LMFDB - Embedded newform 65.3.h.a.12.4

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			12.4
Character	$\chi$	$=$	65.12
Dual form			65.3.h.a.38.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30775 + 1.30775i) q^{2} +(-3.70495 + 3.70495i) q^{3} +0.579580i q^{4} +(1.70825 - 4.69914i) q^{5} -9.69031i q^{6} +(-2.51452 + 2.51452i) q^{7} +(-5.98895 - 5.98895i) q^{8} -18.4534i q^{9} +O(q^{10})$	\(q+(-1.30775 + 1.30775i) q^{2} +(-3.70495 + 3.70495i) q^{3} +0.579580i q^{4} +(1.70825 - 4.69914i) q^{5} -9.69031i q^{6} +(-2.51452 + 2.51452i) q^{7} +(-5.98895 - 5.98895i) q^{8} -18.4534i q^{9} +(3.91133 + 8.37926i) q^{10} +7.77306i q^{11} +(-2.14732 - 2.14732i) q^{12} +(-11.6077 + 5.85337i) q^{13} -6.57674i q^{14} +(11.0811 + 23.7391i) q^{15} +13.3458 q^{16} +(11.0151 + 11.0151i) q^{17} +(24.1324 + 24.1324i) q^{18} -30.0131 q^{19} +(2.72352 + 0.990068i) q^{20} -18.6324i q^{21} +(-10.1652 - 10.1652i) q^{22} +(-2.29100 + 2.29100i) q^{23} +44.3775 q^{24} +(-19.1638 - 16.0546i) q^{25} +(7.52518 - 22.8347i) q^{26} +(35.0243 + 35.0243i) q^{27} +(-1.45737 - 1.45737i) q^{28} +12.1096i q^{29} +(-45.5361 - 16.5535i) q^{30} +54.0761i q^{31} +(6.50285 - 6.50285i) q^{32} +(-28.7988 - 28.7988i) q^{33} -28.8099 q^{34} +(7.52065 + 16.1115i) q^{35} +10.6952 q^{36} +(-12.0160 + 12.0160i) q^{37} +(39.2496 - 39.2496i) q^{38} +(21.3194 - 64.6924i) q^{39} +(-38.3735 + 17.9123i) q^{40} -10.1155i q^{41} +(24.3665 + 24.3665i) q^{42} +(24.7835 - 24.7835i) q^{43} -4.50511 q^{44} +(-86.7149 - 31.5230i) q^{45} -5.99212i q^{46} +(24.5775 - 24.5775i) q^{47} +(-49.4455 + 49.4455i) q^{48} +36.3543i q^{49} +(46.0568 - 4.06600i) q^{50} -81.6206 q^{51} +(-3.39250 - 6.72757i) q^{52} +(-18.7933 + 18.7933i) q^{53} -91.6061 q^{54} +(36.5267 + 13.2783i) q^{55} +30.1187 q^{56} +(111.197 - 111.197i) q^{57} +(-15.8364 - 15.8364i) q^{58} +28.7578 q^{59} +(-13.7587 + 6.42238i) q^{60} +56.9832 q^{61} +(-70.7180 - 70.7180i) q^{62} +(46.4014 + 46.4014i) q^{63} +70.3913i q^{64} +(7.67698 + 64.5451i) q^{65} +75.3233 q^{66} +(-38.6824 + 38.6824i) q^{67} +(-6.38410 + 6.38410i) q^{68} -16.9761i q^{69} +(-30.9050 - 11.2347i) q^{70} +37.5046i q^{71} +(-110.516 + 110.516i) q^{72} +(76.0023 + 76.0023i) q^{73} -31.4278i q^{74} +(130.482 - 11.5193i) q^{75} -17.3950i q^{76} +(-19.5455 - 19.5455i) q^{77} +(56.7210 + 112.482i) q^{78} -84.8869i q^{79} +(22.7979 - 62.7136i) q^{80} -93.4467 q^{81} +(13.2285 + 13.2285i) q^{82} +(-22.4590 - 22.4590i) q^{83} +10.7990 q^{84} +(70.5777 - 32.9448i) q^{85} +64.8213i q^{86} +(-44.8656 - 44.8656i) q^{87} +(46.5524 - 46.5524i) q^{88} +22.1375 q^{89} +(154.626 - 72.1772i) q^{90} +(14.4693 - 43.9062i) q^{91} +(-1.32782 - 1.32782i) q^{92} +(-200.349 - 200.349i) q^{93} +64.2825i q^{94} +(-51.2699 + 141.036i) q^{95} +48.1856i q^{96} +(-86.8554 + 86.8554i) q^{97} +(-47.5424 - 47.5424i) q^{98} +143.439 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 $

$2$	−1.30775	+	1.30775i	−0.653875	+	0.653875i	−0.953924	−	0.300049i	$-0.902997\pi$
$2$	−1.30775	+	1.30775i	−0.653875	+	0.653875i	0.300049	+	0.953924i	$0.402997\pi$
$3$	−3.70495	+	3.70495i	−1.23498	+	1.23498i	−0.272959	+	0.962026i	$0.588002\pi$
$3$	−3.70495	+	3.70495i	−1.23498	+	1.23498i	−0.962026	+	0.272959i	$0.911998\pi$
$4$			0.579580i			0.144895i
$5$	1.70825	−	4.69914i	0.341650	−	0.939827i
$5$	1.70825	−	4.69914i	0.341650	−	0.939827i
$6$		−	9.69031i		−	1.61505i
$7$	−2.51452	+	2.51452i	−0.359218	+	0.359218i	−0.863525	−	0.504307i	$-0.831748\pi$
$7$	−2.51452	+	2.51452i	−0.359218	+	0.359218i	0.504307	+	0.863525i	$0.331748\pi$
$8$	−5.98895	−	5.98895i	−0.748618	−	0.748618i
$9$		−	18.4534i		−	2.05038i
$10$	3.91133	+	8.37926i	0.391133	+	0.837926i
$11$			7.77306i			0.706642i	0.935502	+	0.353321i	$0.114948\pi$
$11$			7.77306i			0.706642i	−0.935502	+	0.353321i	$0.885052\pi$
$12$	−2.14732	−	2.14732i	−0.178943	−	0.178943i
$13$	−11.6077	+	5.85337i	−0.892898	+	0.450259i
$13$	−11.6077	+	5.85337i	−0.892898	+	0.450259i
$14$		−	6.57674i		−	0.469767i
$15$	11.0811	+	23.7391i	0.738740	+	1.58261i
$16$	13.3458			0.834111
$17$	11.0151	+	11.0151i	0.647944	+	0.647944i	0.952496	−	0.304551i	$-0.0985065\pi$
$17$	11.0151	+	11.0151i	0.647944	+	0.647944i	−0.304551	+	0.952496i	$0.598507\pi$
$18$	24.1324	+	24.1324i	1.34069	+	1.34069i
$19$	−30.0131			−1.57964			−0.789819	−	0.613341i	$-0.789825\pi$
$19$	−30.0131			−1.57964			−0.789819	+	0.613341i	$0.789825\pi$
$20$	2.72352	+	0.990068i	0.136176	+	0.0495034i
$21$		−	18.6324i		−	0.887257i
$22$	−10.1652	−	10.1652i	−0.462055	−	0.462055i
$23$	−2.29100	+	2.29100i	−0.0996088	+	0.0996088i	−0.755155	−	0.655546i	$-0.772438\pi$
$23$	−2.29100	+	2.29100i	−0.0996088	+	0.0996088i	0.655546	+	0.755155i	$0.272438\pi$
$24$	44.3775			1.84906
$25$	−19.1638	−	16.0546i	−0.766550	−	0.642184i
$26$	7.52518	−	22.8347i	0.289430	−	0.878257i
$27$	35.0243	+	35.0243i	1.29720	+	1.29720i
$28$	−1.45737	−	1.45737i	−0.0520488	−	0.0520488i
$29$			12.1096i			0.417573i	0.977961	+	0.208787i	$0.0669514\pi$
$29$			12.1096i			0.417573i	−0.977961	+	0.208787i	$0.933049\pi$
$30$	−45.5361	−	16.5535i	−1.51787	−	0.551783i
$31$			54.0761i			1.74439i	0.489158	+	0.872195i	$0.337304\pi$
$31$			54.0761i			1.74439i	−0.489158	+	0.872195i	$0.662696\pi$
$32$	6.50285	−	6.50285i	0.203214	−	0.203214i
$33$	−28.7988	−	28.7988i	−0.872692	−	0.872692i
$34$	−28.8099			−0.847349
$35$	7.52065	+	16.1115i	0.214876	+	0.460329i
$36$	10.6952			0.297089
$37$	−12.0160	+	12.0160i	−0.324756	+	0.324756i	−0.850588	−	0.525832i	$-0.823754\pi$
$37$	−12.0160	+	12.0160i	−0.324756	+	0.324756i	0.525832	+	0.850588i	$0.323754\pi$
$38$	39.2496	−	39.2496i	1.03289	−	1.03289i
$39$	21.3194	−	64.6924i	0.546652	−	1.65878i
$40$	−38.3735	+	17.9123i	−0.959337	+	0.447806i
$41$		−	10.1155i		−	0.246718i	−0.992362	−	0.123359i	$-0.960633\pi$
$41$		−	10.1155i		−	0.246718i	0.992362	−	0.123359i	$-0.0393667\pi$
$42$	24.3665	+	24.3665i	0.580155	+	0.580155i
$43$	24.7835	−	24.7835i	0.576361	−	0.576361i	−0.357537	−	0.933899i	$-0.616384\pi$
$43$	24.7835	−	24.7835i	0.576361	−	0.576361i	0.933899	+	0.357537i	$0.116384\pi$
$44$	−4.50511			−0.102389
$45$	−86.7149	−	31.5230i	−1.92700	−	0.700511i
$46$		−	5.99212i		−	0.130263i
$47$	24.5775	−	24.5775i	0.522926	−	0.522926i	−0.395528	−	0.918454i	$-0.629438\pi$
$47$	24.5775	−	24.5775i	0.522926	−	0.522926i	0.918454	+	0.395528i	$0.129438\pi$
$48$	−49.4455	+	49.4455i	−1.03011	+	1.03011i
$49$			36.3543i			0.741925i
$50$	46.0568	−	4.06600i	0.921136	−	0.0813200i
$51$	−81.6206			−1.60040
$52$	−3.39250	−	6.72757i	−0.0652403	−	0.129376i
$53$	−18.7933	+	18.7933i	−0.354590	+	0.354590i	−0.861814	−	0.507224i	$-0.830672\pi$
$53$	−18.7933	+	18.7933i	−0.354590	+	0.354590i	0.507224	+	0.861814i	$0.330672\pi$
$54$	−91.6061			−1.69641
$55$	36.5267	+	13.2783i	0.664121	+	0.241424i
$56$	30.1187			0.537834
$57$	111.197	−	111.197i	1.95083	−	1.95083i
$58$	−15.8364	−	15.8364i	−0.273041	−	0.273041i
$59$	28.7578			0.487420			0.243710	−	0.969848i	$-0.421635\pi$
$59$	28.7578			0.487420			0.243710	+	0.969848i	$0.421635\pi$
$60$	−13.7587	+	6.42238i	−0.229311	+	0.107040i
$61$	56.9832			0.934152			0.467076	−	0.884217i	$-0.345308\pi$
$61$	56.9832			0.934152			0.467076	+	0.884217i	$0.345308\pi$
$62$	−70.7180	−	70.7180i	−1.14061	−	1.14061i
$63$	46.4014	+	46.4014i	0.736531	+	0.736531i
$64$			70.3913i			1.09986i
$65$	7.67698	+	64.5451i	0.118107	+	0.993001i
$66$	75.3233			1.14126
$67$	−38.6824	+	38.6824i	−0.577349	+	0.577349i	−0.934172	−	0.356823i	$-0.883860\pi$
$67$	−38.6824	+	38.6824i	−0.577349	+	0.577349i	0.356823	+	0.934172i	$0.383860\pi$
$68$	−6.38410	+	6.38410i	−0.0938839	+	0.0938839i
$69$		−	16.9761i		−	0.246031i
$70$	−30.9050	−	11.2347i	−0.441500	−	0.160496i
$71$			37.5046i			0.528234i	0.964491	+	0.264117i	$0.0850806\pi$
$71$			37.5046i			0.528234i	−0.964491	+	0.264117i	$0.914919\pi$
$72$	−110.516	+	110.516i	−1.53495	+	1.53495i
$73$	76.0023	+	76.0023i	1.04113	+	1.04113i	0.999117	+	0.0420103i	$0.0133762\pi$
$73$	76.0023	+	76.0023i	1.04113	+	1.04113i	0.0420103	+	0.999117i	$0.486624\pi$
$74$		−	31.4278i		−	0.424700i
$75$	130.482	−	11.5193i	1.73977	−	0.153590i
$76$		−	17.3950i		−	0.228881i
$77$	−19.5455	−	19.5455i	−0.253838	−	0.253838i
$78$	56.7210	+	112.482i	0.727192	+	1.44208i
$79$		−	84.8869i		−	1.07452i	−0.843418	−	0.537259i	$-0.819460\pi$
$79$		−	84.8869i		−	1.07452i	0.843418	−	0.537259i	$-0.180540\pi$
$80$	22.7979	−	62.7136i	0.284974	−	0.783920i
$81$	−93.4467			−1.15366
$82$	13.2285	+	13.2285i	0.161323	+	0.161323i
$83$	−22.4590	−	22.4590i	−0.270591	−	0.270591i	0.558747	−	0.829338i	$-0.311282\pi$
$83$	−22.4590	−	22.4590i	−0.270591	−	0.270591i	−0.829338	+	0.558747i	$0.811282\pi$
$84$	10.7990			0.128559
$85$	70.5777	−	32.9448i	0.830326	−	0.387586i
$86$			64.8213i			0.753737i
$87$	−44.8656	−	44.8656i	−0.515697	−	0.515697i
$88$	46.5524	−	46.5524i	0.529005	−	0.529005i
$89$	22.1375			0.248736			0.124368	−	0.992236i	$-0.460310\pi$
$89$	22.1375			0.248736			0.124368	+	0.992236i	$0.460310\pi$
$90$	154.626	−	72.1772i	1.71806	−	0.801969i
$91$	14.4693	−	43.9062i	0.159004	−	0.482486i
$92$	−1.32782	−	1.32782i	−0.0144328	−	0.0144328i
$93$	−200.349	−	200.349i	−2.15430	−	2.15430i
$94$			64.2825i			0.683856i
$95$	−51.2699	+	141.036i	−0.539683	+	1.48459i
$96$			48.1856i			0.501933i
$97$	−86.8554	+	86.8554i	−0.895416	+	0.895416i	−0.995027	−	0.0996101i	$-0.968240\pi$
$97$	−86.8554	+	86.8554i	−0.895416	+	0.895416i	0.0996101	+	0.995027i	$0.468240\pi$
$98$	−47.5424	−	47.5424i	−0.485126	−	0.485126i
$99$	143.439			1.44888
$100$	9.30492	−	11.1069i	0.0930492	−	0.111069i
$101$	−159.152			−1.57576			−0.787881	−	0.615828i	$-0.788822\pi$
$101$	−159.152			−1.57576			−0.787881	+	0.615828i	$0.788822\pi$
$102$	106.739	−	106.739i	1.04646	−	1.04646i
$103$	−31.8440	+	31.8440i	−0.309165	+	0.309165i	−0.844586	−	0.535420i	$-0.820153\pi$
$103$	−31.8440	+	31.8440i	−0.309165	+	0.309165i	0.535420	+	0.844586i	$0.320153\pi$
$104$	104.573	+	34.4622i	1.00551	+	0.331367i
$105$	−87.5561	−	31.8288i	−0.833868	−	0.303131i
$106$		−	49.1538i		−	0.463716i
$107$	−44.8475	−	44.8475i	−0.419136	−	0.419136i	0.465770	−	0.884906i	$-0.345777\pi$
$107$	−44.8475	−	44.8475i	−0.419136	−	0.419136i	−0.884906	+	0.465770i	$0.845777\pi$
$108$	−20.2994	+	20.2994i	−0.187957	+	0.187957i
$109$	−57.0295			−0.523206			−0.261603	−	0.965176i	$-0.584251\pi$
$109$	−57.0295			−0.523206			−0.261603	+	0.965176i	$0.584251\pi$
$110$	−65.1325	+	30.4030i	−0.592113	+	0.276391i
$111$		−	89.0372i		−	0.802137i
$112$	−33.5582	+	33.5582i	−0.299627	+	0.299627i
$113$	133.490	−	133.490i	1.18133	−	1.18133i	0.201927	−	0.979400i	$-0.435280\pi$
$113$	133.490	−	133.490i	1.18133	−	1.18133i	0.979400	−	0.201927i	$-0.0647205\pi$
$114$			290.836i			2.55120i
$115$	6.85213	+	14.6793i	0.0595837	+	0.127646i
$116$	−7.01849			−0.0605043
$117$	108.014	+	214.201i	0.923201	+	1.83078i
$118$	−37.6080	+	37.6080i	−0.318712	+	0.318712i
$119$	−55.3952			−0.465506
$120$	75.8080	−	208.536i	0.631733	−	1.73780i
$121$	60.5796			0.500658
$122$	−74.5198	+	74.5198i	−0.610818	+	0.610818i
$123$	37.4773	+	37.4773i	0.304693	+	0.304693i
$124$	−31.3414			−0.252753
$125$	−108.179	+	62.6278i	−0.865434	+	0.501023i
$126$	−121.363			−0.963198
$127$	−92.6870	−	92.6870i	−0.729819	−	0.729819i	0.240764	−	0.970584i	$-0.422602\pi$
$127$	−92.6870	−	92.6870i	−0.729819	−	0.729819i	−0.970584	+	0.240764i	$0.922602\pi$
$128$	−66.0428	−	66.0428i	−0.515959	−	0.515959i
$129$			183.644i			1.42360i
$130$	−94.4484	−	74.3692i	−0.726526	−	0.572071i
$131$	36.3295			0.277324			0.138662	−	0.990340i	$-0.455720\pi$
$131$	36.3295			0.277324			0.138662	+	0.990340i	$0.455720\pi$
$132$	16.6912	−	16.6912i	0.126449	−	0.126449i
$133$	75.4687	−	75.4687i	0.567434	−	0.567434i
$134$		−	101.174i		−	0.755029i
$135$	224.414	−	104.754i	1.66233	−	0.775954i
$136$		−	131.937i		−	0.970126i
$137$	104.928	−	104.928i	0.765896	−	0.765896i	−0.211485	−	0.977381i	$-0.567830\pi$
$137$	104.928	−	104.928i	0.765896	−	0.765896i	0.977381	+	0.211485i	$0.0678301\pi$
$138$	22.2005	+	22.2005i	0.160873	+	0.160873i
$139$			190.381i			1.36965i	0.728708	+	0.684825i	$0.240121\pi$
$139$			190.381i			1.36965i	−0.728708	+	0.684825i	$0.759879\pi$
$140$	−9.33791	+	4.35882i	−0.0666994	+	0.0311344i
$141$			182.117i			1.29161i
$142$	−49.0467	−	49.0467i	−0.345399	−	0.345399i
$143$	−45.4986	−	90.2271i	−0.318172	−	0.630959i
$144$		−	246.274i		−	1.71024i
$145$	56.9048	+	20.6863i	0.392447	+	0.142664i
$146$	−198.784			−1.36153
$147$	−134.691	−	134.691i	−0.916267	−	0.916267i
$148$	−6.96421	−	6.96421i	−0.0470555	−	0.0470555i
$149$	−124.370			−0.834700			−0.417350	−	0.908746i	$-0.637041\pi$
$149$	−124.370			−0.834700			−0.417350	+	0.908746i	$0.637041\pi$
$150$	−155.574	+	185.703i	−1.03716	+	1.23802i
$151$		−	216.930i		−	1.43662i	−0.695721	−	0.718312i	$-0.744915\pi$
$151$		−	216.930i		−	1.43662i	0.695721	−	0.718312i	$-0.255085\pi$
$152$	179.747	+	179.747i	1.18255	+	1.18255i
$153$	203.265	−	203.265i	1.32853	−	1.32853i
$154$	51.1214			0.331957
$155$	254.111	+	92.3755i	1.63943	+	0.595971i
$156$	37.4944	+	12.3563i	0.240349	+	0.0792071i
$157$	67.4230	+	67.4230i	0.429446	+	0.429446i	0.888439	−	0.458994i	$-0.151790\pi$
$157$	67.4230	+	67.4230i	0.429446	+	0.429446i	−0.458994	+	0.888439i	$0.651790\pi$
$158$	111.011	+	111.011i	0.702600	+	0.702600i
$159$		−	139.257i		−	0.875827i
$160$	−19.4493	−	41.6663i	−0.121558	−	0.260414i
$161$		−	11.5216i		−	0.0715625i
$162$	122.205	−	122.205i	0.754351	−	0.754351i
$163$	134.632	+	134.632i	0.825965	+	0.825965i	0.986956	−	0.160991i	$-0.0514689\pi$
$163$	134.632	+	134.632i	0.825965	+	0.825965i	−0.160991	+	0.986956i	$0.551469\pi$
$164$	5.86271			0.0357482
$165$	−184.525	+	86.1340i	−1.11833	+	0.522024i
$166$	58.7416			0.353865
$167$	−64.1934	+	64.1934i	−0.384392	+	0.384392i	−0.872682	−	0.488290i	$-0.837621\pi$
$167$	−64.1934	+	64.1934i	−0.384392	+	0.384392i	0.488290	+	0.872682i	$0.337621\pi$
$168$	−111.588	+	111.588i	−0.664217	+	0.664217i
$169$	100.476	−	135.888i	0.594533	−	0.804071i
$170$	−49.2145	+	135.382i	−0.289497	+	0.796362i
$171$			553.843i			3.23885i
$172$	14.3640	+	14.3640i	0.0835118	+	0.0835118i
$173$	−70.7661	+	70.7661i	−0.409053	+	0.409053i	−0.881408	−	0.472355i	$-0.843404\pi$
$173$	−70.7661	+	70.7661i	−0.409053	+	0.409053i	0.472355	+	0.881408i	$0.343404\pi$
$174$	117.346			0.674402
$175$	88.5574	−	7.81804i	0.506042	−	0.0446745i
$176$			103.737i			0.589417i
$177$	−106.546	+	106.546i	−0.601956	+	0.601956i
$178$	−28.9503	+	28.9503i	−0.162642	+	0.162642i
$179$			115.149i			0.643293i	0.946860	+	0.321646i	$0.104236\pi$
$179$			115.149i			0.643293i	−0.946860	+	0.321646i	$0.895764\pi$
$180$	18.2701	−	50.2582i	0.101500	−	0.279212i
$181$	−86.3110			−0.476856			−0.238428	−	0.971160i	$-0.576632\pi$
$181$	−86.3110			−0.476856			−0.238428	+	0.971160i	$0.576632\pi$
$182$	38.4961	+	76.3406i	0.211517	+	0.419454i
$183$	−211.120	+	211.120i	−1.15366	+	1.15366i
$184$	27.4414			0.149138
$185$	35.9384	+	76.9910i	0.194262	+	0.416167i
$186$	524.014			2.81728
$187$	−85.6207	+	85.6207i	−0.457865	+	0.457865i
$188$	14.2446	+	14.2446i	0.0757693	+	0.0757693i
$189$	−176.139			−0.931952
$190$	−117.391	−	251.488i	−0.617848	−	1.32362i
$191$	249.862			1.30818			0.654089	−	0.756417i	$-0.273052\pi$
$191$	249.862			1.30818			0.654089	+	0.756417i	$0.273052\pi$
$192$	−260.797	−	260.797i	−1.35832	−	1.35832i
$193$	93.4298	+	93.4298i	0.484092	+	0.484092i	0.906436	−	0.422344i	$-0.138792\pi$
$193$	93.4298	+	93.4298i	0.484092	+	0.484092i	−0.422344	+	0.906436i	$0.638792\pi$
$194$		−	227.170i		−	1.17098i
$195$	−267.579	−	210.694i	−1.37220	−	1.08048i
$196$	−21.0702			−0.107501
$197$	215.730	−	215.730i	1.09507	−	1.09507i	0.100096	−	0.994978i	$-0.468085\pi$
$197$	215.730	−	215.730i	1.09507	−	1.09507i	0.994978	−	0.100096i	$-0.0319151\pi$
$198$	−187.583	+	187.583i	−0.947387	+	0.947387i
$199$		−	84.2954i		−	0.423595i	−0.977314	−	0.211797i	$-0.932068\pi$
$199$		−	84.2954i		−	0.423595i	0.977314	−	0.211797i	$-0.0679317\pi$
$200$	18.6206	+	210.921i	0.0931028	+	1.05460i
$201$		−	286.633i		−	1.42604i
$202$	208.131	−	208.131i	1.03035	−	1.03035i
$203$	−30.4499	−	30.4499i	−0.150000	−	0.150000i
$204$		−	47.3056i		−	0.231890i
$205$	−47.5339	−	17.2797i	−0.231873	−	0.0842914i
$206$		−	83.2880i		−	0.404311i
$207$	42.2767	+	42.2767i	0.204235	+	0.204235i
$208$	−154.913	+	78.1178i	−0.744775	+	0.375566i
$209$		−	233.294i		−	1.11624i
$210$	156.126	−	72.8774i	0.743455	−	0.347035i
$211$	46.9607			0.222563			0.111281	−	0.993789i	$-0.464505\pi$
$211$	46.9607			0.222563			0.111281	+	0.993789i	$0.464505\pi$
$212$	−10.8922	−	10.8922i	−0.0513783	−	0.0513783i
$213$	−138.953	−	138.953i	−0.652361	−	0.652361i
$214$	117.299			0.548125
$215$	−74.1247	−	158.798i	−0.344766	−	0.738594i
$216$		−	419.518i		−	1.94221i
$217$	−135.976	−	135.976i	−0.626616	−	0.626616i
$218$	74.5803	−	74.5803i	0.342111	−	0.342111i
$219$	−563.170			−2.57155
$220$	−7.69585	+	21.1701i	−0.0349811	+	0.0962278i
$221$	−192.334	−	63.3839i	−0.870291	−	0.286805i
$222$	116.438	+	116.438i	0.524497	+	0.524497i
$223$	164.636	+	164.636i	0.738279	+	0.738279i	0.972245	−	0.233966i	$-0.0751704\pi$
$223$	164.636	+	164.636i	0.738279	+	0.738279i	−0.233966	+	0.972245i	$0.575170\pi$
$224$			32.7032i			0.145996i
$225$	−296.262	+	353.636i	−1.31672	+	1.57172i
$226$			349.143i			1.54488i
$227$	−164.535	+	164.535i	−0.724824	+	0.724824i	−0.969584	−	0.244760i	$-0.921291\pi$
$227$	−164.535	+	164.535i	−0.724824	+	0.724824i	0.244760	+	0.969584i	$0.421291\pi$
$228$	64.4476	+	64.4476i	0.282665	+	0.282665i
$229$	42.3079			0.184751			0.0923753	−	0.995724i	$-0.470554\pi$
$229$	42.3079			0.184751			0.0923753	+	0.995724i	$0.470554\pi$
$230$	−28.1578	−	10.2360i	−0.122425	−	0.0445045i
$231$	144.831			0.626972
$232$	72.5239	−	72.5239i	0.312603	−	0.312603i
$233$	8.84358	−	8.84358i	0.0379553	−	0.0379553i	−0.687874	−	0.725830i	$-0.741456\pi$
$233$	8.84358	−	8.84358i	0.0379553	−	0.0379553i	0.725830	+	0.687874i	$0.241456\pi$
$234$	−421.377	−	138.865i	−1.80076	−	0.593440i
$235$	−73.5085	−	157.478i	−0.312802	−	0.670118i
$236$			16.6674i			0.0706247i
$237$	314.502	+	314.502i	1.32701	+	1.32701i
$238$	72.4431	−	72.4431i	0.304383	−	0.304383i
$239$	−137.905			−0.577007			−0.288504	−	0.957479i	$-0.593158\pi$
$239$	−137.905			−0.577007			−0.288504	+	0.957479i	$0.593158\pi$
$240$	147.886	+	316.816i	0.616190	+	1.32007i
$241$		−	197.257i		−	0.818494i	−0.912424	−	0.409247i	$-0.865791\pi$
$241$		−	197.257i		−	0.818494i	0.912424	−	0.409247i	$-0.134209\pi$
$242$	−79.2229	+	79.2229i	−0.327368	+	0.327368i
$243$	30.9968	−	30.9968i	0.127559	−	0.127559i
$244$			33.0263i			0.135354i
$245$	170.834	+	62.1023i	0.697282	+	0.253479i
$246$	−98.0219			−0.398463
$247$	348.382	−	175.678i	1.41045	−	0.711246i
$248$	323.859	−	323.859i	1.30588	−	1.30588i
$249$	166.419			0.668350
$250$	59.5699	−	223.373i	0.238280	−	0.893492i
$251$	−361.018			−1.43832			−0.719160	−	0.694844i	$-0.755473\pi$
$251$	−361.018			−1.43832			−0.719160	+	0.694844i	$0.755473\pi$
$252$	−26.8933	+	26.8933i	−0.106720	+	0.106720i
$253$	−17.8081	−	17.8081i	−0.0703877	−	0.0703877i
$254$	242.423			0.954421
$255$	−139.428	+	383.546i	−0.546778	+	1.50410i
$256$	−108.830			−0.425118
$257$	139.238	+	139.238i	0.541782	+	0.541782i	0.924051	−	0.382269i	$-0.124857\pi$
$257$	139.238	+	139.238i	0.541782	+	0.541782i	−0.382269	+	0.924051i	$0.624857\pi$
$258$	−240.160	−	240.160i	−0.930853	−	0.930853i
$259$		−	60.4289i		−	0.233316i
$260$	−37.4090	+	4.44942i	−0.143881	+	0.0171132i
$261$	223.463			0.856182
$262$	−47.5099	+	47.5099i	−0.181335	+	0.181335i
$263$	−141.566	+	141.566i	−0.538275	+	0.538275i	−0.923022	−	0.384747i	$-0.874289\pi$
$263$	−141.566	+	141.566i	−0.538275	+	0.538275i	0.384747	+	0.923022i	$0.374289\pi$
$264$			344.949i			1.30663i
$265$	56.2086	+	120.416i	0.212108	+	0.454399i
$266$			197.388i			0.742061i
$267$	−82.0185	+	82.0185i	−0.307185	+	0.307185i
$268$	−22.4195	−	22.4195i	−0.0836550	−	0.0836550i
$269$		−	194.943i		−	0.724695i	−0.932043	−	0.362347i	$-0.881975\pi$
$269$		−	194.943i		−	0.724695i	0.932043	−	0.362347i	$-0.118025\pi$
$270$	−156.486	+	430.470i	−0.579579	+	1.59433i
$271$		−	14.0696i		−	0.0519174i	−0.999663	−	0.0259587i	$-0.991736\pi$
$271$		−	14.0696i		−	0.0519174i	0.999663	−	0.0259587i	$-0.00826384\pi$
$272$	147.004	+	147.004i	0.540457	+	0.540457i
$273$	109.062	+	216.279i	0.399496	+	0.792230i
$274$			274.438i			1.00160i
$275$	124.793	−	148.961i	0.453794	−	0.541676i
$276$	9.83902			0.0356486
$277$	−9.25252	−	9.25252i	−0.0334026	−	0.0334026i	0.690208	−	0.723611i	$-0.257519\pi$
$277$	−9.25252	−	9.25252i	−0.0334026	−	0.0334026i	−0.723611	+	0.690208i	$0.757519\pi$
$278$	−248.971	−	248.971i	−0.895580	−	0.895580i
$279$	997.886			3.57665
$280$	51.4503	−	141.532i	0.183751	−	0.505471i
$281$			215.855i			0.768169i	0.923298	+	0.384084i	$0.125483\pi$
$281$			215.855i			0.768169i	−0.923298	+	0.384084i	$0.874517\pi$
$282$	−238.164	−	238.164i	−0.844552	−	0.844552i
$283$	−201.227	+	201.227i	−0.711051	+	0.711051i	−0.966755	−	0.255704i	$-0.917693\pi$
$283$	−201.227	+	201.227i	−0.711051	+	0.711051i	0.255704	+	0.966755i	$0.417693\pi$
$284$	−21.7369			−0.0765385
$285$	−332.578	−	712.483i	−1.16694	−	2.49994i
$286$	177.495	+	58.4937i	0.620613	+	0.204523i
$287$	25.4355	+	25.4355i	0.0886256	+	0.0886256i
$288$	−120.000	−	120.000i	−0.416665	−	0.416665i
$289$		−	46.3371i		−	0.160336i
$290$	−101.470	+	47.3648i	−0.349896	+	0.163327i
$291$		−	643.591i		−	2.21165i
$292$	−44.0494	+	44.0494i	−0.150854	+	0.150854i
$293$	243.563	+	243.563i	0.831272	+	0.831272i	0.987691	−	0.156419i	$-0.0499951\pi$
$293$	243.563	+	243.563i	0.831272	+	0.831272i	−0.156419	+	0.987691i	$0.549995\pi$
$294$	352.285			1.19825
$295$	49.1255	−	135.137i	0.166527	−	0.458091i
$296$	143.926			0.486236
$297$	−272.246	+	272.246i	−0.916654	+	0.916654i
$298$	162.645	−	162.645i	0.545789	−	0.545789i
$299$	13.1831	−	40.0033i	0.0440907	−	0.133790i
$300$	6.67634	+	75.6250i	0.0222545	+	0.252083i
$301$			124.638i			0.414078i
$302$	283.690	+	283.690i	0.939372	+	0.939372i
$303$	589.651	−	589.651i	1.94604	−	1.94604i
$304$	−400.548			−1.31759
$305$	97.3417	−	267.772i	0.319153	−	0.877941i
$306$			531.640i			1.73738i
$307$	−58.3779	+	58.3779i	−0.190156	+	0.190156i	−0.795763	−	0.605608i	$-0.792930\pi$
$307$	−58.3779	+	58.3779i	−0.190156	+	0.190156i	0.605608	+	0.795763i	$0.292930\pi$
$308$	11.3282	−	11.3282i	0.0367799	−	0.0367799i
$309$		−	235.961i		−	0.763629i
$310$	−453.118	+	211.509i	−1.46167	+	0.682289i
$311$	−249.834			−0.803323			−0.401662	−	0.915788i	$-0.631567\pi$
$311$	−249.834			−0.803323			−0.401662	+	0.915788i	$0.631567\pi$
$312$	−515.120	+	259.758i	−1.65103	+	0.832559i
$313$	−235.473	+	235.473i	−0.752308	+	0.752308i	−0.974910	−	0.222601i	$-0.928545\pi$
$313$	−235.473	+	235.473i	−0.752308	+	0.752308i	0.222601	+	0.974910i	$0.428545\pi$
$314$	−176.345			−0.561608
$315$	297.312	−	138.781i	0.943848	−	0.440576i
$316$	49.1987			0.155692
$317$	100.058	−	100.058i	0.315640	−	0.315640i	−0.531450	−	0.847090i	$-0.678353\pi$
$317$	100.058	−	100.058i	0.315640	−	0.315640i	0.847090	+	0.531450i	$0.178353\pi$
$318$	182.113	+	182.113i	0.572682	+	0.572682i
$319$	−94.1288			−0.295075
$320$	330.778	+	120.246i	1.03368	+	0.375769i
$321$	332.316			1.03525
$322$	15.0673	+	15.0673i	0.0467929	+	0.0467929i
$323$	−330.596	−	330.596i	−1.02352	−	1.02352i
$324$		−	54.1598i		−	0.167160i
$325$	316.420	+	74.1839i	0.973601	+	0.228258i
$326$	−352.131			−1.08016
$327$	211.292	−	211.292i	0.646151	−	0.646151i
$328$	−60.5809	+	60.5809i	−0.184698	+	0.184698i
$329$			123.601i			0.375688i
$330$	128.671	−	353.955i	0.389912	−	1.07259i
$331$			127.752i			0.385958i	0.981203	+	0.192979i	$0.0618150\pi$
$331$			127.752i			0.385958i	−0.981203	+	0.192979i	$0.938185\pi$
$332$	13.0168	−	13.0168i	0.0392072	−	0.0392072i
$333$	221.735	+	221.735i	0.665871	+	0.665871i
$334$		−	167.898i		−	0.502688i
$335$	115.695	+	247.853i	0.345357	+	0.739860i
$336$		−	248.664i		−	0.740070i
$337$	255.749	+	255.749i	0.758900	+	0.758900i	0.976122	−	0.217222i	$-0.0696995\pi$
$337$	255.749	+	255.749i	0.758900	+	0.758900i	−0.217222	+	0.976122i	$0.569700\pi$
$338$	46.3100	+	309.105i	0.137012	+	0.914512i
$339$			989.149i			2.91784i
$340$	19.0941	+	40.9054i	0.0561592	+	0.120310i
$341$	−420.337			−1.23266
$342$	−724.288	−	724.288i	−2.11780	−	2.11780i
$343$	−214.626	−	214.626i	−0.625730	−	0.625730i
$344$	−296.855			−0.862949
$345$	−79.7731	−	28.9995i	−0.231226	−	0.0840564i
$346$		−	185.089i		−	0.534939i
$347$	−263.579	−	263.579i	−0.759595	−	0.759595i	0.216654	−	0.976249i	$-0.430486\pi$
$347$	−263.579	−	263.579i	−0.759595	−	0.759595i	−0.976249	+	0.216654i	$0.930486\pi$
$348$	26.0032	−	26.0032i	0.0747218	−	0.0747218i
$349$	264.700			0.758453			0.379227	−	0.925304i	$-0.376190\pi$
$349$	264.700			0.758453			0.379227	+	0.925304i	$0.376190\pi$
$350$	−105.587	+	126.035i	−0.301677	+	0.360100i
$351$	−611.561	−	201.540i	−1.74234	−	0.574189i
$352$	50.5471	+	50.5471i	0.143600	+	0.143600i
$353$	−240.510	−	240.510i	−0.681332	−	0.681332i	0.278968	−	0.960300i	$-0.410008\pi$
$353$	−240.510	−	240.510i	−0.681332	−	0.681332i	−0.960300	+	0.278968i	$0.910008\pi$
$354$		−	278.672i		−	0.787208i
$355$	176.239	+	64.0673i	0.496449	+	0.180471i
$356$			12.8305i			0.0360406i
$357$	205.237	−	205.237i	0.574893	−	0.574893i
$358$	−150.587	−	150.587i	−0.420633	−	0.420633i
$359$	−463.561			−1.29126			−0.645628	−	0.763652i	$-0.723404\pi$
$359$	−463.561			−1.29126			−0.645628	+	0.763652i	$0.723404\pi$
$360$	330.541	+	708.120i	0.918171	+	1.96700i
$361$	539.787			1.49525
$362$	112.873	−	112.873i	0.311804	−	0.311804i
$363$	−224.445	+	224.445i	−0.618305	+	0.618305i
$364$	25.4472	+	8.38613i	0.0699098	+	0.0230388i
$365$	486.976	−	227.314i	1.33418	−	0.622779i
$366$		−	552.185i		−	1.50870i
$367$	−11.1729	−	11.1729i	−0.0304438	−	0.0304438i	0.691721	−	0.722165i	$-0.256853\pi$
$367$	−11.1729	−	11.1729i	−0.0304438	−	0.0304438i	−0.722165	+	0.691721i	$0.756853\pi$
$368$	−30.5752	+	30.5752i	−0.0830848	+	0.0830848i
$369$	−186.664			−0.505865
$370$	−147.683	−	53.6865i	−0.399144	−	0.145099i
$371$		−	94.5123i		−	0.254750i
$372$	116.118	−	116.118i	0.312146	−	0.312146i
$373$	−421.366	+	421.366i	−1.12967	+	1.12967i	−0.139437	+	0.990231i	$0.544529\pi$
$373$	−421.366	+	421.366i	−1.12967	+	1.12967i	−0.990231	+	0.139437i	$0.955471\pi$
$374$		−	223.941i		−	0.598772i
$375$	168.766	−	632.833i	0.450043	−	1.68755i
$376$	−294.387			−0.782944
$377$	−70.8822	−	140.565i	−0.188016	−	0.372850i
$378$	230.346	−	230.346i	0.609380	−	0.609380i
$379$	−156.851			−0.413854			−0.206927	−	0.978356i	$-0.566346\pi$
$379$	−156.851			−0.413854			−0.206927	+	0.978356i	$0.566346\pi$
$380$	−81.7414	−	29.7150i	−0.215109	−	0.0781974i
$381$	686.803			1.80263
$382$	−326.757	+	326.757i	−0.855385	+	0.855385i
$383$	514.785	+	514.785i	1.34409	+	1.34409i	0.891948	+	0.452138i	$0.149339\pi$
$383$	514.785	+	514.785i	1.34409	+	1.34409i	0.452138	+	0.891948i	$0.350661\pi$
$384$	489.371			1.27440
$385$	−125.236	+	58.4585i	−0.325288	+	0.151840i
$386$	−244.366			−0.633072
$387$	−457.340	−	457.340i	−1.18176	−	1.18176i
$388$	−50.3396	−	50.3396i	−0.129741	−	0.129741i
$389$		−	103.977i		−	0.267293i	−0.991029	−	0.133647i	$-0.957331\pi$
$389$		−	103.977i		−	0.267293i	0.991029	−	0.133647i	$-0.0426687\pi$
$390$	625.461	−	74.3923i	1.60375	−	0.190750i
$391$	−50.4710			−0.129082
$392$	217.724	−	217.724i	0.555419	−	0.555419i
$393$	−134.599	+	134.599i	−0.342491	+	0.342491i
$394$			564.241i			1.43208i
$395$	−398.895	−	145.008i	−1.00986	−	0.367109i
$396$			83.1344i			0.209935i
$397$	−72.3240	+	72.3240i	−0.182176	+	0.182176i	−0.792303	−	0.610127i	$-0.791118\pi$
$397$	−72.3240	+	72.3240i	−0.182176	+	0.182176i	0.610127	+	0.792303i	$0.291118\pi$
$398$	110.237	+	110.237i	0.276978	+	0.276978i
$399$			559.216i			1.40154i
$400$	−255.755	−	214.261i	−0.639388	−	0.535653i
$401$			541.291i			1.34985i	0.737885	+	0.674926i	$0.235824\pi$
$401$			541.291i			1.34985i	−0.737885	+	0.674926i	$0.764176\pi$
$402$	374.845	+	374.845i	0.932449	+	0.932449i
$403$	−316.527	−	627.697i	−0.785428	−	1.55756i
$404$		−	92.2412i		−	0.228320i
$405$	−159.630	+	439.119i	−0.394149	+	1.08424i
$406$	79.6418			0.196162
$407$	−93.4008	−	93.4008i	−0.229486	−	0.229486i
$408$	488.821	+	488.821i	1.19809	+	1.19809i
$409$	−178.015			−0.435245			−0.217622	−	0.976033i	$-0.569830\pi$
$409$	−178.015			−0.435245			−0.217622	+	0.976033i	$0.569830\pi$
$410$	84.7600	−	39.5649i	0.206732	−	0.0964997i
$411$			777.505i			1.89174i
$412$	−18.4562	−	18.4562i	−0.0447965	−	0.0447965i
$413$	−72.3121	+	72.3121i	−0.175090	+	0.175090i
$414$	−110.575			−0.267089
$415$	−143.904	+	67.1723i	−0.346756	+	0.161861i
$416$	−37.4194	+	113.547i	−0.0899504	+	0.272949i
$417$	−705.354	−	705.354i	−1.69150	−	1.69150i
$418$	305.090	+	305.090i	0.729880	+	0.729880i
$419$		−	278.825i		−	0.665453i	−0.943023	−	0.332727i	$-0.892031\pi$
$419$		−	278.825i		−	0.665453i	0.943023	−	0.332727i	$-0.107969\pi$
$420$	18.4473	−	50.7458i	0.0439222	−	0.120823i
$421$			787.251i			1.86996i	0.354706	+	0.934978i	$0.384581\pi$
$421$			787.251i			1.86996i	−0.354706	+	0.934978i	$0.615419\pi$
$422$	−61.4129	+	61.4129i	−0.145528	+	0.145528i
$423$	−453.538	−	453.538i	−1.07219	−	1.07219i
$424$	225.104			0.530906
$425$	−34.2475	−	387.932i	−0.0805824	−	0.912782i
$426$	363.431			0.853126
$427$	−143.286	+	143.286i	−0.335564	+	0.335564i
$428$	25.9927	−	25.9927i	0.0607306	−	0.0607306i
$429$	502.858	+	165.717i	1.17216	+	0.386287i
$430$	304.604	+	110.731i	0.708382	+	0.257514i
$431$		−	314.438i		−	0.729554i	−0.931095	−	0.364777i	$-0.881145\pi$
$431$		−	314.438i		−	0.729554i	0.931095	−	0.364777i	$-0.118855\pi$
$432$	467.427	+	467.427i	1.08201	+	1.08201i
$433$	147.355	−	147.355i	0.340311	−	0.340311i	−0.516173	−	0.856484i	$-0.672644\pi$
$433$	147.355	−	147.355i	0.340311	−	0.340311i	0.856484	+	0.516173i	$0.172644\pi$
$434$	355.644			0.819457
$435$	−287.471	+	134.188i	−0.660854	+	0.308478i
$436$		−	33.0531i		−	0.0758099i
$437$	68.7601	−	68.7601i	0.157346	−	0.157346i
$438$	736.486	−	736.486i	1.68147	−	1.68147i
$439$		−	59.6718i		−	0.135927i	−0.997688	−	0.0679634i	$-0.978350\pi$
$439$		−	59.6718i		−	0.135927i	0.997688	−	0.0679634i	$-0.0216501\pi$
$440$	−139.233	−	298.279i	−0.316439	−	0.677908i
$441$	670.860			1.52123
$442$	334.416	−	168.635i	0.756596	−	0.381527i
$443$	436.619	−	436.619i	0.985595	−	0.985595i	−0.0143028	−	0.999898i	$-0.504553\pi$
$443$	436.619	−	436.619i	0.985595	−	0.985595i	0.999898	+	0.0143028i	$0.00455288\pi$
$444$	51.6042			0.116226
$445$	37.8164	−	104.027i	0.0849807	−	0.233769i
$446$	−430.606			−0.965484
$447$	460.786	−	460.786i	1.03084	−	1.03084i
$448$	−177.001	−	177.001i	−0.395091	−	0.395091i
$449$	96.6815			0.215326			0.107663	−	0.994187i	$-0.465663\pi$
$449$	96.6815			0.215326			0.107663	+	0.994187i	$0.465663\pi$
$450$	−75.0314	−	849.904i	−0.166736	−	1.88867i
$451$	78.6280			0.174341
$452$	77.3681	+	77.3681i	0.171168	+	0.171168i
$453$	803.716	+	803.716i	1.77421	+	1.77421i
$454$		−	430.342i		−	0.947889i
$455$	−181.604	−	142.996i	−0.399130	−	0.314277i
$456$	−1331.91			−2.92085
$457$	−546.226	+	546.226i	−1.19524	+	1.19524i	−0.219670	+	0.975574i	$0.570498\pi$
$457$	−546.226	+	546.226i	−1.19524	+	1.19524i	−0.975574	+	0.219670i	$0.929502\pi$
$458$	−55.3281	+	55.3281i	−0.120804	+	0.120804i
$459$			771.590i			1.68102i
$460$	−8.50785	+	3.97135i	−0.0184953	+	0.00863338i
$461$		−	279.826i		−	0.606997i	−0.952832	−	0.303499i	$-0.901845\pi$
$461$		−	279.826i		−	0.606997i	0.952832	−	0.303499i	$-0.0981548\pi$
$462$	−189.402	+	189.402i	−0.409962	+	0.409962i
$463$	−251.254	−	251.254i	−0.542666	−	0.542666i	0.381644	−	0.924309i	$-0.375358\pi$
$463$	−251.254	−	251.254i	−0.542666	−	0.542666i	−0.924309	+	0.381644i	$0.875358\pi$
$464$			161.612i			0.348302i
$465$	−1283.72	+	599.222i	−2.76068	+	1.28865i
$466$			23.1304i			0.0496360i
$467$	218.674	+	218.674i	0.468253	+	0.468253i	0.901348	−	0.433095i	$-0.142579\pi$
$467$	218.674	+	218.674i	0.468253	+	0.468253i	−0.433095	+	0.901348i	$0.642579\pi$
$468$	−124.146	+	62.6030i	−0.265270	+	0.133767i
$469$		−	194.536i		−	0.414788i
$470$	302.072	+	109.811i	0.642707	+	0.233640i
$471$	−499.598			−1.06072
$472$	−172.229	−	172.229i	−0.364891	−	0.364891i
$473$	192.644	+	192.644i	0.407281	+	0.407281i
$474$	−822.580			−1.73540
$475$	575.164	+	481.849i	1.21087	+	1.01442i
$476$		−	32.1060i		−	0.0674495i
$477$	346.800	+	346.800i	0.727043	+	0.727043i
$478$	180.345	−	180.345i	0.377291	−	0.377291i
$479$	688.239			1.43683			0.718413	−	0.695617i	$-0.244869\pi$
$479$	688.239			1.43683			0.718413	+	0.695617i	$0.244869\pi$
$480$	226.430	+	82.3130i	0.471730	+	0.171485i
$481$	69.1435	−	209.811i	0.143749	−	0.436198i
$482$	257.963	+	257.963i	0.535193	+	0.535193i
$483$	42.6869	+	42.6869i	0.0883786	+	0.0883786i
$484$			35.1107i			0.0725428i
$485$	259.775	+	556.516i	0.535618	+	1.14746i
$486$			81.0721i			0.166815i
$487$	332.778	−	332.778i	0.683322	−	0.683322i	−0.277426	−	0.960747i	$-0.589481\pi$
$487$	332.778	−	332.778i	0.683322	−	0.683322i	0.960747	+	0.277426i	$0.0894812\pi$
$488$	−341.270	−	341.270i	−0.699323	−	0.699323i
$489$	−997.614			−2.04011
$490$	−304.622	+	142.194i	−0.621679	+	0.290192i
$491$	446.818			0.910017			0.455008	−	0.890487i	$-0.349636\pi$
$491$	446.818			0.910017			0.455008	+	0.890487i	$0.349636\pi$
$492$	−21.7211	+	21.7211i	−0.0441485	+	0.0441485i
$493$	−133.388	+	133.388i	−0.270564	+	0.270564i
$494$	−225.854	+	685.340i	−0.457195	+	1.38733i
$495$	245.030	−	674.040i	0.495010	−	1.36170i
$496$			721.687i			1.45501i
$497$	−94.3063	−	94.3063i	−0.189751	−	0.189751i
$498$	−217.635	+	217.635i	−0.437018	+	0.437018i
$499$	714.831			1.43253			0.716264	−	0.697830i	$-0.245851\pi$
$499$	714.831			1.43253			0.716264	+	0.697830i	$0.245851\pi$
$500$	−36.2978	−	62.6985i	−0.0725956	−	0.125397i
$501$		−	475.667i		−	0.949436i
$502$	472.122	−	472.122i	0.940482	−	0.940482i
$503$	73.6511	−	73.6511i	0.146424	−	0.146424i	−0.630095	−	0.776518i	$-0.716984\pi$
$503$	73.6511	−	73.6511i	0.146424	−	0.146424i	0.776518	+	0.630095i	$0.216984\pi$
$504$		−	555.792i		−	1.10276i
$505$	−271.871	+	747.876i	−0.538359	+	1.48094i
$506$	46.5771			0.0920495
$507$	131.200	+	875.718i	0.258777	+	1.72725i
$508$	53.7195	−	53.7195i	0.105747	−	0.105747i
$509$	339.398			0.666793			0.333397	−	0.942787i	$-0.391805\pi$
$509$	339.398			0.666793			0.333397	+	0.942787i	$0.391805\pi$
$510$	−319.245	−	683.920i	−0.625971	−	1.34102i
$511$	−382.219			−0.747983
$512$	406.494	−	406.494i	0.793933	−	0.793933i
$513$	−1051.19	−	1051.19i	−2.04910	−	2.04910i
$514$	−364.177			−0.708516
$515$	95.2418	+	204.037i	0.184936	+	0.396188i
$516$	−106.436			−0.206272
$517$	191.042	+	191.042i	0.369521	+	0.369521i
$518$	79.0259	+	79.0259i	0.152560	+	0.152560i
$519$		−	524.371i		−	1.01035i
$520$	340.580	−	432.534i	0.654961	−	0.831796i
$521$	907.389			1.74163			0.870815	−	0.491611i	$-0.163592\pi$
$521$	907.389			1.74163			0.870815	+	0.491611i	$0.163592\pi$
$522$	−292.234	+	292.234i	−0.559836	+	0.559836i
$523$	−420.112	+	420.112i	−0.803274	+	0.803274i	−0.983606	−	0.180332i	$-0.942283\pi$
$523$	−420.112	+	420.112i	−0.803274	+	0.803274i	0.180332	+	0.983606i	$0.442283\pi$
$524$			21.0558i			0.0401829i
$525$	−299.136	+	357.067i	−0.569782	+	0.680127i
$526$		−	370.267i		−	0.703930i
$527$	−595.651	+	595.651i	−1.13027	+	1.13027i
$528$	−384.342	−	384.342i	−0.727921	−	0.727921i
$529$			518.503i			0.980156i
$530$	−230.981	−	83.9671i	−0.435812	−	0.158428i
$531$		−	530.678i		−	0.999394i
$532$	43.7401	+	43.7401i	0.0822183	+	0.0822183i
$533$	59.2095	+	117.417i	0.111087	+	0.220294i
$534$		−	214.519i		−	0.401722i
$535$	−287.355	+	134.134i	−0.537113	+	0.250717i
$536$	463.334			0.864429
$537$	−426.623	−	426.623i	−0.794456	−	0.794456i
$538$	254.937	+	254.937i	0.473860	+	0.473860i
$539$	−282.584			−0.524275
$540$	60.7132	+	130.066i	0.112432	+	0.240863i
$541$		−	903.965i		−	1.67091i	−0.549556	−	0.835457i	$-0.685203\pi$
$541$		−	903.965i		−	1.67091i	0.549556	−	0.835457i	$-0.314797\pi$
$542$	18.3995	+	18.3995i	0.0339475	+	0.0339475i
$543$	319.778	−	319.778i	0.588910	−	0.588910i
$544$	143.259			0.263343
$545$	−97.4206	+	267.989i	−0.178753	+	0.491723i
$546$	−425.465	−	140.212i	−0.779239	−	0.256799i
$547$	−469.877	−	469.877i	−0.859007	−	0.859007i	0.132214	−	0.991221i	$-0.457791\pi$
$547$	−469.877	−	469.877i	−0.859007	−	0.859007i	−0.991221	+	0.132214i	$0.957791\pi$
$548$	60.8140	+	60.8140i	0.110974	+	0.110974i
$549$		−	1051.53i		−	1.91536i
$550$	31.6052	+	358.002i	0.0574641	+	0.650913i
$551$		−	363.447i		−	0.659614i
$552$	−101.669	+	101.669i	−0.184183	+	0.184183i
$553$	213.450	+	213.450i	0.385986	+	0.385986i
$554$	24.2000			0.0436822
$555$	−418.398	−	152.098i	−0.753870	−	0.274050i
$556$	−110.341			−0.198455
$557$	408.107	−	408.107i	0.732687	−	0.732687i	−0.238464	−	0.971151i	$-0.576644\pi$
$557$	408.107	−	408.107i	0.732687	−	0.732687i	0.971151	+	0.238464i	$0.0766439\pi$
$558$	−1304.99	+	1304.99i	−2.33868	+	2.33868i
$559$	−142.612	+	432.746i	−0.255120	+	0.774144i
$560$	100.369	+	215.021i	0.179230	+	0.383966i
$561$		−	634.441i		−	1.13091i
$562$	−282.285	−	282.285i	−0.502286	−	0.502286i
$563$	429.933	−	429.933i	0.763646	−	0.763646i	−0.213333	−	0.976980i	$-0.568432\pi$
$563$	429.933	−	429.933i	0.763646	−	0.763646i	0.976980	+	0.213333i	$0.0684320\pi$
$564$	−105.551			−0.187148
$565$	−399.253	−	855.322i	−0.706643	−	1.51384i
$566$		−	526.310i		−	0.929877i
$567$	234.974	−	234.974i	0.414416	−	0.414416i
$568$	224.613	−	224.613i	0.395446	−	0.395446i
$569$		−	65.7028i		−	0.115471i	−0.998332	−	0.0577353i	$-0.981612\pi$
$569$		−	65.7028i		−	0.115471i	0.998332	−	0.0577353i	$-0.0183879\pi$
$570$	1366.68	+	496.821i	2.39768	+	0.871616i
$571$	675.735			1.18342			0.591712	−	0.806150i	$-0.298452\pi$
$571$	675.735			1.18342			0.591712	+	0.806150i	$0.298452\pi$
$572$	52.2938	−	26.3701i	0.0914227	−	0.0461015i
$573$	−925.728	+	925.728i	−1.61558	+	1.61558i
$574$	−66.5267			−0.115900
$575$	80.6854	−	7.12308i	0.140322	−	0.0123880i
$576$	1298.96			2.25513
$577$	−52.9985	+	52.9985i	−0.0918519	+	0.0918519i	−0.751540	−	0.659688i	$-0.770688\pi$
$577$	−52.9985	+	52.9985i	−0.0918519	+	0.0918519i	0.659688	+	0.751540i	$0.270688\pi$
$578$	60.5973	+	60.5973i	0.104840	+	0.104840i
$579$	−692.306			−1.19569
$580$	−11.9893	+	32.9809i	−0.0206713	+	0.0568636i
$581$	112.947			0.194402
$582$	841.656	+	841.656i	1.44614	+	1.44614i
$583$	−146.081	−	146.081i	−0.250568	−	0.250568i
$584$		−	910.347i		−	1.55881i
$585$	1191.07	−	141.666i	2.03602	−	0.242164i
$586$	−637.038			−1.08710
$587$	−668.195	+	668.195i	−1.13832	+	1.13832i	−0.149572	+	0.988751i	$0.547789\pi$
$587$	−668.195	+	668.195i	−1.13832	+	1.13832i	−0.988751	+	0.149572i	$0.952211\pi$
$588$	78.0643	−	78.0643i	0.132762	−	0.132762i
$589$		−	1622.99i		−	2.75550i
$590$	112.481	+	240.969i	0.190646	+	0.408422i
$591$			1598.54i			2.70480i
$592$	−160.362	+	160.362i	−0.270882	+	0.270882i
$593$	−111.621	−	111.621i	−0.188232	−	0.188232i	0.606700	−	0.794931i	$-0.292493\pi$
$593$	−111.621	−	111.621i	−0.188232	−	0.188232i	−0.794931	+	0.606700i	$0.792493\pi$
$594$		−	712.060i		−	1.19875i
$595$	−94.6290	+	260.310i	−0.159040	+	0.437495i
$596$		−	72.0825i		−	0.120944i
$597$	312.311	+	312.311i	0.523133	+	0.523133i
$598$	35.0741	+	69.5545i	0.0586523	+	0.116312i
$599$			679.649i			1.13464i	0.823497	+	0.567320i	$0.192020\pi$
$599$			679.649i			1.13464i	−0.823497	+	0.567320i	$0.807980\pi$
$600$	−850.441	−	712.464i	−1.41740	−	1.18744i
$601$	−195.614			−0.325482			−0.162741	−	0.986669i	$-0.552033\pi$
$601$	−195.614			−0.325482			−0.162741	+	0.986669i	$0.552033\pi$
$602$	−162.995	−	162.995i	−0.270755	−	0.270755i
$603$	713.821	+	713.821i	1.18378	+	1.18378i
$604$	125.728			0.208160
$605$	103.485	−	284.672i	0.171050	−	0.470532i
$606$			1542.23i			2.54494i
$607$	59.8198	+	59.8198i	0.0985499	+	0.0985499i	0.754663	−	0.656113i	$-0.227800\pi$
$607$	59.8198	+	59.8198i	0.0985499	+	0.0985499i	−0.656113	+	0.754663i	$0.727800\pi$
$608$	−195.171	+	195.171i	−0.321005	+	0.321005i
$609$	225.631			0.370495
$610$	222.880	+	477.477i	0.365378	+	0.782750i
$611$	−141.426	+	429.149i	−0.231467	+	0.702372i
$612$	117.808	+	117.808i	0.192497	+	0.192497i
$613$	170.058	+	170.058i	0.277419	+	0.277419i	0.832078	−	0.554659i	$-0.187151\pi$
$613$	170.058	+	170.058i	0.277419	+	0.277419i	−0.554659	+	0.832078i	$0.687151\pi$
$614$		−	152.687i		−	0.248676i
$615$	240.132	−	112.090i	0.390458	−	0.182261i
$616$			234.114i			0.380056i
$617$	−420.256	+	420.256i	−0.681128	+	0.681128i	−0.960254	−	0.279126i	$-0.909955\pi$
$617$	−420.256	+	420.256i	−0.681128	+	0.681128i	0.279126	+	0.960254i	$0.409955\pi$
$618$	308.578	+	308.578i	0.499318	+	0.499318i
$619$	1004.33			1.62250			0.811249	−	0.584701i	$-0.198788\pi$
$619$	1004.33			1.62250			0.811249	+	0.584701i	$0.198788\pi$
$620$	−53.5390	+	147.278i	−0.0863532	+	0.237544i
$621$	−160.482			−0.258425
$622$	326.720	−	326.720i	0.525273	−	0.525273i
$623$	−55.6653	+	55.6653i	−0.0893504	+	0.0893504i
$624$	284.524	−	863.369i	0.455968	−	1.38360i
$625$	109.499	+	615.333i	0.175199	+	0.984533i
$626$		−	615.878i		−	0.983831i
$627$	864.342	+	864.342i	1.37854	+	1.37854i
$628$	−39.0770	+	39.0770i	−0.0622245	+	0.0622245i
$629$	−264.713			−0.420848
$630$	−207.318	+	570.301i	−0.329077	+	0.905240i
$631$		−	143.995i		−	0.228201i	−0.993469	−	0.114100i	$-0.963601\pi$
$631$		−	143.995i		−	0.228201i	0.993469	−	0.114100i	$-0.0363986\pi$
$632$	−508.383	+	508.383i	−0.804403	+	0.804403i
$633$	−173.987	+	173.987i	−0.274861	+	0.274861i
$634$			261.701i			0.412778i
$635$	−593.882	+	277.216i	−0.935247	+	0.436561i
$636$	80.7103			0.126903
$637$	−212.795	−	421.989i	−0.334059	−	0.662463i
$638$	123.097	−	123.097i	0.192942	−	0.192942i
$639$	692.087			1.08308
$640$	−423.162	+	197.526i	−0.661190	+	0.308635i
$641$	−451.324			−0.704094			−0.352047	−	0.935982i	$-0.614514\pi$
$641$	−451.324			−0.704094			−0.352047	+	0.935982i	$0.614514\pi$
$642$	−434.586	+	434.586i	−0.676926	+	0.676926i
$643$	−28.7003	−	28.7003i	−0.0446350	−	0.0446350i	0.684437	−	0.729072i	$-0.260048\pi$
$643$	−28.7003	−	28.7003i	−0.0446350	−	0.0446350i	−0.729072	+	0.684437i	$0.760048\pi$
$644$	6.67766			0.0103690
$645$	862.967	+	313.710i	1.33793	+	0.486371i
$646$	864.674			1.33850
$647$	−744.210	−	744.210i	−1.15025	−	1.15025i	−0.986503	−	0.163744i	$-0.947643\pi$
$647$	−744.210	−	744.210i	−1.15025	−	1.15025i	−0.163744	−	0.986503i	$-0.552357\pi$
$648$	559.647	+	559.647i	0.863653	+	0.863653i
$649$			223.536i			0.344431i
$650$	−510.813	+	316.784i	−0.785866	+	0.487361i
$651$	1007.57			1.54772
$652$	−78.0302	+	78.0302i	−0.119678	+	0.119678i
$653$	−69.9151	+	69.9151i	−0.107068	+	0.107068i	−0.758611	−	0.651544i	$-0.774122\pi$
$653$	−69.9151	+	69.9151i	−0.107068	+	0.107068i	0.651544	+	0.758611i	$0.274122\pi$
$654$			552.633i			0.845005i
$655$	62.0598	−	170.717i	0.0947478	−	0.260637i
$656$		−	134.998i		−	0.205790i
$657$	1402.50	−	1402.50i	2.13470	−	2.13470i
$658$	−161.640	−	161.640i	−0.245653	−	0.245653i
$659$			654.497i			0.993167i	0.867989	+	0.496583i	$0.165412\pi$
$659$			654.497i			0.993167i	−0.867989	+	0.496583i	$0.834588\pi$
$660$	−49.9215	−	106.947i	−0.0756387	−	0.162041i
$661$		−	159.464i		−	0.241246i	−0.992698	−	0.120623i	$-0.961511\pi$
$661$		−	159.464i		−	0.241246i	0.992698	−	0.120623i	$-0.0384893\pi$
$662$	−167.068	−	167.068i	−0.252368	−	0.252368i
$663$	947.425	−	477.756i	1.42900	−	0.720597i
$664$			269.012i			0.405138i
$665$	−225.718	−	483.557i	−0.339426	−	0.727153i
$666$	−579.948			−0.870793
$667$	−27.7432	−	27.7432i	−0.0415940	−	0.0415940i
$668$	−37.2052	−	37.2052i	−0.0556964	−	0.0556964i
$669$	−1219.94			−1.82353
$670$	−475.430	−	172.830i	−0.709597	−	0.257956i
$671$			442.934i			0.660110i
$672$	−121.164	−	121.164i	−0.180303	−	0.180303i
$673$	−10.4801	+	10.4801i	−0.0155723	+	0.0155723i	−0.714850	−	0.699278i	$-0.753505\pi$
$673$	−10.4801	+	10.4801i	−0.0155723	+	0.0155723i	0.699278	+	0.714850i	$0.253505\pi$
$674$	−668.913			−0.992452
$675$	−108.896	−	1233.50i	−0.161328	−	1.82741i
$676$	78.7580	+	58.2339i	0.116506	+	0.0861448i
$677$	49.8492	+	49.8492i	0.0736324	+	0.0736324i	0.742964	−	0.669331i	$-0.233419\pi$
$677$	49.8492	+	49.8492i	0.0736324	+	0.0736324i	−0.669331	+	0.742964i	$0.733419\pi$
$678$	−1293.56	−	1293.56i	−1.90791	−	1.90791i
$679$		−	436.800i		−	0.643299i
$680$	−619.991	−	225.382i	−0.911751	−	0.331444i
$681$		−	1219.19i		−	1.79029i
$682$	549.695	−	549.695i	0.806005	−	0.806005i
$683$	94.2947	+	94.2947i	0.138060	+	0.138060i	0.772759	−	0.634699i	$-0.218876\pi$
$683$	94.2947	+	94.2947i	0.138060	+	0.138060i	−0.634699	+	0.772759i	$0.718876\pi$
$684$	−320.996			−0.469293
$685$	−313.827	−	672.313i	−0.458141	−	0.981478i
$686$	561.353			0.818299
$687$	−156.749	+	156.749i	−0.228164	+	0.228164i
$688$	330.755	−	330.755i	0.480749	−	0.480749i
$689$	108.142	−	328.150i	0.156955	−	0.476271i
$690$	142.247	−	66.3992i	0.206156	−	0.0962308i
$691$		−	433.267i		−	0.627014i	−0.949586	−	0.313507i	$-0.898496\pi$
$691$		−	433.267i		−	0.627014i	0.949586	−	0.313507i	$-0.101504\pi$
$692$	−41.0146	−	41.0146i	−0.0592697	−	0.0592697i
$693$	−360.681	+	360.681i	−0.520463	+	0.520463i
$694$	689.392			0.993360
$695$	894.628	+	325.219i	1.28723	+	0.467941i
$696$			537.395i			0.772120i
$697$	111.422	−	111.422i	0.159860	−	0.159860i
$698$	−346.162	+	346.162i	−0.495934	+	0.495934i
$699$			65.5301i			0.0937484i
$700$	4.53118	+	51.3261i	0.00647312	+	0.0733230i
$701$	−786.537			−1.12202			−0.561011	−	0.827809i	$-0.689587\pi$
$701$	−786.537			−1.12202			−0.561011	+	0.827809i	$0.689587\pi$
$702$	1063.33	−	536.205i	1.51472	−	0.763824i
$703$	360.637	−	360.637i	0.512996	−	0.512996i
$704$	−547.156			−0.777210
$705$	855.793	+	311.102i	1.21389	+	0.441279i
$706$	629.055			0.891012
$707$	400.191	−	400.191i	0.566041	−	0.566041i
$708$	−61.7521	−	61.7521i	−0.0872204	−	0.0872204i
$709$	−776.234			−1.09483			−0.547415	−	0.836862i	$-0.684388\pi$
$709$	−776.234			−1.09483			−0.547415	+	0.836862i	$0.684388\pi$
$710$	−314.261	+	146.693i	−0.442621	+	0.206610i
$711$	−1566.45			−2.20316
$712$	−132.580	−	132.580i	−0.186208	−	0.186208i
$713$	−123.888	−	123.888i	−0.173757	−	0.173757i
$714$			536.797i			0.751816i
$715$	−501.712	+	59.6736i	−0.701696	+	0.0834596i
$716$	−66.7382			−0.0932098
$717$	510.931	−	510.931i	0.712595	−	0.712595i
$718$	606.222	−	606.222i	0.844320	−	0.844320i
$719$			1291.56i			1.79632i	0.439665	+	0.898162i	$0.355097\pi$
$719$			1291.56i			1.79632i	−0.439665	+	0.898162i	$0.644903\pi$
$720$	−1157.28	−	420.699i	−1.60733	−	0.584303i
$721$		−	160.145i		−	0.222115i
$722$	−705.906	+	705.906i	−0.977709	+	0.977709i
$723$	730.828	+	730.828i	1.01083	+	1.01083i
$724$		−	50.0241i		−	0.0690941i
$725$	194.415	−	232.066i	0.268159	−	0.320091i
$726$		−	587.035i		−	0.808588i
$727$	−16.1647	−	16.1647i	−0.0222347	−	0.0222347i	0.695902	−	0.718137i	$-0.255005\pi$
$727$	−16.1647	−	16.1647i	−0.0222347	−	0.0222347i	−0.718137	+	0.695902i	$0.755005\pi$
$728$	−349.608	+	176.296i	−0.480231	+	0.242165i
$729$		−	611.337i		−	0.838596i
$730$	−339.573	+	934.113i	−0.465168	+	1.27961i
$731$	545.984			0.746900
$732$	−122.361	−	122.361i	−0.167160	−	0.167160i
$733$	−539.313	−	539.313i	−0.735762	−	0.735762i	0.235993	−	0.971755i	$-0.424166\pi$
$733$	−539.313	−	539.313i	−0.735762	−	0.735762i	−0.971755	+	0.235993i	$0.924166\pi$
$734$	29.2227			0.0398129
$735$	−863.018	+	402.846i	−1.17417	+	0.548090i
$736$			29.7961i			0.0404838i
$737$	−300.681	−	300.681i	−0.407979	−	0.407979i
$738$	244.110	−	244.110i	0.330773	−	0.330773i
$739$	347.892			0.470760			0.235380	−	0.971903i	$-0.424367\pi$
$739$	347.892			0.470760			0.235380	+	0.971903i	$0.424367\pi$
$740$	−44.6224	+	20.8292i	−0.0603005	+	0.0281475i
$741$	−639.862	+	1941.62i	−0.863511	+	2.62027i
$742$	123.599	+	123.599i	0.166575	+	0.166575i
$743$	109.562	+	109.562i	0.147458	+	0.147458i	0.776982	−	0.629523i	$-0.216750\pi$
$743$	109.562	+	109.562i	0.147458	+	0.147458i	−0.629523	+	0.776982i	$0.716750\pi$
$744$			2399.76i			3.22549i
$745$	−212.456	+	584.433i	−0.285175	+	0.784473i
$746$		−	1102.08i		−	1.47732i
$747$	−414.445	+	414.445i	−0.554812	+	0.554812i
$748$	−49.6240	−	49.6240i	−0.0663423	−	0.0663423i
$749$	225.540			0.301122
$750$	606.883	+	1048.29i	0.809177	+	1.39772i
$751$	−344.182			−0.458298			−0.229149	−	0.973391i	$-0.573594\pi$
$751$	−344.182			−0.458298			−0.229149	+	0.973391i	$0.573594\pi$
$752$	328.006	−	328.006i	0.436178	−	0.436178i
$753$	1337.56	−	1337.56i	1.77630	−	1.77630i
$754$	276.519	+	91.1272i	0.366737	+	0.120858i
$755$	−1019.38	−	370.571i	−1.35018	−	0.490823i
$756$		−	102.087i		−	0.135035i
$757$	733.280	+	733.280i	0.968666	+	0.968666i	0.999524	−	0.0308578i	$-0.00982391\pi$
$757$	733.280	+	733.280i	0.968666	+	0.968666i	−0.0308578	+	0.999524i	$0.509824\pi$
$758$	205.121	−	205.121i	0.270609	−	0.270609i
$759$	131.956			0.173856
$760$	1151.71	−	537.602i	1.51540	−	0.707371i
$761$			1449.86i			1.90521i	0.304212	+	0.952604i	$0.401607\pi$
$761$			1449.86i			1.90521i	−0.304212	+	0.952604i	$0.598393\pi$
$762$	−898.166	+	898.166i	−1.17870	+	1.17870i
$763$	143.402	−	143.402i	0.187945	−	0.187945i
$764$			144.815i			0.189548i
$765$	−607.942	−	1302.40i	−0.794696	−	1.70248i
$766$	−1346.42			−1.75773
$767$	−333.811	+	168.330i	−0.435216	+	0.219465i
$768$	403.211	−	403.211i	0.525014	−	0.525014i
$769$	−1088.45			−1.41541			−0.707703	−	0.706510i	$-0.750269\pi$
$769$	−1088.45			−1.41541			−0.707703	+	0.706510i	$0.750269\pi$
$770$	87.3281	−	240.226i	0.113413	−	0.311982i
$771$	−1031.74			−1.33819
$772$	−54.1500	+	54.1500i	−0.0701425	+	0.0701425i
$773$	−162.908	−	162.908i	−0.210748	−	0.210748i	0.593837	−	0.804585i	$-0.297612\pi$
$773$	−162.908	−	162.908i	−0.210748	−	0.210748i	−0.804585	+	0.593837i	$0.797612\pi$
$774$	1196.17			1.54544
$775$	868.170	−	1036.30i	1.12022	−	1.33716i
$776$	1040.34			1.34065
$777$	223.886	+	223.886i	0.288142	+	0.288142i
$778$	135.976	+	135.976i	0.174776	+	0.174776i
$779$			303.596i			0.389726i
$780$	122.114	−	155.084i	0.156556	−	0.198825i
$781$	−291.526			−0.373272
$782$	66.0035	−	66.0035i	0.0844035	−	0.0844035i
$783$	−424.131	+	424.131i	−0.541675	+	0.541675i
$784$			485.177i			0.618848i
$785$	432.005	−	201.654i	0.550325	−	0.256885i
$786$		−	352.044i		−	0.447893i
$787$	928.395	−	928.395i	1.17966	−	1.17966i	0.199834	−	0.979830i	$-0.435960\pi$
$787$	928.395	−	928.395i	1.17966	−	1.17966i	0.979830	−	0.199834i	$-0.0640402\pi$
$788$	125.033	+	125.033i	0.158671	+	0.158671i
$789$		−	1048.99i		−	1.32952i
$790$	711.289	−	332.021i	0.900366	−	0.420279i
$791$			671.328i			0.848708i
$792$	−859.049	−	859.049i	−1.08466	−	1.08466i
$793$	−661.443	+	333.544i	−0.834102	+	0.420611i
$794$		−	189.163i		−	0.238241i
$795$	−654.386	−	237.885i	−0.823126	−	0.299227i
$796$	48.8559			0.0613768
$797$	825.935	+	825.935i	1.03631	+	1.03631i	0.999316	+	0.0369899i	$0.0117769\pi$
$797$	825.935	+	825.935i	1.03631	+	1.03631i	0.0369899	+	0.999316i	$0.488223\pi$
$798$	−731.315	−	731.315i	−0.916434	−	0.916434i
$799$	541.445			0.677654
$800$	−229.020	+	20.2184i	−0.286275	+	0.0252730i
$801$		−	408.512i		−	0.510002i
$802$	−707.873	−	707.873i	−0.882634	−	0.882634i
$803$	−590.770	+	590.770i	−0.735704	+	0.735704i
$804$	166.127			0.206625
$805$	−54.1414	−	19.6817i	−0.0672564	−	0.0244493i
$806$	1234.81	+	406.933i	1.53202	+	0.504879i
$807$	722.254	+	722.254i	0.894987	+	0.894987i
$808$	953.152	+	953.152i	1.17964	+	1.17964i
$809$			838.884i			1.03694i	0.855096	+	0.518470i	$0.173498\pi$
$809$			838.884i			1.03694i	−0.855096	+	0.518470i	$0.826502\pi$
$810$	−365.501	−	783.014i	−0.451236	−	0.966684i
$811$			664.797i			0.819725i	0.912147	+	0.409862i	$0.134423\pi$
$811$			664.797i			0.819725i	−0.912147	+	0.409862i	$0.865577\pi$
$812$	17.6482	−	17.6482i	0.0217342	−	0.0217342i
$813$	52.1273	+	52.1273i	0.0641172	+	0.0641172i
$814$	244.290			0.300110
$815$	862.642	−	402.670i	1.05846	−	0.494074i
$816$	−1089.29			−1.33491
$817$	−743.831	+	743.831i	−0.910442	+	0.910442i
$818$	232.799	−	232.799i	0.284596	−	0.284596i
$819$	−810.218	−	267.008i	−0.989277	−	0.326017i
$820$	10.0150	−	27.5497i	0.0122134	−	0.0335972i
$821$		−	1007.42i		−	1.22706i	−0.789672	−	0.613529i	$-0.789749\pi$
$821$		−	1007.42i		−	1.22706i	0.789672	−	0.613529i	$-0.210251\pi$
$822$	−1016.78	−	1016.78i	−1.23696	−	1.23696i
$823$	563.739	−	563.739i	0.684981	−	0.684981i	−0.276137	−	0.961118i	$-0.589054\pi$
$823$	563.739	−	563.739i	0.684981	−	0.684981i	0.961118	+	0.276137i	$0.0890545\pi$
$824$	381.424			0.462893
$825$	89.5400	+	1014.25i	0.108533	+	1.22939i
$826$		−	189.132i		−	0.228974i
$827$	735.131	−	735.131i	0.888913	−	0.888913i	−0.105506	−	0.994419i	$-0.533646\pi$
$827$	735.131	−	735.131i	0.888913	−	0.888913i	0.994419	+	0.105506i	$0.0336462\pi$
$828$	−24.5027	+	24.5027i	−0.0295927	+	0.0295927i
$829$			629.637i			0.759513i	0.925086	+	0.379757i	$0.123992\pi$
$829$			629.637i			0.759513i	−0.925086	+	0.379757i	$0.876008\pi$
$830$	100.345	−	276.035i	0.120898	−	0.332572i
$831$	68.5603			0.0825034
$832$	−412.026	−	817.079i	−0.495224	−	0.982066i
$833$	−400.445	+	400.445i	−0.480726	+	0.480726i
$834$	1844.85			2.21205
$835$	191.995	+	411.312i	0.229934	+	0.492589i
$836$	135.212			0.161737
$837$	−1893.98	+	1893.98i	−2.26282	+	2.26282i
$838$	364.633	+	364.633i	0.435123	+	0.435123i
$839$	326.568			0.389235			0.194617	−	0.980879i	$-0.437653\pi$
$839$	326.568			0.389235			0.194617	+	0.980879i	$0.437653\pi$
$840$	333.748	+	714.990i	0.397319	+	0.851178i
$841$	694.357			0.825633
$842$	−1029.53	−	1029.53i	−1.22272	−	1.22272i
$843$	−799.734	−	799.734i	−0.948677	−	0.948677i
$844$			27.2175i			0.0322482i
$845$	−466.918	−	704.282i	−0.552566	−	0.833469i
$846$	1186.23			1.40216
$847$	−152.329	+	152.329i	−0.179845	+	0.179845i
$848$	−250.811	+	250.811i	−0.295768	+	0.295768i
$849$		−	1491.08i		−	1.75627i
$850$	552.106	+	462.531i	0.649536	+	0.544154i
$851$		−	55.0572i		−	0.0646971i
$852$	80.5343	−	80.5343i	0.0945239	−	0.0945239i
$853$	−616.178	−	616.178i	−0.722366	−	0.722366i	0.246721	−	0.969087i	$-0.420647\pi$
$853$	−616.178	−	616.178i	−0.722366	−	0.722366i	−0.969087	+	0.246721i	$0.920647\pi$
$854$		−	374.764i		−	0.438833i
$855$	2602.58	+	946.103i	3.04396	+	1.10655i
$856$			537.179i			0.627545i
$857$	−400.795	−	400.795i	−0.467673	−	0.467673i	0.433487	−	0.901160i	$-0.357283\pi$
$857$	−400.795	−	400.795i	−0.467673	−	0.467673i	−0.901160	+	0.433487i	$0.857283\pi$
$858$	−874.328	+	440.895i	−1.01903	+	0.513864i
$859$		−	751.068i		−	0.874351i	−0.899376	−	0.437176i	$-0.855979\pi$
$859$		−	751.068i		−	0.874351i	0.899376	−	0.437176i	$-0.144021\pi$
$860$	92.0359	−	42.9612i	0.107019	−	0.0499549i
$861$	−188.475			−0.218903
$862$	411.206	+	411.206i	0.477037	+	0.477037i
$863$	606.098	+	606.098i	0.702315	+	0.702315i	0.964907	−	0.262592i	$-0.0845773\pi$
$863$	606.098	+	606.098i	0.702315	+	0.702315i	−0.262592	+	0.964907i	$0.584577\pi$
$864$	455.516			0.527218
$865$	211.653	+	453.426i	0.244686	+	0.524192i
$866$			385.406i			0.445042i
$867$	171.677	+	171.677i	0.198012	+	0.198012i
$868$	78.8087	−	78.8087i	0.0907934	−	0.0907934i
$869$	659.831			0.759299
$870$	200.456	−	551.425i	0.230410	−	0.633822i
$871$	222.590	−	675.435i	0.255557	−	0.775471i
$872$	341.546	+	341.546i	0.391682	+	0.391682i
$873$	1602.78	+	1602.78i	1.83594	+	1.83594i
$874$			179.842i			0.205769i
$875$	114.540	−	429.498i	0.130903	−	0.490855i
$876$		−	326.402i		−	0.372605i
$877$	−685.799	+	685.799i	−0.781983	+	0.781983i	−0.980165	−	0.198182i	$-0.936496\pi$
$877$	−685.799	+	685.799i	−0.781983	+	0.781983i	0.198182	+	0.980165i	$0.436496\pi$
$878$	78.0358	+	78.0358i	0.0888791	+	0.0888791i
$879$	−1804.78			−2.05322
$880$	487.476	+	177.210i	0.553950	+	0.201374i
$881$	540.457			0.613458			0.306729	−	0.951797i	$-0.400765\pi$
$881$	540.457			0.613458			0.306729	+	0.951797i	$0.400765\pi$
$882$	−877.318	+	877.318i	−0.994691	+	0.994691i
$883$	335.688	−	335.688i	0.380168	−	0.380168i	−0.490995	−	0.871162i	$-0.663367\pi$
$883$	335.688	−	335.688i	0.380168	−	0.380168i	0.871162	+	0.490995i	$0.163367\pi$
$884$	36.7360	−	111.473i	0.0415566	−	0.126101i
$885$	318.668	+	682.683i	0.360076	+	0.771393i
$886$			1141.98i			1.28891i
$887$	−783.772	−	783.772i	−0.883621	−	0.883621i	0.110280	−	0.993901i	$-0.464825\pi$
$887$	−783.772	−	783.772i	−0.883621	−	0.883621i	−0.993901	+	0.110280i	$0.964825\pi$
$888$	−533.239	+	533.239i	−0.600495	+	0.600495i
$889$	466.128			0.524328
$890$	86.5871	+	185.496i	0.0972889	+	0.208422i
$891$		−	726.366i		−	0.815226i
$892$	−95.4198	+	95.4198i	−0.106973	+	0.106973i
$893$	−737.647	+	737.647i	−0.826033	+	0.826033i
$894$			1205.19i			1.34808i
$895$	541.103	+	196.704i	0.604584	+	0.219781i
$896$	332.132			0.370683
$897$	99.3676	+	197.053i	0.110778	+	0.219680i
$898$	−126.435	+	126.435i	−0.140797	+	0.140797i
$899$	−654.841			−0.728411
$900$	−204.960	−	171.707i	−0.227734	−	0.190786i
$901$	−414.018			−0.459510
$902$	−102.826	+	102.826i	−0.113998	+	0.113998i
$903$	−461.777	−	461.777i	−0.511380	−	0.511380i
$904$	−1598.93			−1.76873
$905$	−147.441	+	405.587i	−0.162918	+	0.448163i
$906$	−2102.12			−2.32022
$907$	−549.601	−	549.601i	−0.605955	−	0.605955i	0.335931	−	0.941886i	$-0.390949\pi$
$907$	−549.601	−	549.601i	−0.605955	−	0.605955i	−0.941886	+	0.335931i	$0.890949\pi$
$908$	−95.3612	−	95.3612i	−0.105023	−	0.105023i
$909$			2936.89i			3.23090i
$910$	424.496	−	50.4895i	0.466479	−	0.0554830i
$911$	−1456.76			−1.59908			−0.799541	−	0.600612i	$-0.794924\pi$
$911$	−1456.76			−1.59908			−0.799541	+	0.600612i	$0.794924\pi$
$912$	1484.01	−	1484.01i	1.62721	−	1.62721i
$913$	174.575	−	174.575i	0.191211	−	0.191211i
$914$		−	1428.66i		−	1.56308i
$915$	631.437	+	1352.73i	0.690095	+	1.47839i
$916$			24.5208i			0.0267694i
$917$	−91.3513	+	91.3513i	−0.0996197	+	0.0996197i
$918$	−1009.05	−	1009.05i	−1.09918	−	1.09918i
$919$		−	496.540i		−	0.540305i	−0.962818	−	0.270152i	$-0.912926\pi$
$919$		−	496.540i		−	0.540305i	0.962818	−	0.270152i	$-0.0870741\pi$
$920$	46.8768	−	128.951i	0.0509530	−	0.140164i
$921$		−	432.575i		−	0.469679i
$922$	365.942	+	365.942i	0.396900	+	0.396900i
$923$	−219.529	−	435.341i	−0.237842	−	0.471659i
$924$			83.9409i			0.0908451i
$925$	423.183	−	37.3595i	0.457495	−	0.0403887i
$926$	657.155			0.709671
$927$	587.630	+	587.630i	0.633905	+	0.633905i
$928$	78.7471	+	78.7471i	0.0848568	+	0.0848568i
$929$	1162.92			1.25180			0.625901	−	0.779903i	$-0.284732\pi$
$929$	1162.92			1.25180			0.625901	+	0.779903i	$0.284732\pi$
$930$	895.147	−	2462.41i	0.962524	−	2.64776i
$931$		−	1091.11i		−	1.17197i
$932$	5.12556	+	5.12556i	0.00549953	+	0.00549953i
$933$	925.622	−	925.622i	0.992092	−	0.992092i
$934$	−571.942			−0.612358
$935$	256.082	+	548.605i	0.273884	+	0.586743i
$936$	635.944	−	1929.73i	0.679427	−	2.06168i
$937$	236.759	+	236.759i	0.252677	+	0.252677i	0.822067	−	0.569390i	$-0.192821\pi$
$937$	236.759	+	236.759i	0.252677	+	0.252677i	−0.569390	+	0.822067i	$0.692821\pi$
$938$	254.404	+	254.404i	0.271220	+	0.271220i
$939$		−	1744.83i		−	1.85818i
$940$	91.2708	−	42.6041i	0.0970966	−	0.0453235i
$941$		−	829.678i		−	0.881699i	−0.897581	−	0.440849i	$-0.854677\pi$
$941$		−	829.678i		−	0.881699i	0.897581	−	0.440849i	$-0.145323\pi$
$942$	653.349	−	653.349i	0.693577	−	0.693577i
$943$	23.1745	+	23.1745i	0.0245753	+	0.0245753i
$944$	383.795			0.406562
$945$	−300.890	+	827.701i	−0.318402	+	0.875874i
$946$	−503.860			−0.532622
$947$	51.0146	−	51.0146i	0.0538697	−	0.0538697i	−0.679659	−	0.733528i	$-0.737872\pi$
$947$	51.0146	−	51.0146i	0.0538697	−	0.0538697i	0.733528	+	0.679659i	$0.237872\pi$
$948$	−182.279	+	182.279i	−0.192277	+	0.192277i
$949$	−1327.08	−	437.340i	−1.39840	−	0.460843i
$950$	−1382.31	+	122.033i	−1.45506	+	0.128456i
$951$			741.420i			0.779621i
$952$	331.759	+	331.759i	0.348486	+	0.348486i
$953$	437.752	−	437.752i	0.459341	−	0.459341i	−0.439098	−	0.898439i	$-0.644702\pi$
$953$	437.752	−	437.752i	0.459341	−	0.459341i	0.898439	+	0.439098i	$0.144702\pi$
$954$	−907.054			−0.950791
$955$	426.827	−	1174.14i	0.446939	−	1.22946i
$956$		−	79.9268i		−	0.0836054i
$957$	348.743	−	348.743i	0.364413	−	0.364413i
$958$	−900.045	+	900.045i	−0.939504	+	0.939504i
$959$			527.686i			0.550247i
$960$	−1671.02	+	780.012i	−1.74065	+	0.812513i
$961$	−1963.22			−2.04290
$962$	183.958	+	364.803i	0.191225	+	0.379213i
$963$	−827.588	+	827.588i	−0.859385	+	0.859385i
$964$	114.326			0.118596
$965$	598.641	−	279.438i	0.620353	−	0.289573i
$966$	−111.647			−0.115577
$967$	−635.405	+	635.405i	−0.657089	+	0.657089i	−0.954690	−	0.297601i	$-0.903813\pi$
$967$	−635.405	+	635.405i	−0.657089	+	0.657089i	0.297601	+	0.954690i	$0.403813\pi$
$968$	−362.808	−	362.808i	−0.374801	−	0.374801i
$969$	2449.69			2.52806
$970$	−1067.50	−	388.064i	−1.10052	−	0.400066i
$971$	1240.59			1.27764			0.638822	−	0.769354i	$-0.279422\pi$
$971$	1240.59			1.27764			0.638822	+	0.769354i	$0.279422\pi$
$972$	17.9651	+	17.9651i	0.0184826	+	0.0184826i
$973$	−478.718	−	478.718i	−0.492002	−	0.492002i
$974$			870.380i			0.893614i
$975$	−1447.17	+	897.474i	−1.48428	+	0.920486i
$976$	760.485			0.779186
$977$	128.037	−	128.037i	0.131051	−	0.131051i	−0.638539	−	0.769590i	$-0.720461\pi$
$977$	128.037	−	128.037i	0.131051	−	0.131051i	0.769590	+	0.638539i	$0.220461\pi$
$978$	1304.63	−	1304.63i	1.33398	−	1.33398i
$979$			172.076i			0.175767i
$980$	−35.9933	+	99.0119i	−0.0367278	+	0.101033i
$981$			1052.39i			1.07277i
$982$	−584.327	+	584.327i	−0.595037	+	0.595037i
$983$	−320.204	−	320.204i	−0.325742	−	0.325742i	0.525223	−	0.850965i	$-0.323982\pi$
$983$	−320.204	−	320.204i	−0.325742	−	0.325742i	−0.850965	+	0.525223i	$0.823982\pi$
$984$		−	448.899i		−	0.456198i
$985$	−645.223	−	1382.26i	−0.655048	−	1.40331i
$986$		−	348.877i		−	0.353830i
$987$	−457.938	−	457.938i	−0.463969	−	0.463969i
$988$	101.819	+	201.915i	0.103056	+	0.204368i
$989$			113.558i			0.114821i
$990$	561.038	+	1201.91i	0.566705	+	1.21405i
$991$	−171.042			−0.172595			−0.0862977	−	0.996269i	$-0.527504\pi$
$991$	−171.042			−0.172595			−0.0862977	+	0.996269i	$0.527504\pi$
$992$	351.649	+	351.649i	0.354485	+	0.354485i
$993$	−473.316	−	473.316i	−0.476653	−	0.476653i
$994$	246.658			0.248147
$995$	−396.115	−	143.998i	−0.398106	−	0.144721i
$996$			96.4532i			0.0968406i
$997$	1012.25	+	1012.25i	1.01530	+	1.01530i	0.999881	+	0.0154174i	$0.00490770\pi$
$997$	1012.25	+	1012.25i	1.01530	+	1.01530i	0.0154174	+	0.999881i	$0.495092\pi$
$998$	−934.821	+	934.821i	−0.936694	+	0.936694i
$999$	−841.702			−0.842545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.3.h.a.12.4	✓	24
5.2	odd	4		325.3.h.b.168.4		24
5.3	odd	4	inner	65.3.h.a.38.9	yes	24
5.4	even	2		325.3.h.b.207.9		24
13.12	even	2	inner	65.3.h.a.12.9	yes	24
65.12	odd	4		325.3.h.b.168.9		24
65.38	odd	4	inner	65.3.h.a.38.4	yes	24
65.64	even	2		325.3.h.b.207.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.h.a.12.4	✓	24	1.1	even	1	trivial
65.3.h.a.12.9	yes	24	13.12	even	2	inner
65.3.h.a.38.4	yes	24	65.38	odd	4	inner
65.3.h.a.38.9	yes	24	5.3	odd	4	inner
325.3.h.b.168.4		24	5.2	odd	4
325.3.h.b.168.9		24	65.12	odd	4
325.3.h.b.207.4		24	65.64	even	2
325.3.h.b.207.9		24	5.4	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)

\(f(q)\)	\(=\)	\(q+(-1.30775 + 1.30775i) q^{2} +(-3.70495 + 3.70495i) q^{3} +0.579580i q^{4} +(1.70825 - 4.69914i) q^{5} -9.69031i q^{6} +(-2.51452 + 2.51452i) q^{7} +(-5.98895 - 5.98895i) q^{8} -18.4534i q^{9} +O(q^{10})\)	\(q+(-1.30775 + 1.30775i) q^{2} +(-3.70495 + 3.70495i) q^{3} +0.579580i q^{4} +(1.70825 - 4.69914i) q^{5} -9.69031i q^{6} +(-2.51452 + 2.51452i) q^{7} +(-5.98895 - 5.98895i) q^{8} -18.4534i q^{9} +(3.91133 + 8.37926i) q^{10} +7.77306i q^{11} +(-2.14732 - 2.14732i) q^{12} +(-11.6077 + 5.85337i) q^{13} -6.57674i q^{14} +(11.0811 + 23.7391i) q^{15} +13.3458 q^{16} +(11.0151 + 11.0151i) q^{17} +(24.1324 + 24.1324i) q^{18} -30.0131 q^{19} +(2.72352 + 0.990068i) q^{20} -18.6324i q^{21} +(-10.1652 - 10.1652i) q^{22} +(-2.29100 + 2.29100i) q^{23} +44.3775 q^{24} +(-19.1638 - 16.0546i) q^{25} +(7.52518 - 22.8347i) q^{26} +(35.0243 + 35.0243i) q^{27} +(-1.45737 - 1.45737i) q^{28} +12.1096i q^{29} +(-45.5361 - 16.5535i) q^{30} +54.0761i q^{31} +(6.50285 - 6.50285i) q^{32} +(-28.7988 - 28.7988i) q^{33} -28.8099 q^{34} +(7.52065 + 16.1115i) q^{35} +10.6952 q^{36} +(-12.0160 + 12.0160i) q^{37} +(39.2496 - 39.2496i) q^{38} +(21.3194 - 64.6924i) q^{39} +(-38.3735 + 17.9123i) q^{40} -10.1155i q^{41} +(24.3665 + 24.3665i) q^{42} +(24.7835 - 24.7835i) q^{43} -4.50511 q^{44} +(-86.7149 - 31.5230i) q^{45} -5.99212i q^{46} +(24.5775 - 24.5775i) q^{47} +(-49.4455 + 49.4455i) q^{48} +36.3543i q^{49} +(46.0568 - 4.06600i) q^{50} -81.6206 q^{51} +(-3.39250 - 6.72757i) q^{52} +(-18.7933 + 18.7933i) q^{53} -91.6061 q^{54} +(36.5267 + 13.2783i) q^{55} +30.1187 q^{56} +(111.197 - 111.197i) q^{57} +(-15.8364 - 15.8364i) q^{58} +28.7578 q^{59} +(-13.7587 + 6.42238i) q^{60} +56.9832 q^{61} +(-70.7180 - 70.7180i) q^{62} +(46.4014 + 46.4014i) q^{63} +70.3913i q^{64} +(7.67698 + 64.5451i) q^{65} +75.3233 q^{66} +(-38.6824 + 38.6824i) q^{67} +(-6.38410 + 6.38410i) q^{68} -16.9761i q^{69} +(-30.9050 - 11.2347i) q^{70} +37.5046i q^{71} +(-110.516 + 110.516i) q^{72} +(76.0023 + 76.0023i) q^{73} -31.4278i q^{74} +(130.482 - 11.5193i) q^{75} -17.3950i q^{76} +(-19.5455 - 19.5455i) q^{77} +(56.7210 + 112.482i) q^{78} -84.8869i q^{79} +(22.7979 - 62.7136i) q^{80} -93.4467 q^{81} +(13.2285 + 13.2285i) q^{82} +(-22.4590 - 22.4590i) q^{83} +10.7990 q^{84} +(70.5777 - 32.9448i) q^{85} +64.8213i q^{86} +(-44.8656 - 44.8656i) q^{87} +(46.5524 - 46.5524i) q^{88} +22.1375 q^{89} +(154.626 - 72.1772i) q^{90} +(14.4693 - 43.9062i) q^{91} +(-1.32782 - 1.32782i) q^{92} +(-200.349 - 200.349i) q^{93} +64.2825i q^{94} +(-51.2699 + 141.036i) q^{95} +48.1856i q^{96} +(-86.8554 + 86.8554i) q^{97} +(-47.5424 - 47.5424i) q^{98} +143.439 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

Varieties

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Representations

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Database

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