LMFDB - Embedded newform 349.2.k.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(3,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(174))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("349.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.k (of order $174$, degree $56$, 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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$1624$
Relative dimension:	$29$ over $\Q(\zeta_{174})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{174}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	349.3
Dual form			349.2.k.a.233.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03001 - 0.485425i) q^{2} +(-0.306098 + 0.0558749i) q^{3} +(2.10166 + 1.06608i) q^{4} +(0.440893 + 3.46988i) q^{5} +(0.648506 + 0.0351610i) q^{6} +(2.50769 + 0.0452815i) q^{7} +(-0.567264 - 0.481838i) q^{8} +(-2.71595 + 1.02571i) q^{9} +O(q^{10})$	\(q+(-2.03001 - 0.485425i) q^{2} +(-0.306098 + 0.0558749i) q^{3} +(2.10166 + 1.06608i) q^{4} +(0.440893 + 3.46988i) q^{5} +(0.648506 + 0.0351610i) q^{6} +(2.50769 + 0.0452815i) q^{7} +(-0.567264 - 0.481838i) q^{8} +(-2.71595 + 1.02571i) q^{9} +(0.789345 - 7.25791i) q^{10} +(-0.335804 + 1.52557i) q^{11} +(-0.702882 - 0.208894i) q^{12} +(-1.27228 - 1.24952i) q^{13} +(-5.06865 - 1.30922i) q^{14} +(-0.328836 - 1.03749i) q^{15} +(-1.86643 - 2.54951i) q^{16} +(-0.891437 - 1.04948i) q^{17} +(6.01132 - 0.763817i) q^{18} +(-0.630772 - 0.0917483i) q^{19} +(-2.77254 + 7.76253i) q^{20} +(-0.770129 + 0.126256i) q^{21} +(1.42224 - 2.93393i) q^{22} +(-4.26523 + 4.34294i) q^{23} +(0.200561 + 0.115794i) q^{24} +(-7.00453 + 1.80925i) q^{25} +(1.97620 + 3.15413i) q^{26} +(1.57388 - 0.946975i) q^{27} +(5.22204 + 2.76855i) q^{28} +(4.41861 - 1.31319i) q^{29} +(0.163918 + 2.26574i) q^{30} +(-2.96251 + 5.58789i) q^{31} +(3.12713 + 7.45421i) q^{32} +(0.0175478 - 0.485739i) q^{33} +(1.30018 + 2.56319i) q^{34} +(0.948501 + 8.72132i) q^{35} +(-6.80149 - 0.739707i) q^{36} +(-0.362744 - 1.30649i) q^{37} +(1.23594 + 0.492443i) q^{38} +(0.459260 + 0.311386i) q^{39} +(1.42182 - 2.18078i) q^{40} +(-0.460451 + 0.542084i) q^{41} +(1.62466 + 0.117538i) q^{42} +(1.66096 + 1.51740i) q^{43} +(-2.33212 + 2.84825i) q^{44} +(-4.75653 - 8.97178i) q^{45} +(10.7666 - 6.74578i) q^{46} +(-1.70995 + 5.07495i) q^{47} +(0.713764 + 0.676113i) q^{48} +(-0.708996 - 0.0256132i) q^{49} +(15.0975 - 0.272618i) q^{50} +(0.331507 + 0.271435i) q^{51} +(-1.34183 - 3.98241i) q^{52} +(-5.27972 + 11.4119i) q^{53} +(-3.65469 + 1.15837i) q^{54} +(-5.44161 - 0.492583i) q^{55} +(-1.40070 - 1.23399i) q^{56} +(0.198205 - 0.00716033i) q^{57} +(-9.60728 + 0.520891i) q^{58} +(-0.537688 - 2.94560i) q^{59} +(0.414938 - 2.53101i) q^{60} +(-1.79784 - 1.89796i) q^{61} +(8.72643 - 9.90540i) q^{62} +(-6.85720 + 2.44918i) q^{63} +(-1.70729 - 10.4140i) q^{64} +(3.77473 - 4.96557i) q^{65} +(-0.271412 + 0.977537i) q^{66} +(-2.26208 + 5.67740i) q^{67} +(-0.754674 - 3.15599i) q^{68} +(1.06292 - 1.56769i) q^{69} +(2.30808 - 18.1648i) q^{70} +(2.07620 - 11.3740i) q^{71} +(2.03489 + 0.726800i) q^{72} +(4.99947 - 2.76732i) q^{73} +(0.102174 + 2.82827i) q^{74} +(2.04298 - 0.945185i) q^{75} +(-1.22786 - 0.865274i) q^{76} +(-0.911172 + 3.81046i) q^{77} +(-0.781149 - 0.855054i) q^{78} +(-2.92816 - 6.32911i) q^{79} +(8.02357 - 7.60033i) q^{80} +(6.10635 - 5.37956i) q^{81} +(1.19786 - 0.876923i) q^{82} +(8.60289 + 3.60901i) q^{83} +(-1.75315 - 0.555667i) q^{84} +(3.24854 - 3.55589i) q^{85} +(-2.63519 - 3.88662i) q^{86} +(-1.27915 + 0.648855i) q^{87} +(0.925570 - 0.703600i) q^{88} +(-0.0380208 + 0.0184308i) q^{89} +(5.30070 + 20.5218i) q^{90} +(-3.13391 - 3.19101i) q^{91} +(-13.5940 + 4.58034i) q^{92} +(0.594596 - 1.87597i) q^{93} +(5.93473 - 9.47216i) q^{94} +(0.0402520 - 2.22915i) q^{95} +(-1.37371 - 2.10699i) q^{96} +(18.3862 + 2.33621i) q^{97} +(1.42684 + 0.396159i) q^{98} +(-0.652772 - 4.48782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9}+O(q^{10}) $ 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9	\( 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9} - 58 q^{10} - 58 q^{11} - 57 q^{12} - 55 q^{13} - 48 q^{14} - 59 q^{15} - 29 q^{16} - 48 q^{17} + 43 q^{18} + 67 q^{19} - 58 q^{20} + 58 q^{21} - 55 q^{22} - 41 q^{23} - 39 q^{24} - 29 q^{25} - 112 q^{26} - 76 q^{27} - 58 q^{28} - 56 q^{29} - 67 q^{30} - 90 q^{31} - 67 q^{32} - 46 q^{33} + 5 q^{34} - 82 q^{36} + 45 q^{37} - 58 q^{38} - 58 q^{39} - 112 q^{40} + 10 q^{41} + 305 q^{42} - 13 q^{43} + 40 q^{44} - 56 q^{45} - 85 q^{46} - 58 q^{47} - 122 q^{48} - 93 q^{49} - 441 q^{50} - 160 q^{51} + 58 q^{52} - 58 q^{53} - 85 q^{54} + 34 q^{55} - 69 q^{56} - 29 q^{57} - 58 q^{58} - 40 q^{59} + 522 q^{60} + 87 q^{61} - 49 q^{62} - 37 q^{63} + 335 q^{64} - 58 q^{65} - 565 q^{66} - 116 q^{67} - 58 q^{68} + 16 q^{69} - 98 q^{70} - 34 q^{71} + 44 q^{72} - 52 q^{73} - 204 q^{74} - 95 q^{76} - 54 q^{77} + 439 q^{78} - 58 q^{79} - 192 q^{80} - 209 q^{81} - 79 q^{82} + 162 q^{83} + 330 q^{84} - 192 q^{85} + 126 q^{86} - 190 q^{87} - 8 q^{88} + 345 q^{89} - 46 q^{90} - 30 q^{91} + 62 q^{92} - 89 q^{93} - 87 q^{94} - 350 q^{95} + 990 q^{96} - 43 q^{97} - 464 q^{98} - 97 q^{99}+O(q^{100}) \) 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9 - 58 * q^10 - 58 * q^11 - 57 * q^12 - 55 * q^13 - 48 * q^14 - 59 * q^15 - 29 * q^16 - 48 * q^17 + 43 * q^18 + 67 * q^19 - 58 * q^20 + 58 * q^21 - 55 * q^22 - 41 * q^23 - 39 * q^24 - 29 * q^25 - 112 * q^26 - 76 * q^27 - 58 * q^28 - 56 * q^29 - 67 * q^30 - 90 * q^31 - 67 * q^32 - 46 * q^33 + 5 * q^34 - 82 * q^36 + 45 * q^37 - 58 * q^38 - 58 * q^39 - 112 * q^40 + 10 * q^41 + 305 * q^42 - 13 * q^43 + 40 * q^44 - 56 * q^45 - 85 * q^46 - 58 * q^47 - 122 * q^48 - 93 * q^49 - 441 * q^50 - 160 * q^51 + 58 * q^52 - 58 * q^53 - 85 * q^54 + 34 * q^55 - 69 * q^56 - 29 * q^57 - 58 * q^58 - 40 * q^59 + 522 * q^60 + 87 * q^61 - 49 * q^62 - 37 * q^63 + 335 * q^64 - 58 * q^65 - 565 * q^66 - 116 * q^67 - 58 * q^68 + 16 * q^69 - 98 * q^70 - 34 * q^71 + 44 * q^72 - 52 * q^73 - 204 * q^74 - 95 * q^76 - 54 * q^77 + 439 * q^78 - 58 * q^79 - 192 * q^80 - 209 * q^81 - 79 * q^82 + 162 * q^83 + 330 * q^84 - 192 * q^85 + 126 * q^86 - 190 * q^87 - 8 * q^88 + 345 * q^89 - 46 * q^90 - 30 * q^91 + 62 * q^92 - 89 * q^93 - 87 * q^94 - 350 * q^95 + 990 * q^96 - 43 * q^97 - 464 * q^98 - 97 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{174}\right)$

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 $

$2$	−2.03001	−	0.485425i	−1.43544	−	0.343247i	−0.560769	−	0.827972i	$-0.689494\pi$
$2$	−2.03001	−	0.485425i	−1.43544	−	0.343247i	−0.874667	+	0.484725i	$0.838920\pi$
$3$	−0.306098	+	0.0558749i	−0.176726	+	0.0322594i	−0.267209	−	0.963639i	$-0.586101\pi$
$3$	−0.306098	+	0.0558749i	−0.176726	+	0.0322594i	0.0904831	+	0.995898i	$0.471159\pi$
$4$	2.10166	+	1.06608i	1.05083	+	0.533038i
$5$	0.440893	+	3.46988i	0.197174	+	1.55178i	0.716737	+	0.697344i	$0.245635\pi$
$5$	0.440893	+	3.46988i	0.197174	+	1.55178i	−0.519564	+	0.854432i	$0.673905\pi$
$6$	0.648506	+	0.0351610i	0.264752	+	0.0143544i
$7$	2.50769	+	0.0452815i	0.947816	+	0.0171148i	0.489805	−	0.871832i	$-0.337068\pi$
$7$	2.50769	+	0.0452815i	0.947816	+	0.0171148i	0.458011	+	0.888947i	$0.348562\pi$
$8$	−0.567264	−	0.481838i	−0.200558	−	0.170356i
$9$	−2.71595	+	1.02571i	−0.905316	+	0.341904i
$10$	0.789345	−	7.25791i	0.249613	−	2.29515i
$11$	−0.335804	+	1.52557i	−0.101249	+	0.459978i	0.898529	+	0.438914i	$0.144637\pi$
$11$	−0.335804	+	1.52557i	−0.101249	+	0.459978i	−0.999778	+	0.0210645i	$0.993294\pi$
$12$	−0.702882	−	0.208894i	−0.202905	−	0.0603024i
$13$	−1.27228	−	1.24952i	−0.352868	−	0.346554i	0.502498	−	0.864579i	$-0.332415\pi$
$13$	−1.27228	−	1.24952i	−0.352868	−	0.346554i	−0.855366	+	0.518025i	$0.826667\pi$
$14$	−5.06865	−	1.30922i	−1.35465	−	0.349903i
$15$	−0.328836	−	1.03749i	−0.0849050	−	0.267878i
$16$	−1.86643	−	2.54951i	−0.466607	−	0.637377i
$17$	−0.891437	−	1.04948i	−0.216205	−	0.254537i	0.643358	−	0.765565i	$-0.277541\pi$
$17$	−0.891437	−	1.04948i	−0.216205	−	0.254537i	−0.859564	+	0.511029i	$0.829265\pi$
$18$	6.01132	−	0.763817i	1.41688	−	0.180033i
$19$	−0.630772	−	0.0917483i	−0.144709	−	0.0210485i	0.0711995	−	0.997462i	$-0.477317\pi$
$19$	−0.630772	−	0.0917483i	−0.144709	−	0.0210485i	−0.215909	+	0.976414i	$0.569271\pi$
$20$	−2.77254	+	7.76253i	−0.619958	+	1.73575i
$21$	−0.770129	+	0.126256i	−0.168056	+	0.0275514i
$22$	1.42224	−	2.93393i	0.303222	−	0.625515i
$23$	−4.26523	+	4.34294i	−0.889362	+	0.905566i	−0.996056	−	0.0887259i	$-0.971720\pi$
$23$	−4.26523	+	4.34294i	−0.889362	+	0.905566i	0.106694	+	0.994292i	$0.465973\pi$
$24$	0.200561	+	0.115794i	0.0409394	+	0.0236364i
$25$	−7.00453	+	1.80925i	−1.40091	+	0.361849i
$26$	1.97620	+	3.15413i	0.387565	+	0.618576i
$27$	1.57388	−	0.946975i	0.302894	−	0.182245i
$28$	5.22204	+	2.76855i	0.986872	+	0.523206i
$29$	4.41861	−	1.31319i	0.820514	−	0.243853i	0.152787	−	0.988259i	$-0.451175\pi$
$29$	4.41861	−	1.31319i	0.820514	−	0.243853i	0.667728	+	0.744406i	$0.267267\pi$
$30$	0.163918	+	2.26574i	0.0299272	+	0.413665i
$31$	−2.96251	+	5.58789i	−0.532082	+	1.00361i	0.461134	+	0.887331i	$0.347443\pi$
$31$	−2.96251	+	5.58789i	−0.532082	+	1.00361i	−0.993216	+	0.116283i	$0.962902\pi$
$32$	3.12713	+	7.45421i	0.552803	+	1.31773i
$33$	0.0175478	−	0.485739i	0.00305468	−	0.0845563i
$34$	1.30018	+	2.56319i	0.222980	+	0.439583i
$35$	0.948501	+	8.72132i	0.160326	+	1.47417i
$36$	−6.80149	−	0.739707i	−1.13358	−	0.123284i
$37$	−0.362744	−	1.30649i	−0.0596348	−	0.214785i	0.927729	−	0.373254i	$-0.121758\pi$
$37$	−0.362744	−	1.30649i	−0.0596348	−	0.214785i	−0.987364	+	0.158469i	$0.949344\pi$
$38$	1.23594	+	0.492443i	0.200496	+	0.0798848i
$39$	0.459260	+	0.311386i	0.0735405	+	0.0498617i
$40$	1.42182	−	2.18078i	0.224809	−	0.344811i
$41$	−0.460451	+	0.542084i	−0.0719103	+	0.0846593i	−0.796941	−	0.604057i	$-0.793550\pi$
$41$	−0.460451	+	0.542084i	−0.0719103	+	0.0846593i	0.725031	+	0.688717i	$0.241826\pi$
$42$	1.62466	+	0.117538i	0.250690	+	0.0181365i
$43$	1.66096	+	1.51740i	0.253295	+	0.231402i	0.791130	−	0.611648i	$-0.209493\pi$
$43$	1.66096	+	1.51740i	0.253295	+	0.231402i	−0.537835	+	0.843050i	$0.680758\pi$
$44$	−2.33212	+	2.84825i	−0.351581	+	0.429390i
$45$	−4.75653	−	8.97178i	−0.709062	−	1.33743i
$46$	10.7666	−	6.74578i	1.58745	−	0.994610i
$47$	−1.70995	+	5.07495i	−0.249422	+	0.740258i	0.747672	+	0.664069i	$0.231172\pi$
$47$	−1.70995	+	5.07495i	−0.249422	+	0.740258i	−0.997093	+	0.0761889i	$0.975725\pi$
$48$	0.713764	+	0.676113i	0.103023	+	0.0975885i
$49$	−0.708996	−	0.0256132i	−0.101285	−	0.00365902i
$50$	15.0975	−	0.272618i	2.13511	−	0.0385540i
$51$	0.331507	+	0.271435i	0.0464203	+	0.0380085i
$52$	−1.34183	−	3.98241i	−0.186078	−	0.552261i
$53$	−5.27972	+	11.4119i	−0.725225	+	1.56755i	0.0949812	+	0.995479i	$0.469721\pi$
$53$	−5.27972	+	11.4119i	−0.725225	+	1.56755i	−0.820206	+	0.572068i	$0.806141\pi$
$54$	−3.65469	+	1.15837i	−0.497340	+	0.157634i
$55$	−5.44161	−	0.492583i	−0.733746	−	0.0664199i
$56$	−1.40070	−	1.23399i	−0.187177	−	0.164898i
$57$	0.198205	−	0.00716033i	0.0262528	−	0.000948409i
$58$	−9.60728	+	0.520891i	−1.26150	+	0.0683964i
$59$	−0.537688	−	2.94560i	−0.0700010	−	0.383485i	−0.999878	−	0.0156146i	$-0.995030\pi$
$59$	−0.537688	−	2.94560i	−0.0700010	−	0.383485i	0.929877	−	0.367870i	$-0.119913\pi$
$60$	0.414938	−	2.53101i	0.0535683	−	0.326752i
$61$	−1.79784	−	1.89796i	−0.230190	−	0.243009i	0.600661	−	0.799504i	$-0.294904\pi$
$61$	−1.79784	−	1.89796i	−0.230190	−	0.243009i	−0.830851	+	0.556496i	$0.812146\pi$
$62$	8.72643	−	9.90540i	1.10826	−	1.25799i
$63$	−6.85720	+	2.44918i	−0.863925	+	0.308568i
$64$	−1.70729	−	10.4140i	−0.213412	−	1.30175i
$65$	3.77473	−	4.96557i	0.468197	−	0.615903i
$66$	−0.271412	+	0.977537i	−0.0334085	+	0.120327i
$67$	−2.26208	+	5.67740i	−0.276357	+	0.693605i	0.723637	+	0.690181i	$0.242469\pi$
$67$	−2.26208	+	5.67740i	−0.276357	+	0.693605i	−0.999994	+	0.00342380i	$0.998910\pi$
$68$	−0.754674	−	3.15599i	−0.0915177	−	0.382720i
$69$	1.06292	−	1.56769i	0.127960	−	0.188727i
$70$	2.30808	−	18.1648i	0.275868	−	2.17111i
$71$	2.07620	−	11.3740i	0.246400	−	1.34985i	−0.592504	−	0.805568i	$-0.701861\pi$
$71$	2.07620	−	11.3740i	0.246400	−	1.34985i	0.838904	−	0.544280i	$-0.183197\pi$
$72$	2.03489	+	0.726800i	0.239814	+	0.0856542i
$73$	4.99947	−	2.76732i	0.585143	−	0.323890i	−0.163832	−	0.986488i	$-0.552385\pi$
$73$	4.99947	−	2.76732i	0.585143	−	0.323890i	0.748975	+	0.662598i	$0.230546\pi$
$74$	0.102174	+	2.82827i	0.0118775	+	0.328780i
$75$	2.04298	−	0.945185i	0.235903	−	0.109141i
$76$	−1.22786	−	0.865274i	−0.140845	−	0.0992538i
$77$	−0.911172	+	3.81046i	−0.103838	+	0.434242i
$78$	−0.781149	−	0.855054i	−0.0884478	−	0.0968158i
$79$	−2.92816	−	6.32911i	−0.329444	−	0.712081i	0.670101	−	0.742270i	$-0.266251\pi$
$79$	−2.92816	−	6.32911i	−0.329444	−	0.712081i	−0.999544	+	0.0301895i	$0.990389\pi$
$80$	8.02357	−	7.60033i	0.897063	−	0.849743i
$81$	6.10635	−	5.37956i	0.678484	−	0.597729i
$82$	1.19786	−	0.876923i	0.132282	−	0.0968400i
$83$	8.60289	+	3.60901i	0.944290	+	0.396141i	0.804441	−	0.594032i	$-0.202465\pi$
$83$	8.60289	+	3.60901i	0.944290	+	0.396141i	0.139848	+	0.990173i	$0.455338\pi$
$84$	−1.75315	−	0.555667i	−0.191284	−	0.0606282i
$85$	3.24854	−	3.55589i	0.352354	−	0.385690i
$86$	−2.63519	−	3.88662i	−0.284160	−	0.419105i
$87$	−1.27915	+	0.648855i	−0.137140	+	0.0695645i
$88$	0.925570	−	0.703600i	0.0986661	−	0.0750040i
$89$	−0.0380208	+	0.0184308i	−0.00403019	+	0.00195366i	−0.438220	−	0.898868i	$-0.644391\pi$
$89$	−0.0380208	+	0.0184308i	−0.00403019	+	0.00195366i	0.434190	+	0.900821i	$0.357035\pi$
$90$	5.30070	+	20.5218i	0.558743	+	2.16318i
$91$	−3.13391	−	3.19101i	−0.328523	−	0.334508i
$92$	−13.5940	+	4.58034i	−1.41727	+	0.477534i
$93$	0.594596	−	1.87597i	0.0616568	−	0.194529i
$94$	5.93473	−	9.47216i	0.612120	−	0.976978i
$95$	0.0402520	−	2.22915i	0.00412977	−	0.228706i
$96$	−1.37371	−	2.10699i	−0.140204	−	0.215044i
$97$	18.3862	+	2.33621i	1.86683	+	0.237206i	0.976100	−	0.217321i	$-0.0697318\pi$
$97$	18.3862	+	2.33621i	1.86683	+	0.237206i	0.890733	+	0.454527i	$0.150192\pi$
$98$	1.42684	+	0.396159i	0.144132	+	0.0400181i
$99$	−0.652772	−	4.48782i	−0.0656060	−	0.451043i
$100$	−16.6500	−	3.66493i	−1.66500	−	0.366493i
$101$	−12.4410	+	4.95693i	−1.23792	+	0.493233i	−0.894973	−	0.446121i	$-0.852805\pi$
$101$	−12.4410	+	4.95693i	−1.23792	+	0.493233i	−0.342949	+	0.939354i	$0.611426\pi$
$102$	−0.541202	−	0.711939i	−0.0535870	−	0.0704924i
$103$	−9.33227	+	9.85195i	−0.919536	+	0.970742i	−0.999661	−	0.0260430i	$-0.991709\pi$
$103$	−9.33227	+	9.85195i	−0.919536	+	0.970742i	0.0801253	+	0.996785i	$0.474468\pi$
$104$	0.119655	+	1.32184i	0.0117332	+	0.129617i
$105$	−0.777638	−	2.61658i	−0.0758897	−	0.255352i
$106$	16.2575	−	20.6034i	1.57907	−	2.00118i
$107$	2.60823	+	2.05807i	0.252147	+	0.198962i	0.737482	−	0.675367i	$-0.236015\pi$
$107$	2.60823	+	2.05807i	0.252147	+	0.198962i	−0.485334	+	0.874329i	$0.661302\pi$
$108$	4.31732	−	0.312342i	0.415434	−	0.0300552i
$109$	11.3631	−	15.5218i	1.08839	−	1.48672i	0.230372	−	0.973103i	$-0.426006\pi$
$109$	11.3631	−	15.5218i	1.08839	−	1.48672i	0.858018	−	0.513619i	$-0.171696\pi$
$110$	10.8074	+	3.64144i	1.03045	+	0.347198i
$111$	0.184035	+	0.379645i	0.0174678	+	0.0360343i
$112$	−4.56497	−	6.47788i	−0.431349	−	0.612102i
$113$	−1.82134	+	6.12843i	−0.171338	+	0.576514i	0.828525	+	0.559952i	$0.189180\pi$
$113$	−1.82134	+	6.12843i	−0.171338	+	0.576514i	−0.999863	+	0.0165625i	$0.994728\pi$
$114$	−0.405834	−	0.0816779i	−0.0380098	−	0.00764984i
$115$	−16.9500	−	12.8850i	−1.58059	−	1.20154i
$116$	10.6864	+	1.95068i	0.992205	+	0.181116i
$117$	4.73710	+	2.08863i	0.437945	+	0.193094i
$118$	−0.338357	+	6.24062i	−0.0311482	+	0.574496i
$119$	−2.18792	−	2.67214i	−0.200567	−	0.244954i
$120$	−0.313365	+	0.746975i	−0.0286062	+	0.0681892i
$121$	7.76872	+	3.59419i	0.706247	+	0.326745i
$122$	2.72832	+	4.72559i	0.247011	+	0.427835i
$123$	0.110654	−	0.191659i	0.00997735	−	0.0172813i
$124$	−12.1833	+	8.58559i	−1.09409	+	0.771009i
$125$	−2.89281	−	7.26042i	−0.258741	−	0.649391i
$126$	15.1091	−	1.64321i	1.34602	−	0.146389i
$127$	3.85418	+	17.5097i	0.342003	+	1.55374i	0.762832	+	0.646596i	$0.223808\pi$
$127$	3.85418	+	17.5097i	0.342003	+	1.55374i	−0.420829	+	0.907140i	$0.638261\pi$
$128$	−0.422817	+	5.84435i	−0.0373721	+	0.516572i
$129$	−0.593203	−	0.371668i	−0.0522286	−	0.0327235i
$130$	−10.0732	+	8.24782i	−0.883474	+	0.723381i
$131$	−12.9701	+	11.0169i	−1.13320	+	0.962552i	−0.999594	−	0.0284816i	$-0.990933\pi$
$131$	−12.9701	+	11.0169i	−1.13320	+	0.962552i	−0.133610	+	0.991034i	$0.542657\pi$
$132$	0.554713	−	1.00215i	0.0482816	−	0.0872261i
$133$	−1.57762	−	0.258638i	−0.136797	−	0.0224268i
$134$	7.34801	−	10.4271i	0.634771	−	0.900766i
$135$	3.97980	+	5.04367i	0.342527	+	0.434090i
$136$			1.02486i			0.0878812i
$137$	3.81805	−	3.01270i	0.326198	−	0.257393i	−0.442833	−	0.896604i	$-0.646027\pi$
$137$	3.81805	−	3.01270i	0.326198	−	0.257393i	0.769031	+	0.639212i	$0.220739\pi$
$138$	−2.91873	+	2.66646i	−0.248459	+	0.226984i
$139$	−0.824463	−	15.2063i	−0.0699300	−	1.28978i	−0.797319	−	0.603558i	$-0.793749\pi$
$139$	−0.824463	−	15.2063i	−0.0699300	−	1.28978i	0.727389	−	0.686225i	$-0.240734\pi$
$140$	−7.30416	+	19.3404i	−0.617314	+	1.63457i
$141$	0.239850	−	1.64898i	0.0201990	−	0.138869i
$142$	−9.73595	+	22.0815i	−0.817023	+	1.85304i
$143$	2.33347	−	1.52137i	0.195135	−	0.127223i
$144$	7.68418	+	5.00991i	0.640348	+	0.417493i
$145$	6.50474	+	14.7530i	0.540189	+	1.22517i
$146$	−11.4923	+	3.19082i	−0.951110	+	0.264074i
$147$	0.218453	−	0.0317749i	0.0180177	−	0.00262075i
$148$	0.630447	−	3.13251i	0.0518224	−	0.257490i
$149$	1.97045	+	0.955189i	0.161426	+	0.0782521i	0.515161	−	0.857094i	$-0.327732\pi$
$149$	1.97045	+	0.955189i	0.161426	+	0.0782521i	−0.353735	+	0.935346i	$0.615089\pi$
$150$	−4.60610	+	0.927021i	−0.376086	+	0.0756910i
$151$	−2.01541	+	22.2644i	−0.164012	+	1.81185i	0.331719	+	0.943378i	$0.392371\pi$
$151$	−2.01541	+	22.2644i	−0.164012	+	1.81185i	−0.495731	+	0.868476i	$0.665100\pi$
$152$	0.313606	+	0.355976i	0.0254368	+	0.0288734i
$153$	3.49756	+	1.93598i	0.282761	+	0.156515i
$154$	3.69938	−	7.29297i	0.298105	−	0.587684i
$155$	−20.6954	−	7.81588i	−1.66230	−	0.627786i
$156$	0.633249	+	1.14403i	0.0507005	+	0.0915961i
$157$	−1.72530	−	4.83049i	−0.137694	−	0.385515i	0.852949	−	0.521995i	$-0.174812\pi$
$157$	−1.72530	−	4.83049i	−0.137694	−	0.385515i	−0.990643	+	0.136480i	$0.956421\pi$
$158$	2.87189	+	14.2696i	0.228475	+	1.13523i
$159$	0.978472	−	3.78817i	0.0775979	−	0.300422i
$160$	−24.4864	+	14.1373i	−1.93582	+	1.11765i
$161$	−10.8925	+	10.6976i	−0.858450	+	0.843089i
$162$	−15.0073	+	7.95639i	−1.17909	+	0.625113i
$163$	1.53659	−	2.55384i	0.120355	−	0.200032i	−0.790822	−	0.612046i	$-0.790347\pi$
$163$	1.53659	−	2.55384i	0.120355	−	0.200032i	0.911178	+	0.412014i	$0.135174\pi$
$164$	−1.54561	+	0.648403i	−0.120692	+	0.0506318i
$165$	1.69319	−	0.153270i	0.131815	−	0.0119321i
$166$	−15.7121	−	11.5024i	−1.21949	−	0.892759i
$167$	0.710390	+	1.18068i	0.0549716	+	0.0913635i	0.883124	−	0.469139i	$-0.155436\pi$
$167$	0.710390	+	1.18068i	0.0549716	+	0.0913635i	−0.828153	+	0.560502i	$0.810608\pi$
$168$	0.497701	+	0.299457i	0.0383985	+	0.0231036i
$169$	−0.177292	−	9.81840i	−0.0136378	−	0.755262i
$170$	−8.32069	+	5.64157i	−0.638168	+	0.432688i
$171$	1.80725	−	0.397806i	0.138204	−	0.0304210i
$172$	1.87312	+	4.95978i	0.142824	+	0.378180i
$173$	12.9400	−	5.70536i	0.983810	−	0.433770i	0.151727	−	0.988422i	$-0.451516\pi$
$173$	12.9400	−	5.70536i	0.983810	−	0.433770i	0.832082	+	0.554652i	$0.187149\pi$
$174$	2.91167	−	0.696250i	0.220733	−	0.0527826i
$175$	−17.6471	+	4.21985i	−1.33400	+	0.318990i
$176$	4.51622	−	1.99124i	0.340423	−	0.150095i
$177$	0.329171	+	0.871601i	0.0247420	+	0.0655135i
$178$	0.0861294	−	0.0189585i	0.00645567	−	0.00142100i
$179$	9.03331	−	6.12474i	0.675181	−	0.457784i	−0.174795	−	0.984605i	$-0.555926\pi$
$179$	9.03331	−	6.12474i	0.675181	−	0.457784i	0.849977	+	0.526820i	$0.176616\pi$
$180$	−0.432042	−	23.9265i	−0.0322025	−	1.78337i
$181$	18.6416	+	11.2163i	1.38562	+	0.833699i	0.996177	−	0.0873527i	$-0.0278407\pi$
$181$	18.6416	+	11.2163i	1.38562	+	0.833699i	0.389441	+	0.921052i	$0.372668\pi$
$182$	4.81288	+	7.99906i	0.356754	+	0.592930i
$183$	0.656364	+	0.480507i	0.0485198	+	0.0355201i
$184$	4.51211	−	0.408444i	0.332637	−	0.0301109i
$185$	4.37341	−	1.83470i	0.321540	−	0.134890i
$186$	−2.11768	+	3.51961i	−0.155276	+	0.258071i
$187$	1.90041	−	1.00753i	0.138972	−	0.0736781i
$188$	−9.00401	+	8.84290i	−0.656685	+	0.644934i
$189$	3.98969	−	2.30345i	0.290207	−	0.167551i
$190$	−1.16380	+	4.50567i	−0.0844308	+	0.326875i
$191$	0.441432	+	2.19335i	0.0319409	+	0.158705i	0.993096	−	0.117303i	$-0.0374250\pi$
$191$	0.441432	+	2.19335i	0.0319409	+	0.158705i	−0.961155	+	0.276008i	$0.910988\pi$
$192$	1.10448	+	3.09232i	0.0797091	+	0.223169i
$193$	9.45410	+	17.0799i	0.680521	+	1.22944i	0.962829	+	0.270113i	$0.0870610\pi$
$193$	9.45410	+	17.0799i	0.680521	+	1.22944i	−0.282308	+	0.959324i	$0.591100\pi$
$194$	−36.1901	−	13.6676i	−2.59830	−	0.981279i
$195$	−0.877987	+	1.73086i	−0.0628739	+	0.123950i
$196$	−1.46276	−	0.809673i	−0.104483	−	0.0578338i
$197$	−5.58039	−	6.33432i	−0.397586	−	0.451302i	0.516823	−	0.856092i	$-0.327115\pi$
$197$	−5.58039	−	6.33432i	−0.397586	−	0.451302i	−0.914409	+	0.404791i	$0.867344\pi$
$198$	−0.853366	+	9.42720i	−0.0606461	+	0.669962i
$199$	18.5552	−	3.73442i	1.31534	−	0.264726i	0.511355	−	0.859369i	$-0.329144\pi$
$199$	18.5552	−	3.73442i	1.31534	−	0.264726i	0.803989	+	0.594643i	$0.202707\pi$
$200$	4.84518	+	2.34873i	0.342606	+	0.166080i
$201$	0.375195	−	1.86424i	0.0264642	−	0.131493i
$202$	27.6615	−	4.02348i	1.94626	−	0.283091i
$203$	11.1399	−	3.09299i	0.781871	−	0.217085i
$204$	0.407345	+	0.923877i	0.0285199	+	0.0646843i
$205$	−2.08397	−	1.35870i	−0.145551	−	0.0948960i
$206$	23.7270	−	15.4695i	1.65314	−	1.07781i
$207$	7.12954	−	16.1701i	0.495537	−	1.12390i
$208$	−0.811026	+	5.57583i	−0.0562346	+	0.386614i
$209$	0.351785	−	0.931480i	0.0243335	−	0.0644318i
$210$	0.308459	+	5.68918i	0.0212857	+	0.392591i
$211$	18.6019	−	16.9941i	1.28061	−	1.16992i	0.304532	−	0.952502i	$-0.401500\pi$
$211$	18.6019	−	16.9941i	1.28061	−	1.16992i	0.976078	−	0.217421i	$-0.0697643\pi$
$212$	−23.2621	+	18.3554i	−1.59765	+	1.26066i
$213$			3.59757i			0.246502i
$214$	−4.29570	−	5.44402i	−0.293648	−	0.372145i
$215$	−4.53289	+	6.43235i	−0.309141	+	0.438683i
$216$	−1.34910	−	0.221173i	−0.0917945	−	0.0150489i
$217$	−7.68207	+	13.8785i	−0.521493	+	0.942135i
$218$	−30.6020	+	25.9936i	−2.07263	+	1.76051i
$219$	−1.37570	+	1.12642i	−0.0929615	+	0.0761161i
$220$	−10.9113	−	6.83640i	−0.735639	−	0.460910i
$221$	−0.177184	+	2.44910i	−0.0119187	+	0.164745i
$222$	−0.189305	−	0.860019i	−0.0127053	−	0.0577207i
$223$	−1.34087	+	0.145829i	−0.0897916	+	0.00976542i	−0.152904	−	0.988241i	$-0.548863\pi$
$223$	−1.34087	+	0.145829i	−0.0897916	+	0.00976542i	0.0631129	+	0.998006i	$0.479897\pi$
$224$	7.50432	+	18.8344i	0.501403	+	1.25843i
$225$	17.1682	−	12.0985i	1.14455	−	0.806563i
$226$	6.67224	−	11.5567i	0.443831	−	0.768738i
$227$	−13.4460	−	23.2891i	−0.892440	−	1.54575i	−0.836941	−	0.547293i	$-0.815658\pi$
$227$	−13.4460	−	23.2891i	−0.892440	−	1.54575i	−0.0554991	−	0.998459i	$-0.517675\pi$
$228$	0.424193	+	0.196252i	0.0280928	+	0.0129971i
$229$	−1.78242	+	4.24879i	−0.117785	+	0.280768i	−0.970287	−	0.241957i	$-0.922211\pi$
$229$	−1.78242	+	4.24879i	−0.117785	+	0.280768i	0.852502	+	0.522725i	$0.175084\pi$
$230$	28.1539	+	34.3847i	1.85642	+	2.26726i
$231$	0.0659993	−	1.21729i	0.00434244	−	0.0800915i
$232$	−3.13926	−	1.38413i	−0.206103	−	0.0908725i
$233$	28.8828	+	5.27224i	1.89217	+	0.345396i	0.995296	−	0.0968822i	$-0.0308870\pi$
$233$	28.8828	+	5.27224i	1.89217	+	0.345396i	0.896878	+	0.442278i	$0.145830\pi$
$234$	−8.60250	−	6.53945i	−0.562363	−	0.427497i
$235$	−18.3633	−	3.69580i	−1.19789	−	0.241087i
$236$	2.01020	−	6.76388i	0.130853	−	0.440291i
$237$	1.24994	+	1.77372i	0.0811925	+	0.115215i
$238$	3.14439	+	6.48654i	0.203820	+	0.420460i
$239$	−5.80503	−	1.95594i	−0.375496	−	0.126519i	0.125224	−	0.992128i	$-0.460035\pi$
$239$	−5.80503	−	1.95594i	−0.375496	−	0.126519i	−0.500720	+	0.865609i	$0.666931\pi$
$240$	−2.03133	+	2.77476i	−0.131122	+	0.179110i
$241$	25.8036	−	1.86680i	1.66216	−	0.120251i	0.791184	−	0.611579i	$-0.209465\pi$
$241$	25.8036	−	1.86680i	1.66216	−	0.120251i	0.870975	+	0.491327i	$0.163488\pi$
$242$	−14.0259	−	11.0674i	−0.901618	−	0.711438i
$243$	−4.98199	+	6.31376i	−0.319595	+	0.405028i
$244$	−1.75509	−	5.90550i	−0.112358	−	0.378061i
$245$	−0.223717	−	2.47142i	−0.0142928	−	0.157893i
$246$	−0.317665	+	0.335355i	−0.0202536	+	0.0213815i
$247$	0.687880	+	0.904890i	0.0437687	+	0.0575768i
$248$	4.37298	−	1.74236i	0.277685	−	0.110640i
$249$	−2.83498	−	0.624027i	−0.179660	−	0.0395461i
$250$	2.34806	+	16.1430i	0.148504	+	1.02097i
$251$	−21.5751	−	5.99031i	−1.36181	−	0.378105i	−0.491616	−	0.870812i	$-0.663593\pi$
$251$	−21.5751	−	5.99031i	−1.36181	−	0.378105i	−0.870195	+	0.492707i	$0.836007\pi$
$252$	−17.0225	−	2.16294i	−1.07232	−	0.136252i
$253$	−5.19320	−	7.96530i	−0.326494	−	0.500774i
$254$	0.675622	−	37.4159i	0.0423923	−	2.34768i
$255$	−0.795687	+	1.26996i	−0.0498279	+	0.0795281i
$256$	−2.68168	+	8.46081i	−0.167605	+	0.528800i
$257$	14.1154	−	4.75605i	0.880497	−	0.296674i	0.157495	−	0.987520i	$-0.449658\pi$
$257$	14.1154	−	4.75605i	0.880497	−	0.296674i	0.723002	+	0.690846i	$0.242762\pi$
$258$	1.02379	+	1.04245i	0.0637385	+	0.0648999i
$259$	−0.850489	−	3.29268i	−0.0528468	−	0.204597i
$260$	13.2269	−	6.41180i	0.820296	−	0.397643i
$261$	−10.6538	+	8.09877i	−0.659451	+	0.501301i
$262$	31.6774	−	16.0685i	1.95703	−	0.992712i
$263$	−9.96156	−	14.6922i	−0.614256	−	0.905960i	0.385604	−	0.922664i	$-0.373993\pi$
$263$	−9.96156	−	14.6922i	−0.614256	−	0.905960i	−0.999860	+	0.0167043i	$0.994683\pi$
$264$	−0.244002	+	0.267087i	−0.0150173	+	0.0164381i
$265$	−41.9257	−	13.2885i	−2.57548	−	0.816307i
$266$	3.07705	+	1.29086i	0.188666	+	0.0791475i
$267$	0.0106083	−	0.00776604i	0.000649215	−	0.000475274i
$268$	−10.8067	+	9.52043i	−0.660122	+	0.581553i
$269$	−4.55318	+	4.31300i	−0.277612	+	0.262968i	−0.813819	−	0.581118i	$-0.802615\pi$
$269$	−4.55318	+	4.31300i	−0.277612	+	0.262968i	0.536207	+	0.844087i	$0.319857\pi$
$270$	−5.63072	−	12.1706i	−0.342675	−	0.740679i
$271$	10.5717	+	11.5719i	0.642183	+	0.702940i	0.970357	−	0.241677i	$-0.0776975\pi$
$271$	10.5717	+	11.5719i	0.642183	+	0.702940i	−0.328174	+	0.944617i	$0.606433\pi$
$272$	−1.01186	+	4.23151i	−0.0613527	+	0.256573i
$273$	1.13758	+	0.801655i	0.0688495	+	0.0485184i
$274$	−9.21313	+	4.26245i	−0.556585	+	0.257504i
$275$	−0.407988	−	11.2935i	−0.0246026	−	0.681023i
$276$	3.90516	−	2.16160i	0.235063	−	0.130113i
$277$	−9.51541	−	3.39861i	−0.571726	−	0.204203i	0.0346248	−	0.999400i	$-0.488976\pi$
$277$	−9.51541	−	3.39861i	−0.571726	−	0.204203i	−0.606351	+	0.795197i	$0.707367\pi$
$278$	−5.70786	+	31.2692i	−0.342335	+	1.87540i
$279$	2.31447	−	18.2151i	0.138564	−	1.09051i
$280$	3.66422	−	5.40432i	0.218979	−	0.322970i
$281$	2.05619	+	8.59882i	0.122662	+	0.512963i	0.999483	+	0.0321465i	$0.0102343\pi$
$281$	2.05619	+	8.59882i	0.122662	+	0.512963i	−0.876821	+	0.480816i	$0.840340\pi$
$282$	−1.28735	+	3.23101i	−0.0766608	+	0.192404i
$283$	−5.43991	+	19.5928i	−0.323369	+	1.16467i	0.605984	+	0.795477i	$0.292780\pi$
$283$	−5.43991	+	19.5928i	−0.323369	+	1.16467i	−0.929353	+	0.369193i	$0.879634\pi$
$284$	16.4890	−	21.6909i	0.978444	−	1.28712i
$285$	0.112233	+	0.684588i	0.00664808	+	0.0405515i
$286$	−5.47548	+	1.95567i	−0.323772	+	0.115641i
$287$	−1.17921	+	1.33853i	−0.0696067	+	0.0790108i
$288$	−16.1390	−	17.0377i	−0.950999	−	1.00396i
$289$	2.44354	−	14.9050i	0.143738	−	0.876762i
$290$	−6.04321	−	33.1064i	−0.354870	−	1.94407i
$291$	−5.75851	+	0.312217i	−0.337570	+	0.0183025i
$292$	13.4574	−	0.486160i	0.787532	−	0.0284504i
$293$	7.75321	+	6.83040i	0.452947	+	0.399036i	0.856686	−	0.515838i	$-0.172519\pi$
$293$	7.75321	+	6.83040i	0.452947	+	0.399036i	−0.403739	+	0.914874i	$0.632289\pi$
$294$	−0.458888	−	0.0415393i	−0.0267629	−	0.00242262i
$295$	9.98381	−	3.16441i	0.581280	−	0.184239i
$296$	−0.423744	+	0.915907i	−0.0246296	+	0.0532360i
$297$	0.916164	+	2.71908i	0.0531612	+	0.157777i
$298$	−3.53637	−	2.89555i	−0.204856	−	0.167735i
$299$	10.8532	−	0.195977i	0.627654	−	0.0113336i
$300$	5.30130	+	0.191515i	0.306071	+	0.0110571i
$301$	4.09647	+	3.88038i	0.236117	+	0.223661i
$302$	14.8990	−	44.2187i	0.857343	−	2.54450i
$303$	3.53119	−	2.21245i	0.202861	−	0.127102i
$304$	0.943378	+	1.77940i	0.0541064	+	0.102056i
$305$	5.79302	−	7.07508i	0.331707	−	0.405118i
$306$	−6.16032	−	5.62787i	−0.352162	−	0.321724i
$307$	8.01619	+	0.579942i	0.457508	+	0.0330990i	0.298988	−	0.954257i	$-0.403351\pi$
$307$	8.01619	+	0.579942i	0.457508	+	0.0330990i	0.158520	+	0.987356i	$0.449328\pi$
$308$	−5.97721	+	7.03691i	−0.340583	+	0.400965i
$309$	2.30611	−	3.53711i	0.131190	−	0.201219i
$310$	38.2179	+	25.9124i	2.17063	+	1.47173i
$311$	18.1879	+	7.24673i	1.03134	+	0.410924i	0.823547	−	0.567248i	$-0.191992\pi$
$311$	18.1879	+	7.24673i	1.03134	+	0.410924i	0.207795	+	0.978172i	$0.433371\pi$
$312$	−0.110484	−	0.397928i	−0.00625493	−	0.0225282i
$313$	9.04095	+	0.983262i	0.511024	+	0.0555773i	0.359999	−	0.932953i	$-0.382777\pi$
$313$	9.04095	+	0.983262i	0.511024	+	0.0555773i	0.151025	+	0.988530i	$0.451743\pi$
$314$	1.15755	+	10.6435i	0.0653241	+	0.600645i
$315$	−11.5216	−	22.7138i	−0.649171	−	1.27978i
$316$	0.593307	−	16.4233i	0.0333761	−	0.923882i
$317$	−8.79452	−	20.9637i	−0.493950	−	1.17744i	−0.956733	−	0.290968i	$-0.906023\pi$
$317$	−8.79452	−	20.9637i	−0.493950	−	1.17744i	0.462783	−	0.886471i	$-0.346851\pi$
$318$	−3.82518	+	7.21506i	−0.214506	+	0.404600i
$319$	0.519583	+	7.18189i	0.0290911	+	0.402108i
$320$	35.3826	−	10.5156i	1.97795	−	0.587838i
$321$	−0.913370	−	0.484238i	−0.0509793	−	0.0270275i
$322$	27.3048	−	16.4288i	1.52164	−	0.915539i
$323$	0.466006	+	0.743771i	0.0259292	+	0.0413845i
$324$	18.5685	−	4.79618i	1.03158	−	0.266455i
$325$	11.1724	+	6.45041i	0.619735	+	0.357804i
$326$	−4.35900	+	4.43842i	−0.241423	+	0.245821i
$327$	−2.61095	+	5.38612i	−0.144386	+	0.297853i
$328$	0.522394	−	0.0856422i	0.0288444	−	0.00472880i
$329$	−4.51782	+	12.6490i	−0.249075	+	0.697359i
$330$	−3.51160	−	0.510776i	−0.193307	−	0.0281173i
$331$	−20.5335	+	2.60906i	−1.12862	+	0.143407i	−0.667981	−	0.744178i	$-0.732841\pi$
$331$	−20.5335	+	2.60906i	−1.12862	+	0.143407i	−0.460644	+	0.887585i	$0.652381\pi$
$332$	14.2329	+	16.7562i	0.781131	+	0.919619i
$333$	2.32527	+	3.17628i	0.127424	+	0.174059i
$334$	−0.868970	−	2.74163i	−0.0475479	−	0.150015i
$335$	−20.6972	−	5.34602i	−1.13081	−	0.292084i
$336$	1.75928	+	1.72780i	0.0959766	+	0.0942592i
$337$	−29.5717	−	8.78857i	−1.61087	−	0.478744i	−0.650975	−	0.759099i	$-0.725640\pi$
$337$	−29.5717	−	8.78857i	−1.61087	−	0.478744i	−0.959896	+	0.280355i	$0.909548\pi$
$338$	−4.40619	+	20.0175i	−0.239665	+	1.08881i
$339$	0.215084	−	1.97767i	0.0116818	−	0.107412i
$340$	10.6182	−	4.01008i	0.575851	−	0.217477i
$341$	−7.52991	−	6.39596i	−0.407768	−	0.346361i
$342$	−3.86185	−	0.0697338i	−0.208825	−	0.00377077i
$343$	−19.3077	−	1.04683i	−1.04252	−	0.0565237i
$344$	−0.211063	−	1.66108i	−0.0113797	−	0.0895597i
$345$	5.90831	+	2.99701i	0.318093	+	0.161354i
$346$	−29.0379	+	5.30055i	−1.56109	+	0.284959i
$347$	6.87295	+	1.64349i	0.368959	+	0.0882271i	0.412825	−	0.910810i	$-0.364542\pi$
$347$	6.87295	+	1.64349i	0.368959	+	0.0882271i	−0.0438657	+	0.999037i	$0.513967\pi$
$348$	−3.38007			−0.181191
$349$	−7.28402	+	17.2030i	−0.389904	+	0.920855i
$349$	−7.28402	+	17.2030i	−0.389904	+	0.920855i
$350$	37.8722			2.02436
$351$	−3.18569	−	0.761775i	−0.170040	−	0.0406606i
$352$	−12.4221	+	2.26751i	−0.662098	+	0.120859i
$353$	−7.14690	−	3.62529i	−0.380391	−	0.192955i	0.251778	−	0.967785i	$-0.418985\pi$
$353$	−7.14690	−	3.62529i	−0.380391	−	0.192955i	−0.632169	+	0.774830i	$0.717835\pi$
$354$	−0.245124	−	1.92915i	−0.0130282	−	0.102533i
$355$	40.3818	+	2.18944i	2.14324	+	0.116203i
$356$	−0.0995554	−	0.00179768i	−0.00527642	−	9.52769e-5i
$357$	0.819025	+	0.695686i	0.0433474	+	0.0368196i
$358$	−21.3108	+	8.04830i	−1.12631	+	0.425366i
$359$	−0.800349	+	7.35909i	−0.0422408	+	0.388398i	0.953865	+	0.300235i	$0.0970651\pi$
$359$	−0.800349	+	7.35909i	−0.0422408	+	0.388398i	−0.996106	+	0.0881628i	$0.971900\pi$
$360$	−1.62474	+	7.38125i	−0.0856311	+	0.389026i
$361$	−17.8232	−	5.29699i	−0.938065	−	0.278789i
$362$	−32.3980	−	31.8183i	−1.70280	−	1.67233i
$363$	−2.57882	−	0.666099i	−0.135353	−	0.0349611i
$364$	−3.18456	−	10.0474i	−0.166916	−	0.526627i
$365$	11.8065	+	16.1274i	0.617979	+	0.844148i
$366$	−1.09918	−	1.29405i	−0.0574549	−	0.0676411i
$367$	32.0231	−	4.06896i	1.67159	−	0.212398i	0.767898	−	0.640572i	$-0.221303\pi$
$367$	32.0231	−	4.06896i	1.67159	−	0.212398i	0.903696	+	0.428174i	$0.140843\pi$
$368$	19.0331	+	2.76844i	0.992169	+	0.144315i
$369$	0.694538	−	1.94456i	0.0361562	−	0.101230i
$370$	−9.76869	+	1.60150i	−0.507850	+	0.0832578i
$371$	−13.7566	+	28.3784i	−0.714208	+	1.47334i
$372$	3.24957	−	3.30877i	0.168482	−	0.171552i
$373$	−7.82805	−	4.51953i	−0.405321	−	0.234012i	0.283456	−	0.958985i	$-0.408519\pi$
$373$	−7.82805	−	4.51953i	−0.405321	−	0.234012i	−0.688777	+	0.724973i	$0.741852\pi$
$374$	−4.34694	+	1.12280i	−0.224775	+	0.0580585i
$375$	1.29116	+	2.06077i	0.0666752	+	0.106417i
$376$	3.41530	−	2.05492i	0.176131	−	0.105974i
$377$	−7.26257	−	3.85037i	−0.374041	−	0.198304i
$378$	−9.21727	+	2.73933i	−0.474085	+	0.140896i
$379$	1.44908	+	20.0298i	0.0744342	+	1.02886i	0.891708	+	0.452610i	$0.149507\pi$
$379$	1.44908	+	20.0298i	0.0744342	+	1.02886i	−0.817274	+	0.576249i	$0.804516\pi$
$380$	2.46104	−	4.64201i	0.126249	−	0.238130i
$381$	−2.15811	−	5.14434i	−0.110563	−	0.263553i
$382$	0.168593	−	4.66680i	0.00862595	−	0.238774i
$383$	2.99381	+	5.90200i	0.152976	+	0.301578i	0.955473	−	0.295079i	$-0.0953459\pi$
$383$	2.99381	+	5.90200i	0.152976	+	0.301578i	−0.802496	+	0.596657i	$0.796495\pi$
$384$	−0.197129	−	1.81257i	−0.0100597	−	0.0924973i
$385$	−13.6235	−	1.48165i	−0.694320	−	0.0755118i
$386$	−10.9009	−	39.2616i	−0.554843	−	1.99836i
$387$	−6.06751	−	2.41752i	−0.308429	−	0.122889i
$388$	36.1510	+	24.5110i	1.83529	+	1.24436i
$389$	6.63113	−	10.1708i	0.336212	−	0.515680i	−0.628911	−	0.777477i	$-0.716499\pi$
$389$	6.63113	−	10.1708i	0.336212	−	0.515680i	0.965123	+	0.261797i	$0.0843152\pi$
$390$	2.62253	−	3.08748i	0.132797	−	0.156341i
$391$	8.36002	+	0.604817i	0.422784	+	0.0305869i
$392$	0.389846	+	0.356151i	0.0196902	+	0.0179883i
$393$	3.35456	−	4.09696i	0.169215	−	0.206664i
$394$	8.25342	+	15.5676i	0.415801	+	0.784285i
$395$	20.6702	−	12.9508i	1.04003	−	0.651626i
$396$	3.41245	−	10.1278i	0.171482	−	0.508940i
$397$	21.6345	+	20.4933i	1.08580	+	1.02853i	0.999479	+	0.0322606i	$0.0102706\pi$
$397$	21.6345	+	20.4933i	1.08580	+	1.02853i	0.0863240	+	0.996267i	$0.472488\pi$
$398$	−39.4801	−	1.42626i	−1.97896	−	0.0714918i
$399$	0.497359	−	0.00898086i	0.0248991	−	0.000449606i
$400$	17.6861	+	14.4813i	0.884307	+	0.724064i
$401$	11.6652	+	34.6211i	0.582532	+	1.72889i	0.679568	+	0.733612i	$0.262167\pi$
$401$	11.6652	+	34.6211i	0.582532	+	1.72889i	−0.0970364	+	0.995281i	$0.530936\pi$
$402$	−1.66660	+	3.60229i	−0.0831224	+	0.179666i
$403$	10.7513	−	3.40767i	0.535561	−	0.169748i
$404$	−31.4312	−	2.84520i	−1.56376	−	0.141554i
$405$	21.3586	+	18.8165i	1.06132	+	0.934998i
$406$	−24.1156	+	0.871200i	−1.19684	+	0.0432369i
$407$	2.11495	−	0.114669i	0.104834	−	0.00568395i
$408$	−0.0572641	−	0.313708i	−0.00283499	−	0.0155309i
$409$	1.18918	−	7.25366i	0.0588010	−	0.358670i	−0.940994	−	0.338423i	$-0.890106\pi$
$409$	1.18918	−	7.25366i	0.0588010	−	0.358670i	0.999795	−	0.0202470i	$-0.00644527\pi$
$410$	3.57094	+	3.76980i	0.176356	+	0.186177i
$411$	−1.00036	+	1.13552i	−0.0493443	+	0.0560109i
$412$	−30.1162	+	10.7566i	−1.48372	+	0.529939i
$413$	−1.21497	−	7.41100i	−0.0597848	−	0.364671i
$414$	−22.3224	+	29.3647i	−1.09709	+	1.44319i
$415$	−8.72987	+	31.4421i	−0.428532	+	1.54343i
$416$	5.33557	−	13.3913i	0.261598	−	0.656561i
$417$	1.10202	+	4.60856i	0.0539661	+	0.225682i
$418$	−1.16629	+	1.72015i	−0.0570452	+	0.0841353i
$419$	1.58073	−	12.4405i	0.0772238	−	0.607759i	−0.905723	−	0.423870i	$-0.860671\pi$
$419$	1.58073	−	12.4405i	0.0772238	−	0.607759i	0.982947	−	0.183889i	$-0.0588688\pi$
$420$	1.15514	−	6.32820i	0.0563652	−	0.308784i
$421$	−4.31487	−	1.54114i	−0.210294	−	0.0751105i	0.229109	−	0.973401i	$-0.426419\pi$
$421$	−4.31487	−	1.54114i	−0.210294	−	0.0751105i	−0.439402	+	0.898290i	$0.644810\pi$
$422$	−46.0115	+	25.4684i	−2.23981	+	1.23978i
$423$	−0.561297	−	15.5372i	−0.0272912	−	0.755446i
$424$	8.49369	−	3.92960i	0.412490	−	0.190838i
$425$	8.14287	+	5.73829i	0.394987	+	0.278348i
$426$	1.74635	−	7.30312i	0.0846110	−	0.353837i
$427$	−4.42248	−	4.84089i	−0.214019	−	0.234267i
$428$	3.28756	+	7.10595i	0.158910	+	0.343479i
$429$	−0.629264	+	0.596071i	−0.0303812	+	0.0287786i
$430$	12.3242	−	10.8574i	0.594328	−	0.523589i
$431$	−15.3706	+	11.2525i	−0.740378	+	0.542012i	−0.895056	−	0.445953i	$-0.852865\pi$
$431$	−15.3706	+	11.2525i	−0.740378	+	0.542012i	0.154678	+	0.987965i	$0.450566\pi$
$432$	−5.35186	−	2.24517i	−0.257492	−	0.108021i
$433$	37.7458	+	11.9637i	1.81395	+	0.574937i	0.999982	−	0.00597747i	$-0.00190270\pi$
$433$	37.7458	+	11.9637i	1.81395	+	0.574937i	0.813964	+	0.580915i	$0.197305\pi$
$434$	22.3317	−	24.4445i	1.07195	−	1.17337i
$435$	−2.81541	−	4.15243i	−0.134989	−	0.199094i
$436$	40.4289	−	20.5077i	1.93619	−	0.982140i
$437$	3.08884	−	2.34808i	0.147759	−	0.112324i
$438$	3.33949	−	1.61884i	0.159567	−	0.0773510i
$439$	9.46136	+	36.6298i	0.451566	+	1.74825i	0.642153	+	0.766577i	$0.278041\pi$
$439$	9.46136	+	36.6298i	0.451566	+	1.74825i	−0.190587	+	0.981670i	$0.561039\pi$
$440$	2.84948	+	2.90140i	0.135844	+	0.138319i
$441$	1.95187	−	0.657661i	0.0929461	−	0.0313172i
$442$	1.54854	−	4.88570i	0.0736566	−	0.232389i
$443$	−15.0376	+	24.0008i	−0.714457	+	1.14031i	0.269688	+	0.962948i	$0.413079\pi$
$443$	−15.0376	+	24.0008i	−0.714457	+	1.14031i	−0.984145	+	0.177365i	$0.943243\pi$
$444$	−0.0179502	+	0.994081i	−0.000851879	+	0.0471770i
$445$	−0.0807156	−	0.123801i	−0.00382629	−	0.00586874i
$446$	2.79278	+	0.354859i	0.132242	+	0.0168031i
$447$	−0.656523	−	0.182283i	−0.0310525	−	0.00862168i
$448$	−3.80979	−	26.1924i	−0.179996	−	1.23748i
$449$	−29.7518	−	6.54887i	−1.40407	−	0.309060i	−0.552596	−	0.833449i	$-0.686363\pi$
$449$	−29.7518	−	6.54887i	−1.40407	−	0.309060i	−0.851479	+	0.524389i	$0.824294\pi$
$450$	−40.7245	+	16.2261i	−1.91977	+	0.764907i
$451$	−0.672369	−	0.884486i	−0.0316606	−	0.0416488i
$452$	−10.3612	+	10.9382i	−0.487350	+	0.514490i
$453$	−0.627109	−	6.92772i	−0.0294641	−	0.325492i
$454$	15.9904	+	53.8042i	0.750465	+	2.52515i
$455$	9.69068	−	12.2812i	0.454306	−	0.575750i
$456$	−0.115885	−	0.0914408i	−0.00542679	−	0.00428211i
$457$	−2.09559	+	0.151608i	−0.0980275	+	0.00709193i	−0.121084	−	0.992642i	$-0.538637\pi$
$457$	−2.09559	+	0.151608i	−0.0980275	+	0.00709193i	0.0230568	+	0.999734i	$0.492660\pi$
$458$	5.68079	−	7.75986i	0.265446	−	0.362594i
$459$	−2.39685	−	0.807594i	−0.111875	−	0.0376952i
$460$	−21.8867	−	45.1499i	−1.02047	−	2.10513i
$461$	−12.2879	−	17.4371i	−0.572306	−	0.812125i	0.423278	−	0.906000i	$-0.360879\pi$
$461$	−12.2879	−	17.4371i	−0.572306	−	0.812125i	−0.995584	+	0.0938746i	$0.970075\pi$
$462$	−0.724880	+	2.43907i	−0.0337245	+	0.113476i
$463$	6.61205	+	1.33074i	0.307288	+	0.0618447i	0.348509	−	0.937305i	$-0.386688\pi$
$463$	6.61205	+	1.33074i	0.307288	+	0.0618447i	−0.0412211	+	0.999150i	$0.513125\pi$
$464$	−11.5950	−	8.81429i	−0.538284	−	0.409193i
$465$	6.77154	+	1.23607i	0.314023	+	0.0573214i
$466$	−56.0731	−	24.7231i	−2.59754	−	1.14528i
$467$	0.509324	−	9.39394i	0.0235687	−	0.434700i	−0.962807	−	0.270191i	$-0.912913\pi$
$467$	0.509324	−	9.39394i	0.0235687	−	0.434700i	0.986376	−	0.164509i	$-0.0526040\pi$
$468$	7.72915	+	9.43970i	0.357280	+	0.436350i
$469$	−5.92968	+	14.1347i	−0.273807	+	0.652680i
$470$	35.4838	+	16.4165i	1.63674	+	0.757239i
$471$	0.798015	+	1.38220i	0.0367706	+	0.0636885i
$472$	−1.11429	+	1.93001i	−0.0512895	+	0.0888361i
$473$	−2.87267	+	2.02438i	−0.132086	+	0.0930809i
$474$	−1.67639	−	4.20743i	−0.0769992	−	0.193253i
$475$	4.58426	−	0.498568i	0.210340	−	0.0228759i
$476$	−1.74958	−	7.94842i	−0.0801918	−	0.364315i
$477$	2.63411	−	36.4097i	0.120607	−	1.66708i
$478$	10.8348	+	6.78849i	0.495573	+	0.310498i
$479$	−1.91547	+	1.56837i	−0.0875199	+	0.0716606i	−0.676266	−	0.736657i	$-0.736403\pi$
$479$	−1.91547	+	1.56837i	−0.0875199	+	0.0716606i	0.588747	+	0.808318i	$0.299622\pi$
$480$	6.70534	−	5.69557i	0.306056	−	0.259966i
$481$	−1.17096	+	2.11548i	−0.0533913	+	0.0964574i
$482$	−53.2879	−	8.73611i	−2.42720	−	0.397919i
$483$	2.73645	−	3.88314i	0.124513	−	0.176689i
$484$	12.4955	+	15.8358i	0.567979	+	0.719810i
$485$			64.8278i			2.94368i
$486$	13.1784	−	10.3986i	0.597783	−	0.471691i
$487$	−14.5989	+	13.3371i	−0.661540	+	0.604361i	−0.933771	−	0.357871i	$-0.883503\pi$
$487$	−14.5989	+	13.3371i	−0.661540	+	0.604361i	0.272231	+	0.962232i	$0.412238\pi$
$488$	0.105342	+	1.94291i	0.00476859	+	0.0879515i
$489$	−0.327653	+	0.867582i	−0.0148170	+	0.0392334i
$490$	−0.745540	+	5.12561i	−0.0336801	+	0.231551i
$491$	−1.18867	+	2.69595i	−0.0536438	+	0.121666i	−0.939806	−	0.341709i	$-0.888994\pi$
$491$	−1.18867	+	2.69595i	−0.0536438	+	0.121666i	0.886162	+	0.463376i	$0.153362\pi$
$492$	0.436880	−	0.284836i	0.0196961	−	0.0128414i
$493$	−5.31708	−	3.46662i	−0.239469	−	0.156129i
$494$	−0.957148	−	2.17085i	−0.0430641	−	0.0976713i
$495$	15.2844	−	4.24369i	0.686982	−	0.190740i
$496$	19.7757	−	2.87645i	0.887953	−	0.129156i
$497$	5.72150	−	28.4284i	0.256644	−	1.27519i
$498$	5.45213	+	2.64295i	0.244316	+	0.118434i
$499$	−5.35454	+	1.07765i	−0.239702	+	0.0482423i	−0.315674	−	0.948868i	$-0.602231\pi$
$499$	−5.35454	+	1.07765i	−0.239702	+	0.0482423i	0.0759724	+	0.997110i	$0.475794\pi$
$500$	1.66043	−	18.3429i	0.0742567	−	0.820319i
$501$	−0.283419	−	0.321710i	−0.0126622	−	0.0143729i
$502$	40.8899	+	22.6335i	1.82501	+	1.01018i
$503$	−7.32425	+	14.4390i	−0.326572	+	0.643805i	−0.994989	−	0.0999815i	$-0.968122\pi$
$503$	−7.32425	+	14.4390i	−0.326572	+	0.643805i	0.668417	+	0.743787i	$0.266972\pi$
$504$	5.06995	+	1.91473i	0.225834	+	0.0852888i
$505$	−22.6851	−	40.9831i	−1.00947	−	1.82372i
$506$	6.67570	+	18.6906i	0.296771	+	0.830897i
$507$	0.602871	+	2.99549i	0.0267744	+	0.133034i
$508$	−10.5665	+	40.9084i	−0.468812	+	1.81502i
$509$	14.0014	−	8.08371i	0.620601	−	0.358304i	−0.156502	−	0.987678i	$-0.550022\pi$
$509$	14.0014	−	8.08371i	0.620601	−	0.358304i	0.777103	+	0.629374i	$0.216688\pi$
$510$	2.23173	−	2.19179i	0.0988225	−	0.0970542i
$511$	12.6624	−	6.71318i	0.560152	−	0.296974i
$512$	15.5928	−	25.9155i	0.689113	−	1.14531i
$513$	−1.07965	+	0.452924i	−0.0476675	+	0.0199971i
$514$	−30.9632	+	2.80284i	−1.36573	+	0.123628i
$515$	−38.2996	−	28.0381i	−1.68768	−	1.23551i
$516$	−0.850487	−	1.41352i	−0.0374406	−	0.0622267i
$517$	−7.16801	−	4.31285i	−0.315249	−	0.189679i
$518$	0.128152	+	7.09704i	0.00563067	+	0.311826i
$519$	−3.64212	+	2.46942i	−0.159872	+	0.108396i
$520$	−4.53387	+	0.997980i	−0.198823	+	0.0437643i
$521$	−14.0816	−	37.2863i	−0.616927	−	1.63354i	−0.764600	−	0.644506i	$-0.777063\pi$
$521$	−14.0816	−	37.2863i	−0.616927	−	1.63354i	0.147673	−	0.989036i	$-0.452822\pi$
$522$	25.5586	−	11.2690i	1.11867	−	0.493231i
$523$	−37.9510	+	9.07499i	−1.65948	+	0.396822i	−0.951069	−	0.308978i	$-0.900013\pi$
$523$	−37.9510	+	9.07499i	−1.65948	+	0.396822i	−0.708411	+	0.705800i	$0.750588\pi$
$524$	−39.0037	+	9.32672i	−1.70388	+	0.407440i
$525$	5.16596	−	2.27772i	0.225461	−	0.0994078i
$526$	13.0901	+	34.6609i	0.570757	+	1.51129i
$527$	8.50527	−	1.87215i	0.370495	−	0.0815522i
$528$	−1.27115	+	0.861858i	−0.0553195	+	0.0375076i
$529$	−0.253721	−	14.0510i	−0.0110313	−	0.610914i
$530$	78.6591	+	47.3276i	3.41674	+	2.05578i
$531$	4.48167	+	7.44860i	0.194488	+	0.323242i
$532$	−3.03990	−	2.22544i	−0.131797	−	0.0964849i
$533$	1.26317	−	0.114344i	0.0547138	−	0.00495279i
$534$	−0.0253047	+	0.0106156i	−0.00109504	+	0.000459383i
$535$	−5.99131	+	9.95763i	−0.259027	+	0.430506i
$536$	4.01879	−	2.13063i	0.173585	−	0.0920291i
$537$	−2.42286	+	2.37951i	−0.104554	+	0.102683i
$538$	11.3366	−	6.54522i	0.488758	−	0.282184i
$539$	0.277159	−	1.07302i	0.0119381	−	0.0462184i
$540$	2.98727	+	14.8429i	0.128552	+	0.638735i
$541$	−10.6310	−	29.7647i	−0.457064	−	1.27969i	−0.919520	−	0.393043i	$-0.871422\pi$
$541$	−10.6310	−	29.7647i	−0.457064	−	1.27969i	0.462456	−	0.886642i	$-0.346968\pi$
$542$	−15.8433	−	28.6228i	−0.680530	−	1.22945i
$543$	−6.33287	−	2.39168i	−0.271769	−	0.102637i
$544$	5.03541	−	9.92682i	0.215892	−	0.425609i
$545$	58.8687	+	32.5852i	2.52166	+	1.39580i
$546$	−1.92016	−	2.17958i	−0.0821752	−	0.0932774i
$547$	−1.60883	+	17.7729i	−0.0687886	+	0.759913i	0.886206	+	0.463291i	$0.153331\pi$
$547$	−1.60883	+	17.7729i	−0.0687886	+	0.759913i	−0.954995	+	0.296622i	$0.904140\pi$
$548$	11.2360	−	2.26136i	0.479979	−	0.0966004i
$549$	6.82960	+	3.31069i	0.291480	+	0.141297i
$550$	−4.65392	+	23.1240i	−0.198444	+	0.986009i
$551$	−2.90762	+	0.422924i	−0.123869	+	0.0180172i
$552$	−1.35833	+	0.377138i	−0.0578142	+	0.0160520i
$553$	−7.05631	−	16.0040i	−0.300065	−	0.680560i
$554$	17.6666	+	11.5182i	0.750583	+	0.489364i
$555$	−1.23618	+	0.805962i	−0.0524729	+	0.0342112i
$556$	14.4783	−	32.8375i	0.614018	−	1.39262i
$557$	2.99110	−	20.5639i	0.126737	−	0.871319i	−0.825160	−	0.564900i	$-0.808915\pi$
$557$	2.99110	−	20.5639i	0.126737	−	0.871319i	0.951897	−	0.306420i	$-0.0991311\pi$
$558$	−13.5405	+	35.8534i	−0.573213	+	1.51779i
$559$	−0.217197	−	4.00597i	−0.00918647	−	0.169434i
$560$	20.4648	−	18.6959i	0.864794	−	0.790047i
$561$	−0.525416	+	0.414589i	−0.0221831	+	0.0175040i
$562$		−	18.4538i		−	0.778428i
$563$	14.7051	+	18.6361i	0.619748	+	0.785417i	0.989627	−	0.143663i	$-0.0458881\pi$
$563$	14.7051	+	18.6361i	0.619748	+	0.785417i	−0.369879	+	0.929080i	$0.620601\pi$
$564$	2.26202	−	3.20989i	0.0952481	−	0.135161i
$565$	−22.0679	−	3.61785i	−0.928404	−	0.152204i
$566$	20.5539	−	37.1329i	0.863945	−	1.56081i
$567$	15.5564	−	13.2137i	0.653308	−	0.554925i
$568$	−6.65819	+	5.45168i	−0.279372	+	0.228747i
$569$	−6.72204	−	4.21165i	−0.281802	−	0.176562i	0.382648	−	0.923894i	$-0.375012\pi$
$569$	−6.72204	−	4.21165i	−0.281802	−	0.176562i	−0.664450	+	0.747333i	$0.731334\pi$
$570$	0.104483	−	1.44420i	0.00437630	−	0.0604910i
$571$	−4.72144	−	21.4497i	−0.197586	−	0.897643i	−0.966172	−	0.257897i	$-0.916971\pi$
$571$	−4.72144	−	21.4497i	−0.197586	−	0.897643i	0.768586	−	0.639746i	$-0.220961\pi$
$572$	6.52606	−	0.709752i	0.272868	−	0.0296762i
$573$	−0.257674	−	0.646714i	−0.0107645	−	0.0270169i
$574$	3.04357	−	2.14481i	0.127036	−	0.0895226i
$575$	22.0185	−	38.1371i	0.918234	−	1.59043i
$576$	15.3187	+	26.5328i	0.638279	+	1.10553i
$577$	−19.8738	−	9.19459i	−0.827356	−	0.382776i	−0.0399434	−	0.999202i	$-0.512718\pi$
$577$	−19.8738	−	9.19459i	−0.827356	−	0.382776i	−0.787413	+	0.616426i	$0.788580\pi$
$578$	−12.1957	+	29.0711i	−0.507273	+	1.20920i
$579$	−3.84822	−	4.69988i	−0.159927	−	0.195320i
$580$	−2.05707	+	37.9404i	−0.0854152	+	1.57539i
$581$	21.4099	+	9.43982i	0.888233	+	0.391630i
$582$	11.8414	+	2.16152i	0.490842	+	0.0895979i
$583$	−15.6368	−	11.8868i	−0.647609	−	0.492300i
$584$	−4.16942	−	0.839135i	−0.172532	−	0.0347237i
$585$	−5.15873	+	17.3580i	−0.213287	+	0.717665i
$586$	−12.4235	−	17.6294i	−0.513209	−	0.728264i
$587$	3.91373	+	8.07360i	0.161537	+	0.333233i	0.965055	−	0.262047i	$-0.0843975\pi$
$587$	3.91373	+	8.07360i	0.161537	+	0.333233i	−0.803518	+	0.595280i	$0.797041\pi$
$588$	0.492990	+	0.166108i	0.0203306	+	0.00685016i
$589$	2.38135	−	3.25288i	0.0981217	−	0.134032i
$590$	−21.8033	+	1.57739i	−0.897630	+	0.0649402i
$591$	2.06208	+	1.62712i	0.0848225	+	0.0669308i
$592$	−2.65386	+	3.36328i	−0.109073	+	0.138230i
$593$	−9.15592	−	30.8077i	−0.375988	−	1.26512i	−0.908210	−	0.418515i	$-0.862551\pi$
$593$	−9.15592	−	30.8077i	−0.375988	−	1.26512i	0.532221	−	0.846605i	$-0.321357\pi$
$594$	−0.539916	−	5.96449i	−0.0221530	−	0.244726i
$595$	8.30733	−	8.76995i	0.340568	−	0.359533i
$596$	3.12292	+	4.10814i	0.127920	+	0.168276i
$597$	−5.47106	+	2.17987i	−0.223916	+	0.0892161i
$598$	−22.1272	−	4.87056i	−0.904848	−	0.199172i
$599$	2.74801	+	18.8927i	0.112281	+	0.771933i	0.967355	+	0.253427i	$0.0815577\pi$
$599$	2.74801	+	18.8927i	0.112281	+	0.771933i	−0.855074	+	0.518506i	$0.826488\pi$
$600$	−1.61434	−	0.448219i	−0.0659051	−	0.0182985i
$601$	−14.7041	−	1.86835i	−0.599792	−	0.0762115i	−0.179744	−	0.983713i	$-0.557527\pi$
$601$	−14.7041	−	1.86835i	−0.599792	−	0.0762115i	−0.420048	+	0.907502i	$0.637987\pi$
$602$	−6.43225	−	9.86575i	−0.262159	−	0.402098i
$603$	0.320329	−	17.7398i	0.0130448	−	0.722420i
$604$	−27.9713	+	44.6437i	−1.13814	+	1.81653i
$605$	−9.04622	+	28.5411i	−0.367781	+	1.16036i
$606$	−8.24233	+	2.77716i	−0.334822	+	0.112815i
$607$	7.21132	+	7.34271i	0.292699	+	0.298032i	0.844075	−	0.536225i	$-0.180150\pi$
$607$	7.21132	+	7.34271i	0.292699	+	0.298032i	−0.551377	+	0.834256i	$0.685897\pi$
$608$	−1.28859	−	4.98882i	−0.0522594	−	0.202323i
$609$	−3.23710	+	1.56920i	−0.131174	+	0.0635873i
$610$	−15.1943	+	11.5504i	−0.615200	+	0.467663i
$611$	8.51678	−	4.32016i	0.344552	−	0.174775i
$612$	5.28680	+	7.79744i	0.213706	+	0.315193i
$613$	21.0187	−	23.0073i	0.848936	−	0.929254i	−0.149290	−	0.988793i	$-0.547699\pi$
$613$	21.0187	−	23.0073i	0.848936	−	0.929254i	0.998226	+	0.0595391i	$0.0189631\pi$
$614$	−15.9914	−	5.06855i	−0.645362	−	0.204550i
$615$	0.713818	+	0.299455i	0.0287839	+	0.0120752i
$616$	2.35290	−	1.72250i	0.0948010	−	0.0694014i
$617$	1.76291	−	1.55309i	0.0709722	−	0.0625249i	−0.624815	−	0.780773i	$-0.714826\pi$
$617$	1.76291	−	1.55309i	0.0709722	−	0.0625249i	0.695787	+	0.718248i	$0.255056\pi$
$618$	−6.39844	+	6.06092i	−0.257383	+	0.243806i
$619$	−12.2490	−	26.4757i	−0.492328	−	1.06415i	−0.981412	−	0.191912i	$-0.938531\pi$
$619$	−12.2490	−	26.4757i	−0.492328	−	1.06415i	0.489084	−	0.872237i	$-0.337331\pi$
$620$	−35.1625	−	38.4892i	−1.41216	−	1.54576i
$621$	−2.60032	+	10.8744i	−0.104347	+	0.436373i
$622$	−33.4040	−	23.5398i	−1.33938	−	0.943861i
$623$	−0.0961787	+	0.0444970i	−0.00385332	+	0.00178273i
$624$	−0.0632951	−	1.75207i	−0.00253383	−	0.0701388i
$625$	−7.73007	+	4.27877i	−0.309203	+	0.171151i
$626$	−17.8759	−	6.38473i	−0.714466	−	0.255185i
$627$	−0.0556344	+	0.304780i	−0.00222182	+	0.0121718i
$628$	1.52366	−	11.9914i	0.0608006	−	0.478507i
$629$	−1.04777	+	1.54534i	−0.0417773	+	0.0616169i
$630$	12.3632	+	51.7021i	0.492563	+	2.05986i
$631$	−16.8496	+	42.2894i	−0.670774	+	1.68352i	0.0576038	+	0.998340i	$0.481654\pi$
$631$	−16.8496	+	42.2894i	−0.670774	+	1.68352i	−0.728378	+	0.685176i	$0.759725\pi$
$632$	−1.38857	+	5.00118i	−0.0552344	+	0.198936i
$633$	−4.74447	+	6.24125i	−0.188576	+	0.248067i
$634$	7.67668	+	46.8257i	0.304880	+	1.85968i
$635$	−59.0573	+	21.0934i	−2.34362	+	0.837068i
$636$	6.09489	−	6.91833i	0.241678	−	0.274330i
$637$	0.870039	+	0.918489i	0.0344722	+	0.0363919i
$638$	2.43151	−	14.8315i	0.0962643	−	0.587186i
$639$	6.02759	+	33.0208i	0.238448	+	1.30628i
$640$	−20.4656	+	1.10961i	−0.808973	+	0.0438612i
$641$	−1.56191	+	0.0564255i	−0.0616917	+	0.00222867i	−0.0669311	−	0.997758i	$-0.521321\pi$
$641$	−1.56191	+	0.0564255i	−0.0616917	+	0.00222867i	0.00523935	+	0.999986i	$0.498332\pi$
$642$	1.61909	+	1.42638i	0.0639004	+	0.0562948i
$643$	14.7661	+	1.33665i	0.582316	+	0.0527123i	0.377373	−	0.926061i	$-0.376828\pi$
$643$	14.7661	+	1.33665i	0.582316	+	0.0527123i	0.204944	+	0.978774i	$0.434299\pi$
$644$	−34.2968	+	10.8705i	−1.35148	+	0.428358i
$645$	1.02810	−	2.22221i	0.0404815	−	0.0874993i
$646$	−0.584952	−	1.73608i	−0.0230146	−	0.0683050i
$647$	15.3281	+	12.5506i	0.602612	+	0.493414i	0.884816	−	0.465941i	$-0.154284\pi$
$647$	15.3281	+	12.5506i	0.602612	+	0.493414i	−0.282204	+	0.959354i	$0.591066\pi$
$648$	−6.05599	+	0.109354i	−0.237902	+	0.00429582i
$649$	4.67430	+	0.168863i	0.183482	+	0.00662847i
$650$	−19.5490	−	18.5178i	−0.766774	−	0.726327i
$651$	1.57601	−	4.67743i	0.0617686	−	0.183323i
$652$	5.95198	−	3.72918i	0.233098	−	0.146046i
$653$	15.6904	+	29.5952i	0.614012	+	1.15815i	0.974289	+	0.225303i	$0.0723373\pi$
$653$	15.6904	+	29.5952i	0.614012	+	1.15815i	−0.360277	+	0.932845i	$0.617318\pi$
$654$	7.91482	−	9.66646i	0.309494	−	0.377989i
$655$	−43.9458	−	40.1474i	−1.71710	−	1.56869i
$656$	2.24144	+	0.162160i	0.0875137	+	0.00633130i
$657$	−10.7398	+	12.6439i	−0.419001	+	0.493286i
$658$	15.3113	−	23.4845i	0.596898	−	0.915520i
$659$	11.1476	+	7.55825i	0.434248	+	0.294428i	0.758658	−	0.651489i	$-0.225855\pi$
$659$	11.1476	+	7.55825i	0.434248	+	0.294428i	−0.324410	+	0.945917i	$0.605166\pi$
$660$	3.72191	+	1.48294i	0.144875	+	0.0577235i
$661$	3.88068	+	13.9769i	0.150941	+	0.543640i	0.999885	+	0.0151576i	$0.00482499\pi$
$661$	3.88068	+	13.9769i	0.150941	+	0.543640i	−0.848944	+	0.528482i	$0.822761\pi$
$662$	42.9498	+	4.67107i	1.66929	+	0.181546i
$663$	−0.0826078	−	0.759566i	−0.00320822	−	0.0294991i
$664$	−3.14115	−	6.19247i	−0.121900	−	0.240314i
$665$	0.201879	−	5.58819i	0.00782852	−	0.216701i
$666$	−3.17849	−	7.57663i	−0.123164	−	0.293589i
$667$	−13.1433	+	24.7908i	−0.508909	+	0.959904i
$668$	0.234309	+	3.23871i	0.00906569	+	0.125310i
$669$	0.402291	−	0.119559i	0.0155535	−	0.00462243i
$670$	39.4205	+	20.8994i	1.52295	+	0.807415i
$671$	3.49920	−	2.10540i	0.135085	−	0.0812780i
$672$	−3.34943	−	5.34588i	−0.129207	−	0.206222i
$673$	18.2587	−	4.71615i	0.703820	−	0.181794i	0.118925	−	0.992903i	$-0.462055\pi$
$673$	18.2587	−	4.71615i	0.703820	−	0.181794i	0.584895	+	0.811109i	$0.301136\pi$
$674$	55.7646	+	32.1957i	2.14797	+	1.24013i
$675$	−9.31102	+	9.48066i	−0.358381	+	0.364911i
$676$	10.0945	−	20.8240i	0.388252	−	0.800922i
$677$	−6.31096	+	1.03463i	−0.242550	+	0.0397641i	−0.281831	−	0.959464i	$-0.590942\pi$
$677$	−6.31096	+	1.03463i	−0.242550	+	0.0397641i	0.0392806	+	0.999228i	$0.487493\pi$
$678$	−1.39663	+	3.91028i	−0.0536374	+	0.150174i
$679$	46.0010	+	6.69103i	1.76536	+	0.256778i
$680$	−3.55614	+	0.451855i	−0.136372	+	0.0173278i
$681$	5.41706	+	6.37746i	0.207582	+	0.244385i
$682$	12.1810	+	16.6391i	0.466437	+	0.637144i
$683$	5.75533	+	18.1583i	0.220222	+	0.694807i	0.997817	+	0.0660418i	$0.0210371\pi$
$683$	5.75533	+	18.1583i	0.220222	+	0.694807i	−0.777595	+	0.628765i	$0.783561\pi$
$684$	4.22233	+	1.09061i	0.161445	+	0.0417006i
$685$	12.1371	+	11.9199i	0.463733	+	0.455435i
$686$	38.6867	+	11.4975i	1.47707	+	0.438977i
$687$	0.308194	−	1.40014i	0.0117583	−	0.0534186i
$688$	0.768557	−	7.06676i	0.0293010	−	0.269418i
$689$	20.9767	−	7.92210i	0.799148	−	0.301808i
$690$	−10.5391	−	8.95201i	−0.401217	−	0.340797i
$691$	−17.1910	−	0.310419i	−0.653976	−	0.0118089i	−0.309927	−	0.950760i	$-0.600305\pi$
$691$	−17.1910	−	0.310419i	−0.653976	−	0.0118089i	−0.344049	+	0.938952i	$0.611799\pi$
$692$	33.2778	+	1.80427i	1.26503	+	0.0685881i
$693$	−1.43373	−	11.2836i	−0.0544629	−	0.428629i
$694$	−13.1544	−	6.67260i	−0.499334	−	0.253289i
$695$	52.4006	−	9.56515i	1.98767	−	0.362827i
$696$	1.03826	+	0.248273i	0.0393552	+	0.00941077i
$697$	0.979370			0.0370963
$698$	23.1374	−	31.3864i	0.875764	−	1.18799i
$699$	−9.13555			−0.345538
$700$	−41.5869	−	9.94444i	−1.57184	−	0.375864i
$701$	6.31954	−	1.15356i	0.238686	−	0.0435695i	−0.0589028	−	0.998264i	$-0.518760\pi$
$701$	6.31954	−	1.15356i	0.238686	−	0.0435695i	0.297589	+	0.954694i	$0.403818\pi$
$702$	6.09720	+	3.09283i	0.230124	+	0.116731i
$703$	0.108941	+	0.857376i	0.00410879	+	0.0323366i
$704$	16.4607	+	0.892472i	0.620385	+	0.0336363i
$705$	5.82749	+	0.105228i	0.219476	+	0.00396310i
$706$	12.7485	+	10.8287i	0.479796	+	0.407542i
$707$	−31.4225	+	11.8671i	−1.18176	+	0.446308i
$708$	−0.237386	+	2.18273i	−0.00892153	+	0.0820321i
$709$	−2.18430	+	9.92337i	−0.0820330	+	0.372680i	−0.999695	−	0.0246813i	$-0.992143\pi$
$709$	−2.18430	+	9.92337i	−0.0820330	+	0.372680i	0.917662	+	0.397361i	$0.130074\pi$
$710$	−80.9127	−	24.0469i	−3.03660	−	0.902465i
$711$	14.4446	+	14.1861i	0.541714	+	0.532020i
$712$	0.0304485	+	0.00786474i	0.00114110	+	0.000294743i
$713$	−11.6321	−	36.6996i	−0.435625	−	1.37441i
$714$	−1.32493	−	1.80983i	−0.0495841	−	0.0677310i
$715$	6.30777	+	7.42609i	0.235897	+	0.277720i
$716$	25.5144	−	3.24194i	0.953518	−	0.121157i
$717$	1.88620	+	0.274355i	0.0704413	+	0.0102460i
$718$	5.19700	−	14.5505i	0.193950	−	0.543021i
$719$	20.4318	−	3.34962i	0.761977	−	0.124920i	0.231750	−	0.972775i	$-0.425555\pi$
$719$	20.4318	−	3.34962i	0.761977	−	0.124920i	0.530227	+	0.847856i	$0.322107\pi$
$720$	−13.9959	+	28.8720i	−0.521595	+	1.07600i
$721$	−23.8485	+	24.2830i	−0.888165	+	0.904347i
$722$	33.6101	+	19.4048i	1.25084	+	0.722172i
$723$	−7.79414	+	2.01320i	−0.289867	+	0.0748717i
$724$	27.2209	+	43.4461i	1.01166	+	1.61466i
$725$	−28.5744	+	17.1926i	−1.06123	+	0.638518i
$726$	4.91169	+	2.60401i	0.182290	+	0.0966439i
$727$	38.5171	−	11.4471i	1.42852	−	0.424551i	0.524271	−	0.851552i	$-0.324338\pi$
$727$	38.5171	−	11.4471i	1.42852	−	0.424551i	0.904251	+	0.427001i	$0.140430\pi$
$728$	0.240203	+	3.32018i	0.00890252	+	0.123054i
$729$	−10.2635	+	19.3591i	−0.380131	+	0.717003i
$730$	−16.1386	−	38.4700i	−0.597318	−	1.42384i
$731$	0.111839	−	3.09582i	0.00413653	−	0.114503i
$732$	0.867199	+	1.70960i	0.0320526	+	0.0631885i
$733$	−1.87982	−	17.2847i	−0.0694329	−	0.638425i	−0.976212	−	0.216819i	$-0.930432\pi$
$733$	−1.87982	−	17.2847i	−0.0694329	−	0.638425i	0.906779	−	0.421606i	$-0.138534\pi$
$734$	−66.9826	−	7.28479i	−2.47237	−	0.268887i
$735$	0.206570	+	0.743997i	0.00761944	+	0.0274427i
$736$	−45.7111	−	18.2130i	−1.68493	−	0.671339i
$737$	−7.90168	−	5.35747i	−0.291062	−	0.197345i
$738$	−2.35386	+	3.61034i	−0.0866468	+	0.132898i
$739$	8.02771	−	9.45095i	0.295304	−	0.347659i	−0.594422	−	0.804153i	$-0.702619\pi$
$739$	8.02771	−	9.45095i	0.295304	−	0.347659i	0.889726	+	0.456494i	$0.150895\pi$
$740$	11.1474	+	0.806471i	0.409785	+	0.0296465i
$741$	−0.261119	−	0.238550i	−0.00959246	−	0.00876336i
$742$	41.7017	−	50.9308i	1.53092	−	1.86973i
$743$	14.7841	+	27.8857i	0.542375	+	1.02303i	0.991567	+	0.129593i	$0.0413671\pi$
$743$	14.7841	+	27.8857i	0.542375	+	1.02303i	−0.449192	+	0.893435i	$0.648288\pi$
$744$	−1.24121	+	0.777672i	−0.0455049	+	0.0285108i
$745$	−2.44563	+	7.25836i	−0.0896009	+	0.265926i
$746$	13.6971	+	12.9746i	0.501488	+	0.475035i
$747$	−27.0668	−	0.977815i	−0.990323	−	0.0357764i
$748$	5.06813	−	0.0915156i	0.185309	−	0.00334614i
$749$	6.44744	+	5.27911i	0.235584	+	0.192894i
$750$	−1.62072	−	4.81014i	−0.0591805	−	0.175641i
$751$	12.5986	−	27.2313i	0.459728	−	0.993685i	−0.529636	−	0.848225i	$-0.677672\pi$
$751$	12.5986	−	27.2313i	0.459728	−	0.993685i	0.989364	−	0.145460i	$-0.0464663\pi$
$752$	16.1301	−	5.11250i	0.588205	−	0.186434i
$753$	6.93882	+	0.628114i	0.252865	+	0.0228897i
$754$	12.8740	+	11.3417i	0.468845	+	0.413042i
$755$	−78.1434	+	2.82301i	−2.84393	+	0.102740i
$756$	10.8406	−	0.587762i	0.394270	−	0.0213767i
$757$	−5.35286	−	29.3244i	−0.194553	−	1.06581i	−0.924176	−	0.381966i	$-0.875247\pi$
$757$	−5.35286	−	29.3244i	−0.194553	−	1.06581i	0.729624	−	0.683849i	$-0.239695\pi$
$758$	6.78129	−	41.3641i	0.246308	−	1.50241i
$759$	2.03469	+	2.14800i	0.0738546	+	0.0779673i
$760$	−1.09692	+	1.24512i	−0.0397896	+	0.0451653i
$761$	15.9688	−	5.70358i	0.578870	−	0.206755i	−0.0306433	−	0.999530i	$-0.509756\pi$
$761$	15.9688	−	5.70358i	0.578870	−	0.206755i	0.609514	+	0.792776i	$0.291365\pi$
$762$	1.88380	+	11.4907i	0.0682429	+	0.416263i
$763$	29.1980	−	38.4093i	1.05704	−	1.39051i
$764$	−1.41053	+	5.08027i	−0.0510312	+	0.183798i
$765$	−5.17556	+	12.9897i	−0.187123	+	0.469642i
$766$	−3.21249	−	13.4344i	−0.116072	−	0.485405i
$767$	−2.99649	+	4.41949i	−0.108197	+	0.159579i
$768$	0.348112	−	2.73968i	0.0125614	−	0.0988596i
$769$	2.21045	−	12.1095i	0.0797109	−	0.436678i	−0.919354	−	0.393432i	$-0.871288\pi$
$769$	2.21045	−	12.1095i	0.0797109	−	0.436678i	0.999064	−	0.0432459i	$-0.0137699\pi$
$770$	26.9367	+	9.62097i	0.970732	+	0.346716i
$771$	−4.05497	+	2.24452i	−0.146036	+	0.0808343i
$772$	1.66089	+	45.9749i	0.0597767	+	1.65467i
$773$	9.77883	−	4.52417i	0.351720	−	0.162723i	−0.236071	−	0.971736i	$-0.575860\pi$
$773$	9.77883	−	4.52417i	0.351720	−	0.162723i	0.587791	+	0.809013i	$0.299998\pi$
$774$	11.1436	+	7.85291i	0.400549	+	0.282267i
$775$	10.6411	−	44.5004i	0.382241	−	1.59850i
$776$	−9.30414	−	10.1844i	−0.333999	−	0.365599i
$777$	0.444312	+	0.960364i	0.0159396	+	0.0344529i
$778$	−18.3984	+	17.4279i	−0.659616	+	0.624821i
$779$	0.340175	−	0.299686i	0.0121880	−	0.0107374i
$780$	−3.69046	+	2.70169i	−0.132140	+	0.0967361i
$781$	16.6547	+	6.98684i	0.595952	+	0.250009i
$782$	−16.6773	−	5.28595i	−0.596381	−	0.189025i
$783$	5.71082	−	6.25112i	0.204088	−	0.223397i
$784$	1.25799	+	1.85539i	0.0449282	+	0.0662641i
$785$	16.0005	−	8.11631i	0.571083	−	0.289684i
$786$	−8.79857	+	6.68850i	−0.313834	+	0.238571i
$787$	2.96553	−	1.43756i	0.105710	−	0.0512435i	−0.382598	−	0.923915i	$-0.624971\pi$
$787$	2.96553	−	1.43756i	0.105710	−	0.0512435i	0.488308	+	0.872671i	$0.337614\pi$
$788$	−4.97524	−	19.2617i	−0.177235	−	0.686170i
$789$	3.87014	+	3.94066i	0.137781	+	0.140291i
$790$	−48.2475	+	16.2565i	−1.71657	+	0.578379i
$791$	−4.84486	+	15.2857i	−0.172263	+	0.543497i
$792$	−1.79211	+	2.86031i	−0.0636799	+	0.101637i
$793$	−0.0841672	+	4.66117i	−0.00298887	+	0.165523i
$794$	−33.9703	−	52.1035i	−1.20556	−	1.84908i
$795$	13.5759	+	1.72500i	0.481487	+	0.0611793i
$796$	42.9780	+	11.9328i	1.52331	+	0.422946i
$797$	−4.76382	−	32.7514i	−0.168743	−	1.16011i	−0.886129	−	0.463438i	$-0.846616\pi$
$797$	−4.76382	−	32.7514i	−0.168743	−	1.16011i	0.717386	−	0.696676i	$-0.245338\pi$
$798$	−1.01401	−	0.223199i	−0.0358954	−	0.00790117i
$799$	6.85038	−	2.72944i	0.242349	−	0.0965606i
$800$	−35.3906	−	46.5555i	−1.25125	−	1.64599i
$801$	0.0843578	−	0.0890554i	0.00298064	−	0.00314662i
$802$	−6.87456	−	75.9437i	−0.242749	−	2.68167i
$803$	2.54291	+	8.55634i	0.0897372	+	0.301947i
$804$	2.77595	−	3.51801i	0.0979002	−	0.124071i
$805$	−41.9218	−	33.0792i	−1.47755	−	1.16589i
$806$	−23.4795	+	1.69865i	−0.827028	+	0.0598325i
$807$	1.15273	−	1.57461i	0.0405781	−	0.0554289i
$808$	9.44575	+	3.18264i	0.332300	+	0.111965i
$809$	2.54465	+	5.24933i	0.0894650	+	0.184557i	0.939835	−	0.341628i	$-0.110978\pi$
$809$	2.54465	+	5.24933i	0.0894650	+	0.184557i	−0.850370	+	0.526185i	$0.823622\pi$
$810$	−34.2243	−	48.5657i	−1.20252	−	1.70642i
$811$	4.22677	−	14.2222i	0.148422	−	0.499408i	−0.851257	−	0.524749i	$-0.824159\pi$
$811$	4.22677	−	14.2222i	0.148422	−	0.499408i	0.999679	+	0.0253413i	$0.00806724\pi$
$812$	26.7097	+	5.37559i	0.937328	+	0.188646i
$813$	−3.88255	−	2.95143i	−0.136167	−	0.103511i
$814$	−4.34904	−	0.793871i	−0.152434	−	0.0278252i
$815$	9.53897	+	4.20581i	0.334135	+	0.147323i
$816$	0.0732921	−	1.35179i	0.00256574	−	0.0473222i
$817$	−0.908471	−	1.10953i	−0.0317834	−	0.0388174i
$818$	−5.93515	+	14.1478i	−0.207518	+	0.494665i
$819$	11.7846	+	5.45213i	0.411787	+	0.190513i
$820$	−2.93133	−	5.07721i	−0.102366	−	0.177304i
$821$	16.3987	−	28.4033i	0.572318	−	0.991283i	−0.424010	−	0.905658i	$-0.639378\pi$
$821$	16.3987	−	28.4033i	0.572318	−	0.991283i	0.996327	−	0.0856257i	$-0.0272889\pi$
$822$	2.58196	−	1.81951i	0.0900561	−	0.0634627i
$823$	−12.1905	−	30.5959i	−0.424935	−	1.06651i	−0.973151	−	0.230169i	$-0.926072\pi$
$823$	−12.1905	−	30.5959i	−0.424935	−	1.06651i	0.548216	−	0.836337i	$-0.315307\pi$
$824$	10.0409	−	1.09201i	0.349792	−	0.0380421i
$825$	0.755907	+	3.43412i	0.0263173	+	0.119561i
$826$	−1.13108	+	15.6342i	−0.0393552	+	0.543983i
$827$	−21.2215	−	13.2962i	−0.737943	−	0.462354i	0.108997	−	0.994042i	$-0.465236\pi$
$827$	−21.2215	−	13.2962i	−0.737943	−	0.462354i	−0.846940	+	0.531688i	$0.821558\pi$
$828$	32.2224	−	26.3835i	1.11981	−	0.916889i
$829$	18.8665	−	16.0253i	0.655260	−	0.556583i	−0.256889	−	0.966441i	$-0.582698\pi$
$829$	18.8665	−	16.0253i	0.655260	−	0.556583i	0.912149	+	0.409858i	$0.134422\pi$
$830$	32.9845	−	59.5902i	1.14491	−	2.06841i
$831$	3.10255	+	0.508637i	0.107626	+	0.0176444i
$832$	−10.8403	+	15.3829i	−0.375821	+	0.533305i
$833$	0.605145	+	0.766910i	0.0209670	+	0.0265719i
$834$		−	9.89039i		−	0.342476i
$835$	−3.78360	+	2.98552i	−0.130937	+	0.103318i
$836$	1.73236	−	1.58263i	0.0599149	−	0.0547363i
$837$	0.628940	+	11.6001i	0.0217393	+	0.400958i
$838$	−9.24784	+	24.4871i	−0.319461	+	0.845892i
$839$	2.96245	−	20.3669i	0.102275	−	0.703145i	−0.873891	−	0.486121i	$-0.838411\pi$
$839$	2.96245	−	20.3669i	0.102275	−	0.703145i	0.976166	−	0.217023i	$-0.0696347\pi$
$840$	−0.819645	+	1.85899i	−0.0282804	+	0.0641413i
$841$	−6.49329	+	4.23348i	−0.223906	+	0.145982i
$842$	8.01113	+	5.22307i	0.276082	+	0.179999i
$843$	−1.10985	−	2.51720i	−0.0382254	−	0.0866968i
$844$	57.2120	−	15.8848i	1.96932	−	0.546778i
$845$	33.9905	−	4.94405i	1.16931	−	0.170080i
$846$	−6.40272	+	31.8132i	−0.220130	+	1.09376i
$847$	19.3188	+	9.36488i	0.663800	+	0.321781i
$848$	38.9490	−	7.83885i	1.33751	−	0.269187i
$849$	0.570402	−	6.30127i	0.0195761	−	0.216259i
$850$	−13.7446	−	15.6016i	−0.471436	−	0.535129i
$851$	7.22118	+	3.99709i	0.247539	+	0.137018i
$852$	−3.83528	+	7.56088i	−0.131395	+	0.259032i
$853$	−16.1866	−	6.11306i	−0.554218	−	0.209307i	0.0603411	−	0.998178i	$-0.480781\pi$
$853$	−16.1866	−	6.11306i	−0.554218	−	0.209307i	−0.614559	+	0.788870i	$0.710666\pi$
$854$	6.62780	+	11.9738i	0.226798	+	0.409737i
$855$	2.17714	+	6.09555i	0.0744567	+	0.208463i
$856$	−0.487897	−	2.42422i	−0.0166760	−	0.0828581i
$857$	−9.89447	+	38.3066i	−0.337989	+	1.30853i	0.544724	+	0.838616i	$0.316635\pi$
$857$	−9.89447	+	38.3066i	−0.337989	+	1.30853i	−0.882712	+	0.469914i	$0.844285\pi$
$858$	1.56676	−	0.904571i	0.0534884	−	0.0308815i
$859$	−24.2889	+	23.8543i	−0.828727	+	0.813898i	−0.984772	−	0.173852i	$-0.944379\pi$
$859$	−24.2889	+	23.8543i	−0.828727	+	0.813898i	0.156045	+	0.987750i	$0.450126\pi$
$860$	−16.3840	+	8.68623i	−0.558689	+	0.296198i
$861$	0.286165	−	0.475609i	0.00975246	−	0.0162087i
$862$	36.6648	−	15.3813i	1.24881	−	0.523890i
$863$	−40.6038	+	3.67552i	−1.38217	+	0.125116i	−0.756000	−	0.654572i	$-0.772849\pi$
$863$	−40.6038	+	3.67552i	−1.38217	+	0.125116i	−0.626168	+	0.779688i	$0.715378\pi$
$864$	11.9807	+	8.77075i	0.407591	+	0.298387i
$865$	25.5020	+	42.3847i	0.867096	+	1.44112i
$866$	−70.8169	−	42.6091i	−2.40646	−	1.44792i
$867$	0.0848487	+	4.69891i	0.00288161	+	0.159583i
$868$	−30.9407	+	20.9783i	−1.05019	+	0.712050i
$869$	10.6388	−	2.34178i	0.360897	−	0.0794395i
$870$	3.69963	+	9.79615i	0.125429	+	0.332120i
$871$	9.97202	−	4.39675i	0.337889	−	0.148978i
$872$	−13.9249	+	3.32978i	−0.471557	+	0.112761i
$873$	−52.3322	+	12.5139i	−1.77118	+	0.423531i
$874$	−7.41021	+	3.26723i	−0.250654	+	0.110516i
$875$	−6.92551	−	18.3378i	−0.234125	−	0.619932i
$876$	−4.09211	+	0.900741i	−0.138260	+	0.0304332i
$877$	−5.10637	+	3.46221i	−0.172430	+	0.116910i	−0.644349	−	0.764731i	$-0.722872\pi$
$877$	−5.10637	+	3.46221i	−0.172430	+	0.116910i	0.471919	+	0.881642i	$0.343561\pi$
$878$	−1.42564	−	78.9518i	−0.0481130	−	2.66449i
$879$	−2.75489	−	1.65756i	−0.0929202	−	0.0559082i
$880$	8.90052	+	14.7928i	0.300037	+	0.498665i
$881$	18.6723	+	13.6695i	0.629085	+	0.460537i	0.858515	−	0.512788i	$-0.171387\pi$
$881$	18.6723	+	13.6695i	0.629085	+	0.460537i	−0.229430	+	0.973325i	$0.573686\pi$
$882$	−4.28156	+	0.387574i	−0.144168	+	0.0130503i
$883$	−25.6801	+	10.7731i	−0.864204	+	0.362544i	−0.773852	−	0.633366i	$-0.781673\pi$
$883$	−25.6801	+	10.7731i	−0.864204	+	0.362544i	−0.0903517	+	0.995910i	$0.528799\pi$
$884$	−2.98331	+	4.95830i	−0.100340	+	0.166766i
$885$	−2.87922	+	1.52646i	−0.0967838	+	0.0513115i
$886$	42.1770	−	41.4223i	1.41697	−	1.39161i
$887$	−0.878348	+	0.507114i	−0.0294920	+	0.0170272i	−0.514674	−	0.857386i	$-0.672087\pi$
$887$	−0.878348	+	0.507114i	−0.0294920	+	0.0170272i	0.485182	+	0.874413i	$0.338754\pi$
$888$	0.0785310	−	0.304034i	0.00263533	−	0.0102027i
$889$	8.87221	+	44.0834i	0.297564	+	1.47851i
$890$	0.103758	+	0.290499i	0.00347796	+	0.00973756i
$891$	6.15638	+	11.1222i	0.206246	+	0.372607i
$892$	−2.97353	−	1.12299i	−0.0995611	−	0.0376005i
$893$	1.54421	−	3.04425i	0.0516749	−	0.101872i
$894$	1.24427	+	0.688729i	0.0416145	+	0.0230345i
$895$	25.2348	+	28.6441i	0.843506	+	0.957467i
$896$	−1.32493	+	14.6366i	−0.0442629	+	0.488976i
$897$	−3.31118	+	0.666407i	−0.110557	+	0.0222507i
$898$	57.2176	+	27.7366i	1.90937	+	0.925581i
$899$	−5.75220	+	28.5810i	−0.191847	+	0.953230i
$900$	48.9796	−	7.12428i	1.63265	−	0.237476i
$901$	16.6831	−	4.63205i	0.555796	−	0.154316i
$902$	0.935565	+	2.12190i	0.0311509	+	0.0706516i
$903$	−1.47074	−	0.958888i	−0.0489431	−	0.0319098i
$904$	3.98610	−	2.59884i	0.132576	−	0.0864363i
$905$	−30.7001	+	69.6292i	−1.02051	+	2.31455i
$906$	−2.08985	+	14.3678i	−0.0694306	+	0.477337i
$907$	14.8467	−	39.3121i	0.492976	−	1.30534i	−0.423736	−	0.905786i	$-0.639281\pi$
$907$	14.8467	−	39.3121i	0.492976	−	1.30534i	0.916712	−	0.399550i	$-0.130834\pi$
$908$	−3.43095	−	63.2802i	−0.113860	−	2.10003i
$909$	28.7046	−	26.2236i	0.952073	−	0.869782i
$910$	−25.6338	+	20.2268i	−0.849752	+	0.670512i
$911$		−	57.4897i		−	1.90472i	−0.304979	−	0.952359i	$-0.598650\pi$
$911$		−	57.4897i		−	1.90472i	0.304979	−	0.952359i	$-0.401350\pi$
$912$	−0.388190	−	0.491960i	−0.0128543	−	0.0162904i
$913$	−8.39470	+	11.9124i	−0.277824	+	0.394244i
$914$	4.32766	+	0.709485i	0.143146	+	0.0234677i
$915$	−1.37791	+	2.48935i	−0.0455524	+	0.0822955i
$916$	−8.27556	+	7.02933i	−0.273432	+	0.232255i
$917$	−33.0238	+	27.0397i	−1.09054	+	0.892928i
$918$	4.47361	+	2.80292i	0.147651	+	0.0925100i
$919$	0.744670	−	10.2931i	0.0245644	−	0.339539i	−0.970556	−	0.240874i	$-0.922566\pi$
$919$	0.744670	−	10.2931i	0.0245644	−	0.339539i	0.995121	−	0.0986647i	$-0.0314571\pi$
$920$	3.40661	+	15.4764i	0.112313	+	0.510241i
$921$	−2.48615	+	0.270385i	−0.0819213	+	0.00890948i
$922$	16.4803	+	41.3623i	0.542748	+	1.36220i
$923$	−16.8535	+	11.8767i	−0.554741	+	0.390927i
$924$	1.43643	−	2.48796i	0.0472550	−	0.0818480i
$925$	4.90461	+	8.49503i	0.161263	+	0.279315i
$926$	−12.7766	−	5.91107i	−0.419864	−	0.194250i
$927$	15.2407	−	36.3296i	0.500570	−	1.19322i
$928$	23.6063	+	28.8307i	0.774916	+	0.946414i
$929$	2.91342	−	53.7348i	0.0955862	−	1.76298i	−0.421293	−	0.906925i	$-0.638424\pi$
$929$	2.91342	−	53.7348i	0.0955862	−	1.76298i	0.516879	−	0.856058i	$-0.327094\pi$
$930$	−13.1463	−	5.79632i	−0.431084	−	0.190069i
$931$	0.444865	+	0.0812052i	0.0145799	+	0.00266139i
$932$	55.0812	+	41.8717i	1.80425	+	1.37155i
$933$	−5.97220	−	1.20196i	−0.195521	−	0.0393505i
$934$	−5.59399	+	18.8226i	−0.183041	+	0.615893i
$935$	4.33389	+	6.14997i	0.141733	+	0.201126i
$936$	−1.68081	−	3.46732i	−0.0549388	−	0.113333i
$937$	−42.5260	−	14.3287i	−1.38926	−	0.468097i	−0.477434	−	0.878668i	$-0.658433\pi$
$937$	−42.5260	−	14.3287i	−1.38926	−	0.468097i	−0.911829	+	0.410571i	$0.865329\pi$
$938$	18.8987	−	25.8152i	0.617063	−	0.842897i
$939$	−2.82236	+	0.204187i	−0.0921041	+	0.00666340i
$940$	−34.6536	−	27.3440i	−1.13027	−	0.891864i
$941$	−28.6458	+	36.3033i	−0.933827	+	1.18346i	0.0489762	+	0.998800i	$0.484404\pi$
$941$	−28.6458	+	36.3033i	−0.933827	+	1.18346i	−0.982803	+	0.184655i	$0.940883\pi$
$942$	−0.949024	−	3.19326i	−0.0309209	−	0.104042i
$943$	−0.390314	−	4.31182i	−0.0127104	−	0.140412i
$944$	−6.50628	+	6.86860i	−0.211761	+	0.223554i
$945$	9.75171	+	12.8282i	0.317223	+	0.417300i
$946$	6.81424	−	2.71504i	0.221550	−	0.0882736i
$947$	9.03041	+	1.98774i	0.293449	+	0.0645930i	0.359255	−	0.933239i	$-0.383031\pi$
$947$	9.03041	+	1.98774i	0.293449	+	0.0645930i	−0.0658060	+	0.997832i	$0.520962\pi$
$948$	0.736040	+	5.06029i	0.0239055	+	0.164351i
$949$	−9.81855	−	2.72611i	−0.318724	−	0.0884932i
$950$	−9.54812	−	1.21321i	−0.309782	−	0.0393619i
$951$	3.86333	+	5.92556i	0.125277	+	0.192150i
$952$	−0.0464073	+	2.57003i	−0.00150407	+	0.0832952i
$953$	−30.3762	+	48.4822i	−0.983983	+	1.57049i	−0.173415	+	0.984849i	$0.555480\pi$
$953$	−30.3762	+	48.4822i	−0.983983	+	1.57049i	−0.810569	+	0.585644i	$0.800842\pi$
$954$	−23.0214	+	72.6334i	−0.745346	+	2.35159i
$955$	−7.41601	+	2.49874i	−0.239976	+	0.0808575i
$956$	−10.1150	−	10.2993i	−0.327143	−	0.333104i
$957$	−0.560331	−	2.16933i	−0.0181129	−	0.0701245i
$958$	4.64974	−	2.25399i	0.150226	−	0.0728232i
$959$	9.71089	−	7.38203i	0.313581	−	0.238378i
$960$	−10.2430	+	5.19580i	−0.330591	+	0.167694i
$961$	−5.05120	−	7.44996i	−0.162942	−	0.240321i
$962$	3.40398	−	3.72603i	0.109749	−	0.120132i
$963$	−9.19482	−	2.91433i	−0.296299	−	0.0939130i
$964$	56.2207	+	23.5852i	1.81075	+	0.759629i
$965$	−55.0968	+	40.3350i	−1.77363	+	1.29843i
$966$	−7.44000	+	6.55447i	−0.239378	+	0.210887i
$967$	−14.2740	+	13.5210i	−0.459020	+	0.434807i	−0.881941	−	0.471360i	$-0.843763\pi$
$967$	−14.2740	+	13.5210i	−0.459020	+	0.434807i	0.422921	+	0.906166i	$0.361005\pi$
$968$	−2.67509	−	5.78212i	−0.0859808	−	0.185844i
$969$	−0.184202	−	0.201629i	−0.00591741	−	0.00647726i
$970$	31.4690	−	131.601i	1.01041	−	4.22546i
$971$	−23.5888	−	16.6231i	−0.757002	−	0.533461i	0.132063	−	0.991241i	$-0.457840\pi$
$971$	−23.5888	−	16.6231i	−0.757002	−	0.533461i	−0.889065	+	0.457781i	$0.848644\pi$
$972$	−17.2014	+	7.95822i	−0.551735	+	0.255260i
$973$	−1.37893	−	38.1700i	−0.0442064	−	1.22367i
$974$	36.1101	−	19.9878i	1.15704	−	0.640449i
$975$	−3.78028	−	1.35020i	−0.121066	−	0.0432410i
$976$	−1.48331	+	8.12601i	−0.0474797	+	0.260107i
$977$	−0.816644	+	6.42707i	−0.0261268	+	0.205620i	−0.999745	−	0.0225608i	$-0.992818\pi$
$977$	−0.816644	+	6.42707i	−0.0261268	+	0.205620i	0.973619	+	0.228181i	$0.0732778\pi$
$978$	1.08629	−	1.60215i	0.0347356	−	0.0512311i
$979$	−0.0153500	−	0.0641926i	−0.000490588	−	0.00205161i
$980$	2.16454	−	5.43259i	0.0691437	−	0.173538i
$981$	−14.9408	+	53.8118i	−0.477022	+	1.71808i
$982$	3.72169	−	4.89580i	0.118764	−	0.156231i
$983$	0.125163	+	0.763461i	0.00399208	+	0.0243506i	0.988747	−	0.149594i	$-0.0477968\pi$
$983$	0.125163	+	0.763461i	0.00399208	+	0.0243506i	−0.984755	+	0.173945i	$0.944349\pi$
$984$	−0.155119	+	0.0554036i	−0.00494500	+	0.00176620i
$985$	19.5189	−	22.1560i	0.621925	−	0.705950i
$986$	9.11095	+	9.61831i	0.290152	+	0.306310i
$987$	0.676137	−	4.12426i	0.0215217	−	0.131276i
$988$	0.481010	+	2.63510i	0.0153030	+	0.0838339i
$989$	−13.6744	+	0.741404i	−0.434820	+	0.0235753i
$990$	−33.0875	+	1.19532i	−1.05159	+	0.0379896i
$991$	−4.63509	−	4.08341i	−0.147239	−	0.129714i	0.584232	−	0.811586i	$-0.301396\pi$
$991$	−4.63509	−	4.08341i	−0.147239	−	0.129714i	−0.731471	+	0.681873i	$0.761166\pi$
$992$	−50.9174	−	4.60913i	−1.61663	−	0.146340i
$993$	6.13950	−	1.94594i	0.194831	−	0.0617524i
$994$	−25.4146	+	54.9327i	−0.806102	+	1.74236i
$995$	21.1388	+	62.7378i	0.670146	+	1.98892i
$996$	−5.29292	−	4.33380i	−0.167712	−	0.137322i
$997$	19.5210	−	0.352492i	0.618235	−	0.0111635i	0.291948	−	0.956434i	$-0.405697\pi$
$997$	19.5210	−	0.352492i	0.618235	−	0.0111635i	0.326287	+	0.945271i	$0.394202\pi$
$998$	11.3929	+	0.411579i	0.360636	+	0.0130283i
$999$	−1.80813	−	1.71275i	−0.0572066	−	0.0541890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.k.a.3.5	✓	1624
349.233	even	174	inner	349.2.k.a.233.5	yes	1624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.k.a.3.5	✓	1624	1.1	even	1	trivial
349.2.k.a.233.5	yes	1624	349.233	even	174	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.k (of order \(174\), degree \(56\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03001 - 0.485425i) q^{2} +(-0.306098 + 0.0558749i) q^{3} +(2.10166 + 1.06608i) q^{4} +(0.440893 + 3.46988i) q^{5} +(0.648506 + 0.0351610i) q^{6} +(2.50769 + 0.0452815i) q^{7} +(-0.567264 - 0.481838i) q^{8} +(-2.71595 + 1.02571i) q^{9} +O(q^{10})\)	\(q+(-2.03001 - 0.485425i) q^{2} +(-0.306098 + 0.0558749i) q^{3} +(2.10166 + 1.06608i) q^{4} +(0.440893 + 3.46988i) q^{5} +(0.648506 + 0.0351610i) q^{6} +(2.50769 + 0.0452815i) q^{7} +(-0.567264 - 0.481838i) q^{8} +(-2.71595 + 1.02571i) q^{9} +(0.789345 - 7.25791i) q^{10} +(-0.335804 + 1.52557i) q^{11} +(-0.702882 - 0.208894i) q^{12} +(-1.27228 - 1.24952i) q^{13} +(-5.06865 - 1.30922i) q^{14} +(-0.328836 - 1.03749i) q^{15} +(-1.86643 - 2.54951i) q^{16} +(-0.891437 - 1.04948i) q^{17} +(6.01132 - 0.763817i) q^{18} +(-0.630772 - 0.0917483i) q^{19} +(-2.77254 + 7.76253i) q^{20} +(-0.770129 + 0.126256i) q^{21} +(1.42224 - 2.93393i) q^{22} +(-4.26523 + 4.34294i) q^{23} +(0.200561 + 0.115794i) q^{24} +(-7.00453 + 1.80925i) q^{25} +(1.97620 + 3.15413i) q^{26} +(1.57388 - 0.946975i) q^{27} +(5.22204 + 2.76855i) q^{28} +(4.41861 - 1.31319i) q^{29} +(0.163918 + 2.26574i) q^{30} +(-2.96251 + 5.58789i) q^{31} +(3.12713 + 7.45421i) q^{32} +(0.0175478 - 0.485739i) q^{33} +(1.30018 + 2.56319i) q^{34} +(0.948501 + 8.72132i) q^{35} +(-6.80149 - 0.739707i) q^{36} +(-0.362744 - 1.30649i) q^{37} +(1.23594 + 0.492443i) q^{38} +(0.459260 + 0.311386i) q^{39} +(1.42182 - 2.18078i) q^{40} +(-0.460451 + 0.542084i) q^{41} +(1.62466 + 0.117538i) q^{42} +(1.66096 + 1.51740i) q^{43} +(-2.33212 + 2.84825i) q^{44} +(-4.75653 - 8.97178i) q^{45} +(10.7666 - 6.74578i) q^{46} +(-1.70995 + 5.07495i) q^{47} +(0.713764 + 0.676113i) q^{48} +(-0.708996 - 0.0256132i) q^{49} +(15.0975 - 0.272618i) q^{50} +(0.331507 + 0.271435i) q^{51} +(-1.34183 - 3.98241i) q^{52} +(-5.27972 + 11.4119i) q^{53} +(-3.65469 + 1.15837i) q^{54} +(-5.44161 - 0.492583i) q^{55} +(-1.40070 - 1.23399i) q^{56} +(0.198205 - 0.00716033i) q^{57} +(-9.60728 + 0.520891i) q^{58} +(-0.537688 - 2.94560i) q^{59} +(0.414938 - 2.53101i) q^{60} +(-1.79784 - 1.89796i) q^{61} +(8.72643 - 9.90540i) q^{62} +(-6.85720 + 2.44918i) q^{63} +(-1.70729 - 10.4140i) q^{64} +(3.77473 - 4.96557i) q^{65} +(-0.271412 + 0.977537i) q^{66} +(-2.26208 + 5.67740i) q^{67} +(-0.754674 - 3.15599i) q^{68} +(1.06292 - 1.56769i) q^{69} +(2.30808 - 18.1648i) q^{70} +(2.07620 - 11.3740i) q^{71} +(2.03489 + 0.726800i) q^{72} +(4.99947 - 2.76732i) q^{73} +(0.102174 + 2.82827i) q^{74} +(2.04298 - 0.945185i) q^{75} +(-1.22786 - 0.865274i) q^{76} +(-0.911172 + 3.81046i) q^{77} +(-0.781149 - 0.855054i) q^{78} +(-2.92816 - 6.32911i) q^{79} +(8.02357 - 7.60033i) q^{80} +(6.10635 - 5.37956i) q^{81} +(1.19786 - 0.876923i) q^{82} +(8.60289 + 3.60901i) q^{83} +(-1.75315 - 0.555667i) q^{84} +(3.24854 - 3.55589i) q^{85} +(-2.63519 - 3.88662i) q^{86} +(-1.27915 + 0.648855i) q^{87} +(0.925570 - 0.703600i) q^{88} +(-0.0380208 + 0.0184308i) q^{89} +(5.30070 + 20.5218i) q^{90} +(-3.13391 - 3.19101i) q^{91} +(-13.5940 + 4.58034i) q^{92} +(0.594596 - 1.87597i) q^{93} +(5.93473 - 9.47216i) q^{94} +(0.0402520 - 2.22915i) q^{95} +(-1.37371 - 2.10699i) q^{96} +(18.3862 + 2.33621i) q^{97} +(1.42684 + 0.396159i) q^{98} +(-0.652772 - 4.48782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9}+O(q^{10}) \) 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9	\( 1624 q - 55 q^{2} - 58 q^{3} - 85 q^{4} - 60 q^{5} - 58 q^{6} - 58 q^{7} - 145 q^{8} - 29 q^{9} - 58 q^{10} - 58 q^{11} - 57 q^{12} - 55 q^{13} - 48 q^{14} - 59 q^{15} - 29 q^{16} - 48 q^{17} + 43 q^{18} + 67 q^{19} - 58 q^{20} + 58 q^{21} - 55 q^{22} - 41 q^{23} - 39 q^{24} - 29 q^{25} - 112 q^{26} - 76 q^{27} - 58 q^{28} - 56 q^{29} - 67 q^{30} - 90 q^{31} - 67 q^{32} - 46 q^{33} + 5 q^{34} - 82 q^{36} + 45 q^{37} - 58 q^{38} - 58 q^{39} - 112 q^{40} + 10 q^{41} + 305 q^{42} - 13 q^{43} + 40 q^{44} - 56 q^{45} - 85 q^{46} - 58 q^{47} - 122 q^{48} - 93 q^{49} - 441 q^{50} - 160 q^{51} + 58 q^{52} - 58 q^{53} - 85 q^{54} + 34 q^{55} - 69 q^{56} - 29 q^{57} - 58 q^{58} - 40 q^{59} + 522 q^{60} + 87 q^{61} - 49 q^{62} - 37 q^{63} + 335 q^{64} - 58 q^{65} - 565 q^{66} - 116 q^{67} - 58 q^{68} + 16 q^{69} - 98 q^{70} - 34 q^{71} + 44 q^{72} - 52 q^{73} - 204 q^{74} - 95 q^{76} - 54 q^{77} + 439 q^{78} - 58 q^{79} - 192 q^{80} - 209 q^{81} - 79 q^{82} + 162 q^{83} + 330 q^{84} - 192 q^{85} + 126 q^{86} - 190 q^{87} - 8 q^{88} + 345 q^{89} - 46 q^{90} - 30 q^{91} + 62 q^{92} - 89 q^{93} - 87 q^{94} - 350 q^{95} + 990 q^{96} - 43 q^{97} - 464 q^{98} - 97 q^{99}+O(q^{100}) \) 1624 * q - 55 * q^2 - 58 * q^3 - 85 * q^4 - 60 * q^5 - 58 * q^6 - 58 * q^7 - 145 * q^8 - 29 * q^9 - 58 * q^10 - 58 * q^11 - 57 * q^12 - 55 * q^13 - 48 * q^14 - 59 * q^15 - 29 * q^16 - 48 * q^17 + 43 * q^18 + 67 * q^19 - 58 * q^20 + 58 * q^21 - 55 * q^22 - 41 * q^23 - 39 * q^24 - 29 * q^25 - 112 * q^26 - 76 * q^27 - 58 * q^28 - 56 * q^29 - 67 * q^30 - 90 * q^31 - 67 * q^32 - 46 * q^33 + 5 * q^34 - 82 * q^36 + 45 * q^37 - 58 * q^38 - 58 * q^39 - 112 * q^40 + 10 * q^41 + 305 * q^42 - 13 * q^43 + 40 * q^44 - 56 * q^45 - 85 * q^46 - 58 * q^47 - 122 * q^48 - 93 * q^49 - 441 * q^50 - 160 * q^51 + 58 * q^52 - 58 * q^53 - 85 * q^54 + 34 * q^55 - 69 * q^56 - 29 * q^57 - 58 * q^58 - 40 * q^59 + 522 * q^60 + 87 * q^61 - 49 * q^62 - 37 * q^63 + 335 * q^64 - 58 * q^65 - 565 * q^66 - 116 * q^67 - 58 * q^68 + 16 * q^69 - 98 * q^70 - 34 * q^71 + 44 * q^72 - 52 * q^73 - 204 * q^74 - 95 * q^76 - 54 * q^77 + 439 * q^78 - 58 * q^79 - 192 * q^80 - 209 * q^81 - 79 * q^82 + 162 * q^83 + 330 * q^84 - 192 * q^85 + 126 * q^86 - 190 * q^87 - 8 * q^88 + 345 * q^89 - 46 * q^90 - 30 * q^91 + 62 * q^92 - 89 * q^93 - 87 * q^94 - 350 * q^95 + 990 * q^96 - 43 * q^97 - 464 * q^98 - 97 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more