LMFDB - Embedded newform 65.3.h.a.12.3

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			12.3
Character	$\chi$	$=$	65.12
Dual form			65.3.h.a.38.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78036 + 1.78036i) q^{2} +(0.433767 - 0.433767i) q^{3} -2.33933i q^{4} +(3.33534 + 3.72498i) q^{5} +1.54452i q^{6} +(-5.63522 + 5.63522i) q^{7} +(-2.95658 - 2.95658i) q^{8} +8.62369i q^{9} +O(q^{10})$	\(q+(-1.78036 + 1.78036i) q^{2} +(0.433767 - 0.433767i) q^{3} -2.33933i q^{4} +(3.33534 + 3.72498i) q^{5} +1.54452i q^{6} +(-5.63522 + 5.63522i) q^{7} +(-2.95658 - 2.95658i) q^{8} +8.62369i q^{9} +(-12.5699 - 0.693690i) q^{10} -7.95860i q^{11} +(-1.01472 - 1.01472i) q^{12} +(-7.09417 + 10.8937i) q^{13} -20.0654i q^{14} +(3.06254 + 0.169011i) q^{15} +19.8849 q^{16} +(4.22084 + 4.22084i) q^{17} +(-15.3532 - 15.3532i) q^{18} +28.4044 q^{19} +(8.71395 - 7.80247i) q^{20} +4.88875i q^{21} +(14.1691 + 14.1691i) q^{22} +(16.8593 - 16.8593i) q^{23} -2.56494 q^{24} +(-2.75095 + 24.8482i) q^{25} +(-6.76452 - 32.0248i) q^{26} +(7.64458 + 7.64458i) q^{27} +(13.1826 + 13.1826i) q^{28} -50.7219i q^{29} +(-5.75331 + 5.15151i) q^{30} -5.26889i q^{31} +(-23.5758 + 23.5758i) q^{32} +(-3.45218 - 3.45218i) q^{33} -15.0292 q^{34} +(-39.7865 - 2.19568i) q^{35} +20.1736 q^{36} +(16.4223 - 16.4223i) q^{37} +(-50.5700 + 50.5700i) q^{38} +(1.64811 + 7.80255i) q^{39} +(1.15199 - 20.8744i) q^{40} +61.6304i q^{41} +(-8.70370 - 8.70370i) q^{42} +(-18.6744 + 18.6744i) q^{43} -18.6178 q^{44} +(-32.1231 + 28.7630i) q^{45} +60.0309i q^{46} +(21.8727 - 21.8727i) q^{47} +(8.62540 - 8.62540i) q^{48} -14.5113i q^{49} +(-39.3409 - 49.1363i) q^{50} +3.66173 q^{51} +(25.4840 + 16.5956i) q^{52} +(38.2818 - 38.2818i) q^{53} -27.2201 q^{54} +(29.6456 - 26.5447i) q^{55} +33.3220 q^{56} +(12.3209 - 12.3209i) q^{57} +(90.3030 + 90.3030i) q^{58} +12.8470 q^{59} +(0.395373 - 7.16428i) q^{60} -45.4020 q^{61} +(9.38049 + 9.38049i) q^{62} +(-48.5964 - 48.5964i) q^{63} -4.40705i q^{64} +(-64.2403 + 9.90861i) q^{65} +12.2922 q^{66} +(22.7910 - 22.7910i) q^{67} +(9.87393 - 9.87393i) q^{68} -14.6260i q^{69} +(74.7431 - 66.9249i) q^{70} -0.496956i q^{71} +(25.4967 - 25.4967i) q^{72} +(18.8385 + 18.8385i) q^{73} +58.4750i q^{74} +(9.58506 + 11.9716i) q^{75} -66.4473i q^{76} +(44.8484 + 44.8484i) q^{77} +(-16.8255 - 10.9571i) q^{78} +73.0902i q^{79} +(66.3228 + 74.0707i) q^{80} -70.9813 q^{81} +(-109.724 - 109.724i) q^{82} +(-70.8434 - 70.8434i) q^{83} +11.4364 q^{84} +(-1.64459 + 29.8005i) q^{85} -66.4941i q^{86} +(-22.0015 - 22.0015i) q^{87} +(-23.5303 + 23.5303i) q^{88} -2.26468 q^{89} +(5.98216 - 108.399i) q^{90} +(-21.4112 - 101.366i) q^{91} +(-39.4393 - 39.4393i) q^{92} +(-2.28547 - 2.28547i) q^{93} +77.8822i q^{94} +(94.7386 + 105.806i) q^{95} +20.4528i q^{96} +(-85.2235 + 85.2235i) q^{97} +(25.8353 + 25.8353i) q^{98} +68.6325 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 $

$2$	−1.78036	+	1.78036i	−0.890178	+	0.890178i	−0.994539	−	0.104362i	$-0.966720\pi$
$2$	−1.78036	+	1.78036i	−0.890178	+	0.890178i	0.104362	+	0.994539i	$0.466720\pi$
$3$	0.433767	−	0.433767i	0.144589	−	0.144589i	−0.631107	−	0.775696i	$-0.717399\pi$
$3$	0.433767	−	0.433767i	0.144589	−	0.144589i	0.775696	+	0.631107i	$0.217399\pi$
$4$		−	2.33933i		−	0.584832i
$5$	3.33534	+	3.72498i	0.667069	+	0.744996i
$5$	3.33534	+	3.72498i	0.667069	+	0.744996i
$6$			1.54452i			0.257420i
$7$	−5.63522	+	5.63522i	−0.805031	+	0.805031i	−0.983877	−	0.178846i	$-0.942764\pi$
$7$	−5.63522	+	5.63522i	−0.805031	+	0.805031i	0.178846	+	0.983877i	$0.442764\pi$
$8$	−2.95658	−	2.95658i	−0.369573	−	0.369573i
$9$			8.62369i			0.958188i
$10$	−12.5699	−	0.693690i	−1.25699	−	0.0693690i
$11$		−	7.95860i		−	0.723509i	−0.932273	−	0.361755i	$-0.882178\pi$
$11$		−	7.95860i		−	0.723509i	0.932273	−	0.361755i	$-0.117822\pi$
$12$	−1.01472	−	1.01472i	−0.0845604	−	0.0845604i
$13$	−7.09417	+	10.8937i	−0.545705	+	0.837977i
$13$	−7.09417	+	10.8937i	−0.545705	+	0.837977i
$14$		−	20.0654i		−	1.43324i
$15$	3.06254	+	0.169011i	0.204169	+	0.0112674i
$16$	19.8849			1.24280
$17$	4.22084	+	4.22084i	0.248285	+	0.248285i	0.820266	−	0.571982i	$-0.193825\pi$
$17$	4.22084	+	4.22084i	0.248285	+	0.248285i	−0.571982	+	0.820266i	$0.693825\pi$
$18$	−15.3532	−	15.3532i	−0.852957	−	0.852957i
$19$	28.4044			1.49497			0.747485	−	0.664279i	$-0.231261\pi$
$19$	28.4044			1.49497			0.747485	+	0.664279i	$0.231261\pi$
$20$	8.71395	−	7.80247i	0.435698	−	0.390123i
$21$			4.88875i			0.232797i
$22$	14.1691	+	14.1691i	0.644052	+	0.644052i
$23$	16.8593	−	16.8593i	0.733011	−	0.733011i	−0.238204	−	0.971215i	$-0.576559\pi$
$23$	16.8593	−	16.8593i	0.733011	−	0.733011i	0.971215	+	0.238204i	$0.0765587\pi$
$24$	−2.56494			−0.106873
$25$	−2.75095	+	24.8482i	−0.110038	+	0.993927i
$26$	−6.76452	−	32.0248i	−0.260174	−	1.23172i
$27$	7.64458	+	7.64458i	0.283133	+	0.283133i
$28$	13.1826	+	13.1826i	0.470808	+	0.470808i
$29$		−	50.7219i		−	1.74903i	−0.484998	−	0.874515i	$-0.661180\pi$
$29$		−	50.7219i		−	1.74903i	0.484998	−	0.874515i	$-0.338820\pi$
$30$	−5.75331	+	5.15151i	−0.191777	+	0.171717i
$31$		−	5.26889i		−	0.169964i	−0.996382	−	0.0849821i	$-0.972917\pi$
$31$		−	5.26889i		−	0.169964i	0.996382	−	0.0849821i	$-0.0270833\pi$
$32$	−23.5758	+	23.5758i	−0.736743	+	0.736743i
$33$	−3.45218	−	3.45218i	−0.104612	−	0.104612i
$34$	−15.0292			−0.442035
$35$	−39.7865	−	2.19568i	−1.13676	−	0.0627337i
$36$	20.1736			0.560379
$37$	16.4223	−	16.4223i	0.443845	−	0.443845i	−0.449457	−	0.893302i	$-0.648382\pi$
$37$	16.4223	−	16.4223i	0.443845	−	0.443845i	0.893302	+	0.449457i	$0.148382\pi$
$38$	−50.5700	+	50.5700i	−1.33079	+	1.33079i
$39$	1.64811	+	7.80255i	0.0422593	+	0.200065i
$40$	1.15199	−	20.8744i	0.0287998	−	0.521861i
$41$			61.6304i			1.50318i	0.659631	+	0.751590i	$0.270713\pi$
$41$			61.6304i			1.50318i	−0.659631	+	0.751590i	$0.729287\pi$
$42$	−8.70370	−	8.70370i	−0.207231	−	0.207231i
$43$	−18.6744	+	18.6744i	−0.434288	+	0.434288i	−0.890084	−	0.455796i	$-0.849355\pi$
$43$	−18.6744	+	18.6744i	−0.434288	+	0.434288i	0.455796	+	0.890084i	$0.349355\pi$
$44$	−18.6178			−0.423131
$45$	−32.1231	+	28.7630i	−0.713846	+	0.639177i
$46$			60.0309i			1.30502i
$47$	21.8727	−	21.8727i	0.465376	−	0.465376i	−0.435037	−	0.900413i	$-0.643265\pi$
$47$	21.8727	−	21.8727i	0.465376	−	0.465376i	0.900413	+	0.435037i	$0.143265\pi$
$48$	8.62540	−	8.62540i	0.179696	−	0.179696i
$49$		−	14.5113i		−	0.296149i
$50$	−39.3409	−	49.1363i	−0.786818	−	0.982725i
$51$	3.66173			0.0717985
$52$	25.4840	+	16.5956i	0.490076	+	0.319146i
$53$	38.2818	−	38.2818i	0.722298	−	0.722298i	−0.246775	−	0.969073i	$-0.579371\pi$
$53$	38.2818	−	38.2818i	0.722298	−	0.722298i	0.969073	+	0.246775i	$0.0793708\pi$
$54$	−27.2201			−0.504077
$55$	29.6456	−	26.5447i	0.539011	−	0.482630i
$56$	33.3220			0.595036
$57$	12.3209	−	12.3209i	0.216156	−	0.216156i
$58$	90.3030	+	90.3030i	1.55695	+	1.55695i
$59$	12.8470			0.217746			0.108873	−	0.994056i	$-0.465276\pi$
$59$	12.8470			0.217746			0.108873	+	0.994056i	$0.465276\pi$
$60$	0.395373	−	7.16428i	0.00658955	−	0.119405i
$61$	−45.4020			−0.744296			−0.372148	−	0.928173i	$-0.621379\pi$
$61$	−45.4020			−0.744296			−0.372148	+	0.928173i	$0.621379\pi$
$62$	9.38049	+	9.38049i	0.151298	+	0.151298i
$63$	−48.5964	−	48.5964i	−0.771371	−	0.771371i
$64$		−	4.40705i		−	0.0688601i
$65$	−64.2403	+	9.90861i	−0.988313	+	0.152440i
$66$	12.2922			0.186246
$67$	22.7910	−	22.7910i	0.340164	−	0.340164i	−0.516265	−	0.856429i	$-0.672678\pi$
$67$	22.7910	−	22.7910i	0.340164	−	0.340164i	0.856429	+	0.516265i	$0.172678\pi$
$68$	9.87393	−	9.87393i	0.145205	−	0.145205i
$69$		−	14.6260i		−	0.211971i
$70$	74.7431	−	66.9249i	1.06776	−	0.956070i
$71$		−	0.496956i		−	0.00699938i	−0.999994	−	0.00349969i	$-0.998886\pi$
$71$		−	0.496956i		−	0.00699938i	0.999994	−	0.00349969i	$-0.00111399\pi$
$72$	25.4967	−	25.4967i	0.354120	−	0.354120i
$73$	18.8385	+	18.8385i	0.258061	+	0.258061i	0.824265	−	0.566204i	$-0.191588\pi$
$73$	18.8385	+	18.8385i	0.258061	+	0.258061i	−0.566204	+	0.824265i	$0.691588\pi$
$74$			58.4750i			0.790203i
$75$	9.58506	+	11.9716i	0.127801	+	0.159621i
$76$		−	66.4473i		−	0.874306i
$77$	44.8484	+	44.8484i	0.582447	+	0.582447i
$78$	−16.8255	−	10.9571i	−0.215712	−	0.140475i
$79$			73.0902i			0.925192i	0.886569	+	0.462596i	$0.153082\pi$
$79$			73.0902i			0.925192i	−0.886569	+	0.462596i	$0.846918\pi$
$80$	66.3228	+	74.0707i	0.829036	+	0.925884i
$81$	−70.9813			−0.876312
$82$	−109.724	−	109.724i	−1.33810	−	1.33810i
$83$	−70.8434	−	70.8434i	−0.853536	−	0.853536i	0.137031	−	0.990567i	$-0.456244\pi$
$83$	−70.8434	−	70.8434i	−0.853536	−	0.853536i	−0.990567	+	0.137031i	$0.956244\pi$
$84$	11.4364			0.136147
$85$	−1.64459	+	29.8005i	−0.0193481	+	0.350594i
$86$		−	66.4941i		−	0.773187i
$87$	−22.0015	−	22.0015i	−0.252891	−	0.252891i
$88$	−23.5303	+	23.5303i	−0.267390	+	0.267390i
$89$	−2.26468			−0.0254459			−0.0127229	−	0.999919i	$-0.504050\pi$
$89$	−2.26468			−0.0254459			−0.0127229	+	0.999919i	$0.504050\pi$
$90$	5.98216	−	108.399i	0.0664685	−	1.20443i
$91$	−21.4112	−	101.366i	−0.235288	−	1.11391i
$92$	−39.4393	−	39.4393i	−0.428688	−	0.428688i
$93$	−2.28547	−	2.28547i	−0.0245750	−	0.0245750i
$94$			77.8822i			0.828534i
$95$	94.7386	+	105.806i	0.997248	+	1.11375i
$96$			20.4528i			0.213050i
$97$	−85.2235	+	85.2235i	−0.878593	+	0.878593i	−0.993389	−	0.114796i	$-0.963378\pi$
$97$	−85.2235	+	85.2235i	−0.878593	+	0.878593i	0.114796	+	0.993389i	$0.463378\pi$
$98$	25.8353	+	25.8353i	0.263626	+	0.263626i
$99$	68.6325			0.693258
$100$	58.1281	+	6.43538i	0.581281	+	0.0643538i
$101$	−30.6953			−0.303914			−0.151957	−	0.988387i	$-0.548557\pi$
$101$	−30.6953			−0.303914			−0.151957	+	0.988387i	$0.548557\pi$
$102$	−6.51917	+	6.51917i	−0.0639135	+	0.0639135i
$103$	120.944	−	120.944i	1.17421	−	1.17421i	0.193020	−	0.981195i	$-0.438172\pi$
$103$	120.944	−	120.944i	1.17421	−	1.17421i	0.981195	−	0.193020i	$-0.0618283\pi$
$104$	53.1827	−	11.2336i	0.511372	−	0.108016i
$105$	−18.2105	+	16.3057i	−0.173433	+	0.155292i
$106$			136.310i			1.28595i
$107$	92.6405	+	92.6405i	0.865799	+	0.865799i	0.992004	−	0.126205i	$-0.0402797\pi$
$107$	92.6405	+	92.6405i	0.865799	+	0.865799i	−0.126205	+	0.992004i	$0.540280\pi$
$108$	17.8832	−	17.8832i	0.165585	−	0.165585i
$109$	−116.041			−1.06460			−0.532298	−	0.846557i	$-0.678671\pi$
$109$	−116.041			−1.06460			−0.532298	+	0.846557i	$0.678671\pi$
$110$	−5.52080	+	100.039i	−0.0501891	+	0.909443i
$111$		−	14.2469i		−	0.128350i
$112$	−112.055	+	112.055i	−1.00050	+	1.00050i
$113$	67.8000	−	67.8000i	0.600000	−	0.600000i	−0.340313	−	0.940312i	$-0.610533\pi$
$113$	67.8000	−	67.8000i	0.600000	−	0.600000i	0.940312	+	0.340313i	$0.110533\pi$
$114$			43.8712i			0.384835i
$115$	119.032	+	6.56896i	1.03506	+	0.0571214i
$116$	−118.655			−1.02289
$117$	−93.9439	−	61.1779i	−0.802940	−	0.522888i
$118$	−22.8722	+	22.8722i	−0.193832	+	0.193832i
$119$	−47.5707			−0.399754
$120$	−8.55496	−	9.55435i	−0.0712913	−	0.0796196i
$121$	57.6607			0.476534
$122$	80.8317	−	80.8317i	0.662555	−	0.662555i
$123$	26.7332	+	26.7332i	0.217343	+	0.217343i
$124$	−12.3257			−0.0994005
$125$	−101.734	+	72.6300i	−0.813875	+	0.581040i
$126$	173.038			1.37331
$127$	−128.144	−	128.144i	−1.00901	−	1.00901i	−0.999959	−	0.00904741i	$-0.997120\pi$
$127$	−128.144	−	128.144i	−1.00901	−	1.00901i	−0.00904741	−	0.999959i	$-0.502880\pi$
$128$	−86.4570	−	86.4570i	−0.675445	−	0.675445i
$129$			16.2007i			0.125587i
$130$	96.7297	−	132.011i	0.744075	−	1.01547i
$131$	−165.385			−1.26248			−0.631239	−	0.775589i	$-0.717453\pi$
$131$	−165.385			−1.26248			−0.631239	+	0.775589i	$0.717453\pi$
$132$	−8.07579	+	8.07579i	−0.0611802	+	0.0611802i
$133$	−160.065	+	160.065i	−1.20350	+	1.20350i
$134$			81.1521i			0.605613i
$135$	−2.97860	+	53.9732i	−0.0220637	+	0.399802i
$136$		−	24.9585i		−	0.183519i
$137$	−71.1667	+	71.1667i	−0.519465	+	0.519465i	−0.917409	−	0.397945i	$-0.869724\pi$
$137$	−71.1667	+	71.1667i	−0.519465	+	0.519465i	0.397945	+	0.917409i	$0.369724\pi$
$138$	26.0395	+	26.0395i	0.188692	+	0.188692i
$139$		−	87.3453i		−	0.628384i	−0.949360	−	0.314192i	$-0.898267\pi$
$139$		−	87.3453i		−	0.628384i	0.949360	−	0.314192i	$-0.101733\pi$
$140$	−5.13642	+	93.0736i	−0.0366887	+	0.664811i
$141$		−	18.9753i		−	0.134577i
$142$	0.884758	+	0.884758i	0.00623069	+	0.00623069i
$143$	86.6986	+	56.4597i	0.606284	+	0.394823i
$144$			171.481i			1.19084i
$145$	188.938	−	169.175i	1.30302	−	1.16672i
$146$	−67.0784			−0.459441
$147$	−6.29454	−	6.29454i	−0.0428200	−	0.0428200i
$148$	−38.4171	−	38.4171i	−0.259575	−	0.259575i
$149$	200.517			1.34575			0.672875	−	0.739756i	$-0.265059\pi$
$149$	200.517			1.34575			0.672875	+	0.739756i	$0.265059\pi$
$150$	−38.3785	−	4.24890i	−0.255857	−	0.0283260i
$151$		−	282.461i		−	1.87061i	−0.353849	−	0.935303i	$-0.615127\pi$
$151$		−	282.461i		−	1.87061i	0.353849	−	0.935303i	$-0.384873\pi$
$152$	−83.9801	−	83.9801i	−0.552501	−	0.552501i
$153$	−36.3992	+	36.3992i	−0.237903	+	0.237903i
$154$	−159.692			−1.03696
$155$	19.6265	−	17.5736i	0.126623	−	0.113378i
$156$	18.2527	−	3.85548i	0.117005	−	0.0247146i
$157$	144.002	+	144.002i	0.917212	+	0.917212i	0.996826	−	0.0796134i	$-0.0253686\pi$
$157$	144.002	+	144.002i	0.917212	+	0.917212i	−0.0796134	+	0.996826i	$0.525369\pi$
$158$	−130.126	−	130.126i	−0.823585	−	0.823585i
$159$		−	33.2108i		−	0.208873i
$160$	−166.453	−	9.18596i	−1.04033	−	0.0574122i
$161$			190.011i			1.18019i
$162$	126.372	−	126.372i	0.780073	−	0.780073i
$163$	78.4288	+	78.4288i	0.481158	+	0.481158i	0.905502	−	0.424343i	$-0.139495\pi$
$163$	78.4288	+	78.4288i	0.481158	+	0.481158i	−0.424343	+	0.905502i	$0.639495\pi$
$164$	144.174			0.879108
$165$	1.34509	−	24.3735i	0.00815208	−	0.147718i
$166$	252.253			1.51960
$167$	125.294	−	125.294i	0.750263	−	0.750263i	−0.224265	−	0.974528i	$-0.571998\pi$
$167$	125.294	−	125.294i	0.750263	−	0.750263i	0.974528	+	0.224265i	$0.0719982\pi$
$168$	14.4540	−	14.4540i	0.0860357	−	0.0860357i
$169$	−68.3455	−	154.564i	−0.404411	−	0.914577i
$170$	−50.1275	−	55.9834i	−0.294868	−	0.329314i
$171$			244.951i			1.43246i
$172$	43.6855	+	43.6855i	0.253986	+	0.253986i
$173$	144.598	−	144.598i	0.835825	−	0.835825i	−0.152481	−	0.988306i	$-0.548726\pi$
$173$	144.598	−	144.598i	0.835825	−	0.835825i	0.988306	+	0.152481i	$0.0487263\pi$
$174$	78.3410			0.450235
$175$	−124.523	−	155.527i	−0.711558	−	0.888726i
$176$		−	158.256i		−	0.899180i
$177$	5.57261	−	5.57261i	0.0314837	−	0.0314837i
$178$	4.03194	−	4.03194i	0.0226514	−	0.0226514i
$179$			14.1047i			0.0787971i	0.999224	+	0.0393985i	$0.0125442\pi$
$179$			14.1047i			0.0787971i	−0.999224	+	0.0393985i	$0.987456\pi$
$180$	67.2861	+	75.1464i	0.373811	+	0.417480i
$181$	149.600			0.826517			0.413259	−	0.910614i	$-0.364391\pi$
$181$	149.600			0.826517			0.413259	+	0.910614i	$0.364391\pi$
$182$	218.586	+	142.347i	1.20102	+	0.782127i
$183$	−19.6939	+	19.6939i	−0.107617	+	0.107617i
$184$	−99.6916			−0.541802
$185$	115.947	+	6.39870i	0.626739	+	0.0345876i
$186$	8.13790			0.0437522
$187$	33.5920	−	33.5920i	0.179636	−	0.179636i
$188$	−51.1673	−	51.1673i	−0.272167	−	0.272167i
$189$	−86.1578			−0.455861
$190$	−357.040	−	19.7039i	−1.87916	−	0.103704i
$191$	−202.051			−1.05786			−0.528930	−	0.848665i	$-0.677407\pi$
$191$	−202.051			−1.05786			−0.528930	+	0.848665i	$0.677407\pi$
$192$	−1.91163	−	1.91163i	−0.00995642	−	0.00995642i
$193$	120.889	+	120.889i	0.626366	+	0.626366i	0.947152	−	0.320786i	$-0.103947\pi$
$193$	120.889	+	120.889i	0.626366	+	0.626366i	−0.320786	+	0.947152i	$0.603947\pi$
$194$		−	303.456i		−	1.56421i
$195$	−23.5673	+	32.1634i	−0.120858	+	0.164940i
$196$	−33.9468			−0.173198
$197$	24.3108	−	24.3108i	0.123405	−	0.123405i	−0.642707	−	0.766112i	$-0.722189\pi$
$197$	24.3108	−	24.3108i	0.123405	−	0.123405i	0.766112	+	0.642707i	$0.222189\pi$
$198$	−122.190	+	122.190i	−0.617123	+	0.617123i
$199$			111.235i			0.558969i	0.960150	+	0.279485i	$0.0901636\pi$
$199$			111.235i			0.558969i	−0.960150	+	0.279485i	$0.909836\pi$
$200$	81.5992	−	65.3323i	0.407996	−	0.326662i
$201$		−	19.7720i		−	0.0983681i
$202$	54.6485	−	54.6485i	0.270537	−	0.270537i
$203$	285.829	+	285.829i	1.40802	+	1.40802i
$204$		−	8.56598i		−	0.0419901i
$205$	−229.572	+	205.558i	−1.11986	+	1.00272i
$206$			430.647i			2.09052i
$207$	145.389	+	145.389i	0.702362	+	0.702362i
$208$	−141.067	+	216.620i	−0.678205	+	1.04144i
$209$		−	226.060i		−	1.08162i
$210$	3.39127	−	61.4510i	0.0161489	−	0.292624i
$211$	−86.7166			−0.410979			−0.205490	−	0.978659i	$-0.565879\pi$
$211$	−86.7166			−0.410979			−0.205490	+	0.978659i	$0.565879\pi$
$212$	−89.5537	−	89.5537i	−0.422423	−	0.422423i
$213$	−0.215563	−	0.215563i	−0.00101203	−	0.00101203i
$214$	−329.866			−1.54143
$215$	−131.847	−	7.27620i	−0.613243	−	0.0338428i
$216$		−	45.2037i		−	0.209276i
$217$	29.6913	+	29.6913i	0.136826	+	0.136826i
$218$	206.594	−	206.594i	0.947679	−	0.947679i
$219$	16.3430			0.0746258
$220$	−62.0967	−	69.3509i	−0.282258	−	0.315231i
$221$	−75.9239	+	16.0372i	−0.343547	+	0.0725666i
$222$	25.3645	+	25.3645i	0.114255	+	0.114255i
$223$	−185.893	−	185.893i	−0.833601	−	0.833601i	0.154406	−	0.988007i	$-0.450654\pi$
$223$	−185.893	−	185.893i	−0.833601	−	0.833601i	−0.988007	+	0.154406i	$0.950654\pi$
$224$		−	265.709i		−	1.18620i
$225$	−214.283	−	23.7234i	−0.952369	−	0.105437i
$226$			241.416i			1.06821i
$227$	−34.9372	+	34.9372i	−0.153908	+	0.153908i	−0.779861	−	0.625953i	$-0.784710\pi$
$227$	−34.9372	+	34.9372i	−0.153908	+	0.153908i	0.625953	+	0.779861i	$0.284710\pi$
$228$	−28.8227	−	28.8227i	−0.126415	−	0.126415i
$229$	242.528			1.05907			0.529537	−	0.848287i	$-0.322366\pi$
$229$	242.528			1.05907			0.529537	+	0.848287i	$0.322366\pi$
$230$	−223.614	+	200.224i	−0.972235	+	0.870538i
$231$	38.9076			0.168431
$232$	−149.964	+	149.964i	−0.646395	+	0.646395i
$233$	−238.192	+	238.192i	−1.02228	+	1.02228i	−0.0225371	+	0.999746i	$0.507174\pi$
$233$	−238.192	+	238.192i	−1.02228	+	1.02228i	−0.999746	+	0.0225371i	$0.992826\pi$
$234$	276.172	−	58.3351i	1.18022	−	0.249295i
$235$	154.428	+	8.52236i	0.657141	+	0.0362654i
$236$		−	30.0534i		−	0.127345i
$237$	31.7041	+	31.7041i	0.133773	+	0.133773i
$238$	84.6927	−	84.6927i	0.355852	−	0.355852i
$239$	−342.001			−1.43097			−0.715484	−	0.698629i	$-0.753794\pi$
$239$	−342.001			−1.43097			−0.715484	+	0.698629i	$0.753794\pi$
$240$	60.8981	+	3.36076i	0.253742	+	0.0140032i
$241$		−	176.477i		−	0.732268i	−0.930562	−	0.366134i	$-0.880681\pi$
$241$		−	176.477i		−	0.732268i	0.930562	−	0.366134i	$-0.119319\pi$
$242$	−102.656	+	102.656i	−0.424200	+	0.424200i
$243$	−99.5906	+	99.5906i	−0.409838	+	0.409838i
$244$			106.210i			0.435288i
$245$	54.0544	−	48.4003i	0.220630	−	0.197552i
$246$	−95.1893			−0.386948
$247$	−201.506	+	309.429i	−0.815813	+	1.25275i
$248$	−15.5779	+	15.5779i	−0.0628142	+	0.0628142i
$249$	−61.4592			−0.246824
$250$	51.8161	−	310.431i	0.207264	−	1.24172i
$251$	314.765			1.25404			0.627022	−	0.779002i	$-0.284274\pi$
$251$	314.765			1.25404			0.627022	+	0.779002i	$0.284274\pi$
$252$	−113.683	+	113.683i	−0.451123	+	0.451123i
$253$	−134.176	−	134.176i	−0.530340	−	0.530340i
$254$	456.283			1.79639
$255$	12.2131	+	13.6399i	0.0478946	+	0.0534896i
$256$	325.476			1.27139
$257$	−13.8093	−	13.8093i	−0.0537327	−	0.0537327i	0.679730	−	0.733463i	$-0.262097\pi$
$257$	−13.8093	−	13.8093i	−0.0537327	−	0.0537327i	−0.733463	+	0.679730i	$0.762097\pi$
$258$	−28.8430	−	28.8430i	−0.111794	−	0.111794i
$259$			185.086i			0.714619i
$260$	23.1795	+	150.279i	0.0891519	+	0.577997i
$261$	437.410			1.67590
$262$	294.443	−	294.443i	1.12383	−	1.12383i
$263$	108.910	−	108.910i	0.414106	−	0.414106i	−0.469060	−	0.883166i	$-0.655407\pi$
$263$	108.910	−	108.910i	0.414106	−	0.414106i	0.883166	+	0.469060i	$0.155407\pi$
$264$			20.4133i			0.0773232i
$265$	270.282	+	14.9159i	1.01993	+	0.0562866i
$266$		−	569.945i		−	2.14265i
$267$	−0.982346	+	0.982346i	−0.00367920	+	0.00367920i
$268$	−53.3156	−	53.3156i	−0.198939	−	0.198939i
$269$			43.8038i			0.162839i	0.996680	+	0.0814197i	$0.0259454\pi$
$269$			43.8038i			0.162839i	−0.996680	+	0.0814197i	$0.974055\pi$
$270$	−90.7886	−	101.395i	−0.336254	−	0.375535i
$271$			243.960i			0.900220i	0.892973	+	0.450110i	$0.148615\pi$
$271$			243.960i			0.900220i	−0.892973	+	0.450110i	$0.851385\pi$
$272$	83.9308	+	83.9308i	0.308569	+	0.308569i
$273$	−53.2566	−	34.6816i	−0.195079	−	0.127039i
$274$		−	253.404i		−	0.924832i
$275$	197.757	+	21.8937i	0.719116	+	0.0796136i
$276$	−34.2150			−0.123967
$277$	−120.428	−	120.428i	−0.434758	−	0.434758i	0.455486	−	0.890243i	$-0.349466\pi$
$277$	−120.428	−	120.428i	−0.434758	−	0.434758i	−0.890243	+	0.455486i	$0.849466\pi$
$278$	155.506	+	155.506i	0.559373	+	0.559373i
$279$	45.4373			0.162858
$280$	111.140	+	124.124i	0.396930	+	0.443299i
$281$		−	358.582i		−	1.27609i	−0.769999	−	0.638045i	$-0.779743\pi$
$281$		−	358.582i		−	1.27609i	0.769999	−	0.638045i	$-0.220257\pi$
$282$	33.7828	+	33.7828i	0.119797	+	0.119797i
$283$	175.165	−	175.165i	0.618959	−	0.618959i	−0.326305	−	0.945264i	$-0.605804\pi$
$283$	175.165	−	175.165i	0.618959	−	0.618959i	0.945264	+	0.326305i	$0.105804\pi$
$284$	−1.16254			−0.00409346
$285$	86.9897	+	4.80067i	0.305227	+	0.0168444i
$286$	−254.873	+	53.8361i	−0.891163	+	0.188238i
$287$	−347.300	−	347.300i	−1.21011	−	1.21011i
$288$	−203.310	−	203.310i	−0.705938	−	0.705938i
$289$		−	253.369i		−	0.876709i
$290$	−35.1852	+	637.568i	−0.121328	+	2.19851i
$291$			73.9344i			0.254070i
$292$	44.0694	−	44.0694i	0.150923	−	0.150923i
$293$	−221.222	−	221.222i	−0.755025	−	0.755025i	0.220388	−	0.975412i	$-0.429268\pi$
$293$	−221.222	−	221.222i	−0.755025	−	0.755025i	−0.975412	+	0.220388i	$0.929268\pi$
$294$	22.4130			0.0762348
$295$	42.8492	+	47.8548i	0.145251	+	0.162220i
$296$	−97.1077			−0.328067
$297$	60.8402	−	60.8402i	0.204849	−	0.204849i
$298$	−356.991	+	356.991i	−1.19796	+	1.19796i
$299$	64.0573	+	303.262i	0.214238	+	1.01425i
$300$	28.0055	−	22.4226i	0.0933517	−	0.0747420i
$301$		−	210.468i		−	0.699231i
$302$	502.882	+	502.882i	1.66517	+	1.66517i
$303$	−13.3146	+	13.3146i	−0.0439426	+	0.0439426i
$304$	564.818			1.85795
$305$	−151.431	−	169.122i	−0.496497	−	0.554497i
$306$		−	129.607i		−	0.423553i
$307$	2.13802	−	2.13802i	0.00696423	−	0.00696423i	−0.703616	−	0.710580i	$-0.748432\pi$
$307$	2.13802	−	2.13802i	0.00696423	−	0.00696423i	0.710580	+	0.703616i	$0.248432\pi$
$308$	104.915	−	104.915i	0.340634	−	0.340634i
$309$		−	104.923i		−	0.339557i
$310$	−3.65497	+	66.2293i	−0.0117902	+	0.213643i
$311$	−464.344			−1.49307			−0.746534	−	0.665347i	$-0.768284\pi$
$311$	−464.344			−1.49307			−0.746534	+	0.665347i	$0.768284\pi$
$312$	18.1961	−	27.9417i	0.0583209	−	0.0895567i
$313$	−29.3689	+	29.3689i	−0.0938304	+	0.0938304i	−0.752464	−	0.658633i	$-0.771135\pi$
$313$	−29.3689	+	29.3689i	−0.0938304	+	0.0938304i	0.658633	+	0.752464i	$0.271135\pi$
$314$	−512.751			−1.63296
$315$	18.9349	−	343.106i	0.0601107	−	1.08923i
$316$	170.982			0.541082
$317$	−133.383	+	133.383i	−0.420765	+	0.420765i	−0.885467	−	0.464702i	$-0.846161\pi$
$317$	−133.383	+	133.383i	−0.420765	+	0.420765i	0.464702	+	0.885467i	$0.346161\pi$
$318$	59.1270	+	59.1270i	0.185934	+	0.185934i
$319$	−403.675			−1.26544
$320$	16.4162	−	14.6990i	0.0513005	−	0.0459344i
$321$	80.3689			0.250370
$322$	−338.287	−	338.287i	−1.05058	−	1.05058i
$323$	119.891	+	119.891i	0.371178	+	0.371178i
$324$			166.049i			0.512496i
$325$	−251.173	−	206.245i	−0.772840	−	0.634601i
$326$	−279.262			−0.856633
$327$	−50.3348	+	50.3348i	−0.153929	+	0.153929i
$328$	182.215	−	182.215i	0.555535	−	0.555535i
$329$			246.514i			0.749284i
$330$	40.9988	+	45.7883i	0.124239	+	0.138752i
$331$		−	83.9623i		−	0.253663i	−0.991924	−	0.126831i	$-0.959519\pi$
$331$		−	83.9623i		−	0.253663i	0.991924	−	0.126831i	$-0.0404807\pi$
$332$	−165.726	+	165.726i	−0.499175	+	0.499175i
$333$	141.621	+	141.621i	0.425287	+	0.425287i
$334$			446.135i			1.33573i
$335$	160.912	+	8.88018i	0.480334	+	0.0265080i
$336$			97.2120i			0.289321i
$337$	92.5815	+	92.5815i	0.274722	+	0.274722i	0.830998	−	0.556276i	$-0.187770\pi$
$337$	92.5815	+	92.5815i	0.274722	+	0.274722i	−0.556276	+	0.830998i	$0.687770\pi$
$338$	396.857	+	153.499i	1.17413	+	0.454138i
$339$		−	58.8188i		−	0.173507i
$340$	69.7132	+	3.84723i	0.205039	+	0.0113154i
$341$	−41.9330			−0.122971
$342$	−436.100	−	436.100i	−1.27515	−	1.27515i
$343$	−194.351	−	194.351i	−0.566621	−	0.566621i
$344$	110.425			0.321002
$345$	54.4815	−	48.7827i	0.157917	−	0.141399i
$346$			514.871i			1.48807i
$347$	−263.764	−	263.764i	−0.760126	−	0.760126i	0.216219	−	0.976345i	$-0.430628\pi$
$347$	−263.764	−	263.764i	−0.760126	−	0.760126i	−0.976345	+	0.216219i	$0.930628\pi$
$348$	−51.4687	+	51.4687i	−0.147899	+	0.147899i
$349$	479.339			1.37346			0.686732	−	0.726911i	$-0.259045\pi$
$349$	479.339			1.37346			0.686732	+	0.726911i	$0.259045\pi$
$350$	498.588	+	55.1989i	1.42454	+	0.157711i
$351$	−137.510	+	29.0458i	−0.391766	+	0.0827517i
$352$	187.630	+	187.630i	0.533040	+	0.533040i
$353$	−10.9905	−	10.9905i	−0.0311344	−	0.0311344i	0.691368	−	0.722503i	$-0.257008\pi$
$353$	−10.9905	−	10.9905i	−0.0311344	−	0.0311344i	−0.722503	+	0.691368i	$0.757008\pi$
$354$			19.8424i			0.0560521i
$355$	1.85115	−	1.65752i	0.00521451	−	0.00466907i
$356$			5.29784i			0.0148816i
$357$	−20.6346	+	20.6346i	−0.0578000	+	0.0578000i
$358$	−25.1113	−	25.1113i	−0.0701434	−	0.0701434i
$359$	−394.878			−1.09994			−0.549969	−	0.835185i	$-0.685361\pi$
$359$	−394.878			−1.09994			−0.549969	+	0.835185i	$0.685361\pi$
$360$	180.015	+	9.93441i	0.500041	+	0.0275956i
$361$	445.811			1.23493
$362$	−266.340	+	266.340i	−0.735747	+	0.735747i
$363$	25.0113	−	25.0113i	0.0689017	−	0.0689017i
$364$	−237.127	+	50.0878i	−0.651449	+	0.137604i
$365$	−7.34014	+	133.006i	−0.0201100	+	0.364399i
$366$		−	70.1244i		−	0.191597i
$367$	−32.7622	−	32.7622i	−0.0892703	−	0.0892703i	0.661061	−	0.750332i	$-0.270106\pi$
$367$	−32.7622	−	32.7622i	−0.0892703	−	0.0892703i	−0.750332	+	0.661061i	$0.770106\pi$
$368$	335.244	−	335.244i	0.910989	−	0.910989i
$369$	−531.481			−1.44033
$370$	−217.818	+	195.034i	−0.588698	+	0.527120i
$371$			431.452i			1.16294i
$372$	−5.34647	+	5.34647i	−0.0143722	+	0.0143722i
$373$	−42.9772	+	42.9772i	−0.115221	+	0.115221i	−0.762366	−	0.647146i	$-0.775963\pi$
$373$	−42.9772	+	42.9772i	−0.115221	+	0.115221i	0.647146	+	0.762366i	$0.275963\pi$
$374$			119.611i			0.319816i
$375$	−12.6245	+	75.6336i	−0.0336654	+	0.201690i
$376$	−129.337			−0.343981
$377$	552.549	+	359.830i	1.46565	+	0.954455i
$378$	153.391	−	153.391i	0.405797	−	0.405797i
$379$	494.557			1.30490			0.652449	−	0.757832i	$-0.273742\pi$
$379$	494.557			1.30490			0.652449	+	0.757832i	$0.273742\pi$
$380$	247.515	−	221.625i	0.651355	−	0.583223i
$381$	−111.169			−0.291783
$382$	359.723	−	359.723i	0.941684	−	0.941684i
$383$	−43.8046	−	43.8046i	−0.114372	−	0.114372i	0.647604	−	0.761977i	$-0.275771\pi$
$383$	−43.8046	−	43.8046i	−0.114372	−	0.114372i	−0.761977	+	0.647604i	$0.775771\pi$
$384$	−75.0044			−0.195324
$385$	−17.4745	+	316.645i	−0.0453884	+	0.822453i
$386$	−430.450			−1.11515
$387$	−161.042	−	161.042i	−0.416130	−	0.416130i
$388$	199.366	+	199.366i	0.513829	+	0.513829i
$389$		−	341.940i		−	0.879023i	−0.898237	−	0.439511i	$-0.855152\pi$
$389$		−	341.940i		−	0.879023i	0.898237	−	0.439511i	$-0.144848\pi$
$390$	−15.3041	−	99.2205i	−0.0392412	−	0.254411i
$391$	142.320			0.363991
$392$	−42.9040	+	42.9040i	−0.109449	+	0.109449i
$393$	−71.7384	+	71.7384i	−0.182541	+	0.182541i
$394$			86.5637i			0.219705i
$395$	−272.259	+	243.781i	−0.689264	+	0.617167i
$396$		−	160.554i		−	0.405439i
$397$	266.811	−	266.811i	0.672069	−	0.672069i	−0.286124	−	0.958193i	$-0.592367\pi$
$397$	266.811	−	266.811i	0.672069	−	0.672069i	0.958193	+	0.286124i	$0.0923669\pi$
$398$	−198.038	−	198.038i	−0.497582	−	0.497582i
$399$			138.862i			0.348025i
$400$	−54.7023	+	494.103i	−0.136756	+	1.23526i
$401$		−	259.256i		−	0.646523i	−0.946310	−	0.323261i	$-0.895221\pi$
$401$		−	259.256i		−	0.646523i	0.946310	−	0.323261i	$-0.104779\pi$
$402$	35.2011	+	35.2011i	0.0875650	+	0.0875650i
$403$	57.3977	+	37.3784i	0.142426	+	0.0927503i
$404$			71.8064i			0.177739i
$405$	−236.747	−	264.404i	−0.584561	−	0.652849i
$406$	−1017.75			−2.50678
$407$	−130.698	−	130.698i	−0.321126	−	0.321126i
$408$	−10.8262	−	10.8262i	−0.0265348	−	0.0265348i
$409$	422.900			1.03399			0.516993	−	0.855990i	$-0.327051\pi$
$409$	422.900			1.03399			0.516993	+	0.855990i	$0.327051\pi$
$410$	42.7523	−	774.687i	0.104274	−	1.88948i
$411$			61.7396i			0.150218i
$412$	−282.928	−	282.928i	−0.686719	−	0.686719i
$413$	−72.3956	+	72.3956i	−0.175292	+	0.175292i
$414$	−517.688			−1.25045
$415$	27.6031	−	500.178i	0.0665135	−	1.20525i
$416$	−89.5769	−	424.078i	−0.215329	−	1.01942i
$417$	−37.8876	−	37.8876i	−0.0908574	−	0.0908574i
$418$	402.466	+	402.466i	0.962838	+	0.962838i
$419$			572.404i			1.36612i	0.730363	+	0.683060i	$0.239351\pi$
$419$			572.404i			1.36612i	−0.730363	+	0.683060i	$0.760649\pi$
$420$	38.1443	+	42.6003i	0.0908197	+	0.101429i
$421$			335.328i			0.796502i	0.917276	+	0.398251i	$0.130383\pi$
$421$			335.328i			0.796502i	−0.917276	+	0.398251i	$0.869617\pi$
$422$	154.386	−	154.386i	0.365845	−	0.365845i
$423$	188.623	+	188.623i	0.445917	+	0.445917i
$424$	−226.367			−0.533884
$425$	−116.492	+	93.2689i	−0.274098	+	0.219456i
$426$	0.767558			0.00180178
$427$	255.850	−	255.850i	0.599181	−	0.599181i
$428$	216.717	−	216.717i	0.506347	−	0.506347i
$429$	62.0974	−	13.1167i	0.144749	−	0.0305750i
$430$	247.689	−	221.781i	0.576021	−	0.515769i
$431$			79.0478i			0.183406i	0.995786	+	0.0917028i	$0.0292310\pi$
$431$			79.0478i			0.183406i	−0.995786	+	0.0917028i	$0.970769\pi$
$432$	152.011	+	152.011i	0.351878	+	0.351878i
$433$	−4.42481	+	4.42481i	−0.0102190	+	0.0102190i	−0.712198	−	0.701979i	$-0.752300\pi$
$433$	−4.42481	+	4.42481i	−0.0102190	+	0.0102190i	0.701979	+	0.712198i	$0.252300\pi$
$434$	−105.722			−0.243600
$435$	8.57257	−	155.338i	0.0197070	−	0.357098i
$436$			271.458i			0.622610i
$437$	478.878	−	478.878i	1.09583	−	1.09583i
$438$	−29.0964	+	29.0964i	−0.0664302	+	0.0664302i
$439$			786.635i			1.79188i	0.444176	+	0.895940i	$0.353496\pi$
$439$			786.635i			1.79188i	−0.444176	+	0.895940i	$0.646504\pi$
$440$	−166.131	−	9.16823i	−0.377571	−	0.0208369i
$441$	125.141			0.283767
$442$	106.620	−	163.724i	0.241221	−	0.370415i
$443$	−434.735	+	434.735i	−0.981343	+	0.981343i	−0.999829	−	0.0184863i	$-0.994115\pi$
$443$	−434.735	+	434.735i	−0.981343	+	0.981343i	0.0184863	+	0.999829i	$0.494115\pi$
$444$	−33.3282			−0.0750635
$445$	−7.55350	−	8.43590i	−0.0169742	−	0.0189571i
$446$	661.911			1.48411
$447$	86.9776	−	86.9776i	0.194581	−	0.194581i
$448$	24.8347	+	24.8347i	0.0554345	+	0.0554345i
$449$	−40.5436			−0.0902976			−0.0451488	−	0.998980i	$-0.514376\pi$
$449$	−40.5436			−0.0902976			−0.0451488	+	0.998980i	$0.514376\pi$
$450$	423.736	−	339.264i	0.941636	−	0.753920i
$451$	490.491			1.08756
$452$	−158.606	−	158.606i	−0.350899	−	0.350899i
$453$	−122.523	−	122.523i	−0.270469	−	0.270469i
$454$		−	124.401i		−	0.274012i
$455$	306.171	−	417.845i	0.672903	−	0.918341i
$456$	−72.8557			−0.159771
$457$	142.776	−	142.776i	0.312419	−	0.312419i	−0.533427	−	0.845846i	$-0.679096\pi$
$457$	142.776	−	142.776i	0.312419	−	0.312419i	0.845846	+	0.533427i	$0.179096\pi$
$458$	−431.786	+	431.786i	−0.942764	+	0.942764i
$459$			64.5331i			0.140595i
$460$	15.3670	−	278.455i	0.0334065	−	0.605336i
$461$			615.794i			1.33578i	0.744260	+	0.667889i	$0.232802\pi$
$461$			615.794i			1.33578i	−0.744260	+	0.667889i	$0.767198\pi$
$462$	−69.2693	+	69.2693i	−0.149934	+	0.149934i
$463$	−476.235	−	476.235i	−1.02859	−	1.02859i	−0.999579	−	0.0290068i	$-0.990766\pi$
$463$	−476.235	−	476.235i	−1.02859	−	1.02859i	−0.0290068	−	0.999579i	$-0.509234\pi$
$464$		−	1008.60i		−	2.17370i
$465$	0.890501	−	16.1362i	0.00191506	−	0.0347015i
$466$		−	848.133i		−	1.82003i
$467$	−164.188	−	164.188i	−0.351580	−	0.351580i	0.509117	−	0.860697i	$-0.329972\pi$
$467$	−164.188	−	164.188i	−0.351580	−	0.351580i	−0.860697	+	0.509117i	$0.829972\pi$
$468$	−143.115	+	219.766i	−0.305802	+	0.469585i
$469$			256.864i			0.547685i
$470$	−290.110	+	259.764i	−0.617254	+	0.552689i
$471$	124.927			0.265238
$472$	−37.9832	−	37.9832i	−0.0804730	−	0.0804730i
$473$	148.622	+	148.622i	0.314211	+	0.314211i
$474$	−112.889			−0.238163
$475$	−78.1392	+	705.798i	−0.164504	+	1.48589i
$476$			111.283i			0.233789i
$477$	330.130	+	330.130i	0.692097	+	0.692097i
$478$	608.884	−	608.884i	1.27382	−	1.27382i
$479$	366.297			0.764712			0.382356	−	0.924015i	$-0.375113\pi$
$479$	366.297			0.764712			0.382356	+	0.924015i	$0.375113\pi$
$480$	−76.1863	+	68.2171i	−0.158721	+	0.142119i
$481$	62.3970	+	295.402i	0.129724	+	0.614141i
$482$	314.191	+	314.191i	0.651849	+	0.651849i
$483$	82.4206	+	82.4206i	0.170643	+	0.170643i
$484$		−	134.887i		−	0.278693i
$485$	−601.706	−	33.2061i	−1.24063	−	0.0684662i
$486$		−	354.613i		−	0.729657i
$487$	−480.523	+	480.523i	−0.986701	+	0.986701i	−0.999913	−	0.0132120i	$-0.995794\pi$
$487$	−480.523	+	480.523i	−0.986701	+	0.986701i	0.0132120	+	0.999913i	$0.495794\pi$
$488$	134.235	+	134.235i	0.275072	+	0.275072i
$489$	68.0397			0.139141
$490$	−10.0664	+	182.406i	−0.0205436	+	0.372256i
$491$	138.516			0.282110			0.141055	−	0.990002i	$-0.454951\pi$
$491$	138.516			0.282110			0.141055	+	0.990002i	$0.454951\pi$
$492$	62.5378	−	62.5378i	0.127109	−	0.127109i
$493$	214.089	−	214.089i	0.434258	−	0.434258i
$494$	−192.142	−	909.646i	−0.388952	−	1.84139i
$495$	228.913	+	255.655i	0.462451	+	0.516474i
$496$		−	104.771i		−	0.211232i
$497$	2.80045	+	2.80045i	0.00563472	+	0.00563472i
$498$	109.419	−	109.419i	0.219717	−	0.219717i
$499$	508.021			1.01808			0.509040	−	0.860743i	$-0.330001\pi$
$499$	508.021			1.01808			0.509040	+	0.860743i	$0.330001\pi$
$500$	169.905	+	237.990i	0.339811	+	0.475980i
$501$		−	108.697i		−	0.216960i
$502$	−560.394	+	560.394i	−1.11632	+	1.11632i
$503$	415.356	−	415.356i	0.825756	−	0.825756i	−0.161170	−	0.986927i	$-0.551527\pi$
$503$	415.356	−	415.356i	0.825756	−	0.825756i	0.986927	+	0.161170i	$0.0515268\pi$
$504$			287.359i			0.570156i
$505$	−102.379	−	114.339i	−0.202731	−	0.226415i
$506$	477.762			0.944194
$507$	−96.6907	−	37.3986i	−0.190711	−	0.0737644i
$508$	−299.771	+	299.771i	−0.590099	+	0.590099i
$509$	−94.4082			−0.185478			−0.0927389	−	0.995690i	$-0.529562\pi$
$509$	−94.4082			−0.185478			−0.0927389	+	0.995690i	$0.529562\pi$
$510$	−46.0275	−	2.54010i	−0.0902499	−	0.00498059i
$511$	−212.318			−0.415495
$512$	−233.636	+	233.636i	−0.456320	+	0.456320i
$513$	217.140	+	217.140i	0.423275	+	0.423275i
$514$	49.1709			0.0956632
$515$	853.905	+	47.1241i	1.65807	+	0.0915032i
$516$	37.8987			0.0734471
$517$	−174.076	−	174.076i	−0.336704	−	0.336704i
$518$	−329.519	−	329.519i	−0.636137	−	0.636137i
$519$		−	125.444i		−	0.241703i
$520$	219.228	+	160.636i	0.421592	+	0.308916i
$521$	−782.708			−1.50232			−0.751159	−	0.660121i	$-0.770505\pi$
$521$	−782.708			−1.50232			−0.751159	+	0.660121i	$0.770505\pi$
$522$	−778.745	+	778.745i	−1.49185	+	1.49185i
$523$	−617.667	+	617.667i	−1.18101	+	1.18101i	−0.201525	+	0.979483i	$0.564590\pi$
$523$	−617.667	+	617.667i	−1.18101	+	1.18101i	−0.979483	+	0.201525i	$0.935410\pi$
$524$			386.889i			0.738337i
$525$	−121.476	−	13.4487i	−0.231384	−	0.0256166i
$526$			387.796i			0.737255i
$527$	22.2391	−	22.2391i	0.0421995	−	0.0421995i
$528$	−68.6461	−	68.6461i	−0.130012	−	0.130012i
$529$		−	39.4690i		−	0.0746107i
$530$	−507.754	+	454.642i	−0.958026	+	0.857815i
$531$			110.789i			0.208641i
$532$	374.445	+	374.445i	0.703844	+	0.703844i
$533$	−671.383	−	437.216i	−1.25963	−	0.820293i
$534$		−	3.49785i		−	0.00655028i
$535$	−36.0960	+	654.072i	−0.0674692	+	1.22256i
$536$	−134.767			−0.251431
$537$	6.11815	+	6.11815i	0.0113932	+	0.0113932i
$538$	−77.9863	−	77.9863i	−0.144956	−	0.144956i
$539$	−115.490			−0.214267
$540$	126.261	+	6.96793i	0.233817	+	0.0129036i
$541$			381.768i			0.705671i	0.935685	+	0.352835i	$0.114782\pi$
$541$			381.768i			0.705671i	−0.935685	+	0.352835i	$0.885218\pi$
$542$	−434.335	−	434.335i	−0.801356	−	0.801356i
$543$	64.8914	−	64.8914i	0.119505	−	0.119505i
$544$	−199.019			−0.365844
$545$	−387.036	−	432.250i	−0.710159	−	0.793119i
$546$	156.561	−	33.0700i	0.286742	−	0.0605678i
$547$	−1.21491	−	1.21491i	−0.00222105	−	0.00222105i	0.705995	−	0.708216i	$-0.250500\pi$
$547$	−1.21491	−	1.21491i	−0.00222105	−	0.00222105i	−0.708216	+	0.705995i	$0.750500\pi$
$548$	166.482	+	166.482i	0.303800	+	0.303800i
$549$		−	391.533i		−	0.713175i
$550$	−391.056	+	313.099i	−0.711011	+	0.569270i
$551$		−	1440.73i		−	2.61475i
$552$	−43.2430	+	43.2430i	−0.0783387	+	0.0783387i
$553$	−411.879	−	411.879i	−0.744808	−	0.744808i
$554$	428.809			0.774023
$555$	53.0694	−	47.5183i	0.0956206	−	0.0856186i
$556$	−204.329			−0.367499
$557$	−639.049	+	639.049i	−1.14730	+	1.14730i	−0.160224	+	0.987081i	$0.551222\pi$
$557$	−639.049	+	639.049i	−1.14730	+	1.14730i	−0.987081	+	0.160224i	$0.948778\pi$
$558$	−80.8945	+	80.8945i	−0.144972	+	0.144972i
$559$	−70.9540	−	335.913i	−0.126930	−	0.600917i
$560$	−791.148	−	43.6608i	−1.41276	−	0.0779657i
$561$		−	29.1422i		−	0.0519469i
$562$	638.402	+	638.402i	1.13595	+	1.13595i
$563$	387.288	−	387.288i	0.687901	−	0.687901i	−0.273867	−	0.961768i	$-0.588303\pi$
$563$	387.288	−	387.288i	0.687901	−	0.687901i	0.961768	+	0.273867i	$0.0883027\pi$
$564$	−44.3894			−0.0787047
$565$	478.690	+	26.4173i	0.847239	+	0.0467562i
$566$			623.713i			1.10197i
$567$	399.995	−	399.995i	0.705458	−	0.705458i
$568$	−1.46929	+	1.46929i	−0.00258678	+	0.00258678i
$569$		−	661.698i		−	1.16291i	−0.813577	−	0.581457i	$-0.802483\pi$
$569$		−	661.698i		−	1.16291i	0.813577	−	0.581457i	$-0.197517\pi$
$570$	−163.419	+	146.326i	−0.286701	+	0.256712i
$571$	−545.786			−0.955843			−0.477921	−	0.878403i	$-0.658610\pi$
$571$	−545.786			−0.955843			−0.477921	+	0.878403i	$0.658610\pi$
$572$	132.078	−	202.817i	0.230905	−	0.354574i
$573$	−87.6433	+	87.6433i	−0.152955	+	0.152955i
$574$	1236.64			2.15442
$575$	372.543	+	465.301i	0.647901	+	0.809219i
$576$	38.0050			0.0659809
$577$	−377.513	+	377.513i	−0.654268	+	0.654268i	−0.954018	−	0.299750i	$-0.903097\pi$
$577$	−377.513	+	377.513i	−0.654268	+	0.654268i	0.299750	+	0.954018i	$0.403097\pi$
$578$	451.087	+	451.087i	0.780427	+	0.780427i
$579$	104.875			0.181132
$580$	−395.756	−	441.988i	−0.682338	−	0.762048i
$581$	798.436			1.37424
$582$	−131.629	−	131.629i	−0.226167	−	0.226167i
$583$	−304.670	−	304.670i	−0.522589	−	0.522589i
$584$		−	111.395i		−	0.190745i
$585$	−85.4488	−	553.989i	−0.146066	−	0.946989i
$586$	787.708			1.34421
$587$	−80.0625	+	80.0625i	−0.136393	+	0.136393i	−0.772007	−	0.635614i	$-0.780747\pi$
$587$	−80.0625	+	80.0625i	−0.136393	+	0.136393i	0.635614	+	0.772007i	$0.280747\pi$
$588$	−14.7250	+	14.7250i	−0.0250425	+	0.0250425i
$589$		−	149.660i		−	0.254091i
$590$	−161.485	−	8.91183i	−0.273704	−	0.0151048i
$591$		−	21.0905i		−	0.0356861i
$592$	326.555	−	326.555i	0.551613	−	0.551613i
$593$	263.292	+	263.292i	0.444000	+	0.444000i	0.893354	−	0.449354i	$-0.148346\pi$
$593$	263.292	+	263.292i	0.444000	+	0.444000i	−0.449354	+	0.893354i	$0.648346\pi$
$594$			216.634i			0.364704i
$595$	−158.665	−	177.200i	−0.266663	−	0.297815i
$596$		−	469.074i		−	0.787038i
$597$	48.2501	+	48.2501i	0.0808209	+	0.0808209i
$598$	−653.959	−	425.870i	−1.09358	−	0.712156i
$599$		−	386.253i		−	0.644830i	−0.946598	−	0.322415i	$-0.895505\pi$
$599$		−	386.253i		−	0.644830i	0.946598	−	0.322415i	$-0.104495\pi$
$600$	7.05603	−	63.7341i	0.0117601	−	0.106224i
$601$	714.402			1.18869			0.594345	−	0.804210i	$-0.297411\pi$
$601$	714.402			1.18869			0.594345	+	0.804210i	$0.297411\pi$
$602$	374.709	+	374.709i	0.622439	+	0.622439i
$603$	196.543	+	196.543i	0.325941	+	0.325941i
$604$	−660.770			−1.09399
$605$	192.318	+	214.785i	0.317881	+	0.355016i
$606$		−	47.4095i		−	0.0782335i
$607$	360.380	+	360.380i	0.593706	+	0.593706i	0.938631	−	0.344924i	$-0.112095\pi$
$607$	360.380	+	360.380i	0.593706	+	0.593706i	−0.344924	+	0.938631i	$0.612095\pi$
$608$	−669.656	+	669.656i	−1.10141	+	1.10141i
$609$	247.966			0.407170
$610$	570.698	+	31.4949i	0.935571	+	0.0516310i
$611$	83.1059	+	393.443i	0.136016	+	0.643932i
$612$	85.1497	+	85.1497i	0.139134	+	0.139134i
$613$	597.005	+	597.005i	0.973906	+	0.973906i	0.999668	−	0.0257619i	$-0.00820116\pi$
$613$	597.005	+	597.005i	0.973906	+	0.973906i	−0.0257619	+	0.999668i	$0.508201\pi$
$614$			7.61286i			0.0123988i
$615$	−10.4162	+	188.745i	−0.0169369	+	0.306903i
$616$		−	265.196i		−	0.430514i
$617$	145.770	−	145.770i	0.236256	−	0.236256i	−0.579042	−	0.815298i	$-0.696573\pi$
$617$	145.770	−	145.770i	0.236256	−	0.236256i	0.815298	+	0.579042i	$0.196573\pi$
$618$	186.801	+	186.801i	0.302266	+	0.302266i
$619$	−1024.63			−1.65530			−0.827648	−	0.561247i	$-0.810322\pi$
$619$	−1024.63			−1.65530			−0.827648	+	0.561247i	$0.810322\pi$
$620$	−41.1103	−	45.9128i	−0.0663070	−	0.0740530i
$621$	257.764			0.415079
$622$	826.698	−	826.698i	1.32910	−	1.32910i
$623$	12.7620	−	12.7620i	0.0204847	−	0.0204847i
$624$	32.7725	+	155.153i	0.0525200	+	0.248642i
$625$	−609.865	−	136.712i	−0.975783	−	0.218740i
$626$		−	104.574i		−	0.167052i
$627$	−98.0572	−	98.0572i	−0.156391	−	0.156391i
$628$	336.869	−	336.869i	0.536415	−	0.536415i
$629$	138.632			0.220400
$630$	577.140	+	644.562i	0.916095	+	1.02311i
$631$		−	680.647i		−	1.07868i	−0.842088	−	0.539340i	$-0.818674\pi$
$631$		−	680.647i		−	1.07868i	0.842088	−	0.539340i	$-0.181326\pi$
$632$	216.097	−	216.097i	0.341926	−	0.341926i
$633$	−37.6149	+	37.6149i	−0.0594232	+	0.0594232i
$634$		−	474.936i		−	0.749111i
$635$	49.9294	−	904.737i	0.0786290	−	1.42478i
$636$	−77.6910			−0.122156
$637$	158.082	+	102.946i	0.248166	+	0.161610i
$638$	718.685	−	718.685i	1.12647	−	1.12647i
$639$	4.28559			0.00670672
$640$	33.6867	−	610.414i	0.0526355	−	0.953772i
$641$	555.853			0.867165			0.433582	−	0.901114i	$-0.357249\pi$
$641$	555.853			0.867165			0.433582	+	0.901114i	$0.357249\pi$
$642$	−143.085	+	143.085i	−0.222874	+	0.222874i
$643$	−545.418	−	545.418i	−0.848240	−	0.848240i	0.141673	−	0.989913i	$-0.454752\pi$
$643$	−545.418	−	545.418i	−0.848240	−	0.848240i	−0.989913	+	0.141673i	$0.954752\pi$
$644$	444.498			0.690215
$645$	−60.3472	+	54.0349i	−0.0935616	+	0.0837750i
$646$	−426.895			−0.660829
$647$	248.574	+	248.574i	0.384195	+	0.384195i	0.872611	−	0.488416i	$-0.162425\pi$
$647$	248.574	+	248.574i	0.384195	+	0.384195i	−0.488416	+	0.872611i	$0.662425\pi$
$648$	209.862	+	209.862i	0.323861	+	0.323861i
$649$		−	102.244i		−	0.157541i
$650$	814.367	−	79.9873i	1.25287	−	0.123057i
$651$	25.7583			0.0395672
$652$	183.471	−	183.471i	0.281397	−	0.281397i
$653$	−166.637	+	166.637i	−0.255186	+	0.255186i	−0.823093	−	0.567907i	$-0.807753\pi$
$653$	−166.637	+	166.637i	−0.255186	+	0.255186i	0.567907	+	0.823093i	$0.307753\pi$
$654$		−	179.228i		−	0.274048i
$655$	−551.614	−	616.054i	−0.842159	−	0.940541i
$656$			1225.51i			1.86816i
$657$	−162.457	+	162.457i	−0.247271	+	0.247271i
$658$	−438.883	−	438.883i	−0.666995	−	0.666995i
$659$			1000.82i			1.51870i	0.650685	+	0.759348i	$0.274482\pi$
$659$			1000.82i			1.51870i	−0.650685	+	0.759348i	$0.725518\pi$
$660$	−57.0177	−	3.14661i	−0.0863904	−	0.00476760i
$661$		−	387.180i		−	0.585749i	−0.956151	−	0.292874i	$-0.905388\pi$
$661$		−	387.180i		−	0.585749i	0.956151	−	0.292874i	$-0.0946118\pi$
$662$	149.483	+	149.483i	0.225805	+	0.225805i
$663$	−25.9769	+	39.8898i	−0.0391808	+	0.0601655i
$664$			418.909i			0.630888i
$665$	−1130.11	−	62.3670i	−1.69942	−	0.0937850i
$666$	−504.270			−0.757163
$667$	−855.133	−	855.133i	−1.28206	−	1.28206i
$668$	−293.104	−	293.104i	−0.438778	−	0.438778i
$669$	−161.269			−0.241059
$670$	−302.290	+	270.670i	−0.451179	+	0.403986i
$671$			361.337i			0.538505i
$672$	−115.256	−	115.256i	−0.171512	−	0.171512i
$673$	−384.504	+	384.504i	−0.571329	+	0.571329i	−0.932500	−	0.361171i	$-0.882377\pi$
$673$	−384.504	+	384.504i	−0.571329	+	0.571329i	0.361171	+	0.932500i	$0.382377\pi$
$674$	−329.656			−0.489103
$675$	−210.984	+	168.924i	−0.312569	+	0.250258i
$676$	−361.575	+	159.883i	−0.534874	+	0.236513i
$677$	358.805	+	358.805i	0.529993	+	0.529993i	0.920570	−	0.390577i	$-0.127725\pi$
$677$	358.805	+	358.805i	0.529993	+	0.529993i	−0.390577	+	0.920570i	$0.627725\pi$
$678$	104.718	+	104.718i	0.154452	+	0.154452i
$679$		−	960.506i		−	1.41459i
$680$	92.9701	−	83.2453i	0.136721	−	0.122420i
$681$			30.3093i			0.0445070i
$682$	74.6556	−	74.6556i	0.109466	−	0.109466i
$683$	646.688	+	646.688i	0.946835	+	0.946835i	0.998656	−	0.0518212i	$-0.0165026\pi$
$683$	646.688	+	646.688i	0.946835	+	0.946835i	−0.0518212	+	0.998656i	$0.516503\pi$
$684$	573.021			0.837750
$685$	−502.460	−	27.7291i	−0.733518	−	0.0404804i
$686$	692.028			1.00879
$687$	105.201	−	105.201i	0.153131	−	0.153131i
$688$	−371.338	+	371.338i	−0.539735	+	0.539735i
$689$	145.453	+	688.608i	0.211107	+	0.999431i
$690$	−10.1459	+	183.847i	−0.0147042	+	0.266445i
$691$		−	363.653i		−	0.526270i	−0.964759	−	0.263135i	$-0.915244\pi$
$691$		−	363.653i		−	0.526270i	0.964759	−	0.263135i	$-0.0847565\pi$
$692$	−338.262	−	338.262i	−0.488818	−	0.488818i
$693$	−386.759	+	386.759i	−0.558094	+	0.558094i
$694$	939.186			1.35329
$695$	325.360	−	291.327i	0.468143	−	0.419175i
$696$			130.099i			0.186923i
$697$	−260.132	+	260.132i	−0.373216	+	0.373216i
$698$	−853.393	+	853.393i	−1.22263	+	1.22263i
$699$			206.640i			0.295622i
$700$	−363.829	+	291.299i	−0.519756	+	0.416142i
$701$	−743.139			−1.06011			−0.530056	−	0.847962i	$-0.677829\pi$
$701$	−743.139			−1.06011			−0.530056	+	0.847962i	$0.677829\pi$
$702$	193.104	−	296.528i	0.275077	−	0.422405i
$703$	466.466	−	466.466i	0.663536	−	0.663536i
$704$	−35.0739			−0.0498209
$705$	70.6826	−	63.2891i	0.100259	−	0.0897718i
$706$	39.1338			0.0554303
$707$	172.975	−	172.975i	0.244660	−	0.244660i
$708$	−13.0362	−	13.0362i	−0.0184127	−	0.0184127i
$709$	−1179.60			−1.66376			−0.831879	−	0.554957i	$-0.812735\pi$
$709$	−1179.60			−1.66376			−0.831879	+	0.554957i	$0.812735\pi$
$710$	−0.344733	+	6.24668i	−0.000485540	+	0.00879814i
$711$	−630.307			−0.886508
$712$	6.69573	+	6.69573i	0.00940412	+	0.00940412i
$713$	−88.8295	−	88.8295i	−0.124586	−	0.124586i
$714$		−	73.4739i		−	0.102905i
$715$	78.8587	+	511.263i	0.110292	+	0.715053i
$716$	32.9955			0.0460831
$717$	−148.349	+	148.349i	−0.206902	+	0.206902i
$718$	703.023	−	703.023i	0.979141	−	0.979141i
$719$		−	160.358i		−	0.223029i	−0.993763	−	0.111514i	$-0.964430\pi$
$719$		−	160.358i		−	0.223029i	0.993763	−	0.111514i	$-0.0355702\pi$
$720$	−638.763	+	571.948i	−0.887171	+	0.794372i
$721$			1363.09i			1.89056i
$722$	−793.703	+	793.703i	−1.09931	+	1.09931i
$723$	−76.5498	−	76.5498i	−0.105878	−	0.105878i
$724$		−	349.963i		−	0.483374i
$725$	1260.35	+	139.534i	1.73841	+	0.192460i
$726$			89.0581i			0.122670i
$727$	482.308	+	482.308i	0.663422	+	0.663422i	0.956185	−	0.292763i	$-0.0945747\pi$
$727$	482.308	+	482.308i	0.663422	+	0.663422i	−0.292763	+	0.956185i	$0.594575\pi$
$728$	−236.392	+	363.000i	−0.324714	+	0.498626i
$729$		−	552.433i		−	0.757796i
$730$	−223.730	−	249.866i	−0.306479	−	0.342282i
$731$	−157.643			−0.215654
$732$	46.0706	+	46.0706i	0.0629379	+	0.0629379i
$733$	611.314	+	611.314i	0.833989	+	0.833989i	0.988060	−	0.154071i	$-0.0492383\pi$
$733$	611.314	+	611.314i	0.833989	+	0.833989i	−0.154071	+	0.988060i	$0.549238\pi$
$734$	116.657			0.158933
$735$	2.45258	−	44.4415i	0.00333684	−	0.0604646i
$736$			794.940i			1.08008i
$737$	−181.384	−	181.384i	−0.246112	−	0.246112i
$738$	946.225	−	946.225i	1.28215	−	1.28215i
$739$	−346.783			−0.469259			−0.234630	−	0.972085i	$-0.575388\pi$
$739$	−346.783			−0.469259			−0.234630	+	0.972085i	$0.575388\pi$
$740$	14.9687	−	271.237i	0.0202279	−	0.366537i
$741$	46.8137	+	221.627i	0.0631764	+	0.299092i
$742$	−768.139	−	768.139i	−1.03523	−	1.03523i
$743$	551.121	+	551.121i	0.741750	+	0.741750i	0.972915	−	0.231164i	$-0.0742535\pi$
$743$	551.121	+	551.121i	0.741750	+	0.741750i	−0.231164	+	0.972915i	$0.574253\pi$
$744$			13.5144i			0.0181645i
$745$	668.792	+	746.921i	0.897708	+	1.00258i
$746$		−	153.030i		−	0.205133i
$747$	610.932	−	610.932i	0.817847	−	0.817847i
$748$	−78.5827	−	78.5827i	−0.105057	−	0.105057i
$749$	−1044.10			−1.39399
$750$	−112.179	−	157.131i	−0.149571	−	0.209508i
$751$	−714.986			−0.952045			−0.476023	−	0.879433i	$-0.657922\pi$
$751$	−714.986			−0.952045			−0.476023	+	0.879433i	$0.657922\pi$
$752$	434.935	−	434.935i	0.578370	−	0.578370i
$753$	136.535	−	136.535i	0.181321	−	0.181321i
$754$	−1624.36	+	343.109i	−2.15432	+	0.455052i
$755$	1052.16	−	942.106i	1.39359	−	1.24782i
$756$			201.551i			0.266602i
$757$	111.760	+	111.760i	0.147636	+	0.147636i	0.777061	−	0.629425i	$-0.216710\pi$
$757$	111.760	+	111.760i	0.147636	+	0.147636i	−0.629425	+	0.777061i	$0.716710\pi$
$758$	−880.486	+	880.486i	−1.16159	+	1.16159i
$759$	−116.402			−0.153363
$760$	32.7216	−	592.927i	0.0430548	−	0.780167i
$761$		−	624.616i		−	0.820784i	−0.911909	−	0.410392i	$-0.865392\pi$
$761$		−	624.616i		−	0.820784i	0.911909	−	0.410392i	$-0.134608\pi$
$762$	197.921	−	197.921i	0.259738	−	0.259738i
$763$	653.916	−	653.916i	0.857032	−	0.857032i
$764$			472.665i			0.618671i
$765$	−256.990	−	14.1824i	−0.335935	−	0.0185391i
$766$	155.975			0.203623
$767$	−91.1388	+	139.951i	−0.118825	+	0.182466i
$768$	141.181	−	141.181i	0.183829	−	0.183829i
$769$	486.144			0.632177			0.316088	−	0.948730i	$-0.397630\pi$
$769$	486.144			0.632177			0.316088	+	0.948730i	$0.397630\pi$
$770$	−532.629	−	594.851i	−0.691726	−	0.772533i
$771$	−11.9800			−0.0155383
$772$	282.798	−	282.798i	0.366319	−	0.366319i
$773$	−95.7264	−	95.7264i	−0.123838	−	0.123838i	0.642472	−	0.766309i	$-0.277909\pi$
$773$	−95.7264	−	95.7264i	−0.123838	−	0.123838i	−0.766309	+	0.642472i	$0.777909\pi$
$774$	573.424			0.740858
$775$	130.922	+	14.4945i	0.168932	+	0.0187025i
$776$	503.941			0.649409
$777$	80.2844	+	80.2844i	0.103326	+	0.103326i
$778$	608.774	+	608.774i	0.782486	+	0.782486i
$779$			1750.58i			2.24721i
$780$	75.2407	+	55.1317i	0.0964625	+	0.0706817i
$781$	−3.95507			−0.00506411
$782$	−253.381	+	253.381i	−0.324017	+	0.324017i
$783$	387.748	−	387.748i	0.495208	−	0.495208i
$784$		−	288.556i		−	0.368056i
$785$	−56.1084	+	1016.70i	−0.0714757	+	1.29516i
$786$		−	255.440i		−	0.324987i
$787$	89.0150	−	89.0150i	0.113107	−	0.113107i	−0.648288	−	0.761395i	$-0.724515\pi$
$787$	89.0150	−	89.0150i	0.113107	−	0.113107i	0.761395	+	0.648288i	$0.224515\pi$
$788$	−56.8709	−	56.8709i	−0.0721712	−	0.0721712i
$789$		−	94.4831i		−	0.119750i
$790$	50.7019	−	918.735i	0.0641796	−	1.16296i
$791$			764.135i			0.966037i
$792$	−202.918	−	202.918i	−0.256209	−	0.256209i
$793$	322.090	−	494.596i	0.406166	−	0.623703i
$794$			950.037i			1.19652i
$795$	123.710	−	110.769i	0.155610	−	0.139333i
$796$	260.215			0.326903
$797$	−471.659	−	471.659i	−0.591794	−	0.591794i	0.346322	−	0.938116i	$-0.387430\pi$
$797$	−471.659	−	471.659i	−0.591794	−	0.591794i	−0.938116	+	0.346322i	$0.887430\pi$
$798$	−247.224	−	247.224i	−0.309804	−	0.309804i
$799$	184.642			0.231091
$800$	−520.959	−	650.671i	−0.651199	−	0.813338i
$801$		−	19.5299i		−	0.0243819i
$802$	461.567	+	461.567i	0.575520	+	0.575520i
$803$	149.928	−	149.928i	0.186710	−	0.186710i
$804$	−46.2532			−0.0575288
$805$	−707.788	+	633.753i	−0.879239	+	0.787270i
$806$	−168.735	+	35.6415i	−0.209349	+	0.0442202i
$807$	19.0007	+	19.0007i	0.0235448	+	0.0235448i
$808$	90.7532	+	90.7532i	0.112318	+	0.112318i
$809$		−	148.398i		−	0.183434i	−0.995785	−	0.0917168i	$-0.970765\pi$
$809$		−	148.398i		−	0.183434i	0.995785	−	0.0917168i	$-0.0292355\pi$
$810$	892.227	+	49.2390i	1.10151	+	0.0607889i
$811$		−	1205.54i		−	1.48648i	−0.669024	−	0.743241i	$-0.733288\pi$
$811$		−	1205.54i		−	1.48648i	0.669024	−	0.743241i	$-0.266712\pi$
$812$	668.647	−	668.647i	0.823457	−	0.823457i
$813$	105.822	+	105.822i	0.130162	+	0.130162i
$814$	465.379			0.571719
$815$	−30.5587	+	553.733i	−0.0374953	+	0.679427i
$816$	72.8129			0.0892315
$817$	−530.435	+	530.435i	−0.649248	+	0.649248i
$818$	−752.912	+	752.912i	−0.920430	+	0.920430i
$819$	874.145	−	184.644i	1.06733	−	0.225450i
$820$	480.869	+	537.044i	0.586425	+	0.654932i
$821$		−	1294.13i		−	1.57629i	−0.615491	−	0.788144i	$-0.711042\pi$
$821$		−	1294.13i		−	1.57629i	0.615491	−	0.788144i	$-0.288958\pi$
$822$	−109.918	−	109.918i	−0.133721	−	0.133721i
$823$	−709.426	+	709.426i	−0.861999	+	0.861999i	−0.991570	−	0.129571i	$-0.958640\pi$
$823$	−709.426	+	709.426i	−0.861999	+	0.861999i	0.129571	+	0.991570i	$0.458640\pi$
$824$	−715.163			−0.867917
$825$	95.2772	−	76.2837i	0.115488	−	0.0924650i
$826$		−	257.780i		−	0.312082i
$827$	578.353	−	578.353i	0.699338	−	0.699338i	−0.264930	−	0.964268i	$-0.585349\pi$
$827$	578.353	−	578.353i	0.699338	−	0.699338i	0.964268	+	0.264930i	$0.0853488\pi$
$828$	340.113	−	340.113i	0.410764	−	0.410764i
$829$		−	422.793i		−	0.510004i	−0.966941	−	0.255002i	$-0.917924\pi$
$829$		−	422.793i		−	0.510004i	0.966941	−	0.255002i	$-0.0820761\pi$
$830$	841.351	+	939.637i	1.01368	+	1.13209i
$831$	−104.475			−0.125722
$832$	48.0090	+	31.2643i	0.0577032	+	0.0375773i
$833$	61.2500	−	61.2500i	0.0735294	−	0.0735294i
$834$	134.907			0.161758
$835$	884.616	+	48.8190i	1.05942	+	0.0584658i
$836$	−528.827			−0.632569
$837$	40.2785	−	40.2785i	0.0481224	−	0.0481224i
$838$	−1019.08	−	1019.08i	−1.21609	−	1.21609i
$839$	651.223			0.776189			0.388095	−	0.921620i	$-0.373133\pi$
$839$	651.223			0.776189			0.388095	+	0.921620i	$0.373133\pi$
$840$	102.050	+	5.63179i	0.121488	+	0.00670451i
$841$	−1731.71			−2.05911
$842$	−597.002	−	597.002i	−0.709029	−	0.709029i
$843$	−155.541	−	155.541i	−0.184509	−	0.184509i
$844$			202.859i			0.240354i
$845$	347.790	−	770.108i	0.411586	−	0.911371i
$846$	−671.632			−0.793891
$847$	−324.930	+	324.930i	−0.383625	+	0.383625i
$848$	761.228	−	761.228i	0.897675	−	0.897675i
$849$		−	151.962i		−	0.178990i
$850$	41.3446	−	373.448i	0.0486407	−	0.439351i
$851$		−	553.735i		−	0.650687i
$852$	−0.504273	+	0.504273i	−0.000591870	+	0.000591870i
$853$	266.180	+	266.180i	0.312052	+	0.312052i	0.845704	−	0.533652i	$-0.179181\pi$
$853$	266.180	+	266.180i	0.312052	+	0.312052i	−0.533652	+	0.845704i	$0.679181\pi$
$854$			911.009i			1.06675i
$855$	−912.438	+	816.996i	−1.06718	+	0.955551i
$856$		−	547.799i		−	0.639952i
$857$	−313.015	−	313.015i	−0.365245	−	0.365245i	0.500495	−	0.865740i	$-0.333152\pi$
$857$	−313.015	−	313.015i	−0.365245	−	0.365245i	−0.865740	+	0.500495i	$0.833152\pi$
$858$	−87.2031	+	133.908i	−0.101635	+	0.156070i
$859$		−	515.308i		−	0.599892i	−0.953956	−	0.299946i	$-0.903031\pi$
$859$		−	515.308i		−	0.599892i	0.953956	−	0.299946i	$-0.0969687\pi$
$860$	−17.0214	+	308.434i	−0.0197924	+	0.358644i
$861$	−301.295			−0.349936
$862$	−140.733	−	140.733i	−0.163264	−	0.163264i
$863$	324.876	+	324.876i	0.376449	+	0.376449i	0.869819	−	0.493370i	$-0.164235\pi$
$863$	324.876	+	324.876i	0.376449	+	0.376449i	−0.493370	+	0.869819i	$0.664235\pi$
$864$	−360.454			−0.417192
$865$	1020.91	+	56.3404i	1.18024	+	0.0651334i
$866$		−	15.7555i		−	0.0181934i
$867$	−109.903	−	109.903i	−0.126763	−	0.126763i
$868$	69.4578	−	69.4578i	0.0800205	−	0.0800205i
$869$	581.695			0.669385
$870$	261.294	+	291.819i	0.300338	+	0.335424i
$871$	86.5951	+	409.962i	0.0994204	+	0.470679i
$872$	343.085	+	343.085i	0.393446	+	0.393446i
$873$	−734.941	−	734.941i	−0.841857	−	0.841857i
$874$			1705.14i			1.95097i
$875$	164.009	−	982.581i	0.187439	−	1.12295i
$876$		−	38.2317i		−	0.0436435i
$877$	−1176.18	+	1176.18i	−1.34114	+	1.34114i	−0.446223	+	0.894922i	$0.647231\pi$
$877$	−1176.18	+	1176.18i	−1.34114	+	1.34114i	−0.894922	+	0.446223i	$0.852769\pi$
$878$	−1400.49	−	1400.49i	−1.59509	−	1.59509i
$879$	−191.918			−0.218337
$880$	589.499	−	527.837i	0.669885	−	0.599815i
$881$	−60.9585			−0.0691924			−0.0345962	−	0.999401i	$-0.511015\pi$
$881$	−60.9585			−0.0691924			−0.0345962	+	0.999401i	$0.511015\pi$
$882$	−222.796	+	222.796i	−0.252603	+	0.252603i
$883$	452.293	−	452.293i	0.512223	−	0.512223i	−0.402984	−	0.915207i	$-0.632027\pi$
$883$	452.293	−	452.293i	0.512223	−	0.512223i	0.915207	+	0.402984i	$0.132027\pi$
$884$	37.5163	+	177.611i	0.0424393	+	0.200917i
$885$	39.3444	+	2.17129i	0.0444570	+	0.00245343i
$886$		−	1547.96i		−	1.74714i
$887$	−1048.86	−	1048.86i	−1.18248	−	1.18248i	−0.979101	−	0.203376i	$-0.934809\pi$
$887$	−1048.86	−	1048.86i	−1.18248	−	1.18248i	−0.203376	−	0.979101i	$-0.565191\pi$
$888$	−42.1222	+	42.1222i	−0.0474349	+	0.0474349i
$889$	1444.24			1.62456
$890$	28.4668	+	1.57099i	0.0319852	+	0.00176515i
$891$			564.912i			0.634020i
$892$	−434.865	+	434.865i	−0.487517	+	0.487517i
$893$	621.280	−	621.280i	0.695723	−	0.695723i
$894$			309.702i			0.346423i
$895$	−52.5396	+	47.0440i	−0.0587035	+	0.0525631i
$896$	974.407			1.08751
$897$	159.331	+	103.759i	0.177627	+	0.115674i
$898$	72.1820	−	72.1820i	0.0803809	−	0.0803809i
$899$	−267.248			−0.297272
$900$	−55.4968	+	501.279i	−0.0616631	+	0.556976i
$901$	323.163			0.358671
$902$	−873.249	+	873.249i	−0.968125	+	0.968125i
$903$	−91.2943	−	91.2943i	−0.101101	−	0.101101i
$904$	−400.913			−0.443488
$905$	498.966	+	557.255i	0.551344	+	0.615752i
$906$	436.267			0.481531
$907$	490.097	+	490.097i	0.540350	+	0.540350i	0.923632	−	0.383282i	$-0.125206\pi$
$907$	490.097	+	490.097i	0.540350	+	0.540350i	−0.383282	+	0.923632i	$0.625206\pi$
$908$	81.7296	+	81.7296i	0.0900106	+	0.0900106i
$909$		−	264.707i		−	0.291206i
$910$	198.820	+	1289.01i	0.218484	+	1.41649i
$911$	487.918			0.535585			0.267793	−	0.963477i	$-0.413706\pi$
$911$	487.918			0.535585			0.267793	+	0.963477i	$0.413706\pi$
$912$	245.000	−	245.000i	0.268640	−	0.268640i
$913$	−563.815	+	563.815i	−0.617541	+	0.617541i
$914$			508.383i			0.556218i
$915$	−139.046	−	7.67345i	−0.151962	−	0.00838629i
$916$		−	567.353i		−	0.619381i
$917$	931.978	−	931.978i	1.01633	−	1.01633i
$918$	−114.892	−	114.892i	−0.125155	−	0.125155i
$919$			199.701i			0.217303i	0.994080	+	0.108651i	$0.0346532\pi$
$919$			199.701i			0.217303i	−0.994080	+	0.108651i	$0.965347\pi$
$920$	−332.506	−	371.349i	−0.361420	−	0.403641i
$921$		−	1.85481i		−	0.00201390i
$922$	−1096.33	−	1096.33i	−1.18908	−	1.18908i
$923$	5.41369	+	3.52549i	0.00586532	+	0.00381960i
$924$		−	91.0176i		−	0.0985039i
$925$	362.887	+	453.241i	0.392310	+	0.489990i
$926$	1695.74			1.83125
$927$	1042.98	+	1042.98i	1.12512	+	1.12512i
$928$	1195.81	+	1195.81i	1.28859	+	1.28859i
$929$	−617.232			−0.664405			−0.332202	−	0.943208i	$-0.607792\pi$
$929$	−617.232			−0.664405			−0.332202	+	0.943208i	$0.607792\pi$
$930$	27.1427	+	30.3135i	0.0291857	+	0.0325952i
$931$		−	412.186i		−	0.442734i
$932$	557.209	+	557.209i	0.597864	+	0.597864i
$933$	−201.417	+	201.417i	−0.215882	+	0.215882i
$934$	584.625			0.625937
$935$	237.170	+	13.0886i	0.253658	+	0.0139985i
$936$	96.8755	+	458.631i	0.103499	+	0.489990i
$937$	−434.493	−	434.493i	−0.463706	−	0.463706i	0.436162	−	0.899868i	$-0.356338\pi$
$937$	−434.493	−	434.493i	−0.463706	−	0.463706i	−0.899868	+	0.436162i	$0.856338\pi$
$938$	−457.310	−	457.310i	−0.487537	−	0.487537i
$939$			25.4786i			0.0271337i
$940$	19.9366	−	361.258i	0.0212092	−	0.384317i
$941$			1594.74i			1.69473i	0.531008	+	0.847367i	$0.321813\pi$
$941$			1594.74i			1.69473i	−0.531008	+	0.847367i	$0.678187\pi$
$942$	−222.415	+	222.415i	−0.236109	+	0.236109i
$943$	1039.04	+	1039.04i	1.10185	+	1.10185i
$944$	255.461			0.270615
$945$	−287.366	−	320.936i	−0.304091	−	0.339615i
$946$	−529.200			−0.559408
$947$	−1127.45	+	1127.45i	−1.19055	+	1.19055i	−0.213639	+	0.976913i	$0.568532\pi$
$947$	−1127.45	+	1127.45i	−1.19055	+	1.19055i	−0.976913	+	0.213639i	$0.931468\pi$
$948$	74.1664	−	74.1664i	0.0782346	−	0.0782346i
$949$	−338.864	+	71.5774i	−0.357075	+	0.0754241i
$950$	−1117.46	−	1395.69i	−1.17627	−	1.46914i
$951$			115.714i			0.121676i
$952$	140.647	+	140.647i	0.147738	+	0.147738i
$953$	976.109	−	976.109i	1.02425	−	1.02425i	0.0245499	−	0.999699i	$-0.492185\pi$
$953$	976.109	−	976.109i	1.02425	−	1.02425i	0.999699	−	0.0245499i	$-0.00781526\pi$
$954$	−1175.50			−1.23218
$955$	−673.911	−	752.637i	−0.705666	−	0.788102i
$956$			800.053i			0.836876i
$957$	−175.101	+	175.101i	−0.182969	+	0.182969i
$958$	−652.139	+	652.139i	−0.680729	+	0.680729i
$959$		−	802.079i		−	0.836370i
$960$	0.744840	−	13.4967i	0.000775875	−	0.0140591i
$961$	933.239			0.971112
$962$	−637.009	−	414.831i	−0.662172	−	0.431218i
$963$	−798.903	+	798.903i	−0.829598	+	0.829598i
$964$	−412.837			−0.428254
$965$	−47.1025	+	853.514i	−0.0488109	+	0.884470i
$966$	−293.476			−0.303805
$967$	−23.8217	+	23.8217i	−0.0246346	+	0.0246346i	−0.719317	−	0.694682i	$-0.755545\pi$
$967$	−23.8217	+	23.8217i	−0.0246346	+	0.0246346i	0.694682	+	0.719317i	$0.255545\pi$
$968$	−170.479	−	170.479i	−0.176114	−	0.176114i
$969$	104.009			0.107337
$970$	1130.37	−	1012.13i	1.16533	−	1.04343i
$971$	375.513			0.386728			0.193364	−	0.981127i	$-0.438060\pi$
$971$	375.513			0.386728			0.193364	+	0.981127i	$0.438060\pi$
$972$	232.975	+	232.975i	0.239686	+	0.239686i
$973$	492.210	+	492.210i	0.505868	+	0.505868i
$974$		−	1711.00i		−	1.75668i
$975$	−198.413	+	19.4882i	−0.203501	+	0.0199879i
$976$	−902.813			−0.925013
$977$	90.3668	−	90.3668i	0.0924942	−	0.0924942i	−0.659346	−	0.751840i	$-0.729167\pi$
$977$	90.3668	−	90.3668i	0.0924942	−	0.0924942i	0.751840	+	0.659346i	$0.229167\pi$
$978$	−121.135	+	121.135i	−0.123860	+	0.123860i
$979$			18.0237i			0.0184103i
$980$	−113.224	−	126.451i	−0.115535	−	0.129032i
$981$		−	1000.70i		−	1.02008i
$982$	−246.608	+	246.608i	−0.251128	+	0.251128i
$983$	−792.321	−	792.321i	−0.806024	−	0.806024i	0.178006	−	0.984029i	$-0.443035\pi$
$983$	−792.321	−	792.321i	−0.806024	−	0.806024i	−0.984029	+	0.178006i	$0.943035\pi$
$984$		−	158.078i		−	0.160649i
$985$	171.642	+	9.47235i	0.174256	+	0.00961660i
$986$			762.309i			0.773133i
$987$	106.930	+	106.930i	0.108338	+	0.108338i
$988$	723.857	+	471.388i	0.732649	+	0.477114i
$989$			629.673i			0.636676i
$990$	−862.703	−	47.6097i	−0.871417	−	0.0480906i
$991$	−395.791			−0.399386			−0.199693	−	0.979859i	$-0.563994\pi$
$991$	−395.791			−0.399386			−0.199693	+	0.979859i	$0.563994\pi$
$992$	124.218	+	124.218i	0.125220	+	0.125220i
$993$	−36.4201	−	36.4201i	−0.0366769	−	0.0366769i
$994$	−9.97160			−0.0100318
$995$	−414.348	+	371.007i	−0.416430	+	0.372871i
$996$			143.773i			0.144351i
$997$	151.445	+	151.445i	0.151900	+	0.151900i	0.778966	−	0.627066i	$-0.215744\pi$
$997$	151.445	+	151.445i	0.151900	+	0.151900i	−0.627066	+	0.778966i	$0.715744\pi$
$998$	−904.459	+	904.459i	−0.906271	+	0.906271i
$999$	251.083			0.251334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.3.h.a.12.3	✓	24
5.2	odd	4		325.3.h.b.168.3		24
5.3	odd	4	inner	65.3.h.a.38.10	yes	24
5.4	even	2		325.3.h.b.207.10		24
13.12	even	2	inner	65.3.h.a.12.10	yes	24
65.12	odd	4		325.3.h.b.168.10		24
65.38	odd	4	inner	65.3.h.a.38.3	yes	24
65.64	even	2		325.3.h.b.207.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.h.a.12.3	✓	24	1.1	even	1	trivial
65.3.h.a.12.10	yes	24	13.12	even	2	inner
65.3.h.a.38.3	yes	24	65.38	odd	4	inner
65.3.h.a.38.10	yes	24	5.3	odd	4	inner
325.3.h.b.168.3		24	5.2	odd	4
325.3.h.b.168.10		24	65.12	odd	4
325.3.h.b.207.3		24	65.64	even	2
325.3.h.b.207.10		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)

\(f(q)\)	\(=\)	\(q+(-1.78036 + 1.78036i) q^{2} +(0.433767 - 0.433767i) q^{3} -2.33933i q^{4} +(3.33534 + 3.72498i) q^{5} +1.54452i q^{6} +(-5.63522 + 5.63522i) q^{7} +(-2.95658 - 2.95658i) q^{8} +8.62369i q^{9} +O(q^{10})\)	\(q+(-1.78036 + 1.78036i) q^{2} +(0.433767 - 0.433767i) q^{3} -2.33933i q^{4} +(3.33534 + 3.72498i) q^{5} +1.54452i q^{6} +(-5.63522 + 5.63522i) q^{7} +(-2.95658 - 2.95658i) q^{8} +8.62369i q^{9} +(-12.5699 - 0.693690i) q^{10} -7.95860i q^{11} +(-1.01472 - 1.01472i) q^{12} +(-7.09417 + 10.8937i) q^{13} -20.0654i q^{14} +(3.06254 + 0.169011i) q^{15} +19.8849 q^{16} +(4.22084 + 4.22084i) q^{17} +(-15.3532 - 15.3532i) q^{18} +28.4044 q^{19} +(8.71395 - 7.80247i) q^{20} +4.88875i q^{21} +(14.1691 + 14.1691i) q^{22} +(16.8593 - 16.8593i) q^{23} -2.56494 q^{24} +(-2.75095 + 24.8482i) q^{25} +(-6.76452 - 32.0248i) q^{26} +(7.64458 + 7.64458i) q^{27} +(13.1826 + 13.1826i) q^{28} -50.7219i q^{29} +(-5.75331 + 5.15151i) q^{30} -5.26889i q^{31} +(-23.5758 + 23.5758i) q^{32} +(-3.45218 - 3.45218i) q^{33} -15.0292 q^{34} +(-39.7865 - 2.19568i) q^{35} +20.1736 q^{36} +(16.4223 - 16.4223i) q^{37} +(-50.5700 + 50.5700i) q^{38} +(1.64811 + 7.80255i) q^{39} +(1.15199 - 20.8744i) q^{40} +61.6304i q^{41} +(-8.70370 - 8.70370i) q^{42} +(-18.6744 + 18.6744i) q^{43} -18.6178 q^{44} +(-32.1231 + 28.7630i) q^{45} +60.0309i q^{46} +(21.8727 - 21.8727i) q^{47} +(8.62540 - 8.62540i) q^{48} -14.5113i q^{49} +(-39.3409 - 49.1363i) q^{50} +3.66173 q^{51} +(25.4840 + 16.5956i) q^{52} +(38.2818 - 38.2818i) q^{53} -27.2201 q^{54} +(29.6456 - 26.5447i) q^{55} +33.3220 q^{56} +(12.3209 - 12.3209i) q^{57} +(90.3030 + 90.3030i) q^{58} +12.8470 q^{59} +(0.395373 - 7.16428i) q^{60} -45.4020 q^{61} +(9.38049 + 9.38049i) q^{62} +(-48.5964 - 48.5964i) q^{63} -4.40705i q^{64} +(-64.2403 + 9.90861i) q^{65} +12.2922 q^{66} +(22.7910 - 22.7910i) q^{67} +(9.87393 - 9.87393i) q^{68} -14.6260i q^{69} +(74.7431 - 66.9249i) q^{70} -0.496956i q^{71} +(25.4967 - 25.4967i) q^{72} +(18.8385 + 18.8385i) q^{73} +58.4750i q^{74} +(9.58506 + 11.9716i) q^{75} -66.4473i q^{76} +(44.8484 + 44.8484i) q^{77} +(-16.8255 - 10.9571i) q^{78} +73.0902i q^{79} +(66.3228 + 74.0707i) q^{80} -70.9813 q^{81} +(-109.724 - 109.724i) q^{82} +(-70.8434 - 70.8434i) q^{83} +11.4364 q^{84} +(-1.64459 + 29.8005i) q^{85} -66.4941i q^{86} +(-22.0015 - 22.0015i) q^{87} +(-23.5303 + 23.5303i) q^{88} -2.26468 q^{89} +(5.98216 - 108.399i) q^{90} +(-21.4112 - 101.366i) q^{91} +(-39.4393 - 39.4393i) q^{92} +(-2.28547 - 2.28547i) q^{93} +77.8822i q^{94} +(94.7386 + 105.806i) q^{95} +20.4528i q^{96} +(-85.2235 + 85.2235i) q^{97} +(25.8353 + 25.8353i) q^{98} +68.6325 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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