LMFDB - Embedded newform 65.3.h.a.12.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,3,Mod(12,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("65.12");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	65.h (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:	$1.77112171834$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.8
Character	$\chi$	$=$	65.12
Dual form			65.3.h.a.38.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.474292 - 0.474292i) q^{2} +(-0.839739 + 0.839739i) q^{3} +3.55009i q^{4} +(4.99852 - 0.121682i) q^{5} +0.796563i q^{6} +(1.35251 - 1.35251i) q^{7} +(3.58095 + 3.58095i) q^{8} +7.58968i q^{9} +O(q^{10})$	\(q+(0.474292 - 0.474292i) q^{2} +(-0.839739 + 0.839739i) q^{3} +3.55009i q^{4} +(4.99852 - 0.121682i) q^{5} +0.796563i q^{6} +(1.35251 - 1.35251i) q^{7} +(3.58095 + 3.58095i) q^{8} +7.58968i q^{9} +(2.31304 - 2.42847i) q^{10} -7.57957i q^{11} +(-2.98115 - 2.98115i) q^{12} +(1.13612 - 12.9503i) q^{13} -1.28296i q^{14} +(-4.09527 + 4.29964i) q^{15} -10.8035 q^{16} +(-4.65336 - 4.65336i) q^{17} +(3.59972 + 3.59972i) q^{18} -25.1549 q^{19} +(0.431984 + 17.7452i) q^{20} +2.27150i q^{21} +(-3.59493 - 3.59493i) q^{22} +(8.91747 - 8.91747i) q^{23} -6.01413 q^{24} +(24.9704 - 1.21646i) q^{25} +(-5.60335 - 6.68105i) q^{26} +(-13.9310 - 13.9310i) q^{27} +(4.80152 + 4.80152i) q^{28} +16.0851i q^{29} +(0.0969277 + 3.98164i) q^{30} -33.0966i q^{31} +(-19.4478 + 19.4478i) q^{32} +(6.36487 + 6.36487i) q^{33} -4.41410 q^{34} +(6.59595 - 6.92510i) q^{35} -26.9441 q^{36} +(46.0851 - 46.0851i) q^{37} +(-11.9308 + 11.9308i) q^{38} +(9.92080 + 11.8289i) q^{39} +(18.3352 + 17.4637i) q^{40} +32.9969i q^{41} +(1.07736 + 1.07736i) q^{42} +(15.7297 - 15.7297i) q^{43} +26.9082 q^{44} +(0.923530 + 37.9371i) q^{45} -8.45897i q^{46} +(8.32632 - 8.32632i) q^{47} +(9.07217 - 9.07217i) q^{48} +45.3415i q^{49} +(11.2663 - 12.4202i) q^{50} +7.81521 q^{51} +(45.9746 + 4.03333i) q^{52} +(-44.5135 + 44.5135i) q^{53} -13.2147 q^{54} +(-0.922300 - 37.8866i) q^{55} +9.68650 q^{56} +(21.1236 - 21.1236i) q^{57} +(7.62903 + 7.62903i) q^{58} -59.1142 q^{59} +(-15.2641 - 14.5386i) q^{60} +28.3754 q^{61} +(-15.6975 - 15.6975i) q^{62} +(10.2651 + 10.2651i) q^{63} -24.7663i q^{64} +(4.10309 - 64.8704i) q^{65} +6.03761 q^{66} +(-72.9658 + 72.9658i) q^{67} +(16.5199 - 16.5199i) q^{68} +14.9767i q^{69} +(-0.156114 - 6.41292i) q^{70} +127.928i q^{71} +(-27.1782 + 27.1782i) q^{72} +(-28.4135 - 28.4135i) q^{73} -43.7156i q^{74} +(-19.9471 + 21.9901i) q^{75} -89.3024i q^{76} +(-10.2514 - 10.2514i) q^{77} +(10.3157 + 0.904990i) q^{78} -96.0038i q^{79} +(-54.0017 + 1.31460i) q^{80} -44.9102 q^{81} +(15.6501 + 15.6501i) q^{82} +(-47.5821 - 47.5821i) q^{83} -8.06405 q^{84} +(-23.8261 - 22.6937i) q^{85} -14.9210i q^{86} +(-13.5073 - 13.5073i) q^{87} +(27.1421 - 27.1421i) q^{88} +88.2023 q^{89} +(18.4313 + 17.5553i) q^{90} +(-15.9787 - 19.0519i) q^{91} +(31.6579 + 31.6579i) q^{92} +(27.7925 + 27.7925i) q^{93} -7.89821i q^{94} +(-125.737 + 3.06091i) q^{95} -32.6622i q^{96} +(-58.1358 + 58.1358i) q^{97} +(21.5051 + 21.5051i) q^{98} +57.5265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3}+O(q^{10}) $ 24 * q - 4 * q^3	$ 24 q - 4 q^{3} + 16 q^{10} + 72 q^{12} - 36 q^{13} - 104 q^{16} - 48 q^{17} + 8 q^{22} - 104 q^{23} - 88 q^{25} + 88 q^{26} + 56 q^{27} - 24 q^{30} - 64 q^{35} + 256 q^{36} + 124 q^{38} - 368 q^{40} + 216 q^{42} + 8 q^{43} + 196 q^{48} - 296 q^{51} + 16 q^{52} + 220 q^{53} + 332 q^{55} + 584 q^{56} - 8 q^{61} - 596 q^{62} + 420 q^{65} - 360 q^{66} - 640 q^{68} - 184 q^{75} + 388 q^{77} - 636 q^{78} - 224 q^{81} - 1004 q^{82} - 52 q^{87} + 780 q^{88} + 452 q^{90} - 512 q^{91} + 812 q^{92} - 136 q^{95}+O(q^{100}) $ 24 * q - 4 * q^3 + 16 * q^10 + 72 * q^12 - 36 * q^13 - 104 * q^16 - 48 * q^17 + 8 * q^22 - 104 * q^23 - 88 * q^25 + 88 * q^26 + 56 * q^27 - 24 * q^30 - 64 * q^35 + 256 * q^36 + 124 * q^38 - 368 * q^40 + 216 * q^42 + 8 * q^43 + 196 * q^48 - 296 * q^51 + 16 * q^52 + 220 * q^53 + 332 * q^55 + 584 * q^56 - 8 * q^61 - 596 * q^62 + 420 * q^65 - 360 * q^66 - 640 * q^68 - 184 * q^75 + 388 * q^77 - 636 * q^78 - 224 * q^81 - 1004 * q^82 - 52 * q^87 + 780 * q^88 + 452 * q^90 - 512 * q^91 + 812 * q^92 - 136 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.474292	−	0.474292i	0.237146	−	0.237146i	−0.578521	−	0.815667i	$-0.696370\pi$
$2$	0.474292	−	0.474292i	0.237146	−	0.237146i	0.815667	+	0.578521i	$0.196370\pi$
$3$	−0.839739	+	0.839739i	−0.279913	+	0.279913i	−0.833074	−	0.553161i	$-0.813421\pi$
$3$	−0.839739	+	0.839739i	−0.279913	+	0.279913i	0.553161	+	0.833074i	$0.313421\pi$
$4$			3.55009i			0.887524i
$5$	4.99852	−	0.121682i	0.999704	−	0.0243365i
$5$	4.99852	−	0.121682i	0.999704	−	0.0243365i
$6$			0.796563i			0.132761i
$7$	1.35251	−	1.35251i	0.193215	−	0.193215i	−0.603869	−	0.797084i	$-0.706375\pi$
$7$	1.35251	−	1.35251i	0.193215	−	0.193215i	0.797084	+	0.603869i	$0.206375\pi$
$8$	3.58095	+	3.58095i	0.447619	+	0.447619i
$9$			7.58968i			0.843297i
$10$	2.31304	−	2.42847i	0.231304	−	0.242847i
$11$		−	7.57957i		−	0.689052i	−0.938777	−	0.344526i	$-0.888040\pi$
$11$		−	7.57957i		−	0.689052i	0.938777	−	0.344526i	$-0.111960\pi$
$12$	−2.98115	−	2.98115i	−0.248430	−	0.248430i
$13$	1.13612	−	12.9503i	0.0873937	−	0.996174i
$13$	1.13612	−	12.9503i	0.0873937	−	0.996174i
$14$		−	1.28296i		−	0.0916403i
$15$	−4.09527	+	4.29964i	−0.273018	+	0.286642i
$16$	−10.8035			−0.675222
$17$	−4.65336	−	4.65336i	−0.273727	−	0.273727i	0.556872	−	0.830599i	$-0.312001\pi$
$17$	−4.65336	−	4.65336i	−0.273727	−	0.273727i	−0.830599	+	0.556872i	$0.812001\pi$
$18$	3.59972	+	3.59972i	0.199985	+	0.199985i
$19$	−25.1549			−1.32394			−0.661972	−	0.749528i	$-0.730280\pi$
$19$	−25.1549			−1.32394			−0.661972	+	0.749528i	$0.730280\pi$
$20$	0.431984	+	17.7452i	0.0215992	+	0.887261i
$21$			2.27150i			0.108167i
$22$	−3.59493	−	3.59493i	−0.163406	−	0.163406i
$23$	8.91747	−	8.91747i	0.387716	−	0.387716i	−0.486156	−	0.873872i	$-0.661601\pi$
$23$	8.91747	−	8.91747i	0.387716	−	0.387716i	0.873872	+	0.486156i	$0.161601\pi$
$24$	−6.01413			−0.250589
$25$	24.9704	−	1.21646i	0.998815	−	0.0486585i
$26$	−5.60335	−	6.68105i	−0.215514	−	0.256964i
$27$	−13.9310	−	13.9310i	−0.515963	−	0.515963i
$28$	4.80152	+	4.80152i	0.171483	+	0.171483i
$29$			16.0851i			0.554659i	0.960775	+	0.277329i	$0.0894493\pi$
$29$			16.0851i			0.554659i	−0.960775	+	0.277329i	$0.910551\pi$
$30$	0.0969277	+	3.98164i	0.00323092	+	0.132721i
$31$		−	33.0966i		−	1.06763i	−0.845600	−	0.533817i	$-0.820757\pi$
$31$		−	33.0966i		−	1.06763i	0.845600	−	0.533817i	$-0.179243\pi$
$32$	−19.4478	+	19.4478i	−0.607745	+	0.607745i
$33$	6.36487	+	6.36487i	0.192875	+	0.192875i
$34$	−4.41410			−0.129826
$35$	6.59595	−	6.92510i	0.188456	−	0.197860i
$36$	−26.9441			−0.748446
$37$	46.0851	−	46.0851i	1.24554	−	1.24554i	0.287875	−	0.957668i	$-0.407051\pi$
$37$	46.0851	−	46.0851i	1.24554	−	1.24554i	0.957668	−	0.287875i	$-0.0929487\pi$
$38$	−11.9308	+	11.9308i	−0.313968	+	0.313968i
$39$	9.92080	+	11.8289i	0.254380	+	0.303305i
$40$	18.3352	+	17.4637i	0.458379	+	0.436593i
$41$			32.9969i			0.804801i	0.915464	+	0.402401i	$0.131824\pi$
$41$			32.9969i			0.804801i	−0.915464	+	0.402401i	$0.868176\pi$
$42$	1.07736	+	1.07736i	0.0256513	+	0.0256513i
$43$	15.7297	−	15.7297i	0.365808	−	0.365808i	−0.500138	−	0.865946i	$-0.666717\pi$
$43$	15.7297	−	15.7297i	0.365808	−	0.365808i	0.865946	+	0.500138i	$0.166717\pi$
$44$	26.9082			0.611550
$45$	0.923530	+	37.9371i	0.0205229	+	0.843047i
$46$		−	8.45897i		−	0.183891i
$47$	8.32632	−	8.32632i	0.177156	−	0.177156i	−0.612959	−	0.790115i	$-0.710021\pi$
$47$	8.32632	−	8.32632i	0.177156	−	0.177156i	0.790115	+	0.612959i	$0.210021\pi$
$48$	9.07217	−	9.07217i	0.189003	−	0.189003i
$49$			45.3415i			0.925336i
$50$	11.2663	−	12.4202i	0.225326	−	0.248404i
$51$	7.81521			0.153239
$52$	45.9746	+	4.03333i	0.884128	+	0.0775640i
$53$	−44.5135	+	44.5135i	−0.839878	+	0.839878i	−0.988843	−	0.148964i	$-0.952406\pi$
$53$	−44.5135	+	44.5135i	−0.839878	+	0.839878i	0.148964	+	0.988843i	$0.452406\pi$
$54$	−13.2147			−0.244717
$55$	−0.922300	−	37.8866i	−0.0167691	−	0.688848i
$56$	9.68650			0.172973
$57$	21.1236	−	21.1236i	0.370589	−	0.370589i
$58$	7.62903	+	7.62903i	0.131535	+	0.131535i
$59$	−59.1142			−1.00193			−0.500967	−	0.865466i	$-0.667022\pi$
$59$	−59.1142			−1.00193			−0.500967	+	0.865466i	$0.667022\pi$
$60$	−15.2641	−	14.5386i	−0.254402	−	0.242310i
$61$	28.3754			0.465171			0.232585	−	0.972576i	$-0.425281\pi$
$61$	28.3754			0.465171			0.232585	+	0.972576i	$0.425281\pi$
$62$	−15.6975	−	15.6975i	−0.253185	−	0.253185i
$63$	10.2651	+	10.2651i	0.162938	+	0.162938i
$64$		−	24.7663i		−	0.386973i
$65$	4.10309	−	64.8704i	0.0631245	−	0.998006i
$66$	6.03761			0.0914789
$67$	−72.9658	+	72.9658i	−1.08904	+	1.08904i	−0.0934149	+	0.995627i	$0.529778\pi$
$67$	−72.9658	+	72.9658i	−1.08904	+	1.08904i	−0.995627	+	0.0934149i	$0.970222\pi$
$68$	16.5199	−	16.5199i	0.242939	−	0.242939i
$69$			14.9767i			0.217054i
$70$	−0.156114	−	6.41292i	−0.00223020	−	0.0916132i
$71$			127.928i			1.80180i	0.434027	+	0.900900i	$0.357092\pi$
$71$			127.928i			1.80180i	−0.434027	+	0.900900i	$0.642908\pi$
$72$	−27.1782	+	27.1782i	−0.377475	+	0.377475i
$73$	−28.4135	−	28.4135i	−0.389226	−	0.389226i	0.485185	−	0.874411i	$-0.338752\pi$
$73$	−28.4135	−	28.4135i	−0.389226	−	0.389226i	−0.874411	+	0.485185i	$0.838752\pi$
$74$		−	43.7156i		−	0.590751i
$75$	−19.9471	+	21.9901i	−0.265961	+	0.293202i
$76$		−	89.3024i		−	1.17503i
$77$	−10.2514	−	10.2514i	−0.133135	−	0.133135i
$78$	10.3157	+	0.904990i	0.132253	+	0.0116024i
$79$		−	96.0038i		−	1.21524i	−0.794229	−	0.607619i	$-0.792125\pi$
$79$		−	96.0038i		−	1.21524i	0.794229	−	0.607619i	$-0.207875\pi$
$80$	−54.0017	+	1.31460i	−0.675022	+	0.0164325i
$81$	−44.9102			−0.554447
$82$	15.6501	+	15.6501i	0.190855	+	0.190855i
$83$	−47.5821	−	47.5821i	−0.573278	−	0.573278i	0.359765	−	0.933043i	$-0.382857\pi$
$83$	−47.5821	−	47.5821i	−0.573278	−	0.573278i	−0.933043	+	0.359765i	$0.882857\pi$
$84$	−8.06405			−0.0960006
$85$	−23.8261	−	22.6937i	−0.280307	−	0.266984i
$86$		−	14.9210i		−	0.173500i
$87$	−13.5073	−	13.5073i	−0.155256	−	0.155256i
$88$	27.1421	−	27.1421i	0.308432	−	0.308432i
$89$	88.2023			0.991037			0.495519	−	0.868597i	$-0.334978\pi$
$89$	88.2023			0.991037			0.495519	+	0.868597i	$0.334978\pi$
$90$	18.4313	+	17.5553i	0.204792	+	0.195058i
$91$	−15.9787	−	19.0519i	−0.175590	−	0.209362i
$92$	31.6579	+	31.6579i	0.344107	+	0.344107i
$93$	27.7925	+	27.7925i	0.298845	+	0.298845i
$94$		−	7.89821i		−	0.0840235i
$95$	−125.737	+	3.06091i	−1.32355	+	0.0322201i
$96$		−	32.6622i		−	0.340231i
$97$	−58.1358	+	58.1358i	−0.599338	+	0.599338i	−0.940136	−	0.340798i	$-0.889303\pi$
$97$	−58.1358	+	58.1358i	−0.599338	+	0.599338i	0.340798	+	0.940136i	$0.389303\pi$
$98$	21.5051	+	21.5051i	0.219440	+	0.219440i
$99$	57.5265			0.581076
$100$	4.31856	+	88.6472i	0.0431856	+	0.886472i
$101$	113.917			1.12789			0.563944	−	0.825813i	$-0.309283\pi$
$101$	113.917			1.12789			0.563944	+	0.825813i	$0.309283\pi$
$102$	3.70669	−	3.70669i	0.0363401	−	0.0363401i
$103$	−21.8259	+	21.8259i	−0.211902	+	0.211902i	−0.805075	−	0.593173i	$-0.797875\pi$
$103$	−21.8259	+	21.8259i	−0.211902	+	0.211902i	0.593173	+	0.805075i	$0.297875\pi$
$104$	50.4426	−	42.3058i	0.485025	−	0.406787i
$105$	0.276402	+	11.3542i	0.00263240	+	0.108135i
$106$			42.2248i			0.398347i
$107$	100.018	+	100.018i	0.934750	+	0.934750i	0.997998	−	0.0632479i	$-0.0201459\pi$
$107$	100.018	+	100.018i	0.934750	+	0.934750i	−0.0632479	+	0.997998i	$0.520146\pi$
$108$	49.4564	−	49.4564i	0.457929	−	0.457929i
$109$	41.8546			0.383987			0.191993	−	0.981396i	$-0.438505\pi$
$109$	41.8546			0.383987			0.191993	+	0.981396i	$0.438505\pi$
$110$	−18.4068	−	17.5319i	−0.167334	−	0.159381i
$111$			77.3989i			0.697288i
$112$	−14.6119	+	14.6119i	−0.130463	+	0.130463i
$113$	−96.8435	+	96.8435i	−0.857022	+	0.857022i	−0.990986	−	0.133964i	$-0.957229\pi$
$113$	−96.8435	+	96.8435i	−0.857022	+	0.857022i	0.133964	+	0.990986i	$0.457229\pi$
$114$		−	20.0375i		−	0.175768i
$115$	43.4891	−	45.6593i	0.378166	−	0.397037i
$116$	−57.1036			−0.492273
$117$	98.2883	+	8.62277i	0.840071	+	0.0736989i
$118$	−28.0374	+	28.0374i	−0.237605	+	0.237605i
$119$	−12.5874			−0.105776
$120$	−30.0617	+	0.731813i	−0.250514	+	0.00609845i
$121$	63.5501			0.525207
$122$	13.4582	−	13.4582i	0.110313	−	0.110313i
$123$	−27.7088	−	27.7088i	−0.225275	−	0.225275i
$124$	117.496			0.947550
$125$	124.667	−	9.11897i	0.997335	−	0.0729518i
$126$	9.73728			0.0772800
$127$	−103.615	−	103.615i	−0.815862	−	0.815862i	0.169643	−	0.985506i	$-0.445738\pi$
$127$	−103.615	−	103.615i	−0.815862	−	0.815862i	−0.985506	+	0.169643i	$0.945738\pi$
$128$	−89.5378	−	89.5378i	−0.699514	−	0.699514i
$129$			26.4178i			0.204789i
$130$	−28.8214	−	32.7136i	−0.221703	−	0.251643i
$131$	159.070			1.21427			0.607136	−	0.794598i	$-0.292318\pi$
$131$	159.070			1.21427			0.607136	+	0.794598i	$0.292318\pi$
$132$	−22.5959	+	22.5959i	−0.171181	+	0.171181i
$133$	−34.0222	+	34.0222i	−0.255806	+	0.255806i
$134$			69.2142i			0.516524i
$135$	−71.3296	−	67.9392i	−0.528367	−	0.503254i
$136$		−	33.3269i		−	0.245050i
$137$	4.74606	−	4.74606i	0.0346428	−	0.0346428i	−0.689573	−	0.724216i	$-0.742202\pi$
$137$	4.74606	−	4.74606i	0.0346428	−	0.0346428i	0.724216	+	0.689573i	$0.242202\pi$
$138$	7.10333	+	7.10333i	0.0514734	+	0.0514734i
$139$		−	45.1532i		−	0.324843i	−0.986721	−	0.162422i	$-0.948069\pi$
$139$		−	45.1532i		−	0.324843i	0.986721	−	0.162422i	$-0.0519305\pi$
$140$	24.5848	+	23.4162i	0.175605	+	0.167259i
$141$			13.9839i			0.0991765i
$142$	60.6751	+	60.6751i	0.427290	+	0.427290i
$143$	−98.1574	−	8.61129i	−0.686416	−	0.0602188i
$144$		−	81.9954i		−	0.569413i
$145$	1.95727	+	80.4017i	0.0134984	+	0.554494i
$146$	−26.9526			−0.184607
$147$	−38.0750	−	38.0750i	−0.259014	−	0.259014i
$148$	163.606	+	163.606i	1.10545	+	1.10545i
$149$	−81.6178			−0.547771			−0.273885	−	0.961762i	$-0.588309\pi$
$149$	−81.6178			−0.547771			−0.273885	+	0.961762i	$0.588309\pi$
$150$	0.968990	+	19.8905i	0.00645993	+	0.132603i
$151$			117.641i			0.779078i	0.921010	+	0.389539i	$0.127366\pi$
$151$			117.641i			0.779078i	−0.921010	+	0.389539i	$0.872634\pi$
$152$	−90.0785	−	90.0785i	−0.592622	−	0.592622i
$153$	35.3175	−	35.3175i	0.230833	−	0.230833i
$154$	−9.72432			−0.0631449
$155$	−4.02728	−	165.434i	−0.0259824	−	1.06732i
$156$	−41.9937	+	35.2198i	−0.269190	+	0.225768i
$157$	−19.2300	−	19.2300i	−0.122484	−	0.122484i	0.643208	−	0.765692i	$-0.277603\pi$
$157$	−19.2300	−	19.2300i	−0.122484	−	0.122484i	−0.765692	+	0.643208i	$0.777603\pi$
$158$	−45.5338	−	45.5338i	−0.288189	−	0.288189i
$159$		−	74.7596i		−	0.470186i
$160$	−94.8439	+	99.5768i	−0.592774	+	0.622355i
$161$		−	24.1219i		−	0.149825i
$162$	−21.3006	+	21.3006i	−0.131485	+	0.131485i
$163$	−90.0452	−	90.0452i	−0.552424	−	0.552424i	0.374715	−	0.927140i	$-0.377740\pi$
$163$	−90.0452	−	90.0452i	−0.552424	−	0.552424i	−0.927140	+	0.374715i	$0.877740\pi$
$164$	−117.142			−0.714280
$165$	32.5894	+	31.0404i	0.197511	+	0.188124i
$166$	−45.1356			−0.271901
$167$	−70.3760	+	70.3760i	−0.421413	+	0.421413i	−0.885690	−	0.464277i	$-0.846314\pi$
$167$	−70.3760	+	70.3760i	−0.421413	+	0.421413i	0.464277	+	0.885690i	$0.346314\pi$
$168$	−8.13414	+	8.13414i	−0.0484175	+	0.0484175i
$169$	−166.418	−	29.4261i	−0.984725	−	0.174119i
$170$	−22.0639	+	0.537118i	−0.129788	+	0.00315952i
$171$		−	190.918i		−	1.11648i
$172$	55.8421	+	55.8421i	0.324663	+	0.324663i
$173$	160.905	−	160.905i	0.930086	−	0.930086i	−0.0676247	−	0.997711i	$-0.521542\pi$
$173$	160.905	−	160.905i	0.930086	−	0.930086i	0.997711	+	0.0676247i	$0.0215421\pi$
$174$	−12.8128			−0.0736368
$175$	32.1273	−	35.4179i	0.183585	−	0.202388i
$176$			81.8863i			0.465263i
$177$	49.6405	−	49.6405i	0.280455	−	0.280455i
$178$	41.8336	−	41.8336i	0.235021	−	0.235021i
$179$			159.790i			0.892682i	0.894863	+	0.446341i	$0.147273\pi$
$179$			159.790i			0.892682i	−0.894863	+	0.446341i	$0.852727\pi$
$180$	−134.680	+	3.27862i	−0.748225	+	0.0182145i
$181$	−173.370			−0.957846			−0.478923	−	0.877857i	$-0.658973\pi$
$181$	−173.370			−0.957846			−0.478923	+	0.877857i	$0.658973\pi$
$182$	−16.6147	−	1.45760i	−0.0912897	−	0.00800879i
$183$	−23.8280	+	23.8280i	−0.130207	+	0.130207i
$184$	63.8660			0.347098
$185$	224.749	−	235.965i	1.21486	−	1.27549i
$186$	26.3636			0.141740
$187$	−35.2704	+	35.2704i	−0.188612	+	0.188612i
$188$	29.5592	+	29.5592i	0.157230	+	0.157230i
$189$	−37.6835			−0.199384
$190$	−58.1845	+	61.0880i	−0.306234	+	0.321516i
$191$	118.091			0.618277			0.309138	−	0.951017i	$-0.399959\pi$
$191$	118.091			0.618277			0.309138	+	0.951017i	$0.399959\pi$
$192$	20.7972	+	20.7972i	0.108319	+	0.108319i
$193$	146.487	+	146.487i	0.758999	+	0.758999i	0.976140	−	0.217141i	$-0.0696732\pi$
$193$	146.487	+	146.487i	0.758999	+	0.758999i	−0.217141	+	0.976140i	$0.569673\pi$
$194$			55.1467i			0.284261i
$195$	51.0287	+	57.9197i	0.261686	+	0.297024i
$196$	−160.966			−0.821257
$197$	161.211	−	161.211i	0.818327	−	0.818327i	−0.167538	−	0.985866i	$-0.553582\pi$
$197$	161.211	−	161.211i	0.818327	−	0.818327i	0.985866	+	0.167538i	$0.0535817\pi$
$198$	27.2843	−	27.2843i	0.137800	−	0.137800i
$199$			98.2606i			0.493772i	0.969045	+	0.246886i	$0.0794073\pi$
$199$			98.2606i			0.493772i	−0.969045	+	0.246886i	$0.920593\pi$
$200$	93.7738	+	85.0616i	0.468869	+	0.425308i
$201$		−	122.545i		−	0.609674i
$202$	54.0297	−	54.0297i	0.267474	−	0.267474i
$203$	21.7552	+	21.7552i	0.107168	+	0.107168i
$204$			27.7447i			0.136004i
$205$	4.01514	+	164.935i	0.0195860	+	0.804563i
$206$			20.7037i			0.100503i
$207$	67.6807	+	67.6807i	0.326960	+	0.326960i
$208$	−12.2741	+	139.909i	−0.0590102	+	0.672638i
$209$			190.664i			0.912266i
$210$	5.51628	+	5.25409i	0.0262680	+	0.0250195i
$211$	−225.759			−1.06995			−0.534974	−	0.844868i	$-0.679679\pi$
$211$	−225.759			−1.06995			−0.534974	+	0.844868i	$0.679679\pi$
$212$	−158.027	−	158.027i	−0.745412	−	0.745412i
$213$	−107.426	−	107.426i	−0.504348	−	0.504348i
$214$	94.8757			0.443344
$215$	76.7114	−	80.5394i	0.356797	−	0.374602i
$216$		−	99.7724i		−	0.461909i
$217$	−44.7634	−	44.7634i	−0.206283	−	0.206283i
$218$	19.8513	−	19.8513i	0.0910609	−	0.0910609i
$219$	47.7199			0.217899
$220$	134.501	−	3.27425i	0.611369	−	0.0148830i
$221$	−65.5489	+	54.9754i	−0.296601	+	0.248757i
$222$	36.7097	+	36.7097i	0.165359	+	0.165359i
$223$	203.948	+	203.948i	0.914566	+	0.914566i	0.996627	−	0.0820617i	$-0.0261505\pi$
$223$	203.948	+	203.948i	0.914566	+	0.914566i	−0.0820617	+	0.996627i	$0.526150\pi$
$224$			52.6066i			0.234851i
$225$	9.23256	+	189.517i	0.0410336	+	0.842298i
$226$			91.8642i			0.406479i
$227$	293.776	−	293.776i	1.29417	−	1.29417i	0.361984	−	0.932184i	$-0.382099\pi$
$227$	293.776	−	293.776i	1.29417	−	1.29417i	0.932184	−	0.361984i	$-0.117901\pi$
$228$	74.9908	+	74.9908i	0.328907	+	0.328907i
$229$	−198.628			−0.867371			−0.433686	−	0.901064i	$-0.642787\pi$
$229$	−198.628			−0.867371			−0.433686	+	0.901064i	$0.642787\pi$
$230$	−1.02931	−	42.2823i	−0.00447525	−	0.183836i
$231$	17.2170			0.0745326
$232$	−57.5999	+	57.5999i	−0.248275	+	0.248275i
$233$	−29.7894	+	29.7894i	−0.127852	+	0.127852i	−0.768137	−	0.640285i	$-0.778816\pi$
$233$	−29.7894	+	29.7894i	−0.127852	+	0.127852i	0.640285	+	0.768137i	$0.278816\pi$
$234$	50.7070	−	42.5276i	0.216697	−	0.181742i
$235$	40.6061	−	42.6324i	0.172792	−	0.181415i
$236$		−	209.861i		−	0.889241i
$237$	80.6182	+	80.6182i	0.340161	+	0.340161i
$238$	−5.97009	+	5.97009i	−0.0250844	+	0.0250844i
$239$	−193.873			−0.811185			−0.405593	−	0.914054i	$-0.632935\pi$
$239$	−193.873			−0.811185			−0.405593	+	0.914054i	$0.632935\pi$
$240$	44.2435	−	46.4513i	0.184348	−	0.193547i
$241$		−	314.594i		−	1.30537i	−0.757629	−	0.652685i	$-0.773643\pi$
$241$		−	314.594i		−	1.30537i	0.757629	−	0.652685i	$-0.226357\pi$
$242$	30.1413	−	30.1413i	0.124551	−	0.124551i
$243$	163.092	−	163.092i	0.671160	−	0.671160i
$244$			100.735i			0.412850i
$245$	5.51726	+	226.640i	0.0225194	+	0.925062i
$246$	−26.2841			−0.106846
$247$	−28.5790	+	325.763i	−0.115704	+	1.31888i
$248$	118.517	−	118.517i	0.477892	−	0.477892i
$249$	79.9131			0.320936
$250$	54.8035	−	63.4536i	0.219214	−	0.253814i
$251$	271.800			1.08287			0.541435	−	0.840743i	$-0.317881\pi$
$251$	271.800			1.08287			0.541435	+	0.840743i	$0.317881\pi$
$252$	−36.4420	+	36.4420i	−0.144611	+	0.144611i
$253$	−67.5906	−	67.5906i	−0.267157	−	0.267157i
$254$	−98.2870			−0.386957
$255$	39.0645	−	0.950974i	0.153194	−	0.00372931i
$256$	14.1311			0.0551998
$257$	−355.414	−	355.414i	−1.38293	−	1.38293i	−0.839363	−	0.543572i	$-0.817072\pi$
$257$	−355.414	−	355.414i	−1.38293	−	1.38293i	−0.543572	−	0.839363i	$-0.682928\pi$
$258$	12.5297	+	12.5297i	0.0485648	+	0.0485648i
$259$		−	124.661i		−	0.481315i
$260$	230.296	+	14.5664i	0.885754	+	0.0560245i
$261$	−122.081			−0.467742
$262$	75.4454	−	75.4454i	0.287960	−	0.287960i
$263$	−334.181	+	334.181i	−1.27065	+	1.27065i	−0.324901	+	0.945748i	$0.605331\pi$
$263$	−334.181	+	334.181i	−1.27065	+	1.27065i	−0.945748	+	0.324901i	$0.894669\pi$
$264$			45.5845i			0.172669i
$265$	−217.085	+	227.918i	−0.819190	+	0.860069i
$266$			32.2729i			0.121327i
$267$	−74.0670	+	74.0670i	−0.277404	+	0.277404i
$268$	−259.036	−	259.036i	−0.966551	−	0.966551i
$269$			335.882i			1.24863i	0.781171	+	0.624317i	$0.214623\pi$
$269$			335.882i			1.24863i	−0.781171	+	0.624317i	$0.785377\pi$
$270$	−66.0541	+	1.60800i	−0.244645	+	0.00595555i
$271$			349.861i			1.29100i	0.763761	+	0.645500i	$0.223351\pi$
$271$			349.861i			1.29100i	−0.763761	+	0.645500i	$0.776649\pi$
$272$	50.2728	+	50.2728i	0.184826	+	0.184826i
$273$	29.4166	+	2.58070i	0.107753	+	0.00945311i
$274$		−	4.50203i		−	0.0164308i
$275$	−9.22027	−	189.265i	−0.0335283	−	0.688236i
$276$	−53.1687			−0.192640
$277$	−362.018	−	362.018i	−1.30692	−	1.30692i	−0.923625	−	0.383298i	$-0.874788\pi$
$277$	−362.018	−	362.018i	−1.30692	−	1.30692i	−0.383298	−	0.923625i	$-0.625212\pi$
$278$	−21.4158	−	21.4158i	−0.0770353	−	0.0770353i
$279$	251.193			0.900332
$280$	48.4182	−	1.17868i	0.172922	−	0.00420956i
$281$			323.880i			1.15260i	0.817240	+	0.576298i	$0.195503\pi$
$281$			323.880i			1.15260i	−0.817240	+	0.576298i	$0.804497\pi$
$282$	6.63244	+	6.63244i	0.0235193	+	0.0235193i
$283$	228.523	−	228.523i	0.807502	−	0.807502i	−0.176754	−	0.984255i	$-0.556560\pi$
$283$	228.523	−	228.523i	0.807502	−	0.807502i	0.984255	+	0.176754i	$0.0565596\pi$
$284$	−454.156			−1.59914
$285$	103.016	−	108.157i	0.361461	−	0.379498i
$286$	−50.6395	+	42.4710i	−0.177061	+	0.148500i
$287$	44.6284	+	44.6284i	0.155500	+	0.155500i
$288$	−147.603	−	147.603i	−0.512509	−	0.512509i
$289$		−	245.693i		−	0.850147i
$290$	39.0622	+	37.2055i	0.134697	+	0.128295i
$291$		−	97.6379i		−	0.335525i
$292$	100.871	−	100.871i	0.345448	−	0.345448i
$293$	−107.760	−	107.760i	−0.367780	−	0.367780i	0.498887	−	0.866667i	$-0.333742\pi$
$293$	−107.760	−	107.760i	−0.367780	−	0.367780i	−0.866667	+	0.498887i	$0.833742\pi$
$294$	−36.1173			−0.122848
$295$	−295.483	+	7.19315i	−1.00164	+	0.0243836i
$296$	330.057			1.11506
$297$	−105.591	+	105.591i	−0.355525	+	0.355525i
$298$	−38.7107	+	38.7107i	−0.129902	+	0.129902i
$299$	−105.352	−	125.615i	−0.352349	−	0.420117i
$300$	−78.0670	−	70.8141i	−0.260223	−	0.236047i
$301$		−	42.5491i		−	0.141359i
$302$	55.7961	+	55.7961i	0.184755	+	0.184755i
$303$	−95.6603	+	95.6603i	−0.315711	+	0.315711i
$304$	271.763			0.893956
$305$	141.835	−	3.45279i	0.465033	−	0.0113206i
$306$		−	33.5016i		−	0.109482i
$307$	25.1232	−	25.1232i	0.0818345	−	0.0818345i	−0.665005	−	0.746839i	$-0.731570\pi$
$307$	25.1232	−	25.1232i	0.0818345	−	0.0818345i	0.746839	+	0.665005i	$0.231570\pi$
$308$	36.3935	−	36.3935i	0.118161	−	0.118161i
$309$		−	36.6561i		−	0.118628i
$310$	−80.3742	−	76.5540i	−0.259272	−	0.246948i
$311$	6.13773			0.0197355			0.00986773	−	0.999951i	$-0.496859\pi$
$311$	6.13773			0.0197355			0.00986773	+	0.999951i	$0.496859\pi$
$312$	−6.83276	+	77.8845i	−0.0218999	+	0.249630i
$313$	30.0089	−	30.0089i	0.0958751	−	0.0958751i	−0.657542	−	0.753418i	$-0.728404\pi$
$313$	30.0089	−	30.0089i	0.0958751	−	0.0958751i	0.753418	+	0.657542i	$0.228404\pi$
$314$	−18.2413			−0.0580932
$315$	52.5593	+	50.0611i	0.166855	+	0.158924i
$316$	340.822			1.07855
$317$	−271.543	+	271.543i	−0.856602	+	0.856602i	−0.990936	−	0.134334i	$-0.957110\pi$
$317$	−271.543	+	271.543i	−0.856602	+	0.856602i	0.134334	+	0.990936i	$0.457110\pi$
$318$	−35.4578	−	35.4578i	−0.111503	−	0.111503i
$319$	121.918			0.382189
$320$	−3.01362	−	123.795i	−0.00941757	−	0.386859i
$321$	−167.979			−0.523298
$322$	−11.4408	−	11.4408i	−0.0355304	−	0.0355304i
$323$	117.055	+	117.055i	0.362399	+	0.362399i
$324$		−	159.436i		−	0.492085i
$325$	12.6158	−	324.755i	0.0388179	−	0.999246i
$326$	−85.4154			−0.262010
$327$	−35.1469	+	35.1469i	−0.107483	+	0.107483i
$328$	−118.160	+	118.160i	−0.360244	+	0.360244i
$329$		−	22.5228i		−	0.0684583i
$330$	30.1791	−	0.734671i	0.0914518	−	0.00222627i
$331$		−	461.986i		−	1.39573i	−0.716231	−	0.697863i	$-0.754134\pi$
$331$		−	461.986i		−	1.39573i	0.716231	−	0.697863i	$-0.245866\pi$
$332$	168.921	−	168.921i	0.508798	−	0.508798i
$333$	349.771	+	349.771i	1.05036	+	1.05036i
$334$			66.7575i			0.199873i
$335$	−355.842	+	373.600i	−1.06222	+	1.11522i
$336$		−	24.5403i		−	0.0730366i
$337$	251.956	+	251.956i	0.747645	+	0.747645i	0.974036	−	0.226391i	$-0.0726928\pi$
$337$	251.956	+	251.956i	0.747645	+	0.747645i	−0.226391	+	0.974036i	$0.572693\pi$
$338$	−92.8875	+	64.9744i	−0.274815	+	0.192232i
$339$		−	162.647i		−	0.479784i
$340$	80.5646	−	84.5850i	0.236955	−	0.248779i
$341$	−250.858			−0.735655
$342$	−90.5508	−	90.5508i	−0.264768	−	0.264768i
$343$	127.597	+	127.597i	0.372004	+	0.372004i
$344$	112.655			0.327485
$345$	1.82240	+	74.8614i	0.00528232	+	0.216989i
$346$		−	152.632i		−	0.441132i
$347$	158.608	+	158.608i	0.457084	+	0.457084i	0.897697	−	0.440613i	$-0.145239\pi$
$347$	158.608	+	158.608i	0.457084	+	0.457084i	−0.440613	+	0.897697i	$0.645239\pi$
$348$	47.9522	−	47.9522i	0.137794	−	0.137794i
$349$	100.147			0.286953			0.143476	−	0.989654i	$-0.454172\pi$
$349$	100.147			0.286953			0.143476	+	0.989654i	$0.454172\pi$
$350$	−1.56068	−	32.0361i	−0.00445908	−	0.0915318i
$351$	−196.237	+	164.583i	−0.559081	+	0.468897i
$352$	147.406	+	147.406i	0.418768	+	0.418768i
$353$	−168.954	−	168.954i	−0.478623	−	0.478623i	0.426068	−	0.904691i	$-0.359898\pi$
$353$	−168.954	−	168.954i	−0.478623	−	0.478623i	−0.904691	+	0.426068i	$0.859898\pi$
$354$		−	47.0882i		−	0.133017i
$355$	15.5666	+	639.450i	0.0438495	+	1.80127i
$356$			313.127i			0.879569i
$357$	10.5701	−	10.5701i	0.0296082	−	0.0296082i
$358$	75.7872	+	75.7872i	0.211696	+	0.211696i
$359$	660.165			1.83890			0.919451	−	0.393206i	$-0.128634\pi$
$359$	660.165			1.83890			0.919451	+	0.393206i	$0.128634\pi$
$360$	−132.544	+	139.158i	−0.368177	+	0.386550i
$361$	271.771			0.752828
$362$	−82.2280	+	82.2280i	−0.227149	+	0.227149i
$363$	−53.3655	+	53.3655i	−0.147012	+	0.147012i
$364$	67.6361	−	56.7259i	0.185813	−	0.155840i
$365$	−145.483	−	138.568i	−0.398583	−	0.379639i
$366$			22.6028i			0.0617563i
$367$	372.681	+	372.681i	1.01548	+	1.01548i	0.999878	+	0.0156001i	$0.00496585\pi$
$367$	372.681	+	372.681i	1.01548	+	1.01548i	0.0156001	+	0.999878i	$0.495034\pi$
$368$	−96.3404	+	96.3404i	−0.261794	+	0.261794i
$369$	−250.435			−0.678687
$370$	−5.31941	−	218.513i	−0.0143768	−	0.590576i
$371$			120.410i			0.324554i
$372$	−98.6662	+	98.6662i	−0.265232	+	0.265232i
$373$	356.949	−	356.949i	0.956968	−	0.956968i	−0.0421435	−	0.999112i	$-0.513419\pi$
$373$	356.949	−	356.949i	0.956968	−	0.956968i	0.999112	+	0.0421435i	$0.0134187\pi$
$374$			33.4570i			0.0894571i
$375$	−97.0302	+	112.345i	−0.258747	+	0.299587i
$376$	59.6323			0.158596
$377$	208.306	+	18.2746i	0.552536	+	0.0484737i
$378$	−17.8730	+	17.8730i	−0.0472830	+	0.0472830i
$379$	512.720			1.35282			0.676411	−	0.736524i	$-0.263534\pi$
$379$	512.720			1.35282			0.676411	+	0.736524i	$0.263534\pi$
$380$	−10.8665	−	446.380i	−0.0285961	−	1.17468i
$381$	174.018			0.456741
$382$	56.0095	−	56.0095i	0.146622	−	0.146622i
$383$	−33.6454	−	33.6454i	−0.0878471	−	0.0878471i	0.661818	−	0.749665i	$-0.269785\pi$
$383$	−33.6454	−	33.6454i	−0.0878471	−	0.0878471i	−0.749665	+	0.661818i	$0.769785\pi$
$384$	150.377			0.391606
$385$	−52.4893	−	49.9945i	−0.136336	−	0.129856i
$386$	138.955			0.359987
$387$	119.384	+	119.384i	0.308485	+	0.308485i
$388$	−206.388	−	206.388i	−0.531927	−	0.531927i
$389$		−	127.432i		−	0.327589i	−0.986494	−	0.163795i	$-0.947627\pi$
$389$		−	127.432i		−	0.327589i	0.986494	−	0.163795i	$-0.0523735\pi$
$390$	51.6733	+	3.26837i	0.132496	+	0.00838044i
$391$	−82.9924			−0.212257
$392$	−162.365	+	162.365i	−0.414198	+	0.414198i
$393$	−133.577	+	133.577i	−0.339891	+	0.339891i
$394$		−	152.922i		−	0.388126i
$395$	−11.6820	−	479.877i	−0.0295746	−	1.21488i
$396$			204.224i			0.515718i
$397$	46.0480	−	46.0480i	0.115990	−	0.115990i	−0.646730	−	0.762719i	$-0.723864\pi$
$397$	46.0480	−	46.0480i	0.115990	−	0.115990i	0.762719	+	0.646730i	$0.223864\pi$
$398$	46.6042	+	46.6042i	0.117096	+	0.117096i
$399$		−	57.1396i		−	0.143207i
$400$	−269.769	+	13.1421i	−0.674422	+	0.0328553i
$401$		−	158.263i		−	0.394672i	−0.980336	−	0.197336i	$-0.936771\pi$
$401$		−	158.263i		−	0.394672i	0.980336	−	0.197336i	$-0.0632290\pi$
$402$	−58.1219	−	58.1219i	−0.144582	−	0.144582i
$403$	−428.610	−	37.6017i	−1.06355	−	0.0933045i
$404$			404.415i			1.00103i
$405$	−224.485	+	5.46479i	−0.554283	+	0.0134933i
$406$	20.6366			0.0508291
$407$	−349.305	−	349.305i	−0.858244	−	0.858244i
$408$	27.9859	+	27.9859i	0.0685928	+	0.0685928i
$409$	−600.151			−1.46736			−0.733681	−	0.679494i	$-0.762200\pi$
$409$	−600.151			−1.46736			−0.733681	+	0.679494i	$0.762200\pi$
$410$	80.1319	+	76.3232i	0.195444	+	0.186154i
$411$			7.97091i			0.0193939i
$412$	−77.4840	−	77.4840i	−0.188068	−	0.188068i
$413$	−79.9522	+	79.9522i	−0.193589	+	0.193589i
$414$	64.2008			0.155074
$415$	−243.630	−	232.050i	−0.587060	−	0.559157i
$416$	229.759	+	273.949i	0.552306	+	0.658532i
$417$	37.9170	+	37.9170i	0.0909280	+	0.0909280i
$418$	90.4302	+	90.4302i	0.216340	+	0.216340i
$419$		−	794.846i		−	1.89701i	−0.316768	−	0.948503i	$-0.602598\pi$
$419$		−	794.846i		−	1.89701i	0.316768	−	0.948503i	$-0.397402\pi$
$420$	−40.3083	+	0.981253i	−0.0959722	+	0.00233632i
$421$		−	53.4119i		−	0.126869i	−0.997986	−	0.0634346i	$-0.979795\pi$
$421$		−	53.4119i		−	0.126869i	0.997986	−	0.0634346i	$-0.0202054\pi$
$422$	−107.076	+	107.076i	−0.253734	+	0.253734i
$423$	63.1941	+	63.1941i	0.149395	+	0.149395i
$424$	−318.801			−0.751890
$425$	−121.857	−	110.535i	−0.286722	−	0.260083i
$426$	−101.903			−0.239208
$427$	38.3779	−	38.3779i	0.0898780	−	0.0898780i
$428$	−355.074	+	355.074i	−0.829613	+	0.829613i
$429$	89.6579	−	75.1954i	0.208993	−	0.175281i
$430$	−1.81562	−	74.5828i	−0.00422237	−	0.173448i
$431$			236.100i			0.547795i	0.961759	+	0.273898i	$0.0883130\pi$
$431$			236.100i			0.547795i	−0.961759	+	0.273898i	$0.911687\pi$
$432$	150.504	+	150.504i	0.348390	+	0.348390i
$433$	430.853	−	430.853i	0.995043	−	0.995043i	−0.00494518	−	0.999988i	$-0.501574\pi$
$433$	430.853	−	430.853i	0.995043	−	0.995043i	0.999988	+	0.00494518i	$0.00157411\pi$
$434$	−42.4618			−0.0978383
$435$	−69.1601	−	65.8729i	−0.158989	−	0.151432i
$436$			148.588i			0.340797i
$437$	−224.319	+	224.319i	−0.513315	+	0.513315i
$438$	22.6332	−	22.6332i	0.0516739	−	0.0516739i
$439$		−	72.0697i		−	0.164168i	−0.996625	−	0.0820839i	$-0.973842\pi$
$439$		−	72.0697i		−	0.164168i	0.996625	−	0.0820839i	$-0.0261576\pi$
$440$	132.367	−	138.973i	0.300835	−	0.315847i
$441$	−344.127			−0.780333
$442$	−5.01494	+	57.1637i	−0.0113460	+	0.129330i
$443$	2.86569	−	2.86569i	0.00646883	−	0.00646883i	−0.703865	−	0.710334i	$-0.748544\pi$
$443$	2.86569	−	2.86569i	0.00646883	−	0.00646883i	0.710334	+	0.703865i	$0.248544\pi$
$444$	−274.774			−0.618859
$445$	440.881	−	10.7327i	0.990744	−	0.0241184i
$446$	193.462			0.433771
$447$	68.5377	−	68.5377i	0.153328	−	0.153328i
$448$	−33.4966	−	33.4966i	−0.0747691	−	0.0747691i
$449$	−83.6740			−0.186356			−0.0931782	−	0.995649i	$-0.529703\pi$
$449$	−83.6740			−0.186356			−0.0931782	+	0.995649i	$0.529703\pi$
$450$	94.2654	+	85.5075i	0.209479	+	0.190017i
$451$	250.102			0.554550
$452$	−343.804	−	343.804i	−0.760627	−	0.760627i
$453$	−98.7876	−	98.7876i	−0.218074	−	0.218074i
$454$		−	278.671i		−	0.613814i
$455$	−82.1881	−	93.2870i	−0.180633	−	0.205026i
$456$	151.285			0.331765
$457$	159.614	−	159.614i	0.349265	−	0.349265i	−0.510571	−	0.859836i	$-0.670566\pi$
$457$	159.614	−	159.614i	0.349265	−	0.349265i	0.859836	+	0.510571i	$0.170566\pi$
$458$	−94.2077	+	94.2077i	−0.205694	+	0.205694i
$459$			129.652i			0.282466i
$460$	162.095	+	154.390i	0.352380	+	0.335631i
$461$			327.810i			0.711084i	0.934660	+	0.355542i	$0.115704\pi$
$461$			327.810i			0.711084i	−0.934660	+	0.355542i	$0.884296\pi$
$462$	8.16590	−	8.16590i	0.0176751	−	0.0176751i
$463$	−342.712	−	342.712i	−0.740199	−	0.740199i	0.232418	−	0.972616i	$-0.425336\pi$
$463$	−342.712	−	342.712i	−0.740199	−	0.740199i	−0.972616	+	0.232418i	$0.925336\pi$
$464$		−	173.776i		−	0.374518i
$465$	142.303	+	135.540i	0.306029	+	0.291483i
$466$			28.2578i			0.0606390i
$467$	625.306	+	625.306i	1.33898	+	1.33898i	0.897045	+	0.441939i	$0.145709\pi$
$467$	625.306	+	625.306i	1.33898	+	1.33898i	0.441939	+	0.897045i	$0.354291\pi$
$468$	−30.6117	+	348.933i	−0.0654095	+	0.745583i
$469$			197.373i			0.420839i
$470$	−0.961073	−	39.4794i	−0.00204484	−	0.0839987i
$471$	32.2964			0.0685699
$472$	−211.685	−	211.685i	−0.448485	−	0.448485i
$473$	−119.225	−	119.225i	−0.252061	−	0.252061i
$474$	76.4731			0.161336
$475$	−628.129	+	30.6001i	−1.32238	+	0.0644212i
$476$		−	44.6864i		−	0.0938789i
$477$	−337.843	−	337.843i	−0.708267	−	0.708267i
$478$	−91.9525	+	91.9525i	−0.192369	+	0.192369i
$479$	274.459			0.572983			0.286491	−	0.958083i	$-0.407511\pi$
$479$	274.459			0.572983			0.286491	+	0.958083i	$0.407511\pi$
$480$	−3.97442	−	163.263i	−0.00828004	−	0.340131i
$481$	−544.456	−	649.172i	−1.13192	−	1.34963i
$482$	−149.209	−	149.209i	−0.309563	−	0.309563i
$483$	20.2561	+	20.2561i	0.0419381	+	0.0419381i
$484$			225.609i			0.466134i
$485$	−283.519	+	297.667i	−0.584575	+	0.613746i
$486$		−	154.706i		−	0.318326i
$487$	−265.442	+	265.442i	−0.545055	+	0.545055i	−0.925006	−	0.379952i	$-0.875941\pi$
$487$	−265.442	+	265.442i	−0.545055	+	0.545055i	0.379952	+	0.925006i	$0.375941\pi$
$488$	101.611	+	101.611i	0.208219	+	0.208219i
$489$	151.229			0.309262
$490$	110.110	+	104.877i	0.224715	+	0.214034i
$491$	575.012			1.17110			0.585552	−	0.810635i	$-0.300878\pi$
$491$	575.012			1.17110			0.585552	+	0.810635i	$0.300878\pi$
$492$	98.3687	−	98.3687i	0.199936	−	0.199936i
$493$	74.8497	−	74.8497i	0.151825	−	0.151825i
$494$	140.952	+	168.062i	0.285328	+	0.340206i
$495$	287.547	−	6.99996i	0.580904	−	0.0141413i
$496$			357.561i			0.720889i
$497$	173.023	+	173.023i	0.348135	+	0.348135i
$498$	37.9022	−	37.9022i	0.0761087	−	0.0761087i
$499$	484.104			0.970148			0.485074	−	0.874473i	$-0.338793\pi$
$499$	484.104			0.970148			0.485074	+	0.874473i	$0.338793\pi$
$500$	32.3732	+	442.579i	0.0647464	+	0.885159i
$501$		−	118.195i		−	0.235918i
$502$	128.913	−	128.913i	0.256798	−	0.256798i
$503$	−165.310	+	165.310i	−0.328648	+	0.328648i	−0.852072	−	0.523424i	$-0.824654\pi$
$503$	−165.310	+	165.310i	−0.328648	+	0.328648i	0.523424	+	0.852072i	$0.324654\pi$
$504$			73.5174i			0.145868i
$505$	569.415	−	13.8616i	1.12755	−	0.0274488i
$506$	−64.1154			−0.126710
$507$	164.458	−	115.038i	0.324376	−	0.226899i
$508$	367.841	−	367.841i	0.724097	−	0.724097i
$509$	−487.485			−0.957731			−0.478865	−	0.877888i	$-0.658952\pi$
$509$	−487.485			−0.957731			−0.478865	+	0.877888i	$0.658952\pi$
$510$	18.0769	−	18.9790i	0.0354450	−	0.0372137i
$511$	−76.8589			−0.150409
$512$	364.853	−	364.853i	0.712604	−	0.712604i
$513$	350.434	+	350.434i	0.683106	+	0.683106i
$514$	−337.140			−0.655915
$515$	−106.441	+	111.753i	−0.206682	+	0.216996i
$516$	−93.7856			−0.181755
$517$	−63.1099	−	63.1099i	−0.122070	−	0.122070i
$518$	−59.1255	−	59.1255i	−0.114142	−	0.114142i
$519$			270.236i			0.520687i
$520$	246.990	−	217.604i	0.474982	−	0.418470i
$521$	−121.288			−0.232798			−0.116399	−	0.993203i	$-0.537135\pi$
$521$	−121.288			−0.232798			−0.116399	+	0.993203i	$0.537135\pi$
$522$	−57.9019	+	57.9019i	−0.110923	+	0.110923i
$523$	−26.5332	+	26.5332i	−0.0507326	+	0.0507326i	−0.732018	−	0.681285i	$-0.761421\pi$
$523$	−26.5332	+	26.5332i	−0.0507326	+	0.0507326i	0.681285	+	0.732018i	$0.261421\pi$
$524$			564.712i			1.07770i
$525$	2.76320	+	56.7203i	0.00526324	+	0.108039i
$526$			316.998i			0.602659i
$527$	−154.010	+	154.010i	−0.292240	+	0.292240i
$528$	−68.7631	−	68.7631i	−0.130233	−	0.130233i
$529$			369.957i			0.699352i
$530$	5.13802	+	211.062i	0.00969437	+	0.398229i
$531$		−	448.657i		−	0.844929i
$532$	−120.782	−	120.782i	−0.227034	−	0.227034i
$533$	427.318	+	37.4883i	0.801722	+	0.0703346i
$534$			70.2587i			0.131571i
$535$	512.114	+	487.773i	0.957222	+	0.911725i
$536$	−522.574			−0.974951
$537$	−134.182	−	134.182i	−0.249873	−	0.249873i
$538$	159.306	+	159.306i	0.296108	+	0.296108i
$539$	343.669			0.637605
$540$	241.191	−	253.227i	0.446649	−	0.468938i
$541$		−	613.710i		−	1.13440i	−0.823580	−	0.567200i	$-0.808027\pi$
$541$		−	613.710i		−	1.13440i	0.823580	−	0.567200i	$-0.191973\pi$
$542$	165.936	+	165.936i	0.306155	+	0.306155i
$543$	145.586	−	145.586i	0.268114	−	0.268114i
$544$	180.995			0.332712
$545$	209.211	−	5.09296i	0.383873	−	0.00934489i
$546$	15.1760	−	12.7280i	0.0277950	−	0.0233114i
$547$	−100.400	−	100.400i	−0.183546	−	0.183546i	0.609353	−	0.792899i	$-0.291429\pi$
$547$	−100.400	−	100.400i	−0.183546	−	0.183546i	−0.792899	+	0.609353i	$0.791429\pi$
$548$	16.8490	+	16.8490i	0.0307463	+	0.0307463i
$549$			215.360i			0.392277i
$550$	−94.1399	−	85.3937i	−0.171163	−	0.155261i
$551$		−	404.620i		−	0.734337i
$552$	−53.6308	+	53.6308i	−0.0971573	+	0.0971573i
$553$	−129.846	−	129.846i	−0.234802	−	0.234802i
$554$	−343.404			−0.619863
$555$	9.41809	+	386.880i	0.0169695	+	0.697081i
$556$	160.298			0.288306
$557$	653.897	−	653.897i	1.17396	−	1.17396i	0.192706	−	0.981257i	$-0.438274\pi$
$557$	653.897	−	653.897i	1.17396	−	1.17396i	0.981257	−	0.192706i	$-0.0617263\pi$
$558$	119.139	−	119.139i	0.213510	−	0.213510i
$559$	−185.833	−	221.575i	−0.332439	−	0.396378i
$560$	−71.2596	+	74.8157i	−0.127249	+	0.133599i
$561$		−	59.2360i		−	0.105590i
$562$	153.613	+	153.613i	0.273333	+	0.273333i
$563$	418.387	−	418.387i	0.743139	−	0.743139i	−0.230042	−	0.973181i	$-0.573886\pi$
$563$	418.387	−	418.387i	0.743139	−	0.743139i	0.973181	+	0.230042i	$0.0738863\pi$
$564$	−49.6441			−0.0880215
$565$	−472.290	+	495.858i	−0.835911	+	0.877625i
$566$		−	216.773i		−	0.382991i
$567$	−60.7413	+	60.7413i	−0.107128	+	0.107128i
$568$	−458.103	+	458.103i	−0.806519	+	0.806519i
$569$		−	142.839i		−	0.251036i	−0.992091	−	0.125518i	$-0.959941\pi$
$569$		−	142.839i		−	0.251036i	0.992091	−	0.125518i	$-0.0400593\pi$
$570$	−2.43821	−	100.158i	−0.00427756	−	0.175715i
$571$	−576.933			−1.01039			−0.505195	−	0.863005i	$-0.668580\pi$
$571$	−576.933			−1.01039			−0.505195	+	0.863005i	$0.668580\pi$
$572$	30.5709	−	348.468i	0.0534456	−	0.609210i
$573$	−99.1655	+	99.1655i	−0.173064	+	0.173064i
$574$	42.3338			0.0737523
$575$	211.825	−	233.521i	0.368391	−	0.406123i
$576$	187.968			0.326334
$577$	328.514	−	328.514i	0.569349	−	0.569349i	−0.362597	−	0.931946i	$-0.618110\pi$
$577$	328.514	−	328.514i	0.569349	−	0.569349i	0.931946	+	0.362597i	$0.118110\pi$
$578$	−116.530	−	116.530i	−0.201609	−	0.201609i
$579$	−246.021			−0.424908
$580$	−285.434	+	6.94851i	−0.492127	+	0.0119802i
$581$	−128.710			−0.221532
$582$	−46.3088	−	46.3088i	−0.0795684	−	0.0795684i
$583$	337.394	+	337.394i	0.578720	+	0.578720i
$584$		−	203.495i		−	0.348450i
$585$	492.345	+	31.1411i	0.841615	+	0.0532327i
$586$	−102.219			−0.174435
$587$	−592.826	+	592.826i	−1.00993	+	1.00993i	−0.00997554	+	0.999950i	$0.503175\pi$
$587$	−592.826	+	592.826i	−1.00993	+	1.00993i	−0.999950	+	0.00997554i	$0.996825\pi$
$588$	135.170	−	135.170i	0.229881	−	0.229881i
$589$			832.544i			1.41349i
$590$	−136.734	+	143.557i	−0.231752	+	0.243317i
$591$			270.750i			0.458121i
$592$	−497.882	+	497.882i	−0.841018	+	0.841018i
$593$	389.824	+	389.824i	0.657376	+	0.657376i	0.954758	−	0.297383i	$-0.0961137\pi$
$593$	389.824	+	389.824i	0.657376	+	0.657376i	−0.297383	+	0.954758i	$0.596114\pi$
$594$			100.162i			0.168623i
$595$	−62.9182	+	1.53166i	−0.105745	+	0.00257422i
$596$		−	289.751i		−	0.486159i
$597$	−82.5133	−	82.5133i	−0.138213	−	0.138213i
$598$	−109.546	−	9.61039i	−0.183187	−	0.0160709i
$599$		−	313.658i		−	0.523636i	−0.965117	−	0.261818i	$-0.915678\pi$
$599$		−	313.658i		−	0.523636i	0.965117	−	0.261818i	$-0.0843221\pi$
$600$	−150.175	+	7.31597i	−0.250292	+	0.0121933i
$601$	−135.295			−0.225116			−0.112558	−	0.993645i	$-0.535904\pi$
$601$	−135.295			−0.225116			−0.112558	+	0.993645i	$0.535904\pi$
$602$	−20.1807	−	20.1807i	−0.0335227	−	0.0335227i
$603$	−553.787	−	553.787i	−0.918386	−	0.918386i
$604$	−417.636			−0.691450
$605$	317.656	−	7.73293i	0.525052	−	0.0127817i
$606$			90.7418i			0.149739i
$607$	−667.362	−	667.362i	−1.09944	−	1.09944i	−0.994476	−	0.104968i	$-0.966526\pi$
$607$	−667.362	−	667.362i	−1.09944	−	1.09944i	−0.104968	−	0.994476i	$-0.533474\pi$
$608$	489.209	−	489.209i	0.804620	−	0.804620i
$609$	−36.5374			−0.0599957
$610$	65.6336	−	68.9088i	0.107596	−	0.112965i
$611$	−98.3683	−	117.288i	−0.160996	−	0.191960i
$612$	125.380	+	125.380i	0.204870	+	0.204870i
$613$	334.033	+	334.033i	0.544915	+	0.544915i	0.924966	−	0.380050i	$-0.124093\pi$
$613$	334.033	+	334.033i	0.544915	+	0.544915i	−0.380050	+	0.924966i	$0.624093\pi$
$614$		−	23.8314i		−	0.0388134i
$615$	−141.874	−	135.131i	−0.230690	−	0.219725i
$616$		−	73.4195i		−	0.119188i
$617$	−636.131	+	636.131i	−1.03101	+	1.03101i	−0.0315024	+	0.999504i	$0.510029\pi$
$617$	−636.131	+	636.131i	−1.03101	+	1.03101i	−0.999504	+	0.0315024i	$0.989971\pi$
$618$	−17.3857	−	17.3857i	−0.0281322	−	0.0281322i
$619$	−308.253			−0.497986			−0.248993	−	0.968505i	$-0.580100\pi$
$619$	−308.253			−0.497986			−0.248993	+	0.968505i	$0.580100\pi$
$620$	587.307	−	14.2972i	0.947269	−	0.0230600i
$621$	−248.459			−0.400095
$622$	2.91107	−	2.91107i	0.00468018	−	0.00468018i
$623$	119.294	−	119.294i	0.191483	−	0.191483i
$624$	−107.180	−	127.794i	−0.171763	−	0.204798i
$625$	622.040	−	60.7511i	0.995265	−	0.0972018i
$626$		−	28.4660i		−	0.0454728i
$627$	−160.108	−	160.108i	−0.255355	−	0.255355i
$628$	68.2684	−	68.2684i	0.108708	−	0.108708i
$629$	−428.901			−0.681877
$630$	48.6720	−	1.18486i	0.0772571	−	0.00188072i
$631$			889.835i			1.41020i	0.709109	+	0.705099i	$0.249098\pi$
$631$			889.835i			1.41020i	−0.709109	+	0.705099i	$0.750902\pi$
$632$	343.785	−	343.785i	0.543963	−	0.543963i
$633$	189.579	−	189.579i	0.299493	−	0.299493i
$634$			257.581i			0.406279i
$635$	−530.527	−	505.311i	−0.835476	−	0.795766i
$636$	265.403			0.417301
$637$	587.184	+	51.5133i	0.921795	+	0.0808686i
$638$	57.8248	−	57.8248i	0.0906345	−	0.0906345i
$639$	−970.930			−1.51945
$640$	−458.451	−	436.661i	−0.716330	−	0.682283i
$641$	−286.859			−0.447518			−0.223759	−	0.974644i	$-0.571833\pi$
$641$	−286.859			−0.447518			−0.223759	+	0.974644i	$0.571833\pi$
$642$	−79.6709	+	79.6709i	−0.124098	+	0.124098i
$643$	−64.4210	−	64.4210i	−0.100188	−	0.100188i	0.655236	−	0.755424i	$-0.272569\pi$
$643$	−64.4210	−	64.4210i	−0.100188	−	0.100188i	−0.755424	+	0.655236i	$0.772569\pi$
$644$	85.6349			0.132973
$645$	3.21458	+	132.050i	0.00498384	+	0.204728i
$646$	111.036			0.171883
$647$	−401.845	−	401.845i	−0.621089	−	0.621089i	0.324721	−	0.945810i	$-0.394730\pi$
$647$	−401.845	−	401.845i	−0.621089	−	0.621089i	−0.945810	+	0.324721i	$0.894730\pi$
$648$	−160.821	−	160.821i	−0.248181	−	0.248181i
$649$			448.060i			0.690385i
$650$	−148.045	−	160.012i	−0.227762	−	0.246173i
$651$	75.1791			0.115483
$652$	319.669	−	319.669i	0.490290	−	0.490290i
$653$	−395.274	+	395.274i	−0.605320	+	0.605320i	−0.941719	−	0.336400i	$-0.890791\pi$
$653$	−395.274	+	395.274i	−0.605320	+	0.605320i	0.336400	+	0.941719i	$0.390791\pi$
$654$			33.3398i			0.0509783i
$655$	795.113	−	19.3560i	1.21391	−	0.0295511i
$656$		−	356.483i		−	0.543420i
$657$	215.649	−	215.649i	0.328233	−	0.328233i
$658$	−10.6824	−	10.6824i	−0.0162346	−	0.0162346i
$659$		−	107.196i		−	0.162665i	−0.996687	−	0.0813324i	$-0.974082\pi$
$659$		−	107.196i		−	0.162665i	0.996687	−	0.0813324i	$-0.0259175\pi$
$660$	−110.196	+	115.695i	−0.166964	+	0.175296i
$661$			71.8876i			0.108756i	0.998520	+	0.0543779i	$0.0173176\pi$
$661$			71.8876i			0.108756i	−0.998520	+	0.0543779i	$0.982682\pi$
$662$	−219.116	−	219.116i	−0.330991	−	0.330991i
$663$	8.87901	−	101.209i	0.0133922	−	0.152653i
$664$		−	340.778i		−	0.513220i
$665$	−165.921	+	174.200i	−0.249505	+	0.261956i
$666$	331.787			0.498179
$667$	143.438	+	143.438i	0.215050	+	0.215050i
$668$	−249.841	−	249.841i	−0.374014	−	0.374014i
$669$	−342.527			−0.511998
$670$	8.42215	+	345.968i	0.0125704	+	0.516371i
$671$		−	215.073i		−	0.320527i
$672$	−44.1758	−	44.1758i	−0.0657378	−	0.0657378i
$673$	−173.678	+	173.678i	−0.258065	+	0.258065i	−0.824267	−	0.566202i	$-0.808412\pi$
$673$	−173.678	+	173.678i	−0.258065	+	0.258065i	0.566202	+	0.824267i	$0.308412\pi$
$674$	239.002			0.354602
$675$	−364.809	−	330.916i	−0.540458	−	0.490246i
$676$	104.465	−	590.801i	0.154534	−	0.873966i
$677$	−202.765	−	202.765i	−0.299506	−	0.299506i	0.541314	−	0.840820i	$-0.317927\pi$
$677$	−202.765	−	202.765i	−0.299506	−	0.299506i	−0.840820	+	0.541314i	$0.817927\pi$
$678$	−77.1420	−	77.1420i	−0.113779	−	0.113779i
$679$			157.258i			0.231602i
$680$	−4.05529	−	166.585i	−0.00596366	−	0.244978i
$681$			493.391i			0.724510i
$682$	−118.980	+	118.980i	−0.174458	+	0.174458i
$683$	148.074	+	148.074i	0.216799	+	0.216799i	0.807148	−	0.590349i	$-0.201010\pi$
$683$	148.074	+	148.074i	0.216799	+	0.216799i	−0.590349	+	0.807148i	$0.701010\pi$
$684$	677.776			0.990901
$685$	23.1458	−	24.3008i	0.0337894	−	0.0354756i
$686$	121.037			0.176438
$687$	166.796	−	166.796i	0.242789	−	0.242789i
$688$	−169.937	+	169.937i	−0.247001	+	0.247001i
$689$	525.889	+	627.035i	0.763265	+	0.910065i
$690$	36.3705	+	34.6418i	0.0527109	+	0.0502055i
$691$			1074.87i			1.55553i	0.628553	+	0.777767i	$0.283648\pi$
$691$			1074.87i			1.55553i	−0.628553	+	0.777767i	$0.716352\pi$
$692$	571.228	+	571.228i	0.825473	+	0.825473i
$693$	77.8049	−	77.8049i	0.112273	−	0.112273i
$694$	150.453			0.216791
$695$	−5.49436	−	225.699i	−0.00790555	−	0.324747i
$696$		−	96.7378i		−	0.138991i
$697$	153.546	−	153.546i	0.220296	−	0.220296i
$698$	47.4987	−	47.4987i	0.0680497	−	0.0680497i
$699$		−	50.0308i		−	0.0715748i
$700$	125.737	+	114.055i	0.179624	+	0.162936i
$701$	479.308			0.683750			0.341875	−	0.939746i	$-0.388938\pi$
$701$	479.308			0.683750			0.341875	+	0.939746i	$0.388938\pi$
$702$	−15.0135	+	171.134i	−0.0213867	+	0.243781i
$703$	−1159.27	+	1159.27i	−1.64903	+	1.64903i
$704$	−187.718			−0.266645
$705$	1.70159	+	69.8987i	0.00241361	+	0.0991471i
$706$	−160.267			−0.227007
$707$	154.073	−	154.073i	0.217925	−	0.217925i
$708$	176.228	+	176.228i	0.248910	+	0.248910i
$709$	854.943			1.20584			0.602922	−	0.797800i	$-0.294003\pi$
$709$	854.943			1.20584			0.602922	+	0.797800i	$0.294003\pi$
$710$	310.669	+	295.903i	0.437562	+	0.416764i
$711$	728.637			1.02481
$712$	315.848	+	315.848i	0.443607	+	0.443607i
$713$	−295.138	−	295.138i	−0.413939	−	0.413939i
$714$		−	10.0266i		−	0.0140429i
$715$	−491.690	−	31.0997i	−0.687678	−	0.0434961i
$716$	−567.270			−0.792277
$717$	162.803	−	162.803i	0.227061	−	0.227061i
$718$	313.111	−	313.111i	0.436088	−	0.436088i
$719$		−	590.382i		−	0.821115i	−0.911835	−	0.410557i	$-0.865334\pi$
$719$		−	590.382i		−	0.821115i	0.911835	−	0.410557i	$-0.134666\pi$
$720$	−9.97740	−	409.856i	−0.0138575	−	0.569244i
$721$			59.0393i			0.0818853i
$722$	128.899	−	128.899i	0.178530	−	0.178530i
$723$	264.177	+	264.177i	0.365390	+	0.365390i
$724$		−	615.480i		−	0.850111i
$725$	19.5669	+	401.651i	0.0269889	+	0.554002i
$726$			50.6217i			0.0697268i
$727$	244.483	+	244.483i	0.336290	+	0.336290i	0.854969	−	0.518679i	$-0.173576\pi$
$727$	244.483	+	244.483i	0.336290	+	0.336290i	−0.518679	+	0.854969i	$0.673576\pi$
$728$	11.0050	−	125.443i	0.0151168	−	0.172311i
$729$		−	130.283i		−	0.178714i
$730$	−134.723	+	3.27966i	−0.184552	+	0.00449268i
$731$	−146.392			−0.200263
$732$	−84.5915	−	84.5915i	−0.115562	−	0.115562i
$733$	735.257	+	735.257i	1.00308	+	1.00308i	0.999995	+	0.00308383i	$0.000981616\pi$
$733$	735.257	+	735.257i	1.00308	+	1.00308i	0.00308383	+	0.999995i	$0.499018\pi$
$734$	353.519			0.481633
$735$	−194.952	−	185.686i	−0.265240	−	0.252633i
$736$			346.851i			0.471265i
$737$	553.050	+	553.050i	0.750407	+	0.750407i
$738$	−118.779	+	118.779i	−0.160948	+	0.160948i
$739$	−369.838			−0.500457			−0.250229	−	0.968187i	$-0.580506\pi$
$739$	−369.838			−0.500457			−0.250229	+	0.968187i	$0.580506\pi$
$740$	837.698	+	797.882i	1.13202	+	1.07822i
$741$	−249.557	−	297.555i	−0.336784	−	0.401559i
$742$	57.1093	+	57.1093i	0.0769667	+	0.0769667i
$743$	−761.247	−	761.247i	−1.02456	−	1.02456i	−0.999691	−	0.0248675i	$-0.992084\pi$
$743$	−761.247	−	761.247i	−1.02456	−	1.02456i	−0.0248675	−	0.999691i	$-0.507916\pi$
$744$			199.047i			0.267537i
$745$	−407.968	+	9.93145i	−0.547608	+	0.0133308i
$746$		−	338.596i		−	0.453882i
$747$	361.133	−	361.133i	0.483444	−	0.483444i
$748$	−125.213	−	125.213i	−0.167398	−	0.167398i
$749$	270.550			0.361216
$750$	7.26384	+	99.3051i	0.00968512	+	0.132407i
$751$	−435.407			−0.579770			−0.289885	−	0.957061i	$-0.593617\pi$
$751$	−435.407			−0.579770			−0.289885	+	0.957061i	$0.593617\pi$
$752$	−89.9538	+	89.9538i	−0.119619	+	0.119619i
$753$	−228.241	+	228.241i	−0.303109	+	0.303109i
$754$	107.465	−	90.1305i	0.142527	−	0.119536i
$755$	14.3148	+	588.030i	0.0189600	+	0.778847i
$756$		−	133.780i		−	0.176958i
$757$	−544.880	−	544.880i	−0.719788	−	0.719788i	0.248774	−	0.968562i	$-0.419973\pi$
$757$	−544.880	−	544.880i	−0.719788	−	0.719788i	−0.968562	+	0.248774i	$0.919973\pi$
$758$	243.179	−	243.179i	0.320816	−	0.320816i
$759$	113.517			0.149561
$760$	−461.220	−	439.298i	−0.606869	−	0.578024i
$761$		−	425.922i		−	0.559687i	−0.960046	−	0.279843i	$-0.909717\pi$
$761$		−	425.922i		−	0.559687i	0.960046	−	0.279843i	$-0.0902826\pi$
$762$	82.5355	−	82.5355i	0.108314	−	0.108314i
$763$	56.6085	−	56.6085i	0.0741920	−	0.0741920i
$764$			419.234i			0.548735i
$765$	172.237	−	180.832i	0.225147	−	0.236382i
$766$	−31.9155			−0.0416652
$767$	−67.1607	+	765.544i	−0.0875628	+	0.998101i
$768$	−11.8665	+	11.8665i	−0.0154511	+	0.0154511i
$769$	700.592			0.911043			0.455522	−	0.890225i	$-0.349453\pi$
$769$	700.592			0.911043			0.455522	+	0.890225i	$0.349453\pi$
$770$	−48.6072	+	1.18328i	−0.0631262	+	0.00153673i
$771$	596.911			0.774203
$772$	−520.042	+	520.042i	−0.673629	+	0.673629i
$773$	361.969	+	361.969i	0.468265	+	0.468265i	0.901352	−	0.433087i	$-0.142576\pi$
$773$	361.969	+	361.969i	0.468265	+	0.468265i	−0.433087	+	0.901352i	$0.642576\pi$
$774$	113.245			0.146312
$775$	−40.2608	−	826.436i	−0.0519495	−	1.06637i
$776$	−416.363			−0.536550
$777$	104.682	+	104.682i	0.134726	+	0.134726i
$778$	−60.4401	−	60.4401i	−0.0776865	−	0.0776865i
$779$		−	830.034i		−	1.06551i
$780$	−205.621	+	181.157i	−0.263616	+	0.232252i
$781$	969.638			1.24153
$782$	−39.3626	+	39.3626i	−0.0503358	+	0.0503358i
$783$	224.082	−	224.082i	0.286183	−	0.286183i
$784$		−	489.849i		−	0.624807i
$785$	−98.4615	−	93.7816i	−0.125429	−	0.119467i
$786$			126.709i			0.161207i
$787$	−375.706	+	375.706i	−0.477389	+	0.477389i	−0.904296	−	0.426906i	$-0.859603\pi$
$787$	−375.706	+	375.706i	−0.477389	+	0.477389i	0.426906	+	0.904296i	$0.359603\pi$
$788$	572.313	+	572.313i	0.726285	+	0.726285i
$789$		−	561.250i		−	0.711343i
$790$	−233.142	−	222.061i	−0.295117	−	0.281090i
$791$			261.963i			0.331179i
$792$	205.999	+	205.999i	0.260100	+	0.260100i
$793$	32.2378	−	367.469i	0.0406530	−	0.463391i
$794$		−	43.6804i		−	0.0550131i
$795$	−9.09692	−	373.687i	−0.0114427	−	0.470047i
$796$	−348.834			−0.438234
$797$	672.906	+	672.906i	0.844299	+	0.844299i	0.989415	−	0.145116i	$-0.0463555\pi$
$797$	672.906	+	672.906i	0.844299	+	0.844299i	−0.145116	+	0.989415i	$0.546355\pi$
$798$	−27.1008	−	27.1008i	−0.0339609	−	0.0339609i
$799$	−77.4907			−0.0969846
$800$	−461.962	+	509.277i	−0.577453	+	0.636597i
$801$			669.427i			0.835739i
$802$	−75.0630	−	75.0630i	−0.0935948	−	0.0935948i
$803$	−215.362	+	215.362i	−0.268197	+	0.268197i
$804$	435.045			0.541100
$805$	−2.93521	−	120.574i	−0.00364622	−	0.149781i
$806$	−221.120	+	185.452i	−0.274343	+	0.230089i
$807$	−282.054	−	282.054i	−0.349509	−	0.349509i
$808$	407.930	+	407.930i	0.504863	+	0.504863i
$809$		−	308.731i		−	0.381621i	−0.981627	−	0.190810i	$-0.938888\pi$
$809$		−	308.731i		−	0.381621i	0.981627	−	0.190810i	$-0.0611116\pi$
$810$	−103.879	+	109.063i	−0.128246	+	0.134646i
$811$			274.480i			0.338446i	0.985578	+	0.169223i	$0.0541258\pi$
$811$			274.480i			0.338446i	−0.985578	+	0.169223i	$0.945874\pi$
$812$	−77.2330	+	77.2330i	−0.0951145	+	0.0951145i
$813$	−293.792	−	293.792i	−0.361368	−	0.361368i
$814$	−331.345			−0.407058
$815$	−461.049	−	439.136i	−0.565705	−	0.538817i
$816$	−84.4320			−0.103471
$817$	−395.681	+	395.681i	−0.484309	+	0.484309i
$818$	−284.647	+	284.647i	−0.347979	+	0.347979i
$819$	144.598	−	121.273i	0.176554	−	0.148075i
$820$	−585.536	+	14.2541i	−0.714069	+	0.0173831i
$821$		−	440.073i		−	0.536021i	−0.963416	−	0.268011i	$-0.913634\pi$
$821$		−	440.073i		−	0.536021i	0.963416	−	0.268011i	$-0.0863662\pi$
$822$	3.78054	+	3.78054i	0.00459919	+	0.00459919i
$823$	−237.638	+	237.638i	−0.288746	+	0.288746i	−0.836584	−	0.547838i	$-0.815451\pi$
$823$	−237.638	+	237.638i	−0.288746	+	0.288746i	0.547838	+	0.836584i	$0.315451\pi$
$824$	−156.315			−0.189702
$825$	166.676	+	151.191i	0.202031	+	0.183261i
$826$			75.8414i			0.0918176i
$827$	−304.685	+	304.685i	−0.368422	+	0.368422i	−0.866902	−	0.498479i	$-0.833892\pi$
$827$	−304.685	+	304.685i	−0.368422	+	0.368422i	0.498479	+	0.866902i	$0.333892\pi$
$828$	−240.273	+	240.273i	−0.290185	+	0.290185i
$829$		−	126.772i		−	0.152921i	−0.997073	−	0.0764606i	$-0.975638\pi$
$829$		−	126.772i		−	0.152921i	0.997073	−	0.0764606i	$-0.0243620\pi$
$830$	−225.611	+	5.49221i	−0.271821	+	0.00661712i
$831$	608.001			0.731650
$832$	−320.730	−	28.1375i	−0.385493	−	0.0338191i
$833$	210.990	−	210.990i	0.253289	−	0.253289i
$834$	35.9674			0.0431264
$835$	−343.212	+	360.339i	−0.411032	+	0.431544i
$836$	−676.874			−0.809658
$837$	−461.069	+	461.069i	−0.550859	+	0.550859i
$838$	−376.989	−	376.989i	−0.449867	−	0.449867i
$839$	−131.400			−0.156615			−0.0783077	−	0.996929i	$-0.524952\pi$
$839$	−131.400			−0.156615			−0.0783077	+	0.996929i	$0.524952\pi$
$840$	−39.6689	+	41.6484i	−0.0472248	+	0.0495815i
$841$	582.270			0.692354
$842$	−25.3328	−	25.3328i	−0.0300865	−	0.0300865i
$843$	−271.974	−	271.974i	−0.322627	−	0.322627i
$844$		−	801.466i		−	0.949604i
$845$	−835.427	−	126.837i	−0.988670	−	0.150102i
$846$	59.9449			0.0708568
$847$	85.9518	−	85.9518i	0.101478	−	0.101478i
$848$	480.904	−	480.904i	0.567104	−	0.567104i
$849$			383.799i			0.452061i
$850$	−110.222	+	5.36959i	−0.129673	+	0.00631716i
$851$		−	821.925i		−	0.965835i
$852$	381.373	−	381.373i	0.447620	−	0.447620i
$853$	−1110.43	−	1110.43i	−1.30180	−	1.30180i	−0.927179	−	0.374619i	$-0.877773\pi$
$853$	−1110.43	−	1110.43i	−1.30180	−	1.30180i	−0.374619	−	0.927179i	$-0.622227\pi$
$854$		−	36.4047i		−	0.0426284i
$855$	−23.2313	−	954.306i	−0.0271712	−	1.11615i
$856$			716.320i			0.836823i
$857$	−840.910	−	840.910i	−0.981225	−	0.981225i	0.0186020	−	0.999827i	$-0.494078\pi$
$857$	−840.910	−	840.910i	−0.981225	−	0.981225i	−0.999827	+	0.0186020i	$0.994078\pi$
$858$	6.85944	−	78.1886i	0.00799468	−	0.0911289i
$859$		−	694.617i		−	0.808634i	−0.914619	−	0.404317i	$-0.867509\pi$
$859$		−	694.617i		−	0.808634i	0.914619	−	0.404317i	$-0.132491\pi$
$860$	285.923	+	272.333i	0.332468	+	0.316666i
$861$	−74.9525			−0.0870529
$862$	111.980	+	111.980i	0.129907	+	0.129907i
$863$	−383.841	−	383.841i	−0.444775	−	0.444775i	0.448838	−	0.893613i	$-0.351838\pi$
$863$	−383.841	−	383.841i	−0.444775	−	0.444775i	−0.893613	+	0.448838i	$0.851838\pi$
$864$	541.856			0.627148
$865$	784.707	−	823.866i	0.907176	−	0.952446i
$866$		−	408.701i		−	0.471941i
$867$	206.318	+	206.318i	0.237967	+	0.237967i
$868$	158.914	−	158.914i	0.183081	−	0.183081i
$869$	−727.667			−0.837362
$870$	−64.0450	+	1.55909i	−0.0736150	+	0.00179206i
$871$	862.029	+	1027.82i	0.989700	+	1.18005i
$872$	149.879	+	149.879i	0.171880	+	0.171880i
$873$	−441.232	−	441.232i	−0.505420	−	0.505420i
$874$			212.785i			0.243461i
$875$	156.279	−	180.946i	0.178605	−	0.206796i
$876$			169.410i			0.193391i
$877$	466.543	−	466.543i	0.531976	−	0.531976i	−0.389184	−	0.921160i	$-0.627243\pi$
$877$	466.543	−	466.543i	0.531976	−	0.531976i	0.921160	+	0.389184i	$0.127243\pi$
$878$	−34.1821	−	34.1821i	−0.0389317	−	0.0389317i
$879$	180.980			0.205893
$880$	9.96412	+	409.310i	0.0113229	+	0.465125i
$881$	102.759			0.116639			0.0583193	−	0.998298i	$-0.481426\pi$
$881$	102.759			0.116639			0.0583193	+	0.998298i	$0.481426\pi$
$882$	−163.217	+	163.217i	−0.185053	+	0.185053i
$883$	308.176	−	308.176i	0.349010	−	0.349010i	−0.510731	−	0.859741i	$-0.670625\pi$
$883$	308.176	−	308.176i	0.349010	−	0.349010i	0.859741	+	0.510731i	$0.170625\pi$
$884$	−195.168	−	232.705i	−0.220778	−	0.263241i
$885$	242.089	−	254.169i	0.273546	−	0.287197i
$886$		−	2.71835i		−	0.00306811i
$887$	168.082	+	168.082i	0.189495	+	0.189495i	0.795478	−	0.605983i	$-0.207220\pi$
$887$	168.082	+	168.082i	0.189495	+	0.189495i	−0.605983	+	0.795478i	$0.707220\pi$
$888$	−277.162	+	277.162i	−0.312119	+	0.312119i
$889$	−280.278			−0.315274
$890$	204.016	−	214.197i	0.229231	−	0.240670i
$891$			340.400i			0.382043i
$892$	−724.035	+	724.035i	−0.811699	+	0.811699i
$893$	−209.448	+	209.448i	−0.234544	+	0.234544i
$894$		−	65.0137i		−	0.0727223i
$895$	19.4436	+	798.714i	0.0217247	+	0.892418i
$896$	−242.201			−0.270313
$897$	193.952	+	17.0153i	0.216223	+	0.0189691i
$898$	−39.6859	+	39.6859i	−0.0441937	+	0.0441937i
$899$	532.363			0.592172
$900$	−672.804	+	32.7765i	−0.747560	+	0.0364183i
$901$	414.275			0.459794
$902$	118.621	−	118.621i	0.131509	−	0.131509i
$903$	35.7302	+	35.7302i	0.0395683	+	0.0395683i
$904$	−693.583			−0.767238
$905$	−866.594	+	21.0961i	−0.957562	+	0.0233106i
$906$	−93.7083			−0.103431
$907$	251.066	+	251.066i	0.276810	+	0.276810i	0.831834	−	0.555024i	$-0.187291\pi$
$907$	251.066	+	251.066i	0.276810	+	0.276810i	−0.555024	+	0.831834i	$0.687291\pi$
$908$	1042.93	+	1042.93i	1.14861	+	1.14861i
$909$			864.590i			0.951144i
$910$	−83.2264	−	5.26412i	−0.0914576	−	0.00578475i
$911$	999.093			1.09670			0.548350	−	0.836249i	$-0.315256\pi$
$911$	999.093			1.09670			0.548350	+	0.836249i	$0.315256\pi$
$912$	−228.210	+	228.210i	−0.250230	+	0.250230i
$913$	−360.652	+	360.652i	−0.395019	+	0.395019i
$914$		−	151.407i		−	0.165653i
$915$	−116.205	+	122.004i	−0.127000	+	0.133338i
$916$		−	705.148i		−	0.769813i
$917$	215.143	−	215.143i	0.234616	−	0.234616i
$918$	61.4928	+	61.4928i	0.0669856	+	0.0669856i
$919$			1415.85i			1.54064i	0.637659	+	0.770318i	$0.279903\pi$
$919$			1415.85i			1.54064i	−0.637659	+	0.770318i	$0.720097\pi$
$920$	319.236	−	7.77137i	0.346995	−	0.00844714i
$921$			42.1939i			0.0458131i
$922$	155.477	+	155.477i	0.168631	+	0.168631i
$923$	1656.70	+	145.341i	1.79491	+	0.157466i
$924$			61.1221i			0.0661494i
$925$	1094.70	−	1206.82i	1.18346	−	1.30467i
$926$	−325.091			−0.351070
$927$	−165.651	−	165.651i	−0.178696	−	0.178696i
$928$	−312.820	−	312.820i	−0.337091	−	0.337091i
$929$	698.290			0.751657			0.375829	−	0.926689i	$-0.377358\pi$
$929$	698.290			0.751657			0.375829	+	0.926689i	$0.377358\pi$
$930$	131.779	−	3.20798i	0.141698	−	0.00344944i
$931$		−	1140.56i		−	1.22509i
$932$	−105.755	−	105.755i	−0.113471	−	0.113471i
$933$	−5.15409	+	5.15409i	−0.00552422	+	0.00552422i
$934$	593.155			0.635069
$935$	−172.008	+	180.592i	−0.183966	+	0.193146i
$936$	321.088	+	382.843i	0.343042	+	0.409020i
$937$	−198.313	−	198.313i	−0.211646	−	0.211646i	0.593320	−	0.804967i	$-0.297817\pi$
$937$	−198.313	−	198.313i	−0.211646	−	0.211646i	−0.804967	+	0.593320i	$0.797817\pi$
$938$	93.6126	+	93.6126i	0.0998002	+	0.0998002i
$939$			50.3993i			0.0536734i
$940$	151.349	+	144.156i	0.161010	+	0.153357i
$941$			1388.60i			1.47567i	0.674983	+	0.737833i	$0.264151\pi$
$941$			1388.60i			1.47567i	−0.674983	+	0.737833i	$0.735849\pi$
$942$	15.3179	−	15.3179i	0.0162611	−	0.0162611i
$943$	294.249	+	294.249i	0.312035	+	0.312035i
$944$	638.643			0.676528
$945$	−188.362	+	4.58542i	−0.199325	+	0.00485230i
$946$	−113.095			−0.119550
$947$	−725.571	+	725.571i	−0.766179	+	0.766179i	−0.977431	−	0.211253i	$-0.932246\pi$
$947$	−725.571	+	725.571i	−0.766179	+	0.766179i	0.211253	+	0.977431i	$0.432246\pi$
$948$	−286.202	+	286.202i	−0.301901	+	0.301901i
$949$	−400.244	+	335.681i	−0.421753	+	0.353721i
$950$	−283.403	+	312.430i	−0.298319	+	0.328873i
$951$		−	456.050i		−	0.479548i
$952$	−45.0747	−	45.0747i	−0.0473474	−	0.0473474i
$953$	−395.957	+	395.957i	−0.415485	+	0.415485i	−0.883644	−	0.468159i	$-0.844917\pi$
$953$	−395.957	+	395.957i	−0.415485	+	0.415485i	0.468159	+	0.883644i	$0.344917\pi$
$954$	−320.473			−0.335925
$955$	590.279	−	14.3696i	0.618094	−	0.0150467i
$956$		−	688.268i		−	0.719946i
$957$	−102.379	+	102.379i	−0.106980	+	0.106980i
$958$	130.174	−	130.174i	0.135881	−	0.135881i
$959$		−	12.8381i		−	0.0133870i
$960$	106.486	+	101.425i	0.110923	+	0.105651i
$961$	−134.387			−0.139841
$962$	−566.128	−	49.6661i	−0.588491	−	0.0516279i
$963$	−759.106	+	759.106i	−0.788272	+	0.788272i
$964$	1116.84			1.15855
$965$	750.042	+	714.392i	0.777245	+	0.740303i
$966$	19.2146			0.0198909
$967$	1000.43	−	1000.43i	1.03457	−	1.03457i	0.0351922	−	0.999381i	$-0.488796\pi$
$967$	1000.43	−	1000.43i	1.03457	−	1.03457i	0.999381	−	0.0351922i	$-0.0112043\pi$
$968$	227.570	+	227.570i	0.235093	+	0.235093i
$969$	−196.591			−0.202880
$970$	6.71038	+	275.652i	0.00691792	+	0.284177i
$971$	−1605.87			−1.65383			−0.826915	−	0.562326i	$-0.809907\pi$
$971$	−1605.87			−1.65383			−0.826915	+	0.562326i	$0.809907\pi$
$972$	578.992	+	578.992i	0.595671	+	0.595671i
$973$	−61.0700	−	61.0700i	−0.0627647	−	0.0627647i
$974$			251.794i			0.258515i
$975$	262.116	+	283.304i	0.268837	+	0.290568i
$976$	−306.555			−0.314093
$977$	834.436	−	834.436i	0.854080	−	0.854080i	−0.136553	−	0.990633i	$-0.543602\pi$
$977$	834.436	−	834.436i	0.854080	−	0.854080i	0.990633	+	0.136553i	$0.0436023\pi$
$978$	71.7267	−	71.7267i	0.0733402	−	0.0733402i
$979$		−	668.536i		−	0.682876i
$980$	−804.594	+	19.5868i	−0.821014	+	0.0199865i
$981$			317.663i			0.323815i
$982$	272.724	−	272.724i	0.277723	−	0.277723i
$983$	−359.602	−	359.602i	−0.365821	−	0.365821i	0.500130	−	0.865951i	$-0.333286\pi$
$983$	−359.602	−	359.602i	−0.365821	−	0.365821i	−0.865951	+	0.500130i	$0.833286\pi$
$984$		−	198.447i		−	0.201674i
$985$	786.197	−	825.430i	0.798170	−	0.838000i
$986$		−	71.0012i		−	0.0720093i
$987$	18.9133	+	18.9133i	0.0191624	+	0.0191624i
$988$	−1156.49	−	101.458i	−1.17054	−	0.102690i
$989$		−	280.539i		−	0.283659i
$990$	133.061	−	139.701i	0.134405	−	0.141112i
$991$	1612.32			1.62697			0.813483	−	0.581588i	$-0.197568\pi$
$991$	1612.32			1.62697			0.813483	+	0.581588i	$0.197568\pi$
$992$	643.658	+	643.658i	0.648848	+	0.648848i
$993$	387.948	+	387.948i	0.390682	+	0.390682i
$994$	164.127			0.165118
$995$	11.9566	+	491.157i	0.0120167	+	0.493625i
$996$			283.699i			0.284839i
$997$	400.327	+	400.327i	0.401532	+	0.401532i	0.878773	−	0.477241i	$-0.158363\pi$
$997$	400.327	+	400.327i	0.401532	+	0.401532i	−0.477241	+	0.878773i	$0.658363\pi$
$998$	229.606	−	229.606i	0.230067	−	0.230067i
$999$	−1284.02			−1.28531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.3.h.a.12.8	yes	24
5.2	odd	4		325.3.h.b.168.8		24
5.3	odd	4	inner	65.3.h.a.38.5	yes	24
5.4	even	2		325.3.h.b.207.5		24
13.12	even	2	inner	65.3.h.a.12.5	✓	24
65.12	odd	4		325.3.h.b.168.5		24
65.38	odd	4	inner	65.3.h.a.38.8	yes	24
65.64	even	2		325.3.h.b.207.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.h.a.12.5	✓	24	13.12	even	2	inner
65.3.h.a.12.8	yes	24	1.1	even	1	trivial
65.3.h.a.38.5	yes	24	5.3	odd	4	inner
65.3.h.a.38.8	yes	24	65.38	odd	4	inner
325.3.h.b.168.5		24	65.12	odd	4
325.3.h.b.168.8		24	5.2	odd	4
325.3.h.b.207.5		24	5.4	even	2
325.3.h.b.207.8		24	65.64	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	65.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.474292 - 0.474292i) q^{2} +(-0.839739 + 0.839739i) q^{3} +3.55009i q^{4} +(4.99852 - 0.121682i) q^{5} +0.796563i q^{6} +(1.35251 - 1.35251i) q^{7} +(3.58095 + 3.58095i) q^{8} +7.58968i q^{9} +O(q^{10})\)	\(q+(0.474292 - 0.474292i) q^{2} +(-0.839739 + 0.839739i) q^{3} +3.55009i q^{4} +(4.99852 - 0.121682i) q^{5} +0.796563i q^{6} +(1.35251 - 1.35251i) q^{7} +(3.58095 + 3.58095i) q^{8} +7.58968i q^{9} +(2.31304 - 2.42847i) q^{10} -7.57957i q^{11} +(-2.98115 - 2.98115i) q^{12} +(1.13612 - 12.9503i) q^{13} -1.28296i q^{14} +(-4.09527 + 4.29964i) q^{15} -10.8035 q^{16} +(-4.65336 - 4.65336i) q^{17} +(3.59972 + 3.59972i) q^{18} -25.1549 q^{19} +(0.431984 + 17.7452i) q^{20} +2.27150i q^{21} +(-3.59493 - 3.59493i) q^{22} +(8.91747 - 8.91747i) q^{23} -6.01413 q^{24} +(24.9704 - 1.21646i) q^{25} +(-5.60335 - 6.68105i) q^{26} +(-13.9310 - 13.9310i) q^{27} +(4.80152 + 4.80152i) q^{28} +16.0851i q^{29} +(0.0969277 + 3.98164i) q^{30} -33.0966i q^{31} +(-19.4478 + 19.4478i) q^{32} +(6.36487 + 6.36487i) q^{33} -4.41410 q^{34} +(6.59595 - 6.92510i) q^{35} -26.9441 q^{36} +(46.0851 - 46.0851i) q^{37} +(-11.9308 + 11.9308i) q^{38} +(9.92080 + 11.8289i) q^{39} +(18.3352 + 17.4637i) q^{40} +32.9969i q^{41} +(1.07736 + 1.07736i) q^{42} +(15.7297 - 15.7297i) q^{43} +26.9082 q^{44} +(0.923530 + 37.9371i) q^{45} -8.45897i q^{46} +(8.32632 - 8.32632i) q^{47} +(9.07217 - 9.07217i) q^{48} +45.3415i q^{49} +(11.2663 - 12.4202i) q^{50} +7.81521 q^{51} +(45.9746 + 4.03333i) q^{52} +(-44.5135 + 44.5135i) q^{53} -13.2147 q^{54} +(-0.922300 - 37.8866i) q^{55} +9.68650 q^{56} +(21.1236 - 21.1236i) q^{57} +(7.62903 + 7.62903i) q^{58} -59.1142 q^{59} +(-15.2641 - 14.5386i) q^{60} +28.3754 q^{61} +(-15.6975 - 15.6975i) q^{62} +(10.2651 + 10.2651i) q^{63} -24.7663i q^{64} +(4.10309 - 64.8704i) q^{65} +6.03761 q^{66} +(-72.9658 + 72.9658i) q^{67} +(16.5199 - 16.5199i) q^{68} +14.9767i q^{69} +(-0.156114 - 6.41292i) q^{70} +127.928i q^{71} +(-27.1782 + 27.1782i) q^{72} +(-28.4135 - 28.4135i) q^{73} -43.7156i q^{74} +(-19.9471 + 21.9901i) q^{75} -89.3024i q^{76} +(-10.2514 - 10.2514i) q^{77} +(10.3157 + 0.904990i) q^{78} -96.0038i q^{79} +(-54.0017 + 1.31460i) q^{80} -44.9102 q^{81} +(15.6501 + 15.6501i) q^{82} +(-47.5821 - 47.5821i) q^{83} -8.06405 q^{84} +(-23.8261 - 22.6937i) q^{85} -14.9210i q^{86} +(-13.5073 - 13.5073i) q^{87} +(27.1421 - 27.1421i) q^{88} +88.2023 q^{89} +(18.4313 + 17.5553i) q^{90} +(-15.9787 - 19.0519i) q^{91} +(31.6579 + 31.6579i) q^{92} +(27.7925 + 27.7925i) q^{93} -7.89821i q^{94} +(-125.737 + 3.06091i) q^{95} -32.6622i q^{96} +(-58.1358 + 58.1358i) q^{97} +(21.5051 + 21.5051i) q^{98} +57.5265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3}+O(q^{10}) \) 24 * q - 4 * q^3	\( 24 q - 4 q^{3} + 16 q^{10} + 72 q^{12} - 36 q^{13} - 104 q^{16} - 48 q^{17} + 8 q^{22} - 104 q^{23} - 88 q^{25} + 88 q^{26} + 56 q^{27} - 24 q^{30} - 64 q^{35} + 256 q^{36} + 124 q^{38} - 368 q^{40} + 216 q^{42} + 8 q^{43} + 196 q^{48} - 296 q^{51} + 16 q^{52} + 220 q^{53} + 332 q^{55} + 584 q^{56} - 8 q^{61} - 596 q^{62} + 420 q^{65} - 360 q^{66} - 640 q^{68} - 184 q^{75} + 388 q^{77} - 636 q^{78} - 224 q^{81} - 1004 q^{82} - 52 q^{87} + 780 q^{88} + 452 q^{90} - 512 q^{91} + 812 q^{92} - 136 q^{95}+O(q^{100}) \) 24 * q - 4 * q^3 + 16 * q^10 + 72 * q^12 - 36 * q^13 - 104 * q^16 - 48 * q^17 + 8 * q^22 - 104 * q^23 - 88 * q^25 + 88 * q^26 + 56 * q^27 - 24 * q^30 - 64 * q^35 + 256 * q^36 + 124 * q^38 - 368 * q^40 + 216 * q^42 + 8 * q^43 + 196 * q^48 - 296 * q^51 + 16 * q^52 + 220 * q^53 + 332 * q^55 + 584 * q^56 - 8 * q^61 - 596 * q^62 + 420 * q^65 - 360 * q^66 - 640 * q^68 - 184 * q^75 + 388 * q^77 - 636 * q^78 - 224 * q^81 - 1004 * q^82 - 52 * q^87 + 780 * q^88 + 452 * q^90 - 512 * q^91 + 812 * q^92 - 136 * q^95

Introduction

L-functions

Modular forms

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