LMFDB - Embedded newform 322.2.i.d.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	322.71
Dual form			322.2.i.d.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{2} +(-0.311523 - 2.16669i) q^{3} +(0.415415 + 0.909632i) q^{4} +(3.63410 + 1.06707i) q^{5} +(0.909331 - 1.99116i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-1.71902 + 0.504749i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{2} +(-0.311523 - 2.16669i) q^{3} +(0.415415 + 0.909632i) q^{4} +(3.63410 + 1.06707i) q^{5} +(0.909331 - 1.99116i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-1.71902 + 0.504749i) q^{9} +(2.48030 + 2.86241i) q^{10} +(-4.18629 + 2.69037i) q^{11} +(1.84148 - 1.18345i) q^{12} +(-0.479443 - 0.553307i) q^{13} +(0.959493 - 0.281733i) q^{14} +(1.17990 - 8.20638i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.29192 - 2.82891i) q^{17} +(-1.71902 - 0.504749i) q^{18} +(0.406772 + 0.890707i) q^{19} +(0.539020 + 3.74897i) q^{20} +(-1.84148 - 1.18345i) q^{21} -4.97625 q^{22} +(-0.648138 - 4.75183i) q^{23} +2.18897 q^{24} +(7.86176 + 5.05245i) q^{25} +(-0.104193 - 0.724677i) q^{26} +(-1.09884 - 2.40613i) q^{27} +(0.959493 + 0.281733i) q^{28} +(-0.0957505 + 0.209664i) q^{29} +(5.42930 - 6.26574i) q^{30} +(-1.20953 + 8.41249i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(7.13331 + 8.23228i) q^{33} +(2.61625 - 1.68136i) q^{34} +(3.18626 - 2.04769i) q^{35} +(-1.17324 - 1.35399i) q^{36} +(-5.60670 + 1.64628i) q^{37} +(-0.139354 + 0.969228i) q^{38} +(-1.04949 + 1.21117i) q^{39} +(-1.57339 + 3.44525i) q^{40} +(0.499980 + 0.146807i) q^{41} +(-0.909331 - 1.99116i) q^{42} +(-1.47048 - 10.2274i) q^{43} +(-4.18629 - 2.69037i) q^{44} -6.78568 q^{45} +(2.02379 - 4.34791i) q^{46} -11.5810 q^{47} +(1.84148 + 1.18345i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(3.88217 + 8.50078i) q^{50} +(-6.53182 - 1.91792i) q^{51} +(0.304138 - 0.665968i) q^{52} +(-1.08408 + 1.25109i) q^{53} +(0.376447 - 2.61825i) q^{54} +(-18.0842 + 5.31000i) q^{55} +(0.654861 + 0.755750i) q^{56} +(1.80317 - 1.15882i) q^{57} +(-0.193904 + 0.124614i) q^{58} +(7.56933 + 8.73548i) q^{59} +(7.95493 - 2.33578i) q^{60} +(-1.65471 + 11.5087i) q^{61} +(-5.56566 + 6.42311i) q^{62} +(-0.744253 + 1.62969i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.15193 - 2.52237i) q^{65} +(1.55022 + 10.7820i) q^{66} +(-3.56617 - 2.29184i) q^{67} +3.10995 q^{68} +(-10.0938 + 2.88462i) q^{69} +3.78752 q^{70} +(3.45379 + 2.21961i) q^{71} +(-0.254970 - 1.77335i) q^{72} +(3.34650 + 7.32782i) q^{73} +(-5.60670 - 1.64628i) q^{74} +(8.49796 - 18.6079i) q^{75} +(-0.641236 + 0.740026i) q^{76} +(-0.708195 + 4.92560i) q^{77} +(-1.53769 + 0.451507i) q^{78} +(2.51647 + 2.90416i) q^{79} +(-3.18626 + 2.04769i) q^{80} +(-9.39257 + 6.03624i) q^{81} +(0.341240 + 0.393812i) q^{82} +(-5.41640 + 1.59040i) q^{83} +(0.311523 - 2.16669i) q^{84} +(7.71359 - 8.90196i) q^{85} +(4.29231 - 9.39885i) q^{86} +(0.484106 + 0.142146i) q^{87} +(-2.06721 - 4.52656i) q^{88} +(-2.52535 - 17.5642i) q^{89} +(-5.70848 - 3.66862i) q^{90} -0.732130 q^{91} +(4.05317 - 2.56355i) q^{92} +18.6040 q^{93} +(-9.74257 - 6.26117i) q^{94} +(0.527805 + 3.67097i) q^{95} +(0.909331 + 1.99116i) q^{96} +(7.31030 + 2.14650i) q^{97} +(0.415415 - 0.909632i) q^{98} +(5.83835 - 6.73781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$3$	−0.311523	−	2.16669i	−0.179858	−	1.25094i	−0.857089	−	0.515168i	$-0.827729\pi$
$3$	−0.311523	−	2.16669i	−0.179858	−	1.25094i	0.677231	−	0.735770i	$-0.263180\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	3.63410	+	1.06707i	1.62522	+	0.477207i	0.962414	−	0.271587i	$-0.0875483\pi$
$5$	3.63410	+	1.06707i	1.62522	+	0.477207i	0.662803	+	0.748793i	$0.269366\pi$
$6$	0.909331	−	1.99116i	0.371233	−	0.812887i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	−1.71902	+	0.504749i	−0.573006	+	0.168250i
$10$	2.48030	+	2.86241i	0.784339	+	0.905175i
$11$	−4.18629	+	2.69037i	−1.26221	+	0.811176i	−0.988586	−	0.150660i	$-0.951860\pi$
$11$	−4.18629	+	2.69037i	−1.26221	+	0.811176i	−0.273628	+	0.961835i	$0.588224\pi$
$12$	1.84148	−	1.18345i	0.531589	−	0.341632i
$13$	−0.479443	−	0.553307i	−0.132974	−	0.153460i	0.685358	−	0.728207i	$-0.259646\pi$
$13$	−0.479443	−	0.553307i	−0.132974	−	0.153460i	−0.818331	+	0.574747i	$0.805100\pi$
$14$	0.959493	−	0.281733i	0.256435	−	0.0752962i
$15$	1.17990	−	8.20638i	0.304649	−	2.11888i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	1.29192	−	2.82891i	0.313336	−	0.686111i	−0.685795	−	0.727795i	$-0.740545\pi$
$17$	1.29192	−	2.82891i	0.313336	−	0.686111i	0.999131	+	0.0416845i	$0.0132724\pi$
$18$	−1.71902	−	0.504749i	−0.405176	−	0.118971i
$19$	0.406772	+	0.890707i	0.0933199	+	0.204342i	0.950536	−	0.310615i	$-0.100535\pi$
$19$	0.406772	+	0.890707i	0.0933199	+	0.204342i	−0.857216	+	0.514957i	$0.827808\pi$
$20$	0.539020	+	3.74897i	0.120529	+	0.838294i
$21$	−1.84148	−	1.18345i	−0.401844	−	0.258249i
$22$	−4.97625			−1.06094
$23$	−0.648138	−	4.75183i	−0.135146	−	0.990826i
$23$	−0.648138	−	4.75183i	−0.135146	−	0.990826i
$24$	2.18897			0.446822
$25$	7.86176	+	5.05245i	1.57235	+	1.01049i
$26$	−0.104193	−	0.724677i	−0.0204339	−	0.142121i
$27$	−1.09884	−	2.40613i	−0.211473	−	0.463061i
$28$	0.959493	+	0.281733i	0.181327	+	0.0532424i
$29$	−0.0957505	+	0.209664i	−0.0177804	+	0.0389337i	−0.918314	−	0.395853i	$-0.870449\pi$
$29$	−0.0957505	+	0.209664i	−0.0177804	+	0.0389337i	0.900533	+	0.434787i	$0.143176\pi$
$30$	5.42930	−	6.26574i	0.991249	−	1.14396i
$31$	−1.20953	+	8.41249i	−0.217239	+	1.51093i	0.530928	+	0.847417i	$0.321843\pi$
$31$	−1.20953	+	8.41249i	−0.217239	+	1.51093i	−0.748167	+	0.663511i	$0.769066\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	7.13331	+	8.23228i	1.24175	+	1.43306i
$34$	2.61625	−	1.68136i	0.448684	−	0.288352i
$35$	3.18626	−	2.04769i	0.538577	−	0.346122i
$36$	−1.17324	−	1.35399i	−0.195540	−	0.225666i
$37$	−5.60670	+	1.64628i	−0.921736	+	0.270646i	−0.707973	−	0.706239i	$-0.750390\pi$
$37$	−5.60670	+	1.64628i	−0.921736	+	0.270646i	−0.213763	+	0.976886i	$0.568572\pi$
$38$	−0.139354	+	0.969228i	−0.0226062	+	0.157230i
$39$	−1.04949	+	1.21117i	−0.168052	+	0.193943i
$40$	−1.57339	+	3.44525i	−0.248775	+	0.544741i
$41$	0.499980	+	0.146807i	0.0780837	+	0.0229274i	0.320541	−	0.947235i	$-0.396135\pi$
$41$	0.499980	+	0.146807i	0.0780837	+	0.0229274i	−0.242457	+	0.970162i	$0.577953\pi$
$42$	−0.909331	−	1.99116i	−0.140313	−	0.307242i
$43$	−1.47048	−	10.2274i	−0.224246	−	1.55967i	−0.721719	−	0.692186i	$-0.756648\pi$
$43$	−1.47048	−	10.2274i	−0.224246	−	1.55967i	0.497473	−	0.867479i	$-0.334261\pi$
$44$	−4.18629	−	2.69037i	−0.631107	−	0.405588i
$45$	−6.78568			−1.01155
$46$	2.02379	−	4.34791i	0.298391	−	0.641064i
$47$	−11.5810			−1.68926			−0.844632	−	0.535347i	$-0.820181\pi$
$47$	−11.5810			−1.68926			−0.844632	+	0.535347i	$0.820181\pi$
$48$	1.84148	+	1.18345i	0.265795	+	0.170816i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	3.88217	+	8.50078i	0.549022	+	1.20219i
$51$	−6.53182	−	1.91792i	−0.914638	−	0.268562i
$52$	0.304138	−	0.665968i	0.0421763	−	0.0923532i
$53$	−1.08408	+	1.25109i	−0.148910	+	0.171851i	−0.825304	−	0.564689i	$-0.808996\pi$
$53$	−1.08408	+	1.25109i	−0.148910	+	0.171851i	0.676394	+	0.736540i	$0.263542\pi$
$54$	0.376447	−	2.61825i	0.0512280	−	0.356299i
$55$	−18.0842	+	5.31000i	−2.43847	+	0.716000i
$56$	0.654861	+	0.755750i	0.0875094	+	0.100991i
$57$	1.80317	−	1.15882i	0.238835	−	0.153490i
$58$	−0.193904	+	0.124614i	−0.0254608	+	0.0163627i
$59$	7.56933	+	8.73548i	0.985443	+	1.13726i	0.990533	+	0.137275i	$0.0438344\pi$
$59$	7.56933	+	8.73548i	0.985443	+	1.13726i	−0.00508982	+	0.999987i	$0.501620\pi$
$60$	7.95493	−	2.33578i	1.02698	−	0.301548i
$61$	−1.65471	+	11.5087i	−0.211863	+	1.47354i	0.555064	+	0.831808i	$0.312694\pi$
$61$	−1.65471	+	11.5087i	−0.211863	+	1.47354i	−0.766927	+	0.641734i	$0.778215\pi$
$62$	−5.56566	+	6.42311i	−0.706839	+	0.815736i
$63$	−0.744253	+	1.62969i	−0.0937671	+	0.205321i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−1.15193	−	2.52237i	−0.142879	−	0.312861i
$66$	1.55022	+	10.7820i	0.190819	+	1.32717i
$67$	−3.56617	−	2.29184i	−0.435676	−	0.279992i	0.304362	−	0.952556i	$-0.401557\pi$
$67$	−3.56617	−	2.29184i	−0.435676	−	0.279992i	−0.740039	+	0.672564i	$0.765193\pi$
$68$	3.10995			0.377136
$69$	−10.0938	+	2.88462i	−1.21516	+	0.347267i
$70$	3.78752			0.452695
$71$	3.45379	+	2.21961i	0.409889	+	0.263420i	0.729297	−	0.684198i	$-0.239847\pi$
$71$	3.45379	+	2.21961i	0.409889	+	0.263420i	−0.319407	+	0.947617i	$0.603484\pi$
$72$	−0.254970	−	1.77335i	−0.0300485	−	0.208992i
$73$	3.34650	+	7.32782i	0.391679	+	0.857657i	0.998047	+	0.0624725i	$0.0198986\pi$
$73$	3.34650	+	7.32782i	0.391679	+	0.857657i	−0.606368	+	0.795184i	$0.707374\pi$
$74$	−5.60670	−	1.64628i	−0.651766	−	0.191376i
$75$	8.49796	−	18.6079i	0.981260	−	2.14866i
$76$	−0.641236	+	0.740026i	−0.0735548	+	0.0848868i
$77$	−0.708195	+	4.92560i	−0.0807063	+	0.561324i
$78$	−1.53769	+	0.451507i	−0.174109	+	0.0511231i
$79$	2.51647	+	2.90416i	0.283125	+	0.326744i	0.879443	−	0.476005i	$-0.157916\pi$
$79$	2.51647	+	2.90416i	0.283125	+	0.326744i	−0.596318	+	0.802749i	$0.703370\pi$
$80$	−3.18626	+	2.04769i	−0.356235	+	0.228938i
$81$	−9.39257	+	6.03624i	−1.04362	+	0.670693i
$82$	0.341240	+	0.393812i	0.0376836	+	0.0434892i
$83$	−5.41640	+	1.59040i	−0.594527	+	0.174569i	−0.565134	−	0.824999i	$-0.691176\pi$
$83$	−5.41640	+	1.59040i	−0.594527	+	0.174569i	−0.0293927	+	0.999568i	$0.509357\pi$
$84$	0.311523	−	2.16669i	0.0339899	−	0.236405i
$85$	7.71359	−	8.90196i	0.836656	−	0.965553i
$86$	4.29231	−	9.39885i	0.462852	−	1.01350i
$87$	0.484106	+	0.142146i	0.0519016	+	0.0152397i
$88$	−2.06721	−	4.52656i	−0.220365	−	0.482533i
$89$	−2.52535	−	17.5642i	−0.267686	−	1.86180i	−0.470255	−	0.882530i	$-0.655838\pi$
$89$	−2.52535	−	17.5642i	−0.267686	−	1.86180i	0.202569	−	0.979268i	$-0.435071\pi$
$90$	−5.70848	−	3.66862i	−0.601726	−	0.386706i
$91$	−0.732130			−0.0767480
$92$	4.05317	−	2.56355i	0.422572	−	0.267269i
$93$	18.6040			1.92915
$94$	−9.74257	−	6.26117i	−1.00487	−	0.645790i
$95$	0.527805	+	3.67097i	0.0541517	+	0.376633i
$96$	0.909331	+	1.99116i	0.0928082	+	0.203222i
$97$	7.31030	+	2.14650i	0.742249	+	0.217944i	0.630929	−	0.775841i	$-0.282674\pi$
$97$	7.31030	+	2.14650i	0.742249	+	0.217944i	0.111320	+	0.993785i	$0.464492\pi$
$98$	0.415415	−	0.909632i	0.0419633	−	0.0918867i
$99$	5.83835	−	6.73781i	0.586776	−	0.677176i
$100$	−1.32997	+	9.25017i	−0.132997	+	0.925017i
$101$	0.273380	−	0.0802717i	0.0272023	−	0.00798733i	−0.268103	−	0.963390i	$-0.586397\pi$
$101$	0.273380	−	0.0802717i	0.0272023	−	0.00798733i	0.295305	+	0.955403i	$0.404579\pi$
$102$	−4.45802	−	5.14482i	−0.441409	−	0.509414i
$103$	12.9958	−	8.35188i	1.28051	−	0.822935i	0.289561	−	0.957160i	$-0.406491\pi$
$103$	12.9958	−	8.35188i	1.28051	−	0.822935i	0.990951	+	0.134225i	$0.0428543\pi$
$104$	0.615907	−	0.395819i	0.0603946	−	0.0388133i
$105$	−5.42930	−	6.26574i	−0.529845	−	0.611474i
$106$	−1.58838	+	0.466389i	−0.154277	+	0.0452997i
$107$	−1.90501	+	13.2497i	−0.184165	+	1.28089i	0.662620	+	0.748956i	$0.269445\pi$
$107$	−1.90501	+	13.2497i	−0.184165	+	1.28089i	−0.846784	+	0.531937i	$0.821464\pi$
$108$	1.73222	−	1.99909i	0.166683	−	0.192362i
$109$	2.84450	−	6.22860i	0.272454	−	0.596591i	−0.723104	−	0.690739i	$-0.757285\pi$
$109$	2.84450	−	6.22860i	0.272454	−	0.596591i	0.995558	+	0.0941478i	$0.0300126\pi$
$110$	−18.0842	−	5.31000i	−1.72426	−	0.506288i
$111$	5.31359	+	11.6351i	0.504343	+	1.10436i
$112$	0.142315	+	0.989821i	0.0134475	+	0.0935293i
$113$	−12.5174	−	8.04444i	−1.17754	−	0.756757i	−0.202606	−	0.979260i	$-0.564941\pi$
$113$	−12.5174	−	8.04444i	−1.17754	−	0.756757i	−0.974932	+	0.222503i	$0.928577\pi$
$114$	2.14343			0.200750
$115$	2.71513	−	17.9602i	0.253187	−	1.67480i
$116$	−0.230494			−0.0214008
$117$	1.10345	+	0.709146i	0.102014	+	0.0655605i
$118$	1.64497	+	11.4410i	0.151432	+	1.05323i
$119$	−1.29192	−	2.82891i	−0.118430	−	0.259325i
$120$	7.95493	+	2.33578i	0.726182	+	0.213226i
$121$	5.71740	−	12.5194i	0.519763	−	1.13812i
$122$	−7.61411	+	8.78716i	−0.689350	+	0.795552i
$123$	0.162331	−	1.12903i	0.0146369	−	0.101802i
$124$	−8.15473	+	2.39444i	−0.732316	+	0.215027i
$125$	10.7776	+	12.4380i	0.963979	+	1.11249i
$126$	−1.50718	+	0.968607i	−0.134270	+	0.0862903i
$127$	7.69442	−	4.94491i	0.682770	−	0.438790i	−0.152739	−	0.988267i	$-0.548809\pi$
$127$	7.69442	−	4.94491i	0.682770	−	0.438790i	0.835509	+	0.549477i	$0.185173\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	−21.7015	+	6.37214i	−1.91071	+	0.561036i
$130$	0.394632	−	2.74473i	0.0346116	−	0.240729i
$131$	6.30955	−	7.28161i	0.551268	−	0.636197i	−0.409910	−	0.912126i	$-0.634440\pi$
$131$	6.30955	−	7.28161i	0.551268	−	0.636197i	0.961178	+	0.275929i	$0.0889853\pi$
$132$	−4.52506	+	9.90850i	−0.393856	+	0.862424i
$133$	0.939530	+	0.275871i	0.0814676	+	0.0239210i
$134$	−1.76099	−	3.85603i	−0.152126	−	0.333110i
$135$	−1.42580	−	9.91667i	−0.122713	−	0.853491i
$136$	2.61625	+	1.68136i	0.224342	+	0.144176i
$137$	0.382566			0.0326848			0.0163424	−	0.999866i	$-0.494798\pi$
$137$	0.382566			0.0326848			0.0163424	+	0.999866i	$0.494798\pi$
$138$	−10.0510	−	3.03044i	−0.855600	−	0.257969i
$139$	20.9958			1.78084			0.890421	−	0.455138i	$-0.150410\pi$
$139$	20.9958			1.78084			0.890421	+	0.455138i	$0.150410\pi$
$140$	3.18626	+	2.04769i	0.269288	+	0.173061i
$141$	3.60775	+	25.0925i	0.303827	+	2.11317i
$142$	1.70550	+	3.73452i	0.143122	+	0.313394i
$143$	3.49568	+	1.02643i	0.292324	+	0.0858340i
$144$	0.744253	−	1.62969i	0.0620211	−	0.135807i
$145$	−0.571692	+	0.659768i	−0.0474765	+	0.0547908i
$146$	−1.14646	+	7.97381i	−0.0948818	+	0.659917i
$147$	−2.10030	+	0.616704i	−0.173230	+	0.0508649i
$148$	−3.82661	−	4.41615i	−0.314546	−	0.363005i
$149$	−10.5421	+	6.77498i	−0.863641	+	0.555028i	−0.895801	−	0.444454i	$-0.853398\pi$
$149$	−10.5421	+	6.77498i	−0.863641	+	0.555028i	0.0321607	+	0.999483i	$0.489761\pi$
$150$	17.2092	−	11.0597i	1.40512	−	0.903017i
$151$	−6.08017	−	7.01689i	−0.494797	−	0.571026i	0.452344	−	0.891843i	$-0.350588\pi$
$151$	−6.08017	−	7.01689i	−0.494797	−	0.571026i	−0.947141	+	0.320817i	$0.896042\pi$
$152$	−0.939530	+	0.275871i	−0.0762060	+	0.0223761i
$153$	−0.792942	+	5.51504i	−0.0641056	+	0.445864i
$154$	−3.25875	+	3.76080i	−0.262598	+	0.303054i
$155$	−13.3722	+	29.2811i	−1.07408	+	2.35192i
$156$	−1.53769	−	0.451507i	−0.123114	−	0.0361495i
$157$	3.46635	+	7.59025i	0.276645	+	0.605768i	0.996047	−	0.0888258i	$-0.0283114\pi$
$157$	3.46635	+	7.59025i	0.276645	+	0.605768i	−0.719402	+	0.694594i	$0.755584\pi$
$158$	0.546881	+	3.80364i	0.0435075	+	0.302601i
$159$	3.04844	+	1.95912i	0.241757	+	0.155368i
$160$	−3.78752			−0.299430
$161$	−4.01564	−	2.62196i	−0.316476	−	0.206639i
$162$	−11.1650			−0.877203
$163$	20.5361	+	13.1978i	1.60852	+	1.03373i	0.962823	+	0.270132i	$0.0870673\pi$
$163$	20.5361	+	13.1978i	1.60852	+	1.03373i	0.645692	+	0.763598i	$0.276569\pi$
$164$	0.0741585	+	0.515783i	0.00579080	+	0.0402759i
$165$	17.1388	+	37.5286i	1.33425	+	2.92160i
$166$	−5.41640	−	1.59040i	−0.420394	−	0.123439i
$167$	2.16920	−	4.74989i	0.167858	−	0.367558i	−0.806945	−	0.590627i	$-0.798880\pi$
$167$	2.16920	−	4.74989i	0.167858	−	0.367558i	0.974803	+	0.223070i	$0.0716077\pi$
$168$	1.43347	−	1.65431i	0.110595	−	0.127633i
$169$	1.77381	−	12.3371i	0.136447	−	0.949009i
$170$	11.3018	−	3.31852i	0.866812	−	0.254519i
$171$	−1.14883	−	1.32582i	−0.0878534	−	0.101388i
$172$	8.69232	−	5.58621i	0.662783	−	0.425945i
$173$	9.21231	−	5.92040i	0.700399	−	0.450119i	−0.141370	−	0.989957i	$-0.545151\pi$
$173$	9.21231	−	5.92040i	0.700399	−	0.450119i	0.841769	+	0.539838i	$0.181514\pi$
$174$	0.330406	+	0.381309i	0.0250480	+	0.0289069i
$175$	8.96674	−	2.63287i	0.677822	−	0.199026i
$176$	0.708195	−	4.92560i	0.0533822	−	0.371281i
$177$	16.5690	−	19.1217i	1.24541	−	1.43727i
$178$	7.37145	−	16.1412i	0.552514	−	1.20984i
$179$	−18.0357	−	5.29576i	−1.34805	−	0.395824i	−0.473517	−	0.880785i	$-0.657016\pi$
$179$	−18.0357	−	5.29576i	−1.34805	−	0.395824i	−0.874536	+	0.484961i	$0.838834\pi$
$180$	−2.81887	−	6.17247i	−0.210106	−	0.460069i
$181$	−1.21009	−	8.41635i	−0.0899451	−	0.625582i	−0.984072	−	0.177769i	$-0.943112\pi$
$181$	−1.21009	−	8.41635i	−0.0899451	−	0.625582i	0.894127	−	0.447813i	$-0.147797\pi$
$182$	−0.615907	−	0.395819i	−0.0456540	−	0.0293401i
$183$	25.4513			1.88142
$184$	4.79571	+	0.0347153i	0.353544	+	0.00255924i
$185$	−22.1320			−1.62718
$186$	15.6507	+	10.0581i	1.14757	+	0.737496i
$187$	2.20245	+	15.3184i	0.161059	+	1.12019i
$188$	−4.81093	−	10.5345i	−0.350873	−	0.768304i
$189$	−2.53803	−	0.745231i	−0.184614	−	0.0542076i
$190$	−1.54066	+	3.37357i	−0.111771	+	0.244744i
$191$	−16.5026	+	19.0450i	−1.19408	+	1.37805i	−0.286552	+	0.958065i	$0.592509\pi$
$191$	−16.5026	+	19.0450i	−1.19408	+	1.37805i	−0.907532	+	0.419983i	$0.862036\pi$
$192$	−0.311523	+	2.16669i	−0.0224822	+	0.156367i
$193$	6.08791	−	1.78757i	0.438218	−	0.128672i	−0.0551795	−	0.998476i	$-0.517573\pi$
$193$	6.08791	−	1.78757i	0.438218	−	0.128672i	0.493397	+	0.869804i	$0.335755\pi$
$194$	4.98933	+	5.75800i	0.358213	+	0.413400i
$195$	−5.10634	+	3.28164i	−0.365672	+	0.235003i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	−7.78935	−	8.98939i	−0.554968	−	0.640467i	0.407065	−	0.913399i	$-0.366552\pi$
$197$	−7.78935	−	8.98939i	−0.554968	−	0.640467i	−0.962033	+	0.272932i	$0.912007\pi$
$198$	8.55427	−	2.51176i	0.607925	−	0.178503i
$199$	1.20767	−	8.39950i	0.0856091	−	0.595424i	−0.901184	−	0.433437i	$-0.857301\pi$
$199$	1.20767	−	8.39950i	0.0856091	−	0.595424i	0.986793	−	0.161987i	$-0.0517903\pi$
$200$	−6.11986	+	7.06270i	−0.432740	+	0.499408i
$201$	−3.85475	+	8.44073i	−0.271893	+	0.595363i
$202$	0.273380	+	0.0802717i	0.0192350	+	0.00564789i
$203$	0.0957505	+	0.209664i	0.00672037	+	0.0147156i
$204$	−0.968819	−	6.73829i	−0.0678309	−	0.471774i
$205$	1.66032	+	1.06702i	0.115962	+	0.0745242i
$206$	15.4481			1.07632
$207$	3.51265	+	7.84134i	0.244146	+	0.545011i
$208$	0.732130			0.0507640
$209$	−4.09919	−	2.63439i	−0.283547	−	0.182225i
$210$	−1.17990	−	8.20638i	−0.0814207	−	0.566294i
$211$	−4.63404	−	10.1471i	−0.319021	−	0.698558i	0.680391	−	0.732849i	$-0.261810\pi$
$211$	−4.63404	−	10.1471i	−0.319021	−	0.698558i	−0.999412	+	0.0342914i	$0.989083\pi$
$212$	−1.58838	−	0.466389i	−0.109090	−	0.0320318i
$213$	3.73328	−	8.17474i	0.255800	−	0.560124i
$214$	−8.76590	+	10.1164i	−0.599225	+	0.691542i
$215$	5.56947	−	38.7365i	0.379834	−	2.64181i
$216$	2.53803	−	0.745231i	0.172691	−	0.0507066i
$217$	5.56566	+	6.42311i	0.377821	+	0.436029i
$218$	5.76038	−	3.70197i	0.390142	−	0.250729i
$219$	14.8346	−	9.53362i	1.00243	−	0.644222i
$220$	−12.3426	−	14.2441i	−0.832137	−	0.960337i
$221$	−2.18465	+	0.641472i	−0.146956	+	0.0431501i
$222$	−1.82035	+	12.6608i	−0.122174	+	0.849740i
$223$	2.68371	−	3.09716i	0.179714	−	0.207401i	−0.658744	−	0.752367i	$-0.728912\pi$
$223$	2.68371	−	3.09716i	0.179714	−	0.207401i	0.838458	+	0.544966i	$0.183457\pi$
$224$	−0.415415	+	0.909632i	−0.0277561	+	0.0607773i
$225$	−16.0647	−	4.71703i	−1.07098	−	0.314469i
$226$	−6.18115	−	13.5348i	−0.411164	−	0.900324i
$227$	0.180137	+	1.25288i	0.0119561	+	0.0831566i	0.994926	−	0.100611i	$-0.0320797\pi$
$227$	0.180137	+	1.25288i	0.0119561	+	0.0831566i	−0.982970	+	0.183768i	$0.941171\pi$
$228$	1.80317	+	1.15882i	0.119418	+	0.0767450i
$229$	−3.41706			−0.225806			−0.112903	−	0.993606i	$-0.536015\pi$
$229$	−3.41706			−0.225806			−0.112903	+	0.993606i	$0.536015\pi$
$230$	11.9941	−	13.6412i	0.790870	−	0.899474i
$231$	10.8929			0.716698
$232$	−0.193904	−	0.124614i	−0.0127304	−	0.00818133i
$233$	−1.65378	−	11.5023i	−0.108343	−	0.753541i	−0.969480	−	0.245169i	$-0.921156\pi$
$233$	−1.65378	−	11.5023i	−0.108343	−	0.753541i	0.861137	−	0.508372i	$-0.169753\pi$
$234$	0.544890	+	1.19314i	0.0356206	+	0.0779982i
$235$	−42.0865	−	12.3577i	−2.74542	−	0.806128i
$236$	−4.80165	+	10.5142i	−0.312561	+	0.684413i
$237$	5.50848	−	6.35712i	0.357814	−	0.412939i
$238$	0.442591	−	3.07829i	0.0286889	−	0.199536i
$239$	20.7209	−	6.08421i	1.34032	−	0.393555i	0.468539	−	0.883443i	$-0.344780\pi$
$239$	20.7209	−	6.08421i	1.34032	−	0.393555i	0.871785	+	0.489888i	$0.162962\pi$
$240$	5.42930	+	6.26574i	0.350460	+	0.404452i
$241$	−14.3888	+	9.24715i	−0.926867	+	0.595661i	−0.914642	−	0.404264i	$-0.867528\pi$
$241$	−14.3888	+	9.24715i	−0.926867	+	0.595661i	−0.0122247	+	0.999925i	$0.503891\pi$
$242$	11.5783	−	7.44089i	0.744278	−	0.478319i
$243$	10.8080	+	12.4731i	0.693334	+	0.800150i
$244$	−11.1561	+	3.27573i	−0.714196	+	0.209707i
$245$	0.539020	−	3.74897i	0.0344367	−	0.239513i
$246$	0.746963	−	0.862042i	0.0476246	−	0.0549618i
$247$	0.297810	−	0.652113i	0.0189492	−	0.0414929i
$248$	−8.15473	−	2.39444i	−0.517826	−	0.152047i
$249$	5.13323	+	11.2402i	0.325305	+	0.712319i
$250$	2.34220	+	16.2904i	0.148134	+	1.03029i
$251$	8.93322	+	5.74103i	0.563860	+	0.362371i	0.791306	−	0.611420i	$-0.209401\pi$
$251$	8.93322	+	5.74103i	0.563860	+	0.362371i	−0.227447	+	0.973791i	$0.573038\pi$
$252$	−1.79159			−0.112860
$253$	15.4975	+	18.1488i	0.974317	+	1.14101i
$254$	9.14638			0.573895
$255$	−21.6907	−	13.9398i	−1.35833	−	0.872943i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−0.216538	−	0.474153i	−0.0135073	−	0.0295769i	0.902758	−	0.430149i	$-0.141539\pi$
$257$	−0.216538	−	0.474153i	−0.0135073	−	0.0295769i	−0.916265	+	0.400572i	$0.868812\pi$
$258$	−21.7015	−	6.37214i	−1.35108	−	0.396712i
$259$	−2.42744	+	5.31534i	−0.150834	+	0.330279i
$260$	1.81590	−	2.09566i	0.112617	−	0.129967i
$261$	0.0587689	−	0.408747i	0.00363770	−	0.0253008i
$262$	9.24467	−	2.71448i	0.571138	−	0.167701i
$263$	3.37692	+	3.89718i	0.208230	+	0.240310i	0.850252	−	0.526376i	$-0.176450\pi$
$263$	3.37692	+	3.89718i	0.208230	+	0.240310i	−0.642022	+	0.766686i	$0.721904\pi$
$264$	−9.16366	+	5.88913i	−0.563985	+	0.362451i
$265$	−5.27464	+	3.38981i	−0.324019	+	0.208234i
$266$	0.641236	+	0.740026i	0.0393167	+	0.0453739i
$267$	−37.2694	+	10.9433i	−2.28085	+	0.669718i
$268$	0.603288	−	4.19596i	0.0368517	−	0.256309i
$269$	1.14466	−	1.32101i	0.0697912	−	0.0805434i	−0.719780	−	0.694202i	$-0.755757\pi$
$269$	1.14466	−	1.32101i	0.0697912	−	0.0805434i	0.789571	+	0.613659i	$0.210303\pi$
$270$	4.16189	−	9.11328i	0.253285	−	0.554616i
$271$	−5.06320	−	1.48669i	−0.307567	−	0.0903099i	0.124307	−	0.992244i	$-0.460329\pi$
$271$	−5.06320	−	1.48669i	−0.307567	−	0.0903099i	−0.431874	+	0.901934i	$0.642147\pi$
$272$	1.29192	+	2.82891i	0.0783341	+	0.171528i
$273$	0.228075	+	1.58630i	0.0138037	+	0.0960071i
$274$	0.321835	+	0.206831i	0.0194427	+	0.0124951i
$275$	−46.5045			−2.80433
$276$	−6.81707	−	7.98336i	−0.410340	−	0.480542i
$277$	−9.54025			−0.573218			−0.286609	−	0.958048i	$-0.592528\pi$
$277$	−9.54025			−0.573218			−0.286609	+	0.958048i	$0.592528\pi$
$278$	17.6628	+	11.3512i	1.05934	+	0.680799i
$279$	−2.16699	−	15.0717i	−0.129734	−	0.902321i
$280$	1.57339	+	3.44525i	0.0940281	+	0.205893i
$281$	17.7580	+	5.21422i	1.05935	+	0.311055i	0.764591	−	0.644516i	$-0.222941\pi$
$281$	17.7580	+	5.21422i	1.05935	+	0.311055i	0.294763	+	0.955570i	$0.404759\pi$
$282$	−10.5310	+	23.0596i	−0.627110	+	1.37318i
$283$	16.7723	−	19.3563i	0.997012	−	1.15061i	0.00842433	−	0.999965i	$-0.497318\pi$
$283$	16.7723	−	19.3563i	0.997012	−	1.15061i	0.988587	−	0.150648i	$-0.0481361\pi$
$284$	−0.584277	+	4.06374i	−0.0346705	+	0.241138i
$285$	7.78942	−	2.28718i	0.461406	−	0.135481i
$286$	2.38583	+	2.75339i	0.141077	+	0.162812i
$287$	0.438367	−	0.281721i	0.0258760	−	0.0166295i
$288$	1.50718	−	0.968607i	0.0888115	−	0.0570757i
$289$	4.79897	+	5.53831i	0.282293	+	0.325783i
$290$	−0.837636	+	0.245952i	−0.0491877	+	0.0144428i
$291$	2.37347	−	16.5078i	0.139135	−	0.967707i
$292$	−5.27543	+	6.08817i	−0.308721	+	0.356283i
$293$	−5.65450	+	12.3816i	−0.330339	+	0.723343i	−0.999810	−	0.0194961i	$-0.993794\pi$
$293$	−5.65450	+	12.3816i	−0.330339	+	0.723343i	0.669470	+	0.742839i	$0.266521\pi$
$294$	−2.10030	−	0.616704i	−0.122492	−	0.0359669i
$295$	18.1863	+	39.8225i	1.05885	+	2.31856i
$296$	−0.831603	−	5.78392i	−0.0483359	−	0.336184i
$297$	11.0735	+	7.11648i	0.642548	+	0.412940i
$298$	−12.5314			−0.725924
$299$	−2.31848	+	2.63685i	−0.134081	+	0.152493i
$300$	20.4566			1.18106
$301$	−8.69232	−	5.58621i	−0.501017	−	0.321984i
$302$	−1.32135	−	9.19017i	−0.0760349	−	0.528835i
$303$	−0.259088	−	0.567324i	−0.0148842	−	0.0325919i
$304$	−0.939530	−	0.275871i	−0.0538858	−	0.0158223i
$305$	−18.2939	+	40.0581i	−1.04751	+	2.29372i
$306$	−3.64872	+	4.21085i	−0.208583	+	0.240718i
$307$	2.81309	−	19.5655i	0.160552	−	1.11666i	−0.737045	−	0.675844i	$-0.763779\pi$
$307$	2.81309	−	19.5655i	0.160552	−	1.11666i	0.897597	−	0.440818i	$-0.145311\pi$
$308$	−4.77468	+	1.40197i	−0.272063	+	0.0798848i
$309$	−22.1444	−	25.5560i	−1.25975	−	1.45383i
$310$	−27.0800	+	17.4033i	−1.53804	+	0.988440i
$311$	18.0066	−	11.5722i	1.02106	−	0.656197i	0.0808290	−	0.996728i	$-0.474243\pi$
$311$	18.0066	−	11.5722i	1.02106	−	0.656197i	0.940233	+	0.340531i	$0.110607\pi$
$312$	−1.04949	−	1.21117i	−0.0594155	−	0.0685691i
$313$	6.54668	−	1.92228i	0.370040	−	0.108654i	−0.0914249	−	0.995812i	$-0.529142\pi$
$313$	6.54668	−	1.92228i	0.370040	−	0.108654i	0.461465	+	0.887158i	$0.347324\pi$
$314$	−1.18752	+	8.25938i	−0.0670156	+	0.466104i
$315$	−4.44367	+	5.12827i	−0.250373	+	0.288946i
$316$	−1.59634	+	3.49549i	−0.0898010	+	0.196637i
$317$	0.877206	+	0.257571i	0.0492688	+	0.0144666i	0.306274	−	0.951943i	$-0.400918\pi$
$317$	0.877206	+	0.257571i	0.0492688	+	0.0144666i	−0.257005	+	0.966410i	$0.582736\pi$
$318$	1.50534	+	3.29623i	0.0844151	+	0.184843i
$319$	−0.163234	−	1.13532i	−0.00913937	−	0.0635657i
$320$	−3.18626	−	2.04769i	−0.178118	−	0.114469i
$321$	29.3013			1.63544
$322$	−1.96063	−	4.37675i	−0.109262	−	0.243907i
$323$	3.04524			0.169442
$324$	−9.39257	−	6.03624i	−0.521810	−	0.335347i
$325$	−0.973713	−	6.77232i	−0.0540119	−	0.375661i
$326$	10.1408	+	22.2054i	0.561650	+	1.22984i
$327$	−14.3816	−	4.22281i	−0.795302	−	0.233522i
$328$	−0.216467	+	0.473998i	−0.0119524	+	0.0261721i
$329$	−7.58395	+	8.75234i	−0.418117	+	0.482532i
$330$	−5.87147	+	40.8370i	−0.323214	+	2.24800i
$331$	−14.1812	+	4.16399i	−0.779472	+	0.228874i	−0.647180	−	0.762337i	$-0.724052\pi$
$331$	−14.1812	+	4.16399i	−0.779472	+	0.228874i	−0.132292	+	0.991211i	$0.542234\pi$
$332$	−3.69673	−	4.26625i	−0.202884	−	0.234141i
$333$	8.80706	−	5.65996i	0.482624	−	0.310164i
$334$	4.39283	−	2.82310i	0.240365	−	0.154473i
$335$	−10.5142	−	12.1341i	−0.574455	−	0.662956i
$336$	2.10030	−	0.616704i	0.114581	−	0.0336440i
$337$	4.03801	−	28.0850i	0.219964	−	1.52989i	−0.518196	−	0.855262i	$-0.673396\pi$
$337$	4.03801	−	28.0850i	0.219964	−	1.52989i	0.738161	−	0.674625i	$-0.235695\pi$
$338$	8.16218	−	9.41965i	0.443964	−	0.512362i
$339$	−13.5304	+	29.6273i	−0.734868	+	1.60914i
$340$	11.3018	+	3.31852i	0.612929	+	0.179972i
$341$	−17.5692	−	38.4712i	−0.951426	−	2.08333i
$342$	−0.249665	−	1.73646i	−0.0135003	−	0.0938969i
$343$	−0.841254	−	0.540641i	−0.0454234	−	0.0291919i
$344$	10.3326			0.557095
$345$	−39.7601	−	0.287816i	−2.14061	−	0.0154955i
$346$	10.9507			0.588713
$347$	−3.03207	−	1.94859i	−0.162770	−	0.104606i	0.456720	−	0.889610i	$-0.349024\pi$
$347$	−3.03207	−	1.94859i	−0.162770	−	0.104606i	−0.619490	+	0.785005i	$0.712660\pi$
$348$	0.0718040	+	0.499408i	0.00384910	+	0.0267711i
$349$	12.8153	+	28.0616i	0.685989	+	1.50211i	0.856171	+	0.516693i	$0.172837\pi$
$349$	12.8153	+	28.0616i	0.685989	+	1.50211i	−0.170182	+	0.985413i	$0.554436\pi$
$350$	8.96674	+	2.63287i	0.479292	+	0.140733i
$351$	−0.804497	+	1.76160i	−0.0429409	+	0.0940273i
$352$	3.25875	−	3.76080i	0.173692	−	0.200451i
$353$	−3.51868	+	24.4729i	−0.187280	+	1.30256i	0.651732	+	0.758450i	$0.274043\pi$
$353$	−3.51868	+	24.4729i	−0.187280	+	1.30256i	−0.839012	+	0.544113i	$0.816866\pi$
$354$	24.2767	−	7.12829i	1.29029	−	0.378864i
$355$	10.1829	+	11.7517i	0.540453	+	0.623716i
$356$	14.9279	−	9.59356i	0.791175	−	0.508457i
$357$	−5.72690	+	3.68045i	−0.303100	+	0.194790i
$358$	−12.3095	−	14.2059i	−0.650578	−	0.750807i
$359$	−1.96016	+	0.575556i	−0.103453	+	0.0303767i	−0.333050	−	0.942909i	$-0.608078\pi$
$359$	−1.96016	+	0.575556i	−0.103453	+	0.0303767i	0.229596	+	0.973286i	$0.426259\pi$
$360$	0.965703	−	6.71661i	0.0508970	−	0.353996i
$361$	11.8145	−	13.6346i	0.621814	−	0.717611i
$362$	3.53223	−	7.73450i	0.185650	−	0.406516i
$363$	−28.9066	−	8.48776i	−1.51721	−	0.445492i
$364$	−0.304138	−	0.665968i	−0.0159411	−	0.0349062i
$365$	4.34224	+	30.2010i	0.227283	+	1.58079i
$366$	21.4110	+	13.7600i	1.11917	+	0.719248i
$367$	8.42071			0.439558			0.219779	−	0.975550i	$-0.429466\pi$
$367$	8.42071			0.439558			0.219779	+	0.975550i	$0.429466\pi$
$368$	4.01564	+	2.62196i	0.209329	+	0.136679i
$369$	−0.933575			−0.0486000
$370$	−18.6186	−	11.9655i	−0.967935	−	0.622054i
$371$	0.235593	+	1.63858i	0.0122314	+	0.0850710i
$372$	7.72840	+	16.9228i	0.400699	+	0.877408i
$373$	3.44871	+	1.01263i	0.178567	+	0.0524321i	0.369794	−	0.929114i	$-0.379428\pi$
$373$	3.44871	+	1.01263i	0.178567	+	0.0524321i	−0.191226	+	0.981546i	$0.561246\pi$
$374$	−6.42891	+	14.0774i	−0.332431	+	0.727923i
$375$	23.5919	−	27.2265i	1.21828	−	1.40597i
$376$	1.64815	−	11.4631i	0.0849968	−	0.591166i
$377$	0.161916	−	0.0475427i	0.00833907	−	0.00244857i
$378$	−1.73222	−	1.99909i	−0.0890958	−	0.102822i
$379$	−22.2430	+	14.2947i	−1.14254	+	0.734269i	−0.968141	−	0.250405i	$-0.919436\pi$
$379$	−22.2430	+	14.2947i	−1.14254	+	0.734269i	−0.174404	+	0.984674i	$0.555800\pi$
$380$	−3.11997	+	2.00508i	−0.160051	+	0.102859i
$381$	−13.1111	−	15.1310i	−0.671700	−	0.775183i
$382$	−24.1794	+	7.09970i	−1.23712	+	0.363252i
$383$	−3.81586	+	26.5399i	−0.194981	+	1.35612i	0.623605	+	0.781740i	$0.285667\pi$
$383$	−3.81586	+	26.5399i	−0.194981	+	1.35612i	−0.818586	+	0.574384i	$0.805242\pi$
$384$	−1.43347	+	1.65431i	−0.0731515	+	0.0844213i
$385$	−7.82960	+	17.1444i	−0.399033	+	0.873761i
$386$	6.08791	+	1.78757i	0.309867	+	0.0909851i
$387$	7.69006	+	16.8389i	0.390908	+	0.855968i
$388$	1.08429	+	7.54137i	0.0550463	+	0.382855i
$389$	−18.6200	−	11.9663i	−0.944070	−	0.606717i	−0.0245237	−	0.999699i	$-0.507807\pi$
$389$	−18.6200	−	11.9663i	−0.944070	−	0.606717i	−0.919546	+	0.392983i	$0.871443\pi$
$390$	−6.06991			−0.307362
$391$	−14.2798	−	4.30546i	−0.722162	−	0.217736i
$392$	1.00000			0.0505076
$393$	−17.7426	−	11.4025i	−0.894994	−	0.575178i
$394$	−1.69279	−	11.7736i	−0.0852814	−	0.593145i
$395$	6.04616	+	13.2392i	0.304215	+	0.666138i
$396$	8.55427	+	2.51176i	0.429868	+	0.126221i
$397$	−7.55379	+	16.5405i	−0.379114	+	0.830143i	0.619854	+	0.784717i	$0.287192\pi$
$397$	−7.55379	+	16.5405i	−0.379114	+	0.830143i	−0.998968	+	0.0454259i	$0.985535\pi$
$398$	5.55706	−	6.41319i	0.278550	−	0.321464i
$399$	0.305042	−	2.12161i	0.0152712	−	0.106213i
$400$	−8.96674	+	2.63287i	−0.448337	+	0.131644i
$401$	−13.5382	−	15.6239i	−0.676065	−	0.780220i	0.309248	−	0.950982i	$-0.399923\pi$
$401$	−13.5382	−	15.6239i	−0.676065	−	0.780220i	−0.985312	+	0.170761i	$0.945377\pi$
$402$	−7.80623	+	5.01676i	−0.389339	+	0.250213i
$403$	5.23459	−	3.36406i	0.260753	−	0.167576i
$404$	0.186584	+	0.215329i	0.00928290	+	0.0107130i
$405$	−40.5746	+	11.9138i	−2.01617	+	0.592000i
$406$	−0.0328027	+	0.228147i	−0.00162797	+	0.0113228i
$407$	19.0422	−	21.9759i	0.943887	−	1.08930i
$408$	2.82797	−	6.19239i	0.140005	−	0.306569i
$409$	27.5961	+	8.10294i	1.36454	+	0.400664i	0.880360	−	0.474305i	$-0.157301\pi$
$409$	27.5961	+	8.10294i	1.36454	+	0.400664i	0.484177	+	0.874970i	$0.339119\pi$
$410$	0.819875	+	1.79527i	0.0404907	+	0.0886623i
$411$	−0.119178	−	0.828901i	−0.00587862	−	0.0408867i
$412$	12.9958	+	8.35188i	0.640256	+	0.411468i
$413$	11.5587			0.568766
$414$	−1.28432	+	8.49563i	−0.0631210	+	0.417538i
$415$	−21.3808			−1.04954
$416$	0.615907	+	0.395819i	0.0301973	+	0.0194066i
$417$	−6.54068	−	45.4914i	−0.320298	−	2.22772i
$418$	−2.02420	−	4.43238i	−0.0990069	−	0.216795i
$419$	−4.63031	−	1.35958i	−0.226205	−	0.0664199i	0.166666	−	0.986013i	$-0.446700\pi$
$419$	−4.63031	−	1.35958i	−0.226205	−	0.0664199i	−0.392871	+	0.919594i	$0.628518\pi$
$420$	3.44411	−	7.54154i	0.168055	−	0.367990i
$421$	9.22774	−	10.6494i	0.449732	−	0.519019i	−0.484931	−	0.874552i	$-0.661155\pi$
$421$	9.22774	−	10.6494i	0.449732	−	0.519019i	0.934664	+	0.355533i	$0.115701\pi$
$422$	1.58755	−	11.0417i	0.0772808	−	0.537500i
$423$	19.9080	−	5.84551i	0.967958	−	0.284218i
$424$	−1.08408	−	1.25109i	−0.0526475	−	0.0607584i
$425$	24.4496	−	15.7128i	1.18598	−	0.762184i
$426$	7.56024	−	4.85867i	0.366295	−	0.235403i
$427$	7.61411	+	8.78716i	0.368473	+	0.425240i
$428$	−12.8437	+	3.77125i	−0.620823	+	0.182290i
$429$	1.13496	−	7.89382i	0.0547964	−	0.381117i
$430$	25.6279	−	29.5761i	1.23589	−	1.42629i
$431$	6.10086	−	13.3590i	0.293868	−	0.643482i	−0.703897	−	0.710302i	$-0.748558\pi$
$431$	6.10086	−	13.3590i	0.293868	−	0.643482i	0.997765	+	0.0668206i	$0.0212855\pi$
$432$	2.53803	+	0.745231i	0.122111	+	0.0358550i
$433$	−13.3122	−	29.1496i	−0.639742	−	1.40084i	−0.900253	−	0.435368i	$-0.856618\pi$
$433$	−13.3122	−	29.1496i	−0.639742	−	1.40084i	0.260511	−	0.965471i	$-0.416109\pi$
$434$	1.20953	+	8.41249i	0.0580594	+	0.403812i
$435$	1.60761	+	1.03315i	0.0770789	+	0.0495356i
$436$	6.84738			0.327930
$437$	3.96884	−	2.51021i	0.189856	−	0.120080i
$438$	17.6339			0.842582
$439$	23.1995	+	14.9094i	1.10725	+	0.711588i	0.960693	−	0.277614i	$-0.0895437\pi$
$439$	23.1995	+	14.9094i	1.10725	+	0.711588i	0.146559	+	0.989202i	$0.453180\pi$
$440$	−2.68230	−	18.6558i	−0.127874	−	0.889381i
$441$	0.744253	+	1.62969i	0.0354406	+	0.0776042i
$442$	−2.18465	−	0.641472i	−0.103913	−	0.0305117i
$443$	−3.38650	+	7.41540i	−0.160897	+	0.352316i	−0.972860	−	0.231393i	$-0.925672\pi$
$443$	−3.38650	+	7.41540i	−0.160897	+	0.352316i	0.811963	+	0.583709i	$0.198399\pi$
$444$	−8.37634	+	9.66681i	−0.397524	+	0.458767i
$445$	9.56480	−	66.5246i	0.453415	−	3.15357i
$446$	3.93213	−	1.15458i	0.186192	−	0.0546709i
$447$	17.9634	+	20.7308i	0.849639	+	0.980536i
$448$	−0.841254	+	0.540641i	−0.0397455	+	0.0255429i
$449$	−3.11588	+	2.00245i	−0.147047	+	0.0945016i	−0.612096	−	0.790784i	$-0.709673\pi$
$449$	−3.11588	+	2.00245i	−0.147047	+	0.0945016i	0.465048	+	0.885285i	$0.346037\pi$
$450$	−10.9643	−	12.6535i	−0.516861	−	0.596490i
$451$	−2.48803	+	0.730550i	−0.117157	+	0.0344003i
$452$	2.11757	−	14.7280i	0.0996020	−	0.692747i
$453$	−13.3093	+	15.3598i	−0.625326	+	0.721664i
$454$	−0.525818	+	1.15138i	−0.0246778	+	0.0540369i
$455$	−2.66063	−	0.781231i	−0.124732	−	0.0366247i
$456$	0.890412	+	1.94973i	0.0416974	+	0.0913045i
$457$	−3.87282	−	26.9361i	−0.181163	−	1.26002i	−0.854019	−	0.520242i	$-0.825842\pi$
$457$	−3.87282	−	26.9361i	−0.181163	−	1.26002i	0.672856	−	0.739774i	$-0.265067\pi$
$458$	−2.87461	−	1.84740i	−0.134322	−	0.0863234i
$459$	−8.22635			−0.383973
$460$	17.4651	−	4.99118i	0.814315	−	0.232715i
$461$	33.9562			1.58150			0.790749	−	0.612140i	$-0.209691\pi$
$461$	33.9562			1.58150			0.790749	+	0.612140i	$0.209691\pi$
$462$	9.16366	+	5.88913i	0.426332	+	0.273987i
$463$	4.09508	+	28.4819i	0.190315	+	1.32367i	0.831175	+	0.556010i	$0.187668\pi$
$463$	4.09508	+	28.4819i	0.190315	+	1.32367i	−0.640861	+	0.767657i	$0.721422\pi$
$464$	−0.0957505	−	0.209664i	−0.00444511	−	0.00973342i
$465$	67.6089	+	19.8518i	3.13529	+	0.920604i
$466$	4.82737	−	10.5705i	0.223624	−	0.489667i
$467$	−21.3693	+	24.6615i	−0.988855	+	1.14120i	0.00112594	+	0.999999i	$0.499642\pi$
$467$	−21.3693	+	24.6615i	−0.988855	+	1.14120i	−0.989981	+	0.141200i	$0.954904\pi$
$468$	−0.186671	+	1.29832i	−0.00862887	+	0.0600151i
$469$	−4.06740	+	1.19430i	−0.187815	+	0.0551474i
$470$	−28.7243	−	33.1497i	−1.32496	−	1.52908i
$471$	15.3659	−	9.87504i	0.708022	−	0.455018i
$472$	−9.72379	+	6.24910i	−0.447574	+	0.287638i
$473$	33.6713	+	38.8588i	1.54821	+	1.78673i
$474$	8.07094	−	2.36984i	0.370711	−	0.108850i
$475$	−1.30230	+	9.05772i	−0.0597538	+	0.415596i
$476$	2.03658	−	2.35034i	0.0933466	−	0.107728i
$477$	1.23206	−	2.69784i	0.0564122	−	0.123526i
$478$	20.7209	+	6.08421i	0.947753	+	0.278285i
$479$	−14.2822	−	31.2736i	−0.652570	−	1.42893i	−0.889287	−	0.457350i	$-0.848799\pi$
$479$	−14.2822	−	31.2736i	−0.652570	−	1.42893i	0.236716	−	0.971579i	$-0.423929\pi$
$480$	1.17990	+	8.20638i	0.0538548	+	0.374568i
$481$	3.59899	+	2.31293i	0.164100	+	0.105461i
$482$	−17.1041			−0.779068
$483$	−4.43001	+	9.51744i	−0.201572	+	0.433058i
$484$	13.7631			0.625595
$485$	24.2759	+	15.6012i	1.10231	+	0.708413i
$486$	2.34880	+	16.3363i	0.106544	+	0.741029i
$487$	4.92851	+	10.7919i	0.223332	+	0.489029i	0.987818	−	0.155611i	$-0.0497346\pi$
$487$	4.92851	+	10.7919i	0.223332	+	0.489029i	−0.764486	+	0.644640i	$0.777007\pi$
$488$	−11.1561	−	3.27573i	−0.505013	−	0.148285i
$489$	22.1980	−	48.6069i	1.00383	−	2.19808i
$490$	2.48030	−	2.86241i	0.112048	−	0.129311i
$491$	−5.32543	+	37.0392i	−0.240333	+	1.67156i	0.410137	+	0.912024i	$0.365481\pi$
$491$	−5.32543	+	37.0392i	−0.240333	+	1.67156i	−0.650471	+	0.759531i	$0.725428\pi$
$492$	1.09444	−	0.321357i	0.0493412	−	0.0144879i
$493$	0.469419	+	0.541738i	0.0211416	+	0.0243987i
$494$	0.603092	−	0.387584i	0.0271344	−	0.0174382i
$495$	28.4068	−	18.2560i	1.27679	−	0.820544i
$496$	−5.56566	−	6.42311i	−0.249905	−	0.288406i
$497$	3.93922	−	1.15666i	0.176698	−	0.0518833i
$498$	−1.75857	+	12.2311i	−0.0788032	+	0.548088i
$499$	−6.76079	+	7.80236i	−0.302654	+	0.349282i	−0.886622	−	0.462495i	$-0.846954\pi$
$499$	−6.76079	+	7.80236i	−0.302654	+	0.349282i	0.583967	+	0.811777i	$0.301500\pi$
$500$	−6.83685	+	14.9706i	−0.305753	+	0.669506i
$501$	−10.9673	−	3.22029i	−0.489983	−	0.143872i
$502$	4.41127	+	9.65933i	0.196884	+	0.431117i
$503$	1.00900	+	7.01775i	0.0449891	+	0.312906i	0.999873	+	0.0159272i	$0.00507000\pi$
$503$	1.00900	+	7.01775i	0.0449891	+	0.312906i	−0.954884	+	0.296979i	$0.904021\pi$
$504$	−1.50718	−	0.968607i	−0.0671352	−	0.0431452i
$505$	1.07915			0.0480213
$506$	3.22530	+	23.6463i	0.143382	+	1.05121i
$507$	−27.2833			−1.21169
$508$	7.69442	+	4.94491i	0.341385	+	0.219395i
$509$	−1.54184	−	10.7237i	−0.0683408	−	0.475321i	−0.995037	−	0.0995086i	$-0.968273\pi$
$509$	−1.54184	−	10.7237i	−0.0683408	−	0.475321i	0.926696	−	0.375812i	$-0.122636\pi$
$510$	−10.7110	−	23.4538i	−0.474291	−	1.03855i
$511$	7.72949	+	2.26958i	0.341933	+	0.100400i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	1.69618	−	1.95750i	0.0748882	−	0.0864256i
$514$	0.0741828	−	0.515953i	0.00327206	−	0.0227577i
$515$	56.1399	−	16.4842i	2.47382	−	0.726379i
$516$	−14.8114	−	17.0933i	−0.652038	−	0.752492i
$517$	48.4815	−	31.1572i	2.13221	−	1.37029i
$518$	−4.91578	+	3.15918i	−0.215987	+	0.138806i
$519$	−15.6975	−	18.1159i	−0.689044	−	0.795199i
$520$	2.66063	−	0.781231i	0.116676	−	0.0342593i
$521$	−2.39794	+	16.6780i	−0.105056	+	0.730678i	0.867404	+	0.497605i	$0.165787\pi$
$521$	−2.39794	+	16.6780i	−0.105056	+	0.730678i	−0.972459	+	0.233073i	$0.925122\pi$
$522$	0.270425	−	0.312087i	0.0118362	−	0.0136597i
$523$	−16.4468	+	36.0134i	−0.719167	+	1.57476i	0.0959014	+	0.995391i	$0.469427\pi$
$523$	−16.4468	+	36.0134i	−0.719167	+	1.57476i	−0.815068	+	0.579365i	$0.803301\pi$
$524$	9.24467	+	2.71448i	0.403855	+	0.118583i
$525$	−8.49796	−	18.6079i	−0.370882	−	0.812117i
$526$	0.733876	+	5.10422i	0.0319985	+	0.222554i
$527$	22.2355	+	14.2899i	0.968595	+	0.622478i
$528$	−10.8929			−0.474051
$529$	−22.1598	+	6.15969i	−0.963471	+	0.267813i
$530$	−6.26998			−0.272351
$531$	−17.4210	−	11.1958i	−0.756009	−	0.485857i
$532$	0.139354	+	0.969228i	0.00604176	+	0.0420214i
$533$	−0.158482	−	0.347028i	−0.00686463	−	0.0150314i
$534$	−37.2694	−	10.9433i	−1.61280	−	0.473562i
$535$	−21.0613	+	46.1178i	−0.910558	+	1.99384i
$536$	2.77603	−	3.20370i	0.119906	−	0.138379i
$537$	−5.85574	+	40.7276i	−0.252694	+	1.75752i
$538$	1.67714	−	0.492453i	0.0723067	−	0.0212312i
$539$	3.25875	+	3.76080i	0.140364	+	0.161989i
$540$	8.42822	−	5.41649i	0.362693	−	0.233088i
$541$	−10.4307	+	6.70340i	−0.448451	+	0.288202i	−0.745308	−	0.666720i	$-0.767698\pi$
$541$	−10.4307	+	6.70340i	−0.448451	+	0.288202i	0.296858	+	0.954922i	$0.404061\pi$
$542$	−3.45567	−	3.98805i	−0.148434	−	0.171302i
$543$	−17.8586	+	5.24377i	−0.766388	+	0.225032i
$544$	−0.442591	+	3.07829i	−0.0189760	+	0.131981i
$545$	16.9835	−	19.6000i	0.727495	−	0.839573i
$546$	−0.665748	+	1.45778i	−0.0284914	+	0.0623874i
$547$	−6.16877	−	1.81131i	−0.263757	−	0.0774462i	0.147180	−	0.989110i	$-0.452980\pi$
$547$	−6.16877	−	1.81131i	−0.263757	−	0.0774462i	−0.410937	+	0.911664i	$0.634799\pi$
$548$	0.158924	+	0.347994i	0.00678888	+	0.0148656i
$549$	−2.96455	−	20.6189i	−0.126524	−	0.879994i
$550$	−39.1221	−	25.1422i	−1.66817	−	1.07207i
$551$	−0.225698			−0.00961506
$552$	−1.41876	−	10.4016i	−0.0603862	−	0.442722i
$553$	3.84275			0.163411
$554$	−8.02577	−	5.15785i	−0.340982	−	0.219136i
$555$	6.89462	+	47.9531i	0.292660	+	2.03550i
$556$	8.72198	+	19.0985i	0.369894	+	0.809955i
$557$	20.4421	+	6.00234i	0.866159	+	0.254327i	0.684481	−	0.729031i	$-0.260029\pi$
$557$	20.4421	+	6.00234i	0.866159	+	0.254327i	0.181678	+	0.983358i	$0.441847\pi$
$558$	6.32541	−	13.8507i	0.267776	−	0.586347i
$559$	−4.95388	+	5.71708i	−0.209527	+	0.241807i
$560$	−0.539020	+	3.74897i	−0.0227778	+	0.158423i
$561$	32.5040	−	9.54404i	1.37232	−	0.402950i
$562$	12.1200	+	13.9872i	0.511250	+	0.590014i
$563$	5.82104	−	3.74095i	0.245327	−	0.157662i	−0.412199	−	0.911094i	$-0.635239\pi$
$563$	5.82104	−	3.74095i	0.245327	−	0.157662i	0.657526	+	0.753431i	$0.271603\pi$
$564$	−21.3262	+	13.7055i	−0.897994	+	0.577106i
$565$	−36.9055	−	42.5912i	−1.55262	−	1.79182i
$566$	24.5746	−	7.21575i	1.03295	−	0.303301i
$567$	−1.58894	+	11.0513i	−0.0667293	+	0.464112i
$568$	−2.68855	+	3.10275i	−0.112809	+	0.130188i
$569$	−14.5165	+	31.7867i	−0.608563	+	1.33257i	0.314990	+	0.949095i	$0.397999\pi$
$569$	−14.5165	+	31.7867i	−0.608563	+	1.33257i	−0.923553	+	0.383471i	$0.874729\pi$
$570$	7.78942	+	2.28718i	0.326263	+	0.0957995i
$571$	12.1660	+	26.6399i	0.509132	+	1.11484i	0.973392	+	0.229145i	$0.0735929\pi$
$571$	12.1660	+	26.6399i	0.509132	+	1.11484i	−0.464260	+	0.885699i	$0.653680\pi$
$572$	0.518490	+	3.60618i	0.0216792	+	0.150782i
$573$	46.4055	+	29.8230i	1.93862	+	1.24587i
$574$	0.521087			0.0217498
$575$	18.9129	−	40.6324i	0.788721	−	1.69449i
$576$	1.79159			0.0746496
$577$	−3.53971	−	2.27483i	−0.147360	−	0.0947026i	0.464883	−	0.885372i	$-0.346096\pi$
$577$	−3.53971	−	2.27483i	−0.147360	−	0.0947026i	−0.612243	+	0.790669i	$0.709733\pi$
$578$	1.04292	+	7.25365i	0.0433796	+	0.301712i
$579$	−5.76964	−	12.6337i	−0.239778	−	0.525041i
$580$	−0.837636	−	0.245952i	−0.0347809	−	0.0102126i
$581$	−2.34504	+	5.13493i	−0.0972888	+	0.213033i
$582$	10.9215	−	12.6041i	0.452711	−	0.522456i
$583$	1.17237	−	8.15400i	0.0485546	−	0.337704i
$584$	−7.72949	+	2.26958i	−0.319849	+	0.0939160i
$585$	3.25335	+	3.75456i	0.134509	+	0.155232i
$586$	−11.4509	+	7.35904i	−0.473032	+	0.303999i
$587$	−17.5373	+	11.2705i	−0.723842	+	0.465185i	−0.849971	−	0.526829i	$-0.823381\pi$
$587$	−17.5373	+	11.2705i	−0.723842	+	0.465185i	0.126129	+	0.992014i	$0.459745\pi$
$588$	−1.43347	−	1.65431i	−0.0591153	−	0.0682227i
$589$	−7.98506	+	2.34463i	−0.329019	+	0.0966086i
$590$	−6.23037	+	43.3331i	−0.256500	+	1.78400i
$591$	−17.0507	+	19.6775i	−0.701370	+	0.809424i
$592$	2.42744	−	5.31534i	0.0997670	−	0.218459i
$593$	5.12145	+	1.50379i	0.210313	+	0.0617534i	0.385192	−	0.922837i	$-0.374135\pi$
$593$	5.12145	+	1.50379i	0.210313	+	0.0617534i	−0.174879	+	0.984590i	$0.555953\pi$
$594$	5.46813	+	11.9735i	0.224360	+	0.491280i
$595$	−1.67632	−	11.6591i	−0.0687225	−	0.477976i
$596$	−10.5421	−	6.77498i	−0.431820	−	0.277514i
$597$	−18.5753			−0.760237
$598$	−3.37601	+	0.964798i	−0.138056	+	0.0394535i
$599$	−24.5079			−1.00136			−0.500682	−	0.865631i	$-0.666917\pi$
$599$	−24.5079			−1.00136			−0.500682	+	0.865631i	$0.666917\pi$
$600$	17.2092	+	11.0597i	0.702561	+	0.451508i
$601$	−5.42353	−	37.7215i	−0.221231	−	1.53869i	−0.733394	−	0.679804i	$-0.762065\pi$
$601$	−5.42353	−	37.7215i	−0.221231	−	1.53869i	0.512163	−	0.858888i	$-0.328844\pi$
$602$	−4.29231	−	9.39885i	−0.174941	−	0.383068i
$603$	7.28711	+	2.13969i	0.296754	+	0.0871348i
$604$	3.85699	−	8.44563i	0.156939	−	0.343648i
$605$	34.1366	−	39.3957i	1.38785	−	1.60166i
$606$	0.0887596	−	0.617336i	0.00360561	−	0.0250776i
$607$	21.1148	−	6.19987i	0.857024	−	0.251645i	0.176437	−	0.984312i	$-0.443543\pi$
$607$	21.1148	−	6.19987i	0.857024	−	0.251645i	0.680587	+	0.732667i	$0.261725\pi$
$608$	−0.641236	−	0.740026i	−0.0260056	−	0.0300120i
$609$	0.424449	−	0.272777i	0.0171995	−	0.0110535i
$610$	−37.0469	+	23.8086i	−1.49999	+	0.963982i
$611$	5.55243	+	6.40785i	0.224627	+	0.259234i
$612$	−5.34605	+	1.56974i	−0.216101	+	0.0634531i
$613$	−4.91941	+	34.2153i	−0.198693	+	1.38194i	0.609389	+	0.792871i	$0.291415\pi$
$613$	−4.91941	+	34.2153i	−0.198693	+	1.38194i	−0.808082	+	0.589070i	$0.799494\pi$
$614$	12.9444	−	14.9387i	0.522394	−	0.602875i
$615$	1.79468	−	3.92980i	0.0723685	−	0.158465i
$616$	−4.77468	−	1.40197i	−0.192377	−	0.0564871i
$617$	−16.4871	−	36.1017i	−0.663745	−	1.45340i	−0.878991	−	0.476838i	$-0.841783\pi$
$617$	−16.4871	−	36.1017i	−0.663745	−	1.45340i	0.215247	−	0.976560i	$-0.430944\pi$
$618$	−4.81244	−	33.4713i	−0.193585	−	1.34641i
$619$	−3.32114	−	2.13437i	−0.133488	−	0.0857874i	0.472193	−	0.881495i	$-0.343463\pi$
$619$	−3.32114	−	2.13437i	−0.133488	−	0.0857874i	−0.605680	+	0.795708i	$0.707099\pi$
$620$	−32.1901			−1.29279
$621$	−10.7213	+	6.78103i	−0.430233	+	0.272114i
$622$	21.4045			0.858243
$623$	−14.9279	−	9.59356i	−0.598072	−	0.384358i
$624$	−0.228075	−	1.58630i	−0.00913031	−	0.0635027i
$625$	6.48380	+	14.1975i	0.259352	+	0.567902i
$626$	6.54668	+	1.92228i	0.261658	+	0.0768297i
$627$	−4.43092	+	9.70235i	−0.176954	+	0.387475i
$628$	−5.46436	+	6.30621i	−0.218052	+	0.251645i
$629$	−2.58624	+	17.9877i	−0.103120	+	0.717216i
$630$	−6.51081	+	1.91175i	−0.259397	+	0.0761658i
$631$	24.0227	+	27.7237i	0.956329	+	1.10366i	0.994536	+	0.104392i	$0.0332897\pi$
$631$	24.0227	+	27.7237i	0.956329	+	1.10366i	−0.0382077	+	0.999270i	$0.512165\pi$
$632$	−3.23273	+	2.07755i	−0.128591	+	0.0826405i
$633$	−20.5421	+	13.2016i	−0.816474	+	0.524716i
$634$	0.598699	+	0.690936i	0.0237774	+	0.0274406i
$635$	33.2388	−	9.75980i	1.31904	−	0.387306i
$636$	−0.515705	+	3.58681i	−0.0204490	+	0.142226i
$637$	−0.479443	+	0.553307i	−0.0189962	+	0.0219228i
$638$	0.476479	−	1.04334i	0.0188640	−	0.0413063i
$639$	−7.05747	−	2.07226i	−0.279189	−	0.0819774i
$640$	−1.57339	−	3.44525i	−0.0621938	−	0.136185i
$641$	−3.37736	−	23.4901i	−0.133398	−	0.927802i	−0.941080	−	0.338184i	$-0.890187\pi$
$641$	−3.37736	−	23.4901i	−0.133398	−	0.927802i	0.807682	−	0.589618i	$-0.200722\pi$
$642$	24.6499	+	15.8415i	0.972852	+	0.625214i
$643$	10.5744			0.417015			0.208507	−	0.978021i	$-0.433139\pi$
$643$	10.5744			0.417015			0.208507	+	0.978021i	$0.433139\pi$
$644$	0.716862	−	4.74195i	0.0282483	−	0.186859i
$645$	−85.6650			−3.37305
$646$	2.56182	+	1.64638i	0.100793	+	0.0647760i
$647$	−1.49301	−	10.3841i	−0.0586964	−	0.408243i	−0.997894	−	0.0648654i	$-0.979338\pi$
$647$	−1.49301	−	10.3841i	−0.0586964	−	0.408243i	0.939198	−	0.343377i	$-0.111571\pi$
$648$	−4.63810	−	10.1560i	−0.182202	−	0.398966i
$649$	−55.1890	−	16.2050i	−2.16636	−	0.636101i
$650$	2.84225	−	6.22367i	0.111482	−	0.244112i
$651$	12.1831	−	14.0600i	0.477492	−	0.551055i
$652$	−3.47410	+	24.1629i	−0.136056	+	0.946292i
$653$	−10.1857	+	2.99080i	−0.398598	+	0.117039i	−0.474887	−	0.880047i	$-0.657511\pi$
$653$	−10.1857	+	2.99080i	−0.398598	+	0.117039i	0.0762890	+	0.997086i	$0.475693\pi$
$654$	−9.81552	−	11.3277i	−0.383817	−	0.442949i
$655$	30.6995	−	19.7294i	1.19953	−	0.770890i
$656$	−0.438367	+	0.281721i	−0.0171153	+	0.0109994i
$657$	−9.45141	−	10.9075i	−0.368735	−	0.425543i
$658$	−11.1119	+	3.26275i	−0.433187	+	0.127195i
$659$	6.72966	−	46.8058i	0.262150	−	1.82330i	−0.254469	−	0.967081i	$-0.581901\pi$
$659$	6.72966	−	46.8058i	0.262150	−	1.82330i	0.516619	−	0.856215i	$-0.327190\pi$
$660$	−27.0175	+	31.1799i	−1.05166	+	1.21368i
$661$	−2.52405	+	5.52691i	−0.0981743	+	0.214972i	−0.952346	−	0.305019i	$-0.901337\pi$
$661$	−2.52405	+	5.52691i	−0.0981743	+	0.214972i	0.854172	+	0.519991i	$0.174065\pi$
$662$	−14.1812	−	4.16399i	−0.551170	−	0.161838i
$663$	2.07044	+	4.53363i	0.0804092	+	0.176072i
$664$	−0.803376	−	5.58760i	−0.0311770	−	0.216841i
$665$	3.11997	+	2.00508i	0.120987	+	0.0777538i
$666$	10.4690			0.405665
$667$	1.05835	+	0.319099i	0.0409795	+	0.0123556i
$668$	5.22177			0.202036
$669$	−7.54663	−	4.84993i	−0.291770	−	0.187509i
$670$	−2.28496	−	15.8923i	−0.0882759	−	0.613972i
$671$	−24.0356	−	52.6306i	−0.927884	−	2.03178i
$672$	2.10030	+	0.616704i	0.0810209	+	0.0237899i
$673$	−15.7897	+	34.5746i	−0.608648	+	1.33275i	0.314846	+	0.949143i	$0.398047\pi$
$673$	−15.7897	+	34.5746i	−0.608648	+	1.33275i	−0.923495	+	0.383611i	$0.874680\pi$
$674$	18.5809	−	21.4435i	0.715709	−	0.825972i
$675$	3.51801	−	24.4683i	0.135408	−	0.941785i
$676$	11.9591	−	3.51151i	0.459966	−	0.135058i
$677$	−17.9465	−	20.7114i	−0.689742	−	0.796005i	0.297586	−	0.954695i	$-0.403818\pi$
$677$	−17.9465	−	20.7114i	−0.689742	−	0.796005i	−0.987328	+	0.158690i	$0.949273\pi$
$678$	−27.4002	+	17.6090i	−1.05230	+	0.676271i
$679$	6.40945	−	4.11910i	0.245972	−	0.158077i
$680$	7.71359	+	8.90196i	0.295803	+	0.341374i
$681$	2.65849	−	0.780602i	0.101873	−	0.0299127i
$682$	6.01894	−	41.8627i	0.230477	−	1.60300i
$683$	−27.2820	+	31.4851i	−1.04392	+	1.20475i	−0.0655553	+	0.997849i	$0.520882\pi$
$683$	−27.2820	+	31.4851i	−1.04392	+	1.20475i	−0.978363	+	0.206897i	$0.933664\pi$
$684$	0.728769	−	1.59578i	0.0278652	−	0.0610162i
$685$	1.39028	+	0.408223i	0.0531199	+	0.0155974i
$686$	−0.415415	−	0.909632i	−0.0158606	−	0.0347299i
$687$	1.06449	+	7.40371i	0.0406129	+	0.282469i
$688$	8.69232	+	5.58621i	0.331392	+	0.212972i
$689$	1.21199			0.0461732
$690$	−33.2927	−	21.7380i	−1.26743	−	0.827553i
$691$	−8.38377			−0.318933			−0.159467	−	0.987203i	$-0.550977\pi$
$691$	−8.38377			−0.318933			−0.159467	+	0.987203i	$0.550977\pi$
$692$	9.21231	+	5.92040i	0.350200	+	0.225060i
$693$	−1.26879	−	8.82466i	−0.0481975	−	0.335221i
$694$	−1.49725	−	3.27852i	−0.0568348	−	0.124451i
$695$	76.3008	+	22.4039i	2.89425	+	0.849830i
$696$	−0.209595	+	0.458949i	−0.00794468	+	0.0173964i
$697$	1.06124	−	1.22473i	0.0401972	−	0.0463901i
$698$	−4.39033	+	30.5354i	−0.166177	+	1.15578i
$699$	−24.4067	+	7.16647i	−0.923148	+	0.271061i
$700$	6.11986	+	7.06270i	0.231309	+	0.266945i
$701$	16.8022	−	10.7981i	0.634611	−	0.407840i	−0.183403	−	0.983038i	$-0.558711\pi$
$701$	16.8022	−	10.7981i	0.634611	−	0.407840i	0.818014	+	0.575198i	$0.195075\pi$
$702$	−1.62918	+	1.04701i	−0.0614894	+	0.0395168i
$703$	−3.74700	−	4.32427i	−0.141321	−	0.163093i
$704$	4.77468	−	1.40197i	0.179953	−	0.0528388i
$705$	−13.6644	+	95.0381i	−0.514632	+	3.57934i
$706$	−16.1912	+	18.6856i	−0.609363	+	0.703242i
$707$	0.118361	−	0.259174i	0.00445141	−	0.00974723i
$708$	24.2767	+	7.12829i	0.912376	+	0.267898i
$709$	12.8840	+	28.2121i	0.483870	+	1.05953i	0.981381	+	0.192070i	$0.0615199\pi$
$709$	12.8840	+	28.2121i	0.483870	+	1.05953i	−0.497512	+	0.867457i	$0.665753\pi$
$710$	2.21296	+	15.3915i	0.0830509	+	0.577632i
$711$	−5.79173	−	3.72212i	−0.217207	−	0.139590i
$712$	17.7448			0.665014
$713$	40.7587	+	0.295045i	1.52642	+	0.0110495i
$714$	−6.80758			−0.254767
$715$	11.6084	+	7.46026i	0.434129	+	0.278998i
$716$	−2.67511	−	18.6058i	−0.0999736	−	0.695332i
$717$	−19.6376	−	43.0004i	−0.733381	−	1.60588i
$718$	−1.96016	−	0.575556i	−0.0731526	−	0.0214796i
$719$	13.7406	−	30.0878i	0.512440	−	1.12209i	−0.459784	−	0.888031i	$-0.652073\pi$
$719$	13.7406	−	30.0878i	0.512440	−	1.12209i	0.972223	−	0.234055i	$-0.0751997\pi$
$720$	4.44367	−	5.12827i	0.165606	−	0.191119i
$721$	2.19850	−	15.2909i	0.0818762	−	0.569462i
$722$	17.3104	−	5.08279i	0.644226	−	0.189162i
$723$	24.5182	+	28.2955i	0.911840	+	1.05232i
$724$	7.15309	−	4.59701i	0.265842	−	0.170847i
$725$	−1.81209	+	1.16456i	−0.0672991	+	0.0432505i
$726$	−19.7290	−	22.7685i	−0.732212	−	0.845017i
$727$	−18.5943	+	5.45978i	−0.689625	+	0.202492i	−0.607724	−	0.794148i	$-0.707917\pi$
$727$	−18.5943	+	5.45978i	−0.689625	+	0.202492i	−0.0819008	+	0.996640i	$0.526099\pi$
$728$	0.104193	−	0.724677i	0.00386165	−	0.0268583i
$729$	1.72388	−	1.98947i	0.0638476	−	0.0736840i
$730$	−12.6749	+	27.7543i	−0.469121	+	1.02723i
$731$	−30.8321	−	9.05313i	−1.14037	−	0.334842i
$732$	10.5729	+	23.1513i	0.390784	+	0.855698i
$733$	3.25767	+	22.6576i	0.120325	+	0.836876i	0.957189	+	0.289465i	$0.0934774\pi$
$733$	3.25767	+	22.6576i	0.120325	+	0.836876i	−0.836864	+	0.547411i	$0.815613\pi$
$734$	7.08395	+	4.55258i	0.261473	+	0.168039i
$735$	−8.29076			−0.305809
$736$	1.96063	+	4.37675i	0.0722698	+	0.161329i
$737$	21.0949			0.777040
$738$	−0.785373	−	0.504729i	−0.0289100	−	0.0185793i
$739$	6.85476	+	47.6759i	0.252156	+	1.75379i	0.585213	+	0.810880i	$0.301011\pi$
$739$	6.85476	+	47.6759i	0.252156	+	1.75379i	−0.333056	+	0.942907i	$0.608080\pi$
$740$	−9.19396	−	20.1320i	−0.337977	−	0.740066i
$741$	−1.50570	−	0.442113i	−0.0553133	−	0.0162414i
$742$	−0.687692	+	1.50583i	−0.0252460	+	0.0552809i
$743$	1.66142	−	1.91738i	0.0609515	−	0.0703418i	−0.724455	−	0.689322i	$-0.757908\pi$
$743$	1.66142	−	1.91738i	0.0609515	−	0.0703418i	0.785407	+	0.618980i	$0.212454\pi$
$744$	−2.64763	+	18.4147i	−0.0970669	+	0.675115i
$745$	−45.5403	+	13.3718i	−1.66847	+	0.489906i
$746$	2.35377	+	2.71639i	0.0861776	+	0.0994543i
$747$	8.50813	−	5.46784i	0.311296	−	0.200058i
$748$	−13.0191	+	8.36689i	−0.476027	+	0.305924i
$749$	8.76590	+	10.1164i	0.320299	+	0.369645i
$750$	34.5665	−	10.1496i	1.26219	−	0.370612i
$751$	4.00139	−	27.8303i	0.146013	−	1.01554i	−0.776650	−	0.629933i	$-0.783082\pi$
$751$	4.00139	−	27.8303i	0.146013	−	1.01554i	0.922662	−	0.385609i	$-0.126008\pi$
$752$	7.58395	−	8.75234i	0.276558	−	0.319165i
$753$	9.65613	−	21.1440i	0.351889	−	0.770529i
$754$	0.161916	+	0.0475427i	0.00589662	+	0.00173140i
$755$	−14.6084	−	31.9880i	−0.531655	−	1.16416i
$756$	−0.376447	−	2.61825i	−0.0136913	−	0.0952248i
$757$	33.2193	+	21.3487i	1.20737	+	0.775933i	0.980217	−	0.197925i	$-0.0634204\pi$
$757$	33.2193	+	21.3487i	1.20737	+	0.775933i	0.227158	+	0.973858i	$0.427057\pi$
$758$	−26.4403			−0.960354
$759$	34.4951	−	39.2320i	1.25209	−	1.42403i
$760$	−3.70872			−0.134529
$761$	2.75703	+	1.77183i	0.0999422	+	0.0642289i	0.589657	−	0.807654i	$-0.299263\pi$
$761$	2.75703	+	1.77183i	0.0999422	+	0.0642289i	−0.489715	+	0.871883i	$0.662899\pi$
$762$	−2.84931	−	19.8174i	−0.103220	−	0.717907i
$763$	−2.84450	−	6.22860i	−0.102978	−	0.225490i
$764$	−24.1794	−	7.09970i	−0.874778	−	0.256858i
$765$	−8.76654	+	19.1961i	−0.316955	+	0.694035i
$766$	−17.5586	+	20.2637i	−0.634419	+	0.732159i
$767$	1.20433	−	8.37632i	0.0434860	−	0.302451i
$768$	−2.10030	+	0.616704i	−0.0757881	+	0.0222534i
$769$	−15.6627	−	18.0757i	−0.564810	−	0.651826i	0.399459	−	0.916751i	$-0.369198\pi$
$769$	−15.6627	−	18.0757i	−0.564810	−	0.651826i	−0.964269	+	0.264925i	$0.914653\pi$
$770$	−15.8556	+	10.1898i	−0.571398	+	0.367215i
$771$	−0.959886	+	0.616881i	−0.0345694	+	0.0222164i
$772$	4.15504	+	4.79518i	0.149543	+	0.172582i
$773$	−12.1896	+	3.57920i	−0.438430	+	0.128735i	−0.493496	−	0.869748i	$-0.664281\pi$
$773$	−12.1896	+	3.57920i	−0.438430	+	0.128735i	0.0550659	+	0.998483i	$0.482463\pi$
$774$	−2.63450	+	18.3233i	−0.0946950	+	0.658618i
$775$	−52.0127	+	60.0258i	−1.86835	+	2.15619i
$776$	−3.16502	+	6.93042i	−0.113617	+	0.248787i
$777$	12.2729	+	3.60365i	0.440288	+	0.129280i
$778$	−9.19463	−	20.1334i	−0.329643	−	0.721818i
$779$	0.0726156	+	0.505052i	0.00260172	+	0.0180954i
$780$	−5.10634	−	3.28164i	−0.182836	−	0.117502i
$781$	−20.4301			−0.731048
$782$	−9.68525	−	11.3422i	−0.346344	−	0.405598i
$783$	0.609695			0.0217887
$784$	0.841254	+	0.540641i	0.0300448	+	0.0193086i
$785$	4.49775	+	31.2825i	0.160532	+	1.11652i
$786$	−8.76136	−	19.1847i	−0.312507	−	0.684296i
$787$	−11.5845	−	3.40150i	−0.412941	−	0.121250i	0.0686618	−	0.997640i	$-0.478127\pi$
$787$	−11.5845	−	3.40150i	−0.412941	−	0.121250i	−0.481603	+	0.876390i	$0.659945\pi$
$788$	4.94122	−	10.8198i	0.176024	−	0.385438i
$789$	7.39199	−	8.53081i	0.263162	−	0.303705i
$790$	−2.07132	+	14.4064i	−0.0736943	+	0.512555i
$791$	−14.2767	+	4.19203i	−0.507622	+	0.149051i
$792$	5.83835	+	6.73781i	0.207457	+	0.239418i
$793$	7.16119	−	4.60222i	0.254301	−	0.163430i
$794$	−15.2971	+	9.83085i	−0.542874	+	0.348884i
$795$	8.98783	+	10.3725i	0.318766	+	0.367875i
$796$	8.14213	−	2.39075i	0.288590	−	0.0847377i
$797$	−3.25862	+	22.6642i	−0.115426	+	0.802808i	0.847064	+	0.531491i	$0.178368\pi$
$797$	−3.25862	+	22.6642i	−0.115426	+	0.802808i	−0.962490	+	0.271317i	$0.912541\pi$
$798$	1.40365	−	1.61989i	0.0496885	−	0.0573436i
$799$	−14.9617	+	32.7616i	−0.529308	+	1.15902i
$800$	−8.96674	−	2.63287i	−0.317022	−	0.0930861i
$801$	13.2066	+	28.9185i	0.466633	+	1.02178i
$802$	−2.94213	−	20.4630i	−0.103890	−	0.722572i
$803$	−33.7240	−	21.6731i	−1.19009	−	0.764826i
$804$	−9.27928			−0.327255
$805$	−11.7954	−	13.8134i	−0.415733	−	0.486859i
$806$	6.22236			0.219173
$807$	−3.21881	−	2.06860i	−0.113307	−	0.0728182i
$808$	0.0405486	+	0.282021i	0.00142649	+	0.00992148i
$809$	−3.89599	−	8.53102i	−0.136976	−	0.299935i	0.828697	−	0.559698i	$-0.189083\pi$
$809$	−3.89599	−	8.53102i	−0.136976	−	0.299935i	−0.965672	+	0.259763i	$0.916356\pi$
$810$	−40.5746	−	11.9138i	−1.42565	−	0.418607i
$811$	17.3548	−	38.0017i	0.609409	−	1.33442i	−0.313569	−	0.949565i	$-0.601525\pi$
$811$	17.3548	−	38.0017i	0.609409	−	1.33442i	0.922978	−	0.384853i	$-0.125748\pi$
$812$	−0.150941	+	0.174195i	−0.00529700	+	0.00611306i
$813$	−1.64389	+	11.4335i	−0.0576538	+	0.400991i
$814$	27.9004	−	8.19229i	0.977907	−	0.287139i
$815$	60.5474	+	69.8755i	2.12088	+	2.44763i
$816$	5.72690	−	3.68045i	0.200482	−	0.128842i
$817$	8.51147	−	5.46999i	0.297779	−	0.191371i
$818$	18.8345	+	21.7362i	0.658533	+	0.759988i
$819$	1.25854	−	0.369542i	0.0439771	−	0.0129128i
$820$	−0.280876	+	1.95354i	−0.00980863	+	0.0682205i
$821$	21.5215	−	24.8371i	0.751105	−	0.866821i	−0.243570	−	0.969883i	$-0.578319\pi$
$821$	21.5215	−	24.8371i	0.751105	−	0.866821i	0.994675	+	0.103062i	$0.0328640\pi$
$822$	0.347879	−	0.761748i	0.0121337	−	0.0265690i
$823$	−5.55712	−	1.63172i	−0.193709	−	0.0568781i	0.183439	−	0.983031i	$-0.441277\pi$
$823$	−5.55712	−	1.63172i	−0.193709	−	0.0568781i	−0.377148	+	0.926153i	$0.623095\pi$
$824$	6.41738	+	14.0521i	0.223560	+	0.489528i
$825$	14.4872	+	100.761i	0.504381	+	3.50804i
$826$	9.72379	+	6.24910i	0.338334	+	0.217434i
$827$	−46.7711			−1.62639			−0.813195	−	0.581991i	$-0.802274\pi$
$827$	−46.7711			−1.62639			−0.813195	+	0.581991i	$0.802274\pi$
$828$	−5.67353	+	6.45262i	−0.197169	+	0.224244i
$829$	−28.5619			−0.991997			−0.495998	−	0.868323i	$-0.665198\pi$
$829$	−28.5619			−0.991997			−0.495998	+	0.868323i	$0.665198\pi$
$830$	−17.9866	−	11.5593i	−0.624326	−	0.401230i
$831$	2.97201	+	20.6708i	0.103098	+	0.717061i
$832$	0.304138	+	0.665968i	0.0105441	+	0.0230883i
$833$	−2.98397	−	0.876173i	−0.103388	−	0.0303576i
$834$	19.0921	−	41.8060i	0.661107	−	1.44762i
$835$	12.9515	−	14.9469i	0.448207	−	0.517258i
$836$	0.693460	−	4.82312i	0.0239838	−	0.166811i
$837$	21.5707	−	6.33372i	0.745591	−	0.218925i
$838$	−3.16022	−	3.64709i	−0.109168	−	0.125987i
$839$	−20.4382	+	13.1348i	−0.705605	+	0.453465i	−0.843603	−	0.536968i	$-0.819570\pi$
$839$	−20.4382	+	13.1348i	−0.705605	+	0.453465i	0.137998	+	0.990433i	$0.455933\pi$
$840$	6.97463	−	4.48232i	0.240648	−	0.154655i
$841$	18.9562	+	21.8766i	0.653661	+	0.754365i
$842$	13.5204	−	3.96993i	0.465942	−	0.136813i
$843$	5.76558	−	40.1005i	0.198577	−	1.38113i
$844$	7.30511	−	8.43055i	0.251452	−	0.290191i
$845$	19.6107	−	42.9415i	0.674630	−	1.47723i
$846$	19.9080	+	5.84551i	0.684450	+	0.200973i
$847$	−5.71740	−	12.5194i	−0.196452	−	0.430170i
$848$	−0.235593	−	1.63858i	−0.00809029	−	0.0562692i
$849$	−47.1641	−	30.3105i	−1.61867	−	1.04025i
$850$	29.0634			0.996865
$851$	11.4567	+	25.5751i	0.392732	+	0.876703i
$852$	8.98687			0.307885
$853$	4.16334	+	2.67562i	0.142550	+	0.0916114i	0.609972	−	0.792423i	$-0.291181\pi$
$853$	4.16334	+	2.67562i	0.142550	+	0.0916114i	−0.467422	+	0.884034i	$0.654817\pi$
$854$	1.65471	+	11.5087i	0.0566228	+	0.393821i
$855$	−2.76023	−	6.04405i	−0.0943977	−	0.206702i
$856$	−12.8437	−	3.77125i	−0.438988	−	0.128899i
$857$	−1.11344	+	2.43810i	−0.0380345	+	0.0832840i	−0.927696	−	0.373337i	$-0.878213\pi$
$857$	−1.11344	+	2.43810i	−0.0380345	+	0.0832840i	0.889661	+	0.456621i	$0.150941\pi$
$858$	5.22251	−	6.02710i	0.178294	−	0.205762i
$859$	−1.29565	+	9.01142i	−0.0442069	+	0.307466i	0.955707	+	0.294321i	$0.0950934\pi$
$859$	−1.29565	+	9.01142i	−0.0442069	+	0.307466i	−0.999914	+	0.0131449i	$0.995816\pi$
$860$	37.5496	−	11.0256i	1.28043	−	0.375968i
$861$	−0.746963	−	0.862042i	−0.0254564	−	0.0293783i
$862$	12.3548	−	7.93995i	0.420806	−	0.270436i
$863$	15.9753	−	10.2667i	0.543806	−	0.349483i	−0.239720	−	0.970842i	$-0.577056\pi$
$863$	15.9753	−	10.2667i	0.543806	−	0.349483i	0.783526	+	0.621359i	$0.213419\pi$
$864$	1.73222	+	1.99909i	0.0589313	+	0.0680104i
$865$	39.7959	−	11.6851i	1.35310	−	0.397306i
$866$	4.56054	−	31.7193i	0.154974	−	1.07786i
$867$	10.5048	−	12.1232i	0.356762	−	0.411725i
$868$	−3.53061	+	7.73096i	−0.119837	+	0.262406i
$869$	−18.3479	−	5.38744i	−0.622411	−	0.182756i
$870$	0.793845	+	1.73828i	0.0269139	+	0.0589331i
$871$	0.441685	+	3.07199i	0.0149659	+	0.104090i
$872$	5.76038	+	3.70197i	0.195071	+	0.125365i
$873$	−13.6500			−0.461982
$874$	4.69593	+	0.0339930i	0.158842	+	0.00114983i
$875$	16.4579			0.556377
$876$	14.8346	+	9.53362i	0.501215	+	0.322111i
$877$	−3.97432	−	27.6420i	−0.134203	−	0.933404i	−0.939991	−	0.341199i	$-0.889167\pi$
$877$	−3.97432	−	27.6420i	−0.134203	−	0.933404i	0.805788	−	0.592204i	$-0.201742\pi$
$878$	11.4560	+	25.0852i	0.386622	+	0.846584i
$879$	28.5887	+	8.39439i	0.964271	+	0.283136i
$880$	7.82960	−	17.1444i	0.263936	−	0.577938i
$881$	−18.4348	+	21.2749i	−0.621086	+	0.716771i	−0.975913	−	0.218161i	$-0.929994\pi$
$881$	−18.4348	+	21.2749i	−0.621086	+	0.716771i	0.354827	+	0.934932i	$0.384540\pi$
$882$	−0.254970	+	1.77335i	−0.00858528	+	0.0597119i
$883$	0.487701	−	0.143202i	0.0164125	−	0.00481913i	−0.273516	−	0.961867i	$-0.588187\pi$
$883$	0.487701	−	0.143202i	0.0164125	−	0.00481913i	0.289928	+	0.957048i	$0.406368\pi$
$884$	−1.49104	−	1.72075i	−0.0501492	−	0.0578752i
$885$	80.6176	−	51.8098i	2.70993	−	1.74157i
$886$	−6.85797	+	4.40735i	−0.230398	+	0.148068i
$887$	−6.13435	−	7.07942i	−0.205971	−	0.237704i	0.643360	−	0.765564i	$-0.277540\pi$
$887$	−6.13435	−	7.07942i	−0.205971	−	0.237704i	−0.849331	+	0.527860i	$0.822994\pi$
$888$	−12.2729	+	3.60365i	−0.411852	+	0.120931i
$889$	1.30167	−	9.05328i	0.0436565	−	0.303637i
$890$	44.0123	−	50.7929i	1.47530	−	1.70258i
$891$	23.0804	−	50.5389i	0.773221	−	1.69312i
$892$	3.93213	+	1.15458i	0.131658	+	0.0386581i
$893$	−4.71083	−	10.3153i	−0.157642	−	0.345188i
$894$	3.90382	+	27.1516i	0.130563	+	0.908087i
$895$	−59.8926	−	38.4906i	−2.00199	−	1.28660i
$896$	−1.00000			−0.0334077
$897$	6.43550	+	4.20198i	0.214875	+	0.140300i
$898$	−3.70385			−0.123599
$899$	−1.64799	−	1.05910i	−0.0549634	−	0.0353228i
$900$	−2.38277	−	16.5725i	−0.0794256	−	0.552417i
$901$	2.13868	+	4.68306i	0.0712499	+	0.156016i
$902$	−2.48803	−	0.730550i	−0.0828422	−	0.0243247i
$903$	−9.39574	+	20.5738i	−0.312670	+	0.684653i
$904$	9.74397	−	11.2451i	0.324080	−	0.374008i
$905$	4.58323	−	31.8771i	0.152352	−	1.05963i
$906$	−19.5006	+	5.72589i	−0.647864	+	0.190230i
$907$	−19.2565	−	22.2232i	−0.639402	−	0.737909i	0.339867	−	0.940474i	$-0.389618\pi$
$907$	−19.2565	−	22.2232i	−0.639402	−	0.737909i	−0.979269	+	0.202564i	$0.935073\pi$
$908$	−1.06483	+	0.684324i	−0.0353376	+	0.0227101i
$909$	−0.429428	+	0.275977i	−0.0142432	+	0.00915358i
$910$	−1.81590	−	2.09566i	−0.0601964	−	0.0694704i
$911$	19.7991	−	5.81355i	0.655974	−	0.192611i	0.0632259	−	0.997999i	$-0.479861\pi$
$911$	19.7991	−	5.81355i	0.655974	−	0.192611i	0.592748	+	0.805388i	$0.298043\pi$
$912$	−0.305042	+	2.12161i	−0.0101009	+	0.0702535i
$913$	18.3959	−	21.2299i	0.608814	−	0.702609i
$914$	11.3047	−	24.7539i	0.373927	−	0.818785i
$915$	92.4926	+	27.1583i	3.05771	+	0.897824i
$916$	−1.41950	−	3.10827i	−0.0469015	−	0.102700i
$917$	−1.37120	−	9.53688i	−0.0452809	−	0.314936i
$918$	−6.92044	−	4.44750i	−0.228409	−	0.146789i
$919$	0.109138			0.00360014			0.00180007	−	0.999998i	$-0.499427\pi$
$919$	0.109138			0.00360014			0.00180007	+	0.999998i	$0.499427\pi$
$920$	17.3910	+	5.24350i	0.573365	+	0.172873i
$921$	−43.2687			−1.42575
$922$	28.5658	+	18.3581i	0.940764	+	0.604592i
$923$	−0.427766	−	2.97518i	−0.0140801	−	0.0979293i
$924$	4.52506	+	9.90850i	0.148864	+	0.325966i
$925$	−52.3963	−	15.3849i	−1.72278	−	0.505853i
$926$	−11.9535	+	26.1745i	−0.392816	+	0.860147i
$927$	−18.1244	+	20.9166i	−0.595282	+	0.686993i
$928$	0.0328027	−	0.228147i	0.00107680	−	0.00748931i
$929$	3.46927	−	1.01867i	0.113823	−	0.0334214i	−0.224325	−	0.974514i	$-0.572018\pi$
$929$	3.46927	−	1.01867i	0.113823	−	0.0334214i	0.338148	+	0.941093i	$0.390200\pi$
$930$	46.1436	+	53.2525i	1.51311	+	1.74622i
$931$	0.823751	−	0.529393i	0.0269973	−	0.0173501i
$932$	9.77586	−	6.28257i	0.320219	−	0.205792i
$933$	−30.6827	−	35.4098i	−1.00451	−	1.15926i
$934$	−31.3101	+	9.19346i	−1.02450	+	0.300819i
$935$	−8.34181	+	58.0185i	−0.272806	+	1.89741i
$936$	−0.858965	+	0.991299i	−0.0280762	+	0.0324016i
$937$	−8.41848	+	18.4339i	−0.275020	+	0.602209i	−0.995861	−	0.0908911i	$-0.971028\pi$
$937$	−8.41848	+	18.4339i	−0.275020	+	0.602209i	0.720841	+	0.693100i	$0.243756\pi$
$938$	−4.06740	−	1.19430i	−0.132805	−	0.0389951i
$939$	−6.20442	−	13.5858i	−0.202474	−	0.443355i
$940$	−6.24240	−	43.4168i	−0.203605	−	1.41610i
$941$	19.3450	+	12.4323i	0.630630	+	0.405282i	0.816543	−	0.577285i	$-0.195888\pi$
$941$	19.3450	+	12.4323i	0.630630	+	0.405282i	−0.185912	+	0.982566i	$0.559524\pi$
$942$	18.2654			0.595120
$943$	0.373548	−	2.47097i	0.0121644	−	0.0804659i
$944$	−11.5587			−0.376203
$945$	−8.42822	−	5.41649i	−0.274170	−	0.176198i
$946$	7.31748	+	50.8942i	0.237912	+	1.65471i
$947$	2.25252	+	4.93233i	0.0731970	+	0.160279i	0.942693	−	0.333660i	$-0.108284\pi$
$947$	2.25252	+	4.93233i	0.0731970	+	0.160279i	−0.869496	+	0.493939i	$0.835557\pi$
$948$	8.07094	+	2.36984i	0.262132	+	0.0769689i
$949$	2.45007	−	5.36491i	0.0795328	−	0.174152i
$950$	−5.99254	+	6.91576i	−0.194424	+	0.224377i
$951$	0.284806	−	1.98087i	0.00923548	−	0.0642342i
$952$	2.98397	−	0.876173i	0.0967111	−	0.0283969i
$953$	−14.5359	−	16.7754i	−0.470865	−	0.543408i	0.469787	−	0.882780i	$-0.344331\pi$
$953$	−14.5359	−	16.7754i	−0.470865	−	0.543408i	−0.940652	+	0.339372i	$0.889785\pi$
$954$	2.49504	−	1.60346i	0.0807798	−	0.0519140i
$955$	−80.2942	+	51.6020i	−2.59826	+	1.66980i
$956$	14.1422	+	16.3209i	0.457391	+	0.527857i
$957$	−2.40903	+	0.707356i	−0.0778730	+	0.0228656i
$958$	4.89286	−	34.0306i	0.158081	−	1.09948i
$959$	0.250527	−	0.289124i	0.00808995	−	0.00933630i
$960$	−3.44411	+	7.54154i	−0.111158	+	0.243402i
$961$	−39.5627	−	11.6167i	−1.27622	−	0.374731i
$962$	1.77720	+	3.89152i	0.0572992	+	0.125468i
$963$	−3.41300	−	23.7380i	−0.109982	−	0.764945i
$964$	−14.3888	−	9.24715i	−0.463434	−	0.297831i
$965$	24.0315			0.773602
$966$	−8.87227	+	5.61153i	−0.285461	+	0.180548i
$967$	20.7678			0.667847			0.333924	−	0.942600i	$-0.391627\pi$
$967$	20.7678			0.667847			0.333924	+	0.942600i	$0.391627\pi$
$968$	11.5783	+	7.44089i	0.372139	+	0.239159i
$969$	−0.948663	−	6.59809i	−0.0304754	−	0.211961i
$970$	11.9876	+	26.2491i	0.384897	+	0.842807i
$971$	−40.3761	−	11.8555i	−1.29573	−	0.380461i	−0.440055	−	0.897971i	$-0.645041\pi$
$971$	−40.3761	−	11.8555i	−1.29573	−	0.380461i	−0.855677	+	0.517510i	$0.826859\pi$
$972$	−6.85612	+	15.0128i	−0.219910	+	0.481536i
$973$	13.7493	−	15.8676i	0.440783	−	0.508691i
$974$	−1.68843	+	11.7433i	−0.0541008	+	0.376280i
$975$	−14.3702	+	4.21947i	−0.460214	+	0.135131i
$976$	−7.61411	−	8.78716i	−0.243722	−	0.281270i
$977$	−10.2939	+	6.61548i	−0.329331	+	0.211648i	−0.694848	−	0.719157i	$-0.744528\pi$
$977$	−10.2939	+	6.61548i	−0.329331	+	0.211648i	0.365518	+	0.930804i	$0.380892\pi$
$978$	44.9530	−	28.8895i	1.43744	−	0.923786i
$979$	57.8259	+	66.7346i	1.84812	+	2.13285i
$980$	3.63410	−	1.06707i	0.116087	−	0.0340862i
$981$	−1.74588	+	12.1428i	−0.0557415	+	0.387691i
$982$	−24.5049	+	28.2802i	−0.781984	+	0.902458i
$983$	22.7883	−	49.8994i	0.726833	−	1.59154i	−0.0772406	−	0.997012i	$-0.524611\pi$
$983$	22.7883	−	49.8994i	0.726833	−	1.59154i	0.804074	−	0.594530i	$-0.202662\pi$
$984$	1.09444	+	0.321357i	0.0348895	+	0.0102445i
$985$	−18.7150	−	40.9801i	−0.596309	−	1.30573i
$986$	0.102014	+	0.709526i	0.00324880	+	0.0225959i
$987$	21.3262	+	13.7055i	0.678820	+	0.436251i
$988$	0.716897			0.0228075
$989$	−47.6459	+	13.6162i	−1.51505	+	0.432971i
$990$	33.7673			1.07319
$991$	−5.44588	−	3.49985i	−0.172994	−	0.111177i	0.451278	−	0.892383i	$-0.350968\pi$
$991$	−5.44588	−	3.49985i	−0.172994	−	0.111177i	−0.624272	+	0.781207i	$0.714604\pi$
$992$	−1.20953	−	8.41249i	−0.0384027	−	0.267097i
$993$	13.4399	+	29.4292i	0.426501	+	0.933907i
$994$	3.93922	+	1.15666i	0.124945	+	0.0366870i
$995$	13.3516	−	29.2359i	0.423274	−	0.926841i
$996$	−8.09203	+	9.33870i	−0.256406	+	0.295908i
$997$	−1.34349	+	9.34415i	−0.0425486	+	0.295932i	0.957425	+	0.288682i	$0.0932170\pi$
$997$	−1.34349	+	9.34415i	−0.0425486	+	0.295932i	−0.999974	+	0.00725037i	$0.997692\pi$
$998$	−9.90581	+	2.90861i	−0.313563	+	0.0920704i
$999$	10.1221	+	11.6815i	0.320248	+	0.369585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.71.2	✓	40
23.9	even	11		7406.2.a.bu.1.14		20
23.12	even	11	inner	322.2.i.d.127.2	yes	40
23.14	odd	22		7406.2.a.bv.1.14		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.71.2	✓	40	1.1	even	1	trivial
322.2.i.d.127.2	yes	40	23.12	even	11	inner
7406.2.a.bu.1.14		20	23.9	even	11
7406.2.a.bv.1.14		20	23.14	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(-0.311523 - 2.16669i) q^{3} +(0.415415 + 0.909632i) q^{4} +(3.63410 + 1.06707i) q^{5} +(0.909331 - 1.99116i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-1.71902 + 0.504749i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{2} +(-0.311523 - 2.16669i) q^{3} +(0.415415 + 0.909632i) q^{4} +(3.63410 + 1.06707i) q^{5} +(0.909331 - 1.99116i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-1.71902 + 0.504749i) q^{9} +(2.48030 + 2.86241i) q^{10} +(-4.18629 + 2.69037i) q^{11} +(1.84148 - 1.18345i) q^{12} +(-0.479443 - 0.553307i) q^{13} +(0.959493 - 0.281733i) q^{14} +(1.17990 - 8.20638i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.29192 - 2.82891i) q^{17} +(-1.71902 - 0.504749i) q^{18} +(0.406772 + 0.890707i) q^{19} +(0.539020 + 3.74897i) q^{20} +(-1.84148 - 1.18345i) q^{21} -4.97625 q^{22} +(-0.648138 - 4.75183i) q^{23} +2.18897 q^{24} +(7.86176 + 5.05245i) q^{25} +(-0.104193 - 0.724677i) q^{26} +(-1.09884 - 2.40613i) q^{27} +(0.959493 + 0.281733i) q^{28} +(-0.0957505 + 0.209664i) q^{29} +(5.42930 - 6.26574i) q^{30} +(-1.20953 + 8.41249i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(7.13331 + 8.23228i) q^{33} +(2.61625 - 1.68136i) q^{34} +(3.18626 - 2.04769i) q^{35} +(-1.17324 - 1.35399i) q^{36} +(-5.60670 + 1.64628i) q^{37} +(-0.139354 + 0.969228i) q^{38} +(-1.04949 + 1.21117i) q^{39} +(-1.57339 + 3.44525i) q^{40} +(0.499980 + 0.146807i) q^{41} +(-0.909331 - 1.99116i) q^{42} +(-1.47048 - 10.2274i) q^{43} +(-4.18629 - 2.69037i) q^{44} -6.78568 q^{45} +(2.02379 - 4.34791i) q^{46} -11.5810 q^{47} +(1.84148 + 1.18345i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(3.88217 + 8.50078i) q^{50} +(-6.53182 - 1.91792i) q^{51} +(0.304138 - 0.665968i) q^{52} +(-1.08408 + 1.25109i) q^{53} +(0.376447 - 2.61825i) q^{54} +(-18.0842 + 5.31000i) q^{55} +(0.654861 + 0.755750i) q^{56} +(1.80317 - 1.15882i) q^{57} +(-0.193904 + 0.124614i) q^{58} +(7.56933 + 8.73548i) q^{59} +(7.95493 - 2.33578i) q^{60} +(-1.65471 + 11.5087i) q^{61} +(-5.56566 + 6.42311i) q^{62} +(-0.744253 + 1.62969i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.15193 - 2.52237i) q^{65} +(1.55022 + 10.7820i) q^{66} +(-3.56617 - 2.29184i) q^{67} +3.10995 q^{68} +(-10.0938 + 2.88462i) q^{69} +3.78752 q^{70} +(3.45379 + 2.21961i) q^{71} +(-0.254970 - 1.77335i) q^{72} +(3.34650 + 7.32782i) q^{73} +(-5.60670 - 1.64628i) q^{74} +(8.49796 - 18.6079i) q^{75} +(-0.641236 + 0.740026i) q^{76} +(-0.708195 + 4.92560i) q^{77} +(-1.53769 + 0.451507i) q^{78} +(2.51647 + 2.90416i) q^{79} +(-3.18626 + 2.04769i) q^{80} +(-9.39257 + 6.03624i) q^{81} +(0.341240 + 0.393812i) q^{82} +(-5.41640 + 1.59040i) q^{83} +(0.311523 - 2.16669i) q^{84} +(7.71359 - 8.90196i) q^{85} +(4.29231 - 9.39885i) q^{86} +(0.484106 + 0.142146i) q^{87} +(-2.06721 - 4.52656i) q^{88} +(-2.52535 - 17.5642i) q^{89} +(-5.70848 - 3.66862i) q^{90} -0.732130 q^{91} +(4.05317 - 2.56355i) q^{92} +18.6040 q^{93} +(-9.74257 - 6.26117i) q^{94} +(0.527805 + 3.67097i) q^{95} +(0.909331 + 1.99116i) q^{96} +(7.31030 + 2.14650i) q^{97} +(0.415415 - 0.909632i) q^{98} +(5.83835 - 6.73781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

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