LMFDB - Embedded newform 197.2.b.a.196.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,2,Mod(196,197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("197.196"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	197.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.57305291982$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 228x^{12} + 1095x^{10} + 2834x^{8} + 3942x^{6} + 2795x^{4} + 925x^{2} + 112 $ x^16 + 24x^14 + 228x^12 + 1095x^10 + 2834x^8 + 3942x^6 + 2795x^4 + 925*x^2 + 112
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			196.3
Root			$-2.21923i$ of defining polynomial
Character	$\chi$	$=$	197.196
Dual form			197.2.b.a.196.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.21923i q^{2} +2.10111i q^{3} -2.92500 q^{4} -0.563008i q^{5} +4.66286 q^{6} +4.64533 q^{7} +2.05279i q^{8} -1.41466 q^{9} -1.24945 q^{10} +3.29649i q^{11} -6.14575i q^{12} -4.12885i q^{13} -10.3091i q^{14} +1.18294 q^{15} -1.29438 q^{16} -2.75853i q^{17} +3.13947i q^{18} +0.189181 q^{19} +1.64680i q^{20} +9.76035i q^{21} +7.31568 q^{22} -0.612588 q^{23} -4.31314 q^{24} +4.68302 q^{25} -9.16289 q^{26} +3.33096i q^{27} -13.5876 q^{28} -7.36081 q^{29} -2.62522i q^{30} +6.71818i q^{31} +6.97811i q^{32} -6.92629 q^{33} -6.12182 q^{34} -2.61536i q^{35} +4.13789 q^{36} -3.73416 q^{37} -0.419838i q^{38} +8.67517 q^{39} +1.15574 q^{40} +1.64174 q^{41} +21.6605 q^{42} +1.97103 q^{43} -9.64223i q^{44} +0.796468i q^{45} +1.35948i q^{46} -10.2897 q^{47} -2.71963i q^{48} +14.5791 q^{49} -10.3927i q^{50} +5.79597 q^{51} +12.0769i q^{52} -7.36742 q^{53} +7.39219 q^{54} +1.85595 q^{55} +9.53588i q^{56} +0.397491i q^{57} +16.3354i q^{58} -7.15391 q^{59} -3.46010 q^{60} -9.57237 q^{61} +14.9092 q^{62} -6.57158 q^{63} +12.8973 q^{64} -2.32458 q^{65} +15.3711i q^{66} -15.7183i q^{67} +8.06869i q^{68} -1.28711i q^{69} -5.80409 q^{70} -8.27498i q^{71} -2.90401i q^{72} +13.8460i q^{73} +8.28698i q^{74} +9.83955i q^{75} -0.553355 q^{76} +15.3133i q^{77} -19.2522i q^{78} -3.46481i q^{79} +0.728746i q^{80} -11.2427 q^{81} -3.64340i q^{82} +3.54792 q^{83} -28.5490i q^{84} -1.55307 q^{85} -4.37418i q^{86} -15.4659i q^{87} -6.76700 q^{88} -9.42287i q^{89} +1.76755 q^{90} -19.1799i q^{91} +1.79182 q^{92} -14.1156 q^{93} +22.8352i q^{94} -0.106511i q^{95} -14.6618 q^{96} +6.44242 q^{97} -32.3544i q^{98} -4.66343i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 10 q^{6} + 2 q^{7} - 18 q^{9} + 4 q^{10} + 14 q^{15} + 16 q^{16} - 14 q^{19} + 4 q^{22} + 8 q^{23} + 40 q^{24} - 4 q^{25} - 22 q^{26} - 32 q^{28} + 20 q^{29} - 20 q^{33} - 24 q^{34} + 26 q^{36}+ \cdots + 18 q^{97}+O(q^{100}) $ 16 * q - 16 * q^4 - 10 * q^6 + 2 * q^7 - 18 * q^9 + 4 * q^10 + 14 * q^15 + 16 * q^16 - 14 * q^19 + 4 * q^22 + 8 * q^23 + 40 * q^24 - 4 * q^25 - 22 * q^26 - 32 * q^28 + 20 * q^29 - 20 * q^33 - 24 * q^34 + 26 * q^36 - 14 * q^37 + 6 * q^39 + 2 * q^40 - 14 * q^41 + 2 * q^42 + 22 * q^43 - 14 * q^47 - 2 * q^49 + 26 * q^51 - 2 * q^53 + 78 * q^54 + 22 * q^55 - 18 * q^59 - 74 * q^60 - 10 * q^61 - 6 * q^62 - 58 * q^63 - 10 * q^64 + 50 * q^65 + 50 * q^70 + 50 * q^76 + 4 * q^81 - 4 * q^85 + 64 * q^88 - 112 * q^90 - 100 * q^92 + 10 * q^93 - 60 * q^96 + 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	2.21923i		−	1.56924i	−0.619980	−	0.784618i	$-0.712859\pi$
$2$		−	2.21923i		−	1.56924i	0.619980	−	0.784618i	$-0.287141\pi$
$3$			2.10111i			1.21308i	0.795054	+	0.606538i	$0.207442\pi$
$3$			2.10111i			1.21308i	−0.795054	+	0.606538i	$0.792558\pi$
$4$	−2.92500			−1.46250
$5$		−	0.563008i		−	0.251785i	−0.992044	−	0.125892i	$-0.959821\pi$
$5$		−	0.563008i		−	0.251785i	0.992044	−	0.125892i	$-0.0401794\pi$
$6$	4.66286			1.90360
$7$	4.64533			1.75577			0.877885	−	0.478872i	$-0.158954\pi$
$7$	4.64533			1.75577			0.877885	+	0.478872i	$0.158954\pi$
$8$			2.05279i			0.725770i
$9$	−1.41466			−0.471555
$10$	−1.24945			−0.395110
$11$			3.29649i			0.993929i	0.867771	+	0.496964i	$0.165552\pi$
$11$			3.29649i			0.993929i	−0.867771	+	0.496964i	$0.834448\pi$
$12$		−	6.14575i		−	1.77412i
$13$		−	4.12885i		−	1.14514i	−0.819857	−	0.572569i	$-0.805947\pi$
$13$		−	4.12885i		−	1.14514i	0.819857	−	0.572569i	$-0.194053\pi$
$14$		−	10.3091i		−	2.75522i
$15$	1.18294			0.305434
$16$	−1.29438			−0.323595
$17$		−	2.75853i		−	0.669041i	−0.942388	−	0.334521i	$-0.891426\pi$
$17$		−	2.75853i		−	0.669041i	0.942388	−	0.334521i	$-0.108574\pi$
$18$			3.13947i			0.739981i
$19$	0.189181			0.0434012			0.0217006	−	0.999765i	$-0.493092\pi$
$19$	0.189181			0.0434012			0.0217006	+	0.999765i	$0.493092\pi$
$20$			1.64680i			0.368235i
$21$			9.76035i			2.12988i
$22$	7.31568			1.55971
$23$	−0.612588			−0.127733			−0.0638667	−	0.997958i	$-0.520343\pi$
$23$	−0.612588			−0.127733			−0.0638667	+	0.997958i	$0.520343\pi$
$24$	−4.31314			−0.880415
$25$	4.68302			0.936604
$26$	−9.16289			−1.79699
$27$			3.33096i			0.641044i
$28$	−13.5876			−2.56781
$29$	−7.36081			−1.36687			−0.683434	−	0.730012i	$-0.739514\pi$
$29$	−7.36081			−1.36687			−0.683434	+	0.730012i	$0.739514\pi$
$30$		−	2.62522i		−	0.479298i
$31$			6.71818i			1.20662i	0.797506	+	0.603311i	$0.206152\pi$
$31$			6.71818i			1.20662i	−0.797506	+	0.603311i	$0.793848\pi$
$32$			6.97811i			1.23357i
$33$	−6.92629			−1.20571
$34$	−6.12182			−1.04988
$35$		−	2.61536i		−	0.442076i
$36$	4.13789			0.689649
$37$	−3.73416			−0.613892			−0.306946	−	0.951727i	$-0.599307\pi$
$37$	−3.73416			−0.613892			−0.306946	+	0.951727i	$0.599307\pi$
$38$		−	0.419838i		−	0.0681067i
$39$	8.67517			1.38914
$40$	1.15574			0.182738
$41$	1.64174			0.256396			0.128198	−	0.991749i	$-0.459081\pi$
$41$	1.64174			0.256396			0.128198	+	0.991749i	$0.459081\pi$
$42$	21.6605			3.34229
$43$	1.97103			0.300580			0.150290	−	0.988642i	$-0.451979\pi$
$43$	1.97103			0.300580			0.150290	+	0.988642i	$0.451979\pi$
$44$		−	9.64223i		−	1.45362i
$45$			0.796468i			0.118730i
$46$			1.35948i			0.200444i
$47$	−10.2897			−1.50090			−0.750450	−	0.660927i	$-0.770163\pi$
$47$	−10.2897			−1.50090			−0.750450	+	0.660927i	$0.770163\pi$
$48$		−	2.71963i		−	0.392545i
$49$	14.5791			2.08273
$50$		−	10.3927i		−	1.46975i
$51$	5.79597			0.811598
$52$			12.0769i			1.67476i
$53$	−7.36742			−1.01199			−0.505996	−	0.862536i	$-0.668875\pi$
$53$	−7.36742			−1.01199			−0.505996	+	0.862536i	$0.668875\pi$
$54$	7.39219			1.00595
$55$	1.85595			0.250256
$56$			9.53588i			1.27429i
$57$			0.397491i			0.0526489i
$58$			16.3354i			2.14494i
$59$	−7.15391			−0.931359			−0.465680	−	0.884953i	$-0.654190\pi$
$59$	−7.15391			−0.931359			−0.465680	+	0.884953i	$0.654190\pi$
$60$	−3.46010			−0.446697
$61$	−9.57237			−1.22562			−0.612808	−	0.790232i	$-0.709960\pi$
$61$	−9.57237			−1.22562			−0.612808	+	0.790232i	$0.709960\pi$
$62$	14.9092			1.89347
$63$	−6.57158			−0.827942
$64$	12.8973			1.61216
$65$	−2.32458			−0.288328
$66$			15.3711i			1.89205i
$67$		−	15.7183i		−	1.92029i	−0.279495	−	0.960147i	$-0.590167\pi$
$67$		−	15.7183i		−	1.92029i	0.279495	−	0.960147i	$-0.409833\pi$
$68$			8.06869i			0.978473i
$69$		−	1.28711i		−	0.154950i
$70$	−5.80409			−0.693721
$71$		−	8.27498i		−	0.982059i	−0.871143	−	0.491030i	$-0.836621\pi$
$71$		−	8.27498i		−	0.982059i	0.871143	−	0.491030i	$-0.163379\pi$
$72$		−	2.90401i		−	0.342241i
$73$			13.8460i			1.62055i	0.586049	+	0.810276i	$0.300683\pi$
$73$			13.8460i			1.62055i	−0.586049	+	0.810276i	$0.699317\pi$
$74$			8.28698i			0.963342i
$75$			9.83955i			1.13617i
$76$	−0.553355			−0.0634742
$77$			15.3133i			1.74511i
$78$		−	19.2522i		−	2.17989i
$79$		−	3.46481i		−	0.389822i	−0.980821	−	0.194911i	$-0.937558\pi$
$79$		−	3.46481i		−	0.389822i	0.980821	−	0.194911i	$-0.0624418\pi$
$80$			0.728746i			0.0814763i
$81$	−11.2427			−1.24919
$82$		−	3.64340i		−	0.402346i
$83$	3.54792			0.389435			0.194718	−	0.980859i	$-0.437621\pi$
$83$	3.54792			0.389435			0.194718	+	0.980859i	$0.437621\pi$
$84$		−	28.5490i		−	3.11495i
$85$	−1.55307			−0.168454
$86$		−	4.37418i		−	0.471680i
$87$		−	15.4659i		−	1.65812i
$88$	−6.76700			−0.721364
$89$		−	9.42287i		−	0.998822i	−0.866365	−	0.499411i	$-0.833550\pi$
$89$		−	9.42287i		−	0.998822i	0.866365	−	0.499411i	$-0.166450\pi$
$90$	1.76755			0.186316
$91$		−	19.1799i		−	2.01060i
$92$	1.79182			0.186810
$93$	−14.1156			−1.46372
$94$			22.8352i			2.35527i
$95$		−	0.106511i		−	0.0109278i
$96$	−14.6618			−1.49641
$97$	6.44242			0.654129			0.327064	−	0.945002i	$-0.393941\pi$
$97$	6.44242			0.654129			0.327064	+	0.945002i	$0.393941\pi$
$98$		−	32.3544i		−	3.26829i
$99$		−	4.66343i		−	0.468692i
$100$	−13.6978			−1.36978
$101$	6.55750			0.652496			0.326248	−	0.945284i	$-0.394216\pi$
$101$	6.55750			0.652496			0.326248	+	0.945284i	$0.394216\pi$
$102$		−	12.8626i		−	1.27359i
$103$			10.2904i			1.01395i	0.861962	+	0.506973i	$0.169236\pi$
$103$			10.2904i			1.01395i	−0.861962	+	0.506973i	$0.830764\pi$
$104$	8.47566			0.831107
$105$	5.49516			0.536272
$106$			16.3500i			1.58805i
$107$	19.7908			1.91325			0.956625	−	0.291322i	$-0.0940950\pi$
$107$	19.7908			1.91325			0.956625	+	0.291322i	$0.0940950\pi$
$108$		−	9.74307i		−	0.937527i
$109$	−15.4089			−1.47590			−0.737952	−	0.674853i	$-0.764207\pi$
$109$	−15.4089			−1.47590			−0.737952	+	0.674853i	$0.764207\pi$
$110$		−	4.11879i		−	0.392711i
$111$		−	7.84589i		−	0.744699i
$112$	−6.01282			−0.568158
$113$			2.98691i			0.280985i	0.990082	+	0.140492i	$0.0448685\pi$
$113$			2.98691i			0.280985i	−0.990082	+	0.140492i	$0.955131\pi$
$114$	0.882125			0.0826186
$115$			0.344892i			0.0321613i
$116$	21.5304			1.99904
$117$			5.84094i			0.539995i
$118$			15.8762i			1.46152i
$119$		−	12.8143i		−	1.17468i
$120$			2.42833i			0.221675i
$121$	0.133160			0.0121054
$122$			21.2433i			1.92328i
$123$			3.44947i			0.311028i
$124$		−	19.6507i		−	1.76468i
$125$		−	5.45162i		−	0.487608i
$126$			14.5839i			1.29924i
$127$	−5.93996			−0.527087			−0.263543	−	0.964648i	$-0.584891\pi$
$127$	−5.93996			−0.527087			−0.263543	+	0.964648i	$0.584891\pi$
$128$		−	14.6659i		−	1.29629i
$129$			4.14136i			0.364626i
$130$			5.15878i			0.452455i
$131$			4.86484i			0.425043i	0.977156	+	0.212522i	$0.0681676\pi$
$131$			4.86484i			0.425043i	−0.977156	+	0.212522i	$0.931832\pi$
$132$	20.2594			1.76335
$133$	0.878810			0.0762025
$134$	−34.8825			−3.01339
$135$	1.87536			0.161405
$136$	5.66268			0.485570
$137$	13.5581			1.15835			0.579175	−	0.815203i	$-0.303375\pi$
$137$	13.5581			1.15835			0.579175	+	0.815203i	$0.303375\pi$
$138$	−2.85641			−0.243154
$139$			10.8222i			0.917928i	0.888455	+	0.458964i	$0.151779\pi$
$139$			10.8222i			0.917928i	−0.888455	+	0.458964i	$0.848221\pi$
$140$			7.64992i			0.646536i
$141$		−	21.6197i		−	1.82071i
$142$	−18.3641			−1.54108
$143$	13.6107			1.13819
$144$	1.83111			0.152593
$145$			4.14420i			0.344157i
$146$	30.7275			2.54303
$147$			30.6323i			2.52651i
$148$	10.9224			0.897817
$149$			20.5178i			1.68088i	0.541904	+	0.840440i	$0.317704\pi$
$149$			20.5178i			1.68088i	−0.541904	+	0.840440i	$0.682296\pi$
$150$	21.8363			1.78292
$151$		−	2.82986i		−	0.230290i	−0.993349	−	0.115145i	$-0.963267\pi$
$151$		−	2.82986i		−	0.230290i	0.993349	−	0.115145i	$-0.0367333\pi$
$152$			0.388349i			0.0314993i
$153$			3.90239i			0.315490i
$154$	33.9837			2.73849
$155$	3.78239			0.303809
$156$	−25.3749			−2.03162
$157$	−7.95930			−0.635221			−0.317611	−	0.948221i	$-0.602880\pi$
$157$	−7.95930			−0.635221			−0.317611	+	0.948221i	$0.602880\pi$
$158$	−7.68923			−0.611722
$159$		−	15.4798i		−	1.22762i
$160$	3.92873			0.310593
$161$	−2.84567			−0.224270
$162$			24.9502i			1.96027i
$163$	8.50043			0.665805			0.332903	−	0.942961i	$-0.391972\pi$
$163$	8.50043			0.665805			0.332903	+	0.942961i	$0.391972\pi$
$164$	−4.80208			−0.374979
$165$			3.89956i			0.303580i
$166$		−	7.87367i		−	0.611116i
$167$			13.1042i			1.01403i	0.861936	+	0.507017i	$0.169252\pi$
$167$			13.1042i			1.01403i	−0.861936	+	0.507017i	$0.830748\pi$
$168$	−20.0359			−1.54581
$169$	−4.04742			−0.311340
$170$			3.44663i			0.264345i
$171$	−0.267628			−0.0204660
$172$	−5.76527			−0.439598
$173$	15.5407			1.18154			0.590770	−	0.806840i	$-0.298824\pi$
$173$	15.5407			1.18154			0.590770	+	0.806840i	$0.298824\pi$
$174$	−34.3224			−2.60197
$175$	21.7542			1.64446
$176$		−	4.26691i		−	0.321630i
$177$		−	15.0311i		−	1.12981i
$178$	−20.9116			−1.56739
$179$		−	18.4693i		−	1.38046i	−0.723590	−	0.690230i	$-0.757509\pi$
$179$		−	18.4693i		−	1.38046i	0.723590	−	0.690230i	$-0.242491\pi$
$180$		−	2.32967i		−	0.173643i
$181$	19.5704			1.45466			0.727328	−	0.686289i	$-0.240762\pi$
$181$	19.5704			1.45466			0.727328	+	0.686289i	$0.240762\pi$
$182$	−42.5646			−3.15510
$183$		−	20.1126i		−	1.48677i
$184$		−	1.25751i		−	0.0927051i
$185$			2.10236i			0.154569i
$186$			31.3259i			2.29693i
$187$	9.09346			0.664979
$188$	30.0972			2.19507
$189$			15.4734i			1.12553i
$190$	−0.236372			−0.0171482
$191$	−19.3057			−1.39691			−0.698457	−	0.715652i	$-0.746130\pi$
$191$	−19.3057			−1.39691			−0.698457	+	0.715652i	$0.746130\pi$
$192$			27.0986i			1.95568i
$193$	−11.5650			−0.832465			−0.416233	−	0.909258i	$-0.636650\pi$
$193$	−11.5650			−0.832465			−0.416233	+	0.909258i	$0.636650\pi$
$194$		−	14.2972i		−	1.02648i
$195$		−	4.88419i		−	0.349764i
$196$	−42.6438			−3.04599
$197$	−6.11357	−	12.6342i	−0.435574	−	0.900153i
$197$	−6.11357	−	12.6342i	−0.435574	−	0.900153i
$198$	−10.3492			−0.735488
$199$		−	10.0560i		−	0.712853i	−0.934323	−	0.356427i	$-0.883995\pi$
$199$		−	10.0560i		−	0.712853i	0.934323	−	0.356427i	$-0.116005\pi$
$200$			9.61325i			0.679760i
$201$	33.0259			2.32946
$202$		−	14.5526i		−	1.02392i
$203$	−34.1934			−2.39991
$204$	−16.9532			−1.18696
$205$		−	0.924311i		−	0.0645567i
$206$	22.8369			1.59112
$207$	0.866606			0.0602333
$208$			5.34430i			0.370561i
$209$			0.623634i			0.0431377i
$210$		−	12.1950i		−	0.841537i
$211$		−	19.2753i		−	1.32697i	−0.748191	−	0.663483i	$-0.769077\pi$
$211$		−	19.2753i		−	1.32697i	0.748191	−	0.663483i	$-0.230923\pi$
$212$	21.5497			1.48004
$213$	17.3866			1.19131
$214$		−	43.9204i		−	3.00234i
$215$		−	1.10971i		−	0.0756814i
$216$	−6.83777			−0.465251
$217$			31.2082i			2.11855i
$218$			34.1959i			2.31604i
$219$	−29.0920			−1.96585
$220$	−5.42865			−0.366000
$221$	−11.3896			−0.766144
$222$	−17.4119			−1.16861
$223$	22.9146			1.53448			0.767238	−	0.641363i	$-0.221631\pi$
$223$	22.9146			1.53448			0.767238	+	0.641363i	$0.221631\pi$
$224$			32.4156i			2.16586i
$225$	−6.62491			−0.441660
$226$	6.62865			0.440931
$227$			5.65166i			0.375114i	0.982254	+	0.187557i	$0.0600569\pi$
$227$			5.65166i			0.375114i	−0.982254	+	0.187557i	$0.939943\pi$
$228$		−	1.16266i		−	0.0769991i
$229$			2.48643i			0.164308i	0.996620	+	0.0821539i	$0.0261799\pi$
$229$			2.48643i			0.164308i	−0.996620	+	0.0821539i	$0.973820\pi$
$230$	0.765396			0.0504687
$231$	−32.1749			−2.11695
$232$		−	15.1102i		−	0.992033i
$233$	9.66588			0.633233			0.316617	−	0.948554i	$-0.397453\pi$
$233$	9.66588			0.633233			0.316617	+	0.948554i	$0.397453\pi$
$234$	12.9624			0.847380
$235$			5.79316i			0.377904i
$236$	20.9252			1.36211
$237$	7.27995			0.472884
$238$	−28.4379			−1.84335
$239$	7.21102			0.466442			0.233221	−	0.972424i	$-0.425073\pi$
$239$	7.21102			0.466442			0.233221	+	0.972424i	$0.425073\pi$
$240$	−1.53118			−0.0988370
$241$		−	25.8732i		−	1.66664i	−0.552790	−	0.833321i	$-0.686437\pi$
$241$		−	25.8732i		−	1.66664i	0.552790	−	0.833321i	$-0.313563\pi$
$242$		−	0.295512i		−	0.0189962i
$243$		−	13.6293i		−	0.874320i
$244$	27.9992			1.79246
$245$		−	8.20814i		−	0.524399i
$246$	7.65518			0.488076
$247$		−	0.781102i		−	0.0497003i
$248$	−13.7910			−0.875730
$249$			7.45458i			0.472415i
$250$	−12.0984			−0.765171
$251$	−15.1941			−0.959045			−0.479522	−	0.877530i	$-0.659190\pi$
$251$	−15.1941			−0.959045			−0.479522	+	0.877530i	$0.659190\pi$
$252$	19.2219			1.21086
$253$		−	2.01939i		−	0.126958i
$254$			13.1822i			0.827123i
$255$		−	3.26318i		−	0.204348i
$256$	−6.75246			−0.422029
$257$	2.60948			0.162775			0.0813876	−	0.996683i	$-0.474065\pi$
$257$	2.60948			0.162775			0.0813876	+	0.996683i	$0.474065\pi$
$258$	9.19064			0.572184
$259$	−17.3464			−1.07785
$260$	6.79938			0.421680
$261$	10.4131			0.644554
$262$	10.7962			0.666993
$263$			19.5944i			1.20824i	0.796892	+	0.604122i	$0.206476\pi$
$263$			19.5944i			1.20824i	−0.796892	+	0.604122i	$0.793524\pi$
$264$		−	14.2182i		−	0.875070i
$265$			4.14791i			0.254804i
$266$		−	1.95028i		−	0.119580i
$267$	19.7985			1.21165
$268$			45.9760i			2.80843i
$269$			8.61415i			0.525214i	0.964903	+	0.262607i	$0.0845823\pi$
$269$			8.61415i			0.525214i	−0.964903	+	0.262607i	$0.915418\pi$
$270$		−	4.16186i		−	0.253283i
$271$		−	4.58387i		−	0.278450i	−0.990261	−	0.139225i	$-0.955539\pi$
$271$		−	4.58387i		−	0.278450i	0.990261	−	0.139225i	$-0.0444611\pi$
$272$			3.57058i			0.216498i
$273$	40.2990			2.43901
$274$		−	30.0887i		−	1.81772i
$275$			15.4375i			0.930918i
$276$			3.76481i			0.226615i
$277$		−	19.6946i		−	1.18333i	−0.806183	−	0.591666i	$-0.798471\pi$
$277$		−	19.6946i		−	1.18333i	0.806183	−	0.591666i	$-0.201529\pi$
$278$	24.0170			1.44045
$279$		−	9.50398i		−	0.568988i
$280$	5.36878			0.320846
$281$		−	6.26461i		−	0.373715i	−0.982387	−	0.186858i	$-0.940170\pi$
$281$		−	6.26461i		−	0.373715i	0.982387	−	0.186858i	$-0.0598303\pi$
$282$	−47.9792			−2.85712
$283$			9.80509i			0.582852i	0.956593	+	0.291426i	$0.0941297\pi$
$283$			9.80509i			0.582852i	−0.956593	+	0.291426i	$0.905870\pi$
$284$			24.2043i			1.43626i
$285$	0.223791			0.0132562
$286$		−	30.2054i		−	1.78608i
$287$	7.62641			0.450173
$288$		−	9.87168i		−	0.581695i
$289$	9.39052			0.552384
$290$	9.19694			0.540063
$291$			13.5362i			0.793508i
$292$		−	40.4995i		−	2.37006i
$293$	−18.1583			−1.06082			−0.530410	−	0.847741i	$-0.677962\pi$
$293$	−18.1583			−1.06082			−0.530410	+	0.847741i	$0.677962\pi$
$294$	67.9802			3.96468
$295$			4.02771i			0.234502i
$296$		−	7.66544i		−	0.445545i
$297$	−10.9805			−0.637152
$298$	45.5337			2.63770
$299$			2.52928i			0.146272i
$300$		−	28.7807i		−	1.66165i
$301$	9.15610			0.527749
$302$	−6.28011			−0.361380
$303$			13.7780i			0.791527i
$304$	−0.244872			−0.0140444
$305$			5.38932i			0.308592i
$306$	8.66032			0.495078
$307$			20.1126i			1.14789i	0.818895	+	0.573944i	$0.194587\pi$
$307$			20.1126i			1.14789i	−0.818895	+	0.573944i	$0.805413\pi$
$308$		−	44.7913i		−	2.55222i
$309$	−21.6213			−1.23000
$310$		−	8.39401i		−	0.476748i
$311$	18.3336			1.03960			0.519802	−	0.854287i	$-0.326006\pi$
$311$	18.3336			1.03960			0.519802	+	0.854287i	$0.326006\pi$
$312$			17.8083i			1.00820i
$313$	−23.5484			−1.33103			−0.665516	−	0.746384i	$-0.731788\pi$
$313$	−23.5484			−1.33103			−0.665516	+	0.746384i	$0.731788\pi$
$314$			17.6635i			0.996812i
$315$			3.69985i			0.208463i
$316$			10.1346i			0.570114i
$317$		−	13.0967i		−	0.735587i	−0.929908	−	0.367793i	$-0.880113\pi$
$317$		−	13.0967i		−	0.735587i	0.929908	−	0.367793i	$-0.119887\pi$
$318$	−34.3532			−1.92643
$319$		−	24.2648i		−	1.35857i
$320$		−	7.26128i		−	0.405918i
$321$			41.5827i			2.32092i
$322$			6.31521i			0.351933i
$323$		−	0.521862i		−	0.0290372i
$324$	32.8849			1.82694
$325$		−	19.3355i		−	1.07254i
$326$		−	18.8644i		−	1.04481i
$327$		−	32.3758i		−	1.79038i
$328$			3.37014i			0.186085i
$329$	−47.7989			−2.63524
$330$	8.65402			0.476388
$331$	−32.4860			−1.78559			−0.892796	−	0.450462i	$-0.851259\pi$
$331$	−32.4860			−1.78559			−0.892796	+	0.450462i	$0.851259\pi$
$332$	−10.3777			−0.569549
$333$	5.28259			0.289484
$334$	29.0813			1.59126
$335$	−8.84952			−0.483501
$336$		−	12.6336i		−	0.689219i
$337$			3.97241i			0.216391i	0.994130	+	0.108195i	$0.0345072\pi$
$337$			3.97241i			0.216391i	−0.994130	+	0.108195i	$0.965493\pi$
$338$			8.98217i			0.488566i
$339$	−6.27582			−0.340856
$340$	4.54274			0.246365
$341$	−22.1464			−1.19930
$342$			0.593929i			0.0321160i
$343$	35.2074			1.90102
$344$			4.04611i			0.218152i
$345$	−0.724656			−0.0390142
$346$		−	34.4885i		−	1.85411i
$347$	8.52685			0.457746			0.228873	−	0.973456i	$-0.426496\pi$
$347$	8.52685			0.457746			0.228873	+	0.973456i	$0.426496\pi$
$348$			45.2377i			2.42499i
$349$			21.5768i			1.15498i	0.816399	+	0.577489i	$0.195967\pi$
$349$			21.5768i			1.15498i	−0.816399	+	0.577489i	$0.804033\pi$
$350$		−	48.2776i		−	2.58055i
$351$	13.7531			0.734084
$352$	−23.0033			−1.22608
$353$	−15.5581			−0.828074			−0.414037	−	0.910260i	$-0.635882\pi$
$353$	−15.5581			−0.828074			−0.414037	+	0.910260i	$0.635882\pi$
$354$	−33.3576			−1.77294
$355$	−4.65888			−0.247268
$356$			27.5619i			1.46078i
$357$	26.9242			1.42498
$358$	−40.9877			−2.16627
$359$		−	16.9281i		−	0.893429i	−0.894676	−	0.446715i	$-0.852594\pi$
$359$		−	16.9281i		−	0.893429i	0.894676	−	0.446715i	$-0.147406\pi$
$360$	−1.63498			−0.0861710
$361$	−18.9642			−0.998116
$362$		−	43.4313i		−	2.28270i
$363$			0.279783i			0.0146848i
$364$			56.1011i			2.94050i
$365$	7.79541			0.408030
$366$	−44.6346			−2.33309
$367$			19.4678i			1.01621i	0.861295	+	0.508105i	$0.169654\pi$
$367$			19.4678i			1.01621i	−0.861295	+	0.508105i	$0.830346\pi$
$368$	0.792921			0.0413339
$369$	−2.32251			−0.120905
$370$	4.66563			0.242555
$371$	−34.2241			−1.77683
$372$	41.2882			2.14070
$373$			14.9999i			0.776665i	0.921519	+	0.388332i	$0.126949\pi$
$373$			14.9999i			0.776665i	−0.921519	+	0.388332i	$0.873051\pi$
$374$		−	20.1805i		−	1.04351i
$375$	11.4545			0.591505
$376$		−	21.1225i		−	1.08931i
$377$			30.3917i			1.56525i
$378$	34.3392			1.76622
$379$	12.4468			0.639351			0.319675	−	0.947527i	$-0.396426\pi$
$379$	12.4468			0.639351			0.319675	+	0.947527i	$0.396426\pi$
$380$			0.311543i			0.0159818i
$381$		−	12.4805i		−	0.639396i
$382$			42.8439i			2.19209i
$383$			9.30081i			0.475249i	0.971357	+	0.237625i	$0.0763688\pi$
$383$			9.30081i			0.475249i	−0.971357	+	0.237625i	$0.923631\pi$
$384$	30.8147			1.57250
$385$	8.62150			0.439392
$386$			25.6654i			1.30633i
$387$	−2.78835			−0.141740
$388$	−18.8441			−0.956663
$389$		−	26.1257i		−	1.32463i	−0.749227	−	0.662313i	$-0.769575\pi$
$389$		−	26.1257i		−	1.32463i	0.749227	−	0.662313i	$-0.230425\pi$
$390$	−10.8392			−0.548862
$391$			1.68984i			0.0854589i
$392$			29.9278i			1.51158i
$393$	−10.2216			−0.515610
$394$	−28.0384	+	13.5674i	−1.41255	+	0.683518i
$395$	−1.95072			−0.0981512
$396$			13.6405i			0.685462i
$397$		−	22.0168i		−	1.10499i	−0.833516	−	0.552495i	$-0.813676\pi$
$397$		−	22.0168i		−	1.10499i	0.833516	−	0.552495i	$-0.186324\pi$
$398$	−22.3167			−1.11863
$399$			1.84648i			0.0924394i
$400$	−6.06161			−0.303080
$401$	27.5377			1.37517			0.687583	−	0.726105i	$-0.258672\pi$
$401$	27.5377			1.37517			0.687583	+	0.726105i	$0.258672\pi$
$402$		−	73.2921i		−	3.65548i
$403$	27.7384			1.38175
$404$	−19.1807			−0.954275
$405$			6.32974i			0.314527i
$406$			75.8831i			3.76602i
$407$		−	12.3096i		−	0.610165i
$408$			11.8979i			0.589034i
$409$	19.7440			0.976280			0.488140	−	0.872765i	$-0.337675\pi$
$409$	19.7440			0.976280			0.488140	+	0.872765i	$0.337675\pi$
$410$	−2.05126			−0.101305
$411$			28.4871i			1.40517i
$412$		−	30.0995i		−	1.48290i
$413$	−33.2323			−1.63525
$414$		−	1.92320i		−	0.0945202i
$415$		−	1.99751i		−	0.0980539i
$416$	28.8116			1.41260
$417$	−22.7387			−1.11352
$418$	1.38399			0.0676932
$419$	18.4085			0.899316			0.449658	−	0.893201i	$-0.351546\pi$
$419$	18.4085			0.899316			0.449658	+	0.893201i	$0.351546\pi$
$420$	−16.0733			−0.784298
$421$		−	10.4114i		−	0.507420i	−0.967280	−	0.253710i	$-0.918349\pi$
$421$		−	10.4114i		−	0.507420i	0.967280	−	0.253710i	$-0.0816510\pi$
$422$	−42.7764			−2.08232
$423$	14.5564			0.707757
$424$		−	15.1238i		−	0.734474i
$425$		−	12.9182i		−	0.626627i
$426$		−	38.5850i		−	1.86945i
$427$	−44.4668			−2.15190
$428$	−57.8881			−2.79813
$429$			28.5976i			1.38071i
$430$	−2.46270			−0.118762
$431$	11.5080			0.554321			0.277160	−	0.960824i	$-0.410607\pi$
$431$	11.5080			0.554321			0.277160	+	0.960824i	$0.410607\pi$
$432$		−	4.31153i		−	0.207439i
$433$	−2.43909			−0.117215			−0.0586077	−	0.998281i	$-0.518666\pi$
$433$	−2.43909			−0.117215			−0.0586077	+	0.998281i	$0.518666\pi$
$434$	69.2582			3.32450
$435$	−8.70741			−0.417488
$436$	45.0710			2.15851
$437$	−0.115890			−0.00554378
$438$			64.5619i			3.08489i
$439$		−	31.8967i		−	1.52234i	−0.648550	−	0.761172i	$-0.724624\pi$
$439$		−	31.8967i		−	1.52234i	0.648550	−	0.761172i	$-0.275376\pi$
$440$			3.80987i			0.181629i
$441$	−20.6245			−0.982120
$442$			25.2761i			1.20226i
$443$	23.1491			1.09985			0.549923	−	0.835215i	$-0.314657\pi$
$443$	23.1491			1.09985			0.549923	+	0.835215i	$0.314657\pi$
$444$			22.9492i			1.08912i
$445$	−5.30515			−0.251488
$446$		−	50.8529i		−	2.40795i
$447$	−43.1101			−2.03904
$448$	59.9122			2.83058
$449$	29.3535			1.38528			0.692638	−	0.721285i	$-0.256448\pi$
$449$	29.3535			1.38528			0.692638	+	0.721285i	$0.256448\pi$
$450$			14.7022i			0.693069i
$451$			5.41197i			0.254840i
$452$		−	8.73670i		−	0.410940i
$453$	5.94584			0.279360
$454$	12.5424			0.588642
$455$	−10.7984			−0.506238
$456$	−0.815965			−0.0382110
$457$	20.1237			0.941346			0.470673	−	0.882308i	$-0.344011\pi$
$457$	20.1237			0.941346			0.470673	+	0.882308i	$0.344011\pi$
$458$	5.51796			0.257838
$459$	9.18856			0.428885
$460$		−	1.00881i		−	0.0470359i
$461$			35.1172i			1.63557i	0.575525	+	0.817785i	$0.304798\pi$
$461$			35.1172i			1.63557i	−0.575525	+	0.817785i	$0.695202\pi$
$462$			71.4036i			3.32200i
$463$			10.6702i			0.495885i	0.968775	+	0.247942i	$0.0797544\pi$
$463$			10.6702i			0.495885i	−0.968775	+	0.247942i	$0.920246\pi$
$464$	9.52768			0.442312
$465$			7.94722i			0.368543i
$466$		−	21.4509i		−	0.993692i
$467$		−	3.33874i		−	0.154498i	−0.997012	−	0.0772492i	$-0.975386\pi$
$467$		−	3.33874i		−	0.154498i	0.997012	−	0.0772492i	$-0.0246137\pi$
$468$		−	17.0847i		−	0.789743i
$469$		−	73.0166i		−	3.37159i
$470$	12.8564			0.593020
$471$		−	16.7234i		−	0.770572i
$472$		−	14.6855i		−	0.675953i
$473$			6.49749i			0.298755i
$474$		−	16.1559i		−	0.742066i
$475$	0.885940			0.0406497
$476$			37.4817i			1.71797i
$477$	10.4224			0.477210
$478$		−	16.0029i		−	0.731957i
$479$	15.4474			0.705810			0.352905	−	0.935659i	$-0.385194\pi$
$479$	15.4474			0.705810			0.352905	+	0.935659i	$0.385194\pi$
$480$			8.25470i			0.376774i
$481$			15.4178i			0.702991i
$482$	−57.4188			−2.61535
$483$		−	5.97907i		−	0.272057i
$484$	−0.389492			−0.0177042
$485$		−	3.62713i		−	0.164700i
$486$	−30.2466			−1.37201
$487$	−34.3593			−1.55697			−0.778484	−	0.627665i	$-0.784011\pi$
$487$	−34.3593			−1.55697			−0.778484	+	0.627665i	$0.784011\pi$
$488$		−	19.6500i		−	0.889516i
$489$			17.8603i			0.807673i
$490$	−18.2158			−0.822905
$491$	−11.0066			−0.496719			−0.248360	−	0.968668i	$-0.579891\pi$
$491$	−11.0066			−0.496719			−0.248360	+	0.968668i	$0.579891\pi$
$492$		−	10.0897i		−	0.454879i
$493$			20.3050i			0.914491i
$494$	−1.73345			−0.0779915
$495$	−2.62555			−0.118010
$496$		−	8.69588i		−	0.390456i
$497$		−	38.4400i		−	1.72427i
$498$	16.5435			0.741330
$499$	38.2261			1.71124			0.855618	−	0.517608i	$-0.173177\pi$
$499$	38.2261			1.71124			0.855618	+	0.517608i	$0.173177\pi$
$500$			15.9460i			0.713126i
$501$	−27.5334			−1.23010
$502$			33.7193i			1.50497i
$503$	−1.02627			−0.0457591			−0.0228795	−	0.999738i	$-0.507283\pi$
$503$	−1.02627			−0.0457591			−0.0228795	+	0.999738i	$0.507283\pi$
$504$		−	13.4901i		−	0.600896i
$505$		−	3.69193i		−	0.164289i
$506$	−4.48150			−0.199227
$507$		−	8.50407i		−	0.377679i
$508$	17.3744			0.770864
$509$			26.0268i			1.15362i	0.816879	+	0.576809i	$0.195702\pi$
$509$			26.0268i			1.15362i	−0.816879	+	0.576809i	$0.804298\pi$
$510$	−7.24176			−0.320670
$511$			64.3192i			2.84531i
$512$		−	14.3465i		−	0.634032i
$513$			0.630156i			0.0278221i
$514$		−	5.79105i		−	0.255432i
$515$	5.79360			0.255296
$516$		−	12.1135i		−	0.533266i
$517$		−	33.9197i		−	1.49179i
$518$			38.4957i			1.69141i
$519$			32.6528i			1.43330i
$520$		−	4.77186i		−	0.209260i
$521$	−31.0693			−1.36117			−0.680585	−	0.732669i	$-0.738275\pi$
$521$	−31.0693			−1.36117			−0.680585	+	0.732669i	$0.738275\pi$
$522$		−	23.1091i		−	1.01146i
$523$			9.62558i			0.420897i	0.977605	+	0.210449i	$0.0674925\pi$
$523$			9.62558i			0.420897i	−0.977605	+	0.210449i	$0.932508\pi$
$524$		−	14.2297i		−	0.621625i
$525$			45.7079i			1.99486i
$526$	43.4846			1.89602
$527$	18.5323			0.807279
$528$	8.96525			0.390162
$529$	−22.6247			−0.983684
$530$	9.20519			0.399848
$531$	10.1204			0.439187
$532$	−2.57052			−0.111446
$533$		−	6.77849i		−	0.293609i
$534$		−	43.9375i		−	1.90136i
$535$		−	11.1424i		−	0.481727i
$536$	32.2663			1.39369
$537$	38.8060			1.67460
$538$	19.1168			0.824185
$539$			48.0598i			2.07008i
$540$	−5.48542			−0.236055
$541$		−	3.41893i		−	0.146991i	−0.997296	−	0.0734956i	$-0.976585\pi$
$541$		−	3.41893i		−	0.146991i	0.997296	−	0.0734956i	$-0.0234155\pi$
$542$	−10.1727			−0.436954
$543$			41.1196i			1.76461i
$544$	19.2493			0.825307
$545$			8.67533i			0.371610i
$546$		−	89.4330i		−	3.82738i
$547$			19.7270i			0.843465i	0.906720	+	0.421733i	$0.138578\pi$
$547$			19.7270i			0.843465i	−0.906720	+	0.421733i	$0.861422\pi$
$548$	−39.6575			−1.69409
$549$	13.5417			0.577945
$550$	34.2595			1.46083
$551$	−1.39253			−0.0593237
$552$	2.64217			0.112458
$553$		−	16.0952i		−	0.684437i
$554$	−43.7068			−1.85693
$555$	−4.41730			−0.187504
$556$		−	31.6550i		−	1.34247i
$557$	7.49167			0.317432			0.158716	−	0.987324i	$-0.449265\pi$
$557$	7.49167			0.317432			0.158716	+	0.987324i	$0.449265\pi$
$558$	−21.0915			−0.892876
$559$		−	8.13810i		−	0.344205i
$560$			3.38527i			0.143054i
$561$			19.1064i			0.806671i
$562$	−13.9026			−0.586447
$563$	38.4566			1.62075			0.810376	−	0.585910i	$-0.199263\pi$
$563$	38.4566			1.62075			0.810376	+	0.585910i	$0.199263\pi$
$564$			63.2376i			2.66278i
$565$	1.68165			0.0707477
$566$	21.7598			0.914632
$567$	−52.2261			−2.19329
$568$	16.9868			0.712749
$569$	−27.1633			−1.13874			−0.569372	−	0.822080i	$-0.692813\pi$
$569$	−27.1633			−1.13874			−0.569372	+	0.822080i	$0.692813\pi$
$570$		−	0.496643i		−	0.0208021i
$571$			17.5516i			0.734513i	0.930120	+	0.367256i	$0.119703\pi$
$571$			17.5516i			0.734513i	−0.930120	+	0.367256i	$0.880297\pi$
$572$	−39.8113			−1.66460
$573$		−	40.5635i		−	1.69456i
$574$		−	16.9248i		−	0.706427i
$575$	−2.86876			−0.119636
$576$	−18.2453			−0.760223
$577$		−	37.2580i		−	1.55107i	−0.631303	−	0.775536i	$-0.717480\pi$
$577$		−	37.2580i		−	1.55107i	0.631303	−	0.775536i	$-0.282520\pi$
$578$		−	20.8398i		−	0.866820i
$579$		−	24.2993i		−	1.00984i
$580$		−	12.1218i		−	0.503329i
$581$	16.4813			0.683759
$582$	30.0401			1.24520
$583$		−	24.2866i		−	1.00585i
$584$	−28.4229			−1.17615
$585$	3.28850			0.135963
$586$			40.2975i			1.66468i
$587$	5.65818			0.233538			0.116769	−	0.993159i	$-0.462746\pi$
$587$	5.65818			0.233538			0.116769	+	0.993159i	$0.462746\pi$
$588$		−	89.5994i		−	3.69502i
$589$			1.27095i			0.0523688i
$590$	8.93842			0.367989
$591$	26.5459	−	12.8453i	1.09195	−	0.528385i
$592$	4.83342			0.198652
$593$		−	25.1377i		−	1.03228i	−0.856504	−	0.516141i	$-0.827368\pi$
$593$		−	25.1377i		−	1.03228i	0.856504	−	0.516141i	$-0.172632\pi$
$594$			24.3683i			0.999842i
$595$	−7.21454			−0.295767
$596$		−	60.0144i		−	2.45829i
$597$	21.1288			0.864746
$598$	5.61307			0.229536
$599$		−	20.0911i		−	0.820899i	−0.911883	−	0.410449i	$-0.865372\pi$
$599$		−	20.0911i		−	0.820899i	0.911883	−	0.410449i	$-0.134628\pi$
$600$	−20.1985			−0.824601
$601$	−11.6052			−0.473385			−0.236692	−	0.971585i	$-0.576063\pi$
$601$	−11.6052			−0.473385			−0.236692	+	0.971585i	$0.576063\pi$
$602$		−	20.3195i		−	0.828162i
$603$			22.2361i			0.905524i
$604$			8.27733i			0.336800i
$605$		−	0.0749699i		−	0.00304796i
$606$	30.5767			1.24209
$607$	−3.40247			−0.138102			−0.0690510	−	0.997613i	$-0.521997\pi$
$607$	−3.40247			−0.138102			−0.0690510	+	0.997613i	$0.521997\pi$
$608$			1.32013i			0.0535383i
$609$		−	71.8441i		−	2.91127i
$610$	11.9602			0.484253
$611$			42.4845i			1.71874i
$612$		−	11.4145i		−	0.461404i
$613$	3.42289			0.138249			0.0691246	−	0.997608i	$-0.477979\pi$
$613$	3.42289			0.138249			0.0691246	+	0.997608i	$0.477979\pi$
$614$	44.6346			1.80131
$615$	1.94208			0.0783122
$616$	−31.4349			−1.26655
$617$	−22.4885			−0.905353			−0.452677	−	0.891675i	$-0.649531\pi$
$617$	−22.4885			−0.905353			−0.452677	+	0.891675i	$0.649531\pi$
$618$			47.9828i			1.93015i
$619$	7.15723			0.287674			0.143837	−	0.989601i	$-0.454056\pi$
$619$	7.15723			0.287674			0.143837	+	0.989601i	$0.454056\pi$
$620$	−11.0635			−0.444320
$621$		−	2.04051i		−	0.0818828i
$622$		−	40.6866i		−	1.63138i
$623$		−	43.7723i		−	1.75370i
$624$	−11.2290			−0.449518
$625$	20.3458			0.813832
$626$			52.2593i			2.08870i
$627$	−1.31032			−0.0523293
$628$	23.2809			0.929011
$629$			10.3008i			0.410719i
$630$	8.21084			0.327128
$631$	−14.7372			−0.586679			−0.293339	−	0.956008i	$-0.594767\pi$
$631$	−14.7372			−0.586679			−0.293339	+	0.956008i	$0.594767\pi$
$632$	7.11253			0.282921
$633$	40.4995			1.60971
$634$	−29.0647			−1.15431
$635$			3.34425i			0.132712i
$636$			45.2783i			1.79540i
$637$		−	60.1949i		−	2.38501i
$638$	−53.8493			−2.13192
$639$			11.7063i			0.463095i
$640$	−8.25702			−0.326387
$641$			24.3146i			0.960371i	0.877167	+	0.480185i	$0.159431\pi$
$641$			24.3146i			0.960371i	−0.877167	+	0.480185i	$0.840569\pi$
$642$	92.2817			3.64207
$643$			0.910967i			0.0359250i	0.999839	+	0.0179625i	$0.00571795\pi$
$643$			0.910967i			0.0359250i	−0.999839	+	0.0179625i	$0.994282\pi$
$644$	8.32359			0.327995
$645$	2.33162			0.0918074
$646$	−1.15813			−0.0455662
$647$			1.39145i			0.0547034i	0.999626	+	0.0273517i	$0.00870741\pi$
$647$			1.39145i			0.0547034i	−0.999626	+	0.0273517i	$0.991293\pi$
$648$		−	23.0789i		−	0.906626i
$649$		−	23.5828i		−	0.925705i
$650$	−42.9100			−1.68307
$651$	−65.5718			−2.56996
$652$	−24.8638			−0.973740
$653$	33.2909			1.30277			0.651387	−	0.758746i	$-0.274187\pi$
$653$	33.2909			1.30277			0.651387	+	0.758746i	$0.274187\pi$
$654$	−71.8494			−2.80953
$655$	2.73894			0.107019
$656$	−2.12503			−0.0829685
$657$		−	19.5874i		−	0.764179i
$658$			106.077i			4.13531i
$659$			12.1850i			0.474659i	0.971429	+	0.237329i	$0.0762721\pi$
$659$			12.1850i			0.474659i	−0.971429	+	0.237329i	$0.923728\pi$
$660$		−	11.4062i		−	0.443986i
$661$	−6.49886			−0.252776			−0.126388	−	0.991981i	$-0.540338\pi$
$661$	−6.49886			−0.252776			−0.126388	+	0.991981i	$0.540338\pi$
$662$			72.0940i			2.80201i
$663$		−	23.9307i		−	0.929392i
$664$			7.28314i			0.282641i
$665$		−	0.494777i		−	0.0191866i
$666$		−	11.7233i		−	0.454269i
$667$	4.50914			0.174595
$668$		−	38.3298i		−	1.48302i
$669$			48.1461i			1.86144i
$670$			19.6392i			0.758727i
$671$		−	31.5552i		−	1.21818i
$672$	−68.1088			−2.62735
$673$		−	27.3951i		−	1.05600i	−0.849243	−	0.528002i	$-0.822941\pi$
$673$		−	27.3951i		−	1.05600i	0.849243	−	0.528002i	$-0.177059\pi$
$674$	8.81570			0.339568
$675$			15.5990i			0.600405i
$676$	11.8387			0.455334
$677$			40.3684i			1.55148i	0.631050	+	0.775742i	$0.282624\pi$
$677$			40.3684i			1.55148i	−0.631050	+	0.775742i	$0.717376\pi$
$678$			13.9275i			0.534883i
$679$	29.9272			1.14850
$680$		−	3.18813i		−	0.122259i
$681$	−11.8748			−0.455042
$682$			49.1481i			1.88198i
$683$	8.87986			0.339778			0.169889	−	0.985463i	$-0.445659\pi$
$683$	8.87986			0.339778			0.169889	+	0.985463i	$0.445659\pi$
$684$	0.782812			0.0299316
$685$		−	7.63334i		−	0.291655i
$686$		−	78.1334i		−	2.98315i
$687$	−5.22426			−0.199318
$688$	−2.55127			−0.0972661
$689$			30.4190i			1.15887i
$690$			1.60818i			0.0612224i
$691$	−30.1086			−1.14539			−0.572693	−	0.819770i	$-0.694101\pi$
$691$	−30.1086			−1.14539			−0.572693	+	0.819770i	$0.694101\pi$
$692$	−45.4566			−1.72800
$693$		−	21.6632i		−	0.822915i
$694$		−	18.9231i		−	0.718310i
$695$	6.09299			0.231120
$696$	31.7482			1.20341
$697$		−	4.52878i		−	0.171540i
$698$	47.8839			1.81243
$699$			20.3091i			0.768160i
$700$	−63.6310			−2.40502
$701$		−	24.2916i		−	0.917480i	−0.888571	−	0.458740i	$-0.848301\pi$
$701$		−	24.2916i		−	0.917480i	0.888571	−	0.458740i	$-0.151699\pi$
$702$		−	30.5213i		−	1.15195i
$703$	−0.706434			−0.0266436
$704$			42.5158i			1.60237i
$705$	−12.1721			−0.458427
$706$			34.5271i			1.29944i
$707$	30.4618			1.14563
$708$			43.9661i			1.65235i
$709$		−	29.2050i		−	1.09682i	−0.836211	−	0.548408i	$-0.815234\pi$
$709$		−	29.2050i		−	1.09682i	0.836211	−	0.548408i	$-0.184766\pi$
$710$			10.3391i			0.388021i
$711$			4.90155i			0.183822i
$712$	19.3432			0.724916
$713$		−	4.11548i		−	0.154126i
$714$		−	59.7511i		−	2.23613i
$715$		−	7.66294i		−	0.286578i
$716$			54.0227i			2.01892i
$717$			15.1511i			0.565830i
$718$	−37.5674			−1.40200
$719$			26.8815i			1.00251i	0.865299	+	0.501256i	$0.167128\pi$
$719$			26.8815i			1.00251i	−0.865299	+	0.501256i	$0.832872\pi$
$720$		−	1.03093i		−	0.0384205i
$721$			47.8025i			1.78026i
$722$			42.0860i			1.56628i
$723$	54.3625			2.02176
$724$	−57.2434			−2.12743
$725$	−34.4708			−1.28021
$726$	0.620904			0.0230439
$727$	12.0876			0.448304			0.224152	−	0.974554i	$-0.428039\pi$
$727$	12.0876			0.448304			0.224152	+	0.974554i	$0.428039\pi$
$728$	39.3722			1.45923
$729$	−5.09149			−0.188574
$730$		−	17.2998i		−	0.640295i
$731$		−	5.43715i		−	0.201100i
$732$			58.8293i			2.17439i
$733$	19.9267			0.736008			0.368004	−	0.929824i	$-0.380041\pi$
$733$	19.9267			0.736008			0.368004	+	0.929824i	$0.380041\pi$
$734$	43.2035			1.59467
$735$	17.2462			0.636136
$736$		−	4.27470i		−	0.157568i
$737$	51.8152			1.90864
$738$			5.15419i			0.189728i
$739$	−16.0317			−0.589735			−0.294867	−	0.955538i	$-0.595275\pi$
$739$	−16.0317			−0.589735			−0.294867	+	0.955538i	$0.595275\pi$
$740$		−	6.14941i		−	0.226057i
$741$	1.64118			0.0602903
$742$			75.9512i			2.78826i
$743$		−	31.0245i		−	1.13818i	−0.822276	−	0.569088i	$-0.807296\pi$
$743$		−	31.0245i		−	1.13818i	0.822276	−	0.569088i	$-0.192704\pi$
$744$		−	28.9764i		−	1.06233i
$745$	11.5517			0.423220
$746$	33.2883			1.21877
$747$	−5.01912			−0.183640
$748$	−26.5984			−0.972532
$749$	91.9349			3.35923
$750$		−	25.4201i		−	0.928211i
$751$	13.0874			0.477566			0.238783	−	0.971073i	$-0.423252\pi$
$751$	13.0874			0.477566			0.238783	+	0.971073i	$0.423252\pi$
$752$	13.3187			0.485684
$753$		−	31.9245i		−	1.16339i
$754$	67.4463			2.45625
$755$	−1.59323			−0.0579836
$756$		−	45.2598i		−	1.64608i
$757$		−	32.2239i		−	1.17120i	−0.810601	−	0.585599i	$-0.800859\pi$
$757$		−	32.2239i		−	1.17120i	0.810601	−	0.585599i	$-0.199141\pi$
$758$		−	27.6224i		−	1.00329i
$759$	4.24296			0.154010
$760$	0.218644			0.00793104
$761$		−	17.1597i		−	0.622038i	−0.950404	−	0.311019i	$-0.899330\pi$
$761$		−	17.1597i		−	0.622038i	0.950404	−	0.311019i	$-0.100670\pi$
$762$	−27.6972			−1.00336
$763$	−71.5793			−2.59135
$764$	56.4692			2.04298
$765$	2.19708			0.0794355
$766$	20.6407			0.745778
$767$			29.5374i			1.06653i
$768$		−	14.1877i		−	0.511954i
$769$	19.7214			0.711172			0.355586	−	0.934643i	$-0.384281\pi$
$769$	19.7214			0.711172			0.355586	+	0.934643i	$0.384281\pi$
$770$		−	19.1331i		−	0.689510i
$771$			5.48281i			0.197459i
$772$	33.8275			1.21748
$773$	−16.7080			−0.600944			−0.300472	−	0.953791i	$-0.597144\pi$
$773$	−16.7080			−0.600944			−0.300472	+	0.953791i	$0.597144\pi$
$774$			6.18800i			0.222423i
$775$			31.4614i			1.13013i
$776$			13.2249i			0.474747i
$777$		−	36.4467i		−	1.30752i
$778$	−57.9790			−2.07865
$779$	0.310586			0.0111279
$780$			14.2863i			0.511530i
$781$	27.2784			0.976097
$782$	3.75015			0.134105
$783$		−	24.5186i		−	0.876223i
$784$	−18.8709			−0.673960
$785$			4.48115i			0.159939i
$786$			22.6840i			0.809113i
$787$	20.4294			0.728230			0.364115	−	0.931354i	$-0.381371\pi$
$787$	20.4294			0.728230			0.364115	+	0.931354i	$0.381371\pi$
$788$	17.8822	+	36.9552i	0.637027	+	1.31647i
$789$	−41.1701			−1.46569
$790$			4.32910i			0.154022i
$791$			13.8752i			0.493344i
$792$	9.57303			0.340163
$793$			39.5229i			1.40350i
$794$	−48.8604			−1.73399
$795$	−8.71523			−0.309097
$796$			29.4139i			1.04255i
$797$	−45.2801			−1.60390			−0.801951	−	0.597390i	$-0.796205\pi$
$797$	−45.2801			−1.60390			−0.801951	+	0.597390i	$0.796205\pi$
$798$	4.09776			0.145059
$799$			28.3843i			1.00416i
$800$			32.6786i			1.15536i
$801$			13.3302i			0.471000i
$802$		−	61.1126i		−	2.15796i
$803$	−45.6432			−1.61071
$804$	−96.6006			−3.40684
$805$			1.60214i			0.0564679i
$806$		−	61.5579i		−	2.16829i
$807$	−18.0993			−0.637125
$808$			13.4612i			0.473562i
$809$		−	5.71448i		−	0.200910i	−0.994942	−	0.100455i	$-0.967970\pi$
$809$		−	5.71448i		−	0.200910i	0.994942	−	0.100455i	$-0.0320299\pi$
$810$	14.0472			0.493567
$811$	−38.8381			−1.36379			−0.681895	−	0.731450i	$-0.738844\pi$
$811$	−38.8381			−1.36379			−0.681895	+	0.731450i	$0.738844\pi$
$812$	100.016			3.50986
$813$	9.63121			0.337781
$814$	−27.3179			−0.957493
$815$		−	4.78581i		−	0.167640i
$816$	−7.50219			−0.262629
$817$	0.372883			0.0130455
$818$		−	43.8167i		−	1.53201i
$819$			27.1331i			0.948107i
$820$			2.70361i			0.0944141i
$821$	18.8602			0.658227			0.329113	−	0.944290i	$-0.393250\pi$
$821$	18.8602			0.658227			0.329113	+	0.944290i	$0.393250\pi$
$822$	63.2196			2.20504
$823$			11.1260i			0.387827i	0.981019	+	0.193914i	$0.0621182\pi$
$823$			11.1260i			0.387827i	−0.981019	+	0.193914i	$0.937882\pi$
$824$	−21.1241			−0.735893
$825$	−32.4360			−1.12928
$826$			73.7501i			2.56610i
$827$	−15.1190			−0.525738			−0.262869	−	0.964832i	$-0.584669\pi$
$827$	−15.1190			−0.525738			−0.262869	+	0.964832i	$0.584669\pi$
$828$	−2.53482			−0.0880912
$829$	−21.2211			−0.737039			−0.368519	−	0.929620i	$-0.620135\pi$
$829$	−21.2211			−0.737039			−0.368519	+	0.929620i	$0.620135\pi$
$830$	−4.43294			−0.153870
$831$	41.3804			1.43547
$832$		−	53.2510i		−	1.84615i
$833$		−	40.2168i		−	1.39343i
$834$			50.4624i			1.74737i
$835$	7.37777			0.255318
$836$		−	1.82413i		−	0.0630888i
$837$	−22.3780			−0.773498
$838$		−	40.8529i		−	1.41124i
$839$	17.7199			0.611760			0.305880	−	0.952070i	$-0.401049\pi$
$839$	17.7199			0.611760			0.305880	+	0.952070i	$0.401049\pi$
$840$			11.2804i			0.389210i
$841$	25.1815			0.868329
$842$	−23.1053			−0.796262
$843$	13.1626			0.453345
$844$			56.3802i			1.94069i
$845$			2.27873i			0.0783907i
$846$		−	32.3041i		−	1.11064i
$847$	0.618570			0.0212543
$848$	9.53623			0.327476
$849$	−20.6016			−0.707044
$850$	−28.6686			−0.983325
$851$	2.28750			0.0784146
$852$	−50.8559			−1.74229
$853$	−20.7795			−0.711475			−0.355738	−	0.934586i	$-0.615770\pi$
$853$	−20.7795			−0.711475			−0.355738	+	0.934586i	$0.615770\pi$
$854$			98.6822i			3.37684i
$855$			0.150677i			0.00515304i
$856$			40.6264i			1.38858i
$857$			24.5073i			0.837155i	0.908181	+	0.418577i	$0.137471\pi$
$857$			24.5073i			0.837155i	−0.908181	+	0.418577i	$0.862529\pi$
$858$	63.4648			2.16665
$859$			56.3100i			1.92127i	0.277807	+	0.960637i	$0.410393\pi$
$859$			56.3100i			1.92127i	−0.277807	+	0.960637i	$0.589607\pi$
$860$			3.24589i			0.110684i
$861$			16.0239i			0.546094i
$862$		−	25.5389i		−	0.869860i
$863$			11.8034i			0.401791i	0.979613	+	0.200896i	$0.0643852\pi$
$863$			11.8034i			0.401791i	−0.979613	+	0.200896i	$0.935615\pi$
$864$	−23.2438			−0.790771
$865$		−	8.74956i		−	0.297494i
$866$			5.41292i			0.183938i
$867$			19.7305i			0.670084i
$868$		−	91.2839i		−	3.09838i
$869$	11.4217			0.387455
$870$			19.3238i			0.655138i
$871$	−64.8985			−2.19900
$872$		−	31.6312i		−	1.07117i
$873$	−9.11386			−0.308458
$874$			0.257187i			0.00869949i
$875$		−	25.3246i		−	0.856127i
$876$	85.0940			2.87506
$877$		−	16.4938i		−	0.556955i	−0.960443	−	0.278477i	$-0.910170\pi$
$877$		−	16.4938i		−	0.556955i	0.960443	−	0.278477i	$-0.0898298\pi$
$878$	−70.7862			−2.38892
$879$		−	38.1526i		−	1.28686i
$880$	−2.40230			−0.0809816
$881$	−13.2005			−0.444735			−0.222368	−	0.974963i	$-0.571379\pi$
$881$	−13.2005			−0.444735			−0.222368	+	0.974963i	$0.571379\pi$
$882$			45.7706i			1.54118i
$883$			9.49893i			0.319664i	0.987144	+	0.159832i	$0.0510953\pi$
$883$			9.49893i			0.319664i	−0.987144	+	0.159832i	$0.948905\pi$
$884$	33.3144			1.12049
$885$	−8.46266			−0.284469
$886$		−	51.3732i		−	1.72592i
$887$		−	48.3450i		−	1.62327i	−0.584167	−	0.811634i	$-0.698579\pi$
$887$		−	48.3450i		−	1.62327i	0.584167	−	0.811634i	$-0.301421\pi$
$888$	16.1059			0.540480
$889$	−27.5931			−0.925443
$890$			11.7734i			0.394644i
$891$		−	37.0615i		−	1.24161i
$892$	−67.0252			−2.24417
$893$	−1.94661			−0.0651409
$894$			95.6714i			3.19973i
$895$	−10.3984			−0.347579
$896$		−	68.1279i		−	2.27599i
$897$	−5.31431			−0.177440
$898$		−	65.1422i		−	2.17382i
$899$		−	49.4513i		−	1.64929i
$900$	19.3778			0.645928
$901$			20.3232i			0.677065i
$902$	12.0104			0.399903
$903$			19.2380i			0.640200i
$904$	−6.13149			−0.203930
$905$		−	11.0183i		−	0.366261i
$906$		−	13.1952i		−	0.438382i
$907$		−	20.8861i		−	0.693512i	−0.937955	−	0.346756i	$-0.887283\pi$
$907$		−	20.8861i		−	0.693512i	0.937955	−	0.346756i	$-0.112717\pi$
$908$		−	16.5311i		−	0.548604i
$909$	−9.27667			−0.307688
$910$			23.9642i			0.794406i
$911$		−	38.2625i		−	1.26769i	−0.773459	−	0.633846i	$-0.781475\pi$
$911$		−	38.2625i		−	1.26769i	0.773459	−	0.633846i	$-0.218525\pi$
$912$		−	0.514504i		−	0.0170369i
$913$			11.6957i			0.387071i
$914$		−	44.6592i		−	1.47719i
$915$	−11.3236			−0.374345
$916$		−	7.27280i		−	0.240300i
$917$			22.5988i			0.746278i
$918$		−	20.3916i		−	0.673022i
$919$			1.45866i			0.0481167i	0.999711	+	0.0240583i	$0.00765875\pi$
$919$			1.45866i			0.0481167i	−0.999711	+	0.0240583i	$0.992341\pi$
$920$	−0.707990			−0.0233417
$921$	−42.2588			−1.39248
$922$	77.9332			2.56659
$923$	−34.1662			−1.12459
$924$	94.1115			3.09604
$925$	−17.4872			−0.574974
$926$	23.6796			0.778160
$927$		−	14.5575i		−	0.478132i
$928$		−	51.3645i		−	1.68612i
$929$		−	2.41889i		−	0.0793611i	−0.999212	−	0.0396805i	$-0.987366\pi$
$929$		−	2.41889i		−	0.0793611i	0.999212	−	0.0396805i	$-0.0126340\pi$
$930$	17.6367			0.578331
$931$	2.75809			0.0903928
$932$	−28.2727			−0.926103
$933$			38.5210i			1.26112i
$934$	−7.40944			−0.242444
$935$		−	5.11969i		−	0.167432i
$936$	−11.9902			−0.391913
$937$		−	58.0778i		−	1.89732i	−0.316297	−	0.948660i	$-0.602440\pi$
$937$		−	58.0778i		−	1.89732i	0.316297	−	0.948660i	$-0.397560\pi$
$938$	−162.041			−5.29082
$939$		−	49.4777i		−	1.61464i
$940$		−	16.9450i		−	0.552684i
$941$			0.0666861i			0.00217390i	0.999999	+	0.00108695i	$0.000345988\pi$
$941$			0.0666861i			0.00217390i	−0.999999	+	0.00108695i	$0.999654\pi$
$942$	−37.1131			−1.20921
$943$	−1.00571			−0.0327503
$944$	9.25987			0.301383
$945$	8.71166			0.283390
$946$	14.4194			0.468817
$947$		−	13.0942i		−	0.425505i	−0.977106	−	0.212753i	$-0.931757\pi$
$947$		−	13.0942i		−	0.425505i	0.977106	−	0.212753i	$-0.0682429\pi$
$948$	−21.2939			−0.691592
$949$	57.1681			1.85575
$950$		−	1.96611i		−	0.0637890i
$951$	27.5177			0.892323
$952$	26.3050			0.852550
$953$		−	11.9768i		−	0.387966i	−0.981005	−	0.193983i	$-0.937859\pi$
$953$		−	11.9768i		−	0.387966i	0.981005	−	0.193983i	$-0.0621407\pi$
$954$		−	23.1298i		−	0.748855i
$955$			10.8693i			0.351722i
$956$	−21.0922			−0.682171
$957$	50.9831			1.64805
$958$		−	34.2814i		−	1.10758i
$959$	62.9820			2.03380
$960$	15.2568			0.492410
$961$	−14.1340			−0.455934
$962$	34.2157			1.10316
$963$	−27.9974			−0.902203
$964$			75.6792i			2.43746i
$965$			6.51117i			0.209602i
$966$	−13.2690			−0.426922
$967$			53.4857i			1.71998i	0.510308	+	0.859992i	$0.329531\pi$
$967$			53.4857i			1.71998i	−0.510308	+	0.859992i	$0.670469\pi$
$968$			0.273348i			0.00878575i
$969$	1.09649			0.0352243
$970$	−8.04946			−0.258452
$971$		−	1.92870i		−	0.0618948i	−0.999521	−	0.0309474i	$-0.990148\pi$
$971$		−	1.92870i		−	0.0618948i	0.999521	−	0.0309474i	$-0.00985244\pi$
$972$			39.8657i			1.27869i
$973$			50.2727i			1.61167i
$974$			76.2513i			2.44325i
$975$	40.6260			1.30107
$976$	12.3903			0.396603
$977$		−	12.2966i		−	0.393405i	−0.980463	−	0.196702i	$-0.936977\pi$
$977$		−	12.2966i		−	0.393405i	0.980463	−	0.196702i	$-0.0630232\pi$
$978$	39.6363			1.26743
$979$	31.0624			0.992758
$980$			24.0088i			0.766933i
$981$	21.7984			0.695970
$982$			24.4261i			0.779469i
$983$			12.0532i			0.384437i	0.981352	+	0.192219i	$0.0615683\pi$
$983$			12.0532i			0.384437i	−0.981352	+	0.192219i	$0.938432\pi$
$984$	−7.08103			−0.225735
$985$	−7.11318	+	3.44199i	−0.226645	+	0.109671i
$986$	45.0616			1.43505
$987$		−	100.431i		−	3.19674i
$988$			2.28472i			0.0726867i
$989$	−1.20743			−0.0383941
$990$			5.82670i			0.185185i
$991$	−9.89610			−0.314360			−0.157180	−	0.987570i	$-0.550240\pi$
$991$	−9.89610			−0.314360			−0.157180	+	0.987570i	$0.550240\pi$
$992$	−46.8802			−1.48845
$993$		−	68.2566i		−	2.16606i
$994$	−85.3073			−2.70578
$995$	−5.66163			−0.179486
$996$		−	21.8046i		−	0.690907i
$997$			36.1230i			1.14403i	0.820244	+	0.572014i	$0.193838\pi$
$997$			36.1230i			1.14403i	−0.820244	+	0.572014i	$0.806162\pi$
$998$		−	84.8327i		−	2.68533i
$999$		−	12.4384i		−	0.393532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.b.a.196.3	✓	16
3.2	odd	2		1773.2.b.b.1378.14		16
4.3	odd	2		3152.2.b.c.1969.4		16
197.196	even	2	inner	197.2.b.a.196.14	yes	16
591.590	odd	2		1773.2.b.b.1378.3		16
788.787	odd	2		3152.2.b.c.1969.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.b.a.196.3	✓	16	1.1	even	1	trivial
197.2.b.a.196.14	yes	16	197.196	even	2	inner
1773.2.b.b.1378.3		16	591.590	odd	2
1773.2.b.b.1378.14		16	3.2	odd	2
3152.2.b.c.1969.4		16	4.3	odd	2
3152.2.b.c.1969.13		16	788.787	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.21923i q^{2} +2.10111i q^{3} -2.92500 q^{4} -0.563008i q^{5} +4.66286 q^{6} +4.64533 q^{7} +2.05279i q^{8} -1.41466 q^{9} -1.24945 q^{10} +3.29649i q^{11} -6.14575i q^{12} -4.12885i q^{13} -10.3091i q^{14} +1.18294 q^{15} -1.29438 q^{16} -2.75853i q^{17} +3.13947i q^{18} +0.189181 q^{19} +1.64680i q^{20} +9.76035i q^{21} +7.31568 q^{22} -0.612588 q^{23} -4.31314 q^{24} +4.68302 q^{25} -9.16289 q^{26} +3.33096i q^{27} -13.5876 q^{28} -7.36081 q^{29} -2.62522i q^{30} +6.71818i q^{31} +6.97811i q^{32} -6.92629 q^{33} -6.12182 q^{34} -2.61536i q^{35} +4.13789 q^{36} -3.73416 q^{37} -0.419838i q^{38} +8.67517 q^{39} +1.15574 q^{40} +1.64174 q^{41} +21.6605 q^{42} +1.97103 q^{43} -9.64223i q^{44} +0.796468i q^{45} +1.35948i q^{46} -10.2897 q^{47} -2.71963i q^{48} +14.5791 q^{49} -10.3927i q^{50} +5.79597 q^{51} +12.0769i q^{52} -7.36742 q^{53} +7.39219 q^{54} +1.85595 q^{55} +9.53588i q^{56} +0.397491i q^{57} +16.3354i q^{58} -7.15391 q^{59} -3.46010 q^{60} -9.57237 q^{61} +14.9092 q^{62} -6.57158 q^{63} +12.8973 q^{64} -2.32458 q^{65} +15.3711i q^{66} -15.7183i q^{67} +8.06869i q^{68} -1.28711i q^{69} -5.80409 q^{70} -8.27498i q^{71} -2.90401i q^{72} +13.8460i q^{73} +8.28698i q^{74} +9.83955i q^{75} -0.553355 q^{76} +15.3133i q^{77} -19.2522i q^{78} -3.46481i q^{79} +0.728746i q^{80} -11.2427 q^{81} -3.64340i q^{82} +3.54792 q^{83} -28.5490i q^{84} -1.55307 q^{85} -4.37418i q^{86} -15.4659i q^{87} -6.76700 q^{88} -9.42287i q^{89} +1.76755 q^{90} -19.1799i q^{91} +1.79182 q^{92} -14.1156 q^{93} +22.8352i q^{94} -0.106511i q^{95} -14.6618 q^{96} +6.44242 q^{97} -32.3544i q^{98} -4.66343i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 10 q^{6} + 2 q^{7} - 18 q^{9} + 4 q^{10} + 14 q^{15} + 16 q^{16} - 14 q^{19} + 4 q^{22} + 8 q^{23} + 40 q^{24} - 4 q^{25} - 22 q^{26} - 32 q^{28} + 20 q^{29} - 20 q^{33} - 24 q^{34} + 26 q^{36}+ \cdots + 18 q^{97}+O(q^{100}) \) 16 * q - 16 * q^4 - 10 * q^6 + 2 * q^7 - 18 * q^9 + 4 * q^10 + 14 * q^15 + 16 * q^16 - 14 * q^19 + 4 * q^22 + 8 * q^23 + 40 * q^24 - 4 * q^25 - 22 * q^26 - 32 * q^28 + 20 * q^29 - 20 * q^33 - 24 * q^34 + 26 * q^36 - 14 * q^37 + 6 * q^39 + 2 * q^40 - 14 * q^41 + 2 * q^42 + 22 * q^43 - 14 * q^47 - 2 * q^49 + 26 * q^51 - 2 * q^53 + 78 * q^54 + 22 * q^55 - 18 * q^59 - 74 * q^60 - 10 * q^61 - 6 * q^62 - 58 * q^63 - 10 * q^64 + 50 * q^65 + 50 * q^70 + 50 * q^76 + 4 * q^81 - 4 * q^85 + 64 * q^88 - 112 * q^90 - 100 * q^92 + 10 * q^93 - 60 * q^96 + 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more