LMFDB - Embedded newform 322.2.i.d.127.2

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			127.2
Character	$\chi$	$=$	322.127
Dual form			322.2.i.d.71.2

$q$-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 $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

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	0.677231	+	0.735770i	$0.263180\pi$
$3$	−0.311523	+	2.16669i	−0.179858	+	1.25094i	−0.857089	+	0.515168i	$0.827729\pi$
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	3.63410	−	1.06707i	1.62522	−	0.477207i	0.662803	−	0.748793i	$-0.269366\pi$
$5$	3.63410	−	1.06707i	1.62522	−	0.477207i	0.962414	+	0.271587i	$0.0875483\pi$
$6$	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	−0.273628	−	0.961835i	$-0.588224\pi$
$11$	−4.18629	−	2.69037i	−1.26221	−	0.811176i	−0.988586	+	0.150660i	$0.951860\pi$
$12$	1.84148	+	1.18345i	0.531589	+	0.341632i
$13$	−0.479443	+	0.553307i	−0.132974	+	0.153460i	−0.818331	−	0.574747i	$-0.805100\pi$
$13$	−0.479443	+	0.553307i	−0.132974	+	0.153460i	0.685358	+	0.728207i	$0.259646\pi$
$14$	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	0.999131	−	0.0416845i	$-0.0132724\pi$
$17$	1.29192	+	2.82891i	0.313336	+	0.686111i	−0.685795	+	0.727795i	$0.740545\pi$
$18$	−1.71902	+	0.504749i	−0.405176	+	0.118971i
$19$	0.406772	−	0.890707i	0.0933199	−	0.204342i	−0.857216	−	0.514957i	$-0.827808\pi$
$19$	0.406772	−	0.890707i	0.0933199	−	0.204342i	0.950536	+	0.310615i	$0.100535\pi$
$20$	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	0.900533	−	0.434787i	$-0.143176\pi$
$29$	−0.0957505	−	0.209664i	−0.0177804	−	0.0389337i	−0.918314	+	0.395853i	$0.870449\pi$
$30$	5.42930	+	6.26574i	0.991249	+	1.14396i
$31$	−1.20953	−	8.41249i	−0.217239	−	1.51093i	−0.748167	−	0.663511i	$-0.769066\pi$
$31$	−1.20953	−	8.41249i	−0.217239	−	1.51093i	0.530928	−	0.847417i	$-0.321843\pi$
$32$	−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	−0.213763	−	0.976886i	$-0.568572\pi$
$37$	−5.60670	−	1.64628i	−0.921736	−	0.270646i	−0.707973	+	0.706239i	$0.750390\pi$
$38$	−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	−0.242457	−	0.970162i	$-0.577953\pi$
$41$	0.499980	−	0.146807i	0.0780837	−	0.0229274i	0.320541	+	0.947235i	$0.396135\pi$
$42$	−0.909331	+	1.99116i	−0.140313	+	0.307242i
$43$	−1.47048	+	10.2274i	−0.224246	+	1.55967i	0.497473	+	0.867479i	$0.334261\pi$
$43$	−1.47048	+	10.2274i	−0.224246	+	1.55967i	−0.721719	+	0.692186i	$0.756648\pi$
$44$	−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	0.676394	−	0.736540i	$-0.263542\pi$
$53$	−1.08408	−	1.25109i	−0.148910	−	0.171851i	−0.825304	+	0.564689i	$0.808996\pi$
$54$	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	−0.00508982	−	0.999987i	$-0.501620\pi$
$59$	7.56933	−	8.73548i	0.985443	−	1.13726i	0.990533	−	0.137275i	$-0.0438344\pi$
$60$	7.95493	+	2.33578i	1.02698	+	0.301548i
$61$	−1.65471	−	11.5087i	−0.211863	−	1.47354i	−0.766927	−	0.641734i	$-0.778215\pi$
$61$	−1.65471	−	11.5087i	−0.211863	−	1.47354i	0.555064	−	0.831808i	$-0.312694\pi$
$62$	−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	−0.740039	−	0.672564i	$-0.765193\pi$
$67$	−3.56617	+	2.29184i	−0.435676	+	0.279992i	0.304362	+	0.952556i	$0.401557\pi$
$68$	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	−0.319407	−	0.947617i	$-0.603484\pi$
$71$	3.45379	−	2.21961i	0.409889	−	0.263420i	0.729297	+	0.684198i	$0.239847\pi$
$72$	−0.254970	+	1.77335i	−0.0300485	+	0.208992i
$73$	3.34650	−	7.32782i	0.391679	−	0.857657i	−0.606368	−	0.795184i	$-0.707374\pi$
$73$	3.34650	−	7.32782i	0.391679	−	0.857657i	0.998047	−	0.0624725i	$-0.0198986\pi$
$74$	−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	−0.596318	−	0.802749i	$-0.703370\pi$
$79$	2.51647	−	2.90416i	0.283125	−	0.326744i	0.879443	+	0.476005i	$0.157916\pi$
$80$	−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	−0.0293927	−	0.999568i	$-0.509357\pi$
$83$	−5.41640	−	1.59040i	−0.594527	−	0.174569i	−0.565134	+	0.824999i	$0.691176\pi$
$84$	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	0.202569	+	0.979268i	$0.435071\pi$
$89$	−2.52535	+	17.5642i	−0.267686	+	1.86180i	−0.470255	+	0.882530i	$0.655838\pi$
$90$	−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	0.111320	−	0.993785i	$-0.464492\pi$
$97$	7.31030	−	2.14650i	0.742249	−	0.217944i	0.630929	+	0.775841i	$0.282674\pi$
$98$	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	0.295305	−	0.955403i	$-0.404579\pi$
$101$	0.273380	+	0.0802717i	0.0272023	+	0.00798733i	−0.268103	+	0.963390i	$0.586397\pi$
$102$	−4.45802	+	5.14482i	−0.441409	+	0.509414i
$103$	12.9958	+	8.35188i	1.28051	+	0.822935i	0.990951	−	0.134225i	$-0.0428543\pi$
$103$	12.9958	+	8.35188i	1.28051	+	0.822935i	0.289561	+	0.957160i	$0.406491\pi$
$104$	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	−0.846784	−	0.531937i	$-0.821464\pi$
$107$	−1.90501	−	13.2497i	−0.184165	−	1.28089i	0.662620	−	0.748956i	$-0.269445\pi$
$108$	1.73222	+	1.99909i	0.166683	+	0.192362i
$109$	2.84450	+	6.22860i	0.272454	+	0.596591i	0.995558	−	0.0941478i	$-0.0300126\pi$
$109$	2.84450	+	6.22860i	0.272454	+	0.596591i	−0.723104	+	0.690739i	$0.757285\pi$
$110$	−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	−0.974932	−	0.222503i	$-0.928577\pi$
$113$	−12.5174	+	8.04444i	−1.17754	+	0.756757i	−0.202606	+	0.979260i	$0.564941\pi$
$114$	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	0.835509	−	0.549477i	$-0.185173\pi$
$127$	7.69442	+	4.94491i	0.682770	+	0.438790i	−0.152739	+	0.988267i	$0.548809\pi$
$128$	−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	0.961178	−	0.275929i	$-0.0889853\pi$
$131$	6.30955	+	7.28161i	0.551268	+	0.636197i	−0.409910	+	0.912126i	$0.634440\pi$
$132$	−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	0.0321607	−	0.999483i	$-0.489761\pi$
$149$	−10.5421	−	6.77498i	−0.863641	−	0.555028i	−0.895801	+	0.444454i	$0.853398\pi$
$150$	17.2092	+	11.0597i	1.40512	+	0.903017i
$151$	−6.08017	+	7.01689i	−0.494797	+	0.571026i	−0.947141	−	0.320817i	$-0.896042\pi$
$151$	−6.08017	+	7.01689i	−0.494797	+	0.571026i	0.452344	+	0.891843i	$0.350588\pi$
$152$	−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	−0.719402	−	0.694594i	$-0.755584\pi$
$157$	3.46635	−	7.59025i	0.276645	−	0.605768i	0.996047	+	0.0888258i	$0.0283114\pi$
$158$	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	0.645692	−	0.763598i	$-0.276569\pi$
$163$	20.5361	−	13.1978i	1.60852	−	1.03373i	0.962823	−	0.270132i	$-0.0870673\pi$
$164$	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	0.974803	−	0.223070i	$-0.0716077\pi$
$167$	2.16920	+	4.74989i	0.167858	+	0.367558i	−0.806945	+	0.590627i	$0.798880\pi$
$168$	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	0.841769	−	0.539838i	$-0.181514\pi$
$173$	9.21231	+	5.92040i	0.700399	+	0.450119i	−0.141370	+	0.989957i	$0.545151\pi$
$174$	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	−0.874536	−	0.484961i	$-0.838834\pi$
$179$	−18.0357	+	5.29576i	−1.34805	+	0.395824i	−0.473517	+	0.880785i	$0.657016\pi$
$180$	−2.81887	+	6.17247i	−0.210106	+	0.460069i
$181$	−1.21009	+	8.41635i	−0.0899451	+	0.625582i	0.894127	+	0.447813i	$0.147797\pi$
$181$	−1.21009	+	8.41635i	−0.0899451	+	0.625582i	−0.984072	+	0.177769i	$0.943112\pi$
$182$	−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	−0.907532	−	0.419983i	$-0.862036\pi$
$191$	−16.5026	−	19.0450i	−1.19408	−	1.37805i	−0.286552	−	0.958065i	$-0.592509\pi$
$192$	−0.311523	−	2.16669i	−0.0224822	−	0.156367i
$193$	6.08791	+	1.78757i	0.438218	+	0.128672i	0.493397	−	0.869804i	$-0.335755\pi$
$193$	6.08791	+	1.78757i	0.438218	+	0.128672i	−0.0551795	+	0.998476i	$0.517573\pi$
$194$	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	−0.962033	−	0.272932i	$-0.912007\pi$
$197$	−7.78935	+	8.98939i	−0.554968	+	0.640467i	0.407065	+	0.913399i	$0.366552\pi$
$198$	8.55427	+	2.51176i	0.607925	+	0.178503i
$199$	1.20767	+	8.39950i	0.0856091	+	0.595424i	0.986793	+	0.161987i	$0.0517903\pi$
$199$	1.20767	+	8.39950i	0.0856091	+	0.595424i	−0.901184	+	0.433437i	$0.857301\pi$
$200$	−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	−0.999412	−	0.0342914i	$-0.989083\pi$
$211$	−4.63404	+	10.1471i	−0.319021	+	0.698558i	0.680391	+	0.732849i	$0.261810\pi$
$212$	−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	0.838458	−	0.544966i	$-0.183457\pi$
$223$	2.68371	+	3.09716i	0.179714	+	0.207401i	−0.658744	+	0.752367i	$0.728912\pi$
$224$	−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	−0.982970	−	0.183768i	$-0.941171\pi$
$227$	0.180137	−	1.25288i	0.0119561	−	0.0831566i	0.994926	+	0.100611i	$0.0320797\pi$
$228$	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	0.861137	+	0.508372i	$0.169753\pi$
$233$	−1.65378	+	11.5023i	−0.108343	+	0.753541i	−0.969480	+	0.245169i	$0.921156\pi$
$234$	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	0.871785	−	0.489888i	$-0.162962\pi$
$239$	20.7209	+	6.08421i	1.34032	+	0.393555i	0.468539	+	0.883443i	$0.344780\pi$
$240$	5.42930	−	6.26574i	0.350460	−	0.404452i
$241$	−14.3888	−	9.24715i	−0.926867	−	0.595661i	−0.0122247	−	0.999925i	$-0.503891\pi$
$241$	−14.3888	−	9.24715i	−0.926867	−	0.595661i	−0.914642	+	0.404264i	$0.867528\pi$
$242$	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	−0.227447	−	0.973791i	$-0.573038\pi$
$251$	8.93322	−	5.74103i	0.563860	−	0.362371i	0.791306	+	0.611420i	$0.209401\pi$
$252$	−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	−0.916265	−	0.400572i	$-0.868812\pi$
$257$	−0.216538	+	0.474153i	−0.0135073	+	0.0295769i	0.902758	+	0.430149i	$0.141539\pi$
$258$	−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	−0.642022	−	0.766686i	$-0.721904\pi$
$263$	3.37692	−	3.89718i	0.208230	−	0.240310i	0.850252	+	0.526376i	$0.176450\pi$
$264$	−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	0.789571	−	0.613659i	$-0.210303\pi$
$269$	1.14466	+	1.32101i	0.0697912	+	0.0805434i	−0.719780	+	0.694202i	$0.755757\pi$
$270$	4.16189	+	9.11328i	0.253285	+	0.554616i
$271$	−5.06320	+	1.48669i	−0.307567	+	0.0903099i	−0.431874	−	0.901934i	$-0.642147\pi$
$271$	−5.06320	+	1.48669i	−0.307567	+	0.0903099i	0.124307	+	0.992244i	$0.460329\pi$
$272$	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	0.294763	−	0.955570i	$-0.404759\pi$
$281$	17.7580	−	5.21422i	1.05935	−	0.311055i	0.764591	+	0.644516i	$0.222941\pi$
$282$	−10.5310	−	23.0596i	−0.627110	−	1.37318i
$283$	16.7723	+	19.3563i	0.997012	+	1.15061i	0.988587	+	0.150648i	$0.0481361\pi$
$283$	16.7723	+	19.3563i	0.997012	+	1.15061i	0.00842433	+	0.999965i	$0.497318\pi$
$284$	−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	0.669470	−	0.742839i	$-0.266521\pi$
$293$	−5.65450	−	12.3816i	−0.330339	−	0.723343i	−0.999810	+	0.0194961i	$0.993794\pi$
$294$	−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	0.897597	+	0.440818i	$0.145311\pi$
$307$	2.81309	+	19.5655i	0.160552	+	1.11666i	−0.737045	+	0.675844i	$0.763779\pi$
$308$	−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	0.940233	−	0.340531i	$-0.110607\pi$
$311$	18.0066	+	11.5722i	1.02106	+	0.656197i	0.0808290	+	0.996728i	$0.474243\pi$
$312$	−1.04949	+	1.21117i	−0.0594155	+	0.0685691i
$313$	6.54668	+	1.92228i	0.370040	+	0.108654i	0.461465	−	0.887158i	$-0.347324\pi$
$313$	6.54668	+	1.92228i	0.370040	+	0.108654i	−0.0914249	+	0.995812i	$0.529142\pi$
$314$	−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	−0.257005	−	0.966410i	$-0.582736\pi$
$317$	0.877206	−	0.257571i	0.0492688	−	0.0144666i	0.306274	+	0.951943i	$0.400918\pi$
$318$	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	−0.132292	−	0.991211i	$-0.542234\pi$
$331$	−14.1812	−	4.16399i	−0.779472	−	0.228874i	−0.647180	+	0.762337i	$0.724052\pi$
$332$	−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	0.738161	+	0.674625i	$0.235695\pi$
$337$	4.03801	+	28.0850i	0.219964	+	1.52989i	−0.518196	+	0.855262i	$0.673396\pi$
$338$	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	−0.619490	−	0.785005i	$-0.712660\pi$
$347$	−3.03207	+	1.94859i	−0.162770	+	0.104606i	0.456720	+	0.889610i	$0.349024\pi$
$348$	0.0718040	−	0.499408i	0.00384910	−	0.0267711i
$349$	12.8153	−	28.0616i	0.685989	−	1.50211i	−0.170182	−	0.985413i	$-0.554436\pi$
$349$	12.8153	−	28.0616i	0.685989	−	1.50211i	0.856171	−	0.516693i	$-0.172837\pi$
$350$	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	−0.839012	−	0.544113i	$-0.816866\pi$
$353$	−3.51868	−	24.4729i	−0.187280	−	1.30256i	0.651732	−	0.758450i	$-0.274043\pi$
$354$	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	0.229596	−	0.973286i	$-0.426259\pi$
$359$	−1.96016	−	0.575556i	−0.103453	−	0.0303767i	−0.333050	+	0.942909i	$0.608078\pi$
$360$	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	−0.191226	−	0.981546i	$-0.561246\pi$
$373$	3.44871	−	1.01263i	0.178567	−	0.0524321i	0.369794	+	0.929114i	$0.379428\pi$
$374$	−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	−0.174404	−	0.984674i	$-0.555800\pi$
$379$	−22.2430	−	14.2947i	−1.14254	−	0.734269i	−0.968141	+	0.250405i	$0.919436\pi$
$380$	−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	−0.818586	−	0.574384i	$-0.805242\pi$
$383$	−3.81586	−	26.5399i	−0.194981	−	1.35612i	0.623605	−	0.781740i	$-0.285667\pi$
$384$	−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	−0.919546	−	0.392983i	$-0.871443\pi$
$389$	−18.6200	+	11.9663i	−0.944070	+	0.606717i	−0.0245237	+	0.999699i	$0.507807\pi$
$390$	−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	−0.998968	−	0.0454259i	$-0.985535\pi$
$397$	−7.55379	−	16.5405i	−0.379114	−	0.830143i	0.619854	−	0.784717i	$-0.287192\pi$
$398$	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	−0.985312	−	0.170761i	$-0.945377\pi$
$401$	−13.5382	+	15.6239i	−0.676065	+	0.780220i	0.309248	+	0.950982i	$0.399923\pi$
$402$	−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	0.484177	−	0.874970i	$-0.339119\pi$
$409$	27.5961	−	8.10294i	1.36454	−	0.400664i	0.880360	+	0.474305i	$0.157301\pi$
$410$	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	−0.392871	−	0.919594i	$-0.628518\pi$
$419$	−4.63031	+	1.35958i	−0.226205	+	0.0664199i	0.166666	+	0.986013i	$0.446700\pi$
$420$	3.44411	+	7.54154i	0.168055	+	0.367990i
$421$	9.22774	+	10.6494i	0.449732	+	0.519019i	0.934664	−	0.355533i	$-0.115701\pi$
$421$	9.22774	+	10.6494i	0.449732	+	0.519019i	−0.484931	+	0.874552i	$0.661155\pi$
$422$	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	0.997765	−	0.0668206i	$-0.0212855\pi$
$431$	6.10086	+	13.3590i	0.293868	+	0.643482i	−0.703897	+	0.710302i	$0.748558\pi$
$432$	2.53803	−	0.745231i	0.122111	−	0.0358550i
$433$	−13.3122	+	29.1496i	−0.639742	+	1.40084i	0.260511	+	0.965471i	$0.416109\pi$
$433$	−13.3122	+	29.1496i	−0.639742	+	1.40084i	−0.900253	+	0.435368i	$0.856618\pi$
$434$	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	0.146559	−	0.989202i	$-0.453180\pi$
$439$	23.1995	−	14.9094i	1.10725	−	0.711588i	0.960693	+	0.277614i	$0.0895437\pi$
$440$	−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	0.811963	−	0.583709i	$-0.198399\pi$
$443$	−3.38650	−	7.41540i	−0.160897	−	0.352316i	−0.972860	+	0.231393i	$0.925672\pi$
$444$	−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	0.465048	−	0.885285i	$-0.346037\pi$
$449$	−3.11588	−	2.00245i	−0.147047	−	0.0945016i	−0.612096	+	0.790784i	$0.709673\pi$
$450$	−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	0.672856	+	0.739774i	$0.265067\pi$
$457$	−3.87282	+	26.9361i	−0.181163	+	1.26002i	−0.854019	+	0.520242i	$0.825842\pi$
$458$	−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	−0.640861	−	0.767657i	$-0.721422\pi$
$463$	4.09508	−	28.4819i	0.190315	−	1.32367i	0.831175	−	0.556010i	$-0.187668\pi$
$464$	−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	−0.989981	−	0.141200i	$-0.954904\pi$
$467$	−21.3693	−	24.6615i	−0.988855	−	1.14120i	0.00112594	−	0.999999i	$-0.499642\pi$
$468$	−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	0.236716	+	0.971579i	$0.423929\pi$
$479$	−14.2822	+	31.2736i	−0.652570	+	1.42893i	−0.889287	+	0.457350i	$0.848799\pi$
$480$	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	−0.764486	−	0.644640i	$-0.777007\pi$
$487$	4.92851	−	10.7919i	0.223332	−	0.489029i	0.987818	+	0.155611i	$0.0497346\pi$
$488$	−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	−0.650471	−	0.759531i	$-0.725428\pi$
$491$	−5.32543	−	37.0392i	−0.240333	−	1.67156i	0.410137	−	0.912024i	$-0.365481\pi$
$492$	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	0.583967	−	0.811777i	$-0.301500\pi$
$499$	−6.76079	−	7.80236i	−0.302654	−	0.349282i	−0.886622	+	0.462495i	$0.846954\pi$
$500$	−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	−0.954884	−	0.296979i	$-0.904021\pi$
$503$	1.00900	−	7.01775i	0.0449891	−	0.312906i	0.999873	−	0.0159272i	$-0.00507000\pi$
$504$	−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	0.926696	+	0.375812i	$0.122636\pi$
$509$	−1.54184	+	10.7237i	−0.0683408	+	0.475321i	−0.995037	+	0.0995086i	$0.968273\pi$
$510$	−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	−0.972459	−	0.233073i	$-0.925122\pi$
$521$	−2.39794	−	16.6780i	−0.105056	−	0.730678i	0.867404	−	0.497605i	$-0.165787\pi$
$522$	0.270425	+	0.312087i	0.0118362	+	0.0136597i
$523$	−16.4468	−	36.0134i	−0.719167	−	1.57476i	−0.815068	−	0.579365i	$-0.803301\pi$
$523$	−16.4468	−	36.0134i	−0.719167	−	1.57476i	0.0959014	−	0.995391i	$-0.469427\pi$
$524$	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	0.296858	−	0.954922i	$-0.404061\pi$
$541$	−10.4307	−	6.70340i	−0.448451	−	0.288202i	−0.745308	+	0.666720i	$0.767698\pi$
$542$	−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	−0.410937	−	0.911664i	$-0.634799\pi$
$547$	−6.16877	+	1.81131i	−0.263757	+	0.0774462i	0.147180	+	0.989110i	$0.452980\pi$
$548$	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	0.181678	−	0.983358i	$-0.441847\pi$
$557$	20.4421	−	6.00234i	0.866159	−	0.254327i	0.684481	+	0.729031i	$0.260029\pi$
$558$	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	0.657526	−	0.753431i	$-0.271603\pi$
$563$	5.82104	+	3.74095i	0.245327	+	0.157662i	−0.412199	+	0.911094i	$0.635239\pi$
$564$	−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	−0.923553	−	0.383471i	$-0.874729\pi$
$569$	−14.5165	−	31.7867i	−0.608563	−	1.33257i	0.314990	−	0.949095i	$-0.397999\pi$
$570$	7.78942	−	2.28718i	0.326263	−	0.0957995i
$571$	12.1660	−	26.6399i	0.509132	−	1.11484i	−0.464260	−	0.885699i	$-0.653680\pi$
$571$	12.1660	−	26.6399i	0.509132	−	1.11484i	0.973392	−	0.229145i	$-0.0735929\pi$
$572$	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	−0.612243	−	0.790669i	$-0.709733\pi$
$577$	−3.53971	+	2.27483i	−0.147360	+	0.0947026i	0.464883	+	0.885372i	$0.346096\pi$
$578$	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	0.126129	−	0.992014i	$-0.459745\pi$
$587$	−17.5373	−	11.2705i	−0.723842	−	0.465185i	−0.849971	+	0.526829i	$0.823381\pi$
$588$	−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	−0.174879	−	0.984590i	$-0.555953\pi$
$593$	5.12145	−	1.50379i	0.210313	−	0.0617534i	0.385192	+	0.922837i	$0.374135\pi$
$594$	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	0.512163	+	0.858888i	$0.328844\pi$
$601$	−5.42353	+	37.7215i	−0.221231	+	1.53869i	−0.733394	+	0.679804i	$0.762065\pi$
$602$	−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	0.680587	−	0.732667i	$-0.261725\pi$
$607$	21.1148	+	6.19987i	0.857024	+	0.251645i	0.176437	+	0.984312i	$0.443543\pi$
$608$	−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	−0.808082	−	0.589070i	$-0.799494\pi$
$613$	−4.91941	−	34.2153i	−0.198693	−	1.38194i	0.609389	−	0.792871i	$-0.291415\pi$
$614$	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	0.215247	+	0.976560i	$0.430944\pi$
$617$	−16.4871	+	36.1017i	−0.663745	+	1.45340i	−0.878991	+	0.476838i	$0.841783\pi$
$618$	−4.81244	+	33.4713i	−0.193585	+	1.34641i
$619$	−3.32114	+	2.13437i	−0.133488	+	0.0857874i	−0.605680	−	0.795708i	$-0.707099\pi$
$619$	−3.32114	+	2.13437i	−0.133488	+	0.0857874i	0.472193	+	0.881495i	$0.343463\pi$
$620$	−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	−0.0382077	−	0.999270i	$-0.512165\pi$
$631$	24.0227	−	27.7237i	0.956329	−	1.10366i	0.994536	−	0.104392i	$-0.0332897\pi$
$632$	−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	0.807682	+	0.589618i	$0.200722\pi$
$641$	−3.37736	+	23.4901i	−0.133398	+	0.927802i	−0.941080	+	0.338184i	$0.890187\pi$
$642$	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	0.939198	+	0.343377i	$0.111571\pi$
$647$	−1.49301	+	10.3841i	−0.0586964	+	0.408243i	−0.997894	+	0.0648654i	$0.979338\pi$
$648$	−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	0.0762890	−	0.997086i	$-0.475693\pi$
$653$	−10.1857	−	2.99080i	−0.398598	−	0.117039i	−0.474887	+	0.880047i	$0.657511\pi$
$654$	−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	0.516619	+	0.856215i	$0.327190\pi$
$659$	6.72966	+	46.8058i	0.262150	+	1.82330i	−0.254469	+	0.967081i	$0.581901\pi$
$660$	−27.0175	−	31.1799i	−1.05166	−	1.21368i
$661$	−2.52405	−	5.52691i	−0.0981743	−	0.214972i	0.854172	−	0.519991i	$-0.174065\pi$
$661$	−2.52405	−	5.52691i	−0.0981743	−	0.214972i	−0.952346	+	0.305019i	$0.901337\pi$
$662$	−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	−0.923495	−	0.383611i	$-0.874680\pi$
$673$	−15.7897	−	34.5746i	−0.608648	−	1.33275i	0.314846	−	0.949143i	$-0.398047\pi$
$674$	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	−0.987328	−	0.158690i	$-0.949273\pi$
$677$	−17.9465	+	20.7114i	−0.689742	+	0.796005i	0.297586	+	0.954695i	$0.403818\pi$
$678$	−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	−0.978363	−	0.206897i	$-0.933664\pi$
$683$	−27.2820	−	31.4851i	−1.04392	−	1.20475i	−0.0655553	−	0.997849i	$-0.520882\pi$
$684$	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	0.818014	−	0.575198i	$-0.195075\pi$
$701$	16.8022	+	10.7981i	0.634611	+	0.407840i	−0.183403	+	0.983038i	$0.558711\pi$
$702$	−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	−0.497512	−	0.867457i	$-0.665753\pi$
$709$	12.8840	−	28.2121i	0.483870	−	1.05953i	0.981381	−	0.192070i	$-0.0615199\pi$
$710$	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	0.972223	+	0.234055i	$0.0751997\pi$
$719$	13.7406	+	30.0878i	0.512440	+	1.12209i	−0.459784	+	0.888031i	$0.652073\pi$
$720$	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	−0.0819008	−	0.996640i	$-0.526099\pi$
$727$	−18.5943	−	5.45978i	−0.689625	−	0.202492i	−0.607724	+	0.794148i	$0.707917\pi$
$728$	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	−0.836864	−	0.547411i	$-0.815613\pi$
$733$	3.25767	−	22.6576i	0.120325	−	0.836876i	0.957189	−	0.289465i	$-0.0934774\pi$
$734$	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	−0.333056	−	0.942907i	$-0.608080\pi$
$739$	6.85476	−	47.6759i	0.252156	−	1.75379i	0.585213	−	0.810880i	$-0.301011\pi$
$740$	−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	0.785407	−	0.618980i	$-0.212454\pi$
$743$	1.66142	+	1.91738i	0.0609515	+	0.0703418i	−0.724455	+	0.689322i	$0.757908\pi$
$744$	−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	0.922662	+	0.385609i	$0.126008\pi$
$751$	4.00139	+	27.8303i	0.146013	+	1.01554i	−0.776650	+	0.629933i	$0.783082\pi$
$752$	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	0.227158	−	0.973858i	$-0.427057\pi$
$757$	33.2193	−	21.3487i	1.20737	−	0.775933i	0.980217	+	0.197925i	$0.0634204\pi$
$758$	−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	−0.489715	−	0.871883i	$-0.662899\pi$
$761$	2.75703	−	1.77183i	0.0999422	−	0.0642289i	0.589657	+	0.807654i	$0.299263\pi$
$762$	−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	−0.964269	−	0.264925i	$-0.914653\pi$
$769$	−15.6627	+	18.0757i	−0.564810	+	0.651826i	0.399459	+	0.916751i	$0.369198\pi$
$770$	−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	0.0550659	−	0.998483i	$-0.482463\pi$
$773$	−12.1896	−	3.57920i	−0.438430	−	0.128735i	−0.493496	+	0.869748i	$0.664281\pi$
$774$	−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	−0.481603	−	0.876390i	$-0.659945\pi$
$787$	−11.5845	+	3.40150i	−0.412941	+	0.121250i	0.0686618	+	0.997640i	$0.478127\pi$
$788$	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	−0.962490	−	0.271317i	$-0.912541\pi$
$797$	−3.25862	−	22.6642i	−0.115426	−	0.802808i	0.847064	−	0.531491i	$-0.178368\pi$
$798$	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	−0.965672	−	0.259763i	$-0.916356\pi$
$809$	−3.89599	+	8.53102i	−0.136976	+	0.299935i	0.828697	+	0.559698i	$0.189083\pi$
$810$	−40.5746	+	11.9138i	−1.42565	+	0.418607i
$811$	17.3548	+	38.0017i	0.609409	+	1.33442i	0.922978	+	0.384853i	$0.125748\pi$
$811$	17.3548	+	38.0017i	0.609409	+	1.33442i	−0.313569	+	0.949565i	$0.601525\pi$
$812$	−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	0.994675	−	0.103062i	$-0.0328640\pi$
$821$	21.5215	+	24.8371i	0.751105	+	0.866821i	−0.243570	+	0.969883i	$0.578319\pi$
$822$	0.347879	+	0.761748i	0.0121337	+	0.0265690i
$823$	−5.55712	+	1.63172i	−0.193709	+	0.0568781i	−0.377148	−	0.926153i	$-0.623095\pi$
$823$	−5.55712	+	1.63172i	−0.193709	+	0.0568781i	0.183439	+	0.983031i	$0.441277\pi$
$824$	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	0.137998	−	0.990433i	$-0.455933\pi$
$839$	−20.4382	−	13.1348i	−0.705605	−	0.453465i	−0.843603	+	0.536968i	$0.819570\pi$
$840$	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	−0.467422	−	0.884034i	$-0.654817\pi$
$853$	4.16334	−	2.67562i	0.142550	−	0.0916114i	0.609972	+	0.792423i	$0.291181\pi$
$854$	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	0.889661	−	0.456621i	$-0.150941\pi$
$857$	−1.11344	−	2.43810i	−0.0380345	−	0.0832840i	−0.927696	+	0.373337i	$0.878213\pi$
$858$	5.22251	+	6.02710i	0.178294	+	0.205762i
$859$	−1.29565	−	9.01142i	−0.0442069	−	0.307466i	−0.999914	−	0.0131449i	$-0.995816\pi$
$859$	−1.29565	−	9.01142i	−0.0442069	−	0.307466i	0.955707	−	0.294321i	$-0.0950934\pi$
$860$	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	0.783526	−	0.621359i	$-0.213419\pi$
$863$	15.9753	+	10.2667i	0.543806	+	0.349483i	−0.239720	+	0.970842i	$0.577056\pi$
$864$	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	0.805788	+	0.592204i	$0.201742\pi$
$877$	−3.97432	+	27.6420i	−0.134203	+	0.933404i	−0.939991	+	0.341199i	$0.889167\pi$
$878$	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	0.354827	−	0.934932i	$-0.384540\pi$
$881$	−18.4348	−	21.2749i	−0.621086	−	0.716771i	−0.975913	+	0.218161i	$0.929994\pi$
$882$	−0.254970	−	1.77335i	−0.00858528	−	0.0597119i
$883$	0.487701	+	0.143202i	0.0164125	+	0.00481913i	0.289928	−	0.957048i	$-0.406368\pi$
$883$	0.487701	+	0.143202i	0.0164125	+	0.00481913i	−0.273516	+	0.961867i	$0.588187\pi$
$884$	−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	−0.849331	−	0.527860i	$-0.822994\pi$
$887$	−6.13435	+	7.07942i	−0.205971	+	0.237704i	0.643360	+	0.765564i	$0.277540\pi$
$888$	−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	−0.979269	−	0.202564i	$-0.935073\pi$
$907$	−19.2565	+	22.2232i	−0.639402	+	0.737909i	0.339867	+	0.940474i	$0.389618\pi$
$908$	−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	0.592748	−	0.805388i	$-0.298043\pi$
$911$	19.7991	+	5.81355i	0.655974	+	0.192611i	0.0632259	+	0.997999i	$0.479861\pi$
$912$	−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	0.338148	−	0.941093i	$-0.390200\pi$
$929$	3.46927	+	1.01867i	0.113823	+	0.0334214i	−0.224325	+	0.974514i	$0.572018\pi$
$930$	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	0.720841	−	0.693100i	$-0.243756\pi$
$937$	−8.41848	−	18.4339i	−0.275020	−	0.602209i	−0.995861	+	0.0908911i	$0.971028\pi$
$938$	−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	−0.185912	−	0.982566i	$-0.559524\pi$
$941$	19.3450	−	12.4323i	0.630630	−	0.405282i	0.816543	+	0.577285i	$0.195888\pi$
$942$	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	−0.869496	−	0.493939i	$-0.835557\pi$
$947$	2.25252	−	4.93233i	0.0731970	−	0.160279i	0.942693	+	0.333660i	$0.108284\pi$
$948$	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	−0.940652	−	0.339372i	$-0.889785\pi$
$953$	−14.5359	+	16.7754i	−0.470865	+	0.543408i	0.469787	+	0.882780i	$0.344331\pi$
$954$	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	−0.855677	−	0.517510i	$-0.826859\pi$
$971$	−40.3761	+	11.8555i	−1.29573	+	0.380461i	−0.440055	+	0.897971i	$0.645041\pi$
$972$	−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	0.365518	−	0.930804i	$-0.380892\pi$
$977$	−10.2939	−	6.61548i	−0.329331	−	0.211648i	−0.694848	+	0.719157i	$0.744528\pi$
$978$	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	0.804074	+	0.594530i	$0.202662\pi$
$983$	22.7883	+	49.8994i	0.726833	+	1.59154i	−0.0772406	+	0.997012i	$0.524611\pi$
$984$	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	−0.624272	−	0.781207i	$-0.714604\pi$
$991$	−5.44588	+	3.49985i	−0.172994	+	0.111177i	0.451278	+	0.892383i	$0.350968\pi$
$992$	−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	−0.999974	−	0.00725037i	$-0.997692\pi$
$997$	−1.34349	−	9.34415i	−0.0425486	−	0.295932i	0.957425	−	0.288682i	$-0.0932170\pi$
$998$	−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.127.2	yes	40
23.2	even	11	inner	322.2.i.d.71.2	✓	40
23.5	odd	22		7406.2.a.bv.1.14		20
23.18	even	11		7406.2.a.bu.1.14		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.71.2	✓	40	23.2	even	11	inner
322.2.i.d.127.2	yes	40	1.1	even	1	trivial
7406.2.a.bu.1.14		20	23.18	even	11
7406.2.a.bv.1.14		20	23.5	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

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