LMFDB - Embedded newform 1408.2.i.b.351.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1408,2,Mod(351,1408)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1408, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("1408.351");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1408 = 2^{7} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1408.i (of order $4$, degree $2$, not 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:	$11.2429366046$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 176)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			351.19
Character	$\chi$	$=$	1408.351
Dual form			1408.2.i.b.1055.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82463 - 1.82463i) q^{3} +(2.57632 - 2.57632i) q^{5} -2.30642i q^{7} -3.65855i q^{9} +O(q^{10})$	\(q+(1.82463 - 1.82463i) q^{3} +(2.57632 - 2.57632i) q^{5} -2.30642i q^{7} -3.65855i q^{9} +(-2.61242 + 2.04334i) q^{11} +(2.25903 - 2.25903i) q^{13} -9.40167i q^{15} +1.40277i q^{17} +(5.03186 + 5.03186i) q^{19} +(-4.20837 - 4.20837i) q^{21} -3.12111 q^{23} -8.27488i q^{25} +(-1.20161 - 1.20161i) q^{27} +(0.452394 - 0.452394i) q^{29} +3.35465i q^{31} +(-1.03837 + 8.49505i) q^{33} +(-5.94209 - 5.94209i) q^{35} +(3.56280 - 3.56280i) q^{37} -8.24377i q^{39} -10.6795 q^{41} +(1.58250 - 1.58250i) q^{43} +(-9.42561 - 9.42561i) q^{45} +7.74416i q^{47} +1.68042 q^{49} +(2.55954 + 2.55954i) q^{51} +(3.56645 - 3.56645i) q^{53} +(-1.46614 + 11.9948i) q^{55} +18.3626 q^{57} +(2.93608 + 2.93608i) q^{59} +(-6.88773 + 6.88773i) q^{61} -8.43816 q^{63} -11.6400i q^{65} +(-6.98769 + 6.98769i) q^{67} +(-5.69487 + 5.69487i) q^{69} -2.69084 q^{71} +2.27278 q^{73} +(-15.0986 - 15.0986i) q^{75} +(4.71280 + 6.02535i) q^{77} -10.2158 q^{79} +6.59065 q^{81} +(-1.15150 - 1.15150i) q^{83} +(3.61399 + 3.61399i) q^{85} -1.65090i q^{87} +16.8749i q^{89} +(-5.21027 - 5.21027i) q^{91} +(6.12099 + 6.12099i) q^{93} +25.9274 q^{95} +6.48153 q^{97} +(7.47567 + 9.55769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5	$ 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1408\mathbb{Z}\right)^\times$.

$n$	$133$	$639$	$1025$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.82463	−	1.82463i	1.05345	−	1.05345i	0.0549624	−	0.998488i	$-0.482496\pi$
$3$	1.82463	−	1.82463i	1.05345	−	1.05345i	0.998488	−	0.0549624i	$-0.0175039\pi$
$4$		0			0
$5$	2.57632	−	2.57632i	1.15217	−	1.15217i	0.166049	−	0.986117i	$-0.446899\pi$
$5$	2.57632	−	2.57632i	1.15217	−	1.15217i	0.986117	−	0.166049i	$-0.0531010\pi$
$6$		0			0
$7$		−	2.30642i		−	0.871745i	−0.900008	−	0.435873i	$-0.856440\pi$
$7$		−	2.30642i		−	0.871745i	0.900008	−	0.435873i	$-0.143560\pi$
$8$		0			0
$9$		−	3.65855i		−	1.21952i
$10$		0			0
$11$	−2.61242	+	2.04334i	−0.787675	+	0.616090i
$11$	−2.61242	+	2.04334i	−0.787675	+	0.616090i
$12$		0			0
$13$	2.25903	−	2.25903i	0.626541	−	0.626541i	−0.320655	−	0.947196i	$-0.603903\pi$
$13$	2.25903	−	2.25903i	0.626541	−	0.626541i	0.947196	+	0.320655i	$0.103903\pi$
$14$		0			0
$15$		−	9.40167i		−	2.42750i
$16$		0			0
$17$			1.40277i			0.340222i	0.985425	+	0.170111i	$0.0544127\pi$
$17$			1.40277i			0.340222i	−0.985425	+	0.170111i	$0.945587\pi$
$18$		0			0
$19$	5.03186	+	5.03186i	1.15439	+	1.15439i	0.985663	+	0.168724i	$0.0539648\pi$
$19$	5.03186	+	5.03186i	1.15439	+	1.15439i	0.168724	+	0.985663i	$0.446035\pi$
$20$		0			0
$21$	−4.20837	−	4.20837i	−0.918341	−	0.918341i
$22$		0			0
$23$	−3.12111			−0.650796			−0.325398	−	0.945577i	$-0.605498\pi$
$23$	−3.12111			−0.650796			−0.325398	+	0.945577i	$0.605498\pi$
$24$		0			0
$25$		−	8.27488i		−	1.65498i
$26$		0			0
$27$	−1.20161	−	1.20161i	−0.231251	−	0.231251i
$28$		0			0
$29$	0.452394	−	0.452394i	0.0840074	−	0.0840074i	−0.663854	−	0.747862i	$-0.731081\pi$
$29$	0.452394	−	0.452394i	0.0840074	−	0.0840074i	0.747862	+	0.663854i	$0.231081\pi$
$30$		0			0
$31$			3.35465i			0.602513i	0.953543	+	0.301256i	$0.0974060\pi$
$31$			3.35465i			0.602513i	−0.953543	+	0.301256i	$0.902594\pi$
$32$		0			0
$33$	−1.03837	+	8.49505i	−0.180756	+	1.47880i
$34$		0			0
$35$	−5.94209	−	5.94209i	−1.00440	−	1.00440i
$36$		0			0
$37$	3.56280	−	3.56280i	0.585721	−	0.585721i	−0.350749	−	0.936470i	$-0.614073\pi$
$37$	3.56280	−	3.56280i	0.585721	−	0.585721i	0.936470	+	0.350749i	$0.114073\pi$
$38$		0			0
$39$		−	8.24377i		−	1.32006i
$40$		0			0
$41$	−10.6795			−1.66786			−0.833930	−	0.551870i	$-0.813915\pi$
$41$	−10.6795			−1.66786			−0.833930	+	0.551870i	$0.813915\pi$
$42$		0			0
$43$	1.58250	−	1.58250i	0.241329	−	0.241329i	−0.576071	−	0.817400i	$-0.695415\pi$
$43$	1.58250	−	1.58250i	0.241329	−	0.241329i	0.817400	+	0.576071i	$0.195415\pi$
$44$		0			0
$45$	−9.42561	−	9.42561i	−1.40509	−	1.40509i
$46$		0			0
$47$			7.74416i			1.12960i	0.825227	+	0.564801i	$0.191047\pi$
$47$			7.74416i			1.12960i	−0.825227	+	0.564801i	$0.808953\pi$
$48$		0			0
$49$	1.68042			0.240060
$50$		0			0
$51$	2.55954	+	2.55954i	0.358408	+	0.358408i
$52$		0			0
$53$	3.56645	−	3.56645i	0.489890	−	0.489890i	−0.418381	−	0.908271i	$-0.637402\pi$
$53$	3.56645	−	3.56645i	0.489890	−	0.489890i	0.908271	+	0.418381i	$0.137402\pi$
$54$		0			0
$55$	−1.46614	+	11.9948i	−0.197695	+	1.61737i
$56$		0			0
$57$	18.3626			2.43218
$58$		0			0
$59$	2.93608	+	2.93608i	0.382245	+	0.382245i	0.871910	−	0.489666i	$-0.162881\pi$
$59$	2.93608	+	2.93608i	0.382245	+	0.382245i	−0.489666	+	0.871910i	$0.662881\pi$
$60$		0			0
$61$	−6.88773	+	6.88773i	−0.881884	+	0.881884i	−0.993726	−	0.111842i	$-0.964325\pi$
$61$	−6.88773	+	6.88773i	−0.881884	+	0.881884i	0.111842	+	0.993726i	$0.464325\pi$
$62$		0			0
$63$	−8.43816			−1.06311
$64$		0			0
$65$		−	11.6400i		−	1.44376i
$66$		0			0
$67$	−6.98769	+	6.98769i	−0.853682	+	0.853682i	−0.990585	−	0.136902i	$-0.956285\pi$
$67$	−6.98769	+	6.98769i	−0.853682	+	0.853682i	0.136902	+	0.990585i	$0.456285\pi$
$68$		0			0
$69$	−5.69487	+	5.69487i	−0.685581	+	0.685581i
$70$		0			0
$71$	−2.69084			−0.319343			−0.159672	−	0.987170i	$-0.551044\pi$
$71$	−2.69084			−0.319343			−0.159672	+	0.987170i	$0.551044\pi$
$72$		0			0
$73$	2.27278			0.266009			0.133004	−	0.991115i	$-0.457538\pi$
$73$	2.27278			0.266009			0.133004	+	0.991115i	$0.457538\pi$
$74$		0			0
$75$	−15.0986	−	15.0986i	−1.74344	−	1.74344i
$76$		0			0
$77$	4.71280	+	6.02535i	0.537074	+	0.686652i
$78$		0			0
$79$	−10.2158			−1.14936			−0.574681	−	0.818377i	$-0.694874\pi$
$79$	−10.2158			−1.14936			−0.574681	+	0.818377i	$0.694874\pi$
$80$		0			0
$81$	6.59065			0.732295
$82$		0			0
$83$	−1.15150	−	1.15150i	−0.126393	−	0.126393i	0.641080	−	0.767474i	$-0.278486\pi$
$83$	−1.15150	−	1.15150i	−0.126393	−	0.126393i	−0.767474	+	0.641080i	$0.778486\pi$
$84$		0			0
$85$	3.61399	+	3.61399i	0.391993	+	0.391993i
$86$		0			0
$87$		−	1.65090i		−	0.176995i
$88$		0			0
$89$			16.8749i			1.78873i	0.447336	+	0.894366i	$0.352373\pi$
$89$			16.8749i			1.78873i	−0.447336	+	0.894366i	$0.647627\pi$
$90$		0			0
$91$	−5.21027	−	5.21027i	−0.546184	−	0.546184i
$92$		0			0
$93$	6.12099	+	6.12099i	0.634717	+	0.634717i
$94$		0			0
$95$	25.9274			2.66009
$96$		0			0
$97$	6.48153			0.658100			0.329050	−	0.944313i	$-0.393272\pi$
$97$	6.48153			0.658100			0.329050	+	0.944313i	$0.393272\pi$
$98$		0			0
$99$	7.47567	+	9.55769i	0.751333	+	0.960584i
$100$		0			0
$101$	6.01839	+	6.01839i	0.598852	+	0.598852i	0.940007	−	0.341155i	$-0.110818\pi$
$101$	6.01839	+	6.01839i	0.598852	+	0.598852i	−0.341155	+	0.940007i	$0.610818\pi$
$102$		0			0
$103$	−18.1047			−1.78391			−0.891953	−	0.452128i	$-0.850665\pi$
$103$	−18.1047			−1.78391			−0.891953	+	0.452128i	$0.850665\pi$
$104$		0			0
$105$	−21.6842			−2.11616
$106$		0			0
$107$	4.81575	−	4.81575i	0.465556	−	0.465556i	−0.434915	−	0.900471i	$-0.643222\pi$
$107$	4.81575	−	4.81575i	0.465556	−	0.465556i	0.900471	+	0.434915i	$0.143222\pi$
$108$		0			0
$109$	10.2051	−	10.2051i	0.977474	−	0.977474i	−0.0222774	−	0.999752i	$-0.507092\pi$
$109$	10.2051	−	10.2051i	0.977474	−	0.977474i	0.999752	+	0.0222774i	$0.00709170\pi$
$110$		0			0
$111$		−	13.0016i		−	1.23406i
$112$		0			0
$113$	−1.51861			−0.142859			−0.0714294	−	0.997446i	$-0.522756\pi$
$113$	−1.51861			−0.142859			−0.0714294	+	0.997446i	$0.522756\pi$
$114$		0			0
$115$	−8.04098	+	8.04098i	−0.749825	+	0.749825i
$116$		0			0
$117$	−8.26476	−	8.26476i	−0.764078	−	0.764078i
$118$		0			0
$119$	3.23538			0.296587
$120$		0			0
$121$	2.64952	−	10.6761i	0.240865	−	0.970559i
$122$		0			0
$123$	−19.4862	+	19.4862i	−1.75701	+	1.75701i
$124$		0			0
$125$	−8.43714	−	8.43714i	−0.754641	−	0.754641i
$126$		0			0
$127$	5.94078			0.527159			0.263579	−	0.964638i	$-0.415097\pi$
$127$	5.94078			0.527159			0.263579	+	0.964638i	$0.415097\pi$
$128$		0			0
$129$		−	5.77495i		−	0.508456i
$130$		0			0
$131$	−11.1164	−	11.1164i	−0.971246	−	0.971246i	0.0283520	−	0.999598i	$-0.490974\pi$
$131$	−11.1164	−	11.1164i	−0.971246	−	0.971246i	−0.999598	+	0.0283520i	$0.990974\pi$
$132$		0			0
$133$	11.6056	−	11.6056i	1.00633	−	1.00633i
$134$		0			0
$135$	−6.19149			−0.532879
$136$		0			0
$137$		−	5.12979i		−	0.438268i	−0.975695	−	0.219134i	$-0.929677\pi$
$137$		−	5.12979i		−	0.438268i	0.975695	−	0.219134i	$-0.0703231\pi$
$138$		0			0
$139$	5.80600	−	5.80600i	0.492458	−	0.492458i	−0.416622	−	0.909080i	$-0.636786\pi$
$139$	5.80600	−	5.80600i	0.492458	−	0.492458i	0.909080	+	0.416622i	$0.136786\pi$
$140$		0			0
$141$	14.1302	+	14.1302i	1.18998	+	1.18998i
$142$		0			0
$143$	−1.28557	+	10.5175i	−0.107505	+	0.879517i
$144$		0			0
$145$		−	2.33102i		−	0.193581i
$146$		0			0
$147$	3.06615	−	3.06615i	0.252891	−	0.252891i
$148$		0			0
$149$	−9.18535	−	9.18535i	−0.752493	−	0.752493i	0.222451	−	0.974944i	$-0.428594\pi$
$149$	−9.18535	−	9.18535i	−0.752493	−	0.752493i	−0.974944	+	0.222451i	$0.928594\pi$
$150$		0			0
$151$		−	3.68858i		−	0.300173i	−0.988673	−	0.150086i	$-0.952045\pi$
$151$		−	3.68858i		−	0.300173i	0.988673	−	0.150086i	$-0.0479552\pi$
$152$		0			0
$153$	5.13212			0.414907
$154$		0			0
$155$	8.64266	+	8.64266i	0.694195	+	0.694195i
$156$		0			0
$157$	−3.07918	−	3.07918i	−0.245746	−	0.245746i	0.573476	−	0.819222i	$-0.305594\pi$
$157$	−3.07918	−	3.07918i	−0.245746	−	0.245746i	−0.819222	+	0.573476i	$0.805594\pi$
$158$		0			0
$159$		−	13.0149i		−	1.03215i
$160$		0			0
$161$			7.19859i			0.567328i
$162$		0			0
$163$	8.86782	−	8.86782i	0.694581	−	0.694581i	−0.268655	−	0.963236i	$-0.586579\pi$
$163$	8.86782	−	8.86782i	0.694581	−	0.694581i	0.963236	+	0.268655i	$0.0865793\pi$
$164$		0			0
$165$	19.2108	+	24.5612i	1.49556	+	1.91208i
$166$		0			0
$167$			9.21961i			0.713435i	0.934212	+	0.356718i	$0.116104\pi$
$167$			9.21961i			0.713435i	−0.934212	+	0.356718i	$0.883896\pi$
$168$		0			0
$169$			2.79360i			0.214893i
$170$		0			0
$171$	18.4093	−	18.4093i	1.40780	−	1.40780i
$172$		0			0
$173$	5.28581	−	5.28581i	0.401873	−	0.401873i	−0.477020	−	0.878892i	$-0.658283\pi$
$173$	5.28581	−	5.28581i	0.401873	−	0.401873i	0.878892	+	0.477020i	$0.158283\pi$
$174$		0			0
$175$	−19.0854			−1.44272
$176$		0			0
$177$	10.7145			0.805352
$178$		0			0
$179$	−0.195531	+	0.195531i	−0.0146147	+	0.0146147i	−0.714376	−	0.699762i	$-0.753290\pi$
$179$	−0.195531	+	0.195531i	−0.0146147	+	0.0146147i	0.699762	+	0.714376i	$0.253290\pi$
$180$		0			0
$181$	1.38314	−	1.38314i	0.102808	−	0.102808i	−0.653832	−	0.756640i	$-0.726840\pi$
$181$	1.38314	−	1.38314i	0.102808	−	0.102808i	0.756640	+	0.653832i	$0.226840\pi$
$182$		0			0
$183$			25.1351i			1.85804i
$184$		0			0
$185$		−	18.3579i		−	1.34970i
$186$		0			0
$187$	−2.86634	−	3.66464i	−0.209608	−	0.267985i
$188$		0			0
$189$	−2.77143	+	2.77143i	−0.201592	+	0.201592i
$190$		0			0
$191$		−	1.73357i		−	0.125437i	−0.998031	−	0.0627183i	$-0.980023\pi$
$191$		−	1.73357i		−	0.125437i	0.998031	−	0.0627183i	$-0.0199770\pi$
$192$		0			0
$193$		−	2.28898i		−	0.164764i	−0.996601	−	0.0823821i	$-0.973747\pi$
$193$		−	2.28898i		−	0.164764i	0.996601	−	0.0823821i	$-0.0262528\pi$
$194$		0			0
$195$	−21.2386	−	21.2386i	−1.52093	−	1.52093i
$196$		0			0
$197$	1.78891	+	1.78891i	0.127454	+	0.127454i	0.767956	−	0.640502i	$-0.221274\pi$
$197$	1.78891	+	1.78891i	0.127454	+	0.127454i	−0.640502	+	0.767956i	$0.721274\pi$
$198$		0			0
$199$	14.9845			1.06223			0.531113	−	0.847301i	$-0.321774\pi$
$199$	14.9845			1.06223			0.531113	+	0.847301i	$0.321774\pi$
$200$		0			0
$201$			25.4999i			1.79862i
$202$		0			0
$203$	−1.04341	−	1.04341i	−0.0732331	−	0.0732331i
$204$		0			0
$205$	−27.5139	+	27.5139i	−1.92165	+	1.92165i
$206$		0			0
$207$			11.4187i			0.793657i
$208$		0			0
$209$	−23.4272	−	2.86355i	−1.62049	−	0.198076i
$210$		0			0
$211$	−5.47937	−	5.47937i	−0.377215	−	0.377215i	0.492881	−	0.870097i	$-0.335944\pi$
$211$	−5.47937	−	5.47937i	−0.377215	−	0.377215i	−0.870097	+	0.492881i	$0.835944\pi$
$212$		0			0
$213$	−4.90978	+	4.90978i	−0.336413	+	0.336413i
$214$		0			0
$215$		−	8.15405i		−	0.556101i
$216$		0			0
$217$	7.73723			0.525238
$218$		0			0
$219$	4.14698	−	4.14698i	0.280227	−	0.280227i
$220$		0			0
$221$	3.16890	+	3.16890i	0.213163	+	0.213163i
$222$		0			0
$223$		−	6.96622i		−	0.466492i	−0.972418	−	0.233246i	$-0.925065\pi$
$223$		−	6.96622i		−	0.466492i	0.972418	−	0.233246i	$-0.0749348\pi$
$224$		0			0
$225$	−30.2741			−2.01827
$226$		0			0
$227$	18.5015	+	18.5015i	1.22799	+	1.22799i	0.964724	+	0.263262i	$0.0847985\pi$
$227$	18.5015	+	18.5015i	1.22799	+	1.22799i	0.263262	+	0.964724i	$0.415202\pi$
$228$		0			0
$229$	−14.4781	+	14.4781i	−0.956742	+	0.956742i	−0.999102	−	0.0423605i	$-0.986512\pi$
$229$	−14.4781	+	14.4781i	−0.956742	+	0.956742i	0.0423605	+	0.999102i	$0.486512\pi$
$230$		0			0
$231$	19.5932	+	2.39491i	1.28914	+	0.157574i
$232$		0			0
$233$	0.323337			0.0211825			0.0105912	−	0.999944i	$-0.496629\pi$
$233$	0.323337			0.0211825			0.0105912	+	0.999944i	$0.496629\pi$
$234$		0			0
$235$	19.9515	+	19.9515i	1.30149	+	1.30149i
$236$		0			0
$237$	−18.6400	+	18.6400i	−1.21080	+	1.21080i
$238$		0			0
$239$	−15.6605			−1.01300			−0.506498	−	0.862241i	$-0.669060\pi$
$239$	−15.6605			−1.01300			−0.506498	+	0.862241i	$0.669060\pi$
$240$		0			0
$241$		−	21.7928i		−	1.40380i	−0.712277	−	0.701899i	$-0.752336\pi$
$241$		−	21.7928i		−	1.40380i	0.712277	−	0.701899i	$-0.247664\pi$
$242$		0			0
$243$	15.6303	−	15.6303i	1.00269	−	1.00269i
$244$		0			0
$245$	4.32930	−	4.32930i	0.276589	−	0.276589i
$246$		0			0
$247$	22.7342			1.44654
$248$		0			0
$249$	−4.20212			−0.266298
$250$		0			0
$251$	6.22698	+	6.22698i	0.393044	+	0.393044i	0.875771	−	0.482727i	$-0.160354\pi$
$251$	6.22698	+	6.22698i	0.393044	+	0.393044i	−0.482727	+	0.875771i	$0.660354\pi$
$252$		0			0
$253$	8.15366	−	6.37748i	0.512616	−	0.400949i
$254$		0			0
$255$	13.1884			0.825890
$256$		0			0
$257$	14.3219			0.893373			0.446687	−	0.894690i	$-0.352604\pi$
$257$	14.3219			0.893373			0.446687	+	0.894690i	$0.352604\pi$
$258$		0			0
$259$	−8.21732	−	8.21732i	−0.510599	−	0.510599i
$260$		0			0
$261$	−1.65511	−	1.65511i	−0.102448	−	0.102448i
$262$		0			0
$263$		−	17.8792i		−	1.10248i	−0.834347	−	0.551240i	$-0.814155\pi$
$263$		−	17.8792i		−	1.10248i	0.834347	−	0.551240i	$-0.185845\pi$
$264$		0			0
$265$		−	18.3767i		−	1.12887i
$266$		0			0
$267$	30.7904	+	30.7904i	1.88434	+	1.88434i
$268$		0			0
$269$	−13.3395	−	13.3395i	−0.813324	−	0.813324i	0.171806	−	0.985131i	$-0.445040\pi$
$269$	−13.3395	−	13.3395i	−0.813324	−	0.813324i	−0.985131	+	0.171806i	$0.945040\pi$
$270$		0			0
$271$	7.67677			0.466331			0.233165	−	0.972437i	$-0.425092\pi$
$271$	7.67677			0.466331			0.233165	+	0.972437i	$0.425092\pi$
$272$		0			0
$273$	−19.0136			−1.15076
$274$		0			0
$275$	16.9084	+	21.6175i	1.01961	+	1.30358i
$276$		0			0
$277$	−17.1475	−	17.1475i	−1.03030	−	1.03030i	−0.999527	−	0.0307686i	$-0.990204\pi$
$277$	−17.1475	−	17.1475i	−1.03030	−	1.03030i	−0.0307686	−	0.999527i	$-0.509796\pi$
$278$		0			0
$279$	12.2732			0.734775
$280$		0			0
$281$	−8.25178			−0.492260			−0.246130	−	0.969237i	$-0.579159\pi$
$281$	−8.25178			−0.492260			−0.246130	+	0.969237i	$0.579159\pi$
$282$		0			0
$283$	5.07874	−	5.07874i	0.301900	−	0.301900i	−0.539857	−	0.841757i	$-0.681522\pi$
$283$	5.07874	−	5.07874i	0.301900	−	0.301900i	0.841757	+	0.539857i	$0.181522\pi$
$284$		0			0
$285$	47.3079	−	47.3079i	2.80228	−	2.80228i
$286$		0			0
$287$			24.6315i			1.45395i
$288$		0			0
$289$	15.0322			0.884249
$290$		0			0
$291$	11.8264	−	11.8264i	0.693276	−	0.693276i
$292$		0			0
$293$	20.8776	+	20.8776i	1.21968	+	1.21968i	0.967743	+	0.251940i	$0.0810686\pi$
$293$	20.8776	+	20.8776i	1.21968	+	1.21968i	0.251940	+	0.967743i	$0.418931\pi$
$294$		0			0
$295$	15.1286			0.880819
$296$		0			0
$297$	5.59443	+	0.683819i	0.324622	+	0.0396792i
$298$		0			0
$299$	−7.05066	+	7.05066i	−0.407750	+	0.407750i
$300$		0			0
$301$	−3.64991	−	3.64991i	−0.210377	−	0.210377i
$302$		0			0
$303$	21.9627			1.26172
$304$		0			0
$305$			35.4900i			2.03215i
$306$		0			0
$307$	13.5255	+	13.5255i	0.771941	+	0.771941i	0.978446	−	0.206505i	$-0.0662088\pi$
$307$	13.5255	+	13.5255i	0.771941	+	0.771941i	−0.206505	+	0.978446i	$0.566209\pi$
$308$		0			0
$309$	−33.0343	+	33.0343i	−1.87926	+	1.87926i
$310$		0			0
$311$	−0.460770			−0.0261279			−0.0130639	−	0.999915i	$-0.504159\pi$
$311$	−0.460770			−0.0261279			−0.0130639	+	0.999915i	$0.504159\pi$
$312$		0			0
$313$			19.7545i			1.11659i	0.829642	+	0.558296i	$0.188545\pi$
$313$			19.7545i			1.11659i	−0.829642	+	0.558296i	$0.811455\pi$
$314$		0			0
$315$	−21.7394	+	21.7394i	−1.22488	+	1.22488i
$316$		0			0
$317$	−8.32098	−	8.32098i	−0.467353	−	0.467353i	0.433703	−	0.901056i	$-0.357207\pi$
$317$	−8.32098	−	8.32098i	−0.467353	−	0.467353i	−0.901056	+	0.433703i	$0.857207\pi$
$318$		0			0
$319$	−0.257450	+	2.10624i	−0.0144144	+	0.117927i
$320$		0			0
$321$		−	17.5739i		−	0.980881i
$322$		0			0
$323$	−7.05855	+	7.05855i	−0.392748	+	0.392748i
$324$		0			0
$325$	−18.6932	−	18.6932i	−1.03691	−	1.03691i
$326$		0			0
$327$		−	37.2412i		−	2.05944i
$328$		0			0
$329$	17.8613			0.984725
$330$		0			0
$331$	−8.60533	−	8.60533i	−0.472992	−	0.472992i	0.429890	−	0.902881i	$-0.358552\pi$
$331$	−8.60533	−	8.60533i	−0.472992	−	0.472992i	−0.902881	+	0.429890i	$0.858552\pi$
$332$		0			0
$333$	−13.0347	−	13.0347i	−0.714297	−	0.714297i
$334$		0			0
$335$			36.0051i			1.96717i
$336$		0			0
$337$			26.2867i			1.43193i	0.698137	+	0.715964i	$0.254012\pi$
$337$			26.2867i			1.43193i	−0.698137	+	0.715964i	$0.745988\pi$
$338$		0			0
$339$	−2.77090	+	2.77090i	−0.150495	+	0.150495i
$340$		0			0
$341$	−6.85469	−	8.76376i	−0.371202	−	0.474584i
$342$		0			0
$343$		−	20.0207i		−	1.08102i
$344$		0			0
$345$			29.3436i			1.57981i
$346$		0			0
$347$	4.50647	−	4.50647i	0.241920	−	0.241920i	−0.575724	−	0.817644i	$-0.695280\pi$
$347$	4.50647	−	4.50647i	0.241920	−	0.241920i	0.817644	+	0.575724i	$0.195280\pi$
$348$		0			0
$349$	−13.0519	+	13.0519i	−0.698653	+	0.698653i	−0.964120	−	0.265467i	$-0.914474\pi$
$349$	−13.0519	+	13.0519i	−0.698653	+	0.698653i	0.265467	+	0.964120i	$0.414474\pi$
$350$		0			0
$351$	−5.42895			−0.289776
$352$		0			0
$353$	−23.6735			−1.26001			−0.630006	−	0.776591i	$-0.716947\pi$
$353$	−23.6735			−1.26001			−0.630006	+	0.776591i	$0.716947\pi$
$354$		0			0
$355$	−6.93246	+	6.93246i	−0.367937	+	0.367937i
$356$		0			0
$357$	5.90338	−	5.90338i	0.312440	−	0.312440i
$358$		0			0
$359$			8.59616i			0.453688i	0.973931	+	0.226844i	$0.0728407\pi$
$359$			8.59616i			0.453688i	−0.973931	+	0.226844i	$0.927159\pi$
$360$		0			0
$361$			31.6392i			1.66522i
$362$		0			0
$363$	−14.6456	−	24.3144i	−0.768696	−	1.27618i
$364$		0			0
$365$	5.85541	−	5.85541i	0.306486	−	0.306486i
$366$		0			0
$367$			10.2443i			0.534750i	0.963593	+	0.267375i	$0.0861562\pi$
$367$			10.2443i			0.534750i	−0.963593	+	0.267375i	$0.913844\pi$
$368$		0			0
$369$			39.0716i			2.03399i
$370$		0			0
$371$	−8.22574	−	8.22574i	−0.427059	−	0.427059i
$372$		0			0
$373$	5.94105	+	5.94105i	0.307616	+	0.307616i	0.843984	−	0.536368i	$-0.180204\pi$
$373$	5.94105	+	5.94105i	0.307616	+	0.307616i	−0.536368	+	0.843984i	$0.680204\pi$
$374$		0			0
$375$	−30.7893			−1.58995
$376$		0			0
$377$		−	2.04394i		−	0.105268i
$378$		0			0
$379$	−8.68605	−	8.68605i	−0.446172	−	0.446172i	0.447908	−	0.894080i	$-0.352169\pi$
$379$	−8.68605	−	8.68605i	−0.446172	−	0.446172i	−0.894080	+	0.447908i	$0.852169\pi$
$380$		0			0
$381$	10.8397	−	10.8397i	0.555336	−	0.555336i
$382$		0			0
$383$		−	9.96890i		−	0.509387i	−0.967022	−	0.254693i	$-0.918025\pi$
$383$		−	9.96890i		−	0.509387i	0.967022	−	0.254693i	$-0.0819746\pi$
$384$		0			0
$385$	27.6650	+	3.38154i	1.40994	+	0.172339i
$386$		0			0
$387$	−5.78965	−	5.78965i	−0.294304	−	0.294304i
$388$		0			0
$389$	−14.7897	+	14.7897i	−0.749867	+	0.749867i	−0.974454	−	0.224587i	$-0.927897\pi$
$389$	−14.7897	+	14.7897i	−0.749867	+	0.749867i	0.224587	+	0.974454i	$0.427897\pi$
$390$		0			0
$391$		−	4.37820i		−	0.221415i
$392$		0			0
$393$	−40.5667			−2.04632
$394$		0			0
$395$	−26.3191	+	26.3191i	−1.32426	+	1.32426i
$396$		0			0
$397$	24.3586	+	24.3586i	1.22252	+	1.22252i	0.966733	+	0.255788i	$0.0823349\pi$
$397$	24.3586	+	24.3586i	1.22252	+	1.22252i	0.255788	+	0.966733i	$0.417665\pi$
$398$		0			0
$399$		−	42.3518i		−	2.12024i
$400$		0			0
$401$	22.5817			1.12767			0.563837	−	0.825886i	$-0.309324\pi$
$401$	22.5817			1.12767			0.563837	+	0.825886i	$0.309324\pi$
$402$		0			0
$403$	7.57824	+	7.57824i	0.377499	+	0.377499i
$404$		0			0
$405$	16.9796	−	16.9796i	0.843726	−	0.843726i
$406$		0			0
$407$	−2.02753	+	16.5876i	−0.100501	+	0.822215i
$408$		0			0
$409$	15.3317			0.758104			0.379052	−	0.925375i	$-0.376250\pi$
$409$	15.3317			0.758104			0.379052	+	0.925375i	$0.376250\pi$
$410$		0			0
$411$	−9.35997	−	9.35997i	−0.461693	−	0.461693i
$412$		0			0
$413$	6.77183	−	6.77183i	0.333220	−	0.333220i
$414$		0			0
$415$	−5.93326			−0.291252
$416$		0			0
$417$		−	21.1876i		−	1.03756i
$418$		0			0
$419$	−11.7507	+	11.7507i	−0.574059	+	0.574059i	−0.933260	−	0.359201i	$-0.883049\pi$
$419$	−11.7507	+	11.7507i	−0.574059	+	0.574059i	0.359201	+	0.933260i	$0.383049\pi$
$420$		0			0
$421$	−4.03675	+	4.03675i	−0.196739	+	0.196739i	−0.798601	−	0.601861i	$-0.794426\pi$
$421$	−4.03675	+	4.03675i	−0.196739	+	0.196739i	0.601861	+	0.798601i	$0.294426\pi$
$422$		0			0
$423$	28.3324			1.37757
$424$		0			0
$425$	11.6078			0.563060
$426$		0			0
$427$	15.8860	+	15.8860i	0.768778	+	0.768778i
$428$		0			0
$429$	16.8448	+	21.5362i	0.813277	+	1.03978i
$430$		0			0
$431$	−14.5861			−0.702586			−0.351293	−	0.936266i	$-0.614258\pi$
$431$	−14.5861			−0.702586			−0.351293	+	0.936266i	$0.614258\pi$
$432$		0			0
$433$	11.6300			0.558902			0.279451	−	0.960160i	$-0.409847\pi$
$433$	11.6300			0.558902			0.279451	+	0.960160i	$0.409847\pi$
$434$		0			0
$435$	−4.25326	−	4.25326i	−0.203928	−	0.203928i
$436$		0			0
$437$	−15.7050	−	15.7050i	−0.751271	−	0.751271i
$438$		0			0
$439$			26.7375i			1.27611i	0.769991	+	0.638055i	$0.220261\pi$
$439$			26.7375i			1.27611i	−0.769991	+	0.638055i	$0.779739\pi$
$440$		0			0
$441$		−	6.14790i		−	0.292757i
$442$		0			0
$443$	5.04822	+	5.04822i	0.239848	+	0.239848i	0.816787	−	0.576939i	$-0.195753\pi$
$443$	5.04822	+	5.04822i	0.239848	+	0.239848i	−0.576939	+	0.816787i	$0.695753\pi$
$444$		0			0
$445$	43.4751	+	43.4751i	2.06092	+	2.06092i
$446$		0			0
$447$	−33.5197			−1.58543
$448$		0			0
$449$	−24.3369			−1.14853			−0.574266	−	0.818669i	$-0.694712\pi$
$449$	−24.3369			−1.14853			−0.574266	+	0.818669i	$0.694712\pi$
$450$		0			0
$451$	27.8994	−	21.8219i	1.31373	−	1.02755i
$452$		0			0
$453$	−6.73030	−	6.73030i	−0.316217	−	0.316217i
$454$		0			0
$455$	−26.8467			−1.25859
$456$		0			0
$457$	5.84239			0.273296			0.136648	−	0.990620i	$-0.456367\pi$
$457$	5.84239			0.273296			0.136648	+	0.990620i	$0.456367\pi$
$458$		0			0
$459$	1.68559	−	1.68559i	0.0786767	−	0.0786767i
$460$		0			0
$461$	−24.7318	+	24.7318i	−1.15187	+	1.15187i	−0.165696	+	0.986177i	$0.552987\pi$
$461$	−24.7318	+	24.7318i	−1.15187	+	1.15187i	−0.986177	+	0.165696i	$0.947013\pi$
$462$		0			0
$463$		−	9.71871i		−	0.451667i	−0.974166	−	0.225833i	$-0.927490\pi$
$463$		−	9.71871i		−	0.451667i	0.974166	−	0.225833i	$-0.0725105\pi$
$464$		0			0
$465$	31.5393			1.46260
$466$		0			0
$467$	−12.8617	+	12.8617i	−0.595167	+	0.595167i	−0.939023	−	0.343856i	$-0.888267\pi$
$467$	−12.8617	+	12.8617i	−0.595167	+	0.595167i	0.343856	+	0.939023i	$0.388267\pi$
$468$		0			0
$469$	16.1166	+	16.1166i	0.744194	+	0.744194i
$470$		0			0
$471$	−11.2367			−0.517762
$472$		0			0
$473$	−0.900573	+	7.36774i	−0.0414084	+	0.338769i
$474$		0			0
$475$	41.6380	−	41.6380i	1.91048	−	1.91048i
$476$		0			0
$477$	−13.0481	−	13.0481i	−0.597429	−	0.597429i
$478$		0			0
$479$	−2.44971			−0.111930			−0.0559650	−	0.998433i	$-0.517824\pi$
$479$	−2.44971			−0.111930			−0.0559650	+	0.998433i	$0.517824\pi$
$480$		0			0
$481$		−	16.0969i		−	0.733956i
$482$		0			0
$483$	13.1348	+	13.1348i	0.597652	+	0.597652i
$484$		0			0
$485$	16.6985	−	16.6985i	0.758240	−	0.758240i
$486$		0			0
$487$	−29.6860			−1.34520			−0.672600	−	0.740007i	$-0.734822\pi$
$487$	−29.6860			−1.34520			−0.672600	+	0.740007i	$0.734822\pi$
$488$		0			0
$489$		−	32.3610i		−	1.46341i
$490$		0			0
$491$	11.6835	−	11.6835i	0.527268	−	0.527268i	−0.392489	−	0.919757i	$-0.628386\pi$
$491$	11.6835	−	11.6835i	0.527268	−	0.527268i	0.919757	+	0.392489i	$0.128386\pi$
$492$		0			0
$493$	0.634605	+	0.634605i	0.0285812	+	0.0285812i
$494$		0			0
$495$	43.8834	+	5.36396i	1.97241	+	0.241092i
$496$		0			0
$497$			6.20620i			0.278386i
$498$		0			0
$499$	21.9899	−	21.9899i	0.984403	−	0.984403i	−0.0154773	−	0.999880i	$-0.504927\pi$
$499$	21.9899	−	21.9899i	0.984403	−	0.984403i	0.999880	+	0.0154773i	$0.00492678\pi$
$500$		0			0
$501$	16.8224	+	16.8224i	0.751569	+	0.751569i
$502$		0			0
$503$			4.56805i			0.203679i	0.994801	+	0.101840i	$0.0324729\pi$
$503$			4.56805i			0.203679i	−0.994801	+	0.101840i	$0.967527\pi$
$504$		0			0
$505$	31.0106			1.37996
$506$		0			0
$507$	5.09729	+	5.09729i	0.226379	+	0.226379i
$508$		0			0
$509$	−8.08245	−	8.08245i	−0.358248	−	0.358248i	0.504919	−	0.863167i	$-0.331522\pi$
$509$	−8.08245	−	8.08245i	−0.358248	−	0.358248i	−0.863167	+	0.504919i	$0.831522\pi$
$510$		0			0
$511$		−	5.24198i		−	0.231892i
$512$		0			0
$513$		−	12.0927i		−	0.533906i
$514$		0			0
$515$	−46.6435	+	46.6435i	−2.05536	+	2.05536i
$516$		0			0
$517$	−15.8240	−	20.2310i	−0.695937	−	0.889760i
$518$		0			0
$519$		−	19.2893i		−	0.846706i
$520$		0			0
$521$		−	0.244590i		−	0.0107157i	−0.999986	−	0.00535785i	$-0.998295\pi$
$521$		−	0.244590i		−	0.0107157i	0.999986	−	0.00535785i	$-0.00170546\pi$
$522$		0			0
$523$	−19.9640	+	19.9640i	−0.872963	+	0.872963i	−0.992794	−	0.119831i	$-0.961765\pi$
$523$	−19.9640	+	19.9640i	−0.872963	+	0.872963i	0.119831	+	0.992794i	$0.461765\pi$
$524$		0			0
$525$	−34.8237	+	34.8237i	−1.51983	+	1.51983i
$526$		0			0
$527$	−4.70581			−0.204988
$528$		0			0
$529$	−13.2587			−0.576465
$530$		0			0
$531$	10.7418	−	10.7418i	0.466154	−	0.466154i
$532$		0			0
$533$	−24.1253	+	24.1253i	−1.04498	+	1.04498i
$534$		0			0
$535$		−	24.8139i		−	1.07280i
$536$		0			0
$537$			0.713544i			0.0307917i
$538$		0			0
$539$	−4.38997	+	3.43367i	−0.189089	+	0.147899i
$540$		0			0
$541$	22.1416	−	22.1416i	0.951942	−	0.951942i	−0.0469555	−	0.998897i	$-0.514952\pi$
$541$	22.1416	−	22.1416i	0.951942	−	0.951942i	0.998897	+	0.0469555i	$0.0149519\pi$
$542$		0			0
$543$		−	5.04744i		−	0.216607i
$544$		0			0
$545$		−	52.5834i		−	2.25243i
$546$		0			0
$547$	0.219631	+	0.219631i	0.00939075	+	0.00939075i	0.711787	−	0.702396i	$-0.247886\pi$
$547$	0.219631	+	0.219631i	0.00939075	+	0.00939075i	−0.702396	+	0.711787i	$0.747886\pi$
$548$		0			0
$549$	25.1991	+	25.1991i	1.07547	+	1.07547i
$550$		0			0
$551$	4.55276			0.193954
$552$		0			0
$553$			23.5618i			1.00195i
$554$		0			0
$555$	−33.4963	−	33.4963i	−1.42184	−	1.42184i
$556$		0			0
$557$	27.9997	−	27.9997i	1.18639	−	1.18639i	0.208328	−	0.978059i	$-0.433198\pi$
$557$	27.9997	−	27.9997i	1.18639	−	1.18639i	0.978059	−	0.208328i	$-0.0668021\pi$
$558$		0			0
$559$		−	7.14981i		−	0.302405i
$560$		0			0
$561$	−11.9166	−	1.45659i	−0.503120	−	0.0614974i
$562$		0			0
$563$	−26.9865	−	26.9865i	−1.13734	−	1.13734i	−0.988925	−	0.148419i	$-0.952582\pi$
$563$	−26.9865	−	26.9865i	−1.13734	−	1.13734i	−0.148419	−	0.988925i	$-0.547418\pi$
$564$		0			0
$565$	−3.91243	+	3.91243i	−0.164597	+	0.164597i
$566$		0			0
$567$		−	15.2008i		−	0.638375i
$568$		0			0
$569$	−29.8110			−1.24974			−0.624871	−	0.780728i	$-0.714849\pi$
$569$	−29.8110			−1.24974			−0.624871	+	0.780728i	$0.714849\pi$
$570$		0			0
$571$	−14.9978	+	14.9978i	−0.627637	+	0.627637i	−0.947473	−	0.319836i	$-0.896372\pi$
$571$	−14.9978	+	14.9978i	−0.627637	+	0.627637i	0.319836	+	0.947473i	$0.396372\pi$
$572$		0			0
$573$	−3.16312	−	3.16312i	−0.132141	−	0.132141i
$574$		0			0
$575$			25.8268i			1.07705i
$576$		0			0
$577$	−36.8973			−1.53606			−0.768028	−	0.640416i	$-0.778762\pi$
$577$	−36.8973			−1.53606			−0.768028	+	0.640416i	$0.778762\pi$
$578$		0			0
$579$	−4.17654	−	4.17654i	−0.173571	−	0.173571i
$580$		0			0
$581$	−2.65584	+	2.65584i	−0.110183	+	0.110183i
$582$		0			0
$583$	−2.02961	+	16.6046i	−0.0840578	+	0.687691i
$584$		0			0
$585$	−42.5854			−1.76069
$586$		0			0
$587$	16.9590	+	16.9590i	0.699972	+	0.699972i	0.964404	−	0.264432i	$-0.0851845\pi$
$587$	16.9590	+	16.9590i	0.699972	+	0.699972i	−0.264432	+	0.964404i	$0.585184\pi$
$588$		0			0
$589$	−16.8801	+	16.8801i	−0.695533	+	0.695533i
$590$		0			0
$591$	6.52818			0.268534
$592$		0			0
$593$			40.5127i			1.66366i	0.555034	+	0.831828i	$0.312705\pi$
$593$			40.5127i			1.66366i	−0.555034	+	0.831828i	$0.687295\pi$
$594$		0			0
$595$	8.33540	−	8.33540i	0.341718	−	0.341718i
$596$		0			0
$597$	27.3412	−	27.3412i	1.11900	−	1.11900i
$598$		0			0
$599$	−38.4028			−1.56909			−0.784547	−	0.620069i	$-0.787105\pi$
$599$	−38.4028			−1.56909			−0.784547	+	0.620069i	$0.787105\pi$
$600$		0			0
$601$	35.6934			1.45596			0.727982	−	0.685596i	$-0.240458\pi$
$601$	35.6934			1.45596			0.727982	+	0.685596i	$0.240458\pi$
$602$		0			0
$603$	25.5648	+	25.5648i	1.04108	+	1.04108i
$604$		0			0
$605$	−20.6792	−	34.3312i	−0.840728	−	1.39576i
$606$		0			0
$607$	−4.91053			−0.199312			−0.0996562	−	0.995022i	$-0.531774\pi$
$607$	−4.91053			−0.199312			−0.0996562	+	0.995022i	$0.531774\pi$
$608$		0			0
$609$	−3.80768			−0.154295
$610$		0			0
$611$	17.4943	+	17.4943i	0.707742	+	0.707742i
$612$		0			0
$613$	−6.87970	−	6.87970i	−0.277869	−	0.277869i	0.554389	−	0.832258i	$-0.312952\pi$
$613$	−6.87970	−	6.87970i	−0.277869	−	0.277869i	−0.832258	+	0.554389i	$0.812952\pi$
$614$		0			0
$615$			100.405i			4.04873i
$616$		0			0
$617$		−	36.6461i		−	1.47532i	−0.675174	−	0.737658i	$-0.735932\pi$
$617$		−	36.6461i		−	1.47532i	0.675174	−	0.737658i	$-0.264068\pi$
$618$		0			0
$619$	−16.1029	−	16.1029i	−0.647231	−	0.647231i	0.305092	−	0.952323i	$-0.401313\pi$
$619$	−16.1029	−	16.1029i	−0.647231	−	0.647231i	−0.952323	+	0.305092i	$0.901313\pi$
$620$		0			0
$621$	3.75037	+	3.75037i	0.150497	+	0.150497i
$622$		0			0
$623$	38.9206			1.55932
$624$		0			0
$625$	−2.09921			−0.0839682
$626$		0			0
$627$	−47.9708	+	37.5210i	−1.91577	+	1.49844i
$628$		0			0
$629$	4.99780	+	4.99780i	0.199275	+	0.199275i
$630$		0			0
$631$	30.0101			1.19468			0.597341	−	0.801988i	$-0.296224\pi$
$631$	30.0101			1.19468			0.597341	+	0.801988i	$0.296224\pi$
$632$		0			0
$633$	−19.9956			−0.794755
$634$		0			0
$635$	15.3054	−	15.3054i	0.607375	−	0.607375i
$636$		0			0
$637$	3.79611	−	3.79611i	0.150407	−	0.150407i
$638$		0			0
$639$			9.84456i			0.389445i
$640$		0			0
$641$	−28.8851			−1.14089			−0.570447	−	0.821335i	$-0.693230\pi$
$641$	−28.8851			−1.14089			−0.570447	+	0.821335i	$0.693230\pi$
$642$		0			0
$643$	15.6360	−	15.6360i	0.616625	−	0.616625i	−0.328039	−	0.944664i	$-0.606388\pi$
$643$	15.6360	−	15.6360i	0.616625	−	0.616625i	0.944664	+	0.328039i	$0.106388\pi$
$644$		0			0
$645$	−14.8781	−	14.8781i	−0.585826	−	0.585826i
$646$		0			0
$647$	12.6873			0.498789			0.249394	−	0.968402i	$-0.419768\pi$
$647$	12.6873			0.498789			0.249394	+	0.968402i	$0.419768\pi$
$648$		0			0
$649$	−13.6697	−	1.67087i	−0.536582	−	0.0655875i
$650$		0			0
$651$	14.1176	−	14.1176i	0.553312	−	0.553312i
$652$		0			0
$653$	−21.8991	−	21.8991i	−0.856977	−	0.856977i	0.134004	−	0.990981i	$-0.457217\pi$
$653$	−21.8991	−	21.8991i	−0.856977	−	0.856977i	−0.990981	+	0.134004i	$0.957217\pi$
$654$		0			0
$655$	−57.2790			−2.23807
$656$		0			0
$657$		−	8.31508i		−	0.324402i
$658$		0			0
$659$	1.61652	+	1.61652i	0.0629706	+	0.0629706i	0.737891	−	0.674920i	$-0.235822\pi$
$659$	1.61652	+	1.61652i	0.0629706	+	0.0629706i	−0.674920	+	0.737891i	$0.735822\pi$
$660$		0			0
$661$	10.8521	−	10.8521i	0.422097	−	0.422097i	−0.463828	−	0.885925i	$-0.653525\pi$
$661$	10.8521	−	10.8521i	0.422097	−	0.422097i	0.885925	+	0.463828i	$0.153525\pi$
$662$		0			0
$663$	11.5641			0.449114
$664$		0			0
$665$		−	59.7995i		−	2.31892i
$666$		0			0
$667$	−1.41197	+	1.41197i	−0.0546717	+	0.0546717i
$668$		0			0
$669$	−12.7108	−	12.7108i	−0.491427	−	0.491427i
$670$		0			0
$671$	3.91969	−	32.0677i	0.151318	−	1.23796i
$672$		0			0
$673$		−	9.75446i		−	0.376007i	−0.982168	−	0.188003i	$-0.939798\pi$
$673$		−	9.75446i		−	0.376007i	0.982168	−	0.188003i	$-0.0602016\pi$
$674$		0			0
$675$	−9.94321	+	9.94321i	−0.382714	+	0.382714i
$676$		0			0
$677$	27.2847	+	27.2847i	1.04864	+	1.04864i	0.998755	+	0.0498807i	$0.0158841\pi$
$677$	27.2847	+	27.2847i	1.04864	+	1.04864i	0.0498807	+	0.998755i	$0.484116\pi$
$678$		0			0
$679$		−	14.9491i		−	0.573695i
$680$		0			0
$681$	67.5167			2.58725
$682$		0			0
$683$	−11.8640	−	11.8640i	−0.453963	−	0.453963i	0.442704	−	0.896668i	$-0.354019\pi$
$683$	−11.8640	−	11.8640i	−0.453963	−	0.453963i	−0.896668	+	0.442704i	$0.854019\pi$
$684$		0			0
$685$	−13.2160	−	13.2160i	−0.504957	−	0.504957i
$686$		0			0
$687$			52.8345i			2.01576i
$688$		0			0
$689$		−	16.1134i		−	0.613872i
$690$		0			0
$691$	30.4947	−	30.4947i	1.16007	−	1.16007i	0.175615	−	0.984459i	$-0.443809\pi$
$691$	30.4947	−	30.4947i	1.16007	−	1.16007i	0.984459	−	0.175615i	$-0.0561913\pi$
$692$		0			0
$693$	22.0441	−	17.2420i	0.837385	−	0.654971i
$694$		0			0
$695$		−	29.9162i		−	1.13479i
$696$		0			0
$697$		−	14.9809i		−	0.567443i
$698$		0			0
$699$	0.589970	−	0.589970i	0.0223147	−	0.0223147i
$700$		0			0
$701$	−26.0339	+	26.0339i	−0.983285	+	0.983285i	−0.999863	−	0.0165776i	$-0.994723\pi$
$701$	−26.0339	+	26.0339i	−0.983285	+	0.983285i	0.0165776	+	0.999863i	$0.494723\pi$
$702$		0			0
$703$	35.8550			1.35230
$704$		0			0
$705$	72.8081			2.74211
$706$		0			0
$707$	13.8809	−	13.8809i	0.522047	−	0.522047i
$708$		0			0
$709$	6.64692	−	6.64692i	0.249630	−	0.249630i	−0.571189	−	0.820819i	$-0.693517\pi$
$709$	6.64692	−	6.64692i	0.249630	−	0.249630i	0.820819	+	0.571189i	$0.193517\pi$
$710$		0			0
$711$			37.3749i			1.40167i
$712$		0			0
$713$		−	10.4702i		−	0.392113i
$714$		0			0
$715$	23.7844	+	30.4085i	0.889486	+	1.13721i
$716$		0			0
$717$	−28.5747	+	28.5747i	−1.06714	+	1.06714i
$718$		0			0
$719$		−	17.5365i		−	0.654001i	−0.945024	−	0.327000i	$-0.893962\pi$
$719$		−	17.5365i		−	0.654001i	0.945024	−	0.327000i	$-0.106038\pi$
$720$		0			0
$721$			41.7570i			1.55511i
$722$		0			0
$723$	−39.7638	−	39.7638i	−1.47883	−	1.47883i
$724$		0			0
$725$	−3.74350	−	3.74350i	−0.139030	−	0.139030i
$726$		0			0
$727$	20.9383			0.776559			0.388280	−	0.921542i	$-0.373069\pi$
$727$	20.9383			0.776559			0.388280	+	0.921542i	$0.373069\pi$
$728$		0			0
$729$		−	37.2673i		−	1.38027i
$730$		0			0
$731$	2.21988	+	2.21988i	0.0821054	+	0.0821054i
$732$		0			0
$733$	14.9727	−	14.9727i	0.553028	−	0.553028i	−0.374285	−	0.927314i	$-0.622112\pi$
$733$	14.9727	−	14.9727i	0.553028	−	0.553028i	0.927314	+	0.374285i	$0.122112\pi$
$734$		0			0
$735$		−	15.7988i		−	0.582746i
$736$		0			0
$737$	3.97658	−	32.5330i	0.146479	−	1.19837i
$738$		0			0
$739$	22.2057	+	22.2057i	0.816850	+	0.816850i	0.985650	−	0.168800i	$-0.0539893\pi$
$739$	22.2057	+	22.2057i	0.816850	+	0.816850i	−0.168800	+	0.985650i	$0.553989\pi$
$740$		0			0
$741$	41.4815	−	41.4815i	1.52386	−	1.52386i
$742$		0			0
$743$			1.52927i			0.0561034i	0.999606	+	0.0280517i	$0.00893030\pi$
$743$			1.52927i			0.0561034i	−0.999606	+	0.0280517i	$0.991070\pi$
$744$		0			0
$745$	−47.3288			−1.73399
$746$		0			0
$747$	−4.21281	+	4.21281i	−0.154139	+	0.154139i
$748$		0			0
$749$	−11.1071	−	11.1071i	−0.405846	−	0.405846i
$750$		0			0
$751$		−	53.1709i		−	1.94023i	−0.242637	−	0.970117i	$-0.578012\pi$
$751$		−	53.1709i		−	1.94023i	0.242637	−	0.970117i	$-0.421988\pi$
$752$		0			0
$753$	22.7239			0.828105
$754$		0			0
$755$	−9.50298	−	9.50298i	−0.345849	−	0.345849i
$756$		0			0
$757$	7.25028	−	7.25028i	0.263516	−	0.263516i	−0.562965	−	0.826481i	$-0.690339\pi$
$757$	7.25028	−	7.25028i	0.263516	−	0.263516i	0.826481	+	0.562965i	$0.190339\pi$
$758$		0			0
$759$	3.24085	−	26.5140i	0.117636	−	0.962396i
$760$		0			0
$761$	−45.4603			−1.64794			−0.823968	−	0.566637i	$-0.808244\pi$
$761$	−45.4603			−1.64794			−0.823968	+	0.566637i	$0.808244\pi$
$762$		0			0
$763$	−23.5373	−	23.5373i	−0.852109	−	0.852109i
$764$		0			0
$765$	13.2220	−	13.2220i	0.478042	−	0.478042i
$766$		0			0
$767$	13.2653			0.478984
$768$		0			0
$769$			4.63104i			0.167000i	0.996508	+	0.0834998i	$0.0266098\pi$
$769$			4.63104i			0.167000i	−0.996508	+	0.0834998i	$0.973390\pi$
$770$		0			0
$771$	26.1321	−	26.1321i	0.941125	−	0.941125i
$772$		0			0
$773$	−22.7135	+	22.7135i	−0.816949	+	0.816949i	−0.985665	−	0.168716i	$-0.946038\pi$
$773$	−22.7135	+	22.7135i	−0.816949	+	0.816949i	0.168716	+	0.985665i	$0.446038\pi$
$774$		0			0
$775$	27.7593			0.997144
$776$		0			0
$777$	−29.9871			−1.07578
$778$		0			0
$779$	−53.7378	−	53.7378i	−1.92536	−	1.92536i
$780$		0			0
$781$	7.02960	−	5.49829i	0.251539	−	0.196744i
$782$		0			0
$783$	−1.08721			−0.0388535
$784$		0			0
$785$	−15.8659			−0.566280
$786$		0			0
$787$	−33.9423	−	33.9423i	−1.20991	−	1.20991i	−0.971055	−	0.238856i	$-0.923227\pi$
$787$	−33.9423	−	33.9423i	−1.20991	−	1.20991i	−0.238856	−	0.971055i	$-0.576773\pi$
$788$		0			0
$789$	−32.6230	−	32.6230i	−1.16141	−	1.16141i
$790$		0			0
$791$			3.50255i			0.124536i
$792$		0			0
$793$			31.1191i			1.10507i
$794$		0			0
$795$	−33.5306	−	33.5306i	−1.18921	−	1.18921i
$796$		0			0
$797$	2.13455	+	2.13455i	0.0756095	+	0.0756095i	0.743900	−	0.668291i	$-0.232974\pi$
$797$	2.13455	+	2.13455i	0.0756095	+	0.0756095i	−0.668291	+	0.743900i	$0.732974\pi$
$798$		0			0
$799$	−10.8633			−0.384316
$800$		0			0
$801$	61.7376			2.18139
$802$		0			0
$803$	−5.93746	+	4.64406i	−0.209528	+	0.163885i
$804$		0			0
$805$	18.5459	+	18.5459i	0.653657	+	0.653657i
$806$		0			0
$807$	−48.6794			−1.71359
$808$		0			0
$809$	5.98492			0.210419			0.105209	−	0.994450i	$-0.466449\pi$
$809$	5.98492			0.210419			0.105209	+	0.994450i	$0.466449\pi$
$810$		0			0
$811$	−1.03817	+	1.03817i	−0.0364551	+	0.0364551i	−0.725099	−	0.688644i	$-0.758206\pi$
$811$	−1.03817	+	1.03817i	−0.0364551	+	0.0364551i	0.688644	+	0.725099i	$0.258206\pi$
$812$		0			0
$813$	14.0073	−	14.0073i	0.491256	−	0.491256i
$814$		0			0
$815$		−	45.6927i		−	1.60055i
$816$		0			0
$817$	15.9258			0.557173
$818$		0			0
$819$	−19.0620	+	19.0620i	−0.666081	+	0.666081i
$820$		0			0
$821$	−16.9715	−	16.9715i	−0.592309	−	0.592309i	0.345945	−	0.938255i	$-0.387558\pi$
$821$	−16.9715	−	16.9715i	−0.592309	−	0.592309i	−0.938255	+	0.345945i	$0.887558\pi$
$822$		0			0
$823$	−33.4356			−1.16549			−0.582747	−	0.812654i	$-0.698022\pi$
$823$	−33.4356			−1.16549			−0.582747	+	0.812654i	$0.698022\pi$
$824$		0			0
$825$	70.2955	+	8.59236i	2.44737	+	0.299147i
$826$		0			0
$827$	14.5957	−	14.5957i	0.507544	−	0.507544i	−0.406228	−	0.913772i	$-0.633156\pi$
$827$	14.5957	−	14.5957i	0.507544	−	0.507544i	0.913772	+	0.406228i	$0.133156\pi$
$828$		0			0
$829$	−14.5397	−	14.5397i	−0.504986	−	0.504986i	0.407997	−	0.912983i	$-0.366227\pi$
$829$	−14.5397	−	14.5397i	−0.504986	−	0.504986i	−0.912983	+	0.407997i	$0.866227\pi$
$830$		0			0
$831$	−62.5758			−2.17073
$832$		0			0
$833$			2.35725i			0.0816738i
$834$		0			0
$835$	23.7527	+	23.7527i	0.821996	+	0.821996i
$836$		0			0
$837$	4.03099	−	4.03099i	0.139331	−	0.139331i
$838$		0			0
$839$	−5.57499			−0.192470			−0.0962351	−	0.995359i	$-0.530680\pi$
$839$	−5.57499			−0.192470			−0.0962351	+	0.995359i	$0.530680\pi$
$840$		0			0
$841$			28.5907i			0.985886i
$842$		0			0
$843$	−15.0564	+	15.0564i	−0.518572	+	0.518572i
$844$		0			0
$845$	7.19723	+	7.19723i	0.247592	+	0.247592i
$846$		0			0
$847$	−24.6237	−	6.11091i	−0.846080	−	0.209973i
$848$		0			0
$849$		−	18.5336i		−	0.636073i
$850$		0			0
$851$	−11.1199	+	11.1199i	−0.381185	+	0.381185i
$852$		0			0
$853$	25.0564	+	25.0564i	0.857914	+	0.857914i	0.991092	−	0.133178i	$-0.0425182\pi$
$853$	25.0564	+	25.0564i	0.857914	+	0.857914i	−0.133178	+	0.991092i	$0.542518\pi$
$854$		0			0
$855$		−	94.8567i		−	3.24403i
$856$		0			0
$857$	−7.64685			−0.261211			−0.130606	−	0.991434i	$-0.541692\pi$
$857$	−7.64685			−0.261211			−0.130606	+	0.991434i	$0.541692\pi$
$858$		0			0
$859$	−12.6183	−	12.6183i	−0.430531	−	0.430531i	0.458278	−	0.888809i	$-0.348466\pi$
$859$	−12.6183	−	12.6183i	−0.430531	−	0.430531i	−0.888809	+	0.458278i	$0.848466\pi$
$860$		0			0
$861$	44.9433	+	44.9433i	1.53166	+	1.53166i
$862$		0			0
$863$		−	6.93071i		−	0.235924i	−0.993018	−	0.117962i	$-0.962364\pi$
$863$		−	6.93071i		−	0.235924i	0.993018	−	0.117962i	$-0.0376361\pi$
$864$		0			0
$865$		−	27.2359i		−	0.926048i
$866$		0			0
$867$	27.4283	−	27.4283i	0.931513	−	0.931513i
$868$		0			0
$869$	26.6879	−	20.8743i	0.905325	−	0.708111i
$870$		0			0
$871$			31.5708i			1.06973i
$872$		0			0
$873$		−	23.7130i		−	0.802564i
$874$		0			0
$875$	−19.4596	+	19.4596i	−0.657855	+	0.657855i
$876$		0			0
$877$	−4.48288	+	4.48288i	−0.151376	+	0.151376i	−0.778732	−	0.627356i	$-0.784137\pi$
$877$	−4.48288	+	4.48288i	−0.151376	+	0.151376i	0.627356	+	0.778732i	$0.284137\pi$
$878$		0			0
$879$	76.1878			2.56975
$880$		0			0
$881$	−33.2923			−1.12165			−0.560823	−	0.827936i	$-0.689515\pi$
$881$	−33.2923			−1.12165			−0.560823	+	0.827936i	$0.689515\pi$
$882$		0			0
$883$	−15.2202	+	15.2202i	−0.512202	+	0.512202i	−0.915201	−	0.402999i	$-0.867968\pi$
$883$	−15.2202	+	15.2202i	−0.512202	+	0.512202i	0.402999	+	0.915201i	$0.367968\pi$
$884$		0			0
$885$	27.6040	−	27.6040i	0.927900	−	0.927900i
$886$		0			0
$887$			40.5311i			1.36090i	0.732794	+	0.680450i	$0.238216\pi$
$887$			40.5311i			1.36090i	−0.732794	+	0.680450i	$0.761784\pi$
$888$		0			0
$889$		−	13.7019i		−	0.459548i
$890$		0			0
$891$	−17.2176	+	13.4669i	−0.576811	+	0.451160i
$892$		0			0
$893$	−38.9675	+	38.9675i	−1.30400	+	1.30400i
$894$		0			0
$895$			1.00750i			0.0336771i
$896$		0			0
$897$			25.7297i			0.859090i
$898$		0			0
$899$	1.51762	+	1.51762i	0.0506155	+	0.0506155i
$900$		0			0
$901$	5.00292	+	5.00292i	0.166672	+	0.166672i
$902$		0			0
$903$	−13.3195			−0.443244
$904$		0			0
$905$		−	7.12684i		−	0.236904i
$906$		0			0
$907$	−23.5136	−	23.5136i	−0.780756	−	0.780756i	0.199202	−	0.979958i	$-0.436165\pi$
$907$	−23.5136	−	23.5136i	−0.780756	−	0.780756i	−0.979958	+	0.199202i	$0.936165\pi$
$908$		0			0
$909$	22.0186	−	22.0186i	0.730311	−	0.730311i
$910$		0			0
$911$			26.4160i			0.875200i	0.899170	+	0.437600i	$0.144171\pi$
$911$			26.4160i			0.875200i	−0.899170	+	0.437600i	$0.855829\pi$
$912$		0			0
$913$	5.36110	+	0.655298i	0.177427	+	0.0216872i
$914$		0			0
$915$	64.7562	+	64.7562i	2.14077	+	2.14077i
$916$		0			0
$917$	−25.6391	+	25.6391i	−0.846679	+	0.846679i
$918$		0			0
$919$			22.5351i			0.743363i	0.928360	+	0.371682i	$0.121219\pi$
$919$			22.5351i			0.743363i	−0.928360	+	0.371682i	$0.878781\pi$
$920$		0			0
$921$	49.3581			1.62640
$922$		0			0
$923$	−6.07867	+	6.07867i	−0.200082	+	0.200082i
$924$		0			0
$925$	−29.4817	−	29.4817i	−0.969354	−	0.969354i
$926$		0			0
$927$			66.2369i			2.17551i
$928$		0			0
$929$	−17.6500			−0.579077			−0.289539	−	0.957166i	$-0.593502\pi$
$929$	−17.6500			−0.579077			−0.289539	+	0.957166i	$0.593502\pi$
$930$		0			0
$931$	8.45564	+	8.45564i	0.277122	+	0.277122i
$932$		0			0
$933$	−0.840736	+	0.840736i	−0.0275244	+	0.0275244i
$934$		0			0
$935$	−16.8259	−	2.05666i	−0.550266	−	0.0672601i
$936$		0			0
$937$	−51.9895			−1.69842			−0.849211	−	0.528054i	$-0.822922\pi$
$937$	−51.9895			−1.69842			−0.849211	+	0.528054i	$0.822922\pi$
$938$		0			0
$939$	36.0447	+	36.0447i	1.17628	+	1.17628i
$940$		0			0
$941$	−7.17207	+	7.17207i	−0.233803	+	0.233803i	−0.814278	−	0.580475i	$-0.802867\pi$
$941$	−7.17207	+	7.17207i	−0.233803	+	0.233803i	0.580475	+	0.814278i	$0.302867\pi$
$942$		0			0
$943$	33.3319			1.08544
$944$		0			0
$945$			14.2802i			0.464535i
$946$		0			0
$947$	−38.9044	+	38.9044i	−1.26422	+	1.26422i	−0.315196	+	0.949027i	$0.602070\pi$
$947$	−38.9044	+	38.9044i	−1.26422	+	1.26422i	−0.949027	+	0.315196i	$0.897930\pi$
$948$		0			0
$949$	5.13426	−	5.13426i	0.166665	−	0.166665i
$950$		0			0
$951$	−30.3654			−0.984666
$952$		0			0
$953$	25.6514			0.830931			0.415465	−	0.909609i	$-0.363619\pi$
$953$	25.6514			0.830931			0.415465	+	0.909609i	$0.363619\pi$
$954$		0			0
$955$	−4.46623	−	4.46623i	−0.144524	−	0.144524i
$956$		0			0
$957$	3.37336	+	4.31286i	0.109045	+	0.139415i
$958$		0			0
$959$	−11.8315			−0.382058
$960$		0			0
$961$	19.7463			0.636979
$962$		0			0
$963$	−17.6187	−	17.6187i	−0.567754	−	0.567754i
$964$		0			0
$965$	−5.89714	−	5.89714i	−0.189836	−	0.189836i
$966$		0			0
$967$		−	0.325063i		−	0.0104533i	−0.999986	−	0.00522666i	$-0.998336\pi$
$967$		−	0.325063i		−	0.0104533i	0.999986	−	0.00522666i	$-0.00166371\pi$
$968$		0			0
$969$			25.7585i			0.827482i
$970$		0			0
$971$	26.5110	+	26.5110i	0.850779	+	0.850779i	0.990229	−	0.139450i	$-0.0445334\pi$
$971$	26.5110	+	26.5110i	0.850779	+	0.850779i	−0.139450	+	0.990229i	$0.544533\pi$
$972$		0			0
$973$	−13.3911	−	13.3911i	−0.429298	−	0.429298i
$974$		0			0
$975$	−68.2162			−2.18467
$976$		0			0
$977$	5.77233			0.184673			0.0923365	−	0.995728i	$-0.470566\pi$
$977$	5.77233			0.184673			0.0923365	+	0.995728i	$0.470566\pi$
$978$		0			0
$979$	−34.4811	−	44.0843i	−1.10202	−	1.40894i
$980$		0			0
$981$	−37.3360	−	37.3360i	−1.19205	−	1.19205i
$982$		0			0
$983$	20.6509			0.658663			0.329331	−	0.944214i	$-0.393177\pi$
$983$	20.6509			0.658663			0.329331	+	0.944214i	$0.393177\pi$
$984$		0			0
$985$	9.21760			0.293697
$986$		0			0
$987$	32.5903	−	32.5903i	1.03736	−	1.03736i
$988$		0			0
$989$	−4.93914	+	4.93914i	−0.157056	+	0.157056i
$990$		0			0
$991$			13.8044i			0.438511i	0.975667	+	0.219256i	$0.0703629\pi$
$991$			13.8044i			0.438511i	−0.975667	+	0.219256i	$0.929637\pi$
$992$		0			0
$993$	−31.4031			−0.996547
$994$		0			0
$995$	38.6050	−	38.6050i	1.22386	−	1.22386i
$996$		0			0
$997$	22.4165	+	22.4165i	0.709936	+	0.709936i	0.966522	−	0.256585i	$-0.0825974\pi$
$997$	22.4165	+	22.4165i	0.709936	+	0.709936i	−0.256585	+	0.966522i	$0.582597\pi$
$998$		0			0
$999$	−8.56222			−0.270897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1408.2.i.b.351.19		44
4.3	odd	2		1408.2.i.a.351.4		44
8.3	odd	2		704.2.i.a.175.20		44
8.5	even	2		176.2.i.a.131.6	yes	44
11.10	odd	2	inner	1408.2.i.b.351.20		44
16.3	odd	4		176.2.i.a.43.17	yes	44
16.5	even	4		1408.2.i.a.1055.3		44
16.11	odd	4	inner	1408.2.i.b.1055.20		44
16.13	even	4		704.2.i.a.527.20		44
44.43	even	2		1408.2.i.a.351.3		44
88.21	odd	2		176.2.i.a.131.17	yes	44
88.43	even	2		704.2.i.a.175.19		44
176.21	odd	4		1408.2.i.a.1055.4		44
176.43	even	4	inner	1408.2.i.b.1055.19		44
176.109	odd	4		704.2.i.a.527.19		44
176.131	even	4		176.2.i.a.43.6	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.i.a.43.6	✓	44	176.131	even	4
176.2.i.a.43.17	yes	44	16.3	odd	4
176.2.i.a.131.6	yes	44	8.5	even	2
176.2.i.a.131.17	yes	44	88.21	odd	2
704.2.i.a.175.19		44	88.43	even	2
704.2.i.a.175.20		44	8.3	odd	2
704.2.i.a.527.19		44	176.109	odd	4
704.2.i.a.527.20		44	16.13	even	4
1408.2.i.a.351.3		44	44.43	even	2
1408.2.i.a.351.4		44	4.3	odd	2
1408.2.i.a.1055.3		44	16.5	even	4
1408.2.i.a.1055.4		44	176.21	odd	4
1408.2.i.b.351.19		44	1.1	even	1	trivial
1408.2.i.b.351.20		44	11.10	odd	2	inner
1408.2.i.b.1055.19		44	176.43	even	4	inner
1408.2.i.b.1055.20		44	16.11	odd	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:	\( N \)	\(=\)	\( 1408 = 2^{7} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1408.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.82463 - 1.82463i) q^{3} +(2.57632 - 2.57632i) q^{5} -2.30642i q^{7} -3.65855i q^{9} +O(q^{10})\)	\(q+(1.82463 - 1.82463i) q^{3} +(2.57632 - 2.57632i) q^{5} -2.30642i q^{7} -3.65855i q^{9} +(-2.61242 + 2.04334i) q^{11} +(2.25903 - 2.25903i) q^{13} -9.40167i q^{15} +1.40277i q^{17} +(5.03186 + 5.03186i) q^{19} +(-4.20837 - 4.20837i) q^{21} -3.12111 q^{23} -8.27488i q^{25} +(-1.20161 - 1.20161i) q^{27} +(0.452394 - 0.452394i) q^{29} +3.35465i q^{31} +(-1.03837 + 8.49505i) q^{33} +(-5.94209 - 5.94209i) q^{35} +(3.56280 - 3.56280i) q^{37} -8.24377i q^{39} -10.6795 q^{41} +(1.58250 - 1.58250i) q^{43} +(-9.42561 - 9.42561i) q^{45} +7.74416i q^{47} +1.68042 q^{49} +(2.55954 + 2.55954i) q^{51} +(3.56645 - 3.56645i) q^{53} +(-1.46614 + 11.9948i) q^{55} +18.3626 q^{57} +(2.93608 + 2.93608i) q^{59} +(-6.88773 + 6.88773i) q^{61} -8.43816 q^{63} -11.6400i q^{65} +(-6.98769 + 6.98769i) q^{67} +(-5.69487 + 5.69487i) q^{69} -2.69084 q^{71} +2.27278 q^{73} +(-15.0986 - 15.0986i) q^{75} +(4.71280 + 6.02535i) q^{77} -10.2158 q^{79} +6.59065 q^{81} +(-1.15150 - 1.15150i) q^{83} +(3.61399 + 3.61399i) q^{85} -1.65090i q^{87} +16.8749i q^{89} +(-5.21027 - 5.21027i) q^{91} +(6.12099 + 6.12099i) q^{93} +25.9274 q^{95} +6.48153 q^{97} +(7.47567 + 9.55769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5	\( 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Introduction

L-functions

Modular forms

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Database

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