.299926	−	0.656746i
$846$	9.07002	−	15.8870i	0.311834	−	0.546207i
$847$	0.376387	−	0.171890i	0.0129328	−	0.00590621i
$848$	−0.468693	−	3.25983i	−0.0160950	−	0.111943i
$849$	0.986998	+	10.0782i	0.0338737	+	0.345884i
$850$		−	5.79819i		−	0.198876i
$851$	42.9120	+	21.7822i	1.47100	+	0.746683i
$852$	−0.146532	−	0.185404i	−0.00502010	−	0.00635184i
$853$	−32.8779	−	21.1293i	−1.12572	−	0.723454i	−0.161055	−	0.986946i	$-0.551489\pi$
$853$	−32.8779	−	21.1293i	−1.12572	−	0.723454i	−0.964662	+	0.263492i	$0.915126\pi$
$854$	55.4172	−	7.96779i	1.89634	−	0.272652i
$855$	0.673980	+	3.40800i	0.0230496	+	0.116551i
$856$	2.90586	−	9.89644i	0.0993202	−	0.338253i
$857$	−44.7098	−	20.4183i	−1.52726	−	0.697475i	−0.537904	−	0.843006i	$-0.680784\pi$
$857$	−44.7098	−	20.4183i	−1.52726	−	0.697475i	−0.989354	+	0.145531i	$0.953511\pi$
$858$	−33.5841	−	1.51827i	−1.14654	−	0.0518330i
$859$	2.89003	−	20.1006i	0.0986067	−	0.685825i	−0.879221	−	0.476414i	$-0.841936\pi$
$859$	2.89003	−	20.1006i	0.0986067	−	0.685825i	0.977828	−	0.209411i	$-0.0671545\pi$
$860$	1.06682	+	3.63324i	0.0363781	+	0.123892i
$861$	57.3398	+	10.9073i	1.95414	+	0.371721i
$862$	−1.44199	−	2.24378i	−0.0491143	−	0.0764234i
$863$	17.5450	+	27.3005i	0.597238	+	0.929320i	0.999902	+	0.0139726i	$0.00444776\pi$
$863$	17.5450	+	27.3005i	0.597238	+	0.929320i	−0.402665	+	0.915348i	$0.631916\pi$
$864$	4.74215	+	2.12415i	0.161331	+	0.0722651i
$865$	0.432309	+	1.47231i	0.0146990	+	0.0500600i
$866$	−2.19800	+	15.2874i	−0.0746911	+	0.519488i
$867$	−1.29999	+	28.7556i	−0.0441499	+	0.976592i
$868$	−0.338359	−	0.154524i	−0.0114847	−	0.00524487i
$869$	6.12812	−	20.8705i	0.207882	−	0.707982i
$870$	2.38718	+	1.22337i	0.0809331	+	0.0414760i
$871$	46.4519	−	6.67877i	1.57396	−	0.226301i
$872$	1.31027	+	0.842060i	0.0443714	+	0.0285158i
$873$	−40.1320	−	9.53026i	−1.35826	−	0.322550i
$874$	−3.46038	−	4.34373i	−0.117049	−	0.146929i
$875$		−	4.89874i		−	0.165608i
$876$	12.2820	−	1.20282i	0.414969	−	0.0406395i
$877$	−4.17664	−	29.0492i	−0.141035	−	0.980921i	−0.930282	−	0.366845i	$-0.880438\pi$
$877$	−4.17664	−	29.0492i	−0.141035	−	0.980921i	0.789247	−	0.614076i	$-0.210471\pi$
$878$	17.4046	−	7.94842i	0.587377	−	0.268246i
$879$	−9.43423	+	3.80344i	−0.318209	+	0.128287i
$880$	1.38306	−	3.02847i	0.0466228	−	0.102090i
$881$	12.7779	−	14.7465i	0.430499	−	0.496822i	−0.498508	−	0.866885i	$-0.666118\pi$
$881$	12.7779	−	14.7465i	0.430499	−	0.496822i	0.929007	+	0.370063i	$0.120664\pi$
$882$	−18.7226	+	47.4316i	−0.630423	+	1.59710i
$883$	41.9855	−	12.3281i	1.41293	−	0.414872i	0.515823	−	0.856695i	$-0.327486\pi$
$883$	41.9855	−	12.3281i	1.41293	−	0.414872i	0.897102	+	0.441823i	$0.145668\pi$
$884$	−22.1361	−	25.5464i	−0.744517	−	0.859219i
$885$	4.01770	+	1.37965i	0.135053	+	0.0463764i
$886$	22.4818	−	14.4482i	0.755290	−	0.485396i
$887$	3.81866	−	3.30889i	0.128218	−	0.111102i	−0.588391	−	0.808576i	$-0.700238\pi$
$887$	3.81866	−	3.30889i	0.128218	−	0.111102i	0.716609	+	0.697475i	$0.245693\pi$
$888$	10.0472	−	14.1819i	0.337163	−	0.475915i
$889$	62.4054	+	8.97254i	2.09301	+	0.300929i
$890$	−13.9657	−	12.1014i	−0.468133	−	0.405639i
$891$	−23.3727	+	18.7499i	−0.783015	+	0.628145i
$892$	20.5360	+	6.02991i	0.687596	+	0.201896i
$893$	2.93341	+	6.42328i	0.0981630	+	0.214947i
$894$	23.1305	−	24.3765i	0.773599	−	0.815272i
$895$	−4.81508	+	7.49240i	−0.160950	+	0.250443i
$896$	4.89874			0.163656
$897$	33.7222	+	34.7555i	1.12595	+	1.16045i
$898$	−19.4567			−0.649278
$899$	0.0635770	−	0.0989277i	0.00212041	−	0.00329942i
$900$	2.98776	+	0.270695i	0.0995921	+	0.00902317i
$901$	7.93255	+	17.3699i	0.264272	+	0.578674i
$902$	21.9750	+	6.45244i	0.731688	+	0.214843i
$903$	−7.65033	−	31.2049i	−0.254587	−	1.03843i
$904$	7.95886	+	6.89640i	0.264708	+	0.229371i
$905$	6.81543	+	0.979911i	0.226553	+	0.0325733i
$906$	11.8652	+	8.40592i	0.394195	+	0.279268i
$907$	−11.7819	+	10.2090i	−0.391210	+	0.338986i	−0.828151	−	0.560505i	$-0.810607\pi$
$907$	−11.7819	+	10.2090i	−0.391210	+	0.338986i	0.436941	+	0.899490i	$0.356062\pi$
$908$	2.58361	−	1.66039i	0.0857402	−	0.0551019i
$909$	18.3085	−	6.43612i	0.607253	−	0.213473i
$910$	−18.7022	−	21.5835i	−0.619972	−	0.715486i
$911$	43.1223	−	12.6618i	1.42871	−	0.419506i	0.526265	−	0.850321i	$-0.323592\pi$
$911$	43.1223	−	12.6618i	1.42871	−	0.419506i	0.902440	+	0.430815i	$0.141774\pi$
$912$	−1.73457	+	1.00706i	−0.0574373	+	0.0333472i
$913$	22.2286	−	25.6532i	0.735659	−	0.848996i
$914$	9.67042	−	21.1753i	0.319869	−	0.700415i
$915$	7.40170	+	18.3595i	0.244693	+	0.606947i
$916$	10.7807	−	4.92338i	0.356204	−	0.162673i
$917$	8.90981	+	61.9691i	0.294228	+	2.04640i
$918$	−29.8520	−	4.07086i	−0.985263	−	0.134358i
$919$			50.6555i			1.67097i	0.549512	+	0.835486i	$0.314814\pi$
$919$			50.6555i			1.67097i	−0.549512	+	0.835486i	$0.685186\pi$
$920$	−4.44100	+	1.81039i	−0.146415	+	0.0596869i
$921$	−22.8893	+	18.0903i	−0.754229	+	0.596095i
$922$	−20.5918	−	13.2336i	−0.678156	−	0.435825i
$923$	−0.787323	+	0.113200i	−0.0259150	+	0.00372602i
$924$	−12.8836	+	25.1400i	−0.423838	+	0.827044i
$925$	2.82705	−	9.62804i	0.0929527	−	0.316568i
$926$	−11.8582	−	5.41547i	−0.389686	−	0.177963i
$927$	43.6594	−	31.4096i	1.43396	−	1.03163i
$928$	−0.220401	+	1.53292i	−0.00723501	+	0.0503206i
$929$	6.78000	+	23.0905i	0.222444	+	0.757576i	0.992781	+	0.119939i	$0.0382699\pi$
$929$	6.78000	+	23.0905i	0.222444	+	0.757576i	−0.770337	+	0.637637i	$0.779912\pi$
$930$	0.0245772	−	0.129202i	0.000805918	−	0.00423671i
$931$	−10.6416	−	16.5587i	−0.348765	−	0.542689i
$932$	4.25882	+	6.62685i	0.139502	+	0.217070i
$933$	−5.46144	+	28.7108i	−0.178800	+	0.939948i
$934$	2.12395	+	7.23352i	0.0694979	+	0.236688i
$935$	−2.74726	+	19.1076i	−0.0898451	+	0.624886i
$936$	14.1973	−	10.2139i	0.464054	−	0.333851i
$937$	32.6584	+	14.9146i	1.06690	+	0.487238i	0.869932	−	0.493171i	$-0.164162\pi$
$937$	32.6584	+	14.9146i	1.06690	+	0.487238i	0.196971	+	0.980409i	$0.436890\pi$
$938$	11.1099	−	37.8367i	0.362750	−	1.23541i
$939$	15.1080	−	29.4805i	0.493030	−	0.962060i
$940$	6.03586	−	0.867826i	0.196868	−	0.0283053i
$941$	−47.6822	−	30.6435i	−1.55440	−	0.998950i	−0.984122	−	0.177495i	$-0.943201\pi$
$941$	−47.6822	−	30.6435i	−1.55440	−	0.998950i	−0.570274	−	0.821454i	$-0.693163\pi$
$942$	−14.3694	+	11.3566i	−0.468179	+	0.370019i
$943$	−16.6748	−	28.4666i	−0.543006	−	0.927001i
$944$			2.45257i			0.0798244i
$945$	−25.2212	−	3.43936i	−0.820445	−	0.111882i
$946$	−1.79416	−	12.4786i	−0.0583330	−	0.405715i
$947$	−35.7086	+	16.3075i	−1.16037	+	0.529924i	−0.900131	−	0.435619i	$-0.856529\pi$
$947$	−35.7086	+	16.3075i	−1.16037	+	0.529924i	−0.260241	+	0.965544i	$0.583802\pi$
$948$	4.23118	+	10.4952i	0.137422	+	0.340869i
$949$	17.2553	−	37.7838i	0.560130	−	1.22651i
$950$	−0.758330	+	0.875159i	−0.0246035	+	0.0283939i
$951$	0.263455	−	0.152958i	0.00854311	−	0.00496000i
$952$	−27.2533	+	8.00229i	−0.883284	+	0.259356i
$953$	−23.6928	−	27.3430i	−0.767486	−	0.885726i	0.228654	−	0.973508i	$-0.426568\pi$
$953$	−23.6928	−	27.3430i	−0.767486	−	0.885726i	−0.996140	+	0.0877818i	$0.972022\pi$
$954$	−9.32090	+	3.27665i	−0.301775	+	0.106085i
$955$	1.37107	−	0.881132i	0.0443667	−	0.0285128i
$956$	−17.4826	+	15.1488i	−0.565428	+	0.489946i
$957$	−7.28719	−	5.16262i	−0.235561	−	0.166884i
$958$	29.4888	+	4.23985i	0.952741	+	0.136983i
$959$	−39.1711	−	33.9419i	−1.26490	−	1.09604i
$960$	0.412423	+	1.68223i	0.0133109	+	0.0542938i
$961$	29.7387	+	8.73208i	0.959315	+	0.281680i
$962$	−24.3018	−	53.2134i	−0.783520	−	1.71567i
$963$	−30.8165	−	2.79202i	−0.993048	−	0.0899714i
$964$	10.4575	−	16.2722i	0.336813	−	0.524091i
$965$	17.2357			0.554836
$966$	38.3366	−	13.6435i	1.23346	−	0.438973i
$967$	9.75777			0.313789			0.156894	−	0.987615i	$-0.449852\pi$
$967$	9.75777			0.313789			0.156894	+	0.987615i	$0.449852\pi$
$968$	−0.0456660	+	0.0710576i	−0.00146776	+	0.00228388i
$969$	8.00488	−	8.43610i	0.257154	−	0.271007i
$970$	−5.71168	−	12.5068i	−0.183391	−	0.401571i
$971$	−8.02687	−	2.35690i	−0.257594	−	0.0756365i	0.150386	−	0.988627i	$-0.451948\pi$
$971$	−8.02687	−	2.35690i	−0.257594	−	0.0756365i	−0.407980	+	0.912991i	$0.633767\pi$
$972$	3.49135	−	15.1924i	0.111985	−	0.487298i
$973$	−74.5359	−	64.5857i	−2.38951	−	2.07052i
$974$	4.59793	+	0.661083i	0.147327	+	0.0211825i
$975$	5.83726	−	8.23946i	0.186942	−	0.263874i
$976$	−8.63736	+	7.48431i	−0.276475	+	0.239567i
$977$	42.7832	−	27.4951i	1.36875	−	0.879645i	0.369976	−	0.929041i	$-0.379366\pi$
$977$	42.7832	−	27.4951i	1.36875	−	0.879645i	0.998779	+	0.0493960i	$0.0157296\pi$
$978$	20.0171	+	6.87372i	0.640075	+	0.219797i
$979$	40.2896	+	46.4966i	1.28766	+	1.48604i
$980$	−16.3092	+	4.78880i	−0.520977	+	0.152973i
$981$	1.71558	−	4.34623i	0.0547743	−	0.138764i
$982$	−14.0849	+	16.2548i	−0.449466	+	0.518711i
$983$	16.8501	−	36.8966i	0.537434	−	1.17682i	−0.424973	−	0.905206i	$-0.639716\pi$
$983$	16.8501	−	36.8966i	0.537434	−	1.17682i	0.962407	−	0.271611i	$-0.0875564\pi$
$984$	−11.0507	+	4.45511i	−0.352282	+	0.142024i
$985$	−2.08422	+	0.951833i	−0.0664089	+	0.0303279i
$986$	−1.27793	−	8.88817i	−0.0406975	−	0.283057i
$987$	−51.4938	+	5.04297i	−1.63907	+	0.160520i
$988$			6.75101i			0.214778i
$989$	−10.4406	+	14.8587i	−0.331992	+	0.472478i
$990$	−9.71775	−	2.30770i	−0.308850	−	0.0733437i
$991$	41.4978	+	26.6690i	1.31822	+	0.847168i	0.995070	−	0.0991795i	$-0.0316218\pi$
$991$	41.4978	+	26.6690i	1.31822	+	0.847168i	0.323150	+	0.946348i	$0.395258\pi$
$992$	0.0751597	−	0.0108063i	0.00238632	−	0.000343101i
$993$	−17.8518	−	9.14856i	−0.566509	−	0.290321i
$994$	−0.188303	+	0.641303i	−0.00597262	+	0.0203409i
$995$	−1.84885	−	0.844343i	−0.0586126	−	0.0267675i
$996$	−0.797515	+	17.6410i	−0.0252702	+	0.558976i
$997$	−0.767507	+	5.33813i	−0.0243072	+	0.169060i	−0.998359	−	0.0572648i	$-0.981762\pi$
$997$	−0.767507	+	5.33813i	−0.0243072	+	0.169060i	0.974052	+	0.226325i	$0.0726711\pi$
$998$	11.8658	+	40.4111i	0.375605	+	1.27919i
$999$	−47.5851	−	21.3148i	−1.50553	−	0.674371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.a.251.10	yes	160
3.2	odd	2		690.2.q.b.251.6	yes	160
23.11	odd	22		690.2.q.b.11.6	yes	160
69.11	even	22	inner	690.2.q.a.11.10	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.10	✓	160	69.11	even	22	inner
690.2.q.a.251.10	yes	160	1.1	even	1	trivial
690.2.q.b.11.6	yes	160	23.11	odd	22
690.2.q.b.251.6	yes	160	3.2	odd	2

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.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 - 0.841254i) q^{2} +(-1.25644 - 1.19221i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.68223 + 0.412423i) q^{6} +(3.70222 + 3.20799i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(0.157263 + 2.99588i) q^{9} +O(q^{10})\)	\(q+(0.540641 - 0.841254i) q^{2} +(-1.25644 - 1.19221i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.68223 + 0.412423i) q^{6} +(3.70222 + 3.20799i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(0.157263 + 2.99588i) q^{9} +(-0.755750 + 0.654861i) q^{10} +(2.80081 - 1.79997i) q^{11} +(-0.562531 + 1.63816i) q^{12} +(3.81776 + 4.40593i) q^{13} +(4.70031 - 1.38014i) q^{14} +(0.869657 + 1.49790i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.40866 - 5.27422i) q^{17} +(2.60531 + 1.48739i) q^{18} +(-1.05335 + 0.481051i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-0.826998 - 8.44447i) q^{21} -3.32933i q^{22} +(-3.28761 + 3.49165i) q^{23} +(1.07398 + 1.35889i) q^{24} +(0.841254 + 0.540641i) q^{25} +(5.77054 - 0.829678i) q^{26} +(3.37413 - 3.95162i) q^{27} +(1.38014 - 4.70031i) q^{28} +(1.40873 + 0.643347i) q^{29} +(1.73028 + 0.0782228i) q^{30} +(0.0108063 - 0.0751597i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-5.66499 - 1.07761i) q^{33} +(-3.13474 - 4.87775i) q^{34} +(-2.64846 - 4.12108i) q^{35} +(2.65981 - 1.38758i) q^{36} +(-2.82705 - 9.62804i) q^{37} +(-0.164801 + 1.14621i) q^{38} +(0.456029 - 10.0873i) q^{39} +(0.909632 + 0.415415i) q^{40} +(-1.93806 + 6.60042i) q^{41} +(-7.55105 - 3.86971i) q^{42} +(3.74808 - 0.538893i) q^{43} +(-2.80081 - 1.79997i) q^{44} +(0.693143 - 2.91883i) q^{45} +(1.15995 + 4.65344i) q^{46} -6.09793i q^{47} +(1.72380 - 0.168818i) q^{48} +(2.41902 + 16.8247i) q^{49} +(0.909632 - 0.415415i) q^{50} +(-9.31431 + 3.75509i) q^{51} +(2.42182 - 5.30304i) q^{52} +(-2.15669 + 2.48895i) q^{53} +(-1.50012 - 4.97490i) q^{54} +(-3.19447 + 0.937982i) q^{55} +(-3.20799 - 3.70222i) q^{56} +(1.89699 + 0.651412i) q^{57} +(1.30284 - 0.837282i) q^{58} +(1.85353 - 1.60609i) q^{59} +(1.00127 - 1.41332i) q^{60} +(11.3125 + 1.62650i) q^{61} +(-0.0573860 - 0.0497252i) q^{62} +(-9.02853 + 11.5959i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-2.42182 - 5.30304i) q^{65} +(-3.96927 + 4.18310i) q^{66} +(4.35207 - 6.77195i) q^{67} -5.79819 q^{68} +(8.29346 - 0.467509i) q^{69} -4.89874 q^{70} +(-0.0737642 + 0.114779i) q^{71} +(0.270695 - 2.98776i) q^{72} +(-2.95980 - 6.48106i) q^{73} +(-9.62804 - 2.82705i) q^{74} +(-0.412423 - 1.68223i) q^{75} +(0.875159 + 0.758330i) q^{76} +(16.1435 + 2.32109i) q^{77} +(-8.23946 - 5.83726i) q^{78} +(4.93755 - 4.27841i) q^{79} +(0.841254 - 0.540641i) q^{80} +(-8.95054 + 0.942281i) q^{81} +(4.50483 + 5.19886i) q^{82} +(9.78245 - 2.87239i) q^{83} +(-7.33782 + 4.26022i) q^{84} +(-3.79701 + 4.38198i) q^{85} +(1.57302 - 3.44444i) q^{86} +(-1.00298 - 2.48783i) q^{87} +(-3.02847 + 1.38306i) q^{88} +(2.62988 + 18.2912i) q^{89} +(-2.08073 - 2.16115i) q^{90} +28.5591i q^{91} +(4.54184 + 1.54003i) q^{92} +(-0.103184 + 0.0815499i) q^{93} +(-5.12990 - 3.29679i) q^{94} +(1.14621 - 0.164801i) q^{95} +(0.789940 - 1.54143i) q^{96} +(-3.87364 + 13.1924i) q^{97} +(15.4616 + 7.06109i) q^{98} +(5.83296 + 8.10782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Introduction

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