LMFDB - Embedded newform 322.2.i.d.29.1

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			29.1
Character	$\chi$	$=$	322.29
Dual form			322.2.i.d.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-2.49681 - 0.733130i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.90645 + 1.22520i) q^{5} +(-1.70409 + 1.96663i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(3.17283 + 2.03906i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-2.49681 - 0.733130i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.90645 + 1.22520i) q^{5} +(-1.70409 + 1.96663i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(3.17283 + 2.03906i) q^{9} +(0.322515 + 2.24314i) q^{10} +(2.57290 + 5.63387i) q^{11} +(1.08100 + 2.36706i) q^{12} +(-0.405547 - 2.82064i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(5.65829 - 1.66142i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-3.20248 + 3.69586i) q^{17} +(3.17283 - 2.03906i) q^{18} +(3.80365 + 4.38965i) q^{19} +(2.17441 + 0.638464i) q^{20} +(-1.08100 + 2.36706i) q^{21} +6.19357 q^{22} +(3.07454 - 3.68066i) q^{23} +2.60222 q^{24} +(0.0563685 - 0.123430i) q^{25} +(-2.73422 - 0.802838i) q^{26} +(-1.31480 - 1.51736i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-4.57668 + 5.28177i) q^{29} +(0.839255 - 5.83715i) q^{30} +(-6.66582 + 1.95726i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-2.29369 - 15.9530i) q^{33} +(2.03151 + 4.44840i) q^{34} +(0.941416 + 2.06141i) q^{35} +(-0.536748 - 3.73317i) q^{36} +(-7.09832 - 4.56181i) q^{37} +(5.57306 - 1.63640i) q^{38} +(-1.05532 + 7.33993i) q^{39} +(1.48405 - 1.71268i) q^{40} +(-1.48345 + 0.953356i) q^{41} +(1.70409 + 1.96663i) q^{42} +(7.43289 + 2.18249i) q^{43} +(2.57290 - 5.63387i) q^{44} -8.54712 q^{45} +(-2.07083 - 4.32570i) q^{46} +0.254073 q^{47} +(1.08100 - 2.36706i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-0.0888594 - 0.102549i) q^{50} +(10.7055 - 6.88004i) q^{51} +(-1.86612 + 2.15362i) q^{52} +(-1.47999 + 10.2935i) q^{53} +(-1.92643 + 0.565650i) q^{54} +(-11.8078 - 7.58838i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-6.27882 - 13.7487i) q^{57} +(2.90325 + 6.35723i) q^{58} +(-0.441520 - 3.07084i) q^{59} +(-4.96102 - 3.18825i) q^{60} +(-6.24521 + 1.83376i) q^{61} +(-0.988695 + 6.87652i) q^{62} +(2.46984 - 2.85035i) q^{63} +(0.841254 - 0.540641i) q^{64} +(4.22902 + 4.88054i) q^{65} +(-15.4642 - 4.54069i) q^{66} +(-4.96443 + 10.8706i) q^{67} +4.89033 q^{68} +(-10.3749 + 6.93587i) q^{69} +2.26621 q^{70} +(0.394376 - 0.863562i) q^{71} +(-3.61878 - 1.06257i) q^{72} +(-2.31619 - 2.67303i) q^{73} +(-7.09832 + 4.56181i) q^{74} +(-0.231232 + 0.266856i) q^{75} +(0.826613 - 5.74922i) q^{76} +(5.94268 - 1.74493i) q^{77} +(6.23824 + 4.00907i) q^{78} +(-1.28937 - 8.96779i) q^{79} +(-0.941416 - 2.06141i) q^{80} +(-2.52990 - 5.53970i) q^{81} +(0.250955 + 1.74543i) q^{82} +(5.47724 + 3.52001i) q^{83} +(2.49681 - 0.733130i) q^{84} +(1.57720 - 10.9697i) q^{85} +(5.07300 - 5.85456i) q^{86} +(15.2994 - 9.83230i) q^{87} +(-4.05592 - 4.68079i) q^{88} +(12.6959 + 3.72785i) q^{89} +(-3.55060 + 7.77473i) q^{90} -2.84965 q^{91} +(-4.79505 + 0.0867377i) q^{92} +18.0782 q^{93} +(0.105546 - 0.231113i) q^{94} +(-12.6297 - 3.70842i) q^{95} +(-1.70409 - 1.96663i) q^{96} +(-2.77410 + 1.78281i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(-3.32439 + 23.1216i) 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 $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	−2.49681	−	0.733130i	−1.44154	−	0.423273i	−0.534802	−	0.844977i	$-0.679614\pi$
$3$	−2.49681	−	0.733130i	−1.44154	−	0.423273i	−0.906733	+	0.421704i	$0.861432\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−1.90645	+	1.22520i	−0.852592	+	0.547928i	−0.892382	−	0.451280i	$-0.850967\pi$
$5$	−1.90645	+	1.22520i	−0.852592	+	0.547928i	0.0397900	+	0.999208i	$0.487331\pi$
$6$	−1.70409	+	1.96663i	−0.695693	+	0.802872i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$7$	0.142315	−	0.989821i	0.0537900	−	0.374117i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	3.17283	+	2.03906i	1.05761	+	0.679685i
$10$	0.322515	+	2.24314i	0.101988	+	0.709343i
$11$	2.57290	+	5.63387i	0.775759	+	1.69867i	0.713542	+	0.700612i	$0.247090\pi$
$11$	2.57290	+	5.63387i	0.775759	+	1.69867i	0.0622164	+	0.998063i	$0.480183\pi$
$12$	1.08100	+	2.36706i	0.312058	+	0.683312i
$13$	−0.405547	−	2.82064i	−0.112478	−	0.782305i	−0.965495	−	0.260421i	$-0.916139\pi$
$13$	−0.405547	−	2.82064i	−0.112478	−	0.782305i	0.853017	−	0.521884i	$-0.174771\pi$
$14$	−0.841254	−	0.540641i	−0.224834	−	0.144492i
$15$	5.65829	−	1.66142i	1.46097	−	0.428978i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−3.20248	+	3.69586i	−0.776716	+	0.896378i	−0.996868	−	0.0790875i	$-0.974799\pi$
$17$	−3.20248	+	3.69586i	−0.776716	+	0.896378i	0.220152	+	0.975466i	$0.429345\pi$
$18$	3.17283	−	2.03906i	0.747844	−	0.480610i
$19$	3.80365	+	4.38965i	0.872618	+	1.00705i	0.999885	+	0.0151861i	$0.00483407\pi$
$19$	3.80365	+	4.38965i	0.872618	+	1.00705i	−0.127267	+	0.991869i	$0.540620\pi$
$20$	2.17441	+	0.638464i	0.486213	+	0.142765i
$21$	−1.08100	+	2.36706i	−0.235894	+	0.516536i
$22$	6.19357			1.32047
$23$	3.07454	−	3.68066i	0.641085	−	0.767470i
$23$	3.07454	−	3.68066i	0.641085	−	0.767470i
$24$	2.60222			0.531176
$25$	0.0563685	−	0.123430i	0.0112737	−	0.0246860i
$26$	−2.73422	−	0.802838i	−0.536224	−	0.157449i
$27$	−1.31480	−	1.51736i	−0.253033	−	0.292016i
$28$	−0.841254	+	0.540641i	−0.158982	+	0.102172i
$29$	−4.57668	+	5.28177i	−0.849869	+	0.980801i	−0.999969	−	0.00786993i	$-0.997495\pi$
$29$	−4.57668	+	5.28177i	−0.849869	+	0.980801i	0.150100	+	0.988671i	$0.452040\pi$
$30$	0.839255	−	5.83715i	0.153226	−	1.06571i
$31$	−6.66582	+	1.95726i	−1.19722	+	0.351535i	−0.818788	−	0.574096i	$-0.805354\pi$
$31$	−6.66582	+	1.95726i	−1.19722	+	0.351535i	−0.378429	+	0.925630i	$0.623536\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	−2.29369	−	15.9530i	−0.399281	−	2.77706i
$34$	2.03151	+	4.44840i	0.348402	+	0.762894i
$35$	0.941416	+	2.06141i	0.159128	+	0.348443i
$36$	−0.536748	−	3.73317i	−0.0894580	−	0.622194i
$37$	−7.09832	−	4.56181i	−1.16696	−	0.749958i	−0.194013	−	0.980999i	$-0.562150\pi$
$37$	−7.09832	−	4.56181i	−1.16696	−	0.749958i	−0.972944	+	0.231041i	$0.925787\pi$
$38$	5.57306	−	1.63640i	0.904070	−	0.265459i
$39$	−1.05532	+	7.33993i	−0.168987	+	1.17533i
$40$	1.48405	−	1.71268i	0.234649	−	0.270799i
$41$	−1.48345	+	0.953356i	−0.231676	+	0.148889i	−0.651329	−	0.758796i	$-0.725788\pi$
$41$	−1.48345	+	0.953356i	−0.231676	+	0.148889i	0.419653	+	0.907685i	$0.362152\pi$
$42$	1.70409	+	1.96663i	0.262947	+	0.303457i
$43$	7.43289	+	2.18249i	1.13351	+	0.332827i	0.794085	−	0.607807i	$-0.207951\pi$
$43$	7.43289	+	2.18249i	1.13351	+	0.332827i	0.339421	+	0.940635i	$0.389769\pi$
$44$	2.57290	−	5.63387i	0.387879	−	0.849337i
$45$	−8.54712			−1.27413
$46$	−2.07083	−	4.32570i	−0.305328	−	0.637789i
$47$	0.254073			0.0370604			0.0185302	−	0.999828i	$-0.494101\pi$
$47$	0.254073			0.0370604			0.0185302	+	0.999828i	$0.494101\pi$
$48$	1.08100	−	2.36706i	0.156029	−	0.341656i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	−0.0888594	−	0.102549i	−0.0125666	−	0.0145026i
$51$	10.7055	−	6.88004i	1.49908	−	0.963398i
$52$	−1.86612	+	2.15362i	−0.258784	+	0.298653i
$53$	−1.47999	+	10.2935i	−0.203292	+	1.41392i	0.591139	+	0.806570i	$0.298678\pi$
$53$	−1.47999	+	10.2935i	−0.203292	+	1.41392i	−0.794431	+	0.607355i	$0.792231\pi$
$54$	−1.92643	+	0.565650i	−0.262153	+	0.0769752i
$55$	−11.8078	−	7.58838i	−1.59216	−	1.02322i
$56$	0.142315	+	0.989821i	0.0190176	+	0.132270i
$57$	−6.27882	−	13.7487i	−0.831650	−	1.82106i
$58$	2.90325	+	6.35723i	0.381215	+	0.834745i
$59$	−0.441520	−	3.07084i	−0.0574810	−	0.399789i	−0.998167	−	0.0605121i	$-0.980727\pi$
$59$	−0.441520	−	3.07084i	−0.0574810	−	0.399789i	0.940686	−	0.339277i	$-0.110182\pi$
$60$	−4.96102	−	3.18825i	−0.640464	−	0.411601i
$61$	−6.24521	+	1.83376i	−0.799618	+	0.234789i	−0.655918	−	0.754832i	$-0.727718\pi$
$61$	−6.24521	+	1.83376i	−0.799618	+	0.234789i	−0.143700	+	0.989621i	$0.545900\pi$
$62$	−0.988695	+	6.87652i	−0.125564	+	0.873319i
$63$	2.46984	−	2.85035i	0.311171	−	0.359110i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	4.22902	+	4.88054i	0.524545	+	0.605357i
$66$	−15.4642	−	4.54069i	−1.90351	−	0.558921i
$67$	−4.96443	+	10.8706i	−0.606502	+	1.32805i	0.318439	+	0.947943i	$0.396841\pi$
$67$	−4.96443	+	10.8706i	−0.606502	+	1.32805i	−0.924941	+	0.380110i	$0.875886\pi$
$68$	4.89033			0.593039
$69$	−10.3749	+	6.93587i	−1.24900	+	0.834981i
$70$	2.26621			0.270863
$71$	0.394376	−	0.863562i	0.0468038	−	0.102486i	−0.884786	−	0.465998i	$-0.845695\pi$
$71$	0.394376	−	0.863562i	0.0468038	−	0.102486i	0.931589	+	0.363512i	$0.118423\pi$
$72$	−3.61878	−	1.06257i	−0.426477	−	0.125225i
$73$	−2.31619	−	2.67303i	−0.271090	−	0.312855i	0.603838	−	0.797107i	$-0.293637\pi$
$73$	−2.31619	−	2.67303i	−0.271090	−	0.312855i	−0.874929	+	0.484252i	$0.839092\pi$
$74$	−7.09832	+	4.56181i	−0.825163	+	0.530300i
$75$	−0.231232	+	0.266856i	−0.0267003	+	0.0308138i
$76$	0.826613	−	5.74922i	0.0948190	−	0.659481i
$77$	5.94268	−	1.74493i	0.677232	−	0.198853i
$78$	6.23824	+	4.00907i	0.706341	+	0.453938i
$79$	−1.28937	−	8.96779i	−0.145066	−	1.00896i	−0.924148	−	0.382034i	$-0.875224\pi$
$79$	−1.28937	−	8.96779i	−0.145066	−	1.00896i	0.779083	−	0.626921i	$-0.215685\pi$
$80$	−0.941416	−	2.06141i	−0.105254	−	0.230473i
$81$	−2.52990	−	5.53970i	−0.281099	−	0.615522i
$82$	0.250955	+	1.74543i	0.0277134	+	0.192751i
$83$	5.47724	+	3.52001i	0.601206	+	0.386371i	0.805550	−	0.592528i	$-0.201870\pi$
$83$	5.47724	+	3.52001i	0.601206	+	0.386371i	−0.204345	+	0.978899i	$0.565506\pi$
$84$	2.49681	−	0.733130i	0.272425	−	0.0799911i
$85$	1.57720	−	10.9697i	0.171072	−	1.18983i
$86$	5.07300	−	5.85456i	0.547036	−	0.631313i
$87$	15.2994	−	9.83230i	1.64026	−	1.05413i
$88$	−4.05592	−	4.68079i	−0.432363	−	0.498973i
$89$	12.6959	+	3.72785i	1.34576	+	0.395151i	0.873721	−	0.486427i	$-0.161700\pi$
$89$	12.6959	+	3.72785i	1.34576	+	0.395151i	0.472039	+	0.881578i	$0.343518\pi$
$90$	−3.55060	+	7.77473i	−0.374266	+	0.819529i
$91$	−2.84965			−0.298724
$92$	−4.79505	+	0.0867377i	−0.499918	+	0.00904303i
$93$	18.0782			1.87463
$94$	0.105546	−	0.231113i	0.0108862	−	0.0238375i
$95$	−12.6297	−	3.70842i	−1.29578	−	0.380475i
$96$	−1.70409	−	1.96663i	−0.173923	−	0.200718i
$97$	−2.77410	+	1.78281i	−0.281667	+	0.181017i	−0.673845	−	0.738873i	$-0.735358\pi$
$97$	−2.77410	+	1.78281i	−0.281667	+	0.181017i	0.392177	+	0.919890i	$0.371722\pi$
$98$	−0.654861	+	0.755750i	−0.0661509	+	0.0763422i
$99$	−3.32439	+	23.1216i	−0.334113	+	2.32381i
$100$	−0.130196	+	0.0382289i	−0.0130196	+	0.00382289i
$101$	4.82449	+	3.10051i	0.480055	+	0.308513i	0.758195	−	0.652028i	$-0.226082\pi$
$101$	4.82449	+	3.10051i	0.480055	+	0.308513i	−0.278140	+	0.960541i	$0.589718\pi$
$102$	−1.81106	−	12.5962i	−0.179321	−	1.24721i
$103$	4.55274	+	9.96910i	0.448595	+	0.982285i	0.989940	+	0.141485i	$0.0451877\pi$
$103$	4.55274	+	9.96910i	0.448595	+	0.982285i	−0.541346	+	0.840800i	$0.682085\pi$
$104$	1.18379	+	2.59213i	0.116080	+	0.254179i
$105$	−0.839255	−	5.83715i	−0.0819029	−	0.569647i
$106$	8.74851	+	5.62233i	0.849731	+	0.546089i
$107$	−9.49113	+	2.78685i	−0.917542	+	0.269415i	−0.706212	−	0.708000i	$-0.749598\pi$
$107$	−9.49113	+	2.78685i	−0.917542	+	0.269415i	−0.211330	+	0.977415i	$0.567779\pi$
$108$	−0.285733	+	1.98732i	−0.0274947	+	0.191230i
$109$	7.14608	−	8.24702i	0.684471	−	0.789921i	−0.302097	−	0.953277i	$-0.597687\pi$
$109$	7.14608	−	8.24702i	0.684471	−	0.789921i	0.986567	+	0.163356i	$0.0522320\pi$
$110$	−11.8078	+	7.58838i	−1.12583	+	0.723524i
$111$	14.3788	+	16.5940i	1.36477	+	1.57503i
$112$	0.959493	+	0.281733i	0.0906636	+	0.0266212i
$113$	6.40315	−	14.0209i	0.602358	−	1.31898i	−0.325322	−	0.945603i	$-0.605473\pi$
$113$	6.40315	−	14.0209i	0.602358	−	1.31898i	0.927680	−	0.373376i	$-0.121800\pi$
$114$	−15.1146			−1.41561
$115$	−1.35191	+	10.7839i	−0.126066	+	1.00561i
$116$	6.98879			0.648893
$117$	4.46471	−	9.77635i	0.412763	−	0.903824i
$118$	−2.97675	−	0.874052i	−0.274032	−	0.0804630i
$119$	3.20248	+	3.69586i	0.293571	+	0.338799i
$120$	−4.96102	+	3.18825i	−0.452877	+	0.291046i
$121$	−17.9172	+	20.6775i	−1.62883	+	1.87977i
$122$	−0.926309	+	6.44262i	−0.0838640	+	0.583287i
$123$	4.40283	−	1.29279i	0.396990	−	0.116567i
$124$	5.84439	+	3.75596i	0.524841	+	0.337295i
$125$	−1.56881	−	10.9113i	−0.140319	−	0.975938i
$126$	−1.56676	−	3.43073i	−0.139578	−	0.305633i
$127$	−6.38064	−	13.9717i	−0.566191	−	1.23978i	−0.948801	−	0.315875i	$-0.897702\pi$
$127$	−6.38064	−	13.9717i	−0.566191	−	1.23978i	0.382610	−	0.923910i	$-0.375025\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	−16.9585	−	10.8986i	−1.49311	−	0.959565i
$130$	6.19630	−	1.81940i	0.543451	−	0.159572i
$131$	−0.724048	+	5.03587i	−0.0632604	+	0.439986i	0.933434	+	0.358748i	$0.116796\pi$
$131$	−0.724048	+	5.03587i	−0.0632604	+	0.439986i	−0.996695	+	0.0812375i	$0.974113\pi$
$132$	−10.5544	+	12.1804i	−0.918643	+	1.06017i
$133$	4.88629	−	3.14022i	0.423695	−	0.272292i
$134$	7.82594	+	9.03161i	0.676058	+	0.780212i
$135$	4.36568	+	1.28188i	0.375738	+	0.110327i
$136$	2.03151	−	4.44840i	0.174201	−	0.381447i
$137$	0.996620			0.0851470			0.0425735	−	0.999093i	$-0.486444\pi$
$137$	0.996620			0.0851470			0.0425735	+	0.999093i	$0.486444\pi$
$138$	1.99919	+	12.3186i	0.170182	+	1.04863i
$139$	11.1151			0.942772			0.471386	−	0.881927i	$-0.343754\pi$
$139$	11.1151			0.942772			0.471386	+	0.881927i	$0.343754\pi$
$140$	0.941416	−	2.06141i	0.0795642	−	0.174221i
$141$	−0.634373	−	0.186269i	−0.0534238	−	0.0156867i
$142$	−0.621694	−	0.717473i	−0.0521714	−	0.0602090i
$143$	14.8477	−	9.54203i	1.24163	−	0.797944i
$144$	−2.46984	+	2.85035i	−0.205820	+	0.237529i
$145$	2.25399	−	15.6768i	0.187184	−	1.30189i
$146$	−3.39366	+	0.996467i	−0.280861	+	0.0824682i
$147$	2.18913	+	1.40687i	0.180556	+	0.116036i
$148$	1.20082	+	8.35191i	0.0987070	+	0.686522i
$149$	1.36791	+	2.99530i	0.112063	+	0.245384i	0.957351	−	0.288927i	$-0.0932984\pi$
$149$	1.36791	+	2.99530i	0.112063	+	0.245384i	−0.845288	+	0.534311i	$0.820571\pi$
$150$	0.146683	+	0.321192i	0.0119766	+	0.0262252i
$151$	0.0603959	+	0.420063i	0.00491495	+	0.0341842i	0.992131	−	0.125202i	$-0.0399577\pi$
$151$	0.0603959	+	0.420063i	0.00491495	+	0.0341842i	−0.987216	+	0.159386i	$0.949049\pi$
$152$	−4.88629	−	3.14022i	−0.396330	−	0.254706i
$153$	−17.6970	+	5.19631i	−1.43072	+	0.420097i
$154$	0.881436	−	6.13053i	0.0710282	−	0.494012i
$155$	10.3100	−	11.8984i	0.828122	−	0.955704i
$156$	6.23824	−	4.00907i	0.499459	−	0.320983i
$157$	6.73275	+	7.77000i	0.537332	+	0.620114i	0.957884	−	0.287154i	$-0.0927093\pi$
$157$	6.73275	+	7.77000i	0.537332	+	0.620114i	−0.420553	+	0.907268i	$0.638164\pi$
$158$	−8.69301	−	2.55250i	−0.691579	−	0.203066i
$159$	11.2417	−	24.6160i	0.891528	−	1.95217i
$160$	−2.26621			−0.179159
$161$	−3.20564	−	3.56705i	−0.252640	−	0.281123i
$162$	−6.09004			−0.478479
$163$	−0.630306	+	1.38018i	−0.0493694	+	0.108104i	−0.932709	−	0.360629i	$-0.882562\pi$
$163$	−0.630306	+	1.38018i	−0.0493694	+	0.108104i	0.883340	+	0.468733i	$0.155289\pi$
$164$	1.69195	+	0.496802i	0.132119	+	0.0387937i
$165$	23.9185	+	27.6034i	1.86205	+	2.14892i
$166$	5.47724	−	3.52001i	0.425116	−	0.273206i
$167$	−3.47877	+	4.01472i	−0.269195	+	0.310668i	−0.874212	−	0.485545i	$-0.838621\pi$
$167$	−3.47877	+	4.01472i	−0.269195	+	0.310668i	0.605016	+	0.796213i	$0.293167\pi$
$168$	0.370335	−	2.57573i	0.0285719	−	0.198722i
$169$	4.68186	−	1.37472i	0.360143	−	0.105748i
$170$	−9.32318	−	5.99165i	−0.715055	−	0.459538i
$171$	3.11761	+	21.6835i	0.238410	+	1.65818i
$172$	−3.21809	−	7.04664i	−0.245377	−	0.537301i
$173$	2.42358	+	5.30690i	0.184261	+	0.403476i	0.979110	−	0.203332i	$-0.0651770\pi$
$173$	2.42358	+	5.30690i	0.184261	+	0.403476i	−0.794848	+	0.606808i	$0.792450\pi$
$174$	−2.58819	−	18.0013i	−0.196210	−	1.36467i
$175$	−0.114151	−	0.0733606i	−0.00862903	−	0.00554554i
$176$	−5.94268	+	1.74493i	−0.447947	+	0.131529i
$177$	−1.14893	+	7.99100i	−0.0863591	+	0.600641i
$178$	8.66502	−	9.99997i	0.649471	−	0.749530i
$179$	−11.3981	+	7.32512i	−0.851935	+	0.547506i	−0.892178	−	0.451684i	$-0.850823\pi$
$179$	−11.3981	+	7.32512i	−0.851935	+	0.547506i	0.0402425	+	0.999190i	$0.487187\pi$
$180$	5.59717	+	6.45948i	0.417189	+	0.481461i
$181$	−13.9839	−	4.10603i	−1.03941	−	0.305199i	−0.282880	−	0.959155i	$-0.591290\pi$
$181$	−13.9839	−	4.10603i	−1.03941	−	0.305199i	−0.756532	+	0.653956i	$0.773108\pi$
$182$	−1.18379	+	2.59213i	−0.0877480	+	0.192141i
$183$	16.9375			1.25206
$184$	−1.91304	+	4.39776i	−0.141031	+	0.324207i
$185$	19.1218			1.40586
$186$	7.50997	−	16.4445i	0.550658	−	1.20577i
$187$	−29.0617	−	8.53327i	−2.12520	−	0.624015i
$188$	−0.166382	−	0.192016i	−0.0121347	−	0.0140042i
$189$	−1.68903	+	1.08547i	−0.122859	+	0.0789566i
$190$	−8.61986	+	9.94785i	−0.625351	+	0.721693i
$191$	−1.98108	+	13.7787i	−0.143346	+	0.996993i	0.783457	+	0.621446i	$0.213454\pi$
$191$	−1.98108	+	13.7787i	−0.143346	+	0.996993i	−0.926803	+	0.375547i	$0.877455\pi$
$192$	−2.49681	+	0.733130i	−0.180192	+	0.0529091i
$193$	−17.3744	−	11.1659i	−1.25064	−	0.803737i	−0.263665	−	0.964614i	$-0.584931\pi$
$193$	−17.3744	−	11.1659i	−1.25064	−	0.803737i	−0.986974	+	0.160877i	$0.948568\pi$
$194$	0.469294	+	3.26401i	0.0336934	+	0.234343i
$195$	−6.98099	−	15.2862i	−0.499919	−	1.09467i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	2.39541	+	16.6605i	0.170666	+	1.18701i	0.877481	+	0.479611i	$0.159222\pi$
$197$	2.39541	+	16.6605i	0.170666	+	1.18701i	−0.706815	+	0.707398i	$0.749869\pi$
$198$	19.6512	+	12.6290i	1.39655	+	0.897506i
$199$	2.58113	−	0.757889i	0.182972	−	0.0537253i	−0.188963	−	0.981984i	$-0.560513\pi$
$199$	2.58113	−	0.757889i	0.182972	−	0.0537253i	0.371935	+	0.928259i	$0.378694\pi$
$200$	−0.0193110	+	0.134311i	−0.00136549	+	0.00949721i
$201$	20.3648	−	23.5022i	1.43642	−	1.65772i
$202$	4.82449	−	3.10051i	0.339450	−	0.218151i
$203$	4.57668	+	5.28177i	0.321220	+	0.370708i
$204$	−12.2102	−	3.58525i	−0.854887	−	0.251017i
$205$	1.66008	−	3.63506i	0.115945	−	0.253884i
$206$	10.9595			0.763584
$207$	17.2601	−	5.40896i	1.19966	−	0.375948i
$208$	2.84965			0.197587
$209$	−14.9443	+	32.7234i	−1.03372	+	2.26353i
$210$	−5.65829	−	1.66142i	−0.390459	−	0.114649i
$211$	3.44581	+	3.97667i	0.237219	+	0.273766i	0.861860	−	0.507147i	$-0.169300\pi$
$211$	3.44581	+	3.97667i	0.237219	+	0.273766i	−0.624640	+	0.780913i	$0.714754\pi$
$212$	8.74851	−	5.62233i	0.600850	−	0.386143i
$213$	−1.61779	+	1.86702i	−0.110849	+	0.127926i
$214$	−1.40775	+	9.79113i	−0.0962319	+	0.669308i
$215$	−16.8445	+	4.94598i	−1.14878	+	0.337313i
$216$	1.68903	+	1.08547i	0.114924	+	0.0738571i
$217$	0.988695	+	6.87652i	0.0671170	+	0.466809i
$218$	−4.53316	−	9.92624i	−0.307025	−	0.672290i
$219$	3.82342	+	8.37213i	0.258363	+	0.565736i
$220$	1.99752	+	13.8930i	0.134673	+	0.936668i
$221$	11.7235	+	7.53421i	0.788605	+	0.506806i
$222$	21.0676	−	6.18600i	1.41396	−	0.415177i
$223$	0.422667	−	2.93971i	0.0283039	−	0.196858i	−0.970763	−	0.240038i	$-0.922840\pi$
$223$	0.422667	−	2.93971i	0.0283039	−	0.196858i	0.999067	+	0.0431806i	$0.0137491\pi$
$224$	0.654861	−	0.755750i	0.0437547	−	0.0504956i
$225$	0.430528	−	0.276684i	0.0287019	−	0.0184456i
$226$	−10.0939	−	11.6490i	−0.671439	−	0.774881i
$227$	−13.5880	−	3.98981i	−0.901870	−	0.264813i	−0.202255	−	0.979333i	$-0.564827\pi$
$227$	−13.5880	−	3.98981i	−0.901870	−	0.264813i	−0.699615	+	0.714520i	$0.746645\pi$
$228$	−6.27882	+	13.7487i	−0.415825	+	0.910530i
$229$	−9.79829			−0.647489			−0.323745	−	0.946145i	$-0.604942\pi$
$229$	−9.79829			−0.647489			−0.323745	+	0.946145i	$0.604942\pi$
$230$	9.24781	+	5.70955i	0.609782	+	0.376476i
$231$	−16.1170			−1.06042
$232$	2.90325	−	6.35723i	0.190608	−	0.417372i
$233$	13.7081	+	4.02507i	0.898049	+	0.263691i	0.698003	−	0.716095i	$-0.254072\pi$
$233$	13.7081	+	4.02507i	0.898049	+	0.263691i	0.200047	+	0.979786i	$0.435891\pi$
$234$	−7.03818	−	8.12249i	−0.460100	−	0.530984i
$235$	−0.484379	+	0.311291i	−0.0315974	+	0.0203064i
$236$	−2.03165	+	2.34465i	−0.132249	+	0.152624i
$237$	−3.35523	+	23.3362i	−0.217946	+	1.51585i
$238$	4.69223	−	1.37776i	0.304152	−	0.0893072i
$239$	−12.7950	−	8.22284i	−0.827639	−	0.531892i	0.0568876	−	0.998381i	$-0.481882\pi$
$239$	−12.7950	−	8.22284i	−0.827639	−	0.531892i	−0.884527	+	0.466489i	$0.845519\pi$
$240$	0.839255	+	5.83715i	0.0541737	+	0.376786i
$241$	2.61749	+	5.73149i	0.168607	+	0.369198i	0.975008	−	0.222172i	$-0.0713146\pi$
$241$	2.61749	+	5.73149i	0.168607	+	0.369198i	−0.806400	+	0.591370i	$0.798587\pi$
$242$	11.3659	+	24.8878i	0.730626	+	1.59985i
$243$	3.11255	+	21.6483i	0.199670	+	1.38874i
$244$	5.47561	+	3.51896i	0.350540	+	0.225278i
$245$	2.17441	−	0.638464i	0.138918	−	0.0407900i
$246$	0.653041	−	4.54200i	0.0416364	−	0.289587i
$247$	10.8391	−	12.5089i	0.689673	−	0.795925i
$248$	5.84439	−	3.75596i	0.371119	−	0.238504i
$249$	−11.0950	−	12.8043i	−0.703119	−	0.811442i
$250$	−10.5770	−	3.10569i	−0.668948	−	0.196421i
$251$	7.84756	−	17.1838i	0.495333	−	1.08463i	−0.482625	−	0.875827i	$-0.660316\pi$
$251$	7.84756	−	17.1838i	0.495333	−	1.08463i	0.977958	−	0.208802i	$-0.0669563\pi$
$252$	−3.77155			−0.237586
$253$	28.6468	+	7.85156i	1.80101	+	0.493624i
$254$	−15.3597			−0.963752
$255$	−11.9802	+	26.2330i	−0.750229	+	1.64277i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−0.653201	−	0.753835i	−0.0407456	−	0.0470229i	0.735011	−	0.678055i	$-0.237177\pi$
$257$	−0.653201	−	0.753835i	−0.0407456	−	0.0470229i	−0.775757	+	0.631032i	$0.782632\pi$
$258$	−16.9585	+	10.8986i	−1.05579	+	0.678515i
$259$	−5.52558	+	6.37686i	−0.343343	+	0.396239i
$260$	0.919053	−	6.39215i	0.0569972	−	0.396425i
$261$	−25.2909	+	7.42607i	−1.56547	+	0.459662i
$262$	4.28000	+	2.75059i	0.264420	+	0.169932i
$263$	−1.61533	−	11.2349i	−0.0996055	−	0.692772i	−0.977037	−	0.213070i	$-0.931654\pi$
$263$	−1.61533	−	11.2349i	−0.0996055	−	0.692772i	0.877432	−	0.479702i	$-0.159255\pi$
$264$	6.69526	+	14.6606i	0.412065	+	0.902295i
$265$	−9.79014	−	21.4374i	−0.601404	−	1.31689i
$266$	−0.826613	−	5.74922i	−0.0506829	−	0.352507i
$267$	−28.9662	−	18.6155i	−1.77270	−	1.13925i
$268$	11.4665	−	3.36685i	0.700425	−	0.205663i
$269$	2.58657	−	17.9900i	0.157706	−	1.09687i	−0.745142	−	0.666906i	$-0.767618\pi$
$269$	2.58657	−	17.9900i	0.157706	−	1.09687i	0.902847	−	0.429961i	$-0.141473\pi$
$270$	2.97961	−	3.43865i	0.181333	−	0.209270i
$271$	24.5894	−	15.8026i	1.49370	−	0.959942i	0.498012	−	0.867170i	$-0.334064\pi$
$271$	24.5894	−	15.8026i	1.49370	−	0.959942i	0.995687	−	0.0927723i	$-0.0295729\pi$
$272$	−3.20248	−	3.69586i	−0.194179	−	0.224095i
$273$	7.11503	+	2.08916i	0.430621	+	0.126442i
$274$	0.414011	−	0.906557i	0.0250113	−	0.0547671i
$275$	0.840418			0.0506791
$276$	12.0359	+	3.29883i	0.724478	+	0.198566i
$277$	−3.58835			−0.215603			−0.107802	−	0.994172i	$-0.534381\pi$
$277$	−3.58835			−0.215603			−0.107802	+	0.994172i	$0.534381\pi$
$278$	4.61739	−	10.1107i	0.276932	−	0.606398i
$279$	−25.1405	−	7.38192i	−1.50512	−	0.441944i
$280$	−1.48405	−	1.71268i	−0.0886889	−	0.102352i
$281$	−26.5690	+	17.0748i	−1.58497	+	1.01860i	−0.611085	+	0.791565i	$0.709267\pi$
$281$	−26.5690	+	17.0748i	−1.58497	+	1.01860i	−0.973887	+	0.227035i	$0.927097\pi$
$282$	−0.432964	+	0.499667i	−0.0257826	+	0.0297547i
$283$	4.36951	−	30.3906i	0.259740	−	1.80653i	−0.274921	−	0.961467i	$-0.588652\pi$
$283$	4.36951	−	30.3906i	0.259740	−	1.80653i	0.534661	−	0.845066i	$-0.320439\pi$
$284$	−0.910898	+	0.267464i	−0.0540518	+	0.0158711i
$285$	28.8153	+	18.5184i	1.70687	+	1.09694i
$286$	−2.51178	−	17.4698i	−0.148525	−	1.03301i
$287$	0.732535	+	1.60403i	0.0432402	+	0.0946828i
$288$	1.56676	+	3.43073i	0.0923222	+	0.202157i
$289$	−0.984148	−	6.84490i	−0.0578911	−	0.402641i
$290$	−13.3238	−	8.56269i	−0.782401	−	0.502818i
$291$	8.23344	−	2.41756i	0.482653	−	0.141720i
$292$	−0.503357	+	3.50093i	−0.0294568	+	0.204876i
$293$	−11.9534	+	13.7949i	−0.698324	+	0.805909i	−0.988525	−	0.151057i	$-0.951732\pi$
$293$	−11.9534	+	13.7949i	−0.698324	+	0.805909i	0.290201	+	0.956966i	$0.406278\pi$
$294$	2.18913	−	1.40687i	0.127673	−	0.0820501i
$295$	4.60414	+	5.31346i	0.268064	+	0.309362i
$296$	8.09600	+	2.37720i	0.470571	+	0.138172i
$297$	5.16575	−	11.3114i	0.299747	−	0.656355i
$298$	3.29287			0.190751
$299$	−11.6287	−	7.17948i	−0.672504	−	0.415200i
$300$	0.353101			0.0203863
$301$	3.21809	−	7.04664i	0.185488	−	0.406161i
$302$	0.407192	+	0.119562i	0.0234313	+	0.00688004i
$303$	−9.77277	−	11.2784i	−0.561431	−	0.647926i
$304$	−4.88629	+	3.14022i	−0.280248	+	0.180104i
$305$	9.65949	−	11.1476i	0.553101	−	0.638312i
$306$	−2.62487	+	18.2564i	−0.150054	+	1.04365i
$307$	31.9237	−	9.37363i	1.82198	−	0.534982i	0.822548	−	0.568695i	$-0.192552\pi$
$307$	31.9237	−	9.37363i	1.82198	−	0.534982i	0.999432	+	0.0337135i	$0.0107334\pi$
$308$	−5.21036	−	3.34850i	−0.296888	−	0.190798i
$309$	−4.05868	−	28.2287i	−0.230890	−	1.60588i
$310$	−6.54024	−	14.3211i	−0.371461	−	0.813385i
$311$	8.63803	+	18.9146i	0.489818	+	1.07255i	0.979646	+	0.200732i	$0.0643321\pi$
$311$	8.63803	+	18.9146i	0.489818	+	1.07255i	−0.489828	+	0.871819i	$0.662941\pi$
$312$	−1.05532	−	7.33993i	−0.0597459	−	0.415542i
$313$	−0.280926	−	0.180540i	−0.0158789	−	0.0102047i	0.532677	−	0.846318i	$-0.321186\pi$
$313$	−0.280926	−	0.180540i	−0.0158789	−	0.0102047i	−0.548556	+	0.836114i	$0.684822\pi$
$314$	9.86473	−	2.89655i	0.556699	−	0.163461i
$315$	−1.21638	+	8.46012i	−0.0685354	+	0.476674i
$316$	−5.93304	+	6.84710i	−0.333760	+	0.385179i
$317$	−12.5459	+	8.06274i	−0.704646	+	0.452849i	−0.843266	−	0.537497i	$-0.819370\pi$
$317$	−12.5459	+	8.06274i	−0.704646	+	0.452849i	0.138619	+	0.990346i	$0.455734\pi$
$318$	−17.7215	−	20.4517i	−0.993772	−	1.14687i
$319$	−41.5322	−	12.1949i	−2.32535	−	0.682786i
$320$	−0.941416	+	2.06141i	−0.0526268	+	0.115237i
$321$	25.7407			1.43671
$322$	−4.57638	+	1.43415i	−0.255032	+	0.0799218i
$323$	−28.4047			−1.58048
$324$	−2.52990	+	5.53970i	−0.140550	+	0.307761i
$325$	−0.371011	−	0.108939i	−0.0205800	−	0.00604283i
$326$	0.993615	+	1.14669i	0.0550313	+	0.0635095i
$327$	−23.8886	+	15.3523i	−1.32104	+	0.848982i
$328$	1.15477	−	1.33267i	0.0637615	−	0.0735846i
$329$	0.0361584	−	0.251487i	0.00199348	−	0.0138649i
$330$	35.0450	−	10.2901i	1.92916	−	0.566454i
$331$	1.55190	+	0.997348i	0.0853004	+	0.0548192i	0.582596	−	0.812762i	$-0.302037\pi$
$331$	1.55190	+	0.997348i	0.0853004	+	0.0548192i	−0.497295	+	0.867581i	$0.665673\pi$
$332$	−0.926585	−	6.44454i	−0.0508530	−	0.353690i
$333$	−13.2200	−	28.9478i	−0.724451	−	1.58633i
$334$	2.20678	+	4.83217i	0.120750	+	0.264405i
$335$	−3.85422	−	26.8067i	−0.210579	−	1.46461i
$336$	−2.18913	−	1.40687i	−0.119427	−	0.0767509i
$337$	−13.8651	+	4.07116i	−0.755280	+	0.221770i	−0.636634	−	0.771166i	$-0.719674\pi$
$337$	−13.8651	+	4.07116i	−0.755280	+	0.221770i	−0.118646	+	0.992937i	$0.537855\pi$
$338$	0.694428	−	4.82985i	0.0377719	−	0.262709i
$339$	−26.2666	+	30.3133i	−1.42661	+	1.64639i
$340$	−9.32318	+	5.99165i	−0.505621	+	0.324943i
$341$	−28.1775	−	32.5185i	−1.52589	−	1.76098i
$342$	21.0191	+	6.17176i	1.13658	+	0.333731i
$343$	−0.415415	+	0.909632i	−0.0224303	+	0.0491155i
$344$	−7.74669			−0.417673
$345$	11.2815	−	25.9343i	0.607375	−	1.39626i
$346$	5.83412			0.313644
$347$	3.93813	−	8.62330i	0.211410	−	0.462923i	−0.773986	−	0.633203i	$-0.781740\pi$
$347$	3.93813	−	8.62330i	0.211410	−	0.462923i	0.985396	+	0.170280i	$0.0544671\pi$
$348$	−17.4497	−	5.12369i	−0.935402	−	0.274659i
$349$	5.50299	+	6.35079i	0.294568	+	0.339950i	0.883671	−	0.468108i	$-0.155064\pi$
$349$	5.50299	+	6.35079i	0.294568	+	0.339950i	−0.589103	+	0.808058i	$0.700519\pi$
$350$	−0.114151	+	0.0733606i	−0.00610165	+	0.00392129i
$351$	−3.74671	+	4.32394i	−0.199985	+	0.230795i
$352$	−0.881436	+	6.13053i	−0.0469807	+	0.326758i
$353$	−7.49326	+	2.20022i	−0.398826	+	0.117106i	−0.474994	−	0.879989i	$-0.657550\pi$
$353$	−7.49326	+	2.20022i	−0.398826	+	0.117106i	0.0761679	+	0.997095i	$0.475731\pi$
$354$	6.79159	+	4.36469i	0.360969	+	0.231981i
$355$	0.306180	+	2.12953i	0.0162504	+	0.113024i
$356$	−5.49671	−	12.0361i	−0.291325	−	0.637913i
$357$	−5.28645	−	11.5757i	−0.279789	−	0.612652i
$358$	1.92822	+	13.4111i	0.101910	+	0.708796i
$359$	11.5208	+	7.40396i	0.608044	+	0.390766i	0.808123	−	0.589014i	$-0.200484\pi$
$359$	11.5208	+	7.40396i	0.608044	+	0.390766i	−0.200079	+	0.979780i	$0.564120\pi$
$360$	8.20090	−	2.40800i	0.432225	−	0.126913i
$361$	−2.09726	+	14.5868i	−0.110382	+	0.767726i
$362$	−9.54408	+	11.0145i	−0.501626	+	0.578907i
$363$	59.8951	−	38.4923i	3.14368	−	2.02032i
$364$	1.86612	+	2.15362i	0.0978113	+	0.112880i
$365$	7.69073	+	2.25820i	0.402551	+	0.118200i
$366$	7.03610	−	15.4069i	0.367783	−	0.805332i
$367$	−1.21664			−0.0635080			−0.0317540	−	0.999496i	$-0.510109\pi$
$367$	−1.21664			−0.0635080			−0.0317540	+	0.999496i	$0.510109\pi$
$368$	3.20564	+	3.56705i	0.167106	+	0.185946i
$369$	−6.65069			−0.346221
$370$	7.94347	−	17.3938i	0.412962	−	0.904260i
$371$	9.97813	+	2.92984i	0.518039	+	0.152110i
$372$	−11.8387	−	13.6626i	−0.613810	−	0.708374i
$373$	18.5640	−	11.9303i	0.961206	−	0.617730i	0.0368746	−	0.999320i	$-0.488260\pi$
$373$	18.5640	−	11.9303i	0.961206	−	0.617730i	0.924332	+	0.381590i	$0.124623\pi$
$374$	−19.8348	+	22.8906i	−1.02563	+	1.18364i
$375$	−4.08239	+	28.3937i	−0.210814	+	1.46624i
$376$	−0.243781	+	0.0715806i	−0.0125721	+	0.00369149i
$377$	16.7540	+	10.7672i	0.862877	+	0.554538i
$378$	0.285733	+	1.98732i	0.0146965	+	0.102217i
$379$	4.17147	+	9.13425i	0.214274	+	0.469195i	0.985997	−	0.166764i	$-0.0533319\pi$
$379$	4.17147	+	9.13425i	0.214274	+	0.469195i	−0.771723	+	0.635959i	$0.780605\pi$
$380$	5.46806	+	11.9734i	0.280506	+	0.614222i
$381$	5.68822	+	39.5625i	0.291417	+	2.02685i
$382$	11.7106	+	7.52594i	0.599166	+	0.385061i
$383$	−11.3165	+	3.32282i	−0.578245	+	0.169788i	−0.557760	−	0.830002i	$-0.688339\pi$
$383$	−11.3165	+	3.32282i	−0.578245	+	0.169788i	−0.0204847	+	0.999790i	$0.506521\pi$
$384$	−0.370335	+	2.57573i	−0.0188986	+	0.131442i
$385$	−9.19156	+	10.6076i	−0.468445	+	0.540615i
$386$	−17.3744	+	11.1659i	−0.884336	+	0.568328i
$387$	19.1331	+	22.0808i	0.972590	+	1.12243i
$388$	3.16400	+	0.929035i	0.160628	+	0.0471646i
$389$	2.41384	−	5.28556i	0.122386	−	0.267989i	−0.838516	−	0.544878i	$-0.816576\pi$
$389$	2.41384	−	5.28556i	0.122386	−	0.267989i	0.960902	+	0.276889i	$0.0893034\pi$
$390$	−16.8048			−0.850946
$391$	3.75705	+	23.1503i	0.190002	+	1.17076i
$392$	1.00000			0.0505076
$393$	5.49976	−	12.0428i	0.277426	−	0.607479i
$394$	16.1500	+	4.74206i	0.813624	+	0.238902i
$395$	13.4455	+	15.5169i	0.676517	+	0.780742i
$396$	19.6512	−	12.6290i	0.987508	−	0.634633i
$397$	6.56392	−	7.57517i	0.329434	−	0.380187i	−0.566735	−	0.823900i	$-0.691794\pi$
$397$	6.56392	−	7.57517i	0.329434	−	0.380187i	0.896169	+	0.443713i	$0.146339\pi$
$398$	0.382841	−	2.66272i	0.0191901	−	0.133470i
$399$	−14.5023	+	4.25827i	−0.726025	+	0.213180i
$400$	0.114151	+	0.0733606i	0.00570757	+	0.00366803i
$401$	−0.162086	−	1.12733i	−0.00809417	−	0.0562962i	0.985374	−	0.170405i	$-0.0545077\pi$
$401$	−0.162086	−	1.12733i	−0.00809417	−	0.0562962i	−0.993468	+	0.114109i	$0.963599\pi$
$402$	−12.9185	−	28.2877i	−0.644319	−	1.41086i
$403$	8.22404	+	18.0081i	0.409668	+	0.897049i
$404$	−0.816159	−	5.67651i	−0.0406054	−	0.282417i
$405$	11.6104	+	7.46154i	0.576925	+	0.370767i
$406$	6.70569	−	1.96897i	0.332798	−	0.0977183i
$407$	7.43738	−	51.7281i	0.368657	−	2.56407i
$408$	−8.33357	+	9.61745i	−0.412573	+	0.476135i
$409$	18.2357	−	11.7194i	0.901697	−	0.579485i	−0.00559641	−	0.999984i	$-0.501781\pi$
$409$	18.2357	−	11.7194i	0.901697	−	0.579485i	0.907293	+	0.420499i	$0.138145\pi$
$410$	−2.61695	−	3.02012i	−0.129242	−	0.149153i
$411$	−2.48837	−	0.730652i	−0.122742	−	0.0360404i
$412$	4.55274	−	9.96910i	0.224297	−	0.491143i
$413$	−3.10242			−0.152660
$414$	2.24993	−	17.9473i	0.110578	−	0.882060i
$415$	−14.7548			−0.724287
$416$	1.18379	−	2.59213i	0.0580399	−	0.127090i
$417$	−27.7524	−	8.14883i	−1.35904	−	0.399050i
$418$	23.5582	+	27.1876i	1.15227	+	1.32979i
$419$	16.4355	−	10.5624i	0.802924	−	0.516008i	−0.0736446	−	0.997285i	$-0.523463\pi$
$419$	16.4355	−	10.5624i	0.802924	−	0.516008i	0.876569	+	0.481276i	$0.159827\pi$
$420$	−3.86183	+	4.45678i	−0.188438	+	0.217469i
$421$	−1.96789	+	13.6870i	−0.0959091	+	0.667063i	0.883981	+	0.467523i	$0.154854\pi$
$421$	−1.96789	+	13.6870i	−0.0959091	+	0.667063i	−0.979890	+	0.199539i	$0.936055\pi$
$422$	5.04875	−	1.48245i	0.245769	−	0.0721644i
$423$	0.806131	+	0.518069i	0.0391954	+	0.0251894i
$424$	−1.47999	−	10.2935i	−0.0718744	−	0.499898i
$425$	0.275660	+	0.603612i	0.0133715	+	0.0292795i
$426$	1.02625	+	2.24718i	0.0497221	+	0.108876i
$427$	0.926309	+	6.44262i	0.0448272	+	0.311780i
$428$	8.32152	+	5.34792i	0.402236	+	0.258501i
$429$	−44.0674	+	12.9394i	−2.12760	+	0.624718i
$430$	−2.49842	+	17.3769i	−0.120485	+	0.837989i
$431$	20.4473	−	23.5974i	0.984912	−	1.13665i	−0.00570546	−	0.999984i	$-0.501816\pi$
$431$	20.4473	−	23.5974i	0.984912	−	1.13665i	0.990617	−	0.136665i	$-0.0436384\pi$
$432$	1.68903	−	1.08547i	0.0812635	−	0.0522249i
$433$	−1.87813	−	2.16748i	−0.0902571	−	0.104162i	0.708824	−	0.705385i	$-0.249226\pi$
$433$	−1.87813	−	2.16748i	−0.0902571	−	0.104162i	−0.799081	+	0.601223i	$0.794680\pi$
$434$	6.66582	+	1.95726i	0.319970	+	0.0939516i
$435$	−17.1209	+	37.4896i	−0.820887	+	1.79749i
$436$	−10.9124			−0.522608
$437$	27.8513	−	0.503802i	1.33231	−	0.0241001i
$438$	9.20387			0.439778
$439$	−12.0584	+	26.4043i	−0.575517	+	1.26021i	0.368290	+	0.929711i	$0.379943\pi$
$439$	−12.0584	+	26.4043i	−0.575517	+	1.26021i	−0.943807	+	0.330496i	$0.892784\pi$
$440$	13.4673	+	3.95437i	0.642031	+	0.188517i
$441$	−2.46984	−	2.85035i	−0.117612	−	0.135731i
$442$	11.7235	−	7.53421i	0.557628	−	0.358366i
$443$	−1.89608	+	2.18819i	−0.0900855	+	0.103964i	−0.799003	−	0.601328i	$-0.794639\pi$
$443$	−1.89608	+	2.18819i	−0.0900855	+	0.103964i	0.708917	+	0.705292i	$0.249184\pi$
$444$	3.12481	−	21.7335i	0.148297	−	1.03143i
$445$	−28.7715	+	8.44807i	−1.36390	+	0.400477i
$446$	−2.49847	−	1.60567i	−0.118306	−	0.0760308i
$447$	−1.21946	−	8.48155i	−0.0576786	−	0.401164i
$448$	−0.415415	−	0.909632i	−0.0196265	−	0.0429761i
$449$	6.85901	+	15.0191i	0.323697	+	0.708797i	0.999603	−	0.0281913i	$-0.00897474\pi$
$449$	6.85901	+	15.0191i	0.323697	+	0.708797i	−0.675906	+	0.736988i	$0.736247\pi$
$450$	−0.0728324	−	0.506561i	−0.00343335	−	0.0238795i
$451$	−9.18785	−	5.90467i	−0.432639	−	0.278040i
$452$	−14.7895	+	4.34259i	−0.695639	+	0.204258i
$453$	0.157164	−	1.09310i	0.00738419	−	0.0513581i
$454$	−9.27394	+	10.7027i	−0.435247	+	0.502302i
$455$	5.43272	−	3.49140i	0.254690	−	0.163679i
$456$	9.89795	+	11.4228i	0.463514	+	0.534923i
$457$	26.3889	+	7.74847i	1.23442	+	0.362458i	0.832916	−	0.553400i	$-0.186670\pi$
$457$	26.3889	+	7.74847i	1.23442	+	0.362458i	0.401503	+	0.915858i	$0.368488\pi$
$458$	−4.07036	+	8.91284i	−0.190195	+	0.416470i
$459$	9.81857			0.458292
$460$	9.03527	−	6.04027i	0.421271	−	0.281629i
$461$	−20.2816			−0.944608			−0.472304	−	0.881436i	$-0.656578\pi$
$461$	−20.2816			−0.944608			−0.472304	+	0.881436i	$0.656578\pi$
$462$	−6.69526	+	14.6606i	−0.311492	+	0.682071i
$463$	27.7639	+	8.15223i	1.29030	+	0.378866i	0.853688	−	0.520784i	$-0.174360\pi$
$463$	27.7639	+	8.15223i	1.29030	+	0.378866i	0.436611	+	0.899650i	$0.356179\pi$
$464$	−4.57668	−	5.28177i	−0.212467	−	0.245200i
$465$	−34.4653	+	22.1495i	−1.59829	+	1.02716i
$466$	9.35589	−	10.7973i	0.433403	−	0.500174i
$467$	0.339577	−	2.36181i	0.0157138	−	0.109292i	−0.980455	−	0.196744i	$-0.936963\pi$
$467$	0.339577	−	2.36181i	0.0157138	−	0.109292i	0.996169	+	0.0874520i	$0.0278724\pi$
$468$	−10.3122	+	3.02795i	−0.476683	+	0.139967i
$469$	10.0534	+	6.46095i	0.464224	+	0.298339i
$470$	0.0819423	+	0.569921i	0.00377972	+	0.0262885i
$471$	−11.1140	−	24.3362i	−0.512105	−	1.12135i
$472$	1.28879	+	2.82206i	0.0593214	+	0.129896i
$473$	6.82821	+	47.4913i	0.313962	+	2.18365i
$474$	19.8335	+	12.7462i	0.910983	+	0.585453i
$475$	0.756220	−	0.222046i	0.0346977	−	0.0101882i
$476$	0.695966	−	4.84055i	0.0318995	−	0.221866i
$477$	−25.6848	+	29.6419i	−1.17603	+	1.35721i
$478$	−12.7950	+	8.22284i	−0.585229	+	0.376104i
$479$	27.7500	+	32.0252i	1.26793	+	1.46327i	0.823352	+	0.567531i	$0.192101\pi$
$479$	27.7500	+	32.0252i	1.26793	+	1.46327i	0.444580	+	0.895739i	$0.353353\pi$
$480$	5.65829	+	1.66142i	0.258265	+	0.0758333i
$481$	−9.98854	+	21.8718i	−0.455438	+	0.997270i
$482$	6.30089			0.286998
$483$	5.38877	+	11.2564i	0.245197	+	0.512185i
$484$	27.3603			1.24365
$485$	3.10439	−	6.79768i	0.140963	−	0.308667i
$486$	20.9850	+	6.16174i	0.951898	+	0.279502i
$487$	12.4181	+	14.3313i	0.562718	+	0.649412i	0.963799	−	0.266631i	$-0.0859106\pi$
$487$	12.4181	+	14.3313i	0.562718	+	0.649412i	−0.401080	+	0.916043i	$0.631365\pi$
$488$	5.47561	−	3.51896i	0.247869	−	0.159296i
$489$	2.58561	−	2.98395i	0.116925	−	0.134939i
$490$	0.322515	−	2.24314i	0.0145697	−	0.101335i
$491$	14.2638	−	4.18822i	0.643715	−	0.189012i	0.0564487	−	0.998406i	$-0.482022\pi$
$491$	14.2638	−	4.18822i	0.643715	−	0.189012i	0.587266	+	0.809394i	$0.300204\pi$
$492$	−3.86027	−	2.48084i	−0.174034	−	0.111845i
$493$	−4.86396	−	33.8296i	−0.219062	−	1.52361i
$494$	−6.87583	−	15.0560i	−0.309358	−	0.677400i
$495$	−21.9909	−	48.1533i	−0.988417	−	2.16433i
$496$	−0.988695	−	6.87652i	−0.0443937	−	0.308765i
$497$	−0.798647	−	0.513259i	−0.0358242	−	0.0230228i
$498$	−16.2563	+	4.77327i	−0.728461	+	0.213895i
$499$	−3.52290	+	24.5023i	−0.157707	+	1.09687i	0.745139	+	0.666909i	$0.232383\pi$
$499$	−3.52290	+	24.5023i	−0.157707	+	1.09687i	−0.902846	+	0.429965i	$0.858526\pi$
$500$	−7.21887	+	8.33103i	−0.322838	+	0.372575i
$501$	11.6292	−	7.47360i	0.519552	−	0.333896i
$502$	−12.3709	−	14.2768i	−0.552140	−	0.637204i
$503$	29.4102	+	8.63560i	1.31133	+	0.385042i	0.861358	−	0.507998i	$-0.169614\pi$
$503$	29.4102	+	8.63560i	1.31133	+	0.385042i	0.449976	+	0.893041i	$0.351433\pi$
$504$	−1.56676	+	3.43073i	−0.0697890	+	0.152817i
$505$	−12.9964			−0.578334
$506$	19.0423	−	22.7964i	0.846536	−	1.01342i
$507$	−12.6976			−0.563920
$508$	−6.38064	+	13.9717i	−0.283095	+	0.619892i
$509$	0.502152	+	0.147445i	0.0222575	+	0.00653539i	0.292842	−	0.956161i	$-0.405399\pi$
$509$	0.502152	+	0.147445i	0.0222575	+	0.00653539i	−0.270585	+	0.962696i	$0.587217\pi$
$510$	18.8856	+	21.7951i	0.836268	+	0.965104i
$511$	−2.97545	+	1.91221i	−0.131626	+	0.0845911i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	1.65964	−	11.5430i	0.0732747	−	0.509637i
$514$	−0.957062	+	0.281019i	−0.0422142	+	0.0123952i
$515$	−20.8938	−	13.4276i	−0.920689	−	0.591691i
$516$	2.86887	+	19.9534i	0.126295	+	0.878400i
$517$	0.653705	+	1.43141i	0.0287499	+	0.0629535i
$518$	3.50519	+	7.67528i	0.154009	+	0.337233i
$519$	−2.16058	−	15.0271i	−0.0948388	−	0.659618i
$520$	−5.43272	−	3.49140i	−0.238240	−	0.153108i
$521$	−16.0723	+	4.71925i	−0.704139	+	0.206754i	−0.614151	−	0.789189i	$-0.710501\pi$
$521$	−16.0723	+	4.71925i	−0.704139	+	0.206754i	−0.0899888	+	0.995943i	$0.528683\pi$
$522$	−3.75122	+	26.0903i	−0.164186	+	1.14194i
$523$	7.89575	−	9.11218i	0.345257	−	0.398448i	−0.556390	−	0.830922i	$-0.687814\pi$
$523$	7.89575	−	9.11218i	0.345257	−	0.398448i	0.901646	+	0.432474i	$0.142359\pi$
$524$	4.28000	−	2.75059i	0.186973	−	0.120160i
$525$	0.231232	+	0.266856i	0.0100918	+	0.0116465i
$526$	−10.8906	−	3.19778i	−0.474854	−	0.139430i
$527$	14.1134	−	30.9041i	0.614790	−	1.34620i
$528$	16.1170			0.701404
$529$	−4.09446	−	22.6326i	−0.178020	−	0.984027i
$530$	−23.5671			−1.02369
$531$	4.86075	−	10.6435i	0.210938	−	0.461891i
$532$	−5.57306	−	1.63640i	−0.241623	−	0.0709469i
$533$	3.29068	+	3.79765i	0.142535	+	0.164495i
$534$	−28.9662	+	18.6155i	−1.25349	+	0.805570i
$535$	14.6799	−	16.9416i	0.634669	−	0.732447i
$536$	1.70074	−	11.8289i	0.0734607	−	0.510930i
$537$	33.8292	−	9.93316i	1.45984	−	0.428647i
$538$	−15.2897	−	9.82612i	−0.659188	−	0.423634i
$539$	−0.881436	−	6.13053i	−0.0379662	−	0.264060i
$540$	−1.89013	−	4.13881i	−0.0813383	−	0.178106i
$541$	−3.37066	−	7.38072i	−0.144916	−	0.317322i	0.823230	−	0.567708i	$-0.192170\pi$
$541$	−3.37066	−	7.38072i	−0.144916	−	0.317322i	−0.968146	+	0.250386i	$0.919442\pi$
$542$	−4.15979	−	28.9320i	−0.178678	−	1.24273i
$543$	31.9048	+	20.5040i	1.36917	+	0.879910i
$544$	−4.69223	+	1.37776i	−0.201178	+	0.0590711i
$545$	−3.51940	+	24.4780i	−0.150755	+	1.04852i
$546$	4.85606	−	5.60419i	0.207820	−	0.239837i
$547$	−20.6287	+	13.2573i	−0.882020	+	0.566840i	−0.901407	−	0.432972i	$-0.857465\pi$
$547$	−20.6287	+	13.2573i	−0.882020	+	0.566840i	0.0193874	+	0.999812i	$0.493828\pi$
$548$	−0.652647	−	0.753195i	−0.0278797	−	0.0321749i
$549$	−23.5542	−	6.91613i	−1.00527	−	0.295173i
$550$	0.349122	−	0.764471i	0.0148866	−	0.0325971i
$551$	−40.5933			−1.72933
$552$	8.00062	−	9.57788i	0.340529	−	0.407662i
$553$	−9.06001			−0.385271
$554$	−1.49066	+	3.26408i	−0.0633319	+	0.138678i
$555$	−47.7435	−	14.0188i	−2.02660	−	0.595063i
$556$	−7.27885	−	8.40025i	−0.308692	−	0.356250i
$557$	20.4556	−	13.1460i	0.866733	−	0.557015i	−0.0300189	−	0.999549i	$-0.509557\pi$
$557$	20.4556	−	13.1460i	0.866733	−	0.557015i	0.896752	+	0.442534i	$0.145920\pi$
$558$	−17.1586	+	19.8021i	−0.726380	+	0.838288i
$559$	3.14165	−	21.8506i	0.132877	−	0.924183i
$560$	−2.17441	+	0.638464i	−0.0918856	+	0.0269800i
$561$	66.3055	+	42.6120i	2.79942	+	1.79908i
$562$	4.49467	+	31.2611i	0.189596	+	1.31867i
$563$	−5.08253	−	11.1292i	−0.214203	−	0.469040i	0.771779	−	0.635891i	$-0.219367\pi$
$563$	−5.08253	−	11.1292i	−0.214203	−	0.469040i	−0.985982	+	0.166851i	$0.946640\pi$
$564$	0.274653	+	0.601407i	0.0115650	+	0.0253238i
$565$	4.97120	+	34.5755i	0.209140	+	1.45460i
$566$	−25.8291	−	16.5994i	−1.08568	−	0.697723i
$567$	−5.84335	+	1.71576i	−0.245398	+	0.0720553i
$568$	−0.135107	+	0.939690i	−0.00566897	+	0.0394285i
$569$	16.2641	−	18.7698i	0.681827	−	0.786870i	−0.304351	−	0.952560i	$-0.598440\pi$
$569$	16.2641	−	18.7698i	0.681827	−	0.786870i	0.986178	+	0.165690i	$0.0529851\pi$
$570$	28.8153	−	18.5184i	1.20694	−	0.775652i
$571$	12.9176	+	14.9077i	0.540584	+	0.623867i	0.958663	−	0.284543i	$-0.0918419\pi$
$571$	12.9176	+	14.9077i	0.540584	+	0.623867i	−0.418079	+	0.908411i	$0.637296\pi$
$572$	−16.9345	−	4.97243i	−0.708069	−	0.207908i
$573$	15.0480	−	32.9505i	0.628639	−	1.37653i
$574$	1.76338			0.0736021
$575$	−0.280996	−	0.586962i	−0.0117183	−	0.0244780i
$576$	3.77155			0.157148
$577$	7.45460	−	16.3233i	0.310339	−	0.679548i	−0.688622	−	0.725121i	$-0.741784\pi$
$577$	7.45460	−	16.3233i	0.310339	−	0.679548i	0.998961	+	0.0455727i	$0.0145113\pi$
$578$	−6.63517	−	1.94826i	−0.275987	−	0.0810370i
$579$	35.1947	+	40.6168i	1.46264	+	1.68798i
$580$	−13.3238	+	8.56269i	−0.553241	+	0.355546i
$581$	4.26367	−	4.92054i	0.176887	−	0.204139i
$582$	1.22121	−	8.49369i	0.0506207	−	0.352075i
$583$	−61.8002	+	18.1462i	−2.55950	+	0.751538i
$584$	2.97545	+	1.91221i	0.123125	+	0.0791277i
$585$	3.46626	+	24.1084i	0.143312	+	0.996758i
$586$	7.58270	+	16.6038i	0.313239	+	0.685897i
$587$	14.2841	+	31.2778i	0.589568	+	1.29097i	0.935703	+	0.352789i	$0.114767\pi$
$587$	14.2841	+	31.2778i	0.589568	+	1.29097i	−0.346135	+	0.938185i	$0.612506\pi$
$588$	−0.370335	−	2.57573i	−0.0152723	−	0.106221i
$589$	−33.9462	−	21.8159i	−1.39873	−	0.898908i
$590$	6.74593	−	1.98078i	0.277725	−	0.0815475i
$591$	6.23339	−	43.3542i	0.256408	−	1.78335i
$592$	5.52558	−	6.37686i	0.227100	−	0.262087i
$593$	−38.9533	+	25.0338i	−1.59962	+	1.02801i	−0.632212	+	0.774795i	$0.717853\pi$
$593$	−38.9533	+	25.0338i	−1.59962	+	1.02801i	−0.967409	+	0.253219i	$0.918511\pi$
$594$	−8.14330	−	9.39787i	−0.334124	−	0.385599i
$595$	−10.6336	−	3.12230i	−0.435934	−	0.128002i
$596$	1.36791	−	2.99530i	0.0560316	−	0.122692i
$597$	−7.00024			−0.286501
$598$	−11.3614	+	7.59535i	−0.464603	+	0.310597i
$599$	12.2512			0.500569			0.250284	−	0.968172i	$-0.419476\pi$
$599$	12.2512			0.500569			0.250284	+	0.968172i	$0.419476\pi$
$600$	0.146683	−	0.321192i	0.00598832	−	0.0131126i
$601$	39.7485	+	11.6712i	1.62137	+	0.476078i	0.961387	−	0.275200i	$-0.0887440\pi$
$601$	39.7485	+	11.6712i	1.62137	+	0.476078i	0.659986	+	0.751278i	$0.270562\pi$
$602$	−5.07300	−	5.85456i	−0.206760	−	0.238614i
$603$	−37.9171	+	24.3678i	−1.54410	+	0.992334i
$604$	0.277911	−	0.320727i	0.0113081	−	0.0130502i
$605$	8.82409	−	61.3729i	0.358750	−	2.49516i
$606$	−14.3189	+	4.20442i	−0.581667	+	0.170793i
$607$	9.81954	+	6.31064i	0.398563	+	0.256141i	0.724534	−	0.689239i	$-0.242055\pi$
$607$	9.81954	+	6.31064i	0.398563	+	0.256141i	−0.325971	+	0.945380i	$0.605691\pi$
$608$	0.826613	+	5.74922i	0.0335236	+	0.233162i
$609$	−7.55489	−	16.5429i	−0.306140	−	0.670352i
$610$	−6.12755	−	13.4175i	−0.248097	−	0.543258i
$611$	−0.103039	−	0.716649i	−0.00416849	−	0.0289925i
$612$	15.5162	+	9.97165i	0.627205	+	0.403080i
$613$	17.1241	−	5.02809i	0.691635	−	0.203082i	0.0830200	−	0.996548i	$-0.473543\pi$
$613$	17.1241	−	5.02809i	0.691635	−	0.203082i	0.608615	+	0.793465i	$0.291725\pi$
$614$	4.73501	−	32.9327i	0.191090	−	1.32906i
$615$	−6.80987	+	7.85901i	−0.274600	+	0.316906i
$616$	−5.21036	+	3.34850i	−0.209931	+	0.134915i
$617$	4.88892	+	5.64211i	0.196821	+	0.227143i	0.845578	−	0.533853i	$-0.179256\pi$
$617$	4.88892	+	5.64211i	0.196821	+	0.227143i	−0.648757	+	0.760996i	$0.724711\pi$
$618$	−27.3638	−	8.03474i	−1.10073	−	0.323204i
$619$	1.34723	−	2.95003i	0.0541499	−	0.118572i	−0.880623	−	0.473818i	$-0.842876\pi$
$619$	1.34723	−	2.95003i	0.0541499	−	0.118572i	0.934773	+	0.355246i	$0.115603\pi$
$620$	−15.7439			−0.632289
$621$	−9.62728	+	0.174148i	−0.386329	+	0.00698832i
$622$	20.7937			0.833753
$623$	5.49671	−	12.0361i	0.220221	−	0.482217i
$624$	−7.11503	−	2.08916i	−0.284829	−	0.0836334i
$625$	16.8038	+	19.3926i	0.672150	+	0.775703i
$626$	−0.280926	+	0.180540i	−0.0112281	+	0.00721583i
$627$	61.3036	−	70.7481i	2.44823	−	2.82541i
$628$	1.46317	−	10.1765i	0.0583867	−	0.406088i
$629$	39.5921	−	11.6253i	1.57864	−	0.463530i
$630$	7.19030	+	4.62092i	0.286468	+	0.184102i
$631$	5.15149	+	35.8294i	0.205078	+	1.42635i	0.788929	+	0.614485i	$0.210636\pi$
$631$	5.15149	+	35.8294i	0.205078	+	1.42635i	−0.583851	+	0.811861i	$0.698455\pi$
$632$	3.76366	+	8.24127i	0.149710	+	0.327820i
$633$	−5.68812	−	12.4552i	−0.226082	−	0.495051i
$634$	2.12239	+	14.7615i	0.0842907	+	0.586255i
$635$	29.2825	+	18.8187i	1.16204	+	0.746799i
$636$	−25.9653	+	7.62410i	−1.02959	+	0.302315i
$637$	−0.405547	+	2.82064i	−0.0160684	+	0.111758i
$638$	−28.3460	+	32.7130i	−1.12223	+	1.29512i
$639$	3.01214	−	1.93578i	0.119158	−	0.0765784i
$640$	1.48405	+	1.71268i	0.0586622	+	0.0676998i
$641$	40.2702	+	11.8244i	1.59058	+	0.467035i	0.952904	−	0.303273i	$-0.0980793\pi$
$641$	40.2702	+	11.8244i	1.59058	+	0.467035i	0.637672	+	0.770308i	$0.279897\pi$
$642$	10.6931	−	23.4146i	0.422022	−	0.924099i
$643$	−42.3960			−1.67193			−0.835967	−	0.548779i	$-0.815093\pi$
$643$	−42.3960			−1.67193			−0.835967	+	0.548779i	$0.815093\pi$
$644$	−0.596552	+	4.75858i	−0.0235074	+	0.187514i
$645$	45.6835			1.79879
$646$	−11.7997	+	25.8378i	−0.464254	+	1.01657i
$647$	−4.90774	−	1.44104i	−0.192943	−	0.0566533i	0.183833	−	0.982957i	$-0.441149\pi$
$647$	−4.90774	−	1.44104i	−0.192943	−	0.0566533i	−0.376777	+	0.926304i	$0.622968\pi$
$648$	3.98813	+	4.60255i	0.156669	+	0.180805i
$649$	16.1647	−	10.3884i	0.634521	−	0.407782i
$650$	−0.253218	+	0.292229i	−0.00993202	+	0.0114622i
$651$	2.57280	−	17.8942i	0.100836	−	0.701330i
$652$	1.45583	−	0.427471i	0.0570148	−	0.0167410i
$653$	0.669724	+	0.430406i	0.0262083	+	0.0168431i	0.553679	−	0.832730i	$-0.313223\pi$
$653$	0.669724	+	0.430406i	0.0262083	+	0.0168431i	−0.527471	+	0.849573i	$0.676860\pi$
$654$	4.04123	+	28.1074i	0.158025	+	1.09908i
$655$	−4.78960	−	10.4878i	−0.187145	−	0.409790i
$656$	−0.732535	−	1.60403i	−0.0286007	−	0.0626268i
$657$	−1.89844	−	13.2039i	−0.0740652	−	0.515134i
$658$	−0.213740	−	0.137362i	−0.00833245	−	0.00535494i
$659$	−0.731336	+	0.214740i	−0.0284888	+	0.00836507i	−0.295946	−	0.955205i	$-0.595635\pi$
$659$	−0.731336	+	0.214740i	−0.0284888	+	0.00836507i	0.267457	+	0.963570i	$0.413817\pi$
$660$	5.19798	−	36.1528i	0.202331	−	1.40724i
$661$	−9.42970	+	10.8824i	−0.366773	+	0.423278i	−0.908897	−	0.417020i	$-0.863075\pi$
$661$	−9.42970	+	10.8824i	−0.366773	+	0.423278i	0.542125	+	0.840298i	$0.317620\pi$
$662$	1.55190	−	0.997348i	0.0603165	−	0.0387630i
$663$	−23.7477	−	27.4063i	−0.922285	−	1.06437i
$664$	−6.24708	−	1.83431i	−0.242434	−	0.0711849i
$665$	−5.46806	+	11.9734i	−0.212042	+	0.464308i
$666$	−31.8236			−1.23314
$667$	5.36922	+	33.0842i	0.207897	+	1.28103i
$668$	5.31223			0.205536
$669$	−3.21051	+	7.03004i	−0.124126	+	0.271797i
$670$	−25.9854	−	7.62999i	−1.00390	−	0.294772i
$671$	−26.3995	−	30.4666i	−1.01914	−	1.17615i
$672$	−2.18913	+	1.40687i	−0.0844474	+	0.0542711i
$673$	13.2402	−	15.2800i	0.510372	−	0.589000i	−0.440822	−	0.897594i	$-0.645313\pi$
$673$	13.2402	−	15.2800i	0.510372	−	0.589000i	0.951194	+	0.308594i	$0.0998585\pi$
$674$	−2.05651	+	14.3034i	−0.0792139	+	0.550945i
$675$	−0.261401	+	0.0767541i	−0.0100613	+	0.00295427i
$676$	−4.10491	−	2.63807i	−0.157881	−	0.101464i
$677$	−4.10832	−	28.5740i	−0.157896	−	1.09819i	−0.902502	−	0.430685i	$-0.858272\pi$
$677$	−4.10832	−	28.5740i	−0.157896	−	1.09819i	0.744607	−	0.667504i	$-0.232637\pi$
$678$	16.6624	+	36.4856i	0.639916	+	1.40122i
$679$	1.36986	+	2.99958i	0.0525705	+	0.115113i
$680$	1.57720	+	10.9697i	0.0604830	+	0.420668i
$681$	31.0017	+	19.9236i	1.18799	+	0.763475i
$682$	−41.2852	+	12.1224i	−1.58089	+	0.464192i
$683$	5.18045	−	36.0308i	0.198224	−	1.37868i	−0.611209	−	0.791469i	$-0.709317\pi$
$683$	5.18045	−	36.0308i	0.198224	−	1.37868i	0.809434	−	0.587211i	$-0.199774\pi$
$684$	14.3457	−	16.5558i	0.548521	−	0.633027i
$685$	−1.90001	+	1.22106i	−0.0725957	+	0.0466544i
$686$	0.654861	+	0.755750i	0.0250027	+	0.0288547i
$687$	24.4645	+	7.18342i	0.933379	+	0.274065i
$688$	−3.21809	+	7.04664i	−0.122689	+	0.268650i
$689$	29.6345			1.12899
$690$	−18.9042	−	21.0355i	−0.719671	−	0.800809i
$691$	49.2524			1.87365			0.936825	−	0.349800i	$-0.113750\pi$
$691$	49.2524			1.87365			0.936825	+	0.349800i	$0.113750\pi$
$692$	2.42358	−	5.30690i	0.0921307	−	0.201738i
$693$	22.4132	+	6.58110i	0.851405	+	0.249995i
$694$	−6.20807	−	7.16450i	−0.235655	−	0.271961i
$695$	−21.1905	+	13.6183i	−0.803800	+	0.516571i
$696$	−11.9095	+	13.7443i	−0.451430	+	0.520978i
$697$	1.22725	−	8.53573i	0.0464855	−	0.323314i
$698$	8.06291	−	2.36748i	0.305185	−	0.0896105i
$699$	−31.2757	−	20.0997i	−1.18296	−	0.760240i
$700$	0.0193110	+	0.134311i	0.000729887	+	0.00507647i
$701$	−12.6091	−	27.6100i	−0.476238	−	1.04282i	−0.983481	−	0.181013i	$-0.942062\pi$
$701$	−12.6091	−	27.6100i	−0.476238	−	1.04282i	0.507242	−	0.861803i	$-0.330665\pi$
$702$	2.37675	+	5.20436i	0.0897047	+	0.196426i
$703$	−6.97479	−	48.5107i	−0.263059	−	1.82962i
$704$	5.21036	+	3.34850i	0.196373	+	0.126201i
$705$	1.43762	−	0.422123i	0.0541439	−	0.0158981i
$706$	−1.11142	+	7.73011i	−0.0418289	+	0.290927i
$707$	3.75555	−	4.33414i	0.141242	−	0.163002i
$708$	6.79159	−	4.36469i	0.255244	−	0.164035i
$709$	5.93079	+	6.84450i	0.222736	+	0.257051i	0.856108	−	0.516796i	$-0.172875\pi$
$709$	5.93079	+	6.84450i	0.222736	+	0.257051i	−0.633373	+	0.773847i	$0.718330\pi$
$710$	2.06428	+	0.606128i	0.0774711	+	0.0227476i
$711$	14.1949	−	31.0824i	0.532349	−	1.16568i
$712$	−13.2319			−0.495885
$713$	−13.2903	+	30.5523i	−0.497726	+	1.14419i
$714$	−12.7257			−0.476248
$715$	−16.6155	+	36.3829i	−0.621384	+	1.36064i
$716$	13.0001	+	3.81719i	0.485838	+	0.142655i
$717$	25.9183	+	29.9113i	0.967936	+	1.11706i
$718$	11.5208	−	7.40396i	0.429952	−	0.276313i
$719$	−22.3941	+	25.8441i	−0.835158	+	0.963824i	−0.999746	−	0.0225387i	$-0.992825\pi$
$719$	−22.3941	+	25.8441i	−0.835158	+	0.963824i	0.164588	+	0.986362i	$0.447371\pi$
$720$	1.21638	−	8.46012i	0.0453319	−	0.315290i
$721$	10.5156	−	3.08765i	0.391620	−	0.114990i
$722$	12.3974	+	7.96731i	0.461383	+	0.296513i
$723$	−2.33344	−	16.2294i	−0.0867815	−	0.603579i
$724$	6.05435	+	13.2572i	0.225008	+	0.492699i
$725$	0.393948	+	0.862625i	0.0146308	+	0.0320371i
$726$	−10.1325	−	70.4728i	−0.376051	−	2.61549i
$727$	−22.9520	−	14.7503i	−0.851241	−	0.547059i	0.0407205	−	0.999171i	$-0.487035\pi$
$727$	−22.9520	−	14.7503i	−0.851241	−	0.547059i	−0.891962	+	0.452111i	$0.850671\pi$
$728$	2.73422	−	0.802838i	0.101337	−	0.0297552i
$729$	5.49944	−	38.2495i	0.203683	−	1.41665i
$730$	5.24898	−	6.05764i	0.194273	−	0.224203i
$731$	−31.8699	+	20.4815i	−1.17875	+	0.757537i
$732$	−11.0917	−	12.8005i	−0.409962	−	0.473121i
$733$	3.22127	+	0.945850i	0.118980	+	0.0349358i	0.340681	−	0.940179i	$-0.389343\pi$
$733$	3.22127	+	0.945850i	0.118980	+	0.0349358i	−0.221700	+	0.975115i	$0.571161\pi$
$734$	−0.505410	+	1.10669i	−0.0186550	+	0.0408488i
$735$	−5.89717			−0.217520
$736$	4.57638	−	1.43415i	0.168687	−	0.0528633i
$737$	−74.0164			−2.72643
$738$	−2.76280	+	6.04968i	−0.101700	+	0.222692i
$739$	−48.1064	−	14.1253i	−1.76962	−	0.519608i	−0.775838	−	0.630932i	$-0.782673\pi$
$739$	−48.1064	−	14.1253i	−1.76962	−	0.519608i	−0.993784	+	0.111323i	$0.964491\pi$
$740$	−12.5221	−	14.4513i	−0.460322	−	0.531239i
$741$	−36.2338	+	23.2860i	−1.33108	+	0.855434i
$742$	6.81014	−	7.85932i	0.250008	−	0.288525i
$743$	3.99654	−	27.7965i	0.146619	−	1.01976i	−0.775084	−	0.631858i	$-0.782292\pi$
$743$	3.99654	−	27.7965i	0.146619	−	1.01976i	0.921703	−	0.387897i	$-0.126798\pi$
$744$	−17.3459	+	5.09323i	−0.635933	+	0.186727i
$745$	−6.27770	−	4.03443i	−0.229997	−	0.147810i
$746$	−3.14047	−	21.8424i	−0.114981	−	0.799708i
$747$	10.2009	+	22.3368i	0.373231	+	0.817261i
$748$	12.5823	+	27.5514i	0.460055	+	1.00738i
$749$	1.40775	+	9.79113i	0.0514381	+	0.357760i
$750$	24.1319	+	15.5086i	0.881173	+	0.566295i
$751$	18.6060	−	5.46320i	0.678941	−	0.199355i	0.0759602	−	0.997111i	$-0.475798\pi$
$751$	18.6060	−	5.46320i	0.678941	−	0.199355i	0.602981	+	0.797756i	$0.293980\pi$
$752$	−0.0361584	+	0.251487i	−0.00131856	+	0.00917078i
$753$	−32.1918	+	37.1513i	−1.17313	+	1.35387i
$754$	16.7540	−	10.7672i	0.610146	−	0.392117i
$755$	−0.629805	−	0.726833i	−0.0229209	−	0.0264522i
$756$	1.92643	+	0.565650i	0.0700634	+	0.0205725i
$757$	13.2317	−	28.9735i	0.480916	−	1.05306i	−0.501295	−	0.865276i	$-0.667143\pi$
$757$	13.2317	−	28.9735i	0.480916	−	1.05306i	0.982211	−	0.187782i	$-0.0601299\pi$
$758$	10.0417			0.364731
$759$	−65.7695	−	40.6057i	−2.38728	−	1.47389i
$760$	13.1629			0.477468
$761$	20.7230	−	45.3771i	0.751209	−	1.64492i	−0.0129704	−	0.999916i	$-0.504129\pi$
$761$	20.7230	−	45.3771i	0.751209	−	1.64492i	0.764180	−	0.645003i	$-0.223144\pi$
$762$	38.3503	+	11.2607i	1.38928	+	0.407930i
$763$	−7.14608	−	8.24702i	−0.258706	−	0.298562i
$764$	11.7106	−	7.52594i	0.423674	−	0.272279i
$765$	27.3720	−	31.5890i	0.989637	−	1.14210i
$766$	−1.67849	+	11.6742i	−0.0606464	+	0.421805i
$767$	−8.48268	+	2.49074i	−0.306292	+	0.0899354i
$768$	2.18913	+	1.40687i	0.0789933	+	0.0507659i
$769$	3.12926	+	21.7645i	0.112844	+	0.784848i	0.965130	+	0.261772i	$0.0843067\pi$
$769$	3.12926	+	21.7645i	0.112844	+	0.784848i	−0.852286	+	0.523077i	$0.824784\pi$
$770$	5.83072	+	12.7675i	0.210125	+	0.460109i
$771$	1.07826	+	2.36107i	0.0388327	+	0.0850317i
$772$	2.93923	+	20.4428i	0.105785	+	0.735753i
$773$	−11.5732	−	7.43765i	−0.416259	−	0.267514i	0.315704	−	0.948858i	$-0.397759\pi$
$773$	−11.5732	−	7.43765i	−0.416259	−	0.267514i	−0.731963	+	0.681344i	$0.761396\pi$
$774$	28.0336	−	8.23140i	1.00765	−	0.295871i
$775$	−0.134158	+	0.933089i	−0.00481910	+	0.0335175i
$776$	2.15945	−	2.49214i	0.0775199	−	0.0894628i
$777$	18.4714	−	11.8708i	0.662658	−	0.425864i
$778$	−3.80517	−	4.39140i	−0.136422	−	0.157439i
$779$	−9.82743	−	2.88559i	−0.352104	−	0.103387i
$780$	−6.98099	+	15.2862i	−0.249959	+	0.547335i
$781$	5.87988			0.210399
$782$	22.6190	+	6.19945i	0.808853	+	0.221692i
$783$	14.0318			0.501455
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	−22.3555	−	6.56417i	−0.797902	−	0.234285i
$786$	−8.66983	−	10.0055i	−0.309242	−	0.356885i
$787$	−28.2685	+	18.1670i	−1.00766	+	0.647585i	−0.936787	−	0.349900i	$-0.886215\pi$
$787$	−28.2685	+	18.1670i	−1.00766	+	0.647585i	−0.0708747	+	0.997485i	$0.522579\pi$
$788$	11.0225	−	12.7206i	0.392659	−	0.453153i
$789$	−4.20345	+	29.2356i	−0.149647	+	1.04082i
$790$	19.7002	−	5.78449i	0.700900	−	0.205803i
$791$	−12.9670	−	8.33336i	−0.461052	−	0.296300i
$792$	−3.32439	−	23.1216i	−0.118127	−	0.821591i
$793$	7.70511	+	16.8718i	0.273616	+	0.599136i
$794$	−4.16386	−	9.11759i	−0.147770	−	0.323571i
$795$	8.72773	+	60.7027i	0.309541	+	2.15290i
$796$	−2.26306	−	1.45438i	−0.0802120	−	0.0515491i
$797$	−33.0558	+	9.70606i	−1.17090	+	0.343806i	−0.808658	−	0.588279i	$-0.799806\pi$
$797$	−33.0558	+	9.70606i	−1.17090	+	0.343806i	−0.362238	+	0.932086i	$0.617987\pi$
$798$	−2.15103	+	14.9607i	−0.0761456	+	0.529604i
$799$	−0.813664	+	0.939019i	−0.0287854	+	0.0332201i
$800$	0.114151	−	0.0733606i	0.00403586	−	0.00259369i
$801$	32.6806	+	37.7154i	1.15471	+	1.33261i
$802$	−1.09279	−	0.320872i	−0.0385877	−	0.0113304i
$803$	9.10016	−	19.9266i	0.321138	−	0.703194i
$804$	−31.0979			−1.09674
$805$	10.4818	+	2.87286i	0.369434	+	0.101255i
$806$	19.7972			0.697325
$807$	−19.6472	+	43.0213i	−0.691613	+	1.51442i
$808$	−5.50258	−	1.61570i	−0.193580	−	0.0568403i
$809$	18.6799	+	21.5577i	0.656749	+	0.757928i	0.982243	−	0.187616i	$-0.0600760\pi$
$809$	18.6799	+	21.5577i	0.656749	+	0.757928i	−0.325494	+	0.945544i	$0.605531\pi$
$810$	11.6104	−	7.46154i	0.407947	−	0.262172i
$811$	5.14199	−	5.93417i	0.180560	−	0.208377i	−0.658254	−	0.752796i	$-0.728705\pi$
$811$	5.14199	−	5.93417i	0.180560	−	0.208377i	0.838813	+	0.544419i	$0.183250\pi$
$812$	0.994608	−	6.91765i	0.0349039	−	0.242762i
$813$	−72.9805	+	21.4290i	−2.55954	+	0.751548i
$814$	−43.9639	−	28.2539i	−1.54094	−	0.990299i
$815$	−0.489349	−	3.40350i	−0.0171412	−	0.119219i
$816$	5.28645	+	11.5757i	0.185063	+	0.405231i
$817$	18.6918	+	40.9292i	0.653942	+	1.43193i
$818$	−3.08493	−	21.4562i	−0.107862	−	0.750197i
$819$	−9.04145	−	5.81059i	−0.315934	−	0.203038i
$820$	−3.83431	+	1.12586i	−0.133900	+	0.0393166i
$821$	−5.30369	+	36.8880i	−0.185100	+	1.28740i	0.659379	+	0.751811i	$0.270819\pi$
$821$	−5.30369	+	36.8880i	−0.185100	+	1.28740i	−0.844479	+	0.535589i	$0.820090\pi$
$822$	−1.69833	+	1.95998i	−0.0592361	+	0.0683622i
$823$	−45.7396	+	29.3950i	−1.59438	+	1.02465i	−0.624514	+	0.781014i	$0.714703\pi$
$823$	−45.7396	+	29.3950i	−1.59438	+	1.02465i	−0.969867	+	0.243633i	$0.921661\pi$
$824$	−7.17694	−	8.28263i	−0.250021	−	0.288539i
$825$	−2.09837	−	0.616136i	−0.0730557	−	0.0214511i
$826$	−1.28879	+	2.82206i	−0.0448428	+	0.0981920i
$827$	−54.6118			−1.89904			−0.949520	−	0.313706i	$-0.898429\pi$
$827$	−54.6118			−1.89904			−0.949520	+	0.313706i	$0.898429\pi$
$828$	−15.3907	−	9.50217i	−0.534865	−	0.330223i
$829$	−23.0118			−0.799232			−0.399616	−	0.916683i	$-0.630857\pi$
$829$	−23.0118			−0.799232			−0.399616	+	0.916683i	$0.630857\pi$
$830$	−6.12938	+	13.4215i	−0.212754	+	0.465866i
$831$	8.95945	+	2.63073i	0.310800	+	0.0912591i
$832$	−1.86612	−	2.15362i	−0.0646961	−	0.0746633i
$833$	4.11400	−	2.64391i	0.142542	−	0.0916060i
$834$	−18.9412	+	21.8593i	−0.655880	+	0.756926i
$835$	1.71327	−	11.9161i	0.0592903	−	0.412373i
$836$	34.5171	−	10.1351i	1.19380	−	0.350531i
$837$	11.7341	+	7.54104i	0.405589	+	0.260657i
$838$	−2.78038	−	19.3380i	−0.0960468	−	0.668020i
$839$	−3.91956	−	8.58263i	−0.135318	−	0.296305i	0.829827	−	0.558021i	$-0.188439\pi$
$839$	−3.91956	−	8.58263i	−0.135318	−	0.296305i	−0.965145	+	0.261715i	$0.915712\pi$
$840$	2.44977	+	5.36425i	0.0845252	+	0.185084i
$841$	−2.82398	−	19.6412i	−0.0973785	−	0.677283i
$842$	11.6326	+	7.47583i	0.400887	+	0.257634i
$843$	78.8558	−	23.1542i	2.71594	−	0.797472i
$844$	0.748846	−	5.20834i	0.0257763	−	0.179278i
$845$	−7.24145	+	8.35708i	−0.249113	+	0.287492i
$846$	0.806131	−	0.518069i	0.0277154	−	0.0178116i
$847$	17.9172	+	20.6775i	0.615641	+	0.710488i
$848$	−9.97813	−	2.92984i	−0.342650	−	0.100611i
$849$	−33.1901	+	72.6762i	−1.13908	+	2.49424i
$850$	0.663578			0.0227605
$851$	−38.6145	+	12.1010i	−1.32369	+	0.414818i
$852$	2.47043			0.0846354
$853$	2.71024	−	5.93459i	0.0927967	−	0.203196i	−0.857542	−	0.514414i	$-0.828010\pi$
$853$	2.71024	−	5.93459i	0.0927967	−	0.203196i	0.950339	+	0.311218i	$0.100737\pi$
$854$	6.24521	+	1.83376i	0.213707	+	0.0627500i
$855$	−32.5103	−	37.5189i	−1.11183	−	1.28312i
$856$	8.32152	−	5.34792i	0.284424	−	0.182788i
$857$	3.42870	−	3.95693i	0.117122	−	0.135166i	−0.694161	−	0.719820i	$-0.744224\pi$
$857$	3.42870	−	3.95693i	0.117122	−	0.135166i	0.811283	+	0.584654i	$0.198770\pi$
$858$	−6.53621	+	45.4603i	−0.223143	+	1.55199i
$859$	37.9896	−	11.1548i	1.29619	−	0.380596i	0.440345	−	0.897829i	$-0.354856\pi$
$859$	37.9896	−	11.1548i	1.29619	−	0.380596i	0.855845	+	0.517233i	$0.173038\pi$
$860$	14.7687	+	9.49127i	0.503609	+	0.323650i
$861$	−0.653041	−	4.54200i	−0.0222556	−	0.154791i
$862$	−12.9709	−	28.4023i	−0.441790	−	0.967385i
$863$	0.177336	+	0.388311i	0.00603657	+	0.0132183i	0.912626	−	0.408795i	$-0.134051\pi$
$863$	0.177336	+	0.388311i	0.00603657	+	0.0132183i	−0.906590	+	0.422013i	$0.861324\pi$
$864$	−0.285733	−	1.98732i	−0.00972084	−	0.0676099i
$865$	−11.1225	−	7.14799i	−0.378176	−	0.243039i
$866$	−2.75181	+	0.808004i	−0.0935103	+	0.0274571i
$867$	−2.56097	+	17.8119i	−0.0869752	+	0.604925i
$868$	4.54947	−	5.25037i	0.154419	−	0.178209i
$869$	47.2059	−	30.3374i	1.60135	−	1.02913i
$870$	26.9895	+	31.1475i	0.915029	+	1.05600i
$871$	32.6753	+	9.59434i	1.10716	+	0.325092i
$872$	−4.53316	+	9.92624i	−0.153512	+	0.336145i
$873$	−12.4370			−0.420929
$874$	11.1116	−	25.5437i	0.375854	−	0.864028i
$875$	−11.0235			−0.372663
$876$	3.82342	−	8.37213i	0.129182	−	0.282868i
$877$	−16.1071	−	4.72948i	−0.543899	−	0.159703i	−0.00176986	−	0.999998i	$-0.500563\pi$
$877$	−16.1071	−	4.72948i	−0.543899	−	0.159703i	−0.542129	+	0.840295i	$0.682382\pi$
$878$	19.0089	+	21.9375i	0.641520	+	0.740353i
$879$	39.9588	−	25.6800i	1.34778	−	0.866164i
$880$	9.19156	−	10.6076i	0.309847	−	0.357583i
$881$	8.19222	−	56.9782i	0.276003	−	1.91964i	−0.103844	−	0.994594i	$-0.533114\pi$
$881$	8.19222	−	56.9782i	0.276003	−	1.91964i	0.379847	−	0.925049i	$-0.375977\pi$
$882$	−3.61878	+	1.06257i	−0.121851	+	0.0357786i
$883$	−26.9005	−	17.2879i	−0.905273	−	0.581784i	0.00307660	−	0.999995i	$-0.499021\pi$
$883$	−26.9005	−	17.2879i	−0.905273	−	0.581784i	−0.908350	+	0.418212i	$0.862657\pi$
$884$	−1.98326	−	13.7939i	−0.0667041	−	0.463937i
$885$	−7.60022	−	16.6422i	−0.255479	−	0.559420i
$886$	1.20279	+	2.63375i	0.0404086	+	0.0884824i
$887$	5.40609	+	37.6002i	0.181519	+	1.26249i	0.853174	+	0.521627i	$0.174675\pi$
$887$	5.40609	+	37.6002i	0.181519	+	1.26249i	−0.671655	+	0.740864i	$0.734416\pi$
$888$	−18.4714	−	11.8708i	−0.619860	−	0.398360i
$889$	−14.7375	+	4.32732i	−0.494280	+	0.145134i
$890$	−4.26747	+	29.6809i	−0.143046	+	0.994906i
$891$	24.7007	−	28.5062i	0.827506	−	0.954993i
$892$	−2.49847	+	1.60567i	−0.0836551	+	0.0537619i
$893$	0.966406	+	1.11529i	0.0323395	+	0.0373218i
$894$	−8.22167	−	2.41410i	−0.274974	−	0.0807396i
$895$	12.7552	−	27.9300i	0.426360	−	0.933598i
$896$	−1.00000			−0.0334077
$897$	23.7711	+	26.4512i	0.793695	+	0.883178i
$898$	16.5112			0.550986
$899$	20.1695	−	44.1651i	0.672692	−	1.47299i
$900$	−0.491039	−	0.144182i	−0.0163680	−	0.00480607i
$901$	−33.3038	−	38.4347i	−1.10951	−	1.28044i
$902$	−9.18785	+	5.90467i	−0.305922	+	0.196604i
$903$	−13.2011	+	15.2349i	−0.439304	+	0.506984i
$904$	−2.19362	+	15.2570i	−0.0729588	+	0.507439i
$905$	31.6903	−	9.30512i	1.05342	−	0.309313i
$906$	−0.929027	−	0.597050i	−0.0308649	−	0.0198356i
$907$	−0.594715	−	4.13634i	−0.0197472	−	0.137345i	0.977563	−	0.210644i	$-0.0675562\pi$
$907$	−0.594715	−	4.13634i	−0.0197472	−	0.137345i	−0.997310	+	0.0732995i	$0.976647\pi$
$908$	5.88298	+	12.8819i	0.195234	+	0.427502i
$909$	8.98519	+	19.6748i	0.298020	+	0.652573i
$910$	−0.919053	−	6.39215i	−0.0304663	−	0.211898i
$911$	20.5052	+	13.1779i	0.679369	+	0.436604i	0.834292	−	0.551323i	$-0.185877\pi$
$911$	20.5052	+	13.1779i	0.679369	+	0.436604i	−0.154923	+	0.987926i	$0.549513\pi$
$912$	14.5023	−	4.25827i	0.480220	−	0.141005i
$913$	−5.73887	+	39.9147i	−0.189929	+	1.32098i
$914$	18.0106	−	20.7853i	0.595737	−	0.687517i
$915$	−32.2906	+	20.7519i	−1.06749	+	0.686037i
$916$	6.41652	+	7.40505i	0.212008	+	0.244670i
$917$	4.88157	+	1.43336i	0.161203	+	0.0473336i
$918$	4.07878	−	8.93129i	0.134620	−	0.294776i
$919$	29.5485			0.974714			0.487357	−	0.873203i	$-0.337961\pi$
$919$	29.5485			0.974714			0.487357	+	0.873203i	$0.337961\pi$
$920$	−1.74104	−	10.7280i	−0.0574003	−	0.353691i
$921$	−86.5795			−2.85289
$922$	−8.42528	+	18.4488i	−0.277472	+	0.607579i
$923$	−2.59574	−	0.762177i	−0.0854397	−	0.0250874i
$924$	10.5544	+	12.1804i	0.347215	+	0.400707i
$925$	−0.963186	+	0.619002i	−0.0316693	+	0.0203527i
$926$	18.9491	−	21.8684i	0.622705	−	0.718640i
$927$	−5.88249	+	40.9136i	−0.193206	+	1.34378i
$928$	−6.70569	+	1.96897i	−0.220125	+	0.0646346i
$929$	−16.0097	−	10.2888i	−0.525261	−	0.337564i	0.250989	−	0.967990i	$-0.419244\pi$
$929$	−16.0097	−	10.2888i	−0.525261	−	0.337564i	−0.776250	+	0.630425i	$0.782880\pi$
$930$	5.83050	+	40.5520i	0.191190	+	1.32975i
$931$	−2.41287	−	5.28345i	−0.0790787	−	0.173158i
$932$	−5.93497	−	12.9958i	−0.194406	−	0.425691i
$933$	−7.70064	−	53.5591i	−0.252108	−	1.75345i
$934$	−2.00731	−	1.29002i	−0.0656813	−	0.0422108i
$935$	65.8597	−	19.3382i	2.15384	−	0.632426i
$936$	−1.52954	+	10.6382i	−0.0499946	+	0.347720i
$937$	−34.1042	+	39.3583i	−1.11414	+	1.28578i	−0.159766	+	0.987155i	$0.551074\pi$
$937$	−34.1042	+	39.3583i	−1.11414	+	1.28578i	−0.954370	+	0.298626i	$0.903472\pi$
$938$	10.0534	−	6.46095i	0.328256	−	0.210957i
$939$	0.569060	+	0.656730i	0.0185706	+	0.0214316i
$940$	0.552459	+	0.162217i	0.0180192	+	0.00529092i
$941$	−15.2476	+	33.3876i	−0.497057	+	1.08840i	0.480357	+	0.877073i	$0.340507\pi$
$941$	−15.2476	+	33.3876i	−0.497057	+	1.08840i	−0.977415	+	0.211331i	$0.932220\pi$
$942$	−26.7539			−0.871690
$943$	−1.05195	+	8.39120i	−0.0342561	+	0.273255i
$944$	3.10242			0.100975
$945$	1.89013	−	4.13881i	0.0614860	−	0.134636i
$946$	46.0361	+	13.5174i	1.49676	+	0.439489i
$947$	8.69648	+	10.0363i	0.282598	+	0.326135i	0.879246	−	0.476368i	$-0.158047\pi$
$947$	8.69648	+	10.0363i	0.282598	+	0.326135i	−0.596649	+	0.802503i	$0.703501\pi$
$948$	19.8335	−	12.7462i	0.644163	−	0.413978i
$949$	−6.60033	+	7.61719i	−0.214256	+	0.247264i
$950$	0.112165	−	0.780123i	0.00363910	−	0.0253105i
$951$	37.2357	−	10.9334i	1.20745	−	0.354540i
$952$	−4.11400	−	2.64391i	−0.133336	−	0.0856896i
$953$	2.53523	+	17.6329i	0.0821241	+	0.571186i	0.988787	+	0.149330i	$0.0477118\pi$
$953$	2.53523	+	17.6329i	0.0821241	+	0.571186i	−0.906663	+	0.421855i	$0.861379\pi$
$954$	16.2933	+	35.6774i	0.527516	+	1.15510i
$955$	−13.1049	−	28.6957i	−0.424065	−	0.928572i
$956$	2.16453	+	15.0546i	0.0700059	+	0.486901i
$957$	94.7576	+	60.8970i	3.06308	+	1.96852i
$958$	40.6590	−	11.9385i	1.31363	−	0.385717i
$959$	0.141834	−	0.986476i	0.00458005	−	0.0318550i
$960$	3.86183	−	4.45678i	0.124640	−	0.143842i
$961$	14.5235	−	9.33366i	0.468499	−	0.301086i
$962$	15.7459	+	18.1718i	0.507669	+	0.585882i
$963$	−35.7963	−	10.5107i	−1.15352	−	0.338704i
$964$	2.61749	−	5.73149i	0.0843035	−	0.184599i
$965$	46.8040			1.50668
$966$	12.4778	−	0.225711i	0.401466	−	0.00726212i
$967$	41.4376			1.33254			0.666271	−	0.745710i	$-0.267889\pi$
$967$	41.4376			1.33254			0.666271	+	0.745710i	$0.267889\pi$
$968$	11.3659	−	24.8878i	0.365313	−	0.799924i
$969$	70.9211	+	20.8243i	2.27832	+	0.668974i
$970$	−4.89377	−	5.64771i	−0.157130	−	0.181337i
$971$	−27.7537	+	17.8362i	−0.890659	+	0.572392i	−0.904006	−	0.427519i	$-0.859388\pi$
$971$	−27.7537	+	17.8362i	−0.890659	+	0.572392i	0.0133472	+	0.999911i	$0.495751\pi$
$972$	14.3224	−	16.5289i	0.459391	−	0.530165i
$973$	1.58185	−	11.0020i	0.0507117	−	0.352707i
$974$	18.1948	−	5.34249i	0.583001	−	0.171184i
$975$	0.846479	+	0.543999i	0.0271090	+	0.0174219i
$976$	−0.926309	−	6.44262i	−0.0296504	−	0.206223i
$977$	−1.36145	−	2.98116i	−0.0435566	−	0.0953757i	0.886603	−	0.462532i	$-0.153059\pi$
$977$	−1.36145	−	2.98116i	−0.0435566	−	0.0953757i	−0.930159	+	0.367156i	$0.880332\pi$
$978$	−1.64020	−	3.59153i	−0.0524477	−	0.114844i
$979$	11.6630	+	81.1182i	0.372752	+	2.59255i
$980$	−1.90645	−	1.22520i	−0.0608994	−	0.0391377i
$981$	39.4895	−	11.5952i	1.26080	−	0.370205i
$982$	2.11565	−	14.7146i	0.0675130	−	0.469563i
$983$	4.76176	−	5.49536i	0.151876	−	0.175275i	−0.674713	−	0.738080i	$-0.735733\pi$
$983$	4.76176	−	5.49536i	0.151876	−	0.175275i	0.826589	+	0.562806i	$0.190278\pi$
$984$	−3.86027	+	2.48084i	−0.123061	+	0.0790864i
$985$	−24.9792	−	28.8275i	−0.795904	−	0.918522i
$986$	−32.7930	−	9.62890i	−1.04434	−	0.306647i
$987$	−0.274653	+	0.601407i	−0.00874231	+	0.0191430i
$988$	−16.5517			−0.526580
$989$	30.8857	−	20.6478i	0.982108	−	0.656561i
$990$	−52.9372			−1.68245
$991$	11.6947	−	25.6078i	0.371495	−	0.813460i	−0.627887	−	0.778304i	$-0.716080\pi$
$991$	11.6947	−	25.6078i	0.371495	−	0.813460i	0.999382	−	0.0351556i	$-0.0111927\pi$
$992$	−6.66582	−	1.95726i	−0.211640	−	0.0621431i
$993$	−3.14363	−	3.62794i	−0.0997600	−	0.115129i
$994$	−0.798647	+	0.513259i	−0.0253315	+	0.0162796i
$995$	−3.99224	+	4.60730i	−0.126563	+	0.146061i
$996$	−2.41118	+	16.7701i	−0.0764011	+	0.531382i
$997$	1.83221	−	0.537984i	0.0580265	−	0.0170381i	−0.252590	−	0.967573i	$-0.581283\pi$
$997$	1.83221	−	0.537984i	0.0580265	−	0.0170381i	0.310617	+	0.950535i	$0.399464\pi$
$998$	20.8246	+	13.3832i	0.659192	+	0.423637i
$999$	2.41096	+	16.7686i	0.0762793	+	0.530534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.29.1	✓	40
23.2	even	11		7406.2.a.bu.1.16		20
23.4	even	11	inner	322.2.i.d.211.1	yes	40
23.21	odd	22		7406.2.a.bv.1.16		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.29.1	✓	40	1.1	even	1	trivial
322.2.i.d.211.1	yes	40	23.4	even	11	inner
7406.2.a.bu.1.16		20	23.2	even	11
7406.2.a.bv.1.16		20	23.21	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)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-2.49681 - 0.733130i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.90645 + 1.22520i) q^{5} +(-1.70409 + 1.96663i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(3.17283 + 2.03906i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-2.49681 - 0.733130i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-1.90645 + 1.22520i) q^{5} +(-1.70409 + 1.96663i) q^{6} +(0.142315 - 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(3.17283 + 2.03906i) q^{9} +(0.322515 + 2.24314i) q^{10} +(2.57290 + 5.63387i) q^{11} +(1.08100 + 2.36706i) q^{12} +(-0.405547 - 2.82064i) q^{13} +(-0.841254 - 0.540641i) q^{14} +(5.65829 - 1.66142i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-3.20248 + 3.69586i) q^{17} +(3.17283 - 2.03906i) q^{18} +(3.80365 + 4.38965i) q^{19} +(2.17441 + 0.638464i) q^{20} +(-1.08100 + 2.36706i) q^{21} +6.19357 q^{22} +(3.07454 - 3.68066i) q^{23} +2.60222 q^{24} +(0.0563685 - 0.123430i) q^{25} +(-2.73422 - 0.802838i) q^{26} +(-1.31480 - 1.51736i) q^{27} +(-0.841254 + 0.540641i) q^{28} +(-4.57668 + 5.28177i) q^{29} +(0.839255 - 5.83715i) q^{30} +(-6.66582 + 1.95726i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-2.29369 - 15.9530i) q^{33} +(2.03151 + 4.44840i) q^{34} +(0.941416 + 2.06141i) q^{35} +(-0.536748 - 3.73317i) q^{36} +(-7.09832 - 4.56181i) q^{37} +(5.57306 - 1.63640i) q^{38} +(-1.05532 + 7.33993i) q^{39} +(1.48405 - 1.71268i) q^{40} +(-1.48345 + 0.953356i) q^{41} +(1.70409 + 1.96663i) q^{42} +(7.43289 + 2.18249i) q^{43} +(2.57290 - 5.63387i) q^{44} -8.54712 q^{45} +(-2.07083 - 4.32570i) q^{46} +0.254073 q^{47} +(1.08100 - 2.36706i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-0.0888594 - 0.102549i) q^{50} +(10.7055 - 6.88004i) q^{51} +(-1.86612 + 2.15362i) q^{52} +(-1.47999 + 10.2935i) q^{53} +(-1.92643 + 0.565650i) q^{54} +(-11.8078 - 7.58838i) q^{55} +(0.142315 + 0.989821i) q^{56} +(-6.27882 - 13.7487i) q^{57} +(2.90325 + 6.35723i) q^{58} +(-0.441520 - 3.07084i) q^{59} +(-4.96102 - 3.18825i) q^{60} +(-6.24521 + 1.83376i) q^{61} +(-0.988695 + 6.87652i) q^{62} +(2.46984 - 2.85035i) q^{63} +(0.841254 - 0.540641i) q^{64} +(4.22902 + 4.88054i) q^{65} +(-15.4642 - 4.54069i) q^{66} +(-4.96443 + 10.8706i) q^{67} +4.89033 q^{68} +(-10.3749 + 6.93587i) q^{69} +2.26621 q^{70} +(0.394376 - 0.863562i) q^{71} +(-3.61878 - 1.06257i) q^{72} +(-2.31619 - 2.67303i) q^{73} +(-7.09832 + 4.56181i) q^{74} +(-0.231232 + 0.266856i) q^{75} +(0.826613 - 5.74922i) q^{76} +(5.94268 - 1.74493i) q^{77} +(6.23824 + 4.00907i) q^{78} +(-1.28937 - 8.96779i) q^{79} +(-0.941416 - 2.06141i) q^{80} +(-2.52990 - 5.53970i) q^{81} +(0.250955 + 1.74543i) q^{82} +(5.47724 + 3.52001i) q^{83} +(2.49681 - 0.733130i) q^{84} +(1.57720 - 10.9697i) q^{85} +(5.07300 - 5.85456i) q^{86} +(15.2994 - 9.83230i) q^{87} +(-4.05592 - 4.68079i) q^{88} +(12.6959 + 3.72785i) q^{89} +(-3.55060 + 7.77473i) q^{90} -2.84965 q^{91} +(-4.79505 + 0.0867377i) q^{92} +18.0782 q^{93} +(0.105546 - 0.231113i) q^{94} +(-12.6297 - 3.70842i) q^{95} +(-1.70409 - 1.96663i) q^{96} +(-2.77410 + 1.78281i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(-3.32439 + 23.1216i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more