LMFDB - Embedded newform 207.2.o.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46589 + 0.0698289i) q^{2} +(1.15264 + 1.29284i) q^{3} +(0.153011 - 0.0146108i) q^{4} +(1.95685 + 1.86585i) q^{5} +(-1.77992 - 1.81467i) q^{6} +(-0.197460 - 1.02452i) q^{7} +(2.68195 - 0.385606i) q^{8} +(-0.342849 + 2.98034i) q^{9} +O(q^{10})$	\(q+(-1.46589 + 0.0698289i) q^{2} +(1.15264 + 1.29284i) q^{3} +(0.153011 - 0.0146108i) q^{4} +(1.95685 + 1.86585i) q^{5} +(-1.77992 - 1.81467i) q^{6} +(-0.197460 - 1.02452i) q^{7} +(2.68195 - 0.385606i) q^{8} +(-0.342849 + 2.98034i) q^{9} +(-2.99882 - 2.59849i) q^{10} +(-0.977128 + 0.503745i) q^{11} +(0.195256 + 0.180978i) q^{12} +(-0.821376 - 0.158307i) q^{13} +(0.360996 + 1.48805i) q^{14} +(-0.156701 + 4.68054i) q^{15} +(-4.20638 + 0.810712i) q^{16} +(1.94122 + 4.25068i) q^{17} +(0.294464 - 4.39280i) q^{18} +(-2.86472 - 1.30827i) q^{19} +(0.326682 + 0.256906i) q^{20} +(1.09694 - 1.43619i) q^{21} +(1.39719 - 0.806666i) q^{22} +(4.33512 + 2.05104i) q^{23} +(3.58984 + 3.02286i) q^{24} +(0.109946 + 2.30805i) q^{25} +(1.21510 + 0.174705i) q^{26} +(-4.24828 + 2.99201i) q^{27} +(-0.0451828 - 0.153878i) q^{28} +(-0.270294 + 2.83065i) q^{29} +(-0.0971313 - 6.87209i) q^{30} +(0.397166 - 0.312335i) q^{31} +(0.843165 - 0.204550i) q^{32} +(-1.77753 - 0.682631i) q^{33} +(-3.14244 - 6.09547i) q^{34} +(1.52521 - 2.37327i) q^{35} +(-0.00891453 + 0.461036i) q^{36} +(-0.606716 + 2.06629i) q^{37} +(4.29071 + 1.71774i) q^{38} +(-0.742084 - 1.24438i) q^{39} +(5.96766 + 4.24955i) q^{40} +(6.01245 - 6.30568i) q^{41} +(-1.50770 + 2.18189i) q^{42} +(7.28198 - 9.25979i) q^{43} +(-0.142152 + 0.0913553i) q^{44} +(-6.23179 + 5.19238i) q^{45} +(-6.49802 - 2.70388i) q^{46} +(-10.9285 - 6.30957i) q^{47} +(-5.89655 - 4.50369i) q^{48} +(5.48792 - 2.19703i) q^{49} +(-0.322337 - 3.37567i) q^{50} +(-3.25791 + 7.40918i) q^{51} +(-0.127993 - 0.0122218i) q^{52} +(-5.36725 - 6.19414i) q^{53} +(6.01858 - 4.68261i) q^{54} +(-2.85201 - 0.837425i) q^{55} +(-0.924641 - 2.67157i) q^{56} +(-1.61060 - 5.21157i) q^{57} +(0.198560 - 4.16829i) q^{58} +(0.877589 - 4.55336i) q^{59} +(0.0444095 + 0.718465i) q^{60} +(0.973623 - 2.43199i) q^{61} +(-0.560392 + 0.485582i) q^{62} +(3.12113 - 0.237244i) q^{63} +(6.99883 - 2.05504i) q^{64} +(-1.31193 - 1.84235i) q^{65} +(2.65334 + 0.876538i) q^{66} +(0.633742 - 1.22929i) q^{67} +(0.359135 + 0.622040i) q^{68} +(2.34517 + 7.96870i) q^{69} +(-2.07006 + 3.58545i) q^{70} +(4.43366 + 6.89892i) q^{71} +(0.229736 + 8.12534i) q^{72} +(-1.42222 + 3.11423i) q^{73} +(0.745092 - 3.07131i) q^{74} +(-2.85720 + 2.80249i) q^{75} +(-0.457449 - 0.158325i) q^{76} +(0.709041 + 0.901619i) q^{77} +(1.17471 + 1.77230i) q^{78} +(14.4731 - 5.00918i) q^{79} +(-9.74392 - 6.26203i) q^{80} +(-8.76491 - 2.04362i) q^{81} +(-8.37327 + 9.66327i) q^{82} +(9.74971 - 9.29633i) q^{83} +(0.146860 - 0.235780i) q^{84} +(-4.13247 + 11.9400i) q^{85} +(-10.0280 + 14.0823i) q^{86} +(-3.97112 + 2.91327i) q^{87} +(-2.42636 + 1.72780i) q^{88} +(-2.12858 + 14.8046i) q^{89} +(8.77253 - 8.04662i) q^{90} +0.872777i q^{91} +(0.693290 + 0.250493i) q^{92} +(0.861587 + 0.153461i) q^{93} +(16.4606 + 8.48600i) q^{94} +(-3.16478 - 7.90523i) q^{95} +(1.23631 + 0.854302i) q^{96} +(-7.48716 - 1.81637i) q^{97} +(-7.89127 + 3.60382i) q^{98} +(-1.16633 - 3.08489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.46589	+	0.0698289i	−1.03654	+	0.0493765i	−0.558946	−	0.829204i	$-0.688794\pi$
$2$	−1.46589	+	0.0698289i	−1.03654	+	0.0493765i	−0.477594	+	0.878581i	$0.658491\pi$
$3$	1.15264	+	1.29284i	0.665476	+	0.746419i
$3$	1.15264	+	1.29284i	0.665476	+	0.746419i
$4$	0.153011	−	0.0146108i	0.0765057	−	0.00730541i
$5$	1.95685	+	1.86585i	0.875130	+	0.834435i	0.987236	−	0.159261i	$-0.0509113\pi$
$5$	1.95685	+	1.86585i	0.875130	+	0.834435i	−0.112106	+	0.993696i	$0.535760\pi$
$6$	−1.77992	−	1.81467i	−0.726648	−	0.740835i
$7$	−0.197460	−	1.02452i	−0.0746330	−	0.387233i	−0.999967	−	0.00808060i	$-0.997428\pi$
$7$	−0.197460	−	1.02452i	−0.0746330	−	0.387233i	0.925334	−	0.379152i	$-0.123784\pi$
$8$	2.68195	−	0.385606i	0.948213	−	0.136332i
$9$	−0.342849	+	2.98034i	−0.114283	+	0.993448i
$10$	−2.99882	−	2.59849i	−0.948309	−	0.821714i
$11$	−0.977128	+	0.503745i	−0.294615	+	0.151885i	−0.599197	−	0.800601i	$-0.704514\pi$
$11$	−0.977128	+	0.503745i	−0.294615	+	0.151885i	0.304582	+	0.952486i	$0.401483\pi$
$12$	0.195256	+	0.180978i	0.0563656	+	0.0522437i
$13$	−0.821376	−	0.158307i	−0.227809	−	0.0439065i	0.0740693	−	0.997253i	$-0.476401\pi$
$13$	−0.821376	−	0.158307i	−0.227809	−	0.0439065i	−0.301878	+	0.953347i	$0.597614\pi$
$14$	0.360996	+	1.48805i	0.0964803	+	0.397697i
$15$	−0.156701	+	4.68054i	−0.0404599	+	1.20851i
$16$	−4.20638	+	0.810712i	−1.05159	+	0.202678i
$17$	1.94122	+	4.25068i	0.470815	+	1.03094i	0.984888	+	0.173195i	$0.0554090\pi$
$17$	1.94122	+	4.25068i	0.470815	+	1.03094i	−0.514072	+	0.857747i	$0.671864\pi$
$18$	0.294464	−	4.39280i	0.0694059	−	1.03539i
$19$	−2.86472	−	1.30827i	−0.657211	−	0.300138i	0.0587558	−	0.998272i	$-0.481287\pi$
$19$	−2.86472	−	1.30827i	−0.657211	−	0.300138i	−0.715967	+	0.698134i	$0.754014\pi$
$20$	0.326682	+	0.256906i	0.0730483	+	0.0574458i
$21$	1.09694	−	1.43619i	0.239371	−	0.313402i
$22$	1.39719	−	0.806666i	0.297881	−	0.171982i
$23$	4.33512	+	2.05104i	0.903934	+	0.427671i
$23$	4.33512	+	2.05104i	0.903934	+	0.427671i
$24$	3.58984	+	3.02286i	0.732774	+	0.617038i
$25$	0.109946	+	2.30805i	0.0219892	+	0.461610i
$26$	1.21510	+	0.174705i	0.238301	+	0.0342625i
$27$	−4.24828	+	2.99201i	−0.817581	+	0.575813i
$28$	−0.0451828	−	0.153878i	−0.00853874	−	0.0290803i
$29$	−0.270294	+	2.83065i	−0.0501924	+	0.525638i	0.935055	+	0.354502i	$0.115350\pi$
$29$	−0.270294	+	2.83065i	−0.0501924	+	0.525638i	−0.985247	+	0.171136i	$0.945256\pi$
$30$	−0.0971313	−	6.87209i	−0.0177337	−	1.25467i
$31$	0.397166	−	0.312335i	0.0713332	−	0.0560970i	−0.581856	−	0.813292i	$-0.697673\pi$
$31$	0.397166	−	0.312335i	0.0713332	−	0.0560970i	0.653189	+	0.757195i	$0.273431\pi$
$32$	0.843165	−	0.204550i	0.149052	−	0.0361596i
$33$	−1.77753	−	0.682631i	−0.309429	−	0.118831i
$34$	−3.14244	−	6.09547i	−0.538923	−	1.04537i
$35$	1.52521	−	2.37327i	0.257807	−	0.401155i
$36$	−0.00891453	+	0.461036i	−0.00148575	+	0.0768393i
$37$	−0.606716	+	2.06629i	−0.0997435	+	0.339695i	−0.994212	−	0.107436i	$-0.965736\pi$
$37$	−0.606716	+	2.06629i	−0.0997435	+	0.339695i	0.894469	+	0.447131i	$0.147554\pi$
$38$	4.29071	+	1.71774i	0.696046	+	0.278655i
$39$	−0.742084	−	1.24438i	−0.118829	−	0.199260i
$40$	5.96766	+	4.24955i	0.943570	+	0.671913i
$41$	6.01245	−	6.30568i	0.938987	−	0.984781i	−0.0609236	−	0.998142i	$-0.519405\pi$
$41$	6.01245	−	6.30568i	0.938987	−	0.984781i	0.999911	+	0.0133611i	$0.00425310\pi$
$42$	−1.50770	+	2.18189i	−0.232643	+	0.336673i
$43$	7.28198	−	9.25979i	1.11049	−	1.41211i	0.209747	−	0.977756i	$-0.432736\pi$
$43$	7.28198	−	9.25979i	1.11049	−	1.41211i	0.900744	−	0.434350i	$-0.143022\pi$
$44$	−0.142152	+	0.0913553i	−0.0214302	+	0.0137723i
$45$	−6.23179	+	5.19238i	−0.928980	+	0.774035i
$46$	−6.49802	−	2.70388i	−0.958081	−	0.398665i
$47$	−10.9285	−	6.30957i	−1.59408	−	0.920345i	−0.992596	−	0.121464i	$-0.961241\pi$
$47$	−10.9285	−	6.30957i	−1.59408	−	0.920345i	−0.601489	−	0.798881i	$-0.705426\pi$
$48$	−5.89655	−	4.50369i	−0.851093	−	0.650052i
$49$	5.48792	−	2.19703i	0.783989	−	0.313862i
$50$	−0.322337	−	3.37567i	−0.0455854	−	0.477392i
$51$	−3.25791	+	7.40918i	−0.456198	+	1.03749i
$52$	−0.127993	−	0.0122218i	−0.0177494	−	0.00169486i
$53$	−5.36725	−	6.19414i	−0.737249	−	0.850830i	0.256019	−	0.966672i	$-0.417589\pi$
$53$	−5.36725	−	6.19414i	−0.737249	−	0.850830i	−0.993268	+	0.115841i	$0.963044\pi$
$54$	6.01858	−	4.68261i	0.819024	−	0.637223i
$55$	−2.85201	−	0.837425i	−0.384564	−	0.112918i
$56$	−0.924641	−	2.67157i	−0.123560	−	0.357004i
$57$	−1.61060	−	5.21157i	−0.213329	−	0.690290i
$58$	0.198560	−	4.16829i	0.0260722	−	0.547324i
$59$	0.877589	−	4.55336i	0.114252	−	0.592798i	−0.879000	−	0.476822i	$-0.841789\pi$
$59$	0.877589	−	4.55336i	0.114252	−	0.592798i	0.993252	−	0.115975i	$-0.0369993\pi$
$60$	0.0444095	+	0.718465i	0.00573325	+	0.0927535i
$61$	0.973623	−	2.43199i	0.124660	−	0.311385i	−0.852890	−	0.522091i	$-0.825152\pi$
$61$	0.973623	−	2.43199i	0.124660	−	0.311385i	0.977549	+	0.210706i	$0.0675764\pi$
$62$	−0.560392	+	0.485582i	−0.0711698	+	0.0616690i
$63$	3.12113	−	0.237244i	0.393225	−	0.0298899i
$64$	6.99883	−	2.05504i	0.874853	−	0.256880i
$65$	−1.31193	−	1.84235i	−0.162725	−	0.228515i
$66$	2.65334	+	0.876538i	0.326603	+	0.107894i
$67$	0.633742	−	1.22929i	0.0774239	−	0.150181i	−0.846946	−	0.531679i	$-0.821561\pi$
$67$	0.633742	−	1.22929i	0.0774239	−	0.150181i	0.924370	+	0.381498i	$0.124592\pi$
$68$	0.359135	+	0.622040i	0.0435515	+	0.0754334i
$69$	2.34517	+	7.96870i	0.282325	+	0.959319i
$70$	−2.07006	+	3.58545i	−0.247420	+	0.428543i
$71$	4.43366	+	6.89892i	0.526179	+	0.818751i	0.998018	−	0.0629343i	$-0.0200459\pi$
$71$	4.43366	+	6.89892i	0.526179	+	0.818751i	−0.471839	+	0.881685i	$0.656409\pi$
$72$	0.229736	+	8.12534i	0.0270746	+	0.957581i
$73$	−1.42222	+	3.11423i	−0.166458	+	0.364493i	−0.974417	−	0.224746i	$-0.927845\pi$
$73$	−1.42222	+	3.11423i	−0.166458	+	0.364493i	0.807959	+	0.589238i	$0.200572\pi$
$74$	0.745092	−	3.07131i	0.0866152	−	0.357033i
$75$	−2.85720	+	2.80249i	−0.329921	+	0.323604i
$76$	−0.457449	−	0.158325i	−0.0524730	−	0.0181611i
$77$	0.709041	+	0.901619i	0.0808027	+	0.102749i
$78$	1.17471	+	1.77230i	0.133009	+	0.200673i
$79$	14.4731	−	5.00918i	1.62835	−	0.563577i	0.648136	−	0.761525i	$-0.275549\pi$
$79$	14.4731	−	5.00918i	1.62835	−	0.563577i	0.980213	+	0.197948i	$0.0634277\pi$
$80$	−9.74392	−	6.26203i	−1.08940	−	0.700117i
$81$	−8.76491	−	2.04362i	−0.973879	−	0.227068i
$82$	−8.37327	+	9.66327i	−0.924673	+	1.06713i
$83$	9.74971	−	9.29633i	1.07017	−	1.02040i	0.0704315	−	0.997517i	$-0.477562\pi$
$83$	9.74971	−	9.29633i	1.07017	−	1.02040i	0.999738	−	0.0228880i	$-0.00728610\pi$
$84$	0.146860	−	0.235780i	0.0160237	−	0.0257257i
$85$	−4.13247	+	11.9400i	−0.448229	+	1.29507i
$86$	−10.0280	+	14.0823i	−1.08134	+	1.51854i
$87$	−3.97112	+	2.91327i	−0.425748	+	0.312335i
$88$	−2.42636	+	1.72780i	−0.258651	+	0.184185i
$89$	−2.12858	+	14.8046i	−0.225629	+	1.56929i	0.490577	+	0.871398i	$0.336786\pi$
$89$	−2.12858	+	14.8046i	−0.225629	+	1.56929i	−0.716206	+	0.697889i	$0.754123\pi$
$90$	8.77253	−	8.04662i	0.924706	−	0.848188i
$91$			0.872777i			0.0914919i
$92$	0.693290	+	0.250493i	0.0722804	+	0.0261157i
$93$	0.861587	+	0.153461i	0.0893424	+	0.0159132i
$94$	16.4606	+	8.48600i	1.69778	+	0.875265i
$95$	−3.16478	−	7.90523i	−0.324699	−	0.811060i
$96$	1.23631	+	0.854302i	0.126181	+	0.0871918i
$97$	−7.48716	−	1.81637i	−0.760206	−	0.184424i	−0.163125	−	0.986605i	$-0.552158\pi$
$97$	−7.48716	−	1.81637i	−0.760206	−	0.184424i	−0.597080	+	0.802181i	$0.703673\pi$
$98$	−7.89127	+	3.60382i	−0.797139	+	0.364041i
$99$	−1.16633	−	3.08489i	−0.117220	−	0.310043i
$100$	0.0505455	+	0.351552i	0.00505455	+	0.0351552i
$101$	4.83457	+	5.07035i	0.481057	+	0.504518i	0.918877	−	0.394545i	$-0.129098\pi$
$101$	4.83457	+	5.07035i	0.481057	+	0.504518i	−0.437820	+	0.899063i	$0.644249\pi$
$102$	4.25836	−	11.0885i	0.421640	−	1.09793i
$103$	−8.10595	−	0.386134i	−0.798703	−	0.0380469i	−0.355738	−	0.934586i	$-0.615770\pi$
$103$	−8.10595	−	0.386134i	−0.798703	−	0.0380469i	−0.442965	+	0.896539i	$0.646073\pi$
$104$	−2.26393	−	0.107844i	−0.221997	−	0.0105750i
$105$	4.82626	−	0.763678i	0.470994	−	0.0745273i
$106$	8.30033	+	8.70513i	0.806199	+	0.845517i
$107$	0.331396	+	2.30491i	0.0320372	+	0.222824i	0.999550	−	0.0299985i	$-0.00955025\pi$
$107$	0.331396	+	2.30491i	0.0320372	+	0.222824i	−0.967513	+	0.252822i	$0.918641\pi$
$108$	−0.606319	+	0.519883i	−0.0583431	+	0.0500257i
$109$	3.38104	−	1.54407i	0.323845	−	0.147895i	−0.246858	−	0.969052i	$-0.579398\pi$
$109$	3.38104	−	1.54407i	0.323845	−	0.147895i	0.570703	+	0.821157i	$0.306671\pi$
$110$	4.23920	+	1.02842i	0.404192	+	0.0980559i
$111$	−3.37069	+	1.59730i	−0.319932	+	0.151609i
$112$	1.66118	+	4.14944i	0.156967	+	0.392085i
$113$	−1.85847	−	0.958110i	−0.174831	−	0.0901314i	0.368590	−	0.929592i	$-0.379841\pi$
$113$	−1.85847	−	0.958110i	−0.174831	−	0.0901314i	−0.543420	+	0.839461i	$0.682871\pi$
$114$	2.72488	+	7.52712i	0.255209	+	0.704980i
$115$	4.65624	+	12.1023i	0.434196	+	1.12854i
$116$			0.437071i			0.0405810i
$117$	0.753418	−	2.39371i	0.0696535	−	0.221298i
$118$	−0.968492	+	6.73601i	−0.0891569	+	0.620100i
$119$	3.97160	−	2.82816i	0.364076	−	0.259257i
$120$	1.38458	+	12.6134i	0.126394	+	1.15144i
$121$	−5.67961	+	7.97589i	−0.516328	+	0.725081i
$122$	−1.25740	+	3.63302i	−0.113840	+	0.328918i
$123$	15.0824	+	0.504946i	1.35993	+	0.0455294i
$124$	0.0562075	−	0.0535937i	0.00504758	−	0.00481286i
$125$	4.76181	−	5.49542i	0.425909	−	0.491525i
$126$	−4.55866	+	0.565718i	−0.406118	+	0.0503982i
$127$	−5.27382	−	3.38928i	−0.467976	−	0.300750i	0.285319	−	0.958433i	$-0.407900\pi$
$127$	−5.27382	−	3.38928i	−0.467976	−	0.300750i	−0.753295	+	0.657683i	$0.771537\pi$
$128$	−11.7558	+	4.06873i	−1.03908	+	0.359628i
$129$	20.3649	−	1.25879i	1.79303	−	0.110830i
$130$	2.05180	+	2.60907i	0.179954	+	0.228831i
$131$	12.2408	+	4.23658i	1.06948	+	0.370151i	0.804408	−	0.594077i	$-0.202483\pi$
$131$	12.2408	+	4.23658i	1.06948	+	0.370151i	0.265074	+	0.964228i	$0.414604\pi$
$132$	−0.281957	−	0.0784791i	−0.0245412	−	0.00683073i
$133$	−0.774685	+	3.19330i	−0.0671737	+	0.276894i
$134$	−0.843156	+	1.84625i	−0.0728376	+	0.159492i
$135$	−13.8959	−	2.07174i	−1.19597	−	0.178307i
$136$	6.84535	+	10.6516i	0.586984	+	0.913365i
$137$	−4.68128	+	8.10821i	−0.399949	+	0.692731i	−0.993719	−	0.111903i	$-0.964305\pi$
$137$	−4.68128	+	8.10821i	−0.399949	+	0.692731i	0.593771	+	0.804634i	$0.297639\pi$
$138$	−3.99420	−	11.5175i	−0.340009	−	0.980432i
$139$	−6.12117	−	10.6022i	−0.519191	−	0.899265i	−0.999751	−	0.0223035i	$-0.992900\pi$
$139$	−6.12117	−	10.6022i	−0.519191	−	0.899265i	0.480560	−	0.876962i	$-0.340433\pi$
$140$	0.198699	−	0.385421i	0.0167931	−	0.0325740i
$141$	−4.43937	−	21.4014i	−0.373862	−	1.80232i
$142$	−6.98100	−	9.80345i	−0.585833	−	0.822687i
$143$	0.882336	−	0.259077i	0.0737847	−	0.0216651i
$144$	−0.974051	−	12.8144i	−0.0811709	−	1.06787i
$145$	−5.81050	+	5.03483i	−0.482536	+	0.418120i
$146$	1.86735	−	4.66442i	0.154543	−	0.386030i
$147$	9.16599	+	4.56260i	0.755998	+	0.376317i
$148$	−0.0626444	+	0.325030i	−0.00514933	+	0.0267173i
$149$	0.141473	−	2.96989i	0.0115899	−	0.243303i	−0.985637	−	0.168879i	$-0.945985\pi$
$149$	0.141473	−	2.96989i	0.0115899	−	0.243303i	0.997227	−	0.0744237i	$-0.0237117\pi$
$150$	3.99265	−	4.30766i	0.325998	−	0.351719i
$151$	−6.41295	−	18.5290i	−0.521878	−	1.50787i	−0.830684	−	0.556744i	$-0.812051\pi$
$151$	−6.41295	−	18.5290i	−0.521878	−	1.50787i	0.308806	−	0.951125i	$-0.400071\pi$
$152$	−8.18751	−	2.40407i	−0.664095	−	0.194996i
$153$	−13.3340	+	4.32817i	−1.07799	+	0.349912i
$154$	−1.10233	−	1.27216i	−0.0888287	−	0.102514i
$155$	1.35997	+	0.129861i	0.109235	+	0.0104307i
$156$	−0.131729	−	0.179561i	−0.0105467	−	0.0143764i
$157$	−1.46059	−	15.2959i	−0.116567	−	1.22075i	−0.844672	−	0.535284i	$-0.820205\pi$
$157$	−1.46059	−	15.2959i	−0.116567	−	1.22075i	0.728105	−	0.685466i	$-0.240401\pi$
$158$	−20.8661	+	8.35354i	−1.66002	+	0.664572i
$159$	1.82150	−	14.0786i	0.144455	−	1.11650i
$160$	2.03161	+	1.17295i	0.160613	+	0.0927297i
$161$	1.24532	−	4.84642i	0.0981450	−	0.381951i
$162$	12.9911	+	2.38367i	1.02068	+	0.187279i
$163$	−0.973816	+	0.625834i	−0.0762752	+	0.0490191i	−0.578223	−	0.815879i	$-0.696253\pi$
$163$	−0.973816	+	0.625834i	−0.0762752	+	0.0490191i	0.501947	+	0.864898i	$0.332617\pi$
$164$	0.827842	−	1.05269i	0.0646436	−	0.0822011i
$165$	−2.20468	−	4.65242i	−0.171634	−	0.362191i
$166$	−13.6428	+	14.3082i	−1.05889	+	1.11053i
$167$	−20.0273	−	14.2614i	−1.54976	−	1.10358i	−0.953749	−	0.300603i	$-0.902812\pi$
$167$	−20.0273	−	14.2614i	−1.54976	−	1.10358i	−0.596011	−	0.802977i	$-0.703248\pi$
$168$	2.38813	−	4.27477i	0.184248	−	0.329805i
$169$	−11.4192	−	4.57155i	−0.878399	−	0.351658i
$170$	5.22398	−	17.7913i	0.400661	−	1.36453i
$171$	4.88127	−	8.08931i	0.373280	−	0.618605i
$172$	0.978933	−	1.52325i	0.0746429	−	0.116147i
$173$	7.12635	+	13.8232i	0.541806	+	1.05096i	0.987772	+	0.155908i	$0.0498302\pi$
$173$	7.12635	+	13.8232i	0.541806	+	1.05096i	−0.445965	+	0.895050i	$0.647140\pi$
$174$	5.61779	−	4.54783i	0.425883	−	0.344770i
$175$	2.34294	−	0.568391i	0.177109	−	0.0429663i
$176$	3.70178	−	2.91111i	0.279032	−	0.219433i
$177$	6.89830	−	4.11380i	0.518508	−	0.309212i
$178$	2.08648	−	21.8506i	0.156388	−	1.63777i
$179$	4.07254	+	13.8698i	0.304396	+	1.03668i	0.959633	+	0.281254i	$0.0907503\pi$
$179$	4.07254	+	13.8698i	0.304396	+	1.03668i	−0.655238	+	0.755423i	$0.727432\pi$
$180$	−0.877670	+	0.885545i	−0.0654176	+	0.0660046i
$181$	12.9898	+	1.86766i	0.965527	+	0.138822i	0.607004	−	0.794699i	$-0.292371\pi$
$181$	12.9898	+	1.86766i	0.965527	+	0.138822i	0.358523	+	0.933521i	$0.383280\pi$
$182$	−0.0609451	−	1.27939i	−0.00451755	−	0.0948350i
$183$	4.26640	−	1.54447i	0.315382	−	0.114171i
$184$	12.4175	+	3.82914i	0.915427	+	0.282288i
$185$	−5.04264	+	2.91137i	−0.370742	+	0.214048i
$186$	−1.27371	−	0.164794i	−0.0933928	−	0.0120833i
$187$	−4.03808	−	3.17558i	−0.295294	−	0.232221i
$188$	−1.76437	−	0.805762i	−0.128680	−	0.0587662i
$189$	3.90425	+	3.76165i	0.283992	+	0.273620i
$190$	5.19123	+	11.3672i	0.376611	+	0.824664i
$191$	−24.7734	+	4.77468i	−1.79254	+	0.345484i	−0.973576	−	0.228363i	$-0.926663\pi$
$191$	−24.7734	+	4.77468i	−1.79254	+	0.345484i	−0.818963	+	0.573847i	$0.805451\pi$
$192$	10.7239	+	6.67962i	0.773934	+	0.482060i
$193$	4.37964	+	18.0531i	0.315253	+	1.29949i	0.880294	+	0.474429i	$0.157345\pi$
$193$	4.37964	+	18.0531i	0.315253	+	1.29949i	−0.565040	+	0.825063i	$0.691139\pi$
$194$	11.1022	+	2.13977i	0.797090	+	0.153627i
$195$	0.869674	−	3.81968i	0.0622786	−	0.273533i
$196$	0.807614	−	0.416354i	0.0576867	−	0.0297396i
$197$	−14.4226	−	12.4972i	−1.02757	−	0.890391i	−0.0335294	−	0.999438i	$-0.510675\pi$
$197$	−14.4226	−	12.4972i	−1.02757	−	0.890391i	−0.994037	+	0.109047i	$0.965220\pi$
$198$	1.92512	+	4.44066i	0.136812	+	0.315584i
$199$	1.81677	−	0.261211i	0.128787	−	0.0185168i	−0.0776198	−	0.996983i	$-0.524732\pi$
$199$	1.81677	−	0.261211i	0.128787	−	0.0185168i	0.206407	+	0.978466i	$0.433823\pi$
$200$	1.18487	+	6.14768i	0.0837829	+	0.434707i
$201$	2.31974	−	0.597600i	0.163622	−	0.0421515i
$202$	−7.44100	−	7.09497i	−0.523547	−	0.499201i
$203$	2.95343	−	0.282019i	0.207290	−	0.0197938i
$204$	−0.390243	+	1.18129i	−0.0273225	+	0.0827068i
$205$	23.5309	−	1.12092i	1.64347	−	0.0782882i
$206$	11.9094			0.829766
$207$	−7.59910	+	12.2169i	−0.528174	+	0.849136i
$208$	3.58336			0.248461
$209$	3.45823	−	0.164736i	0.239211	−	0.0113950i
$210$	−7.02143	+	1.45648i	−0.484525	+	0.100507i
$211$	−13.4814	+	1.28732i	−0.928101	+	0.0886229i	−0.548147	−	0.836382i	$-0.684666\pi$
$211$	−13.4814	+	1.28732i	−0.928101	+	0.0886229i	−0.379955	+	0.925005i	$0.624060\pi$
$212$	−0.911752	−	0.869354i	−0.0626194	−	0.0597075i
$213$	−3.80875	+	13.6840i	−0.260971	+	0.937609i
$214$	−0.646739	−	3.35560i	−0.0442102	−	0.229384i
$215$	31.5272	−	4.53292i	2.15013	−	0.309143i
$216$	−10.2399	+	9.66259i	−0.696739	+	0.657456i
$217$	−0.398419	−	0.345232i	−0.0270464	−	0.0234358i
$218$	−4.84841	+	2.49953i	−0.328376	+	0.169289i
$219$	−5.66549	+	1.75088i	−0.382838	+	0.118314i
$220$	−0.448625	−	0.0864654i	−0.0302463	−	0.00582949i
$221$	−0.921559	−	3.79872i	−0.0619908	−	0.255529i
$222$	4.82952	−	2.57683i	0.324136	−	0.172946i
$223$	−18.3716	+	3.54084i	−1.23026	+	0.237112i	−0.762642	−	0.646821i	$-0.776098\pi$
$223$	−18.3716	+	3.54084i	−1.23026	+	0.237112i	−0.467614	+	0.883933i	$0.654886\pi$
$224$	−0.376057	−	0.823450i	−0.0251264	−	0.0550191i
$225$	−6.91648	−	0.463636i	−0.461099	−	0.0309091i
$226$	2.79122	+	1.27471i	0.185669	+	0.0847923i
$227$	17.7462	+	13.9558i	1.17786	+	0.926278i	0.998347	−	0.0574778i	$-0.0183059\pi$
$227$	17.7462	+	13.9558i	1.17786	+	0.926278i	0.179512	+	0.983756i	$0.442548\pi$
$228$	−0.322586	−	0.773898i	−0.0213638	−	0.0512527i
$229$	17.6045	−	10.1640i	1.16334	−	0.671655i	0.211238	−	0.977435i	$-0.432250\pi$
$229$	17.6045	−	10.1640i	1.16334	−	0.671655i	0.952102	+	0.305780i	$0.0989171\pi$
$230$	−7.67061	−	17.4154i	−0.505785	−	1.14834i
$231$	−0.348377	+	1.95591i	−0.0229216	+	0.128690i
$232$	0.366600	+	7.69589i	0.0240685	+	0.505260i
$233$	−16.7476	−	2.40795i	−1.09717	−	0.157750i	−0.430129	−	0.902767i	$-0.641532\pi$
$233$	−16.7476	−	2.40795i	−1.09717	−	0.157750i	−0.667045	+	0.745018i	$0.732441\pi$
$234$	−0.937278	+	3.56152i	−0.0612718	+	0.232824i
$235$	−9.61270	−	32.7378i	−0.627063	−	2.13558i
$236$	0.0677527	−	0.709539i	0.00441033	−	0.0461870i
$237$	23.1583	+	12.9375i	1.50429	+	0.840383i
$238$	−5.62444	+	4.42311i	−0.364578	+	0.286707i
$239$	−7.46293	+	1.81049i	−0.482737	+	0.117111i	−0.469740	−	0.882805i	$-0.655652\pi$
$239$	−7.46293	+	1.81049i	−0.482737	+	0.117111i	−0.0129968	+	0.999916i	$0.504137\pi$
$240$	−3.13543	−	19.8151i	−0.202391	−	1.27906i
$241$	12.4430	+	24.1360i	0.801521	+	1.55473i	0.831723	+	0.555191i	$0.187355\pi$
$241$	12.4430	+	24.1360i	0.801521	+	1.55473i	−0.0302015	+	0.999544i	$0.509615\pi$
$242$	7.76872	−	12.0884i	0.499393	−	0.777070i
$243$	−7.46071	−	13.6871i	−0.478605	−	0.878030i
$244$	0.113442	−	0.386348i	0.00726238	−	0.0247334i
$245$	14.8384	+	5.94039i	0.947989	+	0.379518i
$246$	−22.1444	+	0.312992i	−1.41187	+	0.0199556i
$247$	2.14590	+	1.52809i	0.136540	+	0.0972300i
$248$	0.944742	−	0.990817i	0.0599912	−	0.0629169i
$249$	23.2565	+	1.88947i	1.47382	+	0.119740i
$250$	−6.59654	+	8.38819i	−0.417202	+	0.530516i
$251$	3.59135	−	2.30802i	0.226684	−	0.145681i	−0.422369	−	0.906424i	$-0.638802\pi$
$251$	3.59135	−	2.30802i	0.226684	−	0.145681i	0.649053	+	0.760743i	$0.275165\pi$
$252$	0.474102	−	0.0819032i	0.0298656	−	0.00515942i
$253$	−5.26916	+	0.179663i	−0.331270	+	0.0112953i
$254$	7.96751	+	4.60004i	0.499926	+	0.288632i
$255$	−20.1997	+	8.41988i	−1.26495	+	0.527273i
$256$	3.40502	−	1.36316i	0.212814	−	0.0851977i
$257$	1.11705	+	11.6983i	0.0696800	+	0.729722i	0.961037	+	0.276420i	$0.0891480\pi$
$257$	1.11705	+	11.6983i	0.0696800	+	0.729722i	−0.891357	+	0.453302i	$0.850246\pi$
$258$	−29.7648	+	3.26730i	−1.85307	+	0.203413i
$259$	2.23676	+	0.213584i	0.138985	+	0.0132715i
$260$	−0.227659	−	0.262732i	−0.0141188	−	0.0162940i
$261$	−8.34364	−	1.77606i	−0.516458	−	0.109935i
$262$	−18.2395	−	5.35559i	−1.12684	−	0.330869i
$263$	2.55569	+	7.38419i	0.157591	+	0.455329i	0.995962	−	0.0897703i	$-0.0286133\pi$
$263$	2.55569	+	7.38419i	0.157591	+	0.455329i	−0.838372	+	0.545099i	$0.816492\pi$
$264$	−5.03049	−	1.14535i	−0.309605	−	0.0704917i
$265$	1.05444	−	22.1355i	0.0647740	−	1.35977i
$266$	0.912618	−	4.73511i	0.0559562	−	0.290328i
$267$	−21.5934	+	14.3125i	−1.32150	+	0.875909i
$268$	0.0790088	−	0.197355i	0.00482623	−	0.0120553i
$269$	−5.31672	+	4.60697i	−0.324166	+	0.280892i	−0.801706	−	0.597718i	$-0.796074\pi$
$269$	−5.31672	+	4.60697i	−0.324166	+	0.280892i	0.477540	+	0.878610i	$0.341529\pi$
$270$	20.5145	+	2.06661i	1.24847	+	0.125770i
$271$	10.5066	−	3.08500i	0.638228	−	0.187401i	0.0534194	−	0.998572i	$-0.482988\pi$
$271$	10.5066	−	3.08500i	0.638228	−	0.187401i	0.584808	+	0.811172i	$0.301170\pi$
$272$	−11.6116	−	16.3062i	−0.704056	−	0.988708i
$273$	−1.12836	+	1.00600i	−0.0682913	+	0.0608857i
$274$	6.29605	−	12.2126i	0.380358	−	0.737792i
$275$	−1.27010	−	2.19988i	−0.0765899	−	0.132658i
$276$	0.475266	+	1.18504i	0.0286077	+	0.0713309i
$277$	−16.1784	+	28.0218i	−0.972066	+	1.68367i	−0.282771	+	0.959188i	$0.591253\pi$
$277$	−16.1784	+	28.0218i	−0.972066	+	1.68367i	−0.689296	+	0.724480i	$0.742080\pi$
$278$	9.71330	+	15.1142i	0.582565	+	0.906489i
$279$	0.794698	+	1.29078i	0.0475773	+	0.0772768i
$280$	3.17538	−	6.95311i	0.189765	−	0.415528i
$281$	3.76331	−	15.5126i	0.224500	−	0.925402i	−0.742341	−	0.670022i	$-0.766284\pi$
$281$	3.76331	−	15.5126i	0.224500	−	0.925402i	0.966841	−	0.255380i	$-0.0822004\pi$
$282$	8.00206	+	31.0621i	0.476515	+	1.84972i
$283$	−6.37884	−	2.20774i	−0.379183	−	0.131236i	0.130827	−	0.991405i	$-0.458237\pi$
$283$	−6.37884	−	2.20774i	−0.379183	−	0.131236i	−0.510009	+	0.860169i	$0.670358\pi$
$284$	0.779200	+	0.990833i	0.0462370	+	0.0587951i
$285$	6.57232	−	13.2034i	0.389311	−	0.782103i
$286$	−1.27532	+	0.441391i	−0.0754110	+	0.0261000i
$287$	−7.64752	−	4.91476i	−0.451419	−	0.290109i
$288$	0.320550	+	2.58305i	0.0188886	+	0.152208i
$289$	−3.16732	+	3.65528i	−0.186313	+	0.215017i
$290$	8.16597	−	7.78624i	0.479522	−	0.457224i
$291$	−6.28173	−	11.7733i	−0.368241	−	0.690162i
$292$	−0.172114	+	0.497292i	−0.0100722	+	0.0291018i
$293$	−0.301561	+	0.423484i	−0.0176174	+	0.0247402i	−0.823291	−	0.567620i	$-0.807864\pi$
$293$	−0.301561	+	0.423484i	−0.0176174	+	0.0247402i	0.805673	+	0.592360i	$0.201804\pi$
$294$	−13.7549	−	6.04821i	−0.802204	−	0.352739i
$295$	10.2132	−	7.27280i	0.594636	−	0.423439i
$296$	−0.830410	+	5.77563i	−0.0482666	+	0.335702i
$297$	2.64390	−	5.06363i	0.153415	−	0.293821i
$298$			4.36341i			0.252765i
$299$	−3.23607	−	2.37096i	−0.187147	−	0.137116i
$300$	−0.396238	+	0.470559i	−0.0228768	+	0.0271677i
$301$	−10.9248	−	5.63210i	−0.629693	−	0.324629i
$302$	10.6945	+	26.7137i	0.615401	+	1.53720i
$303$	−0.982619	+	12.0946i	−0.0564500	+	0.694815i
$304$	13.1107	+	3.18062i	0.751951	+	0.182421i
$305$	6.44297	−	2.94241i	0.368924	−	0.168482i
$306$	19.2440	−	7.27571i	1.10011	−	0.415925i
$307$	−2.59688	−	18.0617i	−0.148212	−	1.03084i	−0.919145	−	0.393920i	$-0.871119\pi$
$307$	−2.59688	−	18.0617i	−0.148212	−	1.03084i	0.770933	−	0.636916i	$-0.219790\pi$
$308$	0.121665	+	0.127598i	0.00693249	+	0.00727059i
$309$	−8.84402	−	10.9247i	−0.503119	−	0.621486i
$310$	−2.00263	−	0.0953969i	−0.113742	−	0.00541818i
$311$	5.77626	+	0.275157i	0.327542	+	0.0156027i	0.210709	−	0.977549i	$-0.432423\pi$
$311$	5.77626	+	0.275157i	0.327542	+	0.0156027i	0.116833	+	0.993152i	$0.462726\pi$
$312$	−2.47007	−	3.05120i	−0.139840	−	0.172740i
$313$	22.5934	+	23.6952i	1.27705	+	1.33933i	0.913002	+	0.407954i	$0.133758\pi$
$313$	22.5934	+	23.6952i	1.27705	+	1.33933i	0.364050	+	0.931380i	$0.381394\pi$
$314$	3.20916	+	22.3202i	0.181103	+	1.25960i
$315$	6.55024	+	5.35931i	0.369064	+	0.301963i
$316$	2.14136	−	0.977925i	0.120461	−	0.0550126i
$317$	−8.64977	−	2.09841i	−0.485819	−	0.117858i	−0.0146343	−	0.999893i	$-0.504658\pi$
$317$	−8.64977	−	2.09841i	−0.485819	−	0.117858i	−0.471185	+	0.882034i	$0.656174\pi$
$318$	−1.68703	+	20.7648i	−0.0946040	+	1.16443i
$319$	−1.16181	−	2.90207i	−0.0650490	−	0.162485i
$320$	17.5301	+	9.03737i	0.979960	+	0.505205i
$321$	−2.59789	+	3.08517i	−0.145000	+	0.172197i
$322$	−1.48708	+	7.19127i	−0.0828718	+	0.400754i
$323$		−	14.7166i		−	0.818856i
$324$	−1.37099	−	0.184634i	−0.0761661	−	0.0102574i
$325$	0.275074	−	1.91318i	0.0152584	−	0.106124i
$326$	1.38381	−	0.985403i	0.0766419	−	0.0545764i
$327$	5.89334	+	2.59138i	0.325903	+	0.143303i
$328$	13.6936	−	19.2300i	0.756102	−	1.06180i
$329$	−4.30634	+	12.4424i	−0.237416	+	0.685970i
$330$	3.55669	+	6.66599i	0.195789	+	0.366951i
$331$	−6.48978	+	6.18799i	−0.356710	+	0.340123i	−0.847151	−	0.531352i	$-0.821684\pi$
$331$	−6.48978	+	6.18799i	−0.356710	+	0.340123i	0.490441	+	0.871474i	$0.336836\pi$
$332$	1.35599	−	1.56490i	0.0744196	−	0.0858848i
$333$	−5.95023	−	2.51665i	−0.326071	−	0.137911i
$334$	30.3537	+	19.5071i	1.66088	+	1.06738i
$335$	3.53381	−	1.22306i	0.193073	−	0.0668231i
$336$	−3.44980	+	6.93044i	−0.188202	+	0.378087i
$337$	4.83482	+	6.14797i	0.263369	+	0.334901i	0.899695	−	0.436519i	$-0.143789\pi$
$337$	4.83482	+	6.14797i	0.263369	+	0.334901i	−0.636326	+	0.771421i	$0.719546\pi$
$338$	17.0585	+	5.90400i	0.927859	+	0.321135i
$339$	−0.903470	−	3.50706i	−0.0490698	−	0.190477i
$340$	−0.457862	+	1.88733i	−0.0248310	+	0.102355i
$341$	−0.230745	+	0.505262i	−0.0124956	+	0.0273615i
$342$	−6.59053	+	12.1989i	−0.356375	+	0.659640i
$343$	−7.28320	−	11.3329i	−0.393256	−	0.611918i
$344$	15.9593	−	27.6423i	0.860467	−	1.49037i
$345$	−10.2793	+	19.9693i	−0.553418	+	1.07511i
$346$	−11.4117	−	19.7656i	−0.613497	−	1.06261i
$347$	11.8224	−	22.9323i	0.634660	−	1.23107i	−0.323877	−	0.946099i	$-0.604986\pi$
$347$	11.8224	−	22.9323i	0.634660	−	1.23107i	0.958537	−	0.284969i	$-0.0919834\pi$
$348$	−0.565061	+	0.503785i	−0.0302904	+	0.0270057i
$349$	−3.96423	−	5.56698i	−0.212200	−	0.297994i	0.694733	−	0.719268i	$-0.255522\pi$
$349$	−3.96423	−	5.56698i	−0.212200	−	0.297994i	−0.906933	+	0.421274i	$0.861583\pi$
$350$	−3.39480	+	0.996803i	−0.181460	+	0.0532813i
$351$	3.96309	−	1.78503i	0.211534	−	0.0952781i
$352$	−0.720839	+	0.624611i	−0.0384209	+	0.0332919i
$353$	−0.924535	+	2.30938i	−0.0492080	+	0.122916i	−0.950935	−	0.309389i	$-0.899875\pi$
$353$	−0.924535	+	2.30938i	−0.0492080	+	0.122916i	0.901727	+	0.432305i	$0.142300\pi$
$354$	−9.82487	+	6.51208i	−0.522186	+	0.346113i
$355$	−4.19635	+	21.7727i	−0.222719	+	1.15558i
$356$	−0.109390	+	2.29638i	−0.00579765	+	0.121708i
$357$	8.23417	+	1.87478i	0.435798	+	0.0992237i
$358$	−6.93840	−	20.0472i	−0.366706	−	1.05953i
$359$	−17.3286	−	5.08813i	−0.914568	−	0.268541i	−0.209606	−	0.977786i	$-0.567218\pi$
$359$	−17.3286	−	5.08813i	−0.914568	−	0.268541i	−0.704963	+	0.709245i	$0.749036\pi$
$360$	−14.7111	+	16.3287i	−0.775345	+	0.860600i
$361$	−5.94733	−	6.86358i	−0.313017	−	0.361241i
$362$	−19.1721	−	1.83071i	−1.00766	−	0.0962201i
$363$	−16.8580	+	1.85052i	−0.884818	+	0.0971271i
$364$	0.0127520	+	0.133545i	0.000668385	+	0.00699965i
$365$	−8.59376	+	3.44042i	−0.449818	+	0.180080i
$366$	−6.14622	+	2.56195i	−0.321268	+	0.133915i
$367$	−12.3720	−	7.14298i	−0.645814	−	0.372861i	0.141037	−	0.990004i	$-0.454956\pi$
$367$	−12.3720	−	7.14298i	−0.645814	−	0.372861i	−0.786850	+	0.617144i	$0.788290\pi$
$368$	−19.8979	−	5.11291i	−1.03725	−	0.266529i
$369$	16.7317	+	20.0811i	0.871019	+	1.04538i
$370$	7.18865	−	4.61986i	0.373720	−	0.240175i
$371$	−5.28621	+	6.72196i	−0.274446	+	0.348987i
$372$	0.134075	+	0.0108929i	0.00695146	+	0.000564768i
$373$	7.27928	−	7.63429i	0.376907	−	0.395289i	−0.507770	−	0.861492i	$-0.669530\pi$
$373$	7.27928	−	7.63429i	0.376907	−	0.395289i	0.884677	+	0.466204i	$0.154379\pi$
$374$	6.14113	+	4.37308i	0.317550	+	0.226126i
$375$	12.5933	−	0.177996i	0.650316	−	0.00919167i
$376$	−31.7427	−	12.7079i	−1.63700	−	0.655358i
$377$	0.670126	−	2.28224i	0.0345132	−	0.117541i
$378$	−5.98587	−	5.24153i	−0.307880	−	0.269595i
$379$	−1.69081	+	2.63095i	−0.0868511	+	0.135143i	−0.881961	−	0.471322i	$-0.843777\pi$
$379$	−1.69081	+	2.63095i	−0.0868511	+	0.135143i	0.795110	+	0.606465i	$0.207413\pi$
$380$	−0.599749	−	1.16335i	−0.0307665	−	0.0596786i
$381$	−1.69703	−	10.7248i	−0.0869414	−	0.549448i
$382$	35.9816	−	8.72905i	1.84098	−	0.446617i
$383$	−7.35813	+	5.78649i	−0.375983	+	0.295676i	−0.788212	−	0.615404i	$-0.788993\pi$
$383$	−7.35813	+	5.78649i	−0.375983	+	0.295676i	0.412229	+	0.911080i	$0.364750\pi$
$384$	−18.8104	−	10.5086i	−0.959914	−	0.536263i
$385$	−0.294801	+	3.08730i	−0.0150245	+	0.157343i
$386$	−7.68070	−	26.1581i	−0.390937	−	1.33141i
$387$	25.1008	+	24.8775i	1.27594	+	1.26460i
$388$	−1.17216	−	0.168531i	−0.0595074	−	0.00855587i
$389$	0.325950	+	6.84253i	0.0165263	+	0.346930i	0.991953	+	0.126606i	$0.0404084\pi$
$389$	0.325950	+	6.84253i	0.0165263	+	0.346930i	−0.975427	+	0.220324i	$0.929289\pi$
$390$	−1.00812	+	5.65995i	−0.0510482	+	0.286603i
$391$	−0.302895	+	22.4087i	−0.0153181	+	1.13326i
$392$	13.8711	−	8.00851i	0.700599	−	0.404491i
$393$	8.63200	+	20.7086i	0.435427	+	1.04461i
$394$	22.0146	+	17.3124i	1.10908	+	0.872189i
$395$	37.6680	+	17.2024i	1.89528	+	0.865547i
$396$	−0.223534	−	0.454982i	−0.0112330	−	0.0228637i
$397$	−6.03124	−	13.2066i	−0.302699	−	0.662819i	0.695762	−	0.718272i	$-0.255067\pi$
$397$	−6.03124	−	13.2066i	−0.302699	−	0.662819i	−0.998461	+	0.0554537i	$0.982339\pi$
$398$	−2.64494	+	0.509770i	−0.132579	+	0.0255524i
$399$	−5.02134	+	2.67918i	−0.251381	+	0.134127i
$400$	−2.33364	−	9.61940i	−0.116682	−	0.480970i
$401$	19.1666	+	3.69405i	0.957132	+	0.184472i	0.643819	−	0.765178i	$-0.277349\pi$
$401$	19.1666	+	3.69405i	0.957132	+	0.184472i	0.313313	+	0.949650i	$0.398561\pi$
$402$	−3.35876	+	1.03800i	−0.167520	+	0.0517708i
$403$	−0.375668	+	0.193670i	−0.0187133	+	0.00964740i
$404$	0.813826	+	0.705184i	0.0404893	+	0.0350842i
$405$	−13.3385	−	20.3531i	−0.662797	−	1.01135i
$406$	−4.30971	+	0.619643i	−0.213887	+	0.0307524i
$407$	−0.448041	−	2.32466i	−0.0222086	−	0.115229i
$408$	−5.88052	+	21.1273i	−0.291129	+	1.04596i
$409$	−15.6525	−	14.9247i	−0.773968	−	0.737977i	0.196159	−	0.980572i	$-0.437153\pi$
$409$	−15.6525	−	14.9247i	−0.773968	−	0.737977i	−0.970128	+	0.242595i	$0.922002\pi$
$410$	−34.4155	+	3.28628i	−1.69966	+	0.162298i
$411$	−15.8784	+	3.29371i	−0.783224	+	0.162467i
$412$	−1.24594	+	0.0593516i	−0.0613832	+	0.00292404i
$413$	−4.83831			−0.238078
$414$	10.2863	−	18.4393i	0.505546	−	0.906243i
$415$	36.4243			1.78800
$416$	−0.724937	+	0.0345330i	−0.0355430	+	0.00169312i
$417$	6.65138	−	20.1342i	0.325719	−	0.985974i
$418$	−5.05788	+	0.482969i	−0.247389	+	0.0236228i
$419$	20.1773	+	19.2390i	0.985723	+	0.939885i	0.998196	−	0.0600369i	$-0.0191218\pi$
$419$	20.1773	+	19.2390i	0.985723	+	0.939885i	−0.0124728	+	0.999922i	$0.503970\pi$
$420$	0.727314	−	0.187367i	0.0354893	−	0.00914257i
$421$	−0.0935334	−	0.485297i	−0.00455854	−	0.0236519i	0.979578	−	0.201063i	$-0.0644398\pi$
$421$	−0.0935334	−	0.485297i	−0.00455854	−	0.0236519i	−0.984137	+	0.177412i	$0.943228\pi$
$422$	19.6724	−	2.82847i	0.957638	−	0.137688i
$423$	22.5515	−	30.4075i	1.09649	−	1.47846i
$424$	−16.7832	−	14.5427i	−0.815064	−	0.706257i
$425$	−9.59736	+	4.94778i	−0.465540	+	0.240003i
$426$	4.62768	−	20.3251i	0.224212	−	0.984755i
$427$	−2.68388	−	0.517276i	−0.129882	−	0.0250327i
$428$	0.0843839	+	0.347835i	0.00407885	+	0.0168133i
$429$	1.35196	+	0.842093i	0.0652732	+	0.0406567i
$430$	−45.8988	+	8.84627i	−2.21344	+	0.426605i
$431$	5.40362	+	11.8323i	0.260283	+	0.569941i	0.993983	−	0.109533i	$-0.0349355\pi$
$431$	5.40362	+	11.8323i	0.260283	+	0.569941i	−0.733700	+	0.679474i	$0.762208\pi$
$432$	15.4442	−	16.0297i	0.743059	−	0.771227i
$433$	22.1861	+	10.1320i	1.06619	+	0.486915i	0.869695	−	0.493589i	$-0.164315\pi$
$433$	22.1861	+	10.1320i	1.06619	+	0.486915i	0.196499	+	0.980504i	$0.437043\pi$
$434$	0.608145	+	0.478250i	0.0291919	+	0.0229567i
$435$	−13.2066	−	1.70869i	−0.633208	−	0.0819253i
$436$	0.494777	−	0.285660i	0.0236955	−	0.0136806i
$437$	−9.73557	−	11.5472i	−0.465715	−	0.552376i
$438$	8.18272	−	2.96221i	0.390985	−	0.141540i
$439$	0.290389	+	6.09602i	0.0138595	+	0.290947i	0.995147	+	0.0983990i	$0.0313721\pi$
$439$	0.290389	+	6.09602i	0.0138595	+	0.290947i	−0.981288	+	0.192548i	$0.938325\pi$
$440$	−7.97186	−	1.14618i	−0.380043	−	0.0546420i
$441$	4.66639	+	17.1091i	0.222209	+	0.814721i
$442$	1.61616	+	5.50415i	0.0768731	+	0.261806i
$443$	0.536572	−	5.61923i	0.0254933	−	0.266978i	−0.973735	−	0.227686i	$-0.926884\pi$
$443$	0.536572	−	5.61923i	0.0254933	−	0.266978i	0.999228	−	0.0392913i	$-0.0125100\pi$
$444$	−0.492416	+	0.293653i	−0.0233691	+	0.0139362i
$445$	−31.7886	+	24.9988i	−1.50692	+	1.18506i
$446$	26.6835	−	6.47336i	1.26350	−	0.306522i
$447$	4.00265	−	3.24031i	0.189319	−	0.153261i
$448$	−3.48742	−	6.76466i	−0.164765	−	0.319600i
$449$	−11.7076	+	18.2173i	−0.552514	+	0.859728i	−0.999392	−	0.0348669i	$-0.988899\pi$
$449$	−11.7076	+	18.2173i	−0.552514	+	0.859728i	0.446878	+	0.894595i	$0.352536\pi$
$450$	10.1712	+	0.196668i	0.479474	+	0.00927104i
$451$	−2.69848	+	9.19019i	−0.127067	+	0.432749i
$452$	−0.298367	−	0.119448i	−0.0140340	−	0.00561836i
$453$	16.5631	−	29.6481i	0.778204	−	1.39299i
$454$	−26.9885	−	19.2184i	−1.26663	−	0.901966i
$455$	−1.62847	+	1.70789i	−0.0763440	+	0.0800673i
$456$	−6.32917	−	13.3561i	−0.296391	−	0.625458i
$457$	12.2370	−	15.5607i	0.572424	−	0.727897i	−0.410509	−	0.911856i	$-0.634649\pi$
$457$	12.2370	−	15.5607i	0.572424	−	0.727897i	0.982934	+	0.183959i	$0.0588915\pi$
$458$	−25.0966	+	16.1286i	−1.17269	+	0.753639i
$459$	−20.9649	−	12.2499i	−0.978560	−	0.571777i
$460$	0.889281	+	1.78375i	0.0414629	+	0.0831679i
$461$	−27.2976	−	15.7603i	−1.27138	−	0.734030i	−0.296130	−	0.955148i	$-0.595696\pi$
$461$	−27.2976	−	15.7603i	−1.27138	−	0.734030i	−0.975247	+	0.221118i	$0.929030\pi$
$462$	0.374103	−	2.89148i	0.0174049	−	0.134524i
$463$	−13.9029	+	5.56587i	−0.646122	+	0.258668i	−0.671494	−	0.741010i	$-0.734347\pi$
$463$	−13.9029	+	5.56587i	−0.646122	+	0.258668i	0.0253724	+	0.999678i	$0.491923\pi$
$464$	−1.15788	−	12.1259i	−0.0537534	−	0.562931i
$465$	1.39966	+	1.90790i	0.0649077	+	0.0884765i
$466$	24.7183	+	2.36031i	1.14505	+	0.109339i
$467$	15.3268	+	17.6881i	0.709239	+	0.818506i	0.989970	−	0.141281i	$-0.0451220\pi$
$467$	15.3268	+	17.6881i	0.709239	+	0.818506i	−0.280730	+	0.959787i	$0.590577\pi$
$468$	0.0803075	−	0.377273i	0.00371222	−	0.0174394i
$469$	−1.38457	−	0.406547i	−0.0639335	−	0.0187726i
$470$	16.3772	+	47.3188i	0.755424	+	2.18265i
$471$	18.0916	−	19.5190i	0.833618	−	0.899388i
$472$	0.597844	−	12.5503i	0.0275180	−	0.577674i
$473$	−2.45086	+	12.7163i	−0.112691	+	0.584694i
$474$	−34.8509	−	17.3479i	−1.60075	−	0.796815i
$475$	2.70460	−	6.75575i	0.124095	−	0.309975i
$476$	0.566378	−	0.490770i	0.0259599	−	0.0224944i
$477$	20.3008	−	13.8726i	0.929511	−	0.635183i
$478$	10.8134	−	3.17510i	0.494593	−	0.145226i
$479$	3.59937	+	5.05461i	0.164459	+	0.230951i	0.888579	−	0.458723i	$-0.151693\pi$
$479$	3.59937	+	5.05461i	0.164459	+	0.230951i	−0.724120	+	0.689674i	$0.757754\pi$
$480$	0.825278	+	3.97852i	0.0376686	+	0.181594i
$481$	0.825450	−	1.60115i	0.0376373	−	0.0730061i
$482$	−19.9254	−	34.5118i	−0.907577	−	1.57197i
$483$	7.70103	−	3.97617i	0.350409	−	0.180922i
$484$	−0.752510	+	1.30339i	−0.0342050	+	0.0592448i
$485$	−11.2622	−	17.5243i	−0.511389	−	0.795737i
$486$	11.8923	+	19.5429i	0.539447	+	0.886482i
$487$	14.0170	−	30.6929i	0.635170	−	1.39083i	−0.268785	−	0.963200i	$-0.586622\pi$
$487$	14.0170	−	30.6929i	0.635170	−	1.39083i	0.903955	−	0.427628i	$-0.140651\pi$
$488$	1.67342	−	6.89792i	0.0757520	−	0.312254i
$489$	−1.93156	−	0.537624i	−0.0873481	−	0.0243122i
$490$	−22.1662	−	7.67181i	−1.00137	−	0.346577i
$491$	21.2704	+	27.0475i	0.959918	+	1.22063i	0.975330	+	0.220754i	$0.0708517\pi$
$491$	21.2704	+	27.0475i	0.959918	+	1.22063i	−0.0154118	+	0.999881i	$0.504906\pi$
$492$	2.31515	−	0.143104i	0.104375	−	0.00645161i
$493$	−12.5569	+	4.34598i	−0.565534	+	0.195733i
$494$	−3.25236	−	2.09016i	−0.146331	−	0.0940409i
$495$	3.47362	−	8.21285i	0.156128	−	0.369140i
$496$	−1.41742	+	1.63579i	−0.0636439	+	0.0734490i
$497$	6.19261	−	5.90465i	0.277777	−	0.264860i
$498$	−34.2234	−	1.14577i	−1.53359	−	0.0513433i
$499$	−6.72618	+	19.4340i	−0.301105	+	0.869987i	0.688380	+	0.725351i	$0.258322\pi$
$499$	−6.72618	+	19.4340i	−0.301105	+	0.869987i	−0.989485	+	0.144636i	$0.953799\pi$
$500$	0.648318	−	0.910436i	0.0289937	−	0.0407159i
$501$	−4.64662	−	42.3303i	−0.207596	−	1.89118i
$502$	−5.10335	+	3.63408i	−0.227774	+	0.162197i
$503$	−0.408017	+	2.83782i	−0.0181926	+	0.126532i	−0.996894	−	0.0787577i	$-0.974905\pi$
$503$	−0.408017	+	2.83782i	−0.0181926	+	0.126532i	0.978701	+	0.205290i	$0.0658137\pi$
$504$	8.27922	−	1.83980i	0.368786	−	0.0819513i
$505$			18.9425i			0.842930i
$506$	7.71147	−	0.631306i	0.342817	−	0.0280650i
$507$	−7.25193	−	20.0325i	−0.322069	−	0.889674i
$508$	−0.856475	−	0.441543i	−0.0379999	−	0.0195903i
$509$	−9.95331	−	24.8622i	−0.441173	−	1.10200i	−0.967760	−	0.251875i	$-0.918953\pi$
$509$	−9.95331	−	24.8622i	−0.441173	−	1.10200i	0.526587	−	0.850121i	$-0.323471\pi$
$510$	29.0225	−	13.7531i	1.28514	−	0.608999i
$511$	3.47142	+	0.842158i	0.153567	+	0.0372549i
$512$	17.7355	−	8.09951i	0.783804	−	0.357951i
$513$	16.0845	−	3.01337i	0.710147	−	0.133043i
$514$	−2.45436	−	17.0705i	−0.108257	−	0.752945i
$515$	−15.1417	−	15.8801i	−0.667221	−	0.699761i
$516$	3.09767	−	0.490156i	0.136367	−	0.0215779i
$517$	13.8570	+	0.660088i	0.609428	+	0.0290306i
$518$	−3.29375	−	0.156901i	−0.144719	−	0.00689382i
$519$	−9.65701	+	25.1463i	−0.423896	+	1.10380i
$520$	−4.22896	−	4.43520i	−0.185452	−	0.194497i
$521$	−1.89252	−	13.1628i	−0.0829129	−	0.576672i	−0.988351	−	0.152193i	$-0.951366\pi$
$521$	−1.89252	−	13.1628i	−0.0829129	−	0.576672i	0.905438	−	0.424479i	$-0.139543\pi$
$522$	12.3549	+	2.02087i	0.540758	+	0.0884512i
$523$	−36.4077	+	16.6268i	−1.59200	+	0.727041i	−0.997052	−	0.0767259i	$-0.975553\pi$
$523$	−36.4077	+	16.6268i	−1.59200	+	0.727041i	−0.594945	+	0.803767i	$0.702826\pi$
$524$	1.93488	+	0.469396i	0.0845256	+	0.0205057i
$525$	3.43540	+	2.37389i	0.149933	+	0.103605i
$526$	−4.26199	−	10.6459i	−0.185832	−	0.464185i
$527$	2.09862	+	1.08192i	0.0914175	+	0.0471290i
$528$	8.03040	+	1.43033i	0.349478	+	0.0622472i
$529$	14.5865	+	17.7830i	0.634195	+	0.773174i
$530$			32.5218i			1.41266i
$531$	13.2697	+	4.17663i	0.575857	+	0.181250i
$532$	−0.0718790	+	0.499929i	−0.00311635	+	0.0216747i
$533$	−5.93672	+	4.22752i	−0.257148	+	0.183114i
$534$	30.6542	−	22.4883i	1.32653	−	0.973166i
$535$	−3.65213	+	5.12870i	−0.157895	+	0.221733i
$536$	1.22564	−	3.54126i	0.0529397	−	0.152959i
$537$	−13.2372	+	21.2520i	−0.571227	+	0.917090i
$538$	7.47203	−	7.12457i	0.322142	−	0.307162i
$539$	−4.25566	+	4.91129i	−0.183304	+	0.211544i
$540$	−2.15650	−	0.113969i	−0.0928010	−	0.00490446i
$541$	35.7999	+	23.0072i	1.53916	+	0.989158i	0.987947	+	0.154793i	$0.0494711\pi$
$541$	35.7999	+	23.0072i	1.53916	+	0.989158i	0.551213	+	0.834365i	$0.314165\pi$
$542$	−15.1860	+	5.25593i	−0.652295	+	0.225762i
$543$	12.5580	+	18.9465i	0.538916	+	0.813070i
$544$	2.50624	+	3.18695i	0.107454	+	0.136639i
$545$	9.49719	+	3.28701i	0.406815	+	0.140800i
$546$	1.58380	−	1.55347i	0.0677803	−	0.0664824i
$547$	−3.98059	+	16.4082i	−0.170198	+	0.701565i	0.821195	+	0.570647i	$0.193308\pi$
$547$	−3.98059	+	16.4082i	−0.170198	+	0.701565i	−0.991393	+	0.130918i	$0.958208\pi$
$548$	−0.597821	+	1.30905i	−0.0255377	+	0.0559197i
$549$	6.91437	+	3.73554i	0.295098	+	0.159429i
$550$	2.01544	+	3.13609i	0.0859387	+	0.133723i
$551$	4.47758	−	7.75539i	0.190751	−	0.330391i
$552$	9.36240	+	20.4674i	0.398490	+	0.871148i
$553$	−7.98987	−	13.8389i	−0.339764	−	0.588488i
$554$	21.7590	−	42.2066i	0.924452	−	1.79319i
$555$	−9.57626	−	3.16355i	−0.406490	−	0.134285i
$556$	−1.09152	−	1.53282i	−0.0462906	−	0.0650060i
$557$	−0.132902	+	0.0390237i	−0.00563126	+	0.00165349i	−0.284547	−	0.958662i	$-0.591843\pi$
$557$	−0.132902	+	0.0390237i	−0.00563126	+	0.00165349i	0.278916	+	0.960316i	$0.410025\pi$
$558$	−1.25507	−	1.83664i	−0.0531315	−	0.0777513i
$559$	−7.44714	+	6.45298i	−0.314980	+	0.272932i
$560$	−4.49155	+	11.2194i	−0.189803	+	0.474104i
$561$	−0.548941	−	8.88087i	−0.0231763	−	0.374951i
$562$	−4.43337	+	23.0025i	−0.187010	+	0.970301i
$563$	0.0418942	−	0.879468i	0.00176563	−	0.0370652i	−0.997813	−	0.0661063i	$-0.978942\pi$
$563$	0.0418942	−	0.879468i	0.00176563	−	0.0370652i	0.999578	+	0.0290411i	$0.00924538\pi$
$564$	−0.991966	−	3.20980i	−0.0417693	−	0.135157i
$565$	−1.84906	−	5.34252i	−0.0777907	−	0.224761i
$566$	9.50484	+	2.79087i	0.399518	+	0.117309i
$567$	−0.363007	+	9.38337i	−0.0152449	+	0.394065i
$568$	14.5511	+	16.7929i	0.610552	+	0.704614i
$569$	−29.5748	−	2.82406i	−1.23984	−	0.118391i	−0.545546	−	0.838081i	$-0.683678\pi$
$569$	−29.5748	−	2.82406i	−1.23984	−	0.118391i	−0.694296	+	0.719690i	$0.744284\pi$
$570$	−8.71232	+	19.8137i	−0.364919	+	0.829904i
$571$	1.83016	+	19.1663i	0.0765897	+	0.802084i	0.949409	+	0.314041i	$0.101683\pi$
$571$	1.83016	+	19.1663i	0.0765897	+	0.802084i	−0.872820	+	0.488043i	$0.837711\pi$
$572$	0.131222	−	0.0525334i	0.00548667	−	0.00219653i
$573$	−34.7276	−	26.5244i	−1.45077	−	1.10807i
$574$	11.5536	+	6.67048i	0.482238	+	0.278421i
$575$	−4.25728	+	10.2312i	−0.177541	+	0.426670i
$576$	3.72519	+	21.5635i	0.155216	+	0.898479i
$577$	−4.05986	+	2.60911i	−0.169014	+	0.108619i	−0.622413	−	0.782689i	$-0.713848\pi$
$577$	−4.05986	+	2.60911i	−0.169014	+	0.108619i	0.453399	+	0.891308i	$0.350211\pi$
$578$	4.38770	−	5.57941i	0.182504	−	0.232073i
$579$	−18.2916	+	26.4709i	−0.760172	+	1.10009i
$580$	−0.815510	+	0.855282i	−0.0338622	+	0.0355136i
$581$	−11.4495	−	8.15313i	−0.475004	−	0.338249i
$582$	10.0304	+	16.8197i	0.415775	+	0.697198i
$583$	8.36476	+	3.34874i	0.346433	+	0.138691i
$584$	−2.61346	+	8.90062i	−0.108146	+	0.368310i
$585$	5.94063	−	3.27836i	0.245615	−	0.135544i
$586$	0.412484	−	0.641838i	0.0170396	−	0.0265141i
$587$	−10.6253	−	20.6102i	−0.438554	−	0.850676i	−0.999736	−	0.0229833i	$-0.992684\pi$
$587$	−10.6253	−	20.6102i	−0.438554	−	0.850676i	0.561182	−	0.827692i	$-0.310347\pi$
$588$	1.46916	+	0.564207i	0.0605873	+	0.0232675i
$589$	−1.54639	+	0.375150i	−0.0637178	+	0.0154578i
$590$	−14.4636	+	11.3743i	−0.595457	+	0.468272i
$591$	−0.467146	−	33.0508i	−0.0192158	−	1.35953i
$592$	0.876913	−	9.18344i	0.0360409	−	0.377437i
$593$	−5.58492	−	19.0205i	−0.229345	−	0.781077i	−0.991089	−	0.133199i	$-0.957475\pi$
$593$	−5.58492	−	19.0205i	−0.229345	−	0.781077i	0.761744	−	0.647878i	$-0.224343\pi$
$594$	−3.52208	+	7.60734i	−0.144513	+	0.312133i
$595$	13.0488	+	1.87613i	0.534947	+	0.0769138i
$596$	−0.0217455	−	0.456494i	−0.000890730	−	0.0186987i
$597$	2.43178	+	2.04770i	0.0995260	+	0.0838067i
$598$	4.90928	+	3.24959i	0.200755	+	0.132885i
$599$	−31.0663	+	17.9361i	−1.26933	+	0.732851i	−0.974862	−	0.222810i	$-0.928477\pi$
$599$	−31.0663	+	17.9361i	−1.26933	+	0.732851i	−0.294472	+	0.955660i	$0.595144\pi$
$600$	−6.58222	+	8.61790i	−0.268718	+	0.351824i
$601$	12.1964	+	9.59132i	0.497500	+	0.391238i	0.835140	−	0.550037i	$-0.185386\pi$
$601$	12.1964	+	9.59132i	0.497500	+	0.391238i	−0.337640	+	0.941275i	$0.609629\pi$
$602$	16.4078	+	7.49318i	0.668731	+	0.305399i
$603$	3.44642	+	2.31023i	0.140349	+	0.0940798i
$604$	−1.25198	−	2.74145i	−0.0509423	−	0.111548i
$605$	−25.9960	+	5.01031i	−1.05689	+	0.203698i
$606$	0.595860	−	17.7979i	0.0242051	−	0.722991i
$607$	4.89823	+	20.1908i	0.198813	+	0.819519i	0.980607	+	0.195982i	$0.0627895\pi$
$607$	4.89823	+	20.1908i	0.198813	+	0.819519i	−0.781794	+	0.623536i	$0.785695\pi$
$608$	−2.68304	−	0.517113i	−0.108811	−	0.0209717i
$609$	3.76884	+	3.49324i	0.152721	+	0.141553i
$610$	−9.23922	+	4.76315i	−0.374085	+	0.192854i
$611$	7.97755	+	6.91259i	0.322737	+	0.279653i
$612$	−1.97702	+	0.857080i	−0.0799164	+	0.0346454i
$613$	21.8606	−	3.14308i	0.882941	−	0.126948i	0.314095	−	0.949392i	$-0.398299\pi$
$613$	21.8606	−	3.14308i	0.882941	−	0.126948i	0.568846	+	0.822444i	$0.307390\pi$
$614$	5.06797	+	26.2951i	0.204527	+	1.06118i
$615$	28.5718	+	29.1296i	1.15213	+	1.17462i
$616$	2.24928	+	2.14469i	0.0906262	+	0.0864119i
$617$	−30.2369	+	2.88727i	−1.21729	+	0.116237i	−0.683864	−	0.729609i	$-0.739702\pi$
$617$	−30.2369	+	2.88727i	−1.21729	+	0.116237i	−0.533426	+	0.845846i	$0.679096\pi$
$618$	13.7272	+	15.3969i	0.552190	+	0.619353i
$619$	6.61605	−	0.315161i	0.265922	−	0.0126674i	0.0858023	−	0.996312i	$-0.472655\pi$
$619$	6.61605	−	0.315161i	0.265922	−	0.0126674i	0.180119	+	0.983645i	$0.442352\pi$
$620$	0.209988			0.00843331
$621$	−24.5535	+	4.25734i	−0.985299	+	0.170841i
$622$	−8.48657			−0.340281
$623$	15.5880	−	0.742546i	0.624518	−	0.0297495i
$624$	4.13032	+	4.63269i	0.165345	+	0.185456i
$625$	31.0728	−	2.96709i	1.24291	−	0.118684i
$626$	−34.7740	−	33.1569i	−1.38985	−	1.32522i
$627$	4.19907	+	4.28104i	0.167695	+	0.170968i
$628$	−0.446972	−	2.31911i	−0.0178361	−	0.0925427i
$629$	−9.96089	+	1.43216i	−0.397167	+	0.0571040i
$630$	−9.97616	−	7.39876i	−0.397460	−	0.294774i
$631$	26.1918	+	22.6953i	1.04268	+	0.903486i	0.995439	−	0.0953975i	$-0.0304122\pi$
$631$	26.1918	+	22.6953i	1.04268	+	0.903486i	0.0472393	+	0.998884i	$0.484958\pi$
$632$	36.8845	−	19.0153i	1.46719	−	0.756387i
$633$	−17.2035	−	15.9455i	−0.683779	−	0.633776i
$634$	12.8261	+	2.47203i	0.509391	+	0.0981770i
$635$	−3.99618	−	16.4725i	−0.158584	−	0.653691i
$636$	0.0730113	−	2.18080i	0.00289508	−	0.0864742i
$637$	−4.85545	+	0.935812i	−0.192380	+	0.0370782i
$638$	1.90574	+	4.17298i	0.0754488	+	0.165210i
$639$	−22.0812	+	10.8486i	−0.873520	+	0.429162i
$640$	−30.5960	−	13.9727i	−1.20941	−	0.552321i
$641$	−15.4386	−	12.1410i	−0.609787	−	0.479542i	0.264870	−	0.964284i	$-0.414671\pi$
$641$	−15.4386	−	12.1410i	−0.609787	−	0.479542i	−0.874657	+	0.484742i	$0.838913\pi$
$642$	3.59278	−	4.70392i	0.141796	−	0.185649i
$643$	41.5551	−	23.9919i	1.63878	−	0.946147i	0.657519	−	0.753438i	$-0.271606\pi$
$643$	41.5551	−	23.9919i	1.63878	−	0.946147i	0.981256	−	0.192710i	$-0.0617275\pi$
$644$	0.119738	−	0.759752i	0.00471834	−	0.0299384i
$645$	42.1997	+	35.5346i	1.66161	+	1.39917i
$646$	1.02765	+	21.5730i	0.0404322	+	0.848777i
$647$	−29.8180	−	4.28718i	−1.17227	−	0.168547i	−0.471454	−	0.881891i	$-0.656271\pi$
$647$	−29.8180	−	4.28718i	−1.17227	−	0.168547i	−0.700814	+	0.713344i	$0.747180\pi$
$648$	−24.2951	−	2.10107i	−0.954401	−	0.0825380i
$649$	1.43622	+	4.89130i	0.0563764	+	0.192000i
$650$	−0.269633	+	2.82372i	−0.0105759	+	0.110756i
$651$	−0.0129047	−	0.913017i	−0.000505776	−	0.0357840i
$652$	−0.139861	+	0.109988i	−0.00547738	+	0.00430746i
$653$	−25.3745	+	6.15579i	−0.992981	+	0.240895i	−0.699159	−	0.714966i	$-0.746442\pi$
$653$	−25.3745	+	6.15579i	−0.992981	+	0.240895i	−0.293821	+	0.955860i	$0.594927\pi$
$654$	−8.81994	−	3.38714i	−0.344887	−	0.132448i
$655$	16.0485	+	31.1298i	0.627069	+	1.21634i
$656$	−20.1785	+	31.3984i	−0.787839	+	1.22590i
$657$	−8.79386	−	5.30641i	−0.343081	−	0.207023i
$658$	5.44379	−	18.5398i	0.212221	−	0.722758i
$659$	23.5592	+	9.43170i	0.917738	+	0.367407i	0.781957	−	0.623332i	$-0.214222\pi$
$659$	23.5592	+	9.43170i	0.917738	+	0.367407i	0.135780	+	0.990739i	$0.456646\pi$
$660$	−0.405317	−	0.679662i	−0.0157769	−	0.0264558i
$661$	−22.3318	−	15.9024i	−0.868605	−	0.618531i	0.0564325	−	0.998406i	$-0.482027\pi$
$661$	−22.3318	−	15.9024i	−0.868605	−	0.618531i	−0.925038	+	0.379876i	$0.875967\pi$
$662$	9.08119	−	9.52408i	0.352951	−	0.370164i
$663$	3.84889	−	5.56997i	0.149479	−	0.216320i
$664$	22.5635	−	28.6918i	0.875634	−	1.11346i
$665$	−7.47416	+	4.80335i	−0.289836	+	0.186266i
$666$	8.89811	+	3.27363i	0.344795	+	0.126850i
$667$	−6.97753	+	11.7168i	−0.270171	+	0.453677i
$668$	−3.27278	−	1.88954i	−0.126628	−	0.0731085i
$669$	−25.7536	−	19.6702i	−0.995691	−	0.760494i
$670$	−5.09477	+	2.03964i	−0.196828	+	0.0787980i
$671$	0.273749	+	2.86683i	0.0105680	+	0.110673i
$672$	0.631128	−	1.43532i	0.0243463	−	0.0553687i
$673$	−17.8823	−	1.70755i	−0.689310	−	0.0658212i	−0.255478	−	0.966815i	$-0.582233\pi$
$673$	−17.8823	−	1.70755i	−0.689310	−	0.0658212i	−0.433832	+	0.900994i	$0.642839\pi$
$674$	−7.51662	−	8.67464i	−0.289529	−	0.334135i
$675$	−7.37280	−	9.47628i	−0.283779	−	0.364742i
$676$	−1.81406	−	0.532656i	−0.0697715	−	0.0204868i
$677$	−7.46630	−	21.5724i	−0.286953	−	0.829096i	−0.992698	−	0.120630i	$-0.961509\pi$
$677$	−7.46630	−	21.5724i	−0.286953	−	0.829096i	0.705745	−	0.708466i	$-0.250613\pi$
$678$	1.56928	+	5.07787i	0.0602679	+	0.195014i
$679$	−0.382488	+	8.02941i	−0.0146785	+	0.308141i
$680$	−6.47894	+	33.6159i	−0.248456	+	1.28911i
$681$	2.41244	+	39.0289i	0.0924450	+	1.49559i
$682$	0.302965	−	0.756771i	0.0116011	−	0.0289782i
$683$	7.05211	−	6.11069i	0.269842	−	0.233819i	−0.509420	−	0.860518i	$-0.670140\pi$
$683$	7.05211	−	6.11069i	0.269842	−	0.233819i	0.779261	+	0.626699i	$0.215594\pi$
$684$	0.628698	−	1.30908i	0.0240389	−	0.0500537i
$685$	−24.2893	+	7.13198i	−0.928046	+	0.272499i
$686$	11.4677	+	16.1042i	0.437840	+	0.614860i
$687$	33.4320	+	11.0444i	1.27551	+	0.421369i
$688$	−23.1237	+	44.8538i	−0.881583	+	1.71003i
$689$	3.42796	+	5.93739i	0.130595	+	0.226197i
$690$	13.6739	−	29.9906i	0.520555	−	1.14172i
$691$	−6.97069	+	12.0736i	−0.265178	+	0.459301i	−0.967610	−	0.252449i	$-0.918764\pi$
$691$	−6.97069	+	12.0736i	−0.265178	+	0.459301i	0.702433	+	0.711750i	$0.252097\pi$
$692$	1.29238	+	2.01098i	0.0491290	+	0.0764461i
$693$	−2.93023	+	1.80407i	−0.111310	+	0.0685309i
$694$	−15.7290	+	34.4417i	−0.597065	+	1.30739i
$695$	7.80389	−	32.1681i	0.296018	−	1.22020i
$696$	−9.52696	+	9.34453i	−0.361119	+	0.354203i
$697$	38.4749	+	13.3163i	1.45734	+	0.504391i
$698$	6.19986	+	7.88376i	0.234668	+	0.298405i
$699$	−16.1909	−	24.4274i	−0.612396	−	0.923930i
$700$	0.350192	−	0.121202i	0.0132360	−	0.00458102i
$701$	1.40337	+	0.901892i	0.0530046	+	0.0340640i	0.566875	−	0.823804i	$-0.308152\pi$
$701$	1.40337	+	0.901892i	0.0530046	+	0.0340640i	−0.513870	+	0.857868i	$0.671789\pi$
$702$	−5.68481	+	2.89340i	−0.214559	+	0.109204i
$703$	4.44133	−	5.12557i	0.167508	−	0.193315i
$704$	−5.80354	+	5.53366i	−0.218729	+	0.208558i
$705$	31.2447	−	50.1625i	1.17674	−	1.88923i
$706$	1.19400	−	3.44985i	0.0449369	−	0.129837i
$707$	4.24004	−	5.95431i	0.159463	−	0.223935i
$708$	0.995412	−	0.730249i	0.0374099	−	0.0274444i
$709$	24.7915	−	17.6539i	0.931064	−	0.663008i	−0.0104627	−	0.999945i	$-0.503330\pi$
$709$	24.7915	−	17.6539i	0.931064	−	0.663008i	0.941527	+	0.336937i	$0.109391\pi$
$710$	4.63101	−	32.2094i	0.173799	−	1.20880i
$711$	9.96701	+	44.8521i	0.373792	+	1.68209i
$712$			40.5261i			1.51878i
$713$	2.36237	−	0.539405i	0.0884716	−	0.0202009i
$714$	−12.2013	−	2.17323i	−0.456622	−	0.0813312i
$715$	2.21000	+	1.13933i	0.0826493	+	0.0426087i
$716$	0.825794	+	2.06273i	0.0308614	+	0.0770879i
$717$	−10.9427	−	7.56150i	−0.408663	−	0.282390i
$718$	25.7571	+	6.24860i	0.961246	+	0.233196i
$719$	−7.80894	+	3.56623i	−0.291224	+	0.132998i	−0.555670	−	0.831403i	$-0.687538\pi$
$719$	−7.80894	+	3.56623i	−0.291224	+	0.132998i	0.264446	+	0.964401i	$0.414811\pi$
$720$	22.0037	−	26.8933i	0.820030	−	1.00225i
$721$	1.20500	+	8.38096i	0.0448766	+	0.312123i
$722$	9.19740	+	9.64595i	0.342292	+	0.358985i
$723$	−16.8616	+	43.9068i	−0.627090	+	1.63291i
$724$	2.01488	+	0.0959806i	0.0748825	+	0.00356709i
$725$	−6.56300	−	0.312634i	−0.243744	−	0.0116109i
$726$	24.5828	−	3.88984i	0.912354	−	0.144365i
$727$	−11.3567	−	11.9106i	−0.421197	−	0.441738i	0.478610	−	0.878028i	$-0.341141\pi$
$727$	−11.3567	−	11.9106i	−0.421197	−	0.441738i	−0.899806	+	0.436289i	$0.856292\pi$
$728$	0.336548	+	2.34074i	0.0124733	+	0.0867537i
$729$	9.09572	−	25.4218i	0.336879	−	0.941548i
$730$	12.3573	−	5.64337i	0.457363	−	0.208870i
$731$	53.4964	+	12.9781i	1.97863	+	0.480012i
$732$	0.630242	−	0.298658i	0.0232944	−	0.0110387i
$733$	−15.8788	−	39.6634i	−0.586497	−	1.46500i	−0.863609	−	0.504162i	$-0.831802\pi$
$733$	−15.8788	−	39.6634i	−0.586497	−	1.46500i	0.277112	−	0.960838i	$-0.410623\pi$
$734$	18.6348	+	9.60690i	0.687822	+	0.354597i
$735$	9.42334	+	26.0307i	0.347585	+	0.960157i
$736$	4.07476	+	0.842618i	0.150198	+	0.0310593i
$737$			1.52042i			0.0560052i
$738$	−25.9291	−	28.2683i	−0.954463	−	1.04057i
$739$	2.37514	−	16.5195i	0.0873711	−	0.607679i	−0.898348	−	0.439284i	$-0.855232\pi$
$739$	2.37514	−	16.5195i	0.0873711	−	0.607679i	0.985719	−	0.168396i	$-0.0538586\pi$
$740$	−0.729043	+	0.519149i	−0.0268002	+	0.0190843i
$741$	0.497880	+	4.53563i	0.0182901	+	0.166621i
$742$	7.27961	−	10.2228i	0.267243	−	0.375290i
$743$	4.97807	−	14.3832i	0.182628	−	0.527668i	−0.816110	−	0.577896i	$-0.803874\pi$
$743$	4.97807	−	14.3832i	0.182628	−	0.527668i	0.998738	+	0.0502287i	$0.0159950\pi$
$744$	2.36991	+	0.0793426i	0.0868851	+	0.00290884i
$745$	5.81822	−	5.54766i	0.213163	−	0.203250i
$746$	−10.1375	+	11.6993i	−0.371161	+	0.428343i
$747$	24.3636	+	32.2447i	0.891417	+	1.17977i
$748$	−0.664270	−	0.426900i	−0.0242881	−	0.0156090i
$749$	2.29599	−	0.794650i	0.0838937	−	0.0290359i
$750$	−18.4480	+	1.14030i	−0.673625	+	0.0416379i
$751$	−5.76826	−	7.33494i	−0.210487	−	0.267656i	0.669334	−	0.742962i	$-0.266580\pi$
$751$	−5.76826	−	7.33494i	−0.210487	−	0.267656i	−0.879820	+	0.475306i	$0.842337\pi$
$752$	51.0846	+	17.6805i	1.86286	+	0.644743i
$753$	7.12342	+	1.98271i	0.259592	+	0.0722541i
$754$	−0.822964	+	3.39230i	−0.0299706	+	0.123540i
$755$	22.0232	−	48.2241i	0.801507	−	1.75505i
$756$	0.652355	+	0.518531i	0.0237259	+	0.0188588i
$757$	−25.6627	−	39.9320i	−0.932727	−	1.45135i	−0.891924	−	0.452185i	$-0.850645\pi$
$757$	−25.6627	−	39.9320i	−0.932727	−	1.45135i	−0.0408031	−	0.999167i	$-0.512992\pi$
$758$	2.29483	−	3.97475i	0.0833518	−	0.144370i
$759$	−6.30572	−	6.60508i	−0.228883	−	0.239749i
$760$	−11.5361	−	19.9811i	−0.418458	−	0.724790i
$761$	11.7890	−	22.8674i	0.427349	−	0.828942i	−0.572609	−	0.819829i	$-0.694069\pi$
$761$	11.7890	−	22.8674i	0.427349	−	0.828942i	0.999958	−	0.00911356i	$-0.00290098\pi$
$762$	3.23656	+	15.6029i	0.117248	+	0.565232i
$763$	−2.24955	−	3.15906i	−0.0814393	−	0.114365i
$764$	−3.72085	+	1.09254i	−0.134616	+	0.0395267i
$765$	−34.1684	−	16.4098i	−1.23536	−	0.593297i
$766$	10.3821	−	8.99617i	0.375122	−	0.325045i
$767$	−1.44166	+	3.60110i	−0.0520554	+	0.130028i
$768$	5.68710	+	2.83089i	0.205216	+	0.102151i
$769$	−0.183527	+	0.952229i	−0.00661815	+	0.0343382i	−0.985088	−	0.172053i	$-0.944960\pi$
$769$	−0.183527	+	0.952229i	−0.00661815	+	0.0343382i	0.978470	+	0.206391i	$0.0661720\pi$
$770$	0.216563	−	4.54623i	0.00780440	−	0.163835i
$771$	−13.8365	+	14.9281i	−0.498308	+	0.537623i
$772$	0.933906	+	2.69834i	0.0336120	+	0.0971155i
$773$	−12.8080	−	3.76076i	−0.460671	−	0.135265i	0.0431586	−	0.999068i	$-0.486258\pi$
$773$	−12.8080	−	3.76076i	−0.460671	−	0.135265i	−0.503830	+	0.863803i	$0.668076\pi$
$774$	−38.5321	−	34.7149i	−1.38501	−	1.24780i
$775$	0.764552	+	0.882340i	0.0274635	+	0.0316946i
$776$	−20.7806	−	1.98431i	−0.745980	−	0.0712324i
$777$	2.30204	+	3.13794i	0.0825853	+	0.112573i
$778$	−0.955613	−	10.0076i	−0.0342604	−	0.358791i
$779$	−25.4735	+	10.1981i	−0.912684	+	0.365383i
$780$	0.0772614	−	0.597161i	0.00276640	−	0.0213818i
$781$	−7.80755	−	4.50769i	−0.279376	−	0.161298i
$782$	−1.12077	−	32.8699i	−0.0400785	−	1.17542i
$783$	−7.32105	−	12.8341i	−0.261633	−	0.458654i
$784$	−21.3031	+	13.6907i	−0.760825	+	0.488952i
$785$	25.6818	−	32.6571i	0.916624	−	1.16558i
$786$	−14.0996	−	29.7537i	−0.502916	−	1.06128i
$787$	−16.0757	+	16.8598i	−0.573038	+	0.600985i	−0.944923	−	0.327294i	$-0.893863\pi$
$787$	−16.0757	+	16.8598i	−0.573038	+	0.600985i	0.371884	+	0.928279i	$0.378712\pi$
$788$	−2.38941	−	1.70149i	−0.0851193	−	0.0606132i
$789$	−6.60075	+	11.8154i	−0.234993	+	0.420639i
$790$	−56.4184	−	22.5865i	−2.00728	−	0.803592i
$791$	−0.614629	+	2.09324i	−0.0218537	+	0.0744269i
$792$	−4.31758	−	7.82377i	−0.153418	−	0.278006i
$793$	−1.18471	+	1.84345i	−0.0420704	+	0.0654628i
$794$	9.76333	+	18.9382i	0.346487	+	0.672092i
$795$	29.8330	−	24.1510i	1.05807	−	0.856548i
$796$	0.274169	−	0.0665127i	0.00971767	−	0.00235748i
$797$	37.6806	−	29.6323i	1.33471	−	1.04963i	0.340724	−	0.940163i	$-0.389328\pi$
$797$	37.6806	−	29.6323i	1.33471	−	1.04963i	0.993990	−	0.109468i	$-0.0349147\pi$
$798$	7.17364	−	4.27801i	0.253944	−	0.151440i
$799$	5.60534	−	58.7018i	0.198303	−	2.07672i
$800$	0.564814	+	1.92358i	0.0199692	+	0.0680088i
$801$	−43.3931	−	11.4197i	−1.53322	−	0.403494i
$802$	−28.3540	−	4.07669i	−1.00121	−	0.143953i
$803$	−0.179084	−	3.75943i	−0.00631973	−	0.132668i
$804$	0.346216	−	0.125333i	0.0122101	−	0.00442015i
$805$	11.4796	−	7.16013i	0.404603	−	0.252361i
$806$	0.537164	−	0.310132i	0.0189208	−	0.0109239i
$807$	−12.0843	−	1.56348i	−0.425388	−	0.0550372i
$808$	14.9212	+	11.7342i	0.524927	+	0.412807i
$809$	−24.2648	−	11.0814i	−0.853106	−	0.389600i	−0.0596437	−	0.998220i	$-0.518996\pi$
$809$	−24.2648	−	11.0814i	−0.853106	−	0.389600i	−0.793462	+	0.608619i	$0.791724\pi$
$810$	20.9740	+	28.9039i	0.736952	+	1.01558i
$811$	−19.8777	−	43.5261i	−0.698000	−	1.52841i	−0.842379	−	0.538885i	$-0.818846\pi$
$811$	−19.8777	−	43.5261i	−0.698000	−	1.52841i	0.144379	−	0.989522i	$-0.453881\pi$
$812$	0.447788	−	0.0863041i	0.0157143	−	0.00302868i
$813$	16.0987	+	10.0274i	0.564605	+	0.351675i
$814$	0.819106	+	3.37640i	0.0287097	+	0.118343i
$815$	−3.07333	−	0.592335i	−0.107654	−	0.0207486i
$816$	7.69727	−	33.8070i	0.269458	−	1.18348i
$817$	−32.9752	+	16.9999i	−1.15365	+	0.594750i
$818$	23.9871	+	20.7849i	0.838688	+	0.726727i
$819$	−2.60118	−	0.299231i	−0.0908924	−	0.0104560i
$820$	3.58412	−	0.515319i	0.125163	−	0.0179957i
$821$	−1.18172	−	6.13133i	−0.0412422	−	0.213985i	0.955461	−	0.295117i	$-0.0953586\pi$
$821$	−1.18172	−	6.13133i	−0.0412422	−	0.213985i	−0.996703	+	0.0811320i	$0.974146\pi$
$822$	23.0460	−	5.93699i	0.803821	−	0.207076i
$823$	24.8978	+	23.7400i	0.867884	+	0.827526i	0.986218	−	0.165448i	$-0.0529071\pi$
$823$	24.8978	+	23.7400i	0.867884	+	0.827526i	−0.118335	+	0.992974i	$0.537756\pi$
$824$	−21.8886	+	2.09011i	−0.762527	+	0.0728125i
$825$	1.38011	−	4.17769i	0.0480494	−	0.145449i
$826$	7.09242	−	0.337854i	0.246777	−	0.0117554i
$827$	−6.97282			−0.242469			−0.121234	−	0.992624i	$-0.538685\pi$
$827$	−6.97282			−0.242469			−0.121234	+	0.992624i	$0.538685\pi$
$828$	−0.984249	+	1.98036i	−0.0342050	+	0.0688223i
$829$	34.2211			1.18855			0.594274	−	0.804263i	$-0.297440\pi$
$829$	34.2211			1.18855			0.594274	+	0.804263i	$0.297440\pi$
$830$	−53.3940	+	2.54347i	−1.85333	+	0.0882851i
$831$	−54.8755	+	11.3830i	−1.90361	+	0.394872i
$832$	−6.07400	+	0.579996i	−0.210578	+	0.0201078i
$833$	19.9922	+	19.0625i	0.692687	+	0.660476i
$834$	−8.34424	+	29.9789i	−0.288937	+	1.03808i
$835$	−12.5808	−	65.2754i	−0.435377	−	2.25895i
$836$	0.526742	−	0.0757340i	0.0182177	−	0.00261932i
$837$	−0.752762	+	2.51521i	−0.0260193	+	0.0869385i
$838$	−30.9211	−	26.7932i	−1.06815	−	0.925557i
$839$	−10.7840	+	5.55953i	−0.372304	+	0.191936i	−0.634216	−	0.773156i	$-0.718677\pi$
$839$	−10.7840	+	5.55953i	−0.372304	+	0.191936i	0.261912	+	0.965092i	$0.415647\pi$
$840$	12.6493	−	3.90918i	0.436442	−	0.134880i
$841$	20.5364	+	3.95807i	0.708152	+	0.136485i
$842$	0.170997	+	0.704861i	0.00589296	+	0.0242911i
$843$	24.3929	−	13.0150i	0.840137	−	0.448262i
$844$	−2.04401	+	0.393950i	−0.0703576	+	0.0135603i
$845$	−13.8158	−	30.2524i	−0.475278	−	1.04071i
$846$	−30.9347	+	46.1487i	−1.06356	+	1.58663i
$847$	9.29297	+	4.24396i	0.319310	+	0.145824i
$848$	27.5983	+	21.7036i	0.947731	+	0.745304i
$849$	−4.49826	−	10.7915i	−0.154380	−	0.370364i
$850$	13.7232	−	7.92308i	0.470701	−	0.271759i
$851$	−6.86822	+	7.71319i	−0.235439	+	0.264405i
$852$	−0.382849	+	2.14945i	−0.0131162	+	0.0736389i
$853$	1.32821	+	27.8827i	0.0454772	+	0.954684i	0.900167	+	0.435545i	$0.143444\pi$
$853$	1.32821	+	27.8827i	0.0454772	+	0.954684i	−0.854690	+	0.519139i	$0.826253\pi$
$854$	3.97039	+	0.570856i	0.135864	+	0.0195343i
$855$	24.6454	−	6.72183i	0.842854	−	0.229882i
$856$	1.77757	+	6.05386i	0.0607562	+	0.206917i
$857$	−0.339055	+	3.55075i	−0.0115819	+	0.121291i	−0.999414	−	0.0342339i	$-0.989101\pi$
$857$	−0.339055	+	3.55075i	−0.0115819	+	0.121291i	0.987832	+	0.155525i	$0.0497069\pi$
$858$	−2.04062	−	1.14001i	−0.0696658	−	0.0389193i
$859$	28.4519	−	22.3748i	0.970766	−	0.763419i	−0.000845921	−	1.00000i	$-0.500269\pi$
$859$	28.4519	−	22.3748i	0.970766	−	0.763419i	0.971612	+	0.236581i	$0.0760268\pi$
$860$	4.75778	−	1.15423i	0.162239	−	0.0393588i
$861$	−2.46085	−	15.5519i	−0.0838654	−	0.530009i
$862$	−8.74734	−	16.9675i	−0.297936	−	0.577915i
$863$	−7.97847	+	12.4147i	−0.271590	+	0.422603i	−0.950080	−	0.312008i	$-0.898999\pi$
$863$	−7.97847	+	12.4147i	−0.271590	+	0.422603i	0.678489	+	0.734610i	$0.262635\pi$
$864$	−2.96998	+	3.39174i	−0.101041	+	0.115389i
$865$	−11.8468	+	40.3466i	−0.402805	+	1.37183i
$866$	−33.2298	−	13.3032i	−1.12920	−	0.452062i
$867$	−8.37645	+	0.118394i	−0.284479	+	0.00402088i
$868$	−0.0660067	−	0.0470032i	−0.00224041	−	0.00159539i
$869$	−11.6187	+	12.1853i	−0.394138	+	0.413360i
$870$	19.4787	+	1.58254i	0.660391	+	0.0536532i
$871$	−0.715146	+	0.909382i	−0.0242318	+	0.0308132i
$872$	8.47238	−	5.44487i	0.286911	−	0.184386i
$873$	7.98036	−	21.6916i	0.270094	−	0.734149i
$874$	15.0776	+	16.2470i	0.510007	+	0.549564i
$875$	−6.57044	−	3.79345i	−0.222121	−	0.128242i
$876$	−0.841302	+	0.350682i	−0.0284250	+	0.0118484i
$877$	−15.0711	+	6.03356i	−0.508915	+	0.203739i	−0.611887	−	0.790945i	$-0.709589\pi$
$877$	−15.0711	+	6.03356i	−0.508915	+	0.203739i	0.102971	+	0.994684i	$0.467165\pi$
$878$	−0.851357	−	8.91581i	−0.0287319	−	0.300894i
$879$	−0.895086	+	0.0982542i	−0.0301905	+	0.00331403i
$880$	12.6755	+	1.21037i	0.427292	+	0.0408014i
$881$	32.0624	+	37.0020i	1.08021	+	1.24663i	0.967465	+	0.253006i	$0.0814191\pi$
$881$	32.0624	+	37.0020i	1.08021	+	1.24663i	0.112746	+	0.993624i	$0.464035\pi$
$882$	−8.03512	−	24.7543i	−0.270557	−	0.833520i
$883$	−1.17065	−	0.343734i	−0.0393955	−	0.0115676i	0.261975	−	0.965075i	$-0.415626\pi$
$883$	−1.17065	−	0.343734i	−0.0393955	−	0.0115676i	−0.301371	+	0.953507i	$0.597444\pi$
$884$	−0.196511	−	0.567782i	−0.00660939	−	0.0190966i
$885$	21.1747	+	4.82110i	0.711779	+	0.162060i
$886$	−0.394170	+	8.27464i	−0.0132424	+	0.277992i
$887$	−8.49931	+	44.0986i	−0.285379	+	1.48069i	0.502350	+	0.864665i	$0.332469\pi$
$887$	−8.49931	+	44.0986i	−0.285379	+	1.48069i	−0.787729	+	0.616022i	$0.788743\pi$
$888$	−8.42410	+	5.58363i	−0.282694	+	0.187374i
$889$	−2.43102	+	6.07239i	−0.0815338	+	0.203661i
$890$	44.8529	−	38.8652i	1.50347	−	1.30277i
$891$	9.59390	−	2.41840i	0.321408	−	0.0810195i
$892$	−2.75934	+	0.810214i	−0.0923894	+	0.0271280i
$893$	23.0524	+	32.3726i	0.771420	+	1.08331i
$894$	−5.64117	+	5.02943i	−0.188669	+	0.168209i
$895$	−17.9096	+	34.7399i	−0.598653	+	1.16123i
$896$	6.48980	+	11.2407i	0.216809	+	0.375524i
$897$	−0.664759	−	6.91656i	−0.0221957	−	0.230937i
$898$	15.8899	−	27.5221i	0.530252	−	0.918424i
$899$	0.776759	+	1.20866i	0.0259064	+	0.0403111i
$900$	−1.06507	+	0.0301139i	−0.0355025	+	0.00100380i
$901$	15.9103	−	34.8387i	0.530049	−	1.16064i
$902$	3.31394	−	13.6602i	0.110342	−	0.454836i
$903$	−5.31091	−	20.6157i	−0.176736	−	0.686048i
$904$	−5.35379	−	1.85296i	−0.178064	−	0.0616287i
$905$	21.9344	+	27.8918i	0.729124	+	0.927156i
$906$	−22.2094	+	44.6175i	−0.737859	+	1.48232i
$907$	−40.0070	+	13.8465i	−1.32841	+	0.459767i	−0.896857	−	0.442321i	$-0.854155\pi$
$907$	−40.0070	+	13.8465i	−1.32841	+	0.459767i	−0.431553	+	0.902088i	$0.642034\pi$
$908$	2.91928	+	1.87611i	0.0968797	+	0.0622608i
$909$	−16.7689	+	12.6703i	−0.556190	+	0.420248i
$910$	2.26790	−	2.61730i	0.0751802	−	0.0867626i
$911$	−0.143846	+	0.137157i	−0.00476582	+	0.00454420i	−0.692458	−	0.721458i	$-0.743472\pi$
$911$	−0.143846	+	0.137157i	−0.00476582	+	0.00454420i	0.687692	+	0.726002i	$0.258624\pi$
$912$	10.9999	+	20.6161i	0.364243	+	0.682667i
$913$	−4.84374	+	13.9951i	−0.160304	+	0.463169i
$914$	−16.8516	+	23.6647i	−0.557400	+	0.782759i
$915$	11.2305	+	4.93818i	0.371268	+	0.163251i
$916$	2.54519	−	1.81242i	0.0840955	−	0.0598841i
$917$	1.92339	−	13.3775i	0.0635161	−	0.441764i
$918$	31.5877	+	16.4931i	1.04255	+	0.544352i
$919$		−	13.8209i		−	0.455910i	−0.973672	−	0.227955i	$-0.926796\pi$
$919$		−	13.8209i		−	0.455910i	0.973672	−	0.227955i	$-0.0732039\pi$
$920$	17.1545	+	30.6622i	0.565567	+	1.01090i
$921$	20.3575	−	24.1759i	0.670804	−	0.796625i
$922$	41.1158	+	21.1967i	1.35408	+	0.698075i
$923$	−2.54956	−	6.36849i	−0.0839197	−	0.209621i
$924$	−0.0247282	+	0.304367i	−0.000813498	+	0.0100130i
$925$	−4.83580	−	1.17315i	−0.159000	−	0.0385730i
$926$	19.9914	−	9.12978i	0.656959	−	0.300023i
$927$	3.92993	−	24.0261i	0.129076	−	0.789122i
$928$	0.351105	+	2.44199i	0.0115256	+	0.0801623i
$929$	14.5567	+	15.2666i	0.477590	+	0.500882i	0.917817	−	0.397005i	$-0.129950\pi$
$929$	14.5567	+	15.2666i	0.477590	+	0.500882i	−0.440226	+	0.897887i	$0.645102\pi$
$930$	−2.18497	−	2.69903i	−0.0716481	−	0.0885046i
$931$	−18.5957	−	0.885821i	−0.609448	−	0.0290316i
$932$	−2.59776	−	0.123747i	−0.0850925	−	0.00405345i
$933$	6.30221	+	7.78491i	0.206325	+	0.254867i
$934$	−23.7025	−	24.8585i	−0.775570	−	0.813395i
$935$	−1.97675	−	13.7486i	−0.0646466	−	0.449627i
$936$	1.09760	−	6.71033i	0.0358762	−	0.219334i
$937$	−7.22931	+	3.30152i	−0.236171	+	0.107856i	−0.529985	−	0.848007i	$-0.677803\pi$
$937$	−7.22931	+	3.30152i	−0.236171	+	0.107856i	0.293814	+	0.955863i	$0.405075\pi$
$938$	2.05802	+	0.499269i	0.0671966	+	0.0163017i
$939$	−4.59207	+	56.5215i	−0.149857	+	1.84451i
$940$	−1.94918	−	4.86881i	−0.0635752	−	0.158803i
$941$	−0.0197931	−	0.0102041i	−0.000645237	−	0.000332643i	0.457904	−	0.889002i	$-0.348600\pi$
$941$	−0.0197931	−	0.0102041i	−0.000645237	−	0.000332643i	−0.458549	+	0.888669i	$0.651631\pi$
$942$	−25.1573	+	29.8760i	−0.819670	+	0.973413i
$943$	38.9979	−	15.0041i	1.26995	−	0.488600i
$944$			19.8646i			0.646539i
$945$	0.621346	+	14.6457i	0.0202124	+	0.476426i
$946$	2.70472	−	18.8118i	0.0879382	−	0.611624i
$947$	−2.49018	+	1.77325i	−0.0809198	+	0.0576227i	−0.619801	−	0.784759i	$-0.712787\pi$
$947$	−2.49018	+	1.77325i	−0.0809198	+	0.0576227i	0.538881	+	0.842382i	$0.318847\pi$
$948$	3.73251	+	1.64123i	0.121226	+	0.0533047i
$949$	1.66118	−	2.33280i	0.0539242	−	0.0757260i
$950$	−3.49289	+	10.0920i	−0.113324	+	0.327429i
$951$	−7.25715	−	13.6014i	−0.235329	−	0.441057i
$952$	9.56108	−	9.11647i	0.309876	−	0.295466i
$953$	29.2523	−	33.7589i	0.947575	−	1.09356i	−0.0479305	−	0.998851i	$-0.515263\pi$
$953$	29.2523	−	33.7589i	0.947575	−	1.09356i	0.995505	−	0.0947087i	$-0.0301920\pi$
$954$	−28.7901	+	21.7533i	−0.932112	+	0.704289i
$955$	−57.3866	−	36.8801i	−1.85699	−	1.19341i
$956$	−1.11546	+	0.386065i	−0.0360766	+	0.0124862i
$957$	2.41275	−	4.84707i	0.0779930	−	0.156683i
$958$	−5.62924	−	7.15816i	−0.181872	−	0.231270i
$959$	9.23140	+	3.19502i	0.298098	+	0.103173i
$960$	8.52198	+	33.0803i	0.275046	+	1.06766i
$961$	−7.24834	+	29.8781i	−0.233817	+	0.963808i
$962$	−1.09821	+	2.40475i	−0.0354078	+	0.0775322i
$963$	−6.98304	+	0.197438i	−0.225025	+	0.00636236i
$964$	2.25656	+	3.51128i	0.0726789	+	0.113091i
$965$	−25.1142	+	43.4990i	−0.808454	+	1.40028i
$966$	−11.0112	+	6.36639i	−0.354280	+	0.204835i
$967$	−13.6653	−	23.6690i	−0.439447	−	0.761144i	0.558200	−	0.829706i	$-0.311492\pi$
$967$	−13.6653	−	23.6690i	−0.439447	−	0.761144i	−0.997647	+	0.0685623i	$0.978159\pi$
$968$	−12.1569	+	23.5810i	−0.390736	+	0.757923i
$969$	19.0262	−	16.9630i	0.611210	−	0.544929i
$970$	17.7328	+	24.9022i	0.569366	+	0.799563i
$971$	−29.7050	+	8.72218i	−0.953280	+	0.279908i	−0.721152	−	0.692777i	$-0.756387\pi$
$971$	−29.7050	+	8.72218i	−0.953280	+	0.279908i	−0.232128	+	0.972685i	$0.574569\pi$
$972$	−1.34155	−	1.98528i	−0.0430304	−	0.0636779i
$973$	−9.65347	+	8.36478i	−0.309476	+	0.268163i
$974$	−18.4041	+	45.9712i	−0.589705	+	1.47301i
$975$	2.79049	−	1.84958i	0.0893673	−	0.0592341i
$976$	−2.12378	+	11.0192i	−0.0679804	+	0.352716i
$977$	−2.23012	+	46.8160i	−0.0713479	+	1.49778i	0.625312	+	0.780375i	$0.284972\pi$
$977$	−2.23012	+	46.8160i	−0.0713479	+	1.49778i	−0.696660	+	0.717402i	$0.745331\pi$
$978$	2.86899	+	0.653219i	0.0917402	+	0.0208876i
$979$	−5.37785	−	15.5383i	−0.171877	−	0.496605i
$980$	2.35724	+	0.692147i	0.0752991	+	0.0221098i
$981$	3.44267	+	10.6060i	0.109916	+	0.338625i
$982$	−33.0687	−	38.1633i	−1.05526	−	1.21784i
$983$	49.3891	+	4.71609i	1.57527	+	0.150420i	0.845764	−	0.533556i	$-0.179145\pi$
$983$	49.3891	+	4.71609i	1.57527	+	0.150420i	0.729504	+	0.683976i	$0.239751\pi$
$984$	40.6449	−	4.46162i	1.29571	−	0.142231i
$985$	−4.90482	−	51.3656i	−0.156281	−	1.63664i
$986$	18.1035	−	7.24756i	0.576534	−	0.230809i
$987$	−21.0496	+	8.77415i	−0.670016	+	0.279284i
$988$	0.350674	+	0.202462i	0.0111564	+	0.00644117i
$989$	50.5604	−	25.2067i	1.60773	−	0.801525i
$990$	−4.51845	+	12.2817i	−0.143606	+	0.390338i
$991$	−17.8109	+	11.4464i	−0.565782	+	0.363606i	−0.792047	−	0.610460i	$-0.790985\pi$
$991$	−17.8109	+	11.4464i	−0.565782	+	0.363606i	0.226266	+	0.974066i	$0.427348\pi$
$992$	0.270989	−	0.344590i	0.00860390	−	0.0109407i
$993$	−15.4804	−	1.25770i	−0.491256	−	0.0399119i
$994$	−8.66537	+	9.08798i	−0.274849	+	0.288253i
$995$	4.04252	+	2.87866i	0.128156	+	0.0912598i
$996$	3.58612	−	0.0506868i	0.113631	−	0.00160607i
$997$	−12.4356	−	4.97846i	−0.393839	−	0.157669i	0.166286	−	0.986078i	$-0.446823\pi$
$997$	−12.4356	−	4.97846i	−0.393839	−	0.157669i	−0.560125	+	0.828408i	$0.689247\pi$
$998$	8.50278	−	28.9578i	0.269151	−	0.916644i
$999$	−3.60485	−	10.5935i	−0.114053	−	0.335162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.7	✓	440
3.2	odd	2		621.2.s.a.494.16		440
9.4	even	3		621.2.s.a.287.16		440
9.5	odd	6	inner	207.2.o.a.149.7	yes	440
23.21	odd	22	inner	207.2.o.a.182.7	yes	440
69.44	even	22		621.2.s.a.251.16		440
207.67	odd	66		621.2.s.a.44.16		440
207.113	even	66	inner	207.2.o.a.113.7	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.7	✓	440	1.1	even	1	trivial
207.2.o.a.113.7	yes	440	207.113	even	66	inner
207.2.o.a.149.7	yes	440	9.5	odd	6	inner
207.2.o.a.182.7	yes	440	23.21	odd	22	inner
621.2.s.a.44.16		440	207.67	odd	66
621.2.s.a.251.16		440	69.44	even	22
621.2.s.a.287.16		440	9.4	even	3
621.2.s.a.494.16		440	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46589 + 0.0698289i) q^{2} +(1.15264 + 1.29284i) q^{3} +(0.153011 - 0.0146108i) q^{4} +(1.95685 + 1.86585i) q^{5} +(-1.77992 - 1.81467i) q^{6} +(-0.197460 - 1.02452i) q^{7} +(2.68195 - 0.385606i) q^{8} +(-0.342849 + 2.98034i) q^{9} +O(q^{10})\)	\(q+(-1.46589 + 0.0698289i) q^{2} +(1.15264 + 1.29284i) q^{3} +(0.153011 - 0.0146108i) q^{4} +(1.95685 + 1.86585i) q^{5} +(-1.77992 - 1.81467i) q^{6} +(-0.197460 - 1.02452i) q^{7} +(2.68195 - 0.385606i) q^{8} +(-0.342849 + 2.98034i) q^{9} +(-2.99882 - 2.59849i) q^{10} +(-0.977128 + 0.503745i) q^{11} +(0.195256 + 0.180978i) q^{12} +(-0.821376 - 0.158307i) q^{13} +(0.360996 + 1.48805i) q^{14} +(-0.156701 + 4.68054i) q^{15} +(-4.20638 + 0.810712i) q^{16} +(1.94122 + 4.25068i) q^{17} +(0.294464 - 4.39280i) q^{18} +(-2.86472 - 1.30827i) q^{19} +(0.326682 + 0.256906i) q^{20} +(1.09694 - 1.43619i) q^{21} +(1.39719 - 0.806666i) q^{22} +(4.33512 + 2.05104i) q^{23} +(3.58984 + 3.02286i) q^{24} +(0.109946 + 2.30805i) q^{25} +(1.21510 + 0.174705i) q^{26} +(-4.24828 + 2.99201i) q^{27} +(-0.0451828 - 0.153878i) q^{28} +(-0.270294 + 2.83065i) q^{29} +(-0.0971313 - 6.87209i) q^{30} +(0.397166 - 0.312335i) q^{31} +(0.843165 - 0.204550i) q^{32} +(-1.77753 - 0.682631i) q^{33} +(-3.14244 - 6.09547i) q^{34} +(1.52521 - 2.37327i) q^{35} +(-0.00891453 + 0.461036i) q^{36} +(-0.606716 + 2.06629i) q^{37} +(4.29071 + 1.71774i) q^{38} +(-0.742084 - 1.24438i) q^{39} +(5.96766 + 4.24955i) q^{40} +(6.01245 - 6.30568i) q^{41} +(-1.50770 + 2.18189i) q^{42} +(7.28198 - 9.25979i) q^{43} +(-0.142152 + 0.0913553i) q^{44} +(-6.23179 + 5.19238i) q^{45} +(-6.49802 - 2.70388i) q^{46} +(-10.9285 - 6.30957i) q^{47} +(-5.89655 - 4.50369i) q^{48} +(5.48792 - 2.19703i) q^{49} +(-0.322337 - 3.37567i) q^{50} +(-3.25791 + 7.40918i) q^{51} +(-0.127993 - 0.0122218i) q^{52} +(-5.36725 - 6.19414i) q^{53} +(6.01858 - 4.68261i) q^{54} +(-2.85201 - 0.837425i) q^{55} +(-0.924641 - 2.67157i) q^{56} +(-1.61060 - 5.21157i) q^{57} +(0.198560 - 4.16829i) q^{58} +(0.877589 - 4.55336i) q^{59} +(0.0444095 + 0.718465i) q^{60} +(0.973623 - 2.43199i) q^{61} +(-0.560392 + 0.485582i) q^{62} +(3.12113 - 0.237244i) q^{63} +(6.99883 - 2.05504i) q^{64} +(-1.31193 - 1.84235i) q^{65} +(2.65334 + 0.876538i) q^{66} +(0.633742 - 1.22929i) q^{67} +(0.359135 + 0.622040i) q^{68} +(2.34517 + 7.96870i) q^{69} +(-2.07006 + 3.58545i) q^{70} +(4.43366 + 6.89892i) q^{71} +(0.229736 + 8.12534i) q^{72} +(-1.42222 + 3.11423i) q^{73} +(0.745092 - 3.07131i) q^{74} +(-2.85720 + 2.80249i) q^{75} +(-0.457449 - 0.158325i) q^{76} +(0.709041 + 0.901619i) q^{77} +(1.17471 + 1.77230i) q^{78} +(14.4731 - 5.00918i) q^{79} +(-9.74392 - 6.26203i) q^{80} +(-8.76491 - 2.04362i) q^{81} +(-8.37327 + 9.66327i) q^{82} +(9.74971 - 9.29633i) q^{83} +(0.146860 - 0.235780i) q^{84} +(-4.13247 + 11.9400i) q^{85} +(-10.0280 + 14.0823i) q^{86} +(-3.97112 + 2.91327i) q^{87} +(-2.42636 + 1.72780i) q^{88} +(-2.12858 + 14.8046i) q^{89} +(8.77253 - 8.04662i) q^{90} +0.872777i q^{91} +(0.693290 + 0.250493i) q^{92} +(0.861587 + 0.153461i) q^{93} +(16.4606 + 8.48600i) q^{94} +(-3.16478 - 7.90523i) q^{95} +(1.23631 + 0.854302i) q^{96} +(-7.48716 - 1.81637i) q^{97} +(-7.89127 + 3.60382i) q^{98} +(-1.16633 - 3.08489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

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