LMFDB - Embedded newform 1300.2.i.h.601.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(601,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1300.601");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.i (of order $3$, 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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 10x^{8} - 5x^{7} + 74x^{6} - 44x^{5} + 166x^{4} - 64x^{3} + 259x^{2} - 126x + 81 $ x^10 - x^9 + 10x^8 - 5x^7 + 74x^6 - 44x^5 + 166x^4 - 64x^3 + 259x^2 - 126x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.5
Root			$1.41443 + 2.44987i$ of defining polynomial
Character	$\chi$	$=$	1300.601
Dual form			1300.2.i.h.1101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41443 + 2.44987i) q^{3} +(2.50124 - 4.33228i) q^{7} +(-2.50124 + 4.33228i) q^{9} +O(q^{10})$	$q+(1.41443 + 2.44987i) q^{3} +(2.50124 - 4.33228i) q^{7} +(-2.50124 + 4.33228i) q^{9} +(-3.09549 - 5.36155i) q^{11} +(3.56575 + 0.534272i) q^{13} +(0.168866 - 0.292485i) q^{17} +(2.33237 - 4.03979i) q^{19} +14.1513 q^{21} +(-1.50869 - 2.61312i) q^{23} -5.66475 q^{27} +(3.74681 + 6.48966i) q^{29} +6.47624 q^{31} +(8.75673 - 15.1671i) q^{33} +(-1.90699 - 3.30300i) q^{37} +(3.73461 + 9.49131i) q^{39} +(4.64905 + 8.05238i) q^{41} +(-0.734613 + 1.27239i) q^{43} -4.48412 q^{47} +(-9.01241 - 15.6099i) q^{49} +0.955399 q^{51} -8.89084 q^{53} +13.1959 q^{57} +(1.42188 - 2.46276i) q^{59} +(-2.07585 + 3.59548i) q^{61} +(12.5124 + 21.6721i) q^{63} +(-1.97894 - 3.42762i) q^{67} +(4.26787 - 7.39216i) q^{69} +(-4.91340 + 8.51027i) q^{71} -3.70935 q^{73} -30.9703 q^{77} +1.45186 q^{79} +(-0.508685 - 0.881068i) q^{81} -0.164117 q^{83} +(-10.5992 + 18.3584i) q^{87} +(2.33858 + 4.05054i) q^{89} +(11.2334 - 14.1115i) q^{91} +(9.16021 + 15.8660i) q^{93} +(-0.257942 + 0.446768i) q^{97} +30.9703 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 10 * q + q^3 + 4 * q^7 - 4 * q^9	$ 10 q + q^{3} + 4 q^{7} - 4 q^{9} - 7 q^{11} + 6 q^{13} + 8 q^{17} - 4 q^{19} + 8 q^{21} + q^{23} - 2 q^{27} - 3 q^{29} + 16 q^{31} + 10 q^{33} - q^{37} + 14 q^{39} + 10 q^{41} + 16 q^{43} - 8 q^{47} - 11 q^{49} + 8 q^{51} - 32 q^{53} + 6 q^{59} - 9 q^{61} + 46 q^{63} + 2 q^{67} + 24 q^{69} + 5 q^{71} + 16 q^{73} - 56 q^{77} + 11 q^{81} - 30 q^{83} - 19 q^{87} + 22 q^{89} - 7 q^{91} - 3 q^{93} - 21 q^{97} + 56 q^{99}+O(q^{100}) $ 10 * q + q^3 + 4 * q^7 - 4 * q^9 - 7 * q^11 + 6 * q^13 + 8 * q^17 - 4 * q^19 + 8 * q^21 + q^23 - 2 * q^27 - 3 * q^29 + 16 * q^31 + 10 * q^33 - q^37 + 14 * q^39 + 10 * q^41 + 16 * q^43 - 8 * q^47 - 11 * q^49 + 8 * q^51 - 32 * q^53 + 6 * q^59 - 9 * q^61 + 46 * q^63 + 2 * q^67 + 24 * q^69 + 5 * q^71 + 16 * q^73 - 56 * q^77 + 11 * q^81 - 30 * q^83 - 19 * q^87 + 22 * q^89 - 7 * q^91 - 3 * q^93 - 21 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.41443	+	2.44987i	0.816623	+	1.41443i	0.908157	+	0.418631i	$0.137490\pi$
$3$	1.41443	+	2.44987i	0.816623	+	1.41443i	−0.0915334	+	0.995802i	$0.529177\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.50124	−	4.33228i	0.945380	−	1.63745i	0.190391	−	0.981708i	$-0.439024\pi$
$7$	2.50124	−	4.33228i	0.945380	−	1.63745i	0.754989	−	0.655738i	$-0.227642\pi$
$8$		0			0
$9$	−2.50124	+	4.33228i	−0.833747	+	1.44409i
$10$		0			0
$11$	−3.09549	−	5.36155i	−0.933326	−	1.61657i	−0.777592	−	0.628769i	$-0.783559\pi$
$11$	−3.09549	−	5.36155i	−0.933326	−	1.61657i	−0.155734	−	0.987799i	$-0.549774\pi$
$12$		0			0
$13$	3.56575	+	0.534272i	0.988960	+	0.148180i
$13$	3.56575	+	0.534272i	0.988960	+	0.148180i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.168866	−	0.292485i	0.0409560	−	0.0709379i	−0.844821	−	0.535049i	$-0.820293\pi$
$17$	0.168866	−	0.292485i	0.0409560	−	0.0709379i	0.885777	+	0.464111i	$0.153626\pi$
$18$		0			0
$19$	2.33237	−	4.03979i	0.535083	−	0.926792i	−0.464076	−	0.885795i	$-0.653614\pi$
$19$	2.33237	−	4.03979i	0.535083	−	0.926792i	0.999159	−	0.0409961i	$-0.0130531\pi$
$20$		0			0
$21$	14.1513			3.08808
$22$		0			0
$23$	−1.50869	−	2.61312i	−0.314583	−	0.544873i	0.664766	−	0.747052i	$-0.268531\pi$
$23$	−1.50869	−	2.61312i	−0.314583	−	0.544873i	−0.979349	+	0.202179i	$0.935198\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.66475			−1.09018
$28$		0			0
$29$	3.74681	+	6.48966i	0.695765	+	1.20510i	0.969922	+	0.243415i	$0.0782676\pi$
$29$	3.74681	+	6.48966i	0.695765	+	1.20510i	−0.274158	+	0.961685i	$0.588399\pi$
$30$		0			0
$31$	6.47624			1.16317			0.581584	−	0.813486i	$-0.302433\pi$
$31$	6.47624			1.16317			0.581584	+	0.813486i	$0.302433\pi$
$32$		0			0
$33$	8.75673	−	15.1671i	1.52435	−	2.64025i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.90699	−	3.30300i	−0.313507	−	0.543010i	0.665612	−	0.746298i	$-0.268171\pi$
$37$	−1.90699	−	3.30300i	−0.313507	−	0.543010i	−0.979119	+	0.203288i	$0.934837\pi$
$38$		0			0
$39$	3.73461	+	9.49131i	0.598017	+	1.51983i
$40$		0			0
$41$	4.64905	+	8.05238i	0.726059	+	1.25757i	0.958537	+	0.284969i	$0.0919834\pi$
$41$	4.64905	+	8.05238i	0.726059	+	1.25757i	−0.232478	+	0.972602i	$0.574683\pi$
$42$		0			0
$43$	−0.734613	+	1.27239i	−0.112027	+	0.194037i	−0.916588	−	0.399834i	$-0.869068\pi$
$43$	−0.734613	+	1.27239i	−0.112027	+	0.194037i	0.804560	+	0.593871i	$0.202401\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.48412			−0.654076			−0.327038	−	0.945011i	$-0.606050\pi$
$47$	−4.48412			−0.654076			−0.327038	+	0.945011i	$0.606050\pi$
$48$		0			0
$49$	−9.01241	−	15.6099i	−1.28749	−	2.22999i
$50$		0			0
$51$	0.955399			0.133783
$52$		0			0
$53$	−8.89084			−1.22125			−0.610625	−	0.791920i	$-0.709082\pi$
$53$	−8.89084			−1.22125			−0.610625	+	0.791920i	$0.709082\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	13.1959			1.74785
$58$		0			0
$59$	1.42188	−	2.46276i	0.185113	−	0.320625i	−0.758502	−	0.651671i	$-0.774068\pi$
$59$	1.42188	−	2.46276i	0.185113	−	0.320625i	0.943614	+	0.331046i	$0.107402\pi$
$60$		0			0
$61$	−2.07585	+	3.59548i	−0.265786	+	0.460355i	−0.967769	−	0.251839i	$-0.918965\pi$
$61$	−2.07585	+	3.59548i	−0.265786	+	0.460355i	0.701983	+	0.712193i	$0.252298\pi$
$62$		0			0
$63$	12.5124	+	21.6721i	1.57641	+	2.73043i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.97894	−	3.42762i	−0.241766	−	0.418751i	0.719451	−	0.694543i	$-0.244393\pi$
$67$	−1.97894	−	3.42762i	−0.241766	−	0.418751i	−0.961217	+	0.275792i	$0.911060\pi$
$68$		0			0
$69$	4.26787	−	7.39216i	0.513791	−	0.889912i
$70$		0			0
$71$	−4.91340	+	8.51027i	−0.583114	+	1.00998i	0.411994	+	0.911187i	$0.364833\pi$
$71$	−4.91340	+	8.51027i	−0.583114	+	1.00998i	−0.995108	+	0.0987962i	$0.968501\pi$
$72$		0			0
$73$	−3.70935			−0.434147			−0.217073	−	0.976155i	$-0.569651\pi$
$73$	−3.70935			−0.434147			−0.217073	+	0.976155i	$0.569651\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−30.9703			−3.52939
$78$		0			0
$79$	1.45186			0.163347			0.0816733	−	0.996659i	$-0.473974\pi$
$79$	1.45186			0.163347			0.0816733	+	0.996659i	$0.473974\pi$
$80$		0			0
$81$	−0.508685	−	0.881068i	−0.0565206	−	0.0978965i
$82$		0			0
$83$	−0.164117			−0.0180142			−0.00900710	−	0.999959i	$-0.502867\pi$
$83$	−0.164117			−0.0180142			−0.00900710	+	0.999959i	$0.502867\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−10.5992	+	18.3584i	−1.13635	+	1.96822i
$88$		0			0
$89$	2.33858	+	4.05054i	0.247889	+	0.429356i	0.962940	−	0.269716i	$-0.0869299\pi$
$89$	2.33858	+	4.05054i	0.247889	+	0.429356i	−0.715051	+	0.699072i	$0.753597\pi$
$90$		0			0
$91$	11.2334	−	14.1115i	1.17758	−	1.47928i
$92$		0			0
$93$	9.16021	+	15.8660i	0.949870	+	1.64522i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.257942	+	0.446768i	−0.0261900	+	0.0453625i	−0.878823	−	0.477147i	$-0.841671\pi$
$97$	−0.257942	+	0.446768i	−0.0261900	+	0.0453625i	0.852633	+	0.522510i	$0.175004\pi$
$98$		0			0
$99$	30.9703			3.11263
$100$		0			0
$101$	0.762691	+	1.32102i	0.0758906	+	0.131446i	0.901473	−	0.432835i	$-0.142487\pi$
$101$	0.762691	+	1.32102i	0.0758906	+	0.131446i	−0.825583	+	0.564281i	$0.809153\pi$
$102$		0			0
$103$	10.5135			1.03592			0.517961	−	0.855404i	$-0.326691\pi$
$103$	10.5135			1.03592			0.517961	+	0.855404i	$0.326691\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.51117	+	9.54562i	0.532784	+	0.922810i	0.999267	+	0.0382794i	$0.0121877\pi$
$107$	5.51117	+	9.54562i	0.532784	+	0.922810i	−0.466483	+	0.884530i	$0.654479\pi$
$108$		0			0
$109$	−4.82887			−0.462521			−0.231261	−	0.972892i	$-0.574285\pi$
$109$	−4.82887			−0.462521			−0.231261	+	0.972892i	$0.574285\pi$
$110$		0			0
$111$	5.39461	−	9.34374i	0.512034	−	0.886869i
$112$		0			0
$113$	7.23936	−	12.5389i	0.681022	−	1.17956i	−0.293647	−	0.955914i	$-0.594869\pi$
$113$	7.23936	−	12.5389i	0.681022	−	1.17956i	0.974669	−	0.223651i	$-0.0717975\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−11.2334	+	14.1115i	−1.03853	+	1.30460i
$118$		0			0
$119$	−0.844749	−	1.46315i	−0.0774380	−	0.134127i
$120$		0			0
$121$	−13.6641	+	23.6670i	−1.24220	+	2.15155i
$122$		0			0
$123$	−13.1515	+	22.7791i	−1.18583	+	2.05392i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.07340	+	15.7156i	0.805134	+	1.39453i	0.916200	+	0.400721i	$0.131240\pi$
$127$	9.07340	+	15.7156i	0.805134	+	1.39453i	−0.111066	+	0.993813i	$0.535426\pi$
$128$		0			0
$129$	−4.15624			−0.365937
$130$		0			0
$131$	5.02439			0.438983			0.219491	−	0.975614i	$-0.429560\pi$
$131$	5.02439			0.438983			0.219491	+	0.975614i	$0.429560\pi$
$132$		0			0
$133$	−11.6677	−	20.2090i	−1.01171	−	1.75234i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.89337	+	5.01147i	−0.247198	+	0.428159i	−0.962747	−	0.270403i	$-0.912843\pi$
$137$	−2.89337	+	5.01147i	−0.247198	+	0.428159i	0.715550	+	0.698562i	$0.246176\pi$
$138$		0			0
$139$	−5.26684	+	9.12243i	−0.446727	+	0.773755i	−0.998171	−	0.0604577i	$-0.980744\pi$
$139$	−5.26684	+	9.12243i	−0.446727	+	0.773755i	0.551443	+	0.834212i	$0.314077\pi$
$140$		0			0
$141$	−6.34248	−	10.9855i	−0.534133	−	0.925146i
$142$		0			0
$143$	−8.17322	−	20.7718i	−0.683479	−	1.73702i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	25.4949	−	44.1584i	2.10278	−	3.64213i
$148$		0			0
$149$	−5.14121	+	8.90483i	−0.421184	+	0.729512i	−0.996056	−	0.0887314i	$-0.971719\pi$
$149$	−5.14121	+	8.90483i	−0.421184	+	0.729512i	0.574871	+	0.818244i	$0.305052\pi$
$150$		0			0
$151$	7.45767			0.606897			0.303448	−	0.952848i	$-0.401862\pi$
$151$	7.45767			0.606897			0.303448	+	0.952848i	$0.401862\pi$
$152$		0			0
$153$	0.844749	+	1.46315i	0.0682939	+	0.118289i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.0351033			−0.00280155			−0.00140077	−	0.999999i	$-0.500446\pi$
$157$	−0.0351033			−0.00280155			−0.00140077	+	0.999999i	$0.500446\pi$
$158$		0			0
$159$	−12.5755	−	21.7814i	−0.997301	−	1.72738i
$160$		0			0
$161$	−15.0943			−1.18960
$162$		0			0
$163$	−4.73670	+	8.20421i	−0.371007	+	0.642603i	−0.989721	−	0.143014i	$-0.954321\pi$
$163$	−4.73670	+	8.20421i	−0.371007	+	0.642603i	0.618714	+	0.785617i	$0.287654\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.42560	−	7.66536i	−0.342463	−	0.593163i	0.642426	−	0.766347i	$-0.277928\pi$
$167$	−4.42560	−	7.66536i	−0.342463	−	0.593163i	−0.984890	+	0.173184i	$0.944594\pi$
$168$		0			0
$169$	12.4291	+	3.81016i	0.956085	+	0.293089i
$170$		0			0
$171$	11.6677	+	20.2090i	0.892248	+	1.54542i
$172$		0			0
$173$	5.82245	−	10.0848i	0.442673	−	0.766731i	−0.555214	−	0.831707i	$-0.687364\pi$
$173$	5.82245	−	10.0848i	0.442673	−	0.766731i	0.997887	+	0.0649760i	$0.0206971\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.04460			0.604669
$178$		0			0
$179$	−5.15029	−	8.92056i	−0.384950	−	0.666754i	0.606812	−	0.794846i	$-0.292448\pi$
$179$	−5.15029	−	8.92056i	−0.384950	−	0.666754i	−0.991762	+	0.128092i	$0.959115\pi$
$180$		0			0
$181$	−3.79624			−0.282173			−0.141086	−	0.989997i	$-0.545059\pi$
$181$	−3.79624			−0.282173			−0.141086	+	0.989997i	$0.545059\pi$
$182$		0			0
$183$	−11.7446			−0.868188
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.09089			−0.152901
$188$		0			0
$189$	−14.1689	+	24.5412i	−1.03064	+	1.78511i
$190$		0			0
$191$	−7.59407	+	13.1533i	−0.549488	+	0.951741i	0.448822	+	0.893621i	$0.351844\pi$
$191$	−7.59407	+	13.1533i	−0.549488	+	0.951741i	−0.998310	+	0.0581194i	$0.981490\pi$
$192$		0			0
$193$	−3.24578	−	5.62185i	−0.233636	−	0.404670i	0.725239	−	0.688497i	$-0.241729\pi$
$193$	−3.24578	−	5.62185i	−0.233636	−	0.404670i	−0.958875	+	0.283827i	$0.908396\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.02397	−	8.70177i	−0.357943	−	0.619975i	0.629674	−	0.776859i	$-0.283188\pi$
$197$	−5.02397	−	8.70177i	−0.357943	−	0.619975i	−0.987617	+	0.156884i	$0.949855\pi$
$198$		0			0
$199$	4.05582	−	7.02489i	0.287510	−	0.497981i	−0.685705	−	0.727879i	$-0.740506\pi$
$199$	4.05582	−	7.02489i	0.287510	−	0.497981i	0.973215	+	0.229898i	$0.0738393\pi$
$200$		0			0
$201$	5.59815	−	9.69629i	0.394863	−	0.683923i
$202$		0			0
$203$	37.4867			2.63105
$204$		0			0
$205$		0			0
$206$		0			0
$207$	15.0943			1.04913
$208$		0			0
$209$	−28.8794			−1.99763
$210$		0			0
$211$	4.77262	+	8.26641i	0.328560	+	0.569083i	0.982226	−	0.187700i	$-0.0601032\pi$
$211$	4.77262	+	8.26641i	0.328560	+	0.569083i	−0.653666	+	0.756783i	$0.726770\pi$
$212$		0			0
$213$	−27.7987			−1.90474
$214$		0			0
$215$		0			0
$216$		0			0
$217$	16.1986	−	28.0569i	1.09964	−	1.90462i
$218$		0			0
$219$	−5.24663	−	9.08742i	−0.354534	−	0.614071i
$220$		0			0
$221$	0.758400	−	0.952706i	0.0510155	−	0.0640859i
$222$		0			0
$223$	−6.24823	−	10.8222i	−0.418412	−	0.724711i	0.577368	−	0.816484i	$-0.304080\pi$
$223$	−6.24823	−	10.8222i	−0.418412	−	0.724711i	−0.995780	+	0.0917729i	$0.970747\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.67259	−	13.2893i	0.509247	−	0.882043i	−0.490695	−	0.871331i	$-0.663257\pi$
$227$	7.67259	−	13.2893i	0.509247	−	0.882043i	0.999943	−	0.0107112i	$-0.00340954\pi$
$228$		0			0
$229$	17.1968			1.13640			0.568198	−	0.822892i	$-0.307641\pi$
$229$	17.1968			1.13640			0.568198	+	0.822892i	$0.307641\pi$
$230$		0			0
$231$	−43.8054	−	75.8731i	−2.88218	−	4.99209i
$232$		0			0
$233$	−7.21495			−0.472667			−0.236333	−	0.971672i	$-0.575946\pi$
$233$	−7.21495			−0.472667			−0.236333	+	0.971672i	$0.575946\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.05355	+	3.55686i	0.133393	+	0.231043i
$238$		0			0
$239$	1.02935			0.0665830			0.0332915	−	0.999446i	$-0.489401\pi$
$239$	1.02935			0.0665830			0.0332915	+	0.999446i	$0.489401\pi$
$240$		0			0
$241$	12.1790	−	21.0947i	0.784519	−	1.35883i	−0.144768	−	0.989466i	$-0.546243\pi$
$241$	12.1790	−	21.0947i	0.784519	−	1.35883i	0.929286	−	0.369360i	$-0.120423\pi$
$242$		0			0
$243$	−7.05812	+	12.2250i	−0.452779	+	0.784236i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.4750	−	13.1588i	0.666509	−	0.837271i
$248$		0			0
$249$	−0.232133	−	0.402066i	−0.0147108	−	0.0254799i
$250$		0			0
$251$	−6.28426	+	10.8847i	−0.396659	+	0.687034i	−0.993311	−	0.115466i	$-0.963164\pi$
$251$	−6.28426	+	10.8847i	−0.396659	+	0.687034i	0.596652	+	0.802500i	$0.296497\pi$
$252$		0			0
$253$	−9.34025	+	16.1778i	−0.587216	+	1.01709i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.72493	+	13.3800i	0.481868	+	0.834620i	0.999783	−	0.0208118i	$-0.00662508\pi$
$257$	7.72493	+	13.3800i	0.481868	+	0.834620i	−0.517915	+	0.855432i	$0.673292\pi$
$258$		0			0
$259$	−19.0793			−1.18553
$260$		0			0
$261$	−37.4867			−2.32037
$262$		0			0
$263$	−9.64160	−	16.6997i	−0.594527	−	1.02975i	−0.993613	−	0.112837i	$-0.964006\pi$
$263$	−9.64160	−	16.6997i	−0.594527	−	1.02975i	0.399087	−	0.916913i	$-0.369327\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.61552	+	11.4584i	−0.404864	+	0.701244i
$268$		0			0
$269$	−4.46139	+	7.72735i	−0.272016	+	0.471145i	−0.969378	−	0.245574i	$-0.921024\pi$
$269$	−4.46139	+	7.72735i	−0.272016	+	0.471145i	0.697362	+	0.716719i	$0.254357\pi$
$270$		0			0
$271$	−2.59803	−	4.49992i	−0.157819	−	0.273351i	0.776263	−	0.630409i	$-0.217113\pi$
$271$	−2.59803	−	4.49992i	−0.157819	−	0.273351i	−0.934082	+	0.357059i	$0.883780\pi$
$272$		0			0
$273$	50.4601	+	7.56067i	3.05399	+	0.457592i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.20566	+	15.9447i	−0.553114	+	0.958022i	0.444933	+	0.895564i	$0.353227\pi$
$277$	−9.20566	+	15.9447i	−0.553114	+	0.958022i	−0.998048	+	0.0624585i	$0.980106\pi$
$278$		0			0
$279$	−16.1986	+	28.0569i	−0.969787	+	1.67972i
$280$		0			0
$281$	27.7127			1.65320			0.826602	−	0.562787i	$-0.190271\pi$
$281$	27.7127			1.65320			0.826602	+	0.562787i	$0.190271\pi$
$282$		0			0
$283$	−5.28714	−	9.15759i	−0.314288	−	0.544362i	0.664998	−	0.746845i	$-0.268432\pi$
$283$	−5.28714	−	9.15759i	−0.314288	−	0.544362i	−0.979286	+	0.202483i	$0.935099\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	46.5135			2.74561
$288$		0			0
$289$	8.44297	+	14.6237i	0.496645	+	0.860215i
$290$		0			0
$291$	−1.45937			−0.0855495
$292$		0			0
$293$	−8.48115	+	14.6898i	−0.495474	+	0.858187i	−0.999986	−	0.00521804i	$-0.998339\pi$
$293$	−8.48115	+	14.6898i	−0.495474	+	0.858187i	0.504512	+	0.863405i	$0.331672\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	17.5352	+	30.3718i	1.01749	+	1.76235i
$298$		0			0
$299$	−3.98347	−	10.1238i	−0.230370	−	0.585473i
$300$		0			0
$301$	3.67489	+	6.36509i	0.211817	+	0.366878i
$302$		0			0
$303$	−2.15755	+	3.73699i	−0.123948	+	0.214684i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−25.7524			−1.46977			−0.734883	−	0.678194i	$-0.762763\pi$
$307$	−25.7524			−1.46977			−0.734883	+	0.678194i	$0.762763\pi$
$308$		0			0
$309$	14.8706	+	25.7566i	0.845958	+	1.46524i
$310$		0			0
$311$	19.7222			1.11834			0.559171	−	0.829052i	$-0.311119\pi$
$311$	19.7222			1.11834			0.559171	+	0.829052i	$0.311119\pi$
$312$		0			0
$313$	8.08969			0.457257			0.228628	−	0.973514i	$-0.426576\pi$
$313$	8.08969			0.457257			0.228628	+	0.973514i	$0.426576\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.11449			−0.0625959			−0.0312979	−	0.999510i	$-0.509964\pi$
$317$	−1.11449			−0.0625959			−0.0312979	+	0.999510i	$0.509964\pi$
$318$		0			0
$319$	23.1964	−	40.1774i	1.29875	−	2.24950i
$320$		0			0
$321$	−15.5903	+	27.0033i	−0.870168	+	1.50718i
$322$		0			0
$323$	−0.787718	−	1.36437i	−0.0438298	−	0.0759154i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.83011	−	11.8301i	−0.377706	−	0.654205i
$328$		0			0
$329$	−11.2159	+	19.4264i	−0.618350	+	1.07101i
$330$		0			0
$331$	−15.0647	+	26.0929i	−0.828034	+	1.43420i	0.0715451	+	0.997437i	$0.477207\pi$
$331$	−15.0647	+	26.0929i	−0.828034	+	1.43420i	−0.899579	+	0.436759i	$0.856126\pi$
$332$		0			0
$333$	19.0793			1.04554
$334$		0			0
$335$		0			0
$336$		0			0
$337$	19.1976			1.04576			0.522879	−	0.852407i	$-0.324858\pi$
$337$	19.1976			1.04576			0.522879	+	0.852407i	$0.324858\pi$
$338$		0			0
$339$	40.9584			2.22455
$340$		0			0
$341$	−20.0472	−	34.7227i	−1.08561	−	1.88034i
$342$		0			0
$343$	−55.1514			−2.97790
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.94067	+	5.09339i	−0.157863	+	0.273427i	−0.934098	−	0.357017i	$-0.883794\pi$
$347$	−2.94067	+	5.09339i	−0.157863	+	0.273427i	0.776235	+	0.630444i	$0.217127\pi$
$348$		0			0
$349$	2.46427	+	4.26823i	0.131909	+	0.228473i	0.924412	−	0.381394i	$-0.124556\pi$
$349$	2.46427	+	4.26823i	0.131909	+	0.228473i	−0.792503	+	0.609868i	$0.791223\pi$
$350$		0			0
$351$	−20.1991	−	3.02652i	−1.07815	−	0.161543i
$352$		0			0
$353$	−5.35304	−	9.27174i	−0.284914	−	0.493485i	0.687675	−	0.726019i	$-0.258632\pi$
$353$	−5.35304	−	9.27174i	−0.284914	−	0.493485i	−0.972588	+	0.232534i	$0.925298\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.38968	−	4.13905i	0.126475	−	0.219062i
$358$		0			0
$359$	−27.1191			−1.43129			−0.715647	−	0.698462i	$-0.753868\pi$
$359$	−27.1191			−1.43129			−0.715647	+	0.698462i	$0.753868\pi$
$360$		0			0
$361$	−1.37994	−	2.39012i	−0.0726284	−	0.125796i
$362$		0			0
$363$	−77.3081			−4.05762
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−14.0159	−	24.2763i	−0.731625	−	1.26721i	−0.956188	−	0.292752i	$-0.905429\pi$
$367$	−14.0159	−	24.2763i	−0.731625	−	1.26721i	0.224564	−	0.974459i	$-0.427904\pi$
$368$		0			0
$369$	−46.5135			−2.42140
$370$		0			0
$371$	−22.2381	+	38.5176i	−1.15455	+	1.99973i
$372$		0			0
$373$	10.5296	−	18.2377i	0.545200	−	0.944314i	−0.453394	−	0.891310i	$-0.649787\pi$
$373$	10.5296	−	18.2377i	0.545200	−	0.944314i	0.998594	−	0.0530042i	$-0.0168797\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.89292	+	25.1423i	0.509511	+	1.29489i
$378$		0			0
$379$	−3.12627	−	5.41485i	−0.160585	−	0.278142i	0.774493	−	0.632582i	$-0.218005\pi$
$379$	−3.12627	−	5.41485i	−0.160585	−	0.278142i	−0.935079	+	0.354440i	$0.884672\pi$
$380$		0			0
$381$	−25.6674	+	44.4573i	−1.31498	+	2.27762i
$382$		0			0
$383$	−6.10127	+	10.5677i	−0.311760	+	0.539985i	−0.978744	−	0.205088i	$-0.934252\pi$
$383$	−6.10127	+	10.5677i	−0.311760	+	0.539985i	0.666983	+	0.745073i	$0.267585\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.67489	−	6.36509i	−0.186805	−	0.323556i
$388$		0			0
$389$	−28.2139			−1.43050			−0.715250	−	0.698869i	$-0.753687\pi$
$389$	−28.2139			−1.43050			−0.715250	+	0.698869i	$0.753687\pi$
$390$		0			0
$391$	−1.01906			−0.0515362
$392$		0			0
$393$	7.10666	+	12.3091i	0.358483	+	0.620912i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−14.1740	+	24.5502i	−0.711375	+	1.23214i	0.252967	+	0.967475i	$0.418594\pi$
$397$	−14.1740	+	24.5502i	−0.711375	+	1.23214i	−0.964341	+	0.264662i	$0.914740\pi$
$398$		0			0
$399$	33.0062	−	57.1685i	1.65238	−	2.86200i
$400$		0			0
$401$	−4.81419	−	8.33842i	−0.240409	−	0.416401i	0.720422	−	0.693536i	$-0.243948\pi$
$401$	−4.81419	−	8.33842i	−0.240409	−	0.416401i	−0.960831	+	0.277135i	$0.910615\pi$
$402$		0			0
$403$	23.0926	+	3.46008i	1.15033	+	0.172359i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.8061	+	20.4488i	−0.585208	+	1.01361i
$408$		0			0
$409$	14.0867	−	24.3988i	0.696540	−	1.20644i	−0.273118	−	0.961980i	$-0.588055\pi$
$409$	14.0867	−	24.3988i	0.696540	−	1.20644i	0.969659	−	0.244463i	$-0.0786116\pi$
$410$		0			0
$411$	−16.3699			−0.807469
$412$		0			0
$413$	−7.11291	−	12.3199i	−0.350004	−	0.606224i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−29.7984			−1.45923
$418$		0			0
$419$	−8.26993	−	14.3239i	−0.404012	−	0.699770i	0.590194	−	0.807262i	$-0.299051\pi$
$419$	−8.26993	−	14.3239i	−0.404012	−	0.699770i	−0.994206	+	0.107492i	$0.965718\pi$
$420$		0			0
$421$	−34.0033			−1.65722			−0.828610	−	0.559826i	$-0.810868\pi$
$421$	−34.0033			−1.65722			−0.828610	+	0.559826i	$0.810868\pi$
$422$		0			0
$423$	11.2159	−	19.4264i	0.545333	−	0.944545i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	10.3844	+	17.9863i	0.502537	+	0.870420i
$428$		0			0
$429$	39.3277	−	49.4036i	1.89876	−	2.38523i
$430$		0			0
$431$	14.1864	+	24.5716i	0.683337	+	1.18357i	0.973956	+	0.226736i	$0.0728054\pi$
$431$	14.1864	+	24.5716i	0.683337	+	1.18357i	−0.290619	+	0.956839i	$0.593861\pi$
$432$		0			0
$433$	−14.1079	+	24.4356i	−0.677984	+	1.17430i	0.297603	+	0.954690i	$0.403813\pi$
$433$	−14.1079	+	24.4356i	−0.677984	+	1.17430i	−0.975587	+	0.219613i	$0.929521\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−14.0753			−0.673312
$438$		0			0
$439$	3.85259	+	6.67288i	0.183874	+	0.318479i	0.943197	−	0.332235i	$-0.107803\pi$
$439$	3.85259	+	6.67288i	0.183874	+	0.318479i	−0.759323	+	0.650714i	$0.774469\pi$
$440$		0			0
$441$	90.1688			4.29375
$442$		0			0
$443$	38.0286			1.80679			0.903396	−	0.428808i	$-0.141066\pi$
$443$	38.0286			1.80679			0.903396	+	0.428808i	$0.141066\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−29.0876			−1.37579
$448$		0			0
$449$	5.29308	−	9.16788i	0.249796	−	0.432659i	−0.713673	−	0.700479i	$-0.752970\pi$
$449$	5.29308	−	9.16788i	0.249796	−	0.432659i	0.963469	+	0.267820i	$0.0863032\pi$
$450$		0			0
$451$	28.7822	−	49.8522i	1.35530	−	2.34745i
$452$		0			0
$453$	10.5484	+	18.2703i	0.495606	+	0.858415i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−20.8283	−	36.0757i	−0.974306	−	1.68755i	−0.682206	−	0.731160i	$-0.738979\pi$
$457$	−20.8283	−	36.0757i	−0.974306	−	1.68755i	−0.292100	−	0.956388i	$-0.594354\pi$
$458$		0			0
$459$	−0.956584	+	1.65685i	−0.0446495	+	0.0773352i
$460$		0			0
$461$	7.17712	−	12.4311i	0.334272	−	0.578976i	−0.649073	−	0.760726i	$-0.724843\pi$
$461$	7.17712	−	12.4311i	0.334272	−	0.578976i	0.983345	+	0.181750i	$0.0581763\pi$
$462$		0			0
$463$	6.50717			0.302414			0.151207	−	0.988502i	$-0.451684\pi$
$463$	6.50717			0.302414			0.151207	+	0.988502i	$0.451684\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−25.6173			−1.18543			−0.592714	−	0.805413i	$-0.701943\pi$
$467$	−25.6173			−1.18543			−0.592714	+	0.805413i	$0.701943\pi$
$468$		0			0
$469$	−19.7992			−0.914243
$470$		0			0
$471$	−0.0496512	−	0.0859985i	−0.00228781	−	0.00396260i
$472$		0			0
$473$	9.09596			0.418233
$474$		0			0
$475$		0			0
$476$		0			0
$477$	22.2381	−	38.5176i	1.01821	−	1.76360i
$478$		0			0
$479$	17.4198	+	30.1720i	0.795932	+	1.37859i	0.922246	+	0.386604i	$0.126352\pi$
$479$	17.4198	+	30.1720i	0.795932	+	1.37859i	−0.126314	+	0.991990i	$0.540315\pi$
$480$		0			0
$481$	−5.03514	−	12.7965i	−0.229582	−	0.583471i
$482$		0			0
$483$	−21.3499	−	36.9792i	−0.971455	−	1.68261i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.16536	+	5.48256i	−0.143436	+	0.248439i	−0.928788	−	0.370611i	$-0.879148\pi$
$487$	−3.16536	+	5.48256i	−0.143436	+	0.248439i	0.785352	+	0.619049i	$0.212482\pi$
$488$		0			0
$489$	−26.7990			−1.21189
$490$		0			0
$491$	12.6931	+	21.9851i	0.572833	+	0.992175i	0.996273	+	0.0862515i	$0.0274889\pi$
$491$	12.6931	+	21.9851i	0.572833	+	0.992175i	−0.423441	+	0.905924i	$0.639178\pi$
$492$		0			0
$493$	2.53083			0.113983
$494$		0			0
$495$		0			0
$496$		0			0
$497$	24.5792	+	42.5724i	1.10253	+	1.90964i
$498$		0			0
$499$	8.12242			0.363610			0.181805	−	0.983335i	$-0.441806\pi$
$499$	8.12242			0.363610			0.181805	+	0.983335i	$0.441806\pi$
$500$		0			0
$501$	12.5194	−	21.6843i	0.559327	−	0.968782i
$502$		0			0
$503$	7.53334	−	13.0481i	0.335895	−	0.581787i	−0.647761	−	0.761843i	$-0.724295\pi$
$503$	7.53334	−	13.0481i	0.335895	−	0.581787i	0.983656	+	0.180056i	$0.0576279\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	8.24575	+	35.8389i	0.366207	+	1.59166i
$508$		0			0
$509$	20.9514	+	36.2890i	0.928656	+	1.60848i	0.785573	+	0.618769i	$0.212368\pi$
$509$	20.9514	+	36.2890i	0.928656	+	1.60848i	0.143083	+	0.989711i	$0.454298\pi$
$510$		0			0
$511$	−9.27797	+	16.0699i	−0.410433	+	0.710892i
$512$		0			0
$513$	−13.2123	+	22.8844i	−0.583338	+	1.01037i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	13.8805	+	24.0418i	0.610466	+	1.05736i
$518$		0			0
$519$	32.9419			1.44599
$520$		0			0
$521$	−27.8437			−1.21986			−0.609928	−	0.792457i	$-0.708802\pi$
$521$	−27.8437			−1.21986			−0.609928	+	0.792457i	$0.708802\pi$
$522$		0			0
$523$	17.7832	+	30.8015i	0.777607	+	1.34685i	0.933318	+	0.359051i	$0.116900\pi$
$523$	17.7832	+	30.8015i	0.777607	+	1.34685i	−0.155711	+	0.987803i	$0.549767\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.09362	−	1.89420i	0.0476387	−	0.0825127i
$528$		0			0
$529$	6.94774	−	12.0338i	0.302076	−	0.523210i
$530$		0			0
$531$	7.11291	+	12.3199i	0.308674	+	0.534639i
$532$		0			0
$533$	12.2752	+	31.1966i	0.531696	+	1.35128i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	14.5695	−	25.2351i	0.628719	−	1.08897i
$538$		0			0
$539$	−55.7957	+	96.6409i	−2.40329	+	4.16262i
$540$		0			0
$541$	−27.8180			−1.19599			−0.597995	−	0.801499i	$-0.704036\pi$
$541$	−27.8180			−1.19599			−0.597995	+	0.801499i	$0.704036\pi$
$542$		0			0
$543$	−5.36953	−	9.30030i	−0.230429	−	0.399114i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	24.9538			1.06695			0.533473	−	0.845817i	$-0.320887\pi$
$547$	24.9538			1.06695			0.533473	+	0.845817i	$0.320887\pi$
$548$		0			0
$549$	−10.3844	−	17.9863i	−0.443196	−	0.767638i
$550$		0			0
$551$	34.9558			1.48917
$552$		0			0
$553$	3.63144	−	6.28984i	0.154425	−	0.267471i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.58848	−	4.48337i	−0.109677	−	0.189967i	0.805962	−	0.591967i	$-0.201648\pi$
$557$	−2.58848	−	4.48337i	−0.109677	−	0.189967i	−0.915640	+	0.402000i	$0.868315\pi$
$558$		0			0
$559$	−3.29925	+	4.14453i	−0.139543	+	0.175295i
$560$		0			0
$561$	−2.95743	−	5.12242i	−0.124863	−	0.216269i
$562$		0			0
$563$	22.9366	−	39.7273i	0.966660	−	1.67430i	0.261574	−	0.965183i	$-0.415758\pi$
$563$	22.9366	−	39.7273i	0.966660	−	1.67430i	0.705086	−	0.709122i	$-0.250908\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−5.08937			−0.213734
$568$		0			0
$569$	16.1491	+	27.9710i	0.677005	+	1.17261i	0.975879	+	0.218314i	$0.0700556\pi$
$569$	16.1491	+	27.9710i	0.677005	+	1.17261i	−0.298874	+	0.954293i	$0.596611\pi$
$570$		0			0
$571$	10.1241			0.423678			0.211839	−	0.977305i	$-0.432055\pi$
$571$	10.1241			0.423678			0.211839	+	0.977305i	$0.432055\pi$
$572$		0			0
$573$	−42.9652			−1.79490
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−13.9748			−0.581780			−0.290890	−	0.956757i	$-0.593951\pi$
$577$	−13.9748			−0.581780			−0.290890	+	0.956757i	$0.593951\pi$
$578$		0			0
$579$	9.18187	−	15.9035i	0.381586	−	0.660926i
$580$		0			0
$581$	−0.410497	+	0.711001i	−0.0170303	+	0.0294973i
$582$		0			0
$583$	27.5215	+	47.6687i	1.13982	+	1.97423i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.89437	−	11.9414i	−0.284561	−	0.492874i	0.687942	−	0.725766i	$-0.258514\pi$
$587$	−6.89437	−	11.9414i	−0.284561	−	0.492874i	−0.972503	+	0.232892i	$0.925181\pi$
$588$		0			0
$589$	15.1050	−	26.1627i	0.622392	−	1.07801i
$590$		0			0
$591$	14.2121	−	24.6161i	0.584609	−	1.01257i
$592$		0			0
$593$	22.7491			0.934193			0.467097	−	0.884206i	$-0.345300\pi$
$593$	22.7491			0.934193			0.467097	+	0.884206i	$0.345300\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	22.9468			0.939148
$598$		0			0
$599$	−0.331916			−0.0135617			−0.00678086	−	0.999977i	$-0.502158\pi$
$599$	−0.331916			−0.0135617			−0.00678086	+	0.999977i	$0.502158\pi$
$600$		0			0
$601$	9.97424	+	17.2759i	0.406858	+	0.704698i	0.994536	−	0.104396i	$-0.0332911\pi$
$601$	9.97424	+	17.2759i	0.406858	+	0.704698i	−0.587678	+	0.809095i	$0.699958\pi$
$602$		0			0
$603$	19.7992			0.806286
$604$		0			0
$605$		0			0
$606$		0			0
$607$	14.3809	−	24.9085i	0.583704	−	1.01101i	−0.411331	−	0.911486i	$-0.634936\pi$
$607$	14.3809	−	24.9085i	0.583704	−	1.01101i	0.995036	−	0.0995198i	$-0.0317306\pi$
$608$		0			0
$609$	53.0224	+	91.8374i	2.14857	+	3.72144i
$610$		0			0
$611$	−15.9892	−	2.39574i	−0.646855	−	0.0969212i
$612$		0			0
$613$	5.76499	+	9.98526i	0.232846	+	0.403301i	0.958644	−	0.284607i	$-0.0918629\pi$
$613$	5.76499	+	9.98526i	0.232846	+	0.403301i	−0.725799	+	0.687907i	$0.758530\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−16.0493	+	27.7981i	−0.646119	+	1.11911i	0.337923	+	0.941174i	$0.390276\pi$
$617$	−16.0493	+	27.7981i	−0.646119	+	1.11911i	−0.984042	+	0.177937i	$0.943058\pi$
$618$		0			0
$619$	−0.651502			−0.0261861			−0.0130930	−	0.999914i	$-0.504168\pi$
$619$	−0.651502			−0.0261861			−0.0130930	+	0.999914i	$0.504168\pi$
$620$		0			0
$621$	8.54632	+	14.8027i	0.342952	+	0.594010i
$622$		0			0
$623$	23.3974			0.937397
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−40.8480	−	70.7507i	−1.63131	−	2.82551i
$628$		0			0
$629$	−1.28810			−0.0513600
$630$		0			0
$631$	11.8775	−	20.5724i	0.472834	−	0.818973i	−0.526683	−	0.850062i	$-0.676564\pi$
$631$	11.8775	−	20.5724i	0.472834	−	0.818973i	0.999517	+	0.0310895i	$0.00989769\pi$
$632$		0			0
$633$	−13.5011	+	23.3846i	−0.536620	+	0.929453i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−23.7960	−	60.4762i	−0.942832	−	2.39615i
$638$		0			0
$639$	−24.5792	−	42.5724i	−0.972339	−	1.68414i
$640$		0			0
$641$	14.7753	−	25.5916i	0.583590	−	1.01081i	−0.411460	−	0.911428i	$-0.634981\pi$
$641$	14.7753	−	25.5916i	0.583590	−	1.01081i	0.995050	−	0.0993791i	$-0.0316856\pi$
$642$		0			0
$643$	10.4256	−	18.0577i	0.411147	−	0.712127i	−0.583869	−	0.811848i	$-0.698462\pi$
$643$	10.4256	−	18.0577i	0.411147	−	0.712127i	0.995015	+	0.0997211i	$0.0317951\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.201092	−	0.348301i	−0.00790574	−	0.0136931i	0.862045	−	0.506831i	$-0.169183\pi$
$647$	−0.201092	−	0.348301i	−0.00790574	−	0.0136931i	−0.869951	+	0.493138i	$0.835850\pi$
$648$		0			0
$649$	−17.6056			−0.691082
$650$		0			0
$651$	91.6476			3.59195
$652$		0			0
$653$	−23.6263	−	40.9220i	−0.924570	−	1.60140i	−0.792252	−	0.610194i	$-0.791091\pi$
$653$	−23.6263	−	40.9220i	−0.924570	−	1.60140i	−0.132318	−	0.991207i	$-0.542242\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	9.27797	−	16.0699i	0.361968	−	0.626947i
$658$		0			0
$659$	−8.75246	+	15.1597i	−0.340948	+	0.590539i	−0.984609	−	0.174772i	$-0.944081\pi$
$659$	−8.75246	+	15.1597i	−0.340948	+	0.590539i	0.643661	+	0.765310i	$0.277415\pi$
$660$		0			0
$661$	4.70405	+	8.14766i	0.182966	+	0.316907i	0.942889	−	0.333106i	$-0.108097\pi$
$661$	4.70405	+	8.14766i	0.182966	+	0.316907i	−0.759923	+	0.650013i	$0.774763\pi$
$662$		0			0
$663$	3.40671	+	0.510443i	0.132306	+	0.0198240i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11.3055	−	19.5817i	0.437751	−	0.758207i
$668$		0			0
$669$	17.6754	−	30.6147i	0.683370	−	1.18363i
$670$		0			0
$671$	25.7032			0.992260
$672$		0			0
$673$	9.40580	+	16.2913i	0.362567	+	0.627984i	0.988383	−	0.151987i	$-0.0485671\pi$
$673$	9.40580	+	16.2913i	0.362567	+	0.627984i	−0.625816	+	0.779971i	$0.715234\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−43.3999			−1.66800			−0.833998	−	0.551768i	$-0.813953\pi$
$677$	−43.3999			−1.66800			−0.833998	+	0.551768i	$0.813953\pi$
$678$		0			0
$679$	1.29035	+	2.23495i	0.0495191	+	0.0857695i
$680$		0			0
$681$	43.4094			1.66345
$682$		0			0
$683$	−19.9451	+	34.5459i	−0.763177	+	1.32186i	0.178027	+	0.984026i	$0.443028\pi$
$683$	−19.9451	+	34.5459i	−0.763177	+	1.32186i	−0.941205	+	0.337836i	$0.890305\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	24.3237	+	42.1299i	0.928008	+	1.60736i
$688$		0			0
$689$	−31.7025	−	4.75012i	−1.20777	−	0.180965i
$690$		0			0
$691$	2.41303	+	4.17949i	0.0917961	+	0.158995i	0.908267	−	0.418391i	$-0.137406\pi$
$691$	2.41303	+	4.17949i	0.0917961	+	0.158995i	−0.816471	+	0.577387i	$0.804073\pi$
$692$		0			0
$693$	77.4641	−	134.172i	2.94262	−	5.09676i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.14027			0.118946
$698$		0			0
$699$	−10.2051	−	17.6757i	−0.385991	−	0.668556i
$700$		0			0
$701$	−32.6358			−1.23264			−0.616319	−	0.787496i	$-0.711377\pi$
$701$	−32.6358			−1.23264			−0.616319	+	0.787496i	$0.711377\pi$
$702$		0			0
$703$	−17.7912			−0.671009
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.63069			0.286982
$708$		0			0
$709$	−9.85365	+	17.0670i	−0.370061	+	0.640965i	−0.989575	−	0.144021i	$-0.953997\pi$
$709$	−9.85365	+	17.0670i	−0.370061	+	0.640965i	0.619513	+	0.784986i	$0.287330\pi$
$710$		0			0
$711$	−3.63144	+	6.28984i	−0.136190	+	0.235888i
$712$		0			0
$713$	−9.77061	−	16.9232i	−0.365912	−	0.633779i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.45594	+	2.52177i	0.0543732	+	0.0941772i
$718$		0			0
$719$	21.3564	−	36.9903i	0.796458	−	1.37951i	−0.125451	−	0.992100i	$-0.540038\pi$
$719$	21.3564	−	36.9903i	0.796458	−	1.37951i	0.921909	−	0.387406i	$-0.126629\pi$
$720$		0			0
$721$	26.2967	−	45.5472i	0.979340	−	1.69627i
$722$		0			0
$723$	68.9055			2.56262
$724$		0			0
$725$		0			0
$726$		0			0
$727$	11.1831			0.414757			0.207379	−	0.978261i	$-0.433507\pi$
$727$	11.1831			0.414757			0.207379	+	0.978261i	$0.433507\pi$
$728$		0			0
$729$	−42.9851			−1.59204
$730$		0			0
$731$	0.248103	+	0.429726i	0.00917641	+	0.0158940i
$732$		0			0
$733$	3.91032			0.144431			0.0722156	−	0.997389i	$-0.476993\pi$
$733$	3.91032			0.144431			0.0722156	+	0.997389i	$0.476993\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.2516	+	21.2204i	−0.451293	+	0.781662i
$738$		0			0
$739$	−10.3101	−	17.8576i	−0.379263	−	0.656903i	0.611692	−	0.791096i	$-0.290489\pi$
$739$	−10.3101	−	17.8576i	−0.379263	−	0.656903i	−0.990955	+	0.134193i	$0.957156\pi$
$740$		0			0
$741$	47.0534	+	7.05022i	1.72855	+	0.258996i
$742$		0			0
$743$	4.18992	+	7.25716i	0.153713	+	0.266239i	0.932590	−	0.360938i	$-0.117543\pi$
$743$	4.18992	+	7.25716i	0.153713	+	0.266239i	−0.778876	+	0.627177i	$0.784210\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.410497	−	0.711001i	0.0150193	−	0.0260142i
$748$		0			0
$749$	55.1390			2.01474
$750$		0			0
$751$	−7.39645	−	12.8110i	−0.269900	−	0.467481i	0.698935	−	0.715185i	$-0.253657\pi$
$751$	−7.39645	−	12.8110i	−0.269900	−	0.467481i	−0.968836	+	0.247703i	$0.920324\pi$
$752$		0			0
$753$	−35.5547			−1.29568
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.60726	−	2.78385i	−0.0584168	−	0.101181i	0.835338	−	0.549737i	$-0.185272\pi$
$757$	−1.60726	−	2.78385i	−0.0584168	−	0.101181i	−0.893755	+	0.448556i	$0.851939\pi$
$758$		0			0
$759$	−52.8446			−1.91814
$760$		0			0
$761$	−20.3923	+	35.3205i	−0.739220	+	1.28037i	0.213627	+	0.976915i	$0.431472\pi$
$761$	−20.3923	+	35.3205i	−0.739220	+	1.28037i	−0.952847	+	0.303451i	$0.901861\pi$
$762$		0			0
$763$	−12.0782	+	20.9200i	−0.437259	+	0.757354i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.38584	−	8.02193i	0.230579	−	0.289655i
$768$		0			0
$769$	−3.52726	−	6.10940i	−0.127196	−	0.220311i	0.795393	−	0.606094i	$-0.207265\pi$
$769$	−3.52726	−	6.10940i	−0.127196	−	0.220311i	−0.922589	+	0.385783i	$0.873931\pi$
$770$		0			0
$771$	−21.8528	+	37.8502i	−0.787009	+	1.36314i
$772$		0			0
$773$	−11.1643	+	19.3372i	−0.401553	+	0.695510i	−0.993914	−	0.110163i	$-0.964863\pi$
$773$	−11.1643	+	19.3372i	−0.401553	+	0.695510i	0.592361	+	0.805673i	$0.298196\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−26.9864	−	46.7419i	−0.968133	−	1.67686i
$778$		0			0
$779$	43.3733			1.55401
$780$		0			0
$781$	60.8376			2.17694
$782$		0			0
$783$	−21.2247	−	36.7623i	−0.758510	−	1.31378i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	17.5112	−	30.3303i	0.624207	−	1.08116i	−0.364487	−	0.931208i	$-0.618756\pi$
$787$	17.5112	−	30.3303i	0.624207	−	1.08116i	0.988694	−	0.149949i	$-0.0479110\pi$
$788$		0			0
$789$	27.2748	−	47.2413i	0.971008	−	1.68184i
$790$		0			0
$791$	−36.2148	−	62.7258i	−1.28765	−	2.23027i
$792$		0			0
$793$	−9.32294	+	11.7115i	−0.331067	+	0.415888i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.56962	−	14.8430i	0.303552	−	0.525767i	−0.673386	−	0.739291i	$-0.735161\pi$
$797$	8.56962	−	14.8430i	0.303552	−	0.525767i	0.976938	+	0.213524i	$0.0684942\pi$
$798$		0			0
$799$	−0.757215	+	1.31154i	−0.0267883	+	0.0463988i
$800$		0			0
$801$	−23.3974			−0.826706
$802$		0			0
$803$	11.4823	+	19.8879i	0.405200	+	0.701827i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−25.2413			−0.888537
$808$		0			0
$809$	−21.9246	−	37.9745i	−0.770827	−	1.33511i	−0.937111	−	0.349033i	$-0.886510\pi$
$809$	−21.9246	−	37.9745i	−0.770827	−	1.33511i	0.166284	−	0.986078i	$-0.446823\pi$
$810$		0			0
$811$	38.9513			1.36776			0.683882	−	0.729592i	$-0.260290\pi$
$811$	38.9513			1.36776			0.683882	+	0.729592i	$0.260290\pi$
$812$		0			0
$813$	7.34947	−	12.7297i	0.257757	−	0.446449i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.42679	+	5.93537i	0.119888	+	0.207652i
$818$		0			0
$819$	33.0373	+	83.9623i	1.15442	+	2.93388i
$820$		0			0
$821$	−9.30596	−	16.1184i	−0.324780	−	0.562536i	0.656687	−	0.754163i	$-0.271957\pi$
$821$	−9.30596	−	16.1184i	−0.324780	−	0.562536i	−0.981468	+	0.191627i	$0.938624\pi$
$822$		0			0
$823$	4.89794	−	8.48349i	0.170732	−	0.295716i	−0.767944	−	0.640517i	$-0.778720\pi$
$823$	4.89794	−	8.48349i	0.170732	−	0.295716i	0.938676	+	0.344801i	$0.112054\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−39.6991			−1.38047			−0.690236	−	0.723584i	$-0.742494\pi$
$827$	−39.6991			−1.38047			−0.690236	+	0.723584i	$0.742494\pi$
$828$		0			0
$829$	15.8405	+	27.4366i	0.550164	+	0.952911i	0.998262	+	0.0589273i	$0.0187680\pi$
$829$	15.8405	+	27.4366i	0.550164	+	0.952911i	−0.448099	+	0.893984i	$0.647899\pi$
$830$		0			0
$831$	−52.0831			−1.80674
$832$		0			0
$833$	−6.08756			−0.210921
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−36.6863			−1.26806
$838$		0			0
$839$	−16.1325	+	27.9423i	−0.556956	+	0.964677i	0.440792	+	0.897609i	$0.354698\pi$
$839$	−16.1325	+	27.9423i	−0.556956	+	0.964677i	−0.997748	+	0.0670676i	$0.978636\pi$
$840$		0			0
$841$	−13.5771	+	23.5163i	−0.468177	+	0.810906i
$842$		0			0
$843$	39.1978	+	67.8926i	1.35004	+	2.33835i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	68.3546	+	118.394i	2.34869	+	4.06806i
$848$		0			0
$849$	14.9566	−	25.9056i	0.513309	−	0.889078i
$850$		0			0
$851$	−5.75409	+	9.96637i	−0.197248	+	0.341643i
$852$		0			0
$853$	−17.3167			−0.592912			−0.296456	−	0.955047i	$-0.595805\pi$
$853$	−17.3167			−0.592912			−0.296456	+	0.955047i	$0.595805\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−40.9024			−1.39720			−0.698600	−	0.715513i	$-0.746193\pi$
$857$	−40.9024			−1.39720			−0.698600	+	0.715513i	$0.746193\pi$
$858$		0			0
$859$	2.14185			0.0730789			0.0365394	−	0.999332i	$-0.488367\pi$
$859$	2.14185			0.0730789			0.0365394	+	0.999332i	$0.488367\pi$
$860$		0			0
$861$	65.7903	+	113.952i	2.24213	+	3.88348i
$862$		0			0
$863$	26.0760			0.887638			0.443819	−	0.896116i	$-0.353623\pi$
$863$	26.0760			0.887638			0.443819	+	0.896116i	$0.353623\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−23.8840	+	41.3683i	−0.811144	+	1.40494i
$868$		0			0
$869$	−4.49421	−	7.78420i	−0.152456	−	0.264061i
$870$		0			0
$871$	−5.22512	−	13.2793i	−0.177046	−	0.449953i
$872$		0			0
$873$	−1.29035	−	2.23495i	−0.0436717	−	0.0756416i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−23.8954	+	41.3881i	−0.806890	+	1.39758i	0.108117	+	0.994138i	$0.465518\pi$
$877$	−23.8954	+	41.3881i	−0.806890	+	1.39758i	−0.915007	+	0.403437i	$0.867815\pi$
$878$		0			0
$879$	−47.9841			−1.61846
$880$		0			0
$881$	23.9463	+	41.4762i	0.806770	+	1.39737i	0.915089	+	0.403251i	$0.132120\pi$
$881$	23.9463	+	41.4762i	0.806770	+	1.39737i	−0.108319	+	0.994116i	$0.534547\pi$
$882$		0			0
$883$	−35.3788			−1.19059			−0.595296	−	0.803507i	$-0.702965\pi$
$883$	−35.3788			−1.19059			−0.595296	+	0.803507i	$0.702965\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.14082	−	7.17211i	−0.139035	−	0.240816i	0.788096	−	0.615552i	$-0.211067\pi$
$887$	−4.14082	−	7.17211i	−0.139035	−	0.240816i	−0.927132	+	0.374736i	$0.877733\pi$
$888$		0			0
$889$	90.7791			3.04463
$890$		0			0
$891$	−3.14926	+	5.45468i	−0.105504	+	0.182739i
$892$		0			0
$893$	−10.4586	+	18.1149i	−0.349985	+	0.606192i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	19.1676	−	24.0784i	0.639986	−	0.803954i
$898$		0			0
$899$	24.2652	+	42.0286i	0.809291	+	1.40173i
$900$		0			0
$901$	−1.50136	+	2.60043i	−0.0500176	+	0.0866330i
$902$		0			0
$903$	−10.3958	+	18.0060i	−0.345949	+	0.599202i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	19.9952	+	34.6327i	0.663929	+	1.14996i	0.979574	+	0.201082i	$0.0644458\pi$
$907$	19.9952	+	34.6327i	0.663929	+	1.14996i	−0.315645	+	0.948877i	$0.602221\pi$
$908$		0			0
$909$	−7.63069			−0.253094
$910$		0			0
$911$	−33.3447			−1.10476			−0.552380	−	0.833592i	$-0.686280\pi$
$911$	−33.3447			−1.10476			−0.552380	+	0.833592i	$0.686280\pi$
$912$		0			0
$913$	0.508024	+	0.879923i	0.0168131	+	0.0291212i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.5672	−	21.7670i	0.415005	−	0.718811i
$918$		0			0
$919$	−27.3791	+	47.4220i	−0.903154	+	1.56431i	−0.0797777	+	0.996813i	$0.525421\pi$
$919$	−27.3791	+	47.4220i	−0.903154	+	1.56431i	−0.823376	+	0.567496i	$0.807912\pi$
$920$		0			0
$921$	−36.4250	−	63.0900i	−1.20025	−	2.07889i
$922$		0			0
$923$	−22.0668	+	27.7204i	−0.726336	+	0.912427i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−26.2967	+	45.5472i	−0.863697	+	1.49597i
$928$		0			0
$929$	29.6237	−	51.3097i	0.971921	−	1.68342i	0.282177	−	0.959362i	$-0.408943\pi$
$929$	29.6237	−	51.3097i	0.971921	−	1.68342i	0.689744	−	0.724054i	$-0.257723\pi$
$930$		0			0
$931$	−84.0812			−2.75565
$932$		0			0
$933$	27.8957	+	48.3168i	0.913264	+	1.58182i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−43.7040			−1.42775			−0.713874	−	0.700274i	$-0.753061\pi$
$937$	−43.7040			−1.42775			−0.713874	+	0.700274i	$0.753061\pi$
$938$		0			0
$939$	11.4423	+	19.8187i	0.373406	+	0.646759i
$940$		0			0
$941$	−2.34191			−0.0763439			−0.0381720	−	0.999271i	$-0.512153\pi$
$941$	−2.34191			−0.0763439			−0.0381720	+	0.999271i	$0.512153\pi$
$942$		0			0
$943$	14.0279	−	24.2970i	0.456811	−	0.791220i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.25510	−	12.5662i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$947$	−7.25510	−	12.5662i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$948$		0			0
$949$	−13.2266	−	1.98180i	−0.429354	−	0.0643320i
$950$		0			0
$951$	−1.57637	−	2.73035i	−0.0511172	−	0.0885376i
$952$		0			0
$953$	16.7272	−	28.9723i	0.541846	−	0.938505i	−0.456952	−	0.889491i	$-0.651059\pi$
$953$	16.7272	−	28.9723i	0.541846	−	0.938505i	0.998798	−	0.0490137i	$-0.0156078\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	131.239			4.24236
$958$		0			0
$959$	14.4740	+	25.0698i	0.467391	+	0.809545i
$960$		0			0
$961$	10.9417			0.352959
$962$		0			0
$963$	−55.1390			−1.77683
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−2.89216			−0.0930056			−0.0465028	−	0.998918i	$-0.514808\pi$
$967$	−2.89216			−0.0930056			−0.0465028	+	0.998918i	$0.514808\pi$
$968$		0			0
$969$	2.22835	−	3.85961i	0.0715848	−	0.123989i
$970$		0			0
$971$	−22.2739	+	38.5795i	−0.714804	+	1.23808i	0.248231	+	0.968701i	$0.420151\pi$
$971$	−22.2739	+	38.5795i	−0.714804	+	1.23808i	−0.963035	+	0.269376i	$0.913183\pi$
$972$		0			0
$973$	26.3473	+	45.6348i	0.844654	+	1.46298i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.12402	−	5.41096i	−0.0999462	−	0.173112i	0.811716	−	0.584052i	$-0.198534\pi$
$977$	−3.12402	−	5.41096i	−0.0999462	−	0.173112i	−0.911662	+	0.410940i	$0.865200\pi$
$978$		0			0
$979$	14.4781	−	25.0768i	0.462722	−	0.801458i
$980$		0			0
$981$	12.0782	−	20.9200i	0.385626	−	0.667923i
$982$		0			0
$983$	−46.2734			−1.47589			−0.737946	−	0.674860i	$-0.764204\pi$
$983$	−46.2734			−1.47589			−0.737946	+	0.674860i	$0.764204\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−63.4563			−2.01984
$988$		0			0
$989$	4.43320			0.140968
$990$		0			0
$991$	−24.0826	−	41.7122i	−0.765008	−	1.32503i	−0.940242	−	0.340506i	$-0.889402\pi$
$991$	−24.0826	−	41.7122i	−0.765008	−	1.32503i	0.175235	−	0.984527i	$-0.443932\pi$
$992$		0			0
$993$	−85.2323			−2.70477
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−5.67053	+	9.82165i	−0.179588	+	0.311055i	−0.941739	−	0.336344i	$-0.890810\pi$
$997$	−5.67053	+	9.82165i	−0.179588	+	0.311055i	0.762152	+	0.647398i	$0.224143\pi$
$998$		0			0
$999$	10.8026	+	18.7107i	0.341779	+	0.591979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.i.h.601.5	yes	10
5.2	odd	4		1300.2.bb.g.549.10		20
5.3	odd	4		1300.2.bb.g.549.1		20
5.4	even	2		1300.2.i.g.601.1	✓	10
13.9	even	3	inner	1300.2.i.h.1101.5	yes	10
65.9	even	6		1300.2.i.g.1101.1	yes	10
65.22	odd	12		1300.2.bb.g.1049.1		20
65.48	odd	12		1300.2.bb.g.1049.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1300.2.i.g.601.1	✓	10	5.4	even	2
1300.2.i.g.1101.1	yes	10	65.9	even	6
1300.2.i.h.601.5	yes	10	1.1	even	1	trivial
1300.2.i.h.1101.5	yes	10	13.9	even	3	inner
1300.2.bb.g.549.1		20	5.3	odd	4
1300.2.bb.g.549.10		20	5.2	odd	4
1300.2.bb.g.1049.1		20	65.22	odd	12
1300.2.bb.g.1049.10		20	65.48	odd	12

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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41443 + 2.44987i) q^{3} +(2.50124 - 4.33228i) q^{7} +(-2.50124 + 4.33228i) q^{9} +O(q^{10})\)	\(q+(1.41443 + 2.44987i) q^{3} +(2.50124 - 4.33228i) q^{7} +(-2.50124 + 4.33228i) q^{9} +(-3.09549 - 5.36155i) q^{11} +(3.56575 + 0.534272i) q^{13} +(0.168866 - 0.292485i) q^{17} +(2.33237 - 4.03979i) q^{19} +14.1513 q^{21} +(-1.50869 - 2.61312i) q^{23} -5.66475 q^{27} +(3.74681 + 6.48966i) q^{29} +6.47624 q^{31} +(8.75673 - 15.1671i) q^{33} +(-1.90699 - 3.30300i) q^{37} +(3.73461 + 9.49131i) q^{39} +(4.64905 + 8.05238i) q^{41} +(-0.734613 + 1.27239i) q^{43} -4.48412 q^{47} +(-9.01241 - 15.6099i) q^{49} +0.955399 q^{51} -8.89084 q^{53} +13.1959 q^{57} +(1.42188 - 2.46276i) q^{59} +(-2.07585 + 3.59548i) q^{61} +(12.5124 + 21.6721i) q^{63} +(-1.97894 - 3.42762i) q^{67} +(4.26787 - 7.39216i) q^{69} +(-4.91340 + 8.51027i) q^{71} -3.70935 q^{73} -30.9703 q^{77} +1.45186 q^{79} +(-0.508685 - 0.881068i) q^{81} -0.164117 q^{83} +(-10.5992 + 18.3584i) q^{87} +(2.33858 + 4.05054i) q^{89} +(11.2334 - 14.1115i) q^{91} +(9.16021 + 15.8660i) q^{93} +(-0.257942 + 0.446768i) q^{97} +30.9703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 10 * q + q^3 + 4 * q^7 - 4 * q^9	\( 10 q + q^{3} + 4 q^{7} - 4 q^{9} - 7 q^{11} + 6 q^{13} + 8 q^{17} - 4 q^{19} + 8 q^{21} + q^{23} - 2 q^{27} - 3 q^{29} + 16 q^{31} + 10 q^{33} - q^{37} + 14 q^{39} + 10 q^{41} + 16 q^{43} - 8 q^{47} - 11 q^{49} + 8 q^{51} - 32 q^{53} + 6 q^{59} - 9 q^{61} + 46 q^{63} + 2 q^{67} + 24 q^{69} + 5 q^{71} + 16 q^{73} - 56 q^{77} + 11 q^{81} - 30 q^{83} - 19 q^{87} + 22 q^{89} - 7 q^{91} - 3 q^{93} - 21 q^{97} + 56 q^{99}+O(q^{100}) \) 10 * q + q^3 + 4 * q^7 - 4 * q^9 - 7 * q^11 + 6 * q^13 + 8 * q^17 - 4 * q^19 + 8 * q^21 + q^23 - 2 * q^27 - 3 * q^29 + 16 * q^31 + 10 * q^33 - q^37 + 14 * q^39 + 10 * q^41 + 16 * q^43 - 8 * q^47 - 11 * q^49 + 8 * q^51 - 32 * q^53 + 6 * q^59 - 9 * q^61 + 46 * q^63 + 2 * q^67 + 24 * q^69 + 5 * q^71 + 16 * q^73 - 56 * q^77 + 11 * q^81 - 30 * q^83 - 19 * q^87 + 22 * q^89 - 7 * q^91 - 3 * q^93 - 21 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more