LMFDB - Embedded newform 588.2.x.a.55.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(55,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 9]))

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

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

chi := DirichletCharacter("588.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.x (of order $14$, degree $6$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			55.25
Character	$\chi$	$=$	588.55
Dual form			588.2.x.a.139.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33820 - 0.457394i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.58158 - 1.22417i) q^{4} +(-1.14386 + 2.37526i) q^{5} +(-1.40414 - 0.168527i) q^{6} +(-1.90517 + 1.83585i) q^{7} +(1.55655 - 2.36160i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(1.33820 - 0.457394i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.58158 - 1.22417i) q^{4} +(-1.14386 + 2.37526i) q^{5} +(-1.40414 - 0.168527i) q^{6} +(-1.90517 + 1.83585i) q^{7} +(1.55655 - 2.36160i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.444296 + 3.70178i) q^{10} +(1.71931 + 1.37111i) q^{11} +(-1.95610 + 0.416719i) q^{12} +(4.11444 + 3.28115i) q^{13} +(-1.70979 + 3.32815i) q^{14} +(2.06117 - 1.64373i) q^{15} +(1.00280 - 3.87226i) q^{16} +(5.43764 + 1.24111i) q^{17} +(1.19196 + 0.761070i) q^{18} -0.503306 q^{19} +(1.09861 + 5.15696i) q^{20} +(2.51304 - 0.827423i) q^{21} +(2.92793 + 1.04842i) q^{22} +(-0.636689 + 0.145320i) q^{23} +(-2.42706 + 1.45237i) q^{24} +(-1.21598 - 1.52480i) q^{25} +(7.00674 + 2.50894i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-0.765777 + 5.23580i) q^{28} +(-0.628356 + 2.75301i) q^{29} +(2.00644 - 3.14242i) q^{30} -4.81514 q^{31} +(-0.429195 - 5.64055i) q^{32} +(-0.954147 - 1.98131i) q^{33} +(7.84435 - 0.826290i) q^{34} +(-2.18137 - 6.62523i) q^{35} +(1.94320 + 0.473271i) q^{36} +(1.54710 - 6.77828i) q^{37} +(-0.673526 + 0.230209i) q^{38} +(-2.28334 - 4.74141i) q^{39} +(3.82893 + 6.39856i) q^{40} +(-4.33461 + 9.00090i) q^{41} +(2.98450 - 2.25671i) q^{42} +(-1.69645 - 3.52271i) q^{43} +(4.39771 + 0.0637802i) q^{44} +(-2.57024 + 0.586641i) q^{45} +(-0.785551 + 0.485685i) q^{46} +(-7.09061 + 8.89135i) q^{47} +(-2.58360 + 3.05369i) q^{48} +(0.259311 - 6.99520i) q^{49} +(-2.32467 - 1.48430i) q^{50} +(-4.36065 - 3.47750i) q^{51} +(10.5240 + 0.152630i) q^{52} +(-0.361207 - 1.58255i) q^{53} +(-0.743705 - 1.20287i) q^{54} +(-5.22340 + 2.51546i) q^{55} +(1.37006 + 7.35683i) q^{56} +(0.453463 + 0.218376i) q^{57} +(0.418340 + 3.97149i) q^{58} +(13.4713 - 6.48743i) q^{59} +(1.24770 - 5.12293i) q^{60} +(-9.44503 - 2.15577i) q^{61} +(-6.44364 + 2.20241i) q^{62} +(-2.62318 - 0.344885i) q^{63} +(-3.15430 - 7.35190i) q^{64} +(-12.5000 + 6.01966i) q^{65} +(-2.18308 - 2.21497i) q^{66} -4.43686i q^{67} +(10.1194 - 4.69370i) q^{68} +(0.636689 + 0.145320i) q^{69} +(-5.94946 - 7.86816i) q^{70} +(15.0105 - 3.42604i) q^{71} +(2.81687 - 0.255473i) q^{72} +(3.33947 - 2.66314i) q^{73} +(-1.03001 - 9.77836i) q^{74} +(0.433980 + 1.90139i) q^{75} +(-0.796019 + 0.616133i) q^{76} +(-5.79272 + 0.544216i) q^{77} +(-5.22427 - 5.30058i) q^{78} +6.44761i q^{79} +(8.05055 + 6.81125i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-1.68363 + 14.0277i) q^{82} +(-1.49505 - 1.87473i) q^{83} +(2.96167 - 4.38503i) q^{84} +(-9.16787 + 11.4961i) q^{85} +(-3.88146 - 3.93816i) q^{86} +(1.76061 - 2.20774i) q^{87} +(5.91420 - 1.92613i) q^{88} +(4.74517 - 3.78415i) q^{89} +(-3.17118 + 1.96066i) q^{90} +(-13.8624 + 1.30235i) q^{91} +(-0.829078 + 1.00925i) q^{92} +(4.33829 + 2.08921i) q^{93} +(-5.42184 + 15.1416i) q^{94} +(0.575714 - 1.19548i) q^{95} +(-2.06065 + 5.26818i) q^{96} -12.9866i q^{97} +(-2.85255 - 9.47961i) q^{98} +2.19908i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	1.33820	−	0.457394i	0.946253	−	0.323426i
$2$	1.33820	−	0.457394i	0.946253	−	0.323426i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$4$	1.58158	−	1.22417i	0.790791	−	0.612086i
$5$	−1.14386	+	2.37526i	−0.511552	+	1.06225i	0.471996	+	0.881601i	$0.343534\pi$
$5$	−1.14386	+	2.37526i	−0.511552	+	1.06225i	−0.983548	+	0.180648i	$0.942181\pi$
$6$	−1.40414	−	0.168527i	−0.573236	−	0.0688010i
$7$	−1.90517	+	1.83585i	−0.720085	+	0.693886i
$7$	−1.90517	+	1.83585i	−0.720085	+	0.693886i
$8$	1.55655	−	2.36160i	0.550324	−	0.834951i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	−0.444296	+	3.70178i	−0.140499	+	1.17061i
$11$	1.71931	+	1.37111i	0.518393	+	0.413404i	0.847426	−	0.530914i	$-0.178151\pi$
$11$	1.71931	+	1.37111i	0.518393	+	0.413404i	−0.329033	+	0.944318i	$0.606723\pi$
$12$	−1.95610	+	0.416719i	−0.564679	+	0.120296i
$13$	4.11444	+	3.28115i	1.14114	+	0.910028i	0.996834	−	0.0795048i	$-0.0253339\pi$
$13$	4.11444	+	3.28115i	1.14114	+	0.910028i	0.144305	+	0.989533i	$0.453905\pi$
$14$	−1.70979	+	3.32815i	−0.456962	+	0.889486i
$15$	2.06117	−	1.64373i	0.532193	−	0.424409i
$16$	1.00280	−	3.87226i	0.250700	−	0.968065i
$17$	5.43764	+	1.24111i	1.31882	+	0.301012i	0.823311	−	0.567590i	$-0.192124\pi$
$17$	5.43764	+	1.24111i	1.31882	+	0.301012i	0.495510	+	0.868602i	$0.334981\pi$
$18$	1.19196	+	0.761070i	0.280948	+	0.179386i
$19$	−0.503306			−0.115466			−0.0577331	−	0.998332i	$-0.518387\pi$
$19$	−0.503306			−0.115466			−0.0577331	+	0.998332i	$0.518387\pi$
$20$	1.09861	+	5.15696i	0.245657	+	1.15313i
$21$	2.51304	−	0.827423i	0.548390	−	0.180559i
$22$	2.92793	+	1.04842i	0.624237	+	0.223523i
$23$	−0.636689	+	0.145320i	−0.132759	+	0.0303013i	−0.288384	−	0.957515i	$-0.593118\pi$
$23$	−0.636689	+	0.145320i	−0.132759	+	0.0303013i	0.155625	+	0.987816i	$0.450261\pi$
$24$	−2.42706	+	1.45237i	−0.495422	+	0.296463i
$25$	−1.21598	−	1.52480i	−0.243197	−	0.304959i
$26$	7.00674	+	2.50894i	1.37413	+	0.492043i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	−0.765777	+	5.23580i	−0.144718	+	0.989473i
$29$	−0.628356	+	2.75301i	−0.116683	+	0.511220i	0.882482	+	0.470347i	$0.155871\pi$
$29$	−0.628356	+	2.75301i	−0.116683	+	0.511220i	−0.999164	+	0.0408735i	$0.986986\pi$
$30$	2.00644	−	3.14242i	0.366324	−	0.573724i
$31$	−4.81514			−0.864824			−0.432412	−	0.901676i	$-0.642337\pi$
$31$	−4.81514			−0.864824			−0.432412	+	0.901676i	$0.642337\pi$
$32$	−0.429195	−	5.64055i	−0.0758717	−	0.997118i
$33$	−0.954147	−	1.98131i	−0.166096	−	0.344901i
$34$	7.84435	−	0.826290i	1.34529	−	0.141708i
$35$	−2.18137	−	6.62523i	−0.368719	−	1.11987i
$36$	1.94320	+	0.473271i	0.323866	+	0.0788785i
$37$	1.54710	−	6.77828i	0.254341	−	1.11434i	−0.672857	−	0.739772i	$-0.734933\pi$
$37$	1.54710	−	6.77828i	0.254341	−	1.11434i	0.927199	−	0.374570i	$-0.122210\pi$
$38$	−0.673526	+	0.230209i	−0.109260	+	0.0373448i
$39$	−2.28334	−	4.74141i	−0.365627	−	0.759232i
$40$	3.82893	+	6.39856i	0.605407	+	1.01170i
$41$	−4.33461	+	9.00090i	−0.676952	+	1.40571i	0.225211	+	0.974310i	$0.427693\pi$
$41$	−4.33461	+	9.00090i	−0.676952	+	1.40571i	−0.902163	+	0.431395i	$0.858022\pi$
$42$	2.98450	−	2.25671i	0.460519	−	0.348218i
$43$	−1.69645	−	3.52271i	−0.258706	−	0.537208i	0.730645	−	0.682757i	$-0.239219\pi$
$43$	−1.69645	−	3.52271i	−0.258706	−	0.537208i	−0.989351	+	0.145549i	$0.953505\pi$
$44$	4.39771	+	0.0637802i	0.662979	+	0.00961522i
$45$	−2.57024	+	0.586641i	−0.383149	+	0.0874512i
$46$	−0.785551	+	0.485685i	−0.115823	+	0.0716104i
$47$	−7.09061	+	8.89135i	−1.03427	+	1.29694i	−0.0803871	+	0.996764i	$0.525616\pi$
$47$	−7.09061	+	8.89135i	−1.03427	+	1.29694i	−0.953885	+	0.300172i	$0.902956\pi$
$48$	−2.58360	+	3.05369i	−0.372911	+	0.440762i
$49$	0.259311	−	6.99520i	0.0370444	−	0.999314i
$50$	−2.32467	−	1.48430i	−0.328758	−	0.209912i
$51$	−4.36065	−	3.47750i	−0.610613	−	0.486948i
$52$	10.5240	+	0.152630i	1.45942	+	0.0211660i
$53$	−0.361207	−	1.58255i	−0.0496156	−	0.217380i	0.944042	−	0.329824i	$-0.106989\pi$
$53$	−0.361207	−	1.58255i	−0.0496156	−	0.217380i	−0.993658	+	0.112444i	$0.964132\pi$
$54$	−0.743705	−	1.20287i	−0.101205	−	0.163690i
$55$	−5.22340	+	2.51546i	−0.704323	+	0.339184i
$56$	1.37006	+	7.35683i	0.183081	+	0.983098i
$57$	0.453463	+	0.218376i	0.0600626	+	0.0289246i
$58$	0.418340	+	3.97149i	0.0549307	+	0.521482i
$59$	13.4713	−	6.48743i	1.75381	−	0.844592i	0.777301	−	0.629128i	$-0.216588\pi$
$59$	13.4713	−	6.48743i	1.75381	−	0.844592i	0.976512	−	0.215463i	$-0.0691262\pi$
$60$	1.24770	−	5.12293i	0.161078	−	0.661367i
$61$	−9.44503	−	2.15577i	−1.20931	−	0.276018i	−0.430102	−	0.902780i	$-0.641522\pi$
$61$	−9.44503	−	2.15577i	−1.20931	−	0.276018i	−0.779210	+	0.626763i	$0.784380\pi$
$62$	−6.44364	+	2.20241i	−0.818343	+	0.279707i
$63$	−2.62318	−	0.344885i	−0.330489	−	0.0434514i
$64$	−3.15430	−	7.35190i	−0.394288	−	0.918987i
$65$	−12.5000	+	6.01966i	−1.55043	+	0.746647i
$66$	−2.18308	−	2.21497i	−0.268719	−	0.272644i
$67$		−	4.43686i		−	0.542049i	−0.962573	−	0.271024i	$-0.912638\pi$
$67$		−	4.43686i		−	0.542049i	0.962573	−	0.271024i	$-0.0873624\pi$
$68$	10.1194	−	4.69370i	1.22716	−	0.569195i
$69$	0.636689	+	0.145320i	0.0766483	+	0.0174945i
$70$	−5.94946	−	7.86816i	−0.711096	−	0.940425i
$71$	15.0105	−	3.42604i	1.78142	−	0.406597i	0.800235	−	0.599686i	$-0.204708\pi$
$71$	15.0105	−	3.42604i	1.78142	−	0.406597i	0.981181	+	0.193089i	$0.0618508\pi$
$72$	2.81687	−	0.255473i	0.331971	−	0.0301078i
$73$	3.33947	−	2.66314i	0.390855	−	0.311697i	−0.408270	−	0.912861i	$-0.633868\pi$
$73$	3.33947	−	2.66314i	0.390855	−	0.311697i	0.799125	+	0.601165i	$0.205296\pi$
$74$	−1.03001	−	9.77836i	−0.119736	−	1.13671i
$75$	0.433980	+	1.90139i	0.0501116	+	0.219553i
$76$	−0.796019	+	0.616133i	−0.0913096	+	0.0706753i
$77$	−5.79272	+	0.544216i	−0.660142	+	0.0620192i
$78$	−5.22427	−	5.30058i	−0.591532	−	0.600173i
$79$			6.44761i			0.725413i	0.931903	+	0.362706i	$0.118147\pi$
$79$			6.44761i			0.725413i	−0.931903	+	0.362706i	$0.881853\pi$
$80$	8.05055	+	6.81125i	0.900079	+	0.761521i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	−1.68363	+	14.0277i	−0.185926	+	1.54910i
$83$	−1.49505	−	1.87473i	−0.164103	−	0.205779i	0.692980	−	0.720957i	$-0.256297\pi$
$83$	−1.49505	−	1.87473i	−0.164103	−	0.205779i	−0.857083	+	0.515178i	$0.827726\pi$
$84$	2.96167	−	4.38503i	0.323145	−	0.478446i
$85$	−9.16787	+	11.4961i	−0.994395	+	1.24693i
$86$	−3.88146	−	3.93816i	−0.418549	−	0.424663i
$87$	1.76061	−	2.20774i	0.188758	−	0.236694i
$88$	5.91420	−	1.92613i	0.630456	−	0.205327i
$89$	4.74517	−	3.78415i	0.502987	−	0.401119i	−0.338858	−	0.940837i	$-0.610041\pi$
$89$	4.74517	−	3.78415i	0.502987	−	0.401119i	0.841846	+	0.539718i	$0.181469\pi$
$90$	−3.17118	+	1.96066i	−0.334272	+	0.206671i
$91$	−13.8624	+	1.30235i	−1.45317	+	0.136523i
$92$	−0.829078	+	1.00925i	−0.0864374	+	0.105222i
$93$	4.33829	+	2.08921i	0.449859	+	0.216641i
$94$	−5.42184	+	15.1416i	−0.559220	+	1.56174i
$95$	0.575714	−	1.19548i	0.0590670	−	0.122654i
$96$	−2.06065	+	5.26818i	−0.210314	+	0.537681i
$97$		−	12.9866i		−	1.31859i	−0.751886	−	0.659294i	$-0.770855\pi$
$97$		−	12.9866i		−	1.31859i	0.751886	−	0.659294i	$-0.229145\pi$
$98$	−2.85255	−	9.47961i	−0.288151	−	0.957585i
$99$			2.19908i			0.221016i
$100$	−3.78979	−	0.923014i	−0.378979	−	0.0923014i
$101$	3.74398	−	7.77446i	0.372540	−	0.773587i	−0.627447	−	0.778659i	$-0.715900\pi$
$101$	3.74398	−	7.77446i	0.372540	−	0.773587i	0.999987	+	0.00507187i	$0.00161443\pi$
$102$	−7.42603	−	2.65907i	−0.735286	−	0.263287i
$103$	4.23303	+	2.03852i	0.417093	+	0.200861i	0.630647	−	0.776070i	$-0.282790\pi$
$103$	4.23303	+	2.03852i	0.417093	+	0.200861i	−0.213554	+	0.976931i	$0.568504\pi$
$104$	14.1531	−	4.60937i	1.38783	−	0.451986i
$105$	−0.909233	+	6.91558i	−0.0887321	+	0.674892i
$106$	−1.20722	−	1.95256i	−0.117255	−	0.189650i
$107$	−1.50916	+	1.20352i	−0.145896	+	0.116348i	−0.693718	−	0.720247i	$-0.744029\pi$
$107$	−1.50916	+	1.20352i	−0.145896	+	0.116348i	0.547822	+	0.836595i	$0.315457\pi$
$108$	−1.54542	−	1.26952i	−0.148708	−	0.122160i
$109$	−11.2975	+	14.1666i	−1.08210	+	1.35691i	−0.152521	+	0.988300i	$0.548739\pi$
$109$	−11.2975	+	14.1666i	−1.08210	+	1.35691i	−0.929583	+	0.368614i	$0.879832\pi$
$110$	−5.83942	+	5.75534i	−0.556767	+	0.548751i
$111$	−4.33487	+	5.43576i	−0.411448	+	0.515939i
$112$	5.19838	+	9.21829i	0.491201	+	0.871046i
$113$	5.18025	+	6.49583i	0.487317	+	0.611076i	0.963316	−	0.268370i	$-0.0864848\pi$
$113$	5.18025	+	6.49583i	0.487317	+	0.611076i	−0.475999	+	0.879446i	$0.657913\pi$
$114$	0.706710	+	0.0848208i	0.0661894	+	0.00794420i
$115$	0.383113	−	1.67853i	0.0357255	−	0.156524i
$116$	2.37636	+	5.12332i	0.220639	+	0.475688i
$117$			5.26256i			0.486524i
$118$	15.0600	−	14.8432i	1.38639	−	1.36643i
$119$	−12.6381	+	7.61818i	−1.15853	+	0.698357i
$120$	−0.673514	−	7.42622i	−0.0614831	−	0.677918i
$121$	−1.37162	−	6.00948i	−0.124693	−	0.546316i
$122$	−13.6254	+	1.43524i	−1.23359	+	0.129941i
$123$	7.81069	−	6.22882i	0.704266	−	0.561634i
$124$	−7.61553	+	5.89456i	−0.683895	+	0.529347i
$125$	−7.83850	+	1.78909i	−0.701097	+	0.160021i
$126$	−3.66809	+	0.738299i	−0.326780	+	0.0657729i
$127$	−10.2775	−	2.34578i	−0.911983	−	0.208154i	−0.259310	−	0.965794i	$-0.583495\pi$
$127$	−10.2775	−	2.34578i	−0.911983	−	0.208154i	−0.652673	+	0.757640i	$0.726352\pi$
$128$	−7.58381	−	8.39558i	−0.670321	−	0.742071i
$129$			3.90991i			0.344249i
$130$	−13.9741	+	13.7729i	−1.22561	+	1.20797i
$131$	−1.24673	+	0.600395i	−0.108928	+	0.0524568i	−0.487554	−	0.873093i	$-0.662111\pi$
$131$	−1.24673	+	0.600395i	−0.108928	+	0.0524568i	0.378626	+	0.925550i	$0.376397\pi$
$132$	−3.93452	−	1.96556i	−0.342456	−	0.171080i
$133$	0.958880	−	0.923993i	0.0831455	−	0.0801204i
$134$	−2.02939	−	5.93742i	−0.175313	−	0.512915i
$135$	2.57024	+	0.586641i	0.221211	+	0.0504900i
$136$	11.3950	−	10.9097i	0.977109	−	0.935498i
$137$	10.2658	−	4.94374i	0.877064	−	0.422372i	0.0595130	−	0.998228i	$-0.481045\pi$
$137$	10.2658	−	4.94374i	0.877064	−	0.422372i	0.817551	+	0.575856i	$0.195331\pi$
$138$	0.918488	−	0.0967496i	0.0781869	−	0.00823587i
$139$	−13.2987	−	6.40433i	−1.12798	−	0.543208i	−0.225634	−	0.974212i	$-0.572445\pi$
$139$	−13.2987	−	6.40433i	−1.12798	−	0.543208i	−0.902350	+	0.431004i	$0.858159\pi$
$140$	−11.5604	−	7.80797i	−0.977035	−	0.659894i
$141$	10.2462	−	4.93432i	0.862888	−	0.415545i
$142$	18.5200	−	11.4505i	1.55417	−	0.960900i
$143$	2.57520	+	11.2827i	0.215349	+	0.943504i
$144$	3.65269	−	1.63029i	0.304391	−	0.135858i
$145$	−5.82035	−	4.64157i	−0.483354	−	0.385462i
$146$	3.25079	−	5.09127i	0.269037	−	0.421357i
$147$	−3.26873	+	6.18994i	−0.269601	+	0.510538i
$148$	−5.85093	−	12.6143i	−0.480943	−	1.03689i
$149$	2.36583	−	2.96666i	0.193817	−	0.243038i	−0.675422	−	0.737432i	$-0.736038\pi$
$149$	2.36583	−	2.96666i	0.193817	−	0.243038i	0.869238	+	0.494393i	$0.164610\pi$
$150$	1.45044	+	2.34595i	0.118428	+	0.191546i
$151$	13.3815	−	3.05423i	1.08897	−	0.248550i	0.359900	−	0.932991i	$-0.382811\pi$
$151$	13.3815	−	3.05423i	1.08897	−	0.248550i	0.729069	+	0.684441i	$0.239954\pi$
$152$	−0.783420	+	1.18861i	−0.0635438	+	0.0964087i
$153$	2.41998	+	5.02513i	0.195644	+	0.406258i
$154$	−7.50293	+	3.37783i	−0.604603	+	0.272193i
$155$	5.50786	−	11.4372i	0.442402	−	0.918658i
$156$	−9.41559	−	4.70372i	−0.753850	−	0.376599i
$157$	−10.2340	−	21.2511i	−0.816762	−	1.69602i	−0.712719	−	0.701450i	$-0.752536\pi$
$157$	−10.2340	−	21.2511i	−0.816762	−	1.69602i	−0.104043	−	0.994573i	$-0.533178\pi$
$158$	2.94910	+	8.62822i	0.234618	+	0.686424i
$159$	−0.361207	+	1.58255i	−0.0286456	+	0.125505i
$160$	13.8887	+	5.43258i	1.09800	+	0.429483i
$161$	0.946212	−	1.44572i	0.0745719	−	0.113939i
$162$	0.148148	+	1.40643i	0.0116396	+	0.110500i
$163$	−5.44841	−	11.3137i	−0.426753	−	0.886161i	−0.997866	−	0.0652898i	$-0.979203\pi$
$163$	−5.44841	−	11.3137i	−0.426753	−	0.886161i	0.571114	−	0.820871i	$-0.306511\pi$
$164$	4.16313	+	19.5420i	0.325086	+	1.52597i
$165$	5.79753			0.451337
$166$	−2.85817	−	1.82495i	−0.221837	−	0.141643i
$167$	3.59184	−	15.7369i	0.277945	−	1.21776i	−0.622442	−	0.782666i	$-0.713860\pi$
$167$	3.59184	−	15.7369i	0.277945	−	1.21776i	0.900387	−	0.435090i	$-0.143283\pi$
$168$	1.95763	−	7.22272i	0.151035	−	0.557245i
$169$	3.26985	+	14.3261i	0.251527	+	1.10201i
$170$	−7.01022	+	19.5775i	−0.537659	+	1.50153i
$171$	−0.313806	−	0.393500i	−0.0239973	−	0.0300917i
$172$	−6.99548	−	3.49471i	−0.533400	−	0.266469i
$173$	−10.8509	+	2.47664i	−0.824976	+	0.188295i	−0.614111	−	0.789220i	$-0.710485\pi$
$173$	−10.8509	+	2.47664i	−0.824976	+	0.188295i	−0.210865	+	0.977515i	$0.567628\pi$
$174$	1.34625	−	3.75970i	0.102059	−	0.285022i
$175$	5.11595	+	0.672624i	0.386729	+	0.0508456i
$176$	7.03341	−	5.28268i	0.530163	−	0.398197i
$177$	−14.9520			−1.12386
$178$	4.61917	−	7.23438i	0.346221	−	0.542240i
$179$	14.7969	+	3.37730i	1.10597	+	0.252431i	0.736249	−	0.676711i	$-0.236595\pi$
$179$	14.7969	+	3.37730i	1.10597	+	0.252431i	0.369724	+	0.929142i	$0.379452\pi$
$180$	−3.34690	+	4.07424i	−0.249463	+	0.303676i
$181$	13.5092	−	10.7732i	1.00413	−	0.800768i	0.0241193	−	0.999709i	$-0.492322\pi$
$181$	13.5092	−	10.7732i	1.00413	−	0.800768i	0.980011	+	0.198942i	$0.0637504\pi$
$182$	−17.9550	+	8.08338i	−1.33091	+	0.599180i
$183$	7.57433	+	6.04032i	0.559910	+	0.446514i
$184$	−0.647850	+	1.72980i	−0.0477602	+	0.127523i
$185$	14.3305	+	11.4282i	1.05360	+	0.840218i
$186$	6.76111	+	0.811482i	0.495748	+	0.0595008i
$187$	7.64732	+	9.58944i	0.559227	+	0.701249i
$188$	−0.329836	+	22.7425i	−0.0240558	+	1.65867i
$189$	2.21376	+	1.44888i	0.161027	+	0.105391i
$190$	0.223616	−	1.86313i	0.0162228	−	0.135165i
$191$	−8.95656	+	18.5985i	−0.648074	+	1.34574i	0.275121	+	0.961410i	$0.411282\pi$
$191$	−8.95656	+	18.5985i	−0.648074	+	1.34574i	−0.923196	+	0.384330i	$0.874432\pi$
$192$	−0.347939	+	7.99243i	−0.0251103	+	0.576804i
$193$	5.05918	+	2.43637i	0.364168	+	0.175374i	0.607015	−	0.794691i	$-0.292367\pi$
$193$	5.05918	+	2.43637i	0.364168	+	0.175374i	−0.242847	+	0.970065i	$0.578081\pi$
$194$	−5.93998	−	17.3787i	−0.426466	−	1.24772i
$195$	13.8739			0.993531
$196$	−8.15321	−	11.3809i	−0.582372	−	0.812922i
$197$	4.30118			0.306446			0.153223	−	0.988192i	$-0.451035\pi$
$197$	4.30118			0.306446			0.153223	+	0.988192i	$0.451035\pi$
$198$	1.00585	+	2.94283i	0.0714825	+	0.209137i
$199$	13.4392	+	6.47197i	0.952679	+	0.458786i	0.844625	−	0.535359i	$-0.179824\pi$
$199$	13.4392	+	6.47197i	0.952679	+	0.458786i	0.108054	+	0.994145i	$0.465538\pi$
$200$	−5.49370	+	0.498246i	−0.388463	+	0.0352313i
$201$	−1.92508	+	3.99747i	−0.135785	+	0.281960i
$202$	1.45422	−	12.1163i	0.102319	−	0.852499i
$203$	−3.85698	−	6.39850i	−0.270707	−	0.449086i
$204$	−11.1538	−	0.161764i	−0.780921	−	0.0113257i
$205$	−16.4213	−	20.5916i	−1.14691	−	1.43818i
$206$	6.59706	+	0.791793i	0.459639	+	0.0551669i
$207$	−0.510585	−	0.407178i	−0.0354881	−	0.0283008i
$208$	16.8314	−	12.6418i	1.16705	−	0.876553i
$209$	−0.865340	−	0.690086i	−0.0598568	−	0.0477342i
$210$	1.94641	+	9.67034i	0.134315	+	0.667317i
$211$	6.79583	−	5.41949i	0.467844	−	0.373093i	−0.361007	−	0.932563i	$-0.617567\pi$
$211$	6.79583	−	5.41949i	0.467844	−	0.373093i	0.828850	+	0.559470i	$0.188995\pi$
$212$	−2.50860	−	2.06076i	−0.172291	−	0.141533i
$213$	−15.0105	−	3.42604i	−1.02850	−	0.234749i
$214$	−1.46908	+	2.30083i	−0.100425	+	0.157282i
$215$	10.3079			0.702990
$216$	−2.64875	−	0.992019i	−0.180225	−	0.0674983i
$217$	9.17363	−	8.83987i	0.622747	−	0.600089i
$218$	−8.63863	+	24.1252i	−0.585082	+	1.63397i
$219$	−4.16425	+	0.950462i	−0.281394	+	0.0642263i
$220$	−5.18188	+	10.3727i	−0.349362	+	0.699330i
$221$	18.3006	+	22.9482i	1.23103	+	1.54366i
$222$	−3.31466	+	9.25690i	−0.222466	+	0.621283i
$223$	−0.400625	−	1.75525i	−0.0268279	−	0.117541i	0.959741	−	0.280887i	$-0.0906285\pi$
$223$	−0.400625	−	1.75525i	−0.0268279	−	0.117541i	−0.986569	+	0.163346i	$0.947771\pi$
$224$	11.1729	+	9.95824i	0.746520	+	0.665363i
$225$	0.433980	−	1.90139i	0.0289320	−	0.126759i
$226$	9.90339	+	6.32333i	0.658763	+	0.420622i
$227$	5.01200			0.332658			0.166329	−	0.986070i	$-0.446809\pi$
$227$	5.01200			0.332658			0.166329	+	0.986070i	$0.446809\pi$
$228$	0.984518	−	0.209737i	0.0652013	−	0.0138902i
$229$	6.22557	+	12.9275i	0.411397	+	0.854275i	0.998982	+	0.0451122i	$0.0143645\pi$
$229$	6.22557	+	12.9275i	0.411397	+	0.854275i	−0.587585	+	0.809163i	$0.699921\pi$
$230$	−0.255065	−	2.42145i	−0.0168185	−	0.159665i
$231$	5.45519	+	2.02305i	0.358925	+	0.133107i
$232$	5.52343	+	5.76912i	0.362631	+	0.378761i
$233$	2.93771	−	12.8709i	0.192456	−	0.843203i	−0.782827	−	0.622240i	$-0.786223\pi$
$233$	2.93771	−	12.8709i	0.192456	−	0.843203i	0.975282	−	0.220963i	$-0.0709200\pi$
$234$	2.40706	+	7.04238i	0.157355	+	0.460375i
$235$	−13.0086	−	27.0125i	−0.848585	−	1.76210i
$236$	13.3642	−	26.7516i	0.869936	−	1.74138i
$237$	2.79751	−	5.80910i	0.181718	−	0.377341i
$238$	−13.4278	+	15.9753i	−0.870397	+	1.03552i
$239$	6.49002	+	13.4767i	0.419805	+	0.871733i	0.998423	+	0.0561351i	$0.0178778\pi$
$239$	6.49002	+	13.4767i	0.419805	+	0.871733i	−0.578618	+	0.815598i	$0.696408\pi$
$240$	−4.29800	−	9.62973i	−0.277435	−	0.621597i
$241$	3.74034	−	0.853709i	0.240937	−	0.0549922i	−0.100347	−	0.994952i	$-0.531995\pi$
$241$	3.74034	−	0.853709i	0.240937	−	0.0549922i	0.341284	+	0.939960i	$0.389138\pi$
$242$	−4.58421	−	7.41454i	−0.294684	−	0.476625i
$243$	0.623490	−	0.781831i	0.0399969	−	0.0501545i
$244$	−17.5771	+	8.15283i	−1.12526	+	0.521932i
$245$	16.3188	+	8.61749i	1.04257	+	0.550551i
$246$	7.60328	−	11.9080i	0.484767	−	0.759226i
$247$	−2.07082	−	1.65142i	−0.131763	−	0.105078i
$248$	−7.49500	+	11.3714i	−0.475933	+	0.722086i
$249$	0.533577	+	2.33775i	0.0338141	+	0.148149i
$250$	−9.67120	+	5.97944i	−0.611660	+	0.378173i
$251$	−6.76839	+	3.25949i	−0.427217	+	0.205737i	−0.635122	−	0.772412i	$-0.719050\pi$
$251$	−6.76839	+	3.25949i	−0.427217	+	0.205737i	0.207904	+	0.978149i	$0.433336\pi$
$252$	−4.57097	+	2.66576i	−0.287944	+	0.167927i
$253$	−1.29392	−	0.623118i	−0.0813479	−	0.0391751i
$254$	−14.8264	+	1.56175i	−0.930290	+	0.0979927i
$255$	13.2480	−	6.37988i	0.829619	−	0.399524i
$256$	−13.9888	−	7.76621i	−0.874299	−	0.485388i
$257$	−17.9291	−	4.09220i	−1.11839	−	0.255264i	−0.376914	−	0.926248i	$-0.623015\pi$
$257$	−17.9291	−	4.09220i	−1.11839	−	0.255264i	−0.741472	+	0.670984i	$0.765872\pi$
$258$	1.78837	+	5.23226i	0.111339	+	0.325746i
$259$	9.49643	+	15.7540i	0.590079	+	0.978905i
$260$	−12.4006	+	24.8227i	−0.769052	+	1.53944i
$261$	−2.54416	+	1.22520i	−0.157480	+	0.0758381i
$262$	−1.39377	+	1.37370i	−0.0861072	+	0.0848675i
$263$			12.2187i			0.753438i	0.926328	+	0.376719i	$0.122948\pi$
$263$			12.2187i			0.753438i	−0.926328	+	0.376719i	$0.877052\pi$
$264$	−6.16423	−	0.830690i	−0.379382	−	0.0511255i
$265$	4.17215	+	0.952265i	0.256293	+	0.0584972i
$266$	0.860549	−	1.67508i	0.0527636	−	0.102706i
$267$	−5.91713	+	1.35055i	−0.362123	+	0.0826522i
$268$	−5.43148	−	7.01725i	−0.331781	−	0.428647i
$269$	2.22813	−	1.77687i	0.135851	−	0.108338i	−0.553207	−	0.833044i	$-0.686596\pi$
$269$	2.22813	−	1.77687i	0.135851	−	0.108338i	0.689058	+	0.724706i	$0.258025\pi$
$270$	3.70783	−	0.390567i	0.225652	−	0.0237692i
$271$	1.65821	+	7.26509i	0.100729	+	0.441323i	0.999992	+	0.00391501i	$0.00124619\pi$
$271$	1.65821	+	7.26509i	0.100729	+	0.441323i	−0.899263	+	0.437408i	$0.855897\pi$
$272$	10.2588	−	19.8114i	0.622028	−	1.20124i
$273$	13.0546	+	4.84129i	0.790103	+	0.293008i
$274$	11.4765	−	11.3112i	0.693319	−	0.683337i
$275$		−	4.28885i		−	0.258627i
$276$	1.18487	−	0.549582i	0.0713209	−	0.0330809i
$277$	4.57588	−	20.0483i	0.274938	−	1.20458i	−0.629166	−	0.777271i	$-0.716603\pi$
$277$	4.57588	−	20.0483i	0.274938	−	1.20458i	0.904104	−	0.427312i	$-0.140539\pi$
$278$	−20.7257	−	2.48755i	−1.24305	−	0.149193i
$279$	−3.00219	−	3.76462i	−0.179736	−	0.225382i
$280$	−19.0415	−	5.16098i	−1.13795	−	0.308428i
$281$	−11.9753	+	15.0165i	−0.714386	+	0.895812i	−0.998006	−	0.0631253i	$-0.979893\pi$
$281$	−11.9753	+	15.0165i	−0.714386	+	0.895812i	0.283620	+	0.958937i	$0.408465\pi$
$282$	11.4546	−	11.2897i	0.682113	−	0.672292i
$283$	−9.10794	+	11.4210i	−0.541411	+	0.678908i	−0.975000	−	0.222203i	$-0.928675\pi$
$283$	−9.10794	+	11.4210i	−0.541411	+	0.678908i	0.433590	+	0.901110i	$0.357247\pi$
$284$	19.5462	−	23.7940i	1.15986	−	1.41191i
$285$	−1.03740	+	0.827299i	−0.0614503	+	0.0490050i
$286$	8.60676	+	13.9206i	0.508928	+	0.823144i
$287$	−8.26616	−	25.1059i	−0.487936	−	1.48195i
$288$	4.14236	−	3.85238i	0.244091	−	0.227004i
$289$	12.7111	+	6.12135i	0.747712	+	0.360079i
$290$	−9.91185	−	3.54918i	−0.582044	−	0.208415i
$291$	−5.63466	+	11.7005i	−0.330310	+	0.685896i
$292$	2.02150	−	8.30005i	0.118299	−	0.485724i
$293$		−	32.2796i		−	1.88579i	−0.333085	−	0.942897i	$-0.608090\pi$
$293$		−	32.2796i		−	1.88579i	0.333085	−	0.942897i	$-0.391910\pi$
$294$	−1.54299	+	9.77851i	−0.0899890	+	0.570294i
$295$			39.4186i			2.29504i
$296$	−13.5994	−	14.2044i	−0.790452	−	0.825612i
$297$	0.954147	−	1.98131i	0.0553652	−	0.114967i
$298$	1.80904	−	5.05212i	0.104795	−	0.292661i
$299$	−3.09643	−	1.49116i	−0.179071	−	0.0862362i
$300$	3.01400	+	2.47594i	0.174014	+	0.142948i
$301$	9.69918	+	3.59692i	0.559051	+	0.207323i
$302$	16.5102	−	10.2078i	0.950053	−	0.587393i
$303$	−6.74642	+	5.38009i	−0.387572	+	0.309078i
$304$	−0.504715	+	1.94893i	−0.0289474	+	0.111779i
$305$	15.9243	−	19.9685i	0.911825	−	1.14339i
$306$	5.53689	+	5.61777i	0.316523	+	0.321147i
$307$	6.31096	−	7.91369i	0.360185	−	0.451658i	−0.568414	−	0.822743i	$-0.692443\pi$
$307$	6.31096	−	7.91369i	0.360185	−	0.451658i	0.928599	+	0.371085i	$0.121014\pi$
$308$	−8.49545	+	7.95202i	−0.484073	+	0.453108i
$309$	−2.92935	−	3.67328i	−0.166645	−	0.208966i
$310$	2.13934	−	17.8246i	0.121507	−	1.01237i
$311$	−3.38380	+	14.8254i	−0.191878	+	0.840672i	0.783721	+	0.621113i	$0.213319\pi$
$311$	−3.38380	+	14.8254i	−0.191878	+	0.840672i	−0.975599	+	0.219559i	$0.929538\pi$
$312$	−14.7514	−	1.98790i	−0.835135	−	0.112543i
$313$			34.5537i			1.95309i	0.215317	+	0.976544i	$0.430922\pi$
$313$			34.5537i			1.95309i	−0.215317	+	0.976544i	$0.569078\pi$
$314$	−23.4153	−	23.7574i	−1.32140	−	1.34071i
$315$	3.81975	−	5.83622i	0.215219	−	0.328834i
$316$	7.89299	+	10.1974i	0.444015	+	0.573650i
$317$	−1.58000	−	6.92243i	−0.0887417	−	0.388803i	0.910979	−	0.412454i	$-0.135328\pi$
$317$	−1.58000	−	6.92243i	−0.0887417	−	0.388803i	−0.999720	+	0.0236510i	$0.992471\pi$
$318$	0.240481	+	2.28299i	0.0134855	+	0.128024i
$319$	−4.85501	+	3.87174i	−0.271828	+	0.216776i
$320$	21.0708	+	0.917286i	1.17789	+	0.0512778i
$321$	1.88189	−	0.429530i	0.105037	−	0.0239740i
$322$	0.604959	−	2.36747i	0.0337131	−	0.131934i
$323$	−2.73679	−	0.624655i	−0.152279	−	0.0347568i
$324$	0.841545	+	1.81433i	0.0467525	+	0.100796i
$325$		−	10.2635i		−	0.569317i
$326$	−12.4659	−	12.6480i	−0.690424	−	0.700510i
$327$	16.3253	−	7.86187i	0.902794	−	0.434762i
$328$	14.5095	+	24.2470i	0.801153	+	1.33881i
$329$	−2.81439	−	29.9568i	−0.155162	−	1.65157i
$330$	7.75829	−	2.65176i	0.427080	−	0.145974i
$331$	2.56968	+	0.586513i	0.141243	+	0.0322377i	0.292558	−	0.956248i	$-0.405494\pi$
$331$	2.56968	+	0.586513i	0.141243	+	0.0322377i	−0.151315	+	0.988486i	$0.548351\pi$
$332$	−4.65954	−	1.13484i	−0.255725	−	0.0622826i
$333$	6.26407	−	3.01662i	0.343269	−	0.165310i
$334$	−2.39133	−	22.7020i	−0.130848	−	1.24220i
$335$	10.5387	+	5.07517i	0.575790	+	0.277286i
$336$	−0.683918	−	10.5609i	−0.0373108	−	0.576143i
$337$	2.42163	−	1.16619i	0.131914	−	0.0635266i	−0.366762	−	0.930315i	$-0.619534\pi$
$337$	2.42163	−	1.16619i	0.131914	−	0.0635266i	0.498677	+	0.866788i	$0.333819\pi$
$338$	10.9284	+	17.6757i	0.594427	+	0.961431i
$339$	−1.84881	−	8.10017i	−0.100414	−	0.439941i
$340$	−0.426465	+	29.4052i	−0.0231283	+	1.59472i
$341$	−8.27873	−	6.60207i	−0.448318	−	0.357522i
$342$	−0.599921	−	0.383051i	−0.0324400	−	0.0207130i
$343$	12.3481	+	13.8031i	0.666735	+	0.745295i
$344$	−10.9598	−	1.47695i	−0.590915	−	0.0796315i
$345$	−1.07346	+	1.34607i	−0.0577931	+	0.0724702i
$346$	−13.3879	+	8.27737i	−0.719736	+	0.444994i
$347$	−18.6447	+	4.25554i	−1.00090	+	0.228449i	−0.691418	−	0.722455i	$-0.743013\pi$
$347$	−18.6447	+	4.25554i	−1.00090	+	0.228449i	−0.309484	+	0.950905i	$0.600156\pi$
$348$	0.0818990	−	5.64701i	0.00439024	−	0.302712i
$349$	−15.6474	−	32.4922i	−0.837587	−	1.73927i	−0.654340	−	0.756200i	$-0.727054\pi$
$349$	−15.6474	−	32.4922i	−0.837587	−	1.73927i	−0.183247	−	0.983067i	$-0.558661\pi$
$350$	7.15383	−	1.43989i	0.382389	−	0.0769656i
$351$	2.28334	−	4.74141i	0.121876	−	0.253077i
$352$	6.99588	−	10.2863i	0.372881	−	0.548264i
$353$	1.57282	+	3.26599i	0.0837126	+	0.173831i	0.938623	−	0.344945i	$-0.112102\pi$
$353$	1.57282	+	3.26599i	0.0837126	+	0.173831i	−0.854910	+	0.518776i	$0.826388\pi$
$354$	−20.0088	+	6.83896i	−1.06346	+	0.363487i
$355$	−9.03222	+	39.5727i	−0.479380	+	2.10030i
$356$	2.87243	−	11.7939i	0.152238	−	0.625073i
$357$	14.6919	−	1.38028i	0.777579	−	0.0730522i
$358$	21.3460	−	2.24850i	1.12817	−	0.118837i
$359$	7.27372	+	15.1040i	0.383892	+	0.797160i	0.999955	+	0.00946355i	$0.00301239\pi$
$359$	7.27372	+	15.1040i	0.383892	+	0.797160i	−0.616063	+	0.787697i	$0.711273\pi$
$360$	−2.61530	+	6.98302i	−0.137838	+	0.368037i
$361$	−18.7467			−0.986668
$362$	13.1505	−	20.5958i	0.691173	−	1.08249i
$363$	−1.37162	+	6.00948i	−0.0719916	+	0.315416i
$364$	−20.3302	+	19.0297i	−1.06559	+	0.997429i
$365$	2.50574	+	10.9784i	0.131157	+	0.574634i
$366$	12.8988	+	4.61874i	0.674231	+	0.241425i
$367$	−12.3348	−	15.4673i	−0.643870	−	0.807388i	0.347611	−	0.937639i	$-0.386993\pi$
$367$	−12.3348	−	15.4673i	−0.643870	−	0.807388i	−0.991481	+	0.130251i	$0.958422\pi$
$368$	−0.0757553	+	2.61115i	−0.00394902	+	0.136116i
$369$	−9.73977	+	2.22304i	−0.507032	+	0.115727i
$370$	24.4043	+	8.73858i	1.26872	+	0.454297i
$371$	3.59349	+	2.35190i	0.186565	+	0.122105i
$372$	9.41891	−	2.00656i	0.488348	−	0.104035i
$373$	11.0833			0.573873			0.286936	−	0.957950i	$-0.407363\pi$
$373$	11.0833			0.573873			0.286936	+	0.957950i	$0.407363\pi$
$374$	14.6198	+	9.33479i	0.755973	+	0.482690i
$375$	7.83850	+	1.78909i	0.404778	+	0.0923880i
$376$	9.96090	+	30.5850i	0.513694	+	1.57730i
$377$	−11.6184	+	9.26534i	−0.598376	+	0.477189i
$378$	3.62517	+	0.926342i	0.186459	+	0.0476459i
$379$	19.9513	+	15.9106i	1.02483	+	0.817273i	0.983323	−	0.181866i	$-0.0582136\pi$
$379$	19.9513	+	15.9106i	1.02483	+	0.817273i	0.0415040	+	0.999138i	$0.486785\pi$
$380$	−0.552938	−	2.59552i	−0.0283651	−	0.133148i
$381$	8.24194	+	6.57273i	0.422247	+	0.336731i
$382$	−3.47887	+	28.9853i	−0.177995	+	1.48302i
$383$	11.1834	+	14.0236i	0.571447	+	0.716572i	0.980628	−	0.195882i	$-0.0627569\pi$
$383$	11.1834	+	14.0236i	0.571447	+	0.716572i	−0.409181	+	0.912453i	$0.634185\pi$
$384$	3.19008	+	10.8546i	0.162793	+	0.553924i
$385$	5.33344	−	14.3817i	0.271817	−	0.732961i
$386$	7.88460	+	0.946326i	0.401315	+	0.0481667i
$387$	1.69645	−	3.52271i	0.0862353	−	0.179069i
$388$	−15.8978	−	20.5393i	−0.807089	−	1.04273i
$389$	28.8371	+	13.8872i	1.46210	+	0.704109i	0.984648	−	0.174550i	$-0.0558470\pi$
$389$	28.8371	+	13.8872i	1.46210	+	0.704109i	0.477450	+	0.878659i	$0.341561\pi$
$390$	18.5661	−	6.34584i	0.940132	−	0.321334i
$391$	−3.64244			−0.184206
$392$	−16.1162	−	11.5008i	−0.813992	−	0.580876i
$393$	1.38377			0.0698020
$394$	5.75585	−	1.96733i	0.289976	−	0.0991127i
$395$	−15.3147	−	7.37519i	−0.770569	−	0.371086i
$396$	2.69206	+	3.47803i	0.135281	+	0.174778i
$397$	−4.13856	+	8.59380i	−0.207708	+	0.431311i	−0.978633	−	0.205616i	$-0.934080\pi$
$397$	−4.13856	+	8.59380i	−0.207708	+	0.431311i	0.770925	+	0.636927i	$0.219795\pi$
$398$	20.9446	+	2.51382i	1.04986	+	0.126006i
$399$	−1.26483	+	0.416447i	−0.0633206	+	0.0208484i
$400$	−7.12379	+	3.17954i	−0.356190	+	0.158977i
$401$	5.93156	+	7.43795i	0.296208	+	0.371433i	0.907558	−	0.419927i	$-0.137944\pi$
$401$	5.93156	+	7.43795i	0.296208	+	0.371433i	−0.611350	+	0.791361i	$0.709373\pi$
$402$	−0.747732	+	6.22995i	−0.0372935	+	0.310722i
$403$	−19.8116	−	15.7992i	−0.986885	−	0.787014i
$404$	−3.59587	−	16.8792i	−0.178901	−	0.839772i
$405$	−2.06117	−	1.64373i	−0.102421	−	0.0816776i
$406$	−8.08807	−	6.79834i	−0.401404	−	0.337396i
$407$	11.9537	−	9.53276i	0.592523	−	0.472521i
$408$	−15.0000	+	4.88520i	−0.742612	+	0.241853i
$409$	14.6535	+	3.34456i	0.724567	+	0.165378i	0.568870	−	0.822427i	$-0.307381\pi$
$409$	14.6535	+	3.34456i	0.724567	+	0.165378i	0.155697	+	0.987805i	$0.450238\pi$
$410$	−31.3935	−	20.0448i	−1.55042	−	0.989943i
$411$	−11.3942			−0.562032
$412$	9.19038	−	1.95787i	0.452777	−	0.0964575i
$413$	−13.7551	+	37.0909i	−0.676844	+	1.82512i
$414$	−0.869507	−	0.311349i	−0.0427340	−	0.0153020i
$415$	6.16311	−	1.40669i	0.302535	−	0.0690517i
$416$	16.7416	−	24.6159i	0.820825	−	1.20690i
$417$	9.20301	+	11.5402i	0.450673	+	0.565126i
$418$	−1.47364	−	0.527674i	−0.0720782	−	0.0258094i
$419$	−2.69174	−	11.7933i	−0.131500	−	0.576140i	−0.997147	−	0.0754845i	$-0.975950\pi$
$419$	−2.69174	−	11.7933i	−0.131500	−	0.576140i	0.865647	−	0.500655i	$-0.166907\pi$
$420$	7.02784	+	12.0506i	0.342924	+	0.588010i
$421$	−0.643723	+	2.82033i	−0.0313731	+	0.137455i	−0.988189	−	0.153240i	$-0.951029\pi$
$421$	−0.643723	+	2.82033i	−0.0313731	+	0.137455i	0.956816	+	0.290695i	$0.0938864\pi$
$422$	6.61536	−	10.3608i	0.322031	−	0.504354i
$423$	−11.3725			−0.552948
$424$	−4.29959	−	1.61030i	−0.208807	−	0.0782029i
$425$	−4.71965	−	9.80045i	−0.228937	−	0.475392i
$426$	−21.6541	+	2.28096i	−1.04915	+	0.110513i
$427$	21.9520	−	13.2326i	1.06233	−	0.640369i
$428$	−0.913550	+	3.75093i	−0.0441581	+	0.181308i
$429$	2.57520	−	11.2827i	0.124332	−	0.544732i
$430$	13.7940	−	4.71475i	0.665207	−	0.227366i
$431$	−16.1488	−	33.5332i	−0.777858	−	1.61524i	−0.788298	−	0.615294i	$-0.789037\pi$
$431$	−16.1488	−	33.5332i	−0.777858	−	1.61524i	0.0104393	−	0.999946i	$-0.496677\pi$
$432$	−3.99832	−	0.116000i	−0.192369	−	0.00558105i
$433$	−7.09903	+	14.7413i	−0.341158	+	0.708422i	−0.998999	−	0.0447353i	$-0.985756\pi$
$433$	−7.09903	+	14.7413i	−0.341158	+	0.708422i	0.657841	+	0.753157i	$0.271470\pi$
$434$	8.23289	−	16.0255i	0.395191	−	0.769249i
$435$	3.23005	+	6.70727i	0.154869	+	0.321589i
$436$	−0.525528	+	36.2357i	−0.0251683	+	1.73538i
$437$	0.320449	−	0.0731404i	0.0153292	−	0.00349878i
$438$	−5.13788	+	3.17661i	−0.245497	+	0.151785i
$439$	−1.03471	+	1.29749i	−0.0493841	+	0.0619257i	−0.805910	−	0.592038i	$-0.798324\pi$
$439$	−1.03471	+	1.29749i	−0.0493841	+	0.0619257i	0.756526	+	0.653964i	$0.226895\pi$
$440$	−2.18998	+	16.2510i	−0.104403	+	0.774736i
$441$	5.63074	−	4.15870i	0.268131	−	0.198033i
$442$	34.9863	+	22.3388i	1.66413	+	1.06255i
$443$	5.02277	+	4.00553i	0.238639	+	0.190308i	0.735506	−	0.677519i	$-0.236945\pi$
$443$	5.02277	+	4.00553i	0.238639	+	0.190308i	−0.496867	+	0.867827i	$0.665516\pi$
$444$	−0.201647	+	13.9037i	−0.00956972	+	0.659842i
$445$	3.56050	+	15.5996i	0.168784	+	0.739491i
$446$	−1.33896	−	2.16565i	−0.0634016	−	0.102546i
$447$	−3.41873	+	1.64637i	−0.161700	+	0.0778708i
$448$	19.5064	+	8.21575i	0.921593	+	0.388158i
$449$	−19.0116	−	9.15551i	−0.897213	−	0.432075i	−0.0723318	−	0.997381i	$-0.523044\pi$
$449$	−19.0116	−	9.15551i	−0.897213	−	0.432075i	−0.824882	+	0.565305i	$0.808758\pi$
$450$	−0.288930	−	2.74295i	−0.0136203	−	0.129304i
$451$	−19.7938	+	9.53217i	−0.932051	+	0.448852i
$452$	16.1450	+	3.93216i	0.759397	+	0.184953i
$453$	−13.3815	−	3.05423i	−0.628716	−	0.143500i
$454$	6.70708	−	2.29246i	0.314779	−	0.107590i
$455$	12.7633	−	34.4165i	0.598352	−	1.61347i
$456$	1.22155	−	0.730984i	0.0572045	−	0.0342315i
$457$	−29.2211	+	14.0721i	−1.36690	+	0.658266i	−0.966165	−	0.257925i	$-0.916961\pi$
$457$	−29.2211	+	14.0721i	−1.36690	+	0.658266i	−0.400740	+	0.916192i	$0.631247\pi$
$458$	14.2441	+	14.4521i	0.665581	+	0.675304i
$459$		−	5.57748i		−	0.260334i
$460$	−1.44888	−	3.12373i	−0.0675546	−	0.145644i
$461$	3.39765	+	0.775491i	0.158244	+	0.0361182i	0.300909	−	0.953653i	$-0.402710\pi$
$461$	3.39765	+	0.775491i	0.158244	+	0.0361182i	−0.142665	+	0.989771i	$0.545567\pi$
$462$	8.22549	+	0.212079i	0.382684	+	0.00986682i
$463$	15.4484	−	3.52599i	0.717947	−	0.163867i	0.152086	−	0.988367i	$-0.451401\pi$
$463$	15.4484	−	3.52599i	0.717947	−	0.163867i	0.565861	+	0.824501i	$0.308544\pi$
$464$	10.0302	+	5.19387i	0.465642	+	0.241119i
$465$	−9.92483	+	7.91479i	−0.460253	+	0.367039i
$466$	−1.95583	−	18.5676i	−0.0906023	−	0.860129i
$467$	−4.39040	−	19.2356i	−0.203163	−	0.890117i	−0.968996	−	0.247077i	$-0.920530\pi$
$467$	−4.39040	−	19.2356i	−0.203163	−	0.890117i	0.765833	−	0.643040i	$-0.222327\pi$
$468$	6.44229	+	8.32317i	0.297795	+	0.384739i
$469$	8.14541	+	8.45295i	0.376120	+	0.390321i
$470$	−29.7635	−	30.1983i	−1.37289	−	1.39294i
$471$			23.5869i			1.08683i
$472$	5.64803	−	41.9118i	0.259972	−	1.92915i
$473$	1.91329	−	8.38266i	0.0879730	−	0.385435i
$474$	1.08660	−	9.05332i	0.0499091	−	0.415833i
$475$	0.612011	+	0.767438i	0.0280810	+	0.0352125i
$476$	−10.6622	+	27.5200i	−0.488701	+	1.26138i
$477$	1.01208	−	1.26911i	0.0463400	−	0.0581085i
$478$	14.8491	+	15.0660i	0.679183	+	0.689105i
$479$	−11.2544	+	14.1126i	−0.514226	+	0.644819i	−0.969372	−	0.245598i	$-0.921016\pi$
$479$	−11.2544	+	14.1126i	−0.514226	+	0.644819i	0.455146	+	0.890417i	$0.349587\pi$
$480$	−10.1562	−	10.9207i	−0.463565	−	0.498458i
$481$	28.6060	−	22.8125i	1.30432	−	1.04016i
$482$	4.61486	−	2.85325i	0.210201	−	0.129962i
$483$	−1.47978	+	0.892006i	−0.0673325	+	0.0405877i
$484$	−9.52598	−	7.82538i	−0.432999	−	0.355699i
$485$	30.8465	+	14.8549i	1.40067	+	0.674526i
$486$	0.476752	−	1.33143i	0.0216259	−	0.0603949i
$487$	15.8480	−	32.9086i	0.718140	−	1.49123i	−0.146698	−	0.989181i	$-0.546865\pi$
$487$	15.8480	−	32.9086i	0.718140	−	1.49123i	0.864838	−	0.502051i	$-0.167421\pi$
$488$	−19.7927	+	18.9498i	−0.895974	+	0.857818i
$489$			12.5573i			0.567861i
$490$	25.7795	+	4.06785i	1.16460	+	0.183767i
$491$		−	17.9464i		−	0.809908i	−0.914337	−	0.404954i	$-0.867287\pi$
$491$		−	17.9464i		−	0.809908i	0.914337	−	0.404954i	$-0.132713\pi$
$492$	4.72809	−	19.4130i	0.213159	−	0.875207i
$493$	−6.83354	+	14.1900i	−0.307767	+	0.639085i
$494$	−3.52653	−	1.26276i	−0.158666	−	0.0568143i
$495$	−5.22340	−	2.51546i	−0.234774	−	0.113061i
$496$	−4.82862	+	18.6455i	−0.216812	+	0.837206i
$497$	−22.3077	+	34.0842i	−1.00064	+	1.52888i
$498$	1.78331	+	2.88434i	0.0799120	+	0.129250i
$499$	5.04556	−	4.02370i	0.225870	−	0.180126i	−0.504016	−	0.863695i	$-0.668145\pi$
$499$	5.04556	−	4.02370i	0.225870	−	0.180126i	0.729886	+	0.683569i	$0.239573\pi$
$500$	−10.2071	+	12.4253i	−0.456474	+	0.555675i
$501$	−10.0641	+	12.6200i	−0.449631	+	0.563819i
$502$	−7.56662	+	7.45768i	−0.337715	+	0.332853i
$503$	−16.5114	+	20.7046i	−0.736205	+	0.923172i	−0.999133	−	0.0416433i	$-0.986741\pi$
$503$	−16.5114	+	20.7046i	−0.736205	+	0.923172i	0.262927	+	0.964816i	$0.415312\pi$
$504$	−4.89759	+	5.65806i	−0.218156	+	0.252030i
$505$	14.1837	+	17.7859i	0.631168	+	0.791460i
$506$	−2.01654	−	0.242029i	−0.0896459	−	0.0107595i
$507$	3.26985	−	14.3261i	0.145219	−	0.636246i
$508$	−19.1264	+	8.87143i	−0.848596	+	0.393606i
$509$			12.3040i			0.545363i	0.962104	+	0.272682i	$0.0879106\pi$
$509$			12.3040i			0.545363i	−0.962104	+	0.272682i	$0.912089\pi$
$510$	14.8104	−	14.5971i	0.655814	−	0.646371i
$511$	−1.47312	+	11.2045i	−0.0651670	+	0.495657i
$512$	−22.2721	−	3.99439i	−0.984295	−	0.176529i
$513$	0.111996	+	0.490687i	0.00494475	+	0.0216643i
$514$	−25.8645	+	2.72446i	−1.14084	+	0.120171i
$515$	−9.68402	+	7.72275i	−0.426729	+	0.340305i
$516$	4.78641	+	6.18385i	0.210710	+	0.272229i
$517$	−24.3820	+	5.56503i	−1.07232	+	0.244750i
$518$	19.9139	+	16.7384i	0.874968	+	0.735445i
$519$	10.8509	+	2.47664i	0.476300	+	0.108712i
$520$	−5.24078	+	38.8898i	−0.229823	+	1.70543i
$521$		−	37.7280i		−	1.65289i	−0.563014	−	0.826447i	$-0.690358\pi$
$521$		−	37.7280i		−	1.65289i	0.563014	−	0.826447i	$-0.309642\pi$
$522$	−2.84421	+	2.80325i	−0.124487	+	0.122695i
$523$	7.95019	−	3.82861i	0.347638	−	0.167413i	−0.251914	−	0.967750i	$-0.581060\pi$
$523$	7.95019	−	3.82861i	0.347638	−	0.167413i	0.599551	+	0.800336i	$0.295346\pi$
$524$	−1.23682	+	2.47579i	−0.0540309	+	0.108155i
$525$	−4.31747	−	2.82574i	−0.188430	−	0.123325i
$526$	5.58877	+	16.3511i	0.243682	+	0.712943i
$527$	−26.1830	−	5.97609i	−1.14055	−	0.260323i
$528$	−8.62895	+	1.70785i	−0.375527	+	0.0743246i
$529$	−20.3380	+	9.79428i	−0.884262	+	0.425838i
$530$	6.01874	−	0.633989i	0.261438	−	0.0275387i
$531$	13.4713	+	6.48743i	0.584604	+	0.281531i
$532$	0.385420	−	2.63521i	0.0167101	−	0.114251i
$533$	−47.3678	+	22.8111i	−2.05173	+	0.988060i
$534$	−7.30060	+	4.51377i	−0.315928	+	0.195330i
$535$	−1.13239	−	4.96131i	−0.0489573	−	0.214496i
$536$	−10.4781	−	6.90619i	−0.452584	−	0.298302i
$537$	−11.8662	−	9.46298i	−0.512064	−	0.408358i
$538$	2.16896	−	3.39695i	0.0935104	−	0.146453i
$539$	10.0370	−	11.6714i	0.432324	−	0.502723i
$540$	4.78320	−	2.21860i	0.205836	−	0.0954733i
$541$	−4.91108	+	6.15830i	−0.211144	+	0.264766i	−0.876114	−	0.482104i	$-0.839873\pi$
$541$	−4.91108	+	6.15830i	−0.211144	+	0.264766i	0.664970	+	0.746870i	$0.268444\pi$
$542$	5.54203	+	8.96372i	0.238051	+	0.385025i
$543$	−16.8457	+	3.84492i	−0.722918	+	0.165001i
$544$	4.66671	−	31.2039i	0.200084	−	1.33786i
$545$	−20.7266	−	43.0391i	−0.887828	−	1.84359i
$546$	19.6842	+	0.507520i	0.842404	+	0.0217199i
$547$	10.4736	−	21.7487i	0.447820	−	0.929909i	−0.547817	−	0.836598i	$-0.684541\pi$
$547$	10.4736	−	21.7487i	0.447820	−	0.929909i	0.995637	−	0.0933102i	$-0.0297448\pi$
$548$	10.1842	−	20.3860i	0.435046	−	0.870847i
$549$	−4.20343	−	8.72852i	−0.179398	−	0.372524i
$550$	−1.96169	−	5.73935i	−0.0836468	−	0.244727i
$551$	0.316255	−	1.38560i	0.0134729	−	0.0590287i
$552$	1.33423	−	1.27741i	0.0567884	−	0.0543700i
$553$	−11.8368	−	12.2838i	−0.503354	−	0.522359i
$554$	−3.04648	−	28.9216i	−0.129433	−	1.22876i
$555$	−7.95283	−	16.5142i	−0.337579	−	0.700990i
$556$	−28.8730	+	6.15097i	−1.22449	+	0.260859i
$557$	0.257749			0.0109212			0.00546059	−	0.999985i	$-0.498262\pi$
$557$	0.257749			0.0109212			0.00546059	+	0.999985i	$0.498262\pi$
$558$	−5.73946	−	3.66465i	−0.242971	−	0.155137i
$559$	4.57863	−	20.0603i	0.193655	−	0.848459i
$560$	−27.8421	+	1.80304i	−1.17654	+	0.0761923i
$561$	−2.72930	−	11.9578i	−0.115231	−	0.504860i
$562$	−9.15691	+	25.5726i	−0.386261	+	1.07872i
$563$	−19.2663	−	24.1592i	−0.811978	−	1.01819i	−0.999355	−	0.0359000i	$-0.988570\pi$
$563$	−19.2663	−	24.1592i	−0.811978	−	1.01819i	0.187378	−	0.982288i	$-0.440001\pi$
$564$	10.1648	−	20.3472i	0.428015	−	0.856772i
$565$	−21.3548	+	4.87409i	−0.898403	+	0.205055i
$566$	−6.96439	+	19.4495i	−0.292735	+	0.817525i
$567$	−1.36588	−	2.26591i	−0.0573617	−	0.0951594i
$568$	15.2736	−	40.7816i	0.640867	−	1.71116i
$569$	−22.4115			−0.939539			−0.469769	−	0.882789i	$-0.655663\pi$
$569$	−22.4115			−0.939539			−0.469769	+	0.882789i	$0.655663\pi$
$570$	−1.00985	+	1.58160i	−0.0422980	+	0.0662457i
$571$	35.3377	+	8.06561i	1.47884	+	0.337535i	0.884447	−	0.466641i	$-0.154536\pi$
$571$	35.3377	+	8.06561i	1.47884	+	0.337535i	0.594392	+	0.804176i	$0.297393\pi$
$572$	17.8848	+	14.6920i	0.747802	+	0.614302i
$573$	16.1392	−	12.8706i	0.674224	−	0.537675i
$574$	−22.5451	−	29.8159i	−0.941014	−	1.24449i
$575$	0.995787	+	0.794113i	0.0415272	+	0.0331168i
$576$	3.78127	−	7.04997i	0.157553	−	0.293749i
$577$	0.554783	+	0.442424i	0.0230959	+	0.0184184i	0.634970	−	0.772537i	$-0.281013\pi$
$577$	0.554783	+	0.442424i	0.0230959	+	0.0184184i	−0.611874	+	0.790955i	$0.709584\pi$
$578$	19.8099	+	2.37763i	0.823984	+	0.0988964i
$579$	−3.50106	−	4.39019i	−0.145499	−	0.182450i
$580$	−14.8874	−	0.215913i	−0.618168	−	0.00896532i
$581$	6.29004	+	0.826990i	0.260955	+	0.0343093i
$582$	−2.18859	+	18.2349i	−0.0907202	+	0.755862i
$583$	1.54882	−	3.21616i	0.0641456	−	0.133200i
$584$	−1.09121	−	12.0318i	−0.0451547	−	0.497879i
$585$	−12.5000	−	6.01966i	−0.516809	−	0.248882i
$586$	−14.7645	−	43.1967i	−0.609915	−	1.78444i
$587$	−7.08222			−0.292314			−0.146157	−	0.989261i	$-0.546691\pi$
$587$	−7.08222			−0.292314			−0.146157	+	0.989261i	$0.546691\pi$
$588$	2.40779	+	13.7914i	0.0992957	+	0.568747i
$589$	2.42348			0.0998579
$590$	18.0298	+	52.7501i	0.742276	+	2.17169i
$591$	−3.87523	−	1.86621i	−0.159405	−	0.0767656i
$592$	−24.6958	−	12.7880i	−1.01499	−	0.525585i
$593$	12.9490	−	26.8889i	0.531753	−	1.10420i	−0.446116	−	0.894975i	$-0.647193\pi$
$593$	12.9490	−	26.8889i	0.531753	−	1.10420i	0.977869	−	0.209220i	$-0.0670926\pi$
$594$	0.370606	−	3.08781i	0.0152062	−	0.126695i
$595$	−3.63889	−	38.7329i	−0.149180	−	1.58789i
$596$	0.110052	−	7.58821i	0.00450791	−	0.310825i
$597$	−9.30021	−	11.6621i	−0.380632	−	0.477298i
$598$	−4.82571	−	0.579192i	−0.197338	−	0.0236849i
$599$	17.5092	+	13.9631i	0.715408	+	0.570519i	0.912110	−	0.409945i	$-0.134452\pi$
$599$	17.5092	+	13.9631i	0.715408	+	0.570519i	−0.196703	+	0.980463i	$0.563023\pi$
$600$	5.16583	+	1.93472i	0.210894	+	0.0789847i
$601$	27.4156	+	21.8632i	1.11831	+	0.891820i	0.994933	−	0.100540i	$-0.0320571\pi$
$601$	27.4156	+	21.8632i	1.11831	+	0.891820i	0.123374	+	0.992360i	$0.460629\pi$
$602$	14.6247	+	0.377071i	0.596058	+	0.0153683i
$603$	3.46888	−	2.76634i	0.141264	−	0.112654i
$604$	17.4250	−	21.2118i	0.709012	−	0.863094i
$605$	15.8430	+	3.61607i	0.644111	+	0.147014i
$606$	−6.56727	+	10.2854i	−0.266777	+	0.417817i
$607$	−1.50475			−0.0610761			−0.0305381	−	0.999534i	$-0.509722\pi$
$607$	−1.50475			−0.0610761			−0.0305381	+	0.999534i	$0.509722\pi$
$608$	0.216016	+	2.83892i	0.00876061	+	0.115133i
$609$	0.698818	+	7.43833i	0.0283175	+	0.301416i
$610$	12.1766	−	34.0056i	0.493014	−	1.37685i
$611$	−58.3478	+	13.3175i	−2.36050	+	0.538768i
$612$	9.97903	+	4.98519i	0.403378	+	0.201514i
$613$	−4.57842	−	5.74115i	−0.184920	−	0.231883i	0.680727	−	0.732537i	$-0.261664\pi$
$613$	−4.57842	−	5.74115i	−0.184920	−	0.231883i	−0.865647	+	0.500655i	$0.833093\pi$
$614$	4.82568	−	13.4767i	0.194748	−	0.543876i
$615$	5.86069	+	25.6773i	0.236326	+	1.03541i
$616$	−7.73144	+	14.5272i	−0.311509	+	0.585317i
$617$	8.25141	−	36.1518i	0.332189	−	1.45542i	−0.482693	−	0.875790i	$-0.660341\pi$
$617$	8.25141	−	36.1518i	0.332189	−	1.45542i	0.814882	−	0.579626i	$-0.196802\pi$
$618$	−5.60020	−	3.57574i	−0.225273	−	0.143837i
$619$	−47.8506			−1.92328			−0.961640	−	0.274315i	$-0.911549\pi$
$619$	−47.8506			−1.92328			−0.961640	+	0.274315i	$0.911549\pi$
$620$	−5.28997	−	24.8314i	−0.212450	−	0.997255i
$621$	0.283353	+	0.588389i	0.0113706	+	0.0236112i
$622$	2.25283	+	21.3872i	0.0903304	+	0.857547i
$623$	−2.09321	+	15.9209i	−0.0838627	+	0.637856i
$624$	−20.6497	+	4.08700i	−0.826649	+	0.163611i
$625$	6.88654	−	30.1719i	0.275461	−	1.20688i
$626$	15.8046	+	46.2399i	0.631680	+	1.84812i
$627$	0.480228	+	0.997203i	0.0191784	+	0.0398244i
$628$	−42.2009	−	21.0822i	−1.68400	−	0.841271i
$629$	16.8251	−	34.9377i	0.670862	−	1.39306i
$630$	2.44215	−	9.55719i	0.0972977	−	0.380768i
$631$	−13.4227	−	27.8725i	−0.534349	−	1.10959i	−0.977068	−	0.212927i	$-0.931700\pi$
$631$	−13.4227	−	27.8725i	−0.534349	−	1.10959i	0.442719	−	0.896661i	$-0.354014\pi$
$632$	15.2267	+	10.0360i	0.605684	+	0.399212i
$633$	−8.47426	+	1.93419i	−0.336821	+	0.0768773i
$634$	−5.28064	−	8.54095i	−0.209721	−	0.339204i
$635$	17.3279	−	21.7285i	0.687638	−	0.862271i
$636$	1.36604	+	2.94512i	0.0541670	+	0.116781i
$637$	24.0192	−	27.9305i	0.951677	−	1.10664i
$638$	−4.72608	+	7.40183i	−0.187107	+	0.293041i
$639$	12.0375	+	9.59956i	0.476195	+	0.379753i
$640$	28.6165	−	8.41012i	1.13117	−	0.332439i
$641$	3.20364	+	14.0361i	0.126536	+	0.554391i	0.997959	+	0.0638586i	$0.0203407\pi$
$641$	3.20364	+	14.0361i	0.126536	+	0.554391i	−0.871423	+	0.490533i	$0.836802\pi$
$642$	2.32189	−	1.43556i	0.0916378	−	0.0566572i
$643$	−27.4146	+	13.2022i	−1.08112	+	0.520642i	−0.887676	−	0.460468i	$-0.847682\pi$
$643$	−27.4146	+	13.2022i	−1.08112	+	0.520642i	−0.193448	+	0.981110i	$0.561967\pi$
$644$	−0.273305	−	3.44486i	−0.0107697	−	0.135746i
$645$	−9.28706	−	4.47241i	−0.365678	−	0.176101i
$646$	−3.94810	+	0.415876i	−0.155336	+	0.0163624i
$647$	−16.4588	+	7.92613i	−0.647061	+	0.311608i	−0.728475	−	0.685072i	$-0.759771\pi$
$647$	−16.4588	+	7.92613i	−0.647061	+	0.311608i	0.0814142	+	0.996680i	$0.474056\pi$
$648$	1.95602	+	2.04303i	0.0768399	+	0.0802578i
$649$	32.0564	+	7.31665i	1.25832	+	0.287204i
$650$	−4.69446	−	13.7347i	−0.184132	−	0.538718i
$651$	−12.1006	+	3.98416i	−0.474261	+	0.156151i
$652$	−22.4671	−	11.2238i	−0.879879	−	0.439558i
$653$	−30.0688	+	14.4804i	−1.17668	+	0.566660i	−0.916943	−	0.399019i	$-0.869351\pi$
$653$	−30.0688	+	14.4804i	−1.17668	+	0.566660i	−0.259739	+	0.965679i	$0.583636\pi$
$654$	18.2507	−	17.9879i	0.713658	−	0.703383i
$655$		−	3.64809i		−	0.142543i
$656$	30.5071	+	25.8108i	1.19110	+	1.00774i
$657$	4.16425	+	0.950462i	0.162463	+	0.0370811i
$658$	−17.4683	−	38.8010i	−0.680984	−	1.51262i
$659$	−18.4112	+	4.20223i	−0.717198	+	0.163696i	−0.565521	−	0.824734i	$-0.691325\pi$
$659$	−18.4112	+	4.20223i	−0.717198	+	0.163696i	−0.151678	+	0.988430i	$0.548468\pi$
$660$	9.16927	−	7.09719i	0.356914	−	0.276258i
$661$	−14.3484	+	11.4425i	−0.558088	+	0.445060i	−0.861470	−	0.507809i	$-0.830456\pi$
$661$	−14.3484	+	11.4425i	−0.558088	+	0.445060i	0.303382	+	0.952869i	$0.401884\pi$
$662$	3.70703	−	0.390482i	0.144078	−	0.0151765i
$663$	−6.53140	−	28.6159i	−0.253658	−	1.11135i
$664$	−6.75449	+	0.612592i	−0.262125	+	0.0237732i
$665$	1.09789	+	3.33451i	0.0425745	+	0.129307i
$666$	7.00283	−	6.90200i	0.271354	−	0.267447i
$667$		−	1.84412i		−	0.0714046i
$668$	−13.5839	−	29.2862i	−0.525575	−	1.13312i
$669$	−0.400625	+	1.75525i	−0.0154891	+	0.0678620i
$670$	16.4243	+	1.97128i	0.634525	+	0.0761571i
$671$	−13.2832	−	16.6566i	−0.512792	−	0.643020i
$672$	−5.74571	−	13.8198i	−0.221645	−	0.533110i
$673$	−16.4292	+	20.6016i	−0.633301	+	0.794134i	−0.990147	−	0.140029i	$-0.955280\pi$
$673$	−16.4292	+	20.6016i	−0.633301	+	0.794134i	0.356847	+	0.934163i	$0.383852\pi$
$674$	2.70722	−	2.66824i	0.104278	−	0.102777i
$675$	−1.21598	+	1.52480i	−0.0468032	+	0.0586894i
$676$	22.7092	+	18.6551i	0.873431	+	0.717504i
$677$	−18.1727	+	14.4922i	−0.698432	+	0.556981i	−0.907053	−	0.421015i	$-0.861674\pi$
$677$	−18.1727	+	14.4922i	−0.698432	+	0.556981i	0.208621	+	0.977996i	$0.433102\pi$
$678$	−6.17905	−	9.99404i	−0.237305	−	0.383819i
$679$	23.8414	+	24.7416i	0.914949	+	0.949495i
$680$	12.8790	+	39.5452i	0.493889	+	1.51649i
$681$	−4.51566	−	2.17463i	−0.173040	−	0.0833319i
$682$	−14.0984	−	5.04827i	−0.539855	−	0.193308i
$683$	−6.86777	+	14.2611i	−0.262788	+	0.545685i	−0.990057	−	0.140668i	$-0.955075\pi$
$683$	−6.86777	+	14.2611i	−0.262788	+	0.545685i	0.727269	+	0.686353i	$0.240789\pi$
$684$	−0.978022	−	0.238200i	−0.0373956	−	0.00910780i
$685$			30.0389i			1.14773i
$686$	22.8377	+	12.8234i	0.871948	+	0.489599i
$687$		−	14.3485i		−	0.547428i
$688$	−15.3420	+	3.03651i	−0.584910	+	0.115766i
$689$	3.70643	−	7.69649i	0.141204	−	0.293213i
$690$	−0.820821	+	2.29232i	−0.0312481	+	0.0872670i
$691$	13.9336	+	6.71007i	0.530060	+	0.255263i	0.679717	−	0.733475i	$-0.262103\pi$
$691$	13.9336	+	6.71007i	0.530060	+	0.255263i	−0.149657	+	0.988738i	$0.547817\pi$
$692$	−14.1297	+	17.2003i	−0.537130	+	0.653859i
$693$	−4.03719	−	4.18962i	−0.153360	−	0.159151i
$694$	−23.0040	+	14.2228i	−0.873220	+	0.539889i
$695$	30.4239	−	24.2623i	1.15404	−	0.920320i
$696$	−2.47331	−	7.59432i	−0.0937507	−	0.287862i
$697$	−34.7411	+	43.5640i	−1.31591	+	1.65010i
$698$	−35.8012	−	36.3242i	−1.35509	−	1.37489i
$699$	−8.23127	+	10.3217i	−0.311335	+	0.390402i
$700$	8.91469	−	5.19899i	0.336944	−	0.196503i
$701$	11.6800	+	14.6462i	0.441146	+	0.553179i	0.951845	−	0.306580i	$-0.0991847\pi$
$701$	11.6800	+	14.6462i	0.441146	+	0.553179i	−0.510699	+	0.859760i	$0.670613\pi$
$702$	0.886886	−	7.38935i	0.0334734	−	0.278893i
$703$	−0.778663	+	3.41155i	−0.0293678	+	0.128669i
$704$	4.65700	−	16.9651i	0.175517	−	0.639396i
$705$			29.9817i			1.12917i
$706$	3.59859	+	3.65116i	0.135435	+	0.137413i
$707$	7.13983	+	21.6850i	0.268521	+	0.815549i
$708$	−23.6478	+	18.3038i	−0.888740	+	0.687901i
$709$	10.3151	+	45.1935i	0.387393	+	1.69728i	0.673587	+	0.739108i	$0.264753\pi$
$709$	10.3151	+	45.1935i	0.387393	+	1.69728i	−0.286194	+	0.958172i	$0.592390\pi$
$710$	6.01337	+	57.0877i	0.225678	+	2.14246i
$711$	−5.04094	+	4.02002i	−0.189050	+	0.150762i
$712$	−1.55054	−	17.0964i	−0.0581091	−	0.640715i
$713$	3.06574	−	0.699736i	0.114813	−	0.0262053i
$714$	19.0295	−	8.56709i	0.712160	−	0.320615i
$715$	−29.7449	−	6.78909i	−1.11240	−	0.253898i
$716$	27.5369	−	12.7725i	1.02910	−	0.477331i
$717$		−	14.9580i		−	0.558616i
$718$	16.6422	+	16.8853i	0.621082	+	0.630155i
$719$	4.46182	−	2.14870i	0.166398	−	0.0801329i	−0.348831	−	0.937186i	$-0.613421\pi$
$719$	4.46182	−	2.14870i	0.166398	−	0.0801329i	0.515229	+	0.857053i	$0.327707\pi$
$720$	−0.305815	+	10.5409i	−0.0113971	+	0.392837i
$721$	−11.8070	+	3.88749i	−0.439717	+	0.144778i
$722$	−25.0869	+	8.57462i	−0.933637	+	0.319114i
$723$	−3.74034	−	0.853709i	−0.139105	−	0.0317498i
$724$	8.17761	−	33.5763i	0.303918	−	1.24785i
$725$	4.96184	−	2.38950i	0.184278	−	0.0887437i
$726$	0.913186	+	8.66929i	0.0338915	+	0.321747i
$727$	2.58698	+	1.24582i	0.0959458	+	0.0462051i	0.481241	−	0.876588i	$-0.340186\pi$
$727$	2.58698	+	1.24582i	0.0959458	+	0.0462051i	−0.385295	+	0.922793i	$0.625900\pi$
$728$	−18.5019	+	34.7646i	−0.685725	+	1.28846i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	8.37463	+	13.5452i	0.309959	+	0.501330i
$731$	−4.85262	−	21.2607i	−0.179480	−	0.786355i
$732$	19.3738	+	0.280980i	0.716077	+	0.0103853i
$733$	12.3074	+	9.81481i	0.454584	+	0.362518i	0.823852	−	0.566804i	$-0.191820\pi$
$733$	12.3074	+	9.81481i	0.454584	+	0.362518i	−0.369269	+	0.929323i	$0.620392\pi$
$734$	−23.5811	−	15.0566i	−0.870395	−	0.555749i
$735$	−10.9637	−	14.8445i	−0.404403	−	0.547549i
$736$	1.09295	+	3.52890i	0.0402866	+	0.130077i
$737$	6.08341	−	7.62835i	0.224085	−	0.280994i
$738$	−12.0170	+	7.42979i	−0.442352	+	0.273494i
$739$	−5.35779	+	1.22288i	−0.197090	+	0.0449844i	−0.319926	−	0.947443i	$-0.603658\pi$
$739$	−5.35779	+	1.22288i	−0.197090	+	0.0449844i	0.122837	+	0.992427i	$0.460801\pi$
$740$	36.6550	+	0.531609i	1.34746	+	0.0195423i
$741$	1.14922	+	2.38638i	0.0422176	+	0.0876657i
$742$	5.88457	+	1.50369i	0.216029	+	0.0552020i
$743$	−17.1343	+	35.5797i	−0.628596	+	1.30529i	0.306828	+	0.951765i	$0.400732\pi$
$743$	−17.1343	+	35.5797i	−0.628596	+	1.30529i	−0.935424	+	0.353528i	$0.884982\pi$
$744$	11.6866	−	6.99334i	0.428453	−	0.256388i
$745$	4.34040	+	9.01293i	0.159020	+	0.330208i
$746$	14.8318	−	5.06945i	0.543029	−	0.185606i
$747$	0.533577	−	2.33775i	0.0195226	−	0.0855339i
$748$	23.8340	+	5.80483i	0.871457	+	0.212246i
$749$	0.665727	−	5.06349i	0.0243251	−	0.185016i
$750$	11.3078	−	1.19112i	0.412904	−	0.0434935i
$751$	8.83820	+	18.3527i	0.322511	+	0.669700i	0.997688	−	0.0679550i	$-0.0216474\pi$
$751$	8.83820	+	18.3527i	0.322511	+	0.669700i	−0.675178	+	0.737655i	$0.735933\pi$
$752$	27.3191	+	36.3729i	0.996226	+	1.32638i
$753$	7.51235			0.273765
$754$	−11.3098	+	17.7131i	−0.411880	+	0.645072i
$755$	−8.05200	+	35.2781i	−0.293042	+	1.28390i
$756$	5.27493	−	0.418497i	0.191847	−	0.0152206i
$757$	−3.16191	−	13.8532i	−0.114922	−	0.503504i	−0.999323	−	0.0367782i	$-0.988291\pi$
$757$	−3.16191	−	13.8532i	−0.114922	−	0.503504i	0.884402	−	0.466726i	$-0.154567\pi$
$758$	33.9763	+	12.1660i	1.23407	+	0.441891i
$759$	0.895418	+	1.12282i	0.0325016	+	0.0407558i
$760$	−1.92712	−	3.22043i	−0.0699040	−	0.116817i
$761$	6.24497	−	1.42537i	0.226380	−	0.0516698i	−0.107826	−	0.994170i	$-0.534389\pi$
$761$	6.24497	−	1.42537i	0.226380	−	0.0516698i	0.334206	+	0.942500i	$0.391532\pi$
$762$	14.0357	+	5.02584i	0.508461	+	0.182067i
$763$	−4.48417	−	47.7302i	−0.162338	−	1.72795i
$764$	8.60224	+	40.3794i	0.311218	+	1.46088i
$765$	−14.7041			−0.531629
$766$	21.3800	+	13.6512i	0.772491	+	0.493237i
$767$	76.7131	+	17.5093i	2.76995	+	0.632223i
$768$	9.23382	+	13.0666i	0.333197	+	0.471501i
$769$	−21.9455	+	17.5010i	−0.791376	+	0.631102i	−0.933431	−	0.358757i	$-0.883201\pi$
$769$	−21.9455	+	17.5010i	−0.791376	+	0.631102i	0.142055	+	0.989859i	$0.454629\pi$
$770$	0.559113	−	21.6852i	0.0201490	−	0.781480i
$771$	14.3780	+	11.4661i	0.517812	+	0.412941i
$772$	10.9840	−	2.33999i	0.395324	−	0.0842180i
$773$	12.2689	+	9.78412i	0.441281	+	0.351910i	0.818787	−	0.574097i	$-0.194647\pi$
$773$	12.2689	+	9.78412i	0.441281	+	0.351910i	−0.377506	+	0.926007i	$0.623218\pi$
$774$	0.658928	−	5.49005i	0.0236847	−	0.197336i
$775$	5.85513	+	7.34210i	0.210322	+	0.263736i
$776$	−30.6691	−	20.2143i	−1.10096	−	0.725650i
$777$	−1.72059	−	18.3142i	−0.0617257	−	0.657018i
$778$	44.9418	+	5.39402i	1.61124	+	0.193385i
$779$	2.18163	−	4.53021i	0.0781651	−	0.162311i
$780$	21.9427	−	16.9841i	0.785675	−	0.608127i
$781$	30.5052	+	14.6905i	1.09156	+	0.525669i
$782$	−4.87433	+	1.66603i	−0.174306	+	0.0595771i
$783$	2.82380			0.100915
$784$	−26.8272	−	8.01891i	−0.958113	−	0.286390i
$785$	62.1832			2.21941
$786$	1.85177	−	0.632928i	0.0660503	−	0.0225758i
$787$	41.8841	+	20.1703i	1.49301	+	0.718994i	0.989437	−	0.144961i	$-0.0463055\pi$
$787$	41.8841	+	20.1703i	1.49301	+	0.718994i	0.503569	+	0.863955i	$0.332020\pi$
$788$	6.80266	−	5.26538i	0.242335	−	0.187572i
$789$	5.30150	−	11.0087i	0.188738	−	0.391919i
$790$	−23.8676	−	2.86464i	−0.849172	−	0.101919i
$791$	−21.7946	−	2.86547i	−0.774927	−	0.101884i
$792$	5.19336	+	3.42299i	0.184538	+	0.121631i
$793$	−31.7876	−	39.8604i	−1.12881	−	1.41548i
$794$	−1.60748	+	13.3932i	−0.0570474	+	0.475307i
$795$	−3.34580	−	2.66819i	−0.118663	−	0.0946309i
$796$	29.1780	−	6.21594i	1.03419	−	0.220318i
$797$	−8.29539	−	6.61535i	−0.293838	−	0.234328i	0.465463	−	0.885067i	$-0.345888\pi$
$797$	−8.29539	−	6.61535i	−0.293838	−	0.234328i	−0.759301	+	0.650739i	$0.774459\pi$
$798$	−1.50212	+	1.13581i	−0.0531744	+	0.0402074i
$799$	−49.5913	+	39.5477i	−1.75441	+	1.39910i
$800$	−8.07879	+	7.51325i	−0.285628	+	0.265634i
$801$	5.91713	+	1.35055i	0.209072	+	0.0477192i
$802$	11.3397	+	7.24043i	0.400419	+	0.255668i
$803$	9.39304			0.331473
$804$	1.84892	+	8.67896i	0.0652065	+	0.306083i
$805$	2.35163	+	3.90121i	0.0828841	+	0.137500i
$806$	−33.7384	−	12.0809i	−1.18838	−	0.425530i
$807$	−2.77843	+	0.634158i	−0.0978052	+	0.0223234i
$808$	−12.5325	−	20.9431i	−0.440890	−	0.736776i
$809$	−16.3079	−	20.4494i	−0.573354	−	0.718964i	0.407609	−	0.913157i	$-0.366363\pi$
$809$	−16.3079	−	20.4494i	−0.573354	−	0.718964i	−0.980963	+	0.194193i	$0.937791\pi$
$810$	−3.51010	−	1.25688i	−0.123332	−	0.0441623i
$811$	−8.66570	−	37.9669i	−0.304294	−	1.33320i	−0.863575	−	0.504220i	$-0.831780\pi$
$811$	−8.66570	−	37.9669i	−0.304294	−	1.33320i	0.559281	−	0.828978i	$-0.311077\pi$
$812$	−13.9330	−	5.39813i	−0.488953	−	0.189437i
$813$	1.65821	−	7.26509i	0.0581559	−	0.254798i
$814$	11.6363	−	18.2243i	0.407851	−	0.638762i
$815$	33.1053			1.15963
$816$	−17.8386	+	13.3983i	−0.624478	+	0.469035i
$817$	0.853832	+	1.77300i	0.0298718	+	0.0620294i
$818$	21.1391	−	2.22670i	0.739112	−	0.0778549i
$819$	−9.66127	−	10.0261i	−0.337592	−	0.350339i
$820$	−51.1793	−	12.4649i	−1.78726	−	0.435292i
$821$	−11.0656	+	48.4817i	−0.386193	+	1.69202i	0.291414	+	0.956597i	$0.405874\pi$
$821$	−11.0656	+	48.4817i	−0.386193	+	1.69202i	−0.677607	+	0.735424i	$0.736983\pi$
$822$	−15.2477	+	5.21162i	−0.531825	+	0.181776i
$823$	22.6255	+	46.9823i	0.788674	+	1.63770i	0.770144	+	0.637870i	$0.220184\pi$
$823$	22.6255	+	46.9823i	0.788674	+	1.63770i	0.0185303	+	0.999828i	$0.494101\pi$
$824$	11.4031	−	6.82366i	0.397245	−	0.237713i
$825$	−1.86086	+	3.86412i	−0.0647868	+	0.134531i
$826$	−1.44197	+	55.9267i	−0.0501725	+	1.94594i
$827$	−4.67940	−	9.71688i	−0.162719	−	0.337889i	0.803628	−	0.595132i	$-0.202900\pi$
$827$	−4.67940	−	9.71688i	−0.162719	−	0.337889i	−0.966347	+	0.257243i	$0.917186\pi$
$828$	−1.30599	−	0.0189408i	−0.0453862	−	0.000658238i
$829$	41.3451	−	9.43675i	1.43597	−	0.327752i	0.567454	−	0.823405i	$-0.307929\pi$
$829$	41.3451	−	9.43675i	1.43597	−	0.327752i	0.868520	+	0.495654i	$0.165071\pi$
$830$	7.60409	−	4.70141i	0.263942	−	0.163188i
$831$	−12.8213	+	16.0775i	−0.444767	+	0.557721i
$832$	11.1445	−	40.5987i	0.386367	−	1.40751i
$833$	10.0918	−	37.7155i	0.349661	−	1.30677i
$834$	17.5939	+	11.2338i	0.609228	+	0.388993i
$835$	33.2706	+	26.5324i	1.15138	+	0.918191i
$836$	−2.21339	−	0.0321009i	−0.0765517	−	0.00111023i
$837$	1.07147	+	4.69441i	0.0370354	+	0.162263i
$838$	−8.99627	−	14.5506i	−0.310771	−	0.502643i
$839$	40.6457	−	19.5739i	1.40324	−	0.675767i	0.429428	−	0.903101i	$-0.358715\pi$
$839$	40.6457	−	19.5739i	1.40324	−	0.675767i	0.973817	+	0.227334i	$0.0730010\pi$
$840$	14.9166	+	12.9117i	0.514671	+	0.445496i
$841$	18.9439	+	9.12290i	0.653238	+	0.314583i
$842$	0.428571	+	4.06862i	0.0147695	+	0.140214i
$843$	17.3048	−	8.33355i	0.596009	−	0.287023i
$844$	4.11376	−	16.8906i	0.141601	−	0.581400i
$845$	−37.7686	−	8.62043i	−1.29928	−	0.296552i
$846$	−15.2187	+	5.20169i	−0.523229	+	0.178838i
$847$	13.6457	+	8.93096i	0.468871	+	0.306871i
$848$	−6.49027	−	0.188297i	−0.222877	−	0.00646615i
$849$	13.1614	−	6.33817i	0.451696	−	0.217526i
$850$	−10.7985	−	10.9563i	−0.370386	−	0.375797i
$851$			4.54048i			0.155646i
$852$	−27.9344	+	12.9569i	−0.957016	+	0.443895i
$853$	23.3212	+	5.32290i	0.798501	+	0.182253i	0.602257	−	0.798302i	$-0.294268\pi$
$853$	23.3212	+	5.32290i	0.798501	+	0.182253i	0.196244	+	0.980555i	$0.437125\pi$
$854$	23.3238	−	27.7486i	0.798123	−	0.949537i
$855$	1.29362	−	0.295260i	0.0442408	−	0.0100977i
$856$	0.493137	+	5.43737i	0.0168551	+	0.185845i
$857$	−18.4446	+	14.7091i	−0.630056	+	0.502453i	−0.885663	−	0.464328i	$-0.846296\pi$
$857$	−18.4446	+	14.7091i	−0.630056	+	0.502453i	0.255608	+	0.966781i	$0.417724\pi$
$858$	−1.71449	−	16.2764i	−0.0585316	−	0.555667i
$859$	−8.63228	−	37.8205i	−0.294530	−	1.29042i	−0.878147	−	0.478390i	$-0.841220\pi$
$859$	−8.63228	−	37.8205i	−0.294530	−	1.29042i	0.583617	−	0.812029i	$-0.301637\pi$
$860$	16.3027	−	12.6186i	0.555918	−	0.430291i
$861$	−3.44548	+	26.2062i	−0.117422	+	0.893104i
$862$	−36.9482	−	37.4880i	−1.25846	−	1.27685i
$863$			11.9786i			0.407758i	0.978996	+	0.203879i	$0.0653549\pi$
$863$			11.9786i			0.407758i	−0.978996	+	0.203879i	$0.934645\pi$
$864$	−5.40362	+	1.67357i	−0.183835	+	0.0569362i
$865$	6.52926	−	28.6066i	0.222002	−	0.972652i
$866$	−2.75738	+	22.9739i	−0.0936996	+	0.780686i
$867$	−8.79636	−	11.0303i	−0.298740	−	0.374608i
$868$	3.68732	−	25.2111i	0.125156	−	0.855720i
$869$	−8.84036	+	11.0855i	−0.299889	+	0.376049i
$870$	7.39033	+	7.49829i	0.250556	+	0.254216i
$871$	14.5580	−	18.2552i	0.493280	−	0.618553i
$872$	15.8707	+	48.7312i	0.537451	+	1.65025i
$873$	10.1533	−	8.09700i	0.343638	−	0.274042i
$874$	0.395372	−	0.244448i	0.0133737	−	0.00826858i
$875$	11.6491	−	17.7988i	0.393813	−	0.601710i
$876$	−5.42257	+	6.60099i	−0.183212	+	0.223027i
$877$	−43.8555	−	21.1197i	−1.48090	−	0.713162i	−0.493254	−	0.869885i	$-0.664193\pi$
$877$	−43.8555	−	21.1197i	−1.48090	−	0.713162i	−0.987643	+	0.156723i	$0.949907\pi$
$878$	−0.791193	+	2.20957i	−0.0267015	+	0.0745695i
$879$	−14.0056	+	29.0829i	−0.472397	+	0.980942i
$880$	4.50247	+	22.7489i	0.151778	+	0.766864i
$881$		−	5.08783i		−	0.171413i	−0.996320	−	0.0857067i	$-0.972685\pi$
$881$		−	5.08783i		−	0.171413i	0.996320	−	0.0857067i	$-0.0273148\pi$
$882$	5.63292	−	8.14065i	0.189670	−	0.274110i
$883$		−	18.5543i		−	0.624403i	−0.950016	−	0.312202i	$-0.898934\pi$
$883$		−	18.5543i		−	0.624403i	0.950016	−	0.312202i	$-0.101066\pi$
$884$	57.0364	+	13.8914i	1.91834	+	0.467217i
$885$	17.1031	−	35.5149i	0.574914	−	1.19382i
$886$	8.55359	+	3.06283i	0.287364	+	0.102898i
$887$	−49.7196	−	23.9437i	−1.66942	−	0.803950i	−0.998023	−	0.0628518i	$-0.979980\pi$
$887$	−49.7196	−	23.9437i	−1.66942	−	0.803950i	−0.671397	−	0.741098i	$-0.734305\pi$
$888$	6.08964	+	18.6983i	0.204355	+	0.627473i
$889$	23.8869	−	14.3989i	0.801141	−	0.482924i
$890$	11.8998	+	19.2469i	0.398883	+	0.645157i
$891$	−1.71931	+	1.37111i	−0.0575992	+	0.0459338i
$892$	−2.78236	−	2.28564i	−0.0931602	−	0.0765290i
$893$	3.56874	−	4.47506i	0.119423	−	0.149752i
$894$	−3.82192	+	3.76689i	−0.127824	+	0.125984i
$895$	−24.9476	+	31.2833i	−0.833907	+	1.04569i
$896$	29.8614	+	2.07222i	0.997601	+	0.0692282i
$897$	2.14280	+	2.68698i	0.0715460	+	0.0897158i
$898$	−29.6291	−	3.55615i	−0.988736	−	0.118670i
$899$	3.02562	−	13.2561i	0.100910	−	0.442116i
$900$	−1.64125	−	3.53847i	−0.0547085	−	0.117949i
$901$		−	9.05365i		−	0.301621i
$902$	−22.1281	+	21.8095i	−0.736786	+	0.726178i
$903$	−7.17801	−	7.44903i	−0.238869	−	0.247888i
$904$	23.4039	−	2.12259i	0.778401	−	0.0705964i
$905$	10.1365	+	44.4110i	0.336949	+	1.47627i
$906$	−19.3041	+	2.03342i	−0.641337	+	0.0675557i
$907$	14.5568	−	11.6087i	0.483351	−	0.385460i	−0.351279	−	0.936271i	$-0.614253\pi$
$907$	14.5568	−	11.6087i	0.483351	−	0.385460i	0.834630	+	0.550811i	$0.185682\pi$
$908$	7.92689	−	6.13556i	0.263063	−	0.203616i
$909$	8.41265	−	1.92013i	0.279030	−	0.0636868i
$910$	1.33800	−	51.8941i	0.0443541	−	1.72027i
$911$	−3.74833	−	0.855531i	−0.124188	−	0.0283450i	0.159975	−	0.987121i	$-0.448859\pi$
$911$	−3.74833	−	0.855531i	−0.124188	−	0.0283450i	−0.284163	+	0.958776i	$0.591716\pi$
$912$	1.30034	−	1.53694i	0.0430586	−	0.0508931i
$913$		−	5.27313i		−	0.174515i
$914$	−32.6673	+	32.1969i	−1.08054	+	1.06498i
$915$	−23.0113	+	11.0817i	−0.760732	+	0.366349i
$916$	25.6718	+	12.8248i	0.848219	+	0.423742i
$917$	1.27300	−	3.43267i	0.0420381	−	0.113357i
$918$	−2.55110	−	7.46381i	−0.0841990	−	0.246342i
$919$	−17.2201	−	3.93038i	−0.568039	−	0.129651i	−0.0711505	−	0.997466i	$-0.522667\pi$
$919$	−17.2201	−	3.93038i	−0.568039	−	0.129651i	−0.496888	+	0.867814i	$0.665524\pi$
$920$	−3.36768	−	3.51747i	−0.111029	−	0.115968i
$921$	−9.11959	+	4.39177i	−0.300501	+	0.144714i
$922$	4.90145	−	0.516298i	0.161421	−	0.0170034i
$923$	73.0011	+	35.1555i	2.40286	+	1.15716i
$924$	11.1044	−	3.47848i	0.365308	−	0.114434i
$925$	−12.2167	+	5.88327i	−0.401684	+	0.193441i
$926$	19.0603	−	11.7845i	0.626361	−	0.387262i
$927$	1.04547	+	4.58051i	0.0343378	+	0.150444i
$928$	15.7981	+	2.36269i	0.518600	+	0.0775592i
$929$	30.2103	+	24.0919i	0.991168	+	0.790430i	0.977813	−	0.209481i	$-0.0671773\pi$
$929$	30.2103	+	24.0919i	0.991168	+	0.790430i	0.0133553	+	0.999911i	$0.495749\pi$
$930$	−9.66127	+	15.1312i	−0.316806	+	0.496170i
$931$	−0.130513	+	3.52072i	−0.00427738	+	0.115387i
$932$	−11.1100	−	23.9527i	−0.363921	−	0.784597i
$933$	9.48121	−	11.8891i	0.310401	−	0.389230i
$934$	−14.6735	−	23.7330i	−0.480131	−	0.776568i
$935$	−31.5249	+	7.19535i	−1.03097	+	0.235313i
$936$	12.4281	+	8.19144i	0.406224	+	0.267746i
$937$	15.8225	+	32.8559i	0.516900	+	1.07335i	0.982137	+	0.188168i	$0.0602549\pi$
$937$	15.8225	+	32.8559i	0.516900	+	1.07335i	−0.465237	+	0.885186i	$0.654031\pi$
$938$	14.7665	+	7.58612i	0.482145	+	0.247695i
$939$	14.9923	−	31.1318i	0.489254	−	1.01595i
$940$	−53.6421	−	26.7978i	−1.74961	−	0.874049i
$941$	−1.21349	−	2.51983i	−0.0395586	−	0.0821442i	0.880253	−	0.474505i	$-0.157373\pi$
$941$	−1.21349	−	2.51983i	−0.0395586	−	0.0821442i	−0.919811	+	0.392361i	$0.871659\pi$
$942$	10.7885	+	31.5642i	0.351509	+	1.02842i
$943$	1.45178	−	6.36068i	0.0472766	−	0.207132i
$944$	−11.6120	−	58.6699i	−0.377938	−	1.90954i
$945$	−5.97372	+	3.60093i	−0.194325	+	0.117138i
$946$	−1.27381	−	12.0928i	−0.0414150	−	0.393172i
$947$	−5.22730	−	10.8546i	−0.169864	−	0.352727i	0.798607	−	0.601853i	$-0.205571\pi$
$947$	−5.22730	−	10.8546i	−0.169864	−	0.352727i	−0.968471	+	0.249126i	$0.919857\pi$
$948$	−2.68684	−	12.6122i	−0.0872646	−	0.409625i
$949$	22.4782			0.729673
$950$	1.17002	+	0.747059i	0.0379604	+	0.0242378i
$951$	−1.58000	+	6.92243i	−0.0512350	+	0.224475i
$952$	−1.68073	+	41.7042i	−0.0544728	+	1.35164i
$953$	2.86877	+	12.5689i	0.0929285	+	0.407146i	0.999901	−	0.0140427i	$-0.00447006\pi$
$953$	2.86877	+	12.5689i	0.0929285	+	0.407146i	−0.906973	+	0.421189i	$0.861613\pi$
$954$	0.773888	−	2.16125i	0.0250555	−	0.0699729i
$955$	−33.9312	−	42.5483i	−1.09799	−	1.37683i
$956$	26.7623	+	13.3695i	0.865554	+	0.432402i
$957$	6.05409	−	1.38181i	0.195701	−	0.0446675i
$958$	−8.60568	+	24.0332i	−0.278037	+	0.776477i
$959$	−10.4820	+	28.2651i	−0.338483	+	0.912726i
$960$	−18.5861	−	9.96871i	−0.599864	−	0.321739i
$961$	−7.81447			−0.252080
$962$	27.8464	−	43.6121i	0.897804	−	1.40611i
$963$	−1.88189	−	0.429530i	−0.0606432	−	0.0138414i
$964$	4.87057	−	5.92904i	0.156871	−	0.190961i
$965$	−11.5740	+	9.22998i	−0.372581	+	0.297124i
$966$	−1.57225	+	1.87053i	−0.0505864	+	0.0601833i
$967$	−43.1387	−	34.4019i	−1.38725	−	1.10629i	−0.981319	−	0.192386i	$-0.938377\pi$
$967$	−43.1387	−	34.4019i	−1.38725	−	1.10629i	−0.405927	−	0.913906i	$-0.633051\pi$
$968$	−16.3270	−	6.11483i	−0.524769	−	0.196538i
$969$	2.19474	+	1.75025i	0.0705052	+	0.0562260i
$970$	48.0735	+	5.76988i	1.54355	+	0.185260i
$971$	30.3377	+	38.0423i	0.973583	+	1.22083i	0.975311	+	0.220836i	$0.0708786\pi$
$971$	30.3377	+	38.0423i	0.973583	+	1.22083i	−0.00172782	+	0.999999i	$0.500550\pi$
$972$	0.0290031	−	1.99979i	0.000930273	−	0.0641433i
$973$	37.0937	−	12.2132i	1.18917	−	0.391536i
$974$	6.15560	−	51.2872i	0.197238	−	1.64335i
$975$	−4.45317	+	9.24710i	−0.142616	+	0.296144i
$976$	−17.8192	+	34.4118i	−0.570378	+	1.10149i
$977$	−21.4068	−	10.3090i	−0.684865	−	0.329813i	0.0588915	−	0.998264i	$-0.481243\pi$
$977$	−21.4068	−	10.3090i	−0.684865	−	0.329813i	−0.743756	+	0.668451i	$0.766958\pi$
$978$	5.74364	+	16.8042i	0.183661	+	0.537340i
$979$	13.3469			0.426569
$980$	36.3588	−	6.34776i	1.16144	−	0.202772i
$981$	−18.1198			−0.578520
$982$	−8.20856	−	24.0159i	−0.261946	−	0.766378i
$983$	3.21004	+	1.54587i	0.102384	+	0.0493057i	0.484375	−	0.874860i	$-0.339047\pi$
$983$	3.21004	+	1.54587i	0.102384	+	0.0493057i	−0.381991	+	0.924166i	$0.624761\pi$
$984$	−2.55224	−	28.1412i	−0.0813625	−	0.897108i
$985$	−4.91996	+	10.2164i	−0.156763	+	0.325522i
$986$	−2.65426	+	22.1147i	−0.0845288	+	0.704277i
$987$	−10.4621	+	28.2112i	−0.333012	+	0.897974i
$988$	−5.29680	−	0.0768197i	−0.168514	−	0.00244396i
$989$	1.59203	+	1.99634i	0.0506236	+	0.0634800i
$990$	−8.14053	−	0.977044i	−0.258723	−	0.0310525i
$991$	−20.0419	−	15.9829i	−0.636652	−	0.507713i	0.251144	−	0.967950i	$-0.419193\pi$
$991$	−20.0419	−	15.9829i	−0.636652	−	0.507713i	−0.887796	+	0.460237i	$0.847765\pi$
$992$	2.06663	+	27.1600i	0.0656156	+	0.862331i
$993$	−2.06073	−	1.64337i	−0.0653951	−	0.0521509i
$994$	−14.2624	+	55.8150i	−0.452377	+	1.77034i
$995$	−30.7452	+	24.5185i	−0.974690	+	0.777289i
$996$	3.70571	+	3.04416i	0.117420	+	0.0964578i
$997$	47.2205	+	10.7778i	1.49549	+	0.341335i	0.890531	−	0.454923i	$-0.150333\pi$
$997$	47.2205	+	10.7778i	1.49549	+	0.341335i	0.604956	+	0.796259i	$0.293191\pi$
$998$	4.91158	−	7.69234i	0.155473	−	0.243497i
$999$	−6.95260			−0.219970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.x.a.55.25	✓	168
4.3	odd	2		588.2.x.b.55.15	yes	168
49.41	odd	14		588.2.x.b.139.15	yes	168
196.139	even	14	inner	588.2.x.a.139.25	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.x.a.55.25	✓	168	1.1	even	1	trivial
588.2.x.a.139.25	yes	168	196.139	even	14	inner
588.2.x.b.55.15	yes	168	4.3	odd	2
588.2.x.b.139.15	yes	168	49.41	odd	14

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.x (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33820 - 0.457394i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.58158 - 1.22417i) q^{4} +(-1.14386 + 2.37526i) q^{5} +(-1.40414 - 0.168527i) q^{6} +(-1.90517 + 1.83585i) q^{7} +(1.55655 - 2.36160i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(1.33820 - 0.457394i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.58158 - 1.22417i) q^{4} +(-1.14386 + 2.37526i) q^{5} +(-1.40414 - 0.168527i) q^{6} +(-1.90517 + 1.83585i) q^{7} +(1.55655 - 2.36160i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.444296 + 3.70178i) q^{10} +(1.71931 + 1.37111i) q^{11} +(-1.95610 + 0.416719i) q^{12} +(4.11444 + 3.28115i) q^{13} +(-1.70979 + 3.32815i) q^{14} +(2.06117 - 1.64373i) q^{15} +(1.00280 - 3.87226i) q^{16} +(5.43764 + 1.24111i) q^{17} +(1.19196 + 0.761070i) q^{18} -0.503306 q^{19} +(1.09861 + 5.15696i) q^{20} +(2.51304 - 0.827423i) q^{21} +(2.92793 + 1.04842i) q^{22} +(-0.636689 + 0.145320i) q^{23} +(-2.42706 + 1.45237i) q^{24} +(-1.21598 - 1.52480i) q^{25} +(7.00674 + 2.50894i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-0.765777 + 5.23580i) q^{28} +(-0.628356 + 2.75301i) q^{29} +(2.00644 - 3.14242i) q^{30} -4.81514 q^{31} +(-0.429195 - 5.64055i) q^{32} +(-0.954147 - 1.98131i) q^{33} +(7.84435 - 0.826290i) q^{34} +(-2.18137 - 6.62523i) q^{35} +(1.94320 + 0.473271i) q^{36} +(1.54710 - 6.77828i) q^{37} +(-0.673526 + 0.230209i) q^{38} +(-2.28334 - 4.74141i) q^{39} +(3.82893 + 6.39856i) q^{40} +(-4.33461 + 9.00090i) q^{41} +(2.98450 - 2.25671i) q^{42} +(-1.69645 - 3.52271i) q^{43} +(4.39771 + 0.0637802i) q^{44} +(-2.57024 + 0.586641i) q^{45} +(-0.785551 + 0.485685i) q^{46} +(-7.09061 + 8.89135i) q^{47} +(-2.58360 + 3.05369i) q^{48} +(0.259311 - 6.99520i) q^{49} +(-2.32467 - 1.48430i) q^{50} +(-4.36065 - 3.47750i) q^{51} +(10.5240 + 0.152630i) q^{52} +(-0.361207 - 1.58255i) q^{53} +(-0.743705 - 1.20287i) q^{54} +(-5.22340 + 2.51546i) q^{55} +(1.37006 + 7.35683i) q^{56} +(0.453463 + 0.218376i) q^{57} +(0.418340 + 3.97149i) q^{58} +(13.4713 - 6.48743i) q^{59} +(1.24770 - 5.12293i) q^{60} +(-9.44503 - 2.15577i) q^{61} +(-6.44364 + 2.20241i) q^{62} +(-2.62318 - 0.344885i) q^{63} +(-3.15430 - 7.35190i) q^{64} +(-12.5000 + 6.01966i) q^{65} +(-2.18308 - 2.21497i) q^{66} -4.43686i q^{67} +(10.1194 - 4.69370i) q^{68} +(0.636689 + 0.145320i) q^{69} +(-5.94946 - 7.86816i) q^{70} +(15.0105 - 3.42604i) q^{71} +(2.81687 - 0.255473i) q^{72} +(3.33947 - 2.66314i) q^{73} +(-1.03001 - 9.77836i) q^{74} +(0.433980 + 1.90139i) q^{75} +(-0.796019 + 0.616133i) q^{76} +(-5.79272 + 0.544216i) q^{77} +(-5.22427 - 5.30058i) q^{78} +6.44761i q^{79} +(8.05055 + 6.81125i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-1.68363 + 14.0277i) q^{82} +(-1.49505 - 1.87473i) q^{83} +(2.96167 - 4.38503i) q^{84} +(-9.16787 + 11.4961i) q^{85} +(-3.88146 - 3.93816i) q^{86} +(1.76061 - 2.20774i) q^{87} +(5.91420 - 1.92613i) q^{88} +(4.74517 - 3.78415i) q^{89} +(-3.17118 + 1.96066i) q^{90} +(-13.8624 + 1.30235i) q^{91} +(-0.829078 + 1.00925i) q^{92} +(4.33829 + 2.08921i) q^{93} +(-5.42184 + 15.1416i) q^{94} +(0.575714 - 1.19548i) q^{95} +(-2.06065 + 5.26818i) q^{96} -12.9866i q^{97} +(-2.85255 - 9.47961i) q^{98} +2.19908i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Introduction

L-functions

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