LMFDB - Embedded newform 345.2.m.c.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	345.121
Dual form			345.2.m.c.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.168180 + 0.368263i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(1.20239 + 1.38763i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.265120 - 0.305964i) q^{6} +(0.179033 - 1.24520i) q^{7} +(-1.49013 + 0.437542i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.168180 + 0.368263i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(1.20239 + 1.38763i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.265120 - 0.305964i) q^{6} +(0.179033 - 1.24520i) q^{7} +(-1.49013 + 0.437542i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.0576160 - 0.400728i) q^{10} +(2.57583 + 5.64029i) q^{11} +(-0.762742 - 1.67017i) q^{12} +(-0.221481 - 1.54043i) q^{13} +(0.428453 + 0.275350i) q^{14} +(0.959493 - 0.281733i) q^{15} +(-0.433128 + 3.01247i) q^{16} +(-4.04103 + 4.66360i) q^{17} +(-0.340581 + 0.218878i) q^{18} +(-1.10180 - 1.27155i) q^{19} +(-1.76172 - 0.517288i) q^{20} +(-0.522595 + 1.14432i) q^{21} -2.51032 q^{22} +(4.02237 + 2.61161i) q^{23} +1.55304 q^{24} +(0.415415 - 0.909632i) q^{25} +(0.604535 + 0.177507i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(1.94315 - 1.24879i) q^{28} +(-2.00401 + 2.31276i) q^{29} +(-0.0576160 + 0.400728i) q^{30} +(-4.06373 + 1.19322i) q^{31} +(-3.64954 - 2.34542i) q^{32} +(-0.882441 - 6.13751i) q^{33} +(-1.03781 - 2.27249i) q^{34} +(0.522595 + 1.14432i) q^{35} +(0.261304 + 1.81741i) q^{36} +(9.83085 + 6.31790i) q^{37} +(0.653566 - 0.191904i) q^{38} +(-0.221481 + 1.54043i) q^{39} +(1.01702 - 1.17371i) q^{40} +(1.48256 - 0.952785i) q^{41} +(-0.333522 - 0.384905i) q^{42} +(-1.62052 - 0.475829i) q^{43} +(-4.72948 + 10.3561i) q^{44} -1.00000 q^{45} +(-1.63825 + 1.04207i) q^{46} -0.384512 q^{47} +(1.26429 - 2.76842i) q^{48} +(5.19797 + 1.52626i) q^{49} +(0.265120 + 0.305964i) q^{50} +(5.19123 - 3.33620i) q^{51} +(1.87125 - 2.15953i) q^{52} +(1.79065 - 12.4542i) q^{53} +(0.388450 - 0.114059i) q^{54} +(-5.21630 - 3.35231i) q^{55} +(0.278046 + 1.93385i) q^{56} +(0.698936 + 1.53046i) q^{57} +(-0.514668 - 1.12696i) q^{58} +(-1.65459 - 11.5079i) q^{59} +(1.54462 + 0.992669i) q^{60} +(9.76902 - 2.86844i) q^{61} +(0.244020 - 1.69720i) q^{62} +(0.823820 - 0.950739i) q^{63} +(-3.64311 + 2.34129i) q^{64} +(1.01914 + 1.17615i) q^{65} +(2.40863 + 0.707238i) q^{66} +(0.406488 - 0.890084i) q^{67} -11.3302 q^{68} +(-3.12366 - 3.63906i) q^{69} -0.509303 q^{70} +(-1.18552 + 2.59592i) q^{71} +(-1.49013 - 0.437542i) q^{72} +(-2.93492 - 3.38708i) q^{73} +(-3.98001 + 2.55780i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.439644 - 3.05779i) q^{76} +(7.48446 - 2.19764i) q^{77} +(-0.530037 - 0.340634i) q^{78} +(-1.93197 - 13.4372i) q^{79} +(-1.26429 - 2.76842i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.101538 + 0.706213i) q^{82} +(-10.8480 - 6.97162i) q^{83} +(-2.21626 + 0.650753i) q^{84} +(0.878200 - 6.10801i) q^{85} +(0.447770 - 0.516755i) q^{86} +(2.57442 - 1.65448i) q^{87} +(-6.30619 - 7.27773i) q^{88} +(15.6789 + 4.60374i) q^{89} +(0.168180 - 0.368263i) q^{90} -1.95781 q^{91} +(1.21250 + 8.72174i) q^{92} +4.23529 q^{93} +(0.0646674 - 0.141602i) q^{94} +(1.61435 + 0.474015i) q^{95} +(2.84093 + 3.27860i) q^{96} +(2.18629 - 1.40504i) q^{97} +(-1.43626 + 1.65754i) q^{98} +(-0.882441 + 6.13751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) $ 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$	$1$

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 $

$2$	−0.168180	+	0.368263i	−0.118921	+	0.260402i	−0.959726	−	0.280937i	$-0.909355\pi$
$2$	−0.168180	+	0.368263i	−0.118921	+	0.260402i	0.840805	+	0.541338i	$0.182082\pi$
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	1.20239	+	1.38763i	0.601194	+	0.693815i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$	0.265120	−	0.305964i	0.108235	−	0.124909i
$7$	0.179033	−	1.24520i	0.0676682	−	0.470642i	−0.927608	−	0.373556i	$-0.878138\pi$
$7$	0.179033	−	1.24520i	0.0676682	−	0.470642i	0.995276	−	0.0970868i	$-0.0309524\pi$
$8$	−1.49013	+	0.437542i	−0.526841	+	0.154694i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.0576160	−	0.400728i	−0.0182198	−	0.126721i
$11$	2.57583	+	5.64029i	0.776643	+	1.70061i	0.711448	+	0.702739i	$0.248040\pi$
$11$	2.57583	+	5.64029i	0.776643	+	1.70061i	0.0651954	+	0.997873i	$0.479233\pi$
$12$	−0.762742	−	1.67017i	−0.220185	−	0.482137i
$13$	−0.221481	−	1.54043i	−0.0614278	−	0.427240i	−0.997209	−	0.0746589i	$-0.976213\pi$
$13$	−0.221481	−	1.54043i	−0.0614278	−	0.427240i	0.935781	−	0.352581i	$-0.114696\pi$
$14$	0.428453	+	0.275350i	0.114509	+	0.0735904i
$15$	0.959493	−	0.281733i	0.247740	−	0.0727430i
$16$	−0.433128	+	3.01247i	−0.108282	+	0.753118i
$17$	−4.04103	+	4.66360i	−0.980094	+	1.13109i	0.0112687	+	0.999937i	$0.496413\pi$
$17$	−4.04103	+	4.66360i	−0.980094	+	1.13109i	−0.991362	+	0.131152i	$0.958132\pi$
$18$	−0.340581	+	0.218878i	−0.0802756	+	0.0515900i
$19$	−1.10180	−	1.27155i	−0.252771	−	0.291713i	0.615156	−	0.788406i	$-0.289093\pi$
$19$	−1.10180	−	1.27155i	−0.252771	−	0.291713i	−0.867927	+	0.496692i	$0.834548\pi$
$20$	−1.76172	−	0.517288i	−0.393933	−	0.115669i
$21$	−0.522595	+	1.14432i	−0.114040	+	0.249712i
$22$	−2.51032			−0.535201
$23$	4.02237	+	2.61161i	0.838723	+	0.544559i
$23$	4.02237	+	2.61161i	0.838723	+	0.544559i
$24$	1.55304			0.317013
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	0.604535	+	0.177507i	0.118559	+	0.0348121i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	1.94315	−	1.24879i	0.367220	−	0.235998i
$29$	−2.00401	+	2.31276i	−0.372136	+	0.429468i	−0.910669	−	0.413136i	$-0.864433\pi$
$29$	−2.00401	+	2.31276i	−0.372136	+	0.429468i	0.538533	+	0.842604i	$0.318979\pi$
$30$	−0.0576160	+	0.400728i	−0.0105192	+	0.0731626i
$31$	−4.06373	+	1.19322i	−0.729867	+	0.214308i	−0.625493	−	0.780230i	$-0.715102\pi$
$31$	−4.06373	+	1.19322i	−0.729867	+	0.214308i	−0.104374	+	0.994538i	$0.533284\pi$
$32$	−3.64954	−	2.34542i	−0.645153	−	0.414615i
$33$	−0.882441	−	6.13751i	−0.153613	−	1.06840i
$34$	−1.03781	−	2.27249i	−0.177983	−	0.389729i
$35$	0.522595	+	1.14432i	0.0883347	+	0.193426i
$36$	0.261304	+	1.81741i	0.0435507	+	0.302901i
$37$	9.83085	+	6.31790i	1.61618	+	1.03866i	0.958392	+	0.285456i	$0.0921450\pi$
$37$	9.83085	+	6.31790i	1.61618	+	1.03866i	0.657790	+	0.753201i	$0.271491\pi$
$38$	0.653566	−	0.191904i	0.106022	−	0.0311310i
$39$	−0.221481	+	1.54043i	−0.0354654	+	0.246667i
$40$	1.01702	−	1.17371i	0.160806	−	0.185580i
$41$	1.48256	−	0.952785i	0.231537	−	0.148800i	−0.419728	−	0.907650i	$-0.637875\pi$
$41$	1.48256	−	0.952785i	0.231537	−	0.148800i	0.651266	+	0.758850i	$0.274238\pi$
$42$	−0.333522	−	0.384905i	−0.0514636	−	0.0593922i
$43$	−1.62052	−	0.475829i	−0.247128	−	0.0725632i	0.155823	−	0.987785i	$-0.450197\pi$
$43$	−1.62052	−	0.475829i	−0.247128	−	0.0725632i	−0.402950	+	0.915222i	$0.632015\pi$
$44$	−4.72948	+	10.3561i	−0.712996	+	1.56124i
$45$	−1.00000			−0.149071
$46$	−1.63825	+	1.04207i	−0.241546	+	0.153645i
$47$	−0.384512			−0.0560869			−0.0280435	−	0.999607i	$-0.508928\pi$
$47$	−0.384512			−0.0560869			−0.0280435	+	0.999607i	$0.508928\pi$
$48$	1.26429	−	2.76842i	0.182485	−	0.399587i
$49$	5.19797	+	1.52626i	0.742568	+	0.218038i
$50$	0.265120	+	0.305964i	0.0374936	+	0.0432699i
$51$	5.19123	−	3.33620i	0.726917	−	0.467161i
$52$	1.87125	−	2.15953i	0.259495	−	0.299474i
$53$	1.79065	−	12.4542i	0.245964	−	1.71072i	−0.375122	−	0.926975i	$-0.622399\pi$
$53$	1.79065	−	12.4542i	0.245964	−	1.71072i	0.621086	−	0.783742i	$-0.286692\pi$
$54$	0.388450	−	0.114059i	0.0528613	−	0.0155215i
$55$	−5.21630	−	3.35231i	−0.703366	−	0.452026i
$56$	0.278046	+	1.93385i	0.0371554	+	0.258421i
$57$	0.698936	+	1.53046i	0.0925763	+	0.202714i
$58$	−0.514668	−	1.12696i	−0.0675792	−	0.147978i
$59$	−1.65459	−	11.5079i	−0.215410	−	1.49821i	−0.754690	−	0.656081i	$-0.772213\pi$
$59$	−1.65459	−	11.5079i	−0.215410	−	1.49821i	0.539281	−	0.842126i	$-0.318696\pi$
$60$	1.54462	+	0.992669i	0.199410	+	0.128153i
$61$	9.76902	−	2.86844i	1.25080	−	0.367267i	0.411734	−	0.911304i	$-0.364923\pi$
$61$	9.76902	−	2.86844i	1.25080	−	0.367267i	0.839061	+	0.544037i	$0.183105\pi$
$62$	0.244020	−	1.69720i	0.0309906	−	0.215544i
$63$	0.823820	−	0.950739i	0.103792	−	0.119782i
$64$	−3.64311	+	2.34129i	−0.455389	+	0.292661i
$65$	1.01914	+	1.17615i	0.126409	+	0.145884i
$66$	2.40863	+	0.707238i	0.296482	+	0.0870550i
$67$	0.406488	−	0.890084i	0.0496604	−	0.108741i	−0.883175	−	0.469043i	$-0.844599\pi$
$67$	0.406488	−	0.890084i	0.0496604	−	0.108741i	0.932836	+	0.360302i	$0.117326\pi$
$68$	−11.3302			−1.37399
$69$	−3.12366	−	3.63906i	−0.376045	−	0.438091i
$70$	−0.509303			−0.0608733
$71$	−1.18552	+	2.59592i	−0.140695	+	0.308079i	−0.966842	−	0.255376i	$-0.917801\pi$
$71$	−1.18552	+	2.59592i	−0.140695	+	0.308079i	0.826147	+	0.563455i	$0.190528\pi$
$72$	−1.49013	−	0.437542i	−0.175614	−	0.0515648i
$73$	−2.93492	−	3.38708i	−0.343507	−	0.396428i	0.557540	−	0.830150i	$-0.311745\pi$
$73$	−2.93492	−	3.38708i	−0.343507	−	0.396428i	−0.901047	+	0.433722i	$0.857200\pi$
$74$	−3.98001	+	2.55780i	−0.462667	+	0.297338i
$75$	−0.654861	+	0.755750i	−0.0756168	+	0.0872664i
$76$	0.439644	−	3.05779i	0.0504306	−	0.350753i
$77$	7.48446	−	2.19764i	0.852934	−	0.250444i
$78$	−0.530037	−	0.340634i	−0.0600149	−	0.0385692i
$79$	−1.93197	−	13.4372i	−0.217364	−	1.51180i	−0.747715	−	0.664020i	$-0.768849\pi$
$79$	−1.93197	−	13.4372i	−0.217364	−	1.51180i	0.530351	−	0.847778i	$-0.322060\pi$
$80$	−1.26429	−	2.76842i	−0.141352	−	0.309519i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	0.101538	+	0.706213i	0.0112130	+	0.0779882i
$83$	−10.8480	−	6.97162i	−1.19073	−	0.765234i	−0.213400	−	0.976965i	$-0.568454\pi$
$83$	−10.8480	−	6.97162i	−1.19073	−	0.765234i	−0.977328	+	0.211731i	$0.932090\pi$
$84$	−2.21626	+	0.650753i	−0.241814	+	0.0710029i
$85$	0.878200	−	6.10801i	0.0952541	−	0.662507i
$86$	0.447770	−	0.516755i	0.0482843	−	0.0557231i
$87$	2.57442	−	1.65448i	0.276006	−	0.177379i
$88$	−6.30619	−	7.27773i	−0.672242	−	0.775809i
$89$	15.6789	+	4.60374i	1.66196	+	0.487995i	0.971828	−	0.235690i	$-0.0757348\pi$
$89$	15.6789	+	4.60374i	1.66196	+	0.487995i	0.690131	+	0.723685i	$0.257553\pi$
$90$	0.168180	−	0.368263i	0.0177278	−	0.0388184i
$91$	−1.95781			−0.205234
$92$	1.21250	+	8.72174i	0.126412	+	0.909304i
$93$	4.23529			0.439179
$94$	0.0646674	−	0.141602i	0.00666993	−	0.0146051i
$95$	1.61435	+	0.474015i	0.165628	+	0.0486329i
$96$	2.84093	+	3.27860i	0.289951	+	0.334621i
$97$	2.18629	−	1.40504i	0.221984	−	0.142661i	−0.424922	−	0.905230i	$-0.639699\pi$
$97$	2.18629	−	1.40504i	0.221984	−	0.142661i	0.646907	+	0.762569i	$0.276062\pi$
$98$	−1.43626	+	1.65754i	−0.145085	+	0.167436i
$99$	−0.882441	+	6.13751i	−0.0886887	+	0.616843i
$100$	1.76172	−	0.517288i	0.176172	−	0.0517288i
$101$	5.24043	+	3.36782i	0.521443	+	0.335111i	0.774742	−	0.632277i	$-0.217880\pi$
$101$	5.24043	+	3.36782i	0.521443	+	0.335111i	−0.253300	+	0.967388i	$0.581516\pi$
$102$	0.355538	+	2.47282i	0.0352035	+	0.244846i
$103$	3.83546	+	8.39850i	0.377920	+	0.827528i	0.999040	+	0.0438131i	$0.0139506\pi$
$103$	3.83546	+	8.39850i	0.377920	+	0.827528i	−0.621120	+	0.783715i	$0.713322\pi$
$104$	1.00404	+	2.19854i	0.0984543	+	0.215585i
$105$	−0.179033	−	1.24520i	−0.0174718	−	0.121519i
$106$	4.28528	+	2.75398i	0.416223	+	0.267490i
$107$	2.86015	−	0.839815i	0.276501	−	0.0811880i	−0.140542	−	0.990075i	$-0.544885\pi$
$107$	2.86015	−	0.839815i	0.276501	−	0.0811880i	0.417043	+	0.908887i	$0.363066\pi$
$108$	0.261304	−	1.81741i	0.0251440	−	0.174880i
$109$	10.0303	−	11.5756i	0.960733	−	1.10875i	−0.0332758	−	0.999446i	$-0.510594\pi$
$109$	10.0303	−	11.5756i	0.960733	−	1.10875i	0.994009	−	0.109299i	$-0.0348606\pi$
$110$	2.11181	−	1.35718i	0.201353	−	0.129402i
$111$	−7.65267	−	8.83166i	−0.726360	−	0.838264i
$112$	3.67359	+	1.07866i	0.347122	+	0.101924i
$113$	2.36683	−	5.18264i	0.222653	−	0.487542i	−0.765033	−	0.643991i	$-0.777277\pi$
$113$	2.36683	−	5.18264i	0.222653	−	0.487542i	0.987686	+	0.156449i	$0.0500047\pi$
$114$	−0.681158			−0.0637963
$115$	−4.79578	−	0.0223689i	−0.447209	−	0.00208591i
$116$	−5.61885			−0.521697
$117$	0.646500	−	1.41564i	0.0597690	−	0.130876i
$118$	4.51623	+	1.32608i	0.415752	+	0.122076i
$119$	5.08365	+	5.86684i	0.466017	+	0.537812i
$120$	−1.30650	+	0.839637i	−0.119267	+	0.0766480i
$121$	−17.9745	+	20.7437i	−1.63404	+	1.88579i
$122$	−0.586614	+	4.07999i	−0.0531095	+	0.369385i
$123$	−1.69094	+	0.496505i	−0.152467	+	0.0447683i
$124$	−6.54192	−	4.20424i	−0.587482	−	0.377552i
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$	0.211572	+	0.463278i	0.0188483	+	0.0412721i
$127$	7.47170	+	16.3607i	0.663006	+	1.45178i	0.879694	+	0.475540i	$0.157747\pi$
$127$	7.47170	+	16.3607i	0.663006	+	1.45178i	−0.216688	+	0.976241i	$0.569525\pi$
$128$	−1.48430	−	10.3235i	−0.131194	−	0.912477i
$129$	1.42082	+	0.913109i	0.125097	+	0.0803947i
$130$	−0.604535	+	0.177507i	−0.0530212	+	0.0155684i
$131$	−0.968029	+	6.73279i	−0.0845771	+	0.588246i	0.902824	+	0.430010i	$0.141490\pi$
$131$	−0.968029	+	6.73279i	−0.0845771	+	0.588246i	−0.987401	+	0.158237i	$0.949419\pi$
$132$	7.45556	−	8.60418i	0.648923	−	0.748897i
$133$	−1.78060	+	1.14432i	−0.154397	+	0.0992250i
$134$	0.259422	+	0.299389i	0.0224107	+	0.0258633i
$135$	0.959493	+	0.281733i	0.0825800	+	0.0242477i
$136$	3.98114	−	8.71749i	0.341380	−	0.747518i
$137$	−8.48431			−0.724864			−0.362432	−	0.932010i	$-0.618053\pi$
$137$	−8.48431			−0.724864			−0.362432	+	0.932010i	$0.618053\pi$
$138$	1.86547	−	0.538313i	0.158799	−	0.0458243i
$139$	−22.3368			−1.89459			−0.947293	−	0.320368i	$-0.896194\pi$
$139$	−22.3368			−1.89459			−0.947293	+	0.320368i	$0.896194\pi$
$140$	−0.959536	+	2.10109i	−0.0810956	+	0.177575i
$141$	0.368937	+	0.108330i	0.0310701	+	0.00912300i
$142$	−0.756602	−	0.873165i	−0.0634926	−	0.0732744i
$143$	8.11800	−	5.21712i	0.678861	−	0.436278i
$144$	−1.99303	+	2.30008i	−0.166086	+	0.191674i
$145$	0.435514	−	3.02907i	0.0361675	−	0.251550i
$146$	1.74093	−	0.511184i	0.144081	−	0.0423059i
$147$	−4.55742	−	2.92888i	−0.375890	−	0.241570i
$148$	3.05359	+	21.2382i	0.251003	+	1.74577i
$149$	2.32764	+	5.09681i	0.190687	+	0.417547i	0.980693	−	0.195552i	$-0.0626499\pi$
$149$	2.32764	+	5.09681i	0.190687	+	0.417547i	−0.790006	+	0.613099i	$0.789923\pi$
$150$	−0.168180	−	0.368263i	−0.0137319	−	0.0300686i
$151$	0.600045	+	4.17340i	0.0488310	+	0.339627i	0.999562	+	0.0296086i	$0.00942608\pi$
$151$	0.600045	+	4.17340i	0.0488310	+	0.339627i	−0.950731	+	0.310018i	$0.899665\pi$
$152$	2.19819	+	1.41269i	0.178296	+	0.114584i
$153$	−5.92086	+	1.73852i	−0.478673	+	0.140551i
$154$	−0.449430	+	3.12585i	−0.0362161	+	0.251889i
$155$	2.77352	−	3.20082i	0.222775	−	0.257096i
$156$	−2.40386	+	1.54487i	−0.192463	+	0.123688i
$157$	2.86541	+	3.30686i	0.228685	+	0.263916i	0.858482	−	0.512843i	$-0.171408\pi$
$157$	2.86541	+	3.30686i	0.228685	+	0.263916i	−0.629798	+	0.776759i	$0.716862\pi$
$158$	5.27333	+	1.54839i	0.419524	+	0.123183i
$159$	−5.22687	+	11.4452i	−0.414518	+	0.907667i
$160$	4.33822			0.342966
$161$	3.97212	−	4.54111i	0.313047	−	0.357889i
$162$	−0.404849			−0.0318079
$163$	−0.0977331	+	0.214006i	−0.00765505	+	0.0167622i	−0.913421	−	0.407016i	$-0.866569\pi$
$163$	−0.0977331	+	0.214006i	−0.00765505	+	0.0167622i	0.905766	+	0.423778i	$0.139297\pi$
$164$	3.10473	+	0.911631i	0.242439	+	0.0711864i
$165$	4.06055	+	4.68612i	0.316113	+	0.364814i
$166$	4.39182	−	2.82245i	0.340871	−	0.219065i
$167$	−9.28584	+	10.7164i	−0.718560	+	0.829262i	−0.991133	−	0.132873i	$-0.957580\pi$
$167$	−9.28584	+	10.7164i	−0.718560	+	0.829262i	0.272573	+	0.962135i	$0.412125\pi$
$168$	0.278046	−	1.93385i	0.0214517	−	0.149200i
$169$	10.1495	−	2.98017i	0.780733	−	0.229244i
$170$	2.10166	+	1.35066i	0.161190	+	0.103591i
$171$	−0.239445	−	1.66537i	−0.0183108	−	0.127354i
$172$	−1.28822	−	2.82082i	−0.0982262	−	0.215085i
$173$	−1.35825	−	2.97415i	−0.103266	−	0.226120i	0.850946	−	0.525254i	$-0.176030\pi$
$173$	−1.35825	−	2.97415i	−0.103266	−	0.226120i	−0.954211	+	0.299134i	$0.903302\pi$
$174$	0.176317	+	1.22631i	0.0133666	+	0.0929666i
$175$	−1.05830	−	0.680130i	−0.0800002	−	0.0514130i
$176$	−18.1069	+	5.31666i	−1.36486	+	0.400758i
$177$	−1.65459	+	11.5079i	−0.124367	+	0.864990i
$178$	−4.33227	+	4.99970i	−0.324717	+	0.374744i
$179$	8.11054	−	5.21233i	0.606210	−	0.389588i	−0.201224	−	0.979545i	$-0.564492\pi$
$179$	8.11054	−	5.21233i	0.606210	−	0.389588i	0.807434	+	0.589958i	$0.200856\pi$
$180$	−1.20239	−	1.38763i	−0.0896207	−	0.103428i
$181$	−2.28520	−	0.670995i	−0.169858	−	0.0498747i	0.195698	−	0.980664i	$-0.437303\pi$
$181$	−2.28520	−	0.670995i	−0.169858	−	0.0498747i	−0.365555	+	0.930790i	$0.619121\pi$
$182$	0.329264	−	0.720989i	0.0244067	−	0.0534432i
$183$	−10.1814			−0.752634
$184$	−7.13655	−	2.13169i	−0.526113	−	0.157150i
$185$	−11.6860			−0.859169
$186$	−0.712292	+	1.55970i	−0.0522278	+	0.114363i
$187$	−36.7131	−	10.7799i	−2.68472	−	0.788306i
$188$	−0.462333	−	0.533561i	−0.0337191	−	0.0389139i
$189$	−1.05830	+	0.680130i	−0.0769802	+	0.0494722i
$190$	−0.446064	+	0.514785i	−0.0323609	+	0.0373464i
$191$	2.85052	−	19.8258i	0.206256	−	1.43454i	−0.578977	−	0.815344i	$-0.696548\pi$
$191$	2.85052	−	19.8258i	0.206256	−	1.43454i	0.785233	−	0.619200i	$-0.212543\pi$
$192$	4.15516	−	1.22006i	0.299873	−	0.0880505i
$193$	0.739622	+	0.475326i	0.0532391	+	0.0342147i	0.566990	−	0.823725i	$-0.308108\pi$
$193$	0.739622	+	0.475326i	0.0532391	+	0.0342147i	−0.513751	+	0.857940i	$0.671744\pi$
$194$	0.149735	+	1.04143i	0.0107504	+	0.0747705i
$195$	−0.646500	−	1.41564i	−0.0462968	−	0.101376i
$196$	4.13209	+	9.04802i	0.295150	+	0.646287i
$197$	0.462788	+	3.21876i	0.0329723	+	0.229327i	0.999644	−	0.0266930i	$-0.00849765\pi$
$197$	0.462788	+	3.21876i	0.0329723	+	0.229327i	−0.966671	+	0.256020i	$0.917589\pi$
$198$	−2.11181	−	1.35718i	−0.150080	−	0.0964506i
$199$	15.1358	−	4.44427i	1.07295	−	0.315046i	0.302894	−	0.953024i	$-0.402047\pi$
$199$	15.1358	−	4.44427i	1.07295	−	0.315046i	0.770054	+	0.637978i	$0.220229\pi$
$200$	−0.221021	+	1.53723i	−0.0156285	+	0.108699i
$201$	−0.640788	+	0.739509i	−0.0451977	+	0.0521609i
$202$	−2.12158	+	1.36346i	−0.149274	+	0.0959326i
$203$	2.52106	+	2.90946i	0.176944	+	0.204204i
$204$	10.8713	+	3.19210i	0.761142	+	0.223491i
$205$	−0.732097	+	1.60307i	−0.0511318	+	0.111963i
$206$	−3.73791			−0.260432
$207$	1.97189	+	4.37169i	0.137056	+	0.303853i
$208$	4.73644			0.328413
$209$	4.33384	−	9.48979i	0.299778	−	0.656422i
$210$	0.488673	+	0.143487i	0.0337216	+	0.00990156i
$211$	1.39564	+	1.61066i	0.0960800	+	0.110882i	0.801753	−	0.597655i	$-0.203901\pi$
$211$	1.39564	+	1.61066i	0.0960800	+	0.110882i	−0.705673	+	0.708537i	$0.749355\pi$
$212$	19.4349	−	12.4900i	1.33479	−	0.857820i
$213$	1.86885	−	2.15677i	0.128052	−	0.147779i
$214$	−0.171747	+	1.19453i	−0.0117404	+	0.0816563i
$215$	1.62052	−	0.475829i	0.110519	−	0.0324512i
$216$	1.30650	+	0.839637i	0.0888961	+	0.0571300i
$217$	0.758257	+	5.27379i	0.0514738	+	0.358008i
$218$	2.57598	+	5.64061i	0.174467	+	0.382030i
$219$	1.86179	+	4.07674i	0.125808	+	0.275481i
$220$	−1.62025	−	11.2691i	−0.109237	−	0.759761i
$221$	8.07898	+	5.19204i	0.543451	+	0.349255i
$222$	4.53940	−	1.33289i	0.304665	−	0.0894577i
$223$	−2.44126	+	16.9793i	−0.163479	+	1.13702i	0.728534	+	0.685010i	$0.240202\pi$
$223$	−2.44126	+	16.9793i	−0.163479	+	1.13702i	−0.892012	+	0.452011i	$0.850707\pi$
$224$	−3.57391	+	4.12451i	−0.238792	+	0.275580i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	1.51052	+	1.74324i	0.100479	+	0.115958i
$227$	0.723923	+	0.212563i	0.0480485	+	0.0141083i	0.305668	−	0.952138i	$-0.401120\pi$
$227$	0.723923	+	0.212563i	0.0480485	+	0.0141083i	−0.257620	+	0.966246i	$0.582938\pi$
$228$	−1.28331	+	2.81007i	−0.0849895	+	0.186101i
$229$	−8.06603			−0.533019			−0.266509	−	0.963832i	$-0.585870\pi$
$229$	−8.06603			−0.533019			−0.266509	+	0.963832i	$0.585870\pi$
$230$	0.814793	−	1.76235i	0.0537259	−	0.116206i
$231$	−7.80044			−0.513231
$232$	1.97432	−	4.32315i	0.129620	−	0.283829i
$233$	−3.52821	−	1.03597i	−0.231140	−	0.0678690i	0.164111	−	0.986442i	$-0.447524\pi$
$233$	−3.52821	−	1.03597i	−0.231140	−	0.0678690i	−0.395252	+	0.918573i	$0.629343\pi$
$234$	0.412599	+	0.476165i	0.0269725	+	0.0311279i
$235$	0.323472	−	0.207883i	0.0211010	−	0.0135608i
$236$	13.9793	−	16.1330i	0.909976	−	1.05017i
$237$	−1.93197	+	13.4372i	−0.125495	+	0.872837i
$238$	−3.01551	+	0.885434i	−0.195467	+	0.0573942i
$239$	−16.8585	−	10.8343i	−1.09049	−	0.700812i	−0.133529	−	0.991045i	$-0.542631\pi$
$239$	−16.8585	−	10.8343i	−1.09049	−	0.700812i	−0.956956	+	0.290232i	$0.906267\pi$
$240$	0.433128	+	3.01247i	0.0279583	+	0.194454i
$241$	10.4629	+	22.9105i	0.673973	+	1.47579i	0.868906	+	0.494978i	$0.164824\pi$
$241$	10.4629	+	22.9105i	0.673973	+	1.47579i	−0.194933	+	0.980817i	$0.562449\pi$
$242$	−4.61618	−	10.1080i	−0.296739	−	0.649768i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	15.7265	+	10.1068i	1.00679	+	0.647022i
$245$	−5.19797	+	1.52626i	−0.332086	+	0.0975093i
$246$	0.101538	−	0.706213i	0.00647384	−	0.0450265i
$247$	−1.71471	+	1.97888i	−0.109104	+	0.125913i
$248$	5.53340	−	3.55610i	0.351371	−	0.225813i
$249$	8.44449	+	9.74547i	0.535148	+	0.617594i
$250$	−0.388450	−	0.114059i	−0.0245677	−	0.00721373i
$251$	6.26946	−	13.7282i	0.395725	−	0.866517i	−0.601961	−	0.798526i	$-0.705614\pi$
$251$	6.26946	−	13.7282i	0.395725	−	0.866517i	0.997686	−	0.0679914i	$-0.0216590\pi$
$252$	2.30982			0.145505
$253$	−4.36928	+	29.4144i	−0.274695	+	1.84927i
$254$	−7.28166			−0.456892
$255$	−2.56345	+	5.61318i	−0.160530	+	0.351511i
$256$	−4.25892	−	1.25053i	−0.266182	−	0.0781582i
$257$	−2.90353	−	3.35085i	−0.181117	−	0.209020i	0.657930	−	0.753079i	$-0.271432\pi$
$257$	−2.90353	−	3.35085i	−0.181117	−	0.209020i	−0.839047	+	0.544059i	$0.816887\pi$
$258$	−0.575219	+	0.369671i	−0.0358116	+	0.0230147i
$259$	9.62712	−	11.1103i	0.598200	−	0.690360i
$260$	−0.406661	+	2.82839i	−0.0252200	+	0.175409i
$261$	−2.93625	+	0.862162i	−0.181750	+	0.0533665i
$262$	−2.31664	−	1.48881i	−0.143122	−	0.0919791i
$263$	1.67093	+	11.6216i	0.103034	+	0.716617i	0.974209	+	0.225645i	$0.0724491\pi$
$263$	1.67093	+	11.6216i	0.103034	+	0.716617i	−0.871175	+	0.490972i	$0.836642\pi$
$264$	4.00037	+	8.75959i	0.246206	+	0.539116i
$265$	5.22687	+	11.4452i	0.321084	+	0.703076i
$266$	−0.121950	−	0.848180i	−0.00747723	−	0.0520053i
$267$	−13.7468	−	8.83451i	−0.841288	−	0.540663i
$268$	1.72386	−	0.506172i	0.105302	−	0.0309194i
$269$	−1.69782	+	11.8086i	−0.103518	+	0.719983i	0.870278	+	0.492561i	$0.163939\pi$
$269$	−1.69782	+	11.8086i	−0.103518	+	0.719983i	−0.973796	+	0.227423i	$0.926970\pi$
$270$	−0.265120	+	0.305964i	−0.0161347	+	0.0186204i
$271$	1.34444	−	0.864020i	0.0816690	−	0.0524855i	−0.499169	−	0.866505i	$-0.666361\pi$
$271$	1.34444	−	0.864020i	0.0816690	−	0.0524855i	0.580838	+	0.814019i	$0.302725\pi$
$272$	−12.2987	−	14.1934i	−0.745716	−	0.860602i
$273$	1.87850	+	0.551578i	0.113692	+	0.0333830i
$274$	1.42689	−	3.12446i	0.0862018	−	0.188756i
$275$	6.20063			0.373912
$276$	1.29381	−	8.71005i	0.0778782	−	0.524283i
$277$	0.510864			0.0306948			0.0153474	−	0.999882i	$-0.495115\pi$
$277$	0.510864			0.0306948			0.0153474	+	0.999882i	$0.495115\pi$
$278$	3.75662	−	8.22584i	0.225307	−	0.493353i
$279$	−4.06373	−	1.19322i	−0.243289	−	0.0714361i
$280$	−1.27942	−	1.47653i	−0.0764602	−	0.0882398i
$281$	5.67104	−	3.64456i	0.338306	−	0.217416i	−0.360446	−	0.932780i	$-0.617375\pi$
$281$	5.67104	−	3.64456i	0.338306	−	0.217416i	0.698752	+	0.715364i	$0.253739\pi$
$282$	−0.101942	+	0.117647i	−0.00607054	+	0.00700578i
$283$	2.49696	−	17.3667i	0.148429	−	1.03235i	−0.770363	−	0.637605i	$-0.779925\pi$
$283$	2.49696	−	17.3667i	0.148429	−	1.03235i	0.918792	−	0.394741i	$-0.129166\pi$
$284$	−5.02763	+	1.47624i	−0.298335	+	0.0875990i
$285$	−1.41541	−	0.909628i	−0.0838416	−	0.0538817i
$286$	0.555988	+	3.86698i	0.0328762	+	0.228659i
$287$	−0.920983	−	2.01667i	−0.0543639	−	0.119040i
$288$	−1.80216	−	3.94618i	−0.106193	−	0.232531i
$289$	−2.99986	−	20.8645i	−0.176462	−	1.22732i
$290$	1.04225	+	0.669813i	0.0612030	+	0.0393328i
$291$	−2.49358	+	0.732181i	−0.146176	+	0.0429212i
$292$	1.17110	−	8.14517i	0.0685334	−	0.476660i
$293$	7.19602	−	8.30464i	0.420396	−	0.485163i	−0.505562	−	0.862790i	$-0.668715\pi$
$293$	7.19602	−	8.30464i	0.420396	−	0.485163i	0.925957	+	0.377628i	$0.123260\pi$
$294$	1.84507	−	1.18575i	0.107606	−	0.0691545i
$295$	7.61360	+	8.78656i	0.443281	+	0.511573i
$296$	−17.4136	−	5.11309i	−1.01214	−	0.297193i
$297$	2.57583	−	5.64029i	0.149465	−	0.327283i
$298$	−2.26843			−0.131407
$299$	3.13214	−	6.77463i	0.181136	−	0.391787i
$300$	−1.83610			−0.106007
$301$	−0.882631	+	1.93269i	−0.0508740	+	0.111398i
$302$	−1.63783	−	0.480910i	−0.0942464	−	0.0276732i
$303$	−4.07933	−	4.70780i	−0.234352	−	0.270456i
$304$	4.30772	−	2.76841i	0.247065	−	0.158779i
$305$	−6.66743	+	7.69462i	−0.381776	+	0.440593i
$306$	0.355538	−	2.47282i	0.0203248	−	0.141362i
$307$	9.60164	−	2.81930i	0.547994	−	0.160906i	0.00399614	−	0.999992i	$-0.498728\pi$
$307$	9.60164	−	2.81930i	0.547994	−	0.160906i	0.543998	+	0.839086i	$0.316910\pi$
$308$	12.0487	+	7.74325i	0.686541	+	0.441213i
$309$	−1.31397	−	9.13887i	−0.0747492	−	0.519892i
$310$	0.712292	+	1.55970i	0.0404555	+	0.0885851i
$311$	−0.137662	−	0.301437i	−0.00780607	−	0.0170929i	0.905689	−	0.423943i	$-0.139354\pi$
$311$	−0.137662	−	0.301437i	−0.00780607	−	0.0170929i	−0.913495	+	0.406850i	$0.866627\pi$
$312$	−0.343969	−	2.39236i	−0.0194734	−	0.135441i
$313$	21.8806	+	14.0618i	1.23676	+	0.794820i	0.984931	−	0.172950i	$-0.0553300\pi$
$313$	21.8806	+	14.0618i	1.23676	+	0.794820i	0.251834	+	0.967770i	$0.418966\pi$
$314$	−1.69970	+	0.499077i	−0.0959197	+	0.0281646i
$315$	−0.179033	+	1.24520i	−0.0100874	+	0.0701592i
$316$	16.3228	−	18.8375i	0.918230	−	1.05969i
$317$	24.0183	−	15.4356i	1.34900	−	0.866950i	0.351402	−	0.936225i	$-0.385705\pi$
$317$	24.0183	−	15.4356i	1.34900	−	0.866950i	0.997598	+	0.0692748i	$0.0220685\pi$
$318$	−3.33581	−	3.84973i	−0.187063	−	0.215882i
$319$	−18.2066	−	5.34595i	−1.01937	−	0.299315i
$320$	1.79899	−	3.93923i	0.100566	−	0.220210i
$321$	−2.98090			−0.166377
$322$	1.00429	+	2.22651i	0.0559669	+	0.124079i
$323$	10.3824			0.577693
$324$	−0.762742	+	1.67017i	−0.0423746	+	0.0927874i
$325$	−1.49324	−	0.438453i	−0.0828298	−	0.0243210i
$326$	−0.0623737	−	0.0719831i	−0.00345456	−	0.00398677i
$327$	−12.8853	+	8.28087i	−0.712558	+	0.457933i
$328$	−1.79233	+	2.06846i	−0.0989648	+	0.114211i
$329$	−0.0688405	+	0.478796i	−0.00379530	+	0.0263969i
$330$	−2.40863	+	0.707238i	−0.132591	+	0.0389322i
$331$	−11.2875	−	7.25403i	−0.620416	−	0.398717i	0.192334	−	0.981330i	$-0.438394\pi$
$331$	−11.2875	−	7.25403i	−0.620416	−	0.398717i	−0.812750	+	0.582612i	$0.802031\pi$
$332$	−3.36954	−	23.4357i	−0.184928	−	1.28620i
$333$	4.85452	+	10.6299i	0.266026	+	0.582516i
$334$	−2.38477	−	5.22193i	−0.130489	−	0.285731i
$335$	0.139257	+	0.968551i	0.00760840	+	0.0529176i
$336$	−3.22089	−	2.06994i	−0.175714	−	0.112925i
$337$	−30.2063	+	8.86936i	−1.64544	+	0.483145i	−0.967689	−	0.252147i	$-0.918863\pi$
$337$	−30.2063	+	8.86936i	−1.64544	+	0.483145i	−0.677751	+	0.735292i	$0.737045\pi$
$338$	−0.609462	+	4.23890i	−0.0331504	+	0.230566i
$339$	−3.73108	+	4.30590i	−0.202644	+	0.233864i
$340$	9.53160	−	6.12559i	0.516923	−	0.332207i
$341$	−17.1976	−	19.8471i	−0.931301	−	1.07478i
$342$	0.653566	+	0.191904i	0.0353408	+	0.0103770i
$343$	6.48928	−	14.2095i	0.350388	−	0.767243i
$344$	2.62299			0.141422
$345$	4.59521	+	1.37259i	0.247398	+	0.0738978i
$346$	1.32370			0.0711626
$347$	4.74427	−	10.3885i	0.254686	−	0.557684i	−0.738496	−	0.674258i	$-0.764464\pi$
$347$	4.74427	−	10.3885i	0.254686	−	0.557684i	0.993182	+	0.116573i	$0.0371910\pi$
$348$	5.39125	+	1.58301i	0.289001	+	0.0848584i
$349$	−16.4144	−	18.9432i	−0.878642	−	1.01401i	−0.999772	−	0.0213700i	$-0.993197\pi$
$349$	−16.4144	−	18.9432i	−0.878642	−	1.01401i	0.121130	−	0.992637i	$-0.461348\pi$
$350$	0.428453	−	0.275350i	0.0229018	−	0.0147181i
$351$	−1.01914	+	1.17615i	−0.0543979	+	0.0627785i
$352$	3.82822	−	26.6259i	0.204045	−	1.41916i
$353$	5.87917	−	1.72628i	0.312916	−	0.0918805i	−0.121504	−	0.992591i	$-0.538772\pi$
$353$	5.87917	−	1.72628i	0.312916	−	0.0918805i	0.434420	+	0.900710i	$0.356953\pi$
$354$	−3.95969	−	2.54474i	−0.210455	−	0.135251i
$355$	−0.406140	−	2.82477i	−0.0215557	−	0.149923i
$356$	12.4638	+	27.2920i	0.660582	+	1.44647i
$357$	−3.22484	−	7.06142i	−0.170677	−	0.373730i
$358$	0.555477	+	3.86342i	0.0293579	+	0.204188i
$359$	8.33352	+	5.35563i	0.439827	+	0.282659i	0.741755	−	0.670671i	$-0.233994\pi$
$359$	8.33352	+	5.35563i	0.439827	+	0.282659i	−0.301928	+	0.953331i	$0.597630\pi$
$360$	1.49013	−	0.437542i	0.0785368	−	0.0230605i
$361$	2.30112	−	16.0046i	0.121111	−	0.842348i
$362$	0.631428	−	0.728707i	0.0331871	−	0.0383000i
$363$	23.0906	−	14.8394i	1.21194	−	0.778866i
$364$	−2.35404	−	2.71671i	−0.123385	−	0.142394i
$365$	4.30021	+	1.26266i	0.225083	+	0.0660904i
$366$	1.71232	−	3.74945i	0.0895043	−	0.195987i
$367$	−5.45507			−0.284752			−0.142376	−	0.989813i	$-0.545474\pi$
$367$	−5.45507			−0.284752			−0.142376	+	0.989813i	$0.545474\pi$
$368$	−9.60961	+	10.9861i	−0.500935	+	0.572691i
$369$	1.76233			0.0917430
$370$	1.96535	−	4.30351i	0.102174	−	0.223729i
$371$	−15.1874	−	4.45943i	−0.788492	−	0.231522i
$372$	5.09246	+	5.87701i	0.264032	+	0.304709i
$373$	−26.4081	+	16.9715i	−1.36736	+	0.878749i	−0.998708	−	0.0508182i	$-0.983817\pi$
$373$	−26.4081	+	16.9715i	−1.36736	+	0.878749i	−0.368652	+	0.929567i	$0.620181\pi$
$374$	10.1443	−	11.7071i	0.524547	−	0.605360i
$375$	0.142315	−	0.989821i	0.00734911	−	0.0511142i
$376$	0.572974	−	0.168240i	0.0295489	−	0.00867633i
$377$	4.00650	+	2.57482i	0.206345	+	0.132610i
$378$	−0.0724814	−	0.504119i	−0.00372804	−	0.0259291i
$379$	−12.7185	−	27.8497i	−0.653306	−	1.43054i	−0.888630	−	0.458624i	$-0.848342\pi$
$379$	−12.7185	−	27.8497i	−0.653306	−	1.43054i	0.235324	−	0.971917i	$-0.424385\pi$
$380$	1.28331	+	2.81007i	0.0658326	+	0.144153i
$381$	−2.55969	−	17.8030i	−0.131137	−	0.912077i
$382$	6.82172	+	4.38405i	0.349029	+	0.224308i
$383$	−22.4946	+	6.60501i	−1.14942	+	0.337500i	−0.800313	−	0.599582i	$-0.795333\pi$
$383$	−22.4946	+	6.60501i	−1.14942	+	0.337500i	−0.349108	+	0.937083i	$0.613515\pi$
$384$	−1.48430	+	10.3235i	−0.0757451	+	0.526819i
$385$	−5.10820	+	5.89518i	−0.260338	+	0.300446i
$386$	−0.299435	+	0.192435i	−0.0152408	+	0.00979469i
$387$	−1.10602	−	1.27641i	−0.0562221	−	0.0648838i
$388$	4.57845	+	1.34436i	0.232436	+	0.0682493i
$389$	−11.6888	+	25.5948i	−0.592644	+	1.29771i	0.341187	+	0.939996i	$0.389171\pi$
$389$	−11.6888	+	25.5948i	−0.592644	+	1.29771i	−0.933831	+	0.357714i	$0.883556\pi$
$390$	0.630056			0.0319041
$391$	−28.4340	+	8.20512i	−1.43797	+	0.414951i
$392$	−8.41346			−0.424944
$393$	2.82566	−	6.18734i	0.142536	−	0.312110i
$394$	−1.26319	−	0.370905i	−0.0636384	−	0.0186859i
$395$	8.88995	+	10.2595i	0.447302	+	0.516214i
$396$	−9.57764	+	6.15517i	−0.481294	+	0.309309i
$397$	22.8255	−	26.3420i	1.14558	−	1.32207i	0.206466	−	0.978454i	$-0.433804\pi$
$397$	22.8255	−	26.3420i	1.14558	−	1.32207i	0.939111	−	0.343613i	$-0.111651\pi$
$398$	−0.908880	+	6.32140i	−0.0455581	+	0.316863i
$399$	2.03086	−	0.596314i	0.101670	−	0.0298531i
$400$	2.56031	+	1.64541i	0.128016	+	0.0822706i
$401$	−4.47921	−	31.1536i	−0.223681	−	1.55574i	−0.723941	−	0.689861i	$-0.757671\pi$
$401$	−4.47921	−	31.1536i	−0.223681	−	1.55574i	0.500260	−	0.865875i	$-0.333238\pi$
$402$	−0.164566	−	0.360350i	−0.00820781	−	0.0179726i
$403$	2.73811	+	5.99563i	0.136395	+	0.298664i
$404$	1.62774	+	11.3212i	0.0809833	+	0.563251i
$405$	−0.841254	−	0.540641i	−0.0418022	−	0.0268647i
$406$	−1.49544	+	0.439102i	−0.0742176	+	0.0217922i
$407$	−10.3122	+	71.7227i	−0.511155	+	3.55516i
$408$	−6.27588	+	7.24275i	−0.310702	+	0.358570i
$409$	17.3273	−	11.1356i	0.856779	−	0.550619i	−0.0369030	−	0.999319i	$-0.511749\pi$
$409$	17.3273	−	11.1356i	0.856779	−	0.550619i	0.893682	+	0.448700i	$0.148113\pi$
$410$	−0.467227	−	0.539209i	−0.0230747	−	0.0266296i
$411$	8.14064	+	2.39031i	0.401548	+	0.117905i
$412$	−7.04229	+	15.4205i	−0.346949	+	0.759711i
$413$	−14.6260			−0.719696
$414$	−1.94157	−	0.00905602i	−0.0954227	−	0.000445079i
$415$	12.8951			0.632996
$416$	−2.80466	+	6.14134i	−0.137510	+	0.301104i
$417$	21.4320	+	6.29302i	1.04953	+	0.308170i
$418$	2.76588	+	3.19199i	0.135283	+	0.156125i
$419$	13.9084	−	8.93837i	0.679468	−	0.436668i	−0.154859	−	0.987937i	$-0.549492\pi$
$419$	13.9084	−	8.93837i	0.679468	−	0.436668i	0.834328	+	0.551269i	$0.185856\pi$
$420$	1.51261	−	1.74565i	0.0738080	−	0.0851789i
$421$	−1.62259	+	11.2854i	−0.0790802	+	0.550015i	0.911311	+	0.411719i	$0.135072\pi$
$421$	−1.62259	+	11.2854i	−0.0790802	+	0.550015i	−0.990391	+	0.138296i	$0.955838\pi$
$422$	−0.827866	+	0.243083i	−0.0402999	+	0.0118331i
$423$	−0.323472	−	0.207883i	−0.0157278	−	0.0101076i
$424$	2.78094	+	19.3419i	0.135055	+	0.939325i
$425$	2.56345	+	5.61318i	0.124346	+	0.272279i
$426$	0.479955	+	1.05096i	0.0232539	+	0.0509190i
$427$	−1.82282	−	12.6780i	−0.0882122	−	0.613529i
$428$	4.60436	+	2.95904i	0.222560	+	0.143031i
$429$	−9.25900	+	2.71869i	−0.447029	+	0.131259i
$430$	−0.0973098	+	0.676805i	−0.00469270	+	0.0326384i
$431$	8.74710	−	10.0947i	0.421333	−	0.486244i	−0.504910	−	0.863172i	$-0.668474\pi$
$431$	8.74710	−	10.0947i	0.421333	−	0.486244i	0.926243	+	0.376928i	$0.123020\pi$
$432$	2.56031	−	1.64541i	0.123183	−	0.0791649i
$433$	20.6092	+	23.7843i	0.990414	+	1.14300i	0.989723	+	0.142999i	$0.0456744\pi$
$433$	20.6092	+	23.7843i	0.990414	+	1.14300i	0.000690753		1.00000i	$0.499780\pi$
$434$	−2.06967	−	0.607709i	−0.0993473	−	0.0291710i
$435$	−1.27126	+	2.78367i	−0.0609522	+	0.133467i
$436$	28.1231			1.34685
$437$	−1.11107	−	7.99212i	−0.0531497	−	0.382315i
$438$	−1.81443			−0.0866969
$439$	−11.2576	+	24.6507i	−0.537295	+	1.17651i	0.425171	+	0.905113i	$0.360214\pi$
$439$	−11.2576	+	24.6507i	−0.537295	+	1.17651i	−0.962467	+	0.271400i	$0.912513\pi$
$440$	9.23975	+	2.71303i	0.440488	+	0.129339i
$441$	3.54765	+	4.09421i	0.168936	+	0.194962i
$442$	−3.27077	+	2.10199i	−0.155574	+	0.0999816i
$443$	−7.91780	+	9.13762i	−0.376186	+	0.434142i	−0.911997	−	0.410196i	$-0.865460\pi$
$443$	−7.91780	+	9.13762i	−0.376186	+	0.434142i	0.535812	+	0.844338i	$0.320006\pi$
$444$	3.05359	−	21.2382i	0.144917	−	1.00792i
$445$	−15.6789	+	4.60374i	−0.743251	+	0.218238i
$446$	−5.84230	−	3.75462i	−0.276641	−	0.177786i
$447$	−0.797413	−	5.54613i	−0.0377163	−	0.262323i
$448$	2.26314	+	4.95558i	0.106923	+	0.234129i
$449$	3.28814	+	7.20002i	0.155177	+	0.339790i	0.971214	−	0.238210i	$-0.0765606\pi$
$449$	3.28814	+	7.20002i	0.155177	+	0.339790i	−0.816037	+	0.578000i	$0.803833\pi$
$450$	0.0576160	+	0.400728i	0.00271604	+	0.0188905i
$451$	9.19282	+	5.90787i	0.432873	+	0.278191i
$452$	10.0374	−	2.94726i	0.472122	−	0.138627i
$453$	0.600045	−	4.17340i	0.0281926	−	0.196084i
$454$	−0.200029	+	0.230846i	−0.00938782	+	0.0108341i
$455$	1.64701	−	1.05847i	0.0772131	−	0.0496218i
$456$	−1.71114	−	1.97477i	−0.0801316	−	0.0924769i
$457$	24.8681	+	7.30195i	1.16328	+	0.341571i	0.805708	−	0.592314i	$-0.201785\pi$
$457$	24.8681	+	7.30195i	1.16328	+	0.341571i	0.357575	+	0.933884i	$0.383604\pi$
$458$	1.35655	−	2.97043i	0.0633873	−	0.138799i
$459$	6.17082			0.288029
$460$	−5.73535	−	6.68166i	−0.267412	−	0.311534i
$461$	15.7472			0.733419			0.366709	−	0.930336i	$-0.380484\pi$
$461$	15.7472			0.733419			0.366709	+	0.930336i	$0.380484\pi$
$462$	1.31188	−	2.87262i	0.0610342	−	0.133646i
$463$	−10.1966	−	2.99399i	−0.473876	−	0.139143i	0.0360693	−	0.999349i	$-0.488516\pi$
$463$	−10.1966	−	2.99399i	−0.473876	−	0.139143i	−0.509946	+	0.860207i	$0.670334\pi$
$464$	−6.09911	−	7.03875i	−0.283144	−	0.326766i
$465$	−3.56295	+	2.28977i	−0.165228	+	0.106185i
$466$	0.974886	−	1.12508i	0.0451607	−	0.0521183i
$467$	−4.54155	+	31.5872i	−0.210158	+	1.46168i	0.562467	+	0.826820i	$0.309852\pi$
$467$	−4.54155	+	31.5872i	−0.210158	+	1.46168i	−0.772625	+	0.634862i	$0.781057\pi$
$468$	2.74173	−	0.805043i	0.126736	−	0.0372131i
$469$	−1.03556	−	0.665515i	−0.0478178	−	0.0307306i
$470$	0.0221541	+	0.154085i	0.00102189	+	0.00710741i
$471$	−1.81769	−	3.98019i	−0.0837548	−	0.183397i
$472$	7.50077	+	16.4244i	0.345251	+	0.755994i
$473$	−1.49039	−	10.3659i	−0.0685281	−	0.476624i
$474$	−4.62349	−	2.97134i	−0.212364	−	0.136478i
$475$	−1.61435	+	0.474015i	−0.0740713	+	0.0217493i
$476$	−2.02849	+	14.1084i	−0.0929755	+	0.646659i
$477$	8.23964	−	9.50905i	0.377267	−	0.435390i
$478$	6.82514	−	4.38625i	0.312175	−	0.200623i
$479$	18.6623	+	21.5375i	0.852704	+	0.984073i	0.999987	−	0.00502159i	$-0.00159843\pi$
$479$	18.6623	+	21.5375i	0.852704	+	0.984073i	−0.147284	+	0.989094i	$0.547053\pi$
$480$	−4.16249	−	1.22222i	−0.189991	−	0.0557863i
$481$	7.55497	−	16.5431i	0.344477	−	0.754300i
$482$	−10.1967			−0.464449
$483$	−5.09060	+	3.23808i	−0.231630	+	0.147338i
$484$	−50.3968			−2.29076
$485$	−1.07960	+	2.36400i	−0.0490222	+	0.107344i
$486$	0.388450	+	0.114059i	0.0176204	+	0.00517383i
$487$	4.49457	+	5.18701i	0.203668	+	0.235046i	0.848390	−	0.529371i	$-0.177572\pi$
$487$	4.49457	+	5.18701i	0.203668	+	0.235046i	−0.644722	+	0.764417i	$0.723027\pi$
$488$	−13.3021	+	8.54871i	−0.602156	+	0.386982i
$489$	0.154067	−	0.177802i	0.00696713	−	0.00804050i
$490$	0.312130	−	2.17091i	0.0141006	−	0.0980718i
$491$	−41.3071	+	12.1289i	−1.86417	+	0.547368i	−0.865223	+	0.501387i	$0.832823\pi$
$491$	−41.3071	+	12.1289i	−1.86417	+	0.547368i	−0.998942	+	0.0459809i	$0.985359\pi$
$492$	−2.72213	−	1.74941i	−0.122723	−	0.0788693i
$493$	−2.68748	−	18.6918i	−0.121038	−	0.841837i
$494$	−0.440369	−	0.964273i	−0.0198131	−	0.0433847i
$495$	−2.57583	−	5.64029i	−0.115775	−	0.253512i
$496$	−1.83442	−	12.7587i	−0.0823679	−	0.572882i
$497$	3.02020	+	1.94097i	0.135475	+	0.0870642i
$498$	−5.00910	+	1.47080i	−0.224463	+	0.0659083i
$499$	−2.96635	+	20.6314i	−0.132792	+	0.923590i	0.809099	+	0.587672i	$0.199955\pi$
$499$	−2.96635	+	20.6314i	−0.132792	+	0.923590i	−0.941891	+	0.335918i	$0.890954\pi$
$500$	−1.20239	+	1.38763i	−0.0537724	+	0.0620567i
$501$	11.9289	−	7.66621i	0.532942	−	0.342501i
$502$	4.00120	+	4.61763i	0.178582	+	0.206095i
$503$	23.5045	+	6.90154i	1.04801	+	0.307724i	0.760014	−	0.649906i	$-0.225192\pi$
$503$	23.5045	+	6.90154i	1.04801	+	0.307724i	0.287999	+	0.957631i	$0.407010\pi$
$504$	−0.811611	+	1.77718i	−0.0361520	+	0.0791619i
$505$	−6.22931			−0.277201
$506$	−10.0974	−	6.55597i	−0.448886	−	0.291449i
$507$	−10.5780			−0.469786
$508$	−13.7188	+	30.0399i	−0.608672	+	1.33281i
$509$	−27.5804	−	8.09834i	−1.22248	−	0.358952i	−0.394073	−	0.919079i	$-0.628934\pi$
$509$	−27.5804	−	8.09834i	−1.22248	−	0.358952i	−0.828407	+	0.560127i	$0.810752\pi$
$510$	−1.63601	−	1.88805i	−0.0724436	−	0.0836043i
$511$	−4.74305	+	3.04817i	−0.209820	+	0.134843i
$512$	14.8367	−	17.1225i	0.655697	−	0.756715i
$513$	−0.239445	+	1.66537i	−0.0105717	+	0.0735281i
$514$	1.72231	−	0.505716i	0.0759678	−	0.0223062i
$515$	−7.76717	−	4.99166i	−0.342262	−	0.219959i
$516$	0.441326	+	3.06949i	0.0194283	+	0.135127i
$517$	−0.990440	−	2.16876i	−0.0435595	−	0.0953820i
$518$	2.47242	+	5.41385i	0.108632	+	0.237871i
$519$	0.465315	+	3.23634i	0.0204251	+	0.142059i
$520$	−2.03327	−	1.30671i	−0.0891650	−	0.0573028i
$521$	15.1446	−	4.44685i	0.663496	−	0.194820i	0.0673913	−	0.997727i	$-0.478532\pi$
$521$	15.1446	−	4.44685i	0.663496	−	0.194820i	0.596105	+	0.802907i	$0.296714\pi$
$522$	0.176317	−	1.22631i	0.00771720	−	0.0536743i
$523$	15.5902	−	17.9920i	0.681711	−	0.786736i	−0.304450	−	0.952528i	$-0.598473\pi$
$523$	15.5902	−	17.9920i	0.681711	−	0.786736i	0.986161	+	0.165792i	$0.0530181\pi$
$524$	−10.5066	+	6.75216i	−0.458981	+	0.294969i
$525$	0.823820	+	0.950739i	0.0359544	+	0.0414936i
$526$	−4.56082	−	1.33918i	−0.198861	−	0.0583909i
$527$	10.8570	−	23.7734i	0.472936	−	1.03559i
$528$	18.8713			0.821268
$529$	9.35897	+	21.0098i	0.406912	+	0.913468i
$530$	−5.09392			−0.221266
$531$	4.82973	−	10.5756i	0.209593	−	0.458944i
$532$	−3.72886	−	1.09489i	−0.161666	−	0.0474696i
$533$	−1.79606	−	2.07277i	−0.0777961	−	0.0897815i
$534$	5.56536	−	3.57664i	0.240837	−	0.154776i
$535$	−1.95207	+	2.25281i	−0.0843954	+	0.0973975i
$536$	−0.216271	+	1.50420i	−0.00934148	+	0.0649714i
$537$	−9.25049	+	2.71619i	−0.399188	+	0.117212i
$538$	−4.06314	−	2.61122i	−0.175174	−	0.112578i
$539$	4.78055	+	33.2495i	0.205913	+	1.43216i
$540$	0.762742	+	1.67017i	0.0328232	+	0.0718728i
$541$	−3.62001	−	7.92672i	−0.155636	−	0.340796i	0.815711	−	0.578459i	$-0.196346\pi$
$541$	−3.62001	−	7.92672i	−0.155636	−	0.340796i	−0.971348	+	0.237663i	$0.923619\pi$
$542$	0.0920785	+	0.640420i	0.00395511	+	0.0275084i
$543$	2.00359	+	1.28763i	0.0859823	+	0.0552575i
$544$	25.6860	−	7.54208i	1.10128	−	0.323364i
$545$	−2.17980	+	15.1609i	−0.0933725	+	0.649420i
$546$	−0.519053	+	0.599019i	−0.0222134	+	0.0256356i
$547$	−8.67123	+	5.57266i	−0.370755	+	0.238270i	−0.712729	−	0.701440i	$-0.752541\pi$
$547$	−8.67123	+	5.57266i	−0.370755	+	0.238270i	0.341974	+	0.939710i	$0.388905\pi$
$548$	−10.2014	−	11.7731i	−0.435784	−	0.502921i
$549$	9.76902	+	2.86844i	0.416932	+	0.122422i
$550$	−1.04282	+	2.28346i	−0.0444661	+	0.0973673i
$551$	5.14881			0.219347
$552$	6.24690	+	4.05594i	0.265886	+	0.172632i
$553$	−17.0779			−0.726225
$554$	−0.0859172	+	0.188132i	−0.00365027	+	0.00799298i
$555$	11.2126	+	3.29231i	0.475948	+	0.139751i
$556$	−26.8576	−	30.9953i	−1.13901	−	1.31449i
$557$	−34.0924	+	21.9099i	−1.44454	+	0.928351i	−0.445082	+	0.895490i	$0.646825\pi$
$557$	−34.0924	+	21.9099i	−1.44454	+	0.928351i	−0.999460	+	0.0328607i	$0.989538\pi$
$558$	1.12286	−	1.29585i	0.0475344	−	0.0548576i
$559$	−0.374068	+	2.60170i	−0.0158214	+	0.110040i
$560$	−3.67359	+	1.07866i	−0.155238	+	0.0455819i
$561$	32.1889	+	20.6865i	1.35901	+	0.873386i
$562$	0.388400	+	2.70138i	0.0163837	+	0.113951i
$563$	9.61363	+	21.0509i	0.405166	+	0.887190i	0.996720	+	0.0809249i	$0.0257874\pi$
$563$	9.61363	+	21.0509i	0.405166	+	0.887190i	−0.591554	+	0.806265i	$0.701485\pi$
$564$	0.293284	+	0.642202i	0.0123495	+	0.0270416i
$565$	0.810841	+	5.63952i	0.0341123	+	0.237257i
$566$	5.97560	+	3.84028i	0.251173	+	0.161419i
$567$	1.20705	−	0.354422i	0.0506913	−	0.0148843i
$568$	0.630752	−	4.38697i	0.0264657	−	0.184073i
$569$	23.0208	−	26.5674i	0.965082	−	1.11376i	−0.0283800	−	0.999597i	$-0.509035\pi$
$569$	23.0208	−	26.5674i	0.965082	−	1.11376i	0.993462	−	0.114166i	$-0.0364197\pi$
$570$	0.573027	−	0.368262i	0.0240014	−	0.0154248i
$571$	−8.08402	−	9.32945i	−0.338306	−	0.390425i	0.560950	−	0.827850i	$-0.310436\pi$
$571$	−8.08402	−	9.32945i	−0.338306	−	0.390425i	−0.899255	+	0.437425i	$0.855891\pi$
$572$	17.0004	+	4.99177i	0.710823	+	0.208717i
$573$	−8.32063	+	18.2196i	−0.347599	+	0.761136i
$574$	0.897558			0.0374633
$575$	4.04656	−	2.57398i	0.168753	−	0.107342i
$576$	−4.33058			−0.180441
$577$	9.18064	−	20.1028i	0.382195	−	0.836891i	−0.616574	−	0.787297i	$-0.711480\pi$
$577$	9.18064	−	20.1028i	0.382195	−	0.836891i	0.998769	−	0.0495940i	$-0.0157927\pi$
$578$	8.18815	+	2.40426i	0.340582	+	0.100004i
$579$	−0.575747	−	0.664448i	−0.0239272	−	0.0276135i
$580$	4.72688	−	3.03778i	0.196273	−	0.126137i
$581$	−10.6232	+	12.2599i	−0.440726	+	0.508625i
$582$	0.149735	−	1.04143i	0.00620673	−	0.0431688i
$583$	74.8578	−	21.9802i	3.10029	−	0.910328i
$584$	5.85541	+	3.76304i	0.242298	+	0.155716i
$585$	0.221481	+	1.54043i	0.00915712	+	0.0636891i
$586$	1.84807	+	4.04671i	0.0763430	+	0.167168i
$587$	−10.2233	−	22.3858i	−0.421959	−	0.923962i	−0.994564	−	0.104130i	$-0.966794\pi$
$587$	−10.2233	−	22.3858i	−0.421959	−	0.923962i	0.572604	−	0.819832i	$-0.305933\pi$
$588$	−1.41559	−	9.84566i	−0.0583780	−	0.406028i
$589$	5.99466	+	3.85254i	0.247006	+	0.158741i
$590$	−4.51623	+	1.32608i	−0.185930	+	0.0545940i
$591$	0.462788	−	3.21876i	0.0190366	−	0.132402i
$592$	−23.2905	+	26.8787i	−0.957234	+	1.10471i
$593$	−26.8993	+	17.2871i	−1.10462	+	0.709897i	−0.960115	−	0.279606i	$-0.909796\pi$
$593$	−26.8993	+	17.2871i	−1.10462	+	0.709897i	−0.144507	+	0.989504i	$0.546160\pi$
$594$	1.64391	+	1.89717i	0.0674504	+	0.0778419i
$595$	−7.44849	−	2.18707i	−0.305358	−	0.0896613i
$596$	−4.27377	+	9.35824i	−0.175060	+	0.383329i
$597$	−15.7748			−0.645619
$598$	1.96808	+	2.29281i	0.0804809	+	0.0937600i
$599$	9.89067			0.404122			0.202061	−	0.979373i	$-0.435236\pi$
$599$	9.89067			0.404122			0.202061	+	0.979373i	$0.435236\pi$
$600$	0.645156	−	1.41269i	0.0263384	−	0.0576730i
$601$	−27.7974	−	8.16206i	−1.13388	−	0.332937i	−0.339649	−	0.940552i	$-0.610308\pi$
$601$	−27.7974	−	8.16206i	−1.13388	−	0.332937i	−0.794232	+	0.607615i	$0.792126\pi$
$602$	−0.563299	−	0.650081i	−0.0229583	−	0.0264953i
$603$	0.823175	−	0.529023i	0.0335223	−	0.0215435i
$604$	−5.06965	+	5.85069i	−0.206281	+	0.238061i
$605$	3.90623	−	27.1684i	0.158811	−	1.10455i
$606$	2.41977	−	0.710510i	0.0982966	−	0.0288625i
$607$	0.763420	+	0.490620i	0.0309862	+	0.0199136i	0.556042	−	0.831154i	$-0.312319\pi$
$607$	0.763420	+	0.490620i	0.0309862	+	0.0199136i	−0.525056	+	0.851068i	$0.675956\pi$
$608$	1.03876	+	7.22475i	0.0421274	+	0.293002i
$609$	−1.59925	−	3.50188i	−0.0648050	−	0.141903i
$610$	−1.71232	−	3.74945i	−0.0693297	−	0.151811i
$611$	0.0851622	+	0.592316i	0.00344530	+	0.0239626i
$612$	−9.53160	−	6.12559i	−0.385292	−	0.247612i
$613$	−4.99824	+	1.46762i	−0.201877	+	0.0592764i	−0.381108	−	0.924531i	$-0.624457\pi$
$613$	−4.99824	+	1.46762i	−0.201877	+	0.0592764i	0.179231	+	0.983807i	$0.442639\pi$
$614$	−0.576563	+	4.01008i	−0.0232682	+	0.161834i
$615$	1.15408	−	1.33188i	0.0465369	−	0.0537065i
$616$	−10.1913	+	6.54953i	−0.410618	+	0.263888i
$617$	−7.21401	−	8.32542i	−0.290425	−	0.335169i	0.591722	−	0.806142i	$-0.298448\pi$
$617$	−7.21401	−	8.32542i	−0.290425	−	0.335169i	−0.882147	+	0.470973i	$0.843903\pi$
$618$	3.58650	+	1.05309i	0.144270	+	0.0423615i
$619$	14.4112	−	31.5561i	0.579235	−	1.26835i	−0.362498	−	0.931985i	$-0.618076\pi$
$619$	14.4112	−	31.5561i	0.579235	−	1.26835i	0.941733	−	0.336363i	$-0.109197\pi$
$620$	7.77640			0.312308
$621$	−0.660369	−	4.75015i	−0.0264997	−	0.190617i
$622$	0.134160			0.00537933
$623$	8.53963	−	18.6992i	0.342133	−	0.749167i
$624$	−4.54459	−	1.33441i	−0.181929	−	0.0534192i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−8.85833	+	5.69291i	−0.354050	+	0.227534i
$627$	−6.83187	+	7.88440i	−0.272839	+	0.314873i
$628$	−1.14336	+	7.95226i	−0.0456251	+	0.317330i
$629$	−69.1909	+	20.3163i	−2.75882	+	0.810063i
$630$	−0.428453	−	0.275350i	−0.0170700	−	0.0109702i
$631$	2.99416	+	20.8249i	0.119196	+	0.829025i	0.958445	+	0.285278i	$0.0920859\pi$
$631$	2.99416	+	20.8249i	0.119196	+	0.829025i	−0.839249	+	0.543747i	$0.817005\pi$
$632$	8.75820	+	19.1778i	0.348383	+	0.762852i
$633$	−0.885335	−	1.93861i	−0.0351889	−	0.0770529i
$634$	1.64497	+	11.4410i	0.0653301	+	0.454381i
$635$	−15.1309	−	9.72403i	−0.600451	−	0.385886i
$636$	−22.1665	+	6.50867i	−0.878958	+	0.258085i
$637$	1.19986	−	8.34518i	0.0475400	−	0.330648i
$638$	5.03071	−	5.80575i	0.199168	−	0.229852i
$639$	−2.40078	+	1.54289i	−0.0949734	+	0.0610357i
$640$	6.82997	+	7.88221i	0.269978	+	0.311572i
$641$	4.28765	+	1.25897i	0.169352	+	0.0497263i	0.365309	−	0.930886i	$-0.380963\pi$
$641$	4.28765	+	1.25897i	0.169352	+	0.0497263i	−0.195957	+	0.980612i	$0.562781\pi$
$642$	0.501328	−	1.09775i	0.0197858	−	0.0433249i
$643$	−1.97280			−0.0777995			−0.0388998	−	0.999243i	$-0.512385\pi$
$643$	−1.97280			−0.0777995			−0.0388998	+	0.999243i	$0.512385\pi$
$644$	11.0774	+	0.0516682i	0.436511	+	0.00203601i
$645$	−1.68894			−0.0665018
$646$	−1.74612	+	3.82346i	−0.0687000	+	0.150432i
$647$	−16.1953	−	4.75538i	−0.636704	−	0.186953i	−0.0525788	−	0.998617i	$-0.516744\pi$
$647$	−16.1953	−	4.75538i	−0.636704	−	0.186953i	−0.584125	+	0.811664i	$0.698562\pi$
$648$	−1.01702	−	1.17371i	−0.0399525	−	0.0461076i
$649$	60.6462	−	38.9750i	2.38057	−	1.52990i
$650$	0.412599	−	0.476165i	0.0161835	−	0.0186767i
$651$	0.758257	−	5.27379i	0.0297184	−	0.206696i
$652$	−0.414474	+	0.121701i	−0.0162320	+	0.00476616i
$653$	35.1531	+	22.5916i	1.37565	+	0.884076i	0.999104	−	0.0423226i	$-0.0134757\pi$
$653$	35.1531	+	22.5916i	1.37565	+	0.884076i	0.376545	+	0.926398i	$0.377112\pi$
$654$	−0.882491	−	6.13786i	−0.0345081	−	0.240009i
$655$	−2.82566	−	6.18734i	−0.110408	−	0.241759i
$656$	2.22810	+	4.87885i	0.0869926	+	0.190487i
$657$	−0.637820	−	4.43613i	−0.0248837	−	0.173070i
$658$	−0.164745	−	0.105875i	−0.00642245	−	0.00412746i
$659$	−20.8454	+	6.12075i	−0.812020	+	0.238431i	−0.661276	−	0.750142i	$-0.729985\pi$
$659$	−20.8454	+	6.12075i	−0.812020	+	0.238431i	−0.150744	+	0.988573i	$0.548167\pi$
$660$	−1.62025	+	11.2691i	−0.0630681	+	0.438648i
$661$	14.4969	−	16.7303i	0.563862	−	0.650732i	−0.400194	−	0.916430i	$-0.631057\pi$
$661$	14.4969	−	16.7303i	0.563862	−	0.650732i	0.964056	+	0.265699i	$0.0856027\pi$
$662$	4.56973	−	2.93678i	0.177607	−	0.114141i
$663$	−6.28896	−	7.25784i	−0.244243	−	0.281871i
$664$	19.2154	+	5.64214i	0.745701	+	0.218958i
$665$	0.879266	−	1.92532i	0.0340965	−	0.0746609i
$666$	−4.73105			−0.183324
$667$	−14.1009	+	4.06906i	−0.545989	+	0.157555i
$668$	−26.0356			−1.00735
$669$	7.12601	−	15.6038i	0.275507	−	0.603277i
$670$	−0.380102	−	0.111608i	−0.0146846	−	0.00431179i
$671$	41.3422	+	47.7115i	1.59600	+	1.84188i
$672$	4.59115	−	2.95055i	0.177107	−	0.113820i
$673$	−17.2993	+	19.9645i	−0.666840	+	0.769574i	−0.983878	−	0.178838i	$-0.942766\pi$
$673$	−17.2993	+	19.9645i	−0.666840	+	0.769574i	0.317039	+	0.948413i	$0.397312\pi$
$674$	1.81384	−	12.6155i	0.0698664	−	0.485931i
$675$	−0.959493	+	0.281733i	−0.0369309	+	0.0108439i
$676$	16.3390	+	10.5005i	0.628424	+	0.403864i
$677$	−0.262865	−	1.82827i	−0.0101027	−	0.0702660i	0.984146	−	0.177358i	$-0.0567551\pi$
$677$	−0.262865	−	1.82827i	−0.0101027	−	0.0702660i	−0.994249	+	0.107092i	$0.965846\pi$
$678$	−0.958210	−	2.09819i	−0.0367998	−	0.0805804i
$679$	−1.35815	−	2.97393i	−0.0521209	−	0.114129i
$680$	1.36388	+	9.48599i	0.0523024	+	0.363771i
$681$	−0.634713	−	0.407906i	−0.0243223	−	0.0156310i
$682$	10.2012	−	2.99536i	0.390626	−	0.114698i
$683$	4.81759	−	33.5070i	0.184340	−	1.28211i	−0.662014	−	0.749491i	$-0.730298\pi$
$683$	4.81759	−	33.5070i	0.184340	−	1.28211i	0.846354	−	0.532620i	$-0.178793\pi$
$684$	2.02302	−	2.33469i	0.0773520	−	0.0892690i
$685$	7.13746	−	4.58696i	0.272708	−	0.175259i
$686$	4.14149	+	4.77953i	0.158123	+	0.182483i
$687$	7.73930	+	2.27246i	0.295273	+	0.0866999i
$688$	2.13531	−	4.67569i	0.0814081	−	0.178259i
$689$	−19.5815			−0.745996
$690$	−1.27830	+	1.46141i	−0.0486640	+	0.0556348i
$691$	−15.9102			−0.605253			−0.302627	−	0.953109i	$-0.597863\pi$
$691$	−15.9102			−0.605253			−0.302627	+	0.953109i	$0.597863\pi$
$692$	2.49388	−	5.46082i	0.0948029	−	0.207589i
$693$	7.48446	+	2.19764i	0.284311	+	0.0834813i
$694$	3.02782	+	3.49428i	0.114934	+	0.132641i
$695$	18.7910	−	12.0762i	0.712781	−	0.458077i
$696$	−3.11231	+	3.59180i	−0.117972	+	0.136147i
$697$	−1.54767	+	10.7643i	−0.0586223	+	0.407727i
$698$	9.73667	−	2.85894i	0.368538	−	0.108213i
$699$	3.09342	+	1.98802i	0.117004	+	0.0751939i
$700$	−0.328722	−	2.28631i	−0.0124245	−	0.0864145i
$701$	4.46279	+	9.77214i	0.168557	+	0.369089i	0.974994	−	0.222232i	$-0.0713342\pi$
$701$	4.46279	+	9.77214i	0.168557	+	0.369089i	−0.806437	+	0.591320i	$0.798607\pi$
$702$	−0.261735	−	0.573119i	−0.00987855	−	0.0216310i
$703$	−2.79814	−	19.4615i	−0.105534	−	0.734004i
$704$	−22.5896	−	14.5174i	−0.851377	−	0.547147i
$705$	−0.368937	+	0.108330i	−0.0138950	+	0.00407993i
$706$	−0.353034	+	2.45541i	−0.0132866	+	0.0924105i
$707$	5.13183	−	5.92245i	0.193002	−	0.222737i
$708$	−17.9582	+	11.5411i	−0.674912	+	0.433739i
$709$	31.2138	+	36.0226i	1.17226	+	1.35286i	0.923177	+	0.384374i	$0.125583\pi$
$709$	31.2138	+	36.0226i	1.17226	+	1.35286i	0.249080	+	0.968483i	$0.419872\pi$
$710$	1.10856	+	0.325503i	0.0416036	+	0.0122159i
$711$	5.63940	−	12.3486i	0.211494	−	0.463107i
$712$	−25.3779			−0.951078
$713$	−19.4621	−	5.81331i	−0.728860	−	0.217710i
$714$	3.14282			0.117617
$715$	−4.00871	+	8.77785i	−0.149917	+	0.328273i
$716$	16.9848	+	4.98718i	0.634751	+	0.186380i
$717$	13.1232	+	15.1450i	0.490096	+	0.565601i
$718$	−3.37382	+	2.16822i	−0.125910	+	0.0809173i
$719$	5.02413	−	5.79816i	0.187369	−	0.216235i	−0.654292	−	0.756242i	$-0.727033\pi$
$719$	5.02413	−	5.79816i	0.187369	−	0.216235i	0.841660	+	0.540007i	$0.181579\pi$
$720$	0.433128	−	3.01247i	0.0161417	−	0.112268i
$721$	11.1445	−	3.27232i	0.415043	−	0.121868i
$722$	5.50691	+	3.53908i	0.204946	+	0.131711i
$723$	−3.58442	−	24.9302i	−0.133306	−	0.927163i
$724$	−1.81660	−	3.97781i	−0.0675135	−	0.147834i
$725$	1.27126	+	2.78367i	0.0472134	+	0.103383i
$726$	1.58143	+	10.9991i	0.0586924	+	0.408215i
$727$	−0.484156	−	0.311148i	−0.0179563	−	0.0115398i	0.531632	−	0.846976i	$-0.321579\pi$
$727$	−0.484156	−	0.311148i	−0.0179563	−	0.0115398i	−0.549588	+	0.835436i	$0.685215\pi$
$728$	2.91739	−	0.856622i	0.108126	−	0.0317485i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−1.18820	+	1.37126i	−0.0439773	+	0.0507525i
$731$	8.76766	−	5.63463i	0.324283	−	0.208404i
$732$	−12.2420	−	14.1281i	−0.452479	−	0.522189i
$733$	−24.3301	−	7.14397i	−0.898654	−	0.263869i	−0.200396	−	0.979715i	$-0.564223\pi$
$733$	−24.3301	−	7.14397i	−0.898654	−	0.263869i	−0.698258	+	0.715846i	$0.746041\pi$
$734$	0.917436	−	2.00890i	0.0338632	−	0.0741500i
$735$	5.41742			0.199824
$736$	−8.55449	−	18.9653i	−0.315323	−	0.699071i
$737$	6.06738			0.223495
$738$	−0.296388	+	0.649000i	−0.0109102	+	0.0238900i
$739$	13.3650	+	3.92431i	0.491639	+	0.144358i	0.518149	−	0.855290i	$-0.326621\pi$
$739$	13.3650	+	3.92431i	0.491639	+	0.144358i	−0.0265101	+	0.999649i	$0.508439\pi$
$740$	−14.0511	−	16.2158i	−0.516527	−	0.596104i
$741$	2.20277	−	1.41563i	0.0809206	−	0.0520045i
$742$	4.19647	−	4.84299i	0.154057	−	0.177792i
$743$	−0.0133009	+	0.0925096i	−0.000487961	+	0.00339385i	−0.990064	−	0.140618i	$-0.955091\pi$
$743$	−0.0133009	+	0.0925096i	−0.000487961	+	0.00339385i	0.989576	+	0.144012i	$0.0460002\pi$
$744$	−6.31113	+	1.85312i	−0.231377	+	0.0679385i
$745$	−4.71368	−	3.02930i	−0.172696	−	0.110985i
$746$	−1.80865	−	12.5794i	−0.0662192	−	0.460565i
$747$	−5.35682	−	11.7298i	−0.195996	−	0.429171i
$748$	−29.1848	−	63.9058i	−1.06710	−	2.33663i
$749$	−0.533679	−	3.71182i	−0.0195002	−	0.135627i
$750$	0.340581	+	0.218878i	0.0124362	+	0.00799229i
$751$	3.72339	−	1.09329i	0.135868	−	0.0398946i	−0.213091	−	0.977032i	$-0.568353\pi$
$751$	3.72339	−	1.09329i	0.135868	−	0.0398946i	0.348960	+	0.937138i	$0.386535\pi$
$752$	0.166543	−	1.15833i	0.00607320	−	0.0422400i
$753$	−9.88319	+	11.4058i	−0.360163	+	0.415651i
$754$	−1.62203	+	1.04241i	−0.0590707	+	0.0379625i
$755$	−2.76110	−	3.18648i	−0.100487	−	0.115968i
$756$	−2.21626	−	0.650753i	−0.0806046	−	0.0236676i
$757$	3.93816	−	8.62337i	0.143135	−	0.313422i	−0.824464	−	0.565915i	$-0.808523\pi$
$757$	3.93816	−	8.62337i	0.143135	−	0.313422i	0.967599	+	0.252493i	$0.0812505\pi$
$758$	12.3950			0.450207
$759$	12.4793	−	26.9920i	0.452970	−	0.979746i
$760$	−2.61299			−0.0947831
$761$	−1.68469	+	3.68895i	−0.0610699	+	0.133724i	−0.937706	−	0.347429i	$-0.887055\pi$
$761$	−1.68469	+	3.68895i	−0.0610699	+	0.133724i	0.876636	+	0.481153i	$0.159782\pi$
$762$	6.98670	+	2.05148i	0.253101	+	0.0743173i
$763$	−12.6183	−	14.5622i	−0.456811	−	0.527189i
$764$	30.9383	−	19.8828i	1.11931	−	0.719336i
$765$	4.04103	−	4.66360i	0.146104	−	0.168613i
$766$	1.35076	−	9.39477i	0.0488051	−	0.339447i
$767$	−17.3608	+	5.09759i	−0.626862	+	0.184063i
$768$	3.73409	+	2.39975i	0.134742	+	0.0865936i
$769$	4.42644	+	30.7866i	0.159622	+	1.11019i	0.899332	+	0.437267i	$0.144054\pi$
$769$	4.42644	+	30.7866i	0.159622	+	1.11019i	−0.739710	+	0.672926i	$0.765037\pi$
$770$	−1.31188	−	2.87262i	−0.0472769	−	0.103522i
$771$	1.84187	+	4.03313i	0.0663333	+	0.145250i
$772$	0.229736	+	1.59785i	0.00826837	+	0.0575078i
$773$	−38.2779	−	24.5997i	−1.37676	−	0.884790i	−0.377609	−	0.925965i	$-0.623253\pi$
$773$	−38.2779	−	24.5997i	−1.37676	−	0.884790i	−0.999152	+	0.0411751i	$0.986890\pi$
$774$	0.656067	−	0.192639i	0.0235818	−	0.00692425i
$775$	−0.602744	+	4.19218i	−0.0216512	+	0.150587i
$776$	−2.64310	+	3.05029i	−0.0948816	+	0.109499i
$777$	−12.3673	+	7.94797i	−0.443674	+	0.285132i
$778$	−7.45982	−	8.60910i	−0.267448	−	0.308651i
$779$	−2.84500	−	0.835369i	−0.101933	−	0.0299302i
$780$	1.18704	−	2.59925i	0.0425028	−	0.0930681i
$781$	−17.6954			−0.633193
$782$	1.76040	−	11.8512i	0.0629517	−	0.423796i
$783$	3.06021			0.109363
$784$	−6.84921	+	14.9977i	−0.244615	+	0.535631i
$785$	−4.19836	−	1.23275i	−0.149846	−	0.0439987i
$786$	1.80335	+	2.08118i	0.0643233	+	0.0742331i
$787$	27.7530	−	17.8358i	0.989289	−	0.635778i	0.0573356	−	0.998355i	$-0.481739\pi$
$787$	27.7530	−	17.8358i	0.989289	−	0.635778i	0.931954	+	0.362577i	$0.118103\pi$
$788$	−3.91000	+	4.51238i	−0.139288	+	0.160747i
$789$	1.67093	−	11.6216i	0.0594867	−	0.413739i
$790$	−5.27333	+	1.54839i	−0.187617	+	0.0550892i
$791$	−6.02970	−	3.87505i	−0.214391	−	0.137781i
$792$	−1.37047	−	9.53180i	−0.0486974	−	0.338698i
$793$	−6.58230	−	14.4132i	−0.233744	−	0.511829i
$794$	5.86200	+	12.8360i	0.208035	+	0.455532i
$795$	−1.79065	−	12.4542i	−0.0635076	−	0.441705i
$796$	24.3661	+	15.6591i	0.863634	+	0.555024i
$797$	21.9350	−	6.44071i	0.776979	−	0.228142i	0.130883	−	0.991398i	$-0.458219\pi$
$797$	21.9350	−	6.44071i	0.776979	−	0.228142i	0.646096	+	0.763256i	$0.276401\pi$
$798$	−0.121950	+	0.848180i	−0.00431698	+	0.0300252i
$799$	1.55383	−	1.79321i	0.0549704	−	0.0634392i
$800$	−3.64954	+	2.34542i	−0.129031	+	0.0829230i
$801$	10.7010	+	12.3496i	0.378100	+	0.436350i
$802$	12.2260	+	3.58989i	0.431717	+	0.126763i
$803$	11.5442	−	25.2784i	0.407388	−	0.892054i
$804$	−1.79664			−0.0633626
$805$	−0.886457	+	5.96771i	−0.0312435	+	0.210334i
$806$	−2.66847			−0.0939928
$807$	4.95591	−	10.8519i	0.174456	−	0.382006i
$808$	−9.28249	−	2.72559i	−0.326557	−	0.0958858i
$809$	−15.4199	−	17.7955i	−0.542134	−	0.625656i	0.416898	−	0.908953i	$-0.363117\pi$
$809$	−15.4199	−	17.7955i	−0.542134	−	0.625656i	−0.959032	+	0.283297i	$0.908572\pi$
$810$	0.340581	−	0.218878i	0.0119668	−	0.00769058i
$811$	5.07389	−	5.85558i	0.178168	−	0.205617i	−0.659640	−	0.751582i	$-0.729291\pi$
$811$	5.07389	−	5.85558i	0.178168	−	0.205617i	0.837808	+	0.545964i	$0.183837\pi$
$812$	−1.00596	+	6.99661i	−0.0353023	+	0.245533i
$813$	−1.53341	+	0.450248i	−0.0537789	+	0.0157909i
$814$	−24.6786	−	15.8599i	−0.864983	−	0.555891i
$815$	−0.0334819	−	0.232872i	−0.00117282	−	0.00815714i
$816$	7.80174	+	17.0834i	0.273115	+	0.598039i
$817$	1.18046	+	2.58484i	0.0412990	+	0.0904322i
$818$	1.18672	+	8.25379i	0.0414926	+	0.288587i
$819$	−1.64701	−	1.05847i	−0.0575512	−	0.0369859i
$820$	−3.10473	+	0.911631i	−0.108422	+	0.0318355i
$821$	6.85302	−	47.6638i	0.239172	−	1.66348i	−0.417029	−	0.908893i	$-0.636929\pi$
$821$	6.85302	−	47.6638i	0.239172	−	1.66348i	0.656201	−	0.754586i	$-0.272162\pi$
$822$	−2.24936	+	2.59590i	−0.0784553	+	0.0905423i
$823$	5.24319	−	3.36959i	0.182766	−	0.117457i	−0.446059	−	0.895004i	$-0.647173\pi$
$823$	5.24319	−	3.36959i	0.182766	−	0.117457i	0.628825	+	0.777547i	$0.283536\pi$
$824$	−9.39004	−	10.8367i	−0.327117	−	0.377514i
$825$	−5.94946	−	1.74692i	−0.207134	−	0.0608199i
$826$	2.45980	−	5.38621i	0.0855873	−	0.187410i
$827$	44.8732			1.56039			0.780197	−	0.625534i	$-0.215119\pi$
$827$	44.8732			1.56039			0.780197	+	0.625534i	$0.215119\pi$
$828$	−3.69530	+	7.99272i	−0.128421	+	0.277766i
$829$	−1.84316			−0.0640156			−0.0320078	−	0.999488i	$-0.510190\pi$
$829$	−1.84316			−0.0640156			−0.0320078	+	0.999488i	$0.510190\pi$
$830$	−2.16870	+	4.74879i	−0.0752767	+	0.164833i
$831$	−0.490170	−	0.143927i	−0.0170038	−	0.00499277i
$832$	4.41348	+	5.09343i	0.153010	+	0.176583i
$833$	−28.1230	+	18.0736i	−0.974405	+	0.626212i
$834$	−5.92194	+	6.83428i	−0.205060	+	0.236652i
$835$	2.01801	−	14.0355i	0.0698360	−	0.485720i
$836$	18.3793	−	5.39664i	0.635660	−	0.186647i
$837$	3.56295	+	2.28977i	0.123154	+	0.0791460i
$838$	0.952560	+	6.62520i	0.0329056	+	0.228864i
$839$	−13.8958	−	30.4275i	−0.479736	−	1.05048i	−0.982536	−	0.186073i	$-0.940424\pi$
$839$	−13.8958	−	30.4275i	−0.479736	−	1.05048i	0.502800	−	0.864403i	$-0.332303\pi$
$840$	0.811611	+	1.77718i	0.0280032	+	0.0613185i
$841$	2.79436	+	19.4352i	0.0963574	+	0.670180i
$842$	−3.88310	−	2.49552i	−0.133820	−	0.0860012i
$843$	−6.46812	+	1.89921i	−0.222774	+	0.0654123i
$844$	−0.556892	+	3.87327i	−0.0191690	+	0.133323i
$845$	−6.92712	+	7.99432i	−0.238300	+	0.275013i
$846$	0.130957	−	0.0841612i	0.00450241	−	0.00289352i
$847$	22.6120	+	26.0957i	0.776959	+	0.896658i
$848$	36.7424	+	10.7885i	1.26174	+	0.370480i
$849$	−7.28859	+	15.9598i	−0.250144	+	0.547739i
$850$	−2.49825			−0.0856893
$851$	23.0434	+	51.0873i	0.789919	+	1.75125i
$852$	5.23988			0.179515
$853$	4.47271	−	9.79388i	0.153143	−	0.335336i	−0.817474	−	0.575965i	$-0.804626\pi$
$853$	4.47271	−	9.79388i	0.153143	−	0.335336i	0.970617	+	0.240629i	$0.0773537\pi$
$854$	4.97539	+	1.46091i	0.170254	+	0.0499912i
$855$	1.10180	+	1.27155i	0.0376809	+	0.0434860i
$856$	−3.89454	+	2.50287i	−0.133113	+	0.0855463i
$857$	−7.02620	+	8.10867i	−0.240011	+	0.276987i	−0.862957	−	0.505278i	$-0.831390\pi$
$857$	−7.02620	+	8.10867i	−0.240011	+	0.276987i	0.622946	+	0.782265i	$0.285936\pi$
$858$	0.555988	−	3.86698i	0.0189811	−	0.132017i
$859$	−32.4069	+	9.51552i	−1.10571	+	0.324665i	−0.783118	−	0.621873i	$-0.786372\pi$
$859$	−32.4069	+	9.51552i	−1.10571	+	0.324665i	−0.322591	+	0.946539i	$0.604554\pi$
$860$	2.60877	+	1.67656i	0.0889584	+	0.0571701i
$861$	0.315515	+	2.19445i	0.0107527	+	0.0747868i
$862$	2.24642	+	4.91896i	0.0765132	+	0.167541i
$863$	2.41991	+	5.29886i	0.0823747	+	0.180375i	0.946337	−	0.323180i	$-0.104752\pi$
$863$	2.41991	+	5.29886i	0.0823747	+	0.180375i	−0.863963	+	0.503556i	$0.832025\pi$
$864$	0.617392	+	4.29406i	0.0210041	+	0.146087i
$865$	2.75058	+	1.76769i	0.0935224	+	0.0601032i
$866$	−12.2249	+	3.58956i	−0.415420	+	0.121978i
$867$	−2.99986	+	20.8645i	−0.101881	+	0.708595i
$868$	−6.40635	+	7.39332i	−0.217446	+	0.250946i
$869$	70.8130	−	45.5087i	2.40217	−	1.54378i
$870$	−0.811323	−	0.936316i	−0.0275064	−	0.0317441i
$871$	−1.46115	−	0.429031i	−0.0495091	−	0.0145372i
$872$	−9.88170	+	21.6379i	−0.334637	+	0.732752i
$873$	2.59885			0.0879578
$874$	3.13007	+	0.934951i	0.105876	+	0.0316252i
$875$	1.25801			0.0425284
$876$	−3.41842	+	7.48530i	−0.115498	+	0.252905i
$877$	−26.1518	−	7.67886i	−0.883084	−	0.259297i	−0.191413	−	0.981510i	$-0.561307\pi$
$877$	−26.1518	−	7.67886i	−0.883084	−	0.259297i	−0.691671	+	0.722213i	$0.743125\pi$
$878$	−7.18464	−	8.29152i	−0.242470	−	0.279825i
$879$	−9.24421	+	5.94090i	−0.311800	+	0.200381i
$880$	12.3581	−	14.2620i	0.416590	−	0.480771i
$881$	−1.57368	+	10.9452i	−0.0530188	+	0.368754i	0.945988	+	0.324201i	$0.105095\pi$
$881$	−1.57368	+	10.9452i	−0.0530188	+	0.368754i	−0.999007	+	0.0445528i	$0.985814\pi$
$882$	−2.10439	+	0.617906i	−0.0708586	+	0.0208060i
$883$	−17.1802	−	11.0410i	−0.578158	−	0.371560i	0.218640	−	0.975806i	$-0.429838\pi$
$883$	−17.1802	−	11.0410i	−0.578158	−	0.371560i	−0.796798	+	0.604246i	$0.793474\pi$
$884$	2.50943	+	17.4535i	0.0844013	+	0.587024i
$885$	−4.82973	−	10.5756i	−0.162350	−	0.355496i
$886$	−2.03344	−	4.45260i	−0.0683146	−	0.149588i
$887$	−0.716922	−	4.98631i	−0.0240719	−	0.167424i	0.974239	−	0.225517i	$-0.0724071\pi$
$887$	−0.716922	−	4.98631i	−0.0240719	−	0.167424i	−0.998311	+	0.0580931i	$0.981498\pi$
$888$	15.2677	+	9.81196i	0.512351	+	0.329268i
$889$	21.7101	−	6.37467i	0.728134	−	0.213800i
$890$	0.941492	−	6.54822i	0.0315589	−	0.219497i
$891$	−4.06055	+	4.68612i	−0.136033	+	0.156991i
$892$	−26.4964	+	17.0282i	−0.887165	+	0.570146i
$893$	0.423657	+	0.488926i	0.0141771	+	0.0163613i
$894$	2.17654	+	0.639091i	0.0727945	+	0.0213744i
$895$	−4.00502	+	8.76977i	−0.133873	+	0.293141i
$896$	−13.1206			−0.438328
$897$	−4.91390	+	5.61778i	−0.164070	+	0.187572i
$898$	−3.20451			−0.106936
$899$	5.38415	−	11.7896i	0.179571	−	0.393206i
$900$	1.76172	+	0.517288i	0.0587241	+	0.0172429i
$901$	50.8454	+	58.6787i	1.69390	+	1.95487i
$902$	−3.72170	+	2.39179i	−0.123919	+	0.0796380i
$903$	1.39138	−	1.60574i	0.0463022	−	0.0534356i
$904$	−1.25927	+	8.75840i	−0.0418826	+	0.291300i
$905$	2.28520	−	0.670995i	0.0759626	−	0.0223046i
$906$	1.43600	+	0.922859i	0.0477078	+	0.0306599i
$907$	2.95785	+	20.5723i	0.0982138	+	0.683092i	0.978135	+	0.207972i	$0.0666863\pi$
$907$	2.95785	+	20.5723i	0.0982138	+	0.683092i	−0.879921	+	0.475120i	$0.842405\pi$
$908$	0.575478	+	1.26012i	0.0190979	+	0.0418186i
$909$	2.58775	+	5.66638i	0.0858303	+	0.187942i
$910$	0.112801	+	0.784548i	0.00373932	+	0.0260075i
$911$	25.5401	+	16.4136i	0.846181	+	0.543808i	0.890382	−	0.455215i	$-0.150438\pi$
$911$	25.5401	+	16.4136i	0.846181	+	0.543808i	−0.0442003	+	0.999023i	$0.514074\pi$
$912$	−4.91318	+	1.44264i	−0.162692	+	0.0477706i
$913$	11.3792	−	79.1439i	0.376596	−	2.61928i
$914$	−6.87137	+	7.92999i	−0.227285	+	0.262301i
$915$	8.56517	−	5.50450i	0.283156	−	0.181973i
$916$	−9.69850	−	11.1927i	−0.320448	−	0.369816i
$917$	8.21038	+	2.41078i	0.271131	+	0.0796111i
$918$	−1.03781	+	2.27249i	−0.0342529	+	0.0750033i
$919$	−43.7684			−1.44379			−0.721893	−	0.692004i	$-0.756728\pi$
$919$	−43.7684			−1.44379			−0.721893	+	0.692004i	$0.756728\pi$
$920$	7.15612	−	2.06502i	0.235930	−	0.0680817i
$921$	−10.0070			−0.329742
$922$	−2.64836	+	5.79911i	−0.0872192	+	0.190983i
$923$	4.26142	+	1.25126i	0.140266	+	0.0411859i
$924$	−9.37915	−	10.8241i	−0.308551	−	0.356087i
$925$	9.83085	−	6.31790i	0.323236	−	0.207731i
$926$	2.81745	−	3.25151i	0.0925870	−	0.106851i
$927$	−1.31397	+	9.13887i	−0.0431565	+	0.300160i
$928$	12.7381	−	3.74024i	0.418149	−	0.122780i
$929$	−29.0043	−	18.6399i	−0.951601	−	0.611557i	−0.0299394	−	0.999552i	$-0.509531\pi$
$929$	−29.0043	−	18.6399i	−0.951601	−	0.611557i	−0.921661	+	0.387995i	$0.873168\pi$
$930$	−0.244020	−	1.69720i	−0.00800174	−	0.0556533i
$931$	−3.78643	−	8.29112i	−0.124095	−	0.271730i
$932$	−2.80472	−	6.14149i	−0.0918718	−	0.201171i
$933$	0.0471607	+	0.328010i	0.00154397	+	0.0107386i
$934$	−10.8686	−	6.98483i	−0.355632	−	0.228551i
$935$	36.7131	−	10.7799i	1.20065	−	0.352541i
$936$	−0.343969	+	2.39236i	−0.0112430	+	0.0781966i
$937$	17.5306	−	20.2314i	0.572699	−	0.660930i	−0.393320	−	0.919402i	$-0.628673\pi$
$937$	17.5306	−	20.2314i	0.572699	−	0.660930i	0.966019	+	0.258472i	$0.0832189\pi$
$938$	0.419246	−	0.269433i	0.0136889	−	0.00879729i
$939$	−17.0326	−	19.6567i	−0.555838	−	0.641471i
$940$	0.677404	+	0.198904i	0.0220945	+	0.00648753i
$941$	−16.4083	+	35.9292i	−0.534895	+	1.17126i	0.428591	+	0.903499i	$0.359010\pi$
$941$	−16.4083	+	35.9292i	−0.534895	+	1.17126i	−0.963486	+	0.267758i	$0.913717\pi$
$942$	1.77146			0.0577172
$943$	8.45173	+	0.0394213i	0.275226	+	0.00128373i
$944$	35.3840			1.15165
$945$	0.522595	−	1.14432i	0.0170000	−	0.0372249i
$946$	4.06803	+	1.19448i	0.132263	+	0.0388359i
$947$	−27.4204	−	31.6449i	−0.891044	−	1.02832i	−0.999415	−	0.0342095i	$-0.989109\pi$
$947$	−27.4204	−	31.6449i	−0.891044	−	1.02832i	0.108370	−	0.994111i	$-0.465437\pi$
$948$	−20.9688	+	13.4758i	−0.681034	+	0.437674i
$949$	−4.56755	+	5.27123i	−0.148269	+	0.171111i
$950$	0.0969389	−	0.674225i	0.00314511	−	0.0218747i
$951$	−27.3941	+	8.04362i	−0.888313	+	0.260832i
$952$	−10.1423	−	6.51805i	−0.328713	−	0.211251i
$953$	−5.12509	−	35.6458i	−0.166018	−	1.15468i	−0.887015	−	0.461742i	$-0.847225\pi$
$953$	−5.12509	−	35.6458i	−0.166018	−	1.15468i	0.720997	−	0.692939i	$-0.243684\pi$
$954$	2.11609	+	4.63359i	0.0685110	+	0.150018i
$955$	8.32063	+	18.2196i	0.269249	+	0.589573i
$956$	−5.23646	−	36.4204i	−0.169359	−	1.17792i
$957$	15.9630	+	10.2588i	0.516010	+	0.331620i
$958$	−11.0701	+	3.25048i	−0.357659	+	0.105018i
$959$	−1.51897	+	10.5647i	−0.0490502	+	0.341152i
$960$	−2.83592	+	3.27283i	−0.0915291	+	0.105630i
$961$	−10.9887	+	7.06204i	−0.354476	+	0.227808i
$962$	4.82162	+	5.56444i	0.155455	+	0.179405i
$963$	2.86015	+	0.839815i	0.0921670	+	0.0270627i
$964$	−19.2108	+	42.0659i	−0.618740	+	1.35485i
$965$	−0.879190			−0.0283021
$966$	−0.336328	−	2.41926i	−0.0108212	−	0.0778386i
$967$	36.7830			1.18286			0.591431	−	0.806356i	$-0.298563\pi$
$967$	36.7830			1.18286			0.591431	+	0.806356i	$0.298563\pi$
$968$	17.7081	−	38.7753i	0.569160	−	1.24629i
$969$	−9.96185	−	2.92506i	−0.320021	−	0.0939665i
$970$	−0.689006	−	0.795156i	−0.0221227	−	0.0255309i
$971$	−17.5170	+	11.2575i	−0.562146	+	0.361270i	−0.790645	−	0.612275i	$-0.790255\pi$
$971$	−17.5170	+	11.2575i	−0.562146	+	0.361270i	0.228499	+	0.973544i	$0.426618\pi$
$972$	1.20239	−	1.38763i	0.0385666	−	0.0445082i
$973$	−3.99904	+	27.8139i	−0.128203	+	0.891673i
$974$	−2.66609	+	0.782833i	−0.0854269	+	0.0250836i
$975$	1.30922	+	0.841386i	0.0419287	+	0.0269459i
$976$	4.40987	+	30.6713i	0.141156	+	0.981764i
$977$	−8.57611	−	18.7791i	−0.274374	−	0.600796i	0.721412	−	0.692507i	$-0.243494\pi$
$977$	−8.57611	−	18.7791i	−0.274374	−	0.600796i	−0.995786	+	0.0917111i	$0.970766\pi$
$978$	0.0395671	+	0.0866400i	0.00126522	+	0.00277044i
$979$	14.4198	+	100.292i	0.460859	+	3.20534i
$980$	−8.36787	−	5.37770i	−0.267302	−	0.171784i
$981$	14.6963	−	4.31523i	0.469218	−	0.137775i
$982$	2.48043	−	17.2517i	0.0791536	−	0.550525i
$983$	−24.6060	+	28.3969i	−0.784811	+	0.905720i	−0.997447	−	0.0714117i	$-0.977250\pi$
$983$	−24.6060	+	28.3969i	−0.784811	+	0.905720i	0.212636	+	0.977131i	$0.431795\pi$
$984$	2.30248	−	1.47971i	0.0734003	−	0.0471715i
$985$	−2.12952	−	2.45759i	−0.0678521	−	0.0783055i
$986$	7.33550	+	2.15390i	0.233610	+	0.0685940i
$987$	0.200944	−	0.440007i	0.00639613	−	0.0140056i
$988$	−4.80770			−0.152953
$989$	−5.27567	−	6.14614i	−0.167757	−	0.195436i
$990$	2.51032			0.0797831
$991$	−19.2394	+	42.1284i	−0.611159	+	1.33825i	0.310619	+	0.950535i	$0.399464\pi$
$991$	−19.2394	+	42.1284i	−0.611159	+	1.33825i	−0.921778	+	0.387718i	$0.873264\pi$
$992$	17.6293	+	5.17644i	0.559732	+	0.164352i
$993$	8.78657	+	10.1402i	0.278833	+	0.321791i
$994$	−1.22272	+	0.785797i	−0.0387825	+	0.0249240i
$995$	−10.3303	+	11.9218i	−0.327492	+	0.377946i
$996$	−3.36954	+	23.4357i	−0.106768	+	0.742587i
$997$	56.4413	−	16.5727i	1.78751	−	0.524861i	0.791271	−	0.611466i	$-0.209420\pi$
$997$	56.4413	−	16.5727i	1.78751	−	0.524861i	0.996243	+	0.0866045i	$0.0276016\pi$
$998$	−7.09892	−	4.56220i	−0.224712	−	0.144414i
$999$	−1.66308	−	11.5670i	−0.0526177	−	0.365964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.c.121.2	✓	50
23.2	even	11		7935.2.a.bv.1.9		25
23.4	even	11	inner	345.2.m.c.211.2	yes	50
23.21	odd	22		7935.2.a.bw.1.9		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.121.2	✓	50	1.1	even	1	trivial
345.2.m.c.211.2	yes	50	23.4	even	11	inner
7935.2.a.bv.1.9		25	23.2	even	11
7935.2.a.bw.1.9		25	23.21	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.168180 + 0.368263i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(1.20239 + 1.38763i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.265120 - 0.305964i) q^{6} +(0.179033 - 1.24520i) q^{7} +(-1.49013 + 0.437542i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.168180 + 0.368263i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(1.20239 + 1.38763i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.265120 - 0.305964i) q^{6} +(0.179033 - 1.24520i) q^{7} +(-1.49013 + 0.437542i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.0576160 - 0.400728i) q^{10} +(2.57583 + 5.64029i) q^{11} +(-0.762742 - 1.67017i) q^{12} +(-0.221481 - 1.54043i) q^{13} +(0.428453 + 0.275350i) q^{14} +(0.959493 - 0.281733i) q^{15} +(-0.433128 + 3.01247i) q^{16} +(-4.04103 + 4.66360i) q^{17} +(-0.340581 + 0.218878i) q^{18} +(-1.10180 - 1.27155i) q^{19} +(-1.76172 - 0.517288i) q^{20} +(-0.522595 + 1.14432i) q^{21} -2.51032 q^{22} +(4.02237 + 2.61161i) q^{23} +1.55304 q^{24} +(0.415415 - 0.909632i) q^{25} +(0.604535 + 0.177507i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(1.94315 - 1.24879i) q^{28} +(-2.00401 + 2.31276i) q^{29} +(-0.0576160 + 0.400728i) q^{30} +(-4.06373 + 1.19322i) q^{31} +(-3.64954 - 2.34542i) q^{32} +(-0.882441 - 6.13751i) q^{33} +(-1.03781 - 2.27249i) q^{34} +(0.522595 + 1.14432i) q^{35} +(0.261304 + 1.81741i) q^{36} +(9.83085 + 6.31790i) q^{37} +(0.653566 - 0.191904i) q^{38} +(-0.221481 + 1.54043i) q^{39} +(1.01702 - 1.17371i) q^{40} +(1.48256 - 0.952785i) q^{41} +(-0.333522 - 0.384905i) q^{42} +(-1.62052 - 0.475829i) q^{43} +(-4.72948 + 10.3561i) q^{44} -1.00000 q^{45} +(-1.63825 + 1.04207i) q^{46} -0.384512 q^{47} +(1.26429 - 2.76842i) q^{48} +(5.19797 + 1.52626i) q^{49} +(0.265120 + 0.305964i) q^{50} +(5.19123 - 3.33620i) q^{51} +(1.87125 - 2.15953i) q^{52} +(1.79065 - 12.4542i) q^{53} +(0.388450 - 0.114059i) q^{54} +(-5.21630 - 3.35231i) q^{55} +(0.278046 + 1.93385i) q^{56} +(0.698936 + 1.53046i) q^{57} +(-0.514668 - 1.12696i) q^{58} +(-1.65459 - 11.5079i) q^{59} +(1.54462 + 0.992669i) q^{60} +(9.76902 - 2.86844i) q^{61} +(0.244020 - 1.69720i) q^{62} +(0.823820 - 0.950739i) q^{63} +(-3.64311 + 2.34129i) q^{64} +(1.01914 + 1.17615i) q^{65} +(2.40863 + 0.707238i) q^{66} +(0.406488 - 0.890084i) q^{67} -11.3302 q^{68} +(-3.12366 - 3.63906i) q^{69} -0.509303 q^{70} +(-1.18552 + 2.59592i) q^{71} +(-1.49013 - 0.437542i) q^{72} +(-2.93492 - 3.38708i) q^{73} +(-3.98001 + 2.55780i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.439644 - 3.05779i) q^{76} +(7.48446 - 2.19764i) q^{77} +(-0.530037 - 0.340634i) q^{78} +(-1.93197 - 13.4372i) q^{79} +(-1.26429 - 2.76842i) q^{80} +(0.415415 + 0.909632i) q^{81} +(0.101538 + 0.706213i) q^{82} +(-10.8480 - 6.97162i) q^{83} +(-2.21626 + 0.650753i) q^{84} +(0.878200 - 6.10801i) q^{85} +(0.447770 - 0.516755i) q^{86} +(2.57442 - 1.65448i) q^{87} +(-6.30619 - 7.27773i) q^{88} +(15.6789 + 4.60374i) q^{89} +(0.168180 - 0.368263i) q^{90} -1.95781 q^{91} +(1.21250 + 8.72174i) q^{92} +4.23529 q^{93} +(0.0646674 - 0.141602i) q^{94} +(1.61435 + 0.474015i) q^{95} +(2.84093 + 3.27860i) q^{96} +(2.18629 - 1.40504i) q^{97} +(-1.43626 + 1.65754i) q^{98} +(-0.882441 + 6.13751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9}+O(q^{10}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9	\( 50 q - 5 q^{3} - 4 q^{4} + 5 q^{5} - 11 q^{6} - 3 q^{7} - 5 q^{9} + 15 q^{11} - 4 q^{12} - 19 q^{13} + 55 q^{14} + 5 q^{15} + 12 q^{16} + 5 q^{17} - 11 q^{19} + 4 q^{20} + 8 q^{21} - 18 q^{22} + 14 q^{23} + 66 q^{24} - 5 q^{25} - 18 q^{26} - 5 q^{27} + 10 q^{28} - 22 q^{29} + 6 q^{31} + 33 q^{32} + 4 q^{33} + 18 q^{34} - 8 q^{35} - 15 q^{36} + 25 q^{37} - 97 q^{38} - 19 q^{39} + 22 q^{40} - 42 q^{41} - 11 q^{42} - 25 q^{43} + 25 q^{44} - 50 q^{45} - 44 q^{46} + 86 q^{47} - 10 q^{48} - 8 q^{49} - 11 q^{50} - 17 q^{51} - 67 q^{52} - 26 q^{53} - 4 q^{55} - 132 q^{56} + 22 q^{57} + 8 q^{58} - 76 q^{59} + 4 q^{60} + 13 q^{61} - 8 q^{62} + 8 q^{63} + 76 q^{64} + 8 q^{65} + 4 q^{66} + 84 q^{67} + 66 q^{68} + 25 q^{69} + 22 q^{70} + 55 q^{71} - 59 q^{73} + 17 q^{74} - 5 q^{75} + 82 q^{76} - 56 q^{77} - 7 q^{78} + 7 q^{79} + 10 q^{80} - 5 q^{81} - 150 q^{82} + 19 q^{83} + 10 q^{84} + 6 q^{85} + 44 q^{86} - 11 q^{87} - 62 q^{88} - 74 q^{89} - 56 q^{91} + 41 q^{92} + 28 q^{93} - 161 q^{94} + 11 q^{95} - 44 q^{96} - 68 q^{97} - 198 q^{98} + 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^3 - 4 * q^4 + 5 * q^5 - 11 * q^6 - 3 * q^7 - 5 * q^9 + 15 * q^11 - 4 * q^12 - 19 * q^13 + 55 * q^14 + 5 * q^15 + 12 * q^16 + 5 * q^17 - 11 * q^19 + 4 * q^20 + 8 * q^21 - 18 * q^22 + 14 * q^23 + 66 * q^24 - 5 * q^25 - 18 * q^26 - 5 * q^27 + 10 * q^28 - 22 * q^29 + 6 * q^31 + 33 * q^32 + 4 * q^33 + 18 * q^34 - 8 * q^35 - 15 * q^36 + 25 * q^37 - 97 * q^38 - 19 * q^39 + 22 * q^40 - 42 * q^41 - 11 * q^42 - 25 * q^43 + 25 * q^44 - 50 * q^45 - 44 * q^46 + 86 * q^47 - 10 * q^48 - 8 * q^49 - 11 * q^50 - 17 * q^51 - 67 * q^52 - 26 * q^53 - 4 * q^55 - 132 * q^56 + 22 * q^57 + 8 * q^58 - 76 * q^59 + 4 * q^60 + 13 * q^61 - 8 * q^62 + 8 * q^63 + 76 * q^64 + 8 * q^65 + 4 * q^66 + 84 * q^67 + 66 * q^68 + 25 * q^69 + 22 * q^70 + 55 * q^71 - 59 * q^73 + 17 * q^74 - 5 * q^75 + 82 * q^76 - 56 * q^77 - 7 * q^78 + 7 * q^79 + 10 * q^80 - 5 * q^81 - 150 * q^82 + 19 * q^83 + 10 * q^84 + 6 * q^85 + 44 * q^86 - 11 * q^87 - 62 * q^88 - 74 * q^89 - 56 * q^91 + 41 * q^92 + 28 * q^93 - 161 * q^94 + 11 * q^95 - 44 * q^96 - 68 * q^97 - 198 * q^98 + 4 * q^99

Introduction

L-functions

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