LMFDB - Embedded newform 114.2.i.c.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	114.61
Dual form			114.2.i.c.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0923963 + 0.0775297i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(2.14543 - 3.71599i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0923963 + 0.0775297i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(2.14543 - 3.71599i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.113341 - 0.0412527i) q^{10} +(-1.28699 - 2.22913i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.141559 - 0.802823i) q^{13} +(-3.28699 + 2.75811i) q^{14} +(0.0923963 + 0.0775297i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.439693 + 0.160035i) q^{17} +1.00000 q^{18} +(3.16637 + 2.99568i) q^{19} -0.120615 q^{20} +(-4.03209 - 1.46756i) q^{21} +(0.446967 + 2.53487i) q^{22} +(4.25490 + 3.57029i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(-0.865715 + 4.90971i) q^{25} +(-0.407604 + 0.705990i) q^{26} +(0.500000 + 0.866025i) q^{27} +(4.03209 - 1.46756i) q^{28} +(-2.20574 + 0.802823i) q^{29} +(-0.0603074 - 0.104455i) q^{30} +(-2.67365 + 4.63089i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-1.97178 + 1.65452i) q^{33} +(-0.358441 - 0.300767i) q^{34} +(0.0898700 + 0.509678i) q^{35} +(-0.939693 - 0.342020i) q^{36} -8.51754 q^{37} +(-1.95084 - 3.89798i) q^{38} -0.815207 q^{39} +(0.113341 + 0.0412527i) q^{40} +(0.666374 + 3.77920i) q^{41} +(3.28699 + 2.75811i) q^{42} +(7.14930 - 5.99898i) q^{43} +(0.446967 - 2.53487i) q^{44} +(0.0603074 - 0.104455i) q^{45} +(-2.77719 - 4.81023i) q^{46} +(8.90420 - 3.24086i) q^{47} +(0.939693 - 0.342020i) q^{48} +(-5.70574 - 9.88263i) q^{49} +(2.49273 - 4.31753i) q^{50} +(0.0812519 - 0.460802i) q^{51} +(0.624485 - 0.524005i) q^{52} +(9.77379 + 8.20118i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(0.291737 + 0.106183i) q^{55} -4.29086 q^{56} +(2.40033 - 3.63846i) q^{57} +2.34730 q^{58} +(-14.1420 - 5.14728i) q^{59} +(0.0209445 + 0.118782i) q^{60} +(-1.31521 - 1.10359i) q^{61} +(4.09627 - 3.43718i) q^{62} +(-0.745100 + 4.22567i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0491630 + 0.0851529i) q^{65} +(2.41875 - 0.880352i) q^{66} +(-10.7652 + 3.91820i) q^{67} +(0.233956 + 0.405223i) q^{68} +(2.77719 - 4.81023i) q^{69} +(0.0898700 - 0.509678i) q^{70} +(10.2135 - 8.57013i) q^{71} +(0.766044 + 0.642788i) q^{72} +(0.396459 + 2.24843i) q^{73} +(8.00387 + 2.91317i) q^{74} +4.98545 q^{75} +(0.500000 + 4.33013i) q^{76} -11.0446 q^{77} +(0.766044 + 0.278817i) q^{78} +(0.843426 + 4.78331i) q^{79} +(-0.0923963 - 0.0775297i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.666374 - 3.77920i) q^{82} +(-1.62449 + 2.81369i) q^{83} +(-2.14543 - 3.71599i) q^{84} +(-0.0530334 + 0.0193026i) q^{85} +(-8.76991 + 3.19199i) q^{86} +(1.17365 + 2.03282i) q^{87} +(-1.28699 + 2.22913i) q^{88} +(0.595800 - 3.37895i) q^{89} +(-0.0923963 + 0.0775297i) q^{90} +(-2.67958 - 2.24843i) q^{91} +(0.964508 + 5.46999i) q^{92} +(5.02481 + 1.82888i) q^{93} -9.47565 q^{94} +(-0.524815 - 0.0313013i) q^{95} -1.00000 q^{96} +(-2.91400 - 1.06061i) q^{97} +(1.98158 + 11.2381i) q^{98} +(1.97178 + 1.65452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^5 - 3 * q^7 - 3 * q^8	$ 6 q + 3 q^{5} - 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{12} + 9 q^{13} - 12 q^{14} - 3 q^{15} - 3 q^{17} + 6 q^{18} - 12 q^{20} - 15 q^{21} + 15 q^{22} + 27 q^{23} - 15 q^{25} - 6 q^{26} + 3 q^{27} + 15 q^{28} - 3 q^{29} - 6 q^{30} - 15 q^{31} + 3 q^{33} + 6 q^{34} + 12 q^{35} - 6 q^{37} - 12 q^{39} - 6 q^{40} - 15 q^{41} + 12 q^{42} + 3 q^{43} + 15 q^{44} + 6 q^{45} - 6 q^{46} + 15 q^{47} - 24 q^{49} - 3 q^{50} + 3 q^{51} - 9 q^{52} + 6 q^{53} + 27 q^{55} + 6 q^{56} + 12 q^{58} - 27 q^{59} - 3 q^{60} - 15 q^{61} - 3 q^{62} - 3 q^{63} - 3 q^{64} + 12 q^{65} + 12 q^{66} - 3 q^{67} + 6 q^{68} + 6 q^{69} + 12 q^{70} + 3 q^{71} + 12 q^{73} + 24 q^{74} - 6 q^{75} + 3 q^{76} - 42 q^{77} + 27 q^{79} + 3 q^{80} - 15 q^{82} + 3 q^{83} + 3 q^{84} + 12 q^{85} - 24 q^{86} + 6 q^{87} + 42 q^{89} + 3 q^{90} - 42 q^{91} - 27 q^{92} + 3 q^{93} - 18 q^{94} + 24 q^{95} - 6 q^{96} + 18 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 - 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^12 + 9 * q^13 - 12 * q^14 - 3 * q^15 - 3 * q^17 + 6 * q^18 - 12 * q^20 - 15 * q^21 + 15 * q^22 + 27 * q^23 - 15 * q^25 - 6 * q^26 + 3 * q^27 + 15 * q^28 - 3 * q^29 - 6 * q^30 - 15 * q^31 + 3 * q^33 + 6 * q^34 + 12 * q^35 - 6 * q^37 - 12 * q^39 - 6 * q^40 - 15 * q^41 + 12 * q^42 + 3 * q^43 + 15 * q^44 + 6 * q^45 - 6 * q^46 + 15 * q^47 - 24 * q^49 - 3 * q^50 + 3 * q^51 - 9 * q^52 + 6 * q^53 + 27 * q^55 + 6 * q^56 + 12 * q^58 - 27 * q^59 - 3 * q^60 - 15 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 + 12 * q^65 + 12 * q^66 - 3 * q^67 + 6 * q^68 + 6 * q^69 + 12 * q^70 + 3 * q^71 + 12 * q^73 + 24 * q^74 - 6 * q^75 + 3 * q^76 - 42 * q^77 + 27 * q^79 + 3 * q^80 - 15 * q^82 + 3 * q^83 + 3 * q^84 + 12 * q^85 - 24 * q^86 + 6 * q^87 + 42 * q^89 + 3 * q^90 - 42 * q^91 - 27 * q^92 + 3 * q^93 - 18 * q^94 + 24 * q^95 - 6 * q^96 + 18 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.0923963	+	0.0775297i	−0.0413209	+	0.0346723i	−0.663214	−	0.748430i	$-0.730808\pi$
$5$	−0.0923963	+	0.0775297i	−0.0413209	+	0.0346723i	0.621893	+	0.783102i	$0.286364\pi$
$6$	−0.173648	+	0.984808i	−0.0708916	+	0.402046i
$7$	2.14543	−	3.71599i	0.810896	−	1.40451i	−0.101341	−	0.994852i	$-0.532313\pi$
$7$	2.14543	−	3.71599i	0.810896	−	1.40451i	0.912238	−	0.409662i	$-0.134353\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	0.113341	−	0.0412527i	0.0358415	−	0.0130452i
$11$	−1.28699	−	2.22913i	−0.388042	−	0.672108i	0.604144	−	0.796875i	$-0.293515\pi$
$11$	−1.28699	−	2.22913i	−0.388042	−	0.672108i	−0.992186	+	0.124767i	$0.960182\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	0.141559	−	0.802823i	0.0392615	−	0.222663i	−0.958864	−	0.283866i	$-0.908383\pi$
$13$	0.141559	−	0.802823i	0.0392615	−	0.222663i	0.998125	+	0.0612035i	$0.0194939\pi$
$14$	−3.28699	+	2.75811i	−0.878485	+	0.737136i
$15$	0.0923963	+	0.0775297i	0.0238566	+	0.0200181i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.439693	+	0.160035i	0.106641	+	0.0388142i	0.394790	−	0.918772i	$-0.370817\pi$
$17$	0.439693	+	0.160035i	0.106641	+	0.0388142i	−0.288149	+	0.957586i	$0.593040\pi$
$18$	1.00000			0.235702
$19$	3.16637	+	2.99568i	0.726416	+	0.687255i
$19$	3.16637	+	2.99568i	0.726416	+	0.687255i
$20$	−0.120615			−0.0269703
$21$	−4.03209	−	1.46756i	−0.879874	−	0.320248i
$22$	0.446967	+	2.53487i	0.0952936	+	0.540437i
$23$	4.25490	+	3.57029i	0.887208	+	0.744456i	0.967648	−	0.252304i	$-0.0811881\pi$
$23$	4.25490	+	3.57029i	0.887208	+	0.744456i	−0.0804401	+	0.996759i	$0.525633\pi$
$24$	−0.766044	+	0.642788i	−0.156368	+	0.131208i
$25$	−0.865715	+	4.90971i	−0.173143	+	0.981942i
$26$	−0.407604	+	0.705990i	−0.0799377	+	0.138456i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	4.03209	−	1.46756i	0.761993	−	0.277343i
$29$	−2.20574	+	0.802823i	−0.409595	+	0.149080i	−0.538596	−	0.842564i	$-0.681045\pi$
$29$	−2.20574	+	0.802823i	−0.409595	+	0.149080i	0.129001	+	0.991644i	$0.458823\pi$
$30$	−0.0603074	−	0.104455i	−0.0110106	−	0.0190709i
$31$	−2.67365	+	4.63089i	−0.480201	+	0.831733i	−0.999742	−	0.0227125i	$-0.992770\pi$
$31$	−2.67365	+	4.63089i	−0.480201	+	0.831733i	0.519541	+	0.854446i	$0.326103\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−1.97178	+	1.65452i	−0.343243	+	0.288015i
$34$	−0.358441	−	0.300767i	−0.0614721	−	0.0515812i
$35$	0.0898700	+	0.509678i	0.0151908	+	0.0861514i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	−8.51754			−1.40028			−0.700138	−	0.714008i	$-0.746878\pi$
$37$	−8.51754			−1.40028			−0.700138	+	0.714008i	$0.746878\pi$
$38$	−1.95084	−	3.89798i	−0.316468	−	0.632336i
$39$	−0.815207			−0.130538
$40$	0.113341	+	0.0412527i	0.0179208	+	0.00652262i
$41$	0.666374	+	3.77920i	0.104070	+	0.590211i	0.991588	+	0.129437i	$0.0413171\pi$
$41$	0.666374	+	3.77920i	0.104070	+	0.590211i	−0.887517	+	0.460774i	$0.847572\pi$
$42$	3.28699	+	2.75811i	0.507193	+	0.425586i
$43$	7.14930	−	5.99898i	1.09026	−	0.914835i	0.0935262	−	0.995617i	$-0.470186\pi$
$43$	7.14930	−	5.99898i	1.09026	−	0.914835i	0.996732	+	0.0807817i	$0.0257417\pi$
$44$	0.446967	−	2.53487i	0.0673827	−	0.382147i
$45$	0.0603074	−	0.104455i	0.00899009	−	0.0155713i
$46$	−2.77719	−	4.81023i	−0.409474	−	0.709230i
$47$	8.90420	−	3.24086i	1.29881	−	0.472729i	0.402202	−	0.915551i	$-0.368245\pi$
$47$	8.90420	−	3.24086i	1.29881	−	0.472729i	0.896609	+	0.442822i	$0.146023\pi$
$48$	0.939693	−	0.342020i	0.135633	−	0.0493664i
$49$	−5.70574	−	9.88263i	−0.815105	−	1.41180i
$50$	2.49273	−	4.31753i	0.352525	−	0.610591i
$51$	0.0812519	−	0.460802i	0.0113775	−	0.0645253i
$52$	0.624485	−	0.524005i	0.0866005	−	0.0726665i
$53$	9.77379	+	8.20118i	1.34253	+	1.12652i	0.980968	+	0.194172i	$0.0622019\pi$
$53$	9.77379	+	8.20118i	1.34253	+	1.12652i	0.361565	+	0.932347i	$0.382243\pi$
$54$	−0.173648	−	0.984808i	−0.0236305	−	0.134015i
$55$	0.291737	+	0.106183i	0.0393378	+	0.0143178i
$56$	−4.29086			−0.573390
$57$	2.40033	−	3.63846i	0.317931	−	0.481926i
$58$	2.34730			0.308215
$59$	−14.1420	−	5.14728i	−1.84113	−	0.670118i	−0.989220	−	0.146439i	$-0.953219\pi$
$59$	−14.1420	−	5.14728i	−1.84113	−	0.670118i	−0.851915	−	0.523680i	$-0.824559\pi$
$60$	0.0209445	+	0.118782i	0.00270393	+	0.0153347i
$61$	−1.31521	−	1.10359i	−0.168395	−	0.141300i	0.554696	−	0.832053i	$-0.312835\pi$
$61$	−1.31521	−	1.10359i	−0.168395	−	0.141300i	−0.723091	+	0.690753i	$0.757279\pi$
$62$	4.09627	−	3.43718i	0.520226	−	0.436522i
$63$	−0.745100	+	4.22567i	−0.0938738	+	0.532385i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.0491630	+	0.0851529i	0.00609792	+	0.0105619i
$66$	2.41875	−	0.880352i	0.297727	−	0.108364i
$67$	−10.7652	+	3.91820i	−1.31517	+	0.478684i	−0.901909	−	0.431926i	$-0.857834\pi$
$67$	−10.7652	+	3.91820i	−1.31517	+	0.478684i	−0.413266	+	0.910611i	$0.635612\pi$
$68$	0.233956	+	0.405223i	0.0283713	+	0.0491405i
$69$	2.77719	−	4.81023i	0.334334	−	0.579084i
$70$	0.0898700	−	0.509678i	0.0107415	−	0.0609182i
$71$	10.2135	−	8.57013i	1.21212	−	1.01709i	0.212918	−	0.977070i	$-0.431703\pi$
$71$	10.2135	−	8.57013i	1.21212	−	1.01709i	0.999199	−	0.0400167i	$-0.0127411\pi$
$72$	0.766044	+	0.642788i	0.0902792	+	0.0757532i
$73$	0.396459	+	2.24843i	0.0464021	+	0.263159i	0.999179	−	0.0405117i	$-0.0128988\pi$
$73$	0.396459	+	2.24843i	0.0464021	+	0.263159i	−0.952777	+	0.303671i	$0.901788\pi$
$74$	8.00387	+	2.91317i	0.930431	+	0.338649i
$75$	4.98545			0.575670
$76$	0.500000	+	4.33013i	0.0573539	+	0.496700i
$77$	−11.0446			−1.25865
$78$	0.766044	+	0.278817i	0.0867375	+	0.0315699i
$79$	0.843426	+	4.78331i	0.0948928	+	0.538164i	0.994780	+	0.102042i	$0.0325375\pi$
$79$	0.843426	+	4.78331i	0.0948928	+	0.538164i	−0.899887	+	0.436122i	$0.856351\pi$
$80$	−0.0923963	−	0.0775297i	−0.0103302	−	0.00866808i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	0.666374	−	3.77920i	0.0735887	−	0.417342i
$83$	−1.62449	+	2.81369i	−0.178310	+	0.308843i	−0.941302	−	0.337566i	$-0.890396\pi$
$83$	−1.62449	+	2.81369i	−0.178310	+	0.308843i	0.762992	+	0.646408i	$0.223730\pi$
$84$	−2.14543	−	3.71599i	−0.234086	−	0.405448i
$85$	−0.0530334	+	0.0193026i	−0.00575228	+	0.00209366i
$86$	−8.76991	+	3.19199i	−0.945684	+	0.344201i
$87$	1.17365	+	2.03282i	0.125828	+	0.217941i
$88$	−1.28699	+	2.22913i	−0.137193	+	0.237626i
$89$	0.595800	−	3.37895i	0.0631547	−	0.358168i	−0.936811	−	0.349837i	$-0.886237\pi$
$89$	0.595800	−	3.37895i	0.0631547	−	0.358168i	0.999965	−	0.00833100i	$-0.00265187\pi$
$90$	−0.0923963	+	0.0775297i	−0.00973942	+	0.00817235i
$91$	−2.67958	−	2.24843i	−0.280896	−	0.235700i
$92$	0.964508	+	5.46999i	0.100557	+	0.570286i
$93$	5.02481	+	1.82888i	0.521049	+	0.189646i
$94$	−9.47565			−0.977339
$95$	−0.524815	−	0.0313013i	−0.0538449	−	0.00321145i
$96$	−1.00000			−0.102062
$97$	−2.91400	−	1.06061i	−0.295872	−	0.107689i	0.189819	−	0.981819i	$-0.439210\pi$
$97$	−2.91400	−	1.06061i	−0.295872	−	0.107689i	−0.485691	+	0.874130i	$0.661432\pi$
$98$	1.98158	+	11.2381i	0.200170	+	1.13522i
$99$	1.97178	+	1.65452i	0.198171	+	0.166286i
$100$	−3.81908	+	3.20459i	−0.381908	+	0.320459i
$101$	−2.90508	+	16.4755i	−0.289066	+	1.63937i	0.401323	+	0.915937i	$0.368550\pi$
$101$	−2.90508	+	16.4755i	−0.289066	+	1.63937i	−0.690389	+	0.723438i	$0.742561\pi$
$102$	−0.233956	+	0.405223i	−0.0231651	+	0.0401230i
$103$	5.19846	+	9.00400i	0.512220	+	0.887191i	0.999900	+	0.0141681i	$0.00451001\pi$
$103$	5.19846	+	9.00400i	0.512220	+	0.887191i	−0.487680	+	0.873023i	$0.662157\pi$
$104$	−0.766044	+	0.278817i	−0.0751168	+	0.0273403i
$105$	0.486329	−	0.177009i	0.0474609	−	0.0172744i
$106$	−6.37939	−	11.0494i	−0.619621	−	1.07321i
$107$	4.55690	−	7.89279i	0.440533	−	0.763025i	−0.557196	−	0.830381i	$-0.688123\pi$
$107$	4.55690	−	7.89279i	0.440533	−	0.763025i	0.997729	+	0.0673560i	$0.0214563\pi$
$108$	−0.173648	+	0.984808i	−0.0167093	+	0.0947632i
$109$	2.93376	−	2.46172i	0.281004	−	0.235790i	−0.491382	−	0.870944i	$-0.663508\pi$
$109$	2.93376	−	2.46172i	0.281004	−	0.235790i	0.772385	+	0.635154i	$0.219064\pi$
$110$	−0.237826	−	0.199560i	−0.0226758	−	0.0190273i
$111$	1.47906	+	8.38814i	0.140386	+	0.796167i
$112$	4.03209	+	1.46756i	0.380997	+	0.138671i
$113$	5.41147			0.509069			0.254534	−	0.967064i	$-0.418078\pi$
$113$	5.41147			0.509069			0.254534	+	0.967064i	$0.418078\pi$
$114$	−3.50000	+	2.59808i	−0.327805	+	0.243332i
$115$	−0.669940			−0.0624722
$116$	−2.20574	−	0.802823i	−0.204798	−	0.0745402i
$117$	0.141559	+	0.802823i	0.0130872	+	0.0742210i
$118$	11.5287	+	9.67372i	1.06130	+	0.890538i
$119$	1.53802	−	1.29055i	0.140990	−	0.118305i
$120$	0.0209445	−	0.118782i	0.00191197	−	0.0108433i
$121$	2.18732	−	3.78855i	0.198847	−	0.344413i
$122$	0.858441	+	1.48686i	0.0777196	+	0.134614i
$123$	3.60607	−	1.31250i	0.325148	−	0.118344i
$124$	−5.02481	+	1.82888i	−0.451242	+	0.164239i
$125$	−0.602196	−	1.04303i	−0.0538621	−	0.0932919i
$126$	2.14543	−	3.71599i	0.191130	−	0.331047i
$127$	0.736482	−	4.17680i	0.0653522	−	0.370631i	−0.934539	−	0.355861i	$-0.884188\pi$
$127$	0.736482	−	4.17680i	0.0653522	−	0.370631i	0.999891	−	0.0147693i	$-0.00470138\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−7.14930	−	5.99898i	−0.629461	−	0.528180i
$130$	−0.0170741	−	0.0968323i	−0.00149750	−	0.00849275i
$131$	−19.7738	−	7.19707i	−1.72764	−	0.628811i	−0.729185	−	0.684316i	$-0.760101\pi$
$131$	−19.7738	−	7.19707i	−1.72764	−	0.628811i	−0.998458	+	0.0555055i	$0.982323\pi$
$132$	−2.57398			−0.224036
$133$	17.9251	−	5.33921i	1.55431	−	0.462968i
$134$	11.4561			0.989652
$135$	−0.113341	−	0.0412527i	−0.00975482	−	0.00355047i
$136$	−0.0812519	−	0.460802i	−0.00696729	−	0.0395135i
$137$	−9.43835	−	7.91971i	−0.806373	−	0.676627i	0.143367	−	0.989670i	$-0.454207\pi$
$137$	−9.43835	−	7.91971i	−0.806373	−	0.676627i	−0.949739	+	0.313043i	$0.898652\pi$
$138$	−4.25490	+	3.57029i	−0.362201	+	0.303923i
$139$	−0.970437	+	5.50362i	−0.0823114	+	0.466811i	0.915593	+	0.402106i	$0.131722\pi$
$139$	−0.970437	+	5.50362i	−0.0823114	+	0.466811i	−0.997904	+	0.0647050i	$0.979389\pi$
$140$	−0.258770	+	0.448204i	−0.0218701	+	0.0378801i
$141$	−4.73783	−	8.20616i	−0.398997	−	0.691083i
$142$	−12.5287	+	4.56007i	−1.05138	+	0.382672i
$143$	−1.97178	+	0.717670i	−0.164889	+	0.0600146i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.141559	−	0.245188i	0.0117559	−	0.0203617i
$146$	0.396459	−	2.24843i	0.0328112	−	0.186082i
$147$	−8.74170	+	7.33515i	−0.721003	+	0.604993i
$148$	−6.52481	−	5.47497i	−0.536336	−	0.450040i
$149$	1.92649	+	10.9257i	0.157824	+	0.895065i	0.956158	+	0.292850i	$0.0946038\pi$
$149$	1.92649	+	10.9257i	0.157824	+	0.895065i	−0.798334	+	0.602215i	$0.794285\pi$
$150$	−4.68479	−	1.70513i	−0.382512	−	0.139223i
$151$	12.5963			1.02507			0.512535	−	0.858666i	$-0.328707\pi$
$151$	12.5963			1.02507			0.512535	+	0.858666i	$0.328707\pi$
$152$	1.01114	−	4.24000i	0.0820146	−	0.343909i
$153$	−0.467911			−0.0378284
$154$	10.3785	+	3.77747i	0.836324	+	0.304397i
$155$	−0.111997	−	0.635164i	−0.00899579	−	0.0510176i
$156$	−0.624485	−	0.524005i	−0.0499988	−	0.0419540i
$157$	−3.04710	+	2.55682i	−0.243185	+	0.204057i	−0.756231	−	0.654304i	$-0.772962\pi$
$157$	−3.04710	+	2.55682i	−0.243185	+	0.204057i	0.513046	+	0.858361i	$0.328517\pi$
$158$	0.843426	−	4.78331i	0.0670994	−	0.380539i
$159$	6.37939	−	11.0494i	0.505918	−	0.876276i
$160$	0.0603074	+	0.104455i	0.00476772	+	0.00825793i
$161$	22.3957	−	8.15138i	1.76503	−	0.642419i
$162$	−0.939693	+	0.342020i	−0.0738292	+	0.0268716i
$163$	−9.60014	−	16.6279i	−0.751941	−	1.30240i	−0.946881	−	0.321584i	$-0.895785\pi$
$163$	−9.60014	−	16.6279i	−0.751941	−	1.30240i	0.194940	−	0.980815i	$-0.437549\pi$
$164$	−1.91875	+	3.32337i	−0.149829	+	0.259512i
$165$	0.0539108	−	0.305743i	0.00419695	−	0.0238021i
$166$	2.48886	−	2.08840i	0.193173	−	0.162091i
$167$	−11.7777	−	9.88263i	−0.911382	−	0.764741i	0.0609991	−	0.998138i	$-0.480571\pi$
$167$	−11.7777	−	9.88263i	−0.911382	−	0.764741i	−0.972381	+	0.233397i	$0.925016\pi$
$168$	0.745100	+	4.22567i	0.0574857	+	0.326018i
$169$	11.5915	+	4.21897i	0.891655	+	0.324536i
$170$	0.0564370			0.00432852
$171$	−4.00000	−	1.73205i	−0.305888	−	0.132453i
$172$	9.33275			0.711615
$173$	6.19594	+	2.25514i	0.471068	+	0.171455i	0.566636	−	0.823968i	$-0.308244\pi$
$173$	6.19594	+	2.25514i	0.471068	+	0.171455i	−0.0955679	+	0.995423i	$0.530467\pi$
$174$	−0.407604	−	2.31164i	−0.0309004	−	0.175245i
$175$	16.3871	+	13.7504i	1.23875	+	1.03943i
$176$	1.97178	−	1.65452i	0.148629	−	0.124714i
$177$	−2.61334	+	14.8210i	−0.196431	+	1.11401i
$178$	−1.71554	+	2.97140i	−0.128585	+	0.222716i
$179$	−0.620615	−	1.07494i	−0.0463869	−	0.0803445i	0.841900	−	0.539634i	$-0.181437\pi$
$179$	−0.620615	−	1.07494i	−0.0463869	−	0.0803445i	−0.888287	+	0.459290i	$0.848104\pi$
$180$	0.113341	−	0.0412527i	0.00844792	−	0.00307479i
$181$	−3.78699	+	1.37835i	−0.281485	+	0.102452i	−0.478905	−	0.877867i	$-0.658966\pi$
$181$	−3.78699	+	1.37835i	−0.281485	+	0.102452i	0.197420	+	0.980319i	$0.436744\pi$
$182$	1.74897	+	3.02931i	0.129642	+	0.224547i
$183$	−0.858441	+	1.48686i	−0.0634578	+	0.109912i
$184$	0.964508	−	5.46999i	0.0711044	−	0.403253i
$185$	0.786989	−	0.660362i	0.0578606	−	0.0485508i
$186$	−4.09627	−	3.43718i	−0.300353	−	0.252026i
$187$	−0.209141	−	1.18610i	−0.0152939	−	0.0867359i
$188$	8.90420	+	3.24086i	0.649406	+	0.236364i
$189$	4.29086			0.312114
$190$	0.482459	+	0.208911i	0.0350013	+	0.0151560i
$191$	−24.0847			−1.74271			−0.871354	−	0.490654i	$-0.836758\pi$
$191$	−24.0847			−1.74271			−0.871354	+	0.490654i	$0.836758\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	−1.71213	−	9.70999i	−0.123242	−	0.698941i	−0.982336	−	0.187123i	$-0.940084\pi$
$193$	−1.71213	−	9.70999i	−0.123242	−	0.698941i	0.859094	−	0.511817i	$-0.171028\pi$
$194$	2.37551	+	1.99329i	0.170552	+	0.143110i
$195$	0.0753221	−	0.0632028i	0.00539393	−	0.00452604i
$196$	1.98158	−	11.2381i	0.141542	−	0.802722i
$197$	3.22803	−	5.59110i	0.229987	−	0.398350i	−0.727817	−	0.685772i	$-0.759465\pi$
$197$	3.22803	−	5.59110i	0.229987	−	0.398350i	0.957804	+	0.287422i	$0.0927982\pi$
$198$	−1.28699	−	2.22913i	−0.0914623	−	0.158417i
$199$	−23.2777	+	8.47237i	−1.65011	+	0.600591i	−0.988763	−	0.149490i	$-0.952237\pi$
$199$	−23.2777	+	8.47237i	−1.65011	+	0.600591i	−0.661346	+	0.750081i	$0.730015\pi$
$200$	4.68479	−	1.70513i	0.331265	−	0.120571i
$201$	5.72803	+	9.92123i	0.404024	+	0.699790i
$202$	8.36484	−	14.4883i	0.588548	−	1.01939i
$203$	−1.74897	+	9.91890i	−0.122754	+	0.696171i
$204$	0.358441	−	0.300767i	0.0250959	−	0.0210579i
$205$	−0.354570	−	0.297520i	−0.0247643	−	0.0207797i
$206$	−1.80541	−	10.2390i	−0.125789	−	0.713383i
$207$	−5.21941	−	1.89971i	−0.362774	−	0.132039i
$208$	0.815207			0.0565245
$209$	2.60266	−	10.9137i	0.180030	−	0.754914i
$210$	−0.517541			−0.0357137
$211$	1.30066	+	0.473401i	0.0895411	+	0.0325903i	0.386402	−	0.922330i	$-0.373718\pi$
$211$	1.30066	+	0.473401i	0.0895411	+	0.0325903i	−0.296861	+	0.954921i	$0.595940\pi$
$212$	2.21554	+	12.5649i	0.152164	+	0.862963i
$213$	−10.2135	−	8.57013i	−0.699816	−	0.587215i
$214$	−6.98158	+	5.85824i	−0.477251	+	0.400461i
$215$	−0.195470	+	1.10857i	−0.0133309	+	0.0756036i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	11.4722	+	19.8705i	0.778787	+	1.34890i
$218$	−3.59879	+	1.30985i	−0.243741	+	0.0887145i
$219$	2.14543	−	0.780873i	0.144975	−	0.0527665i
$220$	0.155230	+	0.268866i	0.0104656	+	0.0181269i
$221$	0.190722	−	0.330341i	0.0128294	−	0.0222211i
$222$	1.47906	−	8.38814i	0.0992677	−	0.562975i
$223$	17.0929	−	14.3426i	1.14462	−	0.960453i	0.145043	−	0.989425i	$-0.453668\pi$
$223$	17.0929	−	14.3426i	1.14462	−	0.960453i	0.999580	+	0.0289729i	$0.00922364\pi$
$224$	−3.28699	−	2.75811i	−0.219621	−	0.184284i
$225$	−0.865715	−	4.90971i	−0.0577143	−	0.327314i
$226$	−5.08512	−	1.85083i	−0.338257	−	0.123116i
$227$	−20.7665			−1.37832			−0.689161	−	0.724608i	$-0.742021\pi$
$227$	−20.7665			−1.37832			−0.689161	+	0.724608i	$0.742021\pi$
$228$	4.17752	−	1.24432i	0.276663	−	0.0824073i
$229$	5.51754			0.364609			0.182305	−	0.983242i	$-0.441644\pi$
$229$	5.51754			0.364609			0.182305	+	0.983242i	$0.441644\pi$
$230$	0.629538	+	0.229133i	0.0415105	+	0.0151086i
$231$	1.91787	+	10.8768i	0.126187	+	0.715640i
$232$	1.79813	+	1.50881i	0.118053	+	0.0990584i
$233$	−11.5569	+	9.69739i	−0.757118	+	0.635297i	−0.937375	−	0.348322i	$-0.886752\pi$
$233$	−11.5569	+	9.69739i	−0.757118	+	0.635297i	0.180257	+	0.983620i	$0.442307\pi$
$234$	0.141559	−	0.802823i	0.00925402	−	0.0524822i
$235$	−0.571452	+	0.989783i	−0.0372774	+	0.0645664i
$236$	−7.52481	−	13.0334i	−0.489824	−	0.848400i
$237$	4.56418	−	1.66122i	0.296475	−	0.107908i
$238$	−1.88666	+	0.686688i	−0.122294	+	0.0445114i
$239$	14.4757	+	25.0726i	0.936352	+	1.62181i	0.772205	+	0.635374i	$0.219154\pi$
$239$	14.4757	+	25.0726i	0.936352	+	1.62181i	0.164147	+	0.986436i	$0.447513\pi$
$240$	−0.0603074	+	0.104455i	−0.00389282	+	0.00674257i
$241$	−3.36349	+	19.0753i	−0.216662	+	1.22875i	0.661338	+	0.750088i	$0.269989\pi$
$241$	−3.36349	+	19.0753i	−0.216662	+	1.22875i	−0.878000	+	0.478661i	$0.841122\pi$
$242$	−3.35117	+	2.81196i	−0.215421	+	0.180760i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	−0.298133	−	1.69080i	−0.0190860	−	0.108242i
$245$	1.29339	+	0.470754i	0.0826314	+	0.0300754i
$246$	−3.83750			−0.244670
$247$	2.85323	−	2.11797i	0.181546	−	0.134763i
$248$	5.34730			0.339554
$249$	3.05303	+	1.11121i	0.193478	+	0.0704203i
$250$	0.209141	+	1.18610i	0.0132272	+	0.0750153i
$251$	−3.32635	−	2.79114i	−0.209957	−	0.176175i	0.531745	−	0.846905i	$-0.321537\pi$
$251$	−3.32635	−	2.79114i	−0.209957	−	0.176175i	−0.741702	+	0.670730i	$0.765981\pi$
$252$	−3.28699	+	2.75811i	−0.207061	+	0.173745i
$253$	2.48262	−	14.0796i	0.156081	−	0.885180i
$254$	−2.12061	+	3.67301i	−0.133059	+	0.230465i
$255$	0.0282185	+	0.0488759i	0.00176711	+	0.00306073i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−16.6951	+	6.07650i	−1.04141	+	0.379042i	−0.805414	−	0.592712i	$-0.798057\pi$
$257$	−16.6951	+	6.07650i	−1.04141	+	0.379042i	−0.235995	+	0.971754i	$0.575835\pi$
$258$	4.66637	+	8.08240i	0.290516	+	0.503188i
$259$	−18.2738	+	31.6511i	−1.13548	+	1.96671i
$260$	−0.0170741	+	0.0968323i	−0.00105889	+	0.00600528i
$261$	1.79813	−	1.50881i	0.111302	−	0.0933932i
$262$	16.1197	+	13.5261i	0.995881	+	0.835643i
$263$	−0.401674	−	2.27801i	−0.0247683	−	0.140468i	0.969916	−	0.243440i	$-0.0782759\pi$
$263$	−0.401674	−	2.27801i	−0.0247683	−	0.140468i	−0.994684	+	0.102972i	$0.967165\pi$
$264$	2.41875	+	0.880352i	0.148864	+	0.0541819i
$265$	−1.53890			−0.0945336
$266$	−18.6702	−	1.11354i	−1.14475	−	0.0682756i
$267$	−3.43107			−0.209978
$268$	−10.7652	−	3.91820i	−0.657587	−	0.239342i
$269$	−0.489322	−	2.77509i	−0.0298345	−	0.169200i	0.966250	−	0.257606i	$-0.0829337\pi$
$269$	−0.489322	−	2.77509i	−0.0298345	−	0.169200i	−0.996084	+	0.0884063i	$0.971823\pi$
$270$	0.0923963	+	0.0775297i	0.00562306	+	0.00471831i
$271$	−5.12449	+	4.29995i	−0.311290	+	0.261204i	−0.785025	−	0.619464i	$-0.787350\pi$
$271$	−5.12449	+	4.29995i	−0.311290	+	0.261204i	0.473735	+	0.880668i	$0.342906\pi$
$272$	−0.0812519	+	0.460802i	−0.00492662	+	0.0279403i
$273$	−1.74897	+	3.02931i	−0.105852	+	0.183342i
$274$	6.16044	+	10.6702i	0.372166	+	0.644611i
$275$	12.0586	−	4.38895i	0.727158	−	0.264664i
$276$	5.21941	−	1.89971i	0.314171	−	0.114349i
$277$	−4.12583	−	7.14615i	−0.247897	−	0.429370i	0.715045	−	0.699078i	$-0.246406\pi$
$277$	−4.12583	−	7.14615i	−0.247897	−	0.429370i	−0.962942	+	0.269708i	$0.913073\pi$
$278$	2.79426	−	4.83981i	0.167589	−	0.290272i
$279$	0.928548	−	5.26606i	0.0555907	−	0.315271i
$280$	0.396459	−	0.332669i	0.0236930	−	0.0198808i
$281$	21.4008	+	17.9574i	1.27666	+	1.07125i	0.993695	+	0.112120i	$0.0357641\pi$
$281$	21.4008	+	17.9574i	1.27666	+	1.07125i	0.282970	+	0.959129i	$0.408680\pi$
$282$	1.64543	+	9.33170i	0.0979839	+	0.555694i
$283$	−2.27972	−	0.829748i	−0.135515	−	0.0493234i	0.273372	−	0.961908i	$-0.411861\pi$
$283$	−2.27972	−	0.829748i	−0.135515	−	0.0493234i	−0.408887	+	0.912585i	$0.634083\pi$
$284$	13.3327			0.791153
$285$	0.0603074	+	0.522277i	0.00357230	+	0.0309370i
$286$	2.09833			0.124077
$287$	15.4731	+	5.63176i	0.913350	+	0.332432i
$288$	0.173648	+	0.984808i	0.0102323	+	0.0580304i
$289$	−12.8550	−	10.7867i	−0.756179	−	0.634509i
$290$	−0.216881	+	0.181985i	−0.0127357	+	0.0106865i
$291$	−0.538485	+	3.05390i	−0.0315666	+	0.179023i
$292$	−1.14156	+	1.97724i	−0.0668047	+	0.115709i
$293$	7.05051	+	12.2118i	0.411895	+	0.713423i	0.995097	−	0.0989041i	$-0.0315337\pi$
$293$	7.05051	+	12.2118i	0.411895	+	0.713423i	−0.583202	+	0.812327i	$0.698200\pi$
$294$	10.7233	−	3.90295i	0.625394	−	0.227625i
$295$	1.70574	−	0.620838i	0.0993119	−	0.0361466i
$296$	4.25877	+	7.37641i	0.247536	+	0.428745i
$297$	1.28699	−	2.22913i	0.0746787	−	0.129347i
$298$	1.92649	−	10.9257i	0.111599	−	0.632907i
$299$	3.46863	−	2.91052i	0.200596	−	0.168320i
$300$	3.81908	+	3.20459i	0.220495	+	0.185017i
$301$	−6.95383	−	39.4371i	−0.400812	−	2.27312i
$302$	−11.8366	−	4.30818i	−0.681121	−	0.247908i
$303$	16.7297			0.961095
$304$	−2.40033	+	3.63846i	−0.137668	+	0.208680i
$305$	0.207081			0.0118574
$306$	0.439693	+	0.160035i	0.0251356	+	0.00914859i
$307$	−3.50892	−	19.9001i	−0.200265	−	1.13576i	−0.904719	−	0.426009i	$-0.859919\pi$
$307$	−3.50892	−	19.9001i	−0.200265	−	1.13576i	0.704454	−	0.709749i	$-0.251192\pi$
$308$	−8.46064	−	7.09932i	−0.482090	−	0.404521i
$309$	7.96451	−	6.68302i	0.453085	−	0.380183i
$310$	−0.111997	+	0.635164i	−0.00636098	+	0.0360749i
$311$	−4.80928	+	8.32991i	−0.272709	+	0.472346i	−0.969555	−	0.244875i	$-0.921253\pi$
$311$	−4.80928	+	8.32991i	−0.272709	+	0.472346i	0.696845	+	0.717221i	$0.254586\pi$
$312$	0.407604	+	0.705990i	0.0230760	+	0.0399688i
$313$	−23.3871	+	8.51222i	−1.32192	+	0.481139i	−0.904073	−	0.427379i	$-0.859437\pi$
$313$	−23.3871	+	8.51222i	−1.32192	+	0.481139i	−0.417846	+	0.908518i	$0.637215\pi$
$314$	3.73783	−	1.36046i	0.210938	−	0.0767751i
$315$	−0.258770	−	0.448204i	−0.0145801	−	0.0252534i
$316$	−2.42855	+	4.20637i	−0.136617	+	0.236627i
$317$	2.99778	−	17.0012i	0.168372	−	0.954885i	−0.777147	−	0.629319i	$-0.783334\pi$
$317$	2.99778	−	17.0012i	0.168372	−	0.954885i	0.945519	−	0.325566i	$-0.105555\pi$
$318$	−9.77379	+	8.20118i	−0.548087	+	0.459899i
$319$	4.62836	+	3.88365i	0.259138	+	0.217443i
$320$	−0.0209445	−	0.118782i	−0.00117083	−	0.00664014i
$321$	−8.56418	−	3.11711i	−0.478006	−	0.173980i
$322$	−23.8331			−1.32816
$323$	0.912818	+	1.82391i	0.0507906	+	0.101485i
$324$	1.00000			0.0555556
$325$	3.81908	+	1.39003i	0.211844	+	0.0771050i
$326$	3.33409	+	18.9086i	0.184658	+	1.04725i
$327$	−2.93376	−	2.46172i	−0.162237	−	0.136133i
$328$	2.93969	−	2.46669i	0.162317	−	0.136200i
$329$	7.06031	−	40.0410i	0.389247	−	2.20753i
$330$	−0.155230	+	0.268866i	−0.00854512	+	0.0148006i
$331$	−4.99525	−	8.65203i	−0.274564	−	0.475559i	0.695461	−	0.718564i	$-0.255200\pi$
$331$	−4.99525	−	8.65203i	−0.274564	−	0.475559i	−0.970025	+	0.243005i	$0.921867\pi$
$332$	−3.05303	+	1.11121i	−0.167557	+	0.0609858i
$333$	8.00387	−	2.91317i	0.438609	−	0.159641i
$334$	7.68732	+	13.3148i	0.420631	+	0.728555i
$335$	0.690884	−	1.19665i	0.0377470	−	0.0653798i
$336$	0.745100	−	4.22567i	0.0406485	−	0.230529i
$337$	5.18139	−	4.34770i	0.282248	−	0.236834i	−0.490662	−	0.871350i	$-0.663245\pi$
$337$	5.18139	−	4.34770i	0.282248	−	0.236834i	0.772910	+	0.634516i	$0.218800\pi$
$338$	−9.44949	−	7.92907i	−0.513985	−	0.431284i
$339$	−0.939693	−	5.32926i	−0.0510371	−	0.289446i
$340$	−0.0530334	−	0.0193026i	−0.00287614	−	0.00104683i
$341$	13.7638			0.745353
$342$	3.16637	+	2.99568i	0.171218	+	0.161988i
$343$	−18.9290			−1.02207
$344$	−8.76991	−	3.19199i	−0.472842	−	0.172100i
$345$	0.116334	+	0.659762i	0.00626320	+	0.0355204i
$346$	−5.05097	−	4.23827i	−0.271542	−	0.227851i
$347$	18.8457	−	15.8134i	1.01169	−	0.848909i	0.0231297	−	0.999732i	$-0.492637\pi$
$347$	18.8457	−	15.8134i	1.01169	−	0.848909i	0.988561	+	0.150823i	$0.0481925\pi$
$348$	−0.407604	+	2.31164i	−0.0218499	+	0.123917i
$349$	3.41740	−	5.91912i	0.182929	−	0.316843i	−0.759947	−	0.649985i	$-0.774775\pi$
$349$	3.41740	−	5.91912i	0.182929	−	0.316843i	0.942877	+	0.333141i	$0.108109\pi$
$350$	−10.6959	−	18.5259i	−0.571722	−	0.990251i
$351$	0.766044	−	0.278817i	0.0408884	−	0.0148822i
$352$	−2.41875	+	0.880352i	−0.128920	+	0.0469229i
$353$	2.54189	+	4.40268i	0.135291	+	0.234331i	0.925709	−	0.378237i	$-0.123470\pi$
$353$	2.54189	+	4.40268i	0.135291	+	0.234331i	−0.790418	+	0.612568i	$0.790136\pi$
$354$	7.52481	−	13.0334i	0.399939	−	0.692715i
$355$	−0.279248	+	1.58370i	−0.0148210	+	0.0840538i
$356$	2.62836	−	2.20545i	0.139303	−	0.116889i
$357$	−1.53802	−	1.29055i	−0.0814006	−	0.0683032i
$358$	0.215537	+	1.22237i	0.0113915	+	0.0646044i
$359$	2.69459	+	0.980752i	0.142215	+	0.0517621i	0.412147	−	0.911117i	$-0.364779\pi$
$359$	2.69459	+	0.980752i	0.142215	+	0.0517621i	−0.269932	+	0.962879i	$0.587001\pi$
$360$	−0.120615			−0.00635696
$361$	1.05185	+	18.9709i	0.0553606	+	0.998466i
$362$	4.03003			0.211814
$363$	−4.11081	−	1.49621i	−0.215762	−	0.0785309i
$364$	−0.607411	−	3.44480i	−0.0318370	−	0.180557i
$365$	−0.210952	−	0.177009i	−0.0110417	−	0.00926510i
$366$	1.31521	−	1.10359i	0.0687470	−	0.0576856i
$367$	3.84507	−	21.8065i	0.200711	−	1.13829i	−0.703336	−	0.710858i	$-0.748307\pi$
$367$	3.84507	−	21.8065i	0.200711	−	1.13829i	0.904047	−	0.427433i	$-0.140582\pi$
$368$	−2.77719	+	4.81023i	−0.144771	+	0.250751i
$369$	−1.91875	−	3.32337i	−0.0998860	−	0.173008i
$370$	−0.965385	+	0.351371i	−0.0501880	+	0.0182669i
$371$	51.4445	−	18.7243i	2.67087	−	0.972115i
$372$	2.67365	+	4.63089i	0.138622	+	0.240101i
$373$	−8.83662	+	15.3055i	−0.457543	+	0.792487i	−0.998830	−	0.0483501i	$-0.984604\pi$
$373$	−8.83662	+	15.3055i	−0.457543	+	0.792487i	0.541288	+	0.840837i	$0.317937\pi$
$374$	−0.209141	+	1.18610i	−0.0108144	+	0.0613315i
$375$	−0.922618	+	0.774169i	−0.0476438	+	0.0399779i
$376$	−7.25877	−	6.09083i	−0.374343	−	0.314111i
$377$	0.332282	+	1.88446i	0.0171134	+	0.0970548i
$378$	−4.03209	−	1.46756i	−0.207388	−	0.0754832i
$379$	−9.75970			−0.501322			−0.250661	−	0.968075i	$-0.580648\pi$
$379$	−9.75970			−0.501322			−0.250661	+	0.968075i	$0.580648\pi$
$380$	−0.381911	−	0.361323i	−0.0195916	−	0.0185355i
$381$	−4.24123			−0.217285
$382$	22.6322	+	8.23746i	1.15797	+	0.421465i
$383$	−3.87505	−	21.9765i	−0.198006	−	1.12295i	−0.908073	−	0.418812i	$-0.862447\pi$
$383$	−3.87505	−	21.9765i	−0.198006	−	1.12295i	0.710067	−	0.704134i	$-0.248665\pi$
$384$	−0.766044	−	0.642788i	−0.0390920	−	0.0328021i
$385$	1.02048	−	0.856282i	0.0520084	−	0.0436402i
$386$	−1.71213	+	9.70999i	−0.0871453	+	0.494226i
$387$	−4.66637	+	8.08240i	−0.237205	+	0.410851i
$388$	−1.55051	−	2.68556i	−0.0787151	−	0.136339i
$389$	−6.59879	+	2.40176i	−0.334572	+	0.121774i	−0.503843	−	0.863795i	$-0.668081\pi$
$389$	−6.59879	+	2.40176i	−0.334572	+	0.121774i	0.169271	+	0.985570i	$0.445859\pi$
$390$	−0.0923963	+	0.0336295i	−0.00467867	+	0.00170290i
$391$	1.29948	+	2.25076i	0.0657174	+	0.113826i
$392$	−5.70574	+	9.88263i	−0.288183	+	0.499148i
$393$	−3.65405	+	20.7231i	−0.184322	+	1.04534i
$394$	−4.94562	+	4.14987i	−0.249157	+	0.209067i
$395$	−0.448778	−	0.376569i	−0.0225805	−	0.0189472i
$396$	0.446967	+	2.53487i	0.0224609	+	0.127382i
$397$	18.7738	+	6.83310i	0.942229	+	0.342943i	0.767046	−	0.641592i	$-0.221726\pi$
$397$	18.7738	+	6.83310i	0.942229	+	0.342943i	0.175184	+	0.984536i	$0.443948\pi$
$398$	24.7716			1.24169
$399$	−8.37077	−	16.7257i	−0.419063	−	0.837331i
$400$	−4.98545			−0.249273
$401$	1.11809	+	0.406951i	0.0558347	+	0.0203222i	0.369787	−	0.929117i	$-0.379431\pi$
$401$	1.11809	+	0.406951i	0.0558347	+	0.0203222i	−0.313952	+	0.949439i	$0.601653\pi$
$402$	−1.98932	−	11.2820i	−0.0992184	−	0.562695i
$403$	3.33931	+	2.80201i	0.166343	+	0.139578i
$404$	−12.8157	+	10.7536i	−0.637604	+	0.535013i
$405$	−0.0209445	+	0.118782i	−0.00104074	+	0.00590234i
$406$	5.03596	−	8.72254i	0.249930	−	0.432892i
$407$	10.9620	+	18.9867i	0.543365	+	0.941136i
$408$	−0.439693	+	0.160035i	−0.0217680	+	0.00792291i
$409$	−8.91622	+	3.24524i	−0.440879	+	0.160467i	−0.552916	−	0.833237i	$-0.686485\pi$
$409$	−8.91622	+	3.24524i	−0.440879	+	0.160467i	0.112037	+	0.993704i	$0.464263\pi$
$410$	0.231429	+	0.400847i	0.0114295	+	0.0197964i
$411$	−6.16044	+	10.6702i	−0.303872	+	0.526322i
$412$	−1.80541	+	10.2390i	−0.0889460	+	0.504438i
$413$	−49.4680	+	41.5086i	−2.43416	+	2.04250i
$414$	4.25490	+	3.57029i	0.209117	+	0.175470i
$415$	−0.0680482	−	0.385920i	−0.00334035	−	0.0189441i
$416$	−0.766044	−	0.278817i	−0.0375584	−	0.0136701i
$417$	5.58853			0.273671
$418$	−6.17840	+	9.36532i	−0.302195	+	0.458073i
$419$	4.72638			0.230899			0.115449	−	0.993313i	$-0.463169\pi$
$419$	4.72638			0.230899			0.115449	+	0.993313i	$0.463169\pi$
$420$	0.486329	+	0.177009i	0.0237304	+	0.00863718i
$421$	0.240819	+	1.36575i	0.0117368	+	0.0665627i	0.990114	−	0.140268i	$-0.0447963\pi$
$421$	0.240819	+	1.36575i	0.0117368	+	0.0665627i	−0.978377	+	0.206830i	$0.933685\pi$
$422$	−1.06031	−	0.889704i	−0.0516150	−	0.0433101i
$423$	−7.25877	+	6.09083i	−0.352933	+	0.296146i
$424$	2.21554	−	12.5649i	0.107596	−	0.610207i
$425$	−1.16637	+	2.02022i	−0.0565775	+	0.0979950i
$426$	6.66637	+	11.5465i	0.322987	+	0.559430i
$427$	−6.92262	+	2.51963i	−0.335009	+	0.121933i
$428$	8.56418	−	3.11711i	0.413965	−	0.150671i
$429$	1.04916	+	1.81720i	0.0506541	+	0.0877354i
$430$	0.562834	−	0.974856i	0.0271422	−	0.0470117i
$431$	0.470904	−	2.67063i	0.0226827	−	0.128640i	−0.971364	−	0.237597i	$-0.923640\pi$
$431$	0.470904	−	2.67063i	0.0226827	−	0.128640i	0.994046	+	0.108958i	$0.0347513\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	−15.5057	−	13.0108i	−0.745155	−	0.625260i	0.189061	−	0.981965i	$-0.439455\pi$
$433$	−15.5057	−	13.0108i	−0.745155	−	0.625260i	−0.934217	+	0.356706i	$0.883900\pi$
$434$	−3.98427	−	22.5959i	−0.191251	−	1.08464i
$435$	−0.266044	−	0.0968323i	−0.0127559	−	0.00464275i
$436$	3.82976			0.183412
$437$	2.77719	+	24.0512i	0.132851	+	1.15052i
$438$	−2.28312			−0.109092
$439$	17.1027	+	6.22486i	0.816266	+	0.297096i	0.716209	−	0.697885i	$-0.245876\pi$
$439$	17.1027	+	6.22486i	0.816266	+	0.297096i	0.100056	+	0.994982i	$0.468098\pi$
$440$	−0.0539108	−	0.305743i	−0.00257009	−	0.0145757i
$441$	8.74170	+	7.33515i	0.416271	+	0.349293i
$442$	−0.292204	+	0.245188i	−0.0138987	+	0.0116624i
$443$	−6.20661	+	35.1995i	−0.294885	+	1.67238i	0.372784	+	0.927918i	$0.378403\pi$
$443$	−6.20661	+	35.1995i	−0.294885	+	1.67238i	−0.667669	+	0.744458i	$0.732708\pi$
$444$	−4.25877	+	7.37641i	−0.202112	+	0.350069i
$445$	0.206919	+	0.358394i	0.00980891	+	0.0169895i
$446$	−20.9675	+	7.63155i	−0.992840	+	0.361364i
$447$	10.4251	−	3.79444i	0.493092	−	0.179471i
$448$	2.14543	+	3.71599i	0.101362	+	0.175564i
$449$	9.49525	−	16.4463i	0.448109	−	0.776147i	−0.550154	−	0.835063i	$-0.685431\pi$
$449$	9.49525	−	16.4463i	0.448109	−	0.776147i	0.998263	+	0.0589161i	$0.0187644\pi$
$450$	−0.865715	+	4.90971i	−0.0408102	+	0.231446i
$451$	7.56670	−	6.34922i	0.356302	−	0.298973i
$452$	4.14543	+	3.47843i	0.194985	+	0.163612i
$453$	−2.18732	−	12.4049i	−0.102769	−	0.582833i
$454$	19.5141	+	7.10257i	0.915844	+	0.333340i
$455$	0.421903			0.0197791
$456$	−4.35117	−	0.259515i	−0.203762	−	0.0121529i
$457$	25.9632			1.21451			0.607253	−	0.794509i	$-0.292272\pi$
$457$	25.9632			1.21451			0.607253	+	0.794509i	$0.292272\pi$
$458$	−5.18479	−	1.88711i	−0.242269	−	0.0881789i
$459$	0.0812519	+	0.460802i	0.00379251	+	0.0215084i
$460$	−0.513204	−	0.430629i	−0.0239282	−	0.0200782i
$461$	−22.3949	+	18.7915i	−1.04303	+	0.875209i	−0.992344	−	0.123506i	$-0.960586\pi$
$461$	−22.3949	+	18.7915i	−1.04303	+	0.875209i	−0.0506891	+	0.998714i	$0.516142\pi$
$462$	1.91787	−	10.8768i	0.0892274	−	0.506034i
$463$	10.5954	−	18.3518i	0.492410	−	0.852878i	−0.507552	−	0.861621i	$-0.669450\pi$
$463$	10.5954	−	18.3518i	0.492410	−	0.852878i	0.999962	+	0.00874269i	$0.00278292\pi$
$464$	−1.17365	−	2.03282i	−0.0544852	−	0.0943712i
$465$	−0.606067	+	0.220590i	−0.0281057	+	0.0102296i
$466$	14.1766	−	5.15988i	0.656720	−	0.239027i
$467$	1.07263	+	1.85786i	0.0496356	+	0.0859713i	0.889776	−	0.456398i	$-0.150861\pi$
$467$	1.07263	+	1.85786i	0.0496356	+	0.0859713i	−0.840140	+	0.542369i	$0.817527\pi$
$468$	−0.407604	+	0.705990i	−0.0188415	+	0.0326344i
$469$	−8.53590	+	48.4095i	−0.394151	+	2.23534i
$470$	0.875515	−	0.734644i	0.0403845	−	0.0338866i
$471$	3.04710	+	2.55682i	0.140403	+	0.117812i
$472$	2.61334	+	14.8210i	0.120289	+	0.682191i
$473$	−22.5736	−	8.21611i	−1.03793	−	0.377777i
$474$	−4.85710			−0.223094
$475$	−17.4491	+	12.9526i	−0.800619	+	0.594305i
$476$	2.00774			0.0920246
$477$	−11.9893	−	4.36376i	−0.548953	−	0.199803i
$478$	−5.02734	−	28.5115i	−0.229945	−	1.30408i
$479$	−2.60220	−	2.18350i	−0.118897	−	0.0997668i	0.581400	−	0.813618i	$-0.302505\pi$
$479$	−2.60220	−	2.18350i	−0.118897	−	0.0997668i	−0.700298	+	0.713851i	$0.746949\pi$
$480$	0.0923963	−	0.0775297i	0.00421729	−	0.00353873i
$481$	−1.20574	+	6.83807i	−0.0549769	+	0.311789i
$482$	9.68479	−	16.7746i	0.441130	−	0.764060i
$483$	−11.9165	−	20.6400i	−0.542221	−	0.939154i
$484$	4.11081	−	1.49621i	0.186855	−	0.0680097i
$485$	0.351471	−	0.127925i	0.0159595	−	0.00580878i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−9.89306	+	17.1353i	−0.448297	+	0.776473i	−0.998275	−	0.0587056i	$-0.981303\pi$
$487$	−9.89306	+	17.1353i	−0.448297	+	0.776473i	0.549978	+	0.835179i	$0.314636\pi$
$488$	−0.298133	+	1.69080i	−0.0134959	+	0.0765388i
$489$	−14.7083	+	12.3417i	−0.665131	+	0.558111i
$490$	−1.05438	−	0.884728i	−0.0476319	−	0.0399679i
$491$	4.36618	+	24.7618i	0.197043	+	1.11749i	0.909479	+	0.415750i	$0.136481\pi$
$491$	4.36618	+	24.7618i	0.197043	+	1.11749i	−0.712436	+	0.701737i	$0.752408\pi$
$492$	3.60607	+	1.31250i	0.162574	+	0.0591721i
$493$	−1.09833			−0.0494661
$494$	−3.40554	+	1.01438i	−0.153223	+	0.0456392i
$495$	−0.310460			−0.0139541
$496$	−5.02481	−	1.82888i	−0.225621	−	0.0821193i
$497$	−9.93423	−	56.3398i	−0.445611	−	2.52719i
$498$	−2.48886	−	2.08840i	−0.111528	−	0.0935833i
$499$	26.9329	−	22.5994i	1.20568	−	1.01169i	0.206232	−	0.978503i	$-0.433880\pi$
$499$	26.9329	−	22.5994i	1.20568	−	1.01169i	0.999449	−	0.0331839i	$-0.0105647\pi$
$500$	0.209141	−	1.18610i	0.00935305	−	0.0530438i
$501$	−7.68732	+	13.3148i	−0.343444	+	0.594863i
$502$	2.17112	+	3.76049i	0.0969019	+	0.167839i
$503$	−19.1186	+	6.95859i	−0.852454	+	0.310268i	−0.731041	−	0.682334i	$-0.760965\pi$
$503$	−19.1186	+	6.95859i	−0.852454	+	0.310268i	−0.121414	+	0.992602i	$0.538743\pi$
$504$	4.03209	−	1.46756i	0.179604	−	0.0653703i
$505$	−1.00892	−	1.74751i	−0.0448965	−	0.0777630i
$506$	−7.14842	+	12.3814i	−0.317786	+	0.550422i
$507$	2.14203	−	12.1480i	0.0951307	−	0.539513i
$508$	3.24897	−	2.72621i	0.144150	−	0.120956i
$509$	−10.0851	−	8.46242i	−0.447015	−	0.375090i	0.391312	−	0.920258i	$-0.372021\pi$
$509$	−10.0851	−	8.46242i	−0.447015	−	0.375090i	−0.838327	+	0.545168i	$0.816466\pi$
$510$	−0.00980018	−	0.0555796i	−0.000433959	−	0.00246111i
$511$	9.20574	+	3.35061i	0.407238	+	0.148222i
$512$	1.00000			0.0441942
$513$	−1.01114	+	4.24000i	−0.0446431	+	0.187201i
$514$	17.7665			0.783647
$515$	−1.17840	−	0.428901i	−0.0519263	−	0.0188996i
$516$	−1.62061	−	9.19096i	−0.0713436	−	0.404610i
$517$	−18.6839	−	15.6777i	−0.821718	−	0.689503i
$518$	27.9971	−	23.4923i	1.23012	−	1.03219i
$519$	1.14496	−	6.49341i	0.0502583	−	0.285029i
$520$	0.0491630	−	0.0851529i	0.00215594	−	0.00373420i
$521$	−10.2456	−	17.7458i	−0.448866	−	0.777459i	0.549446	−	0.835529i	$-0.314839\pi$
$521$	−10.2456	−	17.7458i	−0.448866	−	0.777459i	−0.998313	+	0.0580697i	$0.981505\pi$
$522$	−2.20574	+	0.802823i	−0.0965425	+	0.0351386i
$523$	40.3312	−	14.6793i	1.76356	−	0.641883i	0.763566	−	0.645730i	$-0.223447\pi$
$523$	40.3312	−	14.6793i	1.76356	−	0.641883i	0.999993	+	0.00384740i	$0.00122467\pi$
$524$	−10.5214	−	18.2236i	−0.459630	−	0.796102i
$525$	10.6959	−	18.5259i	0.466809	−	0.808537i
$526$	−0.401674	+	2.27801i	−0.0175138	+	0.0993258i
$527$	−1.91669	+	1.60829i	−0.0834923	+	0.0700583i
$528$	−1.97178	−	1.65452i	−0.0858108	−	0.0720038i
$529$	1.36333	+	7.73183i	0.0592753	+	0.336167i
$530$	1.44609	+	0.526333i	0.0628141	+	0.0228625i
$531$	15.0496			0.653098
$532$	17.1634	+	7.43199i	0.744129	+	0.322217i
$533$	3.12836			0.135504
$534$	3.22416	+	1.17350i	0.139523	+	0.0507822i
$535$	0.190884	+	1.08256i	0.00825265	+	0.0468031i
$536$	8.77584	+	7.36381i	0.379059	+	0.318068i
$537$	−0.950837	+	0.797847i	−0.0410316	+	0.0344296i
$538$	−0.489322	+	2.77509i	−0.0210962	+	0.119642i
$539$	−14.6864	+	25.4377i	−0.632590	+	1.09568i
$540$	−0.0603074	−	0.104455i	−0.00259522	−	0.00449505i
$541$	13.6976	−	4.98551i	0.588905	−	0.214344i	−0.0303426	−	0.999540i	$-0.509660\pi$
$541$	13.6976	−	4.98551i	0.588905	−	0.214344i	0.619248	+	0.785196i	$0.287438\pi$
$542$	6.28611	−	2.28796i	0.270012	−	0.0982762i
$543$	2.01501	+	3.49011i	0.0864726	+	0.149775i
$544$	0.233956	−	0.405223i	0.0100308	−	0.0173738i
$545$	−0.0802124	+	0.454907i	−0.00343592	+	0.0194861i
$546$	2.67958	−	2.24843i	0.114675	−	0.0962240i
$547$	14.2246	+	11.9359i	0.608201	+	0.510341i	0.894070	−	0.447928i	$-0.147838\pi$
$547$	14.2246	+	11.9359i	0.608201	+	0.510341i	−0.285869	+	0.958269i	$0.592282\pi$
$548$	−2.13950	−	12.1337i	−0.0913949	−	0.518326i
$549$	1.61334	+	0.587208i	0.0688557	+	0.0250614i
$550$	−12.8324			−0.547177
$551$	−9.38919	−	4.06564i	−0.399993	−	0.173202i
$552$	−5.55438			−0.236410
$553$	19.5842	+	7.12808i	0.832807	+	0.303117i
$554$	1.43289	+	8.12630i	0.0608775	+	0.345253i
$555$	−0.786989	−	0.660362i	−0.0334058	−	0.0280308i
$556$	−4.28106	+	3.59224i	−0.181557	+	0.152345i
$557$	2.69816	−	15.3020i	0.114325	−	0.648367i	−0.872758	−	0.488154i	$-0.837671\pi$
$557$	2.69816	−	15.3020i	0.114325	−	0.648367i	0.987082	−	0.160214i	$-0.0512183\pi$
$558$	−2.67365	+	4.63089i	−0.113185	+	0.196041i
$559$	−3.80406	−	6.58883i	−0.160895	−	0.278678i
$560$	−0.486329	+	0.177009i	−0.0205512	+	0.00748001i
$561$	−1.13176	+	0.411927i	−0.0477829	+	0.0173916i
$562$	−13.9684	−	24.1939i	−0.589220	−	1.02056i
$563$	6.07785	−	10.5271i	0.256151	−	0.443666i	−0.709057	−	0.705151i	$-0.750879\pi$
$563$	6.07785	−	10.5271i	0.256151	−	0.443666i	0.965207	+	0.261485i	$0.0842123\pi$
$564$	1.64543	−	9.33170i	0.0692851	−	0.392935i
$565$	−0.500000	+	0.419550i	−0.0210352	+	0.0176506i
$566$	1.85844	+	1.55942i	0.0781161	+	0.0655472i
$567$	−0.745100	−	4.22567i	−0.0312913	−	0.177462i
$568$	−12.5287	−	4.56007i	−0.525692	−	0.191336i
$569$	13.6709			0.573113			0.286556	−	0.958063i	$-0.407489\pi$
$569$	13.6709			0.573113			0.286556	+	0.958063i	$0.407489\pi$
$570$	0.121959	−	0.511406i	0.00510830	−	0.0214205i
$571$	28.2003			1.18014			0.590072	−	0.807350i	$-0.299099\pi$
$571$	28.2003			1.18014			0.590072	+	0.807350i	$0.299099\pi$
$572$	−1.97178	−	0.717670i	−0.0824443	−	0.0300073i
$573$	4.18227	+	23.7188i	0.174717	+	0.990868i
$574$	−12.6138	−	10.5842i	−0.526490	−	0.441778i
$575$	−21.2126	+	17.7995i	−0.884627	+	0.742290i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	−10.1095	+	17.5101i	−0.420863	+	0.728956i	−0.996024	−	0.0890843i	$-0.971606\pi$
$577$	−10.1095	+	17.5101i	−0.420863	+	0.728956i	0.575161	+	0.818040i	$0.304939\pi$
$578$	8.39053	+	14.5328i	0.349000	+	0.604486i
$579$	−9.26517	+	3.37225i	−0.385047	+	0.140146i
$580$	0.266044	−	0.0968323i	0.0110469	−	0.00402074i
$581$	6.97044	+	12.0732i	0.289182	+	0.500879i
$582$	1.55051	−	2.68556i	0.0642706	−	0.111320i
$583$	5.70274	−	32.3419i	0.236184	−	1.33946i
$584$	1.74897	−	1.46756i	0.0723729	−	0.0607281i
$585$	−0.0753221	−	0.0632028i	−0.00311419	−	0.00261311i
$586$	−2.44862	−	13.8868i	−0.101151	−	0.573658i
$587$	4.89306	+	1.78093i	0.201958	+	0.0735067i	0.441019	−	0.897498i	$-0.354617\pi$
$587$	4.89306	+	1.78093i	0.201958	+	0.0735067i	−0.239061	+	0.971005i	$0.576839\pi$
$588$	−11.4115			−0.470601
$589$	−22.3384	+	6.65376i	−0.920439	+	0.274163i
$590$	−1.81521			−0.0747309
$591$	−6.06670	−	2.20810i	−0.249551	−	0.0908291i
$592$	−1.47906	−	8.38814i	−0.0607888	−	0.344750i
$593$	−33.3573	−	27.9901i	−1.36982	−	1.14942i	−0.972811	−	0.231602i	$-0.925603\pi$
$593$	−33.3573	−	27.9901i	−1.36982	−	1.14942i	−0.397010	−	0.917814i	$-0.629952\pi$
$594$	−1.97178	+	1.65452i	−0.0809032	+	0.0678858i
$595$	−0.0420512	+	0.238484i	−0.00172393	+	0.00977690i
$596$	−5.54710	+	9.60787i	−0.227218	+	0.393553i
$597$	12.3858	+	21.4528i	0.506916	+	0.878005i
$598$	−4.25490	+	1.54866i	−0.173996	+	0.0633293i
$599$	30.7511	−	11.1925i	1.25646	−	0.457312i	0.373877	−	0.927478i	$-0.378028\pi$
$599$	30.7511	−	11.1925i	1.25646	−	0.457312i	0.882578	+	0.470166i	$0.155806\pi$
$600$	−2.49273	−	4.31753i	−0.101765	−	0.176262i
$601$	10.3867	−	17.9902i	0.423681	−	0.733836i	−0.572616	−	0.819824i	$-0.694071\pi$
$601$	10.3867	−	17.9902i	0.423681	−	0.733836i	0.996296	+	0.0859876i	$0.0274045\pi$
$602$	−6.95383	+	39.4371i	−0.283417	+	1.60734i
$603$	8.77584	−	7.36381i	0.357380	−	0.299877i
$604$	9.64930	+	8.09672i	0.392624	+	0.329451i
$605$	0.0916247	+	0.519630i	0.00372508	+	0.0211260i
$606$	−15.7208	−	5.72189i	−0.638612	−	0.232436i
$607$	−23.0419			−0.935241			−0.467621	−	0.883929i	$-0.654889\pi$
$607$	−23.0419			−0.935241			−0.467621	+	0.883929i	$0.654889\pi$
$608$	3.50000	−	2.59808i	0.141944	−	0.105366i
$609$	10.0719			0.408135
$610$	−0.194593	−	0.0708260i	−0.00787883	−	0.00286766i
$611$	−1.34137	−	7.60727i	−0.0542659	−	0.307757i
$612$	−0.358441	−	0.300767i	−0.0144891	−	0.0121578i
$613$	16.2404	−	13.6273i	0.655942	−	0.550400i	−0.252926	−	0.967486i	$-0.581393\pi$
$613$	16.2404	−	13.6273i	0.655942	−	0.550400i	0.908867	+	0.417085i	$0.136948\pi$
$614$	−3.50892	+	19.9001i	−0.141609	+	0.803102i
$615$	−0.231429	+	0.400847i	−0.00933213	+	0.0161637i
$616$	5.52229	+	9.56488i	0.222499	+	0.385380i
$617$	19.2472	−	7.00541i	0.774864	−	0.282027i	0.0758345	−	0.997120i	$-0.475838\pi$
$617$	19.2472	−	7.00541i	0.774864	−	0.282027i	0.699029	+	0.715093i	$0.253616\pi$
$618$	−9.76991	+	3.55596i	−0.393004	+	0.143042i
$619$	7.87258	+	13.6357i	0.316426	+	0.548065i	0.979740	−	0.200276i	$-0.0641839\pi$
$619$	7.87258	+	13.6357i	0.316426	+	0.548065i	−0.663314	+	0.748341i	$0.730851\pi$
$620$	0.322481	−	0.558554i	0.0129512	−	0.0224321i
$621$	−0.964508	+	5.46999i	−0.0387044	+	0.219503i
$622$	7.36824	−	6.18269i	0.295440	−	0.247903i
$623$	−11.2779	−	9.46329i	−0.451840	−	0.379139i
$624$	−0.141559	−	0.802823i	−0.00566691	−	0.0321386i
$625$	−23.2875	−	8.47594i	−0.931498	−	0.339038i
$626$	24.8881			0.994727
$627$	−11.1998	−	0.667985i	−0.447277	−	0.0266768i
$628$	−3.97771			−0.158728
$629$	−3.74510	−	1.36310i	−0.149327	−	0.0543506i
$630$	0.0898700	+	0.509678i	0.00358051	+	0.0203061i
$631$	−16.2041	−	13.5969i	−0.645077	−	0.541284i	0.260496	−	0.965475i	$-0.416114\pi$
$631$	−16.2041	−	13.5969i	−0.645077	−	0.541284i	−0.905573	+	0.424191i	$0.860558\pi$
$632$	3.72075	−	3.12208i	0.148004	−	0.124190i
$633$	0.240352	−	1.36310i	0.00955314	−	0.0541786i
$634$	−8.63176	+	14.9506i	−0.342811	+	0.593766i
$635$	0.255777	+	0.443020i	0.0101502	+	0.0175807i
$636$	11.9893	−	4.36376i	0.475408	−	0.173034i
$637$	−8.74170	+	3.18172i	−0.346359	+	0.126064i
$638$	−3.02094	−	5.23243i	−0.119600	−	0.207154i
$639$	−6.66637	+	11.5465i	−0.263718	+	0.456772i
$640$	−0.0209445	+	0.118782i	−0.000827905	+	0.00469528i
$641$	6.30200	−	5.28801i	0.248914	−	0.208864i	−0.509790	−	0.860299i	$-0.670277\pi$
$641$	6.30200	−	5.28801i	0.248914	−	0.208864i	0.758705	+	0.651435i	$0.225833\pi$
$642$	6.98158	+	5.85824i	0.275541	+	0.231206i
$643$	−0.742574	−	4.21134i	−0.0292842	−	0.166079i	0.966658	−	0.256069i	$-0.0824276\pi$
$643$	−0.742574	−	4.21134i	−0.0292842	−	0.166079i	−0.995943	+	0.0899901i	$0.971316\pi$
$644$	22.3957	+	8.15138i	0.882516	+	0.321210i
$645$	1.12567			0.0443231
$646$	−0.233956	−	2.02611i	−0.00920486	−	0.0797164i
$647$	0.947682			0.0372572			0.0186286	−	0.999826i	$-0.494070\pi$
$647$	0.947682			0.0372572			0.0186286	+	0.999826i	$0.494070\pi$
$648$	−0.939693	−	0.342020i	−0.0369146	−	0.0134358i
$649$	6.72668	+	38.1489i	0.264045	+	1.49748i
$650$	−3.11334	−	2.61240i	−0.122115	−	0.102467i
$651$	17.5765	−	14.7484i	0.688878	−	0.578037i
$652$	3.33409	−	18.9086i	0.130573	−	0.740517i
$653$	16.4217	−	28.4433i	0.642632	−	1.11307i	−0.342211	−	0.939623i	$-0.611176\pi$
$653$	16.4217	−	28.4433i	0.642632	−	1.11307i	0.984843	−	0.173449i	$-0.0554911\pi$
$654$	1.91488	+	3.31667i	0.0748776	+	0.129692i
$655$	2.38501	−	0.868073i	0.0931901	−	0.0339184i
$656$	−3.60607	+	1.31250i	−0.140793	+	0.0512446i
$657$	−1.14156	−	1.97724i	−0.0445365	−	0.0771394i
$658$	−20.3293	+	35.2115i	−0.792520	+	1.37269i
$659$	0.823826	−	4.67215i	0.0320917	−	0.182001i	−0.964548	−	0.263906i	$-0.914989\pi$
$659$	0.823826	−	4.67215i	0.0320917	−	0.182001i	0.996640	+	0.0819047i	$0.0261003\pi$
$660$	0.237826	−	0.199560i	0.00925736	−	0.00776785i
$661$	30.1864	+	25.3294i	1.17412	+	0.985201i	1.00000		0.000475674i	$0.000151412\pi$
$661$	30.1864	+	25.3294i	1.17412	+	0.985201i	0.174117	+	0.984725i	$0.444293\pi$
$662$	1.73483	+	9.83873i	0.0674262	+	0.382393i
$663$	−0.358441	−	0.130462i	−0.0139207	−	0.00506671i
$664$	3.24897			0.126085
$665$	−1.24227	+	1.88305i	−0.0481731	+	0.0730217i
$666$	−8.51754			−0.330048
$667$	−12.2515	−	4.45918i	−0.474380	−	0.172660i
$668$	−2.66978	−	15.1411i	−0.103297	−	0.585825i
$669$	−17.0929	−	14.3426i	−0.660848	−	0.554518i
$670$	−1.05850	+	0.888184i	−0.0408933	+	0.0343135i
$671$	−0.767389	+	4.35208i	−0.0296247	+	0.168010i
$672$	−2.14543	+	3.71599i	−0.0827617	+	0.143348i
$673$	−8.57145	−	14.8462i	−0.330405	−	0.572279i	0.652186	−	0.758059i	$-0.273852\pi$
$673$	−8.57145	−	14.8462i	−0.330405	−	0.572279i	−0.982591	+	0.185780i	$0.940519\pi$
$674$	−6.35591	+	2.31336i	−0.244821	+	0.0891074i
$675$	−4.68479	+	1.70513i	−0.180318	+	0.0656303i
$676$	6.16772	+	10.6828i	0.237220	+	0.410877i
$677$	−3.56506	+	6.17486i	−0.137016	+	0.237319i	−0.926366	−	0.376625i	$-0.877085\pi$
$677$	−3.56506	+	6.17486i	−0.137016	+	0.237319i	0.789350	+	0.613944i	$0.210418\pi$
$678$	−0.939693	+	5.32926i	−0.0360887	+	0.204669i
$679$	−10.1930	+	8.55294i	−0.391171	+	0.328232i
$680$	0.0432332	+	0.0362770i	0.00165792	+	0.00139116i
$681$	3.60607	+	20.4510i	0.138185	+	0.783685i
$682$	−12.9338	−	4.70750i	−0.495259	−	0.180260i
$683$	−26.0000			−0.994862			−0.497431	−	0.867503i	$-0.665723\pi$
$683$	−26.0000			−0.994862			−0.497431	+	0.867503i	$0.665723\pi$
$684$	−1.95084	−	3.89798i	−0.0745921	−	0.149043i
$685$	1.48608			0.0567802
$686$	17.7875	+	6.47410i	0.679128	+	0.247182i
$687$	−0.958111	−	5.43372i	−0.0365542	−	0.207309i
$688$	7.14930	+	5.99898i	0.272565	+	0.228709i
$689$	7.96766	−	6.68566i	0.303544	−	0.254703i
$690$	0.116334	−	0.659762i	0.00442875	−	0.0251167i
$691$	−19.6857	+	34.0967i	−0.748880	+	1.29710i	0.199479	+	0.979902i	$0.436075\pi$
$691$	−19.6857	+	34.0967i	−0.748880	+	1.29710i	−0.948360	+	0.317197i	$0.897258\pi$
$692$	3.29679	+	5.71021i	0.125325	+	0.217069i
$693$	10.3785	−	3.77747i	0.394247	−	0.143494i
$694$	−23.1177	+	8.41415i	−0.877535	+	0.319397i
$695$	−0.337029	−	0.583752i	−0.0127843	−	0.0221430i
$696$	1.17365	−	2.03282i	0.0444870	−	0.0770538i
$697$	−0.311804	+	1.76833i	−0.0118104	+	0.0669802i
$698$	−5.23577	+	4.39333i	−0.198177	+	0.166290i
$699$	11.5569	+	9.69739i	0.437122	+	0.366789i
$700$	3.71466	+	21.0669i	0.140401	+	0.796253i
$701$	−5.29426	−	1.92695i	−0.199962	−	0.0727801i	0.240098	−	0.970749i	$-0.422820\pi$
$701$	−5.29426	−	1.92695i	−0.199962	−	0.0727801i	−0.440060	+	0.897969i	$0.645043\pi$
$702$	−0.815207			−0.0307680
$703$	−26.9697	−	25.5158i	−1.01718	−	0.962346i
$704$	2.57398			0.0970104
$705$	1.07398	+	0.390896i	0.0404483	+	0.0147220i
$706$	−0.882789	−	5.00654i	−0.0332242	−	0.188424i
$707$	54.9903	+	46.1423i	2.06812	+	1.73536i
$708$	−11.5287	+	9.67372i	−0.433275	+	0.363560i
$709$	5.32517	−	30.2005i	0.199991	−	1.13421i	−0.705139	−	0.709069i	$-0.749115\pi$
$709$	5.32517	−	30.2005i	0.199991	−	1.13421i	0.905130	−	0.425136i	$-0.139774\pi$
$710$	0.804063	−	1.39268i	0.0301760	−	0.0522663i
$711$	−2.42855	−	4.20637i	−0.0910777	−	0.157751i
$712$	−3.22416	+	1.17350i	−0.120830	+	0.0439786i
$713$	−27.9097	+	10.1583i	−1.04523	+	0.380432i
$714$	1.00387	+	1.73875i	0.0375689	+	0.0650713i
$715$	0.126545	−	0.219182i	0.00473250	−	0.00819693i
$716$	0.215537	−	1.22237i	0.00805500	−	0.0456822i
$717$	22.1780	−	18.6095i	0.828252	−	0.694986i
$718$	−2.19665	−	1.84321i	−0.0819783	−	0.0687880i
$719$	1.10085	+	6.24324i	0.0410549	+	0.232834i	0.998430	−	0.0560138i	$-0.0178391\pi$
$719$	1.10085	+	6.24324i	0.0410549	+	0.232834i	−0.957375	+	0.288847i	$0.906728\pi$
$720$	0.113341	+	0.0412527i	0.00422396	+	0.00153740i
$721$	44.6117			1.66143
$722$	5.50000	−	18.1865i	0.204689	−	0.676833i
$723$	19.3696			0.720363
$724$	−3.78699	−	1.37835i	−0.140742	−	0.0512260i
$725$	−2.03209	−	11.5245i	−0.0754699	−	0.428011i
$726$	3.35117	+	2.81196i	0.124373	+	0.104362i
$727$	−17.8806	+	15.0036i	−0.663154	+	0.556452i	−0.911030	−	0.412340i	$-0.864712\pi$
$727$	−17.8806	+	15.0036i	−0.663154	+	0.556452i	0.247877	+	0.968792i	$0.420267\pi$
$728$	−0.607411	+	3.44480i	−0.0225121	+	0.127673i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	0.137689	+	0.238484i	0.00509609	+	0.00882670i
$731$	4.10354	−	1.49357i	0.151775	−	0.0552416i
$732$	−1.61334	+	0.587208i	−0.0596308	+	0.0217038i
$733$	−0.794730	−	1.37651i	−0.0293540	−	0.0508426i	0.850975	−	0.525206i	$-0.176012\pi$
$733$	−0.794730	−	1.37651i	−0.0293540	−	0.0508426i	−0.880329	+	0.474363i	$0.842678\pi$
$734$	−11.0715	+	19.1763i	−0.408655	+	0.707811i
$735$	0.239008	−	1.35548i	0.00881594	−	0.0499977i
$736$	4.25490	−	3.57029i	0.156838	−	0.131602i
$737$	22.5888	+	18.9543i	0.832070	+	0.698190i
$738$	0.666374	+	3.77920i	0.0245296	+	0.139114i
$739$	−3.43882	−	1.25163i	−0.126499	−	0.0460418i	0.277995	−	0.960582i	$-0.410330\pi$
$739$	−3.43882	−	1.25163i	−0.126499	−	0.0460418i	−0.404494	+	0.914541i	$0.632552\pi$
$740$	1.02734			0.0377658
$741$	−2.58125	−	2.44210i	−0.0948247	−	0.0897127i
$742$	−54.7461			−2.00979
$743$	17.2716	+	6.28634i	0.633632	+	0.230623i	0.638811	−	0.769363i	$-0.279426\pi$
$743$	17.2716	+	6.28634i	0.633632	+	0.230623i	−0.00517924	+	0.999987i	$0.501649\pi$
$744$	−0.928548	−	5.26606i	−0.0340422	−	0.193063i
$745$	−1.02506	−	0.860130i	−0.0375554	−	0.0315127i
$746$	13.5385	−	11.3601i	0.495679	−	0.415924i
$747$	0.564178	−	3.19961i	0.0206422	−	0.117068i
$748$	0.602196	−	1.04303i	0.0220185	−	0.0381371i
$749$	−19.5530	−	33.8668i	−0.714452	−	1.23747i
$750$	1.13176	−	0.411927i	0.0413260	−	0.0150414i
$751$	−28.8161	+	10.4882i	−1.05152	+	0.382720i	−0.809235	−	0.587486i	$-0.800118\pi$
$751$	−28.8161	+	10.4882i	−1.05152	+	0.382720i	−0.242281	+	0.970206i	$0.577896\pi$
$752$	4.73783	+	8.20616i	0.172771	+	0.299248i
$753$	−2.17112	+	3.76049i	−0.0791201	+	0.137040i
$754$	0.332282	−	1.88446i	0.0121010	−	0.0686281i
$755$	−1.16385	+	0.976584i	−0.0423568	+	0.0355415i
$756$	3.28699	+	2.75811i	0.119547	+	0.100312i
$757$	−1.35235	−	7.66955i	−0.0491520	−	0.278755i	0.950319	−	0.311278i	$-0.100757\pi$
$757$	−1.35235	−	7.66955i	−0.0491520	−	0.278755i	−0.999471	+	0.0325230i	$0.989646\pi$
$758$	9.17112	+	3.33802i	0.333110	+	0.121242i
$759$	−14.2968			−0.518943
$760$	0.235300	+	0.470154i	0.00853522	+	0.0170543i
$761$	28.3969			1.02939			0.514694	−	0.857374i	$-0.327906\pi$
$761$	28.3969			1.02939			0.514694	+	0.857374i	$0.327906\pi$
$762$	3.98545	+	1.45059i	0.144378	+	0.0525492i
$763$	−2.85355	−	16.1833i	−0.103305	−	0.585874i
$764$	−18.4500	−	15.4814i	−0.667496	−	0.560096i
$765$	0.0432332	−	0.0362770i	0.00156310	−	0.00131160i
$766$	−3.87505	+	21.9765i	−0.140011	+	0.794043i
$767$	−6.13429	+	10.6249i	−0.221496	+	0.383643i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−33.1095	+	12.0509i	−1.19396	+	0.434566i	−0.861112	−	0.508415i	$-0.830232\pi$
$769$	−33.1095	+	12.0509i	−1.19396	+	0.434566i	−0.332848	+	0.942981i	$0.608010\pi$
$770$	−1.25180	+	0.455618i	−0.0451118	+	0.0164193i
$771$	8.88326	+	15.3863i	0.319923	+	0.554122i
$772$	4.92989	−	8.53882i	0.177431	−	0.307319i
$773$	−3.49092	+	19.7980i	−0.125559	+	0.712083i	0.855415	+	0.517944i	$0.173302\pi$
$773$	−3.49092	+	19.7980i	−0.125559	+	0.712083i	−0.980974	+	0.194139i	$0.937809\pi$
$774$	7.14930	−	5.99898i	0.256976	−	0.215629i
$775$	−20.4217	−	17.1359i	−0.733571	−	0.615539i
$776$	0.538485	+	3.05390i	0.0193305	+	0.109629i
$777$	34.3435	+	12.5000i	1.23207	+	0.448435i
$778$	7.02229			0.251761
$779$	−9.21126	+	13.9626i	−0.330028	+	0.500262i
$780$	0.0983261			0.00352064
$781$	−32.2486	−	11.7375i	−1.15394	−	0.420001i
$782$	−0.451304	−	2.55947i	−0.0161386	−	0.0915265i
$783$	−1.79813	−	1.50881i	−0.0642600	−	0.0539206i
$784$	8.74170	−	7.33515i	0.312203	−	0.261970i
$785$	0.0833113	−	0.472482i	0.00297351	−	0.0168636i
$786$	10.5214	−	18.2236i	0.375286	−	0.650015i
$787$	11.9265	+	20.6573i	0.425133	+	0.736353i	0.996433	−	0.0843890i	$-0.0268938\pi$
$787$	11.9265	+	20.6573i	0.425133	+	0.736353i	−0.571299	+	0.820742i	$0.693561\pi$
$788$	6.06670	−	2.20810i	0.216117	−	0.0786603i
$789$	−2.17365	+	0.791143i	−0.0773839	+	0.0281654i
$790$	0.292919	+	0.507350i	0.0104216	+	0.0180507i
$791$	11.6099	−	20.1090i	0.412802	−	0.714994i
$792$	0.446967	−	2.53487i	0.0158823	−	0.0900728i
$793$	−1.07217	+	0.899655i	−0.0380738	+	0.0319477i
$794$	−15.3045	−	12.8420i	−0.543137	−	0.455746i
$795$	0.267226	+	1.51552i	0.00947755	+	0.0537498i
$796$	−23.2777	−	8.47237i	−0.825055	−	0.300295i
$797$	−28.5262			−1.01045			−0.505225	−	0.862988i	$-0.668591\pi$
$797$	−28.5262			−1.01045			−0.505225	+	0.862988i	$0.668591\pi$
$798$	2.14543	+	18.5800i	0.0759474	+	0.657724i
$799$	4.43376			0.156855
$800$	4.68479	+	1.70513i	0.165632	+	0.0602853i
$801$	0.595800	+	3.37895i	0.0210516	+	0.119389i
$802$	−0.911474	−	0.764818i	−0.0321853	−	0.0270066i
$803$	4.50181	−	3.77747i	0.158865	−	0.133304i
$804$	−1.98932	+	11.2820i	−0.0701580	+	0.397886i
$805$	−1.43731	+	2.48949i	−0.0506585	+	0.0877431i
$806$	−2.17958	−	3.77514i	−0.0767724	−	0.132974i
$807$	−2.64796	+	0.963777i	−0.0932125	+	0.0339266i
$808$	15.7208	−	5.72189i	0.553054	−	0.201295i
$809$	−12.4645	−	21.5892i	−0.438229	−	0.759034i	0.559324	−	0.828949i	$-0.311061\pi$
$809$	−12.4645	−	21.5892i	−0.438229	−	0.759034i	−0.997553	+	0.0699145i	$0.977727\pi$
$810$	0.0603074	−	0.104455i	0.00211899	−	0.00367019i
$811$	3.21672	−	18.2429i	0.112954	−	0.640596i	−0.874788	−	0.484505i	$-0.839000\pi$
$811$	3.21672	−	18.2429i	0.112954	−	0.640596i	0.987743	−	0.156091i	$-0.0498892\pi$
$812$	−7.71554	+	6.47410i	−0.270762	+	0.227197i
$813$	5.12449	+	4.29995i	0.179724	+	0.150806i
$814$	−3.80706	−	21.5909i	−0.133437	−	0.756760i
$815$	2.17617	+	0.792063i	0.0762281	+	0.0277447i
$816$	0.467911			0.0163802
$817$	40.6083	+	2.42199i	1.42071	+	0.0847346i
$818$	9.48845			0.331756
$819$	3.28699	+	1.19637i	0.114857	+	0.0418044i
$820$	−0.0803746	−	0.455827i	−0.00280680	−	0.0159182i
$821$	27.2415	+	22.8584i	0.950736	+	0.797762i	0.979421	−	0.201826i	$-0.0646876\pi$
$821$	27.2415	+	22.8584i	0.950736	+	0.797762i	−0.0286853	+	0.999588i	$0.509132\pi$
$822$	9.43835	−	7.91971i	0.329200	−	0.276232i
$823$	−3.21167	+	18.2143i	−0.111952	+	0.634909i	0.876263	+	0.481834i	$0.160029\pi$
$823$	−3.21167	+	18.2143i	−0.111952	+	0.634909i	−0.988214	+	0.153076i	$0.951082\pi$
$824$	5.19846	−	9.00400i	0.181097	−	0.313669i
$825$	−6.41622	−	11.1132i	−0.223384	−	0.386913i
$826$	60.6814	−	22.0862i	2.11138	−	0.768479i
$827$	−29.6891	+	10.8060i	−1.03239	+	0.375760i	−0.801991	−	0.597336i	$-0.796226\pi$
$827$	−29.6891	+	10.8060i	−1.03239	+	0.375760i	−0.230401	+	0.973096i	$0.574004\pi$
$828$	−2.77719	−	4.81023i	−0.0965140	−	0.167167i
$829$	20.5719	−	35.6316i	0.714492	−	1.23754i	−0.248663	−	0.968590i	$-0.579991\pi$
$829$	20.5719	−	35.6316i	0.714492	−	1.23754i	0.963155	−	0.268947i	$-0.0866756\pi$
$830$	−0.0680482	+	0.385920i	−0.00236199	+	0.0133955i
$831$	−6.32114	+	5.30406i	−0.219278	+	0.183996i
$832$	0.624485	+	0.524005i	0.0216501	+	0.0181666i
$833$	−0.927204	−	5.25844i	−0.0321257	−	0.182194i
$834$	−5.25150	−	1.91139i	−0.181844	−	0.0661860i
$835$	1.85441			0.0641744
$836$	9.00892	−	6.68739i	0.311580	−	0.231288i
$837$	−5.34730			−0.184830
$838$	−4.44134	−	1.61652i	−0.153424	−	0.0558416i
$839$	3.46956	+	19.6769i	0.119783	+	0.679320i	0.984271	+	0.176667i	$0.0565316\pi$
$839$	3.46956	+	19.6769i	0.119783	+	0.679320i	−0.864488	+	0.502653i	$0.832357\pi$
$840$	−0.396459	−	0.332669i	−0.0136791	−	0.0114782i
$841$	−17.9945	+	15.0992i	−0.620501	+	0.520662i
$842$	0.240819	−	1.36575i	0.00829917	−	0.0470669i
$843$	13.9684	−	24.1939i	0.481096	−	0.833284i
$844$	0.692066	+	1.19869i	0.0238219	+	0.0412608i
$845$	−1.39811	+	0.508870i	−0.0480964	+	0.0175057i
$846$	8.90420	−	3.24086i	0.306133	−	0.111423i
$847$	−9.38548	−	16.2561i	−0.322489	−	0.558567i
$848$	−6.37939	+	11.0494i	−0.219069	+	0.379439i
$849$	−0.421274	+	2.38917i	−0.0144581	+	0.0819959i
$850$	1.78699	−	1.49946i	0.0612932	−	0.0514311i
$851$	−36.2413	−	30.4100i	−1.24234	−	1.04244i
$852$	−2.31521	−	13.1302i	−0.0793177	−	0.449833i
$853$	17.7939	+	6.47643i	0.609250	+	0.221749i	0.628175	−	0.778072i	$-0.283802\pi$
$853$	17.7939	+	6.47643i	0.609250	+	0.221749i	−0.0189251	+	0.999821i	$0.506024\pi$
$854$	7.36690			0.252090
$855$	0.503870	−	0.150084i	0.0172320	−	0.00513275i
$856$	−9.11381			−0.311504
$857$	20.0532	+	7.29877i	0.685004	+	0.249321i	0.660995	−	0.750391i	$-0.270135\pi$
$857$	20.0532	+	7.29877i	0.685004	+	0.249321i	0.0240095	+	0.999712i	$0.492357\pi$
$858$	−0.364370	−	2.06645i	−0.0124394	−	0.0705474i
$859$	35.1129	+	29.4632i	1.19804	+	1.00527i	0.999684	+	0.0251425i	$0.00800396\pi$
$859$	35.1129	+	29.4632i	1.19804	+	1.00527i	0.198354	+	0.980130i	$0.436440\pi$
$860$	−0.862311	+	0.723565i	−0.0294046	+	0.0246734i
$861$	2.85932	−	16.2160i	0.0974453	−	0.552640i
$862$	−1.35591	+	2.34851i	−0.0461826	+	0.0799907i
$863$	−7.62970	−	13.2150i	−0.259718	−	0.449845i	0.706448	−	0.707765i	$-0.250296\pi$
$863$	−7.62970	−	13.2150i	−0.259718	−	0.449845i	−0.966166	+	0.257920i	$0.916963\pi$
$864$	0.939693	−	0.342020i	0.0319690	−	0.0116358i
$865$	−0.747321	+	0.272003i	−0.0254097	+	0.00924837i
$866$	10.1206	+	17.5294i	0.343912	+	0.595674i
$867$	−8.39053	+	14.5328i	−0.284957	+	0.493561i
$868$	−3.98427	+	22.5959i	−0.135235	+	0.766955i
$869$	9.57713	−	8.03617i	0.324882	−	0.272608i
$870$	0.216881	+	0.181985i	0.00735297	+	0.00616987i
$871$	1.62171	+	9.19718i	0.0549496	+	0.311634i
$872$	−3.59879	−	1.30985i	−0.121871	−	0.0443572i
$873$	3.10101			0.104953
$874$	5.61628	−	23.5506i	0.189973	−	0.796609i
$875$	−5.16788			−0.174706
$876$	2.14543	+	0.780873i	0.0724874	+	0.0263832i
$877$	3.88635	+	22.0406i	0.131233	+	0.744259i	0.977409	+	0.211356i	$0.0677878\pi$
$877$	3.88635	+	22.0406i	0.131233	+	0.744259i	−0.846176	+	0.532903i	$0.821101\pi$
$878$	−13.9422	−	11.6989i	−0.470527	−	0.394819i
$879$	10.8020	−	9.06396i	0.364343	−	0.305720i
$880$	−0.0539108	+	0.305743i	−0.00181733	+	0.0103066i
$881$	13.5052	−	23.3917i	0.455002	−	0.788087i	−0.543686	−	0.839289i	$-0.682972\pi$
$881$	13.5052	−	23.3917i	0.455002	−	0.788087i	0.998688	+	0.0512016i	$0.0163051\pi$
$882$	−5.70574	−	9.88263i	−0.192122	−	0.332765i
$883$	−16.3640	+	5.95599i	−0.550691	+	0.200435i	−0.602354	−	0.798229i	$-0.705770\pi$
$883$	−16.3640	+	5.95599i	−0.550691	+	0.200435i	0.0516624	+	0.998665i	$0.483548\pi$
$884$	0.358441	−	0.130462i	0.0120557	−	0.00438790i
$885$	−0.907604	−	1.57202i	−0.0305088	−	0.0528427i
$886$	17.8712	−	30.9539i	0.600396	−	1.03992i
$887$	10.1718	−	57.6869i	0.341534	−	1.93694i	−0.00788527	−	0.999969i	$-0.502510\pi$
$887$	10.1718	−	57.6869i	0.341534	−	1.93694i	0.349419	−	0.936966i	$-0.386379\pi$
$888$	6.52481	−	5.47497i	0.218958	−	0.183728i
$889$	−13.9409	−	11.6978i	−0.467562	−	0.392331i
$890$	−0.0718623	−	0.407551i	−0.00240883	−	0.0136611i
$891$	−2.41875	−	0.880352i	−0.0810311	−	0.0294929i
$892$	22.3131			0.747099
$893$	37.9026	+	16.4123i	1.26836	+	0.549217i
$894$	−11.0942			−0.371046
$895$	0.140682	+	0.0512040i	0.00470248	+	0.00171156i
$896$	−0.745100	−	4.22567i	−0.0248920	−	0.141170i
$897$	−3.46863	−	2.91052i	−0.115814	−	0.0971795i
$898$	−14.5476	+	12.2069i	−0.485459	+	0.407348i
$899$	2.17958	−	12.3610i	0.0726930	−	0.412262i
$900$	2.49273	−	4.31753i	0.0830909	−	0.143918i
$901$	2.98499	+	5.17015i	0.0994443	+	0.172243i
$902$	−9.28194	+	3.37835i	−0.309055	+	0.112487i
$903$	−37.6305	+	13.6964i	−1.25226	+	0.455787i
$904$	−2.70574	−	4.68647i	−0.0899915	−	0.155870i
$905$	0.243041	−	0.420959i	0.00807894	−	0.0139931i
$906$	−2.18732	+	12.4049i	−0.0726688	+	0.412125i
$907$	−7.55896	+	6.34272i	−0.250991	+	0.210607i	−0.759599	−	0.650392i	$-0.774605\pi$
$907$	−7.55896	+	6.34272i	−0.250991	+	0.210607i	0.508608	+	0.860998i	$0.330160\pi$
$908$	−15.9081	−	13.3485i	−0.527928	−	0.442984i
$909$	−2.90508	−	16.4755i	−0.0963553	−	0.546458i
$910$	−0.396459	−	0.144299i	−0.0131425	−	0.00478348i
$911$	−13.9813			−0.463222			−0.231611	−	0.972808i	$-0.574400\pi$
$911$	−13.9813			−0.463222			−0.231611	+	0.972808i	$0.574400\pi$
$912$	4.00000	+	1.73205i	0.132453	+	0.0573539i
$913$	8.36278			0.276768
$914$	−24.3974	−	8.87992i	−0.806994	−	0.293722i
$915$	−0.0359593	−	0.203935i	−0.00118878	−	0.00674189i
$916$	4.22668	+	3.54661i	0.139653	+	0.117183i
$917$	−69.1675	+	58.0384i	−2.28411	+	1.91660i
$918$	0.0812519	−	0.460802i	0.00268171	−	0.0152087i
$919$	6.36231	−	11.0198i	0.209873	−	0.363511i	−0.741801	−	0.670620i	$-0.766028\pi$
$919$	6.36231	−	11.0198i	0.209873	−	0.363511i	0.951674	+	0.307109i	$0.0993615\pi$
$920$	0.334970	+	0.580185i	0.0110436	+	0.0191281i
$921$	−18.9884	+	6.91123i	−0.625691	+	0.227733i
$922$	27.4714	−	9.99876i	0.904721	−	0.329292i
$923$	−5.43448	−	9.41279i	−0.178878	−	0.309826i
$924$	−5.52229	+	9.56488i	−0.181670	+	0.314662i
$925$	7.37376	−	41.8187i	0.242448	−	1.37499i
$926$	−16.2331	+	13.6212i	−0.533452	+	0.447619i
$927$	−7.96451	−	6.68302i	−0.261589	−	0.219499i
$928$	0.407604	+	2.31164i	0.0133802	+	0.0758832i
$929$	−19.6830	−	7.16404i	−0.645780	−	0.235045i	−0.00169466	−	0.999999i	$-0.500539\pi$
$929$	−19.6830	−	7.16404i	−0.645780	−	0.235045i	−0.644085	+	0.764954i	$0.722762\pi$
$930$	0.644963			0.0211492
$931$	11.5386	−	48.3846i	0.378164	−	1.58574i
$932$	−15.0865			−0.494174
$933$	9.03849	+	3.28974i	0.295907	+	0.107701i
$934$	−0.372522	−	2.11268i	−0.0121893	−	0.0691289i
$935$	0.111281	+	0.0933762i	0.00363929	+	0.00305373i
$936$	0.624485	−	0.524005i	0.0204119	−	0.0171276i
$937$	−1.68866	+	9.57688i	−0.0551662	+	0.312863i	−0.999887	−	0.0150119i	$-0.995221\pi$
$937$	−1.68866	+	9.57688i	−0.0551662	+	0.312863i	0.944721	+	0.327875i	$0.106332\pi$
$938$	24.5782	−	42.5706i	0.802505	−	1.38998i
$939$	12.4440	+	21.5537i	0.406096	+	0.703378i
$940$	−1.07398	+	0.390896i	−0.0350293	+	0.0127496i
$941$	21.7875	−	7.92999i	0.710251	−	0.258510i	0.0384696	−	0.999260i	$-0.487752\pi$
$941$	21.7875	−	7.92999i	0.710251	−	0.258510i	0.671781	+	0.740750i	$0.265530\pi$
$942$	−1.98886	−	3.44480i	−0.0648004	−	0.112238i
$943$	−10.6575	+	18.4592i	−0.347054	+	0.601116i
$944$	2.61334	−	14.8210i	0.0850570	−	0.482382i
$945$	−0.396459	+	0.332669i	−0.0128968	+	0.0108217i
$946$	18.4021	+	15.4412i	0.598305	+	0.502038i
$947$	4.77900	+	27.1031i	0.155297	+	0.880731i	0.958514	+	0.285045i	$0.0920086\pi$
$947$	4.77900	+	27.1031i	0.155297	+	0.880731i	−0.803217	+	0.595686i	$0.796880\pi$
$948$	4.56418	+	1.66122i	0.148238	+	0.0539541i
$949$	1.86122			0.0604176
$950$	20.8268	−	6.20351i	0.675711	−	0.201268i
$951$	−17.2635			−0.559808
$952$	−1.88666	−	0.686688i	−0.0611470	−	0.0222557i
$953$	8.75608	+	49.6582i	0.283637	+	1.60859i	0.710113	+	0.704088i	$0.248644\pi$
$953$	8.75608	+	49.6582i	0.283637	+	1.60859i	−0.426475	+	0.904499i	$0.640245\pi$
$954$	9.77379	+	8.20118i	0.316438	+	0.265523i
$955$	2.22534	−	1.86728i	0.0720102	−	0.0604238i
$956$	−5.02734	+	28.5115i	−0.162596	+	0.922127i
$957$	3.02094	−	5.23243i	0.0976533	−	0.169140i
$958$	1.69846	+	2.94182i	0.0548749	+	0.0950460i
$959$	−49.6789	+	18.0816i	−1.60422	+	0.583887i
$960$	−0.113341	+	0.0412527i	−0.00365806	+	0.00133142i
$961$	1.20321	+	2.08402i	0.0388133	+	0.0672265i
$962$	3.47178	−	6.01330i	0.111935	−	0.193877i
$963$	−1.58260	+	8.97535i	−0.0509984	+	0.289227i
$964$	−14.8380	+	12.4505i	−0.477899	+	0.401005i
$965$	0.911007	+	0.764426i	0.0293264	+	0.0246077i
$966$	4.13857	+	23.4710i	0.133156	+	0.755166i
$967$	−29.9424	−	10.8981i	−0.962882	−	0.350460i	−0.187720	−	0.982223i	$-0.560110\pi$
$967$	−29.9424	−	10.8981i	−0.962882	−	0.350460i	−0.775162	+	0.631762i	$0.782332\pi$
$968$	−4.37464			−0.140606
$969$	1.63769	−	1.21567i	0.0526101	−	0.0390529i
$970$	−0.374028			−0.0120093
$971$	2.10607	+	0.766546i	0.0675869	+	0.0245996i	0.375592	−	0.926785i	$-0.377439\pi$
$971$	2.10607	+	0.766546i	0.0675869	+	0.0245996i	−0.308005	+	0.951385i	$0.599662\pi$
$972$	−0.173648	−	0.984808i	−0.00556977	−	0.0315877i
$973$	18.3694	+	15.4138i	0.588897	+	0.494143i
$974$	15.1570	−	12.7183i	0.485663	−	0.407520i
$975$	0.705737	−	4.00243i	0.0226017	−	0.128180i
$976$	0.858441	−	1.48686i	0.0274780	−	0.0475933i
$977$	0.733956	+	1.27125i	0.0234813	+	0.0406708i	0.877527	−	0.479527i	$-0.159192\pi$
$977$	0.733956	+	1.27125i	0.0234813	+	0.0406708i	−0.854046	+	0.520198i	$0.825858\pi$
$978$	18.0424	−	6.56688i	0.576931	−	0.209986i
$979$	−8.29890	+	3.02055i	−0.265234	+	0.0965373i
$980$	0.688196	+	1.19199i	0.0219836	+	0.0380767i
$981$	−1.91488	+	3.31667i	−0.0611373	+	0.105893i
$982$	4.36618	−	24.7618i	0.139330	−	0.790182i
$983$	22.9957	−	19.2957i	0.733450	−	0.615437i	−0.197620	−	0.980279i	$-0.563321\pi$
$983$	22.9957	−	19.2957i	0.733450	−	0.615437i	0.931070	+	0.364841i	$0.118877\pi$
$984$	−2.93969	−	2.46669i	−0.0937140	−	0.0786354i
$985$	0.135219	+	0.766865i	0.00430844	+	0.0244343i
$986$	1.03209	+	0.375650i	0.0328684	+	0.0119631i
$987$	−40.6587			−1.29418
$988$	3.54710	+	0.211558i	0.112848	+	0.00673057i
$989$	51.8376			1.64834
$990$	0.291737	+	0.106183i	0.00927200	+	0.00337473i
$991$	9.50464	+	53.9035i	0.301925	+	1.71230i	0.637637	+	0.770337i	$0.279912\pi$
$991$	9.50464	+	53.9035i	0.301925	+	1.71230i	−0.335712	+	0.941965i	$0.608977\pi$
$992$	4.09627	+	3.43718i	0.130057	+	0.109130i
$993$	−7.65317	+	6.42177i	−0.242866	+	0.203789i
$994$	−9.93423	+	56.3398i	−0.315095	+	1.78699i
$995$	1.49391	−	2.58752i	0.0473601	−	0.0820300i
$996$	1.62449	+	2.81369i	0.0514738	+	0.0891552i
$997$	45.6896	−	16.6297i	1.44700	−	0.526666i	0.505251	−	0.862972i	$-0.331400\pi$
$997$	45.6896	−	16.6297i	1.44700	−	0.526666i	0.941753	+	0.336306i	$0.109178\pi$
$998$	−33.0381	+	12.0249i	−1.04580	+	0.380641i
$999$	−4.25877	−	7.37641i	−0.134742	−	0.233379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.c.61.1	yes	6
3.2	odd	2		342.2.u.b.289.1		6
4.3	odd	2		912.2.bo.d.289.1		6
19.5	even	9	inner	114.2.i.c.43.1	✓	6
19.9	even	9		2166.2.a.r.1.3		3
19.10	odd	18		2166.2.a.p.1.3		3
57.5	odd	18		342.2.u.b.271.1		6
57.29	even	18		6498.2.a.bu.1.1		3
57.47	odd	18		6498.2.a.bp.1.1		3
76.43	odd	18		912.2.bo.d.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.c.43.1	✓	6	19.5	even	9	inner
114.2.i.c.61.1	yes	6	1.1	even	1	trivial
342.2.u.b.271.1		6	57.5	odd	18
342.2.u.b.289.1		6	3.2	odd	2
912.2.bo.d.289.1		6	4.3	odd	2
912.2.bo.d.385.1		6	76.43	odd	18
2166.2.a.p.1.3		3	19.10	odd	18
2166.2.a.r.1.3		3	19.9	even	9
6498.2.a.bp.1.1		3	57.47	odd	18
6498.2.a.bu.1.1		3	57.29	even	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0923963 + 0.0775297i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(2.14543 - 3.71599i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0923963 + 0.0775297i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(2.14543 - 3.71599i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.113341 - 0.0412527i) q^{10} +(-1.28699 - 2.22913i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.141559 - 0.802823i) q^{13} +(-3.28699 + 2.75811i) q^{14} +(0.0923963 + 0.0775297i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.439693 + 0.160035i) q^{17} +1.00000 q^{18} +(3.16637 + 2.99568i) q^{19} -0.120615 q^{20} +(-4.03209 - 1.46756i) q^{21} +(0.446967 + 2.53487i) q^{22} +(4.25490 + 3.57029i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(-0.865715 + 4.90971i) q^{25} +(-0.407604 + 0.705990i) q^{26} +(0.500000 + 0.866025i) q^{27} +(4.03209 - 1.46756i) q^{28} +(-2.20574 + 0.802823i) q^{29} +(-0.0603074 - 0.104455i) q^{30} +(-2.67365 + 4.63089i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-1.97178 + 1.65452i) q^{33} +(-0.358441 - 0.300767i) q^{34} +(0.0898700 + 0.509678i) q^{35} +(-0.939693 - 0.342020i) q^{36} -8.51754 q^{37} +(-1.95084 - 3.89798i) q^{38} -0.815207 q^{39} +(0.113341 + 0.0412527i) q^{40} +(0.666374 + 3.77920i) q^{41} +(3.28699 + 2.75811i) q^{42} +(7.14930 - 5.99898i) q^{43} +(0.446967 - 2.53487i) q^{44} +(0.0603074 - 0.104455i) q^{45} +(-2.77719 - 4.81023i) q^{46} +(8.90420 - 3.24086i) q^{47} +(0.939693 - 0.342020i) q^{48} +(-5.70574 - 9.88263i) q^{49} +(2.49273 - 4.31753i) q^{50} +(0.0812519 - 0.460802i) q^{51} +(0.624485 - 0.524005i) q^{52} +(9.77379 + 8.20118i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(0.291737 + 0.106183i) q^{55} -4.29086 q^{56} +(2.40033 - 3.63846i) q^{57} +2.34730 q^{58} +(-14.1420 - 5.14728i) q^{59} +(0.0209445 + 0.118782i) q^{60} +(-1.31521 - 1.10359i) q^{61} +(4.09627 - 3.43718i) q^{62} +(-0.745100 + 4.22567i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0491630 + 0.0851529i) q^{65} +(2.41875 - 0.880352i) q^{66} +(-10.7652 + 3.91820i) q^{67} +(0.233956 + 0.405223i) q^{68} +(2.77719 - 4.81023i) q^{69} +(0.0898700 - 0.509678i) q^{70} +(10.2135 - 8.57013i) q^{71} +(0.766044 + 0.642788i) q^{72} +(0.396459 + 2.24843i) q^{73} +(8.00387 + 2.91317i) q^{74} +4.98545 q^{75} +(0.500000 + 4.33013i) q^{76} -11.0446 q^{77} +(0.766044 + 0.278817i) q^{78} +(0.843426 + 4.78331i) q^{79} +(-0.0923963 - 0.0775297i) q^{80} +(0.766044 - 0.642788i) q^{81} +(0.666374 - 3.77920i) q^{82} +(-1.62449 + 2.81369i) q^{83} +(-2.14543 - 3.71599i) q^{84} +(-0.0530334 + 0.0193026i) q^{85} +(-8.76991 + 3.19199i) q^{86} +(1.17365 + 2.03282i) q^{87} +(-1.28699 + 2.22913i) q^{88} +(0.595800 - 3.37895i) q^{89} +(-0.0923963 + 0.0775297i) q^{90} +(-2.67958 - 2.24843i) q^{91} +(0.964508 + 5.46999i) q^{92} +(5.02481 + 1.82888i) q^{93} -9.47565 q^{94} +(-0.524815 - 0.0313013i) q^{95} -1.00000 q^{96} +(-2.91400 - 1.06061i) q^{97} +(1.98158 + 11.2381i) q^{98} +(1.97178 + 1.65452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^5 - 3 * q^7 - 3 * q^8	\( 6 q + 3 q^{5} - 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{12} + 9 q^{13} - 12 q^{14} - 3 q^{15} - 3 q^{17} + 6 q^{18} - 12 q^{20} - 15 q^{21} + 15 q^{22} + 27 q^{23} - 15 q^{25} - 6 q^{26} + 3 q^{27} + 15 q^{28} - 3 q^{29} - 6 q^{30} - 15 q^{31} + 3 q^{33} + 6 q^{34} + 12 q^{35} - 6 q^{37} - 12 q^{39} - 6 q^{40} - 15 q^{41} + 12 q^{42} + 3 q^{43} + 15 q^{44} + 6 q^{45} - 6 q^{46} + 15 q^{47} - 24 q^{49} - 3 q^{50} + 3 q^{51} - 9 q^{52} + 6 q^{53} + 27 q^{55} + 6 q^{56} + 12 q^{58} - 27 q^{59} - 3 q^{60} - 15 q^{61} - 3 q^{62} - 3 q^{63} - 3 q^{64} + 12 q^{65} + 12 q^{66} - 3 q^{67} + 6 q^{68} + 6 q^{69} + 12 q^{70} + 3 q^{71} + 12 q^{73} + 24 q^{74} - 6 q^{75} + 3 q^{76} - 42 q^{77} + 27 q^{79} + 3 q^{80} - 15 q^{82} + 3 q^{83} + 3 q^{84} + 12 q^{85} - 24 q^{86} + 6 q^{87} + 42 q^{89} + 3 q^{90} - 42 q^{91} - 27 q^{92} + 3 q^{93} - 18 q^{94} + 24 q^{95} - 6 q^{96} + 18 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 - 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^12 + 9 * q^13 - 12 * q^14 - 3 * q^15 - 3 * q^17 + 6 * q^18 - 12 * q^20 - 15 * q^21 + 15 * q^22 + 27 * q^23 - 15 * q^25 - 6 * q^26 + 3 * q^27 + 15 * q^28 - 3 * q^29 - 6 * q^30 - 15 * q^31 + 3 * q^33 + 6 * q^34 + 12 * q^35 - 6 * q^37 - 12 * q^39 - 6 * q^40 - 15 * q^41 + 12 * q^42 + 3 * q^43 + 15 * q^44 + 6 * q^45 - 6 * q^46 + 15 * q^47 - 24 * q^49 - 3 * q^50 + 3 * q^51 - 9 * q^52 + 6 * q^53 + 27 * q^55 + 6 * q^56 + 12 * q^58 - 27 * q^59 - 3 * q^60 - 15 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 + 12 * q^65 + 12 * q^66 - 3 * q^67 + 6 * q^68 + 6 * q^69 + 12 * q^70 + 3 * q^71 + 12 * q^73 + 24 * q^74 - 6 * q^75 + 3 * q^76 - 42 * q^77 + 27 * q^79 + 3 * q^80 - 15 * q^82 + 3 * q^83 + 3 * q^84 + 12 * q^85 - 24 * q^86 + 6 * q^87 + 42 * q^89 + 3 * q^90 - 42 * q^91 - 27 * q^92 + 3 * q^93 - 18 * q^94 + 24 * q^95 - 6 * q^96 + 18 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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