LMFDB - Embedded newform 525.2.bp.a.59.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(59,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 5]))

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

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

chi := DirichletCharacter("525.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bp (of order $30$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			59.4
Character	$\chi$	$=$	525.59
Dual form			525.2.bp.a.89.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.275952 + 2.62550i) q^{2} +(-1.15521 - 1.29053i) q^{3} +(-4.86083 - 1.03320i) q^{4} +(-1.85485 - 1.24881i) q^{5} +(3.70709 - 2.67690i) q^{6} +(2.62092 - 0.361651i) q^{7} +(2.42244 - 7.45550i) q^{8} +(-0.330959 + 2.98169i) q^{9} +O(q^{10})$	\(q+(-0.275952 + 2.62550i) q^{2} +(-1.15521 - 1.29053i) q^{3} +(-4.86083 - 1.03320i) q^{4} +(-1.85485 - 1.24881i) q^{5} +(3.70709 - 2.67690i) q^{6} +(2.62092 - 0.361651i) q^{7} +(2.42244 - 7.45550i) q^{8} +(-0.330959 + 2.98169i) q^{9} +(3.79060 - 4.52531i) q^{10} +(0.644250 + 1.44701i) q^{11} +(4.28192 + 7.46664i) q^{12} +(0.652216 - 0.473863i) q^{13} +(0.226271 + 6.98103i) q^{14} +(0.531121 + 3.83639i) q^{15} +(9.82639 + 4.37499i) q^{16} +(-2.56167 + 2.30654i) q^{17} +(-7.73711 - 1.69174i) q^{18} +(-0.199328 - 0.937764i) q^{19} +(7.72585 + 7.98668i) q^{20} +(-3.49445 - 2.96460i) q^{21} +(-3.97691 + 1.29218i) q^{22} +(-0.797238 + 7.58521i) q^{23} +(-12.4200 + 5.48646i) q^{24} +(1.88095 + 4.63271i) q^{25} +(1.06415 + 1.84316i) q^{26} +(4.23030 - 3.01737i) q^{27} +(-13.1135 - 0.950009i) q^{28} +(2.79541 - 0.908283i) q^{29} +(-10.2190 + 0.335801i) q^{30} +(5.14060 - 4.62861i) q^{31} +(-6.35899 + 11.0141i) q^{32} +(1.12317 - 2.50303i) q^{33} +(-5.34893 - 7.36217i) q^{34} +(-5.31305 - 2.60222i) q^{35} +(4.68942 - 14.1515i) q^{36} +(-3.53326 + 7.93583i) q^{37} +(2.51711 - 0.264559i) q^{38} +(-1.36499 - 0.294294i) q^{39} +(-13.8038 + 10.8037i) q^{40} +(-8.18117 + 5.94397i) q^{41} +(8.74787 - 8.35660i) q^{42} +3.56769i q^{43} +(-1.63654 - 7.69930i) q^{44} +(4.33744 - 5.11729i) q^{45} +(-19.6950 - 4.18630i) q^{46} +(8.17346 + 7.35942i) q^{47} +(-5.70551 - 17.7354i) q^{48} +(6.73842 - 1.89572i) q^{49} +(-12.6823 + 3.66005i) q^{50} +(5.93595 + 0.641378i) q^{51} +(-3.65991 + 1.62950i) q^{52} +(9.96212 + 2.11751i) q^{53} +(6.75477 + 11.9393i) q^{54} +(0.612049 - 3.48853i) q^{55} +(3.65272 - 20.4163i) q^{56} +(-0.979951 + 1.34056i) q^{57} +(1.61330 + 7.59000i) q^{58} +(0.491345 + 4.67484i) q^{59} +(1.38208 - 19.1968i) q^{60} +(6.51692 + 0.684956i) q^{61} +(10.7339 + 14.7739i) q^{62} +(0.210914 + 7.93445i) q^{63} +(-9.75868 - 7.09010i) q^{64} +(-1.80153 + 0.0644521i) q^{65} +(6.26178 + 3.63960i) q^{66} +(2.62821 - 2.36645i) q^{67} +(14.8350 - 8.56497i) q^{68} +(10.7100 - 7.73368i) q^{69} +(8.29827 - 13.2313i) q^{70} +(-11.5314 + 3.74677i) q^{71} +(21.4283 + 9.69043i) q^{72} +(0.388484 - 0.172964i) q^{73} +(-19.8605 - 11.4665i) q^{74} +(3.80577 - 7.77921i) q^{75} +4.76426i q^{76} +(2.21184 + 3.55950i) q^{77} +(1.14934 - 3.50256i) q^{78} +(4.01855 - 4.46305i) q^{79} +(-12.7630 - 20.3862i) q^{80} +(-8.78093 - 1.97364i) q^{81} +(-13.3483 - 23.1199i) q^{82} +(-1.51152 - 0.491122i) q^{83} +(13.9229 + 18.0209i) q^{84} +(7.63195 - 1.07925i) q^{85} +(-9.36699 - 0.984510i) q^{86} +(-4.40147 - 2.55831i) q^{87} +(12.3488 - 1.29791i) q^{88} +(1.40466 - 13.3644i) q^{89} +(12.2385 + 12.8001i) q^{90} +(1.53803 - 1.47783i) q^{91} +(11.7123 - 36.0467i) q^{92} +(-11.9119 - 1.28708i) q^{93} +(-21.5777 + 19.4286i) q^{94} +(-0.801365 + 1.98834i) q^{95} +(21.5601 - 4.51714i) q^{96} +(4.25200 + 13.0863i) q^{97} +(3.11774 + 18.2149i) q^{98} +(-4.52775 + 1.44205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.275952	+	2.62550i	−0.195127	+	1.85651i	0.259388	+	0.965773i	$0.416479\pi$
$2$	−0.275952	+	2.62550i	−0.195127	+	1.85651i	−0.454515	+	0.890739i	$0.650188\pi$
$3$	−1.15521	−	1.29053i	−0.666963	−	0.745091i
$3$	−1.15521	−	1.29053i	−0.666963	−	0.745091i
$4$	−4.86083	−	1.03320i	−2.43041	−	0.516601i
$5$	−1.85485	−	1.24881i	−0.829515	−	0.558484i
$5$	−1.85485	−	1.24881i	−0.829515	−	0.558484i
$6$	3.70709	−	2.67690i	1.51341	−	1.09284i
$7$	2.62092	−	0.361651i	0.990614	−	0.136691i
$7$	2.62092	−	0.361651i	0.990614	−	0.136691i
$8$	2.42244	−	7.45550i	0.856462	−	2.63592i
$9$	−0.330959	+	2.98169i	−0.110320	+	0.993896i
$10$	3.79060	−	4.52531i	1.19869	−	1.43103i
$11$	0.644250	+	1.44701i	0.194249	+	0.436290i	0.984242	−	0.176826i	$-0.0565828\pi$
$11$	0.644250	+	1.44701i	0.194249	+	0.436290i	−0.789994	+	0.613115i	$0.789916\pi$
$12$	4.28192	+	7.46664i	1.23608	+	2.15543i
$13$	0.652216	−	0.473863i	0.180892	−	0.131426i	−0.493654	−	0.869658i	$-0.664339\pi$
$13$	0.652216	−	0.473863i	0.180892	−	0.131426i	0.674547	+	0.738232i	$0.264339\pi$
$14$	0.226271	+	6.98103i	0.0604735	+	1.86576i
$15$	0.531121	+	3.83639i	0.137135	+	0.990552i
$16$	9.82639	+	4.37499i	2.45660	+	1.09375i
$17$	−2.56167	+	2.30654i	−0.621297	+	0.559418i	−0.918512	−	0.395392i	$-0.870609\pi$
$17$	−2.56167	+	2.30654i	−0.621297	+	0.559418i	0.297216	+	0.954810i	$0.403942\pi$
$18$	−7.73711	−	1.69174i	−1.82365	−	0.398746i
$19$	−0.199328	−	0.937764i	−0.0457290	−	0.215138i	0.949350	−	0.314220i	$-0.101743\pi$
$19$	−0.199328	−	0.937764i	−0.0457290	−	0.215138i	−0.995079	+	0.0990817i	$0.968409\pi$
$20$	7.72585	+	7.98668i	1.72755	+	1.78588i
$21$	−3.49445	−	2.96460i	−0.762550	−	0.646929i
$22$	−3.97691	+	1.29218i	−0.847880	+	0.275493i
$23$	−0.797238	+	7.58521i	−0.166236	+	1.58163i	0.519948	+	0.854198i	$0.325951\pi$
$23$	−0.797238	+	7.58521i	−0.166236	+	1.58163i	−0.686184	+	0.727428i	$0.740715\pi$
$24$	−12.4200	+	5.48646i	−2.53523	+	1.11992i
$25$	1.88095	+	4.63271i	0.376191	+	0.926542i
$26$	1.06415	+	1.84316i	0.208697	+	0.361473i
$27$	4.23030	−	3.01737i	0.814122	−	0.580694i
$28$	−13.1135	−	0.950009i	−2.47822	−	0.179535i
$29$	2.79541	−	0.908283i	0.519094	−	0.168664i	−0.0377399	−	0.999288i	$-0.512016\pi$
$29$	2.79541	−	0.908283i	0.519094	−	0.168664i	0.556834	+	0.830624i	$0.312016\pi$
$30$	−10.2190	+	0.335801i	−1.86573	+	0.0613086i
$31$	5.14060	−	4.62861i	0.923278	−	0.831323i	−0.0627282	−	0.998031i	$-0.519980\pi$
$31$	5.14060	−	4.62861i	0.923278	−	0.831323i	0.986006	+	0.166707i	$0.0533135\pi$
$32$	−6.35899	+	11.0141i	−1.12412	+	1.94704i
$33$	1.12317	−	2.50303i	0.195519	−	0.435722i
$34$	−5.34893	−	7.36217i	−0.917334	−	1.26260i
$35$	−5.31305	−	2.60222i	−0.898069	−	0.439855i
$36$	4.68942	−	14.1515i	0.781570	−	2.35859i
$37$	−3.53326	+	7.93583i	−0.580864	+	1.30464i	0.349132	+	0.937073i	$0.386476\pi$
$37$	−3.53326	+	7.93583i	−0.580864	+	1.30464i	−0.929996	+	0.367569i	$0.880190\pi$
$38$	2.51711	−	0.264559i	0.408329	−	0.0429171i
$39$	−1.36499	−	0.294294i	−0.218573	−	0.0471248i
$40$	−13.8038	+	10.8037i	−2.18257	+	1.70821i
$41$	−8.18117	+	5.94397i	−1.27768	+	0.928292i	−0.999480	−	0.0322303i	$-0.989739\pi$
$41$	−8.18117	+	5.94397i	−1.27768	+	0.928292i	−0.278204	+	0.960522i	$0.589739\pi$
$42$	8.74787	−	8.35660i	1.34983	−	1.28945i
$43$			3.56769i			0.544068i	0.962288	+	0.272034i	$0.0876963\pi$
$43$			3.56769i			0.544068i	−0.962288	+	0.272034i	$0.912304\pi$
$44$	−1.63654	−	7.69930i	−0.246717	−	1.16071i
$45$	4.33744	−	5.11729i	0.646587	−	0.762840i
$46$	−19.6950	−	4.18630i	−2.90387	−	0.617237i
$47$	8.17346	+	7.35942i	1.19222	+	1.07348i	0.995667	+	0.0929891i	$0.0296422\pi$
$47$	8.17346	+	7.35942i	1.19222	+	1.07348i	0.196555	+	0.980493i	$0.437024\pi$
$48$	−5.70551	−	17.7354i	−0.823520	−	2.55988i
$49$	6.73842	−	1.89572i	0.962631	−	0.270817i
$50$	−12.6823	+	3.66005i	−1.79354	+	0.517609i
$51$	5.93595	+	0.641378i	0.831199	+	0.0898109i
$52$	−3.65991	+	1.62950i	−0.507538	+	0.225970i
$53$	9.96212	+	2.11751i	1.36840	+	0.290863i	0.832784	−	0.553598i	$-0.186746\pi$
$53$	9.96212	+	2.11751i	1.36840	+	0.290863i	0.535618	+	0.844461i	$0.320079\pi$
$54$	6.75477	+	11.9393i	0.919208	+	1.62474i
$55$	0.612049	−	3.48853i	0.0825287	−	0.470394i
$56$	3.65272	−	20.4163i	0.488115	−	2.72825i
$57$	−0.979951	+	1.34056i	−0.129798	+	0.177561i
$58$	1.61330	+	7.59000i	0.211837	+	0.996616i
$59$	0.491345	+	4.67484i	0.0639677	+	0.608612i	0.978806	+	0.204791i	$0.0656515\pi$
$59$	0.491345	+	4.67484i	0.0639677	+	0.608612i	−0.914838	+	0.403821i	$0.867682\pi$
$60$	1.38208	−	19.1968i	0.178426	−	2.47830i
$61$	6.51692	+	0.684956i	0.834406	+	0.0876996i	0.512089	−	0.858932i	$-0.328872\pi$
$61$	6.51692	+	0.684956i	0.834406	+	0.0876996i	0.322317	+	0.946632i	$0.395538\pi$
$62$	10.7339	+	14.7739i	1.36321	+	1.87629i
$63$	0.210914	+	7.93445i	0.0265727	+	0.999647i
$64$	−9.75868	−	7.09010i	−1.21984	−	0.886262i
$65$	−1.80153	+	0.0644521i	−0.223452	+	0.00799429i
$66$	6.26178	+	3.63960i	0.770772	+	0.448004i
$67$	2.62821	−	2.36645i	0.321086	−	0.289108i	−0.492787	−	0.870150i	$-0.664022\pi$
$67$	2.62821	−	2.36645i	0.321086	−	0.289108i	0.813873	+	0.581043i	$0.197355\pi$
$68$	14.8350	−	8.56497i	1.79900	−	1.03866i
$69$	10.7100	−	7.73368i	1.28933	−	0.931026i
$70$	8.29827	−	13.2313i	0.991833	−	1.58145i
$71$	−11.5314	+	3.74677i	−1.36852	+	0.444660i	−0.898879	−	0.438196i	$-0.855618\pi$
$71$	−11.5314	+	3.74677i	−1.36852	+	0.444660i	−0.469644	+	0.882856i	$0.655618\pi$
$72$	21.4283	+	9.69043i	2.52534	+	1.14203i
$73$	0.388484	−	0.172964i	0.0454686	−	0.0202439i	−0.383876	−	0.923384i	$-0.625411\pi$
$73$	0.388484	−	0.172964i	0.0454686	−	0.0202439i	0.429345	+	0.903141i	$0.358744\pi$
$74$	−19.8605	−	11.4665i	−2.30874	−	1.33295i
$75$	3.80577	−	7.77921i	0.439453	−	0.898266i
$76$			4.76426i			0.546498i
$77$	2.21184	+	3.55950i	0.252062	+	0.405642i
$78$	1.14934	−	3.50256i	0.130137	−	0.396587i
$79$	4.01855	−	4.46305i	0.452122	−	0.502132i	−0.473389	−	0.880854i	$-0.656969\pi$
$79$	4.01855	−	4.46305i	0.452122	−	0.502132i	0.925511	+	0.378721i	$0.123636\pi$
$80$	−12.7630	−	20.3862i	−1.42694	−	2.27925i
$81$	−8.78093	−	1.97364i	−0.975659	−	0.219293i
$82$	−13.3483	−	23.1199i	−1.47407	−	2.55317i
$83$	−1.51152	−	0.491122i	−0.165911	−	0.0539077i	0.224884	−	0.974386i	$-0.427800\pi$
$83$	−1.51152	−	0.491122i	−0.165911	−	0.0539077i	−0.390795	+	0.920478i	$0.627800\pi$
$84$	13.9229	+	18.0209i	1.51911	+	1.96624i
$85$	7.63195	−	1.07925i	0.827801	−	0.117061i
$86$	−9.36699	−	0.984510i	−1.01007	−	0.106162i
$87$	−4.40147	−	2.55831i	−0.471887	−	0.274280i
$88$	12.3488	−	1.29791i	1.31639	−	0.138358i
$89$	1.40466	−	13.3644i	0.148893	−	1.41663i	−0.623670	−	0.781688i	$-0.714359\pi$
$89$	1.40466	−	13.3644i	0.148893	−	1.41663i	0.772563	−	0.634938i	$-0.218974\pi$
$90$	12.2385	+	12.8001i	1.29005	+	1.34925i
$91$	1.53803	−	1.47783i	0.161229	−	0.154919i
$92$	11.7123	−	36.0467i	1.22109	−	3.75813i
$93$	−11.9119	−	1.28708i	−1.23520	−	0.133464i
$94$	−21.5777	+	19.4286i	−2.22557	+	2.00391i
$95$	−0.801365	+	1.98834i	−0.0822183	+	0.203999i
$96$	21.5601	−	4.51714i	2.20047	−	0.461029i
$97$	4.25200	+	13.0863i	0.431726	+	1.32871i	0.896405	+	0.443236i	$0.146170\pi$
$97$	4.25200	+	13.0863i	0.431726	+	1.32871i	−0.464679	+	0.885479i	$0.653830\pi$
$98$	3.11774	+	18.2149i	0.314939	+	1.83998i
$99$	−4.52775	+	1.44205i	−0.455056	+	0.144932i
$100$	−4.35647	−	24.4622i	−0.435647	−	2.44622i
$101$	0.988001	−	1.71127i	0.0983098	−	0.170278i	−0.812675	−	0.582717i	$-0.801990\pi$
$101$	0.988001	−	1.71127i	0.0983098	−	0.170278i	0.910985	+	0.412439i	$0.135323\pi$
$102$	−3.32198	+	15.4079i	−0.328925	+	1.52561i
$103$	−8.52477	+	9.46772i	−0.839971	+	0.932882i	−0.998515	−	0.0544698i	$-0.982653\pi$
$103$	−8.52477	+	9.46772i	−0.839971	+	0.932882i	0.158545	+	0.987352i	$0.449320\pi$
$104$	−1.95293	−	6.01050i	−0.191501	−	0.589378i
$105$	2.77946	+	9.86279i	0.271248	+	0.962510i
$106$	−8.30860	+	25.5712i	−0.807003	+	2.48370i
$107$	0.464603	+	0.804715i	0.0449148	+	0.0777948i	0.887609	−	0.460598i	$-0.152365\pi$
$107$	0.464603	+	0.804715i	0.0449148	+	0.0777948i	−0.842694	+	0.538393i	$0.819032\pi$
$108$	−23.6803	+	10.2962i	−2.27864	+	0.990752i
$109$	−1.02711	−	9.77229i	−0.0983792	−	0.936015i	−0.926710	−	0.375777i	$-0.877376\pi$
$109$	−1.02711	−	9.77229i	−0.0983792	−	0.936015i	0.828331	−	0.560239i	$-0.189291\pi$
$110$	8.99026	+	2.56960i	0.857188	+	0.245002i
$111$	14.3231	−	4.60779i	1.35949	−	0.437352i
$112$	27.3364	+	7.91276i	2.58305	+	0.747686i
$113$	0.914212	−	0.664214i	0.0860019	−	0.0624840i	−0.543953	−	0.839115i	$-0.683073\pi$
$113$	0.914212	−	0.664214i	0.0860019	−	0.0624840i	0.629955	+	0.776631i	$0.283073\pi$
$114$	−3.24922	−	2.94279i	−0.304318	−	0.275618i
$115$	10.9512	−	13.0739i	1.02121	−	1.21914i
$116$	−14.5264	+	1.52679i	−1.34875	+	0.141759i
$117$	1.19705	+	2.10153i	0.110668	+	0.194287i
$118$	−12.4094			−1.14238
$119$	−5.87977	+	6.97168i	−0.538997	+	0.639093i
$120$	29.8888	+	5.33366i	2.72847	+	0.486894i
$121$	5.68166	−	6.31012i	0.516515	−	0.573647i
$122$	−3.59671	+	16.9212i	−0.325631	+	1.53197i
$123$	17.1219	+	3.69153i	1.54383	+	0.332854i
$124$	−29.7699	+	17.1876i	−2.67341	+	1.54349i
$125$	2.29648	−	10.9419i	0.205404	−	0.978677i
$126$	−20.8901	−	1.63577i	−1.86104	−	0.145726i
$127$	−10.9584	+	15.0830i	−0.972403	+	1.33840i	−0.0315789	+	0.999501i	$0.510054\pi$
$127$	−10.9584	+	15.0830i	−0.972403	+	1.33840i	−0.940824	+	0.338896i	$0.889946\pi$
$128$	4.28803	−	4.76234i	0.379012	−	0.420935i
$129$	4.60423	−	4.12145i	0.405380	−	0.362873i
$130$	0.327915	−	4.74771i	0.0287601	−	0.416401i
$131$	8.03423	−	1.70773i	0.701954	−	0.149205i	0.156911	−	0.987613i	$-0.449846\pi$
$131$	8.03423	−	1.70773i	0.701954	−	0.149205i	0.545043	+	0.838408i	$0.316513\pi$
$132$	−8.04567	+	11.0064i	−0.700285	+	0.957980i
$133$	−0.861566	−	2.38572i	−0.0747072	−	0.206868i
$134$	5.48786	+	7.55339i	0.474079	+	0.652514i
$135$	−11.6147	+	0.313946i	−0.999635	+	0.0270202i
$136$	10.9909	+	24.6860i	0.942463	+	2.11681i
$137$	−1.49874	−	14.2595i	−0.128046	−	1.21828i	−0.850169	−	0.526510i	$-0.823500\pi$
$137$	−1.49874	−	14.2595i	−0.128046	−	1.21828i	0.722123	−	0.691765i	$-0.243167\pi$
$138$	17.3494	+	30.2532i	1.47688	+	2.57532i
$139$	0.227996	−	0.313810i	0.0193384	−	0.0266170i	−0.799238	−	0.601014i	$-0.794763\pi$
$139$	0.227996	−	0.313810i	0.0193384	−	0.0266170i	0.818577	+	0.574397i	$0.194763\pi$
$140$	23.1372	+	18.1384i	1.95545	+	1.53297i
$141$	0.0554834	−	19.0498i	0.00467255	−	1.60429i
$142$	−6.65506	−	31.3096i	−0.558481	−	2.62744i
$143$	1.10587	+	0.638476i	0.0924778	+	0.0533921i
$144$	−16.2970	+	27.8513i	−1.35808	+	2.32094i
$145$	−6.31934	−	1.80620i	−0.524793	−	0.149997i
$146$	0.346915	+	1.06769i	0.0287109	+	0.0883631i
$147$	−10.2308	−	6.50620i	−0.843823	−	0.536622i
$148$	25.3739	−	34.9241i	2.08572	−	2.87075i
$149$	7.33704	−	4.23604i	0.601074	−	0.347030i	−0.168390	−	0.985720i	$-0.553857\pi$
$149$	7.33704	−	4.23604i	0.601074	−	0.347030i	0.769464	+	0.638690i	$0.220523\pi$
$150$	19.3741	+	12.1388i	1.58189	+	0.991125i
$151$	−9.29689	+	16.1027i	−0.756570	+	1.31042i	0.188020	+	0.982165i	$0.439793\pi$
$151$	−9.29689	+	16.1027i	−0.756570	+	1.31042i	−0.944590	+	0.328252i	$0.893540\pi$
$152$	−7.47436	−	0.785587i	−0.606251	−	0.0637196i
$153$	−6.02957	−	8.40148i	−0.487462	−	0.679219i
$154$	−9.95584	+	4.82494i	−0.802264	+	0.388805i
$155$	−15.3153	+	2.16577i	−1.23015	+	0.173959i
$156$	6.33090	+	2.84082i	0.506877	+	0.227448i
$157$	0.237396	−	0.411182i	0.0189463	−	0.0328159i	−0.856397	−	0.516318i	$-0.827302\pi$
$157$	0.237396	−	0.411182i	0.0189463	−	0.0328159i	0.875343	+	0.483502i	$0.160636\pi$
$158$	10.6088	+	11.7823i	0.843993	+	0.937349i
$159$	−8.77566	−	15.3026i	−0.695955	−	1.21358i
$160$	25.5495	−	12.4884i	2.01986	−	0.987291i
$161$	0.653708	+	20.1685i	0.0515194	+	1.58950i
$162$	7.60490	−	22.5097i	0.597498	−	1.76853i
$163$	0.130771	−	0.293716i	0.0102427	−	0.0230056i	−0.908352	−	0.418207i	$-0.862659\pi$
$163$	0.130771	−	0.293716i	0.0102427	−	0.0230056i	0.918594	+	0.395202i	$0.129325\pi$
$164$	45.9086	−	20.4398i	3.58486	−	1.59608i
$165$	−5.20912	+	3.24013i	−0.405529	+	0.252244i
$166$	1.70655	−	3.83297i	0.132454	−	0.297496i
$167$	−8.43529	−	2.74079i	−0.652742	−	0.212089i	−0.0361193	−	0.999347i	$-0.511500\pi$
$167$	−8.43529	−	2.74079i	−0.652742	−	0.212089i	−0.616623	+	0.787259i	$0.711500\pi$
$168$	−30.5677	+	18.8713i	−2.35835	+	1.45595i
$169$	−3.81638	+	11.7456i	−0.293568	+	0.903509i
$170$	0.727531	+	20.3355i	0.0557991	+	1.55966i
$171$	2.86209	−	0.283972i	0.218870	−	0.0217159i
$172$	3.68614	−	17.3419i	0.281066	−	1.32231i
$173$	−14.6424	−	1.53898i	−1.11324	−	0.117006i	−0.469998	−	0.882667i	$-0.655745\pi$
$173$	−14.6424	−	1.53898i	−1.11324	−	0.117006i	−0.643244	+	0.765661i	$0.722412\pi$
$174$	7.93145	−	10.8501i	0.601281	−	0.822544i
$175$	6.60525	+	11.4617i	0.499310	+	0.866423i
$176$			17.0375i			1.28425i
$177$	5.46543	−	6.03454i	0.410807	−	0.453584i
$178$	34.7007	+	7.37586i	2.60093	+	0.552844i
$179$	3.58695	−	16.8753i	0.268101	−	1.26132i	−0.613641	−	0.789585i	$-0.710296\pi$
$179$	3.58695	−	16.8753i	0.268101	−	1.26132i	0.881742	−	0.471731i	$-0.156371\pi$
$180$	−26.3707	+	20.3928i	−1.96556	+	1.51999i
$181$	12.9629	+	4.21190i	0.963524	+	0.313068i	0.748199	−	0.663475i	$-0.230919\pi$
$181$	12.9629	+	4.21190i	0.963524	+	0.313068i	0.215325	+	0.976542i	$0.430919\pi$
$182$	3.45563	+	4.44592i	0.256148	+	0.329553i
$183$	−6.64448	−	9.20158i	−0.491174	−	0.680200i
$184$	54.6203	+	24.3185i	4.02666	+	1.79279i
$185$	16.4640	−	10.3074i	1.21046	−	0.757817i
$186$	6.66633	−	30.9195i	0.488799	−	2.26713i
$187$	−4.98794	−	2.22077i	−0.364754	−	0.162399i
$188$	−32.1261	−	44.2177i	−2.34303	−	3.22491i
$189$	9.99603	−	9.43818i	0.727104	−	0.686527i
$190$	−4.99925	−	2.65267i	−0.362684	−	0.192445i
$191$	1.39640	−	3.13635i	0.101040	−	0.226939i	−0.855951	−	0.517056i	$-0.827028\pi$
$191$	1.39640	−	3.13635i	0.101040	−	0.226939i	0.956991	+	0.290118i	$0.0936944\pi$
$192$	2.12335	+	20.7845i	0.153240	+	1.49999i
$193$	8.31502	+	4.80068i	0.598528	+	0.345561i	0.768462	−	0.639895i	$-0.221022\pi$
$193$	8.31502	+	4.80068i	0.598528	+	0.345561i	−0.169934	+	0.985455i	$0.554355\pi$
$194$	−35.5315	+	7.55246i	−2.55102	+	0.542235i
$195$	2.16433	+	2.25048i	0.154991	+	0.161160i
$196$	−34.7130	+	2.25262i	−2.47950	+	0.160901i
$197$	0.916166	+	2.81967i	0.0652741	+	0.200893i	0.978374	−	0.206842i	$-0.0663187\pi$
$197$	0.916166	+	2.81967i	0.0652741	+	0.200893i	−0.913100	+	0.407735i	$0.866319\pi$
$198$	−2.53667	−	12.2856i	−0.180273	−	0.873097i
$199$	4.86829	+	2.81071i	0.345104	+	0.199246i	0.662527	−	0.749038i	$-0.269484\pi$
$199$	4.86829	+	2.81071i	0.345104	+	0.199246i	−0.317423	+	0.948284i	$0.602817\pi$
$200$	39.0957	−	2.80099i	2.76448	−	0.198060i
$201$	−6.09012	−	0.658037i	−0.429564	−	0.0464143i
$202$	4.22030	+	3.06623i	0.296939	+	0.215739i
$203$	6.99805	−	3.39150i	0.491167	−	0.238037i
$204$	−28.1910	−	9.25066i	−1.97376	−	0.647676i
$205$	22.5977	−	0.808464i	1.57829	−	0.0564656i
$206$	−22.5051	−	24.9945i	−1.56801	−	1.74145i
$207$	−22.3529	−	4.88751i	−1.55363	−	0.339706i
$208$	8.48208	−	1.80292i	0.588126	−	0.125010i
$209$	1.22854	−	0.892584i	0.0849796	−	0.0617413i
$210$	−26.6618	+	4.57583i	−1.83984	+	0.315763i
$211$	−14.6628	−	10.6531i	−1.00943	−	0.733391i	−0.0453372	−	0.998972i	$-0.514436\pi$
$211$	−14.6628	−	10.6531i	−1.00943	−	0.733391i	−0.964089	+	0.265581i	$0.914436\pi$
$212$	−46.2363	−	20.5857i	−3.17552	−	1.41383i
$213$	18.1566	+	10.5533i	1.24407	+	0.723102i
$214$	−2.24099	+	0.997754i	−0.153191	+	0.0682051i
$215$	4.45536	−	6.61754i	0.303853	−	0.451312i
$216$	−12.2484	−	38.8484i	−0.833398	−	2.64330i
$217$	11.7991	−	13.9903i	0.800977	−	0.949725i
$218$	25.9406			1.75692
$219$	−0.671998	−	0.301541i	−0.0454094	−	0.0203762i
$220$	−6.57942	+	16.3248i	−0.443585	+	1.10062i
$221$	−0.577780	+	2.71824i	−0.0388657	+	0.182849i
$222$	8.14528	+	38.8770i	0.546676	+	2.60925i
$223$	4.33588	+	3.15020i	0.290352	+	0.210953i	0.723420	−	0.690408i	$-0.242569\pi$
$223$	4.33588	+	3.15020i	0.290352	+	0.210953i	−0.433068	+	0.901361i	$0.642569\pi$
$224$	−12.6831	+	31.1668i	−0.847427	+	2.08242i
$225$	−14.4358	+	4.07518i	−0.962388	+	0.271678i
$226$	1.49162	+	2.58356i	0.0992210	+	0.171856i
$227$	7.82393	+	17.5728i	0.519292	+	1.16635i	0.962834	+	0.270096i	$0.0870553\pi$
$227$	7.82393	+	17.5728i	0.519292	+	1.16635i	−0.443541	+	0.896254i	$0.646278\pi$
$228$	6.14844	−	5.50374i	0.407190	−	0.364494i
$229$	9.58860	+	8.63362i	0.633633	+	0.570525i	0.922094	−	0.386966i	$-0.126477\pi$
$229$	9.58860	+	8.63362i	0.633633	+	0.570525i	−0.288461	+	0.957492i	$0.593144\pi$
$230$	31.3034	+	32.3603i	2.06409	+	2.13377i
$231$	2.03851	−	6.96644i	0.134124	−	0.458358i
$232$		−	23.0414i		−	1.51274i
$233$	21.1610	−	4.49791i	1.38630	−	0.294668i	0.546454	−	0.837489i	$-0.315977\pi$
$233$	21.1610	−	4.49791i	1.38630	−	0.294668i	0.839848	+	0.542822i	$0.182644\pi$
$234$	−5.84792	+	2.56295i	−0.382290	+	0.167545i
$235$	−5.97006	−	23.8577i	−0.389444	−	1.55631i
$236$	2.44170	−	23.2313i	0.158941	−	1.51223i
$237$	−10.4020	−	0.0302962i	−0.675683	−	0.00196795i
$238$	−16.6817	−	17.3612i	−1.08131	−	1.12536i
$239$	−4.50426	+	6.19958i	−0.291356	+	0.401018i	−0.929454	−	0.368938i	$-0.879722\pi$
$239$	−4.50426	+	6.19958i	−0.291356	+	0.401018i	0.638098	+	0.769955i	$0.279722\pi$
$240$	−11.5652	+	40.0215i	−0.746530	+	2.58338i
$241$	−20.1725	+	2.12022i	−1.29943	+	0.136575i	−0.728853	−	0.684670i	$-0.759946\pi$
$241$	−20.1725	+	2.12022i	−1.29943	+	0.136575i	−0.570575	+	0.821246i	$0.693279\pi$
$242$	14.9994	+	16.6585i	0.964197	+	1.07085i
$243$	7.59681	+	13.6121i	0.487336	+	0.873215i
$244$	−30.9699	−	10.0627i	−1.98265	−	0.644201i
$245$	−14.8662	−	4.89872i	−0.949764	−	0.312968i
$246$	−14.4169	+	43.9350i	−0.919190	+	2.80119i
$247$	−0.574376	−	0.517171i	−0.0365467	−	0.0329068i
$248$	−22.0559	−	49.5383i	−1.40055	−	3.14568i
$249$	1.11232	+	2.51802i	0.0704903	+	0.159573i
$250$	28.0944	+	9.04887i	1.77685	+	0.572301i
$251$	−23.3368			−1.47301			−0.736503	−	0.676434i	$-0.763524\pi$
$251$	−23.3368			−1.47301			−0.736503	+	0.676434i	$0.763524\pi$
$252$	7.17267	−	38.7859i	0.451835	−	2.44328i
$253$	−11.4895	+	3.73316i	−0.722338	+	0.234702i
$254$	−36.5764	−	32.9336i	−2.29501	−	2.06644i
$255$	−10.2093	−	8.60253i	−0.639334	−	0.538711i
$256$	−4.82239	−	5.35580i	−0.301399	−	0.334738i
$257$	−11.4630	+	6.61814i	−0.715040	+	0.412828i	−0.812924	−	0.582369i	$-0.802126\pi$
$257$	−11.4630	+	6.61814i	−0.715040	+	0.412828i	0.0978846	+	0.995198i	$0.468792\pi$
$258$	9.55034	+	13.2257i	0.594578	+	0.823399i
$259$	−6.39037	+	22.0770i	−0.397079	+	1.37180i
$260$	8.82351	+	1.54805i	0.547211	+	0.0960060i
$261$	1.78305	+	8.63564i	0.110368	+	0.534533i
$262$	2.26659	+	21.5652i	0.140030	+	1.33230i
$263$	−0.621741	−	5.91547i	−0.0383382	−	0.364764i	−0.996825	−	0.0796260i	$-0.974627\pi$
$263$	−0.621741	−	5.91547i	−0.0383382	−	0.364764i	0.958487	−	0.285138i	$-0.0920393\pi$
$264$	−15.9406	−	14.4372i	−0.981073	−	0.888550i
$265$	−15.8339	−	16.3685i	−0.972668	−	1.00551i
$266$	6.50146	−	1.60370i	0.398630	−	0.0983293i
$267$	−18.8699	+	13.6260i	−1.15482	+	0.833898i
$268$	−15.2203	+	8.78743i	−0.929726	+	0.536778i
$269$	3.07503	+	3.41517i	0.187488	+	0.208226i	0.829560	−	0.558418i	$-0.188592\pi$
$269$	3.07503	+	3.41517i	0.187488	+	0.208226i	−0.642072	+	0.766645i	$0.721925\pi$
$270$	2.38083	−	30.5811i	0.144893	−	1.86111i
$271$	−20.1790	−	18.1693i	−1.22579	−	1.10370i	−0.991305	−	0.131584i	$-0.957994\pi$
$271$	−20.1790	−	18.1693i	−1.22579	−	1.10370i	−0.234483	−	0.972120i	$-0.575340\pi$
$272$	−35.2631	+	11.4577i	−2.13814	+	0.694723i
$273$	−3.68395	−	0.277672i	−0.222963	−	0.0168055i
$274$	37.8521			2.28673
$275$	−5.49177	+	5.70638i	−0.331166	+	0.344108i
$276$	−60.0498	+	26.5266i	−3.61457	+	1.59671i
$277$	5.61515	+	12.6118i	0.337382	+	0.757772i	0.999961	+	0.00878053i	$0.00279496\pi$
$277$	5.61515	+	12.6118i	0.337382	+	0.757772i	−0.662580	+	0.748991i	$0.730538\pi$
$278$	0.760993	+	0.685201i	0.0456413	+	0.0410956i
$279$	12.0998	+	16.8595i	0.724393	+	1.00935i
$280$	−32.2714	+	33.3077i	−1.92858	+	1.99052i
$281$	10.3969	+	3.37815i	0.620225	+	0.201523i	0.602240	−	0.798315i	$-0.294275\pi$
$281$	10.3969	+	3.37815i	0.620225	+	0.201523i	0.0179849	+	0.999838i	$0.494275\pi$
$282$	50.0002	+	5.40251i	2.97747	+	0.321715i
$283$	−17.6054	−	19.5527i	−1.04653	−	1.16229i	−0.986444	−	0.164096i	$-0.947529\pi$
$283$	−17.6054	−	19.5527i	−1.04653	−	1.16229i	−0.0600857	−	0.998193i	$-0.519137\pi$
$284$	59.9232	−	6.29819i	3.55579	−	0.373729i
$285$	3.49177	−	1.26277i	0.206834	−	0.0747998i
$286$	−1.98149	+	2.72729i	−0.117168	+	0.161268i
$287$	−19.2925	+	18.5374i	−1.13880	+	1.09423i
$288$	−30.7360	−	22.6057i	−1.81114	−	1.33206i
$289$	−0.534947	+	5.08968i	−0.0314675	+	0.299393i
$290$	6.48602	−	16.0930i	0.380872	−	0.945016i
$291$	11.9764	−	20.6049i	0.702068	−	1.20788i
$292$	−2.06706	+	0.439367i	−0.120965	+	0.0257120i
$293$		−	26.8440i		−	1.56825i	−0.620606	−	0.784123i	$-0.713113\pi$
$293$		−	26.8440i		−	1.56825i	0.620606	−	0.784123i	$-0.286887\pi$
$294$	19.9053	−	25.0656i	1.16090	−	1.46186i
$295$	4.92661	−	9.28473i	0.286838	−	0.540578i
$296$	50.6065	+	45.5663i	2.94144	+	2.64849i
$297$	7.09154	+	4.17734i	0.411493	+	0.242394i
$298$	9.09708	+	20.4324i	0.526980	+	1.18362i
$299$	3.07438	+	5.32498i	0.177796	+	0.307951i
$300$	−26.5367	+	33.8813i	−1.53210	+	1.95614i
$301$	1.29026	+	9.35062i	0.0743694	+	0.538961i
$302$	−39.7122	−	28.8526i	−2.28518	−	1.66028i
$303$	−3.34980	+	0.701832i	−0.192441	+	0.0403192i
$304$	2.14404	−	10.0869i	0.122969	−	0.578523i
$305$	−11.2325	−	9.40887i	−0.643173	−	0.538751i
$306$	23.7220	−	13.5123i	1.35610	−	0.772445i
$307$	−10.8188			−0.617464			−0.308732	−	0.951149i	$-0.599905\pi$
$307$	−10.8188			−0.617464			−0.308732	+	0.951149i	$0.599905\pi$
$308$	−7.07369	−	19.5874i	−0.403061	−	1.11609i
$309$	22.0664	+	0.0642691i	1.25531	+	0.00365614i
$310$	−1.45996	−	40.8080i	−0.0829202	−	2.31774i
$311$	3.80600	−	1.69454i	0.215818	−	0.0960885i	−0.295980	−	0.955194i	$-0.595646\pi$
$311$	3.80600	−	1.69454i	0.215818	−	0.0960885i	0.511798	+	0.859106i	$0.328980\pi$
$312$	−5.50071	+	9.46374i	−0.311416	+	0.535779i
$313$	5.91865	+	2.63515i	0.334542	+	0.148948i	0.567131	−	0.823627i	$-0.308053\pi$
$313$	5.91865	+	2.63515i	0.334542	+	0.148948i	−0.232589	+	0.972575i	$0.574720\pi$
$314$	1.01405	+	0.736752i	0.0572262	+	0.0415773i
$315$	9.51740	−	14.9806i	0.536245	−	0.844063i
$316$	−24.1447	+	17.5421i	−1.35825	+	0.986823i
$317$	13.2622	−	2.81897i	0.744881	−	0.158329i	0.180190	−	0.983632i	$-0.442329\pi$
$317$	13.2622	−	2.81897i	0.744881	−	0.158329i	0.564691	+	0.825302i	$0.308995\pi$
$318$	42.5988	−	18.8177i	2.38882	−	1.05525i
$319$	3.11524	+	3.45982i	0.174420	+	0.193713i
$320$	9.24673	+	25.3378i	0.516908	+	1.41643i
$321$	0.501797	−	1.52920i	0.0280076	−	0.0853519i
$322$	−53.1330	−	3.84923i	−2.96099	−	0.214509i
$323$	2.67360	+	1.94249i	0.148763	+	0.108083i
$324$	40.6435	+	18.6660i	2.25797	+	1.03700i
$325$	3.42206	+	2.13022i	0.189822	+	0.118163i
$326$	0.735065	+	0.424390i	0.0407115	+	0.0235048i
$327$	−11.4249	+	12.6146i	−0.631801	+	0.697589i
$328$	24.4969	+	75.3936i	1.35261	+	4.16292i
$329$	24.0835	+	16.3325i	1.32777	+	0.900439i
$330$	−7.06952	−	14.5707i	−0.389164	−	0.802090i
$331$	−16.6930	+	3.54820i	−0.917530	+	0.195027i	−0.642391	−	0.766377i	$-0.722057\pi$
$331$	−16.6930	+	3.54820i	−0.917530	+	0.195027i	−0.275139	+	0.961404i	$0.588724\pi$
$332$	6.83981	+	3.94896i	0.375383	+	0.216728i
$333$	−22.4928	−	13.1615i	−1.23260	−	0.721246i
$334$	9.52369	−	21.3906i	0.521113	−	1.17044i
$335$	−7.83017	+	1.10728i	−0.427808	+	0.0604973i
$336$	−21.3677	−	44.4195i	−1.16570	−	2.42328i
$337$	−1.47676	−	2.03259i	−0.0804445	−	0.110722i	0.766898	−	0.641769i	$-0.221799\pi$
$337$	−1.47676	−	2.03259i	−0.0804445	−	0.110722i	−0.847343	+	0.531046i	$0.821799\pi$
$338$	−29.7850	−	13.2611i	−1.62009	−	0.721311i
$339$	−1.91330	−	0.412513i	−0.103916	−	0.0224046i
$340$	−38.2127	−	2.63928i	−2.07237	−	0.143135i
$341$	10.0095	+	4.45650i	0.542043	+	0.241333i
$342$	−0.0442290	+	7.59279i	−0.00239163	+	0.410571i
$343$	16.9752	−	7.40548i	0.916577	−	0.399858i
$344$	26.5989	+	8.64252i	1.43412	+	0.465973i
$345$	−29.5233	+	0.970146i	−1.58948	+	0.0522309i
$346$	8.08120	−	38.0191i	0.434448	−	2.04392i
$347$	4.78684	+	1.01747i	0.256971	+	0.0546209i	0.334596	−	0.942362i	$-0.391400\pi$
$347$	4.78684	+	1.01747i	0.256971	+	0.0546209i	−0.0776246	+	0.996983i	$0.524734\pi$
$348$	18.7515	+	16.9831i	1.00519	+	0.910390i
$349$		−	14.4605i		−	0.774050i	−0.922069	−	0.387025i	$-0.873503\pi$
$349$		−	14.4605i		−	0.774050i	0.922069	−	0.387025i	$-0.126497\pi$
$350$	−31.9155	+	14.1792i	−1.70595	+	0.757912i
$351$	1.32925	−	3.97256i	0.0709501	−	0.212040i
$352$	−20.0343	−	2.10569i	−1.06783	−	0.112233i
$353$	0.199480	−	0.938477i	0.0106172	−	0.0499501i	−0.972520	−	0.232819i	$-0.925205\pi$
$353$	0.199480	−	0.938477i	0.0106172	−	0.0499501i	0.983137	+	0.182869i	$0.0585384\pi$
$354$	14.3355	+	16.0148i	0.761924	+	0.851175i
$355$	26.0680	+	7.45078i	1.38355	+	0.395446i
$356$	−20.6359	+	63.5109i	−1.09370	+	3.36607i
$357$	15.7896	−	0.465744i	0.835674	−	0.0246498i
$358$	43.3162	+	14.0743i	2.28933	+	0.743850i
$359$	−6.74199	+	15.1428i	−0.355829	+	0.799204i	0.643598	+	0.765363i	$0.277441\pi$
$359$	−6.74199	+	15.1428i	−0.355829	+	0.799204i	−0.999427	+	0.0338412i	$0.989226\pi$
$360$	−27.6448	−	44.7341i	−1.45701	−	2.35769i
$361$	16.5177	−	7.35415i	0.869352	−	0.387061i
$362$	−14.6355	+	32.8718i	−0.769224	+	1.72771i
$363$	−14.7070	−	0.0428346i	−0.771916	−	0.00224823i
$364$	−9.00300	+	5.59438i	−0.471886	+	0.293225i
$365$	−0.936578	−	0.164319i	−0.0490228	−	0.00860085i
$366$	25.9923	−	14.9059i	1.35864	−	0.779145i
$367$	6.11503	+	6.79143i	0.319202	+	0.354510i	0.881297	−	0.472563i	$-0.156671\pi$
$367$	6.11503	+	6.79143i	0.319202	+	0.354510i	−0.562095	+	0.827073i	$0.690004\pi$
$368$	−41.0192	+	71.0474i	−2.13827	+	3.70360i
$369$	−15.0154	−	26.3609i	−0.781672	−	1.37229i
$370$	22.5189	+	46.0707i	1.17070	+	2.39510i
$371$	26.8757	+	1.94701i	1.39532	+	0.101084i
$372$	56.5718	+	18.5636i	2.93311	+	0.962479i
$373$	−24.1016	−	2.53318i	−1.24793	−	0.131163i	−0.542570	−	0.840011i	$-0.682549\pi$
$373$	−24.1016	−	2.53318i	−1.24793	−	0.131163i	−0.705361	+	0.708848i	$0.749215\pi$
$374$	7.20708	−	12.4830i	0.372669	−	0.645482i
$375$	−16.7739	+	9.67660i	−0.866200	+	0.499698i
$376$	74.6679	−	43.1095i	3.85070	−	2.22320i
$377$	1.39281	−	1.91704i	0.0717333	−	0.0987324i
$378$	22.0216	+	28.8491i	1.13267	+	1.48384i
$379$	10.8863	+	33.5047i	0.559193	+	1.72102i	0.684605	+	0.728915i	$0.259975\pi$
$379$	10.8863	+	33.5047i	0.559193	+	1.72102i	−0.125411	+	0.992105i	$0.540025\pi$
$380$	5.94965	−	8.83700i	0.305211	−	0.453328i
$381$	32.1244	−	3.28184i	1.64578	−	0.168134i
$382$	7.84918	+	4.53172i	0.401599	+	0.231863i
$383$	−0.113386	−	0.533437i	−0.00579373	−	0.0272574i	0.975156	−	0.221520i	$-0.0711019\pi$
$383$	−0.113386	−	0.533437i	−0.00579373	−	0.0272574i	−0.980950	+	0.194263i	$0.937769\pi$
$384$	−11.0995	−	0.0323279i	−0.566421	−	0.00164972i
$385$	0.342498	−	9.36450i	0.0174553	−	0.477259i
$386$	−14.8988	+	20.5064i	−0.758327	+	1.04375i
$387$	−10.6377	−	1.18076i	−0.540747	−	0.0600215i
$388$	−7.14746	−	68.0036i	−0.362857	−	3.45236i
$389$	5.64648	+	12.6822i	0.286288	+	0.643013i	0.998246	−	0.0592092i	$-0.0188579\pi$
$389$	5.64648	+	12.6822i	0.286288	+	0.643013i	−0.711958	+	0.702222i	$0.752191\pi$
$390$	−6.50589	+	5.06143i	−0.329439	+	0.256296i
$391$	−15.4533	−	21.2697i	−0.781509	−	1.07565i
$392$	2.18988	−	54.8305i	0.110606	−	2.76936i
$393$	−11.4851	−	8.39566i	−0.579349	−	0.423505i
$394$	−7.65587	+	1.62731i	−0.385697	+	0.0819824i
$395$	−13.0273	+	3.25990i	−0.655475	+	0.164023i
$396$	23.4986	−	2.33149i	1.18085	−	0.117162i
$397$	9.31208	−	10.3421i	0.467360	−	0.519056i	−0.462674	−	0.886528i	$-0.653110\pi$
$397$	9.31208	−	10.3421i	0.467360	−	0.519056i	0.930034	+	0.367472i	$0.119777\pi$
$398$	−8.72294	+	12.0061i	−0.437241	+	0.601811i
$399$	−2.08356	+	3.86789i	−0.104308	+	0.193637i
$400$	−1.78509	+	53.7520i	−0.0892547	+	2.68760i
$401$	15.9506	−	9.20906i	0.796533	−	0.459879i	−0.0457242	−	0.998954i	$-0.514560\pi$
$401$	15.9506	−	9.20906i	0.796533	−	0.459879i	0.842258	+	0.539075i	$0.181226\pi$
$402$	3.40826	−	15.8081i	0.169988	−	0.788434i
$403$	1.15945	−	5.45479i	0.0577564	−	0.271723i
$404$	−6.57059	+	7.29738i	−0.326899	+	0.363058i
$405$	13.8226	+	14.6265i	0.686852	+	0.726797i
$406$	6.97327	+	19.3093i	0.346078	+	0.958305i
$407$	−13.7595			−0.682034
$408$	19.1613	−	42.7018i	0.948625	−	2.11405i
$409$	16.2273	−	1.70556i	0.802388	−	0.0843344i	0.305548	−	0.952177i	$-0.401160\pi$
$409$	16.2273	−	1.70556i	0.802388	−	0.0843344i	0.496840	+	0.867842i	$0.334494\pi$
$410$	−4.11326	+	59.5536i	−0.203139	+	2.94114i
$411$	−16.6711	+	18.4070i	−0.822323	+	0.907951i
$412$	51.2195	−	37.2132i	2.52340	−	1.83336i
$413$	2.97844	+	12.0747i	0.146559	+	0.594156i
$414$	19.0005	−	57.3389i	0.933824	−	2.81805i
$415$	2.19033	+	2.79856i	0.107519	+	0.137376i
$416$	1.07173	+	10.1969i	0.0525460	+	0.499942i
$417$	−0.668367	+	0.0682806i	−0.0327301	+	0.00334372i
$418$	2.00447	+	3.47184i	0.0980417	+	0.169813i
$419$	2.86047	−	8.80362i	0.139743	−	0.430085i	−0.856555	−	0.516057i	$-0.827399\pi$
$419$	2.86047	−	8.80362i	0.139743	−	0.430085i	0.996298	+	0.0859716i	$0.0273994\pi$
$420$	−3.32024	−	50.8131i	−0.162011	−	2.47942i
$421$	1.06156	+	3.26715i	0.0517373	+	0.159231i	0.973587	−	0.228317i	$-0.0733222\pi$
$421$	1.06156	+	3.26715i	0.0517373	+	0.159231i	−0.921850	+	0.387548i	$0.873322\pi$
$422$	32.0160	−	35.5574i	1.55852	−	1.73091i
$423$	−24.6486	+	21.9351i	−1.19846	+	1.06652i
$424$	39.9197	−	69.1430i	1.93867	−	3.35788i
$425$	−15.5039	−	7.52899i	−0.752050	−	0.365210i
$426$	−32.7181	+	44.7579i	−1.58520	+	2.16853i
$427$	17.3280	−	0.561640i	0.838561	−	0.0271797i
$428$	−1.42692	−	4.39161i	−0.0689729	−	0.212277i
$429$	−0.453545	−	2.16475i	−0.0218974	−	0.104515i
$430$	16.1449	+	13.5237i	0.778577	+	0.652171i
$431$	11.9878	−	10.7939i	0.577432	−	0.519922i	−0.327852	−	0.944729i	$-0.606325\pi$
$431$	11.9878	−	10.7939i	0.577432	−	0.519922i	0.905284	+	0.424807i	$0.139658\pi$
$432$	54.7696	−	11.1424i	2.63510	−	0.536088i
$433$	0.277134	−	0.852930i	0.0133182	−	0.0409892i	−0.944177	−	0.329440i	$-0.893140\pi$
$433$	0.277134	−	0.852930i	0.0133182	−	0.0409892i	0.957495	+	0.288451i	$0.0931401\pi$
$434$	33.4757	+	34.8393i	1.60688	+	1.67234i
$435$	4.96923	+	10.2419i	0.238256	+	0.491061i
$436$	−5.10414	+	48.5626i	−0.244444	+	2.32573i
$437$	7.27205	−	0.764324i	0.347870	−	0.0365626i
$438$	0.977136	−	1.68112i	0.0466894	−	0.0803271i
$439$	2.04621	+	0.215066i	0.0976604	+	0.0102645i	0.153233	−	0.988190i	$-0.451032\pi$
$439$	2.04621	+	0.215066i	0.0976604	+	0.0102645i	−0.0555722	+	0.998455i	$0.517698\pi$
$440$	−24.5261	−	13.0139i	−1.16924	−	0.620413i
$441$	3.42229	+	20.7193i	0.162966	+	0.986632i
$442$	−6.97732	−	2.26707i	−0.331877	−	0.107833i
$443$	15.9897	+	27.6950i	0.759695	+	1.31583i	0.943006	+	0.332776i	$0.107985\pi$
$443$	15.9897	+	27.6950i	0.759695	+	1.31583i	−0.183311	+	0.983055i	$0.558681\pi$
$444$	−74.3831	+	7.59901i	−3.53006	+	0.360633i
$445$	−19.2950	+	23.0349i	−0.914672	+	1.09196i
$446$	−9.46736	+	10.5146i	−0.448292	+	0.497879i
$447$	−13.9426	−	4.57517i	−0.659463	−	0.216398i
$448$	−28.1408	−	15.0533i	−1.32953	−	0.711202i
$449$			22.3219i			1.05343i	0.850041	+	0.526717i	$0.176577\pi$
$449$			22.3219i			1.05343i	−0.850041	+	0.526717i	$0.823423\pi$
$450$	−6.71580	−	39.0259i	−0.316586	−	1.83970i
$451$	−13.8717	−	8.00883i	−0.653193	−	0.377121i
$452$	−5.13010	+	2.28407i	−0.241299	+	0.107433i
$453$	31.5210	−	6.60409i	1.48098	−	0.310287i
$454$	−48.2966	+	15.6925i	−2.26667	+	0.736486i
$455$	−4.69835	+	0.820449i	−0.220262	+	0.0384632i
$456$	7.62067	+	10.5534i	0.356870	+	0.494211i
$457$	−7.10198	+	4.10033i	−0.332217	+	0.191805i	−0.656825	−	0.754043i	$-0.728101\pi$
$457$	−7.10198	+	4.10033i	−0.332217	+	0.191805i	0.324608	+	0.945849i	$0.394768\pi$
$458$	−25.3136	+	22.7925i	−1.18283	+	1.06502i
$459$	−3.87695	+	17.4869i	−0.180960	+	0.816218i
$460$	−66.7400	+	52.2349i	−3.11177	+	2.43547i
$461$	−9.15630	−	6.65244i	−0.426451	−	0.309835i	0.353777	−	0.935330i	$-0.384897\pi$
$461$	−9.15630	−	6.65244i	−0.426451	−	0.309835i	−0.780228	+	0.625495i	$0.784897\pi$
$462$	17.7279	+	7.27451i	0.824776	+	0.338441i
$463$	−7.98929	−	10.9963i	−0.371294	−	0.511042i	0.581958	−	0.813219i	$-0.302287\pi$
$463$	−7.98929	−	10.9963i	−0.371294	−	0.511042i	−0.953252	+	0.302177i	$0.902287\pi$
$464$	31.4425	+	3.30474i	1.45968	+	0.153419i
$465$	20.4875	+	17.2630i	0.950083	+	0.800552i
$466$	5.96986	+	56.7995i	0.276549	+	2.63118i
$467$	0.577848	+	2.71856i	0.0267396	+	0.125800i	0.989493	−	0.144581i	$-0.0461835\pi$
$467$	0.577848	+	2.71856i	0.0267396	+	0.125800i	−0.962753	+	0.270381i	$0.912850\pi$
$468$	−3.64737	−	11.4520i	−0.168600	−	0.529369i
$469$	6.03248	−	7.15276i	0.278554	−	0.330284i
$470$	64.2860	−	9.09084i	2.96529	−	0.419329i
$471$	−0.804889	+	0.168636i	−0.0370873	+	0.00777032i
$472$	36.0435	+	7.66129i	1.65904	+	0.352639i
$473$	−5.16248	+	2.29848i	−0.237371	+	0.105684i
$474$	2.94999	−	27.3021i	0.135498	−	1.25403i
$475$	3.96947	−	2.68732i	0.182132	−	0.123303i
$476$	35.7837	−	27.8132i	1.64014	−	1.27481i
$477$	−9.61082	+	29.0031i	−0.440049	+	1.32796i
$478$	−15.0341	−	13.5367i	−0.687643	−	0.619156i
$479$	−12.6365	−	2.68597i	−0.577377	−	0.122725i	−0.0900384	−	0.995938i	$-0.528699\pi$
$479$	−12.6365	−	2.68597i	−0.577377	−	0.122725i	−0.487339	+	0.873213i	$0.662032\pi$
$480$	−45.6318	−	18.5458i	−2.08280	−	0.846495i
$481$	1.45605	+	6.85015i	0.0663899	+	0.312340i
$482$		−	53.5482i		−	2.43905i
$483$	25.2730	−	24.1426i	1.14996	−	1.09853i
$484$	−34.1372	+	24.8021i	−1.55169	+	1.12737i
$485$	8.45548	−	29.5831i	0.383943	−	1.34330i
$486$	−37.8349	+	16.1892i	−1.71623	+	0.734357i
$487$	−28.6209	+	3.00817i	−1.29694	+	0.136313i	−0.727720	−	0.685875i	$-0.759420\pi$
$487$	−28.6209	+	3.00817i	−1.29694	+	0.136313i	−0.569216	+	0.822188i	$0.692753\pi$
$488$	20.8935	−	46.9276i	0.945805	−	2.12431i
$489$	−0.530118	+	0.170540i	−0.0239728	+	0.00771211i
$490$	16.9640	−	37.6793i	0.766353	−	1.70218i
$491$	−4.54401	−	6.25429i	−0.205068	−	0.282252i	0.694079	−	0.719899i	$-0.255812\pi$
$491$	−4.54401	−	6.25429i	−0.205068	−	0.282252i	−0.899147	+	0.437647i	$0.855812\pi$
$492$	−79.4126	−	35.6343i	−3.58019	−	1.60652i
$493$	−5.06593	+	8.77445i	−0.228158	+	0.395181i
$494$	1.51633	−	1.36531i	0.0682231	−	0.0614284i
$495$	10.1992	+	2.97950i	0.458418	+	0.133919i
$496$	70.7637	−	22.9925i	3.17738	−	1.03239i
$497$	−28.8678	+	13.9903i	−1.29490	+	0.627552i
$498$	−6.91802	+	2.22554i	−0.310004	+	0.0997290i
$499$	13.7877	+	23.8810i	0.617223	+	1.06906i	0.989990	+	0.141137i	$0.0450758\pi$
$499$	13.7877	+	23.8810i	0.617223	+	1.06906i	−0.372767	+	0.927925i	$0.621591\pi$
$500$	−22.4680	+	50.8142i	−1.00480	+	2.27248i
$501$	6.20748	+	14.0522i	0.277330	+	0.627808i
$502$	6.43983	−	61.2709i	0.287424	−	2.73465i
$503$	−3.41272	+	1.10886i	−0.152166	+	0.0494417i	−0.384110	−	0.923288i	$-0.625491\pi$
$503$	−3.41272	+	1.10886i	−0.152166	+	0.0494417i	0.231944	+	0.972729i	$0.425491\pi$
$504$	59.6663	+	17.6483i	2.65775	+	0.786116i
$505$	−3.96964	+	1.94032i	−0.176647	+	0.0863433i
$506$	−6.63089	−	31.1959i	−0.294779	−	1.38683i
$507$	19.5669	−	8.64353i	0.868995	−	0.383873i
$508$	68.8508	−	61.9935i	3.05476	−	2.75052i
$509$	−8.43562	−	3.75578i	−0.373902	−	0.166472i	0.211178	−	0.977448i	$-0.432270\pi$
$509$	−8.43562	−	3.75578i	−0.373902	−	0.166472i	−0.585080	+	0.810976i	$0.698937\pi$
$510$	25.4033	−	24.4308i	1.12488	−	1.08181i
$511$	0.955631	−	0.593820i	0.0422746	−	0.0262690i
$512$	25.7614	−	18.7167i	1.13850	−	0.827170i
$513$	−3.67280	−	3.36558i	−0.162158	−	0.148594i
$514$	−14.2127	−	31.9223i	−0.626897	−	1.40803i
$515$	27.6356	−	6.91541i	1.21777	−	0.304729i
$516$	−26.6387	+	15.2766i	−1.17270	+	0.672513i
$517$	−5.38339	+	16.5684i	−0.236761	+	0.728677i
$518$	−56.1997	−	22.8701i	−2.46927	−	1.00486i
$519$	14.9290	+	20.6744i	0.655311	+	0.907505i
$520$	−3.88357	+	13.5874i	−0.170306	+	0.595848i
$521$	4.01311	+	0.853013i	0.175818	+	0.0373712i	0.294979	−	0.955504i	$-0.404687\pi$
$521$	4.01311	+	0.853013i	0.175818	+	0.0373712i	−0.119162	+	0.992875i	$0.538021\pi$
$522$	−23.1650	+	2.29839i	−1.01390	+	0.100598i
$523$	−2.54537	+	24.2176i	−0.111301	+	1.05896i	0.786207	+	0.617963i	$0.212042\pi$
$523$	−2.54537	+	24.2176i	−0.111301	+	1.05896i	−0.897508	+	0.440997i	$0.854625\pi$
$524$	−40.8175			−1.78312
$525$	7.16125	−	21.7650i	0.312543	−	0.949904i
$526$	15.7027			0.684669
$527$	−2.49244	+	23.7140i	−0.108572	+	1.03300i
$528$	21.9874	−	19.6819i	0.956880	−	0.856546i
$529$	−34.4025	−	7.31247i	−1.49576	−	0.317934i
$530$	47.3448	−	37.0550i	2.05653	−	1.60957i
$531$	−14.1015	−	0.0821432i	−0.611954	−	0.00356471i
$532$	1.72300	+	12.4867i	0.0747016	+	0.541368i
$533$	−2.51927	+	7.75350i	−0.109122	+	0.335841i
$534$	−30.5680	−	53.3032i	−1.32280	−	2.30665i
$535$	0.143166	−	2.07283i	0.00618963	−	0.0896162i
$536$	−11.2764	−	25.3272i	−0.487066	−	1.09397i
$537$	−25.9218	+	14.8655i	−1.11861	+	0.641492i
$538$	−9.81510	+	7.13108i	−0.423159	+	0.307443i
$539$	7.08434	+	8.52923i	0.305144	+	0.367380i
$540$	56.7815	+	10.4743i	2.44349	+	0.450742i
$541$	9.18722	+	4.09041i	0.394989	+	0.175861i	0.594613	−	0.804012i	$-0.297305\pi$
$541$	9.18722	+	4.09041i	0.394989	+	0.175861i	−0.199624	+	0.979873i	$0.563972\pi$
$542$	53.2719	−	47.9663i	2.28823	−	2.06033i
$543$	−9.53931	−	21.5947i	−0.409371	−	0.926717i
$544$	−9.11480	−	42.8818i	−0.390794	−	1.83854i
$545$	−10.2986	+	19.4088i	−0.441143	+	0.831382i
$546$	1.74562	−	9.59559i	0.0747057	−	0.410654i
$547$	23.9057	−	7.76744i	1.02214	−	0.332112i	0.250459	−	0.968127i	$-0.419419\pi$
$547$	23.9057	−	7.76744i	1.02214	−	0.332112i	0.771676	+	0.636015i	$0.219419\pi$
$548$	−7.44787	+	70.8617i	−0.318157	+	3.02706i
$549$	−4.19916	+	19.2047i	−0.179216	+	0.819638i
$550$	−13.4667	−	15.9934i	−0.574220	−	0.681959i
$551$	−1.40896	−	2.44039i	−0.0600237	−	0.103964i
$552$	−31.7143	−	98.5825i	−1.34985	−	4.19595i
$553$	8.91821	−	13.1506i	0.379241	−	0.559220i
$554$	−34.6620	+	11.2624i	−1.47265	+	0.478491i
$555$	−32.3215	−	9.34008i	−1.37197	−	0.396464i
$556$	−1.43248	+	1.28981i	−0.0607507	+	0.0547001i
$557$	9.84636	−	17.0544i	0.417204	−	0.722618i	−0.578453	−	0.815716i	$-0.696343\pi$
$557$	9.84636	−	17.0544i	0.417204	−	0.722618i	0.995657	+	0.0930974i	$0.0296768\pi$
$558$	−47.6037	+	27.1155i	−2.01523	+	1.14789i
$559$	1.69060	+	2.32691i	0.0715046	+	0.0984176i
$560$	−40.8234	−	48.8149i	−1.72510	−	2.06281i
$561$	2.89615	+	9.00258i	0.122276	+	0.380089i
$562$	−11.7384	+	26.3648i	−0.495154	+	1.11213i
$563$	−16.8272	+	1.76861i	−0.709180	+	0.0745378i	−0.452249	−	0.891892i	$-0.649378\pi$
$563$	−16.8272	+	1.76861i	−0.709180	+	0.0745378i	−0.256931	+	0.966430i	$0.582711\pi$
$564$	−19.9520	+	92.5407i	−0.840132	+	3.89667i
$565$	−2.52521	+	0.0903426i	−0.106236	+	0.00380074i
$566$	56.1940	−	40.8273i	2.36201	−	1.71610i
$567$	−23.7279	−	1.99710i	−0.996477	−	0.0838703i
$568$			95.0486i			3.98815i
$569$	2.31432	+	10.8880i	0.0970213	+	0.456450i	0.999661	+	0.0260516i	$0.00829342\pi$
$569$	2.31432	+	10.8880i	0.0970213	+	0.456450i	−0.902639	+	0.430398i	$0.858373\pi$
$570$	2.35184	+	9.51611i	0.0985078	+	0.398586i
$571$	12.1190	+	2.57598i	0.507165	+	0.107801i	0.454386	−	0.890805i	$-0.349859\pi$
$571$	12.1190	+	2.57598i	0.507165	+	0.107801i	0.0527791	+	0.998606i	$0.483192\pi$
$572$	−4.71579	−	4.24612i	−0.197177	−	0.177539i
$573$	−5.66071	+	1.82107i	−0.236480	+	0.0760761i
$574$	−43.3462	−	55.7680i	−1.80923	−	2.32771i
$575$	−36.6397	+	10.5741i	−1.52798	+	0.440969i
$576$	24.3702	−	26.7508i	1.01542	−	1.11462i
$577$	7.37280	−	3.28258i	0.306934	−	0.136656i	−0.247490	−	0.968891i	$-0.579606\pi$
$577$	7.37280	−	3.28258i	0.306934	−	0.136656i	0.554423	+	0.832235i	$0.312939\pi$
$578$	−13.2154	−	2.80901i	−0.549686	−	0.116839i
$579$	−3.41019	−	16.2766i	−0.141723	−	0.676434i
$580$	28.8511	+	15.3088i	1.19798	+	0.635663i
$581$	−4.13918	−	0.740548i	−0.171722	−	0.0307231i
$582$	50.7933	+	37.1300i	2.10545	+	1.53909i
$583$	3.35403	+	15.7795i	0.138910	+	0.653519i
$584$	−0.348456	−	3.31533i	−0.0144192	−	0.137190i
$585$	0.404057	−	5.39293i	0.0167057	−	0.222970i
$586$	70.4791	+	7.40765i	2.91147	+	0.306007i
$587$	3.74724	+	5.15764i	0.154665	+	0.212878i	0.879317	−	0.476237i	$-0.157999\pi$
$587$	3.74724	+	5.15764i	0.154665	+	0.212878i	−0.724652	+	0.689115i	$0.757999\pi$
$588$	43.0080	+	42.1960i	1.77362	+	1.74013i
$589$	−5.36521	−	3.89806i	−0.221070	−	0.160617i
$590$	23.0176	+	15.4970i	0.947620	+	0.638000i
$591$	2.58051	−	4.43966i	0.106148	−	0.182623i
$592$	−69.4384	+	62.5226i	−2.85390	+	2.56966i
$593$	25.0801	−	14.4800i	1.02992	−	0.594622i	0.112956	−	0.993600i	$-0.463968\pi$
$593$	25.0801	−	14.4800i	1.02992	−	0.594622i	0.916961	+	0.398978i	$0.130635\pi$
$594$	−12.9245	+	17.4661i	−0.530301	+	0.716644i
$595$	19.6124	−	5.58873i	0.804030	−	0.229116i
$596$	−40.0408	+	13.0100i	−1.64014	+	0.532912i
$597$	−1.99660	−	9.52966i	−0.0817154	−	0.390023i
$598$	−14.8291	+	6.60236i	−0.606408	+	0.269990i
$599$	0.532949	+	0.307698i	0.0217757	+	0.0125722i	0.510848	−	0.859671i	$-0.329331\pi$
$599$	0.532949	+	0.307698i	0.0217757	+	0.0125722i	−0.489073	+	0.872243i	$0.662665\pi$
$600$	−48.7787	−	47.2186i	−1.99138	−	1.92769i
$601$		−	15.4588i		−	0.630579i	−0.948995	−	0.315290i	$-0.897898\pi$
$601$		−	15.4588i		−	0.630579i	0.948995	−	0.315290i	$-0.102102\pi$
$602$	−24.9062	+	0.807265i	−1.01510	+	0.0329017i
$603$	6.18618	+	8.61969i	0.251921	+	0.351021i
$604$	61.8279	−	68.6668i	2.51574	−	2.79401i
$605$	−18.4188	+	4.60904i	−0.748830	+	0.187384i
$606$	−0.918279	−	8.98860i	−0.0373025	−	0.365137i
$607$	17.0976	+	29.6139i	0.693970	+	1.20199i	0.970527	+	0.240993i	$0.0774731\pi$
$607$	17.0976	+	29.6139i	0.693970	+	1.20199i	−0.276557	+	0.960997i	$0.589194\pi$
$608$	11.5961	+	3.76782i	0.470286	+	0.152805i
$609$	−12.4611	−	5.11332i	−0.504949	−	0.207202i
$610$	27.8027	−	26.8947i	1.12570	−	1.08893i
$611$	8.81822	+	0.926832i	0.356747	+	0.0374956i
$612$	20.6283	+	47.0679i	0.833850	+	1.90261i
$613$	15.3114	−	1.60929i	0.618420	−	0.0649986i	0.209862	−	0.977731i	$-0.432698\pi$
$613$	15.3114	−	1.60929i	0.618420	−	0.0649986i	0.408558	+	0.912732i	$0.366032\pi$
$614$	2.98548	−	28.4049i	0.120484	−	1.14633i
$615$	−27.1486	−	28.2292i	−1.09474	−	1.13831i
$616$	31.8959	−	7.86770i	1.28512	−	0.316999i
$617$	−5.00496	+	15.4037i	−0.201492	+	0.620129i	0.798347	+	0.602198i	$0.205708\pi$
$617$	−5.00496	+	15.4037i	−0.201492	+	0.620129i	−0.999839	+	0.0179316i	$0.994292\pi$
$618$	−6.25799	+	57.9176i	−0.251733	+	2.32979i
$619$	8.91836	−	8.03013i	0.358459	−	0.322758i	−0.470149	−	0.882587i	$-0.655800\pi$
$619$	8.91836	−	8.03013i	0.358459	−	0.322758i	0.828608	+	0.559829i	$0.189133\pi$
$620$	76.6827	+	5.29634i	3.07965	+	0.212706i
$621$	19.5149	+	34.4933i	0.783105	+	1.38417i
$622$	3.39875	+	10.4603i	0.136277	+	0.419419i
$623$	−1.15177	−	35.5350i	−0.0461447	−	1.42368i
$624$	−12.1253	−	8.86365i	−0.485402	−	0.354830i
$625$	−17.9240	+	17.4278i	−0.716961	+	0.697113i
$626$	−8.55187	+	14.8123i	−0.341801	+	0.592018i
$627$	−2.57113	−	0.554343i	−0.102681	−	0.0221383i
$628$	−1.57878	+	1.75341i	−0.0630001	+	0.0699687i
$629$	−9.25325	−	28.4786i	−0.368951	−	1.13552i
$630$	36.7054	+	29.1219i	1.46238	+	1.16024i
$631$	12.6294	−	38.8694i	0.502769	−	1.54737i	−0.301719	−	0.953397i	$-0.597560\pi$
$631$	12.6294	−	38.8694i	0.502769	−	1.54737i	0.804488	−	0.593968i	$-0.202440\pi$
$632$	−23.5396	−	40.7717i	−0.936354	−	1.62181i
$633$	3.19041	+	31.2294i	0.126807	+	1.24126i
$634$	3.74150	+	35.5980i	0.148594	+	1.41378i
$635$	39.1620	−	14.2917i	1.55410	−	0.567149i
$636$	26.8463	+	83.4505i	1.06452	+	3.30903i
$637$	3.49659	−	4.42950i	0.138540	−	0.175503i
$638$	−9.94343	+	7.22432i	−0.393664	+	0.286014i
$639$	−7.35529	−	35.6230i	−0.290971	−	1.40922i
$640$	−13.9009	+	3.47850i	−0.549481	+	0.137500i
$641$	−44.0076	+	4.62538i	−1.73819	+	0.182692i	−0.919912	−	0.392124i	$-0.871740\pi$
$641$	−44.0076	+	4.62538i	−1.73819	+	0.182692i	−0.818283	+	0.574816i	$0.805074\pi$
$642$	3.87646	+	1.73946i	0.152992	+	0.0686509i
$643$	0.475167			0.0187388			0.00936939	−	0.999956i	$-0.497018\pi$
$643$	0.475167			0.0187388			0.00936939	+	0.999956i	$0.497018\pi$
$644$	17.6606	−	98.7113i	0.695925	−	3.88977i
$645$	−13.6871	+	1.89487i	−0.538928	+	0.0746106i
$646$	−5.83779	+	6.48353i	−0.229685	+	0.255091i
$647$	4.07511	−	19.1719i	0.160209	−	0.753725i	−0.822529	−	0.568723i	$-0.807438\pi$
$647$	4.07511	−	19.1719i	0.160209	−	0.753725i	0.982738	−	0.185002i	$-0.0592291\pi$
$648$	−35.9857	+	60.6852i	−1.41365	+	2.38394i
$649$	−6.44799	+	3.72275i	−0.253106	+	0.146131i
$650$	−6.53721	+	8.39679i	−0.256411	+	0.329349i
$651$	−31.6855	+	0.934626i	−1.24185	+	0.0366309i
$652$	−0.939121	+	1.29259i	−0.0367788	+	0.0506217i
$653$	13.5802	−	15.0824i	0.531436	−	0.590219i	−0.416319	−	0.909218i	$-0.636680\pi$
$653$	13.5802	−	15.0824i	0.531436	−	0.590219i	0.947755	+	0.318999i	$0.103347\pi$
$654$	−29.9670	−	33.4773i	−1.17180	−	1.30906i
$655$	−17.0349	−	6.86564i	−0.665610	−	0.268263i
$656$	−106.396	+	22.6152i	−4.15407	+	0.882976i
$657$	0.387152	+	1.21558i	0.0151043	+	0.0474243i
$658$	−49.5269	+	58.7244i	−1.93076	+	2.28932i
$659$	−16.7010	−	22.9870i	−0.650580	−	0.895447i	0.348544	−	0.937292i	$-0.386676\pi$
$659$	−16.7010	−	22.9870i	−0.650580	−	0.895447i	−0.999124	+	0.0418455i	$0.986676\pi$
$660$	28.6684	−	10.3677i	1.11591	−	0.403561i
$661$	−11.7199	−	26.3234i	−0.455852	−	1.02386i	−0.984559	−	0.175055i	$-0.943990\pi$
$661$	−11.7199	−	26.3234i	−0.455852	−	1.02386i	0.528707	−	0.848805i	$-0.322677\pi$
$662$	−4.70937	−	44.8067i	−0.183035	−	1.74146i
$663$	4.17545	−	2.39451i	0.162161	−	0.0929950i
$664$	−7.32313	+	10.0794i	−0.284192	+	0.391157i
$665$	−1.38123	+	5.50108i	−0.0535616	+	0.213323i
$666$	40.7625	−	55.4230i	1.57952	−	2.14760i
$667$	4.66092	+	21.9279i	0.180471	+	0.849051i
$668$	38.1707	+	22.0379i	1.47687	+	0.852671i
$669$	−0.943427	−	9.23476i	−0.0364750	−	0.357036i
$670$	−0.746427	−	20.8637i	−0.0288370	−	0.806035i
$671$	3.20739	+	9.87132i	0.123820	+	0.381078i
$672$	54.8735	−	19.6363i	2.11679	−	0.757486i
$673$	25.5602	−	35.1806i	0.985275	−	1.35611i	0.0513356	−	0.998681i	$-0.483652\pi$
$673$	25.5602	−	35.1806i	0.985275	−	1.35611i	0.933939	−	0.357433i	$-0.116348\pi$
$674$	5.74410	−	3.31635i	0.221254	−	0.127741i
$675$	21.9356	+	13.9222i	0.844303	+	0.535867i
$676$	30.6864	−	53.1503i	1.18024	−	2.04424i
$677$	−19.2019	−	2.01820i	−0.737989	−	0.0775658i	−0.271927	−	0.962318i	$-0.587661\pi$
$677$	−19.2019	−	2.01820i	−0.737989	−	0.0775658i	−0.466062	+	0.884752i	$0.654328\pi$
$678$	1.61103	−	4.90955i	0.0618714	−	0.188550i
$679$	15.8768	+	32.7604i	0.609297	+	1.25723i
$680$	10.4416	−	59.5144i	0.400416	−	2.28227i
$681$	13.6400	−	30.3974i	0.522687	−	1.16483i
$682$	−14.4627	+	25.0501i	−0.553806	+	0.959219i
$683$	−4.41412	−	4.90237i	−0.168901	−	0.187584i	0.652752	−	0.757572i	$-0.273615\pi$
$683$	−4.41412	−	4.90237i	−0.168901	−	0.187584i	−0.821653	+	0.569988i	$0.806948\pi$
$684$	−14.2055	−	1.57678i	−0.543162	−	0.0602896i
$685$	−15.0275	+	28.3210i	−0.574172	+	1.08209i
$686$	14.7588	+	46.6121i	0.563492	+	1.77966i
$687$	0.0650897	−	22.3481i	0.00248333	−	0.852633i
$688$	−15.6086	+	35.0575i	−0.595073	+	1.33656i
$689$	7.50086	−	3.33960i	0.285760	−	0.127229i
$690$	5.59988	−	77.7812i	0.213184	−	2.96108i
$691$	−17.2863	+	38.8257i	−0.657603	+	1.47700i	0.208956	+	0.977925i	$0.432994\pi$
$691$	−17.2863	+	38.8257i	−0.657603	+	1.47700i	−0.866559	+	0.499075i	$0.833673\pi$
$692$	69.5842	+	22.6093i	2.64520	+	0.859476i
$693$	−11.3453	+	5.41696i	−0.430974	+	0.205773i
$694$	−3.99232	+	12.2871i	−0.151546	+	0.466412i
$695$	−0.814788	+	0.297347i	−0.0309067	+	0.0112790i
$696$	−29.7358	+	26.6178i	−1.12713	+	1.00895i
$697$	7.24747	−	34.0967i	0.274518	−	1.29150i
$698$	37.9660	+	3.99039i	1.43703	+	0.151038i
$699$	−30.2502	−	22.1129i	−1.14417	−	0.836388i
$700$	−20.2647	−	62.5380i	−0.765935	−	2.36371i
$701$		−	20.9540i		−	0.791423i	−0.918375	−	0.395712i	$-0.870498\pi$
$701$		−	20.9540i		−	0.791423i	0.918375	−	0.395712i	$-0.129502\pi$
$702$	10.0632	+	4.58618i	0.379810	+	0.173094i
$703$	8.14621	+	1.73153i	0.307240	+	0.0653059i
$704$	3.97240	−	18.6887i	0.149716	−	0.704357i
$705$	−23.8925	+	35.2654i	−0.899845	+	1.32817i
$706$	2.40893	+	0.782709i	0.0906613	+	0.0294576i
$707$	1.97059	−	4.84240i	0.0741115	−	0.182117i
$708$	−32.8014	+	23.6860i	−1.23275	+	0.890174i
$709$	−14.3836	−	6.40400i	−0.540188	−	0.240507i	0.118459	−	0.992959i	$-0.462204\pi$
$709$	−14.3836	−	6.40400i	−0.540188	−	0.240507i	−0.658647	+	0.752452i	$0.728871\pi$
$710$	−26.7556	+	66.3856i	−1.00412	+	2.49141i
$711$	11.9774	+	13.4591i	0.449189	+	0.504757i
$712$	−96.2357	−	42.8469i	−3.60659	−	1.60576i
$713$	31.0107	+	42.6826i	1.16136	+	1.59848i
$714$	−3.13435	+	41.5842i	−0.117300	+	1.55625i
$715$	−1.25390	−	2.56530i	−0.0468931	−	0.0959369i
$716$	−34.8711	+	78.3217i	−1.30319	+	2.92702i
$717$	13.2042	−	1.34894i	0.493119	−	0.0503772i
$718$	−37.8969	−	21.8798i	−1.41430	−	0.816547i
$719$	−23.4029	+	4.97445i	−0.872782	+	0.185516i	−0.622464	−	0.782648i	$-0.713868\pi$
$719$	−23.4029	+	4.97445i	−0.872782	+	0.185516i	−0.250318	+	0.968164i	$0.580535\pi$
$720$	65.0095	−	31.3082i	2.42276	−	1.16679i
$721$	−18.9187	+	27.8971i	−0.704570	+	1.03894i
$722$	14.7503	+	45.3967i	0.548948	+	1.68949i
$723$	26.0398	+	23.5841i	0.968431	+	0.877100i
$724$	−58.6586	−	33.8666i	−2.18003	−	1.25864i
$725$	9.46585	+	11.2419i	0.351553	+	0.417513i
$726$	4.17087	−	38.6014i	0.154796	−	1.43263i
$727$	13.9636	+	10.1451i	0.517881	+	0.376262i	0.815805	−	0.578327i	$-0.196294\pi$
$727$	13.9636	+	10.1451i	0.517881	+	0.376262i	−0.297924	+	0.954590i	$0.596294\pi$
$728$	−7.29218	−	15.0467i	−0.270266	−	0.557670i
$729$	8.79090	−	25.5288i	0.325589	−	0.945511i
$730$	0.689871	−	2.41365i	0.0255333	−	0.0893331i
$731$	−8.22902	−	9.13925i	−0.304361	−	0.338028i
$732$	22.7906	+	51.5924i	0.842364	+	1.90691i
$733$	−15.0018	+	3.18873i	−0.554104	+	0.117778i	−0.476449	−	0.879202i	$-0.658076\pi$
$733$	−15.0018	+	3.18873i	−0.554104	+	0.117778i	−0.0776544	+	0.996980i	$0.524743\pi$
$734$	−19.5184	+	14.1809i	−0.720436	+	0.523428i
$735$	10.8516	+	24.8444i	0.400268	+	0.916398i
$736$	−78.4746	−	57.0151i	−2.89261	−	2.10161i
$737$	5.11749	+	2.27845i	0.188505	+	0.0839279i
$738$	73.3542	−	32.1487i	2.70021	−	1.18341i
$739$	35.6802	−	15.8859i	1.31252	−	0.584370i	0.373306	−	0.927708i	$-0.378224\pi$
$739$	35.6802	−	15.8859i	1.31252	−	0.584370i	0.939212	+	0.343338i	$0.111558\pi$
$740$	−90.6784	+	33.0920i	−3.33340	+	1.21649i
$741$	−0.00389900	+	1.33870i	−0.000143234	+	0.0491782i
$742$	−12.5283	+	70.0250i	−0.459928	+	2.57070i
$743$	2.98106			0.109364			0.0546822	−	0.998504i	$-0.482585\pi$
$743$	2.98106			0.109364			0.0546822	+	0.998504i	$0.482585\pi$
$744$	−38.4516	+	85.6912i	−1.40970	+	3.14159i
$745$	−18.8991	−	1.30533i	−0.692411	−	0.0478236i
$746$	13.3017	−	62.5797i	0.487011	−	2.29121i
$747$	1.96462	−	4.34434i	0.0718819	−	0.158951i
$748$	21.9510	+	15.9484i	0.802609	+	0.583129i
$749$	1.50871	+	1.94107i	0.0551271	+	0.0709251i
$750$	−20.7772	−	46.7102i	−0.758676	−	1.70562i
$751$	4.76773	+	8.25795i	0.173977	+	0.301337i	0.939807	−	0.341706i	$-0.111005\pi$
$751$	4.76773	+	8.25795i	0.173977	+	0.301337i	−0.765830	+	0.643043i	$0.777671\pi$
$752$	48.1183	+	108.075i	1.75469	+	3.94110i
$753$	26.9590	+	30.1170i	0.982441	+	1.09752i
$754$	4.64884	+	4.18584i	0.169301	+	0.152439i
$755$	37.3535	−	18.2581i	1.35943	−	0.664479i
$756$	−58.3406	+	35.5495i	−2.12183	+	1.29292i
$757$		−	20.3449i		−	0.739448i	−0.929142	−	0.369724i	$-0.879452\pi$
$757$		−	20.3449i		−	0.739448i	0.929142	−	0.369724i	$-0.120548\pi$
$758$	−90.9708	+	19.3364i	−3.30421	+	0.702331i
$759$	18.0906	+	10.5150i	0.656647	+	0.381670i
$760$	12.8828	+	10.7912i	0.467308	+	0.391438i
$761$	−5.24709	+	49.9227i	−0.190207	+	1.80970i	0.317599	+	0.948225i	$0.397124\pi$
$761$	−5.24709	+	49.9227i	−0.190207	+	1.80970i	−0.507805	+	0.861472i	$0.669543\pi$
$762$	−0.248290	+	85.2485i	−0.00899458	+	3.08823i
$763$	−6.22613	−	25.2409i	−0.225401	−	0.913782i
$764$	−10.0281	+	13.8025i	−0.362805	+	0.499358i
$765$	0.692126	+	23.1133i	0.0250239	+	0.835662i
$766$	1.43183	−	0.150491i	0.0517341	−	0.00543748i
$767$	2.53570	+	2.81617i	0.0915586	+	0.101686i
$768$	−1.34096	+	12.4106i	−0.0483877	+	0.447828i
$769$	28.4710	+	9.25078i	1.02669	+	0.333591i	0.773480	−	0.633820i	$-0.218514\pi$
$769$	28.4710	+	9.25078i	1.02669	+	0.333591i	0.253209	+	0.967412i	$0.418514\pi$
$770$	24.4920	+	3.48338i	0.882632	+	0.125532i
$771$	21.7831	+	7.14797i	0.784500	+	0.257428i
$772$	−35.4578	−	31.9264i	−1.27616	−	1.14906i
$773$	−19.6951	−	44.2360i	−0.708385	−	1.59106i	−0.803301	−	0.595573i	$-0.796925\pi$
$773$	−19.6951	−	44.2360i	−0.708385	−	1.59106i	0.0949167	−	0.995485i	$-0.469742\pi$
$774$	6.03560	−	27.6036i	0.216945	−	0.992191i
$775$	31.1122	+	15.1087i	1.11758	+	0.542720i
$776$	107.865			3.87214
$777$	35.8733	−	17.2566i	1.28695	−	0.619078i
$778$	−34.8553	+	11.3252i	−1.24962	+	0.406028i
$779$	7.20478	+	6.48721i	0.258138	+	0.232428i
$780$	−8.19524	−	13.1754i	−0.293437	−	0.471754i
$781$	−12.8507	−	14.2722i	−0.459834	−	0.510698i
$782$	60.1080	−	34.7034i	2.14946	−	1.24099i
$783$	9.08479	−	12.2771i	0.324664	−	0.438748i
$784$	74.5081	+	10.8525i	2.66100	+	0.387588i
$785$	−0.953823	+	0.466220i	−0.0340434	+	0.0166401i
$786$	25.2122	−	27.8375i	0.899289	−	0.992931i
$787$	4.97918	+	47.3737i	0.177489	+	1.68869i	0.614248	+	0.789113i	$0.289459\pi$
$787$	4.97918	+	47.3737i	0.177489	+	1.68869i	−0.436759	+	0.899578i	$0.643874\pi$
$788$	−1.54004	−	14.6525i	−0.0548617	−	0.521974i
$789$	−6.91588	+	7.63601i	−0.246212	+	0.271849i
$790$	−4.96397	−	35.1028i	−0.176610	−	1.24890i
$791$	2.15586	−	2.07148i	0.0766536	−	0.0736532i
$792$	−0.216986	+	37.2499i	−0.00771025	+	1.32362i
$793$	4.57501	−	2.64138i	0.162463	−	0.0937983i
$794$	24.5836	+	27.3028i	0.872439	+	0.968941i
$795$	−2.83253	+	39.3432i	−0.100459	+	1.39536i
$796$	−20.7599	−	18.6923i	−0.735815	−	0.662531i
$797$	−18.2450	+	5.92814i	−0.646269	+	0.209986i	−0.613768	−	0.789486i	$-0.710347\pi$
$797$	−18.2450	+	5.92814i	−0.646269	+	0.209986i	−0.0325009	+	0.999472i	$0.510347\pi$
$798$	−9.58021	−	6.53774i	−0.339136	−	0.231433i
$799$	−37.9125			−1.34125
$800$	−62.9861	−	8.74237i	−2.22689	−	0.309090i
$801$	39.3836	+	8.61133i	1.39155	+	0.304266i
$802$	19.7769	+	44.4195i	0.698345	+	1.56851i
$803$	0.500561	+	0.450707i	0.0176644	+	0.0159051i
$804$	28.9232	+	9.49093i	1.02004	+	0.334719i
$805$	23.9741	−	38.2260i	0.844977	−	1.34729i
$806$	14.0016	+	4.54940i	0.493186	+	0.160246i
$807$	0.855072	−	7.91368i	0.0301000	−	0.278575i
$808$	−10.3650	−	11.5115i	−0.364639	−	0.404973i
$809$	21.4657	−	2.25613i	0.754693	−	0.0793214i	0.280634	−	0.959815i	$-0.409455\pi$
$809$	21.4657	−	2.25613i	0.754693	−	0.0793214i	0.474058	+	0.880493i	$0.342789\pi$
$810$	−42.2163	+	32.2552i	−1.48333	+	1.13333i
$811$	28.8956	−	39.7714i	1.01466	−	1.39656i	0.0987848	−	0.995109i	$-0.468504\pi$
$811$	28.8956	−	39.7714i	1.01466	−	1.39656i	0.915879	−	0.401455i	$-0.131496\pi$
$812$	−37.5205	+	9.25510i	−1.31671	+	0.324790i
$813$	−0.136980	+	47.0311i	−0.00480410	+	1.64945i
$814$	3.79696	−	36.1257i	0.133083	−	1.26620i
$815$	−0.609355	+	0.381492i	−0.0213448	+	0.0133631i
$816$	55.5229	+	32.2722i	1.94369	+	1.12975i
$817$	3.34565	−	0.711141i	0.117050	−	0.0248797i
$818$			43.0755i			1.50610i
$819$	3.89740	+	5.07503i	0.136186	+	0.177336i
$820$	−110.679	−	19.4182i	−3.86508	−	0.678113i
$821$	−12.8482	−	11.5686i	−0.448407	−	0.403747i	0.413749	−	0.910391i	$-0.364219\pi$
$821$	−12.8482	−	11.5686i	−0.448407	−	0.403747i	−0.862155	+	0.506644i	$0.830886\pi$
$822$	−43.7273	−	48.8494i	−1.52516	−	1.70382i
$823$	−6.41252	−	14.4028i	−0.223526	−	0.502049i	0.766617	−	0.642104i	$-0.221938\pi$
$823$	−6.41252	−	14.4028i	−0.223526	−	0.502049i	−0.990144	+	0.140056i	$0.955272\pi$
$824$	49.9359	+	86.4914i	1.73960	+	3.01307i
$825$	13.7085	+	0.495229i	0.477267	+	0.0172417i
$826$	−32.5240	+	4.48788i	−1.13166	+	0.156153i
$827$	17.0515	+	12.3886i	0.592938	+	0.430795i	0.843365	−	0.537341i	$-0.180571\pi$
$827$	17.0515	+	12.3886i	0.592938	+	0.430795i	−0.250427	+	0.968135i	$0.580571\pi$
$828$	103.604	+	46.8524i	3.60048	+	1.62823i
$829$	−1.91202	+	8.99537i	−0.0664073	+	0.312422i	−0.998797	−	0.0490323i	$-0.984386\pi$
$829$	−1.91202	+	8.99537i	−0.0664073	+	0.312422i	0.932390	+	0.361454i	$0.117720\pi$
$830$	−7.95205	+	4.97844i	−0.276020	+	0.172804i
$831$	9.78931	−	21.8159i	0.339587	−	0.756786i
$832$	−9.72450			−0.337136
$833$	−12.8891	+	20.3986i	−0.446580	+	0.706771i
$834$	0.00516580	−	1.77364i	0.000178877	−	0.0614162i
$835$	12.2235	+	15.6178i	0.423011	+	0.540477i
$836$	−6.89393	+	3.06937i	−0.238431	+	0.106156i
$837$	7.78001	−	35.0915i	0.268916	−	1.21294i
$838$	22.3246	+	9.93955i	0.771190	+	0.343356i
$839$	−18.8811	−	13.7179i	−0.651847	−	0.473594i	0.212053	−	0.977258i	$-0.431985\pi$
$839$	−18.8811	−	13.7179i	−0.651847	−	0.473594i	−0.863900	+	0.503664i	$0.831985\pi$
$840$	80.2651	+	3.16973i	2.76941	+	0.109366i
$841$	−16.4722	+	11.9677i	−0.568006	+	0.412680i
$842$	−8.87085	+	1.88556i	−0.305710	+	0.0649806i
$843$	−7.65100	−	17.3200i	−0.263514	−	0.596533i
$844$	60.2664	+	66.9326i	2.07445	+	2.30391i
$845$	21.7468	−	17.0204i	0.748114	−	0.585521i
$846$	−50.7888	−	70.7680i	−1.74615	−	2.43305i
$847$	12.6091	−	18.5931i	0.433254	−	0.638866i
$848$	88.6276	+	64.3917i	3.04348	+	2.21122i
$849$	−4.89551	+	45.3079i	−0.168014	+	1.55496i
$850$	24.0457	−	38.6280i	0.824762	−	1.32493i
$851$	−57.3781	−	33.1273i	−1.96690	−	1.13559i
$852$	−77.3522	−	70.0573i	−2.65004	−	2.40012i
$853$	−12.7200	−	39.1481i	−0.435524	−	1.34040i	−0.892549	−	0.450951i	$-0.851085\pi$
$853$	−12.7200	−	39.1481i	−0.435524	−	1.34040i	0.457025	−	0.889454i	$-0.348915\pi$
$854$	−3.30711	+	45.6498i	−0.113167	+	1.56210i
$855$	−5.66338	−	3.04748i	−0.193684	−	0.104222i
$856$	7.12503	−	1.51447i	0.243529	−	0.0517636i
$857$	10.4640	+	6.04138i	0.357443	+	0.206370i	0.667958	−	0.744199i	$-0.267168\pi$
$857$	10.4640	+	6.04138i	0.357443	+	0.206370i	−0.310516	+	0.950568i	$0.600502\pi$
$858$	5.80871	−	0.593420i	0.198306	−	0.0202590i
$859$	10.1956	−	22.8997i	0.347870	−	0.781328i	−0.651866	−	0.758334i	$-0.726013\pi$
$859$	10.1956	−	22.8997i	0.347870	−	0.781328i	0.999736	−	0.0229941i	$-0.00731989\pi$
$860$	−28.4940	+	27.5634i	−0.971638	+	0.939906i
$861$	46.2101	+	3.48303i	1.57484	+	0.118701i
$862$	25.0313	+	34.4526i	0.852569	+	1.17346i
$863$	46.8855	+	20.8748i	1.59600	+	0.710585i	0.995995	−	0.0894106i	$-0.0284983\pi$
$863$	46.8855	+	20.8748i	1.59600	+	0.710585i	0.600006	+	0.799996i	$0.295165\pi$
$864$	6.33320	+	65.7804i	0.215460	+	2.23789i
$865$	25.2376	+	21.1402i	0.858105	+	0.718787i
$866$	2.16290	+	0.962984i	0.0734982	+	0.0327235i
$867$	7.18638	−	5.18930i	0.244062	−	0.176238i
$868$	−71.8084	+	55.8137i	−2.43734	+	1.89444i
$869$	9.04702	+	2.93955i	0.306899	+	0.0997176i
$870$	−28.2614	+	10.2205i	−0.958150	+	0.346507i
$871$	0.592787	−	2.78884i	0.0200858	−	0.0944963i
$872$	−75.3454	−	16.0152i	−2.55152	−	0.542342i
$873$	−40.4266	+	8.34711i	−1.36823	+	0.282507i
$874$			19.3037i			0.652958i
$875$	2.06172	−	29.5085i	0.0696988	−	0.997568i
$876$	2.95491	+	2.16005i	0.0998373	+	0.0729813i
$877$	−14.2695	−	1.49979i	−0.481848	−	0.0506443i	−0.139509	−	0.990221i	$-0.544552\pi$
$877$	−14.2695	−	1.49979i	−0.481848	−	0.0506443i	−0.342339	+	0.939576i	$0.611219\pi$
$878$	−1.12931	+	5.31299i	−0.0381124	+	0.179305i
$879$	−34.6432	+	31.0106i	−1.16848	+	1.04596i
$880$	21.2765	−	31.6020i	0.717232	−	1.06530i
$881$	13.1178	−	40.3724i	0.441950	−	1.36018i	−0.443845	−	0.896104i	$-0.646386\pi$
$881$	13.1178	−	40.3724i	0.441950	−	1.36018i	0.885795	−	0.464077i	$-0.153614\pi$
$882$	−55.3429	+	3.26774i	−1.86349	+	0.110030i
$883$	−23.3227	−	7.57800i	−0.784871	−	0.255020i	−0.110952	−	0.993826i	$-0.535390\pi$
$883$	−23.3227	−	7.57800i	−0.784871	−	0.255020i	−0.673919	+	0.738806i	$0.735390\pi$
$884$	5.61698	−	12.6160i	0.188920	−	0.424320i
$885$	−17.6736	+	4.36790i	−0.594090	+	0.146825i
$886$	−77.1258	+	34.3386i	−2.59109	+	1.15363i
$887$	4.19961	−	9.43248i	0.141009	−	0.316712i	−0.829211	−	0.558935i	$-0.811210\pi$
$887$	4.19961	−	9.43248i	0.141009	−	0.316712i	0.970220	+	0.242224i	$0.0778767\pi$
$888$	0.343529	−	117.948i	0.0115281	−	3.95808i
$889$	−23.2663	+	43.4944i	−0.780328	+	1.45875i
$890$	−55.1537	−	57.0157i	−1.84875	−	1.91117i
$891$	−2.80125	−	13.9776i	−0.0938453	−	0.468267i
$892$	−17.8212	−	19.7924i	−0.596697	−	0.662699i
$893$	5.27220	−	9.13172i	0.176428	−	0.305581i
$894$	15.8596	−	35.3439i	0.530425	−	1.18208i
$895$	−27.7272	+	26.8217i	−0.926819	+	0.896551i
$896$	9.51626	−	14.0325i	0.317916	−	0.468792i
$897$	3.32050	−	10.1191i	0.110868	−	0.337866i
$898$	−58.6061	−	6.15975i	−1.95571	−	0.205554i
$899$	10.1660	−	17.6080i	0.339054	−	0.587259i
$900$	74.3806	−	4.89363i	2.47935	−	0.163121i
$901$	−30.4038	+	17.5536i	−1.01290	+	0.584797i
$902$	24.8551	−	34.2101i	0.827585	−	1.13907i
$903$	10.5768	−	12.4671i	0.351973	−	0.414879i
$904$	−2.73743	−	8.42493i	−0.0910454	−	0.280209i
$905$	−18.7844	−	24.0006i	−0.624414	−	0.797807i
$906$	8.64081	+	84.5808i	0.287072	+	2.81001i
$907$	4.99531	+	2.88404i	0.165866	+	0.0957631i	0.580635	−	0.814164i	$-0.302804\pi$
$907$	4.99531	+	2.88404i	0.165866	+	0.0957631i	−0.414769	+	0.909927i	$0.636138\pi$
$908$	−19.8745	−	93.5022i	−0.659559	−	3.10298i
$909$	4.77548	+	3.51227i	0.158393	+	0.116495i
$910$	−0.857575	−	12.5619i	−0.0284283	−	0.416424i
$911$	24.8541	−	34.2087i	0.823452	−	1.13338i	−0.165655	−	0.986184i	$-0.552974\pi$
$911$	24.8541	−	34.2087i	0.823452	−	1.13338i	0.989107	−	0.147200i	$-0.0470262\pi$
$912$	−15.4943	+	8.88558i	−0.513068	+	0.294231i
$913$	−0.263138	−	2.50359i	−0.00870858	−	0.0828566i
$914$	−8.80564	−	19.7778i	−0.291265	−	0.654191i
$915$	0.833511	+	25.3652i	0.0275550	+	0.838549i
$916$	−37.6883	−	51.8735i	−1.24526	−	1.71395i
$917$	20.4395	−	7.38141i	0.674970	−	0.243756i
$918$	−44.8420	−	15.0045i	−1.48001	−	0.495222i
$919$	−26.6515	+	5.66495i	−0.879152	+	0.186870i	−0.625310	−	0.780376i	$-0.715028\pi$
$919$	−26.6515	+	5.66495i	−0.879152	+	0.186870i	−0.253842	+	0.967246i	$0.581694\pi$
$920$	−70.9434	−	113.318i	−2.33894	−	3.73597i
$921$	12.4981	+	13.9621i	0.411826	+	0.460066i
$922$	19.9927	−	22.2041i	0.658425	−	0.731255i
$923$	−5.74549	+	7.90800i	−0.189115	+	0.260295i
$924$	−17.1066	+	31.7565i	−0.562765	+	1.04471i
$925$	−43.4103	−	1.44165i	−1.42732	−	0.0474011i
$926$	31.0755	−	17.9415i	1.02121	−	0.589593i
$927$	−25.4084	−	28.5516i	−0.834522	−	0.937759i
$928$	−7.77206	+	36.5647i	−0.255130	+	1.20029i
$929$	19.4921	−	21.6482i	0.639515	−	0.710254i	−0.333043	−	0.942912i	$-0.608076\pi$
$929$	19.4921	−	21.6482i	0.639515	−	0.710254i	0.972559	+	0.232658i	$0.0747422\pi$
$930$	−50.9776	+	49.0262i	−1.67162	+	1.60763i
$931$	−3.12089	−	5.94118i	−0.102283	−	0.194714i
$932$	−107.507			−3.52151
$933$	−6.58361	−	2.95422i	−0.215538	−	0.0967167i
$934$	−7.29705	+	0.766951i	−0.238767	+	0.0250954i
$935$	6.47857	+	10.3482i	0.211872	+	0.338422i
$936$	18.5678	−	3.83380i	0.606907	−	0.125312i
$937$	38.7724	−	28.1698i	1.26664	−	0.920268i	0.267577	−	0.963536i	$-0.413777\pi$
$937$	38.7724	−	28.1698i	1.26664	−	0.920268i	0.999063	+	0.0432683i	$0.0137770\pi$
$938$	17.1149	+	17.8121i	0.558822	+	0.581586i
$939$	−3.43656	−	10.6824i	−0.112148	−	0.348607i
$940$	4.36960	+	122.137i	0.142521	+	3.98366i
$941$	4.43665	+	42.2119i	0.144631	+	1.37607i	0.790426	+	0.612557i	$0.209859\pi$
$941$	4.43665	+	42.2119i	0.144631	+	1.37607i	−0.645796	+	0.763510i	$0.723474\pi$
$942$	−0.220643	−	2.15977i	−0.00718895	−	0.0703693i
$943$	−38.5639	−	66.7947i	−1.25581	−	2.17513i
$944$	−15.6242	+	48.0864i	−0.508525	+	1.56508i
$945$	−30.3277	+	5.02330i	−0.986559	+	0.163408i
$946$	−4.61009	−	14.1884i	−0.149887	−	0.461304i
$947$	40.9455	−	45.4746i	1.33055	−	1.47773i	0.585613	−	0.810590i	$-0.300854\pi$
$947$	40.9455	−	45.4746i	1.33055	−	1.47773i	0.744937	−	0.667135i	$-0.232480\pi$
$948$	50.5311	+	10.8946i	1.64117	+	0.353841i
$949$	0.171414	−	0.296898i	0.00556433	−	0.00963771i
$950$	5.96019	+	11.1634i	0.193374	+	0.362189i
$951$	−18.9587	−	13.8589i	−0.614778	−	0.449404i
$952$	37.7340	+	60.7251i	1.22297	+	1.96811i
$953$	−8.61871	−	26.5257i	−0.279187	−	0.859251i	−0.988081	−	0.153935i	$-0.950805\pi$
$953$	−8.61871	−	26.5257i	−0.279187	−	0.859251i	0.708894	−	0.705316i	$-0.249195\pi$
$954$	−73.4957	−	33.2367i	−2.37951	−	1.07608i
$955$	−6.50681	+	4.07364i	−0.210556	+	0.131820i
$956$	28.2999	−	25.4813i	0.915283	−	0.824124i
$957$	0.866252	−	8.01715i	0.0280020	−	0.259158i
$958$	10.5391	−	32.4360i	0.340503	−	1.04796i
$959$	−9.08505	−	36.8311i	−0.293372	−	1.18934i
$960$	22.0174	−	41.2038i	0.710607	−	1.32985i
$961$	1.76128	−	16.7575i	0.0568155	−	0.540564i
$962$	−18.3869	+	1.93254i	−0.592818	+	0.0623076i
$963$	−2.55318	+	1.11897i	−0.0822749	+	0.0360584i
$964$	100.246	+	10.5363i	3.22870	+	0.339350i
$965$	−9.42801	−	19.2884i	−0.303498	−	0.620916i
$966$	56.4124	+	73.0166i	1.81504	+	2.34927i
$967$	−2.44228	−	0.793545i	−0.0785384	−	0.0255187i	0.269484	−	0.963005i	$-0.413147\pi$
$967$	−2.44228	−	0.793545i	−0.0785384	−	0.0255187i	−0.348023	+	0.937486i	$0.613147\pi$
$968$	−33.2817	−	57.6455i	−1.06971	−	1.85280i
$969$	−0.581739	−	5.69437i	−0.0186881	−	0.182929i
$970$	75.3374	+	30.3634i	2.41894	+	0.974910i
$971$	34.3204	−	38.1167i	1.10139	−	1.22322i	0.128564	−	0.991701i	$-0.458963\pi$
$971$	34.3204	−	38.1167i	1.10139	−	1.22322i	0.972830	−	0.231521i	$-0.0743701\pi$
$972$	−22.8628	−	74.0150i	−0.733325	−	2.37403i
$973$	0.484069	−	0.904925i	0.0155186	−	0.0290106i
$974$		−	75.9743i		−	2.43437i
$975$	−1.20409	−	6.87714i	−0.0385618	−	0.220245i
$976$	61.0411	+	35.2421i	1.95388	+	1.12807i
$977$	5.79550	−	2.58032i	0.185414	−	0.0825518i	−0.311930	−	0.950105i	$-0.600975\pi$
$977$	5.79550	−	2.58032i	0.185414	−	0.0825518i	0.497344	+	0.867553i	$0.334309\pi$
$978$	−0.301468	−	1.43889i	−0.00963988	−	0.0460106i
$979$	20.2434	−	6.57747i	0.646981	−	0.210217i
$980$	67.2005	+	39.1716i	2.14664	+	1.25129i
$981$	29.4778	+	0.171712i	0.941155	+	0.00548235i
$982$	17.6746	−	10.2044i	0.564019	−	0.325636i
$983$	4.88300	−	4.39667i	0.155744	−	0.140232i	−0.587575	−	0.809170i	$-0.699917\pi$
$983$	4.88300	−	4.39667i	0.155744	−	0.140232i	0.743319	+	0.668938i	$0.233251\pi$
$984$	68.9990	−	118.710i	2.19961	−	3.78433i
$985$	1.82187	−	6.37418i	0.0580497	−	0.203098i
$986$	−21.6394	−	15.7219i	−0.689139	−	0.500689i
$987$	−6.74399	−	49.9481i	−0.214663	−	1.58987i
$988$	2.25760	+	3.10733i	0.0718240	+	0.0988572i
$989$	−27.0617	−	2.84430i	−0.860512	−	0.0904435i
$990$	−10.6372	+	25.9557i	−0.338072	+	0.824927i
$991$	5.29754	+	50.4027i	0.168282	+	1.60110i	0.674223	+	0.738528i	$0.264479\pi$
$991$	5.29754	+	50.4027i	0.168282	+	1.60110i	−0.505941	+	0.862568i	$0.668855\pi$
$992$	18.2910	+	86.0523i	0.580739	+	2.73216i
$993$	23.8631	+	17.4439i	0.757272	+	0.553567i
$994$	−28.7655	−	79.6531i	−0.912388	−	2.52644i
$995$	−5.51992	−	11.2930i	−0.174993	−	0.358012i
$996$	−2.80517	−	13.3889i	−0.0888852	−	0.424244i
$997$	30.3910	+	6.45981i	0.962493	+	0.204584i	0.662254	−	0.749280i	$-0.269600\pi$
$997$	30.3910	+	6.45981i	0.962493	+	0.204584i	0.300240	+	0.953864i	$0.402933\pi$
$998$	−66.5045	+	29.6097i	−2.10516	+	0.937279i
$999$	8.99862	+	44.2321i	0.284704	+	1.39944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bp.a.59.4	✓	608
3.2	odd	2	inner	525.2.bp.a.59.73	yes	608
7.5	odd	6	inner	525.2.bp.a.509.73	yes	608
21.5	even	6	inner	525.2.bp.a.509.4	yes	608
25.14	even	10	inner	525.2.bp.a.164.4	yes	608
75.14	odd	10	inner	525.2.bp.a.164.73	yes	608
175.89	odd	30	inner	525.2.bp.a.89.73	yes	608
525.89	even	30	inner	525.2.bp.a.89.4	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bp.a.59.4	✓	608	1.1	even	1	trivial
525.2.bp.a.59.73	yes	608	3.2	odd	2	inner
525.2.bp.a.89.4	yes	608	525.89	even	30	inner
525.2.bp.a.89.73	yes	608	175.89	odd	30	inner
525.2.bp.a.164.4	yes	608	25.14	even	10	inner
525.2.bp.a.164.73	yes	608	75.14	odd	10	inner
525.2.bp.a.509.4	yes	608	21.5	even	6	inner
525.2.bp.a.509.73	yes	608	7.5	odd	6	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bp (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.275952 + 2.62550i) q^{2} +(-1.15521 - 1.29053i) q^{3} +(-4.86083 - 1.03320i) q^{4} +(-1.85485 - 1.24881i) q^{5} +(3.70709 - 2.67690i) q^{6} +(2.62092 - 0.361651i) q^{7} +(2.42244 - 7.45550i) q^{8} +(-0.330959 + 2.98169i) q^{9} +O(q^{10})\)	\(q+(-0.275952 + 2.62550i) q^{2} +(-1.15521 - 1.29053i) q^{3} +(-4.86083 - 1.03320i) q^{4} +(-1.85485 - 1.24881i) q^{5} +(3.70709 - 2.67690i) q^{6} +(2.62092 - 0.361651i) q^{7} +(2.42244 - 7.45550i) q^{8} +(-0.330959 + 2.98169i) q^{9} +(3.79060 - 4.52531i) q^{10} +(0.644250 + 1.44701i) q^{11} +(4.28192 + 7.46664i) q^{12} +(0.652216 - 0.473863i) q^{13} +(0.226271 + 6.98103i) q^{14} +(0.531121 + 3.83639i) q^{15} +(9.82639 + 4.37499i) q^{16} +(-2.56167 + 2.30654i) q^{17} +(-7.73711 - 1.69174i) q^{18} +(-0.199328 - 0.937764i) q^{19} +(7.72585 + 7.98668i) q^{20} +(-3.49445 - 2.96460i) q^{21} +(-3.97691 + 1.29218i) q^{22} +(-0.797238 + 7.58521i) q^{23} +(-12.4200 + 5.48646i) q^{24} +(1.88095 + 4.63271i) q^{25} +(1.06415 + 1.84316i) q^{26} +(4.23030 - 3.01737i) q^{27} +(-13.1135 - 0.950009i) q^{28} +(2.79541 - 0.908283i) q^{29} +(-10.2190 + 0.335801i) q^{30} +(5.14060 - 4.62861i) q^{31} +(-6.35899 + 11.0141i) q^{32} +(1.12317 - 2.50303i) q^{33} +(-5.34893 - 7.36217i) q^{34} +(-5.31305 - 2.60222i) q^{35} +(4.68942 - 14.1515i) q^{36} +(-3.53326 + 7.93583i) q^{37} +(2.51711 - 0.264559i) q^{38} +(-1.36499 - 0.294294i) q^{39} +(-13.8038 + 10.8037i) q^{40} +(-8.18117 + 5.94397i) q^{41} +(8.74787 - 8.35660i) q^{42} +3.56769i q^{43} +(-1.63654 - 7.69930i) q^{44} +(4.33744 - 5.11729i) q^{45} +(-19.6950 - 4.18630i) q^{46} +(8.17346 + 7.35942i) q^{47} +(-5.70551 - 17.7354i) q^{48} +(6.73842 - 1.89572i) q^{49} +(-12.6823 + 3.66005i) q^{50} +(5.93595 + 0.641378i) q^{51} +(-3.65991 + 1.62950i) q^{52} +(9.96212 + 2.11751i) q^{53} +(6.75477 + 11.9393i) q^{54} +(0.612049 - 3.48853i) q^{55} +(3.65272 - 20.4163i) q^{56} +(-0.979951 + 1.34056i) q^{57} +(1.61330 + 7.59000i) q^{58} +(0.491345 + 4.67484i) q^{59} +(1.38208 - 19.1968i) q^{60} +(6.51692 + 0.684956i) q^{61} +(10.7339 + 14.7739i) q^{62} +(0.210914 + 7.93445i) q^{63} +(-9.75868 - 7.09010i) q^{64} +(-1.80153 + 0.0644521i) q^{65} +(6.26178 + 3.63960i) q^{66} +(2.62821 - 2.36645i) q^{67} +(14.8350 - 8.56497i) q^{68} +(10.7100 - 7.73368i) q^{69} +(8.29827 - 13.2313i) q^{70} +(-11.5314 + 3.74677i) q^{71} +(21.4283 + 9.69043i) q^{72} +(0.388484 - 0.172964i) q^{73} +(-19.8605 - 11.4665i) q^{74} +(3.80577 - 7.77921i) q^{75} +4.76426i q^{76} +(2.21184 + 3.55950i) q^{77} +(1.14934 - 3.50256i) q^{78} +(4.01855 - 4.46305i) q^{79} +(-12.7630 - 20.3862i) q^{80} +(-8.78093 - 1.97364i) q^{81} +(-13.3483 - 23.1199i) q^{82} +(-1.51152 - 0.491122i) q^{83} +(13.9229 + 18.0209i) q^{84} +(7.63195 - 1.07925i) q^{85} +(-9.36699 - 0.984510i) q^{86} +(-4.40147 - 2.55831i) q^{87} +(12.3488 - 1.29791i) q^{88} +(1.40466 - 13.3644i) q^{89} +(12.2385 + 12.8001i) q^{90} +(1.53803 - 1.47783i) q^{91} +(11.7123 - 36.0467i) q^{92} +(-11.9119 - 1.28708i) q^{93} +(-21.5777 + 19.4286i) q^{94} +(-0.801365 + 1.98834i) q^{95} +(21.5601 - 4.51714i) q^{96} +(4.25200 + 13.0863i) q^{97} +(3.11774 + 18.2149i) q^{98} +(-4.52775 + 1.44205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

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