LMFDB - Embedded newform 128.4.g.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	128.49
Dual form			128.4.g.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.97998 + 2.89120i) q^{3} +(1.57150 - 3.79394i) q^{5} +(-15.6607 - 15.6607i) q^{7} +(21.2692 - 21.2692i) q^{9} +O(q^{10})$	\(q+(-6.97998 + 2.89120i) q^{3} +(1.57150 - 3.79394i) q^{5} +(-15.6607 - 15.6607i) q^{7} +(21.2692 - 21.2692i) q^{9} +(56.0992 + 23.2370i) q^{11} +(14.0971 + 34.0334i) q^{13} +31.0252i q^{15} -26.6088i q^{17} +(30.7752 + 74.2979i) q^{19} +(154.590 + 64.0332i) q^{21} +(141.584 - 141.584i) q^{23} +(76.4640 + 76.4640i) q^{25} +(-8.90248 + 21.4925i) q^{27} +(-11.9990 + 4.97014i) q^{29} +128.572 q^{31} -458.754 q^{33} +(-84.0267 + 34.8050i) q^{35} +(85.1234 - 205.506i) q^{37} +(-196.795 - 196.795i) q^{39} +(-32.3348 + 32.3348i) q^{41} +(-314.016 - 130.070i) q^{43} +(-47.2695 - 114.119i) q^{45} +184.040i q^{47} +147.516i q^{49} +(76.9314 + 185.729i) q^{51} +(277.346 + 114.881i) q^{53} +(176.320 - 176.320i) q^{55} +(-429.620 - 429.620i) q^{57} +(-241.099 + 582.065i) q^{59} +(297.419 - 123.195i) q^{61} -666.181 q^{63} +151.275 q^{65} +(605.866 - 250.958i) q^{67} +(-578.904 + 1397.60i) q^{69} +(-163.321 - 163.321i) q^{71} +(624.709 - 624.709i) q^{73} +(-754.790 - 312.644i) q^{75} +(-514.644 - 1242.46i) q^{77} -139.919i q^{79} +636.381i q^{81} +(226.003 + 545.620i) q^{83} +(-100.952 - 41.8158i) q^{85} +(69.3829 - 69.3829i) q^{87} +(231.313 + 231.313i) q^{89} +(312.217 - 753.759i) q^{91} +(-897.429 + 371.727i) q^{93} +330.245 q^{95} -594.442 q^{97} +(1687.42 - 698.950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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
$3$	−6.97998	+	2.89120i	−1.34330	+	0.556412i	−0.934419	−	0.356177i	$-0.884080\pi$
$3$	−6.97998	+	2.89120i	−1.34330	+	0.556412i	−0.408879	+	0.912589i	$0.634080\pi$
$4$		0			0
$5$	1.57150	−	3.79394i	0.140559	−	0.339340i	−0.837886	−	0.545845i	$-0.816209\pi$
$5$	1.57150	−	3.79394i	0.140559	−	0.339340i	0.978446	+	0.206504i	$0.0662088\pi$
$6$		0			0
$7$	−15.6607	−	15.6607i	−0.845599	−	0.845599i	0.143981	−	0.989580i	$-0.454009\pi$
$7$	−15.6607	−	15.6607i	−0.845599	−	0.845599i	−0.989580	+	0.143981i	$0.954009\pi$
$8$		0			0
$9$	21.2692	−	21.2692i	0.787747	−	0.787747i
$10$		0			0
$11$	56.0992	+	23.2370i	1.53768	+	0.636930i	0.981037	−	0.193819i	$-0.0620874\pi$
$11$	56.0992	+	23.2370i	1.53768	+	0.636930i	0.556647	+	0.830749i	$0.312087\pi$
$12$		0			0
$13$	14.0971	+	34.0334i	0.300757	+	0.726091i	0.999938	+	0.0111463i	$0.00354805\pi$
$13$	14.0971	+	34.0334i	0.300757	+	0.726091i	−0.699181	+	0.714944i	$0.746452\pi$
$14$		0			0
$15$			31.0252i			0.534044i
$16$		0			0
$17$		−	26.6088i		−	0.379622i	−0.981821	−	0.189811i	$-0.939212\pi$
$17$		−	26.6088i		−	0.379622i	0.981821	−	0.189811i	$-0.0607876\pi$
$18$		0			0
$19$	30.7752	+	74.2979i	0.371595	+	0.897110i	0.993481	+	0.114002i	$0.0363670\pi$
$19$	30.7752	+	74.2979i	0.371595	+	0.897110i	−0.621885	+	0.783108i	$0.713633\pi$
$20$		0			0
$21$	154.590	+	64.0332i	1.60639	+	0.665390i
$22$		0			0
$23$	141.584	−	141.584i	1.28358	−	1.28358i	0.344957	−	0.938618i	$-0.387893\pi$
$23$	141.584	−	141.584i	1.28358	−	1.28358i	0.938618	−	0.344957i	$-0.112107\pi$
$24$		0			0
$25$	76.4640	+	76.4640i	0.611712	+	0.611712i
$26$		0			0
$27$	−8.90248	+	21.4925i	−0.0634549	+	0.153194i
$28$		0			0
$29$	−11.9990	+	4.97014i	−0.0768329	+	0.0318252i	−0.420769	−	0.907168i	$-0.638240\pi$
$29$	−11.9990	+	4.97014i	−0.0768329	+	0.0318252i	0.343936	+	0.938993i	$0.388240\pi$
$30$		0			0
$31$	128.572			0.744909			0.372455	−	0.928050i	$-0.378516\pi$
$31$	128.572			0.744909			0.372455	+	0.928050i	$0.378516\pi$
$32$		0			0
$33$	−458.754			−2.41996
$34$		0			0
$35$	−84.0267	+	34.8050i	−0.405803	+	0.168089i
$36$		0			0
$37$	85.1234	−	205.506i	0.378222	−	0.913108i	−0.614078	−	0.789246i	$-0.710472\pi$
$37$	85.1234	−	205.506i	0.378222	−	0.913108i	0.992299	−	0.123863i	$-0.0395282\pi$
$38$		0			0
$39$	−196.795	−	196.795i	−0.808011	−	0.808011i
$40$		0			0
$41$	−32.3348	+	32.3348i	−0.123167	+	0.123167i	−0.766004	−	0.642836i	$-0.777758\pi$
$41$	−32.3348	+	32.3348i	−0.123167	+	0.123167i	0.642836	+	0.766004i	$0.277758\pi$
$42$		0			0
$43$	−314.016	−	130.070i	−1.11365	−	0.461289i	−0.251457	−	0.967868i	$-0.580910\pi$
$43$	−314.016	−	130.070i	−1.11365	−	0.461289i	−0.862193	+	0.506579i	$0.830910\pi$
$44$		0			0
$45$	−47.2695	−	114.119i	−0.156589	−	0.378040i
$46$		0			0
$47$			184.040i			0.571169i	0.958353	+	0.285585i	$0.0921878\pi$
$47$			184.040i			0.571169i	−0.958353	+	0.285585i	$0.907812\pi$
$48$		0			0
$49$			147.516i			0.430076i
$50$		0			0
$51$	76.9314	+	185.729i	0.211227	+	0.509946i
$52$		0			0
$53$	277.346	+	114.881i	0.718801	+	0.297737i	0.711941	−	0.702239i	$-0.247816\pi$
$53$	277.346	+	114.881i	0.718801	+	0.297737i	0.00685997	+	0.999976i	$0.497816\pi$
$54$		0			0
$55$	176.320	−	176.320i	0.432272	−	0.432272i
$56$		0			0
$57$	−429.620	−	429.620i	−0.998326	−	0.998326i
$58$		0			0
$59$	−241.099	+	582.065i	−0.532008	+	1.28438i	0.398184	+	0.917306i	$0.369641\pi$
$59$	−241.099	+	582.065i	−0.532008	+	1.28438i	−0.930192	+	0.367075i	$0.880359\pi$
$60$		0			0
$61$	297.419	−	123.195i	0.624271	−	0.258582i	−0.0480457	−	0.998845i	$-0.515299\pi$
$61$	297.419	−	123.195i	0.624271	−	0.258582i	0.672317	+	0.740264i	$0.265299\pi$
$62$		0			0
$63$	−666.181			−1.33224
$64$		0			0
$65$	151.275			0.288666
$66$		0			0
$67$	605.866	−	250.958i	1.10475	−	0.457603i	0.245624	−	0.969365i	$-0.421007\pi$
$67$	605.866	−	250.958i	1.10475	−	0.457603i	0.859127	+	0.511763i	$0.171007\pi$
$68$		0			0
$69$	−578.904	+	1397.60i	−1.01003	+	2.43842i
$70$		0			0
$71$	−163.321	−	163.321i	−0.272994	−	0.272994i	0.557310	−	0.830304i	$-0.311833\pi$
$71$	−163.321	−	163.321i	−0.272994	−	0.272994i	−0.830304	+	0.557310i	$0.811833\pi$
$72$		0			0
$73$	624.709	−	624.709i	1.00160	−	1.00160i	0.00159983	−	0.999999i	$-0.499491\pi$
$73$	624.709	−	624.709i	1.00160	−	1.00160i	0.999999	−	0.00159983i	$-0.000509242\pi$
$74$		0			0
$75$	−754.790	−	312.644i	−1.16207	−	0.481347i
$76$		0			0
$77$	−514.644	−	1242.46i	−0.761678	−	1.83885i
$78$		0			0
$79$		−	139.919i		−	0.199267i	−0.995024	−	0.0996336i	$-0.968233\pi$
$79$		−	139.919i		−	0.199267i	0.995024	−	0.0996336i	$-0.0317671\pi$
$80$		0			0
$81$			636.381i			0.872951i
$82$		0			0
$83$	226.003	+	545.620i	0.298881	+	0.721562i	0.999964	+	0.00848231i	$0.00270004\pi$
$83$	226.003	+	545.620i	0.298881	+	0.721562i	−0.701083	+	0.713079i	$0.747300\pi$
$84$		0			0
$85$	−100.952	−	41.8158i	−0.128821	−	0.0533595i
$86$		0			0
$87$	69.3829	−	69.3829i	0.0855015	−	0.0855015i
$88$		0			0
$89$	231.313	+	231.313i	0.275496	+	0.275496i	0.831308	−	0.555812i	$-0.187593\pi$
$89$	231.313	+	231.313i	0.275496	+	0.275496i	−0.555812	+	0.831308i	$0.687593\pi$
$90$		0			0
$91$	312.217	−	753.759i	0.359662	−	0.868301i
$92$		0			0
$93$	−897.429	+	371.727i	−1.00063	+	0.414476i
$94$		0			0
$95$	330.245			0.356657
$96$		0			0
$97$	−594.442			−0.622231			−0.311116	−	0.950372i	$-0.600703\pi$
$97$	−594.442			−0.622231			−0.311116	+	0.950372i	$0.600703\pi$
$98$		0			0
$99$	1687.42	−	698.950i	1.71305	−	0.709567i
$100$		0			0
$101$	164.682	−	397.578i	0.162242	−	0.391688i	−0.821762	−	0.569831i	$-0.807009\pi$
$101$	164.682	−	397.578i	0.162242	−	0.391688i	0.984005	+	0.178143i	$0.0570088\pi$
$102$		0			0
$103$	718.153	+	718.153i	0.687007	+	0.687007i	0.961569	−	0.274563i	$-0.0885330\pi$
$103$	718.153	+	718.153i	0.687007	+	0.687007i	−0.274563	+	0.961569i	$0.588533\pi$
$104$		0			0
$105$	485.876	−	485.876i	0.451587	−	0.451587i
$106$		0			0
$107$	−367.941	−	152.406i	−0.332432	−	0.137698i	0.210223	−	0.977653i	$-0.432581\pi$
$107$	−367.941	−	152.406i	−0.332432	−	0.137698i	−0.542655	+	0.839956i	$0.682581\pi$
$108$		0			0
$109$	177.769	+	429.173i	0.156213	+	0.377131i	0.982538	−	0.186062i	$-0.0595726\pi$
$109$	177.769	+	429.173i	0.156213	+	0.377131i	−0.826325	+	0.563193i	$0.809573\pi$
$110$		0			0
$111$			1680.54i			1.43702i
$112$		0			0
$113$			323.520i			0.269329i	0.990891	+	0.134665i	$0.0429957\pi$
$113$			323.520i			0.269329i	−0.990891	+	0.134665i	$0.957004\pi$
$114$		0			0
$115$	−314.661	−	759.659i	−0.255150	−	0.615988i
$116$		0			0
$117$	1023.70	+	424.029i	0.808896	+	0.335056i
$118$		0			0
$119$	−416.713	+	416.713i	−0.321008	+	0.321008i
$120$		0			0
$121$	1666.00	+	1666.00i	1.25169	+	1.25169i
$122$		0			0
$123$	132.210	−	319.183i	0.0969185	−	0.233982i
$124$		0			0
$125$	884.506	−	366.374i	0.632901	−	0.262156i
$126$		0			0
$127$	1147.19			0.801550			0.400775	−	0.916177i	$-0.368741\pi$
$127$	1147.19			0.801550			0.400775	+	0.916177i	$0.368741\pi$
$128$		0			0
$129$	2567.88			1.75263
$130$		0			0
$131$	−1429.33	+	592.049i	−0.953293	+	0.394867i	−0.804468	−	0.593997i	$-0.797549\pi$
$131$	−1429.33	+	592.049i	−0.953293	+	0.394867i	−0.148825	+	0.988863i	$0.547549\pi$
$132$		0			0
$133$	681.596	−	1645.52i	0.444375	−	1.07282i
$134$		0			0
$135$	67.5509	+	67.5509i	0.0430656	+	0.0430656i
$136$		0			0
$137$	−247.558	+	247.558i	−0.154382	+	0.154382i	−0.780072	−	0.625690i	$-0.784817\pi$
$137$	−247.558	+	247.558i	−0.154382	+	0.154382i	0.625690	+	0.780072i	$0.284817\pi$
$138$		0			0
$139$	599.777	+	248.436i	0.365989	+	0.151598i	0.558096	−	0.829776i	$-0.311532\pi$
$139$	599.777	+	248.436i	0.365989	+	0.151598i	−0.192107	+	0.981374i	$0.561532\pi$
$140$		0			0
$141$	−532.096	−	1284.59i	−0.317806	−	0.767250i
$142$		0			0
$143$			2236.82i			1.30806i
$144$		0			0
$145$			53.3340i			0.0305458i
$146$		0			0
$147$	−426.499	−	1029.66i	−0.239299	−	0.577720i
$148$		0			0
$149$	−1776.52	−	735.857i	−0.976765	−	0.404589i	−0.163539	−	0.986537i	$-0.552291\pi$
$149$	−1776.52	−	735.857i	−0.976765	−	0.404589i	−0.813226	+	0.581948i	$0.802291\pi$
$150$		0			0
$151$	1331.94	−	1331.94i	0.717827	−	0.717827i	−0.250333	−	0.968160i	$-0.580540\pi$
$151$	1331.94	−	1331.94i	0.717827	−	0.717827i	0.968160	+	0.250333i	$0.0805401\pi$
$152$		0			0
$153$	−565.947	−	565.947i	−0.299047	−	0.299047i
$154$		0			0
$155$	202.051	−	487.794i	0.104704	−	0.252778i
$156$		0			0
$157$	−2417.43	+	1001.33i	−1.22887	+	0.509013i	−0.900218	−	0.435440i	$-0.856593\pi$
$157$	−2417.43	+	1001.33i	−1.22887	+	0.509013i	−0.328647	+	0.944453i	$0.606593\pi$
$158$		0			0
$159$	−2268.01			−1.13123
$160$		0			0
$161$	−4434.60			−2.17078
$162$		0			0
$163$	−1823.96	+	755.507i	−0.876462	+	0.363042i	−0.775124	−	0.631810i	$-0.782312\pi$
$163$	−1823.96	+	755.507i	−0.876462	+	0.363042i	−0.101338	+	0.994852i	$0.532312\pi$
$164$		0			0
$165$	−720.933	+	1740.49i	−0.340149	+	0.821191i
$166$		0			0
$167$	−2602.55	−	2602.55i	−1.20594	−	1.20594i	−0.972332	−	0.233605i	$-0.924948\pi$
$167$	−2602.55	−	2602.55i	−1.20594	−	1.20594i	−0.233605	−	0.972332i	$-0.575052\pi$
$168$		0			0
$169$	593.967	−	593.967i	0.270354	−	0.270354i
$170$		0			0
$171$	2234.82	+	925.692i	0.999420	+	0.413973i
$172$		0			0
$173$	1666.31	+	4022.82i	0.732295	+	1.76792i	0.634794	+	0.772681i	$0.281085\pi$
$173$	1666.31	+	4022.82i	0.732295	+	1.76792i	0.0975011	+	0.995235i	$0.468915\pi$
$174$		0			0
$175$		−	2394.96i		−	1.03453i
$176$		0			0
$177$		−	4759.87i		−	2.02132i
$178$		0			0
$179$	317.180	+	765.739i	0.132442	+	0.319743i	0.976163	−	0.217039i	$-0.0696398\pi$
$179$	317.180	+	765.739i	0.132442	+	0.319743i	−0.843721	+	0.536782i	$0.819640\pi$
$180$		0			0
$181$	−1556.05	−	644.538i	−0.639008	−	0.264686i	0.0395667	−	0.999217i	$-0.487402\pi$
$181$	−1556.05	−	644.538i	−0.639008	−	0.264686i	−0.678575	+	0.734531i	$0.737402\pi$
$182$		0			0
$183$	−1719.79	+	1719.79i	−0.694704	+	0.694704i
$184$		0			0
$185$	−645.907	−	645.907i	−0.256692	−	0.256692i
$186$		0			0
$187$	618.309	−	1492.73i	0.241793	−	0.583740i
$188$		0			0
$189$	476.007	−	197.168i	0.183198	−	0.0758830i
$190$		0			0
$191$	582.225			0.220567			0.110283	−	0.993900i	$-0.464824\pi$
$191$	582.225			0.220567			0.110283	+	0.993900i	$0.464824\pi$
$192$		0			0
$193$	2115.34			0.788941			0.394471	−	0.918909i	$-0.370928\pi$
$193$	2115.34			0.788941			0.394471	+	0.918909i	$0.370928\pi$
$194$		0			0
$195$	−1055.89	+	437.365i	−0.387764	+	0.160617i
$196$		0			0
$197$	1017.56	−	2456.60i	0.368009	−	0.888453i	−0.626067	−	0.779769i	$-0.715336\pi$
$197$	1017.56	−	2456.60i	0.368009	−	0.888453i	0.994076	−	0.108684i	$-0.0346637\pi$
$198$		0			0
$199$	260.073	+	260.073i	0.0926437	+	0.0926437i	0.751910	−	0.659266i	$-0.229133\pi$
$199$	260.073	+	260.073i	0.0926437	+	0.0926437i	−0.659266	+	0.751910i	$0.729133\pi$
$200$		0			0
$201$	−3503.36	+	3503.36i	−1.22939	+	1.22939i
$202$		0			0
$203$	265.748	+	110.077i	0.0918812	+	0.0380584i
$204$		0			0
$205$	71.8622	+	173.491i	0.0244833	+	0.0591079i
$206$		0			0
$207$		−	6022.74i		−	2.02227i
$208$		0			0
$209$			4883.17i			1.61615i
$210$		0			0
$211$	594.857	+	1436.11i	0.194084	+	0.468560i	0.990723	−	0.135895i	$-0.0433910\pi$
$211$	594.857	+	1436.11i	0.194084	+	0.468560i	−0.796640	+	0.604455i	$0.793391\pi$
$212$		0			0
$213$	1612.17	+	667.781i	0.518610	+	0.214815i
$214$		0			0
$215$	−986.953	+	986.953i	−0.313068	+	0.313068i
$216$		0			0
$217$	−2013.53	−	2013.53i	−0.629895	−	0.629895i
$218$		0			0
$219$	−2554.30	+	6166.62i	−0.788143	+	1.90275i
$220$		0			0
$221$	905.589	−	375.107i	0.275640	−	0.114174i
$222$		0			0
$223$	1890.38			0.567663			0.283832	−	0.958874i	$-0.408394\pi$
$223$	1890.38			0.567663			0.283832	+	0.958874i	$0.408394\pi$
$224$		0			0
$225$	3252.65			0.963749
$226$		0			0
$227$	711.120	−	294.556i	0.207924	−	0.0861248i	−0.276291	−	0.961074i	$-0.589105\pi$
$227$	711.120	−	294.556i	0.207924	−	0.0861248i	0.484215	+	0.874949i	$0.339105\pi$
$228$		0			0
$229$	90.4906	−	218.464i	0.0261126	−	0.0630414i	−0.910285	−	0.413981i	$-0.864138\pi$
$229$	90.4906	−	218.464i	0.0261126	−	0.0630414i	0.936398	+	0.350940i	$0.114138\pi$
$230$		0			0
$231$	7184.41	+	7184.41i	2.04632	+	2.04632i
$232$		0			0
$233$	−2838.71	+	2838.71i	−0.798155	+	0.798155i	−0.982804	−	0.184650i	$-0.940885\pi$
$233$	−2838.71	+	2838.71i	−0.798155	+	0.798155i	0.184650	+	0.982804i	$0.440885\pi$
$234$		0			0
$235$	698.236	+	289.219i	0.193821	+	0.0802832i
$236$		0			0
$237$	404.534	+	976.631i	0.110875	+	0.267675i
$238$		0			0
$239$		−	7044.27i		−	1.90651i	−0.302168	−	0.953255i	$-0.597710\pi$
$239$		−	7044.27i		−	1.90651i	0.302168	−	0.953255i	$-0.402290\pi$
$240$		0			0
$241$		−	5909.62i		−	1.57955i	−0.613395	−	0.789776i	$-0.710197\pi$
$241$		−	5909.62i		−	1.57955i	0.613395	−	0.789776i	$-0.289803\pi$
$242$		0			0
$243$	−2080.27	−	5022.23i	−0.549176	−	1.32583i
$244$		0			0
$245$	559.667	+	231.822i	0.145942	+	0.0604512i
$246$		0			0
$247$	−2094.77	+	2094.77i	−0.539624	+	0.539624i
$248$		0			0
$249$	−3155.00	−	3155.00i	−0.802971	−	0.802971i
$250$		0			0
$251$	−431.008	+	1040.55i	−0.108386	+	0.261668i	−0.968762	−	0.247993i	$-0.920229\pi$
$251$	−431.008	+	1040.55i	−0.108386	+	0.261668i	0.860375	+	0.509661i	$0.170229\pi$
$252$		0			0
$253$	11232.7	−	4652.74i	2.79128	−	1.15619i
$254$		0			0
$255$	825.542			0.202735
$256$		0			0
$257$	−225.266			−0.0546759			−0.0273380	−	0.999626i	$-0.508703\pi$
$257$	−225.266			−0.0546759			−0.0273380	+	0.999626i	$0.508703\pi$
$258$		0			0
$259$	−4551.47	+	1885.28i	−1.09195	+	0.452299i
$260$		0			0
$261$	−149.498	+	360.919i	−0.0354547	+	0.0855951i
$262$		0			0
$263$	−3244.94	−	3244.94i	−0.760803	−	0.760803i	0.215664	−	0.976468i	$-0.430808\pi$
$263$	−3244.94	−	3244.94i	−0.760803	−	0.760803i	−0.976468	+	0.215664i	$0.930808\pi$
$264$		0			0
$265$	871.700	−	871.700i	0.202068	−	0.202068i
$266$		0			0
$267$	−2283.34	−	945.789i	−0.523363	−	0.216784i
$268$		0			0
$269$	83.5926	+	201.810i	0.0189470	+	0.0457420i	0.933070	−	0.359695i	$-0.117119\pi$
$269$	83.5926	+	201.810i	0.0189470	+	0.0457420i	−0.914123	+	0.405437i	$0.867119\pi$
$270$		0			0
$271$			4103.79i			0.919880i	0.887950	+	0.459940i	$0.152129\pi$
$271$			4103.79i			0.919880i	−0.887950	+	0.459940i	$0.847871\pi$
$272$		0			0
$273$			6163.91i			1.36651i
$274$		0			0
$275$	2512.77	+	6066.36i	0.551002	+	1.33024i
$276$		0			0
$277$	−775.002	−	321.016i	−0.168106	−	0.0696318i	0.297043	−	0.954864i	$-0.403999\pi$
$277$	−775.002	−	321.016i	−0.168106	−	0.0696318i	−0.465149	+	0.885232i	$0.653999\pi$
$278$		0			0
$279$	2734.62	−	2734.62i	0.586800	−	0.586800i
$280$		0			0
$281$	1856.75	+	1856.75i	0.394180	+	0.394180i	0.876174	−	0.481994i	$-0.160087\pi$
$281$	1856.75	+	1856.75i	0.394180	+	0.394180i	−0.481994	+	0.876174i	$0.660087\pi$
$282$		0			0
$283$	2964.83	−	7157.74i	0.622760	−	1.50348i	−0.225689	−	0.974199i	$-0.572463\pi$
$283$	2964.83	−	7157.74i	0.622760	−	1.50348i	0.848449	−	0.529277i	$-0.177537\pi$
$284$		0			0
$285$	−2305.10	+	954.805i	−0.479096	+	0.198448i
$286$		0			0
$287$	1012.77			0.208300
$288$		0			0
$289$	4204.97			0.855887
$290$		0			0
$291$	4149.19	−	1718.65i	0.835842	−	0.346217i
$292$		0			0
$293$	316.687	−	764.550i	0.0631435	−	0.152442i	−0.889158	−	0.457600i	$-0.848709\pi$
$293$	316.687	−	764.550i	0.0631435	−	0.152442i	0.952302	+	0.305158i	$0.0987092\pi$
$294$		0			0
$295$	1829.43	+	1829.43i	0.361063	+	0.361063i
$296$		0			0
$297$	−998.843	+	998.843i	−0.195147	+	0.195147i
$298$		0			0
$299$	6814.50	+	2822.66i	1.31804	+	0.545949i
$300$		0			0
$301$	2880.73	+	6954.70i	0.551636	+	1.33177i
$302$		0			0
$303$			3251.22i			0.616427i
$304$		0			0
$305$		−	1321.99i		−	0.248186i
$306$		0			0
$307$	−1040.36	−	2511.64i	−0.193408	−	0.466928i	0.797191	−	0.603727i	$-0.206318\pi$
$307$	−1040.36	−	2511.64i	−0.193408	−	0.466928i	−0.990599	+	0.136799i	$0.956318\pi$
$308$		0			0
$309$	−7089.02	−	2936.37i	−1.30511	−	0.540596i
$310$		0			0
$311$	520.010	−	520.010i	0.0948138	−	0.0948138i	−0.658109	−	0.752923i	$-0.728643\pi$
$311$	520.010	−	520.010i	0.0948138	−	0.0948138i	0.752923	+	0.658109i	$0.228643\pi$
$312$		0			0
$313$	1970.33	+	1970.33i	0.355814	+	0.355814i	0.862267	−	0.506454i	$-0.169044\pi$
$313$	1970.33	+	1970.33i	0.355814	+	0.355814i	−0.506454	+	0.862267i	$0.669044\pi$
$314$		0			0
$315$	−1046.90	+	2527.45i	−0.187258	+	0.452082i
$316$		0			0
$317$	−6426.24	+	2661.83i	−1.13859	+	0.471620i	−0.870693	−	0.491827i	$-0.836329\pi$
$317$	−6426.24	+	2661.83i	−1.13859	+	0.471620i	−0.267898	+	0.963447i	$0.586329\pi$
$318$		0			0
$319$	−788.624			−0.138415
$320$		0			0
$321$	3008.86			0.523172
$322$		0			0
$323$	1976.98	−	818.890i	0.340563	−	0.141066i
$324$		0			0
$325$	−1524.41	+	3680.25i	−0.260182	+	0.628135i
$326$		0			0
$327$	−2481.65	−	2481.65i	−0.419681	−	0.419681i
$328$		0			0
$329$	2882.19	−	2882.19i	0.482980	−	0.482980i
$330$		0			0
$331$	7122.25	+	2950.13i	1.18270	+	0.489891i	0.885372	−	0.464884i	$-0.153904\pi$
$331$	7122.25	+	2950.13i	1.18270	+	0.489891i	0.297330	+	0.954775i	$0.403904\pi$
$332$		0			0
$333$	−2560.44	−	6181.45i	−0.421355	−	1.01724i
$334$		0			0
$335$		−	2693.00i		−	0.439207i
$336$		0			0
$337$		−	8124.62i		−	1.31328i	−0.754203	−	0.656641i	$-0.771977\pi$
$337$		−	8124.62i		−	1.31328i	0.754203	−	0.656641i	$-0.228023\pi$
$338$		0			0
$339$	−935.361	−	2258.16i	−0.149858	−	0.361789i
$340$		0			0
$341$	7212.77	+	2987.63i	1.14544	+	0.474455i
$342$		0			0
$343$	−3061.42	+	3061.42i	−0.481927	+	0.481927i
$344$		0			0
$345$	4392.66	+	4392.66i	0.685486	+	0.685486i
$346$		0			0
$347$	−226.606	+	547.076i	−0.0350572	+	0.0846356i	−0.940438	−	0.339964i	$-0.889585\pi$
$347$	−226.606	+	547.076i	−0.0350572	+	0.0846356i	0.905381	+	0.424600i	$0.139585\pi$
$348$		0			0
$349$	−10769.6	+	4460.93i	−1.65182	+	0.684206i	−0.997409	−	0.0719343i	$-0.977083\pi$
$349$	−10769.6	+	4460.93i	−1.65182	+	0.684206i	−0.654410	+	0.756140i	$0.727083\pi$
$350$		0			0
$351$	−856.962			−0.130317
$352$		0			0
$353$	−8090.20			−1.21982			−0.609912	−	0.792469i	$-0.708795\pi$
$353$	−8090.20			−1.21982			−0.609912	+	0.792469i	$0.708795\pi$
$354$		0			0
$355$	−876.287	+	362.970i	−0.131010	+	0.0542660i
$356$		0			0
$357$	1703.85	−	4113.45i	0.252597	−	0.609823i
$358$		0			0
$359$	−2606.68	−	2606.68i	−0.383218	−	0.383218i	0.489042	−	0.872260i	$-0.337346\pi$
$359$	−2606.68	−	2606.68i	−0.383218	−	0.383218i	−0.872260	+	0.489042i	$0.837346\pi$
$360$		0			0
$361$	276.986	−	276.986i	0.0403828	−	0.0403828i
$362$		0			0
$363$	−16445.4	−	6811.89i	−2.37784	−	0.984935i
$364$		0			0
$365$	−1388.38	−	3351.84i	−0.199099	−	0.480667i
$366$		0			0
$367$			8063.18i			1.14685i	0.819258	+	0.573426i	$0.194386\pi$
$367$			8063.18i			1.14685i	−0.819258	+	0.573426i	$0.805614\pi$
$368$		0			0
$369$			1375.47i			0.194049i
$370$		0			0
$371$	−2544.33	−	6142.55i	−0.356051	−	0.859584i
$372$		0			0
$373$	−7668.37	−	3176.34i	−1.06449	−	0.440924i	−0.219444	−	0.975625i	$-0.570424\pi$
$373$	−7668.37	−	3176.34i	−1.06449	−	0.440924i	−0.845042	+	0.534701i	$0.820424\pi$
$374$		0			0
$375$	−5114.57	+	5114.57i	−0.704307	+	0.704307i
$376$		0			0
$377$	−338.302	−	338.302i	−0.0462160	−	0.0462160i
$378$		0			0
$379$	3822.52	−	9228.39i	0.518073	−	1.25074i	−0.421012	−	0.907055i	$-0.638325\pi$
$379$	3822.52	−	9228.39i	0.518073	−	1.25074i	0.939085	−	0.343685i	$-0.111675\pi$
$380$		0			0
$381$	−8007.38	+	3316.76i	−1.07672	+	0.445992i
$382$		0			0
$383$	−9953.63			−1.32795			−0.663977	−	0.747753i	$-0.731133\pi$
$383$	−9953.63			−1.32795			−0.663977	+	0.747753i	$0.731133\pi$
$384$		0			0
$385$	−5522.59			−0.731058
$386$		0			0
$387$	−9445.34	+	3912.39i	−1.24065	+	0.513896i
$388$		0			0
$389$	3176.18	−	7667.98i	0.413982	−	0.999440i	−0.570076	−	0.821592i	$-0.693086\pi$
$389$	3176.18	−	7667.98i	0.413982	−	0.999440i	0.984058	−	0.177848i	$-0.0569136\pi$
$390$		0			0
$391$	−3767.37	−	3767.37i	−0.487274	−	0.487274i
$392$		0			0
$393$	8264.98	−	8264.98i	1.06085	−	1.06085i
$394$		0			0
$395$	−530.844	−	219.883i	−0.0676194	−	0.0280089i
$396$		0			0
$397$	−60.6257	−	146.363i	−0.00766427	−	0.0185032i	0.920001	−	0.391916i	$-0.128188\pi$
$397$	−60.6257	−	146.363i	−0.00766427	−	0.0185032i	−0.927665	+	0.373413i	$0.878188\pi$
$398$		0			0
$399$			13456.3i			1.68837i
$400$		0			0
$401$			3474.14i			0.432644i	0.976322	+	0.216322i	$0.0694062\pi$
$401$			3474.14i			0.432644i	−0.976322	+	0.216322i	$0.930594\pi$
$402$		0			0
$403$	1812.49	+	4375.74i	0.224036	+	0.540872i
$404$		0			0
$405$	2414.39	+	1000.07i	0.296228	+	0.122701i
$406$		0			0
$407$	9550.71	−	9550.71i	1.16317	−	1.16317i
$408$		0			0
$409$	4584.30	+	4584.30i	0.554228	+	0.554228i	0.927658	−	0.373430i	$-0.121819\pi$
$409$	4584.30	+	4584.30i	0.554228	+	0.554228i	−0.373430	+	0.927658i	$0.621819\pi$
$410$		0			0
$411$	1012.21	−	2443.69i	0.121481	−	0.293280i
$412$		0			0
$413$	12891.3	−	5339.77i	1.53594	−	0.636206i
$414$		0			0
$415$	2425.22			0.286865
$416$		0			0
$417$	−4904.71			−0.575983
$418$		0			0
$419$	10250.7	−	4245.97i	1.19517	−	0.495058i	0.305738	−	0.952116i	$-0.401097\pi$
$419$	10250.7	−	4245.97i	1.19517	−	0.495058i	0.889437	+	0.457058i	$0.151097\pi$
$420$		0			0
$421$	−3016.30	+	7282.00i	−0.349182	+	0.843000i	0.647535	+	0.762036i	$0.275800\pi$
$421$	−3016.30	+	7282.00i	−0.349182	+	0.843000i	−0.996717	+	0.0809641i	$0.974200\pi$
$422$		0			0
$423$	3914.37	+	3914.37i	0.449937	+	0.449937i
$424$		0			0
$425$	2034.61	−	2034.61i	0.232220	−	0.232220i
$426$		0			0
$427$	−6587.10	−	2728.47i	−0.746539	−	0.309227i
$428$		0			0
$429$	−6467.11	−	15613.0i	−0.727820	−	1.75711i
$430$		0			0
$431$			14216.7i			1.58885i	0.607365	+	0.794423i	$0.292227\pi$
$431$			14216.7i			1.58885i	−0.607365	+	0.794423i	$0.707773\pi$
$432$		0			0
$433$			14011.6i			1.55509i	0.628830	+	0.777543i	$0.283534\pi$
$433$			14011.6i			1.55509i	−0.628830	+	0.777543i	$0.716466\pi$
$434$		0			0
$435$	−154.199	−	372.270i	−0.0169961	−	0.0410321i
$436$		0			0
$437$	14876.6	+	6162.10i	1.62848	+	0.674538i
$438$		0			0
$439$	1061.27	−	1061.27i	0.115380	−	0.115380i	−0.647060	−	0.762439i	$-0.724002\pi$
$439$	1061.27	−	1061.27i	0.115380	−	0.115380i	0.762439	+	0.647060i	$0.224002\pi$
$440$		0			0
$441$	3137.54	+	3137.54i	0.338791	+	0.338791i
$442$		0			0
$443$	−2529.77	+	6107.40i	−0.271316	+	0.655014i	−0.999540	−	0.0303248i	$-0.990346\pi$
$443$	−2529.77	+	6107.40i	−0.271316	+	0.655014i	0.728224	+	0.685339i	$0.240346\pi$
$444$		0			0
$445$	1241.10	−	514.080i	0.132211	−	0.0547634i
$446$		0			0
$447$	14527.6			1.53720
$448$		0			0
$449$	1260.27			0.132463			0.0662313	−	0.997804i	$-0.478902\pi$
$449$	1260.27			0.132463			0.0662313	+	0.997804i	$0.478902\pi$
$450$		0			0
$451$	−2565.32	+	1062.59i	−0.267841	+	0.110943i
$452$		0			0
$453$	−5446.01	+	13147.8i	−0.564847	+	1.36366i
$454$		0			0
$455$	−2369.07	−	2369.07i	−0.244096	−	0.244096i
$456$		0			0
$457$	−7126.17	+	7126.17i	−0.729427	+	0.729427i	−0.970506	−	0.241078i	$-0.922499\pi$
$457$	−7126.17	+	7126.17i	−0.729427	+	0.729427i	0.241078	+	0.970506i	$0.422499\pi$
$458$		0			0
$459$	571.889	+	236.884i	0.0581558	+	0.0240889i
$460$		0			0
$461$	−429.245	−	1036.29i	−0.0433665	−	0.104696i	0.900712	−	0.434417i	$-0.143045\pi$
$461$	−429.245	−	1036.29i	−0.0433665	−	0.104696i	−0.944079	+	0.329721i	$0.893045\pi$
$462$		0			0
$463$		−	18501.7i		−	1.85712i	−0.371178	−	0.928562i	$-0.621046\pi$
$463$		−	18501.7i		−	1.85712i	0.371178	−	0.928562i	$-0.378954\pi$
$464$		0			0
$465$			3988.96i			0.397814i
$466$		0			0
$467$	5016.56	+	12111.1i	0.497085	+	1.20007i	0.951046	+	0.309049i	$0.100011\pi$
$467$	5016.56	+	12111.1i	0.497085	+	1.20007i	−0.453961	+	0.891022i	$0.649989\pi$
$468$		0			0
$469$	−13418.5	−	5558.11i	−1.32112	−	0.547228i
$470$		0			0
$471$	13978.5	−	13978.5i	1.36751	−	1.36751i
$472$		0			0
$473$	−14593.6	−	14593.6i	−1.41863	−	1.41863i
$474$		0			0
$475$	−3327.92	+	8034.30i	−0.321464	+	0.776082i
$476$		0			0
$477$	8342.34	−	3455.51i	0.800775	−	0.331692i
$478$		0			0
$479$	−4560.24			−0.434995			−0.217497	−	0.976061i	$-0.569789\pi$
$479$	−4560.24			−0.434995			−0.217497	+	0.976061i	$0.569789\pi$
$480$		0			0
$481$	8194.08			0.776752
$482$		0			0
$483$	30953.4	−	12821.3i	2.91601	−	1.20785i
$484$		0			0
$485$	−934.167	+	2255.28i	−0.0874605	+	0.211148i
$486$		0			0
$487$	14926.4	+	14926.4i	1.38887	+	1.38887i	0.827706	+	0.561162i	$0.189646\pi$
$487$	14926.4	+	14926.4i	1.38887	+	1.38887i	0.561162	+	0.827706i	$0.310354\pi$
$488$		0			0
$489$	10546.9	−	10546.9i	0.975348	−	0.975348i
$490$		0			0
$491$	1750.78	+	725.196i	0.160920	+	0.0666551i	0.461689	−	0.887042i	$-0.347244\pi$
$491$	1750.78	+	725.196i	0.160920	+	0.0666551i	−0.300770	+	0.953697i	$0.597244\pi$
$492$		0			0
$493$	132.249	+	319.278i	0.0120816	+	0.0291675i
$494$		0			0
$495$		−	7500.36i		−	0.681042i
$496$		0			0
$497$			5115.43i			0.461687i
$498$		0			0
$499$	−1646.59	−	3975.23i	−0.147719	−	0.356625i	0.832649	−	0.553801i	$-0.186823\pi$
$499$	−1646.59	−	3975.23i	−0.147719	−	0.356625i	−0.980368	+	0.197176i	$0.936823\pi$
$500$		0			0
$501$	25690.2	+	10641.2i	2.29093	+	0.948934i
$502$		0			0
$503$	−11968.8	+	11968.8i	−1.06096	+	1.06096i	−0.0629447	+	0.998017i	$0.520049\pi$
$503$	−11968.8	+	11968.8i	−1.06096	+	1.06096i	−0.998017	+	0.0629447i	$0.979951\pi$
$504$		0			0
$505$	−1249.59	−	1249.59i	−0.110111	−	0.110111i
$506$		0			0
$507$	−2428.60	+	5863.15i	−0.212737	+	0.513593i
$508$		0			0
$509$	−1912.55	+	792.203i	−0.166546	+	0.0689858i	−0.464399	−	0.885626i	$-0.653730\pi$
$509$	−1912.55	+	792.203i	−0.166546	+	0.0689858i	0.297853	+	0.954612i	$0.403730\pi$
$510$		0			0
$511$	−19566.8			−1.69390
$512$		0			0
$513$	−1870.82			−0.161011
$514$		0			0
$515$	3853.21	−	1596.05i	0.329694	−	0.136564i
$516$		0			0
$517$	−4276.54	+	10324.5i	−0.363795	+	0.878278i
$518$		0			0
$519$	−23261.6	−	23261.6i	−1.96738	−	1.96738i
$520$		0			0
$521$	−1713.04	+	1713.04i	−0.144049	+	0.144049i	−0.775454	−	0.631405i	$-0.782479\pi$
$521$	−1713.04	+	1713.04i	−0.144049	+	0.144049i	0.631405	+	0.775454i	$0.282479\pi$
$522$		0			0
$523$	−12429.1	−	5148.29i	−1.03917	−	0.430438i	−0.203155	−	0.979147i	$-0.565120\pi$
$523$	−12429.1	−	5148.29i	−1.03917	−	0.430438i	−0.836014	+	0.548709i	$0.815120\pi$
$524$		0			0
$525$	6924.32	+	16716.8i	0.575623	+	1.38968i
$526$		0			0
$527$		−	3421.14i		−	0.282784i
$528$		0			0
$529$		−	27924.9i		−	2.29513i
$530$		0			0
$531$	7252.06	+	17508.0i	0.592679	+	1.43085i
$532$		0			0
$533$	−1556.29	−	644.638i	−0.126474	−	0.0523872i
$534$		0			0
$535$	−1156.44	+	1156.44i	−0.0934528	+	0.0934528i
$536$		0			0
$537$	−4427.81	−	4427.81i	−0.355818	−	0.355818i
$538$		0			0
$539$	−3427.83	+	8275.52i	−0.273928	+	0.661321i
$540$		0			0
$541$	5533.67	−	2292.12i	0.439762	−	0.182155i	−0.151806	−	0.988410i	$-0.548509\pi$
$541$	5533.67	−	2292.12i	0.439762	−	0.182155i	0.591568	+	0.806255i	$0.298509\pi$
$542$		0			0
$543$	12724.7			1.00565
$544$		0			0
$545$	1907.62			0.149933
$546$		0			0
$547$	−11530.9	+	4776.23i	−0.901323	+	0.373340i	−0.784729	−	0.619840i	$-0.787198\pi$
$547$	−11530.9	+	4776.23i	−0.901323	+	0.373340i	−0.116594	+	0.993180i	$0.537198\pi$
$548$		0			0
$549$	3705.60	−	8946.10i	0.288071	−	0.695465i
$550$		0			0
$551$	−738.541	−	738.541i	−0.0571015	−	0.0571015i
$552$		0			0
$553$	−2191.23	+	2191.23i	−0.168500	+	0.168500i
$554$		0			0
$555$	6375.86	+	2640.97i	0.487640	+	0.201987i
$556$		0			0
$557$	−6605.12	−	15946.2i	−0.502456	−	1.21304i	−0.948142	−	0.317847i	$-0.897040\pi$
$557$	−6605.12	−	15946.2i	−0.502456	−	1.21304i	0.445686	−	0.895189i	$-0.352960\pi$
$558$		0			0
$559$		−	12520.7i		−	0.947347i
$560$		0			0
$561$			12206.9i			0.918673i
$562$		0			0
$563$	3621.28	+	8742.53i	0.271081	+	0.654447i	0.999530	−	0.0306525i	$-0.00975852\pi$
$563$	3621.28	+	8742.53i	0.271081	+	0.654447i	−0.728449	+	0.685100i	$0.759759\pi$
$564$		0			0
$565$	1227.42	+	508.412i	0.0913943	+	0.0378567i
$566$		0			0
$567$	9966.19	−	9966.19i	0.738167	−	0.738167i
$568$		0			0
$569$	4482.37	+	4482.37i	0.330247	+	0.330247i	0.852680	−	0.522433i	$-0.174976\pi$
$569$	4482.37	+	4482.37i	0.330247	+	0.330247i	−0.522433	+	0.852680i	$0.674976\pi$
$570$		0			0
$571$	−2954.21	+	7132.09i	−0.216515	+	0.522712i	−0.994399	−	0.105696i	$-0.966293\pi$
$571$	−2954.21	+	7132.09i	−0.216515	+	0.522712i	0.777884	+	0.628408i	$0.216293\pi$
$572$		0			0
$573$	−4063.92	+	1683.33i	−0.296287	+	0.122726i
$574$		0			0
$575$	21652.1			1.57036
$576$		0			0
$577$	−25355.5			−1.82940			−0.914699	−	0.404136i	$-0.867572\pi$
$577$	−25355.5			−1.82940			−0.914699	+	0.404136i	$0.867572\pi$
$578$		0			0
$579$	−14765.0	+	6115.88i	−1.05978	+	0.438976i
$580$		0			0
$581$	5005.43	−	12084.2i	0.357419	−	0.862885i
$582$		0			0
$583$	12889.4	+	12889.4i	0.915651	+	0.915651i
$584$		0			0
$585$	3217.48	−	3217.48i	0.227396	−	0.227396i
$586$		0			0
$587$	−11437.3	−	4737.49i	−0.804206	−	0.333113i	−0.0575663	−	0.998342i	$-0.518334\pi$
$587$	−11437.3	−	4737.49i	−0.804206	−	0.333113i	−0.746640	+	0.665229i	$0.768334\pi$
$588$		0			0
$589$	3956.82	+	9552.61i	0.276805	+	0.668266i
$590$		0			0
$591$			20089.0i			1.39822i
$592$		0			0
$593$			2914.83i			0.201851i	0.994894	+	0.100925i	$0.0321804\pi$
$593$			2914.83i			0.201851i	−0.994894	+	0.100925i	$0.967820\pi$
$594$		0			0
$595$	926.119	+	2235.85i	0.0638104	+	0.154052i
$596$		0			0
$597$	−2567.23	−	1063.38i	−0.175996	−	0.0729000i
$598$		0			0
$599$	8115.44	−	8115.44i	0.553569	−	0.553569i	−0.373900	−	0.927469i	$-0.621980\pi$
$599$	8115.44	−	8115.44i	0.553569	−	0.553569i	0.927469	+	0.373900i	$0.121980\pi$
$600$		0			0
$601$	9424.82	+	9424.82i	0.639678	+	0.639678i	0.950476	−	0.310798i	$-0.100596\pi$
$601$	9424.82	+	9424.82i	0.639678	+	0.639678i	−0.310798	+	0.950476i	$0.600596\pi$
$602$		0			0
$603$	7548.60	−	18223.9i	0.509789	−	1.23074i
$604$		0			0
$605$	8938.81	−	3702.58i	0.600685	−	0.248812i
$606$		0			0
$607$	−29374.9			−1.96423			−0.982117	−	0.188274i	$-0.939711\pi$
$607$	−29374.9			−1.96423			−0.982117	+	0.188274i	$0.939711\pi$
$608$		0			0
$609$	−2173.17			−0.144600
$610$		0			0
$611$	−6263.51	+	2594.43i	−0.414721	+	0.171783i
$612$		0			0
$613$	−137.019	+	330.794i	−0.00902800	+	0.0217955i	−0.928329	−	0.371759i	$-0.878755\pi$
$613$	−137.019	+	330.794i	−0.00902800	+	0.0217955i	0.919301	+	0.393555i	$0.128755\pi$
$614$		0			0
$615$	−1003.19	−	1003.19i	−0.0657767	−	0.0657767i
$616$		0			0
$617$	−2046.11	+	2046.11i	−0.133506	+	0.133506i	−0.770702	−	0.637196i	$-0.780094\pi$
$617$	−2046.11	+	2046.11i	−0.133506	+	0.133506i	0.637196	+	0.770702i	$0.280094\pi$
$618$		0			0
$619$	15046.6	+	6232.49i	0.977014	+	0.404693i	0.813319	−	0.581818i	$-0.197659\pi$
$619$	15046.6	+	6232.49i	0.977014	+	0.404693i	0.163696	+	0.986511i	$0.447659\pi$
$620$		0			0
$621$	1782.54	+	4303.43i	0.115187	+	0.278085i
$622$		0			0
$623$		−	7245.06i		−	0.465919i
$624$		0			0
$625$			9585.53i			0.613474i
$626$		0			0
$627$	−14118.2	−	34084.4i	−0.899247	−	2.17097i
$628$		0			0
$629$	−5468.27	−	2265.03i	−0.346636	−	0.143581i
$630$		0			0
$631$	−16948.0	+	16948.0i	−1.06924	+	1.06924i	−0.0718201	+	0.997418i	$0.522881\pi$
$631$	−16948.0	+	16948.0i	−1.06924	+	1.06924i	−0.997418	+	0.0718201i	$0.977119\pi$
$632$		0			0
$633$	−8304.18	−	8304.18i	−0.521424	−	0.521424i
$634$		0			0
$635$	1802.81	−	4352.38i	0.112665	−	0.271998i
$636$		0			0
$637$	−5020.48	+	2079.55i	−0.312274	+	0.129348i
$638$		0			0
$639$	−6947.39			−0.430101
$640$		0			0
$641$	−1901.61			−0.117175			−0.0585876	−	0.998282i	$-0.518660\pi$
$641$	−1901.61			−0.117175			−0.0585876	+	0.998282i	$0.518660\pi$
$642$		0			0
$643$	−23668.9	+	9803.96i	−1.45165	+	0.601291i	−0.962590	−	0.270961i	$-0.912659\pi$
$643$	−23668.9	+	9803.96i	−1.45165	+	0.601291i	−0.489056	+	0.872253i	$0.662659\pi$
$644$		0			0
$645$	4035.43	−	9742.39i	0.246349	−	0.594739i
$646$		0			0
$647$	−15183.7	−	15183.7i	−0.922619	−	0.922619i	0.0745946	−	0.997214i	$-0.476234\pi$
$647$	−15183.7	−	15183.7i	−0.922619	−	0.922619i	−0.997214	+	0.0745946i	$0.976234\pi$
$648$		0			0
$649$	−27050.9	+	27050.9i	−1.63612	+	1.63612i
$650$		0			0
$651$	19875.9	+	8232.86i	1.19662	+	0.495655i
$652$		0			0
$653$	−4239.30	−	10234.6i	−0.254053	−	0.613338i	0.744471	−	0.667655i	$-0.232702\pi$
$653$	−4239.30	−	10234.6i	−0.254053	−	0.613338i	−0.998524	+	0.0543169i	$0.982702\pi$
$654$		0			0
$655$			6353.21i			0.378993i
$656$		0			0
$657$		−	26574.1i		−	1.57801i
$658$		0			0
$659$	−7838.85	−	18924.7i	−0.463366	−	1.11866i	−0.967007	−	0.254751i	$-0.918006\pi$
$659$	−7838.85	−	18924.7i	−0.463366	−	1.11866i	0.503641	−	0.863913i	$-0.331994\pi$
$660$		0			0
$661$	−2051.85	−	849.906i	−0.120738	−	0.0500114i	0.321497	−	0.946911i	$-0.395814\pi$
$661$	−2051.85	−	849.906i	−0.120738	−	0.0500114i	−0.442235	+	0.896899i	$0.645814\pi$
$662$		0			0
$663$	−5236.48	+	5236.48i	−0.306739	+	0.306739i
$664$		0			0
$665$	−5171.87	−	5171.87i	−0.301589	−	0.301589i
$666$		0			0
$667$	−995.169	+	2402.55i	−0.0577707	+	0.139471i
$668$		0			0
$669$	−13194.8	+	5465.46i	−0.762541	+	0.315855i
$670$		0			0
$671$	19547.6			1.12463
$672$		0			0
$673$	17511.0			1.00297			0.501486	−	0.865166i	$-0.332787\pi$
$673$	17511.0			1.00297			0.501486	+	0.865166i	$0.332787\pi$
$674$		0			0
$675$	−2324.12	+	962.682i	−0.132527	+	0.0548943i
$676$		0			0
$677$	−2390.19	+	5770.44i	−0.135691	+	0.327586i	−0.977090	−	0.212828i	$-0.931733\pi$
$677$	−2390.19	+	5770.44i	−0.135691	+	0.327586i	0.841399	+	0.540414i	$0.181733\pi$
$678$		0			0
$679$	9309.39	+	9309.39i	0.526158	+	0.526158i
$680$		0			0
$681$	−4111.98	+	4111.98i	−0.231383	+	0.231383i
$682$		0			0
$683$	1674.92	+	693.777i	0.0938349	+	0.0388677i	0.429107	−	0.903254i	$-0.358828\pi$
$683$	1674.92	+	693.777i	0.0938349	+	0.0388677i	−0.335272	+	0.942121i	$0.608828\pi$
$684$		0			0
$685$	550.182	+	1328.26i	0.0306882	+	0.0740878i
$686$		0			0
$687$			1786.50i			0.0992128i
$688$		0			0
$689$			11058.5i			0.611461i
$690$		0			0
$691$	−8855.39	−	21378.8i	−0.487518	−	1.17697i	−0.955965	−	0.293481i	$-0.905186\pi$
$691$	−8855.39	−	21378.8i	−0.487518	−	1.17697i	0.468447	−	0.883492i	$-0.344814\pi$
$692$		0			0
$693$	−37372.2	−	15480.1i	−2.04856	−	0.848542i
$694$		0			0
$695$	1885.10	−	1885.10i	0.102886	−	0.102886i
$696$		0			0
$697$	860.391	+	860.391i	0.0467570	+	0.0467570i
$698$		0			0
$699$	11606.9	−	28021.4i	0.628056	−	1.51626i
$700$		0			0
$701$	−31059.0	+	12865.1i	−1.67344	+	0.693163i	−0.998980	−	0.0451460i	$-0.985625\pi$
$701$	−31059.0	+	12865.1i	−1.67344	+	0.693163i	−0.674463	+	0.738309i	$0.735625\pi$
$702$		0			0
$703$	17888.4			0.959704
$704$		0			0
$705$	−5709.86			−0.305030
$706$		0			0
$707$	−8805.40	+	3647.31i	−0.468403	+	0.194019i
$708$		0			0
$709$	9260.32	−	22356.4i	0.490520	−	1.18422i	−0.463936	−	0.885869i	$-0.653563\pi$
$709$	9260.32	−	22356.4i	0.490520	−	1.18422i	0.954456	−	0.298352i	$-0.0964368\pi$
$710$		0			0
$711$	−2975.96	−	2975.96i	−0.156972	−	0.156972i
$712$		0			0
$713$	18203.7	−	18203.7i	0.956147	−	0.956147i
$714$		0			0
$715$	8486.37	+	3515.17i	0.443877	+	0.183860i
$716$		0			0
$717$	20366.4	+	49168.8i	1.06080	+	2.56101i
$718$		0			0
$719$		−	2669.74i		−	0.138476i	−0.997600	−	0.0692381i	$-0.977943\pi$
$719$		−	2669.74i		−	0.138476i	0.997600	−	0.0692381i	$-0.0220568\pi$
$720$		0			0
$721$		−	22493.6i		−	1.16186i
$722$		0			0
$723$	17085.9	+	41249.0i	0.878882	+	2.12181i
$724$		0			0
$725$	−1297.53	−	537.453i	−0.0664674	−	0.0275317i
$726$		0			0
$727$	16054.1	−	16054.1i	0.818999	−	0.818999i	−0.166964	−	0.985963i	$-0.553396\pi$
$727$	16054.1	−	16054.1i	0.818999	−	0.818999i	0.985963	+	0.166964i	$0.0533962\pi$
$728$		0			0
$729$	16890.8	+	16890.8i	0.858143	+	0.858143i
$730$		0			0
$731$	−3461.00	+	8355.59i	−0.175116	+	0.422767i
$732$		0			0
$733$	20176.5	−	8357.40i	1.01670	−	0.421129i	0.188802	−	0.982015i	$-0.439539\pi$
$733$	20176.5	−	8357.40i	1.01670	−	0.421129i	0.827893	+	0.560886i	$0.189539\pi$
$734$		0			0
$735$	−4576.71			−0.229679
$736$		0			0
$737$	39820.1			1.99022
$738$		0			0
$739$	16792.0	−	6955.46i	0.835862	−	0.346225i	0.0766414	−	0.997059i	$-0.475580\pi$
$739$	16792.0	−	6955.46i	0.835862	−	0.346225i	0.759221	+	0.650833i	$0.225580\pi$
$740$		0			0
$741$	8565.05	−	20677.9i	0.424622	−	1.02513i
$742$		0			0
$743$	17381.8	+	17381.8i	0.858243	+	0.858243i	0.991131	−	0.132888i	$-0.0424250\pi$
$743$	17381.8	+	17381.8i	0.858243	+	0.858243i	−0.132888	+	0.991131i	$0.542425\pi$
$744$		0			0
$745$	−5583.60	+	5583.60i	−0.274587	+	0.274587i
$746$		0			0
$747$	16411.8	+	6797.99i	0.803851	+	0.332966i
$748$		0			0
$749$	3375.43	+	8149.01i	0.164667	+	0.397541i
$750$		0			0
$751$		−	17302.5i		−	0.840717i	−0.907358	−	0.420358i	$-0.861904\pi$
$751$		−	17302.5i		−	0.840717i	0.907358	−	0.420358i	$-0.138096\pi$
$752$		0			0
$753$		−	8509.12i		−	0.411806i
$754$		0			0
$755$	−2960.16	−	7146.45i	−0.142690	−	0.344485i
$756$		0			0
$757$	−15089.7	−	6250.38i	−0.724499	−	0.300097i	−0.0102100	−	0.999948i	$-0.503250\pi$
$757$	−15089.7	−	6250.38i	−0.724499	−	0.300097i	−0.714289	+	0.699850i	$0.753250\pi$
$758$		0			0
$759$	−64952.1	+	64952.1i	−3.10621	+	3.10621i
$760$		0			0
$761$	21880.6	+	21880.6i	1.04227	+	1.04227i	0.999066	+	0.0432084i	$0.0137579\pi$
$761$	21880.6	+	21880.6i	1.04227	+	1.04227i	0.0432084	+	0.999066i	$0.486242\pi$
$762$		0			0
$763$	3937.16	−	9505.14i	0.186808	−	0.450995i
$764$		0			0
$765$	−3036.56	+	1257.78i	−0.143512	+	0.0594448i
$766$		0			0
$767$	−23208.5			−1.09258
$768$		0			0
$769$	33208.8			1.55727			0.778634	−	0.627479i	$-0.215913\pi$
$769$	33208.8			1.55727			0.778634	+	0.627479i	$0.215913\pi$
$770$		0			0
$771$	1572.35	−	651.290i	0.0734460	−	0.0304223i
$772$		0			0
$773$	−14567.1	+	35168.2i	−0.677805	+	1.63637i	0.0902005	+	0.995924i	$0.471249\pi$
$773$	−14567.1	+	35168.2i	−0.677805	+	1.63637i	−0.768006	+	0.640443i	$0.778751\pi$
$774$		0			0
$775$	9831.11	+	9831.11i	0.455670	+	0.455670i
$776$		0			0
$777$	26318.4	−	26318.4i	1.21515	−	1.21515i
$778$		0			0
$779$	−3397.52	−	1407.30i	−0.156263	−	0.0647262i
$780$		0			0
$781$	−5367.06	−	12957.2i	−0.245901	−	0.593657i
$782$		0			0
$783$		−	302.134i		−	0.0137898i
$784$		0			0
$785$			10745.2i			0.488550i
$786$		0			0
$787$	5755.36	+	13894.7i	0.260682	+	0.629341i	0.998981	−	0.0451318i	$-0.0143708\pi$
$787$	5755.36	+	13894.7i	0.260682	+	0.629341i	−0.738299	+	0.674473i	$0.764371\pi$
$788$		0			0
$789$	32031.3	+	13267.8i	1.44531	+	0.598665i
$790$		0			0
$791$	5066.55	−	5066.55i	0.227744	−	0.227744i
$792$		0			0
$793$	8385.49	+	8385.49i	0.375507	+	0.375507i
$794$		0			0
$795$	−3564.19	+	8604.71i	−0.159005	+	0.383871i
$796$		0			0
$797$	16093.9	−	6666.33i	0.715278	−	0.296278i	0.00479156	−	0.999989i	$-0.498475\pi$
$797$	16093.9	−	6666.33i	0.715278	−	0.296278i	0.710487	+	0.703711i	$0.248475\pi$
$798$		0			0
$799$	4897.08			0.216829
$800$		0			0
$801$	9839.69			0.434043
$802$		0			0
$803$	49562.1	−	20529.3i	2.17809	−	0.902195i
$804$		0			0
$805$	−6968.99	+	16824.6i	−0.305124	+	0.736634i
$806$		0			0
$807$	−1166.95	−	1166.95i	−0.0509028	−	0.0509028i
$808$		0			0
$809$	−23028.6	+	23028.6i	−1.00079	+	1.00079i	−0.000793663		1.00000i	$0.500253\pi$
$809$	−23028.6	+	23028.6i	−1.00079	+	1.00079i	−1.00000		0.000793663i	$0.999747\pi$
$810$		0			0
$811$	909.718	+	376.818i	0.0393891	+	0.0163155i	0.402291	−	0.915512i	$-0.368214\pi$
$811$	909.718	+	376.818i	0.0393891	+	0.0163155i	−0.362902	+	0.931827i	$0.618214\pi$
$812$		0			0
$813$	−11864.9	−	28644.4i	−0.511833	−	1.23567i
$814$		0			0
$815$			8107.26i			0.348448i
$816$		0			0
$817$		−	27333.6i		−	1.17048i
$818$		0			0
$819$	−9391.23	−	22672.4i	−0.400679	−	0.967325i
$820$		0			0
$821$	−3352.70	−	1388.73i	−0.142521	−	0.0590342i	0.310283	−	0.950644i	$-0.399576\pi$
$821$	−3352.70	−	1388.73i	−0.142521	−	0.0590342i	−0.452804	+	0.891610i	$0.649576\pi$
$822$		0			0
$823$	11551.4	−	11551.4i	0.489253	−	0.489253i	−0.418817	−	0.908070i	$-0.637555\pi$
$823$	11551.4	−	11551.4i	0.489253	−	0.489253i	0.908070	+	0.418817i	$0.137555\pi$
$824$		0			0
$825$	−35078.2	−	35078.2i	−1.48032	−	1.48032i
$826$		0			0
$827$	−7178.66	+	17330.8i	−0.301846	+	0.728721i	0.698073	+	0.716026i	$0.254041\pi$
$827$	−7178.66	+	17330.8i	−0.301846	+	0.728721i	−0.999919	+	0.0126945i	$0.995959\pi$
$828$		0			0
$829$	30084.0	−	12461.2i	1.26038	−	0.522068i	0.350357	−	0.936616i	$-0.386060\pi$
$829$	30084.0	−	12461.2i	1.26038	−	0.522068i	0.910028	+	0.414548i	$0.136060\pi$
$830$		0			0
$831$	6337.62			0.264560
$832$		0			0
$833$	3925.22			0.163266
$834$		0			0
$835$	−13963.8	+	5784.01i	−0.578729	+	0.239717i
$836$		0			0
$837$	−1144.61	+	2763.33i	−0.0472681	+	0.114115i
$838$		0			0
$839$	25641.1	+	25641.1i	1.05510	+	1.05510i	0.998391	+	0.0567077i	$0.0180603\pi$
$839$	25641.1	+	25641.1i	1.05510	+	1.05510i	0.0567077	+	0.998391i	$0.481940\pi$
$840$		0			0
$841$	−17126.4	+	17126.4i	−0.702216	+	0.702216i
$842$		0			0
$843$	−18328.4	−	7591.86i	−0.748828	−	0.310175i
$844$		0			0
$845$	−1320.05	−	3186.89i	−0.0537411	−	0.129743i
$846$		0			0
$847$		−	52181.4i		−	2.11685i
$848$		0			0
$849$			58532.8i			2.36613i
$850$		0			0
$851$	−17044.2	−	41148.4i	−0.686567	−	1.65752i
$852$		0			0
$853$	−34256.5	−	14189.5i	−1.37505	−	0.569566i	−0.431899	−	0.901922i	$-0.642156\pi$
$853$	−34256.5	−	14189.5i	−1.37505	−	0.569566i	−0.943154	+	0.332356i	$0.892156\pi$
$854$		0			0
$855$	7024.04	−	7024.04i	0.280956	−	0.280956i
$856$		0			0
$857$	−28481.8	−	28481.8i	−1.13526	−	1.13526i	−0.989289	−	0.145973i	$-0.953369\pi$
$857$	−28481.8	−	28481.8i	−1.13526	−	1.13526i	−0.145973	−	0.989289i	$-0.546631\pi$
$858$		0			0
$859$	13055.3	−	31518.3i	0.518559	−	1.25191i	−0.420230	−	0.907418i	$-0.638051\pi$
$859$	13055.3	−	31518.3i	0.518559	−	1.25191i	0.938789	−	0.344494i	$-0.111949\pi$
$860$		0			0
$861$	−7069.14	+	2928.13i	−0.279809	+	0.115901i
$862$		0			0
$863$	−4609.39			−0.181814			−0.0909070	−	0.995859i	$-0.528977\pi$
$863$	−4609.39			−0.181814			−0.0909070	+	0.995859i	$0.528977\pi$
$864$		0			0
$865$	17881.0			0.702857
$866$		0			0
$867$	−29350.6	+	12157.4i	−1.14971	+	0.476226i
$868$		0			0
$869$	3251.30	−	7849.34i	0.126919	−	0.306410i
$870$		0			0
$871$	17081.9	+	17081.9i	0.664522	+	0.664522i
$872$		0			0
$873$	−12643.3	+	12643.3i	−0.490161	+	0.490161i
$874$		0			0
$875$	−19589.7	−	8114.31i	−0.756859	−	0.313501i
$876$		0			0
$877$	5941.44	+	14343.9i	0.228766	+	0.552291i	0.996028	−	0.0890437i	$-0.0283811\pi$
$877$	5941.44	+	14343.9i	0.228766	+	0.552291i	−0.767261	+	0.641335i	$0.778381\pi$
$878$		0			0
$879$			6252.15i			0.239909i
$880$		0			0
$881$		−	9283.73i		−	0.355025i	−0.984119	−	0.177512i	$-0.943195\pi$
$881$		−	9283.73i		−	0.355025i	0.984119	−	0.177512i	$-0.0568050\pi$
$882$		0			0
$883$	14740.1	+	35585.7i	0.561771	+	1.35623i	0.908349	+	0.418213i	$0.137343\pi$
$883$	14740.1	+	35585.7i	0.561771	+	1.35623i	−0.346578	+	0.938021i	$0.612657\pi$
$884$		0			0
$885$	−18058.7	−	7480.14i	−0.685916	−	0.284116i
$886$		0			0
$887$	5519.29	−	5519.29i	0.208928	−	0.208928i	−0.594884	−	0.803812i	$-0.702802\pi$
$887$	5519.29	−	5519.29i	0.208928	−	0.208928i	0.803812	+	0.594884i	$0.202802\pi$
$888$		0			0
$889$	−17965.9	−	17965.9i	−0.677790	−	0.677790i
$890$		0			0
$891$	−14787.6	+	35700.5i	−0.556009	+	1.34232i
$892$		0			0
$893$	−13673.8	+	5663.86i	−0.512402	+	0.212244i
$894$		0			0
$895$	3403.62			0.127118
$896$		0			0
$897$	−55726.0			−2.07429
$898$		0			0
$899$	−1542.73	+	639.020i	−0.0572335	+	0.0237069i
$900$		0			0
$901$	3056.83	−	7379.85i	0.113028	−	0.272873i
$902$		0			0
$903$	−40214.9	−	40214.9i	−1.48202	−	1.48202i
$904$		0			0
$905$	−4890.68	+	4890.68i	−0.179637	+	0.179637i
$906$		0			0
$907$	24355.0	+	10088.2i	0.891613	+	0.369318i	0.780989	−	0.624544i	$-0.214715\pi$
$907$	24355.0	+	10088.2i	0.891613	+	0.369318i	0.110624	+	0.993862i	$0.464715\pi$
$908$		0			0
$909$	−4953.50	−	11958.8i	−0.180745	−	0.436357i
$910$		0			0
$911$			23518.4i			0.855324i	0.903939	+	0.427662i	$0.140663\pi$
$911$			23518.4i			0.855324i	−0.903939	+	0.427662i	$0.859337\pi$
$912$		0			0
$913$			35860.5i			1.29990i
$914$		0			0
$915$	3822.14	+	9227.46i	0.138094	+	0.333388i
$916$		0			0
$917$	31656.3	+	13112.5i	1.14000	+	0.472205i
$918$		0			0
$919$	−13800.1	+	13800.1i	−0.495345	+	0.495345i	−0.909985	−	0.414640i	$-0.863907\pi$
$919$	−13800.1	+	13800.1i	−0.495345	+	0.495345i	0.414640	+	0.909985i	$0.363907\pi$
$920$		0			0
$921$	14523.3	+	14523.3i	0.519609	+	0.519609i
$922$		0			0
$923$	3256.01	−	7860.71i	0.116114	−	0.280323i
$924$		0			0
$925$	22222.7	−	9204.94i	0.789922	−	0.327196i
$926$		0			0
$927$	30549.0			1.08238
$928$		0			0
$929$	−19436.0			−0.686408			−0.343204	−	0.939261i	$-0.611512\pi$
$929$	−19436.0			−0.686408			−0.343204	+	0.939261i	$0.611512\pi$
$930$		0			0
$931$	−10960.1	+	4539.83i	−0.385825	+	0.159814i
$932$		0			0
$933$	−2126.21	+	5133.12i	−0.0746076	+	0.180119i
$934$		0			0
$935$	−4691.66	−	4691.66i	−0.164100	−	0.164100i
$936$		0			0
$937$	25449.2	−	25449.2i	0.887287	−	0.887287i	−0.106975	−	0.994262i	$-0.534116\pi$
$937$	25449.2	−	25449.2i	0.887287	−	0.887287i	0.994262	+	0.106975i	$0.0341165\pi$
$938$		0			0
$939$	−19449.5	−	8056.24i	−0.675943	−	0.279985i
$940$		0			0
$941$	2720.40	+	6567.63i	0.0942429	+	0.227523i	0.963970	−	0.266010i	$-0.0857054\pi$
$941$	2720.40	+	6567.63i	0.0942429	+	0.227523i	−0.869727	+	0.493532i	$0.835705\pi$
$942$		0			0
$943$			9156.17i			0.316189i
$944$		0			0
$945$		−	2115.79i		−	0.0728325i
$946$		0			0
$947$	−8325.39	−	20099.3i	−0.285680	−	0.689692i	0.714268	−	0.699872i	$-0.246760\pi$
$947$	−8325.39	−	20099.3i	−0.285680	−	0.689692i	−0.999948	+	0.0101799i	$0.996760\pi$
$948$		0			0
$949$	30067.6	+	12454.4i	1.02849	+	0.426014i
$950$		0			0
$951$	37159.1	−	37159.1i	1.26705	−	1.26705i
$952$		0			0
$953$	26308.1	+	26308.1i	0.894230	+	0.894230i	0.994918	−	0.100688i	$-0.0321043\pi$
$953$	26308.1	+	26308.1i	0.894230	+	0.894230i	−0.100688	+	0.994918i	$0.532104\pi$
$954$		0			0
$955$	914.967	−	2208.93i	0.0310028	−	0.0748473i
$956$		0			0
$957$	5504.58	−	2280.07i	0.185933	−	0.0770159i
$958$		0			0
$959$	7753.87			0.261090
$960$		0			0
$961$	−13260.3			−0.445110
$962$		0			0
$963$	−11067.4	+	4584.25i	−0.370343	+	0.153401i
$964$		0			0
$965$	3324.26	−	8025.48i	0.110893	−	0.267720i
$966$		0			0
$967$	−22468.6	−	22468.6i	−0.747200	−	0.747200i	0.226752	−	0.973952i	$-0.427189\pi$
$967$	−22468.6	−	22468.6i	−0.747200	−	0.747200i	−0.973952	+	0.226752i	$0.927189\pi$
$968$		0			0
$969$	−11431.7	+	11431.7i	−0.378987	+	0.378987i
$970$		0			0
$971$	−8065.47	−	3340.83i	−0.266564	−	0.110414i	0.245398	−	0.969422i	$-0.421081\pi$
$971$	−8065.47	−	3340.83i	−0.266564	−	0.110414i	−0.511962	+	0.859008i	$0.671081\pi$
$972$		0			0
$973$	−5502.26	−	13283.6i	−0.181289	−	0.437671i
$974$		0			0
$975$		−	30095.5i		−	0.988540i
$976$		0			0
$977$		−	51239.4i		−	1.67789i	−0.544219	−	0.838943i	$-0.683174\pi$
$977$		−	51239.4i		−	1.67789i	0.544219	−	0.838943i	$-0.316826\pi$
$978$		0			0
$979$	7601.45	+	18351.5i	0.248155	+	0.599098i
$980$		0			0
$981$	12909.2	+	5347.15i	0.420140	+	0.174028i
$982$		0			0
$983$	−11466.1	+	11466.1i	−0.372035	+	0.372035i	−0.868218	−	0.496183i	$-0.834735\pi$
$983$	−11466.1	+	11466.1i	−0.372035	+	0.372035i	0.496183	+	0.868218i	$0.334735\pi$
$984$		0			0
$985$	−7721.09	−	7721.09i	−0.249761	−	0.249761i
$986$		0			0
$987$	−11784.6	+	28450.7i	−0.380050	+	0.917522i
$988$		0			0
$989$	−62875.3	+	26043.8i	−2.02155	+	0.837355i
$990$		0			0
$991$	−49326.7			−1.58114			−0.790572	−	0.612368i	$-0.790217\pi$
$991$	−49326.7			−1.58114			−0.790572	+	0.612368i	$0.790217\pi$
$992$		0			0
$993$	−58242.6			−1.86130
$994$		0			0
$995$	1395.41	−	577.997i	0.0444597	−	0.0184158i
$996$		0			0
$997$	−4441.12	+	10721.8i	−0.141075	+	0.340585i	−0.978587	−	0.205834i	$-0.934009\pi$
$997$	−4441.12	+	10721.8i	−0.141075	+	0.340585i	0.837512	+	0.546419i	$0.184009\pi$
$998$		0			0
$999$	3659.03	+	3659.03i	0.115882	+	0.115882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.49.2		44
4.3	odd	2		32.4.g.a.21.3	✓	44
8.3	odd	2		256.4.g.b.97.2		44
8.5	even	2		256.4.g.a.97.10		44
32.3	odd	8		32.4.g.a.29.3	yes	44
32.13	even	8		256.4.g.a.161.10		44
32.19	odd	8		256.4.g.b.161.2		44
32.29	even	8	inner	128.4.g.a.81.2		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.3	✓	44	4.3	odd	2
32.4.g.a.29.3	yes	44	32.3	odd	8
128.4.g.a.49.2		44	1.1	even	1	trivial
128.4.g.a.81.2		44	32.29	even	8	inner
256.4.g.a.97.10		44	8.5	even	2
256.4.g.a.161.10		44	32.13	even	8
256.4.g.b.97.2		44	8.3	odd	2
256.4.g.b.161.2		44	32.19	odd	8

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.97998 + 2.89120i) q^{3} +(1.57150 - 3.79394i) q^{5} +(-15.6607 - 15.6607i) q^{7} +(21.2692 - 21.2692i) q^{9} +O(q^{10})\)	\(q+(-6.97998 + 2.89120i) q^{3} +(1.57150 - 3.79394i) q^{5} +(-15.6607 - 15.6607i) q^{7} +(21.2692 - 21.2692i) q^{9} +(56.0992 + 23.2370i) q^{11} +(14.0971 + 34.0334i) q^{13} +31.0252i q^{15} -26.6088i q^{17} +(30.7752 + 74.2979i) q^{19} +(154.590 + 64.0332i) q^{21} +(141.584 - 141.584i) q^{23} +(76.4640 + 76.4640i) q^{25} +(-8.90248 + 21.4925i) q^{27} +(-11.9990 + 4.97014i) q^{29} +128.572 q^{31} -458.754 q^{33} +(-84.0267 + 34.8050i) q^{35} +(85.1234 - 205.506i) q^{37} +(-196.795 - 196.795i) q^{39} +(-32.3348 + 32.3348i) q^{41} +(-314.016 - 130.070i) q^{43} +(-47.2695 - 114.119i) q^{45} +184.040i q^{47} +147.516i q^{49} +(76.9314 + 185.729i) q^{51} +(277.346 + 114.881i) q^{53} +(176.320 - 176.320i) q^{55} +(-429.620 - 429.620i) q^{57} +(-241.099 + 582.065i) q^{59} +(297.419 - 123.195i) q^{61} -666.181 q^{63} +151.275 q^{65} +(605.866 - 250.958i) q^{67} +(-578.904 + 1397.60i) q^{69} +(-163.321 - 163.321i) q^{71} +(624.709 - 624.709i) q^{73} +(-754.790 - 312.644i) q^{75} +(-514.644 - 1242.46i) q^{77} -139.919i q^{79} +636.381i q^{81} +(226.003 + 545.620i) q^{83} +(-100.952 - 41.8158i) q^{85} +(69.3829 - 69.3829i) q^{87} +(231.313 + 231.313i) q^{89} +(312.217 - 753.759i) q^{91} +(-897.429 + 371.727i) q^{93} +330.245 q^{95} -594.442 q^{97} +(1687.42 - 698.950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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