LMFDB - Embedded newform 300.2.w.a.163.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			163.14
Character	$\chi$	$=$	300.163
Dual form			300.2.w.a.127.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.180090 - 1.40270i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-1.93514 + 0.505225i) q^{4} +(0.583536 + 2.15858i) q^{5} +(-0.476351 + 1.33157i) q^{6} +(0.889008 + 0.889008i) q^{7} +(1.05718 + 2.62343i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-0.180090 - 1.40270i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-1.93514 + 0.505225i) q^{4} +(0.583536 + 2.15858i) q^{5} +(-0.476351 + 1.33157i) q^{6} +(0.889008 + 0.889008i) q^{7} +(1.05718 + 2.62343i) q^{8} +(0.587785 + 0.809017i) q^{9} +(2.92276 - 1.20727i) q^{10} +(3.50723 - 4.82729i) q^{11} +(1.95359 + 0.428374i) q^{12} +(3.23824 + 0.512887i) q^{13} +(1.08691 - 1.40711i) q^{14} +(0.460042 - 2.18823i) q^{15} +(3.48950 - 1.95536i) q^{16} +(0.313606 + 0.615487i) q^{17} +(1.02895 - 0.970182i) q^{18} +(-1.16061 + 3.57200i) q^{19} +(-2.21979 - 3.88233i) q^{20} +(-0.388511 - 1.19571i) q^{21} +(-7.40286 - 4.05025i) q^{22} +(-1.68898 + 0.267508i) q^{23} +(0.249059 - 2.81744i) q^{24} +(-4.31897 + 2.51922i) q^{25} +(0.136251 - 4.63464i) q^{26} +(-0.156434 - 0.987688i) q^{27} +(-2.16950 - 1.27120i) q^{28} +(8.00770 - 2.60186i) q^{29} +(-3.15228 - 0.251222i) q^{30} +(4.87146 + 1.58283i) q^{31} +(-3.37120 - 4.54257i) q^{32} +(-5.31651 + 2.70890i) q^{33} +(0.806866 - 0.550738i) q^{34} +(-1.40023 + 2.43777i) q^{35} +(-1.54618 - 1.26859i) q^{36} +(-1.22564 + 7.73839i) q^{37} +(5.21947 + 0.984711i) q^{38} +(-2.65245 - 1.92712i) q^{39} +(-5.04599 + 3.81287i) q^{40} +(8.56195 - 6.22062i) q^{41} +(-1.60726 + 0.760300i) q^{42} +(-5.55076 + 5.55076i) q^{43} +(-4.34810 + 11.1134i) q^{44} +(-1.40334 + 1.74087i) q^{45} +(0.679402 + 2.32096i) q^{46} +(4.53317 - 8.89684i) q^{47} +(-3.99688 + 0.158038i) q^{48} -5.41933i q^{49} +(4.31152 + 5.60453i) q^{50} -0.690777i q^{51} +(-6.52555 + 0.643534i) q^{52} +(-2.43953 + 4.78785i) q^{53} +(-1.35726 + 0.397304i) q^{54} +(12.4667 + 4.75375i) q^{55} +(-1.39241 + 3.27209i) q^{56} +(2.65577 - 2.65577i) q^{57} +(-5.09174 - 10.7638i) q^{58} +(-7.86506 + 5.71430i) q^{59} +(0.215306 + 4.46695i) q^{60} +(0.117440 + 0.0853253i) q^{61} +(1.34294 - 7.11825i) q^{62} +(-0.196677 + 1.24177i) q^{63} +(-5.76475 + 5.54686i) q^{64} +(0.782521 + 7.28930i) q^{65} +(4.75722 + 6.96962i) q^{66} +(-6.40031 + 3.26112i) q^{67} +(-0.917829 - 1.03261i) q^{68} +(1.62634 + 0.528429i) q^{69} +(3.67162 + 1.52508i) q^{70} +(-7.03596 + 2.28612i) q^{71} +(-1.50100 + 2.39729i) q^{72} +(-0.769583 - 4.85896i) q^{73} +(11.0754 + 0.325598i) q^{74} +(4.99194 - 0.283873i) q^{75} +(0.441280 - 7.49868i) q^{76} +(7.40945 - 1.17354i) q^{77} +(-2.22549 + 4.06764i) q^{78} +(-0.528568 - 1.62677i) q^{79} +(6.25705 + 6.39135i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-10.2676 - 10.8896i) q^{82} +(-1.79597 - 3.52479i) q^{83} +(1.35592 + 2.11758i) q^{84} +(-1.14558 + 1.03610i) q^{85} +(8.78568 + 6.78641i) q^{86} +(-8.31614 - 1.31715i) q^{87} +(16.3718 + 4.09766i) q^{88} +(-0.274839 + 0.378283i) q^{89} +(2.69465 + 1.65495i) q^{90} +(2.42286 + 3.33478i) q^{91} +(3.13325 - 1.37098i) q^{92} +(-3.62191 - 3.62191i) q^{93} +(-13.2960 - 4.75644i) q^{94} +(-8.38773 - 0.420890i) q^{95} +(0.941479 + 5.57796i) q^{96} +(1.79474 + 0.914467i) q^{97} +(-7.60169 + 0.975968i) q^{98} +5.96686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−0.180090	−	1.40270i	−0.127343	−	0.991859i
$2$	−0.180090	−	1.40270i	−0.127343	−	0.991859i
$3$	−0.891007	−	0.453990i	−0.514423	−	0.262112i
$3$	−0.891007	−	0.453990i	−0.514423	−	0.262112i
$4$	−1.93514	+	0.505225i	−0.967568	+	0.252613i
$5$	0.583536	+	2.15858i	0.260965	+	0.965348i
$5$	0.583536	+	2.15858i	0.260965	+	0.965348i
$6$	−0.476351	+	1.33157i	−0.194469	+	0.543613i
$7$	0.889008	+	0.889008i	0.336013	+	0.336013i	0.854865	−	0.518851i	$-0.173640\pi$
$7$	0.889008	+	0.889008i	0.336013	+	0.336013i	−0.518851	+	0.854865i	$0.673640\pi$
$8$	1.05718	+	2.62343i	0.373769	+	0.927522i
$9$	0.587785	+	0.809017i	0.195928	+	0.269672i
$10$	2.92276	−	1.20727i	0.924257	−	0.381771i
$11$	3.50723	−	4.82729i	1.05747	−	1.45548i	0.175321	−	0.984511i	$-0.443904\pi$
$11$	3.50723	−	4.82729i	1.05747	−	1.45548i	0.882149	−	0.470971i	$-0.156096\pi$
$12$	1.95359	+	0.428374i	0.563952	+	0.123661i
$13$	3.23824	+	0.512887i	0.898126	+	0.142249i	0.588394	−	0.808575i	$-0.299761\pi$
$13$	3.23824	+	0.512887i	0.898126	+	0.142249i	0.309732	+	0.950824i	$0.399761\pi$
$14$	1.08691	−	1.40711i	0.290489	−	0.376067i
$15$	0.460042	−	2.18823i	0.118782	−	0.564999i
$16$	3.48950	−	1.95536i	0.872374	−	0.488839i
$17$	0.313606	+	0.615487i	0.0760607	+	0.149277i	0.925905	−	0.377756i	$-0.123304\pi$
$17$	0.313606	+	0.615487i	0.0760607	+	0.149277i	−0.849844	+	0.527034i	$0.823304\pi$
$18$	1.02895	−	0.970182i	0.242527	−	0.228674i
$19$	−1.16061	+	3.57200i	−0.266263	+	0.819474i	0.725136	+	0.688605i	$0.241777\pi$
$19$	−1.16061	+	3.57200i	−0.266263	+	0.819474i	−0.991400	+	0.130869i	$0.958223\pi$
$20$	−2.21979	−	3.88233i	−0.496361	−	0.868116i
$21$	−0.388511	−	1.19571i	−0.0847800	−	0.260926i
$22$	−7.40286	−	4.05025i	−1.57829	−	0.863515i
$23$	−1.68898	+	0.267508i	−0.352177	+	0.0557793i	−0.330017	−	0.943975i	$-0.607054\pi$
$23$	−1.68898	+	0.267508i	−0.352177	+	0.0557793i	−0.0221601	+	0.999754i	$0.507054\pi$
$24$	0.249059	−	2.81744i	0.0508389	−	0.575108i
$25$	−4.31897	+	2.51922i	−0.863794	+	0.503845i
$26$	0.136251	−	4.63464i	0.0267210	−	0.908929i
$27$	−0.156434	−	0.987688i	−0.0301058	−	0.190081i
$28$	−2.16950	−	1.27120i	−0.409997	−	0.240234i
$29$	8.00770	−	2.60186i	1.48699	−	0.483153i	0.550799	−	0.834638i	$-0.314323\pi$
$29$	8.00770	−	2.60186i	1.48699	−	0.483153i	0.936194	+	0.351484i	$0.114323\pi$
$30$	−3.15228	−	0.251222i	−0.575525	−	0.0458666i
$31$	4.87146	+	1.58283i	0.874940	+	0.284285i	0.711855	−	0.702327i	$-0.247856\pi$
$31$	4.87146	+	1.58283i	0.874940	+	0.284285i	0.163085	+	0.986612i	$0.447856\pi$
$32$	−3.37120	−	4.54257i	−0.595950	−	0.803021i
$33$	−5.31651	+	2.70890i	−0.925485	+	0.471558i
$34$	0.806866	−	0.550738i	0.138376	−	0.0944509i
$35$	−1.40023	+	2.43777i	−0.236682	+	0.412058i
$36$	−1.54618	−	1.26859i	−0.257697	−	0.211432i
$37$	−1.22564	+	7.73839i	−0.201494	+	1.27218i	0.654843	+	0.755765i	$0.272735\pi$
$37$	−1.22564	+	7.73839i	−0.201494	+	1.27218i	−0.856337	+	0.516418i	$0.827265\pi$
$38$	5.21947	+	0.984711i	0.846709	+	0.159741i
$39$	−2.65245	−	1.92712i	−0.424731	−	0.308585i
$40$	−5.04599	+	3.81287i	−0.797841	+	0.602868i
$41$	8.56195	−	6.22062i	1.33715	−	0.971497i	0.337608	−	0.941287i	$-0.390382\pi$
$41$	8.56195	−	6.22062i	1.33715	−	0.971497i	0.999544	−	0.0302103i	$-0.00961769\pi$
$42$	−1.60726	+	0.760300i	−0.248006	+	0.117317i
$43$	−5.55076	+	5.55076i	−0.846482	+	0.846482i	−0.989692	−	0.143210i	$-0.954258\pi$
$43$	−5.55076	+	5.55076i	−0.846482	+	0.846482i	0.143210	+	0.989692i	$0.454258\pi$
$44$	−4.34810	+	11.1134i	−0.655500	+	1.67541i
$45$	−1.40334	+	1.74087i	−0.209197	+	0.259514i
$46$	0.679402	+	2.32096i	0.100172	+	0.342206i
$47$	4.53317	−	8.89684i	0.661230	−	1.29774i	−0.280009	−	0.959997i	$-0.590337\pi$
$47$	4.53317	−	8.89684i	0.661230	−	1.29774i	0.941239	−	0.337740i	$-0.109663\pi$
$48$	−3.99688	+	0.158038i	−0.576899	+	0.0228109i
$49$		−	5.41933i		−	0.774190i
$50$	4.31152	+	5.60453i	0.609741	+	0.792601i
$51$		−	0.690777i		−	0.0967281i
$52$	−6.52555	+	0.643534i	−0.904931	+	0.0892422i
$53$	−2.43953	+	4.78785i	−0.335096	+	0.657662i	−0.995656	−	0.0931109i	$-0.970319\pi$
$53$	−2.43953	+	4.78785i	−0.335096	+	0.657662i	0.660560	+	0.750773i	$0.270319\pi$
$54$	−1.35726	+	0.397304i	−0.184699	+	0.0540662i
$55$	12.4667	+	4.75375i	1.68101	+	0.640996i
$56$	−1.39241	+	3.27209i	−0.186068	+	0.437251i
$57$	2.65577	−	2.65577i	0.351765	−	0.351765i
$58$	−5.09174	−	10.7638i	−0.668578	−	1.41336i
$59$	−7.86506	+	5.71430i	−1.02394	+	0.743938i	−0.967087	−	0.254444i	$-0.918108\pi$
$59$	−7.86506	+	5.71430i	−1.02394	+	0.743938i	−0.0568557	+	0.998382i	$0.518108\pi$
$60$	0.215306	+	4.46695i	0.0277959	+	0.576681i
$61$	0.117440	+	0.0853253i	0.0150367	+	0.0109248i	0.595278	−	0.803520i	$-0.297042\pi$
$61$	0.117440	+	0.0853253i	0.0150367	+	0.0109248i	−0.580242	+	0.814444i	$0.697042\pi$
$62$	1.34294	−	7.11825i	0.170553	−	0.904018i
$63$	−0.196677	+	1.24177i	−0.0247789	+	0.156448i
$64$	−5.76475	+	5.54686i	−0.720594	+	0.693358i
$65$	0.782521	+	7.28930i	0.0970598	+	0.904126i
$66$	4.75722	+	6.96962i	0.585573	+	0.857901i
$67$	−6.40031	+	3.26112i	−0.781923	+	0.398409i	−0.798913	−	0.601446i	$-0.794591\pi$
$67$	−6.40031	+	3.26112i	−0.781923	+	0.398409i	0.0169907	+	0.999856i	$0.494591\pi$
$68$	−0.917829	−	1.03261i	−0.111303	−	0.125222i
$69$	1.62634	+	0.528429i	0.195788	+	0.0636154i
$70$	3.67162	+	1.52508i	0.438843	+	0.182283i
$71$	−7.03596	+	2.28612i	−0.835015	+	0.271313i	−0.695156	−	0.718859i	$-0.744665\pi$
$71$	−7.03596	+	2.28612i	−0.835015	+	0.271313i	−0.139859	+	0.990171i	$0.544665\pi$
$72$	−1.50100	+	2.39729i	−0.176895	+	0.282523i
$73$	−0.769583	−	4.85896i	−0.0900729	−	0.568698i	−0.990909	−	0.134538i	$-0.957045\pi$
$73$	−0.769583	−	4.85896i	−0.0900729	−	0.568698i	0.900836	−	0.434160i	$-0.142955\pi$
$74$	11.0754	+	0.325598i	1.28748	+	0.0378500i
$75$	4.99194	−	0.283873i	0.576419	−	0.0327789i
$76$	0.441280	−	7.49868i	0.0506183	−	0.860158i
$77$	7.40945	−	1.17354i	0.844386	−	0.133738i
$78$	−2.22549	+	4.06764i	−0.251987	+	0.460570i
$79$	−0.528568	−	1.62677i	−0.0594686	−	0.183026i	0.916909	−	0.399096i	$-0.130676\pi$
$79$	−0.528568	−	1.62677i	−0.0594686	−	0.183026i	−0.976378	+	0.216070i	$0.930676\pi$
$80$	6.25705	+	6.39135i	0.699559	+	0.714574i
$81$	−0.309017	+	0.951057i	−0.0343352	+	0.105673i
$82$	−10.2676	−	10.8896i	−1.13386	−	1.20255i
$83$	−1.79597	−	3.52479i	−0.197133	−	0.386896i	0.771187	−	0.636609i	$-0.219664\pi$
$83$	−1.79597	−	3.52479i	−0.197133	−	0.386896i	−0.968320	+	0.249713i	$0.919664\pi$
$84$	1.35592	+	2.11758i	0.147944	+	0.231047i
$85$	−1.14558	+	1.03610i	−0.124256	+	0.112381i
$86$	8.78568	+	6.78641i	0.947384	+	0.731797i
$87$	−8.31614	−	1.31715i	−0.891583	−	0.141213i
$88$	16.3718	+	4.09766i	1.74524	+	0.436812i
$89$	−0.274839	+	0.378283i	−0.0291329	+	0.0400980i	−0.823335	−	0.567556i	$-0.807889\pi$
$89$	−0.274839	+	0.378283i	−0.0291329	+	0.0400980i	0.794202	+	0.607654i	$0.207889\pi$
$90$	2.69465	+	1.65495i	0.284041	+	0.174447i
$91$	2.42286	+	3.33478i	0.253985	+	0.349580i
$92$	3.13325	−	1.37098i	0.326664	−	0.142934i
$93$	−3.62191	−	3.62191i	−0.375575	−	0.375575i
$94$	−13.2960	−	4.75644i	−1.37138	−	0.490589i
$95$	−8.38773	−	0.420890i	−0.860563	−	0.0431824i
$96$	0.941479	+	5.57796i	0.0960893	+	0.569298i
$97$	1.79474	+	0.914467i	0.182228	+	0.0928500i	0.542725	−	0.839911i	$-0.317393\pi$
$97$	1.79474	+	0.914467i	0.182228	+	0.0928500i	−0.360496	+	0.932761i	$0.617393\pi$
$98$	−7.60169	+	0.975968i	−0.767887	+	0.0985877i
$99$	5.96686			0.599692
$100$	7.08502	−	7.05709i	0.708502	−	0.705709i
$101$	−17.6890			−1.76012			−0.880059	−	0.474863i	$-0.842497\pi$
$101$	−17.6890			−1.76012			−0.880059	+	0.474863i	$0.842497\pi$
$102$	−0.968953	+	0.124402i	−0.0959406	+	0.0123176i
$103$	−1.62899	−	0.830010i	−0.160509	−	0.0817834i	0.371891	−	0.928277i	$-0.378710\pi$
$103$	−1.62899	−	0.830010i	−0.160509	−	0.0817834i	−0.532400	+	0.846493i	$0.678710\pi$
$104$	2.07787	+	9.03750i	0.203752	+	0.886200i
$105$	2.35434	−	1.53637i	0.229760	−	0.149935i
$106$	7.15526	+	2.55969i	0.694980	+	0.248619i
$107$	1.33025	+	1.33025i	0.128600	+	0.128600i	0.768477	−	0.639877i	$-0.221015\pi$
$107$	1.33025	+	1.33025i	0.128600	+	0.128600i	−0.639877	+	0.768477i	$0.721015\pi$
$108$	0.801727	+	1.83228i	0.0771462	+	0.176311i
$109$	−0.298615	−	0.411008i	−0.0286021	−	0.0393674i	0.794476	−	0.607295i	$-0.207745\pi$
$109$	−0.298615	−	0.411008i	−0.0286021	−	0.0393674i	−0.823079	+	0.567928i	$0.807745\pi$
$110$	4.42296	−	18.3432i	0.421713	−	1.74895i
$111$	4.60521	−	6.33852i	0.437107	−	0.601626i
$112$	4.84052	+	1.36386i	0.457386	+	0.128873i
$113$	−14.6234	−	2.31612i	−1.37566	−	0.217883i	−0.575563	−	0.817757i	$-0.695217\pi$
$113$	−14.6234	−	2.31612i	−1.37566	−	0.217883i	−0.800094	+	0.599875i	$0.795217\pi$
$114$	−4.20353	−	3.24697i	−0.393696	−	0.304107i
$115$	−1.56302	−	3.48970i	−0.145752	−	0.325417i
$116$	−14.1815	+	9.08064i	−1.31672	+	0.843117i
$117$	1.48846	+	2.92126i	0.137608	+	0.270070i
$118$	9.43187	+	10.0032i	0.868274	+	0.920872i
$119$	−0.268374	+	0.825971i	−0.0246018	+	0.0757166i
$120$	6.22702	−	1.10646i	0.568446	−	0.101006i
$121$	−7.60287	−	23.3992i	−0.691170	−	2.12720i
$122$	0.0985360	−	0.180100i	0.00892103	−	0.0163055i
$123$	−10.4529	+	1.65557i	−0.942502	+	0.149278i
$124$	−10.2266	−	0.601812i	−0.918377	−	0.0540444i
$125$	−7.95823	−	7.85280i	−0.711806	−	0.702376i
$126$	1.77725	+	0.0522483i	0.158330	+	0.00465464i
$127$	−0.348876	−	2.20271i	−0.0309577	−	0.195459i	0.967363	−	0.253396i	$-0.0815477\pi$
$127$	−0.348876	−	2.20271i	−0.0309577	−	0.195459i	−0.998320	+	0.0579371i	$0.981548\pi$
$128$	8.81876	+	7.08728i	0.779475	+	0.626433i
$129$	7.46575	−	2.42577i	0.657323	−	0.213577i
$130$	10.0838	−	2.41037i	0.884406	−	0.211404i
$131$	2.72290	+	0.884725i	0.237901	+	0.0772988i	0.425541	−	0.904939i	$-0.360084\pi$
$131$	2.72290	+	0.884725i	0.237901	+	0.0772988i	−0.187640	+	0.982238i	$0.560084\pi$
$132$	8.91956	−	7.92811i	0.776348	−	0.690054i
$133$	−4.20734	+	2.14374i	−0.364822	+	0.185886i
$134$	5.72701	+	8.39042i	0.494738	+	0.724822i
$135$	2.04072	−	0.914029i	0.175637	−	0.0786671i
$136$	−1.28315	+	1.47340i	−0.110029	+	0.126343i
$137$	−0.0950840	+	0.600336i	−0.00812357	+	0.0512902i	−0.991417	−	0.130737i	$-0.958266\pi$
$137$	−0.0950840	+	0.600336i	−0.00812357	+	0.0512902i	0.983294	+	0.182027i	$0.0582658\pi$
$138$	0.448340	−	2.37643i	0.0381653	−	0.202295i
$139$	16.0216	+	11.6404i	1.35894	+	0.987325i	0.998512	+	0.0545363i	$0.0173680\pi$
$139$	16.0216	+	11.6404i	1.35894	+	0.987325i	0.360424	+	0.932789i	$0.382632\pi$
$140$	1.47801	−	5.42484i	0.124915	−	0.458483i
$141$	−8.07816	+	5.86913i	−0.680304	+	0.494270i
$142$	4.47385	+	9.45763i	0.375437	+	0.793667i
$143$	13.8331	−	13.8331i	1.15678	−	1.15678i
$144$	3.63299	+	1.67373i	0.302749	+	0.139478i
$145$	10.2891	+	15.7670i	0.854465	+	1.30938i
$146$	−6.67706	+	1.95454i	−0.552598	+	0.161759i
$147$	−2.46032	+	4.82866i	−0.202924	+	0.398261i
$148$	−1.53785	−	15.5940i	−0.126410	−	1.28182i
$149$		−	9.98736i		−	0.818197i	−0.912490	−	0.409098i	$-0.865843\pi$
$149$		−	9.98736i		−	0.818197i	0.912490	−	0.409098i	$-0.134157\pi$
$150$	−1.29719	−	6.95106i	−0.105915	−	0.567552i
$151$		−	17.9578i		−	1.46139i	−0.682707	−	0.730693i	$-0.739197\pi$
$151$		−	17.9578i		−	1.46139i	0.682707	−	0.730693i	$-0.260803\pi$
$152$	−10.5979	+	0.731456i	−0.859601	+	0.0593289i
$153$	−0.313606	+	0.615487i	−0.0253536	+	0.0497591i
$154$	−2.98050	−	10.1819i	−0.240175	−	0.820481i
$155$	−0.574005	+	11.4391i	−0.0461052	+	0.918810i
$156$	6.10647	+	2.38915i	0.488909	+	0.191285i
$157$	−4.92861	+	4.92861i	−0.393346	+	0.393346i	−0.875878	−	0.482532i	$-0.839717\pi$
$157$	−4.92861	+	4.92861i	−0.393346	+	0.393346i	0.482532	+	0.875878i	$0.339717\pi$
$158$	−2.18668	+	1.03439i	−0.173963	+	0.0822915i
$159$	4.34728	−	3.15848i	0.344762	−	0.250484i
$160$	7.83831	−	9.92778i	0.619673	−	0.784860i
$161$	−1.73933	−	1.26370i	−0.137079	−	0.0995935i
$162$	1.38970	+	0.262182i	0.109185	+	0.0205990i
$163$	−1.20062	+	7.58039i	−0.0940395	+	0.593742i	0.894997	+	0.446072i	$0.147177\pi$
$163$	−1.20062	+	7.58039i	−0.0940395	+	0.593742i	−0.989037	+	0.147670i	$0.952823\pi$
$164$	−13.4257	+	16.3634i	−1.04837	+	1.27777i
$165$	−8.94976	−	9.89539i	−0.696738	−	0.770355i
$166$	−4.62078	+	3.15399i	−0.358642	+	0.244797i
$167$	14.7520	−	7.51654i	1.14155	−	0.581648i	0.222164	−	0.975009i	$-0.428688\pi$
$167$	14.7520	−	7.51654i	1.14155	−	0.581648i	0.919384	+	0.393362i	$0.128688\pi$
$168$	2.72614	−	2.28331i	0.210326	−	0.176161i
$169$	−2.14059	−	0.695521i	−0.164661	−	0.0535016i
$170$	1.65965	+	1.42031i	0.127289	+	0.108933i
$171$	−3.57200	+	1.16061i	−0.273158	+	0.0887544i
$172$	7.93708	−	13.5458i	0.605197	−	1.03286i
$173$	−2.89459	−	18.2757i	−0.220072	−	1.38948i	−0.812079	−	0.583547i	$-0.801664\pi$
$173$	−2.89459	−	18.2757i	−0.220072	−	1.38948i	0.592008	−	0.805932i	$-0.298336\pi$
$174$	−0.349907	+	11.9022i	−0.0265264	+	0.902307i
$175$	−6.07921	−	1.59999i	−0.459545	−	0.120948i
$176$	2.79939	−	23.7027i	0.211012	−	1.78666i
$177$	9.60205	−	1.52082i	0.721735	−	0.114312i
$178$	0.580114	+	0.317392i	0.0434814	+	0.0237895i
$179$	−4.10815	−	12.6436i	−0.307058	−	0.945026i	−0.978901	−	0.204333i	$-0.934497\pi$
$179$	−4.10815	−	12.6436i	−0.307058	−	0.945026i	0.671844	−	0.740693i	$-0.265503\pi$
$180$	1.83611	−	4.07783i	0.136856	−	0.303943i
$181$	4.57691	−	14.0863i	0.340199	−	1.04702i	−0.623905	−	0.781500i	$-0.714455\pi$
$181$	4.57691	−	14.0863i	0.340199	−	1.04702i	0.964104	−	0.265524i	$-0.0855450\pi$
$182$	4.24136	−	3.99911i	0.314391	−	0.296434i
$183$	−0.0659031	−	0.129342i	−0.00487170	−	0.00956124i
$184$	−2.48734	−	4.14811i	−0.183369	−	0.305803i
$185$	−17.4192	+	1.86998i	−1.28068	+	0.137484i
$186$	−4.42818	+	5.73272i	−0.324690	+	0.420344i
$187$	4.07102	+	0.644786i	0.297703	+	0.0471515i
$188$	−4.27738	+	19.5069i	−0.311960	+	1.42268i
$189$	0.738991	−	1.01713i	0.0537537	−	0.0739856i
$190$	0.920166	+	11.8413i	0.0667558	+	0.859056i
$191$	9.05720	+	12.4662i	0.655356	+	0.902021i	0.999317	−	0.0369636i	$-0.0117686\pi$
$191$	9.05720	+	12.4662i	0.655356	+	0.902021i	−0.343960	+	0.938984i	$0.611769\pi$
$192$	7.65465	−	2.32515i	0.552427	−	0.167803i
$193$	−9.28313	−	9.28313i	−0.668215	−	0.668215i	0.289088	−	0.957303i	$-0.406648\pi$
$193$	−9.28313	−	9.28313i	−0.668215	−	0.668215i	−0.957303	+	0.289088i	$0.906648\pi$
$194$	0.959507	−	2.68217i	0.0688886	−	0.192569i
$195$	2.61204	−	6.85007i	0.187052	−	0.490544i
$196$	2.73798	+	10.4871i	0.195570	+	0.749081i
$197$	18.4968	+	9.42459i	1.31784	+	0.671474i	0.964516	−	0.264026i	$-0.0850505\pi$
$197$	18.4968	+	9.42459i	1.31784	+	0.671474i	0.353327	+	0.935500i	$0.385050\pi$
$198$	−1.07457	−	8.36971i	−0.0763665	−	0.594810i
$199$	−5.43755			−0.385457			−0.192729	−	0.981252i	$-0.561734\pi$
$199$	−5.43755			−0.385457			−0.192729	+	0.981252i	$0.561734\pi$
$200$	−11.1749	−	8.66724i	−0.790186	−	0.612866i
$201$	7.18324			0.506667
$202$	3.18561	+	24.8123i	0.224139	+	1.74579i
$203$	9.43199	+	4.80584i	0.661996	+	0.337304i
$204$	0.348998	+	1.33675i	0.0244347	+	0.0935910i
$205$	18.4239	+	14.8517i	1.28678	+	1.03729i
$206$	−0.870891	+	2.43446i	−0.0606779	+	0.169617i
$207$	−1.20918	−	1.20918i	−0.0840435	−	0.0840435i
$208$	12.3027	−	4.54220i	0.853039	−	0.314945i
$209$	13.1726	+	18.1305i	0.911165	+	1.25411i
$210$	−2.57907	−	3.02574i	−0.177972	−	0.208796i
$211$	−6.08035	+	8.36889i	−0.418589	+	0.576138i	−0.965287	−	0.261192i	$-0.915885\pi$
$211$	−6.08035	+	8.36889i	−0.418589	+	0.576138i	0.546698	+	0.837330i	$0.315885\pi$
$212$	2.30188	−	10.4977i	0.158094	−	0.720982i
$213$	7.30696	+	1.15731i	0.500665	+	0.0792975i
$214$	1.62638	−	2.10550i	0.111177	−	0.143929i
$215$	−15.2208	−	8.74271i	−1.03805	−	0.596248i
$216$	2.42575	−	1.45456i	0.165051	−	0.0989701i
$217$	2.92361	+	5.73791i	0.198468	+	0.389515i
$218$	−0.522743	+	0.492886i	−0.0354047	+	0.0333824i
$219$	−1.52022	+	4.67875i	−0.102727	+	0.316160i
$220$	−26.5265	−	2.90067i	−1.78841	−	0.195563i
$221$	0.699857	+	2.15394i	0.0470775	+	0.144890i
$222$	−9.72040	−	5.31822i	−0.652391	−	0.356935i
$223$	2.70636	−	0.428646i	0.181232	−	0.0287043i	−0.0651589	−	0.997875i	$-0.520755\pi$
$223$	2.70636	−	0.428646i	0.181232	−	0.0287043i	0.246390	+	0.969171i	$0.420755\pi$
$224$	1.04136	−	7.03541i	0.0695787	−	0.470073i
$225$	−4.57672	−	2.01336i	−0.305115	−	0.134224i
$226$	−0.615291	+	20.9294i	−0.0409285	+	1.39220i
$227$	−0.660098	−	4.16770i	−0.0438123	−	0.276620i	0.956050	−	0.293203i	$-0.0947212\pi$
$227$	−0.660098	−	4.16770i	−0.0438123	−	0.276620i	−0.999862	+	0.0165832i	$0.994721\pi$
$228$	−3.79751	+	6.48104i	−0.251496	+	0.429217i
$229$	−3.60946	+	1.17279i	−0.238520	+	0.0774998i	−0.425838	−	0.904800i	$-0.640021\pi$
$229$	−3.60946	+	1.17279i	−0.238520	+	0.0774998i	0.187318	+	0.982299i	$0.440021\pi$
$230$	−4.61352	+	2.82091i	−0.304207	+	0.186005i
$231$	−7.13465	−	2.31819i	−0.469425	−	0.152526i
$232$	15.2914	+	18.2570i	1.00393	+	1.19863i
$233$	−16.3284	+	8.31976i	−1.06971	+	0.545045i	−0.897952	−	0.440093i	$-0.854945\pi$
$233$	−16.3284	+	8.31976i	−1.06971	+	0.545045i	−0.171760	+	0.985139i	$0.554945\pi$
$234$	3.82959	−	2.61395i	0.250348	−	0.170879i
$235$	21.8498	+	4.59359i	1.42533	+	0.299653i
$236$	12.3329	−	15.0316i	0.802806	−	0.978471i
$237$	−0.267579	+	1.68942i	−0.0173811	+	0.109740i
$238$	1.20692	+	0.227699i	0.0782331	+	0.0147596i
$239$	−9.01008	−	6.54621i	−0.582814	−	0.423439i	0.256924	−	0.966432i	$-0.417291\pi$
$239$	−9.01008	−	6.54621i	−0.582814	−	0.423439i	−0.839737	+	0.542993i	$0.817291\pi$
$240$	−2.67346	−	8.53537i	−0.172571	−	0.550956i
$241$	10.5335	−	7.65304i	0.678523	−	0.492976i	−0.194344	−	0.980933i	$-0.562258\pi$
$241$	10.5335	−	7.65304i	0.678523	−	0.492976i	0.872867	+	0.487958i	$0.162258\pi$
$242$	−31.4529	+	14.8785i	−2.02187	+	0.956427i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−0.270371	−	0.105782i	−0.0173087	−	0.00677201i
$245$	11.6981	−	3.16238i	0.747363	−	0.202037i
$246$	4.20472	+	14.3641i	0.268083	+	0.915819i
$247$	−5.59038	+	10.9717i	−0.355707	+	0.698115i
$248$	0.997551	+	14.4533i	0.0633445	+	0.917783i
$249$			3.95596i			0.250699i
$250$	−9.58193	+	12.5772i	−0.606014	+	0.795454i
$251$			4.07587i			0.257267i	0.991692	+	0.128633i	$0.0410590\pi$
$251$			4.07587i			0.257267i	−0.991692	+	0.128633i	$0.958941\pi$
$252$	−0.246776	−	2.50236i	−0.0155454	−	0.157634i
$253$	−4.63230	+	9.09141i	−0.291230	+	0.571572i
$254$	−3.02692	+	0.886055i	−0.189926	+	0.0555961i
$255$	1.49110	−	0.403093i	0.0933763	−	0.0252427i
$256$	8.35316	−	13.6464i	0.522072	−	0.852901i
$257$	−14.0123	+	14.0123i	−0.874061	+	0.874061i	−0.992912	−	0.118851i	$-0.962079\pi$
$257$	−14.0123	+	14.0123i	−0.874061	+	0.874061i	0.118851	+	0.992912i	$0.462079\pi$
$258$	−4.74713	−	10.0354i	−0.295544	−	0.624774i
$259$	−7.96909	+	5.78988i	−0.495175	+	0.359766i
$260$	−5.19702	−	13.7104i	−0.322306	−	0.850285i
$261$	6.81176	+	4.94903i	0.421637	+	0.306337i
$262$	0.750635	−	3.97875i	0.0463744	−	0.245808i
$263$	1.13644	−	7.17523i	0.0700762	−	0.442444i	−0.927557	−	0.373682i	$-0.878095\pi$
$263$	1.13644	−	7.17523i	0.0700762	−	0.442444i	0.997633	−	0.0687618i	$-0.0219048\pi$
$264$	−12.7271	−	11.0837i	−0.783298	−	0.682154i
$265$	−11.7585	−	2.47205i	−0.722322	−	0.151857i
$266$	3.76473	+	5.51556i	0.230830	+	0.338181i
$267$	0.416620	−	0.212279i	0.0254968	−	0.0129912i
$268$	10.7379	−	9.54431i	0.655920	−	0.583012i
$269$	−1.95436	−	0.635011i	−0.119160	−	0.0387173i	0.248830	−	0.968547i	$-0.419954\pi$
$269$	−1.95436	−	0.635011i	−0.119160	−	0.0387173i	−0.367990	+	0.929830i	$0.619954\pi$
$270$	−1.64962	−	2.69791i	−0.100393	−	0.164190i
$271$	−22.9587	+	7.45974i	−1.39464	+	0.453147i	−0.907455	−	0.420150i	$-0.861977\pi$
$271$	−22.9587	+	7.45974i	−1.39464	+	0.453147i	−0.487188	+	0.873297i	$0.661977\pi$
$272$	2.29782	+	1.53453i	0.139326	+	0.0930443i
$273$	−0.644825	−	4.07127i	−0.0390266	−	0.246404i
$274$	0.859216	+	0.0252596i	0.0519071	+	0.00152599i
$275$	−2.98660	+	29.6844i	−0.180099	+	1.79004i
$276$	−3.41416	−	0.200915i	−0.205508	−	0.0120937i
$277$	13.6780	−	2.16637i	0.821829	−	0.130165i	0.268661	−	0.963235i	$-0.413419\pi$
$277$	13.6780	−	2.16637i	0.821829	−	0.130165i	0.553168	+	0.833070i	$0.313419\pi$
$278$	13.4426	−	24.5698i	0.806236	−	1.47360i
$279$	1.58283	+	4.87146i	0.0947617	+	0.291647i
$280$	−7.87560	−	1.09625i	−0.470657	−	0.0655134i
$281$	−8.63244	+	26.5679i	−0.514968	+	1.58491i	0.268371	+	0.963316i	$0.413515\pi$
$281$	−8.63244	+	26.5679i	−0.514968	+	1.58491i	−0.783339	+	0.621594i	$0.786485\pi$
$282$	9.68742	+	10.2743i	0.576878	+	0.611824i
$283$	−0.0314980	−	0.0618183i	−0.00187236	−	0.00367472i	0.890068	−	0.455827i	$-0.150656\pi$
$283$	−0.0314980	−	0.0618183i	−0.00187236	−	0.00367472i	−0.891941	+	0.452152i	$0.850656\pi$
$284$	12.4605	−	7.97870i	0.739396	−	0.473449i
$285$	7.28244	+	4.18297i	0.431375	+	0.247778i
$286$	−21.8949	−	16.9125i	−1.29467	−	1.00006i
$287$	13.1418	+	2.08146i	0.775737	+	0.122865i
$288$	1.69348	−	5.39742i	0.0997891	−	0.318046i
$289$	9.71187	−	13.3672i	0.571287	−	0.786309i
$290$	20.2634	−	17.2720i	1.18991	−	1.01425i
$291$	−1.18397	−	1.62959i	−0.0694054	−	0.0955283i
$292$	3.94411	+	9.01392i	0.230812	+	0.527500i
$293$	13.8584	+	13.8584i	0.809614	+	0.809614i	0.984575	−	0.174961i	$-0.0559801\pi$
$293$	13.8584	+	13.8584i	0.809614	+	0.809614i	−0.174961	+	0.984575i	$0.555980\pi$
$294$	7.21624	+	2.58150i	0.420860	+	0.150556i
$295$	−16.9243	−	13.6429i	−0.985373	−	0.794320i
$296$	−21.5968	+	4.96547i	−1.25529	+	0.288612i
$297$	−5.31651	−	2.70890i	−0.308495	−	0.157186i
$298$	−14.0093	+	1.79863i	−0.811536	+	0.104192i
$299$	−5.60652			−0.324234
$300$	−9.51665	+	3.07138i	−0.549444	+	0.177326i
$301$	−9.86933			−0.568859
$302$	−25.1894	+	3.23402i	−1.44949	+	0.186097i
$303$	15.7610	+	8.03063i	0.905445	+	0.461347i
$304$	2.93459	+	14.7339i	0.168310	+	0.845048i
$305$	−0.115651	+	0.303295i	−0.00662217	+	0.0173666i
$306$	0.919821	+	0.329052i	0.0525826	+	0.0188107i
$307$	−14.4642	−	14.4642i	−0.825517	−	0.825517i	0.161376	−	0.986893i	$-0.448407\pi$
$307$	−14.4642	−	14.4642i	−0.825517	−	0.825517i	−0.986893	+	0.161376i	$0.948407\pi$
$308$	−13.7454	+	6.01440i	−0.783216	+	0.342703i
$309$	1.07462	+	1.47909i	0.0611331	+	0.0841425i
$310$	16.1490	−	1.25491i	0.917201	−	0.0712742i
$311$	−15.9923	+	22.0115i	−0.906840	+	1.24816i	0.0613941	+	0.998114i	$0.480445\pi$
$311$	−15.9923	+	22.0115i	−0.906840	+	1.24816i	−0.968234	+	0.250045i	$0.919555\pi$
$312$	2.25154	−	8.99581i	0.127468	−	0.509287i
$313$	33.5431	+	5.31270i	1.89597	+	0.300292i	0.991892	−	0.127083i	$-0.0405613\pi$
$313$	33.5431	+	5.31270i	1.89597	+	0.300292i	0.904075	+	0.427374i	$0.140561\pi$
$314$	7.80096	+	6.02577i	0.440234	+	0.340054i
$315$	−2.79523	+	0.300073i	−0.157493	+	0.0169072i
$316$	1.84473	+	2.88097i	0.103774	+	0.162067i
$317$	−15.3076	−	30.0429i	−0.859762	−	1.68738i	−0.716380	−	0.697711i	$-0.754202\pi$
$317$	−15.3076	−	30.0429i	−0.859762	−	1.68738i	−0.143382	−	0.989667i	$-0.545798\pi$
$318$	−5.21331	−	5.52912i	−0.292348	−	0.310058i
$319$	15.5249	−	47.7808i	0.869229	−	2.67521i
$320$	−15.3373	−	9.20690i	−0.857381	−	0.514681i
$321$	−0.581340	−	1.78918i	−0.0324472	−	0.0998623i
$322$	−1.45935	+	2.66734i	−0.0813267	+	0.148645i
$323$	−2.56250	+	0.405860i	−0.142581	+	0.0225826i
$324$	0.117492	−	1.99655i	0.00652734	−	0.110919i
$325$	−15.2779	+	5.94271i	−0.847468	+	0.329642i
$326$	10.8492	+	0.318950i	0.600883	+	0.0176650i
$327$	0.0794740	+	0.501779i	0.00439492	+	0.0277485i
$328$	25.3708	+	15.8853i	1.40087	+	0.877122i
$329$	11.9394	−	3.87934i	0.658239	−	0.213875i
$330$	−12.2685	+	14.3359i	−0.675359	+	0.789165i
$331$	0.541262	+	0.175867i	0.0297505	+	0.00966651i	0.323854	−	0.946107i	$-0.395021\pi$
$331$	0.541262	+	0.175867i	0.0297505	+	0.00966651i	−0.294104	+	0.955773i	$0.595021\pi$
$332$	5.25626	+	5.91357i	0.288474	+	0.324550i
$333$	−6.98090	+	3.55695i	−0.382551	+	0.194919i
$334$	−13.2002	−	19.3390i	−0.722280	−	1.05819i
$335$	−10.7742	−	11.9126i	−0.588659	−	0.650857i
$336$	−3.69375	−	3.41276i	−0.201511	−	0.186181i
$337$	−3.65964	+	23.1060i	−0.199353	+	1.25867i	0.661551	+	0.749900i	$0.269898\pi$
$337$	−3.65964	+	23.1060i	−0.199353	+	1.25867i	−0.860905	+	0.508766i	$0.830102\pi$
$338$	−0.590107	+	3.12787i	−0.0320976	+	0.170134i
$339$	11.9781	+	8.70258i	0.650560	+	0.472659i
$340$	1.69338	−	2.58378i	0.0918367	−	0.140125i
$341$	24.7261	−	17.9646i	1.33899	−	0.972836i
$342$	2.27128	+	4.80143i	0.122817	+	0.259632i
$343$	11.0409	−	11.0409i	0.596152	−	0.596152i
$344$	−20.4301	−	8.69387i	−1.10152	−	0.468742i
$345$	−0.191632	+	3.81895i	−0.0103171	+	0.205605i
$346$	−25.1141	+	7.35153i	−1.35014	+	0.395221i
$347$	−15.2550	+	29.9397i	−0.818933	+	1.60725i	−0.0246528	+	0.999696i	$0.507848\pi$
$347$	−15.2550	+	29.9397i	−0.818933	+	1.60725i	−0.794281	+	0.607551i	$0.792152\pi$
$348$	16.7583	−	1.65266i	0.898339	−	0.0885921i
$349$			1.82016i			0.0974309i	0.998813	+	0.0487154i	$0.0155127\pi$
$349$			1.82016i			0.0974309i	−0.998813	+	0.0487154i	$0.984487\pi$
$350$	−1.14950	+	8.81545i	−0.0614433	+	0.471206i
$351$		−	3.27860i		−	0.174999i
$352$	−33.7519	+	0.341917i	−1.79898	+	0.0182242i
$353$	7.29751	−	14.3222i	0.388407	−	0.762293i	−0.611166	−	0.791503i	$-0.709299\pi$
$353$	7.29751	−	14.3222i	0.388407	−	0.762293i	0.999573	+	0.0292100i	$0.00929914\pi$
$354$	−3.86248	−	13.1949i	−0.205289	−	0.701302i
$355$	−9.04052	−	13.8537i	−0.479821	−	0.735277i
$356$	0.340732	−	0.870885i	0.0180588	−	0.0461568i
$357$	0.614106	−	0.614106i	0.0325019	−	0.0325019i
$358$	−16.9953	+	8.03949i	−0.898231	+	0.424900i
$359$	13.1872	−	9.58103i	0.695992	−	0.505668i	−0.182633	−	0.983181i	$-0.558462\pi$
$359$	13.1872	−	9.58103i	0.695992	−	0.505668i	0.878624	+	0.477514i	$0.158462\pi$
$360$	−6.05064	−	1.84114i	−0.318897	−	0.0970366i
$361$	3.95914	+	2.87648i	0.208376	+	0.151394i
$362$	−20.5831	−	3.88323i	−1.08182	−	0.204098i
$363$	−3.84882	+	24.3005i	−0.202011	+	1.27544i
$364$	−6.37338	−	5.22916i	−0.334056	−	0.274083i
$365$	10.0394	−	4.49659i	0.525486	−	0.235362i
$366$	−0.169560	+	0.115736i	−0.00886303	+	0.00604959i
$367$	−4.47934	+	2.28234i	−0.233820	+	0.119137i	−0.566975	−	0.823735i	$-0.691887\pi$
$367$	−4.47934	+	2.28234i	−0.233820	+	0.119137i	0.333156	+	0.942872i	$0.391887\pi$
$368$	−5.37061	+	4.23603i	−0.279963	+	0.220818i
$369$	10.0652	+	3.27037i	0.523972	+	0.170249i
$370$	5.76004	+	24.0971i	0.299450	+	1.25275i
$371$	−6.42520	+	2.08768i	−0.333580	+	0.108387i
$372$	8.83876	+	5.17900i	0.458269	+	0.268519i
$373$	0.445750	+	2.81436i	0.0230801	+	0.145722i	0.996537	−	0.0831473i	$-0.0264972\pi$
$373$	0.445750	+	2.81436i	0.0230801	+	0.145722i	−0.973457	+	0.228869i	$0.926497\pi$
$374$	0.171291	−	5.82654i	0.00885725	−	0.301283i
$375$	3.52574	+	10.6099i	0.182068	+	0.547891i
$376$	28.1326	+	2.48689i	1.45083	+	0.128252i
$377$	27.2653	−	4.31840i	1.40424	−	0.222409i
$378$	−1.55982	−	0.853407i	−0.0802284	−	0.0438945i
$379$	4.96244	+	15.2728i	0.254903	+	0.784512i	0.993849	+	0.110746i	$0.0353241\pi$
$379$	4.96244	+	15.2728i	0.254903	+	0.784512i	−0.738945	+	0.673765i	$0.764676\pi$
$380$	16.4440	−	3.42321i	0.843561	−	0.175607i
$381$	−0.689161	+	2.12102i	−0.0353068	+	0.108663i
$382$	15.8552	−	14.9496i	0.811222	−	0.764887i
$383$	−15.1017	−	29.6388i	−0.771662	−	1.51447i	−0.855391	−	0.517983i	$-0.826683\pi$
$383$	−15.1017	−	29.6388i	−0.771662	−	1.51447i	0.0837286	−	0.996489i	$-0.473317\pi$
$384$	−4.64001	−	10.3184i	−0.236785	−	0.526561i
$385$	6.85687	+	15.3091i	0.349459	+	0.780225i
$386$	−11.3497	+	14.6933i	−0.577682	+	0.747867i
$387$	−7.75331	−	1.22800i	−0.394123	−	0.0624229i
$388$	−3.93508	−	0.862868i	−0.199773	−	0.0438055i
$389$	−11.6281	+	16.0047i	−0.589569	+	0.811472i	−0.994704	−	0.102785i	$-0.967225\pi$
$389$	−11.6281	+	16.0047i	−0.589569	+	0.811472i	0.405135	+	0.914257i	$0.367225\pi$
$390$	−10.0790	−	2.43028i	−0.510370	−	0.123062i
$391$	−0.694322	−	0.955652i	−0.0351134	−	0.0483294i
$392$	14.2172	−	5.72920i	0.718078	−	0.289368i
$393$	−2.02447	−	2.02447i	−0.102121	−	0.102121i
$394$	9.88878	−	27.6427i	0.498189	−	1.39262i
$395$	3.20307	−	2.09024i	0.161164	−	0.105171i
$396$	−11.5467	+	3.01461i	−0.580242	+	0.151490i
$397$	−14.4965	−	7.38633i	−0.727558	−	0.370709i	0.0506495	−	0.998716i	$-0.483871\pi$
$397$	−14.4965	−	7.38633i	−0.727558	−	0.370709i	−0.778208	+	0.628007i	$0.783871\pi$
$398$	0.979249	+	7.62725i	0.0490853	+	0.382319i
$399$	4.72200			0.236396
$400$	−10.1450	+	17.2360i	−0.507252	+	0.861798i
$401$	1.12938			0.0563985			0.0281992	−	0.999602i	$-0.491023\pi$
$401$	1.12938			0.0563985			0.0281992	+	0.999602i	$0.491023\pi$
$402$	−1.29363	−	10.0759i	−0.0645204	−	0.502542i
$403$	14.9631	+	7.62410i	0.745367	+	0.379783i
$404$	34.2306	−	8.93691i	1.70303	−	0.444628i
$405$	−2.23326	−	0.112063i	−0.110971	−	0.00556847i
$406$	5.04254	−	14.0957i	0.250257	−	0.699559i
$407$	33.0568	+	33.0568i	1.63857	+	1.63857i
$408$	1.81220	−	0.730274i	0.0897174	−	0.0361540i
$409$	−15.6753	−	21.5752i	−0.775093	−	1.06682i	−0.995806	−	0.0914855i	$-0.970838\pi$
$409$	−15.6753	−	21.5752i	−0.775093	−	1.06682i	0.220713	−	0.975339i	$-0.429162\pi$
$410$	17.5145	−	28.5179i	0.864982	−	1.40840i
$411$	0.357267	−	0.491736i	0.0176227	−	0.0242556i
$412$	3.57165	+	0.783177i	0.175963	+	0.0385844i
$413$	−12.0722	−	1.91204i	−0.594032	−	0.0940854i
$414$	−1.47835	+	1.91387i	−0.0726570	+	0.0940617i
$415$	6.56054	−	5.93359i	0.322044	−	0.291269i
$416$	−8.58694	−	16.4390i	−0.421009	−	0.805988i
$417$	−8.99074	−	17.6453i	−0.440279	−	0.864095i
$418$	23.0594	−	21.7423i	1.12787	−	1.06345i
$419$	1.24633	−	3.83581i	0.0608873	−	0.187392i	−0.915986	−	0.401210i	$-0.868590\pi$
$419$	1.24633	−	3.83581i	0.0608873	−	0.187392i	0.976874	+	0.213818i	$0.0685899\pi$
$420$	−3.77974	+	4.16256i	−0.184433	+	0.203112i
$421$	6.01598	+	18.5153i	0.293201	+	0.902380i	0.983820	+	0.179161i	$0.0573382\pi$
$421$	6.01598	+	18.5153i	0.293201	+	0.902380i	−0.690619	+	0.723219i	$0.742662\pi$
$422$	12.8341	+	7.02176i	0.624752	+	0.341814i
$423$	9.86222	−	1.56202i	0.479518	−	0.0759481i
$424$	−15.1396	−	1.33833i	−0.735245	−	0.0649949i
$425$	−2.90500	−	1.86822i	−0.140913	−	0.0906222i
$426$	0.307445	−	10.4579i	0.0148958	−	0.506687i
$427$	0.0285504	+	0.180260i	0.00138165	+	0.00872340i
$428$	−3.24629	−	1.90214i	−0.156915	−	0.0919432i
$429$	−18.6055	+	6.04529i	−0.898281	+	0.291869i
$430$	−9.52227	+	22.9247i	−0.459205	+	1.10553i
$431$	24.6627	+	8.01340i	1.18796	+	0.385992i	0.835318	−	0.549766i	$-0.185283\pi$
$431$	24.6627	+	8.01340i	1.18796	+	0.385992i	0.352642	+	0.935758i	$0.385283\pi$
$432$	−2.47716	−	3.14065i	−0.119182	−	0.151105i
$433$	19.3515	−	9.86010i	0.929976	−	0.473846i	0.0777221	−	0.996975i	$-0.475235\pi$
$433$	19.3515	−	9.86010i	0.929976	−	0.473846i	0.852254	+	0.523129i	$0.175235\pi$
$434$	7.52206	−	5.13430i	0.361070	−	0.246454i
$435$	−2.00960	−	18.7197i	−0.0963527	−	0.897540i
$436$	0.785512	+	0.644488i	0.0376192	+	0.0308654i
$437$	1.00471	−	6.34352i	0.0480620	−	0.303452i
$438$	6.83665	+	1.28981i	0.326668	+	0.0616296i
$439$	8.84102	+	6.42338i	0.421959	+	0.306571i	0.778426	−	0.627737i	$-0.216019\pi$
$439$	8.84102	+	6.42338i	0.421959	+	0.306571i	−0.356467	+	0.934308i	$0.616019\pi$
$440$	0.708394	+	37.7311i	0.0337714	+	1.79876i
$441$	4.38433	−	3.18540i	0.208778	−	0.151686i
$442$	2.89529	−	1.36959i	0.137715	−	0.0651449i
$443$	11.6714	−	11.6714i	0.554527	−	0.554527i	−0.373217	−	0.927744i	$-0.621745\pi$
$443$	11.6714	−	11.6714i	0.554527	−	0.554527i	0.927744	+	0.373217i	$0.121745\pi$
$444$	−5.70932	+	14.5926i	−0.270952	+	0.692533i
$445$	−0.976935	−	0.372521i	−0.0463112	−	0.0176592i
$446$	−1.08865	−	3.71902i	−0.0515491	−	0.176101i
$447$	−4.53417	+	8.89881i	−0.214459	+	0.420899i
$448$	−10.0561	−	0.193705i	−0.475107	−	0.00915168i
$449$		−	6.14595i		−	0.290045i	−0.989428	−	0.145023i	$-0.953674\pi$
$449$		−	6.14595i		−	0.290045i	0.989428	−	0.145023i	$-0.0463255\pi$
$450$	−1.99991	+	6.78236i	−0.0942769	+	0.319723i
$451$		−	63.1481i		−	2.97353i
$452$	29.4685	−	2.90611i	1.38608	−	0.136692i
$453$	−8.15267	+	16.0005i	−0.383046	+	0.751770i
$454$	−5.72715	+	1.67648i	−0.268788	+	0.0786811i
$455$	−5.78458	+	7.17591i	−0.271185	+	0.336412i
$456$	9.77485	+	4.15960i	0.457749	+	0.194791i
$457$	−17.1334	+	17.1334i	−0.801466	+	0.801466i	−0.983325	−	0.181859i	$-0.941789\pi$
$457$	−17.1334	+	17.1334i	−0.801466	+	0.801466i	0.181859	+	0.983325i	$0.441789\pi$
$458$	2.29509	+	4.85179i	0.107243	+	0.226709i
$459$	0.558850	−	0.406028i	0.0260849	−	0.0189518i
$460$	4.78774	+	5.96337i	0.223230	+	0.278044i
$461$	20.6031	+	14.9690i	0.959581	+	0.697176i	0.953053	−	0.302802i	$-0.0979222\pi$
$461$	20.6031	+	14.9690i	0.959581	+	0.697176i	0.00652765	+	0.999979i	$0.497922\pi$
$462$	−1.96684	+	10.4253i	−0.0915058	+	0.485027i
$463$	1.06522	−	6.72555i	0.0495051	−	0.312563i	−0.950493	−	0.310745i	$-0.899421\pi$
$463$	1.06522	−	6.72555i	0.0495051	−	0.312563i	0.999998	−	0.00181762i	$-0.000578566\pi$
$464$	22.8553	−	24.7371i	1.06103	−	1.14839i
$465$	5.70468	−	9.93171i	0.264548	−	0.460572i
$466$	14.6107	+	21.4056i	0.676828	+	0.991595i
$467$	19.1476	−	9.75620i	0.886046	−	0.451463i	0.0491291	−	0.998792i	$-0.484355\pi$
$467$	19.1476	−	9.75620i	0.886046	−	0.451463i	0.836917	+	0.547329i	$0.184355\pi$
$468$	−4.35625	−	4.90102i	−0.201368	−	0.226550i
$469$	−8.58909	−	2.79077i	−0.396607	−	0.128866i
$470$	2.50849	−	31.4760i	0.115708	−	1.45188i
$471$	6.62897	−	2.15388i	0.305447	−	0.0992457i
$472$	−23.3058	−	14.5924i	−1.07274	−	0.671669i
$473$	7.32732	+	46.2629i	0.336911	+	2.12717i
$474$	2.41794	+	0.0710837i	0.111060	+	0.00326498i
$475$	−3.98602	−	18.3512i	−0.182891	−	0.842012i
$476$	0.102039	−	1.73395i	0.00467696	−	0.0794757i
$477$	−5.30738	+	0.840606i	−0.243008	+	0.0384887i
$478$	−7.55974	+	13.8174i	−0.345774	+	0.631991i
$479$	−8.36276	−	25.7379i	−0.382104	−	1.17600i	−0.938559	−	0.345118i	$-0.887839\pi$
$479$	−8.36276	−	25.7379i	−0.382104	−	1.17600i	0.556455	−	0.830878i	$-0.312161\pi$
$480$	−11.4911	+	5.28720i	−0.524495	+	0.241327i
$481$	−7.93783	+	24.4301i	−0.361934	+	1.11392i
$482$	−12.6319	−	13.3971i	−0.575368	−	0.610222i
$483$	0.976050	+	1.91561i	0.0444118	+	0.0871631i
$484$	26.5344	+	41.4395i	1.20611	+	1.88361i
$485$	−0.926656	+	4.40773i	−0.0420773	+	0.200145i
$486$	−1.11920	−	0.864516i	−0.0507680	−	0.0392152i
$487$	−1.89556	−	0.300227i	−0.0858958	−	0.0136046i	0.113339	−	0.993556i	$-0.463846\pi$
$487$	−1.89556	−	0.300227i	−0.0858958	−	0.0136046i	−0.199234	+	0.979952i	$0.563846\pi$
$488$	−0.0996896	+	0.398300i	−0.00451273	+	0.0180302i
$489$	4.51118	−	6.20911i	0.204003	−	0.280786i
$490$	−6.54257	−	15.8394i	−0.295563	−	0.715550i
$491$	22.7182	+	31.2689i	1.02526	+	1.41114i	0.908452	+	0.417989i	$0.137265\pi$
$491$	22.7182	+	31.2689i	1.02526	+	1.41114i	0.116804	+	0.993155i	$0.462735\pi$
$492$	19.3912	−	8.48479i	0.874225	−	0.382524i
$493$	4.11268	+	4.11268i	0.185226	+	0.185226i
$494$	16.3968	+	5.86572i	0.737728	+	0.263911i
$495$	3.48188	+	12.8800i	0.156499	+	0.578911i
$496$	20.0939	−	4.00215i	0.902244	−	0.179702i
$497$	−8.28740	−	4.22264i	−0.371741	−	0.189411i
$498$	5.54903	−	0.712430i	0.248658	−	0.0319248i
$499$	−6.28177			−0.281211			−0.140605	−	0.990066i	$-0.544905\pi$
$499$	−6.28177			−0.281211			−0.140605	+	0.990066i	$0.544905\pi$
$500$	19.3677	+	11.1755i	0.866149	+	0.499785i
$501$	−16.5566			−0.739695
$502$	5.71722	−	0.734024i	0.255172	−	0.0327611i
$503$	5.14067	+	2.61930i	0.229211	+	0.116789i	0.564825	−	0.825211i	$-0.308944\pi$
$503$	5.14067	+	2.61930i	0.229211	+	0.116789i	−0.335614	+	0.942000i	$0.608944\pi$
$504$	−3.46561	+	0.796803i	−0.154371	+	0.0354924i
$505$	−10.3222	−	38.1831i	−0.459330	−	1.69913i
$506$	13.5868	+	4.86046i	0.604005	+	0.216074i
$507$	1.59152	+	1.59152i	0.0706820	+	0.0706820i
$508$	1.78799	+	4.08629i	0.0793291	+	0.181300i
$509$	−6.31391	−	8.69035i	−0.279859	−	0.385193i	0.645828	−	0.763483i	$-0.276512\pi$
$509$	−6.31391	−	8.69035i	−0.279859	−	0.385193i	−0.925687	+	0.378290i	$0.876512\pi$
$510$	−0.833952	−	2.01897i	−0.0369280	−	0.0894016i
$511$	3.63549	−	5.00382i	0.160824	−	0.221356i
$512$	−20.6462	−	9.25939i	−0.912440	−	0.409211i
$513$	3.70959	+	0.587541i	0.163782	+	0.0259406i
$514$	22.1785	+	17.1315i	0.978250	+	0.755639i
$515$	0.841074	−	4.00065i	0.0370622	−	0.176290i
$516$	−13.2217	+	8.46607i	−0.582052	+	0.372698i
$517$	−27.0488	−	53.0862i	−1.18960	−	2.33473i
$518$	9.55662	+	10.1355i	0.419894	+	0.445330i
$519$	−5.71791	+	17.5979i	−0.250989	+	0.772463i
$520$	−18.2957	+	9.75897i	−0.802319	+	0.427959i
$521$	−7.60669	−	23.4110i	−0.333255	−	1.02565i	−0.967575	−	0.252584i	$-0.918720\pi$
$521$	−7.60669	−	23.4110i	−0.333255	−	1.02565i	0.634320	−	0.773071i	$-0.281280\pi$
$522$	5.71528	−	10.4461i	0.250151	−	0.457215i
$523$	−34.1236	+	5.40465i	−1.49212	+	0.236329i	−0.848574	−	0.529076i	$-0.822538\pi$
$523$	−34.1236	+	5.40465i	−1.49212	+	0.236329i	−0.643548	+	0.765405i	$0.722538\pi$
$524$	−5.71617	−	0.336383i	−0.249712	−	0.0146950i
$525$	4.69024	+	4.18550i	0.204699	+	0.182670i
$526$	−10.2694	−	0.301903i	−0.447765	−	0.0131636i
$527$	0.553507	+	3.49470i	0.0241111	+	0.152232i
$528$	−13.2551	+	19.8484i	−0.576853	+	0.863789i
$529$	−19.0932	+	6.20376i	−0.830139	+	0.269729i
$530$	−1.34995	+	16.9389i	−0.0586381	+	0.735779i
$531$	−9.24593	−	3.00418i	−0.401239	−	0.130371i
$532$	7.05869	−	6.27409i	0.306033	−	0.272016i
$533$	30.9161	−	15.7525i	1.33912	−	0.682318i
$534$	−0.372793	−	0.546164i	−0.0161323	−	0.0236348i
$535$	−2.09521	+	3.64770i	−0.0905836	+	0.157704i
$536$	−15.3216	−	13.3432i	−0.661792	−	0.576337i
$537$	−2.07968	+	13.1306i	−0.0897448	+	0.566626i
$538$	−0.538769	+	2.85575i	−0.0232280	+	0.123120i
$539$	−26.1607	−	19.0068i	−1.12682	−	0.818683i
$540$	−3.48728	+	2.79979i	−0.150069	+	0.120484i
$541$	−9.35734	+	6.79850i	−0.402303	+	0.292290i	−0.770478	−	0.637466i	$-0.779983\pi$
$541$	−9.35734	+	6.79850i	−0.402303	+	0.292290i	0.368175	+	0.929756i	$0.379983\pi$
$542$	14.5984	+	30.8608i	0.627056	+	1.32558i
$543$	−10.4731	+	10.4731i	−0.449443	+	0.449443i
$544$	1.73866	−	3.49951i	0.0745446	−	0.150040i
$545$	0.712943	−	0.884423i	0.0305391	−	0.0378845i
$546$	−5.59464	+	1.63769i	−0.239428	+	0.0700867i
$547$	13.5824	−	26.6569i	0.580741	−	1.13977i	−0.394556	−	0.918872i	$-0.629102\pi$
$547$	13.5824	−	26.6569i	0.580741	−	1.13977i	0.975297	−	0.220897i	$-0.0708984\pi$
$548$	−0.119305	−	1.20977i	−0.00509644	−	0.0516789i
$549$			0.145164i			0.00619545i
$550$	42.1762	−	1.15656i	1.79840	−	0.0493160i
$551$			31.6233i			1.34720i
$552$	0.333033	+	4.82523i	0.0141748	+	0.205375i
$553$	0.976307	−	1.91611i	0.0415168	−	0.0814813i
$554$	−5.50204	−	18.7959i	−0.233759	−	0.798562i
$555$	16.3695	+	6.24197i	0.694848	+	0.264957i
$556$	−36.8850	−	14.4312i	−1.56427	−	0.612019i
$557$	−11.3351	+	11.3351i	−0.480282	+	0.480282i	−0.905222	−	0.424939i	$-0.860295\pi$
$557$	−11.3351	+	11.3351i	−0.480282	+	0.480282i	0.424939	+	0.905222i	$0.360295\pi$
$558$	6.54814	−	3.09754i	0.277205	−	0.131129i
$559$	−20.8216	+	15.1278i	−0.880659	+	0.639836i
$560$	−0.119391	+	11.2445i	−0.00504520	+	0.475168i
$561$	−3.33458	−	2.42271i	−0.140786	−	0.102287i
$562$	38.8215	+	7.32411i	1.63758	+	0.308949i
$563$	−3.57340	+	22.5616i	−0.150601	+	0.950857i	0.790434	+	0.612547i	$0.209855\pi$
$563$	−3.57340	+	22.5616i	−0.150601	+	0.950857i	−0.941035	+	0.338309i	$0.890145\pi$
$564$	12.6671	−	15.4388i	0.533381	−	0.650093i
$565$	−3.53375	−	32.9175i	−0.148666	−	1.38485i
$566$	−0.0810401	+	0.0553151i	−0.00340637	+	0.00232507i
$567$	−1.12022	+	0.570778i	−0.0470446	+	0.0239704i
$568$	−13.4357	−	16.0415i	−0.563751	−	0.673086i
$569$	−25.9715	−	8.43866i	−1.08878	−	0.353767i	−0.291007	−	0.956721i	$-0.593990\pi$
$569$	−25.9715	−	8.43866i	−1.08878	−	0.353767i	−0.797776	+	0.602954i	$0.793990\pi$
$570$	4.55595	−	10.9684i	0.190828	−	0.459416i
$571$	−29.6950	+	9.64848i	−1.24270	+	0.403776i	−0.855298	−	0.518136i	$-0.826626\pi$
$571$	−29.6950	+	9.64848i	−1.24270	+	0.403776i	−0.387398	+	0.921913i	$0.626626\pi$
$572$	−19.7801	+	33.7578i	−0.827047	+	1.41148i
$573$	−2.41050	−	15.2193i	−0.100700	−	0.635796i
$574$	0.552951	−	18.8089i	0.0230797	−	0.785067i
$575$	6.62074	−	5.41028i	0.276104	−	0.225624i
$576$	−7.87594	−	1.40342i	−0.328164	−	0.0584757i
$577$	22.2278	−	3.52054i	0.925356	−	0.146562i	0.324469	−	0.945896i	$-0.394814\pi$
$577$	22.2278	−	3.52054i	0.925356	−	0.146562i	0.600886	+	0.799334i	$0.294814\pi$
$578$	−20.4993	−	11.2155i	−0.852657	−	0.466505i
$579$	4.05688	+	12.4858i	0.168598	+	0.518892i
$580$	−27.8767	−	25.3130i	−1.15752	−	1.05106i
$581$	1.53693	−	4.73020i	0.0637628	−	0.196242i
$582$	−2.07261	+	1.95422i	−0.0859123	+	0.0810052i
$583$	14.5564	+	28.5684i	0.602862	+	1.18318i
$584$	11.9335	−	7.15573i	0.493813	−	0.296106i
$585$	−5.43721	+	4.91762i	−0.224801	+	0.203318i
$586$	16.9434	−	21.9349i	0.699924	−	0.906121i
$587$	−15.9467	−	2.52570i	−0.658190	−	0.104247i	−0.181599	−	0.983373i	$-0.558127\pi$
$587$	−15.9467	−	2.52570i	−0.658190	−	0.104247i	−0.476590	+	0.879126i	$0.658127\pi$
$588$	2.32150	−	10.5871i	0.0957371	−	0.436606i
$589$	−11.3078	+	15.5638i	−0.465928	+	0.641296i
$590$	−16.0890	+	26.1967i	−0.662372	+	1.07850i
$591$	−12.2021	−	16.7947i	−0.501927	−	0.690843i
$592$	10.8544	+	29.3996i	0.446115	+	1.20832i
$593$	−5.08886	−	5.08886i	−0.208974	−	0.208974i	0.594857	−	0.803831i	$-0.297209\pi$
$593$	−5.08886	−	5.08886i	−0.208974	−	0.208974i	−0.803831	+	0.594857i	$0.797209\pi$
$594$	−2.84232	+	7.94531i	−0.116622	+	0.326000i
$595$	−1.93953	−	0.0973243i	−0.0795131	−	0.00398991i
$596$	5.04587	+	19.3269i	0.206687	+	0.791661i
$597$	4.84489	+	2.46859i	0.198288	+	0.101033i
$598$	1.00968	+	7.86427i	0.0412889	+	0.321594i
$599$	−31.4074			−1.28327			−0.641636	−	0.767009i	$-0.721744\pi$
$599$	−31.4074			−1.28327			−0.641636	+	0.767009i	$0.721744\pi$
$600$	6.02209	+	12.7959i	0.245851	+	0.522390i
$601$	−10.7189			−0.437232			−0.218616	−	0.975811i	$-0.570154\pi$
$601$	−10.7189			−0.437232			−0.218616	+	0.975811i	$0.570154\pi$
$602$	1.77737	+	13.8437i	0.0724402	+	0.564228i
$603$	−6.40031	−	3.26112i	−0.260641	−	0.132803i
$604$	9.07273	+	34.7508i	0.369164	+	1.41399i
$605$	46.0726	−	30.0657i	1.87312	−	1.22235i
$606$	8.42616	−	23.5542i	0.342289	−	0.956823i
$607$	2.32027	+	2.32027i	0.0941769	+	0.0941769i	0.752626	−	0.658449i	$-0.228787\pi$
$607$	2.32027	+	2.32027i	0.0941769	+	0.0941769i	−0.658449	+	0.752626i	$0.728787\pi$
$608$	20.1388	−	6.76978i	0.816735	−	0.274551i
$609$	−6.22216	−	8.56406i	−0.252134	−	0.347033i
$610$	0.446259	+	0.107604i	0.0180685	+	0.00435674i
$611$	19.2425	−	26.4851i	0.778470	−	1.07147i
$612$	0.295911	−	1.34949i	0.0119615	−	0.0545500i
$613$	−17.1447	−	2.71546i	−0.692469	−	0.109676i	−0.199727	−	0.979852i	$-0.564005\pi$
$613$	−17.1447	−	2.71546i	−0.692469	−	0.109676i	−0.492742	+	0.870175i	$0.664005\pi$
$614$	−17.6841	+	22.8938i	−0.713672	+	0.923920i
$615$	−9.67330	−	21.5973i	−0.390065	−	0.870886i
$616$	10.9118	+	18.1975i	0.439650	+	0.733199i
$617$	−16.9930	−	33.3506i	−0.684112	−	1.34264i	−0.927905	−	0.372817i	$-0.878392\pi$
$617$	−16.9930	−	33.3506i	−0.684112	−	1.34264i	0.243793	−	0.969827i	$-0.421608\pi$
$618$	1.88119	−	1.77374i	0.0756726	−	0.0713503i
$619$	−6.63246	+	20.4126i	−0.266581	+	0.820452i	0.724744	+	0.689018i	$0.241958\pi$
$619$	−6.63246	+	20.4126i	−0.266581	+	0.820452i	−0.991325	+	0.131434i	$0.958042\pi$
$620$	−4.66854	−	22.4262i	−0.187493	−	0.900657i
$621$	0.528429	+	1.62634i	0.0212051	+	0.0652627i
$622$	33.7556	+	18.4683i	1.35348	+	0.740513i
$623$	−0.580631	+	0.0919629i	−0.0232625	+	0.00368442i
$624$	−13.0239	−	1.53818i	−0.521373	−	0.0615764i
$625$	12.3070	−	21.7609i	0.492281	−	0.870436i
$626$	1.41135	−	48.0076i	0.0564088	−	1.91877i
$627$	−3.50577	−	22.1346i	−0.140007	−	0.883970i
$628$	7.04747	−	12.0276i	0.281225	−	0.479953i
$629$	−5.14724	+	1.67244i	−0.205234	+	0.0666846i
$630$	0.924306	+	3.86683i	0.0368252	+	0.154058i
$631$	44.1934	+	14.3593i	1.75931	+	0.571635i	0.997129	−	0.0757265i	$-0.0241276\pi$
$631$	44.1934	+	14.3593i	1.75931	+	0.571635i	0.762183	+	0.647362i	$0.224128\pi$
$632$	3.70891	−	3.10644i	0.147533	−	0.123568i
$633$	9.21703	−	4.69631i	0.366344	−	0.186662i
$634$	−39.3844	+	26.8824i	−1.56416	+	1.06764i
$635$	4.55116	−	2.03844i	0.180607	−	0.0808931i
$636$	−6.81683	+	8.30845i	−0.270305	+	0.329451i
$637$	2.77950	−	17.5491i	0.110128	−	0.695320i
$638$	−69.8181	−	13.1720i	−2.76412	−	0.521483i
$639$	−5.98514	−	4.34846i	−0.236769	−	0.172022i
$640$	−10.1524	+	23.1717i	−0.401310	+	0.915942i
$641$	−34.1067	+	24.7799i	−1.34713	+	0.978749i	−0.347983	+	0.937501i	$0.613133\pi$
$641$	−34.1067	+	24.7799i	−1.34713	+	0.978749i	−0.999149	+	0.0412481i	$0.986867\pi$
$642$	−2.40499	+	1.13766i	−0.0949174	+	0.0448998i
$643$	−16.5201	+	16.5201i	−0.651489	+	0.651489i	−0.953352	−	0.301862i	$-0.902392\pi$
$643$	−16.5201	+	16.5201i	−0.651489	+	0.651489i	0.301862	+	0.953352i	$0.402392\pi$
$644$	4.00430	+	1.56667i	0.157791	+	0.0617356i
$645$	9.59276	+	14.6999i	0.377715	+	0.578809i
$646$	1.03078	+	3.52132i	0.0405555	+	0.138545i
$647$	14.8096	−	29.0654i	0.582225	−	1.14268i	−0.392600	−	0.919709i	$-0.628424\pi$
$647$	14.8096	−	29.0654i	0.582225	−	1.14268i	0.974825	−	0.222971i	$-0.0715755\pi$
$648$	−2.82171	+	0.194752i	−0.110847	+	0.00765059i
$649$			58.0083i			2.27702i
$650$	11.0872	+	20.3601i	0.434877	+	0.798590i
$651$		−	6.43981i		−	0.252396i
$652$	−1.50645	−	15.2757i	−0.0589971	−	0.598241i
$653$	19.1784	−	37.6397i	0.750508	−	1.47295i	−0.126238	−	0.992000i	$-0.540290\pi$
$653$	19.1784	−	37.6397i	0.750508	−	1.47295i	0.876746	−	0.480954i	$-0.159710\pi$
$654$	0.689533	−	0.201844i	0.0269629	−	0.00789271i
$655$	−0.320840	+	6.39388i	−0.0125363	+	0.249830i
$656$	17.7133	−	38.4485i	0.691590	−	1.50116i
$657$	3.47863	−	3.47863i	0.135714	−	0.135714i
$658$	−7.59172	−	16.0487i	−0.295956	−	0.625645i
$659$	−4.38671	+	3.18713i	−0.170882	+	0.124153i	−0.669939	−	0.742416i	$-0.733680\pi$
$659$	−4.38671	+	3.18713i	−0.170882	+	0.124153i	0.499057	+	0.866569i	$0.333680\pi$
$660$	22.3184	+	14.6273i	0.868742	+	0.569366i
$661$	25.3251	+	18.3997i	0.985031	+	0.715667i	0.958827	−	0.283990i	$-0.0916583\pi$
$661$	25.3251	+	18.3997i	0.985031	+	0.715667i	0.0262033	+	0.999657i	$0.491658\pi$
$662$	0.149212	−	0.790900i	0.00579930	−	0.0307392i
$663$	0.354290	−	2.23690i	0.0137595	−	0.0868740i
$664$	7.34837	−	8.43793i	0.285172	−	0.327455i
$665$	−7.08258	−	7.83093i	−0.274651	−	0.303671i
$666$	6.24652	+	9.15154i	0.242048	+	0.354615i
$667$	−12.8288	+	6.53662i	−0.496734	+	0.253099i
$668$	−24.7497	+	21.9986i	−0.957593	+	0.851153i
$669$	−2.60599	−	0.846737i	−0.100753	−	0.0327368i
$670$	−14.7695	+	17.2583i	−0.570596	+	0.666748i
$671$	0.823780	−	0.267662i	0.0318017	−	0.0103330i
$672$	−4.12187	+	5.79583i	−0.159004	+	0.223579i
$673$	−1.99690	−	12.6079i	−0.0769748	−	0.485999i	−0.995817	−	0.0913737i	$-0.970874\pi$
$673$	−1.99690	−	12.6079i	−0.0769748	−	0.485999i	0.918842	−	0.394626i	$-0.129126\pi$
$674$	33.0699	+	0.972203i	1.27381	+	0.0374478i
$675$	3.16384	+	3.87170i	0.121776	+	0.149022i
$676$	4.49373	+	0.264446i	0.172836	+	0.0101710i
$677$	−6.23648	+	0.987761i	−0.239687	+	0.0379627i	−0.275122	−	0.961409i	$-0.588718\pi$
$677$	−6.23648	+	0.987761i	−0.239687	+	0.0379627i	0.0354350	+	0.999372i	$0.488718\pi$
$678$	10.0500	−	18.3689i	0.385967	−	0.705453i
$679$	0.782572	+	2.40851i	0.0300323	+	0.0924300i
$680$	−3.92923	−	1.91000i	−0.150679	−	0.0732451i
$681$	−1.30394	+	4.01312i	−0.0499672	+	0.153783i
$682$	−29.6518	−	31.4481i	−1.13543	−	1.20421i
$683$	−12.2876	−	24.1159i	−0.470174	−	0.922768i	−0.997332	−	0.0730008i	$-0.976742\pi$
$683$	−12.2876	−	24.1159i	−0.470174	−	0.922768i	0.527158	−	0.849767i	$-0.323258\pi$
$684$	6.32594	−	4.05061i	0.241878	−	0.154879i
$685$	−1.35136	+	0.145071i	−0.0516329	+	0.00554289i
$686$	−17.4754	−	13.4987i	−0.667214	−	0.515382i
$687$	3.74849	+	0.593702i	0.143014	+	0.0226511i
$688$	−8.51563	+	30.2230i	−0.324655	+	1.15224i
$689$	−10.3554	+	14.2530i	−0.394510	+	0.542997i
$690$	5.39135	−	0.418953i	0.205245	−	0.0159493i
$691$	−2.65374	−	3.65256i	−0.100953	−	0.138950i	0.755552	−	0.655089i	$-0.227369\pi$
$691$	−2.65374	−	3.65256i	−0.100953	−	0.138950i	−0.856505	+	0.516139i	$0.827369\pi$
$692$	14.8348	+	33.9036i	0.563934	+	1.28882i
$693$	5.30458	+	5.30458i	0.201504	+	0.201504i
$694$	44.7437	+	16.0064i	1.69845	+	0.607595i
$695$	−15.7776	+	41.3766i	−0.598477	+	1.56950i
$696$	−5.33620	−	23.2092i	−0.202268	−	0.879744i
$697$	6.51379	+	3.31894i	0.246727	+	0.125714i
$698$	2.55314	−	0.327793i	0.0966376	−	0.0124071i
$699$	18.3258			0.693147
$700$	12.5724	+	0.0248261i	0.475194	+	0.000938337i
$701$	−11.3133			−0.427297			−0.213648	−	0.976911i	$-0.568535\pi$
$701$	−11.3133			−0.427297			−0.213648	+	0.976911i	$0.568535\pi$
$702$	−4.59890	+	0.590444i	−0.173574	+	0.0222849i
$703$	−26.2191	−	13.3593i	−0.988870	−	0.503855i
$704$	6.55799	+	47.2822i	0.247164	+	1.78202i
$705$	−17.3829	−	14.0125i	−0.654678	−	0.527743i
$706$	−21.4039	−	7.65694i	−0.805548	−	0.288173i
$707$	−15.7256	−	15.7256i	−0.591424	−	0.591424i
$708$	−17.8129	+	7.79418i	−0.669450	+	0.292923i
$709$	10.4295	+	14.3550i	0.391688	+	0.539113i	0.958634	−	0.284643i	$-0.0918750\pi$
$709$	10.4295	+	14.3550i	0.391688	+	0.539113i	−0.566945	+	0.823755i	$0.691875\pi$
$710$	−17.8044	+	15.1761i	−0.668189	+	0.569547i
$711$	1.00540	−	1.38381i	0.0377053	−	0.0518969i
$712$	−1.28295	−	0.321107i	−0.0480807	−	0.0120340i
$713$	−8.65121	−	1.37022i	−0.323991	−	0.0513151i
$714$	−0.972001	−	0.750812i	−0.0363762	−	0.0280984i
$715$	37.9320	+	21.7878i	1.41858	+	0.814818i
$716$	14.3377	+	22.3915i	0.535824	+	0.836810i
$717$	5.05613	+	9.92321i	0.188824	+	0.370589i
$718$	−15.8142	−	16.7722i	−0.590181	−	0.625932i
$719$	−1.37168	+	4.22158i	−0.0511549	+	0.157438i	−0.973371	−	0.229237i	$-0.926377\pi$
$719$	−1.37168	+	4.22158i	−0.0511549	+	0.157438i	0.922216	+	0.386676i	$0.126377\pi$
$720$	−1.49291	+	8.81880i	−0.0556374	+	0.328657i
$721$	−0.710297	−	2.18607i	−0.0264528	−	0.0814134i
$722$	3.32184	−	6.07151i	0.123626	−	0.225958i
$723$	−12.8598	+	2.03680i	−0.478262	+	0.0757493i
$724$	−1.74020	+	29.5712i	−0.0646739	+	1.09901i
$725$	−28.0304	+	31.4106i	−1.04102	+	1.16656i
$726$	34.7794	+	1.02246i	1.29079	+	0.0379470i
$727$	5.05252	+	31.9003i	0.187388	+	1.18312i	0.884634	+	0.466287i	$0.154408\pi$
$727$	5.05252	+	31.9003i	0.187388	+	1.18312i	−0.697246	+	0.716832i	$0.745592\pi$
$728$	−6.18716	+	9.88166i	−0.229312	+	0.366239i
$729$	−0.951057	+	0.309017i	−0.0352243	+	0.0114451i
$730$	−8.11536	−	13.2725i	−0.300363	−	0.491236i
$731$	−5.15717	−	1.67567i	−0.190745	−	0.0619767i
$732$	0.192878	+	0.216999i	0.00712899	+	0.00802050i
$733$	5.43837	−	2.77099i	0.200871	−	0.102349i	−0.350662	−	0.936502i	$-0.614043\pi$
$733$	5.43837	−	2.77099i	0.200871	−	0.102349i	0.551532	+	0.834153i	$0.314043\pi$
$734$	4.00812	+	5.87215i	0.147943	+	0.216745i
$735$	−11.8588	−	2.49312i	−0.437417	−	0.0919601i
$736$	6.90907	+	6.77049i	0.254672	+	0.249564i
$737$	−6.70499	+	42.3337i	−0.246982	+	1.55938i
$738$	2.77471	−	14.7074i	0.102139	−	0.541386i
$739$	32.0490	+	23.2850i	1.17894	+	0.856551i	0.992052	−	0.125830i	$-0.0401594\pi$
$739$	32.0490	+	23.2850i	1.17894	+	0.856551i	0.186889	+	0.982381i	$0.440159\pi$
$740$	32.7637	−	12.4193i	1.20442	−	0.456541i
$741$	9.96213	−	7.23791i	0.365968	−	0.265891i
$742$	4.08550	+	8.63667i	0.149983	+	0.317062i
$743$	−0.730435	+	0.730435i	−0.0267970	+	0.0267970i	−0.720378	−	0.693581i	$-0.756032\pi$
$743$	−0.730435	+	0.730435i	−0.0267970	+	0.0267970i	0.693581	+	0.720378i	$0.256032\pi$
$744$	5.67282	−	13.3308i	0.207976	−	0.488732i
$745$	21.5586	−	5.82799i	0.789845	−	0.213521i
$746$	3.86742	−	1.13209i	0.141596	−	0.0414488i
$747$	1.79597	−	3.52479i	0.0657111	−	0.128965i
$748$	−8.20374	+	0.809033i	−0.299958	+	0.0295812i
$749$			2.36520i			0.0864226i
$750$	14.2475	−	6.85629i	0.520245	−	0.250356i
$751$			19.6362i			0.716534i	0.933619	+	0.358267i	$0.116632\pi$
$751$			19.6362i			0.716534i	−0.933619	+	0.358267i	$0.883368\pi$
$752$	−1.57804	−	39.9094i	−0.0575451	−	1.45535i
$753$	1.85041	−	3.63163i	0.0674325	−	0.132344i
$754$	−10.9676	−	37.4674i	−0.399418	−	1.36448i
$755$	38.7634	−	10.4790i	1.41075	−	0.381371i
$756$	−0.916166	+	2.34165i	−0.0333206	+	0.0851649i
$757$	−10.8682	+	10.8682i	−0.395011	+	0.395011i	−0.876469	−	0.481458i	$-0.840107\pi$
$757$	−10.8682	+	10.8682i	−0.395011	+	0.395011i	0.481458	+	0.876469i	$0.340107\pi$
$758$	20.5295	−	9.71129i	0.745665	−	0.352730i
$759$	8.25483	−	5.99748i	0.299631	−	0.217695i
$760$	−7.76315	−	22.4496i	−0.281599	−	0.814331i
$761$	24.6400	+	17.9020i	0.893198	+	0.648946i	0.936710	−	0.350107i	$-0.113855\pi$
$761$	24.6400	+	17.9020i	0.893198	+	0.648946i	−0.0435121	+	0.999053i	$0.513855\pi$
$762$	3.09927	+	0.584711i	0.112275	+	0.0211819i
$763$	0.0999185	−	0.630860i	0.00361729	−	0.0228387i
$764$	−23.8251	−	19.5478i	−0.861963	−	0.707215i
$765$	−1.51158	−	0.317786i	−0.0546513	−	0.0114896i
$766$	−38.8547	+	26.5208i	−1.40388	+	0.958237i
$767$	−28.3997	+	14.4704i	−1.02545	+	0.522495i
$768$	−13.6381	+	8.36680i	−0.492121	+	0.301911i
$769$	34.1192	+	11.0860i	1.23037	+	0.399771i	0.850848	−	0.525411i	$-0.176089\pi$
$769$	34.1192	+	11.0860i	1.23037	+	0.399771i	0.379522	+	0.925183i	$0.376089\pi$
$770$	20.2393	−	12.3752i	0.729372	−	0.445970i
$771$	18.8464	−	6.12358i	0.678738	−	0.220535i
$772$	22.6542	+	13.2740i	0.815342	+	0.477743i
$773$	3.98308	+	25.1482i	0.143261	+	0.904517i	0.949691	+	0.313187i	$0.101397\pi$
$773$	3.98308	+	25.1482i	0.143261	+	0.904517i	−0.806430	+	0.591330i	$0.798603\pi$
$774$	−0.326226	+	11.0967i	−0.0117259	+	0.398863i
$775$	−25.0272	+	5.43609i	−0.899003	+	0.195270i
$776$	−0.501676	+	5.67513i	−0.0180091	+	0.203725i
$777$	9.72906	−	1.54093i	0.349028	−	0.0552806i
$778$	24.5439	+	13.4285i	0.879943	+	0.481434i
$779$	12.2830	+	37.8030i	0.440082	+	1.35443i
$780$	−1.59383	+	14.5755i	−0.0570681	+	0.521886i
$781$	−13.6410	+	41.9826i	−0.488112	+	1.50225i
$782$	−1.21545	+	1.14603i	−0.0434645	+	0.0409819i
$783$	−3.82251	−	7.50209i	−0.136605	−	0.268103i
$784$	−10.5967	−	18.9107i	−0.378455	−	0.675383i
$785$	−13.5148	−	7.76280i	−0.482366	−	0.277066i
$786$	−2.47513	+	3.20431i	−0.0882851	+	0.114294i
$787$	−24.3154	−	3.85118i	−0.866751	−	0.137280i	−0.292804	−	0.956172i	$-0.594588\pi$
$787$	−24.3154	−	3.85118i	−0.866751	−	0.137280i	−0.573947	+	0.818893i	$0.694588\pi$
$788$	−40.5553	−	8.89281i	−1.44472	−	0.316793i
$789$	−4.27007	+	5.87724i	−0.152018	+	0.209235i
$790$	−3.50882	−	4.11652i	−0.124838	−	0.146459i
$791$	−10.9413	−	15.0594i	−0.389028	−	0.535451i
$792$	6.30803	+	15.6536i	0.224146	+	0.556227i
$793$	0.336537	+	0.336537i	0.0119508	+	0.0119508i
$794$	−7.75013	+	21.6644i	−0.275042	+	0.768842i
$795$	9.35465	+	7.54088i	0.331775	+	0.267447i
$796$	10.5224	−	2.74718i	0.372956	−	0.0973714i
$797$	−3.79379	−	1.93303i	−0.134383	−	0.0684714i	0.385506	−	0.922705i	$-0.374027\pi$
$797$	−3.79379	−	1.93303i	−0.134383	−	0.0684714i	−0.519889	+	0.854234i	$0.674027\pi$
$798$	−0.850386	−	6.62355i	−0.0301033	−	0.234471i
$799$	6.89752			0.244017
$800$	26.0039	+	11.1264i	0.919377	+	0.393379i
$801$	−0.467584			−0.0165213
$802$	−0.203390	−	1.58418i	−0.00718195	−	0.0559393i
$803$	−26.1547	−	13.3265i	−0.922979	−	0.470281i
$804$	−13.9005	+	3.62915i	−0.490234	+	0.127990i
$805$	1.71284	−	4.49191i	0.0603696	−	0.158319i
$806$	7.99961	−	22.3618i	0.281774	−	0.787661i
$807$	1.45306	+	1.45306i	0.0511502	+	0.0511502i
$808$	−18.7004	−	46.4058i	−0.657878	−	1.63255i
$809$	1.67229	+	2.30171i	0.0587947	+	0.0809240i	0.837402	−	0.546588i	$-0.184073\pi$
$809$	1.67229	+	2.30171i	0.0587947	+	0.0809240i	−0.778607	+	0.627512i	$0.784073\pi$
$810$	0.244997	+	3.15277i	0.00860831	+	0.110777i
$811$	24.4620	−	33.6690i	0.858977	−	1.18228i	−0.122836	−	0.992427i	$-0.539199\pi$
$811$	24.4620	−	33.6690i	0.858977	−	1.18228i	0.981813	−	0.189853i	$-0.0608011\pi$
$812$	−20.6802	−	4.53467i	−0.725733	−	0.159136i
$813$	23.8430	+	3.77636i	0.836211	+	0.132443i
$814$	40.4156	−	52.3220i	1.41657	−	1.83389i
$815$	−17.0635	+	1.83180i	−0.597709	+	0.0641652i
$816$	−1.35072	−	2.41046i	−0.0472845	−	0.0843831i
$817$	−13.3850	−	26.2696i	−0.468283	−	0.919057i
$818$	−27.4405	+	25.8732i	−0.959436	+	0.904636i
$819$	−1.27377	+	3.92027i	−0.0445092	+	0.136985i
$820$	−43.1563	−	19.4319i	−1.50708	−	0.678590i
$821$	−0.0793176	−	0.244114i	−0.00276820	−	0.00851965i	0.949663	−	0.313274i	$-0.101426\pi$
$821$	−0.0793176	−	0.244114i	−0.00276820	−	0.00851965i	−0.952431	+	0.304754i	$0.901426\pi$
$822$	−0.754099	−	0.412582i	−0.0263022	−	0.0143905i
$823$	42.5661	−	6.74181i	1.48376	−	0.235005i	0.638609	−	0.769531i	$-0.279510\pi$
$823$	42.5661	−	6.74181i	1.48376	−	0.235005i	0.845152	+	0.534527i	$0.179510\pi$
$824$	0.455343	−	5.15100i	0.0158626	−	0.179444i
$825$	16.1375	−	25.0931i	0.561837	−	0.873630i
$826$	−0.507944	+	17.2780i	−0.0176736	+	0.601177i
$827$	−2.82535	−	17.8386i	−0.0982471	−	0.620308i	−0.986851	−	0.161632i	$-0.948324\pi$
$827$	−2.82535	−	17.8386i	−0.0982471	−	0.620308i	0.888604	−	0.458675i	$-0.151676\pi$
$828$	2.95083	+	1.72901i	0.102548	+	0.0600874i
$829$	10.3078	−	3.34920i	0.358004	−	0.116323i	−0.124492	−	0.992221i	$-0.539730\pi$
$829$	10.3078	−	3.34920i	0.358004	−	0.116323i	0.482496	+	0.875898i	$0.339730\pi$
$830$	−9.50454	−	8.13389i	−0.329907	−	0.282331i
$831$	−13.1707	−	4.27941i	−0.456885	−	0.148451i
$832$	−21.5125	+	15.0054i	−0.745813	+	0.520219i
$833$	3.33553	−	1.69954i	0.115569	−	0.0588854i
$834$	−23.1320	+	15.7891i	−0.800994	+	0.546731i
$835$	24.8334	+	27.4574i	0.859397	+	0.950201i
$836$	−34.6506	−	28.4298i	−1.19842	−	0.983265i
$837$	0.801281	−	5.05909i	0.0276963	−	0.174868i
$838$	−5.60495	−	1.05744i	−0.193620	−	0.0365286i
$839$	1.60565	+	1.16657i	0.0554332	+	0.0402746i	0.615157	−	0.788405i	$-0.289093\pi$
$839$	1.60565	+	1.16657i	0.0554332	+	0.0402746i	−0.559724	+	0.828679i	$0.689093\pi$
$840$	6.51952	+	4.55221i	0.224945	+	0.157066i
$841$	33.8921	−	24.6241i	1.16869	−	0.849106i
$842$	24.8880	−	11.7730i	0.857696	−	0.405726i
$843$	19.7532	−	19.7532i	0.680335	−	0.680335i
$844$	7.53813	−	19.2669i	0.259473	−	0.663193i
$845$	0.252227	−	5.02651i	0.00867686	−	0.172917i
$846$	−3.96714	−	13.5524i	−0.136393	−	0.465942i
$847$	14.0431	−	27.5611i	0.482526	−	0.947010i
$848$	0.849225	+	21.4774i	0.0291625	+	0.737535i
$849$			0.0693803i			0.00238113i
$850$	−2.09740	+	4.41130i	−0.0719401	+	0.151306i
$851$		−	13.3978i		−	0.459272i
$852$	−14.7247	+	1.45211i	−0.504459	+	0.0497485i
$853$	−15.2595	+	29.9484i	−0.522475	+	1.02542i	0.467476	+	0.884006i	$0.345163\pi$
$853$	−15.2595	+	29.9484i	−0.522475	+	1.02542i	−0.989951	+	0.141410i	$0.954837\pi$
$854$	0.247709	−	0.0725107i	0.00847643	−	0.00248127i
$855$	−4.58968	−	7.03321i	−0.156964	−	0.240531i
$856$	−2.08350	+	4.89612i	−0.0712126	+	0.167346i
$857$	−7.61766	+	7.61766i	−0.260214	+	0.260214i	−0.825141	−	0.564927i	$-0.808904\pi$
$857$	−7.61766	+	7.61766i	−0.260214	+	0.260214i	0.564927	+	0.825141i	$0.308904\pi$
$858$	11.8304	+	25.0092i	0.403883	+	0.853801i
$859$	28.3958	−	20.6307i	0.968851	−	0.703912i	0.0136617	−	0.999907i	$-0.495651\pi$
$859$	28.3958	−	20.6307i	0.968851	−	0.703912i	0.955189	+	0.295995i	$0.0956512\pi$
$860$	33.8714	+	9.22837i	1.15501	+	0.314685i
$861$	−10.7645	−	7.82085i	−0.366852	−	0.266534i
$862$	6.79888	−	36.0375i	0.231571	−	1.22744i
$863$	6.01670	−	37.9879i	0.204811	−	1.29312i	−0.644244	−	0.764820i	$-0.722828\pi$
$863$	6.01670	−	37.9879i	0.204811	−	1.29312i	0.849055	−	0.528305i	$-0.177172\pi$
$864$	−3.95928	+	4.04031i	−0.134697	+	0.137454i
$865$	37.7606	−	16.9128i	1.28390	−	0.575052i
$866$	−17.3158	−	25.3687i	−0.588415	−	0.862064i
$867$	−14.7219	+	7.50121i	−0.499984	+	0.254754i
$868$	−8.55653	−	9.62656i	−0.290427	−	0.326747i
$869$	−9.70668	−	3.15389i	−0.329277	−	0.106988i
$870$	−25.8962	+	6.19009i	−0.877963	+	0.209864i
$871$	−22.3983	+	7.27766i	−0.758938	+	0.246594i
$872$	0.762561	−	1.21790i	0.0258236	−	0.0412434i
$873$	0.315104	+	1.98949i	0.0106646	+	0.0673339i
$874$	−9.07899	−	0.266908i	−0.307101	−	0.00902829i
$875$	−0.0937283	−	14.0561i	−0.00316859	−	0.475184i
$876$	0.578005	−	9.82206i	0.0195290	−	0.331857i
$877$	34.6520	−	5.48833i	1.17011	−	0.185328i	0.459020	−	0.888426i	$-0.348200\pi$
$877$	34.6520	−	5.48833i	1.17011	−	0.185328i	0.711093	+	0.703098i	$0.248200\pi$
$878$	7.41789	−	13.5581i	0.250342	−	0.457563i
$879$	−6.05632	−	18.6395i	−0.204275	−	0.628693i
$880$	52.7978	−	7.78866i	1.77981	−	0.262556i
$881$	−3.27970	+	10.0939i	−0.110496	+	0.340072i	−0.990981	−	0.134002i	$-0.957217\pi$
$881$	−3.27970	+	10.0939i	−0.110496	+	0.340072i	0.880485	+	0.474074i	$0.157217\pi$
$882$	−5.25774	−	5.57624i	−0.177037	−	0.187762i
$883$	−3.48194	−	6.83369i	−0.117177	−	0.229972i	0.824968	−	0.565180i	$-0.191193\pi$
$883$	−3.48194	−	6.83369i	−0.117177	−	0.229972i	−0.942144	+	0.335208i	$0.891193\pi$
$884$	−2.44254	−	3.81458i	−0.0821515	−	0.128298i
$885$	8.88596	+	19.8394i	0.298698	+	0.666894i
$886$	−18.4734	−	14.2696i	−0.620628	−	0.479397i
$887$	30.7208	+	4.86569i	1.03150	+	0.163374i	0.649164	−	0.760648i	$-0.275119\pi$
$887$	30.7208	+	4.86569i	1.03150	+	0.163374i	0.382339	+	0.924022i	$0.375119\pi$
$888$	21.4972	+	5.38048i	0.721398	+	0.180557i
$889$	1.64808	−	2.26838i	0.0552747	−	0.0760792i
$890$	−0.346599	+	1.43743i	−0.0116180	+	0.0481829i
$891$	3.50723	+	4.82729i	0.117497	+	0.161720i
$892$	−5.02062	+	2.19681i	−0.168103	+	0.0735547i
$893$	26.5183	+	26.5183i	0.887401	+	0.887401i
$894$	13.2989	+	4.75749i	0.444782	+	0.159114i
$895$	24.8950	−	16.2458i	0.832148	−	0.543036i
$896$	1.53930	+	14.1406i	0.0514243	+	0.472404i
$897$	4.99545	+	2.54531i	0.166793	+	0.0849854i
$898$	−8.62092	+	1.10683i	−0.287684	+	0.0369352i
$899$	43.1275			1.43838
$900$	9.87378	+	1.58384i	0.329126	+	0.0527948i
$901$	−3.71191			−0.123662
$902$	−88.5779	+	11.3724i	−2.94932	+	0.378658i
$903$	8.79364	+	4.48058i	0.292634	+	0.149104i
$904$	−9.38339	−	40.8121i	−0.312087	−	1.35739i
$905$	33.0772	+	1.65979i	1.09952	+	0.0551732i
$906$	23.9121	+	8.55422i	0.794428	+	0.284195i
$907$	−11.2357	−	11.2357i	−0.373075	−	0.373075i	0.495521	−	0.868596i	$-0.334977\pi$
$907$	−11.2357	−	11.2357i	−0.373075	−	0.373075i	−0.868596	+	0.495521i	$0.834977\pi$
$908$	3.38300	+	7.73156i	0.112269	+	0.256581i
$909$	−10.3973	−	14.3107i	−0.344857	−	0.474655i
$910$	11.1074	+	6.82172i	0.368207	+	0.226138i
$911$	−9.83174	+	13.5322i	−0.325740	+	0.448343i	−0.940209	−	0.340598i	$-0.889370\pi$
$911$	−9.83174	+	13.5322i	−0.325740	+	0.448343i	0.614469	+	0.788941i	$0.289370\pi$
$912$	4.07432	−	14.4603i	0.134914	−	0.478828i
$913$	−23.3141	−	3.69258i	−0.771583	−	0.122207i
$914$	27.1185	+	20.9474i	0.897002	+	0.692880i
$915$	0.240739	−	0.217733i	0.00795859	−	0.00719804i
$916$	6.39228	−	4.09309i	0.211207	−	0.135239i
$917$	1.63415	+	3.20721i	0.0539645	+	0.105911i
$918$	−0.670180	−	0.710778i	−0.0221192	−	0.0234592i
$919$	−7.63641	+	23.5025i	−0.251902	+	0.775274i	0.742522	+	0.669821i	$0.233629\pi$
$919$	−7.63641	+	23.5025i	−0.251902	+	0.775274i	−0.994424	+	0.105453i	$0.966371\pi$
$920$	7.50260	−	7.78971i	0.247353	−	0.256819i
$921$	6.32110	+	19.4543i	0.208287	+	0.641042i
$922$	17.2866	−	31.5957i	0.569305	−	1.04055i
$923$	−23.9566	+	3.79436i	−0.788542	+	0.124893i
$924$	14.9777	+	0.881404i	0.492731	+	0.0289961i
$925$	−14.2012	−	36.5095i	−0.466933	−	1.20043i
$926$	−9.62576	−	0.282982i	−0.316322	−	0.00929937i
$927$	−0.286002	−	1.80575i	−0.00939354	−	0.0593085i
$928$	−38.8147	−	27.6042i	−1.27416	−	0.906152i
$929$	−39.4625	+	12.8221i	−1.29472	+	0.420681i	−0.873743	−	0.486389i	$-0.838314\pi$
$929$	−39.4625	+	12.8221i	−1.29472	+	0.420681i	−0.420981	+	0.907070i	$0.638314\pi$
$930$	−14.9586	−	6.21335i	−0.490511	−	0.203744i
$931$	19.3579	+	6.28975i	0.634429	+	0.206138i
$932$	27.3944	−	24.3494i	0.897333	−	0.797591i
$933$	24.2423	−	12.3520i	0.793656	−	0.404388i
$934$	−17.1333	−	25.1014i	−0.560620	−	0.821342i
$935$	0.983763	+	9.16390i	0.0321725	+	0.299692i
$936$	−6.09015	+	6.99314i	−0.199063	+	0.228578i
$937$	3.66513	−	23.1407i	0.119734	−	0.755974i	−0.852632	−	0.522513i	$-0.824995\pi$
$937$	3.66513	−	23.1407i	0.119734	−	0.755974i	0.972366	−	0.233461i	$-0.0750052\pi$
$938$	−2.36780	+	12.5505i	−0.0773113	+	0.409789i
$939$	−27.4752	−	19.9619i	−0.896619	−	0.651432i
$940$	−44.6032	+	2.14987i	−1.45480	+	0.0701209i
$941$	1.45471	−	1.05691i	0.0474222	−	0.0344543i	−0.563822	−	0.825897i	$-0.690669\pi$
$941$	1.45471	−	1.05691i	0.0474222	−	0.0344543i	0.611244	+	0.791442i	$0.290669\pi$
$942$	−4.21506	−	8.91056i	−0.137334	−	0.290322i
$943$	−12.7969	+	12.7969i	−0.416724	+	0.416724i
$944$	−16.2716	+	35.3190i	−0.529595	+	1.14954i
$945$	2.62680	+	1.00164i	0.0854497	+	0.0325834i
$946$	63.5734	−	18.6095i	2.06695	−	0.605048i
$947$	15.2838	−	29.9961i	0.496656	−	0.974742i	−0.497569	−	0.867424i	$-0.665774\pi$
$947$	15.2838	−	29.9961i	0.496656	−	0.974742i	0.994225	−	0.107317i	$-0.0342261\pi$
$948$	−0.335739	−	3.40445i	−0.0109043	−	0.110571i
$949$		−	16.1292i		−	0.523575i
$950$	−25.0234	+	8.89607i	−0.811867	+	0.288626i
$951$			33.7179i			1.09338i
$952$	−2.45059	+	0.169138i	−0.0794242	+	0.00548179i
$953$	25.0799	−	49.2221i	0.812418	−	1.59446i	0.00831782	−	0.999965i	$-0.497352\pi$
$953$	25.0799	−	49.2221i	0.812418	−	1.59446i	0.804100	−	0.594494i	$-0.202648\pi$
$954$	2.13492	+	7.29327i	0.0691207	+	0.236128i
$955$	−21.6241	+	26.8252i	−0.699739	+	0.868043i
$956$	20.7430	+	8.11568i	0.670878	+	0.262480i
$957$	−35.5249	+	35.5249i	−1.14836	+	1.14836i
$958$	−34.5965	+	16.3656i	−1.11776	+	0.528748i
$959$	−0.618234	+	0.449173i	−0.0199638	+	0.0145046i
$960$	9.48579	+	15.1664i	0.306153	+	0.489493i
$961$	−3.85379	−	2.79994i	−0.124316	−	0.0903206i
$962$	35.6977	+	6.73477i	1.15094	+	0.217138i
$963$	−0.294293	+	1.85809i	−0.00948347	+	0.0598763i
$964$	−16.5173	+	20.1315i	−0.531985	+	0.648391i
$965$	14.6214	−	25.4555i	0.470679	−	0.819441i
$966$	2.51124	−	1.71409i	0.0807979	−	0.0551498i
$967$	−15.5980	+	7.94759i	−0.501599	+	0.255577i	−0.686434	−	0.727192i	$-0.740825\pi$
$967$	−15.5980	+	7.94759i	−0.501599	+	0.255577i	0.184835	+	0.982770i	$0.440825\pi$
$968$	53.3486	−	44.6827i	1.71469	−	1.43616i
$969$	2.46746	+	0.801726i	0.0792662	+	0.0257551i
$970$	6.34960	+	0.506033i	0.203873	+	0.0162477i
$971$	35.6648	−	11.5882i	1.14454	−	0.371883i	0.325455	−	0.945558i	$-0.394483\pi$
$971$	35.6648	−	11.5882i	1.14454	−	0.371883i	0.819083	+	0.573675i	$0.194483\pi$
$972$	−1.01110	+	1.72560i	−0.0324310	+	0.0553485i
$973$	3.89495	+	24.5917i	0.124866	+	0.788375i
$974$	−0.0797568	+	2.71296i	−0.00255557	+	0.0869290i
$975$	16.3107	+	1.64105i	0.522360	+	0.0525556i
$976$	0.576648	+	0.0681047i	0.0184581	+	0.00217998i
$977$	7.65446	−	1.21235i	0.244888	−	0.0387864i	−0.0327839	−	0.999462i	$-0.510437\pi$
$977$	7.65446	−	1.21235i	0.244888	−	0.0387864i	0.277672	+	0.960676i	$0.410437\pi$
$978$	−9.52194	−	5.20963i	−0.304478	−	0.166586i
$979$	0.862160	+	2.65345i	0.0275547	+	0.0848048i
$980$	−21.0397	+	12.0298i	−0.672087	+	0.384277i
$981$	0.156991	−	0.483169i	0.00501234	−	0.0154264i
$982$	39.7695	−	37.4980i	1.26910	−	1.19661i
$983$	19.4382	+	38.1495i	0.619981	+	1.21678i	0.960954	+	0.276708i	$0.0892436\pi$
$983$	19.4382	+	38.1495i	0.619981	+	1.21678i	−0.340973	+	0.940073i	$0.610756\pi$
$984$	−15.3938	−	25.6721i	−0.490736	−	0.818396i
$985$	−9.55022	+	45.4265i	−0.304295	+	1.44741i
$986$	5.02820	−	6.50950i	0.160130	−	0.207305i
$987$	−12.3993	−	1.96385i	−0.394672	−	0.0625100i
$988$	5.27494	−	24.0562i	0.167818	−	0.765330i
$989$	7.89024	−	10.8600i	0.250895	−	0.345327i
$990$	17.4397	−	7.20359i	0.554269	−	0.228945i
$991$	10.1381	+	13.9539i	0.322047	+	0.443259i	0.939091	−	0.343670i	$-0.111670\pi$
$991$	10.1381	+	13.9539i	0.322047	+	0.443259i	−0.617044	+	0.786929i	$0.711670\pi$
$992$	−9.23254	−	27.4650i	−0.293133	−	0.872015i
$993$	−0.402426	−	0.402426i	−0.0127706	−	0.0127706i
$994$	−4.43062	+	12.3852i	−0.140531	+	0.392835i
$995$	−3.17301	−	11.7374i	−0.100591	−	0.372101i
$996$	−1.99865	−	7.65532i	−0.0633297	−	0.242568i
$997$	14.8156	+	7.54891i	0.469214	+	0.239076i	0.672577	−	0.740027i	$-0.265187\pi$
$997$	14.8156	+	7.54891i	0.469214	+	0.239076i	−0.203363	+	0.979103i	$0.565187\pi$
$998$	1.13129	+	8.81144i	0.0358102	+	0.278921i
$999$	7.83485			0.247884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.163.14	yes	240
3.2	odd	2		900.2.bj.f.163.17		240
4.3	odd	2	inner	300.2.w.a.163.17	yes	240
12.11	even	2		900.2.bj.f.163.14		240
25.2	odd	20	inner	300.2.w.a.127.17	yes	240
75.2	even	20		900.2.bj.f.127.14		240
100.27	even	20	inner	300.2.w.a.127.14	✓	240
300.227	odd	20		900.2.bj.f.127.17		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.14	✓	240	100.27	even	20	inner
300.2.w.a.127.17	yes	240	25.2	odd	20	inner
300.2.w.a.163.14	yes	240	1.1	even	1	trivial
300.2.w.a.163.17	yes	240	4.3	odd	2	inner
900.2.bj.f.127.14		240	75.2	even	20
900.2.bj.f.127.17		240	300.227	odd	20
900.2.bj.f.163.14		240	12.11	even	2
900.2.bj.f.163.17		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.180090 - 1.40270i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-1.93514 + 0.505225i) q^{4} +(0.583536 + 2.15858i) q^{5} +(-0.476351 + 1.33157i) q^{6} +(0.889008 + 0.889008i) q^{7} +(1.05718 + 2.62343i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-0.180090 - 1.40270i) q^{2} +(-0.891007 - 0.453990i) q^{3} +(-1.93514 + 0.505225i) q^{4} +(0.583536 + 2.15858i) q^{5} +(-0.476351 + 1.33157i) q^{6} +(0.889008 + 0.889008i) q^{7} +(1.05718 + 2.62343i) q^{8} +(0.587785 + 0.809017i) q^{9} +(2.92276 - 1.20727i) q^{10} +(3.50723 - 4.82729i) q^{11} +(1.95359 + 0.428374i) q^{12} +(3.23824 + 0.512887i) q^{13} +(1.08691 - 1.40711i) q^{14} +(0.460042 - 2.18823i) q^{15} +(3.48950 - 1.95536i) q^{16} +(0.313606 + 0.615487i) q^{17} +(1.02895 - 0.970182i) q^{18} +(-1.16061 + 3.57200i) q^{19} +(-2.21979 - 3.88233i) q^{20} +(-0.388511 - 1.19571i) q^{21} +(-7.40286 - 4.05025i) q^{22} +(-1.68898 + 0.267508i) q^{23} +(0.249059 - 2.81744i) q^{24} +(-4.31897 + 2.51922i) q^{25} +(0.136251 - 4.63464i) q^{26} +(-0.156434 - 0.987688i) q^{27} +(-2.16950 - 1.27120i) q^{28} +(8.00770 - 2.60186i) q^{29} +(-3.15228 - 0.251222i) q^{30} +(4.87146 + 1.58283i) q^{31} +(-3.37120 - 4.54257i) q^{32} +(-5.31651 + 2.70890i) q^{33} +(0.806866 - 0.550738i) q^{34} +(-1.40023 + 2.43777i) q^{35} +(-1.54618 - 1.26859i) q^{36} +(-1.22564 + 7.73839i) q^{37} +(5.21947 + 0.984711i) q^{38} +(-2.65245 - 1.92712i) q^{39} +(-5.04599 + 3.81287i) q^{40} +(8.56195 - 6.22062i) q^{41} +(-1.60726 + 0.760300i) q^{42} +(-5.55076 + 5.55076i) q^{43} +(-4.34810 + 11.1134i) q^{44} +(-1.40334 + 1.74087i) q^{45} +(0.679402 + 2.32096i) q^{46} +(4.53317 - 8.89684i) q^{47} +(-3.99688 + 0.158038i) q^{48} -5.41933i q^{49} +(4.31152 + 5.60453i) q^{50} -0.690777i q^{51} +(-6.52555 + 0.643534i) q^{52} +(-2.43953 + 4.78785i) q^{53} +(-1.35726 + 0.397304i) q^{54} +(12.4667 + 4.75375i) q^{55} +(-1.39241 + 3.27209i) q^{56} +(2.65577 - 2.65577i) q^{57} +(-5.09174 - 10.7638i) q^{58} +(-7.86506 + 5.71430i) q^{59} +(0.215306 + 4.46695i) q^{60} +(0.117440 + 0.0853253i) q^{61} +(1.34294 - 7.11825i) q^{62} +(-0.196677 + 1.24177i) q^{63} +(-5.76475 + 5.54686i) q^{64} +(0.782521 + 7.28930i) q^{65} +(4.75722 + 6.96962i) q^{66} +(-6.40031 + 3.26112i) q^{67} +(-0.917829 - 1.03261i) q^{68} +(1.62634 + 0.528429i) q^{69} +(3.67162 + 1.52508i) q^{70} +(-7.03596 + 2.28612i) q^{71} +(-1.50100 + 2.39729i) q^{72} +(-0.769583 - 4.85896i) q^{73} +(11.0754 + 0.325598i) q^{74} +(4.99194 - 0.283873i) q^{75} +(0.441280 - 7.49868i) q^{76} +(7.40945 - 1.17354i) q^{77} +(-2.22549 + 4.06764i) q^{78} +(-0.528568 - 1.62677i) q^{79} +(6.25705 + 6.39135i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-10.2676 - 10.8896i) q^{82} +(-1.79597 - 3.52479i) q^{83} +(1.35592 + 2.11758i) q^{84} +(-1.14558 + 1.03610i) q^{85} +(8.78568 + 6.78641i) q^{86} +(-8.31614 - 1.31715i) q^{87} +(16.3718 + 4.09766i) q^{88} +(-0.274839 + 0.378283i) q^{89} +(2.69465 + 1.65495i) q^{90} +(2.42286 + 3.33478i) q^{91} +(3.13325 - 1.37098i) q^{92} +(-3.62191 - 3.62191i) q^{93} +(-13.2960 - 4.75644i) q^{94} +(-8.38773 - 0.420890i) q^{95} +(0.941479 + 5.57796i) q^{96} +(1.79474 + 0.914467i) q^{97} +(-7.60169 + 0.975968i) q^{98} +5.96686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

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