LMFDB - Embedded newform 322.2.e.c.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (of order $3$, degree $2$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$0.373419 + 0.0835272i$ of defining polynomial
Character	$\chi$	$=$	322.277
Dual form			322.2.e.c.93.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.31242 + 2.27317i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.68584 - 2.91996i) q^{5} -2.62484 q^{6} +(-1.55926 - 2.13746i) q^{7} -1.00000 q^{8} +(-1.94488 - 3.36864i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.31242 + 2.27317i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.68584 - 2.91996i) q^{5} -2.62484 q^{6} +(-1.55926 - 2.13746i) q^{7} -1.00000 q^{8} +(-1.94488 - 3.36864i) q^{9} +(1.68584 - 2.91996i) q^{10} +(1.11437 - 1.93015i) q^{11} +(-1.31242 - 2.27317i) q^{12} -3.10674 q^{13} +(1.07146 - 2.41908i) q^{14} +8.85009 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.18584 + 5.51803i) q^{17} +(1.94488 - 3.36864i) q^{18} +(-0.457092 - 0.791706i) q^{19} +3.37167 q^{20} +(6.90521 - 0.739223i) q^{21} +2.22875 q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.31242 - 2.27317i) q^{24} +(-3.18409 + 5.51501i) q^{25} +(-1.55337 - 2.69052i) q^{26} +2.33549 q^{27} +(2.63072 - 0.281626i) q^{28} -4.22526 q^{29} +(4.42505 + 7.66440i) q^{30} +(1.73921 - 3.01240i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.92505 + 5.06633i) q^{33} -6.37167 q^{34} +(-3.61263 + 8.15636i) q^{35} +3.88977 q^{36} +(-4.70891 - 8.15607i) q^{37} +(0.457092 - 0.791706i) q^{38} +(4.07735 - 7.06217i) q^{39} +(1.68584 + 2.91996i) q^{40} -5.85009 q^{41} +(4.09279 + 5.61047i) q^{42} +12.7643 q^{43} +(1.11437 + 1.93015i) q^{44} +(-6.55751 + 11.3579i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-3.28212 - 5.68479i) q^{47} +2.62484 q^{48} +(-2.13744 + 6.66568i) q^{49} -6.36818 q^{50} +(-8.36230 - 14.4839i) q^{51} +(1.55337 - 2.69052i) q^{52} +(-5.57386 + 9.65420i) q^{53} +(1.16774 + 2.02259i) q^{54} -7.51460 q^{55} +(1.55926 + 2.13746i) q^{56} +2.39958 q^{57} +(-2.11263 - 3.65918i) q^{58} +(1.48605 - 2.57391i) q^{59} +(-4.42505 + 7.66440i) q^{60} +(-3.40282 - 5.89385i) q^{61} +3.47842 q^{62} +(-4.16774 + 9.40967i) q^{63} +1.00000 q^{64} +(5.23746 + 9.07155i) q^{65} +(-2.92505 + 5.06633i) q^{66} +(-3.43725 + 5.95350i) q^{67} +(-3.18584 - 5.51803i) q^{68} +2.62484 q^{69} +(-8.86993 + 0.949553i) q^{70} +1.61307 q^{71} +(1.94488 + 3.36864i) q^{72} +(-2.96795 + 5.14065i) q^{73} +(4.70891 - 8.15607i) q^{74} +(-8.35772 - 14.4760i) q^{75} +0.914183 q^{76} +(-5.86320 + 0.627674i) q^{77} +8.15470 q^{78} +(7.37491 + 12.7737i) q^{79} +(-1.68584 + 2.91996i) q^{80} +(2.76951 - 4.79693i) q^{81} +(-2.92505 - 5.06633i) q^{82} -6.51111 q^{83} +(-2.81242 + 6.34970i) q^{84} +21.4832 q^{85} +(6.38214 + 11.0542i) q^{86} +(5.54530 - 9.60474i) q^{87} +(-1.11437 + 1.93015i) q^{88} +(0.792581 + 1.37279i) q^{89} -13.1150 q^{90} +(4.84421 + 6.64053i) q^{91} +1.00000 q^{92} +(4.56514 + 7.90705i) q^{93} +(3.28212 - 5.68479i) q^{94} +(-1.54116 + 2.66937i) q^{95} +(1.31242 + 2.27317i) q^{96} +13.7970 q^{97} +(-6.84137 + 1.48176i) q^{98} -8.66930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 6 q^{15} - 4 q^{16} - 15 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} - q^{21} + 12 q^{22} - 4 q^{23} + q^{24} + 5 q^{25} - q^{26} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 3 q^{30} - 8 q^{31} + 4 q^{32} - 9 q^{33} - 30 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} - q^{38} + 25 q^{39} + 3 q^{40} + 18 q^{41} - 14 q^{42} + 28 q^{43} + 6 q^{44} - 21 q^{45} + 4 q^{46} - 9 q^{47} + 2 q^{48} + 5 q^{49} + 10 q^{50} - 6 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 24 q^{55} + q^{56} + 46 q^{57} + 6 q^{58} - 12 q^{59} - 3 q^{60} - 11 q^{61} - 16 q^{62} - 19 q^{63} + 8 q^{64} + 9 q^{66} + q^{67} - 15 q^{68} + 2 q^{69} - 30 q^{70} - 6 q^{71} + 7 q^{72} + 4 q^{73} + 8 q^{74} - 22 q^{75} - 2 q^{76} - 9 q^{77} + 50 q^{78} - 5 q^{79} - 3 q^{80} + 8 q^{81} + 9 q^{82} + 24 q^{83} - 13 q^{84} + 48 q^{85} + 14 q^{86} + 9 q^{87} - 6 q^{88} - 27 q^{89} - 42 q^{90} - 26 q^{91} + 8 q^{92} + 25 q^{93} + 9 q^{94} + 3 q^{95} + q^{96} + 4 q^{97} - 26 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 2 * q^13 + q^14 + 6 * q^15 - 4 * q^16 - 15 * q^17 + 7 * q^18 + q^19 + 6 * q^20 - q^21 + 12 * q^22 - 4 * q^23 + q^24 + 5 * q^25 - q^26 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 3 * q^30 - 8 * q^31 + 4 * q^32 - 9 * q^33 - 30 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 - q^38 + 25 * q^39 + 3 * q^40 + 18 * q^41 - 14 * q^42 + 28 * q^43 + 6 * q^44 - 21 * q^45 + 4 * q^46 - 9 * q^47 + 2 * q^48 + 5 * q^49 + 10 * q^50 - 6 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 24 * q^55 + q^56 + 46 * q^57 + 6 * q^58 - 12 * q^59 - 3 * q^60 - 11 * q^61 - 16 * q^62 - 19 * q^63 + 8 * q^64 + 9 * q^66 + q^67 - 15 * q^68 + 2 * q^69 - 30 * q^70 - 6 * q^71 + 7 * q^72 + 4 * q^73 + 8 * q^74 - 22 * q^75 - 2 * q^76 - 9 * q^77 + 50 * q^78 - 5 * q^79 - 3 * q^80 + 8 * q^81 + 9 * q^82 + 24 * q^83 - 13 * q^84 + 48 * q^85 + 14 * q^86 + 9 * q^87 - 6 * q^88 - 27 * q^89 - 42 * q^90 - 26 * q^91 + 8 * q^92 + 25 * q^93 + 9 * q^94 + 3 * q^95 + q^96 + 4 * q^97 - 26 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.31242	+	2.27317i	−0.757725	+	1.31242i	0.186283	+	0.982496i	$0.440356\pi$
$3$	−1.31242	+	2.27317i	−0.757725	+	1.31242i	−0.944008	+	0.329922i	$0.892978\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.68584	−	2.91996i	−0.753929	−	1.30584i	−0.945905	−	0.324444i	$-0.894823\pi$
$5$	−1.68584	−	2.91996i	−0.753929	−	1.30584i	0.191976	−	0.981400i	$-0.438511\pi$
$6$	−2.62484			−1.07158
$7$	−1.55926	−	2.13746i	−0.589343	−	0.807883i
$7$	−1.55926	−	2.13746i	−0.589343	−	0.807883i
$8$	−1.00000			−0.353553
$9$	−1.94488	−	3.36864i	−0.648294	−	1.12288i
$10$	1.68584	−	2.91996i	0.533108	−	0.923371i
$11$	1.11437	−	1.93015i	0.335996	−	0.581962i	−0.647680	−	0.761913i	$-0.724260\pi$
$11$	1.11437	−	1.93015i	0.335996	−	0.581962i	0.983676	+	0.179951i	$0.0575938\pi$
$12$	−1.31242	−	2.27317i	−0.378862	−	0.656209i
$13$	−3.10674			−0.861656			−0.430828	−	0.902434i	$-0.641778\pi$
$13$	−3.10674			−0.861656			−0.430828	+	0.902434i	$0.641778\pi$
$14$	1.07146	−	2.41908i	0.286361	−	0.646527i
$15$	8.85009			2.28508
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.18584	+	5.51803i	−0.772679	+	1.33832i	0.163411	+	0.986558i	$0.447750\pi$
$17$	−3.18584	+	5.51803i	−0.772679	+	1.33832i	−0.936090	+	0.351761i	$0.885583\pi$
$18$	1.94488	−	3.36864i	0.458413	−	0.793995i
$19$	−0.457092	−	0.791706i	−0.104864	−	0.181630i	0.808819	−	0.588058i	$-0.200107\pi$
$19$	−0.457092	−	0.791706i	−0.104864	−	0.181630i	−0.913683	+	0.406428i	$0.866774\pi$
$20$	3.37167			0.753929
$21$	6.90521	−	0.739223i	1.50684	−	0.161312i
$22$	2.22875			0.475170
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	1.31242	−	2.27317i	0.267896	−	0.464010i
$25$	−3.18409	+	5.51501i	−0.636818	+	1.10300i
$26$	−1.55337	−	2.69052i	−0.304641	−	0.527654i
$27$	2.33549			0.449465
$28$	2.63072	−	0.281626i	0.497159	−	0.0532224i
$29$	−4.22526			−0.784610			−0.392305	−	0.919835i	$-0.628322\pi$
$29$	−4.22526			−0.784610			−0.392305	+	0.919835i	$0.628322\pi$
$30$	4.42505	+	7.66440i	0.807899	+	1.39932i
$31$	1.73921	−	3.01240i	0.312371	−	0.541043i	−0.666504	−	0.745501i	$-0.732210\pi$
$31$	1.73921	−	3.01240i	0.312371	−	0.541043i	0.978875	+	0.204459i	$0.0655434\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.92505	+	5.06633i	0.509185	+	0.881935i
$34$	−6.37167			−1.09273
$35$	−3.61263	+	8.15636i	−0.610646	+	1.37868i
$36$	3.88977			0.648294
$37$	−4.70891	−	8.15607i	−0.774140	−	1.34085i	−0.935277	−	0.353917i	$-0.884849\pi$
$37$	−4.70891	−	8.15607i	−0.774140	−	1.34085i	0.161137	−	0.986932i	$-0.448484\pi$
$38$	0.457092	−	0.791706i	0.0741500	−	0.128432i
$39$	4.07735	−	7.06217i	0.652898	−	1.13085i
$40$	1.68584	+	2.91996i	0.266554	+	0.461685i
$41$	−5.85009			−0.913631			−0.456815	−	0.889562i	$-0.651010\pi$
$41$	−5.85009			−0.913631			−0.456815	+	0.889562i	$0.651010\pi$
$42$	4.09279	+	5.61047i	0.631531	+	0.865715i
$43$	12.7643			1.94653			0.973267	−	0.229677i	$-0.0737671\pi$
$43$	12.7643			1.94653			0.973267	+	0.229677i	$0.0737671\pi$
$44$	1.11437	+	1.93015i	0.167998	+	0.290981i
$45$	−6.55751	+	11.3579i	−0.977536	+	1.69314i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−3.28212	−	5.68479i	−0.478746	−	0.829212i	0.520957	−	0.853583i	$-0.325575\pi$
$47$	−3.28212	−	5.68479i	−0.478746	−	0.829212i	−0.999703	+	0.0243705i	$0.992242\pi$
$48$	2.62484			0.378862
$49$	−2.13744	+	6.66568i	−0.305349	+	0.952240i
$50$	−6.36818			−0.900597
$51$	−8.36230	−	14.4839i	−1.17096	−	2.02816i
$52$	1.55337	−	2.69052i	0.215414	−	0.373108i
$53$	−5.57386	+	9.65420i	−0.765628	+	1.32611i	0.174286	+	0.984695i	$0.444238\pi$
$53$	−5.57386	+	9.65420i	−0.765628	+	1.32611i	−0.939914	+	0.341412i	$0.889095\pi$
$54$	1.16774	+	2.02259i	0.158910	+	0.275240i
$55$	−7.51460			−1.01327
$56$	1.55926	+	2.13746i	0.208364	+	0.285630i
$57$	2.39958			0.317832
$58$	−2.11263	−	3.65918i	−0.277402	−	0.480474i
$59$	1.48605	−	2.57391i	0.193467	−	0.335094i	−0.752930	−	0.658101i	$-0.771360\pi$
$59$	1.48605	−	2.57391i	0.193467	−	0.335094i	0.946397	+	0.323006i	$0.104693\pi$
$60$	−4.42505	+	7.66440i	−0.571271	+	0.989470i
$61$	−3.40282	−	5.89385i	−0.435686	−	0.754630i	0.561665	−	0.827364i	$-0.310161\pi$
$61$	−3.40282	−	5.89385i	−0.435686	−	0.754630i	−0.997351	+	0.0727344i	$0.976827\pi$
$62$	3.47842			0.441760
$63$	−4.16774	+	9.40967i	−0.525086	+	1.18551i
$64$	1.00000			0.125000
$65$	5.23746	+	9.07155i	0.649627	+	1.12519i
$66$	−2.92505	+	5.06633i	−0.360048	+	0.623622i
$67$	−3.43725	+	5.95350i	−0.419927	+	0.727336i	−0.995932	−	0.0901110i	$-0.971278\pi$
$67$	−3.43725	+	5.95350i	−0.419927	+	0.727336i	0.576004	+	0.817447i	$0.304611\pi$
$68$	−3.18584	−	5.51803i	−0.386339	−	0.669160i
$69$	2.62484			0.315993
$70$	−8.86993	+	0.949553i	−1.06016	+	0.113493i
$71$	1.61307			0.191436			0.0957181	−	0.995408i	$-0.469485\pi$
$71$	1.61307			0.191436			0.0957181	+	0.995408i	$0.469485\pi$
$72$	1.94488	+	3.36864i	0.229207	+	0.396998i
$73$	−2.96795	+	5.14065i	−0.347373	+	0.601667i	−0.985782	−	0.168030i	$-0.946259\pi$
$73$	−2.96795	+	5.14065i	−0.347373	+	0.601667i	0.638409	+	0.769697i	$0.279593\pi$
$74$	4.70891	−	8.15607i	0.547399	−	0.948124i
$75$	−8.35772	−	14.4760i	−0.965066	−	1.67154i
$76$	0.914183			0.104864
$77$	−5.86320	+	0.627674i	−0.668174	+	0.0715301i
$78$	8.15470			0.923337
$79$	7.37491	+	12.7737i	0.829742	+	1.43716i	0.898241	+	0.439504i	$0.144846\pi$
$79$	7.37491	+	12.7737i	0.829742	+	1.43716i	−0.0684986	+	0.997651i	$0.521821\pi$
$80$	−1.68584	+	2.91996i	−0.188482	+	0.326461i
$81$	2.76951	−	4.79693i	0.307723	−	0.532992i
$82$	−2.92505	−	5.06633i	−0.323017	−	0.559482i
$83$	−6.51111			−0.714687			−0.357344	−	0.933973i	$-0.616318\pi$
$83$	−6.51111			−0.714687			−0.357344	+	0.933973i	$0.616318\pi$
$84$	−2.81242	+	6.34970i	−0.306860	+	0.692809i
$85$	21.4832			2.33018
$86$	6.38214	+	11.0542i	0.688204	+	1.19200i
$87$	5.54530	−	9.60474i	0.594519	−	1.02974i
$88$	−1.11437	+	1.93015i	−0.118793	+	0.205755i
$89$	0.792581	+	1.37279i	0.0840134	+	0.145516i	0.904970	−	0.425475i	$-0.139893\pi$
$89$	0.792581	+	1.37279i	0.0840134	+	0.145516i	−0.820957	+	0.570990i	$0.806559\pi$
$90$	−13.1150			−1.38244
$91$	4.84421	+	6.64053i	0.507811	+	0.696117i
$92$	1.00000			0.104257
$93$	4.56514	+	7.90705i	0.473383	+	0.819923i
$94$	3.28212	−	5.68479i	0.338525	−	0.586342i
$95$	−1.54116	+	2.66937i	−0.158120	+	0.273872i
$96$	1.31242	+	2.27317i	0.133948	+	0.232005i
$97$	13.7970			1.40087			0.700435	−	0.713716i	$-0.252989\pi$
$97$	13.7970			1.40087			0.700435	+	0.713716i	$0.252989\pi$
$98$	−6.84137	+	1.48176i	−0.691083	+	0.149680i
$99$	−8.66930			−0.871297
$100$	−3.18409	−	5.51501i	−0.318409	−	0.551501i
$101$	3.53767	−	6.12743i	0.352012	−	0.609702i	−0.634590	−	0.772849i	$-0.718831\pi$
$101$	3.53767	−	6.12743i	0.352012	−	0.609702i	0.986602	+	0.163147i	$0.0521644\pi$
$102$	8.36230	−	14.4839i	0.827991	−	1.43412i
$103$	7.87581	+	13.6413i	0.776027	+	1.34412i	0.934216	+	0.356709i	$0.116101\pi$
$103$	7.87581	+	13.6413i	0.776027	+	1.34412i	−0.158189	+	0.987409i	$0.550565\pi$
$104$	3.10674			0.304641
$105$	−13.7996	−	18.9167i	−1.34670	−	1.84608i
$106$	−11.1477			−1.08276
$107$	−2.88388	−	4.99503i	−0.278795	−	0.482888i	0.692290	−	0.721619i	$-0.256602\pi$
$107$	−2.88388	−	4.99503i	−0.278795	−	0.482888i	−0.971086	+	0.238731i	$0.923268\pi$
$108$	−1.16774	+	2.02259i	−0.112366	+	0.194624i
$109$	9.46033	−	16.3858i	0.906135	−	1.56947i	0.0867484	−	0.996230i	$-0.472352\pi$
$109$	9.46033	−	16.3858i	0.906135	−	1.56947i	0.819387	−	0.573241i	$-0.194314\pi$
$110$	−3.75730	−	6.50784i	−0.358245	−	0.620498i
$111$	24.7202			2.34634
$112$	−1.07146	+	2.41908i	−0.101244	+	0.228582i
$113$	−11.2697			−1.06017			−0.530083	−	0.847946i	$-0.677839\pi$
$113$	−11.2697			−1.06017			−0.530083	+	0.847946i	$0.677839\pi$
$114$	1.19979	+	2.07810i	0.112371	+	0.194632i
$115$	−1.68584	+	2.91996i	−0.157205	+	0.272287i
$116$	2.11263	−	3.65918i	0.196153	−	0.339746i
$117$	6.04225	+	10.4655i	0.558607	+	0.967535i
$118$	2.97209			0.273603
$119$	16.7621	−	1.79443i	1.53658	−	0.164495i
$120$	−8.85009			−0.807899
$121$	3.01635	+	5.22447i	0.274213	+	0.474951i
$122$	3.40282	−	5.89385i	0.308076	−	0.533604i
$123$	7.67777	−	13.2983i	0.692281	−	1.19907i
$124$	1.73921	+	3.01240i	0.156186	+	0.270521i
$125$	4.61307			0.412605
$126$	−10.2329	+	1.09546i	−0.911618	+	0.0975914i
$127$	−20.9743			−1.86117			−0.930583	−	0.366081i	$-0.880699\pi$
$127$	−20.9743			−1.86117			−0.930583	+	0.366081i	$0.880699\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−16.7521	+	29.0154i	−1.47494	+	2.55467i
$130$	−5.23746	+	9.07155i	−0.459356	+	0.795628i
$131$	−1.63795	−	2.83701i	−0.143108	−	0.247871i	0.785557	−	0.618789i	$-0.212376\pi$
$131$	−1.63795	−	2.83701i	−0.143108	−	0.247871i	−0.928666	+	0.370918i	$0.879043\pi$
$132$	−5.85009			−0.509185
$133$	−0.979514	+	2.21149i	−0.0849347	+	0.191760i
$134$	−6.87451			−0.593867
$135$	−3.93725	−	6.81952i	−0.338865	−	0.586931i
$136$	3.18584	−	5.51803i	0.273183	−	0.473167i
$137$	−0.548792	+	0.950535i	−0.0468865	+	0.0812097i	−0.888516	−	0.458845i	$-0.848263\pi$
$137$	−0.548792	+	0.950535i	−0.0468865	+	0.0812097i	0.841630	+	0.540055i	$0.181597\pi$
$138$	1.31242	+	2.27317i	0.111720	+	0.193506i
$139$	−2.44572			−0.207444			−0.103722	−	0.994606i	$-0.533075\pi$
$139$	−2.44572			−0.207444			−0.103722	+	0.994606i	$0.533075\pi$
$140$	−5.25730	−	7.20681i	−0.444323	−	0.609086i
$141$	17.2300			1.45103
$142$	0.806535	+	1.39696i	0.0676829	+	0.117230i
$143$	−3.46207	+	5.99648i	−0.289513	+	0.501451i
$144$	−1.94488	+	3.36864i	−0.162074	+	0.280720i
$145$	7.12309	+	12.3376i	0.591541	+	1.02458i
$146$	−5.93591			−0.491259
$147$	−12.3470	−	13.6069i	−1.01837	−	1.12228i
$148$	9.41782			0.774140
$149$	−9.34377	−	16.1839i	−0.765471	−	1.32583i	−0.939997	−	0.341182i	$-0.889173\pi$
$149$	−9.34377	−	16.1839i	−0.765471	−	1.32583i	0.174526	−	0.984653i	$-0.444161\pi$
$150$	8.35772	−	14.4760i	0.682405	−	1.18196i
$151$	0.267765	−	0.463782i	0.0217904	−	0.0377421i	−0.854925	−	0.518752i	$-0.826397\pi$
$151$	0.267765	−	0.463782i	0.0217904	−	0.0377421i	0.876715	+	0.481010i	$0.159730\pi$
$152$	0.457092	+	0.791706i	0.0370750	+	0.0642158i
$153$	24.7843			2.00369
$154$	−3.47518	−	4.76385i	−0.280038	−	0.383882i
$155$	−11.7281			−0.942023
$156$	4.07735	+	7.06217i	0.326449	+	0.565426i
$157$	5.22028	−	9.04178i	0.416623	−	0.721613i	−0.578974	−	0.815346i	$-0.696547\pi$
$157$	5.22028	−	9.04178i	0.416623	−	0.721613i	0.995597	+	0.0937332i	$0.0298801\pi$
$158$	−7.37491	+	12.7737i	−0.586716	+	1.01622i
$159$	−14.6305	−	25.3407i	−1.16027	−	2.00965i
$160$	−3.37167			−0.266554
$161$	−1.07146	+	2.41908i	−0.0844432	+	0.190650i
$162$	5.53902			0.435186
$163$	−2.08781	−	3.61620i	−0.163530	−	0.283242i	0.772602	−	0.634890i	$-0.218955\pi$
$163$	−2.08781	−	3.61620i	−0.163530	−	0.283242i	−0.936132	+	0.351648i	$0.885621\pi$
$164$	2.92505	−	5.06633i	0.228408	−	0.395614i
$165$	9.86230	−	17.0820i	0.767779	−	1.32983i
$166$	−3.25556	−	5.63879i	−0.252680	−	0.437655i
$167$	−7.26623			−0.562277			−0.281139	−	0.959667i	$-0.590712\pi$
$167$	−7.26623			−0.562277			−0.281139	+	0.959667i	$0.590712\pi$
$168$	−6.90521	+	0.739223i	−0.532748	+	0.0570323i
$169$	−3.34814			−0.257549
$170$	10.7416	+	18.6050i	0.823843	+	1.42694i
$171$	−1.77798	+	3.07955i	−0.135965	+	0.235499i
$172$	−6.38214	+	11.0542i	−0.486633	+	0.842874i
$173$	1.21265	+	2.10037i	0.0921959	+	0.159688i	0.908435	−	0.418026i	$-0.137278\pi$
$173$	1.21265	+	2.10037i	0.0921959	+	0.159688i	−0.816239	+	0.577714i	$0.803945\pi$
$174$	11.0906			0.840777
$175$	16.7529	−	1.79345i	1.26640	−	0.135572i
$176$	−2.22875			−0.167998
$177$	3.90063	+	6.75609i	0.293189	+	0.507819i
$178$	−0.792581	+	1.37279i	−0.0594065	+	0.102895i
$179$	6.93507	−	12.0119i	0.518351	−	0.897811i	−0.481421	−	0.876489i	$-0.659879\pi$
$179$	6.93507	−	12.0119i	0.518351	−	0.897811i	0.999773	−	0.0213215i	$-0.00678736\pi$
$180$	−6.55751	−	11.3579i	−0.488768	−	0.846571i
$181$	3.48271			0.258868			0.129434	−	0.991588i	$-0.458684\pi$
$181$	3.48271			0.258868			0.129434	+	0.991588i	$0.458684\pi$
$182$	−3.32877	+	7.51547i	−0.246744	+	0.557084i
$183$	17.8637			1.32052
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−15.8769	+	27.4996i	−1.16729	+	2.02181i
$186$	−4.56514	+	7.90705i	−0.334732	+	0.579773i
$187$	7.10042	+	12.2983i	0.519234	+	0.899340i
$188$	6.56423			0.478746
$189$	−3.64163	−	4.99201i	−0.264889	−	0.363115i
$190$	−3.08233			−0.223616
$191$	7.42116	+	12.8538i	0.536976	+	0.930070i	0.999065	+	0.0432362i	$0.0137668\pi$
$191$	7.42116	+	12.8538i	0.536976	+	0.930070i	−0.462089	+	0.886834i	$0.652900\pi$
$192$	−1.31242	+	2.27317i	−0.0947156	+	0.164052i
$193$	7.99477	−	13.8473i	0.575476	−	0.996753i	−0.420514	−	0.907286i	$-0.638150\pi$
$193$	7.99477	−	13.8473i	0.575476	−	0.996753i	0.995990	−	0.0894672i	$-0.0285164\pi$
$194$	6.89848	+	11.9485i	0.495282	+	0.857854i
$195$	−27.4950			−1.96896
$196$	−4.70393	−	5.18392i	−0.335995	−	0.370280i
$197$	−14.8954			−1.06126			−0.530628	−	0.847605i	$-0.678044\pi$
$197$	−14.8954			−1.06126			−0.530628	+	0.847605i	$0.678044\pi$
$198$	−4.33465	−	7.50783i	−0.308050	−	0.533558i
$199$	12.0627	−	20.8933i	0.855105	−	1.48109i	−0.0214427	−	0.999770i	$-0.506826\pi$
$199$	12.0627	−	20.8933i	0.855105	−	1.48109i	0.876548	−	0.481315i	$-0.159841\pi$
$200$	3.18409	−	5.51501i	0.225149	−	0.389970i
$201$	−9.02223	−	15.6270i	−0.636379	−	1.10224i
$202$	7.07535			0.497820
$203$	6.58825	+	9.03130i	0.462405	+	0.633873i
$204$	16.7246			1.17096
$205$	9.86230	+	17.0820i	0.688813	+	1.19306i
$206$	−7.87581	+	13.6413i	−0.548734	+	0.950435i
$207$	−1.94488	+	3.36864i	−0.135179	+	0.234136i
$208$	1.55337	+	2.69052i	0.107707	+	0.186554i
$209$	−2.03748			−0.140936
$210$	9.48256	−	21.4091i	0.654359	−	1.47737i
$211$	−18.1067			−1.24652			−0.623260	−	0.782015i	$-0.714192\pi$
$211$	−18.1067			−1.24652			−0.623260	+	0.782015i	$0.714192\pi$
$212$	−5.57386	−	9.65420i	−0.382814	−	0.663054i
$213$	−2.11702	+	3.66679i	−0.145056	+	0.251244i
$214$	2.88388	−	4.99503i	0.197138	−	0.341453i
$215$	−21.5185	−	37.2711i	−1.46755	−	2.54187i
$216$	−2.33549			−0.158910
$217$	−9.15074	+	0.979615i	−0.621193	+	0.0665006i
$218$	18.9207			1.28147
$219$	−7.79039	−	13.4934i	−0.526426	−	0.911797i
$220$	3.75730	−	6.50784i	0.253317	−	0.438758i
$221$	9.89758	−	17.1431i	0.665783	−	1.15317i
$222$	12.3601	+	21.4083i	0.829557	+	1.43683i
$223$	20.1922			1.35217			0.676084	−	0.736824i	$-0.263676\pi$
$223$	20.1922			1.35217			0.676084	+	0.736824i	$0.263676\pi$
$224$	−2.63072	+	0.281626i	−0.175772	+	0.0188170i
$225$	24.7707			1.65138
$226$	−5.63486	−	9.75986i	−0.374825	−	0.649216i
$227$	9.90935	−	17.1635i	0.657706	−	1.13918i	−0.323501	−	0.946228i	$-0.604860\pi$
$227$	9.90935	−	17.1635i	0.657706	−	1.13918i	0.981208	−	0.192953i	$-0.0618066\pi$
$228$	−1.19979	+	2.07810i	−0.0794581	+	0.137625i
$229$	−9.08018	−	15.7273i	−0.600035	−	1.03929i	−0.992815	−	0.119659i	$-0.961820\pi$
$229$	−9.08018	−	15.7273i	−0.600035	−	1.03929i	0.392780	−	0.919633i	$-0.371514\pi$
$230$	−3.37167			−0.222322
$231$	6.26816	−	14.1519i	0.412415	−	0.931124i
$232$	4.22526			0.277402
$233$	−6.20567	−	10.7485i	−0.406547	−	0.704160i	0.587953	−	0.808895i	$-0.299934\pi$
$233$	−6.20567	−	10.7485i	−0.406547	−	0.704160i	−0.994500	+	0.104735i	$0.966601\pi$
$234$	−6.04225	+	10.4655i	−0.394994	+	0.684151i
$235$	−11.0662	+	19.1673i	−0.721881	+	1.25033i
$236$	1.48605	+	2.57391i	0.0967334	+	0.167547i
$237$	−38.7159			−2.51486
$238$	9.93507	+	13.6192i	0.643995	+	0.882800i
$239$	−0.868040			−0.0561489			−0.0280744	−	0.999606i	$-0.508938\pi$
$239$	−0.868040			−0.0561489			−0.0280744	+	0.999606i	$0.508938\pi$
$240$	−4.42505	−	7.66440i	−0.285635	−	0.494735i
$241$	−0.793485	+	1.37436i	−0.0511129	+	0.0885301i	−0.890450	−	0.455081i	$-0.849610\pi$
$241$	−0.793485	+	1.37436i	−0.0511129	+	0.0885301i	0.839337	+	0.543611i	$0.182943\pi$
$242$	−3.01635	+	5.22447i	−0.193898	+	0.335841i
$243$	10.7727	+	18.6589i	0.691072	+	1.19697i
$244$	6.80563			0.435686
$245$	23.0669	−	4.99601i	1.47369	−	0.319184i
$246$	15.3555			0.979033
$247$	1.42007	+	2.45963i	0.0903567	+	0.156502i
$248$	−1.73921	+	3.01240i	−0.110440	+	0.191287i
$249$	8.54530	−	14.8009i	0.541537	−	0.937969i
$250$	2.30653	+	3.99504i	0.145878	+	0.252668i
$251$	−3.09976			−0.195655			−0.0978277	−	0.995203i	$-0.531189\pi$
$251$	−3.09976			−0.195655			−0.0978277	+	0.995203i	$0.531189\pi$
$252$	−6.06514	−	8.31421i	−0.382068	−	0.523746i
$253$	−2.22875			−0.140120
$254$	−10.4871	−	18.1643i	−0.658021	−	1.13973i
$255$	−28.1949	+	48.8351i	−1.76564	+	3.05817i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.48695	+	6.03958i	0.217510	+	0.376738i	0.954046	−	0.299660i	$-0.0968732\pi$
$257$	3.48695	+	6.03958i	0.217510	+	0.376738i	−0.736536	+	0.676398i	$0.763540\pi$
$258$	−33.5041			−2.08588
$259$	−10.0909	+	22.7825i	−0.627015	+	1.41563i
$260$	−10.4749			−0.649627
$261$	8.21763	+	14.2333i	0.508658	+	0.881022i
$262$	1.63795	−	2.83701i	0.101193	−	0.175271i
$263$	−2.28451	+	3.95689i	−0.140869	+	0.243992i	−0.927824	−	0.373018i	$-0.878323\pi$
$263$	−2.28451	+	3.95689i	−0.140869	+	0.243992i	0.786955	+	0.617010i	$0.211656\pi$
$264$	−2.92505	−	5.06633i	−0.180024	−	0.311811i
$265$	37.5865			2.30892
$266$	−2.40496	+	0.257458i	−0.147458	+	0.0157858i
$267$	−4.16079			−0.254636
$268$	−3.43725	−	5.95350i	−0.209964	−	0.363668i
$269$	−14.8758	+	25.7657i	−0.906994	+	1.57096i	−0.0887767	+	0.996052i	$0.528296\pi$
$269$	−14.8758	+	25.7657i	−0.906994	+	1.57096i	−0.818218	+	0.574909i	$0.805038\pi$
$270$	3.93725	−	6.81952i	0.239614	−	0.415023i
$271$	2.69495	+	4.66780i	0.163707	+	0.283549i	0.936195	−	0.351480i	$-0.114322\pi$
$271$	2.69495	+	4.66780i	0.163707	+	0.283549i	−0.772488	+	0.635029i	$0.780988\pi$
$272$	6.37167			0.386339
$273$	−21.4527	+	2.29658i	−1.29838	+	0.138995i
$274$	−1.09758			−0.0663075
$275$	7.09653	+	12.2916i	0.427937	+	0.741208i
$276$	−1.31242	+	2.27317i	−0.0789983	+	0.136829i
$277$	−0.784262	+	1.35838i	−0.0471217	+	0.0816172i	−0.888624	−	0.458636i	$-0.848338\pi$
$277$	−0.784262	+	1.35838i	−0.0471217	+	0.0816172i	0.841503	+	0.540253i	$0.181672\pi$
$278$	−1.22286	−	2.11806i	−0.0733424	−	0.127033i
$279$	−13.5302			−0.810034
$280$	3.61263	−	8.15636i	0.215896	−	0.487436i
$281$	15.4009			0.918739			0.459370	−	0.888245i	$-0.348075\pi$
$281$	15.4009			0.918739			0.459370	+	0.888245i	$0.348075\pi$
$282$	8.61502	+	14.9217i	0.513017	+	0.888572i
$283$	7.99412	−	13.8462i	0.475201	−	0.823072i	−0.524396	−	0.851475i	$-0.675709\pi$
$283$	7.99412	−	13.8462i	0.475201	−	0.823072i	0.999597	+	0.0284026i	$0.00904205\pi$
$284$	−0.806535	+	1.39696i	−0.0478590	+	0.0828943i
$285$	−4.04530	−	7.00667i	−0.239623	−	0.415039i
$286$	−6.92414			−0.409433
$287$	9.12179	+	12.5043i	0.538442	+	0.738107i
$288$	−3.88977			−0.229207
$289$	−11.7991	−	20.4367i	−0.694065	−	1.20216i
$290$	−7.12309	+	12.3376i	−0.418282	+	0.724486i
$291$	−18.1074	+	31.3629i	−1.06147	+	1.83853i
$292$	−2.96795	−	5.14065i	−0.173686	−	0.300834i
$293$	12.8179			0.748830			0.374415	−	0.927261i	$-0.377844\pi$
$293$	12.8179			0.748830			0.374415	+	0.927261i	$0.377844\pi$
$294$	5.61044	−	17.4963i	0.327208	−	1.02041i
$295$	−10.0209			−0.583441
$296$	4.70891	+	8.15607i	0.273700	+	0.474062i
$297$	2.60261	−	4.50785i	0.151019	−	0.261572i
$298$	9.34377	−	16.1839i	0.541270	−	0.937507i
$299$	1.55337	+	2.69052i	0.0898338	+	0.155597i
$300$	16.7154			0.965066
$301$	−19.9028	−	27.2831i	−1.14718	−	1.57257i
$302$	0.535529			0.0308163
$303$	9.28581	+	16.0835i	0.533456	+	0.923973i
$304$	−0.457092	+	0.791706i	−0.0262160	+	0.0454074i
$305$	−11.4732	+	19.8721i	−0.656953	+	1.13788i
$306$	12.3922	+	21.4638i	0.708413	+	1.22701i
$307$	−0.501952			−0.0286479			−0.0143239	−	0.999897i	$-0.504560\pi$
$307$	−0.501952			−0.0286479			−0.0143239	+	0.999897i	$0.504560\pi$
$308$	2.38802	−	5.39152i	0.136070	−	0.307210i
$309$	−41.3454			−2.35206
$310$	−5.86405	−	10.1568i	−0.333055	−	0.576869i
$311$	−7.68365	+	13.3085i	−0.435700	+	0.754654i	−0.997352	−	0.0727189i	$-0.976832\pi$
$311$	−7.68365	+	13.3085i	−0.435700	+	0.754654i	0.561653	+	0.827373i	$0.310166\pi$
$312$	−4.07735	+	7.06217i	−0.230834	+	0.399817i
$313$	3.80983	+	6.59882i	0.215344	+	0.372988i	0.953379	−	0.301775i	$-0.0975792\pi$
$313$	3.80983	+	6.59882i	0.215344	+	0.372988i	−0.738035	+	0.674763i	$0.764246\pi$
$314$	10.4406			0.589194
$315$	34.5019	−	3.69354i	1.94396	−	0.208107i
$316$	−14.7498			−0.829742
$317$	9.14921	+	15.8469i	0.513871	+	0.890050i	0.999871	+	0.0160915i	$0.00512230\pi$
$317$	9.14921	+	15.8469i	0.513871	+	0.890050i	−0.486000	+	0.873959i	$0.661544\pi$
$318$	14.6305	−	25.3407i	0.820436	−	1.42104i
$319$	−4.70851	+	8.15538i	−0.263626	+	0.456613i
$320$	−1.68584	−	2.91996i	−0.0942411	−	0.163230i
$321$	15.1394			0.845001
$322$	−2.63072	+	0.281626i	−0.146604	+	0.0156944i
$323$	5.82488			0.324105
$324$	2.76951	+	4.79693i	0.153862	+	0.266496i
$325$	9.89216	−	17.1337i	0.548718	−	0.950408i
$326$	2.08781	−	3.61620i	0.115633	−	0.200283i
$327$	24.8318	+	43.0100i	1.37320	+	2.37846i
$328$	5.85009			0.323017
$329$	−7.03334	+	15.8794i	−0.387761	+	0.875461i
$330$	19.7246			1.08580
$331$	−5.83639	−	10.1089i	−0.320797	−	0.555637i	0.659856	−	0.751392i	$-0.270617\pi$
$331$	−5.83639	−	10.1089i	−0.320797	−	0.555637i	−0.980653	+	0.195755i	$0.937284\pi$
$332$	3.25556	−	5.63879i	0.178672	−	0.309469i
$333$	−18.3166	+	31.7252i	−1.00374	+	1.73853i
$334$	−3.63311	−	6.29274i	−0.198795	−	0.344323i
$335$	23.1786			1.26638
$336$	−4.09279	−	5.61047i	−0.223280	−	0.306076i
$337$	−24.1242			−1.31413			−0.657064	−	0.753835i	$-0.728202\pi$
$337$	−24.1242			−1.31413			−0.657064	+	0.753835i	$0.728202\pi$
$338$	−1.67407	−	2.89957i	−0.0910574	−	0.157716i
$339$	14.7906	−	25.6180i	0.803314	−	1.39138i
$340$	−10.7416	+	18.6050i	−0.582545	+	1.00900i
$341$	−3.87625	−	6.71387i	−0.209911	−	0.363576i
$342$	−3.55596			−0.192284
$343$	17.5804	−	5.82481i	0.949254	−	0.314510i
$344$	−12.7643			−0.688204
$345$	−4.42505	−	7.66440i	−0.238236	−	0.412638i
$346$	−1.21265	+	2.10037i	−0.0651923	+	0.112916i
$347$	−11.1630	+	19.3349i	−0.599262	+	1.03795i	0.393668	+	0.919253i	$0.371206\pi$
$347$	−11.1630	+	19.3349i	−0.599262	+	1.03795i	−0.992930	+	0.118700i	$0.962127\pi$
$348$	5.54530	+	9.60474i	0.297259	+	0.514868i
$349$	−8.64837			−0.462937			−0.231468	−	0.972842i	$-0.574353\pi$
$349$	−8.64837			−0.462937			−0.231468	+	0.972842i	$0.574353\pi$
$350$	9.92963	+	13.6117i	0.530761	+	0.727577i
$351$	−7.25577			−0.387284
$352$	−1.11437	−	1.93015i	−0.0593963	−	0.102877i
$353$	−15.7845	+	27.3396i	−0.840125	+	1.45514i	0.0496639	+	0.998766i	$0.484185\pi$
$353$	−15.7845	+	27.3396i	−0.840125	+	1.45514i	−0.889789	+	0.456373i	$0.849148\pi$
$354$	−3.90063	+	6.75609i	−0.207316	+	0.359082i
$355$	−2.71937	−	4.71009i	−0.144329	−	0.249986i
$356$	−1.58516			−0.0840134
$357$	−17.9198	+	40.4582i	−0.948417	+	2.14128i
$358$	13.8701			0.733059
$359$	−7.51395	−	13.0145i	−0.396571	−	0.686882i	0.596729	−	0.802443i	$-0.296467\pi$
$359$	−7.51395	−	13.0145i	−0.396571	−	0.686882i	−0.993300	+	0.115561i	$0.963133\pi$
$360$	6.55751	−	11.3579i	0.345611	−	0.598616i
$361$	9.08213	−	15.7307i	0.478007	−	0.827933i
$362$	1.74135	+	3.01611i	0.0915235	+	0.158523i
$363$	−15.8348			−0.831113
$364$	−8.17297	+	0.874941i	−0.428380	+	0.0458594i
$365$	20.0139			1.04758
$366$	8.93183	+	15.4704i	0.466874	+	0.808650i
$367$	17.4935	−	30.2996i	0.913151	−	1.58162i	0.103566	−	0.994623i	$-0.466975\pi$
$367$	17.4935	−	30.2996i	0.913151	−	1.58162i	0.809586	−	0.587002i	$-0.199692\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	11.3777	+	19.7068i	0.592302	+	1.02590i
$370$	−31.7538			−1.65080
$371$	29.3265	−	3.13949i	1.52256	−	0.162994i
$372$	−9.13028			−0.473383
$373$	7.42700	+	12.8639i	0.384555	+	0.666069i	0.991707	−	0.128516i	$-0.0410214\pi$
$373$	7.42700	+	12.8639i	0.384555	+	0.666069i	−0.607152	+	0.794586i	$0.707688\pi$
$374$	−7.10042	+	12.2983i	−0.367154	+	0.635929i
$375$	−6.05428	+	10.4863i	−0.312641	+	0.541511i
$376$	3.28212	+	5.68479i	0.169262	+	0.293171i
$377$	13.1268			0.676064
$378$	2.50239	−	5.64974i	0.128709	−	0.290591i
$379$	3.30019			0.169519			0.0847597	−	0.996401i	$-0.472988\pi$
$379$	3.30019			0.169519			0.0847597	+	0.996401i	$0.472988\pi$
$380$	−1.54116	−	2.66937i	−0.0790600	−	0.136936i
$381$	27.5270	−	47.6782i	1.41025	−	2.44263i
$382$	−7.42116	+	12.8538i	−0.379699	+	0.657659i
$383$	−5.74927	−	9.95803i	−0.293774	−	0.508832i	0.680925	−	0.732353i	$-0.261578\pi$
$383$	−5.74927	−	9.95803i	−0.293774	−	0.508832i	−0.974699	+	0.223522i	$0.928245\pi$
$384$	−2.62484			−0.133948
$385$	11.7172	+	16.0621i	0.597163	+	0.818602i
$386$	15.9895			0.813846
$387$	−24.8250	−	42.9982i	−1.26193	−	2.18572i
$388$	−6.89848	+	11.9485i	−0.350217	+	0.606594i
$389$	−6.22112	+	10.7753i	−0.315423	+	0.546329i	−0.979527	−	0.201311i	$-0.935480\pi$
$389$	−6.22112	+	10.7753i	−0.315423	+	0.546329i	0.664104	+	0.747640i	$0.268813\pi$
$390$	−13.7475	−	23.8113i	−0.696131	−	1.20573i
$391$	6.37167			0.322229
$392$	2.13744	−	6.66568i	0.107957	−	0.336668i
$393$	8.59870			0.433747
$394$	−7.44772	−	12.8998i	−0.375211	−	0.649884i
$395$	24.8658	−	43.0688i	1.25113	−	2.16703i
$396$	4.33465	−	7.50783i	0.217824	−	0.377283i
$397$	−12.0839	−	20.9299i	−0.606473	−	1.05044i	−0.991817	−	0.127668i	$-0.959251\pi$
$397$	−12.0839	−	20.9299i	−0.606473	−	1.05044i	0.385344	−	0.922773i	$-0.374083\pi$
$398$	24.1255			1.20930
$399$	−3.74156	−	5.12900i	−0.187312	−	0.256771i
$400$	6.36818			0.318409
$401$	−2.04156	−	3.53609i	−0.101951	−	0.176584i	0.810538	−	0.585687i	$-0.199175\pi$
$401$	−2.04156	−	3.53609i	−0.101951	−	0.176584i	−0.912488	+	0.409103i	$0.865842\pi$
$402$	9.02223	−	15.6270i	0.449988	−	0.779402i
$403$	−5.40328	+	9.35875i	−0.269156	+	0.466193i
$404$	3.53767	+	6.12743i	0.176006	+	0.304851i
$405$	−18.6758			−0.928006
$406$	−4.52721	+	10.2212i	−0.224682	+	0.507272i
$407$	−20.9899			−1.04043
$408$	8.36230	+	14.4839i	0.413996	+	0.717061i
$409$	−7.11172	+	12.3179i	−0.351652	+	0.609079i	−0.986539	−	0.163526i	$-0.947713\pi$
$409$	−7.11172	+	12.3179i	−0.351652	+	0.609079i	0.634887	+	0.772605i	$0.281047\pi$
$410$	−9.86230	+	17.0820i	−0.487064	+	0.843620i
$411$	−1.44049	−	2.49500i	−0.0710541	−	0.123069i
$412$	−15.7516			−0.776027
$413$	−7.81874	+	0.837020i	−0.384735	+	0.0411871i
$414$	−3.88977			−0.191172
$415$	10.9767	+	19.0122i	0.538824	+	0.933270i
$416$	−1.55337	+	2.69052i	−0.0761603	+	0.131914i
$417$	3.20981	−	5.55956i	0.157185	−	0.272253i
$418$	−1.01874	−	1.76451i	−0.0498282	−	0.0863050i
$419$	13.2679			0.648180			0.324090	−	0.946026i	$-0.394942\pi$
$419$	13.2679			0.648180			0.324090	+	0.946026i	$0.394942\pi$
$420$	23.2821	−	2.49242i	1.13605	−	0.121618i
$421$	−37.5460			−1.82988			−0.914940	−	0.403591i	$-0.867762\pi$
$421$	−37.5460			−1.82988			−0.914940	+	0.403591i	$0.867762\pi$
$422$	−9.05337	−	15.6809i	−0.440711	−	0.763334i
$423$	−12.7667	+	22.1125i	−0.620737	+	1.07515i
$424$	5.57386	−	9.65420i	0.270690	−	0.468850i
$425$	−20.2880	−	35.1398i	−0.984112	−	1.70453i
$426$	−4.23404			−0.205140
$427$	−7.29199	+	16.4634i	−0.352884	+	0.796719i
$428$	5.76776			0.278795
$429$	−9.08737	−	15.7398i	−0.438742	−	0.759924i
$430$	21.5185	−	37.2711i	1.03771	−	1.79737i
$431$	−4.64616	+	8.04739i	−0.223798	+	0.387629i	−0.955958	−	0.293503i	$-0.905179\pi$
$431$	−4.64616	+	8.04739i	−0.223798	+	0.387629i	0.732160	+	0.681132i	$0.238512\pi$
$432$	−1.16774	−	2.02259i	−0.0561831	−	0.0973121i
$433$	−14.1033			−0.677759			−0.338880	−	0.940830i	$-0.610048\pi$
$433$	−14.1033			−0.677759			−0.338880	+	0.940830i	$0.610048\pi$
$434$	−5.42374	−	7.43497i	−0.260348	−	0.356890i
$435$	−37.3939			−1.79290
$436$	9.46033	+	16.3858i	0.453067	+	0.784736i
$437$	−0.457092	+	0.791706i	−0.0218657	+	0.0378724i
$438$	7.79039	−	13.4934i	0.372239	−	0.644738i
$439$	−9.73851	−	16.8676i	−0.464794	−	0.805046i	0.534398	−	0.845233i	$-0.320538\pi$
$439$	−9.73851	−	16.8676i	−0.464794	−	0.805046i	−0.999192	+	0.0401862i	$0.987205\pi$
$440$	7.51460			0.358245
$441$	26.6113	−	5.76370i	1.26721	−	0.274462i
$442$	19.7952			0.941560
$443$	2.96621	+	5.13763i	0.140929	+	0.244096i	0.927847	−	0.372962i	$-0.121658\pi$
$443$	2.96621	+	5.13763i	0.140929	+	0.244096i	−0.786918	+	0.617058i	$0.788324\pi$
$444$	−12.3601	+	21.4083i	−0.586585	+	1.01600i
$445$	2.67233	−	4.62860i	0.126680	−	0.219417i
$446$	10.0961	+	17.4869i	0.478064	+	0.828031i
$447$	49.0517			2.32007
$448$	−1.55926	−	2.13746i	−0.0736679	−	0.100985i
$449$	−5.13864			−0.242507			−0.121254	−	0.992622i	$-0.538691\pi$
$449$	−5.13864			−0.242507			−0.121254	+	0.992622i	$0.538691\pi$
$450$	12.3854	+	21.4521i	0.583852	+	1.01126i
$451$	−6.51918	+	11.2916i	−0.306976	+	0.531699i
$452$	5.63486	−	9.75986i	0.265041	−	0.459065i
$453$	0.702839	+	1.21735i	0.0330222	+	0.0571962i
$454$	19.8187			0.930137
$455$	11.2235	−	25.3397i	0.526166	−	1.18794i
$456$	−2.39958			−0.112371
$457$	−18.3152	−	31.7229i	−0.856749	−	1.48393i	−0.875013	−	0.484100i	$-0.839147\pi$
$457$	−18.3152	−	31.7229i	−0.856749	−	1.48393i	0.0182636	−	0.999833i	$-0.494186\pi$
$458$	9.08018	−	15.7273i	0.424289	−	0.734890i
$459$	−7.44049	+	12.8873i	−0.347292	+	0.601528i
$460$	−1.68584	−	2.91996i	−0.0786025	−	0.136144i
$461$	−16.0663			−0.748281			−0.374140	−	0.927372i	$-0.622062\pi$
$461$	−16.0663			−0.748281			−0.374140	+	0.927372i	$0.622062\pi$
$462$	15.3900	−	1.64754i	0.716005	−	0.0766505i
$463$	14.7503			0.685505			0.342753	−	0.939426i	$-0.388641\pi$
$463$	14.7503			0.685505			0.342753	+	0.939426i	$0.388641\pi$
$464$	2.11263	+	3.65918i	0.0980763	+	0.169873i
$465$	15.3922	−	26.6600i	0.713794	−	1.23633i
$466$	6.20567	−	10.7485i	0.287472	−	0.497917i
$467$	−14.8514	−	25.7234i	−0.687240	−	1.19034i	−0.972727	−	0.231953i	$-0.925489\pi$
$467$	−14.8514	−	25.7234i	−0.687240	−	1.19034i	0.285487	−	0.958383i	$-0.407845\pi$
$468$	−12.0845			−0.558607
$469$	18.0849	−	1.93604i	0.835083	−	0.0893982i
$470$	−22.1325			−1.02089
$471$	13.7024	+	23.7332i	0.631372	+	1.09357i
$472$	−1.48605	+	2.57391i	−0.0684008	+	0.118474i
$473$	14.2242	−	24.6370i	0.654028	−	1.13281i
$474$	−19.3579	−	33.5289i	−0.889139	−	1.54003i
$475$	5.82169			0.267117
$476$	−6.82702	+	15.4136i	−0.312916	+	0.706482i
$477$	43.3620			1.98541
$478$	−0.434020	−	0.751745i	−0.0198516	−	0.0343840i
$479$	6.02332	−	10.4327i	0.275213	−	0.476682i	−0.694976	−	0.719033i	$-0.744585\pi$
$479$	6.02332	−	10.4327i	0.275213	−	0.476682i	0.970189	+	0.242351i	$0.0779184\pi$
$480$	4.42505	−	7.66440i	0.201975	−	0.349831i
$481$	14.6294	+	25.3388i	0.667042	+	1.15535i
$482$	−1.58697			−0.0722845
$483$	−4.09279	−	5.61047i	−0.186228	−	0.255285i
$484$	−6.03269			−0.274213
$485$	−23.2594	−	40.2865i	−1.05616	−	1.82932i
$486$	−10.7727	+	18.6589i	−0.488662	+	0.846387i
$487$	−16.9658	+	29.3856i	−0.768794	+	1.33159i	0.169423	+	0.985543i	$0.445810\pi$
$487$	−16.9658	+	29.3856i	−0.768794	+	1.33159i	−0.938217	+	0.346047i	$0.887524\pi$
$488$	3.40282	+	5.89385i	0.154038	+	0.266802i
$489$	10.9603			0.495643
$490$	15.8601	+	17.4785i	0.716487	+	0.789598i
$491$	−23.1813			−1.04616			−0.523079	−	0.852284i	$-0.675217\pi$
$491$	−23.1813			−1.04616			−0.523079	+	0.852284i	$0.675217\pi$
$492$	7.67777	+	13.2983i	0.346140	+	0.599533i
$493$	13.4610	−	23.3151i	0.606252	−	1.05006i
$494$	−1.42007	+	2.45963i	−0.0638918	+	0.110664i
$495$	14.6150	+	25.3140i	0.656896	+	1.13778i
$496$	−3.47842			−0.156186
$497$	−2.51519	−	3.44787i	−0.112822	−	0.154658i
$498$	17.0906			0.765848
$499$	−4.40107	−	7.62288i	−0.197019	−	0.341247i	0.750542	−	0.660823i	$-0.229793\pi$
$499$	−4.40107	−	7.62288i	−0.197019	−	0.341247i	−0.947561	+	0.319576i	$0.896459\pi$
$500$	−2.30653	+	3.99504i	−0.103151	+	0.178663i
$501$	9.53633	−	16.5174i	0.426052	−	0.737943i
$502$	−1.54988	−	2.68447i	−0.0691746	−	0.119814i
$503$	−31.0653			−1.38513			−0.692566	−	0.721355i	$-0.743520\pi$
$503$	−31.0653			−1.38513			−0.692566	+	0.721355i	$0.743520\pi$
$504$	4.16774	−	9.40967i	0.185646	−	0.419140i
$505$	−23.8558			−1.06157
$506$	−1.11437	−	1.93015i	−0.0495399	−	0.0858056i
$507$	4.39416	−	7.61091i	0.195151	−	0.338012i
$508$	10.4871	−	18.1643i	0.465291	−	0.805908i
$509$	7.37800	+	12.7791i	0.327024	+	0.566422i	0.981920	−	0.189297i	$-0.0606209\pi$
$509$	7.37800	+	12.7791i	0.327024	+	0.566422i	−0.654896	+	0.755719i	$0.727288\pi$
$510$	−56.3899			−2.49699
$511$	15.6157	−	1.67171i	0.690798	−	0.0739521i
$512$	−1.00000			−0.0441942
$513$	−1.06753	−	1.84902i	−0.0471327	−	0.0816363i
$514$	−3.48695	+	6.03958i	−0.153803	+	0.266394i
$515$	26.5547	−	45.9940i	1.17014	−	2.02674i
$516$	−16.7521	−	29.0154i	−0.737469	−	1.27733i
$517$	−14.6300			−0.643427
$518$	−24.7756	+	2.65231i	−1.08858	+	0.116536i
$519$	−6.36600			−0.279437
$520$	−5.23746	−	9.07155i	−0.229678	−	0.397814i
$521$	9.69476	−	16.7918i	0.424735	−	0.735663i	−0.571660	−	0.820490i	$-0.693701\pi$
$521$	9.69476	−	16.7918i	0.424735	−	0.735663i	0.996396	+	0.0848273i	$0.0270339\pi$
$522$	−8.21763	+	14.2333i	−0.359676	+	0.622977i
$523$	2.65365	+	4.59625i	0.116036	+	0.200980i	0.918193	−	0.396132i	$-0.129648\pi$
$523$	2.65365	+	4.59625i	0.116036	+	0.200980i	−0.802157	+	0.597113i	$0.796315\pi$
$524$	3.27590			0.143108
$525$	−17.9100	+	40.4360i	−0.781656	+	1.76477i
$526$	−4.56902			−0.199219
$527$	11.0817	+	19.1940i	0.482725	+	0.836105i
$528$	2.92505	−	5.06633i	0.127296	−	0.220484i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	18.7932	+	32.5508i	0.816326	+	1.41392i
$531$	−11.5607			−0.501694
$532$	−1.42545	−	1.95403i	−0.0618009	−	0.0847178i
$533$	18.1747			0.787235
$534$	−2.08040	−	3.60335i	−0.0900275	−	0.155932i
$535$	−9.72351	+	16.8416i	−0.420384	+	0.728126i
$536$	3.43725	−	5.95350i	0.148467	−	0.257152i
$537$	18.2034	+	31.5292i	0.785535	+	1.36059i
$538$	−29.7516			−1.28268
$539$	10.4839	+	11.5536i	0.451572	+	0.497651i
$540$	7.87451			0.338865
$541$	21.4095	+	37.0824i	0.920468	+	1.59430i	0.798693	+	0.601739i	$0.205525\pi$
$541$	21.4095	+	37.0824i	0.920468	+	1.59430i	0.121775	+	0.992558i	$0.461141\pi$
$542$	−2.69495	+	4.66780i	−0.115758	+	0.200499i
$543$	−4.57077	+	7.91680i	−0.196150	+	0.339742i
$544$	3.18584	+	5.51803i	0.136592	+	0.236584i
$545$	−63.7943			−2.73265
$546$	−12.7153	−	17.4303i	−0.544163	−	0.745948i
$547$	1.51910			0.0649521			0.0324761	−	0.999473i	$-0.489661\pi$
$547$	1.51910			0.0649521			0.0324761	+	0.999473i	$0.489661\pi$
$548$	−0.548792	−	0.950535i	−0.0234432	−	0.0406049i
$549$	−13.2362	+	22.9257i	−0.564905	+	0.978445i
$550$	−7.09653	+	12.2916i	−0.302597	+	0.524113i
$551$	1.93133	+	3.34516i	0.0822774	+	0.142509i
$552$	−2.62484			−0.111720
$553$	15.8039	−	35.6810i	0.672050	−	1.51731i
$554$	−1.56852			−0.0666402
$555$	−41.6743	−	72.1820i	−1.76897	−	3.06395i
$556$	1.22286	−	2.11806i	0.0518609	−	0.0898257i
$557$	6.28851	−	10.8920i	0.266453	−	0.461509i	−0.701491	−	0.712679i	$-0.747482\pi$
$557$	6.28851	−	10.8920i	0.266453	−	0.461509i	0.967943	+	0.251169i	$0.0808151\pi$
$558$	−6.76512	−	11.7175i	−0.286390	−	0.496042i
$559$	−39.6553			−1.67724
$560$	8.86993	−	0.949553i	0.374823	−	0.0401259i
$561$	−37.2749			−1.57375
$562$	7.70044	+	13.3376i	0.324823	+	0.562611i
$563$	5.45510	−	9.44851i	0.229905	−	0.398207i	−0.727875	−	0.685710i	$-0.759492\pi$
$563$	5.45510	−	9.44851i	0.229905	−	0.398207i	0.957780	+	0.287503i	$0.0928251\pi$
$564$	−8.61502	+	14.9217i	−0.362758	+	0.628315i
$565$	18.9989	+	32.9071i	0.799290	+	1.38441i
$566$	15.9882			0.672036
$567$	−14.5716	+	1.55993i	−0.611950	+	0.0655111i
$568$	−1.61307			−0.0676829
$569$	−16.2432	−	28.1340i	−0.680950	−	1.17944i	−0.974691	−	0.223555i	$-0.928234\pi$
$569$	−16.2432	−	28.1340i	−0.680950	−	1.17944i	0.293741	−	0.955885i	$-0.405100\pi$
$570$	4.04530	−	7.00667i	0.169439	−	0.293477i
$571$	−5.40910	+	9.36883i	−0.226364	+	0.392073i	−0.956728	−	0.290985i	$-0.906017\pi$
$571$	−5.40910	+	9.36883i	−0.226364	+	0.392073i	0.730364	+	0.683058i	$0.239350\pi$
$572$	−3.46207	−	5.99648i	−0.144756	−	0.250726i
$573$	−38.9586			−1.62752
$574$	−6.26816	+	14.1519i	−0.261628	+	0.590687i
$575$	6.36818			0.265572
$576$	−1.94488	−	3.36864i	−0.0810368	−	0.140360i
$577$	3.93217	−	6.81072i	0.163698	−	0.283534i	−0.772494	−	0.635022i	$-0.780991\pi$
$577$	3.93217	−	6.81072i	0.163698	−	0.283534i	0.936192	+	0.351488i	$0.114324\pi$
$578$	11.7991	−	20.4367i	0.490778	−	0.850053i
$579$	20.9850	+	36.3470i	0.872105	+	1.51053i
$580$	−14.2462			−0.591541
$581$	10.1525	+	13.9172i	0.421196	+	0.577384i
$582$	−36.2148			−1.50115
$583$	12.4227	+	21.5168i	0.514496	+	0.891133i
$584$	2.96795	−	5.14065i	0.122815	−	0.212722i
$585$	20.3725	−	35.2862i	0.842300	−	1.45891i
$586$	6.40895	+	11.1006i	0.264751	+	0.458563i
$587$	31.4964			1.29999			0.649997	−	0.759937i	$-0.274770\pi$
$587$	31.4964			1.29999			0.649997	+	0.759937i	$0.274770\pi$
$588$	17.9575	−	3.88938i	0.740554	−	0.160395i
$589$	−3.17991			−0.131026
$590$	−5.01046	−	8.67838i	−0.206278	−	0.357283i
$591$	19.5490	−	33.8599i	0.804140	−	1.39281i
$592$	−4.70891	+	8.15607i	−0.193535	+	0.335212i
$593$	−2.67926	−	4.64062i	−0.110024	−	0.190567i	0.805756	−	0.592248i	$-0.201759\pi$
$593$	−2.67926	−	4.64062i	−0.110024	−	0.190567i	−0.915780	+	0.401681i	$0.868426\pi$
$594$	5.20521			0.213572
$595$	−33.4978	−	45.9194i	−1.37328	−	1.88251i
$596$	18.6875			0.765471
$597$	31.6627	+	54.8414i	1.29587	+	2.24451i
$598$	−1.55337	+	2.69052i	−0.0635221	+	0.110024i
$599$	9.54574	−	16.5337i	0.390029	−	0.675549i	−0.602424	−	0.798176i	$-0.705798\pi$
$599$	9.54574	−	16.5337i	0.390029	−	0.675549i	0.992453	+	0.122627i	$0.0391318\pi$
$600$	8.35772	+	14.4760i	0.341202	+	0.590980i
$601$	32.3703			1.32041			0.660206	−	0.751085i	$-0.270469\pi$
$601$	32.3703			1.32041			0.660206	+	0.751085i	$0.270469\pi$
$602$	13.6765	−	30.8778i	0.557411	−	1.25849i
$603$	26.7402			1.08895
$604$	0.267765	+	0.463782i	0.0108952	+	0.0188710i
$605$	10.1701	−	17.6152i	0.413475	−	0.716160i
$606$	−9.28581	+	16.0835i	−0.377210	+	0.653348i
$607$	16.9405	+	29.3418i	0.687593	+	1.19095i	0.972614	+	0.232425i	$0.0746661\pi$
$607$	16.9405	+	29.3418i	0.687593	+	1.19095i	−0.285021	+	0.958521i	$0.592001\pi$
$608$	−0.914183			−0.0370750
$609$	−29.1763	+	3.12341i	−1.18228	+	0.126567i
$610$	−22.9464			−0.929071
$611$	10.1967	+	17.6612i	0.412514	+	0.714496i
$612$	−12.3922	+	21.4638i	−0.500923	+	0.867625i
$613$	−8.47209	+	14.6741i	−0.342185	+	0.592681i	−0.984838	−	0.173476i	$-0.944500\pi$
$613$	−8.47209	+	14.6741i	−0.342185	+	0.592681i	0.642654	+	0.766157i	$0.277833\pi$
$614$	−0.250976	−	0.434703i	−0.0101286	−	0.0175432i
$615$	−51.7738			−2.08772
$616$	5.86320	−	0.627674i	0.236235	−	0.0252897i
$617$	−4.06228			−0.163541			−0.0817707	−	0.996651i	$-0.526058\pi$
$617$	−4.06228			−0.163541			−0.0817707	+	0.996651i	$0.526058\pi$
$618$	−20.6727	−	35.8062i	−0.831579	−	1.44034i
$619$	−3.33355	+	5.77388i	−0.133987	+	0.232072i	−0.925210	−	0.379456i	$-0.876111\pi$
$619$	−3.33355	+	5.77388i	−0.133987	+	0.232072i	0.791223	+	0.611528i	$0.209445\pi$
$620$	5.86405	−	10.1568i	0.235506	−	0.407908i
$621$	−1.16774	−	2.02259i	−0.0468600	−	0.0811639i
$622$	−15.3673			−0.616173
$623$	1.69844	−	3.83464i	0.0680467	−	0.153632i
$624$	−8.15470			−0.326449
$625$	8.14358	+	14.1051i	0.325743	+	0.564204i
$626$	−3.80983	+	6.59882i	−0.152272	+	0.263742i
$627$	2.67403	−	4.63155i	0.106790	−	0.184966i
$628$	5.22028	+	9.04178i	0.208312	+	0.360806i
$629$	60.0073			2.39265
$630$	20.4497	+	28.0328i	0.814734	+	1.11685i
$631$	−11.8611			−0.472181			−0.236091	−	0.971731i	$-0.575866\pi$
$631$	−11.8611			−0.472181			−0.236091	+	0.971731i	$0.575866\pi$
$632$	−7.37491	−	12.7737i	−0.293358	−	0.508111i
$633$	23.7636	−	41.1598i	0.944519	−	1.63596i
$634$	−9.14921	+	15.8469i	−0.363362	+	0.629361i
$635$	35.3592	+	61.2439i	1.40319	+	2.43039i
$636$	29.2609			1.16027
$637$	6.64049	−	20.7086i	0.263106	−	0.820504i
$638$	−9.41702			−0.372823
$639$	−3.13723	−	5.43384i	−0.124107	−	0.214960i
$640$	1.68584	−	2.91996i	0.0666386	−	0.115421i
$641$	−10.9590	+	18.9816i	−0.432856	+	0.749729i	−0.997118	−	0.0758670i	$-0.975828\pi$
$641$	−10.9590	+	18.9816i	−0.432856	+	0.749729i	0.564262	+	0.825596i	$0.309161\pi$
$642$	7.56972	+	13.1111i	0.298753	+	0.517455i
$643$	11.9456			0.471087			0.235544	−	0.971864i	$-0.424313\pi$
$643$	11.9456			0.471087			0.235544	+	0.971864i	$0.424313\pi$
$644$	−1.55926	−	2.13746i	−0.0614433	−	0.0842276i
$645$	112.965			4.44799
$646$	2.91244	+	5.04449i	0.114588	+	0.198473i
$647$	−21.5405	+	37.3093i	−0.846845	+	1.46678i	0.0371647	+	0.999309i	$0.488167\pi$
$647$	−21.5405	+	37.3093i	−0.846845	+	1.46678i	−0.884009	+	0.467469i	$0.845166\pi$
$648$	−2.76951	+	4.79693i	−0.108797	+	0.188441i
$649$	−3.31202	−	5.73659i	−0.130008	−	0.225181i
$650$	19.7843			0.776005
$651$	9.78277	−	22.0869i	0.383417	−	0.865654i
$652$	4.17562			0.163530
$653$	−18.2629	−	31.6323i	−0.714684	−	1.23787i	−0.963081	−	0.269210i	$-0.913237\pi$
$653$	−18.2629	−	31.6323i	−0.714684	−	1.23787i	0.248398	−	0.968658i	$-0.420096\pi$
$654$	−24.8318	+	43.0100i	−0.971001	+	1.68182i
$655$	−5.52263	+	9.56548i	−0.215787	+	0.373754i
$656$	2.92505	+	5.06633i	0.114204	+	0.197807i
$657$	23.0893			0.900799
$658$	−17.2687	+	1.84866i	−0.673203	+	0.0720684i
$659$	49.2823			1.91976			0.959882	−	0.280403i	$-0.0904681\pi$
$659$	49.2823			1.91976			0.959882	+	0.280403i	$0.0904681\pi$
$660$	9.86230	+	17.0820i	0.383890	+	0.664916i
$661$	−16.8683	+	29.2168i	−0.656102	+	1.13640i	0.325514	+	0.945537i	$0.394463\pi$
$661$	−16.8683	+	29.2168i	−0.656102	+	1.13640i	−0.981616	+	0.190865i	$0.938871\pi$
$662$	5.83639	−	10.1089i	0.226838	−	0.392895i
$663$	25.9795	+	44.9979i	1.00896	+	1.74757i
$664$	6.51111			0.252680
$665$	8.10874	−	0.868065i	0.314443	−	0.0336621i
$666$	−36.6331			−1.41950
$667$	2.11263	+	3.65918i	0.0818013	+	0.141684i
$668$	3.63311	−	6.29274i	0.140569	−	0.243473i
$669$	−26.5006	+	45.9003i	−1.02457	+	1.77461i
$670$	11.5893	+	20.0733i	0.447734	+	0.775498i
$671$	−15.1680			−0.585555
$672$	2.81242	−	6.34970i	0.108491	−	0.244945i
$673$	1.47443			0.0568351			0.0284175	−	0.999596i	$-0.490953\pi$
$673$	1.47443			0.0568351			0.0284175	+	0.999596i	$0.490953\pi$
$674$	−12.0621	−	20.8922i	−0.464614	−	0.804736i
$675$	−7.43641	+	12.8802i	−0.286228	+	0.495761i
$676$	1.67407	−	2.89957i	0.0643873	−	0.111522i
$677$	−14.1882	−	24.5747i	−0.545298	−	0.944484i	−0.998588	−	0.0531208i	$-0.983083\pi$
$677$	−14.1882	−	24.5747i	−0.545298	−	0.944484i	0.453290	−	0.891363i	$-0.350250\pi$
$678$	29.5812			1.13606
$679$	−21.5130	−	29.4904i	−0.825593	−	1.13174i
$680$	−21.4832			−0.823843
$681$	26.0104	+	45.0514i	0.996721	+	1.72637i
$682$	3.87625	−	6.71387i	0.148429	−	0.257087i
$683$	19.0782	−	33.0444i	0.730006	−	1.26441i	−0.226874	−	0.973924i	$-0.572850\pi$
$683$	19.0782	−	33.0444i	0.730006	−	1.26441i	0.956880	−	0.290484i	$-0.0938163\pi$
$684$	−1.77798	−	3.07955i	−0.0679827	−	0.117750i
$685$	3.70069			0.141396
$686$	13.8346	+	12.3127i	0.528209	+	0.470101i
$687$	47.6680			1.81865
$688$	−6.38214	−	11.0542i	−0.243317	−	0.421437i
$689$	17.3166	−	29.9931i	0.659708	−	1.14265i
$690$	4.42505	−	7.66440i	0.168459	−	0.291779i
$691$	−12.0540	−	20.8781i	−0.458555	−	0.794240i	0.540330	−	0.841453i	$-0.318299\pi$
$691$	−12.0540	−	20.8781i	−0.458555	−	0.794240i	−0.998885	+	0.0472128i	$0.984966\pi$
$692$	−2.42530			−0.0921959
$693$	13.5177	+	18.5302i	0.513493	+	0.703906i
$694$	−22.3260			−0.847484
$695$	4.12309	+	7.14140i	0.156398	+	0.270889i
$696$	−5.54530	+	9.60474i	−0.210194	+	0.364067i
$697$	18.6374	−	32.2810i	0.705943	−	1.22273i
$698$	−4.32419	−	7.48971i	−0.163673	−	0.283490i
$699$	32.5778			1.23220
$700$	−6.82328	+	15.4052i	−0.257896	+	0.582261i
$701$	−13.3899			−0.505730			−0.252865	−	0.967502i	$-0.581373\pi$
$701$	−13.3899			−0.505730			−0.252865	+	0.967502i	$0.581373\pi$
$702$	−3.62788	−	6.28368i	−0.136926	−	0.237162i
$703$	−4.30480	+	7.45614i	−0.162359	+	0.281214i
$704$	1.11437	−	1.93015i	0.0419995	−	0.0727453i
$705$	−29.0470	−	50.3110i	−1.09397	−	1.89482i
$706$	−31.5690			−1.18812
$707$	−18.6133	+	1.99261i	−0.700024	+	0.0749396i
$708$	−7.80126			−0.293189
$709$	15.1412	+	26.2253i	0.568639	+	0.984911i	0.996701	+	0.0811620i	$0.0258631\pi$
$709$	15.1412	+	26.2253i	0.568639	+	0.984911i	−0.428062	+	0.903749i	$0.640804\pi$
$710$	2.71937	−	4.71009i	0.102056	−	0.176767i
$711$	28.6867	−	49.6868i	1.07583	−	1.86340i
$712$	−0.792581	−	1.37279i	−0.0297032	−	0.0514475i
$713$	−3.47842			−0.130268
$714$	−43.9977	+	4.71009i	−1.64657	+	0.176271i
$715$	23.3459			0.873089
$716$	6.93507	+	12.0119i	0.259176	+	0.448905i
$717$	1.13923	−	1.97321i	0.0425454	−	0.0736908i
$718$	7.51395	−	13.0145i	0.280418	−	0.485699i
$719$	−0.515699	−	0.893216i	−0.0192323	−	0.0333113i	0.856249	−	0.516563i	$-0.172789\pi$
$719$	−0.515699	−	0.893216i	−0.0192323	−	0.0333113i	−0.875481	+	0.483252i	$0.839456\pi$
$720$	13.1150			0.488768
$721$	16.8773	−	38.1045i	0.628544	−	1.41909i
$722$	18.1643			0.676004
$723$	−2.08277	−	3.60746i	−0.0774590	−	0.134163i
$724$	−1.74135	+	3.01611i	−0.0647169	+	0.112093i
$725$	13.4536	−	23.3023i	0.499654	−	0.865426i
$726$	−7.91742	−	13.7134i	−0.293843	−	0.508951i
$727$	−19.4291			−0.720584			−0.360292	−	0.932839i	$-0.617323\pi$
$727$	−19.4291			−0.720584			−0.360292	+	0.932839i	$0.617323\pi$
$728$	−4.84421	−	6.64053i	−0.179538	−	0.246114i
$729$	−39.9363			−1.47912
$730$	10.0070	+	17.3326i	0.370375	+	0.641508i
$731$	−40.6649	+	70.4337i	−1.50405	+	2.60508i
$732$	−8.93183	+	15.4704i	−0.330130	+	0.571802i
$733$	3.40151	+	5.89159i	0.125638	+	0.217611i	0.921982	−	0.387233i	$-0.126569\pi$
$733$	3.40151	+	5.89159i	0.125638	+	0.217611i	−0.796344	+	0.604844i	$0.793236\pi$
$734$	34.9869			1.29139
$735$	−18.9166	+	58.9919i	−0.697748	+	2.17595i
$736$	−1.00000			−0.0368605
$737$	7.66076	+	13.2688i	0.282188	+	0.488764i
$738$	−11.3777	+	19.7068i	−0.418821	+	0.725418i
$739$	−12.3841	+	21.4499i	−0.455558	+	0.789049i	−0.998720	−	0.0505786i	$-0.983893\pi$
$739$	−12.3841	+	21.4499i	−0.455558	+	0.789049i	0.543162	+	0.839628i	$0.317227\pi$
$740$	−15.8769	−	27.4996i	−0.583647	−	1.01091i
$741$	−7.45488			−0.273862
$742$	17.3821	+	23.8278i	0.638118	+	0.874745i
$743$	−46.9124			−1.72105			−0.860524	−	0.509410i	$-0.829864\pi$
$743$	−46.9124			−1.72105			−0.860524	+	0.509410i	$0.829864\pi$
$744$	−4.56514	−	7.90705i	−0.167366	−	0.289887i
$745$	−31.5041	+	54.5668i	−1.15422	+	1.99917i
$746$	−7.42700	+	12.8639i	−0.271922	+	0.470982i
$747$	12.6634	+	21.9336i	0.463328	+	0.802507i
$748$	−14.2008			−0.519234
$749$	−6.17995	+	13.9527i	−0.225811	+	0.509821i
$750$	−12.1086			−0.442142
$751$	−3.83919	−	6.64967i	−0.140094	−	0.242650i	0.787438	−	0.616394i	$-0.211407\pi$
$751$	−3.83919	−	6.64967i	−0.140094	−	0.242650i	−0.927532	+	0.373744i	$0.878074\pi$
$752$	−3.28212	+	5.68479i	−0.119687	+	0.207303i
$753$	4.06819	−	7.04631i	0.148253	−	0.256782i
$754$	6.56339	+	11.3681i	0.239025	+	0.414003i
$755$	−1.80563			−0.0657136
$756$	6.14402	−	0.657736i	0.223456	−	0.0239216i
$757$	−11.3250			−0.411615			−0.205807	−	0.978593i	$-0.565982\pi$
$757$	−11.3250			−0.411615			−0.205807	+	0.978593i	$0.565982\pi$
$758$	1.65009	+	2.85805i	0.0599341	+	0.103809i
$759$	2.92505	−	5.06633i	0.106172	−	0.183896i
$760$	1.54116	−	2.66937i	0.0559039	−	0.0968284i
$761$	9.05776	+	15.6885i	0.328344	+	0.568708i	0.982183	−	0.187925i	$-0.0601763\pi$
$761$	9.05776	+	15.6885i	0.328344	+	0.568708i	−0.653840	+	0.756633i	$0.726843\pi$
$762$	55.0540			1.99440
$763$	−49.7749	+	5.32856i	−1.80197	+	0.192907i
$764$	−14.8423			−0.536976
$765$	−41.7823	−	72.3691i	−1.51064	−	2.61651i
$766$	5.74927	−	9.95803i	0.207730	−	0.359798i
$767$	−4.61677	+	7.99647i	−0.166702	+	0.288736i
$768$	−1.31242	−	2.27317i	−0.0473578	−	0.0820261i
$769$	−37.2805			−1.34437			−0.672184	−	0.740384i	$-0.734644\pi$
$769$	−37.2805			−1.34437			−0.672184	+	0.740384i	$0.734644\pi$
$770$	−8.05163	+	18.1784i	−0.290161	+	0.655106i

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.31242 + 2.27317i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.68584 - 2.91996i) q^{5} -2.62484 q^{6} +(-1.55926 - 2.13746i) q^{7} -1.00000 q^{8} +(-1.94488 - 3.36864i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.31242 + 2.27317i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.68584 - 2.91996i) q^{5} -2.62484 q^{6} +(-1.55926 - 2.13746i) q^{7} -1.00000 q^{8} +(-1.94488 - 3.36864i) q^{9} +(1.68584 - 2.91996i) q^{10} +(1.11437 - 1.93015i) q^{11} +(-1.31242 - 2.27317i) q^{12} -3.10674 q^{13} +(1.07146 - 2.41908i) q^{14} +8.85009 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.18584 + 5.51803i) q^{17} +(1.94488 - 3.36864i) q^{18} +(-0.457092 - 0.791706i) q^{19} +3.37167 q^{20} +(6.90521 - 0.739223i) q^{21} +2.22875 q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.31242 - 2.27317i) q^{24} +(-3.18409 + 5.51501i) q^{25} +(-1.55337 - 2.69052i) q^{26} +2.33549 q^{27} +(2.63072 - 0.281626i) q^{28} -4.22526 q^{29} +(4.42505 + 7.66440i) q^{30} +(1.73921 - 3.01240i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.92505 + 5.06633i) q^{33} -6.37167 q^{34} +(-3.61263 + 8.15636i) q^{35} +3.88977 q^{36} +(-4.70891 - 8.15607i) q^{37} +(0.457092 - 0.791706i) q^{38} +(4.07735 - 7.06217i) q^{39} +(1.68584 + 2.91996i) q^{40} -5.85009 q^{41} +(4.09279 + 5.61047i) q^{42} +12.7643 q^{43} +(1.11437 + 1.93015i) q^{44} +(-6.55751 + 11.3579i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-3.28212 - 5.68479i) q^{47} +2.62484 q^{48} +(-2.13744 + 6.66568i) q^{49} -6.36818 q^{50} +(-8.36230 - 14.4839i) q^{51} +(1.55337 - 2.69052i) q^{52} +(-5.57386 + 9.65420i) q^{53} +(1.16774 + 2.02259i) q^{54} -7.51460 q^{55} +(1.55926 + 2.13746i) q^{56} +2.39958 q^{57} +(-2.11263 - 3.65918i) q^{58} +(1.48605 - 2.57391i) q^{59} +(-4.42505 + 7.66440i) q^{60} +(-3.40282 - 5.89385i) q^{61} +3.47842 q^{62} +(-4.16774 + 9.40967i) q^{63} +1.00000 q^{64} +(5.23746 + 9.07155i) q^{65} +(-2.92505 + 5.06633i) q^{66} +(-3.43725 + 5.95350i) q^{67} +(-3.18584 - 5.51803i) q^{68} +2.62484 q^{69} +(-8.86993 + 0.949553i) q^{70} +1.61307 q^{71} +(1.94488 + 3.36864i) q^{72} +(-2.96795 + 5.14065i) q^{73} +(4.70891 - 8.15607i) q^{74} +(-8.35772 - 14.4760i) q^{75} +0.914183 q^{76} +(-5.86320 + 0.627674i) q^{77} +8.15470 q^{78} +(7.37491 + 12.7737i) q^{79} +(-1.68584 + 2.91996i) q^{80} +(2.76951 - 4.79693i) q^{81} +(-2.92505 - 5.06633i) q^{82} -6.51111 q^{83} +(-2.81242 + 6.34970i) q^{84} +21.4832 q^{85} +(6.38214 + 11.0542i) q^{86} +(5.54530 - 9.60474i) q^{87} +(-1.11437 + 1.93015i) q^{88} +(0.792581 + 1.37279i) q^{89} -13.1150 q^{90} +(4.84421 + 6.64053i) q^{91} +1.00000 q^{92} +(4.56514 + 7.90705i) q^{93} +(3.28212 - 5.68479i) q^{94} +(-1.54116 + 2.66937i) q^{95} +(1.31242 + 2.27317i) q^{96} +13.7970 q^{97} +(-6.84137 + 1.48176i) q^{98} -8.66930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 6 q^{15} - 4 q^{16} - 15 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} - q^{21} + 12 q^{22} - 4 q^{23} + q^{24} + 5 q^{25} - q^{26} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 3 q^{30} - 8 q^{31} + 4 q^{32} - 9 q^{33} - 30 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} - q^{38} + 25 q^{39} + 3 q^{40} + 18 q^{41} - 14 q^{42} + 28 q^{43} + 6 q^{44} - 21 q^{45} + 4 q^{46} - 9 q^{47} + 2 q^{48} + 5 q^{49} + 10 q^{50} - 6 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 24 q^{55} + q^{56} + 46 q^{57} + 6 q^{58} - 12 q^{59} - 3 q^{60} - 11 q^{61} - 16 q^{62} - 19 q^{63} + 8 q^{64} + 9 q^{66} + q^{67} - 15 q^{68} + 2 q^{69} - 30 q^{70} - 6 q^{71} + 7 q^{72} + 4 q^{73} + 8 q^{74} - 22 q^{75} - 2 q^{76} - 9 q^{77} + 50 q^{78} - 5 q^{79} - 3 q^{80} + 8 q^{81} + 9 q^{82} + 24 q^{83} - 13 q^{84} + 48 q^{85} + 14 q^{86} + 9 q^{87} - 6 q^{88} - 27 q^{89} - 42 q^{90} - 26 q^{91} + 8 q^{92} + 25 q^{93} + 9 q^{94} + 3 q^{95} + q^{96} + 4 q^{97} - 26 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 2 * q^13 + q^14 + 6 * q^15 - 4 * q^16 - 15 * q^17 + 7 * q^18 + q^19 + 6 * q^20 - q^21 + 12 * q^22 - 4 * q^23 + q^24 + 5 * q^25 - q^26 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 3 * q^30 - 8 * q^31 + 4 * q^32 - 9 * q^33 - 30 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 - q^38 + 25 * q^39 + 3 * q^40 + 18 * q^41 - 14 * q^42 + 28 * q^43 + 6 * q^44 - 21 * q^45 + 4 * q^46 - 9 * q^47 + 2 * q^48 + 5 * q^49 + 10 * q^50 - 6 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 24 * q^55 + q^56 + 46 * q^57 + 6 * q^58 - 12 * q^59 - 3 * q^60 - 11 * q^61 - 16 * q^62 - 19 * q^63 + 8 * q^64 + 9 * q^66 + q^67 - 15 * q^68 + 2 * q^69 - 30 * q^70 - 6 * q^71 + 7 * q^72 + 4 * q^73 + 8 * q^74 - 22 * q^75 - 2 * q^76 - 9 * q^77 + 50 * q^78 - 5 * q^79 - 3 * q^80 + 8 * q^81 + 9 * q^82 + 24 * q^83 - 13 * q^84 + 48 * q^85 + 14 * q^86 + 9 * q^87 - 6 * q^88 - 27 * q^89 - 42 * q^90 - 26 * q^91 + 8 * q^92 + 25 * q^93 + 9 * q^94 + 3 * q^95 + q^96 + 4 * q^97 - 26 * q^98 - 18 * q^99

Introduction

L-functions

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