LMFDB - Embedded newform 1148.2.k.b.729.2

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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			729.2
Character	$\chi$	$=$	1148.729
Dual form			1148.2.k.b.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32681 + 2.32681i) q^{3} +4.24622i q^{5} +(0.707107 - 0.707107i) q^{7} -7.82813i q^{9} +O(q^{10})$	\(q+(-2.32681 + 2.32681i) q^{3} +4.24622i q^{5} +(0.707107 - 0.707107i) q^{7} -7.82813i q^{9} +(-4.19464 + 4.19464i) q^{11} +(3.56747 - 3.56747i) q^{13} +(-9.88017 - 9.88017i) q^{15} +(-1.77688 - 1.77688i) q^{17} +(-2.53191 - 2.53191i) q^{19} +3.29061i q^{21} -2.95307 q^{23} -13.0304 q^{25} +(11.2341 + 11.2341i) q^{27} +(-1.24311 + 1.24311i) q^{29} -0.673818 q^{31} -19.5203i q^{33} +(3.00253 + 3.00253i) q^{35} +0.962447 q^{37} +16.6017i q^{39} +(0.364205 - 6.39276i) q^{41} -2.97093i q^{43} +33.2399 q^{45} +(5.82139 + 5.82139i) q^{47} -1.00000i q^{49} +8.26894 q^{51} +(-3.22446 + 3.22446i) q^{53} +(-17.8114 - 17.8114i) q^{55} +11.7826 q^{57} +1.27834 q^{59} +0.789980i q^{61} +(-5.53532 - 5.53532i) q^{63} +(15.1483 + 15.1483i) q^{65} +(-0.698946 - 0.698946i) q^{67} +(6.87125 - 6.87125i) q^{69} +(-4.91969 + 4.91969i) q^{71} -9.13102i q^{73} +(30.3193 - 30.3193i) q^{75} +5.93211i q^{77} +(7.06334 - 7.06334i) q^{79} -28.7952 q^{81} -13.7310 q^{83} +(7.54502 - 7.54502i) q^{85} -5.78496i q^{87} +(-5.05584 + 5.05584i) q^{89} -5.04517i q^{91} +(1.56785 - 1.56785i) q^{93} +(10.7511 - 10.7511i) q^{95} +(5.75578 + 5.75578i) q^{97} +(32.8361 + 32.8361i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.32681	+	2.32681i	−1.34339	+	1.34339i	−0.450722	+	0.892664i	$0.648834\pi$
$3$	−2.32681	+	2.32681i	−1.34339	+	1.34339i	−0.892664	+	0.450722i	$0.851166\pi$
$4$		0			0
$5$			4.24622i			1.89897i	0.313816	+	0.949484i	$0.398393\pi$
$5$			4.24622i			1.89897i	−0.313816	+	0.949484i	$0.601607\pi$
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$		−	7.82813i		−	2.60938i
$10$		0			0
$11$	−4.19464	+	4.19464i	−1.26473	+	1.26473i	−0.315957	+	0.948774i	$0.602326\pi$
$11$	−4.19464	+	4.19464i	−1.26473	+	1.26473i	−0.948774	+	0.315957i	$0.897674\pi$
$12$		0			0
$13$	3.56747	−	3.56747i	0.989438	−	0.989438i	−0.0105065	−	0.999945i	$-0.503344\pi$
$13$	3.56747	−	3.56747i	0.989438	−	0.989438i	0.999945	+	0.0105065i	$0.00334437\pi$
$14$		0			0
$15$	−9.88017	−	9.88017i	−2.55105	−	2.55105i
$16$		0			0
$17$	−1.77688	−	1.77688i	−0.430957	−	0.430957i	0.457997	−	0.888954i	$-0.348567\pi$
$17$	−1.77688	−	1.77688i	−0.430957	−	0.430957i	−0.888954	+	0.457997i	$0.848567\pi$
$18$		0			0
$19$	−2.53191	−	2.53191i	−0.580861	−	0.580861i	0.354279	−	0.935140i	$-0.384726\pi$
$19$	−2.53191	−	2.53191i	−0.580861	−	0.580861i	−0.935140	+	0.354279i	$0.884726\pi$
$20$		0			0
$21$			3.29061i			0.718070i
$22$		0			0
$23$	−2.95307			−0.615758			−0.307879	−	0.951426i	$-0.599619\pi$
$23$	−2.95307			−0.615758			−0.307879	+	0.951426i	$0.599619\pi$
$24$		0			0
$25$	−13.0304			−2.60608
$26$		0			0
$27$	11.2341	+	11.2341i	2.16201	+	2.16201i
$28$		0			0
$29$	−1.24311	+	1.24311i	−0.230839	+	0.230839i	−0.813043	−	0.582204i	$-0.802191\pi$
$29$	−1.24311	+	1.24311i	−0.230839	+	0.230839i	0.582204	+	0.813043i	$0.302191\pi$
$30$		0			0
$31$	−0.673818			−0.121021			−0.0605106	−	0.998168i	$-0.519273\pi$
$31$	−0.673818			−0.121021			−0.0605106	+	0.998168i	$0.519273\pi$
$32$		0			0
$33$		−	19.5203i		−	3.39804i
$34$		0			0
$35$	3.00253	+	3.00253i	0.507520	+	0.507520i
$36$		0			0
$37$	0.962447			0.158225			0.0791126	−	0.996866i	$-0.474791\pi$
$37$	0.962447			0.158225			0.0791126	+	0.996866i	$0.474791\pi$
$38$		0			0
$39$			16.6017i			2.65840i
$40$		0			0
$41$	0.364205	−	6.39276i	0.0568793	−	0.998381i
$41$	0.364205	−	6.39276i	0.0568793	−	0.998381i
$42$		0			0
$43$		−	2.97093i		−	0.453063i	−0.974004	−	0.226532i	$-0.927261\pi$
$43$		−	2.97093i		−	0.453063i	0.974004	−	0.226532i	$-0.0727386\pi$
$44$		0			0
$45$	33.2399			4.95512
$46$		0			0
$47$	5.82139	+	5.82139i	0.849137	+	0.849137i	0.990026	−	0.140888i	$-0.0449958\pi$
$47$	5.82139	+	5.82139i	0.849137	+	0.849137i	−0.140888	+	0.990026i	$0.544996\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	8.26894			1.15788
$52$		0			0
$53$	−3.22446	+	3.22446i	−0.442913	+	0.442913i	−0.892990	−	0.450077i	$-0.851397\pi$
$53$	−3.22446	+	3.22446i	−0.442913	+	0.442913i	0.450077	+	0.892990i	$0.351397\pi$
$54$		0			0
$55$	−17.8114	−	17.8114i	−2.40168	−	2.40168i
$56$		0			0
$57$	11.7826			1.56064
$58$		0			0
$59$	1.27834			0.166425			0.0832125	−	0.996532i	$-0.473482\pi$
$59$	1.27834			0.166425			0.0832125	+	0.996532i	$0.473482\pi$
$60$		0			0
$61$			0.789980i			0.101147i	0.998720	+	0.0505733i	$0.0161048\pi$
$61$			0.789980i			0.101147i	−0.998720	+	0.0505733i	$0.983895\pi$
$62$		0			0
$63$	−5.53532	−	5.53532i	−0.697385	−	0.697385i
$64$		0			0
$65$	15.1483	+	15.1483i	1.87891	+	1.87891i
$66$		0			0
$67$	−0.698946	−	0.698946i	−0.0853899	−	0.0853899i	0.663122	−	0.748512i	$-0.269231\pi$
$67$	−0.698946	−	0.698946i	−0.0853899	−	0.0853899i	−0.748512	+	0.663122i	$0.769231\pi$
$68$		0			0
$69$	6.87125	−	6.87125i	0.827201	−	0.827201i
$70$		0			0
$71$	−4.91969	+	4.91969i	−0.583859	+	0.583859i	−0.935962	−	0.352102i	$-0.885467\pi$
$71$	−4.91969	+	4.91969i	−0.583859	+	0.583859i	0.352102	+	0.935962i	$0.385467\pi$
$72$		0			0
$73$		−	9.13102i		−	1.06870i	−0.845262	−	0.534352i	$-0.820556\pi$
$73$		−	9.13102i		−	1.06870i	0.845262	−	0.534352i	$-0.179444\pi$
$74$		0			0
$75$	30.3193	−	30.3193i	3.50097	−	3.50097i
$76$		0			0
$77$			5.93211i			0.676027i
$78$		0			0
$79$	7.06334	−	7.06334i	0.794688	−	0.794688i	−0.187564	−	0.982252i	$-0.560059\pi$
$79$	7.06334	−	7.06334i	0.794688	−	0.794688i	0.982252	+	0.187564i	$0.0600593\pi$
$80$		0			0
$81$	−28.7952			−3.19946
$82$		0			0
$83$	−13.7310			−1.50717			−0.753584	−	0.657352i	$-0.771677\pi$
$83$	−13.7310			−1.50717			−0.753584	+	0.657352i	$0.771677\pi$
$84$		0			0
$85$	7.54502	−	7.54502i	0.818373	−	0.818373i
$86$		0			0
$87$		−	5.78496i		−	0.620212i
$88$		0			0
$89$	−5.05584	+	5.05584i	−0.535918	+	0.535918i	−0.922327	−	0.386410i	$-0.873715\pi$
$89$	−5.05584	+	5.05584i	−0.535918	+	0.535918i	0.386410	+	0.922327i	$0.373715\pi$
$90$		0			0
$91$		−	5.04517i		−	0.528877i
$92$		0			0
$93$	1.56785	−	1.56785i	0.162578	−	0.162578i
$94$		0			0
$95$	10.7511	−	10.7511i	1.10304	−	1.10304i
$96$		0			0
$97$	5.75578	+	5.75578i	0.584411	+	0.584411i	0.936112	−	0.351701i	$-0.114397\pi$
$97$	5.75578	+	5.75578i	0.584411	+	0.584411i	−0.351701	+	0.936112i	$0.614397\pi$
$98$		0			0
$99$	32.8361	+	32.8361i	3.30016	+	3.30016i
$100$		0			0
$101$	8.05190	+	8.05190i	0.801194	+	0.801194i	0.983282	−	0.182088i	$-0.0582857\pi$
$101$	8.05190	+	8.05190i	0.801194	+	0.801194i	−0.182088	+	0.983282i	$0.558286\pi$
$102$		0			0
$103$			10.3626i			1.02106i	0.859861	+	0.510528i	$0.170550\pi$
$103$			10.3626i			1.02106i	−0.859861	+	0.510528i	$0.829450\pi$
$104$		0			0
$105$	−13.9727			−1.36359
$106$		0			0
$107$	−11.6638			−1.12758			−0.563792	−	0.825917i	$-0.690658\pi$
$107$	−11.6638			−1.12758			−0.563792	+	0.825917i	$0.690658\pi$
$108$		0			0
$109$	4.73917	+	4.73917i	0.453930	+	0.453930i	0.896657	−	0.442726i	$-0.145989\pi$
$109$	4.73917	+	4.73917i	0.453930	+	0.453930i	−0.442726	+	0.896657i	$0.645989\pi$
$110$		0			0
$111$	−2.23943	+	2.23943i	−0.212558	+	0.212558i
$112$		0			0
$113$	9.20579			0.866008			0.433004	−	0.901392i	$-0.357454\pi$
$113$	9.20579			0.866008			0.433004	+	0.901392i	$0.357454\pi$
$114$		0			0
$115$		−	12.5394i		−	1.16930i
$116$		0			0
$117$	−27.9266	−	27.9266i	−2.58182	−	2.58182i
$118$		0			0
$119$	−2.51289			−0.230356
$120$		0			0
$121$		−	24.1899i		−	2.19909i
$122$		0			0
$123$	14.0273	+	15.7222i	1.26480	+	1.41762i
$124$		0			0
$125$		−	34.0988i		−	3.04989i
$126$		0			0
$127$	−8.39300			−0.744758			−0.372379	−	0.928081i	$-0.621458\pi$
$127$	−8.39300			−0.744758			−0.372379	+	0.928081i	$0.621458\pi$
$128$		0			0
$129$	6.91281	+	6.91281i	0.608639	+	0.608639i
$130$		0			0
$131$		−	19.8785i		−	1.73679i	−0.495873	−	0.868395i	$-0.665152\pi$
$131$		−	19.8785i		−	1.73679i	0.495873	−	0.868395i	$-0.334848\pi$
$132$		0			0
$133$	−3.58067			−0.310483
$134$		0			0
$135$	−47.7027	+	47.7027i	−4.10559	+	4.10559i
$136$		0			0
$137$	−13.0847	−	13.0847i	−1.11790	−	1.11790i	−0.992050	−	0.125848i	$-0.959835\pi$
$137$	−13.0847	−	13.0847i	−1.11790	−	1.11790i	−0.125848	−	0.992050i	$-0.540165\pi$
$138$		0			0
$139$	8.60496			0.729863			0.364931	−	0.931034i	$-0.381092\pi$
$139$	8.60496			0.729863			0.364931	+	0.931034i	$0.381092\pi$
$140$		0			0
$141$	−27.0906			−2.28144
$142$		0			0
$143$			29.9285i			2.50275i
$144$		0			0
$145$	−5.27851	−	5.27851i	−0.438356	−	0.438356i
$146$		0			0
$147$	2.32681	+	2.32681i	0.191912	+	0.191912i
$148$		0			0
$149$	−4.29787	−	4.29787i	−0.352095	−	0.352095i	0.508793	−	0.860889i	$-0.330092\pi$
$149$	−4.29787	−	4.29787i	−0.352095	−	0.352095i	−0.860889	+	0.508793i	$0.830092\pi$
$150$		0			0
$151$	−10.2354	+	10.2354i	−0.832942	+	0.832942i	−0.987918	−	0.154976i	$-0.950470\pi$
$151$	−10.2354	+	10.2354i	−0.832942	+	0.832942i	0.154976	+	0.987918i	$0.450470\pi$
$152$		0			0
$153$	−13.9096	+	13.9096i	−1.12453	+	1.12453i
$154$		0			0
$155$		−	2.86118i		−	0.229815i
$156$		0			0
$157$	−12.9316	+	12.9316i	−1.03206	+	1.03206i	−0.0325879	+	0.999469i	$0.510375\pi$
$157$	−12.9316	+	12.9316i	−1.03206	+	1.03206i	−0.999469	+	0.0325879i	$0.989625\pi$
$158$		0			0
$159$		−	15.0054i		−	1.19001i
$160$		0			0
$161$	−2.08814	+	2.08814i	−0.164568	+	0.164568i
$162$		0			0
$163$	−24.4625			−1.91605			−0.958024	−	0.286689i	$-0.907445\pi$
$163$	−24.4625			−1.91605			−0.958024	+	0.286689i	$0.907445\pi$
$164$		0			0
$165$	82.8874			6.45278
$166$		0			0
$167$	5.02460	−	5.02460i	0.388815	−	0.388815i	−0.485449	−	0.874265i	$-0.661344\pi$
$167$	5.02460	−	5.02460i	0.388815	−	0.388815i	0.874265	+	0.485449i	$0.161344\pi$
$168$		0			0
$169$		−	12.4537i		−	0.957976i
$170$		0			0
$171$	−19.8201	+	19.8201i	−1.51568	+	1.51568i
$172$		0			0
$173$		−	7.11453i		−	0.540908i	−0.962733	−	0.270454i	$-0.912826\pi$
$173$		−	7.11453i		−	0.540908i	0.962733	−	0.270454i	$-0.0871738\pi$
$174$		0			0
$175$	−9.21388	+	9.21388i	−0.696504	+	0.696504i
$176$		0			0
$177$	−2.97445	+	2.97445i	−0.223573	+	0.223573i
$178$		0			0
$179$	2.38569	+	2.38569i	0.178315	+	0.178315i	0.790621	−	0.612306i	$-0.209758\pi$
$179$	2.38569	+	2.38569i	0.178315	+	0.178315i	−0.612306	+	0.790621i	$0.709758\pi$
$180$		0			0
$181$	11.5967	+	11.5967i	0.861974	+	0.861974i	0.991567	−	0.129593i	$-0.0413672\pi$
$181$	11.5967	+	11.5967i	0.861974	+	0.861974i	−0.129593	+	0.991567i	$0.541367\pi$
$182$		0			0
$183$	−1.83814	−	1.83814i	−0.135879	−	0.135879i
$184$		0			0
$185$			4.08676i			0.300465i
$186$		0			0
$187$	14.9067			1.09009
$188$		0			0
$189$	15.8875			1.15564
$190$		0			0
$191$	0.597809	+	0.597809i	0.0432559	+	0.0432559i	0.728404	−	0.685148i	$-0.240262\pi$
$191$	0.597809	+	0.597809i	0.0432559	+	0.0432559i	−0.685148	+	0.728404i	$0.740262\pi$
$192$		0			0
$193$	−2.21881	+	2.21881i	−0.159713	+	0.159713i	−0.782440	−	0.622726i	$-0.786025\pi$
$193$	−2.21881	+	2.21881i	−0.159713	+	0.159713i	0.622726	+	0.782440i	$0.286025\pi$
$194$		0			0
$195$	−70.4944			−5.04821
$196$		0			0
$197$			10.5596i			0.752338i	0.926551	+	0.376169i	$0.122759\pi$
$197$			10.5596i			0.752338i	−0.926551	+	0.376169i	$0.877241\pi$
$198$		0			0
$199$	13.3700	+	13.3700i	0.947774	+	0.947774i	0.998702	−	0.0509280i	$-0.0162179\pi$
$199$	13.3700	+	13.3700i	0.947774	+	0.947774i	−0.0509280	+	0.998702i	$0.516218\pi$
$200$		0			0
$201$	3.25263			0.229423
$202$		0			0
$203$			1.75802i			0.123389i
$204$		0			0
$205$	27.1451	+	1.54650i	1.89589	+	0.108012i
$206$		0			0
$207$			23.1170i			1.60674i
$208$		0			0
$209$	21.2409			1.46927
$210$		0			0
$211$	−3.28599	−	3.28599i	−0.226217	−	0.226217i	0.584893	−	0.811110i	$-0.301136\pi$
$211$	−3.28599	−	3.28599i	−0.226217	−	0.226217i	−0.811110	+	0.584893i	$0.801136\pi$
$212$		0			0
$213$		−	22.8944i		−	1.56870i
$214$		0			0
$215$	12.6152			0.860352
$216$		0			0
$217$	−0.476461	+	0.476461i	−0.0323443	+	0.0323443i
$218$		0			0
$219$	21.2462	+	21.2462i	1.43568	+	1.43568i
$220$		0			0
$221$	−12.6779			−0.852810
$222$		0			0
$223$	4.96267			0.332325			0.166163	−	0.986098i	$-0.446862\pi$
$223$	4.96267			0.332325			0.166163	+	0.986098i	$0.446862\pi$
$224$		0			0
$225$			102.004i			6.80024i
$226$		0			0
$227$	−14.0028	−	14.0028i	−0.929399	−	0.929399i	0.0682682	−	0.997667i	$-0.478253\pi$
$227$	−14.0028	−	14.0028i	−0.929399	−	0.929399i	−0.997667	+	0.0682682i	$0.978253\pi$
$228$		0			0
$229$	−1.27538	−	1.27538i	−0.0842794	−	0.0842794i	0.663710	−	0.747990i	$-0.268981\pi$
$229$	−1.27538	−	1.27538i	−0.0842794	−	0.0842794i	−0.747990	+	0.663710i	$0.768981\pi$
$230$		0			0
$231$	−13.8029	−	13.8029i	−0.908165	−	0.908165i
$232$		0			0
$233$	−11.0654	+	11.0654i	−0.724917	+	0.724917i	−0.969603	−	0.244685i	$-0.921315\pi$
$233$	−11.0654	+	11.0654i	−0.724917	+	0.724917i	0.244685	+	0.969603i	$0.421315\pi$
$234$		0			0
$235$	−24.7189	+	24.7189i	−1.61248	+	1.61248i
$236$		0			0
$237$			32.8702i			2.13515i
$238$		0			0
$239$	−6.38816	+	6.38816i	−0.413216	+	0.413216i	−0.882857	−	0.469641i	$-0.844383\pi$
$239$	−6.38816	+	6.38816i	−0.413216	+	0.413216i	0.469641	+	0.882857i	$0.344383\pi$
$240$		0			0
$241$		−	13.9312i		−	0.897390i	−0.893685	−	0.448695i	$-0.851889\pi$
$241$		−	13.9312i		−	0.897390i	0.893685	−	0.448695i	$-0.148111\pi$
$242$		0			0
$243$	33.2986	−	33.2986i	2.13610	−	2.13610i
$244$		0			0
$245$	4.24622			0.271281
$246$		0			0
$247$	−18.0651			−1.14945
$248$		0			0
$249$	31.9494	−	31.9494i	2.02471	−	2.02471i
$250$		0			0
$251$		−	11.5202i		−	0.727148i	−0.931565	−	0.363574i	$-0.881556\pi$
$251$		−	11.5202i		−	0.727148i	0.931565	−	0.363574i	$-0.118444\pi$
$252$		0			0
$253$	12.3871	−	12.3871i	0.778768	−	0.778768i
$254$		0			0
$255$			35.1117i			2.19878i
$256$		0			0
$257$	−20.3499	+	20.3499i	−1.26939	+	1.26939i	−0.322993	+	0.946401i	$0.604689\pi$
$257$	−20.3499	+	20.3499i	−1.26939	+	1.26939i	−0.946401	+	0.322993i	$0.895311\pi$
$258$		0			0
$259$	0.680552	−	0.680552i	0.0422875	−	0.0422875i
$260$		0			0
$261$	9.73120	+	9.73120i	0.602346	+	0.602346i
$262$		0			0
$263$	−19.7051	−	19.7051i	−1.21507	−	1.21507i	−0.969338	−	0.245731i	$-0.920972\pi$
$263$	−19.7051	−	19.7051i	−1.21507	−	1.21507i	−0.245731	−	0.969338i	$-0.579028\pi$
$264$		0			0
$265$	−13.6918	−	13.6918i	−0.841078	−	0.841078i
$266$		0			0
$267$		−	23.5280i		−	1.43989i
$268$		0			0
$269$	6.87162			0.418970			0.209485	−	0.977812i	$-0.432821\pi$
$269$	6.87162			0.418970			0.209485	+	0.977812i	$0.432821\pi$
$270$		0			0
$271$	19.6618			1.19437			0.597185	−	0.802104i	$-0.296286\pi$
$271$	19.6618			1.19437			0.597185	+	0.802104i	$0.296286\pi$
$272$		0			0
$273$	11.7392	+	11.7392i	0.710486	+	0.710486i
$274$		0			0
$275$	54.6578	−	54.6578i	3.29599	−	3.29599i
$276$		0			0
$277$	−1.17740			−0.0707429			−0.0353714	−	0.999374i	$-0.511261\pi$
$277$	−1.17740			−0.0707429			−0.0353714	+	0.999374i	$0.511261\pi$
$278$		0			0
$279$			5.27473i			0.315790i
$280$		0			0
$281$	−15.8178	−	15.8178i	−0.943612	−	0.943612i	0.0548806	−	0.998493i	$-0.482522\pi$
$281$	−15.8178	−	15.8178i	−0.943612	−	0.943612i	−0.998493	+	0.0548806i	$0.982522\pi$
$282$		0			0
$283$	−1.44959			−0.0861690			−0.0430845	−	0.999071i	$-0.513718\pi$
$283$	−1.44959			−0.0861690			−0.0430845	+	0.999071i	$0.513718\pi$
$284$		0			0
$285$			50.0315i			2.96361i
$286$		0			0
$287$	−4.26283	−	4.77789i	−0.251627	−	0.282030i
$288$		0			0
$289$		−	10.6854i		−	0.628553i
$290$		0			0
$291$	−26.7853			−1.57018
$292$		0			0
$293$	−0.813256	−	0.813256i	−0.0475109	−	0.0475109i	0.682952	−	0.730463i	$-0.260696\pi$
$293$	−0.813256	−	0.813256i	−0.0475109	−	0.0475109i	−0.730463	+	0.682952i	$0.760696\pi$
$294$		0			0
$295$			5.42809i			0.316036i
$296$		0			0
$297$	−94.2463			−5.46873
$298$		0			0
$299$	−10.5350	+	10.5350i	−0.609255	+	0.609255i
$300$		0			0
$301$	−2.10077	−	2.10077i	−0.121086	−	0.121086i
$302$		0			0
$303$	−37.4705			−2.15263
$304$		0			0
$305$	−3.35443			−0.192074
$306$		0			0
$307$		−	4.11500i		−	0.234855i	−0.993081	−	0.117428i	$-0.962535\pi$
$307$		−	4.11500i		−	0.234855i	0.993081	−	0.117428i	$-0.0374648\pi$
$308$		0			0
$309$	−24.1118	−	24.1118i	−1.37167	−	1.37167i
$310$		0			0
$311$	−11.6645	−	11.6645i	−0.661432	−	0.661432i	0.294286	−	0.955718i	$-0.404918\pi$
$311$	−11.6645	−	11.6645i	−0.661432	−	0.661432i	−0.955718	+	0.294286i	$0.904918\pi$
$312$		0			0
$313$	−5.86970	−	5.86970i	−0.331775	−	0.331775i	0.521485	−	0.853260i	$-0.325378\pi$
$313$	−5.86970	−	5.86970i	−0.331775	−	0.331775i	−0.853260	+	0.521485i	$0.825378\pi$
$314$		0			0
$315$	23.5042	−	23.5042i	1.32431	−	1.32431i
$316$		0			0
$317$	−2.44834	+	2.44834i	−0.137512	+	0.137512i	−0.772512	−	0.635000i	$-0.781000\pi$
$317$	−2.44834	+	2.44834i	−0.137512	+	0.137512i	0.635000	+	0.772512i	$0.281000\pi$
$318$		0			0
$319$		−	10.4288i		−	0.583899i
$320$		0			0
$321$	27.1395	−	27.1395i	1.51478	−	1.51478i
$322$		0			0
$323$			8.99781i			0.500652i
$324$		0			0
$325$	−46.4855	+	46.4855i	−2.57855	+	2.57855i
$326$		0			0
$327$	−22.0543			−1.21961
$328$		0			0
$329$	8.23269			0.453883
$330$		0			0
$331$	7.04942	−	7.04942i	0.387471	−	0.387471i	−0.486313	−	0.873785i	$-0.661659\pi$
$331$	7.04942	−	7.04942i	0.387471	−	0.387471i	0.873785	+	0.486313i	$0.161659\pi$
$332$		0			0
$333$		−	7.53415i		−	0.412869i
$334$		0			0
$335$	2.96788	−	2.96788i	0.162153	−	0.162153i
$336$		0			0
$337$		−	28.6701i		−	1.56176i	−0.624681	−	0.780880i	$-0.714771\pi$
$337$		−	28.6701i		−	1.56176i	0.624681	−	0.780880i	$-0.285229\pi$
$338$		0			0
$339$	−21.4202	+	21.4202i	−1.16338	+	1.16338i
$340$		0			0
$341$	2.82642	−	2.82642i	0.153059	−	0.153059i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	29.1768	+	29.1768i	1.57083	+	1.57083i
$346$		0			0
$347$	12.5714	+	12.5714i	0.674867	+	0.674867i	0.958834	−	0.283967i	$-0.0916507\pi$
$347$	12.5714	+	12.5714i	0.674867	+	0.674867i	−0.283967	+	0.958834i	$0.591651\pi$
$348$		0			0
$349$			10.8944i			0.583165i	0.956546	+	0.291583i	$0.0941818\pi$
$349$			10.8944i			0.583165i	−0.956546	+	0.291583i	$0.905818\pi$
$350$		0			0
$351$	80.1550			4.27836
$352$		0			0
$353$	32.5939			1.73480			0.867399	−	0.497614i	$-0.165790\pi$
$353$	32.5939			1.73480			0.867399	+	0.497614i	$0.165790\pi$
$354$		0			0
$355$	−20.8901	−	20.8901i	−1.10873	−	1.10873i
$356$		0			0
$357$	5.84702	−	5.84702i	0.309457	−	0.309457i
$358$		0			0
$359$	18.9230			0.998718			0.499359	−	0.866395i	$-0.333569\pi$
$359$	18.9230			0.998718			0.499359	+	0.866395i	$0.333569\pi$
$360$		0			0
$361$		−	6.17882i		−	0.325201i
$362$		0			0
$363$	56.2855	+	56.2855i	2.95422	+	2.95422i
$364$		0			0
$365$	38.7723			2.02944
$366$		0			0
$367$			7.25606i			0.378763i	0.981904	+	0.189381i	$0.0606483\pi$
$367$			7.25606i			0.378763i	−0.981904	+	0.189381i	$0.939352\pi$
$368$		0			0
$369$	−50.0433	−	2.85104i	−2.60515	−	0.148419i
$370$		0			0
$371$			4.56007i			0.236747i
$372$		0			0
$373$	−16.9241			−0.876299			−0.438149	−	0.898902i	$-0.644366\pi$
$373$	−16.9241			−0.876299			−0.438149	+	0.898902i	$0.644366\pi$
$374$		0			0
$375$	79.3416	+	79.3416i	4.09718	+	4.09718i
$376$		0			0
$377$			8.86949i			0.456802i
$378$		0			0
$379$	−36.8055			−1.89057			−0.945287	−	0.326240i	$-0.894218\pi$
$379$	−36.8055			−1.89057			−0.945287	+	0.326240i	$0.894218\pi$
$380$		0			0
$381$	19.5289	−	19.5289i	1.00050	−	1.00050i
$382$		0			0
$383$	−23.0952	−	23.0952i	−1.18011	−	1.18011i	−0.979716	−	0.200393i	$-0.935778\pi$
$383$	−23.0952	−	23.0952i	−1.18011	−	1.18011i	−0.200393	−	0.979716i	$-0.564222\pi$
$384$		0			0
$385$	−25.1891			−1.28375
$386$		0			0
$387$	−23.2568			−1.18221
$388$		0			0
$389$		−	20.9557i		−	1.06249i	−0.847217	−	0.531247i	$-0.821724\pi$
$389$		−	20.9557i		−	1.06249i	0.847217	−	0.531247i	$-0.178276\pi$
$390$		0			0
$391$	5.24725	+	5.24725i	0.265365	+	0.265365i
$392$		0			0
$393$	46.2535	+	46.2535i	2.33318	+	2.33318i
$394$		0			0
$395$	29.9925	+	29.9925i	1.50909	+	1.50909i
$396$		0			0
$397$	−19.4766	+	19.4766i	−0.977502	+	0.977502i	−0.999752	−	0.0222503i	$-0.992917\pi$
$397$	−19.4766	+	19.4766i	−0.977502	+	0.977502i	0.0222503	+	0.999752i	$0.492917\pi$
$398$		0			0
$399$	8.33155	−	8.33155i	0.417099	−	0.417099i
$400$		0			0
$401$			19.1947i			0.958537i	0.877668	+	0.479269i	$0.159098\pi$
$401$			19.1947i			0.958537i	−0.877668	+	0.479269i	$0.840902\pi$
$402$		0			0
$403$	−2.40383	+	2.40383i	−0.119743	+	0.119743i
$404$		0			0
$405$		−	122.271i		−	6.07568i
$406$		0			0
$407$	−4.03711	+	4.03711i	−0.200112	+	0.200112i
$408$		0			0
$409$	−0.263444			−0.0130265			−0.00651323	−	0.999979i	$-0.502073\pi$
$409$	−0.263444			−0.0130265			−0.00651323	+	0.999979i	$0.502073\pi$
$410$		0			0
$411$	60.8911			3.00354
$412$		0			0
$413$	0.903919	−	0.903919i	0.0444790	−	0.0444790i
$414$		0			0
$415$		−	58.3047i		−	2.86206i
$416$		0			0
$417$	−20.0221	+	20.0221i	−0.980488	+	0.980488i
$418$		0			0
$419$		−	11.0853i		−	0.541553i	−0.962642	−	0.270776i	$-0.912720\pi$
$419$		−	11.0853i		−	0.541553i	0.962642	−	0.270776i	$-0.0872804\pi$
$420$		0			0
$421$	0.0941971	−	0.0941971i	0.00459089	−	0.00459089i	−0.704808	−	0.709398i	$-0.748967\pi$
$421$	0.0941971	−	0.0941971i	0.00459089	−	0.00459089i	0.709398	+	0.704808i	$0.248967\pi$
$422$		0			0
$423$	45.5706	−	45.5706i	2.21572	−	2.21572i
$424$		0			0
$425$	23.1534	+	23.1534i	1.12311	+	1.12311i
$426$		0			0
$427$	0.558600	+	0.558600i	0.0270325	+	0.0270325i
$428$		0			0
$429$	−69.6380	−	69.6380i	−3.36215	−	3.36215i
$430$		0			0
$431$		−	21.9320i		−	1.05643i	−0.849111	−	0.528215i	$-0.822862\pi$
$431$		−	21.9320i		−	1.05643i	0.849111	−	0.528215i	$-0.177138\pi$
$432$		0			0
$433$	−37.5069			−1.80246			−0.901232	−	0.433336i	$-0.857336\pi$
$433$	−37.5069			−1.80246			−0.901232	+	0.433336i	$0.857336\pi$
$434$		0			0
$435$	24.5642			1.17776
$436$		0			0
$437$	7.47692	+	7.47692i	0.357670	+	0.357670i
$438$		0			0
$439$	−7.42600	+	7.42600i	−0.354424	+	0.354424i	−0.861752	−	0.507329i	$-0.830633\pi$
$439$	−7.42600	+	7.42600i	−0.354424	+	0.354424i	0.507329	+	0.861752i	$0.330633\pi$
$440$		0			0
$441$	−7.82813			−0.372768
$442$		0			0
$443$			2.72125i			0.129290i	0.997908	+	0.0646452i	$0.0205916\pi$
$443$			2.72125i			0.129290i	−0.997908	+	0.0646452i	$0.979408\pi$
$444$		0			0
$445$	−21.4682	−	21.4682i	−1.01769	−	1.01769i
$446$		0			0
$447$	20.0007			0.946000
$448$		0			0
$449$			14.7404i			0.695643i	0.937561	+	0.347821i	$0.113078\pi$
$449$			14.7404i			0.695643i	−0.937561	+	0.347821i	$0.886922\pi$
$450$		0			0
$451$	25.2876	+	28.3430i	1.19075	+	1.33462i
$452$		0			0
$453$		−	47.6316i		−	2.23793i
$454$		0			0
$455$	21.4229			1.00432
$456$		0			0
$457$	11.5351	+	11.5351i	0.539591	+	0.539591i	0.923409	−	0.383818i	$-0.125391\pi$
$457$	11.5351	+	11.5351i	0.539591	+	0.539591i	−0.383818	+	0.923409i	$0.625391\pi$
$458$		0			0
$459$		−	39.9235i		−	1.86347i
$460$		0			0
$461$	−39.9279			−1.85963			−0.929814	−	0.368029i	$-0.880033\pi$
$461$	−39.9279			−1.85963			−0.929814	+	0.368029i	$0.880033\pi$
$462$		0			0
$463$	4.41264	−	4.41264i	0.205073	−	0.205073i	−0.597097	−	0.802169i	$-0.703679\pi$
$463$	4.41264	−	4.41264i	0.205073	−	0.205073i	0.802169	+	0.597097i	$0.203679\pi$
$464$		0			0
$465$	6.65743	+	6.65743i	0.308731	+	0.308731i
$466$		0			0
$467$	−20.5955			−0.953046			−0.476523	−	0.879162i	$-0.658103\pi$
$467$	−20.5955			−0.953046			−0.476523	+	0.879162i	$0.658103\pi$
$468$		0			0
$469$	−0.988459			−0.0456428
$470$		0			0
$471$		−	60.1790i		−	2.77290i
$472$		0			0
$473$	12.4620	+	12.4620i	0.573003	+	0.573003i
$474$		0			0
$475$	32.9918	+	32.9918i	1.51377	+	1.51377i
$476$		0			0
$477$	25.2415	+	25.2415i	1.15573	+	1.15573i
$478$		0			0
$479$	12.3753	−	12.3753i	0.565441	−	0.565441i	−0.365407	−	0.930848i	$-0.619070\pi$
$479$	12.3753	−	12.3753i	0.565441	−	0.565441i	0.930848	+	0.365407i	$0.119070\pi$
$480$		0			0
$481$	3.43350	−	3.43350i	0.156554	−	0.156554i
$482$		0			0
$483$		−	9.71741i		−	0.442158i
$484$		0			0
$485$	−24.4403	+	24.4403i	−1.10978	+	1.10978i
$486$		0			0
$487$			4.31210i			0.195400i	0.995216	+	0.0976998i	$0.0311485\pi$
$487$			4.31210i			0.195400i	−0.995216	+	0.0976998i	$0.968851\pi$
$488$		0			0
$489$	56.9196	−	56.9196i	2.57399	−	2.57399i
$490$		0			0
$491$	15.7780			0.712052			0.356026	−	0.934476i	$-0.384132\pi$
$491$	15.7780			0.712052			0.356026	+	0.934476i	$0.384132\pi$
$492$		0			0
$493$	4.41770			0.198963
$494$		0			0
$495$	−139.430	+	139.430i	−6.26689	+	6.26689i
$496$		0			0
$497$			6.95749i			0.312086i
$498$		0			0
$499$	−10.3963	+	10.3963i	−0.465405	+	0.465405i	−0.900422	−	0.435017i	$-0.856742\pi$
$499$	−10.3963	+	10.3963i	−0.465405	+	0.465405i	0.435017	+	0.900422i	$0.356742\pi$
$500$		0			0
$501$			23.3826i			1.04466i
$502$		0			0
$503$	7.10039	−	7.10039i	0.316591	−	0.316591i	−0.530865	−	0.847456i	$-0.678133\pi$
$503$	7.10039	−	7.10039i	0.316591	−	0.316591i	0.847456	+	0.530865i	$0.178133\pi$
$504$		0			0
$505$	−34.1901	+	34.1901i	−1.52144	+	1.52144i
$506$		0			0
$507$	28.9774	+	28.9774i	1.28693	+	1.28693i
$508$		0			0
$509$	15.4522	+	15.4522i	0.684909	+	0.684909i	0.961102	−	0.276193i	$-0.0890730\pi$
$509$	15.4522	+	15.4522i	0.684909	+	0.684909i	−0.276193	+	0.961102i	$0.589073\pi$
$510$		0			0
$511$	−6.45660	−	6.45660i	−0.285623	−	0.285623i
$512$		0			0
$513$		−	56.8878i		−	2.51166i
$514$		0			0
$515$	−44.0018			−1.93895
$516$		0			0
$517$	−48.8373			−2.14786
$518$		0			0
$519$	16.5542	+	16.5542i	0.726648	+	0.726648i
$520$		0			0
$521$	5.80627	−	5.80627i	0.254377	−	0.254377i	−0.568385	−	0.822763i	$-0.692432\pi$
$521$	5.80627	−	5.80627i	0.254377	−	0.254377i	0.822763	+	0.568385i	$0.192432\pi$
$522$		0			0
$523$	16.3083			0.713113			0.356556	−	0.934274i	$-0.383951\pi$
$523$	16.3083			0.713113			0.356556	+	0.934274i	$0.383951\pi$
$524$		0			0
$525$		−	42.8780i		−	1.87135i
$526$		0			0
$527$	1.19729	+	1.19729i	0.0521549	+	0.0521549i
$528$		0			0
$529$	−14.2794			−0.620842
$530$		0			0
$531$		−	10.0070i		−	0.434265i
$532$		0			0
$533$	−21.5067	−	24.1053i	−0.931558	−	1.04412i
$534$		0			0
$535$		−	49.5271i		−	2.14124i
$536$		0			0
$537$	−11.1021			−0.479092
$538$		0			0
$539$	4.19464	+	4.19464i	0.180676	+	0.180676i
$540$		0			0
$541$			6.45897i			0.277693i	0.990314	+	0.138846i	$0.0443394\pi$
$541$			6.45897i			0.277693i	−0.990314	+	0.138846i	$0.955661\pi$
$542$		0			0
$543$	−53.9666			−2.31593
$544$		0			0
$545$	−20.1236	+	20.1236i	−0.861999	+	0.861999i
$546$		0			0
$547$	23.6067	+	23.6067i	1.00935	+	1.00935i	0.999956	+	0.00939353i	$0.00299010\pi$
$547$	23.6067	+	23.6067i	1.00935	+	1.00935i	0.00939353	+	0.999956i	$0.497010\pi$
$548$		0			0
$549$	6.18406			0.263929
$550$		0			0
$551$	6.29488			0.268171
$552$		0			0
$553$		−	9.98907i		−	0.424779i
$554$		0			0
$555$	−9.50913	−	9.50913i	−0.403640	−	0.403640i
$556$		0			0
$557$	−14.0015	−	14.0015i	−0.593264	−	0.593264i	0.345248	−	0.938512i	$-0.387795\pi$
$557$	−14.0015	−	14.0015i	−0.593264	−	0.593264i	−0.938512	+	0.345248i	$0.887795\pi$
$558$		0			0
$559$	−10.5987	−	10.5987i	−0.448278	−	0.448278i
$560$		0			0
$561$	−34.6852	+	34.6852i	−1.46441	+	1.46441i
$562$		0			0
$563$	−7.83885	+	7.83885i	−0.330368	+	0.330368i	−0.852726	−	0.522358i	$-0.825052\pi$
$563$	−7.83885	+	7.83885i	−0.330368	+	0.330368i	0.522358	+	0.852726i	$0.325052\pi$
$564$		0			0
$565$			39.0898i			1.64452i
$566$		0			0
$567$	−20.3613	+	20.3613i	−0.855093	+	0.855093i
$568$		0			0
$569$			19.7014i			0.825927i	0.910748	+	0.412964i	$0.135506\pi$
$569$			19.7014i			0.825927i	−0.910748	+	0.412964i	$0.864494\pi$
$570$		0			0
$571$	6.75945	−	6.75945i	0.282874	−	0.282874i	−0.551380	−	0.834254i	$-0.685899\pi$
$571$	6.75945	−	6.75945i	0.282874	−	0.282874i	0.834254	+	0.551380i	$0.185899\pi$
$572$		0			0
$573$	−2.78198			−0.116219
$574$		0			0
$575$	38.4797			1.60471
$576$		0			0
$577$	−2.20792	+	2.20792i	−0.0919167	+	0.0919167i	−0.751570	−	0.659653i	$-0.770703\pi$
$577$	−2.20792	+	2.20792i	−0.0919167	+	0.0919167i	0.659653	+	0.751570i	$0.270703\pi$
$578$		0			0
$579$		−	10.3255i		−	0.429113i
$580$		0			0
$581$	−9.70925	+	9.70925i	−0.402808	+	0.402808i
$582$		0			0
$583$		−	27.0509i		−	1.12033i
$584$		0			0
$585$	118.583	−	118.583i	4.90278	−	4.90278i
$586$		0			0
$587$	27.9128	−	27.9128i	1.15208	−	1.15208i	0.165948	−	0.986134i	$-0.446931\pi$
$587$	27.9128	−	27.9128i	1.15208	−	1.15208i	0.986134	−	0.165948i	$-0.0530685\pi$
$588$		0			0
$589$	1.70605	+	1.70605i	0.0702965	+	0.0702965i
$590$		0			0
$591$	−24.5701	−	24.5701i	−1.01068	−	1.01068i
$592$		0			0
$593$	14.3036	+	14.3036i	0.587378	+	0.587378i	0.936921	−	0.349542i	$-0.113663\pi$
$593$	14.3036	+	14.3036i	0.587378	+	0.587378i	−0.349542	+	0.936921i	$0.613663\pi$
$594$		0			0
$595$		−	10.6703i		−	0.437439i
$596$		0			0
$597$	−62.2190			−2.54645
$598$		0			0
$599$	−6.71503			−0.274369			−0.137184	−	0.990546i	$-0.543805\pi$
$599$	−6.71503			−0.274369			−0.137184	+	0.990546i	$0.543805\pi$
$600$		0			0
$601$	32.9853	+	32.9853i	1.34550	+	1.34550i	0.890482	+	0.455018i	$0.150367\pi$
$601$	32.9853	+	32.9853i	1.34550	+	1.34550i	0.455018	+	0.890482i	$0.349633\pi$
$602$		0			0
$603$	−5.47144	+	5.47144i	−0.222814	+	0.222814i
$604$		0			0
$605$	102.716			4.17599
$606$		0			0
$607$		−	24.2536i		−	0.984424i	−0.870475	−	0.492212i	$-0.836188\pi$
$607$		−	24.2536i		−	0.984424i	0.870475	−	0.492212i	$-0.163812\pi$
$608$		0			0
$609$	−4.09058	−	4.09058i	−0.165759	−	0.165759i
$610$		0			0
$611$	41.5353			1.68034
$612$		0			0
$613$			1.38910i			0.0561052i	0.999606	+	0.0280526i	$0.00893059\pi$
$613$			1.38910i			0.0561052i	−0.999606	+	0.0280526i	$0.991069\pi$
$614$		0			0
$615$	−66.7599	+	59.5631i	−2.69202	+	2.40182i
$616$		0			0
$617$			44.3627i			1.78598i	0.450081	+	0.892988i	$0.351395\pi$
$617$			44.3627i			1.78598i	−0.450081	+	0.892988i	$0.648605\pi$
$618$		0			0
$619$	−19.6421			−0.789484			−0.394742	−	0.918792i	$-0.629166\pi$
$619$	−19.6421			−0.789484			−0.394742	+	0.918792i	$0.629166\pi$
$620$		0			0
$621$	−33.1752	−	33.1752i	−1.33128	−	1.33128i
$622$		0			0
$623$			7.15004i			0.286460i
$624$		0			0
$625$	79.6392			3.18557
$626$		0			0
$627$	−49.4237	+	49.4237i	−1.97379	+	1.97379i
$628$		0			0
$629$	−1.71015	−	1.71015i	−0.0681882	−	0.0681882i
$630$		0			0
$631$	18.3307			0.729734			0.364867	−	0.931060i	$-0.381114\pi$
$631$	18.3307			0.729734			0.364867	+	0.931060i	$0.381114\pi$
$632$		0			0
$633$	15.2918			0.607794
$634$		0			0
$635$		−	35.6385i		−	1.41427i
$636$		0			0
$637$	−3.56747	−	3.56747i	−0.141348	−	0.141348i
$638$		0			0
$639$	38.5119	+	38.5119i	1.52351	+	1.52351i
$640$		0			0
$641$	−0.253891	−	0.253891i	−0.0100281	−	0.0100281i	0.702075	−	0.712103i	$-0.252257\pi$
$641$	−0.253891	−	0.253891i	−0.0100281	−	0.0100281i	−0.712103	+	0.702075i	$0.752257\pi$
$642$		0			0
$643$	−28.2154	+	28.2154i	−1.11270	+	1.11270i	−0.119922	+	0.992783i	$0.538264\pi$
$643$	−28.2154	+	28.2154i	−1.11270	+	1.11270i	−0.992783	+	0.119922i	$0.961736\pi$
$644$		0			0
$645$	−29.3533	+	29.3533i	−1.15579	+	1.15579i
$646$		0			0
$647$		−	40.8997i		−	1.60793i	−0.594675	−	0.803966i	$-0.702719\pi$
$647$		−	40.8997i		−	1.60793i	0.594675	−	0.803966i	$-0.297281\pi$
$648$		0			0
$649$	−5.36215	+	5.36215i	−0.210483	+	0.210483i
$650$		0			0
$651$		−	2.21727i		−	0.0869018i
$652$		0			0
$653$	−27.1887	+	27.1887i	−1.06398	+	1.06398i	−0.0661686	+	0.997808i	$0.521078\pi$
$653$	−27.1887	+	27.1887i	−1.06398	+	1.06398i	−0.997808	+	0.0661686i	$0.978922\pi$
$654$		0			0
$655$	84.4084			3.29811
$656$		0			0
$657$	−71.4788			−2.78865
$658$		0			0
$659$	14.2022	−	14.2022i	0.553240	−	0.553240i	−0.374134	−	0.927375i	$-0.622060\pi$
$659$	14.2022	−	14.2022i	0.553240	−	0.553240i	0.927375	+	0.374134i	$0.122060\pi$
$660$		0			0
$661$			15.0450i			0.585182i	0.956238	+	0.292591i	$0.0945174\pi$
$661$			15.0450i			0.585182i	−0.956238	+	0.292591i	$0.905483\pi$
$662$		0			0
$663$	29.4992	−	29.4992i	1.14565	−	1.14565i
$664$		0			0
$665$		−	15.2043i		−	0.589598i
$666$		0			0
$667$	3.67098	−	3.67098i	0.142141	−	0.142141i
$668$		0			0
$669$	−11.5472	+	11.5472i	−0.446441	+	0.446441i
$670$		0			0
$671$	−3.31368	−	3.31368i	−0.127923	−	0.127923i
$672$		0			0
$673$	−1.78627	−	1.78627i	−0.0688558	−	0.0688558i	0.671840	−	0.740696i	$-0.265504\pi$
$673$	−1.78627	−	1.78627i	−0.0688558	−	0.0688558i	−0.740696	+	0.671840i	$0.765504\pi$
$674$		0			0
$675$	−146.385	−	146.385i	−5.63438	−	5.63438i
$676$		0			0
$677$			15.3842i			0.591263i	0.955302	+	0.295632i	$0.0955301\pi$
$677$			15.3842i			0.591263i	−0.955302	+	0.295632i	$0.904470\pi$
$678$		0			0
$679$	8.13990			0.312381
$680$		0			0
$681$	65.1638			2.49708
$682$		0			0
$683$	−12.9936	−	12.9936i	−0.497188	−	0.497188i	0.413374	−	0.910561i	$-0.364350\pi$
$683$	−12.9936	−	12.9936i	−0.497188	−	0.497188i	−0.910561	+	0.413374i	$0.864350\pi$
$684$		0			0
$685$	55.5603	−	55.5603i	2.12285	−	2.12285i
$686$		0			0
$687$	5.93514			0.226440
$688$		0			0
$689$			23.0063i			0.876471i
$690$		0			0
$691$	−5.47679	−	5.47679i	−0.208347	−	0.208347i	0.595218	−	0.803565i	$-0.297066\pi$
$691$	−5.47679	−	5.47679i	−0.208347	−	0.208347i	−0.803565	+	0.595218i	$0.797066\pi$
$692$		0			0
$693$	46.4373			1.76401
$694$		0			0
$695$			36.5385i			1.38599i
$696$		0			0
$697$	−12.0063	+	10.7120i	−0.454771	+	0.405746i
$698$		0			0
$699$		−	51.4942i		−	1.94769i
$700$		0			0
$701$	32.2431			1.21780			0.608902	−	0.793246i	$-0.291610\pi$
$701$	32.2431			1.21780			0.608902	+	0.793246i	$0.291610\pi$
$702$		0			0
$703$	−2.43683	−	2.43683i	−0.0919069	−	0.0919069i
$704$		0			0
$705$		−	115.033i		−	4.33238i
$706$		0			0
$707$	11.3871			0.428256
$708$		0			0
$709$	−1.52044	+	1.52044i	−0.0571012	+	0.0571012i	−0.735081	−	0.677980i	$-0.762856\pi$
$709$	−1.52044	+	1.52044i	−0.0571012	+	0.0571012i	0.677980	+	0.735081i	$0.262856\pi$
$710$		0			0
$711$	−55.2927	−	55.2927i	−2.07364	−	2.07364i
$712$		0			0
$713$	1.98983			0.0745198
$714$		0			0
$715$	−127.083			−4.75263
$716$		0			0
$717$		−	29.7281i		−	1.11022i
$718$		0			0
$719$	−20.5352	−	20.5352i	−0.765833	−	0.765833i	0.211537	−	0.977370i	$-0.432153\pi$
$719$	−20.5352	−	20.5352i	−0.765833	−	0.765833i	−0.977370	+	0.211537i	$0.932153\pi$
$720$		0			0
$721$	7.32746	+	7.32746i	0.272889	+	0.272889i
$722$		0			0
$723$	32.4154	+	32.4154i	1.20554	+	1.20554i
$724$		0			0
$725$	16.1982	−	16.1982i	0.601585	−	0.601585i
$726$		0			0
$727$	−22.6657	+	22.6657i	−0.840625	+	0.840625i	−0.988940	−	0.148315i	$-0.952615\pi$
$727$	−22.6657	+	22.6657i	−0.840625	+	0.840625i	0.148315	+	0.988940i	$0.452615\pi$
$728$		0			0
$729$			68.5736i			2.53976i
$730$		0			0
$731$	−5.27899	+	5.27899i	−0.195251	+	0.195251i
$732$		0			0
$733$			35.9192i			1.32671i	0.748306	+	0.663353i	$0.230867\pi$
$733$			35.9192i			1.32671i	−0.748306	+	0.663353i	$0.769133\pi$
$734$		0			0
$735$	−9.88017	+	9.88017i	−0.364435	+	0.364435i
$736$		0			0
$737$	5.86365			0.215990
$738$		0			0
$739$	11.4531			0.421309			0.210655	−	0.977561i	$-0.432440\pi$
$739$	11.4531			0.421309			0.210655	+	0.977561i	$0.432440\pi$
$740$		0			0
$741$	42.0340	−	42.0340i	1.54416	−	1.54416i
$742$		0			0
$743$			11.6759i			0.428348i	0.976796	+	0.214174i	$0.0687060\pi$
$743$			11.6759i			0.428348i	−0.976796	+	0.214174i	$0.931294\pi$
$744$		0			0
$745$	18.2497	−	18.2497i	0.668617	−	0.668617i
$746$		0			0
$747$			107.488i			3.93277i
$748$		0			0
$749$	−8.24756	+	8.24756i	−0.301359	+	0.301359i
$750$		0			0
$751$	−2.63679	+	2.63679i	−0.0962178	+	0.0962178i	−0.753577	−	0.657359i	$-0.771673\pi$
$751$	−2.63679	+	2.63679i	−0.0962178	+	0.0962178i	0.657359	+	0.753577i	$0.271673\pi$
$752$		0			0
$753$	26.8053	+	26.8053i	0.976841	+	0.976841i
$754$		0			0
$755$	−43.4616	−	43.4616i	−1.58173	−	1.58173i
$756$		0			0
$757$	−24.1160	−	24.1160i	−0.876512	−	0.876512i	0.116659	−	0.993172i	$-0.462781\pi$
$757$	−24.1160	−	24.1160i	−0.876512	−	0.876512i	−0.993172	+	0.116659i	$0.962781\pi$
$758$		0			0
$759$			57.6448i			2.09237i
$760$		0			0
$761$	−21.8556			−0.792263			−0.396132	−	0.918194i	$-0.629648\pi$
$761$	−21.8556			−0.792263			−0.396132	+	0.918194i	$0.629648\pi$
$762$		0			0
$763$	6.70220			0.242636
$764$		0			0
$765$	−59.0634	−	59.0634i	−2.13544	−	2.13544i
$766$		0			0
$767$	4.56042	−	4.56042i	0.164667	−	0.164667i
$768$		0			0
$769$	−3.19153			−0.115089			−0.0575447	−	0.998343i	$-0.518327\pi$
$769$	−3.19153			−0.115089			−0.0575447	+	0.998343i	$0.518327\pi$
$770$		0			0
$771$		−	94.7010i		−	3.41057i
$772$		0			0
$773$	12.0984	+	12.0984i	0.435147	+	0.435147i	0.890375	−	0.455228i	$-0.150442\pi$
$773$	12.0984	+	12.0984i	0.435147	+	0.435147i	−0.455228	+	0.890375i	$0.650442\pi$
$774$		0			0
$775$	8.78011			0.315391
$776$		0			0
$777$			3.16704i			0.113617i
$778$		0			0
$779$	−17.1081	+	15.2638i	−0.612960	+	0.546882i
$780$		0			0
$781$		−	41.2726i		−	1.47685i
$782$		0			0
$783$	−27.9305			−0.998154
$784$		0			0
$785$	−54.9106	−	54.9106i	−1.95984	−	1.95984i
$786$		0			0
$787$			51.3175i			1.82927i	0.404280	+	0.914635i	$0.367522\pi$
$787$			51.3175i			1.82927i	−0.404280	+	0.914635i	$0.632478\pi$
$788$		0			0
$789$	91.7003			3.26462
$790$		0			0
$791$	6.50948	−	6.50948i	0.231450	−	0.231450i
$792$		0			0
$793$	2.81823	+	2.81823i	0.100078	+	0.100078i
$794$		0			0
$795$	63.7163			2.25979
$796$		0			0
$797$	14.1277			0.500429			0.250215	−	0.968190i	$-0.419499\pi$
$797$	14.1277			0.500429			0.250215	+	0.968190i	$0.419499\pi$
$798$		0			0
$799$		−	20.6878i		−	0.731883i
$800$		0			0
$801$	39.5777	+	39.5777i	1.39841	+	1.39841i
$802$		0			0
$803$	38.3013	+	38.3013i	1.35162	+	1.35162i
$804$		0			0
$805$	−8.86669	−	8.86669i	−0.312510	−	0.312510i
$806$		0			0
$807$	−15.9890	+	15.9890i	−0.562838	+	0.562838i
$808$		0			0
$809$	2.68905	−	2.68905i	0.0945420	−	0.0945420i	−0.658254	−	0.752796i	$-0.728705\pi$
$809$	2.68905	−	2.68905i	0.0945420	−	0.0945420i	0.752796	+	0.658254i	$0.228705\pi$
$810$		0			0
$811$			23.3844i			0.821139i	0.911829	+	0.410569i	$0.134670\pi$
$811$			23.3844i			0.821139i	−0.911829	+	0.410569i	$0.865330\pi$
$812$		0			0
$813$	−45.7493	+	45.7493i	−1.60450	+	1.60450i
$814$		0			0
$815$		−	103.873i		−	3.63851i
$816$		0			0
$817$	−7.52215	+	7.52215i	−0.263167	+	0.263167i
$818$		0			0
$819$	−39.4942			−1.38004
$820$		0			0
$821$	0.451175			0.0157461			0.00787305	−	0.999969i	$-0.497494\pi$
$821$	0.451175			0.0157461			0.00787305	+	0.999969i	$0.497494\pi$
$822$		0			0
$823$	24.9031	−	24.9031i	0.868067	−	0.868067i	−0.124191	−	0.992258i	$-0.539634\pi$
$823$	24.9031	−	24.9031i	0.868067	−	0.868067i	0.992258	+	0.124191i	$0.0396336\pi$
$824$		0			0
$825$			254.357i			8.85557i
$826$		0			0
$827$	−1.23323	+	1.23323i	−0.0428838	+	0.0428838i	−0.728223	−	0.685340i	$-0.759654\pi$
$827$	−1.23323	+	1.23323i	−0.0428838	+	0.0428838i	0.685340	+	0.728223i	$0.259654\pi$
$828$		0			0
$829$			31.1302i			1.08120i	0.841281	+	0.540598i	$0.181802\pi$
$829$			31.1302i			1.08120i	−0.841281	+	0.540598i	$0.818198\pi$
$830$		0			0
$831$	2.73958	−	2.73958i	0.0950350	−	0.0950350i
$832$		0			0
$833$	−1.77688	+	1.77688i	−0.0615652	+	0.0615652i
$834$		0			0
$835$	21.3356	+	21.3356i	0.738348	+	0.738348i
$836$		0			0
$837$	−7.56977	−	7.56977i	−0.261650	−	0.261650i
$838$		0			0
$839$	20.9126	+	20.9126i	0.721983	+	0.721983i	0.969009	−	0.247026i	$-0.0794532\pi$
$839$	20.9126	+	20.9126i	0.721983	+	0.721983i	−0.247026	+	0.969009i	$0.579453\pi$
$840$		0			0
$841$			25.9094i			0.893427i
$842$		0			0
$843$	73.6103			2.53527
$844$		0			0
$845$	52.8811			1.81917
$846$		0			0
$847$	−17.1049	−	17.1049i	−0.587731	−	0.587731i
$848$		0			0
$849$	3.37292	−	3.37292i	0.115758	−	0.115758i
$850$		0			0
$851$	−2.84217			−0.0974285
$852$		0			0
$853$			21.9666i			0.752120i	0.926595	+	0.376060i	$0.122721\pi$
$853$			21.9666i			0.752120i	−0.926595	+	0.376060i	$0.877279\pi$
$854$		0			0
$855$	−84.1607	−	84.1607i	−2.87824	−	2.87824i
$856$		0			0
$857$	−3.74412			−0.127897			−0.0639483	−	0.997953i	$-0.520369\pi$
$857$	−3.74412			−0.127897			−0.0639483	+	0.997953i	$0.520369\pi$
$858$		0			0
$859$		−	27.4281i		−	0.935835i	−0.883772	−	0.467917i	$-0.845005\pi$
$859$		−	27.4281i		−	0.935835i	0.883772	−	0.467917i	$-0.154995\pi$
$860$		0			0
$861$	21.0361	+	1.19846i	0.716908	+	0.0408433i
$862$		0			0
$863$		−	23.6965i		−	0.806638i	−0.915059	−	0.403319i	$-0.867856\pi$
$863$		−	23.6965i		−	0.806638i	0.915059	−	0.403319i	$-0.132144\pi$
$864$		0			0
$865$	30.2099			1.02717
$866$		0			0
$867$	24.8629	+	24.8629i	0.844389	+	0.844389i
$868$		0			0
$869$			59.2563i			2.01013i
$870$		0			0
$871$	−4.98694			−0.168976
$872$		0			0
$873$	45.0570	−	45.0570i	1.52495	−	1.52495i
$874$		0			0
$875$	−24.1115	−	24.1115i	−0.815118	−	0.815118i
$876$		0			0
$877$	31.5991			1.06702			0.533512	−	0.845792i	$-0.320872\pi$
$877$	31.5991			1.06702			0.533512	+	0.845792i	$0.320872\pi$
$878$		0			0
$879$	3.78459			0.127651
$880$		0			0
$881$		−	5.87559i		−	0.197954i	−0.995090	−	0.0989769i	$-0.968443\pi$
$881$		−	5.87559i		−	0.197954i	0.995090	−	0.0989769i	$-0.0315570\pi$
$882$		0			0
$883$	13.2928	+	13.2928i	0.447339	+	0.447339i	0.894469	−	0.447130i	$-0.147554\pi$
$883$	13.2928	+	13.2928i	0.447339	+	0.447339i	−0.447130	+	0.894469i	$0.647554\pi$
$884$		0			0
$885$	−12.6302	−	12.6302i	−0.424558	−	0.424558i
$886$		0			0
$887$	34.6734	+	34.6734i	1.16422	+	1.16422i	0.983542	+	0.180678i	$0.0578291\pi$
$887$	34.6734	+	34.6734i	1.16422	+	1.16422i	0.180678	+	0.983542i	$0.442171\pi$
$888$		0			0
$889$	−5.93475	+	5.93475i	−0.199045	+	0.199045i
$890$		0			0
$891$	120.785	−	120.785i	4.04646	−	4.04646i
$892$		0			0
$893$		−	29.4785i		−	0.986461i
$894$		0			0
$895$	−10.1302	+	10.1302i	−0.338615	+	0.338615i
$896$		0			0
$897$		−	49.0260i		−	1.63693i
$898$		0			0
$899$	0.837627	−	0.837627i	0.0279364	−	0.0279364i
$900$		0			0
$901$	11.4589			0.381753
$902$		0			0
$903$	9.77619			0.325331
$904$		0			0
$905$	−49.2420	+	49.2420i	−1.63686	+	1.63686i
$906$		0			0
$907$			11.8740i			0.394268i	0.980377	+	0.197134i	$0.0631634\pi$
$907$			11.8740i			0.394268i	−0.980377	+	0.197134i	$0.936837\pi$
$908$		0			0
$909$	63.0313	−	63.0313i	2.09062	−	2.09062i
$910$		0			0
$911$			42.6779i			1.41398i	0.707223	+	0.706991i	$0.249948\pi$
$911$			42.6779i			1.41398i	−0.707223	+	0.706991i	$0.750052\pi$
$912$		0			0
$913$	57.5964	−	57.5964i	1.90616	−	1.90616i
$914$		0			0
$915$	7.80513	−	7.80513i	0.258030	−	0.258030i
$916$		0			0
$917$	−14.0562	−	14.0562i	−0.464177	−	0.464177i
$918$		0			0
$919$	−5.03181	−	5.03181i	−0.165984	−	0.165984i	0.619228	−	0.785212i	$-0.287446\pi$
$919$	−5.03181	−	5.03181i	−0.165984	−	0.165984i	−0.785212	+	0.619228i	$0.787446\pi$
$920$		0			0
$921$	9.57484	+	9.57484i	0.315502	+	0.315502i
$922$		0			0
$923$			35.1017i			1.15539i
$924$		0			0
$925$	−12.5411			−0.412347
$926$		0			0
$927$	81.1197			2.66432
$928$		0			0
$929$	39.0684	+	39.0684i	1.28179	+	1.28179i	0.939646	+	0.342148i	$0.111155\pi$
$929$	39.0684	+	39.0684i	1.28179	+	1.28179i	0.342148	+	0.939646i	$0.388845\pi$
$930$		0			0
$931$	−2.53191	+	2.53191i	−0.0829801	+	0.0829801i
$932$		0			0
$933$	54.2821			1.77712
$934$		0			0
$935$			63.2973i			2.07004i
$936$		0			0
$937$	−4.15821	−	4.15821i	−0.135843	−	0.135843i	0.635916	−	0.771759i	$-0.280623\pi$
$937$	−4.15821	−	4.15821i	−0.135843	−	0.135843i	−0.771759	+	0.635916i	$0.780623\pi$
$938$		0			0
$939$	27.3154			0.891405
$940$		0			0
$941$		−	25.6027i		−	0.834626i	−0.908763	−	0.417313i	$-0.862972\pi$
$941$		−	25.6027i		−	0.834626i	0.908763	−	0.417313i	$-0.137028\pi$
$942$		0			0
$943$	−1.07552	+	18.8783i	−0.0350239	+	0.614761i
$944$		0			0
$945$			67.4618i			2.19453i
$946$		0			0
$947$	28.1201			0.913780			0.456890	−	0.889523i	$-0.348963\pi$
$947$	28.1201			0.913780			0.456890	+	0.889523i	$0.348963\pi$
$948$		0			0
$949$	−32.5746	−	32.5746i	−1.05742	−	1.05742i
$950$		0			0
$951$		−	11.3937i		−	0.369465i
$952$		0			0
$953$	−37.8099			−1.22478			−0.612392	−	0.790554i	$-0.709793\pi$
$953$	−37.8099			−1.22478			−0.612392	+	0.790554i	$0.709793\pi$
$954$		0			0
$955$	−2.53843	+	2.53843i	−0.0821417	+	0.0821417i
$956$		0			0
$957$	24.2658	+	24.2658i	0.784402	+	0.784402i
$958$		0			0
$959$	−18.5045			−0.597541
$960$		0			0
$961$	−30.5460			−0.985354
$962$		0			0
$963$			91.3058i			2.94229i
$964$		0			0
$965$	−9.42154	−	9.42154i	−0.303290	−	0.303290i
$966$		0			0
$967$	−19.6164	−	19.6164i	−0.630821	−	0.630821i	0.317453	−	0.948274i	$-0.397173\pi$
$967$	−19.6164	−	19.6164i	−0.630821	−	0.630821i	−0.948274	+	0.317453i	$0.897173\pi$
$968$		0			0
$969$	−20.9362	−	20.9362i	−0.672569	−	0.672569i
$970$		0			0
$971$	−24.2959	+	24.2959i	−0.779691	+	0.779691i	−0.979778	−	0.200087i	$-0.935877\pi$
$971$	−24.2959	+	24.2959i	−0.779691	+	0.779691i	0.200087	+	0.979778i	$0.435877\pi$
$972$		0			0
$973$	6.08462	−	6.08462i	0.195064	−	0.195064i
$974$		0			0
$975$		−	216.326i		−	6.92799i
$976$		0			0
$977$	−20.0024	+	20.0024i	−0.639933	+	0.639933i	−0.950539	−	0.310606i	$-0.899468\pi$
$977$	−20.0024	+	20.0024i	−0.639933	+	0.639933i	0.310606	+	0.950539i	$0.399468\pi$
$978$		0			0
$979$		−	42.4148i		−	1.35558i
$980$		0			0
$981$	37.0988	−	37.0988i	1.18447	−	1.18447i
$982$		0			0
$983$	−27.5449			−0.878545			−0.439273	−	0.898354i	$-0.644764\pi$
$983$	−27.5449			−0.878545			−0.439273	+	0.898354i	$0.644764\pi$
$984$		0			0
$985$	−44.8382			−1.42867
$986$		0			0
$987$	−19.1559	+	19.1559i	−0.609740	+	0.609740i
$988$		0			0
$989$			8.77338i			0.278977i
$990$		0			0
$991$	−25.4190	+	25.4190i	−0.807463	+	0.807463i	−0.984249	−	0.176787i	$-0.943430\pi$
$991$	−25.4190	+	25.4190i	−0.807463	+	0.807463i	0.176787	+	0.984249i	$0.443430\pi$
$992$		0			0
$993$			32.8054i			1.04105i
$994$		0			0
$995$	−56.7720	+	56.7720i	−1.79979	+	1.79979i
$996$		0			0
$997$	−18.2025	+	18.2025i	−0.576478	+	0.576478i	−0.933931	−	0.357453i	$-0.883645\pi$
$997$	−18.2025	+	18.2025i	−0.576478	+	0.576478i	0.357453	+	0.933931i	$0.383645\pi$
$998$		0			0
$999$	10.8123	+	10.8123i	0.342085	+	0.342085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.729.2	yes	36
41.9	even	4	inner	1148.2.k.b.337.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.2	✓	36	41.9	even	4	inner
1148.2.k.b.729.2	yes	36	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-2.32681 + 2.32681i) q^{3} +4.24622i q^{5} +(0.707107 - 0.707107i) q^{7} -7.82813i q^{9} +O(q^{10})\)	\(q+(-2.32681 + 2.32681i) q^{3} +4.24622i q^{5} +(0.707107 - 0.707107i) q^{7} -7.82813i q^{9} +(-4.19464 + 4.19464i) q^{11} +(3.56747 - 3.56747i) q^{13} +(-9.88017 - 9.88017i) q^{15} +(-1.77688 - 1.77688i) q^{17} +(-2.53191 - 2.53191i) q^{19} +3.29061i q^{21} -2.95307 q^{23} -13.0304 q^{25} +(11.2341 + 11.2341i) q^{27} +(-1.24311 + 1.24311i) q^{29} -0.673818 q^{31} -19.5203i q^{33} +(3.00253 + 3.00253i) q^{35} +0.962447 q^{37} +16.6017i q^{39} +(0.364205 - 6.39276i) q^{41} -2.97093i q^{43} +33.2399 q^{45} +(5.82139 + 5.82139i) q^{47} -1.00000i q^{49} +8.26894 q^{51} +(-3.22446 + 3.22446i) q^{53} +(-17.8114 - 17.8114i) q^{55} +11.7826 q^{57} +1.27834 q^{59} +0.789980i q^{61} +(-5.53532 - 5.53532i) q^{63} +(15.1483 + 15.1483i) q^{65} +(-0.698946 - 0.698946i) q^{67} +(6.87125 - 6.87125i) q^{69} +(-4.91969 + 4.91969i) q^{71} -9.13102i q^{73} +(30.3193 - 30.3193i) q^{75} +5.93211i q^{77} +(7.06334 - 7.06334i) q^{79} -28.7952 q^{81} -13.7310 q^{83} +(7.54502 - 7.54502i) q^{85} -5.78496i q^{87} +(-5.05584 + 5.05584i) q^{89} -5.04517i q^{91} +(1.56785 - 1.56785i) q^{93} +(10.7511 - 10.7511i) q^{95} +(5.75578 + 5.75578i) q^{97} +(32.8361 + 32.8361i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

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