LMFDB - Embedded newform 336.2.w.b.85.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (of order $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			85.4
Character	$\chi$	$=$	336.85
Dual form			336.2.w.b.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.884433 - 1.10353i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.435558 + 1.95200i) q^{4} +(-1.84737 - 1.84737i) q^{5} +(-1.40570 - 0.154926i) q^{6} -1.00000i q^{7} +(2.53931 - 1.24576i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.884433 - 1.10353i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.435558 + 1.95200i) q^{4} +(-1.84737 - 1.84737i) q^{5} +(-1.40570 - 0.154926i) q^{6} -1.00000i q^{7} +(2.53931 - 1.24576i) q^{8} -1.00000i q^{9} +(-0.404756 + 3.67251i) q^{10} +(-1.28297 - 1.28297i) q^{11} +(1.07228 + 1.68826i) q^{12} +(0.573383 - 0.573383i) q^{13} +(-1.10353 + 0.884433i) q^{14} -2.61258 q^{15} +(-3.62058 - 1.70042i) q^{16} -3.76640 q^{17} +(-1.10353 + 0.884433i) q^{18} +(-5.58859 + 5.58859i) q^{19} +(4.41071 - 2.80143i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(-0.281097 + 2.55050i) q^{22} -8.77599i q^{23} +(0.914679 - 2.67645i) q^{24} +1.82558i q^{25} +(-1.13986 - 0.125627i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.95200 + 0.435558i) q^{28} +(-2.45512 + 2.45512i) q^{29} +(2.31065 + 2.88306i) q^{30} +7.44993 q^{31} +(1.32570 + 5.49932i) q^{32} -1.81440 q^{33} +(3.33113 + 4.15634i) q^{34} +(-1.84737 + 1.84737i) q^{35} +(1.95200 + 0.435558i) q^{36} +(-8.07793 - 8.07793i) q^{37} +(11.1099 + 1.22445i) q^{38} -0.810886i q^{39} +(-6.99243 - 2.38967i) q^{40} +1.18711i q^{41} +(-0.154926 + 1.40570i) q^{42} +(2.55667 + 2.55667i) q^{43} +(3.06317 - 1.94555i) q^{44} +(-1.84737 + 1.84737i) q^{45} +(-9.68457 + 7.76177i) q^{46} +8.68108 q^{47} +(-3.76251 + 1.35776i) q^{48} -1.00000 q^{49} +(2.01459 - 1.61461i) q^{50} +(-2.66325 + 2.66325i) q^{51} +(0.869500 + 1.36898i) q^{52} +(-1.03296 - 1.03296i) q^{53} +(-0.154926 + 1.40570i) q^{54} +4.74026i q^{55} +(-1.24576 - 2.53931i) q^{56} +7.90346i q^{57} +(4.88070 + 0.537912i) q^{58} +(4.49096 + 4.49096i) q^{59} +(1.13793 - 5.09975i) q^{60} +(1.77606 - 1.77606i) q^{61} +(-6.58896 - 8.22122i) q^{62} -1.00000 q^{63} +(4.89618 - 6.32672i) q^{64} -2.11851 q^{65} +(1.60471 + 2.00224i) q^{66} +(9.10323 - 9.10323i) q^{67} +(1.64049 - 7.35200i) q^{68} +(-6.20556 - 6.20556i) q^{69} +(3.67251 + 0.404756i) q^{70} -10.6094i q^{71} +(-1.24576 - 2.53931i) q^{72} -1.67971i q^{73} +(-1.76986 + 16.0586i) q^{74} +(1.29088 + 1.29088i) q^{75} +(-8.47475 - 13.3431i) q^{76} +(-1.28297 + 1.28297i) q^{77} +(-0.894838 + 0.717174i) q^{78} +8.98738 q^{79} +(3.54726 + 9.82987i) q^{80} -1.00000 q^{81} +(1.31001 - 1.04991i) q^{82} +(5.03598 - 5.03598i) q^{83} +(1.68826 - 1.07228i) q^{84} +(6.95796 + 6.95796i) q^{85} +(0.560161 - 5.08256i) q^{86} +3.47207i q^{87} +(-4.85614 - 1.65959i) q^{88} -3.53141i q^{89} +(3.67251 + 0.404756i) q^{90} +(-0.573383 - 0.573383i) q^{91} +(17.1307 + 3.82246i) q^{92} +(5.26789 - 5.26789i) q^{93} +(-7.67783 - 9.57984i) q^{94} +20.6484 q^{95} +(4.82602 + 2.95120i) q^{96} +7.92244 q^{97} +(0.884433 + 1.10353i) q^{98} +(-1.28297 + 1.28297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) $ 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

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 $

$2$	−0.884433	−	1.10353i	−0.625388	−	0.780314i
$2$	−0.884433	−	1.10353i	−0.625388	−	0.780314i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−0.435558	+	1.95200i	−0.217779	+	0.975998i
$5$	−1.84737	−	1.84737i	−0.826171	−	0.826171i	0.160814	−	0.986985i	$-0.448588\pi$
$5$	−1.84737	−	1.84737i	−0.826171	−	0.826171i	−0.986985	+	0.160814i	$0.948588\pi$
$6$	−1.40570	−	0.154926i	−0.573875	−	0.0632481i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.53931	−	1.24576i	0.897781	−	0.440442i
$9$		−	1.00000i		−	0.333333i
$10$	−0.404756	+	3.67251i	−0.127995	+	1.16135i
$11$	−1.28297	−	1.28297i	−0.386831	−	0.386831i	0.486725	−	0.873556i	$-0.338192\pi$
$11$	−1.28297	−	1.28297i	−0.386831	−	0.386831i	−0.873556	+	0.486725i	$0.838192\pi$
$12$	1.07228	+	1.68826i	0.309542	+	0.487358i
$13$	0.573383	−	0.573383i	0.159028	−	0.159028i	−0.623108	−	0.782136i	$-0.714130\pi$
$13$	0.573383	−	0.573383i	0.159028	−	0.159028i	0.782136	+	0.623108i	$0.214130\pi$
$14$	−1.10353	+	0.884433i	−0.294931	+	0.236375i
$15$	−2.61258			−0.674566
$16$	−3.62058	−	1.70042i	−0.905144	−	0.425104i
$17$	−3.76640			−0.913487			−0.456743	−	0.889598i	$-0.650984\pi$
$17$	−3.76640			−0.913487			−0.456743	+	0.889598i	$0.650984\pi$
$18$	−1.10353	+	0.884433i	−0.260105	+	0.208463i
$19$	−5.58859	+	5.58859i	−1.28211	+	1.28211i	−0.342646	+	0.939464i	$0.611323\pi$
$19$	−5.58859	+	5.58859i	−1.28211	+	1.28211i	−0.939464	+	0.342646i	$0.888677\pi$
$20$	4.41071	−	2.80143i	0.986264	−	0.626418i
$21$	−0.707107	−	0.707107i	−0.154303	−	0.154303i
$22$	−0.281097	+	2.55050i	−0.0599300	+	0.543769i
$23$		−	8.77599i		−	1.82992i	−0.403544	−	0.914960i	$-0.632222\pi$
$23$		−	8.77599i		−	1.82992i	0.403544	−	0.914960i	$-0.367778\pi$
$24$	0.914679	−	2.67645i	0.186708	−	0.546327i
$25$			1.82558i			0.365117i
$26$	−1.13986	−	0.125627i	−0.223546	−	0.0246375i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.95200	+	0.435558i	0.368893	+	0.0823128i
$29$	−2.45512	+	2.45512i	−0.455905	+	0.455905i	−0.897309	−	0.441403i	$-0.854481\pi$
$29$	−2.45512	+	2.45512i	−0.455905	+	0.455905i	0.441403	+	0.897309i	$0.354481\pi$
$30$	2.31065	+	2.88306i	0.421865	+	0.526373i
$31$	7.44993			1.33805			0.669023	−	0.743242i	$-0.266713\pi$
$31$	7.44993			1.33805			0.669023	+	0.743242i	$0.266713\pi$
$32$	1.32570	+	5.49932i	0.234352	+	0.972152i
$33$	−1.81440			−0.315846
$34$	3.33113	+	4.15634i	0.571284	+	0.712806i
$35$	−1.84737	+	1.84737i	−0.312263	+	0.312263i
$36$	1.95200	+	0.435558i	0.325333	+	0.0725930i
$37$	−8.07793	−	8.07793i	−1.32800	−	1.32800i	−0.907110	−	0.420894i	$-0.861716\pi$
$37$	−8.07793	−	8.07793i	−1.32800	−	1.32800i	−0.420894	−	0.907110i	$-0.638284\pi$
$38$	11.1099	+	1.22445i	1.80227	+	0.198632i
$39$		−	0.810886i		−	0.129846i
$40$	−6.99243	−	2.38967i	−1.10560	−	0.377841i
$41$			1.18711i			0.185395i	0.995694	+	0.0926974i	$0.0295489\pi$
$41$			1.18711i			0.185395i	−0.995694	+	0.0926974i	$0.970451\pi$
$42$	−0.154926	+	1.40570i	−0.0239055	+	0.216905i
$43$	2.55667	+	2.55667i	0.389888	+	0.389888i	0.874648	−	0.484759i	$-0.161093\pi$
$43$	2.55667	+	2.55667i	0.389888	+	0.389888i	−0.484759	+	0.874648i	$0.661093\pi$
$44$	3.06317	−	1.94555i	0.461790	−	0.293303i
$45$	−1.84737	+	1.84737i	−0.275390	+	0.275390i
$46$	−9.68457	+	7.76177i	−1.42791	+	1.14441i
$47$	8.68108			1.26627			0.633133	−	0.774043i	$-0.281769\pi$
$47$	8.68108			1.26627			0.633133	+	0.774043i	$0.281769\pi$
$48$	−3.76251	+	1.35776i	−0.543072	+	0.195976i
$49$	−1.00000			−0.142857
$50$	2.01459	−	1.61461i	0.284906	−	0.228340i
$51$	−2.66325	+	2.66325i	−0.372929	+	0.372929i
$52$	0.869500	+	1.36898i	0.120578	+	0.189844i
$53$	−1.03296	−	1.03296i	−0.141888	−	0.141888i	0.632595	−	0.774483i	$-0.281990\pi$
$53$	−1.03296	−	1.03296i	−0.141888	−	0.141888i	−0.774483	+	0.632595i	$0.781990\pi$
$54$	−0.154926	+	1.40570i	−0.0210827	+	0.191292i
$55$			4.74026i			0.639177i
$56$	−1.24576	−	2.53931i	−0.166471	−	0.339329i
$57$			7.90346i			1.04684i
$58$	4.88070	+	0.537912i	0.640867	+	0.0706314i
$59$	4.49096	+	4.49096i	0.584673	+	0.584673i	0.936184	−	0.351511i	$-0.114332\pi$
$59$	4.49096	+	4.49096i	0.584673	+	0.584673i	−0.351511	+	0.936184i	$0.614332\pi$
$60$	1.13793	−	5.09975i	0.146906	−	0.658375i
$61$	1.77606	−	1.77606i	0.227401	−	0.227401i	−0.584205	−	0.811606i	$-0.698594\pi$
$61$	1.77606	−	1.77606i	0.227401	−	0.227401i	0.811606	+	0.584205i	$0.198594\pi$
$62$	−6.58896	−	8.22122i	−0.836798	−	1.04410i
$63$	−1.00000			−0.125988
$64$	4.89618	−	6.32672i	0.612022	−	0.790840i
$65$	−2.11851			−0.262768
$66$	1.60471	+	2.00224i	0.197526	+	0.246459i
$67$	9.10323	−	9.10323i	1.11214	−	1.11214i	0.119276	−	0.992861i	$-0.461943\pi$
$67$	9.10323	−	9.10323i	1.11214	−	1.11214i	0.992861	−	0.119276i	$-0.0380573\pi$
$68$	1.64049	−	7.35200i	0.198938	−	0.891561i
$69$	−6.20556	−	6.20556i	−0.747062	−	0.747062i
$70$	3.67251	+	0.404756i	0.438949	+	0.0483776i
$71$		−	10.6094i		−	1.25911i	−0.776957	−	0.629554i	$-0.783238\pi$
$71$		−	10.6094i		−	1.25911i	0.776957	−	0.629554i	$-0.216762\pi$
$72$	−1.24576	−	2.53931i	−0.146814	−	0.299260i
$73$		−	1.67971i		−	0.196596i	−0.995157	−	0.0982978i	$-0.968660\pi$
$73$		−	1.67971i		−	0.196596i	0.995157	−	0.0982978i	$-0.0313398\pi$
$74$	−1.76986	+	16.0586i	−0.205742	+	1.86678i
$75$	1.29088	+	1.29088i	0.149058	+	0.149058i
$76$	−8.47475	−	13.3431i	−0.972121	−	1.53055i
$77$	−1.28297	+	1.28297i	−0.146208	+	0.146208i
$78$	−0.894838	+	0.717174i	−0.101320	+	0.0812040i
$79$	8.98738			1.01116			0.505580	−	0.862780i	$-0.331279\pi$
$79$	8.98738			1.01116			0.505580	+	0.862780i	$0.331279\pi$
$80$	3.54726	+	9.82987i	0.396595	+	1.09901i
$81$	−1.00000			−0.111111
$82$	1.31001	−	1.04991i	0.144666	−	0.115944i
$83$	5.03598	−	5.03598i	0.552770	−	0.552770i	−0.374469	−	0.927239i	$-0.622175\pi$
$83$	5.03598	−	5.03598i	0.552770	−	0.552770i	0.927239	+	0.374469i	$0.122175\pi$
$84$	1.68826	−	1.07228i	0.184204	−	0.116996i
$85$	6.95796	+	6.95796i	0.754696	+	0.754696i
$86$	0.560161	−	5.08256i	0.0604037	−	0.548067i
$87$			3.47207i			0.372245i
$88$	−4.85614	−	1.65959i	−0.517666	−	0.176913i
$89$		−	3.53141i		−	0.374329i	−0.982329	−	0.187164i	$-0.940070\pi$
$89$		−	3.53141i		−	0.374329i	0.982329	−	0.187164i	$-0.0599297\pi$
$90$	3.67251	+	0.404756i	0.387117	+	0.0426650i
$91$	−0.573383	−	0.573383i	−0.0601069	−	0.0601069i
$92$	17.1307	+	3.82246i	1.78600	+	0.398519i
$93$	5.26789	−	5.26789i	0.546255	−	0.546255i
$94$	−7.67783	−	9.57984i	−0.791908	−	0.988085i
$95$	20.6484			2.11849
$96$	4.82602	+	2.95120i	0.492553	+	0.301205i
$97$	7.92244			0.804402			0.402201	−	0.915551i	$-0.368245\pi$
$97$	7.92244			0.804402			0.402201	+	0.915551i	$0.368245\pi$
$98$	0.884433	+	1.10353i	0.0893412	+	0.111473i
$99$	−1.28297	+	1.28297i	−0.128944	+	0.128944i
$100$	−3.56353	−	0.795148i	−0.356353	−	0.0795148i
$101$	−3.02324	−	3.02324i	−0.300823	−	0.300823i	0.540513	−	0.841336i	$-0.318230\pi$
$101$	−3.02324	−	3.02324i	−0.300823	−	0.300823i	−0.841336	+	0.540513i	$0.818230\pi$
$102$	5.29444	+	0.583512i	0.524228	+	0.0577763i
$103$			5.82296i			0.573753i	0.957968	+	0.286877i	$0.0926170\pi$
$103$			5.82296i			0.573753i	−0.957968	+	0.286877i	$0.907383\pi$
$104$	0.741701	−	2.17029i	0.0727297	−	0.212815i
$105$			2.61258i			0.254962i
$106$	−0.226319	+	2.05349i	−0.0219821	+	0.199452i
$107$	4.48343	+	4.48343i	0.433429	+	0.433429i	0.889793	−	0.456364i	$-0.150848\pi$
$107$	4.48343	+	4.48343i	0.433429	+	0.433429i	−0.456364	+	0.889793i	$0.650848\pi$
$108$	1.68826	−	1.07228i	0.162453	−	0.103181i
$109$	6.57337	−	6.57337i	0.629614	−	0.629614i	−0.318357	−	0.947971i	$-0.603131\pi$
$109$	6.57337	−	6.57337i	0.629614	−	0.629614i	0.947971	+	0.318357i	$0.103131\pi$
$110$	5.23103	−	4.19244i	0.498759	−	0.399734i
$111$	−11.4239			−1.08431
$112$	−1.70042	+	3.62058i	−0.160674	+	0.342112i
$113$	−12.6537			−1.19036			−0.595180	−	0.803592i	$-0.702919\pi$
$113$	−12.6537			−1.19036			−0.595180	+	0.803592i	$0.702919\pi$
$114$	8.72171	−	6.99008i	0.816863	−	0.654681i
$115$	−16.2125	+	16.2125i	−1.51183	+	1.51183i
$116$	−3.72304	−	5.86174i	−0.345676	−	0.544249i
$117$	−0.573383	−	0.573383i	−0.0530093	−	0.0530093i
$118$	0.983959	−	8.92786i	0.0905808	−	0.821876i
$119$			3.76640i			0.345266i
$120$	−6.63415	+	3.25464i	−0.605612	+	0.297107i
$121$		−	7.70796i		−	0.700724i
$122$	−3.53075	−	0.389131i	−0.319659	−	0.0352303i
$123$	0.839410	+	0.839410i	0.0756871	+	0.0756871i
$124$	−3.24488	+	14.5422i	−0.291399	+	1.30593i
$125$	−5.86433	+	5.86433i	−0.524522	+	0.524522i
$126$	0.884433	+	1.10353i	0.0787915	+	0.0983103i
$127$	8.72606			0.774313			0.387157	−	0.922014i	$-0.373457\pi$
$127$	8.72606			0.774313			0.387157	+	0.922014i	$0.373457\pi$
$128$	−11.3121	+	0.192479i	−0.999855	+	0.0170129i
$129$	3.61568			0.318343
$130$	1.87368	+	2.33784i	0.164332	+	0.205042i
$131$	−6.31850	+	6.31850i	−0.552050	+	0.552050i	−0.927032	−	0.374982i	$-0.877649\pi$
$131$	−6.31850	+	6.31850i	−0.552050	+	0.552050i	0.374982	+	0.927032i	$0.377649\pi$
$132$	0.790276	−	3.54170i	0.0687847	−	0.308265i
$133$	5.58859	+	5.58859i	0.484592	+	0.484592i
$134$	−18.0969	−	1.99450i	−1.56333	−	0.172298i
$135$			2.61258i			0.224855i
$136$	−9.56406	+	4.69202i	−0.820111	+	0.402338i
$137$			11.0307i			0.942416i	0.882022	+	0.471208i	$0.156182\pi$
$137$			11.0307i			0.942416i	−0.882022	+	0.471208i	$0.843818\pi$
$138$	−1.35963	+	12.3364i	−0.115739	+	1.05015i
$139$	−9.38542	−	9.38542i	−0.796061	−	0.796061i	0.186411	−	0.982472i	$-0.440314\pi$
$139$	−9.38542	−	9.38542i	−0.796061	−	0.796061i	−0.982472	+	0.186411i	$0.940314\pi$
$140$	−2.80143	−	4.41071i	−0.236764	−	0.372773i
$141$	6.13845	−	6.13845i	0.516951	−	0.516951i
$142$	−11.7078	+	9.38332i	−0.982499	+	0.787431i
$143$	−1.47127			−0.123034
$144$	−1.70042	+	3.62058i	−0.141701	+	0.301715i
$145$	9.07107			0.753311
$146$	−1.85361	+	1.48559i	−0.153406	+	0.122949i
$147$	−0.707107	+	0.707107i	−0.0583212	+	0.0583212i
$148$	19.2865	−	12.2497i	1.58534	−	1.00692i
$149$	−6.04303	−	6.04303i	−0.495064	−	0.495064i	0.414833	−	0.909897i	$-0.363840\pi$
$149$	−6.04303	−	6.04303i	−0.495064	−	0.495064i	−0.909897	+	0.414833i	$0.863840\pi$
$150$	0.282830	−	2.56623i	0.0230929	−	0.209532i
$151$		−	2.76077i		−	0.224668i	−0.993671	−	0.112334i	$-0.964167\pi$
$151$		−	2.76077i		−	0.224668i	0.993671	−	0.112334i	$-0.0358327\pi$
$152$	−7.22913	+	21.1532i	−0.586360	+	1.71575i
$153$			3.76640i			0.304496i
$154$	2.55050	+	0.281097i	0.205525	+	0.0226514i
$155$	−13.7628	−	13.7628i	−1.10545	−	1.10545i
$156$	1.58285	+	0.353188i	0.126729	+	0.0282777i
$157$	−12.9246	+	12.9246i	−1.03149	+	1.03149i	−0.0320071	+	0.999488i	$0.510190\pi$
$157$	−12.9246	+	12.9246i	−1.03149	+	1.03149i	−0.999488	+	0.0320071i	$0.989810\pi$
$158$	−7.94873	−	9.91785i	−0.632367	−	0.789022i
$159$	−1.46083			−0.115851
$160$	7.71025	−	12.6084i	0.609549	−	0.996779i
$161$	−8.77599			−0.691645
$162$	0.884433	+	1.10353i	0.0694876	+	0.0867015i
$163$	7.16309	−	7.16309i	0.561056	−	0.561056i	−0.368551	−	0.929608i	$-0.620146\pi$
$163$	7.16309	−	7.16309i	0.561056	−	0.561056i	0.929608	+	0.368551i	$0.120146\pi$
$164$	−2.31723	−	0.517054i	−0.180945	−	0.0403751i
$165$	3.35187	+	3.35187i	0.260943	+	0.260943i
$166$	−10.0113	−	1.10337i	−0.777030	−	0.0856383i
$167$			25.5300i			1.97557i	0.155809	+	0.987787i	$0.450201\pi$
$167$			25.5300i			1.97557i	−0.155809	+	0.987787i	$0.549799\pi$
$168$	−2.67645	−	0.914679i	−0.206492	−	0.0705690i
$169$			12.3425i			0.949420i
$170$	1.52447	−	13.8322i	0.116922	−	1.06088i
$171$	5.58859	+	5.58859i	0.427370	+	0.427370i
$172$	−6.10419	+	3.87703i	−0.465440	+	0.295621i
$173$	9.22288	−	9.22288i	0.701202	−	0.701202i	−0.263466	−	0.964669i	$-0.584866\pi$
$173$	9.22288	−	9.22288i	0.701202	−	0.701202i	0.964669	+	0.263466i	$0.0848657\pi$
$174$	3.83154	−	3.07081i	0.290468	−	0.232798i
$175$	1.82558			0.138001
$176$	2.46352	+	6.82669i	0.185695	+	0.514581i
$177$	6.35117			0.477383
$178$	−3.89702	+	3.12329i	−0.292094	+	0.234101i
$179$	−3.27756	+	3.27756i	−0.244976	+	0.244976i	−0.818905	−	0.573929i	$-0.805419\pi$
$179$	−3.27756	+	3.27756i	−0.244976	+	0.244976i	0.573929	+	0.818905i	$0.305419\pi$
$180$	−2.80143	−	4.41071i	−0.208806	−	0.328755i
$181$	−12.7336	−	12.7336i	−0.946484	−	0.946484i	0.0521551	−	0.998639i	$-0.483391\pi$
$181$	−12.7336	−	12.7336i	−0.946484	−	0.946484i	−0.998639	+	0.0521551i	$0.983391\pi$
$182$	−0.125627	+	1.13986i	−0.00931209	+	0.0844924i
$183$		−	2.51173i		−	0.185673i
$184$	−10.9328	−	22.2850i	−0.805973	−	1.64287i
$185$			29.8459i			2.19432i
$186$	−10.4724	−	1.15418i	−0.767872	−	0.0846289i
$187$	4.83219	+	4.83219i	0.353365	+	0.353365i
$188$	−3.78112	+	16.9454i	−0.275766	+	1.23587i
$189$	−0.707107	+	0.707107i	−0.0514344	+	0.0514344i
$190$	−18.2622	−	22.7862i	−1.32488	−	1.65308i
$191$	−13.1825			−0.953854			−0.476927	−	0.878943i	$-0.658249\pi$
$191$	−13.1825			−0.953854			−0.476927	+	0.878943i	$0.658249\pi$
$192$	−1.01155	−	7.93579i	−0.0730022	−	0.572716i
$193$	24.2115			1.74278			0.871391	−	0.490589i	$-0.163219\pi$
$193$	24.2115			1.74278			0.871391	+	0.490589i	$0.163219\pi$
$194$	−7.00687	−	8.74266i	−0.503064	−	0.627686i
$195$	−1.49801	+	1.49801i	−0.107275	+	0.107275i
$196$	0.435558	−	1.95200i	0.0311113	−	0.139428i
$197$	−4.20130	−	4.20130i	−0.299330	−	0.299330i	0.541421	−	0.840751i	$-0.317886\pi$
$197$	−4.20130	−	4.20130i	−0.299330	−	0.299330i	−0.840751	+	0.541421i	$0.817886\pi$
$198$	2.55050	+	0.281097i	0.181256	+	0.0199767i
$199$		−	8.71100i		−	0.617507i	−0.951142	−	0.308753i	$-0.900088\pi$
$199$		−	8.71100i		−	0.617507i	0.951142	−	0.308753i	$-0.0999118\pi$
$200$	2.27423	+	4.63572i	0.160813	+	0.327795i
$201$		−	12.8739i		−	0.908056i
$202$	−0.662384	+	6.01008i	−0.0466052	+	0.422868i
$203$	2.45512	+	2.45512i	0.172316	+	0.172316i
$204$	−4.03865	−	6.35865i	−0.282762	−	0.445195i
$205$	2.19303	−	2.19303i	0.153168	−	0.153168i
$206$	6.42581	−	5.15002i	0.447708	−	0.358819i
$207$	−8.77599			−0.609974
$208$	−3.05097	+	1.10099i	−0.211547	+	0.0763398i
$209$	14.3400			0.991921
$210$	2.88306	−	2.31065i	0.198950	−	0.159450i
$211$	−2.31830	+	2.31830i	−0.159598	+	0.159598i	−0.782389	−	0.622791i	$-0.785999\pi$
$211$	−2.31830	+	2.31830i	−0.159598	+	0.159598i	0.622791	+	0.782389i	$0.285999\pi$
$212$	2.46625	−	1.56642i	0.169383	−	0.107582i
$213$	−7.50200	−	7.50200i	−0.514029	−	0.514029i
$214$	0.982309	−	8.91289i	0.0671493	−	0.609273i
$215$		−	9.44625i		−	0.644229i
$216$	−2.67645	−	0.914679i	−0.182109	−	0.0622360i
$217$		−	7.44993i		−	0.505734i
$218$	−13.0676	−	1.44021i	−0.885050	−	0.0975433i
$219$	−1.18774	−	1.18774i	−0.0802598	−	0.0802598i
$220$	−9.25298	−	2.06466i	−0.623836	−	0.139199i
$221$	−2.15959	+	2.15959i	−0.145270	+	0.145270i
$222$	10.1037	+	12.6066i	0.678115	+	0.846103i
$223$	9.37037			0.627486			0.313743	−	0.949508i	$-0.398417\pi$
$223$	9.37037			0.627486			0.313743	+	0.949508i	$0.398417\pi$
$224$	5.49932	−	1.32570i	0.367439	−	0.0885768i
$225$	1.82558			0.121706
$226$	11.1913	+	13.9637i	0.744437	+	0.928854i
$227$	5.57766	−	5.57766i	0.370202	−	0.370202i	−0.497349	−	0.867551i	$-0.665693\pi$
$227$	5.57766	−	5.57766i	0.370202	−	0.370202i	0.867551	+	0.497349i	$0.165693\pi$
$228$	−15.4275	−	3.44242i	−1.02171	−	0.227980i
$229$	13.8479	+	13.8479i	0.915097	+	0.915097i	0.996668	−	0.0815703i	$-0.0259935\pi$
$229$	13.8479	+	13.8479i	0.915097	+	0.915097i	−0.0815703	+	0.996668i	$0.525994\pi$
$230$	32.2299	+	3.55213i	2.12518	+	0.234221i
$231$			1.81440i			0.119379i
$232$	−3.17583	+	9.29281i	−0.208504	+	0.610103i
$233$			18.4216i			1.20684i	0.797424	+	0.603419i	$0.206195\pi$
$233$			18.4216i			1.20684i	−0.797424	+	0.603419i	$0.793805\pi$
$234$	−0.125627	+	1.13986i	−0.00821249	+	0.0745153i
$235$	−16.0372	−	16.0372i	−1.04615	−	1.04615i
$236$	−10.7224	+	6.81026i	−0.697969	+	0.443310i
$237$	6.35504	−	6.35504i	0.412804	−	0.412804i
$238$	4.15634	−	3.33113i	0.269415	−	0.215925i
$239$	−14.3108			−0.925691			−0.462845	−	0.886439i	$-0.653172\pi$
$239$	−14.3108			−0.925691			−0.462845	+	0.886439i	$0.653172\pi$
$240$	9.45906	+	4.44248i	0.610579	+	0.286761i
$241$	6.29237			0.405327			0.202664	−	0.979248i	$-0.435040\pi$
$241$	6.29237			0.405327			0.202664	+	0.979248i	$0.435040\pi$
$242$	−8.50597	+	6.81717i	−0.546784	+	0.438224i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	2.69329	+	4.24045i	0.172420	+	0.271467i
$245$	1.84737	+	1.84737i	0.118024	+	0.118024i
$246$	0.183913	−	1.66872i	0.0117259	−	0.106393i
$247$			6.40881i			0.407783i
$248$	18.9177	−	9.28080i	1.20127	−	0.589331i
$249$		−	7.12195i		−	0.451335i
$250$	11.6581	+	1.28486i	0.737322	+	0.0812618i
$251$	16.3705	+	16.3705i	1.03329	+	1.03329i	0.999426	+	0.0338675i	$0.0107824\pi$
$251$	16.3705	+	16.3705i	1.03329	+	1.03329i	0.0338675	+	0.999426i	$0.489218\pi$
$252$	0.435558	−	1.95200i	0.0274376	−	0.122964i
$253$	−11.2594	+	11.2594i	−0.707870	+	0.707870i
$254$	−7.71762	−	9.62948i	−0.484246	−	0.604207i
$255$	9.84004			0.616207
$256$	10.2172	+	12.3130i	0.638573	+	0.769561i
$257$	5.94472			0.370821			0.185411	−	0.982661i	$-0.440638\pi$
$257$	5.94472			0.370821			0.185411	+	0.982661i	$0.440638\pi$
$258$	−3.19782	−	3.99001i	−0.199088	−	0.248407i
$259$	−8.07793	+	8.07793i	−0.501938	+	0.501938i
$260$	0.922733	−	4.13532i	0.0572255	−	0.256461i
$261$	2.45512	+	2.45512i	0.151968	+	0.151968i
$262$	12.5609	+	1.38437i	0.776017	+	0.0855266i
$263$		−	17.5991i		−	1.08521i	−0.839989	−	0.542603i	$-0.817439\pi$
$263$		−	17.5991i		−	1.08521i	0.839989	−	0.542603i	$-0.182561\pi$
$264$	−4.60732	+	2.26030i	−0.283561	+	0.139112i
$265$			3.81653i			0.234447i
$266$	1.22445	−	11.1099i	0.0750757	−	0.681192i
$267$	−2.49708	−	2.49708i	−0.152819	−	0.152819i
$268$	13.8045	+	21.7345i	0.843243	+	1.32764i
$269$	−14.6340	+	14.6340i	−0.892251	+	0.892251i	−0.994735	−	0.102484i	$-0.967321\pi$
$269$	−14.6340	+	14.6340i	−0.892251	+	0.892251i	0.102484	+	0.994735i	$0.467321\pi$
$270$	2.88306	−	2.31065i	0.175458	−	0.140622i
$271$	−1.48973			−0.0904945			−0.0452473	−	0.998976i	$-0.514408\pi$
$271$	−1.48973			−0.0904945			−0.0452473	+	0.998976i	$0.514408\pi$
$272$	13.6366	+	6.40445i	0.826838	+	0.388327i
$273$	−0.810886			−0.0490771
$274$	12.1727	−	9.75591i	0.735380	−	0.589376i
$275$	2.34218	−	2.34218i	0.141239	−	0.141239i
$276$	14.8161	−	9.41035i	0.891826	−	0.566437i
$277$	6.87380	+	6.87380i	0.413006	+	0.413006i	0.882785	−	0.469778i	$-0.155666\pi$
$277$	6.87380	+	6.87380i	0.413006	+	0.413006i	−0.469778	+	0.882785i	$0.655666\pi$
$278$	−2.05632	+	18.6579i	−0.123330	+	1.11902i
$279$		−	7.44993i		−	0.446015i
$280$	−2.38967	+	6.99243i	−0.142810	+	0.417878i
$281$			1.78681i			0.106592i	0.998579	+	0.0532962i	$0.0169727\pi$
$281$			1.78681i			0.106592i	−0.998579	+	0.0532962i	$0.983027\pi$
$282$	−12.2030	−	1.34492i	−0.726679	−	0.0800889i
$283$	−22.5902	−	22.5902i	−1.34285	−	1.34285i	−0.893213	−	0.449634i	$-0.851555\pi$
$283$	−22.5902	−	22.5902i	−1.34285	−	1.34285i	−0.449634	−	0.893213i	$-0.648445\pi$
$284$	20.7096	+	4.62102i	1.22889	+	0.274207i
$285$	14.6007	−	14.6007i	0.864868	−	0.864868i
$286$	1.30124	+	1.62359i	0.0769439	+	0.0960050i
$287$	1.18711			0.0700726
$288$	5.49932	−	1.32570i	0.324051	−	0.0781174i
$289$	−2.81421			−0.165542
$290$	−8.02275	−	10.0102i	−0.471112	−	0.587819i
$291$	5.60201	−	5.60201i	0.328396	−	0.328396i
$292$	3.27879	+	0.731613i	0.191877	+	0.0428144i
$293$	−5.95937	−	5.95937i	−0.348150	−	0.348150i	0.511270	−	0.859420i	$-0.329175\pi$
$293$	−5.95937	−	5.95937i	−0.348150	−	0.348150i	−0.859420	+	0.511270i	$0.829175\pi$
$294$	1.40570	+	0.154926i	0.0819822	+	0.00903544i
$295$		−	16.5930i		−	0.966080i
$296$	−30.5755	−	10.4492i	−1.77717	−	0.607349i
$297$			1.81440i			0.105282i
$298$	−1.32401	+	12.0133i	−0.0766981	+	0.695913i
$299$	−5.03201	−	5.03201i	−0.291008	−	0.291008i
$300$	−3.08205	+	1.95754i	−0.177942	+	0.113019i
$301$	2.55667	−	2.55667i	0.147364	−	0.147364i
$302$	−3.04659	+	2.44171i	−0.175312	+	0.140505i
$303$	−4.27550			−0.245621
$304$	29.7369	−	10.7310i	1.70553	−	0.615465i
$305$	−6.56210			−0.375745
$306$	4.15634	−	3.33113i	0.237602	−	0.190428i
$307$	−19.2863	+	19.2863i	−1.10073	+	1.10073i	−0.106402	+	0.994323i	$0.533933\pi$
$307$	−19.2863	+	19.2863i	−1.10073	+	1.10073i	−0.994323	+	0.106402i	$0.966067\pi$
$308$	−1.94555	−	3.06317i	−0.110858	−	0.174540i
$309$	4.11745	+	4.11745i	0.234234	+	0.234234i
$310$	−3.01540	+	27.3599i	−0.171263	+	1.55394i
$311$		−	30.4880i		−	1.72882i	−0.502791	−	0.864408i	$-0.667694\pi$
$311$		−	30.4880i		−	1.72882i	0.502791	−	0.864408i	$-0.332306\pi$
$312$	−1.01017	−	2.05909i	−0.0571895	−	0.116573i
$313$		−	24.6544i		−	1.39355i	−0.717291	−	0.696774i	$-0.754618\pi$
$313$		−	24.6544i		−	1.39355i	0.717291	−	0.696774i	$-0.245382\pi$
$314$	25.6936	+	2.83175i	1.44997	+	0.159805i
$315$	1.84737	+	1.84737i	0.104088	+	0.104088i
$316$	−3.91453	+	17.5433i	−0.220209	+	0.986890i
$317$	18.9933	−	18.9933i	1.06677	−	1.06677i	0.0691669	−	0.997605i	$-0.477966\pi$
$317$	18.9933	−	18.9933i	1.06677	−	1.06677i	0.997605	−	0.0691669i	$-0.0220341\pi$
$318$	1.29200	+	1.61207i	0.0724519	+	0.0904002i
$319$	6.29972			0.352717
$320$	−20.7329	+	2.64275i	−1.15900	+	0.147734i
$321$	6.34053			0.353894
$322$	7.76177	+	9.68457i	0.432547	+	0.539700i
$323$	21.0489	−	21.0489i	1.17119	−	1.17119i
$324$	0.435558	−	1.95200i	0.0241977	−	0.108444i
$325$	1.04676	+	1.04676i	0.0580638	+	0.0580638i
$326$	−14.2400	−	1.56942i	−0.788678	−	0.0869220i
$327$		−	9.29614i		−	0.514078i
$328$	1.47885	+	3.01443i	0.0816556	+	0.166444i
$329$		−	8.68108i		−	0.478604i
$330$	0.734388	−	6.66340i	0.0404267	−	0.366808i
$331$	13.2656	+	13.2656i	0.729142	+	0.729142i	0.970449	−	0.241307i	$-0.0775759\pi$
$331$	13.2656	+	13.2656i	0.729142	+	0.729142i	−0.241307	+	0.970449i	$0.577576\pi$
$332$	7.63675	+	12.0237i	0.419121	+	0.659885i
$333$	−8.07793	+	8.07793i	−0.442668	+	0.442668i
$334$	28.1732	−	22.5796i	1.54157	−	1.23550i
$335$	−33.6342			−1.83763
$336$	1.35776	+	3.76251i	0.0740718	+	0.205262i
$337$	−5.18645			−0.282524			−0.141262	−	0.989972i	$-0.545116\pi$
$337$	−5.18645			−0.282524			−0.141262	+	0.989972i	$0.545116\pi$
$338$	13.6203	−	10.9161i	0.740846	−	0.593756i
$339$	−8.94752	+	8.94752i	−0.485963	+	0.485963i
$340$	−16.6125	+	10.5513i	−0.900939	+	0.572225i
$341$	−9.55806	−	9.55806i	−0.517598	−	0.517598i
$342$	1.22445	−	11.1099i	0.0662106	−	0.600755i
$343$			1.00000i			0.0539949i
$344$	9.67716	+	3.30718i	0.521758	+	0.178311i
$345$			22.9280i			1.23440i
$346$	−18.3347	−	2.02071i	−0.985682	−	0.108634i
$347$	12.7128	+	12.7128i	0.682457	+	0.682457i	0.960553	−	0.278096i	$-0.0897033\pi$
$347$	12.7128	+	12.7128i	0.682457	+	0.682457i	−0.278096	+	0.960553i	$0.589703\pi$
$348$	−6.77747	−	1.51229i	−0.363310	−	0.0810672i
$349$	0.143369	−	0.143369i	0.00767437	−	0.00767437i	−0.703259	−	0.710934i	$-0.748273\pi$
$349$	0.143369	−	0.143369i	0.00767437	−	0.00767437i	0.710934	+	0.703259i	$0.248273\pi$
$350$	−1.61461	−	2.01459i	−0.0863043	−	0.107684i
$351$	−0.810886			−0.0432819
$352$	5.35465	−	8.75631i	0.285404	−	0.466713i
$353$	7.90240			0.420602			0.210301	−	0.977637i	$-0.432556\pi$
$353$	7.90240			0.420602			0.210301	+	0.977637i	$0.432556\pi$
$354$	−5.61718	−	7.00871i	−0.298550	−	0.372509i
$355$	−19.5996	+	19.5996i	−1.04024	+	1.04024i
$356$	6.89330	+	1.53813i	0.365344	+	0.0815210i
$357$	2.66325	+	2.66325i	0.140954	+	0.140954i
$358$	6.51566	+	0.718106i	0.344364	+	0.0379531i
$359$			4.92045i			0.259691i	0.991534	+	0.129846i	$0.0414482\pi$
$359$			4.92045i			0.259691i	−0.991534	+	0.129846i	$0.958552\pi$
$360$	−2.38967	+	6.99243i	−0.125947	+	0.368534i
$361$		−	43.4647i		−	2.28762i
$362$	−2.78991	+	25.3140i	−0.146635	+	1.33047i
$363$	−5.45035	−	5.45035i	−0.286069	−	0.286069i
$364$	1.36898	−	0.869500i	0.0717542	−	0.0455742i
$365$	−3.10306	+	3.10306i	−0.162421	+	0.162421i
$366$	−2.77177	+	2.22146i	−0.144883	+	0.116117i
$367$	−12.1171			−0.632505			−0.316253	−	0.948675i	$-0.602425\pi$
$367$	−12.1171			−0.632505			−0.316253	+	0.948675i	$0.602425\pi$
$368$	−14.9228	+	31.7742i	−0.777907	+	1.65634i
$369$	1.18711			0.0617983
$370$	32.9359	−	26.3967i	1.71226	−	1.37230i
$371$	−1.03296	+	1.03296i	−0.0536286	+	0.0536286i
$372$	7.98843	+	12.5774i	0.414181	+	0.652107i
$373$	−4.24229	−	4.24229i	−0.219657	−	0.219657i	0.588697	−	0.808354i	$-0.299641\pi$
$373$	−4.24229	−	4.24229i	−0.219657	−	0.219657i	−0.808354	+	0.588697i	$0.799641\pi$
$374$	1.05872	−	9.60622i	0.0547453	−	0.496726i
$375$			8.29342i			0.428270i
$376$	22.0440	−	10.8145i	1.13683	−	0.557716i
$377$			2.81545i			0.145003i
$378$	1.40570	+	0.154926i	0.0723015	+	0.00796851i
$379$	−12.5478	−	12.5478i	−0.644538	−	0.644538i	0.307129	−	0.951668i	$-0.400632\pi$
$379$	−12.5478	−	12.5478i	−0.644538	−	0.644538i	−0.951668	+	0.307129i	$0.900632\pi$
$380$	−8.99360	+	40.3057i	−0.461362	+	2.06764i
$381$	6.17026	−	6.17026i	0.316112	−	0.316112i
$382$	11.6590	+	14.5473i	0.596529	+	0.744305i
$383$	10.6477			0.544073			0.272036	−	0.962287i	$-0.412303\pi$
$383$	10.6477			0.544073			0.272036	+	0.962287i	$0.412303\pi$
$384$	−7.86274	+	8.13495i	−0.401244	+	0.415135i
$385$	4.74026			0.241586
$386$	−21.4134	−	26.7181i	−1.08992	−	1.35992i
$387$	2.55667	−	2.55667i	0.129963	−	0.129963i
$388$	−3.45069	+	15.4646i	−0.175182	+	0.785095i
$389$	−7.72898	−	7.72898i	−0.391875	−	0.391875i	0.483480	−	0.875355i	$-0.339372\pi$
$389$	−7.72898	−	7.72898i	−0.391875	−	0.391875i	−0.875355	+	0.483480i	$0.839372\pi$
$390$	2.97799	+	0.328211i	0.150796	+	0.0166196i
$391$			33.0539i			1.67161i
$392$	−2.53931	+	1.24576i	−0.128254	+	0.0629202i
$393$			8.93571i			0.450747i
$394$	−0.920496	+	8.35203i	−0.0463739	+	0.420769i
$395$	−16.6031	−	16.6031i	−0.835391	−	0.835391i
$396$	−1.94555	−	3.06317i	−0.0977675	−	0.153930i
$397$	−7.15797	+	7.15797i	−0.359248	+	0.359248i	−0.863536	−	0.504288i	$-0.831755\pi$
$397$	−7.15797	+	7.15797i	−0.359248	+	0.359248i	0.504288	+	0.863536i	$0.331755\pi$
$398$	−9.61286	+	7.70429i	−0.481849	+	0.386181i
$399$	7.90346			0.395668
$400$	3.10425	−	6.60967i	0.155213	−	0.330484i
$401$	34.6204			1.72886			0.864431	−	0.502751i	$-0.167679\pi$
$401$	34.6204			1.72886			0.864431	+	0.502751i	$0.167679\pi$
$402$	−14.2068	+	11.3861i	−0.708569	+	0.567888i
$403$	4.27166	−	4.27166i	0.212787	−	0.212787i
$404$	7.21814	−	4.58455i	0.359116	−	0.228090i
$405$	1.84737	+	1.84737i	0.0917968	+	0.0917968i
$406$	0.537912	−	4.88070i	0.0266961	−	0.242225i
$407$			20.7275i			1.02743i
$408$	−3.44505	+	10.0806i	−0.170555	+	0.499063i
$409$		−	22.6531i		−	1.12013i	−0.828450	−	0.560063i	$-0.810777\pi$
$409$		−	22.6531i		−	1.12013i	0.828450	−	0.560063i	$-0.189223\pi$
$410$	−4.35966	−	0.480488i	−0.215308	−	0.0237296i
$411$	7.79988	+	7.79988i	0.384740	+	0.384740i
$412$	−11.3664	−	2.53624i	−0.559982	−	0.124952i
$413$	4.49096	−	4.49096i	0.220986	−	0.220986i
$414$	7.76177	+	9.68457i	0.381470	+	0.475971i
$415$	−18.6067			−0.913366
$416$	3.91335	+	2.39309i	0.191868	+	0.117331i
$417$	−13.2730			−0.649981
$418$	−12.6828	−	15.8247i	−0.620335	−	0.774009i
$419$	16.0963	−	16.0963i	0.786357	−	0.786357i	−0.194538	−	0.980895i	$-0.562321\pi$
$419$	16.0963	−	16.0963i	0.786357	−	0.786357i	0.980895	+	0.194538i	$0.0623208\pi$
$420$	−5.09975	−	1.13793i	−0.248842	−	0.0555254i
$421$	22.1632	+	22.1632i	1.08017	+	1.08017i	0.996493	+	0.0836736i	$0.0266653\pi$
$421$	22.1632	+	22.1632i	1.08017	+	1.08017i	0.0836736	+	0.996493i	$0.473335\pi$
$422$	4.60869	+	0.507934i	0.224347	+	0.0247258i
$423$		−	8.68108i		−	0.422089i
$424$	−3.90982	−	1.33619i	−0.189878	−	0.0648910i
$425$		−	6.87589i		−	0.333529i
$426$	−1.64367	+	14.9137i	−0.0796361	+	0.722571i
$427$	−1.77606	−	1.77606i	−0.0859497	−	0.0859497i
$428$	−10.7044	+	6.79884i	−0.517418	+	0.328634i
$429$	−1.04035	+	1.04035i	−0.0502284	+	0.0502284i
$430$	−10.4242	+	8.35457i	−0.502701	+	0.402893i
$431$	3.65156			0.175889			0.0879447	−	0.996125i	$-0.471970\pi$
$431$	3.65156			0.175889			0.0879447	+	0.996125i	$0.471970\pi$
$432$	1.35776	+	3.76251i	0.0653252	+	0.181024i
$433$	−37.1208			−1.78391			−0.891955	−	0.452123i	$-0.850667\pi$
$433$	−37.1208			−1.78391			−0.891955	+	0.452123i	$0.850667\pi$
$434$	−8.22122	+	6.58896i	−0.394631	+	0.316280i
$435$	6.41422	−	6.41422i	0.307538	−	0.307538i
$436$	9.96810	+	15.6943i	0.477386	+	0.751619i
$437$	49.0454	+	49.0454i	2.34616	+	2.34616i
$438$	−0.260230	+	2.36118i	−0.0124343	+	0.112821i
$439$			23.5707i			1.12497i	0.826807	+	0.562485i	$0.190155\pi$
$439$			23.5707i			1.12497i	−0.826807	+	0.562485i	$0.809845\pi$
$440$	5.90522	+	12.0370i	0.281520	+	0.573841i
$441$			1.00000i			0.0476190i
$442$	4.29319	+	0.473162i	0.204206	+	0.0225060i
$443$	−10.6245	−	10.6245i	−0.504786	−	0.504786i	0.408136	−	0.912921i	$-0.366179\pi$
$443$	−10.6245	−	10.6245i	−0.504786	−	0.504786i	−0.912921	+	0.408136i	$0.866179\pi$
$444$	4.97578	−	22.2995i	0.236140	−	1.05829i
$445$	−6.52383	+	6.52383i	−0.309259	+	0.309259i
$446$	−8.28746	−	10.3405i	−0.392422	−	0.489636i
$447$	−8.54613			−0.404218
$448$	−6.32672	−	4.89618i	−0.298910	−	0.231323i
$449$	−23.9090			−1.12833			−0.564167	−	0.825661i	$-0.690802\pi$
$449$	−23.9090			−1.12833			−0.564167	+	0.825661i	$0.690802\pi$
$450$	−1.61461	−	2.01459i	−0.0761133	−	0.0949686i
$451$	1.52302	−	1.52302i	0.0717164	−	0.0717164i
$452$	5.51143	−	24.7000i	0.259236	−	1.16179i
$453$	−1.95216	−	1.95216i	−0.0917203	−	0.0917203i
$454$	−11.0882	−	1.22205i	−0.520394	−	0.0573538i
$455$			2.11851i			0.0993171i
$456$	9.84579	+	20.0693i	0.461072	+	0.939833i
$457$		−	16.0427i		−	0.750445i	−0.926935	−	0.375222i	$-0.877566\pi$
$457$		−	16.0427i		−	0.750445i	0.926935	−	0.375222i	$-0.122434\pi$
$458$	3.03405	−	27.5292i	0.141772	−	1.28635i
$459$	2.66325	+	2.66325i	0.124310	+	0.124310i
$460$	−24.5853	−	38.7083i	−1.14630	−	1.80478i
$461$	14.6403	−	14.6403i	0.681866	−	0.681866i	−0.278554	−	0.960421i	$-0.589855\pi$
$461$	14.6403	−	14.6403i	0.681866	−	0.681866i	0.960421	+	0.278554i	$0.0898551\pi$
$462$	2.00224	−	1.60471i	0.0931528	−	0.0746580i
$463$	−11.5751			−0.537939			−0.268969	−	0.963149i	$-0.586683\pi$
$463$	−11.5751			−0.537939			−0.268969	+	0.963149i	$0.586683\pi$
$464$	13.0637	−	4.71424i	0.606467	−	0.218853i
$465$	−19.4635			−0.902600
$466$	20.3288	−	16.2926i	0.941712	−	0.754742i
$467$	−3.29239	+	3.29239i	−0.152354	+	0.152354i	−0.779168	−	0.626815i	$-0.784358\pi$
$467$	−3.29239	+	3.29239i	−0.152354	+	0.152354i	0.626815	+	0.779168i	$0.284358\pi$
$468$	1.36898	−	0.869500i	0.0632813	−	0.0401926i
$469$	−9.10323	−	9.10323i	−0.420348	−	0.420348i
$470$	−3.51372	+	31.8814i	−0.162076	+	1.47058i
$471$			18.2781i			0.842212i
$472$	16.9986	+	5.80929i	0.782423	+	0.267394i
$473$		−	6.56028i		−	0.301642i
$474$	−12.6336	−	1.39238i	−0.580280	−	0.0639539i
$475$	−10.2024	−	10.2024i	−0.468120	−	0.468120i
$476$	−7.35200	−	1.64049i	−0.336979	−	0.0751916i
$477$	−1.03296	+	1.03296i	−0.0472960	+	0.0472960i
$478$	12.6570	+	15.7924i	0.578916	+	0.722329i
$479$	1.56900			0.0716893			0.0358447	−	0.999357i	$-0.488588\pi$
$479$	1.56900			0.0716893			0.0358447	+	0.999357i	$0.488588\pi$
$480$	−3.46349	−	14.3674i	−0.158086	−	0.655780i
$481$	−9.26350			−0.422379
$482$	−5.56517	−	6.94382i	−0.253487	−	0.316282i
$483$	−6.20556	+	6.20556i	−0.282363	+	0.282363i
$484$	15.0459	+	3.35727i	0.683905	+	0.152603i
$485$	−14.6357	−	14.6357i	−0.664574	−	0.664574i
$486$	1.40570	+	0.154926i	0.0637639	+	0.00702757i
$487$		−	13.9189i		−	0.630726i	−0.948971	−	0.315363i	$-0.897874\pi$
$487$		−	13.9189i		−	0.630726i	0.948971	−	0.315363i	$-0.102126\pi$
$488$	2.29743	−	6.72251i	0.104000	−	0.304314i
$489$		−	10.1301i		−	0.458101i
$490$	0.404756	−	3.67251i	0.0182850	−	0.165907i
$491$	30.6828	+	30.6828i	1.38469	+	1.38469i	0.836068	+	0.548626i	$0.184849\pi$
$491$	30.6828	+	30.6828i	1.38469	+	1.38469i	0.548626	+	0.836068i	$0.315151\pi$
$492$	−2.00414	+	1.27291i	−0.0903535	+	0.0573874i
$493$	9.24699	−	9.24699i	0.416463	−	0.416463i
$494$	7.07231	−	5.66816i	0.318198	−	0.255023i
$495$	4.74026			0.213059
$496$	−26.9730	−	12.6680i	−1.21113	−	0.568809i
$497$	−10.6094			−0.475898
$498$	−7.85929	+	6.29888i	−0.352183	+	0.282260i
$499$	7.21452	−	7.21452i	0.322966	−	0.322966i	−0.526938	−	0.849904i	$-0.676660\pi$
$499$	7.21452	−	7.21452i	0.322966	−	0.322966i	0.849904	+	0.526938i	$0.176660\pi$
$500$	−8.89290	−	14.0014i	−0.397702	−	0.626162i
$501$	18.0525	+	18.0525i	0.806525	+	0.806525i
$502$	3.58673	−	32.5439i	0.160084	−	1.45250i
$503$			19.8432i			0.884763i	0.896827	+	0.442381i	$0.145866\pi$
$503$			19.8432i			0.884763i	−0.896827	+	0.442381i	$0.854134\pi$
$504$	−2.53931	+	1.24576i	−0.113110	+	0.0554904i
$505$			11.1701i			0.497063i
$506$	22.3832	+	2.46690i	0.995054	+	0.109667i
$507$	8.72744	+	8.72744i	0.387599	+	0.387599i
$508$	−3.80071	+	17.0332i	−0.168629	+	0.755728i
$509$	−4.05195	+	4.05195i	−0.179599	+	0.179599i	−0.791181	−	0.611582i	$-0.790534\pi$
$509$	−4.05195	+	4.05195i	−0.179599	+	0.179599i	0.611582	+	0.791181i	$0.290534\pi$
$510$	−8.70285	−	10.8588i	−0.385369	−	0.480835i
$511$	−1.67971			−0.0743061
$512$	4.55135	−	22.1650i	0.201143	−	0.979562i
$513$	7.90346			0.348946
$514$	−5.25770	−	6.56018i	−0.231907	−	0.289357i
$515$	10.7572	−	10.7572i	0.474018	−	0.474018i
$516$	−1.57484	+	7.05779i	−0.0693284	+	0.310702i
$517$	−11.1376	−	11.1376i	−0.489831	−	0.489831i
$518$	16.0586	+	1.76986i	0.705576	+	0.0777631i
$519$		−	13.0431i		−	0.572529i
$520$	−5.37954	+	2.63914i	−0.235909	+	0.115734i
$521$		−	38.3311i		−	1.67932i	−0.543115	−	0.839658i	$-0.682755\pi$
$521$		−	38.3311i		−	1.67932i	0.543115	−	0.839658i	$-0.317245\pi$
$522$	0.537912	−	4.88070i	0.0235438	−	0.213622i
$523$	11.3713	+	11.3713i	0.497231	+	0.497231i	0.910575	−	0.413344i	$-0.135639\pi$
$523$	11.3713	+	11.3713i	0.497231	+	0.497231i	−0.413344	+	0.910575i	$0.635639\pi$
$524$	−9.58161	−	15.0858i	−0.418575	−	0.659024i
$525$	1.29088	−	1.29088i	0.0563388	−	0.0563388i
$526$	−19.4211	+	15.5652i	−0.846802	+	0.678676i
$527$	−28.0594			−1.22229
$528$	6.56917	+	3.08523i	0.285886	+	0.134268i
$529$	−54.0180			−2.34861
$530$	4.21165	−	3.37546i	0.182943	−	0.146621i
$531$	4.49096	−	4.49096i	0.194891	−	0.194891i
$532$	−13.3431	+	8.47475i	−0.578495	+	0.367427i
$533$	0.680666	+	0.680666i	0.0294829	+	0.0294829i
$534$	−0.547105	+	4.96411i	−0.0236756	+	0.214818i
$535$		−	16.5651i		−	0.716174i
$536$	11.7755	−	34.4563i	0.508624	−	1.48829i
$537$			4.63517i			0.200022i
$538$	29.0918	+	3.20628i	1.25424	+	0.138232i
$539$	1.28297	+	1.28297i	0.0552616	+	0.0552616i
$540$	−5.09975	−	1.13793i	−0.219458	−	0.0489688i
$541$	−13.0681	+	13.0681i	−0.561844	+	0.561844i	−0.929831	−	0.367987i	$-0.880047\pi$
$541$	−13.0681	+	13.0681i	−0.561844	+	0.561844i	0.367987	+	0.929831i	$0.380047\pi$
$542$	1.31756	+	1.64396i	0.0565942	+	0.0706141i
$543$	−18.0081			−0.772801
$544$	−4.99310	−	20.7127i	−0.214078	−	0.888048i
$545$	−24.2869			−1.04034
$546$	0.717174	+	0.894838i	0.0306922	+	0.0382955i
$547$	16.6333	−	16.6333i	0.711189	−	0.711189i	−0.255595	−	0.966784i	$-0.582271\pi$
$547$	16.6333	−	16.6333i	0.711189	−	0.711189i	0.966784	+	0.255595i	$0.0822712\pi$
$548$	−21.5319	−	4.80451i	−0.919796	−	0.205239i
$549$	−1.77606	−	1.77606i	−0.0758005	−	0.0758005i
$550$	−4.65616	−	0.513166i	−0.198539	−	0.0218815i
$551$		−	27.4414i		−	1.16904i
$552$	−23.4885	−	8.02722i	−0.999735	−	0.341661i
$553$		−	8.98738i		−	0.382182i
$554$	1.50603	−	13.6649i	0.0639852	−	0.580564i
$555$	21.1043	+	21.1043i	0.895826	+	0.895826i
$556$	22.4082	−	14.2324i	0.950319	−	0.603588i
$557$	27.1381	−	27.1381i	1.14988	−	1.14988i	0.163300	−	0.986576i	$-0.447786\pi$
$557$	27.1381	−	27.1381i	1.14988	−	1.14988i	0.986576	−	0.163300i	$-0.0522138\pi$
$558$	−8.22122	+	6.58896i	−0.348032	+	0.278933i
$559$	2.93190			0.124006
$560$	9.82987	−	3.54726i	0.415388	−	0.149899i
$561$	6.83375			0.288521
$562$	1.97180	−	1.58032i	0.0831755	−	0.0666616i
$563$	−3.54589	+	3.54589i	−0.149441	+	0.149441i	−0.777869	−	0.628427i	$-0.783699\pi$
$563$	−3.54589	+	3.54589i	−0.149441	+	0.149441i	0.628427	+	0.777869i	$0.283699\pi$
$564$	9.30858	+	14.6559i	0.391962	+	0.617124i
$565$	23.3761	+	23.3761i	0.983441	+	0.983441i
$566$	−4.94946	+	44.9084i	−0.208041	+	1.88764i
$567$			1.00000i			0.0419961i
$568$	−13.2168	−	26.9406i	−0.554563	−	1.13040i
$569$			33.1999i			1.39181i	0.718134	+	0.695905i	$0.244997\pi$
$569$			33.1999i			1.39181i	−0.718134	+	0.695905i	$0.755003\pi$
$570$	−29.0256	−	3.19897i	−1.21575	−	0.133990i
$571$	−25.3515	−	25.3515i	−1.06093	−	1.06093i	−0.998019	−	0.0629072i	$-0.979963\pi$
$571$	−25.3515	−	25.3515i	−1.06093	−	1.06093i	−0.0629072	−	0.998019i	$-0.520037\pi$
$572$	0.640824	−	2.87191i	0.0267942	−	0.120081i
$573$	−9.32145	+	9.32145i	−0.389409	+	0.389409i
$574$	−1.04991	−	1.31001i	−0.0438226	−	0.0546786i
$575$	16.0213			0.668135
$576$	−6.32672	−	4.89618i	−0.263613	−	0.204007i
$577$	−12.8093			−0.533258			−0.266629	−	0.963799i	$-0.585910\pi$
$577$	−12.8093			−0.533258			−0.266629	+	0.963799i	$0.585910\pi$
$578$	2.48898	+	3.10557i	0.103528	+	0.129175i
$579$	17.1201	−	17.1201i	0.711488	−	0.711488i
$580$	−3.95098	+	17.7067i	−0.164056	+	0.735230i
$581$	−5.03598	−	5.03598i	−0.208928	−	0.208928i
$582$	−11.1366	−	1.22739i	−0.461627	−	0.0508769i
$583$			2.65052i			0.109773i
$584$	−2.09251	−	4.26531i	−0.0865888	−	0.176500i
$585$			2.11851i			0.0875895i
$586$	−1.30568	+	11.8470i	−0.0539373	+	0.489395i
$587$	27.9293	+	27.9293i	1.15276	+	1.15276i	0.985996	+	0.166768i	$0.0533330\pi$
$587$	27.9293	+	27.9293i	1.15276	+	1.15276i	0.166768	+	0.985996i	$0.446667\pi$
$588$	−1.07228	−	1.68826i	−0.0442202	−	0.0696225i
$589$	−41.6346	+	41.6346i	−1.71552	+	1.71552i
$590$	−18.3108	+	14.6754i	−0.753845	+	0.604175i
$591$	−5.94154			−0.244402
$592$	15.5109	+	42.9826i	0.637496	+	1.76658i
$593$	−14.6589			−0.601971			−0.300985	−	0.953629i	$-0.597316\pi$
$593$	−14.6589			−0.601971			−0.300985	+	0.953629i	$0.597316\pi$
$594$	2.00224	−	1.60471i	0.0821530	−	0.0658422i
$595$	6.95796	−	6.95796i	0.285248	−	0.285248i
$596$	14.4281	−	9.16388i	0.590996	−	0.375367i
$597$	−6.15961	−	6.15961i	−0.252096	−	0.252096i
$598$	−1.10250	+	10.0034i	−0.0450846	+	0.409071i
$599$			38.6963i			1.58109i	0.612405	+	0.790545i	$0.290202\pi$
$599$			38.6963i			1.58109i	−0.612405	+	0.790545i	$0.709798\pi$
$600$	4.88608	+	1.66982i	0.199473	+	0.0681703i
$601$			33.2012i			1.35430i	0.735843	+	0.677152i	$0.236786\pi$
$601$			33.2012i			1.35430i	−0.735843	+	0.677152i	$0.763214\pi$
$602$	−5.08256	−	0.560161i	−0.207150	−	0.0228304i
$603$	−9.10323	−	9.10323i	−0.370712	−	0.370712i
$604$	5.38901	+	1.20247i	0.219276	+	0.0489280i
$605$	−14.2395	+	14.2395i	−0.578917	+	0.578917i
$606$	3.78139	+	4.71814i	0.153609	+	0.191661i
$607$	11.8393			0.480541			0.240271	−	0.970706i	$-0.422764\pi$
$607$	11.8393			0.480541			0.240271	+	0.970706i	$0.422764\pi$
$608$	−38.1422	−	23.3247i	−1.54687	−	0.945941i
$609$	3.47207			0.140695
$610$	5.80374	+	7.24148i	0.234987	+	0.293199i
$611$	4.97759	−	4.97759i	0.201372	−	0.201372i
$612$	−7.35200	−	1.64049i	−0.297187	−	0.0663128i
$613$	24.5904	+	24.5904i	0.993196	+	0.993196i	0.999977	−	0.00678056i	$-0.00215834\pi$
$613$	24.5904	+	24.5904i	0.993196	+	0.993196i	−0.00678056	+	0.999977i	$0.502158\pi$
$614$	38.3404	+	4.22558i	1.54729	+	0.170530i
$615$		−	3.10141i		−	0.125061i
$616$	−1.65959	+	4.85614i	−0.0668669	+	0.195659i
$617$			30.9399i			1.24559i	0.782383	+	0.622797i	$0.214004\pi$
$617$			30.9399i			1.24559i	−0.782383	+	0.622797i	$0.785996\pi$
$618$	0.902125	−	8.18535i	0.0362888	−	0.329263i
$619$	8.35827	+	8.35827i	0.335947	+	0.335947i	0.854840	−	0.518892i	$-0.173655\pi$
$619$	8.35827	+	8.35827i	0.335947	+	0.335947i	−0.518892	+	0.854840i	$0.673655\pi$
$620$	32.8594	−	20.8704i	1.31967	−	0.838177i
$621$	−6.20556	+	6.20556i	−0.249021	+	0.249021i
$622$	−33.6444	+	26.9646i	−1.34902	+	1.08118i
$623$	−3.53141			−0.141483
$624$	−1.37884	+	2.93588i	−0.0551979	+	0.117529i
$625$	30.7952			1.23181
$626$	−27.2068	+	21.8051i	−1.08740	+	0.871508i
$627$	10.1399	−	10.1399i	0.404950	−	0.404950i
$628$	−19.5993	−	30.8582i	−0.782099	−	1.23137i
$629$	30.4247	+	30.4247i	1.21311	+	1.21311i
$630$	0.404756	−	3.67251i	0.0161259	−	0.146316i
$631$			32.7668i			1.30443i	0.758036	+	0.652213i	$0.226159\pi$
$631$			32.7668i			1.30443i	−0.758036	+	0.652213i	$0.773841\pi$
$632$	22.8217	−	11.1961i	0.907800	−	0.445357i
$633$			3.27857i			0.130311i
$634$	−37.7580	−	4.16140i	−1.49956	−	0.165270i
$635$	−16.1203	−	16.1203i	−0.639715	−	0.639715i
$636$	0.636275	−	2.85153i	0.0252299	−	0.113070i
$637$	−0.573383	+	0.573383i	−0.0227183	+	0.0227183i
$638$	−5.57168	−	6.95193i	−0.220585	−	0.275230i
$639$	−10.6094			−0.419703
$640$	21.2532	+	20.5421i	0.840107	+	0.811996i
$641$	24.2376			0.957327			0.478663	−	0.877998i	$-0.341121\pi$
$641$	24.2376			0.957327			0.478663	+	0.877998i	$0.341121\pi$
$642$	−5.60777	−	6.99696i	−0.221321	−	0.276148i
$643$	16.8282	−	16.8282i	0.663639	−	0.663639i	−0.292597	−	0.956236i	$-0.594519\pi$
$643$	16.8282	−	16.8282i	0.663639	−	0.663639i	0.956236	+	0.292597i	$0.0945195\pi$
$644$	3.82246	−	17.1307i	0.150626	−	0.675044i
$645$	−6.67951	−	6.67951i	−0.263005	−	0.263005i
$646$	−41.8444	−	4.61176i	−1.64635	−	0.181447i
$647$		−	8.62130i		−	0.338938i	−0.985535	−	0.169469i	$-0.945795\pi$
$647$		−	8.62130i		−	0.338938i	0.985535	−	0.169469i	$-0.0542053\pi$
$648$	−2.53931	+	1.24576i	−0.0997535	+	0.0489380i
$649$		−	11.5236i		−	0.452339i
$650$	0.229343	−	2.08092i	0.00899556	−	0.0816204i
$651$	−5.26789	−	5.26789i	−0.206465	−	0.206465i
$652$	10.8624	+	17.1023i	0.425404	+	0.669776i
$653$	−15.8020	+	15.8020i	−0.618380	+	0.618380i	−0.945116	−	0.326736i	$-0.894051\pi$
$653$	−15.8020	+	15.8020i	−0.618380	+	0.618380i	0.326736	+	0.945116i	$0.394051\pi$
$654$	−10.2586	+	8.22181i	−0.401142	+	0.321498i
$655$	23.3453			0.912175
$656$	2.01857	−	4.29801i	0.0788121	−	0.167809i
$657$	−1.67971			−0.0655318
$658$	−9.57984	+	7.67783i	−0.373461	+	0.299313i
$659$	19.8851	−	19.8851i	0.774614	−	0.774614i	−0.204295	−	0.978909i	$-0.565490\pi$
$659$	19.8851	−	19.8851i	0.774614	−	0.774614i	0.978909	+	0.204295i	$0.0654903\pi$
$660$	−8.00278	+	5.08291i	−0.311508	+	0.197852i
$661$	−9.06899	−	9.06899i	−0.352743	−	0.352743i	0.508386	−	0.861129i	$-0.330242\pi$
$661$	−9.06899	−	9.06899i	−0.352743	−	0.352743i	−0.861129	+	0.508386i	$0.830242\pi$
$662$	2.90646	−	26.3715i	0.112963	−	1.02496i
$663$			3.05412i			0.118612i
$664$	6.51430	−	19.0615i	0.252804	−	0.739730i
$665$		−	20.6484i		−	0.800712i
$666$	16.0586	+	1.76986i	0.622259	+	0.0685806i
$667$	21.5462	+	21.5462i	0.834270	+	0.834270i
$668$	−49.8346	−	11.1198i	−1.92816	−	0.430239i
$669$	6.62585	−	6.62585i	0.256170	−	0.256170i
$670$	29.7471	+	37.1163i	1.14923	+	1.43393i
$671$	−4.55728			−0.175932
$672$	2.95120	−	4.82602i	0.113845	−	0.186168i
$673$	26.5522			1.02351			0.511756	−	0.859131i	$-0.328995\pi$
$673$	26.5522			1.02351			0.511756	+	0.859131i	$0.328995\pi$
$674$	4.58707	+	5.72341i	0.176687	+	0.220458i
$675$	1.29088	−	1.29088i	0.0496861	−	0.0496861i
$676$	−24.0924	−	5.37586i	−0.926632	−	0.206764i
$677$	−6.20763	−	6.20763i	−0.238579	−	0.238579i	0.577683	−	0.816261i	$-0.303957\pi$
$677$	−6.20763	−	6.20763i	−0.238579	−	0.238579i	−0.816261	+	0.577683i	$0.803957\pi$
$678$	17.7873	+	1.96038i	0.683118	+	0.0752880i
$679$		−	7.92244i		−	0.304036i
$680$	26.3363	+	9.00048i	1.00995	+	0.345152i
$681$		−	7.88800i		−	0.302269i
$682$	−2.09415	+	19.0011i	−0.0801891	+	0.727588i
$683$	29.4938	+	29.4938i	1.12855	+	1.12855i	0.990414	+	0.138134i	$0.0441105\pi$
$683$	29.4938	+	29.4938i	1.12855	+	1.12855i	0.138134	+	0.990414i	$0.455890\pi$
$684$	−13.3431	+	8.47475i	−0.510185	+	0.324040i
$685$	20.3778	−	20.3778i	0.778597	−	0.778597i
$686$	1.10353	−	0.884433i	0.0421330	−	0.0337678i
$687$	19.5839			0.747174
$688$	−4.90922	−	13.6040i	−0.187162	−	0.518649i
$689$	−1.18456			−0.0451283
$690$	25.3017	−	20.2783i	0.963221	−	0.771980i
$691$	−5.55775	+	5.55775i	−0.211427	+	0.211427i	−0.804873	−	0.593447i	$-0.797767\pi$
$691$	−5.55775	+	5.55775i	−0.211427	+	0.211427i	0.593447	+	0.804873i	$0.297767\pi$
$692$	13.9859	+	22.0201i	0.531665	+	0.837080i
$693$	1.28297	+	1.28297i	0.0487361	+	0.0487361i
$694$	2.78534	−	25.2725i	0.105730	−	0.959332i
$695$			34.6768i			1.31536i
$696$	4.32536	+	8.81666i	0.163952	+	0.334195i
$697$		−	4.47112i		−	0.169356i
$698$	−0.285012	−	0.0314118i	−0.0107879	−	0.00118896i
$699$	13.0260	+	13.0260i	0.492689	+	0.492689i
$700$	−0.795148	+	3.56353i	−0.0300538	+	0.134689i
$701$	13.9287	−	13.9287i	0.526079	−	0.526079i	−0.393322	−	0.919401i	$-0.628674\pi$
$701$	13.9287	−	13.9287i	0.526079	−	0.526079i	0.919401	+	0.393322i	$0.128674\pi$
$702$	0.717174	+	0.894838i	0.0270680	+	0.0337735i
$703$	90.2885			3.40530
$704$	−14.3987	+	1.83535i	−0.542671	+	0.0691724i
$705$	−22.6800			−0.854180
$706$	−6.98914	−	8.72053i	−0.263040	−	0.328202i
$707$	−3.02324	+	3.02324i	−0.113700	+	0.113700i
$708$	−2.76631	+	12.3975i	−0.103964	+	0.465925i
$709$	−16.3323	−	16.3323i	−0.613372	−	0.613372i	0.330451	−	0.943823i	$-0.392799\pi$
$709$	−16.3323	−	16.3323i	−0.613372	−	0.613372i	−0.943823	+	0.330451i	$0.892799\pi$
$710$	38.9633	+	4.29423i	1.46226	+	0.161159i
$711$		−	8.98738i		−	0.337053i
$712$	−4.39928	−	8.96734i	−0.164870	−	0.336065i
$713$		−	65.3805i		−	2.44852i
$714$	0.583512	−	5.29444i	0.0218374	−	0.198139i
$715$	2.71799	+	2.71799i	0.101647	+	0.101647i
$716$	−4.97021	−	7.82535i	−0.185746	−	0.292447i
$717$	−10.1193	+	10.1193i	−0.377912	+	0.377912i
$718$	5.42986	−	4.35180i	0.202641	−	0.162408i
$719$	−11.0810			−0.413253			−0.206627	−	0.978420i	$-0.566249\pi$
$719$	−11.0810			−0.413253			−0.206627	+	0.978420i	$0.566249\pi$
$720$	9.82987	−	3.54726i	0.366338	−	0.132198i
$721$	5.82296			0.216858
$722$	−47.9646	+	38.4416i	−1.78506	+	1.43065i
$723$	4.44938	−	4.44938i	0.165474	−	0.165474i
$724$	30.4023	−	19.3098i	1.12989	−	0.717642i
$725$	−4.48204	−	4.48204i	−0.166459	−	0.166459i
$726$	−1.19416	+	10.8351i	−0.0443194	+	0.402128i
$727$		−	6.33535i		−	0.234965i	−0.993075	−	0.117483i	$-0.962518\pi$
$727$		−	6.33535i		−	0.234965i	0.993075	−	0.117483i	$-0.0374824\pi$
$728$	−2.17029	−	0.741701i	−0.0804364	−	0.0274893i
$729$			1.00000i			0.0370370i
$730$	6.16876	+	0.679873i	0.228316	+	0.0251632i
$731$	−9.62945	−	9.62945i	−0.356158	−	0.356158i
$732$	4.90289	+	1.09401i	0.181216	+	0.0404356i
$733$	−32.0445	+	32.0445i	−1.18359	+	1.18359i	−0.204783	+	0.978807i	$0.565649\pi$
$733$	−32.0445	+	32.0445i	−1.18359	+	1.18359i	−0.978807	+	0.204783i	$0.934351\pi$
$734$	10.7167	+	13.3715i	0.395561	+	0.493552i
$735$	2.61258			0.0963665
$736$	48.2620	−	11.6343i	1.77896	−	0.428846i
$737$	−23.3584			−0.860418
$738$	−1.04991	−	1.31001i	−0.0386479	−	0.0482220i
$739$	−25.1654	+	25.1654i	−0.925724	+	0.925724i	−0.997426	−	0.0717024i	$-0.977157\pi$
$739$	−25.1654	+	25.1654i	−0.925724	+	0.925724i	0.0717024	+	0.997426i	$0.477157\pi$
$740$	−58.2591	−	12.9996i	−2.14165	−	0.477876i
$741$	4.53171	+	4.53171i	0.166477	+	0.166477i
$742$	2.05349	+	0.226319i	0.0753858	+	0.00830844i
$743$		−	11.3500i		−	0.416393i	−0.978087	−	0.208196i	$-0.933241\pi$
$743$		−	11.3500i		−	0.416393i	0.978087	−	0.208196i	$-0.0667593\pi$
$744$	6.81429	−	19.9393i	0.249824	−	0.731011i
$745$			22.3275i			0.818015i
$746$	−0.929476	+	8.43351i	−0.0340305	+	0.308773i
$747$	−5.03598	−	5.03598i	−0.184257	−	0.184257i
$748$	−11.5371	+	7.32772i	−0.421839	+	0.267928i
$749$	4.48343	−	4.48343i	0.163821	−	0.163821i
$750$	9.15204	−	7.33497i	0.334185	−	0.267835i
$751$	−37.7729			−1.37835			−0.689176	−	0.724594i	$-0.742027\pi$
$751$	−37.7729			−1.37835			−0.689176	+	0.724594i	$0.742027\pi$
$752$	−31.4305	−	14.7615i	−1.14615	−	0.538295i
$753$	23.1513			0.843681
$754$	3.10694	−	2.49008i	0.113148	−	0.0906833i
$755$	−5.10017	+	5.10017i	−0.185614	+	0.185614i
$756$	−1.07228	−	1.68826i	−0.0389986	−	0.0614013i
$757$	−24.2029	−	24.2029i	−0.879669	−	0.879669i	0.113831	−	0.993500i	$-0.463688\pi$
$757$	−24.2029	−	24.2029i	−0.879669	−	0.879669i	−0.993500	+	0.113831i	$0.963688\pi$
$758$	−2.74920	+	24.9446i	−0.0998555	+	0.906029i
$759$			15.9231i			0.577973i
$760$	52.4328	−	25.7229i	1.90194	−	0.933069i
$761$		−	50.5222i		−	1.83143i	−0.401831	−	0.915714i	$-0.631626\pi$
$761$		−	50.5222i		−	1.83143i	0.401831	−	0.915714i	$-0.368374\pi$
$762$	−12.2662	−	1.35189i	−0.444359	−	0.0489738i
$763$	−6.57337	−	6.57337i	−0.237972	−	0.237972i
$764$	5.74176	−	25.7322i	0.207729	−	0.930959i
$765$	6.95796	−	6.95796i	0.251565	−	0.251565i
$766$	−9.41719	−	11.7501i	−0.340257	−	0.424548i
$767$	5.15008			0.185959
$768$	15.9312	+	1.48196i	0.574868	+	0.0534757i
$769$	43.7545			1.57783			0.788913	−	0.614505i	$-0.210644\pi$
$769$	43.7545			1.57783			0.788913	+	0.614505i	$0.210644\pi$
$770$	−4.19244	−	5.23103i	−0.151085	−	0.188513i
$771$	4.20355	−	4.20355i	0.151387	−	0.151387i
$772$	−10.5455	+	47.2607i	−0.379541	+	1.70095i
$773$	35.1908	+	35.1908i	1.26572	+	1.26572i	0.948276	+	0.317448i	$0.102826\pi$
$773$	35.1908	+	35.1908i	1.26572	+	1.26572i	0.317448	+	0.948276i	$0.397174\pi$
$774$	−5.08256	−	0.560161i	−0.182689	−	0.0201346i
$775$			13.6005i			0.488543i
$776$	20.1175	−	9.86944i	0.722177	−	0.354292i
$777$			11.4239i			0.409831i
$778$	−1.69340	+	15.3649i	−0.0607114	+	0.550859i
$779$	−6.63425	−	6.63425i	−0.237697	−	0.237697i
$780$	−2.27164	−	3.57658i	−0.0813378	−	0.128062i
$781$	−13.6116	+	13.6116i	−0.487062	+	0.487062i
$782$	36.4760	−	29.2340i	1.30438	−	1.04540i
$783$	3.47207			0.124082
$784$	3.62058	+	1.70042i	0.129306	+	0.0607291i
$785$	47.7531			1.70438
$786$	9.86082	−	7.90303i	0.351724	−	0.281892i
$787$	10.7002	−	10.7002i	0.381423	−	0.381423i	−0.490192	−	0.871615i	$-0.663073\pi$
$787$	10.7002	−	10.7002i	0.381423	−	0.381423i	0.871615	+	0.490192i	$0.163073\pi$
$788$	10.0308	−	6.37101i	0.357334	−	0.226958i
$789$	−12.4444	−	12.4444i	−0.443034	−	0.443034i
$790$	−3.63769	+	33.0063i	−0.129423	+	1.17431i
$791$			12.6537i			0.449914i
$792$	−1.65959	+	4.85614i	−0.0589710	+	0.172555i
$793$		−	2.03673i		−	0.0723264i
$794$	14.2298	+	1.56829i	0.504996	+	0.0556567i
$795$	2.69869	+	2.69869i	0.0957128	+	0.0957128i
$796$	17.0038	+	3.79415i	0.602685	+	0.134480i
$797$	1.80566	−	1.80566i	0.0639597	−	0.0639597i	−0.674403	−	0.738363i	$-0.735599\pi$
$797$	1.80566	−	1.80566i	0.0639597	−	0.0639597i	0.738363	+	0.674403i	$0.235599\pi$
$798$	−6.99008	−	8.72171i	−0.247446	−	0.308745i
$799$	−32.6965			−1.15672
$800$	−10.0395	+	2.42017i	−0.354949	+	0.0855659i
$801$	−3.53141			−0.124776
$802$	−30.6194	−	38.2047i	−1.08121	−	1.34906i
$803$	−2.15503	+	2.15503i	−0.0760492	+	0.0760492i
$804$	25.1298	+	5.60734i	0.886261	+	0.197756i
$805$	16.2125	+	16.2125i	0.571417	+	0.571417i
$806$	−8.49191	−	0.935912i	−0.299115	−	0.0329661i
$807$			20.6956i			0.728520i
$808$	−11.4431	−	3.91071i	−0.402568	−	0.137578i
$809$			27.4525i			0.965177i	0.875847	+	0.482588i	$0.160303\pi$
$809$			27.4525i			0.965177i	−0.875847	+	0.482588i	$0.839697\pi$
$810$	0.404756	−	3.67251i	0.0142217	−	0.129039i
$811$	26.4118	+	26.4118i	0.927444	+	0.927444i	0.997540	−	0.0700961i	$-0.0223306\pi$
$811$	26.4118	+	26.4118i	0.927444	+	0.927444i	−0.0700961	+	0.997540i	$0.522331\pi$
$812$	−5.86174	+	3.72304i	−0.205707	+	0.130653i
$813$	−1.05340	+	1.05340i	−0.0369442	+	0.0369442i
$814$	22.8735	−	18.3321i	0.801715	−	0.642540i
$815$	−26.4658			−0.927057
$816$	14.1711	−	5.11387i	0.496089	−	0.179021i
$817$	−28.5764			−0.999760
$818$	−24.9984	+	20.0352i	−0.874049	+	0.700513i
$819$	−0.573383	+	0.573383i	−0.0200356	+	0.0200356i
$820$	3.32559	+	5.23598i	0.116135	+	0.182848i
$821$	−19.7705	−	19.7705i	−0.689997	−	0.689997i	0.272234	−	0.962231i	$-0.412237\pi$
$821$	−19.7705	−	19.7705i	−0.689997	−	0.689997i	−0.962231	+	0.272234i	$0.912237\pi$
$822$	1.70894	−	15.5059i	0.0596060	−	0.540829i
$823$		−	33.0460i		−	1.15191i	−0.817481	−	0.575955i	$-0.804630\pi$
$823$		−	33.0460i		−	1.15191i	0.817481	−	0.575955i	$-0.195370\pi$
$824$	7.25399	+	14.7863i	0.252705	+	0.515105i
$825$		−	3.31234i		−	0.115321i
$826$	−8.92786	−	0.983959i	−0.310640	−	0.0342363i
$827$	−18.8609	−	18.8609i	−0.655857	−	0.655857i	0.298540	−	0.954397i	$-0.403500\pi$
$827$	−18.8609	−	18.8609i	−0.655857	−	0.655857i	−0.954397	+	0.298540i	$0.903500\pi$
$828$	3.82246	−	17.1307i	0.132840	−	0.595333i
$829$	15.6529	−	15.6529i	0.543646	−	0.543646i	−0.380950	−	0.924596i	$-0.624403\pi$
$829$	15.6529	−	15.6529i	0.543646	−	0.543646i	0.924596	+	0.380950i	$0.124403\pi$
$830$	16.4563	+	20.5330i	0.571208	+	0.712712i
$831$	9.72102			0.337218
$832$	−0.820251	−	6.43502i	−0.0284371	−	0.223094i
$833$	3.76640			0.130498
$834$	11.7391	+	14.6471i	0.406490	+	0.507189i
$835$	47.1636	−	47.1636i	1.63216	−	1.63216i
$836$	−6.24592	+	27.9917i	−0.216020	+	0.968113i
$837$	−5.26789	−	5.26789i	−0.182085	−	0.182085i
$838$	−31.9989	−	3.52667i	−1.10538	−	0.121827i
$839$		−	43.6927i		−	1.50844i	−0.656623	−	0.754219i	$-0.728016\pi$
$839$		−	43.6927i		−	1.50844i	0.656623	−	0.754219i	$-0.271984\pi$
$840$	3.25464	+	6.63415i	0.112296	+	0.228900i
$841$			16.9447i			0.584301i
$842$	4.85590	−	44.0596i	0.167345	−	1.51839i
$843$	1.26347	+	1.26347i	0.0435162	+	0.0435162i
$844$	−3.51555	−	5.53506i	−0.121010	−	0.190525i
$845$	22.8012	−	22.8012i	0.784383	−	0.784383i
$846$	−9.57984	+	7.67783i	−0.329362	+	0.263969i
$847$	−7.70796			−0.264849
$848$	1.98345	+	5.49637i	0.0681120	+	0.188746i
$849$	−31.9473			−1.09643
$850$	−7.58775	+	6.08126i	−0.260258	+	0.208585i
$851$	−70.8919	+	70.8919i	−2.43014	+	2.43014i
$852$	17.9114	−	11.3763i	0.613636	−	0.389746i
$853$	2.25625	+	2.25625i	0.0772526	+	0.0772526i	0.744677	−	0.667425i	$-0.232603\pi$
$853$	2.25625	+	2.25625i	0.0772526	+	0.0772526i	−0.667425	+	0.744677i	$0.732603\pi$
$854$	−0.389131	+	3.53075i	−0.0133158	+	0.120820i
$855$		−	20.6484i		−	0.706162i
$856$	16.9701	+	5.79955i	0.580025	+	0.198224i
$857$		−	22.8421i		−	0.780271i	−0.920757	−	0.390135i	$-0.872428\pi$
$857$		−	22.8421i		−	0.780271i	0.920757	−	0.390135i	$-0.127572\pi$
$858$	2.06817	+	0.227937i	0.0706061	+	0.00778165i
$859$	1.94160	+	1.94160i	0.0662465	+	0.0662465i	0.739454	−	0.673207i	$-0.235084\pi$
$859$	1.94160	+	1.94160i	0.0662465	+	0.0662465i	−0.673207	+	0.739454i	$0.735084\pi$
$860$	18.4390	+	4.11439i	0.628766	+	0.140300i
$861$	0.839410	−	0.839410i	0.0286070	−	0.0286070i
$862$	−3.22956	−	4.02960i	−0.109999	−	0.137249i
$863$	−7.72439			−0.262941			−0.131471	−	0.991320i	$-0.541970\pi$
$863$	−7.72439			−0.262941			−0.131471	+	0.991320i	$0.541970\pi$
$864$	2.95120	−	4.82602i	0.100402	−	0.164184i
$865$	−34.0762			−1.15863
$866$	32.8308	+	40.9639i	1.11564	+	1.39201i
$867$	−1.98995	+	1.98995i	−0.0675822	+	0.0675822i
$868$	14.5422	+	3.24488i	0.493595	+	0.110138i
$869$	−11.5306	−	11.5306i	−0.391148	−	0.391148i
$870$	−12.7512	−	1.40534i	−0.432307	−	0.0476455i
$871$		−	10.4393i		−	0.353722i
$872$	8.50299	−	24.8806i	0.287948	−	0.842564i
$873$		−	7.92244i		−	0.268134i
$874$	10.7457	−	97.5005i	0.363480	−	3.29800i
$875$	5.86433	+	5.86433i	0.198251	+	0.198251i
$876$	2.83578	−	1.80113i	0.0958123	−	0.0608545i
$877$	4.53373	−	4.53373i	0.153093	−	0.153093i	−0.626405	−	0.779498i	$-0.715474\pi$
$877$	4.53373	−	4.53373i	0.153093	−	0.153093i	0.779498	+	0.626405i	$0.215474\pi$
$878$	26.0110	−	20.8467i	0.877830	−	0.703543i
$879$	−8.42782			−0.284263
$880$	8.06042	−	17.1625i	0.271717	−	0.578548i
$881$	4.47594			0.150798			0.0753992	−	0.997153i	$-0.475977\pi$
$881$	4.47594			0.150798			0.0753992	+	0.997153i	$0.475977\pi$
$882$	1.10353	−	0.884433i	0.0371578	−	0.0297804i
$883$	30.3237	−	30.3237i	1.02047	−	1.02047i	0.0206866	−	0.999786i	$-0.493415\pi$
$883$	30.3237	−	30.3237i	1.02047	−	1.02047i	0.999786	−	0.0206866i	$-0.00658523\pi$
$884$	−3.27489	−	5.15614i	−0.110146	−	0.173420i
$885$	−11.7330	−	11.7330i	−0.394400	−	0.394400i
$886$	−2.32781	+	21.1211i	−0.0782042	+	0.709578i
$887$			30.3025i			1.01746i	0.860926	+	0.508730i	$0.169885\pi$
$887$			30.3025i			1.01746i	−0.860926	+	0.508730i	$0.830115\pi$
$888$	−29.0089	+	14.2314i	−0.973474	+	0.477576i
$889$		−	8.72606i		−	0.292663i
$890$	12.9691	+	1.42936i	0.434727	+	0.0479122i
$891$	1.28297	+	1.28297i	0.0429812	+	0.0429812i
$892$	−4.08134	+	18.2909i	−0.136653	+	0.612425i
$893$	−48.5150	+	48.5150i	−1.62349	+	1.62349i
$894$	7.55848	+	9.43092i	0.252793	+	0.315417i
$895$	12.1098			0.404785
$896$	0.192479	+	11.3121i	0.00643026	+	0.377910i
$897$	−7.11633			−0.237607
$898$	21.1459	+	26.3843i	0.705646	+	0.880454i
$899$	−18.2905	+	18.2905i	−0.610022	+	0.610022i
$900$	−0.795148	+	3.56353i	−0.0265049	+	0.118784i
$901$	3.89054	+	3.89054i	0.129613	+	0.129613i
$902$	−3.02772	−	0.333691i	−0.100812	−	0.0111107i
$903$		−	3.61568i		−	0.120322i
$904$	−32.1317	+	15.7634i	−1.06868	+	0.524284i
$905$			47.0476i			1.56392i
$906$	−0.427713	+	3.88081i	−0.0142098	+	0.128931i
$907$	−4.75784	−	4.75784i	−0.157981	−	0.157981i	0.623690	−	0.781672i	$-0.285633\pi$
$907$	−4.75784	−	4.75784i	−0.157981	−	0.157981i	−0.781672	+	0.623690i	$0.785633\pi$
$908$	8.45817	+	13.3170i	0.280694	+	0.441939i
$909$	−3.02324	+	3.02324i	−0.100274	+	0.100274i
$910$	2.33784	−	1.87368i	0.0774985	−	0.0621118i
$911$	11.9935			0.397364			0.198682	−	0.980064i	$-0.436334\pi$
$911$	11.9935			0.397364			0.198682	+	0.980064i	$0.436334\pi$
$912$	13.4392	−	28.6151i	0.445016	−	0.947541i
$913$	−12.9221			−0.427657
$914$	−17.7036	+	14.1887i	−0.585582	+	0.469319i
$915$	−4.64011	+	4.64011i	−0.153397	+	0.153397i
$916$	−33.0627	+	20.9995i	−1.09242	+	0.693844i
$917$	6.31850	+	6.31850i	0.208655	+	0.208655i
$918$	0.583512	−	5.29444i	0.0192588	−	0.174743i
$919$			57.8037i			1.90677i	0.301759	+	0.953384i	$0.402426\pi$
$919$			57.8037i			1.90677i	−0.301759	+	0.953384i	$0.597574\pi$
$920$	−20.9718	+	61.3655i	−0.691418	+	2.02316i
$921$			27.2749i			0.898738i
$922$	−29.1044	−	3.20766i	−0.958501	−	0.105639i
$923$	−6.08327	−	6.08327i	−0.200233	−	0.200233i
$924$	−3.54170	−	0.790276i	−0.116513	−	0.0259982i
$925$	14.7469	−	14.7469i	0.484877	−	0.484877i
$926$	10.2374	+	12.7734i	0.336421	+	0.419761i
$927$	5.82296			0.191251
$928$	−16.7563	−	10.2468i	−0.550051	−	0.336367i
$929$	−5.01856			−0.164654			−0.0823268	−	0.996605i	$-0.526235\pi$
$929$	−5.01856			−0.164654			−0.0823268	+	0.996605i	$0.526235\pi$
$930$	17.2142	+	21.4786i	0.564475	+	0.704311i
$931$	5.58859	−	5.58859i	0.183159	−	0.183159i
$932$	−35.9588	−	8.02367i	−1.17787	−	0.262824i
$933$	−21.5583	−	21.5583i	−0.705786	−	0.705786i
$934$	6.54516	+	0.721356i	0.214164	+	0.0236035i
$935$		−	17.8537i		−	0.583880i
$936$	−2.17029	−	0.741701i	−0.0709382	−	0.0242432i
$937$			14.0317i			0.458395i	0.973380	+	0.229198i	$0.0736102\pi$
$937$			14.0317i			0.458395i	−0.973380	+	0.229198i	$0.926390\pi$
$938$	−1.99450	+	18.0969i	−0.0651227	+	0.590884i
$939$	−17.4333	−	17.4333i	−0.568913	−	0.568913i
$940$	38.2897	−	24.3194i	1.24887	−	0.793212i
$941$	3.87293	−	3.87293i	0.126254	−	0.126254i	−0.641156	−	0.767410i	$-0.721545\pi$
$941$	3.87293	−	3.87293i	0.126254	−	0.126254i	0.767410	+	0.641156i	$0.221545\pi$
$942$	20.1705	−	16.1658i	0.657190	−	0.526709i
$943$	10.4180			0.339258
$944$	−8.62337	−	23.8964i	−0.280667	−	0.777760i
$945$	2.61258			0.0849873
$946$	−7.23947	+	5.80212i	−0.235375	+	0.188643i
$947$	8.14973	−	8.14973i	0.264831	−	0.264831i	−0.562183	−	0.827013i	$-0.690038\pi$
$947$	8.14973	−	8.14973i	0.264831	−	0.264831i	0.827013	+	0.562183i	$0.190038\pi$
$948$	9.63702	+	15.1730i	0.312996	+	0.492796i
$949$	−0.963119	−	0.963119i	−0.0312642	−	0.0312642i
$950$	−2.23533	+	20.2821i	−0.0725238	+	0.658038i
$951$		−	26.8606i		−	0.871016i
$952$	4.69202	+	9.56406i	0.152069	+	0.309973i
$953$		−	41.1170i		−	1.33191i	−0.745992	−	0.665955i	$-0.768024\pi$
$953$		−	41.1170i		−	1.33191i	0.745992	−	0.665955i	$-0.231976\pi$
$954$	2.05349	+	0.226319i	0.0664841	+	0.00732736i
$955$	24.3531	+	24.3531i	0.788046	+	0.788046i
$956$	6.23320	−	27.9347i	0.201596	−	0.903473i
$957$	4.45457	−	4.45457i	0.143996	−	0.143996i
$958$	−1.38767	−	1.73144i	−0.0448337	−	0.0559402i
$959$	11.0307			0.356200
$960$	−12.7917	+	16.5291i	−0.412849	+	0.533474i
$961$	24.5014			0.790368
$962$	8.19294	+	10.2226i	0.264151	+	0.329588i
$963$	4.48343	−	4.48343i	0.144476	−	0.144476i
$964$	−2.74069	+	12.2827i	−0.0882718	+	0.395598i
$965$	−44.7277	−	44.7277i	−1.43984	−	1.43984i
$966$	12.3364	+	1.35963i	0.396918	+	0.0437452i
$967$		−	31.6861i		−	1.01896i	−0.860484	−	0.509478i	$-0.829839\pi$
$967$		−	31.6861i		−	1.01896i	0.860484	−	0.509478i	$-0.170161\pi$
$968$	−9.60224	−	19.5729i	−0.308628	−	0.629096i
$969$		−	29.7676i		−	0.956274i
$970$	−3.20665	+	29.0953i	−0.102959	+	0.934193i
$971$	−3.12339	−	3.12339i	−0.100234	−	0.100234i	0.655211	−	0.755446i	$-0.272580\pi$
$971$	−3.12339	−	3.12339i	−0.100234	−	0.100234i	−0.755446	+	0.655211i	$0.772580\pi$
$972$	−1.07228	−	1.68826i	−0.0343935	−	0.0541508i
$973$	−9.38542	+	9.38542i	−0.300883	+	0.300883i
$974$	−15.3599	+	12.3103i	−0.492164	+	0.394449i
$975$	1.48034			0.0474089
$976$	−9.45042	+	3.41033i	−0.302501	+	0.109162i
$977$	−35.3476			−1.13087			−0.565435	−	0.824793i	$-0.691292\pi$
$977$	−35.3476			−1.13087			−0.565435	+	0.824793i	$0.691292\pi$
$978$	−11.1789	+	8.95942i	−0.357462	+	0.286491i
$979$	−4.53070	+	4.53070i	−0.144802	+	0.144802i
$980$	−4.41071	+	2.80143i	−0.140895	+	0.0894884i
$981$	−6.57337	−	6.57337i	−0.209871	−	0.209871i
$982$	6.72253	−	60.9962i	0.214524	−	1.94647i
$983$			5.27253i			0.168168i	0.996459	+	0.0840838i	$0.0267963\pi$
$983$			5.27253i			0.168168i	−0.996459	+	0.0840838i	$0.973204\pi$
$984$	3.17722	+	1.08582i	0.101286	+	0.0346147i
$985$			15.5227i			0.494596i
$986$	−18.3827	−	2.02599i	−0.585423	−	0.0645208i
$987$	−6.13845	−	6.13845i	−0.195389	−	0.195389i
$988$	−12.5100	−	2.79141i	−0.397995	−	0.0888066i
$989$	22.4373	−	22.4373i	0.713465	−	0.713465i
$990$	−4.19244	−	5.23103i	−0.133245	−	0.166253i
$991$	−15.8030			−0.501999			−0.250999	−	0.967987i	$-0.580759\pi$
$991$	−15.8030			−0.501999			−0.250999	+	0.967987i	$0.580759\pi$
$992$	9.87634	+	40.9695i	0.313574	+	1.30078i
$993$	18.7604			0.595342
$994$	9.38332	+	11.7078i	0.297621	+	0.371350i
$995$	−16.0925	+	16.0925i	−0.510166	+	0.510166i
$996$	13.9020	+	3.10202i	0.440502	+	0.0982914i
$997$	−10.8744	−	10.8744i	−0.344397	−	0.344397i	0.513620	−	0.858018i	$-0.328304\pi$
$997$	−10.8744	−	10.8744i	−0.344397	−	0.344397i	−0.858018	+	0.513620i	$0.828304\pi$
$998$	−14.3422	−	1.58069i	−0.453994	−	0.0500357i
$999$			11.4239i			0.361437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.b.85.4	✓	28
4.3	odd	2		1344.2.w.b.1009.2		28
8.3	odd	2		2688.2.w.c.2017.13		28
8.5	even	2		2688.2.w.d.2017.2		28
16.3	odd	4		1344.2.w.b.337.2		28
16.5	even	4		2688.2.w.d.673.2		28
16.11	odd	4		2688.2.w.c.673.13		28
16.13	even	4	inner	336.2.w.b.253.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.b.85.4	✓	28	1.1	even	1	trivial
336.2.w.b.253.4	yes	28	16.13	even	4	inner
1344.2.w.b.337.2		28	16.3	odd	4
1344.2.w.b.1009.2		28	4.3	odd	2
2688.2.w.c.673.13		28	16.11	odd	4
2688.2.w.c.2017.13		28	8.3	odd	2
2688.2.w.d.673.2		28	16.5	even	4
2688.2.w.d.2017.2		28	8.5	even	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.884433 - 1.10353i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.435558 + 1.95200i) q^{4} +(-1.84737 - 1.84737i) q^{5} +(-1.40570 - 0.154926i) q^{6} -1.00000i q^{7} +(2.53931 - 1.24576i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.884433 - 1.10353i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.435558 + 1.95200i) q^{4} +(-1.84737 - 1.84737i) q^{5} +(-1.40570 - 0.154926i) q^{6} -1.00000i q^{7} +(2.53931 - 1.24576i) q^{8} -1.00000i q^{9} +(-0.404756 + 3.67251i) q^{10} +(-1.28297 - 1.28297i) q^{11} +(1.07228 + 1.68826i) q^{12} +(0.573383 - 0.573383i) q^{13} +(-1.10353 + 0.884433i) q^{14} -2.61258 q^{15} +(-3.62058 - 1.70042i) q^{16} -3.76640 q^{17} +(-1.10353 + 0.884433i) q^{18} +(-5.58859 + 5.58859i) q^{19} +(4.41071 - 2.80143i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(-0.281097 + 2.55050i) q^{22} -8.77599i q^{23} +(0.914679 - 2.67645i) q^{24} +1.82558i q^{25} +(-1.13986 - 0.125627i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.95200 + 0.435558i) q^{28} +(-2.45512 + 2.45512i) q^{29} +(2.31065 + 2.88306i) q^{30} +7.44993 q^{31} +(1.32570 + 5.49932i) q^{32} -1.81440 q^{33} +(3.33113 + 4.15634i) q^{34} +(-1.84737 + 1.84737i) q^{35} +(1.95200 + 0.435558i) q^{36} +(-8.07793 - 8.07793i) q^{37} +(11.1099 + 1.22445i) q^{38} -0.810886i q^{39} +(-6.99243 - 2.38967i) q^{40} +1.18711i q^{41} +(-0.154926 + 1.40570i) q^{42} +(2.55667 + 2.55667i) q^{43} +(3.06317 - 1.94555i) q^{44} +(-1.84737 + 1.84737i) q^{45} +(-9.68457 + 7.76177i) q^{46} +8.68108 q^{47} +(-3.76251 + 1.35776i) q^{48} -1.00000 q^{49} +(2.01459 - 1.61461i) q^{50} +(-2.66325 + 2.66325i) q^{51} +(0.869500 + 1.36898i) q^{52} +(-1.03296 - 1.03296i) q^{53} +(-0.154926 + 1.40570i) q^{54} +4.74026i q^{55} +(-1.24576 - 2.53931i) q^{56} +7.90346i q^{57} +(4.88070 + 0.537912i) q^{58} +(4.49096 + 4.49096i) q^{59} +(1.13793 - 5.09975i) q^{60} +(1.77606 - 1.77606i) q^{61} +(-6.58896 - 8.22122i) q^{62} -1.00000 q^{63} +(4.89618 - 6.32672i) q^{64} -2.11851 q^{65} +(1.60471 + 2.00224i) q^{66} +(9.10323 - 9.10323i) q^{67} +(1.64049 - 7.35200i) q^{68} +(-6.20556 - 6.20556i) q^{69} +(3.67251 + 0.404756i) q^{70} -10.6094i q^{71} +(-1.24576 - 2.53931i) q^{72} -1.67971i q^{73} +(-1.76986 + 16.0586i) q^{74} +(1.29088 + 1.29088i) q^{75} +(-8.47475 - 13.3431i) q^{76} +(-1.28297 + 1.28297i) q^{77} +(-0.894838 + 0.717174i) q^{78} +8.98738 q^{79} +(3.54726 + 9.82987i) q^{80} -1.00000 q^{81} +(1.31001 - 1.04991i) q^{82} +(5.03598 - 5.03598i) q^{83} +(1.68826 - 1.07228i) q^{84} +(6.95796 + 6.95796i) q^{85} +(0.560161 - 5.08256i) q^{86} +3.47207i q^{87} +(-4.85614 - 1.65959i) q^{88} -3.53141i q^{89} +(3.67251 + 0.404756i) q^{90} +(-0.573383 - 0.573383i) q^{91} +(17.1307 + 3.82246i) q^{92} +(5.26789 - 5.26789i) q^{93} +(-7.67783 - 9.57984i) q^{94} +20.6484 q^{95} +(4.82602 + 2.95120i) q^{96} +7.92244 q^{97} +(0.884433 + 1.10353i) q^{98} +(-1.28297 + 1.28297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) \) 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Introduction

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