LMFDB - Embedded newform 430.2.q.c.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			361.2
Character	$\chi$	$=$	430.361
Dual form			430.2.q.c.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 + 0.974928i) q^{2} +(-1.23079 + 0.379647i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(0.365341 - 0.930874i) q^{5} +(-0.644004 - 1.11545i) q^{6} +(1.26969 - 2.19916i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-1.10802 + 0.755432i) q^{9} +O(q^{10})$	\(q+(0.222521 + 0.974928i) q^{2} +(-1.23079 + 0.379647i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(0.365341 - 0.930874i) q^{5} +(-0.644004 - 1.11545i) q^{6} +(1.26969 - 2.19916i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-1.10802 + 0.755432i) q^{9} +(0.988831 + 0.149042i) q^{10} +(3.56146 + 1.71511i) q^{11} +(0.944177 - 0.876068i) q^{12} +(4.90826 - 0.739801i) q^{13} +(2.42655 + 0.748493i) q^{14} +(-0.0962529 + 1.28441i) q^{15} +(0.623490 - 0.781831i) q^{16} +(2.18157 + 5.55856i) q^{17} +(-0.983049 - 0.912136i) q^{18} +(-0.208331 - 0.142038i) q^{19} +(0.0747301 + 0.997204i) q^{20} +(-0.727806 + 3.18873i) q^{21} +(-0.879607 + 3.85381i) q^{22} +(0.224135 + 2.99088i) q^{23} +(1.06420 + 0.725561i) q^{24} +(-0.733052 - 0.680173i) q^{25} +(1.81344 + 4.62058i) q^{26} +(3.48611 - 4.37145i) q^{27} +(-0.189767 + 2.53227i) q^{28} +(-7.51871 - 2.31922i) q^{29} +(-1.27362 + 0.191968i) q^{30} +(5.66401 - 5.25544i) q^{31} +(0.900969 + 0.433884i) q^{32} +(-5.03452 - 0.758832i) q^{33} +(-4.93375 + 3.36377i) q^{34} +(-1.58327 - 1.98536i) q^{35} +(0.670518 - 1.16137i) q^{36} +(4.06894 + 7.04762i) q^{37} +(0.0921186 - 0.234714i) q^{38} +(-5.76015 + 2.77394i) q^{39} +(-0.955573 + 0.294755i) q^{40} +(0.0476591 + 0.208808i) q^{41} -3.27073 q^{42} +(0.105251 + 6.55659i) q^{43} -3.95292 q^{44} +(0.298409 + 1.30741i) q^{45} +(-2.86602 + 0.884049i) q^{46} +(6.56203 - 3.16011i) q^{47} +(-0.470562 + 1.19897i) q^{48} +(0.275797 + 0.477695i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-4.79534 - 6.01317i) q^{51} +(-4.10120 + 2.79615i) q^{52} +(10.3831 + 1.56500i) q^{53} +(5.03758 + 2.42597i) q^{54} +(2.89769 - 2.68867i) q^{55} +(-2.51101 + 0.378474i) q^{56} +(0.310335 + 0.0957257i) q^{57} +(0.587997 - 7.84628i) q^{58} +(2.30594 - 2.89155i) q^{59} +(-0.470562 - 1.19897i) q^{60} +(-9.59261 - 8.90064i) q^{61} +(6.38403 + 4.35256i) q^{62} +(0.254485 + 3.39587i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(1.10453 - 4.83925i) q^{65} +(-0.380480 - 5.07715i) q^{66} +(-8.22517 - 5.60783i) q^{67} +(-4.37730 - 4.06154i) q^{68} +(-1.41134 - 3.59604i) q^{69} +(1.58327 - 1.98536i) q^{70} +(0.581176 - 7.75526i) q^{71} +(1.28146 + 0.395277i) q^{72} +(-8.74793 + 1.31854i) q^{73} +(-5.96550 + 5.53517i) q^{74} +(1.16046 + 0.558846i) q^{75} +(0.249328 + 0.0375801i) q^{76} +(8.29372 - 5.65456i) q^{77} +(-3.98615 - 4.99847i) q^{78} +(2.83745 - 4.91460i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-1.16124 + 2.95880i) q^{81} +(-0.192968 + 0.0929284i) q^{82} +(2.66511 - 0.822078i) q^{83} +(-0.727806 - 3.18873i) q^{84} +5.97134 q^{85} +(-6.36879 + 1.56159i) q^{86} +10.1344 q^{87} +(-0.879607 - 3.85381i) q^{88} +(-16.7107 + 5.15458i) q^{89} +(-1.20823 + 0.581854i) q^{90} +(4.60501 - 11.7334i) q^{91} +(-1.49963 - 2.59744i) q^{92} +(-4.97597 + 8.61864i) q^{93} +(4.54107 + 5.69432i) q^{94} +(-0.208331 + 0.142038i) q^{95} +(-1.27362 - 0.191968i) q^{96} +(9.12818 + 4.39590i) q^{97} +(-0.404348 + 0.375180i) q^{98} +(-5.24180 + 0.790074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{19}{21}\right)$

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 $

$2$	0.222521	+	0.974928i	0.157346	+	0.689378i
$2$	0.222521	+	0.974928i	0.157346	+	0.689378i
$3$	−1.23079	+	0.379647i	−0.710594	+	0.219189i	−0.628920	−	0.777470i	$-0.716503\pi$
$3$	−1.23079	+	0.379647i	−0.710594	+	0.219189i	−0.0816740	+	0.996659i	$0.526027\pi$
$4$	−0.900969	+	0.433884i	−0.450484	+	0.216942i
$5$	0.365341	−	0.930874i	0.163385	−	0.416299i
$5$	0.365341	−	0.930874i	0.163385	−	0.416299i
$6$	−0.644004	−	1.11545i	−0.262914	−	0.455380i
$7$	1.26969	−	2.19916i	0.479896	−	0.831204i	−0.519838	−	0.854265i	$-0.674008\pi$
$7$	1.26969	−	2.19916i	0.479896	−	0.831204i	0.999734	+	0.0230605i	$0.00734105\pi$
$8$	−0.623490	−	0.781831i	−0.220437	−	0.276419i
$9$	−1.10802	+	0.755432i	−0.369339	+	0.251811i
$10$	0.988831	+	0.149042i	0.312696	+	0.0471313i
$11$	3.56146	+	1.71511i	1.07382	+	0.517124i	0.885336	−	0.464952i	$-0.153928\pi$
$11$	3.56146	+	1.71511i	1.07382	+	0.517124i	0.188484	+	0.982076i	$0.439643\pi$
$12$	0.944177	−	0.876068i	0.272560	−	0.252899i
$13$	4.90826	−	0.739801i	1.36131	−	0.205184i	0.572540	−	0.819877i	$-0.305958\pi$
$13$	4.90826	−	0.739801i	1.36131	−	0.205184i	0.788767	+	0.614693i	$0.210720\pi$
$14$	2.42655	+	0.748493i	0.648524	+	0.200043i
$15$	−0.0962529	+	1.28441i	−0.0248524	+	0.331632i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	2.18157	+	5.55856i	0.529109	+	1.34815i	0.906544	+	0.422112i	$0.138711\pi$
$17$	2.18157	+	5.55856i	0.529109	+	1.34815i	−0.377434	+	0.926036i	$0.623194\pi$
$18$	−0.983049	−	0.912136i	−0.231707	−	0.214992i
$19$	−0.208331	−	0.142038i	−0.0477945	−	0.0325857i	0.539187	−	0.842186i	$-0.318732\pi$
$19$	−0.208331	−	0.142038i	−0.0477945	−	0.0325857i	−0.586982	+	0.809600i	$0.699684\pi$
$20$	0.0747301	+	0.997204i	0.0167102	+	0.222982i
$21$	−0.727806	+	3.18873i	−0.158820	+	0.695837i
$22$	−0.879607	+	3.85381i	−0.187533	+	0.821635i
$23$	0.224135	+	2.99088i	0.0467355	+	0.623641i	0.970565	+	0.240838i	$0.0774223\pi$
$23$	0.224135	+	2.99088i	0.0467355	+	0.623641i	−0.923830	+	0.382803i	$0.874959\pi$
$24$	1.06420	+	0.725561i	0.217229	+	0.148104i
$25$	−0.733052	−	0.680173i	−0.146610	−	0.136035i
$26$	1.81344	+	4.62058i	0.355646	+	0.906170i
$27$	3.48611	−	4.37145i	0.670902	−	0.841285i
$28$	−0.189767	+	2.53227i	−0.0358627	+	0.478554i
$29$	−7.51871	−	2.31922i	−1.39619	−	0.430668i	−0.496819	−	0.867854i	$-0.665499\pi$
$29$	−7.51871	−	2.31922i	−1.39619	−	0.430668i	−0.899371	+	0.437187i	$0.855975\pi$
$30$	−1.27362	+	0.191968i	−0.232530	+	0.0350483i
$31$	5.66401	−	5.25544i	1.01729	−	0.943904i	0.0188513	−	0.999822i	$-0.493999\pi$
$31$	5.66401	−	5.25544i	1.01729	−	0.943904i	0.998435	+	0.0559182i	$0.0178086\pi$
$32$	0.900969	+	0.433884i	0.159270	+	0.0767005i
$33$	−5.03452	−	0.758832i	−0.876398	−	0.132096i
$34$	−4.93375	+	3.36377i	−0.846131	+	0.576882i
$35$	−1.58327	−	1.98536i	−0.267622	−	0.335587i
$36$	0.670518	−	1.16137i	0.111753	−	0.193562i
$37$	4.06894	+	7.04762i	0.668930	+	1.15862i	0.978204	+	0.207648i	$0.0665809\pi$
$37$	4.06894	+	7.04762i	0.668930	+	1.15862i	−0.309273	+	0.950973i	$0.600086\pi$
$38$	0.0921186	−	0.234714i	0.0149436	−	0.0380757i
$39$	−5.76015	+	2.77394i	−0.922363	+	0.444186i
$40$	−0.955573	+	0.294755i	−0.151089	+	0.0466049i
$41$	0.0476591	+	0.208808i	0.00744310	+	0.0326104i	0.978513	−	0.206185i	$-0.0661048\pi$
$41$	0.0476591	+	0.208808i	0.00744310	+	0.0326104i	−0.971070	+	0.238795i	$0.923248\pi$
$42$	−3.27073			−0.504685
$43$	0.105251	+	6.55659i	0.0160506	+	0.999871i
$43$	0.105251	+	6.55659i	0.0160506	+	0.999871i
$44$	−3.95292			−0.595925
$45$	0.298409	+	1.30741i	0.0444841	+	0.194898i
$46$	−2.86602	+	0.884049i	−0.422571	+	0.130346i
$47$	6.56203	−	3.16011i	0.957170	−	0.460949i	0.110976	−	0.993823i	$-0.464602\pi$
$47$	6.56203	−	3.16011i	0.957170	−	0.460949i	0.846195	+	0.532874i	$0.178888\pi$
$48$	−0.470562	+	1.19897i	−0.0679198	+	0.173057i
$49$	0.275797	+	0.477695i	0.0393996	+	0.0682421i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−4.79534	−	6.01317i	−0.671482	−	0.842012i
$52$	−4.10120	+	2.79615i	−0.568735	+	0.387757i
$53$	10.3831	+	1.56500i	1.42623	+	0.214969i	0.816365	−	0.577537i	$-0.195986\pi$
$53$	10.3831	+	1.56500i	1.42623	+	0.214969i	0.609864	+	0.792506i	$0.291224\pi$
$54$	5.03758	+	2.42597i	0.685527	+	0.330133i
$55$	2.89769	−	2.68867i	0.390725	−	0.362540i
$56$	−2.51101	+	0.378474i	−0.335548	+	0.0505757i
$57$	0.310335	+	0.0957257i	0.0411049	+	0.0126792i
$58$	0.587997	−	7.84628i	0.0772078	−	1.03027i
$59$	2.30594	−	2.89155i	0.300208	−	0.376448i	−0.608732	−	0.793376i	$-0.708322\pi$
$59$	2.30594	−	2.89155i	0.300208	−	0.376448i	0.908940	+	0.416927i	$0.136893\pi$
$60$	−0.470562	−	1.19897i	−0.0607493	−	0.154787i
$61$	−9.59261	−	8.90064i	−1.22821	−	1.13961i	−0.985530	−	0.169504i	$-0.945784\pi$
$61$	−9.59261	−	8.90064i	−1.22821	−	1.13961i	−0.242678	−	0.970107i	$-0.578026\pi$
$62$	6.38403	+	4.35256i	0.810773	+	0.552776i
$63$	0.254485	+	3.39587i	0.0320621	+	0.427839i
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	1.10453	−	4.83925i	0.137000	−	0.600235i
$66$	−0.380480	−	5.07715i	−0.0468339	−	0.624954i
$67$	−8.22517	−	5.60783i	−1.00486	−	0.685105i	−0.0552330	−	0.998473i	$-0.517590\pi$
$67$	−8.22517	−	5.60783i	−1.00486	−	0.685105i	−0.949632	+	0.313368i	$0.898543\pi$
$68$	−4.37730	−	4.06154i	−0.530825	−	0.492534i
$69$	−1.41134	−	3.59604i	−0.169905	−	0.432912i
$70$	1.58327	−	1.98536i	0.189237	−	0.237296i
$71$	0.581176	−	7.75526i	0.0689729	−	0.920380i	−0.850183	−	0.526487i	$-0.823509\pi$
$71$	0.581176	−	7.75526i	0.0689729	−	0.920380i	0.919156	−	0.393893i	$-0.128872\pi$
$72$	1.28146	+	0.395277i	0.151021	+	0.0465839i
$73$	−8.74793	+	1.31854i	−1.02387	+	0.154323i	−0.639447	−	0.768835i	$-0.720837\pi$
$73$	−8.74793	+	1.31854i	−1.02387	+	0.154323i	−0.384420	+	0.923158i	$0.625599\pi$
$74$	−5.96550	+	5.53517i	−0.693475	+	0.643451i
$75$	1.16046	+	0.558846i	0.133998	+	0.0645299i
$76$	0.249328	+	0.0375801i	0.0285999	+	0.00431074i
$77$	8.29372	−	5.65456i	0.945157	−	0.644397i
$78$	−3.98615	−	4.99847i	−0.451343	−	0.565966i
$79$	2.83745	−	4.91460i	0.319238	−	0.552936i	−0.661092	−	0.750305i	$-0.729907\pi$
$79$	2.83745	−	4.91460i	0.319238	−	0.552936i	0.980329	+	0.197370i	$0.0632399\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−1.16124	+	2.95880i	−0.129027	+	0.328755i
$82$	−0.192968	+	0.0929284i	−0.0213097	+	0.0102622i
$83$	2.66511	−	0.822078i	0.292534	−	0.0902348i	−0.145015	−	0.989430i	$-0.546323\pi$
$83$	2.66511	−	0.822078i	0.292534	−	0.0902348i	0.437549	+	0.899195i	$0.355847\pi$
$84$	−0.727806	−	3.18873i	−0.0794101	−	0.347919i
$85$	5.97134			0.647682
$86$	−6.36879	+	1.56159i	−0.686764	+	0.168391i
$87$	10.1344			1.08652
$88$	−0.879607	−	3.85381i	−0.0937664	−	0.410818i
$89$	−16.7107	+	5.15458i	−1.77134	+	0.546385i	−0.996332	−	0.0855716i	$-0.972728\pi$
$89$	−16.7107	+	5.15458i	−1.77134	+	0.546385i	−0.775004	+	0.631956i	$0.782252\pi$
$90$	−1.20823	+	0.581854i	−0.127359	+	0.0613328i
$91$	4.60501	−	11.7334i	0.482736	−	1.22999i
$92$	−1.49963	−	2.59744i	−0.156348	−	0.270802i
$93$	−4.97597	+	8.61864i	−0.515984	+	0.893711i
$94$	4.54107	+	5.69432i	0.468375	+	0.587324i
$95$	−0.208331	+	0.142038i	−0.0213743	+	0.0145728i
$96$	−1.27362	−	0.191968i	−0.129988	−	0.0195926i
$97$	9.12818	+	4.39590i	0.926827	+	0.446336i	0.835504	−	0.549485i	$-0.185176\pi$
$97$	9.12818	+	4.39590i	0.926827	+	0.446336i	0.0913231	+	0.995821i	$0.470890\pi$
$98$	−0.404348	+	0.375180i	−0.0408453	+	0.0378989i
$99$	−5.24180	+	0.790074i	−0.526820	+	0.0794054i
$100$	0.955573	+	0.294755i	0.0955573	+	0.0294755i
$101$	−0.780740	+	10.4183i	−0.0776866	+	1.03666i	0.813067	+	0.582169i	$0.197796\pi$
$101$	−0.780740	+	10.4183i	−0.0776866	+	1.03666i	−0.890754	+	0.454486i	$0.849823\pi$
$102$	4.79534	−	6.01317i	0.474809	−	0.595392i
$103$	−6.53021	−	16.6387i	−0.643441	−	1.63946i	−0.762819	−	0.646612i	$-0.776185\pi$
$103$	−6.53021	−	16.6387i	−0.643441	−	1.63946i	0.119378	−	0.992849i	$-0.461910\pi$
$104$	−3.63865	−	3.37618i	−0.356799	−	0.331061i
$105$	2.70240	+	1.84247i	0.263728	+	0.179806i
$106$	0.784695	+	10.4710i	0.0762163	+	1.01704i
$107$	0.145163	−	0.636002i	0.0140335	−	0.0614846i	−0.967426	−	0.253153i	$-0.918533\pi$
$107$	0.145163	−	0.636002i	0.0140335	−	0.0614846i	0.981460	+	0.191668i	$0.0613897\pi$
$108$	−1.24418	+	5.45110i	−0.119721	+	0.524533i
$109$	−0.164174	−	2.19075i	−0.0157250	−	0.209836i	−0.999532	−	0.0306026i	$-0.990257\pi$
$109$	−0.164174	−	2.19075i	−0.0157250	−	0.209836i	0.983807	−	0.179233i	$-0.0573617\pi$
$110$	3.26605	+	2.22676i	0.311406	+	0.212313i
$111$	−7.68360	−	7.12934i	−0.729296	−	0.676687i
$112$	−0.927736	−	2.36383i	−0.0876629	−	0.223361i
$113$	−7.31375	+	9.17115i	−0.688019	+	0.862749i	−0.996065	−	0.0886225i	$-0.971754\pi$
$113$	−7.31375	+	9.17115i	−0.688019	+	0.862749i	0.308046	+	0.951371i	$0.400325\pi$
$114$	−0.0242696	+	0.323855i	−0.00227306	+	0.0303318i
$115$	2.86602	+	0.884049i	0.267257	+	0.0824380i
$116$	7.78040	−	1.17271i	0.722392	−	0.108883i
$117$	−4.87956	+	4.52757i	−0.451116	+	0.418574i
$118$	3.33218	+	1.60469i	0.306752	+	0.147724i
$119$	14.9941	+	2.25999i	1.37450	+	0.207173i
$120$	1.06420	−	0.725561i	0.0971479	−	0.0662343i
$121$	2.88399	+	3.61641i	0.262181	+	0.328764i
$122$	6.54293	−	11.3327i	0.592369	−	1.02601i
$123$	−0.137931	−	0.238904i	−0.0124369	−	0.0215413i
$124$	−2.82285	+	7.19251i	−0.253499	+	0.645906i
$125$	−0.900969	+	0.433884i	−0.0805851	+	0.0388077i
$126$	−3.25410	+	1.00376i	−0.289898	+	0.0894216i
$127$	−3.92027	−	17.1758i	−0.347867	−	1.52411i	−0.782012	−	0.623263i	$-0.785806\pi$
$127$	−3.92027	−	17.1758i	−0.347867	−	1.52411i	0.434145	−	0.900843i	$-0.357051\pi$
$128$	−1.00000			−0.0883883
$129$	−2.61873	−	8.02980i	−0.230567	−	0.706985i
$130$	4.96370			0.435346
$131$	4.45547	+	19.5207i	0.389277	+	1.70553i	0.667157	+	0.744917i	$0.267511\pi$
$131$	4.45547	+	19.5207i	0.389277	+	1.70553i	−0.277881	+	0.960616i	$0.589632\pi$
$132$	4.86519	−	1.50071i	0.423461	−	0.130620i
$133$	−0.576879	+	0.277810i	−0.0500217	+	0.0240892i
$134$	3.63695	−	9.26681i	0.314185	−	0.800530i
$135$	−2.79564	−	4.84220i	−0.240611	−	0.416750i
$136$	2.98567	−	5.17133i	0.256019	−	0.443438i
$137$	−4.21755	−	5.28864i	−0.360329	−	0.451839i	0.568314	−	0.822811i	$-0.307596\pi$
$137$	−4.21755	−	5.28864i	−0.360329	−	0.451839i	−0.928644	+	0.370973i	$0.879024\pi$
$138$	3.19183	−	2.17615i	0.271706	−	0.185246i
$139$	−9.85180	−	1.48492i	−0.835618	−	0.125949i	−0.282725	−	0.959201i	$-0.591238\pi$
$139$	−9.85180	−	1.48492i	−0.835618	−	0.125949i	−0.552894	+	0.833252i	$0.686476\pi$
$140$	2.28789	+	1.10179i	0.193362	+	0.0931184i
$141$	−6.87673	+	6.38067i	−0.579125	+	0.537349i
$142$	7.69014	−	1.15910i	0.645342	−	0.0972697i
$143$	18.7494	+	5.78342i	1.56790	+	0.483634i
$144$	−0.100216	+	1.33729i	−0.00835131	+	0.111440i
$145$	−4.90579	+	6.15167i	−0.407404	+	0.510868i
$146$	−3.23208	−	8.23520i	−0.267489	−	0.681550i
$147$	−0.520803	−	0.483234i	−0.0429551	−	0.0398565i
$148$	−6.72384	−	4.58424i	−0.552696	−	0.376822i
$149$	0.00670867	+	0.0895210i	0.000549596	+	0.00733384i	0.997472	−	0.0710627i	$-0.0226390\pi$
$149$	0.00670867	+	0.0895210i	0.000549596	+	0.00733384i	−0.996922	+	0.0783965i	$0.975020\pi$
$150$	−0.286609	+	1.25571i	−0.0234015	+	0.102529i
$151$	0.409829	−	1.79558i	0.0333515	−	0.146122i	−0.955511	−	0.294956i	$-0.904695\pi$
$151$	0.409829	−	1.79558i	0.0333515	−	0.146122i	0.988862	+	0.148834i	$0.0475520\pi$
$152$	0.0188427	+	0.251439i	0.00152835	+	0.0203944i
$153$	−6.61633	−	4.51094i	−0.534899	−	0.364688i
$154$	7.35832	+	6.82752i	0.592950	+	0.550178i
$155$	−2.82285	−	7.19251i	−0.226737	−	0.577716i
$156$	3.98615	−	4.99847i	0.319147	−	0.400198i
$157$	−0.508107	+	6.78022i	−0.0405514	+	0.541121i	0.939522	+	0.342487i	$0.111269\pi$
$157$	−0.508107	+	6.78022i	−0.0405514	+	0.541121i	−0.980074	+	0.198633i	$0.936350\pi$
$158$	5.42277	+	1.67270i	0.431412	+	0.133073i
$159$	−13.3735	+	2.01573i	−1.06059	+	0.159858i
$160$	0.733052	−	0.680173i	0.0579528	−	0.0537724i
$161$	6.86200	+	3.30457i	0.540802	+	0.260436i
$162$	−3.14301	−	0.473733i	−0.246939	−	0.0372200i
$163$	−10.2733	+	7.00423i	−0.804668	+	0.548614i	−0.894356	−	0.447356i	$-0.852366\pi$
$163$	−10.2733	+	7.00423i	−0.804668	+	0.548614i	0.0896874	+	0.995970i	$0.471413\pi$
$164$	−0.133538	−	0.167451i	−0.0104276	−	0.0130757i
$165$	−2.54569	+	4.40927i	−0.198182	+	0.343261i
$166$	1.39451	+	2.41536i	0.108235	+	0.187468i
$167$	−7.39661	+	18.8462i	−0.572367	+	1.45837i	0.292451	+	0.956280i	$0.405529\pi$
$167$	−7.39661	+	18.8462i	−0.572367	+	1.45837i	−0.864818	+	0.502086i	$0.832566\pi$
$168$	2.94683	−	1.41912i	0.227353	−	0.109487i
$169$	11.1213	−	3.43046i	0.855483	−	0.263882i
$170$	1.32875	+	5.82162i	0.101910	+	0.446498i
$171$	0.338134			0.0258578
$172$	−2.93963	−	5.86162i	−0.224144	−	0.446944i
$173$	1.35717			0.103183			0.0515917	−	0.998668i	$-0.483571\pi$
$173$	1.35717			0.103183			0.0515917	+	0.998668i	$0.483571\pi$
$174$	2.25512	+	9.88031i	0.170960	+	0.749025i
$175$	−2.42655	+	0.748493i	−0.183430	+	0.0565807i
$176$	3.56146	−	1.71511i	0.268455	−	0.129281i
$177$	−1.74034	+	4.43433i	−0.130812	+	0.333304i
$178$	−8.74384	−	15.1448i	−0.655378	−	1.13515i
$179$	−2.00082	+	3.46552i	−0.149548	+	0.259025i	−0.931061	−	0.364865i	$-0.881115\pi$
$179$	−2.00082	+	3.46552i	−0.149548	+	0.259025i	0.781512	+	0.623890i	$0.214449\pi$
$180$	−0.836122	−	1.04846i	−0.0623209	−	0.0781479i
$181$	−9.59263	+	6.54014i	−0.713014	+	0.486125i	−0.864690	−	0.502305i	$-0.832485\pi$
$181$	−9.59263	+	6.54014i	−0.713014	+	0.486125i	0.151676	+	0.988430i	$0.451533\pi$
$182$	12.4639	+	1.87863i	0.923886	+	0.139253i
$183$	15.1855	+	7.31297i	1.12255	+	0.540591i
$184$	2.19862	−	2.04002i	0.162084	−	0.150392i
$185$	8.04700	−	1.21289i	0.591627	−	0.0891734i
$186$	−9.50981	−	2.93339i	−0.697293	−	0.215086i
$187$	−1.76394	+	23.5382i	−0.128992	+	1.72128i
$188$	−4.54107	+	5.69432i	−0.331191	+	0.415301i
$189$	−5.18724	−	13.2169i	−0.377316	−	0.961386i
$190$	−0.184835	−	0.171502i	−0.0134093	−	0.0124420i
$191$	−3.28676	−	2.24088i	−0.237822	−	0.162144i	0.438545	−	0.898709i	$-0.355494\pi$
$191$	−3.28676	−	2.24088i	−0.237822	−	0.162144i	−0.676367	+	0.736565i	$0.736446\pi$
$192$	−0.0962529	−	1.28441i	−0.00694646	−	0.0926940i
$193$	4.32685	−	18.9572i	0.311453	−	1.36457i	−0.540674	−	0.841232i	$-0.681831\pi$
$193$	4.32685	−	18.9572i	0.311453	−	1.36457i	0.852128	−	0.523334i	$-0.175312\pi$
$194$	−2.25448	+	9.87750i	−0.161862	+	0.709163i
$195$	0.477771	+	6.37541i	0.0342139	+	0.456553i
$196$	−0.455749	−	0.310724i	−0.0325535	−	0.0221946i
$197$	4.53962	+	4.21215i	0.323434	+	0.300103i	0.825132	−	0.564940i	$-0.191101\pi$
$197$	4.53962	+	4.21215i	0.323434	+	0.300103i	−0.501698	+	0.865043i	$0.667291\pi$
$198$	−1.93667	−	4.93457i	−0.137633	−	0.350684i
$199$	6.23746	−	7.82152i	0.442162	−	0.554453i	−0.509950	−	0.860204i	$-0.670336\pi$
$199$	6.23746	−	7.82152i	0.442162	−	0.554453i	0.952112	+	0.305751i	$0.0989075\pi$
$200$	−0.0747301	+	0.997204i	−0.00528422	+	0.0705130i
$201$	12.2524	+	3.77937i	0.864219	+	0.266576i
$202$	−10.3308	+	1.55711i	−0.726871	+	0.109558i
$203$	−14.6467	+	13.5902i	−1.02800	+	0.953843i
$204$	6.92947	+	3.33705i	0.485160	+	0.233641i
$205$	0.211786	+	0.0319216i	0.0147918	+	0.00222950i
$206$	14.7684	−	10.0689i	1.02897	−	0.701537i
$207$	−2.50775	−	3.14462i	−0.174301	−	0.218566i
$208$	2.48185	−	4.29869i	0.172085	−	0.298061i
$209$	−0.498352	−	0.863172i	−0.0344718	−	0.0597068i
$210$	−1.19493	+	3.04464i	−0.0824581	+	0.210100i
$211$	−11.1707	+	5.37952i	−0.769021	+	0.370341i	−0.776897	−	0.629628i	$-0.783207\pi$
$211$	−11.1707	+	5.37952i	−0.769021	+	0.370341i	0.00787559	+	0.999969i	$0.497493\pi$
$212$	−10.0339	+	3.09504i	−0.689130	+	0.212568i
$213$	2.22896	+	9.76570i	0.152726	+	0.669135i
$214$	0.652358			0.0445942
$215$	6.14181	+	2.29742i	0.418868	+	0.156683i
$216$	−5.59129			−0.380439
$217$	−4.36603	−	19.1288i	−0.296385	−	1.29855i
$218$	2.09929	−	0.647546i	0.142182	−	0.0438573i
$219$	10.2662	−	4.94396i	0.693729	−	0.334082i
$220$	−1.44416	+	3.67967i	−0.0973655	+	0.248083i
$221$	14.8200	+	25.6689i	0.996899	+	1.72668i
$222$	5.24083	−	9.07739i	0.351742	−	0.609234i
$223$	−1.96876	−	2.46875i	−0.131838	−	0.165320i	0.711531	−	0.702655i	$-0.248002\pi$
$223$	−1.96876	−	2.46875i	−0.131838	−	0.165320i	−0.843369	+	0.537335i	$0.819431\pi$
$224$	2.09813	−	1.43048i	0.140187	−	0.0955779i
$225$	1.32606	+	0.199871i	0.0884038	+	0.0133247i
$226$	−10.5687	−	5.08960i	−0.703017	−	0.338555i
$227$	15.6082	−	14.4823i	1.03596	−	0.961226i	0.0366812	−	0.999327i	$-0.488321\pi$
$227$	15.6082	−	14.4823i	1.03596	−	0.961226i	0.999274	+	0.0381012i	$0.0121309\pi$
$228$	−0.321136	+	0.0484035i	−0.0212678	+	0.00320560i
$229$	−12.0557	−	3.71868i	−0.796661	−	0.245737i	−0.130406	−	0.991461i	$-0.541628\pi$
$229$	−12.0557	−	3.71868i	−0.796661	−	0.245737i	−0.666256	+	0.745723i	$0.732104\pi$
$230$	−0.224135	+	2.99088i	−0.0147791	+	0.197213i
$231$	−8.06105	+	10.1082i	−0.530378	+	0.665074i
$232$	2.87460	+	7.32437i	0.188727	+	0.480869i
$233$	−7.99981	−	7.42274i	−0.524085	−	0.486280i	0.373188	−	0.927756i	$-0.378265\pi$
$233$	−7.99981	−	7.42274i	−0.524085	−	0.486280i	−0.897273	+	0.441476i	$0.854455\pi$
$234$	−5.49986	−	3.74974i	−0.359537	−	0.245128i
$235$	−0.544282	−	7.26294i	−0.0355050	−	0.473782i
$236$	−0.822980	+	3.60571i	−0.0535714	+	0.234712i
$237$	−1.62647	+	7.12604i	−0.105651	+	0.462886i
$238$	1.13316	+	15.1210i	0.0734522	+	0.980151i
$239$	−15.9829	−	10.8970i	−1.03385	−	0.704866i	−0.0774698	−	0.996995i	$-0.524684\pi$
$239$	−15.9829	−	10.8970i	−1.03385	−	0.704866i	−0.956379	+	0.292128i	$0.905637\pi$
$240$	0.944177	+	0.876068i	0.0609463	+	0.0565499i
$241$	7.40106	+	18.8576i	0.476744	+	1.21472i	0.943806	+	0.330500i	$0.107217\pi$
$241$	7.40106	+	18.8576i	0.476744	+	1.21472i	−0.467062	+	0.884225i	$0.654687\pi$
$242$	−2.88399	+	3.61641i	−0.185390	+	0.232472i
$243$	−0.947571	+	12.6445i	−0.0607867	+	0.811142i
$244$	12.5045	+	3.85712i	0.800518	+	0.246927i
$245$	0.545434	−	0.0822109i	0.0348465	−	0.00525226i
$246$	0.202222	−	0.187634i	0.0128932	−	0.0119631i
$247$	−1.12762	−	0.543035i	−0.0717490	−	0.0345525i
$248$	−7.64032	−	1.15159i	−0.485161	−	0.0731262i
$249$	−2.96808	+	2.02360i	−0.188094	+	0.128241i
$250$	−0.623490	−	0.781831i	−0.0394330	−	0.0494474i
$251$	−4.18511	+	7.24882i	−0.264162	+	0.457542i	−0.967344	−	0.253468i	$-0.918429\pi$
$251$	−4.18511	+	7.24882i	−0.264162	+	0.457542i	0.703182	+	0.711010i	$0.251762\pi$
$252$	−1.70269	−	2.94915i	−0.107260	−	0.185779i
$253$	−4.33143	+	11.0363i	−0.272315	+	0.693846i
$254$	15.8728	−	7.64395i	0.995950	−	0.479624i
$255$	−7.34943	+	2.26700i	−0.460239	+	0.141965i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$	1.24322			0.0775501			0.0387751	−	0.999248i	$-0.487654\pi$
$257$	1.24322			0.0775501			0.0387751	+	0.999248i	$0.487654\pi$
$258$	7.24575	−	4.33987i	0.451101	−	0.270189i
$259$	20.6651			1.28407
$260$	1.10453	+	4.83925i	0.0684999	+	0.300118i
$261$	10.0829	−	3.11015i	0.624113	−	0.192514i
$262$	−18.0398	+	8.68753i	−1.11451	+	0.536718i
$263$	3.84138	−	9.78768i	0.236870	−	0.603534i	−0.762169	−	0.647378i	$-0.775865\pi$
$263$	3.84138	−	9.78768i	0.236870	−	0.603534i	0.999038	+	0.0438444i	$0.0139606\pi$
$264$	2.54569	+	4.40927i	0.156677	+	0.271372i
$265$	5.25019	−	9.09360i	0.322517	−	0.558615i
$266$	−0.399213	−	0.500597i	−0.0244773	−	0.0306936i
$267$	18.6104	−	12.6884i	1.13894	−	0.776516i
$268$	9.84377	+	1.48371i	0.601304	+	0.0906320i
$269$	14.6368	+	7.04870i	0.892420	+	0.429767i	0.823145	−	0.567831i	$-0.192217\pi$
$269$	14.6368	+	7.04870i	0.892420	+	0.429767i	0.0692746	+	0.997598i	$0.477932\pi$
$270$	4.09870	−	3.80304i	0.249439	−	0.231446i
$271$	−16.9802	+	2.55936i	−1.03147	+	0.155470i	−0.642902	−	0.765948i	$-0.722270\pi$
$271$	−16.9802	+	2.55936i	−1.03147	+	0.155470i	−0.388573	+	0.921418i	$0.627032\pi$
$272$	5.70605	+	1.76008i	0.345980	+	0.106721i
$273$	−1.21324	+	16.1895i	−0.0734285	+	0.979835i
$274$	4.21755	−	5.28864i	0.254791	−	0.319498i
$275$	−1.44416	−	3.67967i	−0.0870863	−	0.221892i
$276$	2.83184	+	2.62756i	0.170457	+	0.158161i
$277$	−13.6440	−	9.30229i	−0.819786	−	0.558921i	0.0792200	−	0.996857i	$-0.474757\pi$
$277$	−13.6440	−	9.30229i	−0.819786	−	0.558921i	−0.899006	+	0.437937i	$0.855709\pi$
$278$	−0.744542	−	9.93522i	−0.0446546	−	0.595875i
$279$	−2.30569	+	10.1019i	−0.138038	+	0.604784i
$280$	−0.565063	+	2.47570i	−0.0337690	+	0.147952i
$281$	−1.54604	−	20.6305i	−0.0922293	−	1.23071i	−0.830813	−	0.556552i	$-0.812124\pi$
$281$	−1.54604	−	20.6305i	−0.0922293	−	1.23071i	0.738583	−	0.674162i	$-0.235495\pi$
$282$	−7.75091	−	5.28448i	−0.461560	−	0.314686i
$283$	−3.56388	−	3.30680i	−0.211851	−	0.196569i	0.567109	−	0.823643i	$-0.308062\pi$
$283$	−3.56388	−	3.30680i	−0.211851	−	0.196569i	−0.778960	+	0.627074i	$0.784252\pi$
$284$	2.84126	+	7.23941i	0.168598	+	0.429580i
$285$	0.202487	−	0.253910i	0.0119943	−	0.0150404i
$286$	−1.46629	+	19.5662i	−0.0867034	+	1.15698i
$287$	0.519715	+	0.160311i	0.0306778	+	0.00946284i
$288$	−1.32606	+	0.199871i	−0.0781387	+	0.0117775i
$289$	−13.6764	+	12.6899i	−0.804496	+	0.746463i
$290$	−7.08907	−	3.41392i	−0.416285	−	0.200472i
$291$	−12.9037	−	1.94492i	−0.756430	−	0.114013i
$292$	7.30952	−	4.98355i	0.427757	−	0.291640i
$293$	15.2415	+	19.1123i	0.890419	+	1.11655i	0.992557	+	0.121779i	$0.0388601\pi$
$293$	15.2415	+	19.1123i	0.890419	+	1.11655i	−0.102139	+	0.994770i	$0.532568\pi$
$294$	0.355229	−	0.615275i	0.0207174	−	0.0358836i
$295$	−1.84922	−	3.20294i	−0.107666	−	0.186482i
$296$	2.97310	−	7.57535i	0.172808	−	0.440308i
$297$	19.9131	−	9.58966i	1.15548	−	0.556448i
$298$	−0.0857837	+	0.0264608i	−0.00496932	+	0.00153283i
$299$	3.31277	+	14.5142i	0.191583	+	0.839378i
$300$	−1.28801			−0.0743632
$301$	14.5526	+	8.09335i	0.838800	+	0.466493i
$302$	1.84176			0.105981
$303$	−2.99434	−	13.1190i	−0.172020	−	0.753669i
$304$	−0.240942	+	0.0743208i	−0.0138190	+	0.00426259i
$305$	−11.7899	+	5.67774i	−0.675090	+	0.325106i
$306$	2.92557	−	7.45423i	0.167244	−	0.426130i
$307$	8.98964	+	15.5705i	0.513066	+	0.888656i	0.999885	+	0.0151536i	$0.00482372\pi$
$307$	8.98964	+	15.5705i	0.513066	+	0.888656i	−0.486819	+	0.873503i	$0.661843\pi$
$308$	−5.01896	+	8.69310i	−0.285982	+	0.495335i
$309$	14.3541	+	17.9995i	0.816578	+	1.02396i
$310$	6.38403	−	4.35256i	0.362589	−	0.247209i
$311$	20.6902	+	3.11855i	1.17324	+	0.176837i	0.706600	−	0.707613i	$-0.250228\pi$
$311$	20.6902	+	3.11855i	1.17324	+	0.176837i	0.466636	+	0.884450i	$0.345466\pi$
$312$	5.76015	+	2.77394i	0.326104	+	0.157044i
$313$	18.8680	−	17.5069i	1.06648	−	0.989551i	0.0665161	−	0.997785i	$-0.478812\pi$
$313$	18.8680	−	17.5069i	1.06648	−	0.989551i	0.999966	+	0.00823452i	$0.00262116\pi$
$314$	−6.72329	+	1.01337i	−0.379417	+	0.0571880i
$315$	3.25410	+	1.00376i	0.183348	+	0.0565552i
$316$	−0.424085	+	5.65902i	−0.0238566	+	0.318345i
$317$	−14.1374	+	17.7278i	−0.794037	+	0.995691i	0.205816	+	0.978591i	$0.434015\pi$
$317$	−14.1374	+	17.7278i	−0.794037	+	0.995691i	−0.999854	+	0.0171007i	$0.994556\pi$
$318$	−4.94108	−	12.5897i	−0.277082	−	0.705994i
$319$	−22.7999	−	21.1552i	−1.27655	−	1.18446i
$320$	0.826239	+	0.563320i	0.0461882	+	0.0314905i
$321$	0.0627913	+	0.837892i	0.00350467	+	0.0467666i
$322$	−1.69477	+	7.42529i	−0.0944461	+	0.413795i
$323$	0.335036	−	1.46789i	0.0186419	−	0.0816754i
$324$	−0.237531	−	3.16963i	−0.0131962	−	0.176090i
$325$	−4.10120	−	2.79615i	−0.227494	−	0.155103i
$326$	−9.11465	−	8.45716i	−0.504814	−	0.468399i
$327$	1.03378	+	2.63402i	0.0571679	+	0.145661i
$328$	0.133538	−	0.167451i	0.00737339	−	0.00924594i
$329$	1.38213	−	18.4433i	0.0761995	−	1.01681i
$330$	−4.86519	−	1.50071i	−0.267820	−	0.0826116i
$331$	−16.9544	+	2.55546i	−0.931897	+	0.140461i	−0.597407	−	0.801938i	$-0.703802\pi$
$331$	−16.9544	+	2.55546i	−0.931897	+	0.140461i	−0.334490	+	0.942399i	$0.608564\pi$
$332$	−2.04450	+	1.89702i	−0.112206	+	0.104112i
$333$	−9.83245	−	4.73506i	−0.538815	−	0.259480i
$334$	−20.0196	−	3.01747i	−1.09543	−	0.165109i
$335$	−8.22517	+	5.60783i	−0.449389	+	0.306388i
$336$	2.03927	+	2.55716i	0.111251	+	0.139504i
$337$	11.3043	−	19.5796i	0.615784	−	1.06657i	−0.374462	−	0.927242i	$-0.622173\pi$
$337$	11.3043	−	19.5796i	0.615784	−	1.06657i	0.990246	−	0.139327i	$-0.0444940\pi$
$338$	5.81917	+	10.0791i	0.316521	+	0.548231i
$339$	5.51985	−	14.0644i	0.299797	−	0.763871i
$340$	−5.37999	+	2.59087i	−0.291771	+	0.140509i
$341$	29.1858	−	9.00262i	1.58050	−	0.487519i
$342$	0.0752419	+	0.329656i	0.00406862	+	0.0178258i
$343$	19.1763			1.03542
$344$	5.06053	−	4.17026i	0.272845	−	0.224845i
$345$	−3.86308			−0.207981
$346$	0.301998	+	1.32314i	0.0162355	+	0.0711324i
$347$	12.7132	−	3.92149i	0.682478	−	0.210517i	0.0659185	−	0.997825i	$-0.479002\pi$
$347$	12.7132	−	3.92149i	0.682478	−	0.210517i	0.616559	+	0.787308i	$0.288526\pi$
$348$	−9.13078	+	4.39715i	−0.489461	+	0.235712i
$349$	−0.000881644		0.00224639i	−4.71933e−5		0.000120247i	−0.930897	−	0.365281i	$-0.880973\pi$
$349$	−0.000881644		0.00224639i	−4.71933e−5		0.000120247i	0.930850	+	0.365401i	$0.119068\pi$
$350$	−1.26969	−	2.19916i	−0.0678675	−	0.117550i
$351$	13.8767	−	24.0352i	0.740686	−	1.28291i
$352$	2.46460	+	3.09052i	0.131364	+	0.164725i
$353$	2.86901	−	1.95606i	0.152702	−	0.104110i	−0.484559	−	0.874759i	$-0.661020\pi$
$353$	2.86901	−	1.95606i	0.152702	−	0.104110i	0.637261	+	0.770648i	$0.280067\pi$
$354$	−4.71041	−	0.709980i	−0.250356	−	0.0377350i
$355$	−7.00684	−	3.37432i	−0.371884	−	0.179090i
$356$	12.8194	−	11.8946i	0.679426	−	0.630415i
$357$	−19.3125	+	2.91089i	−1.02213	+	0.154061i
$358$	−3.82386	−	1.17950i	−0.202097	−	0.0623387i
$359$	−0.0556742	+	0.742920i	−0.00293837	+	0.0392098i	−0.998480	−	0.0551107i	$-0.982449\pi$
$359$	−0.0556742	+	0.742920i	−0.00293837	+	0.0392098i	0.995542	+	0.0943206i	$0.0300679\pi$
$360$	0.836122	−	1.04846i	0.0440675	−	0.0552589i
$361$	−6.91825	−	17.6274i	−0.364119	−	0.927759i
$362$	−8.51073	−	7.89680i	−0.447314	−	0.415047i
$363$	−4.92253	−	3.35613i	−0.258366	−	0.176151i
$364$	0.941949	+	12.5694i	0.0493715	+	0.658818i
$365$	−1.96859	+	8.62493i	−0.103040	+	0.451450i
$366$	−3.75052	+	16.4321i	−0.196043	+	0.858920i
$367$	−1.11742	−	14.9110i	−0.0583289	−	0.778346i	−0.947293	−	0.320369i	$-0.896193\pi$
$367$	−1.11742	−	14.9110i	−0.0583289	−	0.778346i	0.888964	−	0.457977i	$-0.151426\pi$
$368$	2.47811	+	1.68955i	0.129180	+	0.0880737i
$369$	−0.210547	−	0.195359i	−0.0109607	−	0.0101700i
$370$	2.97310	+	7.57535i	0.154564	+	0.393824i
$371$	16.6250	−	20.8470i	0.863125	−	1.08232i
$372$	0.743710	−	9.92412i	0.0385596	−	0.514542i
$373$	22.9650	+	7.08378i	1.18909	+	0.366784i	0.825298	−	0.564698i	$-0.191007\pi$
$373$	22.9650	+	7.08378i	1.18909	+	0.366784i	0.363787	+	0.931482i	$0.381483\pi$
$374$	−23.3406	+	3.51802i	−1.20691	+	0.181913i
$375$	0.944177	−	0.876068i	0.0487571	−	0.0452399i
$376$	−6.56203	−	3.16011i	−0.338411	−	0.162970i
$377$	−38.6196	−	5.82096i	−1.98901	−	0.299795i
$378$	11.7312	−	7.99822i	0.603389	−	0.411384i
$379$	17.2058	+	21.5753i	0.883801	+	1.10825i	0.993449	+	0.114281i	$0.0364563\pi$
$379$	17.2058	+	21.5753i	0.883801	+	1.10825i	−0.109648	+	0.993971i	$0.534972\pi$
$380$	0.126072	−	0.218363i	0.00646736	−	0.0112018i
$381$	11.3458	+	19.6514i	0.581260	+	1.00677i
$382$	1.45332	−	3.70300i	0.0743583	−	0.189462i
$383$	−13.4831	+	6.49314i	−0.688957	+	0.331784i	−0.745396	−	0.666622i	$-0.767740\pi$
$383$	−13.4831	+	6.49314i	−0.688957	+	0.331784i	0.0564394	+	0.998406i	$0.482025\pi$
$384$	1.23079	−	0.379647i	0.0628082	−	0.0193738i
$385$	−2.23365	−	9.78625i	−0.113837	−	0.498754i
$386$	19.4447			0.989708
$387$	−5.06968	−	7.18530i	−0.257706	−	0.365249i
$388$	−10.1315			−0.514350
$389$	−7.74993	−	33.9547i	−0.392937	−	1.72157i	−0.654218	−	0.756306i	$-0.727002\pi$
$389$	−7.74993	−	33.9547i	−0.392937	−	1.72157i	0.261281	−	0.965263i	$-0.415855\pi$
$390$	−6.10925	+	1.88445i	−0.309354	+	0.0954231i
$391$	−16.1360	+	7.77069i	−0.816033	+	0.392981i
$392$	0.201520	−	0.513465i	0.0101783	−	0.0259339i
$393$	−12.8947	−	22.3343i	−0.650452	−	1.12662i
$394$	−3.09638	+	5.36309i	−0.155994	+	0.270189i
$395$	−3.53824	−	4.43681i	−0.178028	−	0.223240i
$396$	4.37990	−	2.98616i	0.220098	−	0.150060i
$397$	−36.5806	−	5.51364i	−1.83593	−	0.276721i	−0.862557	−	0.505960i	$-0.831138\pi$
$397$	−36.5806	−	5.51364i	−1.83593	−	0.276721i	−0.973370	+	0.229239i	$0.926376\pi$
$398$	9.01339	+	4.34062i	0.451800	+	0.217576i
$399$	0.604544	−	0.560935i	0.0302651	−	0.0280819i
$400$	−0.988831	+	0.149042i	−0.0494415	+	0.00745211i
$401$	−31.0177	−	9.56770i	−1.54895	−	0.477788i	−0.601820	−	0.798632i	$-0.705557\pi$
$401$	−31.0177	−	9.56770i	−1.54895	−	0.477788i	−0.947132	+	0.320844i	$0.896034\pi$
$402$	−0.958194	+	12.7862i	−0.0477904	+	0.637718i
$403$	23.9125	−	29.9853i	1.19117	−	1.49367i
$404$	−3.81689	−	9.72527i	−0.189897	−	0.483851i
$405$	2.33002	+	2.16194i	0.115779	+	0.107428i
$406$	−16.5086	−	11.2554i	−0.819310	−	0.558596i
$407$	2.40395	+	32.0785i	0.119159	+	1.59007i
$408$	−1.71144	+	7.49829i	−0.0847287	+	0.371221i
$409$	1.63446	−	7.16102i	0.0808187	−	0.354090i	−0.918308	−	0.395866i	$-0.870445\pi$
$409$	1.63446	−	7.16102i	0.0808187	−	0.354090i	0.999127	+	0.0417762i	$0.0133017\pi$
$410$	0.0160055	+	0.213579i	0.000790457	+	0.0105479i
$411$	7.19871	+	4.90800i	0.355086	+	0.242094i
$412$	13.1028	+	12.1576i	0.645528	+	0.598962i
$413$	−3.43117	−	8.74249i	−0.168837	−	0.430190i
$414$	2.50775	−	3.14462i	0.123249	−	0.154550i
$415$	0.208424	−	2.78122i	0.0102311	−	0.136525i
$416$	4.74318	+	1.46308i	0.232553	+	0.0717333i
$417$	12.6892	−	1.91259i	0.621392	−	0.0936598i
$418$	0.730636	−	0.677931i	0.0357366	−	0.0331587i
$419$	16.3756	+	7.88606i	0.799999	+	0.385259i	0.788778	−	0.614678i	$-0.210714\pi$
$419$	16.3756	+	7.88606i	0.799999	+	0.385259i	0.0112207	+	0.999937i	$0.496428\pi$
$420$	−3.23420	−	0.487477i	−0.157813	−	0.0237864i
$421$	2.91807	−	1.98950i	0.142218	−	0.0969625i	−0.490121	−	0.871654i	$-0.663047\pi$
$421$	2.91807	−	1.98950i	0.142218	−	0.0969625i	0.632339	+	0.774692i	$0.282095\pi$
$422$	−7.73035	−	9.69355i	−0.376308	−	0.471875i
$423$	−4.88359	+	8.45862i	−0.237448	+	0.411272i
$424$	−5.25019	−	9.09360i	−0.254972	−	0.441624i
$425$	2.18157	−	5.55856i	0.105822	−	0.269630i
$426$	−9.02487	+	4.34615i	−0.437256	+	0.210571i
$427$	−31.7535	+	9.79467i	−1.53666	+	0.473997i
$428$	0.145163	+	0.636002i	0.00701673	+	0.0307423i
$429$	−25.2721			−1.22015
$430$	−0.873134	+	6.49905i	−0.0421063	+	0.313412i
$431$	−4.34686			−0.209381			−0.104691	−	0.994505i	$-0.533385\pi$
$431$	−4.34686			−0.209381			−0.104691	+	0.994505i	$0.533385\pi$
$432$	−1.24418	−	5.45110i	−0.0598606	−	0.262266i
$433$	−1.49188	+	0.460185i	−0.0716953	+	0.0221151i	−0.330395	−	0.943843i	$-0.607182\pi$
$433$	−1.49188	+	0.460185i	−0.0716953	+	0.0221151i	0.258700	+	0.965958i	$0.416706\pi$
$434$	17.6777	−	8.51313i	0.848556	−	0.408643i
$435$	3.70251	−	9.43385i	0.177522	−	0.452319i
$436$	1.09845	+	1.90257i	0.0526061	+	0.0911164i
$437$	0.378124	−	0.654929i	0.0180881	−	0.0313295i
$438$	7.10446	+	8.90871i	0.339464	+	0.425675i
$439$	15.5984	−	10.6348i	0.744469	−	0.507571i	−0.130679	−	0.991425i	$-0.541716\pi$
$439$	15.5984	−	10.6348i	0.744469	−	0.507571i	0.875149	+	0.483854i	$0.160763\pi$
$440$	−3.90877	−	0.589152i	−0.186343	−	0.0280867i
$441$	−0.666454	−	0.320947i	−0.0317359	−	0.0152832i
$442$	−21.7276	+	20.1603i	−1.03348	+	0.958926i
$443$	13.6494	−	2.05732i	0.648505	−	0.0977464i	0.183451	−	0.983029i	$-0.441273\pi$
$443$	13.6494	−	2.05732i	0.648505	−	0.0977464i	0.465054	+	0.885282i	$0.346035\pi$
$444$	10.0160	+	3.08953i	0.475338	+	0.146622i
$445$	−1.30686	+	17.4388i	−0.0619509	+	0.826677i
$446$	1.96876	−	2.46875i	0.0932236	−	0.116899i
$447$	−0.0422433	−	0.107634i	−0.00199804	−	0.00509092i
$448$	1.86149	+	1.72721i	0.0879472	+	0.0816030i
$449$	3.74989	+	2.55663i	0.176968	+	0.120655i	0.648565	−	0.761160i	$-0.275370\pi$
$449$	3.74989	+	2.55663i	0.176968	+	0.120655i	−0.471596	+	0.881815i	$0.656322\pi$
$450$	0.100216	+	1.33729i	0.00472421	+	0.0630403i
$451$	−0.188392	+	0.825401i	−0.00887106	+	0.0388666i
$452$	2.61025	−	11.4362i	0.122776	−	0.537915i
$453$	0.177275	+	2.36556i	0.00832908	+	0.111144i
$454$	17.5924	+	11.9943i	0.825652	+	0.562920i
$455$	−9.23989	−	8.57336i	−0.433173	−	0.401925i
$456$	−0.118649	−	0.302314i	−0.00555627	−	0.0141571i
$457$	−15.4559	+	19.3811i	−0.722998	+	0.906611i	−0.998503	−	0.0546885i	$-0.982583\pi$
$457$	−15.4559	+	19.3811i	−0.722998	+	0.906611i	0.275505	+	0.961300i	$0.411155\pi$
$458$	0.942808	−	12.5809i	0.0440545	−	0.587867i
$459$	31.9041	+	9.84113i	1.48916	+	0.459344i
$460$	−2.96577	+	0.447017i	−0.138280	+	0.0208423i
$461$	−13.8600	+	12.8602i	−0.645526	+	0.598961i	−0.933457	−	0.358690i	$-0.883223\pi$
$461$	−13.8600	+	12.8602i	−0.645526	+	0.598961i	0.287930	+	0.957651i	$0.407033\pi$
$462$	−11.6486	−	5.60965i	−0.541940	−	0.260985i
$463$	27.4144	+	4.13205i	1.27405	+	0.192033i	0.751021	−	0.660279i	$-0.229562\pi$
$463$	27.4144	+	4.13205i	1.27405	+	0.192033i	0.523034	+	0.852312i	$0.324800\pi$
$464$	−6.50108	+	4.43236i	−0.301805	+	0.205767i
$465$	6.20494	+	7.78074i	0.287747	+	0.360823i
$466$	5.45651	−	9.45095i	0.252768	−	0.437807i
$467$	−6.68807	−	11.5841i	−0.309487	−	0.536047i	0.668763	−	0.743476i	$-0.266824\pi$
$467$	−6.68807	−	11.5841i	−0.309487	−	0.536047i	−0.978250	+	0.207428i	$0.933491\pi$
$468$	2.43189	−	6.19636i	0.112414	−	0.286427i
$469$	−22.7759	+	10.9683i	−1.05169	+	0.506469i
$470$	6.95973	−	2.14679i	0.321028	−	0.0990241i
$471$	−1.94872	−	8.53790i	−0.0897922	−	0.393406i
$472$	−3.69844			−0.170234
$473$	−10.8704	+	23.5315i	−0.499822	+	1.08198i
$474$	−7.30930			−0.335727
$475$	0.0561073	+	0.245822i	0.00257438	+	0.0112791i
$476$	−14.4898	+	4.46950i	−0.664137	+	0.204859i
$477$	−12.6869	+	6.10968i	−0.580893	+	0.279743i
$478$	7.06722	−	18.0070i	0.323247	−	0.823621i
$479$	−9.90767	−	17.1606i	−0.452693	−	0.784087i	0.545859	−	0.837877i	$-0.316203\pi$
$479$	−9.90767	−	17.1606i	−0.452693	−	0.784087i	−0.998552	+	0.0537898i	$0.982870\pi$
$480$	−0.644004	+	1.11545i	−0.0293946	+	0.0509130i
$481$	25.1853	+	31.5814i	1.14835	+	1.43999i
$482$	−16.7379	+	11.4117i	−0.762391	+	0.519789i
$483$	−9.70022	−	1.46207i	−0.441375	−	0.0665266i
$484$	−4.16749	−	2.00696i	−0.189431	−	0.0912253i
$485$	7.42693	−	6.89118i	0.337239	−	0.312913i
$486$	−12.5383	+	1.88984i	−0.568748	+	0.0857250i
$487$	−23.1273	−	7.13383i	−1.04800	−	0.323265i	−0.277513	−	0.960722i	$-0.589510\pi$
$487$	−23.1273	−	7.13383i	−1.04800	−	0.323265i	−0.770486	+	0.637457i	$0.779986\pi$
$488$	−0.977907	+	13.0493i	−0.0442678	+	0.590712i
$489$	9.98512	−	12.5209i	0.451543	−	0.566216i
$490$	0.201520	+	0.513465i	0.00910375	+	0.0231960i
$491$	−24.9740	−	23.1725i	−1.12706	−	1.04576i	−0.998538	−	0.0540544i	$-0.982786\pi$
$491$	−24.9740	−	23.1725i	−1.12706	−	1.04576i	−0.128524	−	0.991706i	$-0.541024\pi$
$492$	0.227929	+	0.155399i	0.0102758	+	0.00700593i
$493$	−3.51113	−	46.8527i	−0.158133	−	2.11014i
$494$	0.278500	−	1.22019i	0.0125303	−	0.0548989i
$495$	−1.17958	+	5.16810i	−0.0530184	+	0.232289i
$496$	−0.577411	−	7.70501i	−0.0259265	−	0.345965i
$497$	−16.3171	−	11.1248i	−0.731924	−	0.499017i
$498$	−2.63333	−	2.44337i	−0.118002	−	0.109490i
$499$	−1.08560	−	2.76606i	−0.0485981	−	0.123826i	0.904513	−	0.426445i	$-0.140234\pi$
$499$	−1.08560	−	2.76606i	−0.0485981	−	0.123826i	−0.953112	+	0.302619i	$0.902139\pi$
$500$	0.623490	−	0.781831i	0.0278833	−	0.0349646i
$501$	1.94871	−	26.0038i	0.0870621	−	1.16176i
$502$	−7.99836	−	2.46717i	−0.356984	−	0.110115i
$503$	0.0341149	−	0.00514200i	0.00152111	−	0.000229270i	−0.148282	−	0.988945i	$-0.547374\pi$
$503$	0.0341149	−	0.00514200i	0.00152111	−	0.000229270i	0.149803	+	0.988716i	$0.452136\pi$
$504$	2.49633	−	2.31625i	0.111195	−	0.103174i
$505$	9.41284	+	4.53299i	0.418866	+	0.201715i
$506$	−11.7234	−	1.76702i	−0.521170	−	0.0785538i
$507$	−12.3855	+	8.44432i	−0.550062	+	0.375026i
$508$	10.9843	+	13.7739i	0.487351	+	0.611119i
$509$	14.4289	−	24.9916i	0.639550	−	1.10773i	−0.345982	−	0.938241i	$-0.612454\pi$
$509$	14.4289	−	24.9916i	0.639550	−	1.10773i	0.985532	−	0.169491i	$-0.0542125\pi$
$510$	−3.84556	−	6.66071i	−0.170284	−	0.294941i
$511$	−8.20744	+	20.9122i	−0.363076	+	0.925102i
$512$	0.900969	−	0.433884i	0.0398176	−	0.0191751i
$513$	−1.34718	+	0.415549i	−0.0594793	+	0.0183469i
$514$	0.276643	+	1.21205i	0.0122022	+	0.0534614i
$515$	−17.8743			−0.787636
$516$	5.84340	+	6.09838i	0.257241	+	0.268466i
$517$	28.7903			1.26620
$518$	4.59842	+	20.1470i	0.202043	+	0.885209i
$519$	−1.67038	+	0.515244i	−0.0733215	+	0.0226167i
$520$	−4.47214	+	2.15367i	−0.196116	+	0.0944447i
$521$	11.2660	−	28.7054i	0.493574	−	1.25761i	−0.439605	−	0.898191i	$-0.644881\pi$
$521$	11.2660	−	28.7054i	0.493574	−	1.25761i	0.933178	−	0.359414i	$-0.117023\pi$
$522$	5.27582	+	9.13799i	0.230916	+	0.399959i
$523$	−9.29966	+	16.1075i	−0.406646	+	0.704331i	−0.994511	−	0.104627i	$-0.966635\pi$
$523$	−9.29966	+	16.1075i	−0.406646	+	0.704331i	0.587866	+	0.808959i	$0.299968\pi$
$524$	−12.4840	−	15.6544i	−0.545364	−	0.683865i
$525$	2.70240	−	1.84247i	0.117943	−	0.0804119i
$526$	10.3971	+	1.56711i	0.453334	+	0.0683291i
$527$	41.5691	+	20.0186i	1.81078	+	0.872025i
$528$	−3.73225	+	3.46302i	−0.162425	+	0.150709i
$529$	13.8480	−	2.08725i	0.602086	−	0.0907499i
$530$	10.0339	+	3.09504i	0.435844	+	0.134440i
$531$	−0.370642	+	4.94587i	−0.0160845	+	0.214632i
$532$	0.399213	−	0.500597i	0.0173081	−	0.0217036i
$533$	0.388400	+	0.989627i	0.0168235	+	0.0428655i
$534$	16.5115	+	15.3204i	0.714521	+	0.662978i
$535$	−0.539003	−	0.367486i	−0.0233031	−	0.0158878i
$536$	0.743935	+	9.92712i	0.0321331	+	0.428786i
$537$	1.14690	−	5.02492i	0.0494926	−	0.216841i
$538$	−3.61498	+	15.8383i	−0.155853	+	0.682837i
$539$	0.162942	+	2.17431i	0.00701841	+	0.0936542i
$540$	4.61974	+	3.14968i	0.198802	+	0.135541i
$541$	17.9310	+	16.6376i	0.770916	+	0.715305i	0.964007	−	0.265875i	$-0.0856610\pi$
$541$	17.9310	+	16.6376i	0.770916	+	0.715305i	−0.193092	+	0.981181i	$0.561851\pi$
$542$	−6.27364	−	15.9850i	−0.269476	−	0.686614i
$543$	9.32352	−	11.6913i	0.400110	−	0.501723i
$544$	−0.446238	+	5.95464i	−0.0191323	+	0.255303i
$545$	−2.09929	−	0.647546i	−0.0899238	−	0.0277378i
$546$	−16.0536	+	2.41969i	−0.687031	+	0.103553i
$547$	−7.18708	+	6.66864i	−0.307297	+	0.285130i	−0.818713	−	0.574203i	$-0.805312\pi$
$547$	−7.18708	+	6.66864i	−0.307297	+	0.285130i	0.511415	+	0.859334i	$0.329121\pi$
$548$	6.09453	+	2.93497i	0.260345	+	0.125376i
$549$	17.3526	+	2.61548i	0.740591	+	0.111626i
$550$	3.26605	−	2.22676i	0.139265	−	0.0949493i
$551$	1.23697	+	1.55111i	0.0526965	+	0.0660793i
$552$	−1.93154	+	3.34552i	−0.0822118	+	0.142395i
$553$	−7.20533	−	12.4800i	−0.306402	−	0.530703i
$554$	6.03300	−	15.3718i	0.256318	−	0.653086i
$555$	−9.44365	+	4.54782i	−0.400861	+	0.193044i
$556$	9.52044	−	2.93667i	0.403757	−	0.124542i
$557$	−2.73195	−	11.9694i	−0.115756	−	0.507162i	−0.999250	−	0.0387188i	$-0.987672\pi$
$557$	−2.73195	−	11.9694i	−0.115756	−	0.507162i	0.883494	−	0.468443i	$-0.155185\pi$
$558$	−10.3617			−0.438645
$559$	5.36718	+	32.1036i	0.227007	+	1.35784i
$560$	−2.53937			−0.107308
$561$	−6.76517	−	29.6401i	−0.285626	−	1.25141i
$562$	19.7693	−	6.09801i	0.833916	−	0.257229i
$563$	−4.68542	+	2.25638i	−0.197467	+	0.0950950i	−0.530004	−	0.847995i	$-0.677810\pi$
$563$	−4.68542	+	2.25638i	−0.197467	+	0.0950950i	0.332537	+	0.943090i	$0.392095\pi$
$564$	3.42725	−	8.73248i	0.144313	−	0.367704i
$565$	5.86517	+	10.1588i	0.246750	+	0.427383i
$566$	2.43085	−	4.21036i	0.102176	−	0.176975i
$567$	5.03246	+	6.31050i	0.211343	+	0.265016i
$568$	−6.42566	+	4.38094i	−0.269615	+	0.183820i
$569$	20.7946	+	3.13428i	0.871756	+	0.131396i	0.569659	−	0.821881i	$-0.307075\pi$
$569$	20.7946	+	3.13428i	0.871756	+	0.131396i	0.302097	+	0.953277i	$0.402313\pi$
$570$	0.292602	+	0.140910i	0.0122557	+	0.00590205i
$571$	3.22992	−	2.99693i	0.135168	−	0.125418i	−0.609692	−	0.792639i	$-0.708707\pi$
$571$	3.22992	−	2.99693i	0.135168	−	0.125418i	0.744860	+	0.667221i	$0.232516\pi$
$572$	−19.4020	+	2.92437i	−0.811237	+	0.122274i
$573$	4.89604	+	1.51023i	0.204535	+	0.0630907i
$574$	−0.0406440	+	0.542357i	−0.00169645	+	0.0226375i
$575$	1.87001	−	2.34492i	0.0779849	−	0.0977900i
$576$	−0.489935	−	1.24833i	−0.0204140	−	0.0520140i
$577$	2.61472	+	2.42610i	0.108852	+	0.101000i	0.732721	−	0.680529i	$-0.238250\pi$
$577$	2.61472	+	2.42610i	0.108852	+	0.101000i	−0.623869	+	0.781529i	$0.714440\pi$
$578$	−15.4150	−	10.5098i	−0.641180	−	0.437149i
$579$	1.87161	+	24.9749i	0.0777814	+	1.03792i
$580$	1.75086	−	7.67100i	0.0727004	−	0.318521i
$581$	1.57597	−	6.90479i	0.0653824	−	0.286459i
$582$	−0.975189	−	13.0130i	−0.0404229	−	0.539406i
$583$	34.2948	+	23.3818i	1.42035	+	0.968376i
$584$	6.48512	+	6.01731i	0.268356	+	0.248998i
$585$	2.43189	+	6.19636i	0.100546	+	0.256188i
$586$	−15.2415	+	19.1123i	−0.629621	+	0.789520i
$587$	0.383716	−	5.12033i	0.0158377	−	0.211339i	−0.983670	−	0.179979i	$-0.942397\pi$
$587$	0.383716	−	5.12033i	0.0158377	−	0.211339i	0.999508	−	0.0313601i	$-0.00998386\pi$
$588$	0.678895	+	0.209411i	0.0279971	+	0.00863598i
$589$	−1.92646	+	0.290367i	−0.0793784	+	0.0119644i
$590$	2.71115	−	2.51558i	0.111616	−	0.103565i
$591$	−7.18643	−	3.46080i	−0.295610	−	0.142358i
$592$	8.04700	+	1.21289i	0.330730	+	0.0498495i
$593$	−13.3883	+	9.12802i	−0.549793	+	0.374843i	−0.806124	−	0.591746i	$-0.798439\pi$
$593$	−13.3883	+	9.12802i	−0.549793	+	0.374843i	0.256331	+	0.966589i	$0.417486\pi$
$594$	13.7803	+	17.2800i	0.565413	+	0.709006i
$595$	7.58172	−	13.1319i	0.310820	−	0.538356i
$596$	−0.0448860	−	0.0777448i	−0.00183860	−	0.00318455i
$597$	−4.70755	+	11.9946i	−0.192667	+	0.490908i
$598$	−13.4131	+	6.45943i	−0.548504	+	0.264146i
$599$	5.63109	−	1.73696i	0.230080	−	0.0709703i	−0.177571	−	0.984108i	$-0.556824\pi$
$599$	5.63109	−	1.73696i	0.230080	−	0.0709703i	0.407651	+	0.913138i	$0.366348\pi$
$600$	−0.286609	−	1.25571i	−0.0117008	−	0.0512643i
$601$	11.6641			0.475787			0.237893	−	0.971291i	$-0.423543\pi$
$601$	11.6641			0.475787			0.237893	+	0.971291i	$0.423543\pi$
$602$	−4.65217	+	15.9887i	−0.189608	+	0.651651i
$603$	13.3500			0.543652
$604$	0.409829	+	1.79558i	0.0166757	+	0.0730611i
$605$	4.42006	−	1.36341i	0.179701	−	0.0554304i
$606$	12.1238	−	5.83852i	0.492496	−	0.237174i
$607$	−17.5170	+	44.6325i	−0.710991	+	1.81158i	−0.140848	+	0.990031i	$0.544983\pi$
$607$	−17.5170	+	44.6325i	−0.710991	+	1.81158i	−0.570144	+	0.821545i	$0.693113\pi$
$608$	−0.126072	−	0.218363i	−0.00511290	−	0.00885580i
$609$	12.8675	−	22.2872i	0.521418	−	0.903122i
$610$	−8.15890	−	10.2309i	−0.330344	−	0.414238i
$611$	29.8703	−	20.3652i	1.20842	−	0.823889i
$612$	7.91833	+	1.19350i	0.320080	+	0.0482442i
$613$	35.9547	+	17.3149i	1.45220	+	0.699341i	0.982975	−	0.183739i	$-0.0588202\pi$
$613$	35.9547	+	17.3149i	1.45220	+	0.699341i	0.469222	+	0.883080i	$0.344535\pi$
$614$	−13.1797	+	12.2290i	−0.531891	+	0.493523i
$615$	−0.272782	+	0.0411152i	−0.0109996	+	0.00165793i
$616$	−9.59197	−	2.95873i	−0.386471	−	0.119211i
$617$	−1.89666	+	25.3092i	−0.0763567	+	1.01891i	0.819068	+	0.573696i	$0.194491\pi$
$617$	−1.89666	+	25.3092i	−0.0763567	+	1.01891i	−0.895425	+	0.445213i	$0.853128\pi$
$618$	−14.3541	+	17.9995i	−0.577408	+	0.724046i
$619$	2.67426	+	6.81391i	0.107488	+	0.273874i	0.974490	−	0.224429i	$-0.0720518\pi$
$619$	2.67426	+	6.81391i	0.107488	+	0.273874i	−0.867003	+	0.498304i	$0.833957\pi$
$620$	5.66401	+	5.25544i	0.227472	+	0.211063i
$621$	13.8558	+	9.44674i	0.556015	+	0.379085i
$622$	1.56365	+	20.8654i	0.0626966	+	0.836628i
$623$	−9.88164	+	43.2943i	−0.395900	+	1.73455i
$624$	−1.42264	+	6.23299i	−0.0569512	+	0.249519i
$625$	0.0747301	+	0.997204i	0.00298920	+	0.0398882i
$626$	21.2665	+	14.4993i	0.849981	+	0.579508i
$627$	0.941065	+	0.873181i	0.0375825	+	0.0348715i
$628$	−2.48404	−	6.32923i	−0.0991239	−	0.252564i
$629$	−30.2979	+	37.9924i	−1.20806	+	1.51486i
$630$	−0.254485	+	3.39587i	−0.0101389	+	0.135295i
$631$	−29.8948	−	9.22131i	−1.19009	−	0.367095i	−0.364414	−	0.931237i	$-0.618731\pi$
$631$	−29.8948	−	9.22131i	−1.19009	−	0.367095i	−0.825678	+	0.564142i	$0.809207\pi$
$632$	−5.61151	+	0.845798i	−0.223214	+	0.0336441i
$633$	11.7064	−	10.8619i	0.465287	−	0.431724i
$634$	−20.4292	−	9.83818i	−0.811346	−	0.390724i
$635$	−17.4207	−	2.62575i	−0.691321	−	0.104200i
$636$	11.1745	−	7.61866i	0.443099	−	0.302100i
$637$	1.70709	+	2.14062i	0.0676372	+	0.0848143i
$638$	15.5513	−	26.9357i	0.615683	−	1.06639i
$639$	5.21462	+	9.03199i	0.206287	+	0.357300i
$640$	−0.365341	+	0.930874i	−0.0144414	+	0.0367960i
$641$	−2.79271	+	1.34490i	−0.110305	+	0.0531203i	−0.488223	−	0.872719i	$-0.662355\pi$
$641$	−2.79271	+	1.34490i	−0.110305	+	0.0531203i	0.377917	+	0.925839i	$0.376640\pi$
$642$	−0.802912	+	0.247666i	−0.0316884	+	0.00977458i
$643$	−8.17856	−	35.8326i	−0.322531	−	1.41310i	−0.833033	−	0.553223i	$-0.813398\pi$
$643$	−8.17856	−	35.8326i	−0.322531	−	1.41310i	0.510502	−	0.859876i	$-0.329459\pi$
$644$	−7.61625			−0.300122
$645$	−8.43146	−	0.495907i	−0.331988	−	0.0195263i
$646$	1.50564			0.0592385
$647$	5.05938	+	22.1666i	0.198905	+	0.871458i	0.971590	+	0.236669i	$0.0760558\pi$
$647$	5.05938	+	22.1666i	0.198905	+	0.871458i	−0.772686	+	0.634789i	$0.781087\pi$
$648$	3.03730	−	0.936884i	0.119317	−	0.0368043i
$649$	13.1718	−	6.34322i	0.517039	−	0.248993i
$650$	1.81344	−	4.62058i	0.0711291	−	0.181234i
$651$	12.6358	+	21.8859i	0.495238	+	0.857777i
$652$	6.21692	−	10.7680i	0.243473	−	0.421708i
$653$	10.5008	+	13.1676i	0.410927	+	0.515286i	0.943624	−	0.331020i	$-0.107393\pi$
$653$	10.5008	+	13.1676i	0.410927	+	0.515286i	−0.532697	+	0.846306i	$0.678821\pi$
$654$	−2.33794	+	1.59398i	−0.0914207	+	0.0623296i
$655$	19.7991	+	2.98423i	0.773614	+	0.116604i
$656$	0.192968	+	0.0929284i	0.00753412	+	0.00362824i
$657$	8.69678	−	8.06943i	0.339294	−	0.314818i
$658$	18.2884	−	2.75654i	0.712958	−	0.107461i
$659$	−22.1014	−	6.81737i	−0.860947	−	0.265567i	−0.167321	−	0.985902i	$-0.553512\pi$
$659$	−22.1014	−	6.81737i	−0.860947	−	0.265567i	−0.693626	+	0.720335i	$0.743988\pi$
$660$	0.380480	−	5.07715i	0.0148102	−	0.197628i
$661$	20.0498	−	25.1416i	0.779845	−	0.977895i	−0.220152	−	0.975466i	$-0.570655\pi$
$661$	20.0498	−	25.1416i	0.779845	−	0.977895i	0.999997	−	0.00242959i	$-0.000773363\pi$
$662$	−6.26410	−	15.9607i	−0.243461	−	0.620329i
$663$	−27.9853	−	25.9666i	−1.08686	−	1.00846i
$664$	−2.30440	−	1.57111i	−0.0894279	−	0.0609709i
$665$	0.0478487	+	0.638497i	0.00185549	+	0.0247598i
$666$	2.42842	−	10.6396i	0.0940992	−	0.412275i
$667$	5.25128	−	23.0074i	0.203331	−	0.890849i
$668$	−1.51297	−	20.1892i	−0.0585385	−	0.781142i
$669$	3.36038	+	2.29107i	0.129920	+	0.0885777i
$670$	−7.29750	−	6.77109i	−0.281927	−	0.261590i
$671$	−18.8981	−	48.1516i	−0.729553	−	1.85887i
$672$	−2.03927	+	2.55716i	−0.0786664	+	0.0986446i
$673$	0.272536	−	3.63674i	0.0105055	−	0.140186i	−0.989485	−	0.144638i	$-0.953798\pi$
$673$	0.272536	−	3.63674i	0.0105055	−	0.140186i	0.999990	+	0.00445234i	$0.00141723\pi$
$674$	21.6042	+	6.66400i	0.832161	+	0.256688i
$675$	−5.52884	+	0.833338i	−0.212805	+	0.0320752i
$676$	−8.53151	+	7.91608i	−0.328135	+	0.304465i
$677$	−2.25797	−	1.08738i	−0.0867807	−	0.0417914i	0.389990	−	0.920819i	$-0.372478\pi$
$677$	−2.25797	−	1.08738i	−0.0867807	−	0.0417914i	−0.476771	+	0.879028i	$0.658193\pi$
$678$	14.9400	+	2.25184i	0.573768	+	0.0864816i
$679$	21.2572	−	14.4929i	0.815777	−	0.556187i
$680$	−3.72307	−	4.66858i	−0.142773	−	0.179032i
$681$	−13.7122	+	23.7503i	−0.525453	+	0.910112i
$682$	15.2713	+	26.4507i	0.584770	+	1.01285i
$683$	−13.1994	+	33.6315i	−0.505061	+	1.28687i	0.420162	+	0.907449i	$0.361973\pi$
$683$	−13.1994	+	33.6315i	−0.505061	+	1.28687i	−0.925223	+	0.379424i	$0.876122\pi$
$684$	−0.304648	+	0.146711i	−0.0116485	+	0.00560963i
$685$	−6.46390	+	1.99385i	−0.246973	+	0.0761810i
$686$	4.26713	+	18.6955i	0.162920	+	0.713798i
$687$	16.2497			0.619966
$688$	5.19177	+	4.00568i	0.197935	+	0.152715i
$689$	52.1208			1.98564
$690$	−0.859616	−	3.76622i	−0.0327250	−	0.143378i
$691$	26.1724	−	8.07311i	0.995644	−	0.307115i	0.246226	−	0.969213i	$-0.420810\pi$
$691$	26.1724	−	8.07311i	0.995644	−	0.307115i	0.749418	+	0.662097i	$0.230333\pi$
$692$	−1.22276	+	0.588852i	−0.0464825	+	0.0223848i
$693$	−4.91793	+	12.5307i	−0.186817	+	0.476002i
$694$	6.65211	+	11.5218i	0.252511	+	0.437361i
$695$	−4.98154	+	8.62828i	−0.188960	+	0.327289i
$696$	−6.31870	−	7.92340i	−0.239510	−	0.300336i
$697$	−1.05670	+	0.720446i	−0.0400254	+	0.0272888i
$698$	−0.00238625		0.000359670i	−9.03210e−5		1.36137e-5i
$699$	12.6641	+	6.09869i	0.478999	+	0.230674i
$700$	1.86149	−	1.72721i	0.0703577	−	0.0652824i
$701$	−32.5957	+	4.91301i	−1.23112	+	0.185562i	−0.732203	−	0.681086i	$-0.761508\pi$
$701$	−32.5957	+	4.91301i	−1.23112	+	0.185562i	−0.498920	+	0.866648i	$0.666270\pi$
$702$	26.5205	+	8.18049i	1.00095	+	0.308753i
$703$	0.153340	−	2.04618i	0.00578334	−	0.0771732i
$704$	−2.46460	+	3.09052i	−0.0928883	+	0.116478i
$705$	3.42725	+	8.73248i	0.129078	+	0.328884i
$706$	2.54543	+	2.36181i	0.0957984	+	0.0888879i
$707$	21.9201	+	14.9449i	0.824391	+	0.562060i
$708$	−0.355985	−	4.75030i	−0.0133788	−	0.178527i
$709$	−8.45521	+	37.0447i	−0.317542	+	1.39124i	0.524307	+	0.851529i	$0.324324\pi$
$709$	−8.45521	+	37.0447i	−0.317542	+	1.39124i	−0.841849	+	0.539713i	$0.818533\pi$
$710$	1.73055	−	7.58202i	0.0649463	−	0.284548i
$711$	0.568713	+	7.58895i	0.0213284	+	0.284608i
$712$	14.4490	+	9.85116i	0.541499	+	0.369188i
$713$	16.9879	+	15.7624i	0.636201	+	0.590308i
$714$	−7.13534	−	18.1805i	−0.267033	−	0.680390i
$715$	12.2336	−	15.3404i	0.457509	−	0.573698i
$716$	0.299043	−	3.99045i	0.0111758	−	0.149130i
$717$	23.8085	+	7.34396i	0.889146	+	0.274265i
$718$	−0.736683	+	0.111037i	−0.0274928	+	0.00414387i
$719$	−10.0960	+	9.36772i	−0.376517	+	0.349357i	−0.845619	−	0.533787i	$-0.820768\pi$
$719$	−10.0960	+	9.36772i	−0.376517	+	0.349357i	0.469102	+	0.883144i	$0.344578\pi$
$720$	1.20823	+	0.581854i	0.0450281	+	0.0216844i
$721$	−44.8825	−	6.76495i	−1.67151	−	0.251940i
$722$	15.6460	−	10.6673i	0.582284	−	0.396995i
$723$	−16.2684	−	20.3999i	−0.605027	−	0.758679i
$724$	5.80500	−	10.0545i	0.215741	−	0.373674i
$725$	3.93414	+	6.81413i	0.146110	+	0.253070i
$726$	2.17661	−	5.54592i	0.0807817	−	0.205828i
$727$	−24.1163	+	11.6138i	−0.894424	+	0.430732i	−0.823872	−	0.566776i	$-0.808190\pi$
$727$	−24.1163	+	11.6138i	−0.894424	+	0.430732i	−0.0705521	+	0.997508i	$0.522476\pi$
$728$	−12.0447	+	3.71530i	−0.446406	+	0.137698i
$729$	−5.75603	−	25.2188i	−0.213186	−	0.934031i
$730$	−8.84674			−0.327433
$731$	−36.2156	+	14.8887i	−1.33948	+	0.550680i
$732$	−16.8547			−0.622967
$733$	2.71750	+	11.9062i	0.100373	+	0.439764i	0.999995	+	0.00309451i	$0.000985014\pi$
$733$	2.71750	+	11.9062i	0.100373	+	0.439764i	−0.899622	+	0.436670i	$0.856158\pi$
$734$	14.2885	−	4.40741i	0.527397	−	0.162680i
$735$	−0.640101	+	0.308256i	−0.0236105	+	0.0113702i
$736$	−1.09575	+	2.79194i	−0.0403901	+	0.102912i
$737$	−19.6756	−	34.0791i	−0.724759	−	1.25532i
$738$	0.143610	−	0.248740i	0.00528636	−	0.00915625i
$739$	−1.99327	−	2.49948i	−0.0733235	−	0.0919448i	0.743817	−	0.668383i	$-0.233013\pi$
$739$	−1.99327	−	2.49948i	−0.0733235	−	0.0919448i	−0.817140	+	0.576439i	$0.804442\pi$
$740$	−6.72384	+	4.58424i	−0.247173	+	0.168520i
$741$	1.59402	+	0.240261i	0.0585580	+	0.00882619i
$742$	24.0238	+	11.5692i	0.881940	+	0.424720i
$743$	10.4881	−	9.73154i	0.384771	−	0.357015i	−0.463945	−	0.885864i	$-0.653567\pi$
$743$	10.4881	−	9.73154i	0.384771	−	0.357015i	0.848716	+	0.528849i	$0.177376\pi$
$744$	9.84079	−	1.48326i	0.360781	−	0.0543790i
$745$	0.0857837	+	0.0264608i	0.00314287	+	0.000969447i
$746$	−1.79597	+	23.9656i	−0.0657551	+	0.877441i
$747$	−2.33196	+	2.92419i	−0.0853220	+	0.106990i
$748$	−8.62358	−	21.9725i	−0.315309	−	0.803395i
$749$	−1.21436	−	1.12676i	−0.0443717	−	0.0411709i
$750$	1.06420	+	0.725561i	0.0388592	+	0.0264937i
$751$	−0.757974	−	10.1145i	−0.0276589	−	0.369082i	−0.993809	−	0.111102i	$-0.964562\pi$
$751$	−0.757974	−	10.1145i	−0.0276589	−	0.369082i	0.966150	−	0.257980i	$-0.0830569\pi$
$752$	1.62069	−	7.10070i	0.0591004	−	0.258936i
$753$	2.39898	−	10.5106i	0.0874236	−	0.383028i
$754$	−2.91864	−	38.9466i	−0.106291	−	1.41835i
$755$	−1.52173	−	1.03750i	−0.0553815	−	0.0377584i
$756$	10.4081	+	9.65733i	0.378540	+	0.351234i
$757$	−6.62991	−	16.8927i	−0.240968	−	0.613977i	0.758313	−	0.651891i	$-0.226024\pi$
$757$	−6.62991	−	16.8927i	−0.240968	−	0.613977i	−0.999281	+	0.0379139i	$0.987929\pi$
$758$	−17.2058	+	21.5753i	−0.624941	+	0.783652i
$759$	1.14116	−	15.2277i	0.0414215	−	0.552732i
$760$	0.240942	+	0.0743208i	0.00873988	+	0.00269590i
$761$	7.03008	−	1.05961i	0.254840	−	0.0384110i	−0.0203795	−	0.999792i	$-0.506487\pi$
$761$	7.03008	−	1.05961i	0.254840	−	0.0384110i	0.275220	+	0.961381i	$0.411249\pi$
$762$	−16.6340	+	15.4341i	−0.602588	+	0.559120i
$763$	−5.02626	−	2.42052i	−0.181963	−	0.0876287i
$764$	3.93355	+	0.592887i	0.142311	+	0.0214499i
$765$	−6.61633	+	4.51094i	−0.239214	+	0.163093i
$766$	−9.33063	−	11.7002i	−0.337129	−	0.422747i
$767$	9.17897	−	15.8984i	0.331433	−	0.574060i
$768$	0.644004	+	1.11545i	0.0232385	+	0.0402502i
$769$	−0.998058	+	2.54301i	−0.0359909	+	0.0917033i	−0.947739	−	0.319046i	$-0.896638\pi$
$769$	−0.998058	+	2.54301i	−0.0359909	+	0.0917033i	0.911748	+	0.410749i	$0.134733\pi$
$770$	9.04386	−	4.35529i	0.325918	−	0.156954i
$771$	−1.53014	+	0.471986i	−0.0551067	+	0.0169982i
$772$	4.32685	+	18.9572i	0.155727	+	0.682283i
$773$	−40.6674			−1.46271			−0.731353	−	0.681999i	$-0.761111\pi$
$773$	−40.6674			−1.46271			−0.731353	+	0.681999i	$0.761111\pi$
$774$	5.87704	−	6.54145i	0.211246	−	0.235128i
$775$	−7.72662			−0.277548
$776$	−2.25448	−	9.87750i	−0.0809309	−	0.354582i
$777$	−25.4343	+	7.84545i	−0.912451	+	0.281454i
$778$	31.3788	−	15.1112i	1.12499	−	0.541764i
$779$	0.0197298	−	0.0502706i	0.000706892	−	0.00180113i
$780$	−3.19664	−	5.53675i	−0.114458	−	0.198247i
$781$	15.3709	−	26.6232i	0.550015	−	0.952654i
$782$	−11.1665	−	14.0023i	−0.399312	−	0.500721i
$783$	−36.3494	+	24.7826i	−1.29902	+	0.885658i
$784$	0.545434	+	0.0822109i	0.0194798	+	0.00293610i
$785$	6.12590	+	2.95008i	0.218643	+	0.105293i
$786$	18.9050	−	17.5413i	0.674319	−	0.625676i
$787$	−21.9771	+	3.31251i	−0.783398	+	0.118078i	−0.528549	−	0.848903i	$-0.677264\pi$
$787$	−21.9771	+	3.31251i	−0.783398	+	0.118078i	−0.254849	+	0.966981i	$0.582026\pi$
$788$	−5.91764	−	1.82535i	−0.210807	−	0.0650254i
$789$	−1.01205	+	13.5049i	−0.0360300	+	0.480787i
$790$	3.53824	−	4.43681i	0.125885	−	0.157855i
$791$	10.8827	+	27.7286i	0.386943	+	0.985914i
$792$	3.88591	+	3.60560i	0.138080	+	0.128119i
$793$	−53.6678	−	36.5901i	−1.90580	−	1.29935i
$794$	−2.76455	−	36.8903i	−0.0981102	−	1.30919i
$795$	−3.00950	+	13.1855i	−0.106736	+	0.467641i
$796$	−2.22612	+	9.75328i	−0.0789028	+	0.345696i
$797$	−2.14264	−	28.5915i	−0.0758961	−	1.01276i	−0.897013	−	0.442004i	$-0.854268\pi$
$797$	−2.14264	−	28.5915i	−0.0758961	−	1.01276i	0.821117	−	0.570760i	$-0.193351\pi$
$798$	0.681395	+	0.464567i	0.0241211	+	0.0164455i
$799$	31.8812	+	29.5814i	1.12788	+	1.04652i
$800$	−0.365341	−	0.930874i	−0.0129168	−	0.0329114i
$801$	14.6218	−	18.3352i	0.516637	−	0.647842i
$802$	2.42573	−	32.3691i	0.0856554	−	1.14299i
$803$	−33.4168	−	10.3077i	−1.17925	−	0.363751i
$804$	−12.6789	+	1.91103i	−0.447149	+	0.0673968i
$805$	5.58311	−	5.18037i	0.196779	−	0.182584i
$806$	34.5545	+	16.6406i	1.21713	+	0.586140i
$807$	−20.6907	−	3.11863i	−0.728349	−	0.109781i
$808$	8.63210	−	5.88527i	0.303676	−	0.207043i
$809$	−1.46069	−	1.83165i	−0.0513551	−	0.0643973i	0.755491	−	0.655159i	$-0.227399\pi$
$809$	−1.46069	−	1.83165i	−0.0513551	−	0.0643973i	−0.806846	+	0.590762i	$0.798827\pi$
$810$	−1.58926	+	2.75268i	−0.0558408	+	0.0967192i
$811$	12.4530	+	21.5692i	0.437283	+	0.757397i	0.997479	−	0.0709635i	$-0.0226074\pi$
$811$	12.4530	+	21.5692i	0.437283	+	0.757397i	−0.560196	+	0.828360i	$0.689274\pi$
$812$	7.29969	−	18.5993i	0.256169	−	0.652708i
$813$	19.9274	−	9.59651i	0.698883	−	0.336564i
$814$	−30.7393	+	9.48181i	−1.07741	+	0.332337i
$815$	2.76679	+	12.1221i	0.0969164	+	0.424619i
$816$	−7.69113			−0.269243
$817$	0.909357	−	1.38089i	0.0318144	−	0.0483113i
$818$	7.34518			0.256818
$819$	3.76134	+	16.4795i	0.131432	+	0.575841i
$820$	−0.204663	+	0.0631301i	−0.00714713	+	0.00220460i
$821$	−34.8098	+	16.7635i	−1.21487	+	0.585051i	−0.927879	−	0.372881i	$-0.878370\pi$
$821$	−34.8098	+	16.7635i	−1.21487	+	0.585051i	−0.286993	+	0.957933i	$0.592656\pi$
$822$	−3.18308	+	8.11035i	−0.111023	+	0.282881i
$823$	0.439582	+	0.761378i	0.0153229	+	0.0265400i	0.873585	−	0.486671i	$-0.161789\pi$
$823$	0.439582	+	0.761378i	0.0153229	+	0.0265400i	−0.858262	+	0.513211i	$0.828456\pi$
$824$	−8.93715	+	15.4796i	−0.311340	+	0.539257i
$825$	3.17443	+	3.98061i	0.110519	+	0.138587i
$826$	7.75979	−	5.29054i	0.269998	−	0.184081i
$827$	−34.5266	−	5.20405i	−1.20061	−	0.180963i	−0.481870	−	0.876243i	$-0.660042\pi$
$827$	−34.5266	−	5.20405i	−1.20061	−	0.180963i	−0.718739	+	0.695280i	$0.755280\pi$
$828$	3.62381	+	1.74513i	0.125936	+	0.0606476i
$829$	−26.5465	+	24.6316i	−0.921998	+	0.855489i	−0.989837	−	0.142207i	$-0.954580\pi$
$829$	−26.5465	+	24.6316i	−0.921998	+	0.855489i	0.0678386	+	0.997696i	$0.478390\pi$
$830$	2.75787	−	0.415682i	0.0957270	−	0.0144285i
$831$	20.3244	+	6.26924i	0.705044	+	0.217477i
$832$	−0.370938	+	4.94982i	−0.0128600	+	0.171604i
$833$	−2.05362	+	2.57516i	−0.0711538	+	0.0892241i
$834$	4.68825	+	11.9455i	0.162341	+	0.413637i
$835$	14.8412	+	13.7706i	0.513601	+	0.476552i
$836$	0.823516	+	0.561464i	0.0284819	+	0.0194186i
$837$	−3.22847	−	43.0810i	−0.111592	−	1.48910i
$838$	−4.04443	+	17.7198i	−0.139713	+	0.612121i
$839$	−11.3391	+	49.6799i	−0.391470	+	1.71514i	0.268006	+	0.963417i	$0.413635\pi$
$839$	−11.3391	+	49.6799i	−0.391470	+	1.71514i	−0.659477	+	0.751725i	$0.729222\pi$
$840$	−0.244422	−	3.26158i	−0.00843336	−	0.112535i
$841$	27.1913	+	18.5387i	0.937633	+	0.639267i
$842$	2.58895	+	2.40220i	0.0892212	+	0.0827852i
$843$	9.73517	+	24.8048i	0.335297	+	0.854323i
$844$	7.73035	−	9.69355i	0.266090	−	0.333666i
$845$	0.869734	−	11.6058i	0.0299198	−	0.399252i
$846$	−9.33324	−	2.87892i	−0.320884	−	0.0989795i
$847$	11.6148	−	1.75065i	0.399090	−	0.0601531i
$848$	7.69732	−	7.14207i	0.264327	−	0.245260i
$849$	5.64179	+	2.71694i	0.193626	+	0.0932453i
$850$	5.90464	+	0.889981i	0.202527	+	0.0305261i
$851$	−20.1666	+	13.7493i	−0.691302	+	0.471321i
$852$	−6.24540	−	7.83148i	−0.213964	−	0.268302i
$853$	−5.39644	+	9.34691i	−0.184771	+	0.320032i	−0.943499	−	0.331375i	$-0.892488\pi$
$853$	−5.39644	+	9.34691i	−0.184771	+	0.320032i	0.758729	+	0.651407i	$0.225821\pi$
$854$	−16.6149	−	28.7779i	−0.568551	−	0.984759i
$855$	0.123534	−	0.314760i	0.00422478	−	0.0107646i
$856$	−0.587754	+	0.283047i	−0.0200890	+	0.00967436i
$857$	48.5755	−	14.9836i	1.65931	−	0.511828i	0.683405	−	0.730039i	$-0.260498\pi$
$857$	48.5755	−	14.9836i	1.65931	−	0.511828i	0.975902	+	0.218211i	$0.0700220\pi$
$858$	−5.62358	−	24.6385i	−0.191986	−	0.841145i
$859$	42.5479			1.45172			0.725858	−	0.687845i	$-0.241443\pi$
$859$	42.5479			1.45172			0.725858	+	0.687845i	$0.241443\pi$
$860$	−6.53039	+	0.594931i	−0.222685	+	0.0202870i
$861$	−0.700518			−0.0238736
$862$	−0.967268	−	4.23788i	−0.0329453	−	0.144343i
$863$	9.09191	−	2.80448i	0.309492	−	0.0954657i	−0.136118	−	0.990693i	$-0.543463\pi$
$863$	9.09191	−	2.80448i	0.309492	−	0.0954657i	0.445611	+	0.895227i	$0.352987\pi$
$864$	5.03758	−	2.42597i	0.171382	−	0.0825331i
$865$	0.495828	−	1.26335i	0.0168587	−	0.0429552i
$866$	−0.780623	−	1.35208i	−0.0265266	−	0.0459455i
$867$	12.0151	−	20.8107i	0.408054	−	0.706769i
$868$	12.2333	+	15.3401i	0.415227	+	0.520678i
$869$	18.5345	−	12.6366i	0.628740	−	0.428668i
$870$	10.0212	+	1.51045i	0.339751	+	0.0512092i
$871$	−44.5200	−	21.4397i	−1.50850	−	0.726456i
$872$	−1.61044	+	1.49427i	−0.0545363	+	0.0506023i
$873$	−13.4350	+	2.02500i	−0.454705	+	0.0685358i
$874$	0.722649	+	0.222908i	0.0244440	+	0.00753997i
$875$	−0.189767	+	2.53227i	−0.00641531	+	0.0856064i
$876$	−7.10446	+	8.90871i	−0.240038	+	0.300998i
$877$	−5.67296	−	14.4545i	−0.191562	−	0.488093i	0.802532	−	0.596608i	$-0.203485\pi$
$877$	−5.67296	−	14.4545i	−0.191562	−	0.488093i	−0.994095	+	0.108516i	$0.965390\pi$
$878$	13.8391	+	12.8408i	0.467047	+	0.433357i
$879$	−26.0149	−	17.7367i	−0.877462	−	0.598244i
$880$	−0.295402	−	3.94186i	−0.00995800	−	0.132880i
$881$	−2.61642	+	11.4633i	−0.0881493	+	0.386207i	−0.999687	−	0.0250087i	$-0.992039\pi$
$881$	−2.61642	+	11.4633i	−0.0881493	+	0.386207i	0.911538	+	0.411216i	$0.134896\pi$
$882$	0.164601	−	0.721162i	0.00554239	−	0.0242828i
$883$	−2.25422	−	30.0804i	−0.0758604	−	1.01229i	−0.897136	−	0.441755i	$-0.854356\pi$
$883$	−2.25422	−	30.0804i	−0.0758604	−	1.01229i	0.821275	−	0.570532i	$-0.193263\pi$
$884$	−24.4897	−	16.6968i	−0.823676	−	0.561573i
$885$	3.49198	+	3.24008i	0.117382	+	0.108914i
$886$	5.04303	+	12.8494i	0.169424	+	0.431685i
$887$	−16.1663	+	20.2718i	−0.542810	+	0.680662i	−0.975277	−	0.220988i	$-0.929072\pi$
$887$	−16.1663	+	20.2718i	−0.542810	+	0.680662i	0.432467	+	0.901650i	$0.357643\pi$
$888$	−0.783296	+	10.4524i	−0.0262857	+	0.350758i
$889$	−42.7499	−	13.1866i	−1.43378	−	0.442264i
$890$	−17.2924	+	2.60640i	−0.579641	+	0.0873668i
$891$	−9.21037	+	8.54597i	−0.308559	+	0.286301i
$892$	2.84494	+	1.37005i	0.0952558	+	0.0458728i
$893$	−1.81593	−	0.273707i	−0.0607678	−	0.00915927i
$894$	0.0955355	−	0.0651350i	0.00319519	−	0.00217844i
$895$	2.49498	+	3.12861i	0.0833980	+	0.104578i
$896$	−1.26969	+	2.19916i	−0.0424172	+	0.0734688i
$897$	−9.58759	−	16.6062i	−0.320120	−	0.554464i
$898$	−1.65810	+	4.22478i	−0.0553316	+	0.140983i
$899$	−54.7746	+	26.3780i	−1.82683	+	0.879757i
$900$	−1.28146	+	0.395277i	−0.0427152	+	0.0131759i
$901$	13.9524	+	61.1292i	0.464820	+	2.03651i
$902$	−0.846628			−0.0281896
$903$	−20.9838	−	4.43631i	−0.698297	−	0.147631i
$904$	11.7303			0.390145
$905$	2.58347	+	11.3189i	0.0858773	+	0.376253i
$906$	−2.26681	+	0.699217i	−0.0753096	+	0.0232299i
$907$	12.2052	−	5.87772i	0.405267	−	0.195166i	−0.220134	−	0.975470i	$-0.570650\pi$
$907$	12.2052	−	5.87772i	0.405267	−	0.195166i	0.625401	+	0.780303i	$0.284935\pi$
$908$	−7.77889	+	19.8203i	−0.258152	+	0.657759i
$909$	−7.00521	−	12.1334i	−0.232348	−	0.402439i
$910$	6.30234	−	10.9160i	0.208921	−	0.361861i
$911$	10.4911	+	13.1554i	0.347585	+	0.435858i	0.924637	−	0.380849i	$-0.124368\pi$
$911$	10.4911	+	13.1554i	0.347585	+	0.435858i	−0.577052	+	0.816708i	$0.695797\pi$
$912$	0.268332	−	0.182946i	0.00888537	−	0.00605794i
$913$	10.9016	+	1.64316i	0.360791	+	0.0543805i
$914$	−22.3345	−	10.7557i	−0.738759	−	0.355767i
$915$	12.3554	−	11.4641i	0.408456	−	0.378991i
$916$	12.4753	−	1.88034i	0.412194	−	0.0621283i
$917$	48.5862	+	14.9869i	1.60446	+	0.494910i
$918$	−2.49505	+	33.2941i	−0.0823488	+	1.09887i
$919$	3.45652	−	4.33433i	0.114020	−	0.142977i	−0.721546	−	0.692366i	$-0.756568\pi$
$919$	3.45652	−	4.33433i	0.114020	−	0.142977i	0.835566	+	0.549390i	$0.185140\pi$
$920$	−1.09575	−	2.79194i	−0.0361260	−	0.0920475i
$921$	−16.9756	−	15.7511i	−0.559366	−	0.519015i
$922$	−15.6220	−	10.6509i	−0.514482	−	0.350768i
$923$	−2.88479	−	38.4948i	−0.0949539	−	1.26707i
$924$	2.87696	−	12.6048i	0.0946449	−	0.414667i
$925$	1.81085	−	7.93386i	0.0595404	−	0.260864i
$926$	2.07182	+	27.6465i	0.0680842	+	0.908521i
$927$	19.8050	+	13.5028i	0.650482	+	0.443491i
$928$	−5.76786	−	5.35179i	−0.189339	−	0.175681i
$929$	5.43052	+	13.8367i	0.178170	+	0.453969i	0.991861	−	0.127329i	$-0.0406404\pi$
$929$	5.43052	+	13.8367i	0.178170	+	0.453969i	−0.813691	+	0.581298i	$0.802545\pi$
$930$	−6.20494	+	7.78074i	−0.203468	+	0.255141i
$931$	0.0103936	−	0.138692i	0.000340635	−	0.00454546i
$932$	10.4282	+	3.21667i	0.341586	+	0.105365i
$933$	−26.6492	+	4.01672i	−0.872456	+	0.131502i
$934$	9.80541	−	9.09809i	0.320843	−	0.297699i
$935$	21.2666	+	10.2415i	0.695494	+	0.334932i
$936$	6.58215	+	0.992100i	0.215144	+	0.0324278i
$937$	−7.76094	+	5.29132i	−0.253539	+	0.172860i	−0.683420	−	0.730026i	$-0.739508\pi$
$937$	−7.76094	+	5.29132i	−0.253539	+	0.172860i	0.429881	+	0.902886i	$0.358556\pi$
$938$	−15.7614	−	19.7642i	−0.514628	−	0.645323i
$939$	−16.5760	+	28.7105i	−0.540937	+	0.936931i
$940$	3.64165	+	6.30753i	0.118778	+	0.205729i
$941$	3.75465	−	9.56669i	0.122398	−	0.311865i	−0.856522	−	0.516111i	$-0.827379\pi$
$941$	3.75465	−	9.56669i	0.122398	−	0.311865i	0.978920	+	0.204246i	$0.0654743\pi$
$942$	7.89020	−	3.79972i	0.257077	−	0.123802i
$943$	−0.613838	+	0.189344i	−0.0199893	+	0.00616589i
$944$	−0.822980	−	3.60571i	−0.0267857	−	0.117356i
$945$	−14.1984			−0.461873
$946$	−25.3604	−	5.36161i	−0.824539	−	0.174321i
$947$	30.6050			0.994527			0.497264	−	0.867599i	$-0.334338\pi$
$947$	30.6050			0.994527			0.497264	+	0.867599i	$0.334338\pi$
$948$	−1.62647	−	7.12604i	−0.0528254	−	0.231443i
$949$	−41.9617	+	12.9435i	−1.36213	+	0.420163i
$950$	−0.227174	+	0.109401i	−0.00737050	+	0.00354944i
$951$	10.6698	−	27.1863i	0.345993	−	0.881577i
$952$	−7.58172	−	13.1319i	−0.245725	−	0.425608i
$953$	16.5454	−	28.6575i	0.535959	−	0.928308i	−0.463158	−	0.886276i	$-0.653284\pi$
$953$	16.5454	−	28.6575i	0.535959	−	0.928308i	0.999116	−	0.0420317i	$-0.0133830\pi$
$954$	−8.77960	−	11.0093i	−0.284250	−	0.356438i
$955$	−3.28676	+	2.24088i	−0.106357	+	0.0725131i
$956$	19.1281	+	2.88310i	0.618648	+	0.0932462i
$957$	36.0932	+	17.3816i	1.16673	+	0.561867i
$958$	14.5257	−	13.4778i	0.469303	−	0.435450i
$959$	−16.9855	+	2.56015i	−0.548491	+	0.0826717i
$960$	−1.23079	−	0.379647i	−0.0397234	−	0.0122531i
$961$	2.14480	−	28.6204i	0.0691872	−	0.923238i
$962$	−25.1853	+	31.5814i	−0.812006	+	1.01822i
$963$	0.319613	+	0.814361i	0.0102994	+	0.0262424i
$964$	−14.8501	−	13.7789i	−0.478291	−	0.443789i
$965$	−16.0659	−	10.9536i	−0.517181	−	0.352608i
$966$	−0.733086	−	9.78236i	−0.0235867	−	0.314742i
$967$	5.53685	−	24.2585i	0.178053	−	0.780101i	−0.804475	−	0.593987i	$-0.797553\pi$
$967$	5.53685	−	24.2585i	0.178053	−	0.780101i	0.982528	−	0.186115i	$-0.0595896\pi$
$968$	1.02928	−	4.50959i	0.0330824	−	0.144944i
$969$	0.144922	+	1.93385i	0.00465556	+	0.0621242i
$970$	8.37105	+	5.70729i	0.268778	+	0.183250i
$971$	−28.1288	−	26.0997i	−0.902696	−	0.837580i	0.0846089	−	0.996414i	$-0.473036\pi$
$971$	−28.1288	−	26.0997i	−0.902696	−	0.837580i	−0.987305	+	0.158834i	$0.949226\pi$
$972$	−4.63249	−	11.8034i	−0.148587	−	0.378594i
$973$	−15.7743	+	19.7803i	−0.505699	+	0.634127i
$974$	1.80866	−	24.1349i	0.0579532	−	0.773331i
$975$	6.10925	+	1.88445i	0.195653	+	0.0603509i
$976$	−12.9397	+	1.95035i	−0.414190	+	0.0624290i
$977$	−20.9150	+	19.4063i	−0.669130	+	0.620862i	−0.939765	−	0.341820i	$-0.888957\pi$
$977$	−20.9150	+	19.4063i	−0.669130	+	0.620862i	0.270635	+	0.962682i	$0.412766\pi$
$978$	14.4289	+	6.94860i	0.461386	+	0.222192i
$979$	−68.3553	−	10.3029i	−2.18464	−	0.329282i
$980$	−0.455749	+	0.310724i	−0.0145584	+	0.00992573i
$981$	1.83687	+	2.30336i	0.0586468	+	0.0735408i
$982$	17.0343	−	29.5042i	0.543586	−	0.941518i
$983$	18.1294	+	31.4011i	0.578239	+	1.00154i	0.995681	+	0.0928354i	$0.0295930\pi$
$983$	18.1294	+	31.4011i	0.578239	+	1.00154i	−0.417443	+	0.908703i	$0.637074\pi$
$984$	−0.100784	+	0.256794i	−0.00321288	+	0.00818628i
$985$	5.57949	−	2.68694i	0.177777	−	0.0856130i
$986$	44.8968	−	13.8488i	1.42980	−	0.441036i
$987$	5.30083	+	23.2245i	0.168727	+	0.739243i
$988$	1.25157			0.0398177
$989$	−19.5864	+	1.78436i	−0.622811	+	0.0567393i
$990$	−5.30100			−0.168477
$991$	−9.59082	−	42.0201i	−0.304662	−	1.33481i	−0.863002	−	0.505200i	$-0.831419\pi$
$991$	−9.59082	−	42.0201i	−0.304662	−	1.33481i	0.558340	−	0.829612i	$-0.311439\pi$
$992$	7.38335	−	2.27746i	0.234422	−	0.0723095i
$993$	19.8970	−	9.58191i	0.631413	−	0.304073i
$994$	7.21501	−	18.3835i	0.228846	−	0.583091i
$995$	−5.00205	−	8.66381i	−0.158576	−	0.274661i
$996$	1.79614	−	3.11101i	0.0569129	−	0.0985760i
$997$	2.97294	+	3.72795i	0.0941540	+	0.118065i	0.826677	−	0.562677i	$-0.190229\pi$
$997$	2.97294	+	3.72795i	0.0941540	+	0.118065i	−0.732523	+	0.680743i	$0.761657\pi$
$998$	2.45514	−	1.67389i	0.0777162	−	0.0529860i
$999$	44.9931	+	6.78161i	1.42352	+	0.214561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.361.2	yes	48
43.38	even	21	inner	430.2.q.c.81.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.81.2	✓	48	43.38	even	21	inner
430.2.q.c.361.2	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 + 0.974928i) q^{2} +(-1.23079 + 0.379647i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(0.365341 - 0.930874i) q^{5} +(-0.644004 - 1.11545i) q^{6} +(1.26969 - 2.19916i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-1.10802 + 0.755432i) q^{9} +O(q^{10})\)	\(q+(0.222521 + 0.974928i) q^{2} +(-1.23079 + 0.379647i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(0.365341 - 0.930874i) q^{5} +(-0.644004 - 1.11545i) q^{6} +(1.26969 - 2.19916i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-1.10802 + 0.755432i) q^{9} +(0.988831 + 0.149042i) q^{10} +(3.56146 + 1.71511i) q^{11} +(0.944177 - 0.876068i) q^{12} +(4.90826 - 0.739801i) q^{13} +(2.42655 + 0.748493i) q^{14} +(-0.0962529 + 1.28441i) q^{15} +(0.623490 - 0.781831i) q^{16} +(2.18157 + 5.55856i) q^{17} +(-0.983049 - 0.912136i) q^{18} +(-0.208331 - 0.142038i) q^{19} +(0.0747301 + 0.997204i) q^{20} +(-0.727806 + 3.18873i) q^{21} +(-0.879607 + 3.85381i) q^{22} +(0.224135 + 2.99088i) q^{23} +(1.06420 + 0.725561i) q^{24} +(-0.733052 - 0.680173i) q^{25} +(1.81344 + 4.62058i) q^{26} +(3.48611 - 4.37145i) q^{27} +(-0.189767 + 2.53227i) q^{28} +(-7.51871 - 2.31922i) q^{29} +(-1.27362 + 0.191968i) q^{30} +(5.66401 - 5.25544i) q^{31} +(0.900969 + 0.433884i) q^{32} +(-5.03452 - 0.758832i) q^{33} +(-4.93375 + 3.36377i) q^{34} +(-1.58327 - 1.98536i) q^{35} +(0.670518 - 1.16137i) q^{36} +(4.06894 + 7.04762i) q^{37} +(0.0921186 - 0.234714i) q^{38} +(-5.76015 + 2.77394i) q^{39} +(-0.955573 + 0.294755i) q^{40} +(0.0476591 + 0.208808i) q^{41} -3.27073 q^{42} +(0.105251 + 6.55659i) q^{43} -3.95292 q^{44} +(0.298409 + 1.30741i) q^{45} +(-2.86602 + 0.884049i) q^{46} +(6.56203 - 3.16011i) q^{47} +(-0.470562 + 1.19897i) q^{48} +(0.275797 + 0.477695i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-4.79534 - 6.01317i) q^{51} +(-4.10120 + 2.79615i) q^{52} +(10.3831 + 1.56500i) q^{53} +(5.03758 + 2.42597i) q^{54} +(2.89769 - 2.68867i) q^{55} +(-2.51101 + 0.378474i) q^{56} +(0.310335 + 0.0957257i) q^{57} +(0.587997 - 7.84628i) q^{58} +(2.30594 - 2.89155i) q^{59} +(-0.470562 - 1.19897i) q^{60} +(-9.59261 - 8.90064i) q^{61} +(6.38403 + 4.35256i) q^{62} +(0.254485 + 3.39587i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(1.10453 - 4.83925i) q^{65} +(-0.380480 - 5.07715i) q^{66} +(-8.22517 - 5.60783i) q^{67} +(-4.37730 - 4.06154i) q^{68} +(-1.41134 - 3.59604i) q^{69} +(1.58327 - 1.98536i) q^{70} +(0.581176 - 7.75526i) q^{71} +(1.28146 + 0.395277i) q^{72} +(-8.74793 + 1.31854i) q^{73} +(-5.96550 + 5.53517i) q^{74} +(1.16046 + 0.558846i) q^{75} +(0.249328 + 0.0375801i) q^{76} +(8.29372 - 5.65456i) q^{77} +(-3.98615 - 4.99847i) q^{78} +(2.83745 - 4.91460i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-1.16124 + 2.95880i) q^{81} +(-0.192968 + 0.0929284i) q^{82} +(2.66511 - 0.822078i) q^{83} +(-0.727806 - 3.18873i) q^{84} +5.97134 q^{85} +(-6.36879 + 1.56159i) q^{86} +10.1344 q^{87} +(-0.879607 - 3.85381i) q^{88} +(-16.7107 + 5.15458i) q^{89} +(-1.20823 + 0.581854i) q^{90} +(4.60501 - 11.7334i) q^{91} +(-1.49963 - 2.59744i) q^{92} +(-4.97597 + 8.61864i) q^{93} +(4.54107 + 5.69432i) q^{94} +(-0.208331 + 0.142038i) q^{95} +(-1.27362 - 0.191968i) q^{96} +(9.12818 + 4.39590i) q^{97} +(-0.404348 + 0.375180i) q^{98} +(-5.24180 + 0.790074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more