LMFDB - Embedded newform 1148.2.k.a.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.2
Root			$-1.22833i$ of defining polynomial
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.a.729.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.868559 - 0.868559i) q^{3} -4.37966i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.49121i q^{9} +O(q^{10})$	\(q+(-0.868559 - 0.868559i) q^{3} -4.37966i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.49121i q^{9} +(1.10701 + 1.10701i) q^{11} +(0.155874 + 0.155874i) q^{13} +(-3.80399 + 3.80399i) q^{15} +(5.27265 - 5.27265i) q^{17} +(5.24822 - 5.24822i) q^{19} +1.22833i q^{21} +5.28835 q^{23} -14.1814 q^{25} +(-3.90088 + 3.90088i) q^{27} +(-4.12690 - 4.12690i) q^{29} +1.03455 q^{31} -1.92300i q^{33} +(-3.09689 + 3.09689i) q^{35} -2.58579 q^{37} -0.270771i q^{39} +(-4.93089 + 4.08489i) q^{41} +8.71688i q^{43} -6.53099 q^{45} +(-2.00789 + 2.00789i) q^{47} +1.00000i q^{49} -9.15922 q^{51} +(5.98800 + 5.98800i) q^{53} +(4.84832 - 4.84832i) q^{55} -9.11678 q^{57} +6.40829 q^{59} +12.4391i q^{61} +(-1.05444 + 1.05444i) q^{63} +(0.682674 - 0.682674i) q^{65} +(-1.54565 + 1.54565i) q^{67} +(-4.59325 - 4.59325i) q^{69} +(0.123981 + 0.123981i) q^{71} -5.51668i q^{73} +(12.3174 + 12.3174i) q^{75} -1.56555i q^{77} +(-8.20809 - 8.20809i) q^{79} +2.30266 q^{81} -12.8108 q^{83} +(-23.0924 - 23.0924i) q^{85} +7.16891i q^{87} +(11.9756 + 11.9756i) q^{89} -0.220439i q^{91} +(-0.898571 - 0.898571i) q^{93} +(-22.9854 - 22.9854i) q^{95} +(6.20844 - 6.20844i) q^{97} +(1.65078 - 1.65078i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3}+O(q^{10}) $ 8 * q - 4 * q^3	$ 8 q - 4 q^{3} + 12 q^{11} + 4 q^{13} - 8 q^{15} + 8 q^{17} + 8 q^{19} + 28 q^{23} - 4 q^{25} + 8 q^{27} - 16 q^{29} + 28 q^{31} - 8 q^{35} - 32 q^{37} - 4 q^{45} + 20 q^{47} - 20 q^{51} + 32 q^{53} - 4 q^{55} - 36 q^{57} - 20 q^{59} - 8 q^{63} - 4 q^{67} - 44 q^{69} + 8 q^{71} + 12 q^{75} - 12 q^{79} - 16 q^{81} - 64 q^{83} - 56 q^{85} + 4 q^{89} - 4 q^{93} - 52 q^{95} + 56 q^{97} + 12 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 12 * q^11 + 4 * q^13 - 8 * q^15 + 8 * q^17 + 8 * q^19 + 28 * q^23 - 4 * q^25 + 8 * q^27 - 16 * q^29 + 28 * q^31 - 8 * q^35 - 32 * q^37 - 4 * q^45 + 20 * q^47 - 20 * q^51 + 32 * q^53 - 4 * q^55 - 36 * q^57 - 20 * q^59 - 8 * q^63 - 4 * q^67 - 44 * q^69 + 8 * q^71 + 12 * q^75 - 12 * q^79 - 16 * q^81 - 64 * q^83 - 56 * q^85 + 4 * q^89 - 4 * q^93 - 52 * q^95 + 56 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.868559	−	0.868559i	−0.501463	−	0.501463i	0.410429	−	0.911892i	$-0.365379\pi$
$3$	−0.868559	−	0.868559i	−0.501463	−	0.501463i	−0.911892	+	0.410429i	$0.865379\pi$
$4$		0			0
$5$		−	4.37966i		−	1.95864i	−0.202309	−	0.979322i	$-0.564844\pi$
$5$		−	4.37966i		−	1.95864i	0.202309	−	0.979322i	$-0.435156\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$		−	1.49121i		−	0.497070i
$10$		0			0
$11$	1.10701	+	1.10701i	0.333775	+	0.333775i	0.854018	−	0.520243i	$-0.174159\pi$
$11$	1.10701	+	1.10701i	0.333775	+	0.333775i	−0.520243	+	0.854018i	$0.674159\pi$
$12$		0			0
$13$	0.155874	+	0.155874i	0.0432316	+	0.0432316i	0.728392	−	0.685161i	$-0.240268\pi$
$13$	0.155874	+	0.155874i	0.0432316	+	0.0432316i	−0.685161	+	0.728392i	$0.740268\pi$
$14$		0			0
$15$	−3.80399	+	3.80399i	−0.982187	+	0.982187i
$16$		0			0
$17$	5.27265	−	5.27265i	1.27881	−	1.27881i	0.337470	−	0.941336i	$-0.390429\pi$
$17$	5.27265	−	5.27265i	1.27881	−	1.27881i	0.941336	−	0.337470i	$-0.109571\pi$
$18$		0			0
$19$	5.24822	−	5.24822i	1.20402	−	1.20402i	0.231092	−	0.972932i	$-0.425770\pi$
$19$	5.24822	−	5.24822i	1.20402	−	1.20402i	0.972932	−	0.231092i	$-0.0742299\pi$
$20$		0			0
$21$			1.22833i			0.268043i
$22$		0			0
$23$	5.28835			1.10270			0.551349	−	0.834275i	$-0.314113\pi$
$23$	5.28835			1.10270			0.551349	+	0.834275i	$0.314113\pi$
$24$		0			0
$25$	−14.1814			−2.83628
$26$		0			0
$27$	−3.90088	+	3.90088i	−0.750725	+	0.750725i
$28$		0			0
$29$	−4.12690	−	4.12690i	−0.766346	−	0.766346i	0.211115	−	0.977461i	$-0.432290\pi$
$29$	−4.12690	−	4.12690i	−0.766346	−	0.766346i	−0.977461	+	0.211115i	$0.932290\pi$
$30$		0			0
$31$	1.03455			0.185811			0.0929056	−	0.995675i	$-0.470385\pi$
$31$	1.03455			0.185811			0.0929056	+	0.995675i	$0.470385\pi$
$32$		0			0
$33$		−	1.92300i		−	0.334752i
$34$		0			0
$35$	−3.09689	+	3.09689i	−0.523470	+	0.523470i
$36$		0			0
$37$	−2.58579			−0.425101			−0.212550	−	0.977150i	$-0.568177\pi$
$37$	−2.58579			−0.425101			−0.212550	+	0.977150i	$0.568177\pi$
$38$		0			0
$39$		−	0.270771i		−	0.0433581i
$40$		0			0
$41$	−4.93089	+	4.08489i	−0.770076	+	0.637952i
$41$	−4.93089	+	4.08489i	−0.770076	+	0.637952i
$42$		0			0
$43$			8.71688i			1.32931i	0.747150	+	0.664656i	$0.231422\pi$
$43$			8.71688i			1.32931i	−0.747150	+	0.664656i	$0.768578\pi$
$44$		0			0
$45$	−6.53099			−0.973583
$46$		0			0
$47$	−2.00789	+	2.00789i	−0.292881	+	0.292881i	−0.838217	−	0.545336i	$-0.816402\pi$
$47$	−2.00789	+	2.00789i	−0.292881	+	0.292881i	0.545336	+	0.838217i	$0.316402\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−9.15922			−1.28255
$52$		0			0
$53$	5.98800	+	5.98800i	0.822515	+	0.822515i	0.986468	−	0.163953i	$-0.0524246\pi$
$53$	5.98800	+	5.98800i	0.822515	+	0.822515i	−0.163953	+	0.986468i	$0.552425\pi$
$54$		0			0
$55$	4.84832	−	4.84832i	0.653747	−	0.653747i
$56$		0			0
$57$	−9.11678			−1.20755
$58$		0			0
$59$	6.40829			0.834288			0.417144	−	0.908840i	$-0.363031\pi$
$59$	6.40829			0.834288			0.417144	+	0.908840i	$0.363031\pi$
$60$		0			0
$61$			12.4391i			1.59266i	0.604862	+	0.796330i	$0.293228\pi$
$61$			12.4391i			1.59266i	−0.604862	+	0.796330i	$0.706772\pi$
$62$		0			0
$63$	−1.05444	+	1.05444i	−0.132848	+	0.132848i
$64$		0			0
$65$	0.682674	−	0.682674i	0.0846753	−	0.0846753i
$66$		0			0
$67$	−1.54565	+	1.54565i	−0.188832	+	0.188832i	−0.795191	−	0.606359i	$-0.792629\pi$
$67$	−1.54565	+	1.54565i	−0.188832	+	0.188832i	0.606359	+	0.795191i	$0.292629\pi$
$68$		0			0
$69$	−4.59325	−	4.59325i	−0.552962	−	0.552962i
$70$		0			0
$71$	0.123981	+	0.123981i	0.0147138	+	0.0147138i	0.714425	−	0.699712i	$-0.246688\pi$
$71$	0.123981	+	0.123981i	0.0147138	+	0.0147138i	−0.699712	+	0.714425i	$0.746688\pi$
$72$		0			0
$73$		−	5.51668i		−	0.645679i	−0.946454	−	0.322839i	$-0.895363\pi$
$73$		−	5.51668i		−	0.645679i	0.946454	−	0.322839i	$-0.104637\pi$
$74$		0			0
$75$	12.3174	+	12.3174i	1.42229	+	1.42229i
$76$		0			0
$77$		−	1.56555i		−	0.178410i
$78$		0			0
$79$	−8.20809	−	8.20809i	−0.923482	−	0.923482i	0.0737917	−	0.997274i	$-0.476490\pi$
$79$	−8.20809	−	8.20809i	−0.923482	−	0.923482i	−0.997274	+	0.0737917i	$0.976490\pi$
$80$		0			0
$81$	2.30266			0.255852
$82$		0			0
$83$	−12.8108			−1.40617			−0.703087	−	0.711104i	$-0.748195\pi$
$83$	−12.8108			−1.40617			−0.703087	+	0.711104i	$0.748195\pi$
$84$		0			0
$85$	−23.0924	−	23.0924i	−2.50473	−	2.50473i
$86$		0			0
$87$			7.16891i			0.768588i
$88$		0			0
$89$	11.9756	+	11.9756i	1.26942	+	1.26942i	0.946390	+	0.323026i	$0.104700\pi$
$89$	11.9756	+	11.9756i	1.26942	+	1.26942i	0.323026	+	0.946390i	$0.395300\pi$
$90$		0			0
$91$		−	0.220439i		−	0.0231083i
$92$		0			0
$93$	−0.898571	−	0.898571i	−0.0931775	−	0.0931775i
$94$		0			0
$95$	−22.9854	−	22.9854i	−2.35825	−	2.35825i
$96$		0			0
$97$	6.20844	−	6.20844i	0.630371	−	0.630371i	−0.317790	−	0.948161i	$-0.602941\pi$
$97$	6.20844	−	6.20844i	0.630371	−	0.630371i	0.948161	+	0.317790i	$0.102941\pi$
$98$		0			0
$99$	1.65078	−	1.65078i	0.165910	−	0.165910i
$100$		0			0
$101$	2.82012	−	2.82012i	0.280613	−	0.280613i	−0.552741	−	0.833353i	$-0.686418\pi$
$101$	2.82012	−	2.82012i	0.280613	−	0.280613i	0.833353	+	0.552741i	$0.186418\pi$
$102$		0			0
$103$		−	6.30859i		−	0.621604i	−0.950475	−	0.310802i	$-0.899402\pi$
$103$		−	6.30859i		−	0.621604i	0.950475	−	0.310802i	$-0.100598\pi$
$104$		0			0
$105$	5.37966			0.525001
$106$		0			0
$107$	17.5426			1.69591			0.847956	−	0.530067i	$-0.177833\pi$
$107$	17.5426			1.69591			0.847956	+	0.530067i	$0.177833\pi$
$108$		0			0
$109$	−10.6850	+	10.6850i	−1.02344	+	1.02344i	−0.0237172	+	0.999719i	$0.507550\pi$
$109$	−10.6850	+	10.6850i	−1.02344	+	1.02344i	−0.999719	+	0.0237172i	$0.992450\pi$
$110$		0			0
$111$	2.24591	+	2.24591i	0.213172	+	0.213172i
$112$		0			0
$113$	−3.42733			−0.322416			−0.161208	−	0.986920i	$-0.551539\pi$
$113$	−3.42733			−0.322416			−0.161208	+	0.986920i	$0.551539\pi$
$114$		0			0
$115$		−	23.1612i		−	2.15979i
$116$		0			0
$117$	0.232440	−	0.232440i	0.0214891	−	0.0214891i
$118$		0			0
$119$	−7.45666			−0.683551
$120$		0			0
$121$		−	8.54907i		−	0.777188i
$122$		0			0
$123$	7.83074	+	0.734808i	0.706074	+	0.0662554i
$124$		0			0
$125$			40.2115i			3.59663i
$126$		0			0
$127$	21.0195			1.86518			0.932591	−	0.360934i	$-0.117542\pi$
$127$	21.0195			1.86518			0.932591	+	0.360934i	$0.117542\pi$
$128$		0			0
$129$	7.57112	−	7.57112i	0.666600	−	0.666600i
$130$		0			0
$131$			4.79121i			0.418610i	0.977850	+	0.209305i	$0.0671202\pi$
$131$			4.79121i			0.418610i	−0.977850	+	0.209305i	$0.932880\pi$
$132$		0			0
$133$	−7.42210			−0.643578
$134$		0			0
$135$	17.0845	+	17.0845i	1.47040	+	1.47040i
$136$		0			0
$137$	11.4447	−	11.4447i	0.977783	−	0.977783i	−0.0219757	−	0.999759i	$-0.506996\pi$
$137$	11.4447	−	11.4447i	0.977783	−	0.977783i	0.999759	+	0.0219757i	$0.00699563\pi$
$138$		0			0
$139$	13.7262			1.16424			0.582122	−	0.813101i	$-0.302223\pi$
$139$	13.7262			1.16424			0.582122	+	0.813101i	$0.302223\pi$
$140$		0			0
$141$	3.48794			0.293738
$142$		0			0
$143$			0.345107i			0.0288593i
$144$		0			0
$145$	−18.0744	+	18.0744i	−1.50100	+	1.50100i
$146$		0			0
$147$	0.868559	−	0.868559i	0.0716376	−	0.0716376i
$148$		0			0
$149$	−5.91658	+	5.91658i	−0.484705	+	0.484705i	−0.906631	−	0.421925i	$-0.861354\pi$
$149$	−5.91658	+	5.91658i	−0.484705	+	0.484705i	0.421925	+	0.906631i	$0.361354\pi$
$150$		0			0
$151$	−4.68164	−	4.68164i	−0.380986	−	0.380986i	0.490471	−	0.871457i	$-0.336825\pi$
$151$	−4.68164	−	4.68164i	−0.380986	−	0.380986i	−0.871457	+	0.490471i	$0.836825\pi$
$152$		0			0
$153$	−7.86263	−	7.86263i	−0.635656	−	0.635656i
$154$		0			0
$155$		−	4.53099i		−	0.363938i
$156$		0			0
$157$	−6.83898	−	6.83898i	−0.545810	−	0.545810i	0.379416	−	0.925226i	$-0.376125\pi$
$157$	−6.83898	−	6.83898i	−0.545810	−	0.545810i	−0.925226	+	0.379416i	$0.876125\pi$
$158$		0			0
$159$		−	10.4019i		−	0.824921i
$160$		0			0
$161$	−3.73943	−	3.73943i	−0.294708	−	0.294708i
$162$		0			0
$163$	0.0562608			0.00440669			0.00220334	−	0.999998i	$-0.499299\pi$
$163$	0.0562608			0.00440669			0.00220334	+	0.999998i	$0.499299\pi$
$164$		0			0
$165$	−8.42210			−0.655660
$166$		0			0
$167$	17.3830	+	17.3830i	1.34514	+	1.34514i	0.890860	+	0.454277i	$0.150102\pi$
$167$	17.3830	+	17.3830i	1.34514	+	1.34514i	0.454277	+	0.890860i	$0.349898\pi$
$168$		0			0
$169$		−	12.9514i		−	0.996262i
$170$		0			0
$171$	−7.82620	−	7.82620i	−0.598484	−	0.598484i
$172$		0			0
$173$		−	22.1109i		−	1.68106i	−0.541767	−	0.840528i	$-0.682245\pi$
$173$		−	22.1109i		−	1.68106i	0.541767	−	0.840528i	$-0.317755\pi$
$174$		0			0
$175$	10.0278	+	10.0278i	0.758029	+	0.758029i
$176$		0			0
$177$	−5.56598	−	5.56598i	−0.418364	−	0.418364i
$178$		0			0
$179$	−8.88021	+	8.88021i	−0.663738	+	0.663738i	−0.956259	−	0.292521i	$-0.905506\pi$
$179$	−8.88021	+	8.88021i	−0.663738	+	0.663738i	0.292521	+	0.956259i	$0.405506\pi$
$180$		0			0
$181$	2.09192	−	2.09192i	0.155491	−	0.155491i	−0.625074	−	0.780565i	$-0.714931\pi$
$181$	2.09192	−	2.09192i	0.155491	−	0.155491i	0.780565	+	0.625074i	$0.214931\pi$
$182$		0			0
$183$	10.8041	−	10.8041i	0.798660	−	0.798660i
$184$		0			0
$185$			11.3249i			0.832621i
$186$		0			0
$187$	11.6737			0.853668
$188$		0			0
$189$	5.51668			0.401279
$190$		0			0
$191$	−7.26811	+	7.26811i	−0.525902	+	0.525902i	−0.919348	−	0.393446i	$-0.871283\pi$
$191$	−7.26811	+	7.26811i	−0.525902	+	0.525902i	0.393446	+	0.919348i	$0.371283\pi$
$192$		0			0
$193$	−0.804344	−	0.804344i	−0.0578979	−	0.0578979i	0.677565	−	0.735463i	$-0.263035\pi$
$193$	−0.804344	−	0.804344i	−0.0578979	−	0.0578979i	−0.735463	+	0.677565i	$0.763035\pi$
$194$		0			0
$195$	−1.18589			−0.0849230
$196$		0			0
$197$		−	2.18212i		−	0.155470i	−0.996974	−	0.0777349i	$-0.975231\pi$
$197$		−	2.18212i		−	0.155470i	0.996974	−	0.0777349i	$-0.0247688\pi$
$198$		0			0
$199$	−1.70711	+	1.70711i	−0.121014	+	0.121014i	−0.765020	−	0.644006i	$-0.777271\pi$
$199$	−1.70711	+	1.70711i	−0.121014	+	0.121014i	0.644006	+	0.765020i	$0.277271\pi$
$200$		0			0
$201$	2.68498			0.189384
$202$		0			0
$203$			5.83632i			0.409629i
$204$		0			0
$205$	17.8904	+	21.5956i	1.24952	+	1.50830i
$206$		0			0
$207$		−	7.88604i		−	0.548118i
$208$		0			0
$209$	11.6196			0.803747
$210$		0			0
$211$	−6.36627	+	6.36627i	−0.438272	+	0.438272i	−0.891430	−	0.453158i	$-0.850297\pi$
$211$	−6.36627	+	6.36627i	−0.438272	+	0.438272i	0.453158	+	0.891430i	$0.350297\pi$
$212$		0			0
$213$		−	0.215369i		−	0.0147569i
$214$		0			0
$215$	38.1770			2.60365
$216$		0			0
$217$	−0.731540	−	0.731540i	−0.0496602	−	0.0496602i
$218$		0			0
$219$	−4.79156	+	4.79156i	−0.323784	+	0.323784i
$220$		0			0
$221$	1.64374			0.110570
$222$		0			0
$223$	16.4795			1.10355			0.551773	−	0.833994i	$-0.313951\pi$
$223$	16.4795			1.10355			0.551773	+	0.833994i	$0.313951\pi$
$224$		0			0
$225$			21.1475i			1.40983i
$226$		0			0
$227$	11.2174	−	11.2174i	0.744523	−	0.744523i	−0.228922	−	0.973445i	$-0.573520\pi$
$227$	11.2174	−	11.2174i	0.744523	−	0.744523i	0.973445	+	0.228922i	$0.0735201\pi$
$228$		0			0
$229$	−8.73009	+	8.73009i	−0.576900	+	0.576900i	−0.934048	−	0.357148i	$-0.883749\pi$
$229$	−8.73009	+	8.73009i	−0.576900	+	0.576900i	0.357148	+	0.934048i	$0.383749\pi$
$230$		0			0
$231$	−1.35977	+	1.35977i	−0.0894662	+	0.0894662i
$232$		0			0
$233$	16.3305	+	16.3305i	1.06985	+	1.06985i	0.997370	+	0.0724782i	$0.0230908\pi$
$233$	16.3305	+	16.3305i	1.06985	+	1.06985i	0.0724782	+	0.997370i	$0.476909\pi$
$234$		0			0
$235$	8.79387	+	8.79387i	0.573649	+	0.573649i
$236$		0			0
$237$			14.2584i			0.926184i
$238$		0			0
$239$	−4.12956	−	4.12956i	−0.267119	−	0.267119i	0.560819	−	0.827938i	$-0.310486\pi$
$239$	−4.12956	−	4.12956i	−0.267119	−	0.267119i	−0.827938	+	0.560819i	$0.810486\pi$
$240$		0			0
$241$		−	10.2473i		−	0.660084i	−0.943966	−	0.330042i	$-0.892937\pi$
$241$		−	10.2473i		−	0.660084i	0.943966	−	0.330042i	$-0.107063\pi$
$242$		0			0
$243$	9.70264	+	9.70264i	0.622425	+	0.622425i
$244$		0			0
$245$	4.37966			0.279806
$246$		0			0
$247$	1.63612			0.104104
$248$		0			0
$249$	11.1270	+	11.1270i	0.705144	+	0.705144i
$250$		0			0
$251$		−	14.1273i		−	0.891709i	−0.895105	−	0.445855i	$-0.852900\pi$
$251$		−	14.1273i		−	0.891709i	0.895105	−	0.445855i	$-0.147100\pi$
$252$		0			0
$253$	5.85425	+	5.85425i	0.368053	+	0.368053i
$254$		0			0
$255$			40.1143i			2.51205i
$256$		0			0
$257$	−7.25507	−	7.25507i	−0.452559	−	0.452559i	0.443644	−	0.896203i	$-0.353685\pi$
$257$	−7.25507	−	7.25507i	−0.452559	−	0.452559i	−0.896203	+	0.443644i	$0.853685\pi$
$258$		0			0
$259$	1.82843	+	1.82843i	0.113613	+	0.113613i
$260$		0			0
$261$	−6.15407	+	6.15407i	−0.380928	+	0.380928i
$262$		0			0
$263$	−10.4488	+	10.4488i	−0.644303	+	0.644303i	−0.951610	−	0.307307i	$-0.900572\pi$
$263$	−10.4488	+	10.4488i	−0.644303	+	0.644303i	0.307307	+	0.951610i	$0.400572\pi$
$264$		0			0
$265$	26.2254	−	26.2254i	1.61101	−	1.61101i
$266$		0			0
$267$		−	20.8031i		−	1.27313i
$268$		0			0
$269$	−18.9583			−1.15591			−0.577955	−	0.816069i	$-0.696149\pi$
$269$	−18.9583			−1.15591			−0.577955	+	0.816069i	$0.696149\pi$
$270$		0			0
$271$	1.58116			0.0960489			0.0480245	−	0.998846i	$-0.484707\pi$
$271$	1.58116			0.0960489			0.0480245	+	0.998846i	$0.484707\pi$
$272$		0			0
$273$	−0.191464	+	0.191464i	−0.0115879	+	0.0115879i
$274$		0			0
$275$	−15.6989	−	15.6989i	−0.946682	−	0.946682i
$276$		0			0
$277$	4.00642			0.240723			0.120361	−	0.992730i	$-0.461595\pi$
$277$	4.00642			0.240723			0.120361	+	0.992730i	$0.461595\pi$
$278$		0			0
$279$		−	1.54274i		−	0.0923612i
$280$		0			0
$281$	−6.60198	+	6.60198i	−0.393841	+	0.393841i	−0.876054	−	0.482213i	$-0.839833\pi$
$281$	−6.60198	+	6.60198i	−0.393841	+	0.393841i	0.482213	+	0.876054i	$0.339833\pi$
$282$		0			0
$283$	−25.4135			−1.51068			−0.755338	−	0.655335i	$-0.772527\pi$
$283$	−25.4135			−1.51068			−0.755338	+	0.655335i	$0.772527\pi$
$284$		0			0
$285$			39.9284i			2.36515i
$286$		0			0
$287$	6.37512	+	0.598218i	0.376311	+	0.0353117i
$288$		0			0
$289$		−	38.6017i		−	2.27069i
$290$		0			0
$291$	−10.7848			−0.632216
$292$		0			0
$293$	−1.58587	+	1.58587i	−0.0926473	+	0.0926473i	−0.751911	−	0.659264i	$-0.770868\pi$
$293$	−1.58587	+	1.58587i	−0.0926473	+	0.0926473i	0.659264	+	0.751911i	$0.270868\pi$
$294$		0			0
$295$		−	28.0661i		−	1.63407i
$296$		0			0
$297$	−8.63661			−0.501147
$298$		0			0
$299$	0.824315	+	0.824315i	0.0476714	+	0.0476714i
$300$		0			0
$301$	6.16376	−	6.16376i	0.355273	−	0.355273i
$302$		0			0
$303$	−4.89889			−0.281434
$304$		0			0
$305$	54.4789			3.11945
$306$		0			0
$307$			9.98715i			0.569997i	0.958528	+	0.284998i	$0.0919931\pi$
$307$			9.98715i			0.569997i	−0.958528	+	0.284998i	$0.908007\pi$
$308$		0			0
$309$	−5.47939	+	5.47939i	−0.311711	+	0.311711i
$310$		0			0
$311$	−8.19335	+	8.19335i	−0.464602	+	0.464602i	−0.900160	−	0.435558i	$-0.856551\pi$
$311$	−8.19335	+	8.19335i	−0.464602	+	0.464602i	0.435558	+	0.900160i	$0.356551\pi$
$312$		0			0
$313$	15.8900	−	15.8900i	0.898156	−	0.898156i	−0.0971172	−	0.995273i	$-0.530962\pi$
$313$	15.8900	−	15.8900i	0.898156	−	0.898156i	0.995273	+	0.0971172i	$0.0309622\pi$
$314$		0			0
$315$	4.61811	+	4.61811i	0.260201	+	0.260201i
$316$		0			0
$317$	−6.85893	−	6.85893i	−0.385236	−	0.385236i	0.487748	−	0.872984i	$-0.337818\pi$
$317$	−6.85893	−	6.85893i	−0.385236	−	0.385236i	−0.872984	+	0.487748i	$0.837818\pi$
$318$		0			0
$319$		−	9.13702i		−	0.511575i
$320$		0			0
$321$	−15.2368	−	15.2368i	−0.850437	−	0.850437i
$322$		0			0
$323$		−	55.3441i		−	3.07943i
$324$		0			0
$325$	−2.21051	−	2.21051i	−0.122617	−	0.122617i
$326$		0			0
$327$	18.5611			1.02643
$328$		0			0
$329$	2.83958			0.156551
$330$		0			0
$331$	10.1612	+	10.1612i	0.558509	+	0.558509i	0.928883	−	0.370374i	$-0.120770\pi$
$331$	10.1612	+	10.1612i	0.558509	+	0.558509i	−0.370374	+	0.928883i	$0.620770\pi$
$332$		0			0
$333$			3.85595i			0.211305i
$334$		0			0
$335$	6.76944	+	6.76944i	0.369854	+	0.369854i
$336$		0			0
$337$		−	3.07470i		−	0.167490i	−0.996487	−	0.0837448i	$-0.973312\pi$
$337$		−	3.07470i		−	0.167490i	0.996487	−	0.0837448i	$-0.0266881\pi$
$338$		0			0
$339$	2.97684	+	2.97684i	0.161680	+	0.161680i
$340$		0			0
$341$	1.14526	+	1.14526i	0.0620192	+	0.0620192i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	−20.1169	+	20.1169i	−1.08306	+	1.08306i
$346$		0			0
$347$	−19.7853	+	19.7853i	−1.06213	+	1.06213i	−0.0641922	+	0.997938i	$0.520447\pi$
$347$	−19.7853	+	19.7853i	−1.06213	+	1.06213i	−0.997938	+	0.0641922i	$0.979553\pi$
$348$		0			0
$349$			9.92170i			0.531096i	0.964098	+	0.265548i	$0.0855529\pi$
$349$			9.92170i			0.531096i	−0.964098	+	0.265548i	$0.914447\pi$
$350$		0			0
$351$	−1.21609			−0.0649101
$352$		0			0
$353$	8.01578			0.426637			0.213318	−	0.976983i	$-0.431573\pi$
$353$	8.01578			0.426637			0.213318	+	0.976983i	$0.431573\pi$
$354$		0			0
$355$	0.542994	−	0.542994i	0.0288191	−	0.0288191i
$356$		0			0
$357$	6.47655	+	6.47655i	0.342775	+	0.342775i
$358$		0			0
$359$	−15.4833			−0.817178			−0.408589	−	0.912718i	$-0.633979\pi$
$359$	−15.4833			−0.817178			−0.408589	+	0.912718i	$0.633979\pi$
$360$		0			0
$361$		−	36.0876i		−	1.89935i
$362$		0			0
$363$	−7.42537	+	7.42537i	−0.389731	+	0.389731i
$364$		0			0
$365$	−24.1612			−1.26465
$366$		0			0
$367$			17.5727i			0.917289i	0.888620	+	0.458645i	$0.151665\pi$
$367$			17.5727i			0.917289i	−0.888620	+	0.458645i	$0.848335\pi$
$368$		0			0
$369$	6.09142	+	7.35300i	0.317107	+	0.382782i
$370$		0			0
$371$		−	8.46831i		−	0.439653i
$372$		0			0
$373$	11.1630			0.577997			0.288999	−	0.957329i	$-0.406678\pi$
$373$	11.1630			0.577997			0.288999	+	0.957329i	$0.406678\pi$
$374$		0			0
$375$	34.9261	−	34.9261i	1.80358	−	1.80358i
$376$		0			0
$377$		−	1.28655i		−	0.0662607i
$378$		0			0
$379$	25.3324			1.30124			0.650620	−	0.759404i	$-0.274509\pi$
$379$	25.3324			1.30124			0.650620	+	0.759404i	$0.274509\pi$
$380$		0			0
$381$	−18.2567	−	18.2567i	−0.935320	−	0.935320i
$382$		0			0
$383$	−10.3746	+	10.3746i	−0.530119	+	0.530119i	−0.920608	−	0.390489i	$-0.872306\pi$
$383$	−10.3746	+	10.3746i	−0.530119	+	0.530119i	0.390489	+	0.920608i	$0.372306\pi$
$384$		0			0
$385$	−6.85656			−0.349443
$386$		0			0
$387$	12.9987			0.660761
$388$		0			0
$389$			9.08901i			0.460831i	0.973092	+	0.230416i	$0.0740086\pi$
$389$			9.08901i			0.460831i	−0.973092	+	0.230416i	$0.925991\pi$
$390$		0			0
$391$	27.8836	−	27.8836i	1.41014	−	1.41014i
$392$		0			0
$393$	4.16145	−	4.16145i	0.209918	−	0.209918i
$394$		0			0
$395$	−35.9486	+	35.9486i	−1.80877	+	1.80877i
$396$		0			0
$397$	−16.8991	−	16.8991i	−0.848144	−	0.848144i	0.141758	−	0.989901i	$-0.454725\pi$
$397$	−16.8991	−	16.8991i	−0.848144	−	0.848144i	−0.989901	+	0.141758i	$0.954725\pi$
$398$		0			0
$399$	6.44654	+	6.44654i	0.322730	+	0.322730i
$400$		0			0
$401$			17.2355i			0.860701i	0.902662	+	0.430350i	$0.141610\pi$
$401$			17.2355i			0.860701i	−0.902662	+	0.430350i	$0.858390\pi$
$402$		0			0
$403$	0.161260	+	0.161260i	0.00803292	+	0.00803292i
$404$		0			0
$405$		−	10.0849i		−	0.501122i
$406$		0			0
$407$	−2.86249	−	2.86249i	−0.141888	−	0.141888i
$408$		0			0
$409$	6.14926			0.304061			0.152031	−	0.988376i	$-0.451419\pi$
$409$	6.14926			0.304061			0.152031	+	0.988376i	$0.451419\pi$
$410$		0			0
$411$	−19.8807			−0.980644
$412$		0			0
$413$	−4.53134	−	4.53134i	−0.222973	−	0.222973i
$414$		0			0
$415$			56.1072i			2.75419i
$416$		0			0
$417$	−11.9220	−	11.9220i	−0.583825	−	0.583825i
$418$		0			0
$419$			18.6826i			0.912705i	0.889799	+	0.456352i	$0.150844\pi$
$419$			18.6826i			0.912705i	−0.889799	+	0.456352i	$0.849156\pi$
$420$		0			0
$421$	−14.0459	−	14.0459i	−0.684554	−	0.684554i	0.276469	−	0.961023i	$-0.410836\pi$
$421$	−14.0459	−	14.0459i	−0.684554	−	0.684554i	−0.961023	+	0.276469i	$0.910836\pi$
$422$		0			0
$423$	2.99418	+	2.99418i	0.145582	+	0.145582i
$424$		0			0
$425$	−74.7737	+	74.7737i	−3.62706	+	3.62706i
$426$		0			0
$427$	8.79576	−	8.79576i	0.425656	−	0.425656i
$428$		0			0
$429$	0.299746	−	0.299746i	0.0144719	−	0.0144719i
$430$		0			0
$431$		−	12.8378i		−	0.618374i	−0.951001	−	0.309187i	$-0.899943\pi$
$431$		−	12.8378i		−	0.618374i	0.951001	−	0.309187i	$-0.100057\pi$
$432$		0			0
$433$	−5.64434			−0.271250			−0.135625	−	0.990760i	$-0.543304\pi$
$433$	−5.64434			−0.271250			−0.135625	+	0.990760i	$0.543304\pi$
$434$		0			0
$435$	31.3974			1.50539
$436$		0			0
$437$	27.7544	−	27.7544i	1.32767	−	1.32767i
$438$		0			0
$439$	−9.47844	−	9.47844i	−0.452381	−	0.452381i	0.443763	−	0.896144i	$-0.353643\pi$
$439$	−9.47844	−	9.47844i	−0.452381	−	0.452381i	−0.896144	+	0.443763i	$0.853643\pi$
$440$		0			0
$441$	1.49121			0.0710100
$442$		0			0
$443$		−	9.52930i		−	0.452751i	−0.974040	−	0.226375i	$-0.927312\pi$
$443$		−	9.52930i		−	0.452751i	0.974040	−	0.226375i	$-0.0726876\pi$
$444$		0			0
$445$	52.4493	−	52.4493i	2.48633	−	2.48633i
$446$		0			0
$447$	10.2778			0.486123
$448$		0			0
$449$		−	22.0528i		−	1.04074i	−0.853942	−	0.520368i	$-0.825795\pi$
$449$		−	22.0528i		−	1.04074i	0.853942	−	0.520368i	$-0.174205\pi$
$450$		0			0
$451$	−9.98054	−	0.936537i	−0.469965	−	0.0440998i
$452$		0			0
$453$			8.13256i			0.382101i
$454$		0			0
$455$	−0.965447			−0.0452608
$456$		0			0
$457$	18.2147	−	18.2147i	0.852048	−	0.852048i	−0.138337	−	0.990385i	$-0.544176\pi$
$457$	18.2147	−	18.2147i	0.852048	−	0.852048i	0.990385	+	0.138337i	$0.0441758\pi$
$458$		0			0
$459$			41.1360i			1.92006i
$460$		0			0
$461$	−6.79545			−0.316496			−0.158248	−	0.987399i	$-0.550585\pi$
$461$	−6.79545			−0.316496			−0.158248	+	0.987399i	$0.550585\pi$
$462$		0			0
$463$	−5.57774	−	5.57774i	−0.259220	−	0.259220i	0.565517	−	0.824737i	$-0.308677\pi$
$463$	−5.57774	−	5.57774i	−0.259220	−	0.259220i	−0.824737	+	0.565517i	$0.808677\pi$
$464$		0			0
$465$	−3.93543	+	3.93543i	−0.182501	+	0.182501i
$466$		0			0
$467$	36.3150			1.68046			0.840228	−	0.542234i	$-0.182421\pi$
$467$	36.3150			1.68046			0.840228	+	0.542234i	$0.182421\pi$
$468$		0			0
$469$	2.18589			0.100935
$470$		0			0
$471$			11.8801i			0.547407i
$472$		0			0
$473$	−9.64965	+	9.64965i	−0.443691	+	0.443691i
$474$		0			0
$475$	−74.4272	+	74.4272i	−3.41496	+	3.41496i
$476$		0			0
$477$	8.92936	−	8.92936i	0.408847	−	0.408847i
$478$		0			0
$479$	−5.30292	−	5.30292i	−0.242297	−	0.242297i	0.575503	−	0.817800i	$-0.304806\pi$
$479$	−5.30292	−	5.30292i	−0.242297	−	0.242297i	−0.817800	+	0.575503i	$0.804806\pi$
$480$		0			0
$481$	−0.403056	−	0.403056i	−0.0183778	−	0.0183778i
$482$		0			0
$483$			6.49583i			0.295571i
$484$		0			0
$485$	−27.1908	−	27.1908i	−1.23467	−	1.23467i
$486$		0			0
$487$			3.16695i			0.143508i	0.997422	+	0.0717541i	$0.0228597\pi$
$487$			3.16695i			0.143508i	−0.997422	+	0.0717541i	$0.977140\pi$
$488$		0			0
$489$	−0.0488658	−	0.0488658i	−0.00220979	−	0.00220979i
$490$		0			0
$491$	−6.86591			−0.309854			−0.154927	−	0.987926i	$-0.549514\pi$
$491$	−6.86591			−0.309854			−0.154927	+	0.987926i	$0.549514\pi$
$492$		0			0
$493$	−43.5194			−1.96002
$494$		0			0
$495$	−7.22986	−	7.22986i	−0.324958	−	0.324958i
$496$		0			0
$497$		−	0.175335i		−	0.00786487i
$498$		0			0
$499$	2.01551	+	2.01551i	0.0902265	+	0.0902265i	0.750779	−	0.660553i	$-0.229678\pi$
$499$	2.01551	+	2.01551i	0.0902265	+	0.0902265i	−0.660553	+	0.750779i	$0.729678\pi$
$500$		0			0
$501$		−	30.1963i		−	1.34907i
$502$		0			0
$503$	12.2797	+	12.2797i	0.547525	+	0.547525i	0.925724	−	0.378199i	$-0.123457\pi$
$503$	12.2797	+	12.2797i	0.547525	+	0.547525i	−0.378199	+	0.925724i	$0.623457\pi$
$504$		0			0
$505$	−12.3512	−	12.3512i	−0.549620	−	0.549620i
$506$		0			0
$507$	−11.2491	+	11.2491i	−0.499588	+	0.499588i
$508$		0			0
$509$	−0.586823	+	0.586823i	−0.0260105	+	0.0260105i	−0.719992	−	0.693982i	$-0.755855\pi$
$509$	−0.586823	+	0.586823i	−0.0260105	+	0.0260105i	0.693982	+	0.719992i	$0.255855\pi$
$510$		0			0
$511$	−3.90088	+	3.90088i	−0.172565	+	0.172565i
$512$		0			0
$513$			40.9454i			1.80778i
$514$		0			0
$515$	−27.6295			−1.21750
$516$		0			0
$517$	−4.44550			−0.195513
$518$		0			0
$519$	−19.2046	+	19.2046i	−0.842988	+	0.842988i
$520$		0			0
$521$	1.58336	+	1.58336i	0.0693684	+	0.0693684i	0.740940	−	0.671571i	$-0.234380\pi$
$521$	1.58336	+	1.58336i	0.0693684	+	0.0693684i	−0.671571	+	0.740940i	$0.734380\pi$
$522$		0			0
$523$	30.4893			1.33320			0.666602	−	0.745414i	$-0.267748\pi$
$523$	30.4893			1.33320			0.666602	+	0.745414i	$0.267748\pi$
$524$		0			0
$525$		−	17.4194i		−	0.760247i
$526$		0			0
$527$	5.45484	−	5.45484i	0.237617	−	0.237617i
$528$		0			0
$529$	4.96666			0.215942
$530$		0			0
$531$		−	9.55610i		−	0.414699i
$532$		0			0
$533$	−1.40532	−	0.131870i	−0.0608713	−	0.00571194i
$534$		0			0
$535$		−	76.8308i		−	3.32169i
$536$		0			0
$537$	15.4260			0.665680
$538$		0			0
$539$	−1.10701	+	1.10701i	−0.0476822	+	0.0476822i
$540$		0			0
$541$			22.4848i			0.966696i	0.875428	+	0.483348i	$0.160580\pi$
$541$			22.4848i			0.966696i	−0.875428	+	0.483348i	$0.839420\pi$
$542$		0			0
$543$	−3.63391			−0.155946
$544$		0			0
$545$	46.7966	+	46.7966i	2.00455	+	2.00455i
$546$		0			0
$547$	−11.2934	+	11.2934i	−0.482870	+	0.482870i	−0.906047	−	0.423177i	$-0.860915\pi$
$547$	−11.2934	+	11.2934i	−0.482870	+	0.482870i	0.423177	+	0.906047i	$0.360915\pi$
$548$		0			0
$549$	18.5493			0.791664
$550$		0			0
$551$	−43.3177			−1.84540
$552$		0			0
$553$			11.6080i			0.493622i
$554$		0			0
$555$	9.83632	−	9.83632i	0.417528	−	0.417528i
$556$		0			0
$557$	−2.04517	+	2.04517i	−0.0866566	+	0.0866566i	−0.749106	−	0.662450i	$-0.769517\pi$
$557$	−2.04517	+	2.04517i	−0.0866566	+	0.0866566i	0.662450	+	0.749106i	$0.269517\pi$
$558$		0			0
$559$	−1.35873	+	1.35873i	−0.0574682	+	0.0574682i
$560$		0			0
$561$	−10.1393	−	10.1393i	−0.428083	−	0.428083i
$562$		0			0
$563$	5.39793	+	5.39793i	0.227496	+	0.227496i	0.811646	−	0.584150i	$-0.198572\pi$
$563$	5.39793	+	5.39793i	0.227496	+	0.227496i	−0.584150	+	0.811646i	$0.698572\pi$
$564$		0			0
$565$			15.0105i			0.631499i
$566$		0			0
$567$	−1.62823	−	1.62823i	−0.0683792	−	0.0683792i
$568$		0			0
$569$		−	23.2256i		−	0.973666i	−0.873495	−	0.486833i	$-0.838152\pi$
$569$		−	23.2256i		−	0.973666i	0.873495	−	0.486833i	$-0.161848\pi$
$570$		0			0
$571$	−26.4191	−	26.4191i	−1.10561	−	1.10561i	−0.993721	−	0.111884i	$-0.964312\pi$
$571$	−26.4191	−	26.4191i	−1.10561	−	1.10561i	−0.111884	−	0.993721i	$-0.535688\pi$
$572$		0			0
$573$	12.6256			0.527441
$574$		0			0
$575$	−74.9964			−3.12756
$576$		0			0
$577$	20.0881	+	20.0881i	0.836279	+	0.836279i	0.988367	−	0.152088i	$-0.0485996\pi$
$577$	20.0881	+	20.0881i	0.836279	+	0.836279i	−0.152088	+	0.988367i	$0.548600\pi$
$578$		0			0
$579$			1.39724i			0.0580673i
$580$		0			0
$581$	9.05864	+	9.05864i	0.375816	+	0.375816i
$582$		0			0
$583$			13.2575i			0.549070i
$584$		0			0
$585$	−1.01801	−	1.01801i	−0.0420895	−	0.0420895i
$586$		0			0
$587$	24.7778	+	24.7778i	1.02269	+	1.02269i	0.999737	+	0.0229544i	$0.00730725\pi$
$587$	24.7778	+	24.7778i	1.02269	+	1.02269i	0.0229544	+	0.999737i	$0.492693\pi$
$588$		0			0
$589$	5.42956	−	5.42956i	0.223721	−	0.223721i
$590$		0			0
$591$	−1.89530	+	1.89530i	−0.0779623	+	0.0779623i
$592$		0			0
$593$	9.33118	−	9.33118i	0.383185	−	0.383185i	−0.489063	−	0.872248i	$-0.662661\pi$
$593$	9.33118	−	9.33118i	0.383185	−	0.383185i	0.872248	+	0.489063i	$0.162661\pi$
$594$		0			0
$595$			32.6576i			1.33883i
$596$		0			0
$597$	2.96545			0.121368
$598$		0			0
$599$	−6.48082			−0.264799			−0.132400	−	0.991196i	$-0.542268\pi$
$599$	−6.48082			−0.264799			−0.132400	+	0.991196i	$0.542268\pi$
$600$		0			0
$601$	19.0624	−	19.0624i	0.777572	−	0.777572i	−0.201845	−	0.979417i	$-0.564694\pi$
$601$	19.0624	−	19.0624i	0.777572	−	0.777572i	0.979417	+	0.201845i	$0.0646938\pi$
$602$		0			0
$603$	2.30489	+	2.30489i	0.0938626	+	0.0938626i
$604$		0			0
$605$	−37.4420			−1.52223
$606$		0			0
$607$			10.7243i			0.435285i	0.976029	+	0.217642i	$0.0698367\pi$
$607$			10.7243i			0.435285i	−0.976029	+	0.217642i	$0.930163\pi$
$608$		0			0
$609$	5.06919	−	5.06919i	0.205414	−	0.205414i
$610$		0			0
$611$	−0.625954			−0.0253234
$612$		0			0
$613$			32.8034i			1.32492i	0.749099	+	0.662458i	$0.230487\pi$
$613$			32.8034i			1.32492i	−0.749099	+	0.662458i	$0.769513\pi$
$614$		0			0
$615$	3.21821	−	34.2960i	0.129771	−	1.38295i
$616$		0			0
$617$		−	23.6634i		−	0.952654i	−0.879268	−	0.476327i	$-0.841968\pi$
$617$		−	23.6634i		−	0.952654i	0.879268	−	0.476327i	$-0.158032\pi$
$618$		0			0
$619$	8.18699			0.329063			0.164531	−	0.986372i	$-0.447389\pi$
$619$	8.18699			0.329063			0.164531	+	0.986372i	$0.447389\pi$
$620$		0			0
$621$	−20.6292	+	20.6292i	−0.827823	+	0.827823i
$622$		0			0
$623$		−	16.9361i		−	0.678531i
$624$		0			0
$625$	105.206			4.20823
$626$		0			0
$627$	−10.0923	−	10.0923i	−0.403049	−	0.403049i
$628$		0			0
$629$	−13.6340	+	13.6340i	−0.543621	+	0.543621i
$630$		0			0
$631$	25.5192			1.01590			0.507952	−	0.861385i	$-0.330403\pi$
$631$	25.5192			1.01590			0.507952	+	0.861385i	$0.330403\pi$
$632$		0			0
$633$	11.0590			0.439555
$634$		0			0
$635$		−	92.0584i		−	3.65323i
$636$		0			0
$637$	−0.155874	+	0.155874i	−0.00617594	+	0.00617594i
$638$		0			0
$639$	0.184881	−	0.184881i	0.00731380	−	0.00731380i
$640$		0			0
$641$	−16.8663	+	16.8663i	−0.666180	+	0.666180i	−0.956830	−	0.290650i	$-0.906129\pi$
$641$	−16.8663	+	16.8663i	−0.666180	+	0.666180i	0.290650	+	0.956830i	$0.406129\pi$
$642$		0			0
$643$	−31.2517	−	31.2517i	−1.23245	−	1.23245i	−0.963021	−	0.269427i	$-0.913166\pi$
$643$	−31.2517	−	31.2517i	−1.23245	−	1.23245i	−0.269427	−	0.963021i	$-0.586834\pi$
$644$		0			0
$645$	−33.1590	−	33.1590i	−1.30563	−	1.30563i
$646$		0			0
$647$		−	29.3661i		−	1.15450i	−0.816567	−	0.577250i	$-0.804126\pi$
$647$		−	29.3661i		−	1.15450i	0.816567	−	0.577250i	$-0.195874\pi$
$648$		0			0
$649$	7.09402	+	7.09402i	0.278465	+	0.278465i
$650$		0			0
$651$			1.27077i			0.0498054i
$652$		0			0
$653$	−22.0154	−	22.0154i	−0.861530	−	0.861530i	0.129986	−	0.991516i	$-0.458507\pi$
$653$	−22.0154	−	22.0154i	−0.861530	−	0.861530i	−0.991516	+	0.129986i	$0.958507\pi$
$654$		0			0
$655$	20.9839			0.819908
$656$		0			0
$657$	−8.22653			−0.320947
$658$		0			0
$659$	10.7540	+	10.7540i	0.418917	+	0.418917i	0.884830	−	0.465913i	$-0.154274\pi$
$659$	10.7540	+	10.7540i	0.418917	+	0.418917i	−0.465913	+	0.884830i	$0.654274\pi$
$660$		0			0
$661$		−	31.0314i		−	1.20698i	−0.797369	−	0.603492i	$-0.793776\pi$
$661$		−	31.0314i		−	1.20698i	0.797369	−	0.603492i	$-0.206224\pi$
$662$		0			0
$663$	−1.42768	−	1.42768i	−0.0554466	−	0.0554466i
$664$		0			0
$665$			32.5063i			1.26054i
$666$		0			0
$667$	−21.8245	−	21.8245i	−0.845048	−	0.845048i
$668$		0			0
$669$	−14.3134	−	14.3134i	−0.553388	−	0.553388i
$670$		0			0
$671$	−13.7702	+	13.7702i	−0.531591	+	0.531591i
$672$		0			0
$673$	−13.8292	+	13.8292i	−0.533077	+	0.533077i	−0.921487	−	0.388410i	$-0.873024\pi$
$673$	−13.8292	+	13.8292i	−0.533077	+	0.533077i	0.388410	+	0.921487i	$0.373024\pi$
$674$		0			0
$675$	55.3201	−	55.3201i	2.12927	−	2.12927i
$676$		0			0
$677$		−	41.7263i		−	1.60367i	−0.597544	−	0.801836i	$-0.703857\pi$
$677$		−	41.7263i		−	1.60367i	0.597544	−	0.801836i	$-0.296143\pi$
$678$		0			0
$679$	−8.78006			−0.336948
$680$		0			0
$681$	−19.4859			−0.746701
$682$		0			0
$683$	0.539996	−	0.539996i	0.0206624	−	0.0206624i	−0.696700	−	0.717362i	$-0.745349\pi$
$683$	0.539996	−	0.539996i	0.0206624	−	0.0206624i	0.717362	+	0.696700i	$0.245349\pi$
$684$		0			0
$685$	−50.1237	−	50.1237i	−1.91513	−	1.91513i
$686$		0			0
$687$	15.1652			0.578588
$688$		0			0
$689$			1.86674i			0.0711172i
$690$		0			0
$691$	−26.7208	+	26.7208i	−1.01651	+	1.01651i	−0.0166475	+	0.999861i	$0.505299\pi$
$691$	−26.7208	+	26.7208i	−1.01651	+	1.01651i	−0.999861	+	0.0166475i	$0.994701\pi$
$692$		0			0
$693$	−2.33456			−0.0886825
$694$		0			0
$695$		−	60.1162i		−	2.28034i
$696$		0			0
$697$	−4.46070	+	47.5371i	−0.168961	+	1.80059i
$698$		0			0
$699$		−	28.3681i		−	1.07298i
$700$		0			0
$701$	−28.3918			−1.07234			−0.536172	−	0.844109i	$-0.680130\pi$
$701$	−28.3918			−1.07234			−0.536172	+	0.844109i	$0.680130\pi$
$702$		0			0
$703$	−13.5708	+	13.5708i	−0.511831	+	0.511831i
$704$		0			0
$705$		−	15.2760i		−	0.575327i
$706$		0			0
$707$	−3.98826			−0.149994
$708$		0			0
$709$	−7.16891	−	7.16891i	−0.269234	−	0.269234i	0.559557	−	0.828792i	$-0.310971\pi$
$709$	−7.16891	−	7.16891i	−0.269234	−	0.269234i	−0.828792	+	0.559557i	$0.810971\pi$
$710$		0			0
$711$	−12.2400	+	12.2400i	−0.459035	+	0.459035i
$712$		0			0
$713$	5.47108			0.204894
$714$		0			0
$715$	1.51145			0.0565251
$716$		0			0
$717$			7.17353i			0.267901i
$718$		0			0
$719$	−8.38409	+	8.38409i	−0.312674	+	0.312674i	−0.845945	−	0.533271i	$-0.820963\pi$
$719$	−8.38409	+	8.38409i	−0.312674	+	0.312674i	0.533271	+	0.845945i	$0.320963\pi$
$720$		0			0
$721$	−4.46085	+	4.46085i	−0.166131	+	0.166131i
$722$		0			0
$723$	−8.90035	+	8.90035i	−0.331008	+	0.331008i
$724$		0			0
$725$	58.5253	+	58.5253i	2.17358	+	2.17358i
$726$		0			0
$727$	−26.1718	−	26.1718i	−0.970658	−	0.970658i	0.0289234	−	0.999582i	$-0.490792\pi$
$727$	−26.1718	−	26.1718i	−0.970658	−	0.970658i	−0.999582	+	0.0289234i	$0.990792\pi$
$728$		0			0
$729$		−	23.7626i		−	0.880098i
$730$		0			0
$731$	45.9611	+	45.9611i	1.69993	+	1.69993i
$732$		0			0
$733$		−	41.1504i		−	1.51992i	−0.649967	−	0.759962i	$-0.725217\pi$
$733$		−	41.1504i		−	1.51992i	0.649967	−	0.759962i	$-0.274783\pi$
$734$		0			0
$735$	−3.80399	−	3.80399i	−0.140312	−	0.140312i
$736$		0			0
$737$	−3.42210			−0.126055
$738$		0			0
$739$	8.37977			0.308255			0.154127	−	0.988051i	$-0.450743\pi$
$739$	8.37977			0.308255			0.154127	+	0.988051i	$0.450743\pi$
$740$		0			0
$741$	−1.42107	−	1.42107i	−0.0522042	−	0.0522042i
$742$		0			0
$743$			16.7799i			0.615596i	0.951452	+	0.307798i	$0.0995922\pi$
$743$			16.7799i			0.615596i	−0.951452	+	0.307798i	$0.900408\pi$
$744$		0			0
$745$	25.9126	+	25.9126i	0.949365	+	0.949365i
$746$		0			0
$747$			19.1037i			0.698966i
$748$		0			0
$749$	−12.4045	−	12.4045i	−0.453251	−	0.453251i
$750$		0			0
$751$	−12.1427	−	12.1427i	−0.443092	−	0.443092i	0.449958	−	0.893050i	$-0.351439\pi$
$751$	−12.1427	−	12.1427i	−0.443092	−	0.443092i	−0.893050	+	0.449958i	$0.851439\pi$
$752$		0			0
$753$	−12.2704	+	12.2704i	−0.447159	+	0.447159i
$754$		0			0
$755$	−20.5040	+	20.5040i	−0.746216	+	0.746216i
$756$		0			0
$757$	−5.89100	+	5.89100i	−0.214112	+	0.214112i	−0.806012	−	0.591900i	$-0.798378\pi$
$757$	−5.89100	+	5.89100i	−0.214112	+	0.214112i	0.591900	+	0.806012i	$0.298378\pi$
$758$		0			0
$759$		−	10.1695i		−	0.369130i
$760$		0			0
$761$	37.8289			1.37130			0.685648	−	0.727934i	$-0.259519\pi$
$761$	37.8289			1.37130			0.685648	+	0.727934i	$0.259519\pi$
$762$		0			0
$763$	15.1109			0.547050
$764$		0			0
$765$	−34.4357	+	34.4357i	−1.24502	+	1.24502i
$766$		0			0
$767$	0.998883	+	0.998883i	0.0360676	+	0.0360676i
$768$		0			0
$769$	−21.4226			−0.772519			−0.386259	−	0.922390i	$-0.626233\pi$
$769$	−21.4226			−0.772519			−0.386259	+	0.922390i	$0.626233\pi$
$770$		0			0
$771$			12.6029i			0.453883i
$772$		0			0
$773$	18.4236	−	18.4236i	0.662653	−	0.662653i	−0.293352	−	0.956005i	$-0.594771\pi$
$773$	18.4236	−	18.4236i	0.662653	−	0.662653i	0.956005	+	0.293352i	$0.0947708\pi$
$774$		0			0
$775$	−14.6714			−0.527014
$776$		0			0
$777$		−	3.17619i		−	0.113945i
$778$		0			0
$779$	−4.44003	+	47.3168i	−0.159081	+	1.69530i
$780$		0			0
$781$			0.274495i			0.00982222i
$782$		0			0
$783$	32.1971			1.15063
$784$		0			0
$785$	−29.9524	+	29.9524i	−1.06905	+	1.06905i
$786$		0			0
$787$			1.81107i			0.0645578i	0.999479	+	0.0322789i	$0.0102765\pi$
$787$			1.81107i			0.0645578i	−0.999479	+	0.0322789i	$0.989724\pi$
$788$		0			0
$789$	18.1509			0.646189
$790$		0			0
$791$	2.42349	+	2.42349i	0.0861694	+	0.0861694i
$792$		0			0
$793$	−1.93892	+	1.93892i	−0.0688532	+	0.0688532i
$794$		0			0
$795$	−45.5566			−1.61573
$796$		0			0
$797$	32.9410			1.16683			0.583415	−	0.812174i	$-0.301716\pi$
$797$	32.9410			1.16683			0.583415	+	0.812174i	$0.301716\pi$
$798$		0			0
$799$			21.1738i			0.749075i
$800$		0			0
$801$	17.8582	−	17.8582i	0.630989	−	0.630989i
$802$		0			0
$803$	6.10701	−	6.10701i	0.215512	−	0.215512i
$804$		0			0
$805$	−16.3774	+	16.3774i	−0.577229	+	0.577229i
$806$		0			0
$807$	16.4664	+	16.4664i	0.579646	+	0.579646i
$808$		0			0
$809$	28.4128	+	28.4128i	0.998942	+	0.998942i	0.999999	−	0.00105755i	$-0.000336628\pi$
$809$	28.4128	+	28.4128i	0.998942	+	0.998942i	−0.00105755	+	0.999999i	$0.500337\pi$
$810$		0			0
$811$		−	40.5163i		−	1.42272i	−0.702829	−	0.711359i	$-0.748080\pi$
$811$		−	40.5163i		−	1.42272i	0.702829	−	0.711359i	$-0.251920\pi$
$812$		0			0
$813$	−1.37334	−	1.37334i	−0.0481650	−	0.0481650i
$814$		0			0
$815$		−	0.246403i		−	0.00863113i
$816$		0			0
$817$	45.7481	+	45.7481i	1.60052	+	1.60052i
$818$		0			0
$819$	−0.328720			−0.0114864
$820$		0			0
$821$	12.5128			0.436700			0.218350	−	0.975871i	$-0.429933\pi$
$821$	12.5128			0.436700			0.218350	+	0.975871i	$0.429933\pi$
$822$		0			0
$823$	−16.7502	−	16.7502i	−0.583874	−	0.583874i	0.352091	−	0.935966i	$-0.385471\pi$
$823$	−16.7502	−	16.7502i	−0.583874	−	0.583874i	−0.935966	+	0.352091i	$0.885471\pi$
$824$		0			0
$825$			27.2709i			0.949452i
$826$		0			0
$827$	1.64710	+	1.64710i	0.0572754	+	0.0572754i	0.735164	−	0.677889i	$-0.237105\pi$
$827$	1.64710	+	1.64710i	0.0572754	+	0.0572754i	−0.677889	+	0.735164i	$0.737105\pi$
$828$		0			0
$829$		−	1.13120i		−	0.0392883i	−0.999807	−	0.0196442i	$-0.993747\pi$
$829$		−	1.13120i		−	0.0392883i	0.999807	−	0.0196442i	$-0.00625334\pi$
$830$		0			0
$831$	−3.47982	−	3.47982i	−0.120713	−	0.120713i
$832$		0			0
$833$	5.27265	+	5.27265i	0.182687	+	0.182687i
$834$		0			0
$835$	76.1317	−	76.1317i	2.63465	−	2.63465i
$836$		0			0
$837$	−4.03567	+	4.03567i	−0.139493	+	0.139493i
$838$		0			0
$839$	1.30070	−	1.30070i	0.0449053	−	0.0449053i	−0.684298	−	0.729203i	$-0.739891\pi$
$839$	1.30070	−	1.30070i	0.0449053	−	0.0449053i	0.729203	+	0.684298i	$0.239891\pi$
$840$		0			0
$841$			5.06259i			0.174572i
$842$		0			0
$843$	11.4684			0.394993
$844$		0			0
$845$	−56.7228			−1.95132
$846$		0			0
$847$	−6.04510	+	6.04510i	−0.207712	+	0.207712i
$848$		0			0
$849$	22.0731	+	22.0731i	0.757548	+	0.757548i
$850$		0			0
$851$	−13.6745			−0.468757
$852$		0			0
$853$		−	14.7835i		−	0.506177i	−0.967443	−	0.253088i	$-0.918554\pi$
$853$		−	14.7835i		−	0.506177i	0.967443	−	0.253088i	$-0.0814464\pi$
$854$		0			0
$855$	−34.2761	+	34.2761i	−1.17222	+	1.17222i
$856$		0			0
$857$	0.788037			0.0269188			0.0134594	−	0.999909i	$-0.495716\pi$
$857$	0.788037			0.0269188			0.0134594	+	0.999909i	$0.495716\pi$
$858$		0			0
$859$			14.9245i			0.509217i	0.967044	+	0.254609i	$0.0819466\pi$
$859$			14.9245i			0.509217i	−0.967044	+	0.254609i	$0.918053\pi$
$860$		0			0
$861$	−5.01758	−	6.05676i	−0.170999	−	0.206414i
$862$		0			0
$863$			36.5079i			1.24274i	0.783516	+	0.621371i	$0.213424\pi$
$863$			36.5079i			1.24274i	−0.783516	+	0.621371i	$0.786576\pi$
$864$		0			0
$865$	−96.8380			−3.29259
$866$		0			0
$867$	−33.5279	+	33.5279i	−1.13867	+	1.13867i
$868$		0			0
$869$		−	18.1728i		−	0.616471i
$870$		0			0
$871$	−0.481854			−0.0163270
$872$		0			0
$873$	−9.25808	−	9.25808i	−0.313339	−	0.313339i
$874$		0			0
$875$	28.4338	−	28.4338i	0.961239	−	0.961239i
$876$		0			0
$877$	20.2806			0.684829			0.342414	−	0.939549i	$-0.388755\pi$
$877$	20.2806			0.684829			0.342414	+	0.939549i	$0.388755\pi$
$878$		0			0
$879$	2.75484			0.0929184
$880$		0			0
$881$			55.5345i			1.87101i	0.353318	+	0.935503i	$0.385053\pi$
$881$			55.5345i			1.87101i	−0.353318	+	0.935503i	$0.614947\pi$
$882$		0			0
$883$	11.6799	−	11.6799i	0.393060	−	0.393060i	−0.482717	−	0.875777i	$-0.660350\pi$
$883$	11.6799	−	11.6799i	0.393060	−	0.393060i	0.875777	+	0.482717i	$0.160350\pi$
$884$		0			0
$885$	−24.3771	+	24.3771i	−0.819427	+	0.819427i
$886$		0			0
$887$	7.12683	−	7.12683i	0.239296	−	0.239296i	−0.577263	−	0.816558i	$-0.695879\pi$
$887$	7.12683	−	7.12683i	0.239296	−	0.239296i	0.816558	+	0.577263i	$0.195879\pi$
$888$		0			0
$889$	−14.8631	−	14.8631i	−0.498491	−	0.498491i
$890$		0			0
$891$	2.54907	+	2.54907i	0.0853970	+	0.0853970i
$892$		0			0
$893$			21.0757i			0.705271i
$894$		0			0
$895$	38.8923	+	38.8923i	1.30003	+	1.30003i
$896$		0			0
$897$		−	1.43193i		−	0.0478108i
$898$		0			0
$899$	−4.26950	−	4.26950i	−0.142396	−	0.142396i
$900$		0			0
$901$	63.1453			2.10367
$902$		0			0
$903$	−10.7072			−0.356313
$904$		0			0
$905$	−9.16188	−	9.16188i	−0.304551	−	0.304551i
$906$		0			0
$907$		−	13.2975i		−	0.441538i	−0.975326	−	0.220769i	$-0.929143\pi$
$907$		−	13.2975i		−	0.441538i	0.975326	−	0.220769i	$-0.0708567\pi$
$908$		0			0
$909$	−4.20539	−	4.20539i	−0.139484	−	0.139484i
$910$		0			0
$911$			18.3284i			0.607247i	0.952792	+	0.303623i	$0.0981964\pi$
$911$			18.3284i			0.607247i	−0.952792	+	0.303623i	$0.901804\pi$
$912$		0			0
$913$	−14.1817	−	14.1817i	−0.469346	−	0.469346i
$914$		0			0
$915$	−47.3182	−	47.3182i	−1.56429	−	1.56429i
$916$		0			0
$917$	3.38790	−	3.38790i	0.111878	−	0.111878i
$918$		0			0
$919$	10.9667	−	10.9667i	0.361759	−	0.361759i	−0.502701	−	0.864460i	$-0.667660\pi$
$919$	10.9667	−	10.9667i	0.361759	−	0.361759i	0.864460	+	0.502701i	$0.167660\pi$
$920$		0			0
$921$	8.67443	−	8.67443i	0.285832	−	0.285832i
$922$		0			0
$923$			0.0386507i			0.00127220i
$924$		0			0
$925$	36.6701			1.20571
$926$		0			0
$927$	−9.40743			−0.308981
$928$		0			0
$929$	−3.36774	+	3.36774i	−0.110492	+	0.110492i	−0.760191	−	0.649699i	$-0.774895\pi$
$929$	−3.36774	+	3.36774i	−0.110492	+	0.110492i	0.649699	+	0.760191i	$0.274895\pi$
$930$		0			0
$931$	5.24822	+	5.24822i	0.172003	+	0.172003i
$932$		0			0
$933$	14.2328			0.465961
$934$		0			0
$935$		−	51.1270i		−	1.67203i
$936$		0			0
$937$	4.36515	−	4.36515i	0.142603	−	0.142603i	−0.632201	−	0.774804i	$-0.717848\pi$
$937$	4.36515	−	4.36515i	0.142603	−	0.142603i	0.774804	+	0.632201i	$0.217848\pi$
$938$		0			0
$939$	−27.6028			−0.900784
$940$		0			0
$941$		−	18.1833i		−	0.592758i	−0.955070	−	0.296379i	$-0.904221\pi$
$941$		−	18.1833i		−	0.592758i	0.955070	−	0.296379i	$-0.0957791\pi$
$942$		0			0
$943$	−26.0763	+	21.6023i	−0.849161	+	0.703468i
$944$		0			0
$945$		−	24.1612i		−	0.785963i
$946$		0			0
$947$	−9.60761			−0.312205			−0.156103	−	0.987741i	$-0.549893\pi$
$947$	−9.60761			−0.312205			−0.156103	+	0.987741i	$0.549893\pi$
$948$		0			0
$949$	0.859905	−	0.859905i	0.0279137	−	0.0279137i
$950$		0			0
$951$			11.9148i			0.386363i
$952$		0			0
$953$	44.1635			1.43060			0.715299	−	0.698819i	$-0.246291\pi$
$953$	44.1635			1.43060			0.715299	+	0.698819i	$0.246291\pi$
$954$		0			0
$955$	31.8319	+	31.8319i	1.03005	+	1.03005i
$956$		0			0
$957$	−7.93604	+	7.93604i	−0.256536	+	0.256536i
$958$		0			0
$959$	−16.1852			−0.522647
$960$		0			0
$961$	−29.9297			−0.965474
$962$		0			0
$963$		−	26.1598i		−	0.842987i
$964$		0			0
$965$	−3.52275	+	3.52275i	−0.113401	+	0.113401i
$966$		0			0
$967$	−17.2127	+	17.2127i	−0.553523	+	0.553523i	−0.927456	−	0.373933i	$-0.878009\pi$
$967$	−17.2127	+	17.2127i	−0.553523	+	0.553523i	0.373933	+	0.927456i	$0.378009\pi$
$968$		0			0
$969$	−48.0696	+	48.0696i	−1.54422	+	1.54422i
$970$		0			0
$971$	8.80811	+	8.80811i	0.282666	+	0.282666i	0.834171	−	0.551506i	$-0.185946\pi$
$971$	8.80811	+	8.80811i	0.282666	+	0.282666i	−0.551506	+	0.834171i	$0.685946\pi$
$972$		0			0
$973$	−9.70591	−	9.70591i	−0.311157	−	0.311157i
$974$		0			0
$975$			3.83992i			0.122976i
$976$		0			0
$977$	38.6771	+	38.6771i	1.23739	+	1.23739i	0.961064	+	0.276326i	$0.0891170\pi$
$977$	38.6771	+	38.6771i	1.23739	+	1.23739i	0.276326	+	0.961064i	$0.410883\pi$
$978$		0			0
$979$			26.5143i			0.847400i
$980$		0			0
$981$	15.9336	+	15.9336i	0.508719	+	0.508719i
$982$		0			0
$983$	33.8838			1.08072			0.540362	−	0.841433i	$-0.318287\pi$
$983$	33.8838			1.08072			0.540362	+	0.841433i	$0.318287\pi$
$984$		0			0
$985$	−9.55696			−0.304510
$986$		0			0
$987$	−2.46635	−	2.46635i	−0.0785047	−	0.0785047i
$988$		0			0
$989$			46.0979i			1.46583i
$990$		0			0
$991$	−9.42169	−	9.42169i	−0.299290	−	0.299290i	0.541446	−	0.840736i	$-0.317877\pi$
$991$	−9.42169	−	9.42169i	−0.299290	−	0.299290i	−0.840736	+	0.541446i	$0.817877\pi$
$992$		0			0
$993$		−	17.6512i		−	0.560143i
$994$		0			0
$995$	7.47655	+	7.47655i	0.237022	+	0.237022i
$996$		0			0
$997$	31.6502	+	31.6502i	1.00237	+	1.00237i	0.999997	+	0.00237415i	$0.000755717\pi$
$997$	31.6502	+	31.6502i	1.00237	+	1.00237i	0.00237415	+	0.999997i	$0.499244\pi$
$998$		0			0
$999$	10.0868	−	10.0868i	0.319134	−	0.319134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.a.337.2	✓	8
41.32	even	4	inner	1148.2.k.a.729.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.a.337.2	✓	8	1.1	even	1	trivial
1148.2.k.a.729.2	yes	8	41.32	even	4	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.868559 - 0.868559i) q^{3} -4.37966i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.49121i q^{9} +O(q^{10})\)	\(q+(-0.868559 - 0.868559i) q^{3} -4.37966i q^{5} +(-0.707107 - 0.707107i) q^{7} -1.49121i q^{9} +(1.10701 + 1.10701i) q^{11} +(0.155874 + 0.155874i) q^{13} +(-3.80399 + 3.80399i) q^{15} +(5.27265 - 5.27265i) q^{17} +(5.24822 - 5.24822i) q^{19} +1.22833i q^{21} +5.28835 q^{23} -14.1814 q^{25} +(-3.90088 + 3.90088i) q^{27} +(-4.12690 - 4.12690i) q^{29} +1.03455 q^{31} -1.92300i q^{33} +(-3.09689 + 3.09689i) q^{35} -2.58579 q^{37} -0.270771i q^{39} +(-4.93089 + 4.08489i) q^{41} +8.71688i q^{43} -6.53099 q^{45} +(-2.00789 + 2.00789i) q^{47} +1.00000i q^{49} -9.15922 q^{51} +(5.98800 + 5.98800i) q^{53} +(4.84832 - 4.84832i) q^{55} -9.11678 q^{57} +6.40829 q^{59} +12.4391i q^{61} +(-1.05444 + 1.05444i) q^{63} +(0.682674 - 0.682674i) q^{65} +(-1.54565 + 1.54565i) q^{67} +(-4.59325 - 4.59325i) q^{69} +(0.123981 + 0.123981i) q^{71} -5.51668i q^{73} +(12.3174 + 12.3174i) q^{75} -1.56555i q^{77} +(-8.20809 - 8.20809i) q^{79} +2.30266 q^{81} -12.8108 q^{83} +(-23.0924 - 23.0924i) q^{85} +7.16891i q^{87} +(11.9756 + 11.9756i) q^{89} -0.220439i q^{91} +(-0.898571 - 0.898571i) q^{93} +(-22.9854 - 22.9854i) q^{95} +(6.20844 - 6.20844i) q^{97} +(1.65078 - 1.65078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3}+O(q^{10}) \) 8 * q - 4 * q^3	\( 8 q - 4 q^{3} + 12 q^{11} + 4 q^{13} - 8 q^{15} + 8 q^{17} + 8 q^{19} + 28 q^{23} - 4 q^{25} + 8 q^{27} - 16 q^{29} + 28 q^{31} - 8 q^{35} - 32 q^{37} - 4 q^{45} + 20 q^{47} - 20 q^{51} + 32 q^{53} - 4 q^{55} - 36 q^{57} - 20 q^{59} - 8 q^{63} - 4 q^{67} - 44 q^{69} + 8 q^{71} + 12 q^{75} - 12 q^{79} - 16 q^{81} - 64 q^{83} - 56 q^{85} + 4 q^{89} - 4 q^{93} - 52 q^{95} + 56 q^{97} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 12 * q^11 + 4 * q^13 - 8 * q^15 + 8 * q^17 + 8 * q^19 + 28 * q^23 - 4 * q^25 + 8 * q^27 - 16 * q^29 + 28 * q^31 - 8 * q^35 - 32 * q^37 - 4 * q^45 + 20 * q^47 - 20 * q^51 + 32 * q^53 - 4 * q^55 - 36 * q^57 - 20 * q^59 - 8 * q^63 - 4 * q^67 - 44 * q^69 + 8 * q^71 + 12 * q^75 - 12 * q^79 - 16 * q^81 - 64 * q^83 - 56 * q^85 + 4 * q^89 - 4 * q^93 - 52 * q^95 + 56 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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