LMFDB - Embedded newform 448.4.i.p.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,4,Mod(65,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("448.65");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	448.i (of order $3$, 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:	$26.4328556826$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 42 x^{10} - 74 x^{9} + 975 x^{8} - 4602 x^{7} + 21732 x^{6} - 98076 x^{5} + 355026 x^{4} + \cdots + 4977508 $ x^12 + 42x^10 - 74x^9 + 975x^8 - 4602x^7 + 21732x^6 - 98076x^5 + 355026x^4 - 936896x^3 + 2975016x^2 - 3623352x + 4977508
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{2}\cdot 7 $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			65.4
Root			$0.674870 + 1.54726i$ of defining polynomial
Character	$\chi$	$=$	448.65
Dual form			448.4.i.p.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11427 + 1.92998i) q^{3} +(6.72806 - 11.6533i) q^{5} +(-10.1930 + 15.4630i) q^{7} +(11.0168 - 19.0816i) q^{9} +O(q^{10})$	\(q+(1.11427 + 1.92998i) q^{3} +(6.72806 - 11.6533i) q^{5} +(-10.1930 + 15.4630i) q^{7} +(11.0168 - 19.0816i) q^{9} +(24.7053 + 42.7907i) q^{11} -22.0336 q^{13} +29.9876 q^{15} +(19.3955 + 33.5939i) q^{17} +(-65.8356 + 114.031i) q^{19} +(-41.2010 - 2.44230i) q^{21} +(96.9095 - 167.852i) q^{23} +(-28.0336 - 48.5556i) q^{25} +109.274 q^{27} +288.486 q^{29} +(-22.2575 - 38.5511i) q^{31} +(-55.0568 + 95.3612i) q^{33} +(111.616 + 222.818i) q^{35} +(-114.272 + 197.926i) q^{37} +(-24.5514 - 42.5243i) q^{39} +253.399 q^{41} +241.336 q^{43} +(-148.243 - 256.765i) q^{45} +(75.7426 - 131.190i) q^{47} +(-135.206 - 315.228i) q^{49} +(-43.2237 + 74.8656i) q^{51} +(-82.2389 - 142.442i) q^{53} +664.874 q^{55} -293.436 q^{57} +(369.329 + 639.697i) q^{59} +(-138.084 + 239.168i) q^{61} +(182.764 + 364.851i) q^{63} +(-148.243 + 256.765i) q^{65} +(-125.857 - 217.991i) q^{67} +431.935 q^{69} +246.558 q^{71} +(439.589 + 761.390i) q^{73} +(62.4742 - 108.208i) q^{75} +(-913.492 - 54.1497i) q^{77} +(-534.760 + 926.231i) q^{79} +(-175.692 - 304.308i) q^{81} +544.887 q^{83} +521.975 q^{85} +(321.453 + 556.773i) q^{87} +(485.794 - 841.419i) q^{89} +(224.588 - 340.704i) q^{91} +(49.6018 - 85.9129i) q^{93} +(885.892 + 1534.41i) q^{95} -355.197 q^{97} +1088.69 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 72 q^{9}+O(q^{10}) $ 12 * q + 6 * q^5 - 72 * q^9	$ 12 q + 6 q^{5} - 72 q^{9} + 144 q^{13} + 138 q^{17} - 66 q^{21} + 72 q^{25} + 144 q^{29} + 714 q^{33} - 6 q^{37} - 576 q^{41} - 120 q^{45} + 948 q^{49} - 30 q^{53} - 3420 q^{57} - 54 q^{61} - 120 q^{65} - 924 q^{69} + 2694 q^{73} - 4062 q^{77} - 3666 q^{81} + 5268 q^{85} + 3558 q^{89} + 2190 q^{93} - 768 q^{97}+O(q^{100}) $ 12 * q + 6 * q^5 - 72 * q^9 + 144 * q^13 + 138 * q^17 - 66 * q^21 + 72 * q^25 + 144 * q^29 + 714 * q^33 - 6 * q^37 - 576 * q^41 - 120 * q^45 + 948 * q^49 - 30 * q^53 - 3420 * q^57 - 54 * q^61 - 120 * q^65 - 924 * q^69 + 2694 * q^73 - 4062 * q^77 - 3666 * q^81 + 5268 * q^85 + 3558 * q^89 + 2190 * q^93 - 768 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.11427	+	1.92998i	0.214442	+	0.371425i	0.953100	−	0.302656i	$-0.0978733\pi$
$3$	1.11427	+	1.92998i	0.214442	+	0.371425i	−0.738658	+	0.674081i	$0.764540\pi$
$4$		0			0
$5$	6.72806	−	11.6533i	0.601776	−	1.04231i	−0.390776	−	0.920486i	$-0.627793\pi$
$5$	6.72806	−	11.6533i	0.601776	−	1.04231i	0.992552	−	0.121821i	$-0.0388733\pi$
$6$		0			0
$7$	−10.1930	+	15.4630i	−0.550370	+	0.834921i
$7$	−10.1930	+	15.4630i	−0.550370	+	0.834921i
$8$		0			0
$9$	11.0168	−	19.0816i	0.408029	−	0.706727i
$10$		0			0
$11$	24.7053	+	42.7907i	0.677174	+	1.17290i	0.975828	+	0.218538i	$0.0701289\pi$
$11$	24.7053	+	42.7907i	0.677174	+	1.17290i	−0.298654	+	0.954361i	$0.596538\pi$
$12$		0			0
$13$	−22.0336			−0.470078			−0.235039	−	0.971986i	$-0.575522\pi$
$13$	−22.0336			−0.470078			−0.235039	+	0.971986i	$0.575522\pi$
$14$		0			0
$15$	29.9876			0.516184
$16$		0			0
$17$	19.3955	+	33.5939i	0.276711	+	0.479278i	0.970565	−	0.240838i	$-0.0774222\pi$
$17$	19.3955	+	33.5939i	0.276711	+	0.479278i	−0.693854	+	0.720115i	$0.744089\pi$
$18$		0			0
$19$	−65.8356	+	114.031i	−0.794933	+	1.37686i	0.127949	+	0.991781i	$0.459161\pi$
$19$	−65.8356	+	114.031i	−0.794933	+	1.37686i	−0.922882	+	0.385083i	$0.874173\pi$
$20$		0			0
$21$	−41.2010	−	2.44230i	−0.428133	−	0.0253787i
$22$		0			0
$23$	96.9095	−	167.852i	0.878566	−	1.52172i	0.0256515	−	0.999671i	$-0.491834\pi$
$23$	96.9095	−	167.852i	0.878566	−	1.52172i	0.852915	−	0.522050i	$-0.174833\pi$
$24$		0			0
$25$	−28.0336	−	48.5556i	−0.224269	−	0.388445i
$26$		0			0
$27$	109.274			0.778879
$28$		0			0
$29$	288.486			1.84726			0.923631	−	0.383284i	$-0.125207\pi$
$29$	288.486			1.84726			0.923631	+	0.383284i	$0.125207\pi$
$30$		0			0
$31$	−22.2575	−	38.5511i	−0.128954	−	0.223354i	0.794318	−	0.607502i	$-0.207828\pi$
$31$	−22.2575	−	38.5511i	−0.128954	−	0.223354i	−0.923271	+	0.384148i	$0.874495\pi$
$32$		0			0
$33$	−55.0568	+	95.3612i	−0.290429	+	0.503038i
$34$		0			0
$35$	111.616	+	222.818i	0.539044	+	1.07609i
$36$		0			0
$37$	−114.272	+	197.926i	−0.507737	+	0.879427i	0.492223	+	0.870469i	$0.336185\pi$
$37$	−114.272	+	197.926i	−0.507737	+	0.879427i	−0.999960	+	0.00895735i	$0.997149\pi$
$38$		0			0
$39$	−24.5514	−	42.5243i	−0.100805	−	0.174599i
$40$		0			0
$41$	253.399			0.965225			0.482612	−	0.875834i	$-0.339688\pi$
$41$	253.399			0.965225			0.482612	+	0.875834i	$0.339688\pi$
$42$		0			0
$43$	241.336			0.855893			0.427947	−	0.903804i	$-0.359237\pi$
$43$	241.336			0.855893			0.427947	+	0.903804i	$0.359237\pi$
$44$		0			0
$45$	−148.243	−	256.765i	−0.491084	−	0.850583i
$46$		0			0
$47$	75.7426	−	131.190i	0.235068	−	0.407150i	−0.724224	−	0.689564i	$-0.757802\pi$
$47$	75.7426	−	131.190i	0.235068	−	0.407150i	0.959292	+	0.282415i	$0.0911354\pi$
$48$		0			0
$49$	−135.206	−	315.228i	−0.394186	−	0.919031i
$50$		0			0
$51$	−43.2237	+	74.8656i	−0.118677	+	0.205555i
$52$		0			0
$53$	−82.2389	−	142.442i	−0.213139	−	0.369168i	0.739556	−	0.673095i	$-0.235035\pi$
$53$	−82.2389	−	142.442i	−0.213139	−	0.369168i	−0.952695	+	0.303927i	$0.901702\pi$
$54$		0			0
$55$	664.874			1.63003
$56$		0			0
$57$	−293.436			−0.681868
$58$		0			0
$59$	369.329	+	639.697i	0.814959	+	1.41155i	0.909357	+	0.416016i	$0.136574\pi$
$59$	369.329	+	639.697i	0.814959	+	1.41155i	−0.0943985	+	0.995534i	$0.530093\pi$
$60$		0			0
$61$	−138.084	+	239.168i	−0.289833	+	0.502006i	−0.973770	−	0.227536i	$-0.926933\pi$
$61$	−138.084	+	239.168i	−0.289833	+	0.502006i	0.683936	+	0.729542i	$0.260267\pi$
$62$		0			0
$63$	182.764	+	364.851i	0.365494	+	0.729633i
$64$		0			0
$65$	−148.243	+	256.765i	−0.282882	+	0.489965i
$66$		0			0
$67$	−125.857	−	217.991i	−0.229491	−	0.397489i	0.728167	−	0.685400i	$-0.240373\pi$
$67$	−125.857	−	217.991i	−0.229491	−	0.397489i	−0.957657	+	0.287911i	$0.907039\pi$
$68$		0			0
$69$	431.935			0.753606
$70$		0			0
$71$	246.558			0.412128			0.206064	−	0.978539i	$-0.433935\pi$
$71$	246.558			0.412128			0.206064	+	0.978539i	$0.433935\pi$
$72$		0			0
$73$	439.589	+	761.390i	0.704794	+	1.22074i	0.966766	+	0.255664i	$0.0822940\pi$
$73$	439.589	+	761.390i	0.704794	+	1.22074i	−0.261972	+	0.965076i	$0.584373\pi$
$74$		0			0
$75$	62.4742	−	108.208i	0.0961853	−	0.166598i
$76$		0			0
$77$	−913.492	−	54.1497i	−1.35197	−	0.0801419i
$78$		0			0
$79$	−534.760	+	926.231i	−0.761585	+	1.31910i	0.180449	+	0.983584i	$0.442245\pi$
$79$	−534.760	+	926.231i	−0.761585	+	1.31910i	−0.942033	+	0.335519i	$0.891088\pi$
$80$		0			0
$81$	−175.692	−	304.308i	−0.241005	−	0.417432i
$82$		0			0
$83$	544.887			0.720592			0.360296	−	0.932838i	$-0.382676\pi$
$83$	544.887			0.720592			0.360296	+	0.932838i	$0.382676\pi$
$84$		0			0
$85$	521.975			0.666072
$86$		0			0
$87$	321.453	+	556.773i	0.396131	+	0.686118i
$88$		0			0
$89$	485.794	−	841.419i	0.578584	−	1.00214i	−0.417058	−	0.908880i	$-0.636939\pi$
$89$	485.794	−	841.419i	0.578584	−	1.00214i	0.995642	−	0.0932576i	$-0.0297280\pi$
$90$		0			0
$91$	224.588	−	340.704i	0.258717	−	0.392478i
$92$		0			0
$93$	49.6018	−	85.9129i	0.0553061	−	0.0957931i
$94$		0			0
$95$	885.892	+	1534.41i	0.956743	+	1.65713i
$96$		0			0
$97$	−355.197			−0.371802			−0.185901	−	0.982568i	$-0.559520\pi$
$97$	−355.197			−0.371802			−0.185901	+	0.982568i	$0.559520\pi$
$98$		0			0
$99$	1088.69			1.10523
$100$		0			0
$101$	445.395	+	771.447i	0.438797	+	0.760019i	0.997597	−	0.0692838i	$-0.0220714\pi$
$101$	445.395	+	771.447i	0.438797	+	0.760019i	−0.558800	+	0.829302i	$0.688738\pi$
$102$		0			0
$103$	−16.0202	+	27.7478i	−0.0153254	+	0.0265444i	−0.873586	−	0.486669i	$-0.838212\pi$
$103$	−16.0202	+	27.7478i	−0.0153254	+	0.0265444i	0.858261	+	0.513213i	$0.171545\pi$
$104$		0			0
$105$	−305.663	+	463.697i	−0.284092	+	0.430973i
$106$		0			0
$107$	−45.6478	+	79.0644i	−0.0412424	+	0.0714340i	−0.885910	−	0.463858i	$-0.846465\pi$
$107$	−45.6478	+	79.0644i	−0.0412424	+	0.0714340i	0.844667	+	0.535292i	$0.179798\pi$
$108$		0			0
$109$	−60.4235	−	104.657i	−0.0530966	−	0.0919660i	0.838255	−	0.545278i	$-0.183576\pi$
$109$	−60.4235	−	104.657i	−0.0530966	−	0.0919660i	−0.891352	+	0.453312i	$0.850242\pi$
$110$		0			0
$111$	−509.323			−0.435521
$112$		0			0
$113$	234.129			0.194911			0.0974557	−	0.995240i	$-0.468930\pi$
$113$	234.129			0.194911			0.0974557	+	0.995240i	$0.468930\pi$
$114$		0			0
$115$	−1304.03	−	2258.64i	−1.05740	−	1.83147i
$116$		0			0
$117$	−242.739	+	420.437i	−0.191806	+	0.332217i
$118$		0			0
$119$	−717.159	−	42.5115i	−0.552452	−	0.0327481i
$120$		0			0
$121$	−555.199	+	961.632i	−0.417129	+	0.722489i
$122$		0			0
$123$	282.356	+	489.054i	0.206985	+	0.358508i
$124$		0			0
$125$	927.569			0.663714
$126$		0			0
$127$	931.720			0.650999			0.325499	−	0.945542i	$-0.394468\pi$
$127$	931.720			0.650999			0.325499	+	0.945542i	$0.394468\pi$
$128$		0			0
$129$	268.914	+	465.774i	0.183540	+	0.317900i
$130$		0			0
$131$	485.270	−	840.512i	0.323651	−	0.560579i	−0.657588	−	0.753378i	$-0.728423\pi$
$131$	485.270	−	840.512i	0.323651	−	0.560579i	0.981238	+	0.192799i	$0.0617565\pi$
$132$		0			0
$133$	−1092.19	−	2180.33i	−0.712065	−	1.42149i
$134$		0			0
$135$	735.200	−	1273.40i	0.468711	−	0.811831i
$136$		0			0
$137$	−989.298	−	1713.51i	−0.616944	−	1.06858i	−0.990040	−	0.140786i	$-0.955037\pi$
$137$	−989.298	−	1713.51i	−0.616944	−	1.06858i	0.373096	−	0.927793i	$-0.378296\pi$
$138$		0			0
$139$	−2400.83			−1.46501			−0.732504	−	0.680763i	$-0.761648\pi$
$139$	−2400.83			−1.46501			−0.732504	+	0.680763i	$0.761648\pi$
$140$		0			0
$141$	337.592			0.201634
$142$		0			0
$143$	−544.345	−	942.833i	−0.318325	−	0.551354i
$144$		0			0
$145$	1940.95	−	3361.83i	1.11164	−	1.92541i
$146$		0			0
$147$	457.726	−	612.194i	0.256821	−	0.343489i
$148$		0			0
$149$	490.819	−	850.124i	0.269862	−	0.467415i	−0.698964	−	0.715157i	$-0.746355\pi$
$149$	490.819	−	850.124i	0.269862	−	0.467415i	0.968826	+	0.247742i	$0.0796885\pi$
$150$		0			0
$151$	−777.625	−	1346.89i	−0.419087	−	0.725881i	0.576761	−	0.816913i	$-0.304317\pi$
$151$	−777.625	−	1346.89i	−0.419087	−	0.725881i	−0.995848	+	0.0910326i	$0.970983\pi$
$152$		0			0
$153$	854.702			0.451625
$154$		0			0
$155$	−598.998			−0.310405
$156$		0			0
$157$	−73.6182	−	127.510i	−0.0374228	−	0.0648181i	0.846707	−	0.532059i	$-0.178581\pi$
$157$	−73.6182	−	127.510i	−0.0374228	−	0.0648181i	−0.884130	+	0.467241i	$0.845248\pi$
$158$		0			0
$159$	183.273	−	317.439i	0.0914121	−	0.158330i
$160$		0			0
$161$	1607.69	+	3209.42i	0.786981	+	1.57104i
$162$		0			0
$163$	−183.733	+	318.236i	−0.0882891	+	0.152921i	−0.906788	−	0.421587i	$-0.861473\pi$
$163$	−183.733	+	318.236i	−0.0882891	+	0.152921i	0.818499	+	0.574508i	$0.194807\pi$
$164$		0			0
$165$	740.851	+	1283.19i	0.349547	+	0.605433i
$166$		0			0
$167$	−3746.73			−1.73611			−0.868055	−	0.496467i	$-0.834630\pi$
$167$	−3746.73			−1.73611			−0.868055	+	0.496467i	$0.834630\pi$
$168$		0			0
$169$	−1711.52			−0.779027
$170$		0			0
$171$	1450.59	+	2512.50i	0.648711	+	1.12360i
$172$		0			0
$173$	−831.953	+	1440.98i	−0.365620	+	0.633272i	−0.988875	−	0.148746i	$-0.952476\pi$
$173$	−831.953	+	1440.98i	−0.365620	+	0.633272i	0.623256	+	0.782018i	$0.285810\pi$
$174$		0			0
$175$	1036.56	+	61.4448i	0.447751	+	0.0265417i
$176$		0			0
$177$	−823.068	+	1425.60i	−0.349523	+	0.605392i
$178$		0			0
$179$	−247.860	−	429.307i	−0.103497	−	0.179262i	0.809626	−	0.586946i	$-0.199670\pi$
$179$	−247.860	−	429.307i	−0.103497	−	0.179262i	−0.913123	+	0.407684i	$0.866337\pi$
$180$		0			0
$181$	−1800.16			−0.739252			−0.369626	−	0.929181i	$-0.620514\pi$
$181$	−1800.16			−0.739252			−0.369626	+	0.929181i	$0.620514\pi$
$182$		0			0
$183$	−615.453			−0.248610
$184$		0			0
$185$	1537.66	+	2663.31i	0.611088	+	1.05844i
$186$		0			0
$187$	−958.339	+	1659.89i	−0.374763	+	0.649109i
$188$		0			0
$189$	−1113.83	+	1689.69i	−0.428671	+	0.650302i
$190$		0			0
$191$	−1223.14	+	2118.54i	−0.463368	+	0.802576i	−0.999126	−	0.0417948i	$-0.986692\pi$
$191$	−1223.14	+	2118.54i	−0.463368	+	0.802576i	0.535758	+	0.844371i	$0.320026\pi$
$192$		0			0
$193$	−1221.08	−	2114.97i	−0.455415	−	0.788802i	0.543297	−	0.839541i	$-0.317176\pi$
$193$	−1221.08	−	2114.97i	−0.455415	−	0.788802i	−0.998712	+	0.0507385i	$0.983842\pi$
$194$		0			0
$195$	−660.734			−0.242647
$196$		0			0
$197$	2126.21			0.768964			0.384482	−	0.923132i	$-0.374380\pi$
$197$	2126.21			0.768964			0.384482	+	0.923132i	$0.374380\pi$
$198$		0			0
$199$	−1802.28	−	3121.65i	−0.642013	−	1.11200i	−0.984983	−	0.172652i	$-0.944766\pi$
$199$	−1802.28	−	3121.65i	−0.642013	−	1.11200i	0.342970	−	0.939346i	$-0.388567\pi$
$200$		0			0
$201$	280.478	−	485.803i	0.0984249	−	0.170477i
$202$		0			0
$203$	−2940.54	+	4460.85i	−1.01668	+	1.54232i
$204$		0			0
$205$	1704.88	−	2952.94i	0.580849	−	1.00606i
$206$		0			0
$207$	−2135.26	−	3698.38i	−0.716961	−	1.24181i
$208$		0			0
$209$	−6505.94			−2.15323
$210$		0			0
$211$	−2601.68			−0.848848			−0.424424	−	0.905463i	$-0.639523\pi$
$211$	−2601.68			−0.848848			−0.424424	+	0.905463i	$0.639523\pi$
$212$		0			0
$213$	274.733	+	475.852i	0.0883775	+	0.153074i
$214$		0			0
$215$	1623.72	−	2812.37i	0.515056	−	0.892103i
$216$		0			0
$217$	822.984	+	48.7846i	0.257455	+	0.0152613i
$218$		0			0
$219$	−979.645	+	1696.79i	−0.302275	+	0.523556i
$220$		0			0
$221$	−427.351	−	740.194i	−0.130076	−	0.225298i
$222$		0			0
$223$	4235.80			1.27197			0.635987	−	0.771700i	$-0.280593\pi$
$223$	4235.80			1.27197			0.635987	+	0.771700i	$0.280593\pi$
$224$		0			0
$225$	−1235.36			−0.366032
$226$		0			0
$227$	−1390.92	−	2409.14i	−0.406690	−	0.704408i	0.587827	−	0.808987i	$-0.299984\pi$
$227$	−1390.92	−	2409.14i	−0.406690	−	0.704408i	−0.994517	+	0.104579i	$0.966650\pi$
$228$		0			0
$229$	−2525.83	+	4374.86i	−0.728870	+	1.26244i	0.228491	+	0.973546i	$0.426621\pi$
$229$	−2525.83	+	4374.86i	−0.728870	+	1.26244i	−0.957361	+	0.288894i	$0.906713\pi$
$230$		0			0
$231$	−913.372	−	1823.36i	−0.260154	−	0.519343i
$232$		0			0
$233$	3521.24	−	6098.97i	0.990061	−	1.71484i	0.373231	−	0.927738i	$-0.378250\pi$
$233$	3521.24	−	6098.97i	0.990061	−	1.71484i	0.616829	−	0.787097i	$-0.288417\pi$
$234$		0			0
$235$	−1019.20	−	1765.31i	−0.282917	−	0.490026i
$236$		0			0
$237$	−2383.48			−0.653263
$238$		0			0
$239$	−4557.55			−1.23349			−0.616744	−	0.787164i	$-0.711549\pi$
$239$	−4557.55			−1.23349			−0.616744	+	0.787164i	$0.711549\pi$
$240$		0			0
$241$	3262.09	+	5650.11i	0.871908	+	1.51019i	0.860020	+	0.510260i	$0.170451\pi$
$241$	3262.09	+	5650.11i	0.871908	+	1.51019i	0.0118877	+	0.999929i	$0.496216\pi$
$242$		0			0
$243$	1866.73	−	3233.28i	0.492803	−	0.853559i
$244$		0			0
$245$	−4583.13	−	545.270i	−1.19512	−	0.142188i
$246$		0			0
$247$	1450.59	−	2512.50i	0.373680	−	0.647233i
$248$		0			0
$249$	607.153	+	1051.62i	0.154525	+	0.267646i
$250$		0			0
$251$	2962.35			0.744949			0.372474	−	0.928043i	$-0.378509\pi$
$251$	2962.35			0.744949			0.372474	+	0.928043i	$0.378509\pi$
$252$		0			0
$253$	9576.69			2.37977
$254$		0			0
$255$	581.623	+	1007.40i	0.142834	+	0.247396i
$256$		0			0
$257$	2115.21	−	3663.65i	0.513398	−	0.889231i	−0.486481	−	0.873691i	$-0.661720\pi$
$257$	2115.21	−	3663.65i	0.513398	−	0.889231i	0.999879	−	0.0155402i	$-0.00494679\pi$
$258$		0			0
$259$	−1895.74	−	3784.45i	−0.454808	−	0.907930i
$260$		0			0
$261$	3178.19	−	5504.79i	0.753736	−	1.30551i
$262$		0			0
$263$	−2676.52	−	4635.87i	−0.627533	−	1.08692i	−0.988045	−	0.154165i	$-0.950731\pi$
$263$	−2676.52	−	4635.87i	−0.627533	−	1.08692i	0.360512	−	0.932755i	$-0.382602\pi$
$264$		0			0
$265$	−2213.23			−0.513048
$266$		0			0
$267$	2165.23			0.496292
$268$		0			0
$269$	−2700.05	−	4676.62i	−0.611989	−	1.06000i	−0.990905	−	0.134565i	$-0.957036\pi$
$269$	−2700.05	−	4676.62i	−0.611989	−	1.06000i	0.378916	−	0.925431i	$-0.376297\pi$
$270$		0			0
$271$	−4316.80	+	7476.92i	−0.967628	+	1.67598i	−0.265246	+	0.964181i	$0.585453\pi$
$271$	−4316.80	+	7476.92i	−0.967628	+	1.67598i	−0.702382	+	0.711800i	$0.747880\pi$
$272$		0			0
$273$	907.804	+	53.8126i	0.201256	+	0.0119300i
$274$		0			0
$275$	1385.15	−	2399.16i	0.303738	−	0.526089i
$276$		0			0
$277$	1198.09	+	2075.16i	0.259879	+	0.450123i	0.966209	−	0.257759i	$-0.0829841\pi$
$277$	1198.09	+	2075.16i	0.259879	+	0.450123i	−0.706331	+	0.707882i	$0.749651\pi$
$278$		0			0
$279$	−980.823			−0.210467
$280$		0			0
$281$	−7646.23			−1.62326			−0.811630	−	0.584172i	$-0.801419\pi$
$281$	−7646.23			−1.62326			−0.811630	+	0.584172i	$0.801419\pi$
$282$		0			0
$283$	−2601.26	−	4505.51i	−0.546392	−	0.946378i	−0.998518	−	0.0544242i	$-0.982668\pi$
$283$	−2601.26	−	4505.51i	−0.546392	−	0.946378i	0.452126	−	0.891954i	$-0.350666\pi$
$284$		0			0
$285$	−1974.25	+	3419.51i	−0.410332	+	0.710716i
$286$		0			0
$287$	−2582.89	+	3918.29i	−0.531231	+	0.805886i
$288$		0			0
$289$	1704.13	−	2951.64i	0.346862	−	0.600783i
$290$		0			0
$291$	−395.787	−	685.523i	−0.0797300	−	0.138096i
$292$		0			0
$293$	−1999.72			−0.398721			−0.199360	−	0.979926i	$-0.563886\pi$
$293$	−1999.72			−0.398721			−0.199360	+	0.979926i	$0.563886\pi$
$294$		0			0
$295$	9939.48			1.96169
$296$		0			0
$297$	2699.63	+	4675.90i	0.527436	+	0.913547i
$298$		0			0
$299$	−2135.26	+	3698.38i	−0.412995	+	0.715328i
$300$		0			0
$301$	−2459.94	+	3731.77i	−0.471058	+	0.714603i
$302$		0			0
$303$	−992.585	+	1719.21i	−0.188193	+	0.325960i
$304$		0			0
$305$	1858.07	+	3218.28i	0.348829	+	0.604190i
$306$		0			0
$307$	3176.43			0.590516			0.295258	−	0.955418i	$-0.404594\pi$
$307$	3176.43			0.590516			0.295258	+	0.955418i	$0.404594\pi$
$308$		0			0
$309$	−71.4035			−0.0131456
$310$		0			0
$311$	806.614	+	1397.10i	0.147070	+	0.254733i	0.930143	−	0.367196i	$-0.119682\pi$
$311$	806.614	+	1397.10i	0.147070	+	0.254733i	−0.783073	+	0.621930i	$0.786349\pi$
$312$		0			0
$313$	−1017.49	+	1762.34i	−0.183743	+	0.318253i	−0.943152	−	0.332361i	$-0.892155\pi$
$313$	−1017.49	+	1762.34i	−0.183743	+	0.318253i	0.759409	+	0.650614i	$0.225488\pi$
$314$		0			0
$315$	5481.38	+	324.924i	0.980447	+	0.0581187i
$316$		0			0
$317$	1110.49	−	1923.43i	0.196756	−	0.340791i	−0.750719	−	0.660622i	$-0.770293\pi$
$317$	1110.49	−	1923.43i	0.196756	−	0.340791i	0.947475	+	0.319831i	$0.103626\pi$
$318$		0			0
$319$	7127.13	+	12344.5i	1.25092	+	2.16665i
$320$		0			0
$321$	−203.457			−0.0353765
$322$		0			0
$323$	−5107.64			−0.879867
$324$		0			0
$325$	617.680	+	1069.85i	0.105424	+	0.182599i
$326$		0			0
$327$	134.657	−	233.232i	0.0227723	−	0.0394428i
$328$		0			0
$329$	1256.54	+	2508.42i	0.210564	+	0.420346i
$330$		0			0
$331$	761.283	−	1318.58i	0.126417	−	0.218960i	−0.795869	−	0.605469i	$-0.792986\pi$
$331$	761.283	−	1318.58i	0.126417	−	0.218960i	0.922286	+	0.386509i	$0.126319\pi$
$332$		0			0
$333$	2517.83	+	4361.01i	0.414343	+	0.717663i
$334$		0			0
$335$	−3387.09			−0.552408
$336$		0			0
$337$	5089.10			0.822614			0.411307	−	0.911497i	$-0.365072\pi$
$337$	5089.10			0.822614			0.411307	+	0.911497i	$0.365072\pi$
$338$		0			0
$339$	260.884	+	451.864i	0.0417972	+	0.0723949i
$340$		0			0
$341$	1099.75	−	1904.83i	0.174648	−	0.302499i
$342$		0			0
$343$	6252.50	+	1122.43i	0.984266	+	0.176693i
$344$		0			0
$345$	2906.08	−	5033.48i	0.453502	−	0.785489i
$346$		0			0
$347$	2959.08	+	5125.28i	0.457786	+	0.792908i	0.998844	−	0.0480770i	$-0.0153093\pi$
$347$	2959.08	+	5125.28i	0.457786	+	0.792908i	−0.541058	+	0.840985i	$0.681976\pi$
$348$		0			0
$349$	−5743.87			−0.880981			−0.440490	−	0.897757i	$-0.645195\pi$
$349$	−5743.87			−0.880981			−0.440490	+	0.897757i	$0.645195\pi$
$350$		0			0
$351$	−2407.69			−0.366134
$352$		0			0
$353$	−995.069	−	1723.51i	−0.150034	−	0.259867i	0.781205	−	0.624274i	$-0.214605\pi$
$353$	−995.069	−	1723.51i	−0.150034	−	0.259867i	−0.931240	+	0.364407i	$0.881272\pi$
$354$		0			0
$355$	1658.86	−	2873.22i	0.248008	−	0.429563i
$356$		0			0
$357$	−717.065	−	1431.47i	−0.106306	−	0.212217i
$358$		0			0
$359$	−1921.66	+	3328.41i	−0.282510	+	0.489322i	−0.972002	−	0.234971i	$-0.924500\pi$
$359$	−1921.66	+	3328.41i	−0.282510	+	0.489322i	0.689492	+	0.724293i	$0.257834\pi$
$360$		0			0
$361$	−5239.15	−	9074.48i	−0.763836	−	1.32300i
$362$		0			0
$363$	−2474.57			−0.357800
$364$		0			0
$365$	11830.3			1.69651
$366$		0			0
$367$	5458.64	+	9454.65i	0.776400	+	1.34476i	0.934004	+	0.357262i	$0.116290\pi$
$367$	5458.64	+	9454.65i	0.776400	+	1.34476i	−0.157604	+	0.987502i	$0.550377\pi$
$368$		0			0
$369$	2791.64	−	4835.26i	0.393840	−	0.682151i
$370$		0			0
$371$	3040.83	+	180.254i	0.425532	+	0.0252245i
$372$		0			0
$373$	5937.31	−	10283.7i	0.824188	−	1.42754i	−0.0783504	−	0.996926i	$-0.524965\pi$
$373$	5937.31	−	10283.7i	0.824188	−	1.42754i	0.902538	−	0.430609i	$-0.141701\pi$
$374$		0			0
$375$	1033.57	+	1790.19i	0.142328	+	0.246520i
$376$		0			0
$377$	−6356.39			−0.868357
$378$		0			0
$379$	8651.34			1.17253			0.586266	−	0.810119i	$-0.300597\pi$
$379$	8651.34			1.17253			0.586266	+	0.810119i	$0.300597\pi$
$380$		0			0
$381$	1038.19	+	1798.20i	0.139602	+	0.241797i
$382$		0			0
$383$	959.972	−	1662.72i	0.128074	−	0.221830i	−0.794856	−	0.606798i	$-0.792454\pi$
$383$	959.972	−	1662.72i	0.128074	−	0.221830i	0.922930	+	0.384967i	$0.125787\pi$
$384$		0			0
$385$	−6777.05	+	10280.9i	−0.897118	+	1.36094i
$386$		0			0
$387$	2658.75	−	4605.09i	0.349229	−	0.604883i
$388$		0			0
$389$	−100.376	−	173.856i	−0.0130829	−	0.0226602i	0.859410	−	0.511287i	$-0.170831\pi$
$389$	−100.376	−	173.856i	−0.0130829	−	0.0226602i	−0.872493	+	0.488627i	$0.837498\pi$
$390$		0			0
$391$	7518.41			0.972436
$392$		0			0
$393$	2162.89			0.277617
$394$		0			0
$395$	7195.79	+	12463.5i	0.916607	+	1.58761i
$396$		0			0
$397$	−2000.76	+	3465.41i	−0.252935	+	0.438096i	−0.964333	−	0.264694i	$-0.914729\pi$
$397$	−2000.76	+	3465.41i	−0.252935	+	0.438096i	0.711398	+	0.702790i	$0.248063\pi$
$398$		0			0
$399$	2990.99	−	4537.38i	0.375280	−	0.569306i
$400$		0			0
$401$	933.376	−	1616.65i	0.116236	−	0.201326i	−0.802037	−	0.597274i	$-0.796250\pi$
$401$	933.376	−	1616.65i	0.116236	−	0.201326i	0.918273	+	0.395948i	$0.129584\pi$
$402$		0			0
$403$	490.412	+	849.418i	0.0606182	+	0.104994i
$404$		0			0
$405$	−4728.28			−0.580123
$406$		0			0
$407$	−11292.5			−1.37531
$408$		0			0
$409$	6671.19	+	11554.8i	0.806526	+	1.39694i	0.915256	+	0.402872i	$0.131988\pi$
$409$	6671.19	+	11554.8i	0.806526	+	1.39694i	−0.108731	+	0.994071i	$0.534679\pi$
$410$		0			0
$411$	2204.70	−	3818.65i	0.264598	−	0.458297i
$412$		0			0
$413$	−13656.2	−	809.507i	−1.62706	−	0.0964485i
$414$		0			0
$415$	3666.03	−	6349.75i	0.433635	−	0.751077i
$416$		0			0
$417$	−2675.19	−	4633.56i	−0.314159	−	0.544140i
$418$		0			0
$419$	−7096.71			−0.827440			−0.413720	−	0.910404i	$-0.635771\pi$
$419$	−7096.71			−0.827440			−0.413720	+	0.910404i	$0.635771\pi$
$420$		0			0
$421$	−10818.1			−1.25236			−0.626178	−	0.779680i	$-0.715382\pi$
$421$	−10818.1			−1.25236			−0.626178	+	0.779680i	$0.715382\pi$
$422$		0			0
$423$	−1668.88	−	2890.59i	−0.191829	−	0.332258i
$424$		0			0
$425$	1087.45	−	1883.51i	0.124115	−	0.214974i
$426$		0			0
$427$	−2290.76	−	4573.03i	−0.259620	−	0.518277i
$428$		0			0
$429$	1213.10	−	2101.15i	0.136524	−	0.236467i
$430$		0			0
$431$	1183.03	+	2049.06i	0.132214	+	0.229002i	0.924530	−	0.381109i	$-0.124458\pi$
$431$	1183.03	+	2049.06i	0.132214	+	0.229002i	−0.792315	+	0.610112i	$0.791125\pi$
$432$		0			0
$433$	−7040.11			−0.781353			−0.390677	−	0.920528i	$-0.627759\pi$
$433$	−7040.11			−0.781353			−0.390677	+	0.920528i	$0.627759\pi$
$434$		0			0
$435$	8651.02			0.953528
$436$		0			0
$437$	12760.2	+	22101.3i	1.39680	+	2.41933i
$438$		0			0
$439$	5345.70	−	9259.03i	0.581177	−	1.00663i	−0.414164	−	0.910202i	$-0.635926\pi$
$439$	5345.70	−	9259.03i	0.581177	−	1.00663i	0.995340	−	0.0964249i	$-0.0307408\pi$
$440$		0			0
$441$	−7504.59	−	892.847i	−0.810343	−	0.0964093i
$442$		0			0
$443$	−7076.66	+	12257.1i	−0.758967	+	1.31457i	0.184410	+	0.982849i	$0.440962\pi$
$443$	−7076.66	+	12257.1i	−0.758967	+	1.31457i	−0.943378	+	0.331721i	$0.892371\pi$
$444$		0			0
$445$	−6536.90	−	11322.2i	−0.696356	−	1.20612i
$446$		0			0
$447$	2187.63			0.231479
$448$		0			0
$449$	10413.4			1.09452			0.547259	−	0.836963i	$-0.315671\pi$
$449$	10413.4			1.09452			0.547259	+	0.836963i	$0.315671\pi$
$450$		0			0
$451$	6260.28	+	10843.1i	0.653625	+	1.13211i
$452$		0			0
$453$	1732.97	−	3001.60i	0.179740	−	0.311319i
$454$		0			0
$455$	−2459.30	−	4909.48i	−0.253393	−	0.505846i
$456$		0			0
$457$	−3.09097	+	5.35372i	−0.000316388	+	0.000548001i	−0.866184	−	0.499726i	$-0.833434\pi$
$457$	−3.09097	+	5.35372i	−0.000316388	+	0.000548001i	0.865867	+	0.500274i	$0.166767\pi$
$458$		0			0
$459$	2119.41	+	3670.93i	0.215524	+	0.373299i
$460$		0			0
$461$	881.170			0.0890242			0.0445121	−	0.999009i	$-0.485827\pi$
$461$	881.170			0.0890242			0.0445121	+	0.999009i	$0.485827\pi$
$462$		0			0
$463$	15166.1			1.52231			0.761155	−	0.648570i	$-0.224633\pi$
$463$	15166.1			1.52231			0.761155	+	0.648570i	$0.224633\pi$
$464$		0			0
$465$	−667.448	−	1156.05i	−0.0665638	−	0.115292i
$466$		0			0
$467$	−2934.63	+	5082.92i	−0.290789	+	0.503661i	−0.973996	−	0.226563i	$-0.927251\pi$
$467$	−2934.63	+	5082.92i	−0.290789	+	0.503661i	0.683208	+	0.730224i	$0.260584\pi$
$468$		0			0
$469$	4653.64	+	275.857i	0.458177	+	0.0271597i
$470$		0			0
$471$	164.062	−	284.163i	0.0160500	−	0.0277995i
$472$		0			0
$473$	5962.27	+	10326.9i	0.579588	+	1.00388i
$474$		0			0
$475$	7382.43			0.713114
$476$		0			0
$477$	−3624.03			−0.347868
$478$		0			0
$479$	−2857.82	−	4949.90i	−0.272604	−	0.472164i	0.696924	−	0.717145i	$-0.254552\pi$
$479$	−2857.82	−	4949.90i	−0.272604	−	0.472164i	−0.969528	+	0.244981i	$0.921218\pi$
$480$		0			0
$481$	2517.83	−	4361.01i	0.238676	−	0.413399i
$482$		0			0
$483$	−4402.71	+	6678.99i	−0.414762	+	0.629202i
$484$		0			0
$485$	−2389.79	+	4139.23i	−0.223741	+	0.387532i
$486$		0			0
$487$	−1176.90	−	2038.45i	−0.109508	−	0.189673i	0.806063	−	0.591830i	$-0.201594\pi$
$487$	−1176.90	−	2038.45i	−0.109508	−	0.189673i	−0.915571	+	0.402156i	$0.868261\pi$
$488$		0			0
$489$	−818.918			−0.0757316
$490$		0			0
$491$	−13218.9			−1.21499			−0.607493	−	0.794325i	$-0.707825\pi$
$491$	−13218.9			−1.21499			−0.607493	+	0.794325i	$0.707825\pi$
$492$		0			0
$493$	5595.32	+	9691.39i	0.511158	+	0.885351i
$494$		0			0
$495$	7324.77	−	12686.9i	0.665099	−	1.15199i
$496$		0			0
$497$	−2513.16	+	3812.51i	−0.226823	+	0.344094i
$498$		0			0
$499$	3564.20	−	6173.38i	0.319751	−	0.553825i	−0.660685	−	0.750663i	$-0.729734\pi$
$499$	3564.20	−	6173.38i	0.319751	−	0.553825i	0.980436	+	0.196838i	$0.0630674\pi$
$500$		0			0
$501$	−4174.88	−	7231.11i	−0.372295	−	0.644834i
$502$		0			0
$503$	1391.95			0.123388			0.0616938	−	0.998095i	$-0.480350\pi$
$503$	1391.95			0.123388			0.0616938	+	0.998095i	$0.480350\pi$
$504$		0			0
$505$	11986.6			1.05623
$506$		0			0
$507$	−1907.10	−	3303.20i	−0.167056	−	0.289350i
$508$		0			0
$509$	8052.52	−	13947.4i	0.701221	−	1.21455i	−0.266816	−	0.963747i	$-0.585972\pi$
$509$	8052.52	−	13947.4i	0.701221	−	1.21455i	0.968038	−	0.250804i	$-0.0806949\pi$
$510$		0			0
$511$	−16254.1	−	963.504i	−1.40712	−	0.0834107i
$512$		0			0
$513$	−7194.10	+	12460.5i	−0.619156	+	1.07241i
$514$		0			0
$515$	215.569	+	373.377i	0.0184449	+	0.0319475i
$516$		0			0
$517$	7484.96			0.636728
$518$		0			0
$519$	−3708.09			−0.313617
$520$		0			0
$521$	2393.02	+	4144.83i	0.201228	+	0.348538i	0.948924	−	0.315503i	$-0.102173\pi$
$521$	2393.02	+	4144.83i	0.201228	+	0.348538i	−0.747696	+	0.664041i	$0.768840\pi$
$522$		0			0
$523$	−10791.6	+	18691.6i	−0.902261	+	1.56276i	−0.0777098	+	0.996976i	$0.524761\pi$
$523$	−10791.6	+	18691.6i	−0.902261	+	1.56276i	−0.824552	+	0.565787i	$0.808573\pi$
$524$		0			0
$525$	1036.42	+	2069.00i	0.0861585	+	0.171997i
$526$		0			0
$527$	863.387	−	1495.43i	0.0713657	−	0.123609i
$528$		0			0
$529$	−12699.4	−	21996.0i	−1.04376	−	1.80784i
$530$		0			0
$531$	16275.3			1.33011
$532$		0			0
$533$	−5583.28			−0.453731
$534$		0			0
$535$	614.243	+	1063.90i	0.0496374	+	0.0859745i
$536$		0			0
$537$	552.369	−	956.731i	0.0443882	−	0.0768826i
$538$		0			0
$539$	10148.5	−	13573.3i	0.810998	−	1.08468i
$540$		0			0
$541$	−1757.22	+	3043.59i	−0.139646	+	0.241875i	−0.927363	−	0.374163i	$-0.877930\pi$
$541$	−1757.22	+	3043.59i	−0.139646	+	0.241875i	0.787716	+	0.616038i	$0.211263\pi$
$542$		0			0
$543$	−2005.87	−	3474.27i	−0.158527	−	0.274577i
$544$		0			0
$545$	−1626.13			−0.127809
$546$		0			0
$547$	−564.449			−0.0441209			−0.0220604	−	0.999757i	$-0.507023\pi$
$547$	−564.449			−0.0441209			−0.0220604	+	0.999757i	$0.507023\pi$
$548$		0			0
$549$	3042.48	+	5269.73i	0.236521	+	0.409666i
$550$		0			0
$551$	−18992.7	+	32896.3i	−1.46845	+	2.54343i
$552$		0			0
$553$	−8871.47	−	17710.0i	−0.682194	−	1.36186i
$554$		0			0
$555$	−3426.76	+	5935.32i	−0.262086	+	0.453946i
$556$		0			0
$557$	−3687.21	−	6386.43i	−0.280488	−	0.485820i	0.691017	−	0.722839i	$-0.257163\pi$
$557$	−3687.21	−	6386.43i	−0.280488	−	0.485820i	−0.971505	+	0.237019i	$0.923830\pi$
$558$		0			0
$559$	−5317.50			−0.402336
$560$		0			0
$561$	−4271.41			−0.321460
$562$		0			0
$563$	−5017.70	−	8690.91i	−0.375614	−	0.650583i	0.614805	−	0.788680i	$-0.289235\pi$
$563$	−5017.70	−	8690.91i	−0.375614	−	0.650583i	−0.990419	+	0.138097i	$0.955902\pi$
$564$		0			0
$565$	1575.23	−	2728.38i	0.117293	−	0.203158i
$566$		0			0
$567$	6496.33	+	385.088i	0.481165	+	0.0285223i
$568$		0			0
$569$	9298.65	−	16105.7i	0.685096	−	1.18662i	−0.288311	−	0.957537i	$-0.593094\pi$
$569$	9298.65	−	16105.7i	0.685096	−	1.18662i	0.973407	−	0.229084i	$-0.0735731\pi$
$570$		0			0
$571$	−4780.57	−	8280.19i	−0.350369	−	0.606857i	0.635945	−	0.771734i	$-0.280610\pi$
$571$	−4780.57	−	8280.19i	−0.350369	−	0.606857i	−0.986314	+	0.164877i	$0.947277\pi$
$572$		0			0
$573$	−5451.65			−0.397462
$574$		0			0
$575$	−10866.9			−0.788139
$576$		0			0
$577$	9612.84	+	16649.9i	0.693566	+	1.20129i	0.970662	+	0.240449i	$0.0772948\pi$
$577$	9612.84	+	16649.9i	0.693566	+	1.20129i	−0.277096	+	0.960842i	$0.589372\pi$
$578$		0			0
$579$	2721.23	−	4713.31i	0.195320	−	0.338305i
$580$		0			0
$581$	−5554.03	+	8425.56i	−0.396592	+	0.601637i
$582$		0			0
$583$	4063.46	−	7038.13i	0.288665	−	0.499982i
$584$		0			0
$585$	3266.33	+	5657.44i	0.230848	+	0.399840i
$586$		0			0
$587$	−17864.9			−1.25616			−0.628078	−	0.778150i	$-0.716158\pi$
$587$	−17864.9			−1.25616			−0.628078	+	0.778150i	$0.716158\pi$
$588$		0			0
$589$	5861.34			0.410038
$590$		0			0
$591$	2369.18	+	4103.54i	0.164898	+	0.285612i
$592$		0			0
$593$	−4953.99	+	8580.56i	−0.343062	+	0.594201i	−0.985000	−	0.172556i	$-0.944797\pi$
$593$	−4953.99	+	8580.56i	−0.343062	+	0.594201i	0.641938	+	0.766757i	$0.278131\pi$
$594$		0			0
$595$	−5320.49	+	8071.28i	−0.366586	+	0.556118i
$596$		0			0
$597$	4016.48	−	6956.74i	0.275349	−	0.476919i
$598$		0			0
$599$	−3415.15	−	5915.21i	−0.232953	−	0.403487i	0.725723	−	0.687987i	$-0.241506\pi$
$599$	−3415.15	−	5915.21i	−0.232953	−	0.403487i	−0.958676	+	0.284500i	$0.908172\pi$
$600$		0			0
$601$	8230.00			0.558584			0.279292	−	0.960206i	$-0.409900\pi$
$601$	8230.00			0.558584			0.279292	+	0.960206i	$0.409900\pi$
$602$		0			0
$603$	−5546.16			−0.374555
$604$		0			0
$605$	7470.82	+	12939.8i	0.502036	+	0.869553i
$606$		0			0
$607$	2297.46	−	3979.32i	0.153626	−	0.266089i	−0.778932	−	0.627109i	$-0.784238\pi$
$607$	2297.46	−	3979.32i	0.153626	−	0.266089i	0.932558	+	0.361020i	$0.117571\pi$
$608$		0			0
$609$	−11885.9	−	704.570i	−0.790873	−	0.0468811i
$610$		0			0
$611$	−1668.88	+	2890.59i	−0.110500	+	0.191392i
$612$		0			0
$613$	−8339.98	−	14445.3i	−0.549508	−	0.951777i	−0.998308	−	0.0581442i	$-0.981482\pi$
$613$	−8339.98	−	14445.3i	−0.549508	−	0.951777i	0.448800	−	0.893632i	$-0.351852\pi$
$614$		0			0
$615$	7598.82			0.498234
$616$		0			0
$617$	14840.9			0.968353			0.484177	−	0.874970i	$-0.339119\pi$
$617$	14840.9			0.968353			0.484177	+	0.874970i	$0.339119\pi$
$618$		0			0
$619$	−12237.5	−	21195.9i	−0.794613	−	1.37631i	−0.923084	−	0.384597i	$-0.874340\pi$
$619$	−12237.5	−	21195.9i	−0.794613	−	1.37631i	0.128471	−	0.991713i	$-0.458993\pi$
$620$		0			0
$621$	10589.7	−	18341.8i	0.684297	−	1.18524i
$622$		0			0
$623$	8059.13	+	16088.4i	0.518270	+	1.03462i
$624$		0			0
$625$	9744.93	−	16878.7i	0.623676	−	1.08024i
$626$		0			0
$627$	−7249.40	−	12556.3i	−0.461743	−	0.799763i
$628$		0			0
$629$	−8865.46			−0.561986
$630$		0			0
$631$	−19781.0			−1.24797			−0.623985	−	0.781437i	$-0.714487\pi$
$631$	−19781.0			−1.24797			−0.623985	+	0.781437i	$0.714487\pi$
$632$		0			0
$633$	−2898.98	−	5021.19i	−0.182029	−	0.315283i
$634$		0			0
$635$	6268.67	−	10857.7i	0.391755	−	0.678540i
$636$		0			0
$637$	2979.07	+	6945.59i	0.185298	+	0.432016i
$638$		0			0
$639$	2716.28	−	4704.73i	0.168160	−	0.291262i
$640$		0			0
$641$	3087.44	+	5347.61i	0.190244	+	0.329513i	0.945331	−	0.326112i	$-0.105739\pi$
$641$	3087.44	+	5347.61i	0.190244	+	0.329513i	−0.755087	+	0.655625i	$0.772405\pi$
$642$		0			0
$643$	−11826.2			−0.725317			−0.362658	−	0.931922i	$-0.618131\pi$
$643$	−11826.2			−0.725317			−0.362658	+	0.931922i	$0.618131\pi$
$644$		0			0
$645$	7237.09			0.441799
$646$		0			0
$647$	−630.952	−	1092.84i	−0.0383389	−	0.0664049i	0.846219	−	0.532835i	$-0.178873\pi$
$647$	−630.952	−	1092.84i	−0.0383389	−	0.0664049i	−0.884558	+	0.466430i	$0.845540\pi$
$648$		0			0
$649$	−18248.7	+	31607.8i	−1.10374	+	1.91173i
$650$		0			0
$651$	822.876	+	1642.70i	0.0495408	+	0.0988979i
$652$		0			0
$653$	−5351.27	+	9268.68i	−0.320691	+	0.555454i	−0.980631	−	0.195865i	$-0.937249\pi$
$653$	−5351.27	+	9268.68i	−0.320691	+	0.555454i	0.659939	+	0.751319i	$0.270582\pi$
$654$		0			0
$655$	−6529.85	−	11310.0i	−0.389530	−	0.674686i
$656$		0			0
$657$	19371.4			1.15031
$658$		0			0
$659$	−14371.3			−0.849509			−0.424754	−	0.905309i	$-0.639640\pi$
$659$	−14371.3			−0.849509			−0.424754	+	0.905309i	$0.639640\pi$
$660$		0			0
$661$	6637.69	+	11496.8i	0.390584	+	0.676512i	0.992527	−	0.122028i	$-0.0389396\pi$
$661$	6637.69	+	11496.8i	0.390584	+	0.676512i	−0.601942	+	0.798540i	$0.705606\pi$
$662$		0			0
$663$	952.373	−	1649.56i	0.0557875	−	0.0966267i
$664$		0			0
$665$	−32756.4	−	1941.72i	−1.91013	−	0.113228i
$666$		0			0
$667$	27957.1	−	48423.1i	1.62294	−	2.81102i
$668$		0			0
$669$	4719.84	+	8175.01i	0.272765	+	0.472443i
$670$		0			0
$671$	−13645.6			−0.785070
$672$		0			0
$673$	11358.5			0.650577			0.325289	−	0.945615i	$-0.394539\pi$
$673$	11358.5			0.650577			0.325289	+	0.945615i	$0.394539\pi$
$674$		0			0
$675$	−3063.33	−	5305.85i	−0.174678	−	0.302551i
$676$		0			0
$677$	12641.2	−	21895.2i	0.717637	−	1.24298i	−0.244296	−	0.969701i	$-0.578557\pi$
$677$	12641.2	−	21895.2i	0.717637	−	1.24298i	0.961933	−	0.273284i	$-0.0881098\pi$
$678$		0			0
$679$	3620.52	−	5492.39i	0.204629	−	0.310425i
$680$		0			0
$681$	3099.73	−	5368.89i	0.174423	−	0.302109i
$682$		0			0
$683$	−12163.8	−	21068.4i	−0.681459	−	1.18032i	−0.974536	−	0.224233i	$-0.928012\pi$
$683$	−12163.8	−	21068.4i	−0.681459	−	1.18032i	0.293076	−	0.956089i	$-0.405321\pi$
$684$		0			0
$685$	−26624.2			−1.48505
$686$		0			0
$687$	−11257.8			−0.625202
$688$		0			0
$689$	1812.02	+	3138.50i	0.100192	+	0.173538i
$690$		0			0
$691$	8956.82	−	15513.7i	0.493102	−	0.854078i	−0.506866	−	0.862025i	$-0.669196\pi$
$691$	8956.82	−	15513.7i	0.493102	−	0.854078i	0.999968	+	0.00794684i	$0.00252958\pi$
$692$		0			0
$693$	−11097.0	+	16834.4i	−0.608284	+	0.922777i
$694$		0			0
$695$	−16152.9	+	27977.7i	−0.881606	+	1.52699i
$696$		0			0
$697$	4914.78	+	8512.65i	0.267088	+	0.462611i
$698$		0			0
$699$	15694.5			0.849243
$700$		0			0
$701$	2980.76			0.160602			0.0803009	−	0.996771i	$-0.474412\pi$
$701$	2980.76			0.160602			0.0803009	+	0.996771i	$0.474412\pi$
$702$		0			0
$703$	−15046.4	−	26061.1i	−0.807234	−	1.39817i
$704$		0			0
$705$	2271.34	−	3934.08i	0.121338	−	0.210164i
$706$		0			0
$707$	−16468.8	−	976.231i	−0.876056	−	0.0519306i
$708$		0			0
$709$	−10867.3	+	18822.8i	−0.575644	+	0.997044i	0.420328	+	0.907372i	$0.361915\pi$
$709$	−10867.3	+	18822.8i	−0.575644	+	0.997044i	−0.995971	+	0.0896717i	$0.971418\pi$
$710$		0			0
$711$	11782.7	+	20408.2i	0.621498	+	1.07647i
$712$		0			0
$713$	−8627.84			−0.453177
$714$		0			0
$715$	−14649.5			−0.766240
$716$		0			0
$717$	−5078.37	−	8795.99i	−0.264512	−	0.458148i
$718$		0			0
$719$	1210.72	−	2097.03i	0.0627988	−	0.108771i	−0.832917	−	0.553398i	$-0.813331\pi$
$719$	1210.72	−	2097.03i	0.0627988	−	0.108771i	0.895715	+	0.444628i	$0.146664\pi$
$720$		0			0
$721$	−265.769	−	530.552i	−0.0137278	−	0.0274047i
$722$		0			0
$723$	−7269.73	+	12591.5i	−0.373948	+	0.647696i
$724$		0			0
$725$	−8087.30	−	14007.6i	−0.414283	−	0.717559i
$726$		0			0
$727$	−22043.6			−1.12456			−0.562279	−	0.826948i	$-0.690075\pi$
$727$	−22043.6			−1.12456			−0.562279	+	0.826948i	$0.690075\pi$
$728$		0			0
$729$	−1167.18			−0.0592988
$730$		0			0
$731$	4680.82	+	8107.42i	0.236835	+	0.410210i
$732$		0			0
$733$	−1105.01	+	1913.94i	−0.0556816	+	0.0964433i	−0.892523	−	0.451003i	$-0.851066\pi$
$733$	−1105.01	+	1913.94i	−0.0556816	+	0.0964433i	0.836841	+	0.547446i	$0.184400\pi$
$734$		0			0
$735$	−4054.50	−	9452.92i	−0.203473	−	0.474389i
$736$		0			0
$737$	6218.65	−	10771.0i	0.310810	−	0.538339i
$738$		0			0
$739$	18181.1	+	31490.6i	0.905012	+	1.56753i	0.820902	+	0.571070i	$0.193471\pi$
$739$	18181.1	+	31490.6i	0.905012	+	1.56753i	0.0841099	+	0.996456i	$0.473195\pi$
$740$		0			0
$741$	6465.43			0.320531
$742$		0			0
$743$	33576.1			1.65786			0.828929	−	0.559354i	$-0.188951\pi$
$743$	33576.1			1.65786			0.828929	+	0.559354i	$0.188951\pi$
$744$		0			0
$745$	−6604.52	−	11439.4i	−0.324793	−	0.562558i
$746$		0			0
$747$	6002.90	−	10397.3i	0.294022	−	0.509262i
$748$		0			0
$749$	−757.280	−	1511.75i	−0.0369432	−	0.0737493i
$750$		0			0
$751$	−4343.07	+	7522.42i	−0.211026	+	0.365508i	−0.952036	−	0.305986i	$-0.901014\pi$
$751$	−4343.07	+	7522.42i	−0.211026	+	0.365508i	0.741010	+	0.671494i	$0.234347\pi$
$752$		0			0
$753$	3300.87	+	5717.28i	0.159748	+	0.276692i
$754$		0			0
$755$	−20927.6			−1.00879
$756$		0			0
$757$	−7386.71			−0.354656			−0.177328	−	0.984152i	$-0.556745\pi$
$757$	−7386.71			−0.354656			−0.177328	+	0.984152i	$0.556745\pi$
$758$		0			0
$759$	10671.1	+	18482.8i	0.510323	+	0.883905i
$760$		0			0
$761$	−5617.63	+	9730.01i	−0.267594	+	0.463486i	−0.968240	−	0.250023i	$-0.919562\pi$
$761$	−5617.63	+	9730.01i	−0.267594	+	0.463486i	0.700646	+	0.713509i	$0.252895\pi$
$762$		0			0
$763$	2234.20	+	132.438i	0.106007	+	0.00628385i
$764$		0			0
$765$	5750.49	−	9960.14i	0.271777	−	0.470731i
$766$		0			0
$767$	−8137.64	−	14094.8i	−0.383094	−	0.663539i
$768$		0			0
$769$	−29462.9			−1.38161			−0.690806	−	0.723040i	$-0.742744\pi$
$769$	−29462.9			−1.38161			−0.690806	+	0.723040i	$0.742744\pi$
$770$		0			0
$771$	9427.70			0.440377
$772$		0			0
$773$	4117.50	+	7131.71i	0.191586	+	0.331837i	0.945776	−	0.324819i	$-0.105304\pi$
$773$	4117.50	+	7131.71i	0.191586	+	0.331837i	−0.754190	+	0.656656i	$0.771970\pi$
$774$		0			0
$775$	−1247.91	+	2161.45i	−0.0578405	+	0.100183i
$776$		0			0
$777$	5191.53	−	7875.64i	0.239698	−	0.363626i
$778$		0			0
$779$	−16682.7	+	28895.2i	−0.767289	+	1.32898i
$780$		0			0
$781$	6091.28	+	10550.4i	0.279082	+	0.483384i
$782$		0			0
$783$	31524.0			1.43879
$784$		0			0
$785$	−1981.23			−0.0900805
$786$		0			0
$787$	14699.4	+	25460.2i	0.665792	+	1.15319i	0.979070	+	0.203524i	$0.0652396\pi$
$787$	14699.4	+	25460.2i	0.665792	+	1.15319i	−0.313278	+	0.949662i	$0.601427\pi$
$788$		0			0
$789$	5964.75	−	10331.3i	0.269139	−	0.466163i
$790$		0			0
$791$	−2386.47	+	3620.32i	−0.107273	+	0.162736i
$792$		0			0
$793$	3042.48	−	5269.73i	0.136244	−	0.235982i
$794$		0			0
$795$	−2466.15	−	4271.49i	−0.110019	−	0.190559i
$796$		0			0
$797$	6175.40			0.274459			0.137229	−	0.990539i	$-0.456180\pi$
$797$	6175.40			0.274459			0.137229	+	0.990539i	$0.456180\pi$
$798$		0			0
$799$	5876.25			0.260184
$800$		0			0
$801$	−10703.8	−	18539.5i	−0.472159	−	0.817803i
$802$		0			0
$803$	−21720.3	+	37620.7i	−0.954537	+	1.65331i
$804$		0			0
$805$	48217.1	+	2858.20i	2.11109	+	0.125141i
$806$		0			0
$807$	6017.19	−	10422.1i	0.262472	−	0.454615i
$808$		0			0
$809$	4118.69	+	7133.78i	0.178993	+	0.310025i	0.941536	−	0.336912i	$-0.109383\pi$
$809$	4118.69	+	7133.78i	0.178993	+	0.310025i	−0.762543	+	0.646938i	$0.776049\pi$
$810$		0			0
$811$	9126.93			0.395179			0.197589	−	0.980285i	$-0.436689\pi$
$811$	9126.93			0.395179			0.197589	+	0.980285i	$0.436689\pi$
$812$		0			0
$813$	−19240.4			−0.830001
$814$		0			0
$815$	2472.34	+	4282.22i	0.106260	+	0.184049i
$816$		0			0
$817$	−15888.5	+	27519.7i	−0.680377	+	1.17845i
$818$		0			0
$819$	−4026.95	−	8038.97i	−0.171811	−	0.342985i
$820$		0			0
$821$	11926.2	−	20656.7i	0.506974	−	0.878105i	−0.492993	−	0.870033i	$-0.664097\pi$
$821$	11926.2	−	20656.7i	0.506974	−	0.878105i	0.999967	−	0.00807192i	$-0.00256940\pi$
$822$		0			0
$823$	−6462.75	−	11193.8i	−0.273727	−	0.474109i	0.696086	−	0.717958i	$-0.254923\pi$
$823$	−6462.75	−	11193.8i	−0.273727	−	0.474109i	−0.969813	+	0.243849i	$0.921590\pi$
$824$		0			0
$825$	6173.76			0.260537
$826$		0			0
$827$	44737.5			1.88111			0.940553	−	0.339646i	$-0.110307\pi$
$827$	44737.5			1.88111			0.940553	+	0.339646i	$0.110307\pi$
$828$		0			0
$829$	−2189.34	−	3792.05i	−0.0917237	−	0.158870i	0.816513	−	0.577327i	$-0.195904\pi$
$829$	−2189.34	−	3792.05i	−0.0917237	−	0.158870i	−0.908237	+	0.418457i	$0.862571\pi$
$830$		0			0
$831$	−2670.01	+	4624.59i	−0.111458	+	0.193051i
$832$		0			0
$833$	7967.35	−	10656.1i	0.331395	−	0.443230i
$834$		0			0
$835$	−25208.2	+	43661.9i	−1.04475	+	1.80956i
$836$		0			0
$837$	−2432.16	−	4212.62i	−0.100439	−	0.173966i
$838$		0			0
$839$	−20533.2			−0.844915			−0.422457	−	0.906383i	$-0.638832\pi$
$839$	−20533.2			−0.844915			−0.422457	+	0.906383i	$0.638832\pi$
$840$		0			0
$841$	58835.4			2.41237
$842$		0			0
$843$	−8520.00	−	14757.1i	−0.348095	−	0.602919i
$844$		0			0
$845$	−11515.2	+	19944.9i	−0.468800	+	0.811985i
$846$		0			0
$847$	−9210.54	−	18386.9i	−0.373646	−	0.745906i
$848$		0			0
$849$	5797.03	−	10040.8i	0.234339	−	0.405887i
$850$		0			0
$851$	22148.2	+	38361.8i	0.892162	+	1.54527i
$852$		0			0
$853$	−15790.3			−0.633822			−0.316911	−	0.948455i	$-0.602646\pi$
$853$	−15790.3			−0.633822			−0.316911	+	0.948455i	$0.602646\pi$
$854$		0			0
$855$	39038.7			1.56152
$856$		0			0
$857$	−18510.3	−	32060.8i	−0.737807	−	1.27792i	−0.953481	−	0.301454i	$-0.902528\pi$
$857$	−18510.3	−	32060.8i	−0.737807	−	1.27792i	0.215673	−	0.976466i	$-0.430805\pi$
$858$		0			0
$859$	16500.9	−	28580.3i	0.655416	−	1.13521i	−0.326373	−	0.945241i	$-0.605827\pi$
$859$	16500.9	−	28580.3i	0.655416	−	1.13521i	0.981789	−	0.189973i	$-0.0608400\pi$
$860$		0			0
$861$	−10440.3	−	618.875i	−0.413244	−	0.0244962i
$862$		0			0
$863$	15016.5	−	26009.3i	0.592314	−	1.02592i	−0.401606	−	0.915813i	$-0.631548\pi$
$863$	15016.5	−	26009.3i	0.592314	−	1.02592i	0.993920	−	0.110106i	$-0.0351189\pi$
$864$		0			0
$865$	11194.9	+	19390.1i	0.440042	+	0.762176i
$866$		0			0
$867$	7595.48			0.297527
$868$		0			0
$869$	−52845.5			−2.06290
$870$		0			0
$871$	2773.08	+	4803.11i	0.107879	+	0.186851i
$872$		0			0
$873$	−3913.13	+	6777.74i	−0.151706	+	0.262763i
$874$		0			0
$875$	−9454.70	+	14343.0i	−0.365288	+	0.554149i
$876$		0			0
$877$	12151.9	−	21047.7i	0.467890	−	0.810410i	−0.531436	−	0.847098i	$-0.678348\pi$
$877$	12151.9	−	21047.7i	0.467890	−	0.810410i	0.999327	+	0.0366884i	$0.0116809\pi$
$878$		0			0
$879$	−2228.24	−	3859.43i	−0.0855025	−	0.148095i
$880$		0			0
$881$	11547.5			0.441594			0.220797	−	0.975320i	$-0.429134\pi$
$881$	11547.5			0.441594			0.220797	+	0.975320i	$0.429134\pi$
$882$		0			0
$883$	18653.3			0.710911			0.355455	−	0.934693i	$-0.384326\pi$
$883$	18653.3			0.710911			0.355455	+	0.934693i	$0.384326\pi$
$884$		0			0
$885$	11075.3	+	19183.0i	0.420669	+	0.728620i
$886$		0			0
$887$	11296.3	−	19565.8i	0.427614	−	0.740649i	−0.569047	−	0.822305i	$-0.692688\pi$
$887$	11296.3	−	19565.8i	0.427614	−	0.740649i	0.996661	+	0.0816563i	$0.0260210\pi$
$888$		0			0
$889$	−9497.02	+	14407.1i	−0.358290	+	0.543532i
$890$		0			0
$891$	8681.05	−	15036.0i	0.326404	−	0.565349i
$892$		0			0
$893$	9973.12	+	17274.0i	0.373727	+	0.647313i
$894$		0			0
$895$	−6670.48			−0.249128
$896$		0			0
$897$	−9517.07			−0.354254
$898$		0			0
$899$	−6420.98	−	11121.5i	−0.238211	−	0.412593i
$900$		0			0
$901$	3190.12	−	5525.45i	0.117956	−	0.204306i
$902$		0			0
$903$	−9943.28	−	589.415i	−0.366436	−	0.0217215i
$904$		0			0
$905$	−12111.6	+	20977.8i	−0.444864	+	0.770527i
$906$		0			0
$907$	3686.57	+	6385.33i	0.134962	+	0.233761i	0.925583	−	0.378545i	$-0.123575\pi$
$907$	3686.57	+	6385.33i	0.134962	+	0.233761i	−0.790621	+	0.612306i	$0.790242\pi$
$908$		0			0
$909$	19627.3			0.716168
$910$		0			0
$911$	−5827.84			−0.211948			−0.105974	−	0.994369i	$-0.533796\pi$
$911$	−5827.84			−0.211948			−0.105974	+	0.994369i	$0.533796\pi$
$912$		0			0
$913$	13461.6	+	23316.1i	0.487966	+	0.845182i
$914$		0			0
$915$	−4140.81	+	7172.09i	−0.149607	+	0.259128i
$916$		0			0
$917$	8050.44	+	16071.0i	0.289912	+	0.578748i
$918$		0			0
$919$	−3341.49	+	5787.62i	−0.119941	+	0.207743i	−0.919744	−	0.392519i	$-0.871604\pi$
$919$	−3341.49	+	5787.62i	−0.119941	+	0.207743i	0.799803	+	0.600262i	$0.204937\pi$
$920$		0			0
$921$	3539.41	+	6130.45i	0.126632	+	0.219332i
$922$		0			0
$923$	−5432.55			−0.193732
$924$		0			0
$925$	12813.9			0.455478
$926$		0			0
$927$	352.982	+	611.382i	0.0125064	+	0.0216617i
$928$		0			0
$929$	13079.1	−	22653.6i	0.461906	−	0.800045i	−0.537150	−	0.843487i	$-0.680499\pi$
$929$	13079.1	−	22653.6i	0.461906	−	0.800045i	0.999056	+	0.0434417i	$0.0138323\pi$
$930$		0			0
$931$	44846.9	+	5335.60i	1.57873	+	0.187827i
$932$		0			0
$933$	−1797.58	+	3113.50i	−0.0630761	+	0.109251i
$934$		0			0
$935$	12895.5	+	22335.7i	0.451047	+	0.781236i
$936$		0			0
$937$	−41986.5			−1.46386			−0.731932	−	0.681378i	$-0.761381\pi$
$937$	−41986.5			−1.46386			−0.731932	+	0.681378i	$0.761381\pi$
$938$		0			0
$939$	−4535.03			−0.157609
$940$		0			0
$941$	8001.18	+	13858.5i	0.277185	+	0.480098i	0.970684	−	0.240359i	$-0.0772652\pi$
$941$	8001.18	+	13858.5i	0.277185	+	0.480098i	−0.693499	+	0.720458i	$0.743932\pi$
$942$		0			0
$943$	24556.7	−	42533.5i	0.848014	−	1.46880i
$944$		0			0
$945$	12196.7	+	24348.2i	0.419850	+	0.838143i
$946$		0			0
$947$	22745.3	−	39396.0i	0.780488	−	1.35185i	−0.151169	−	0.988508i	$-0.548304\pi$
$947$	22745.3	−	39396.0i	0.780488	−	1.35185i	0.931658	−	0.363338i	$-0.118363\pi$
$948$		0			0
$949$	−9685.71	−	16776.1i	−0.331308	−	0.573843i
$950$		0			0
$951$	4949.58			0.168771
$952$		0			0
$953$	−6352.15			−0.215914			−0.107957	−	0.994156i	$-0.534431\pi$
$953$	−6352.15			−0.215914			−0.107957	+	0.994156i	$0.534431\pi$
$954$		0			0
$955$	16458.7	+	28507.3i	0.557687	+	0.965942i
$956$		0			0
$957$	−15883.1	+	27510.4i	−0.536499	+	0.929243i
$958$		0			0
$959$	36579.9	+	2168.37i	1.23173	+	0.0730139i
$960$		0			0
$961$	13904.7	−	24083.7i	0.466742	−	0.808421i
$962$		0			0
$963$	1005.78	+	1742.07i	0.0336562	+	0.0582943i
$964$		0			0
$965$	−32861.9			−1.09623
$966$		0			0
$967$	−4181.81			−0.139067			−0.0695336	−	0.997580i	$-0.522151\pi$
$967$	−4181.81			−0.139067			−0.0695336	+	0.997580i	$0.522151\pi$
$968$		0			0
$969$	−5691.32	−	9857.65i	−0.188681	−	0.326804i
$970$		0			0
$971$	−12727.5	+	22044.7i	−0.420644	+	0.728577i	−0.996003	−	0.0893242i	$-0.971529\pi$
$971$	−12727.5	+	22044.7i	−0.420644	+	0.728577i	0.575358	+	0.817901i	$0.304863\pi$
$972$		0			0
$973$	24471.7	−	37124.0i	0.806296	−	1.22317i
$974$		0			0
$975$	−1376.53	+	2384.22i	−0.0452146	+	0.0783139i
$976$		0			0
$977$	−5531.20	−	9580.32i	−0.181125	−	0.313717i	0.761139	−	0.648589i	$-0.224640\pi$
$977$	−5531.20	−	9580.32i	−0.181125	−	0.313717i	−0.942264	+	0.334871i	$0.891307\pi$
$978$		0			0
$979$	48006.6			1.56721
$980$		0			0
$981$	−2662.69			−0.0866598
$982$		0			0
$983$	2610.67	+	4521.81i	0.0847074	+	0.146717i	0.905266	−	0.424844i	$-0.139671\pi$
$983$	2610.67	+	4521.81i	0.0847074	+	0.146717i	−0.820559	+	0.571562i	$0.806338\pi$
$984$		0			0
$985$	14305.2	−	24777.4i	0.462744	−	0.801496i
$986$		0			0
$987$	−3441.07	+	5220.17i	−0.110973	+	0.168348i
$988$		0			0
$989$	23387.7	−	40508.8i	0.751959	−	1.30243i
$990$		0			0
$991$	15615.8	+	27047.4i	0.500558	+	0.866992i	1.00000		0.000644310i	$0.000205090\pi$
$991$	15615.8	+	27047.4i	0.500558	+	0.866992i	−0.499442	+	0.866347i	$0.666462\pi$
$992$		0			0
$993$	3393.11			0.108436
$994$		0			0
$995$	−48503.5			−1.54539
$996$		0			0
$997$	−13705.3	−	23738.3i	−0.435358	−	0.754062i	0.561967	−	0.827160i	$-0.310045\pi$
$997$	−13705.3	−	23738.3i	−0.435358	−	0.754062i	−0.997325	+	0.0730974i	$0.976712\pi$
$998$		0			0
$999$	−12487.0	+	21628.1i	−0.395466	+	0.684967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.4.i.p.65.4		12
4.3	odd	2	inner	448.4.i.p.65.3		12
7.4	even	3	inner	448.4.i.p.193.4		12
8.3	odd	2		224.4.i.d.65.4	yes	12
8.5	even	2		224.4.i.d.65.3	✓	12
28.11	odd	6	inner	448.4.i.p.193.3		12
56.5	odd	6		1568.4.a.bg.1.3		6
56.11	odd	6		224.4.i.d.193.4	yes	12
56.19	even	6		1568.4.a.bg.1.4		6
56.37	even	6		1568.4.a.bh.1.4		6
56.51	odd	6		1568.4.a.bh.1.3		6
56.53	even	6		224.4.i.d.193.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.4.i.d.65.3	✓	12	8.5	even	2
224.4.i.d.65.4	yes	12	8.3	odd	2
224.4.i.d.193.3	yes	12	56.53	even	6
224.4.i.d.193.4	yes	12	56.11	odd	6
448.4.i.p.65.3		12	4.3	odd	2	inner
448.4.i.p.65.4		12	1.1	even	1	trivial
448.4.i.p.193.3		12	28.11	odd	6	inner
448.4.i.p.193.4		12	7.4	even	3	inner
1568.4.a.bg.1.3		6	56.5	odd	6
1568.4.a.bg.1.4		6	56.19	even	6
1568.4.a.bh.1.3		6	56.51	odd	6
1568.4.a.bh.1.4		6	56.37	even	6

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11427 + 1.92998i) q^{3} +(6.72806 - 11.6533i) q^{5} +(-10.1930 + 15.4630i) q^{7} +(11.0168 - 19.0816i) q^{9} +O(q^{10})\)	\(q+(1.11427 + 1.92998i) q^{3} +(6.72806 - 11.6533i) q^{5} +(-10.1930 + 15.4630i) q^{7} +(11.0168 - 19.0816i) q^{9} +(24.7053 + 42.7907i) q^{11} -22.0336 q^{13} +29.9876 q^{15} +(19.3955 + 33.5939i) q^{17} +(-65.8356 + 114.031i) q^{19} +(-41.2010 - 2.44230i) q^{21} +(96.9095 - 167.852i) q^{23} +(-28.0336 - 48.5556i) q^{25} +109.274 q^{27} +288.486 q^{29} +(-22.2575 - 38.5511i) q^{31} +(-55.0568 + 95.3612i) q^{33} +(111.616 + 222.818i) q^{35} +(-114.272 + 197.926i) q^{37} +(-24.5514 - 42.5243i) q^{39} +253.399 q^{41} +241.336 q^{43} +(-148.243 - 256.765i) q^{45} +(75.7426 - 131.190i) q^{47} +(-135.206 - 315.228i) q^{49} +(-43.2237 + 74.8656i) q^{51} +(-82.2389 - 142.442i) q^{53} +664.874 q^{55} -293.436 q^{57} +(369.329 + 639.697i) q^{59} +(-138.084 + 239.168i) q^{61} +(182.764 + 364.851i) q^{63} +(-148.243 + 256.765i) q^{65} +(-125.857 - 217.991i) q^{67} +431.935 q^{69} +246.558 q^{71} +(439.589 + 761.390i) q^{73} +(62.4742 - 108.208i) q^{75} +(-913.492 - 54.1497i) q^{77} +(-534.760 + 926.231i) q^{79} +(-175.692 - 304.308i) q^{81} +544.887 q^{83} +521.975 q^{85} +(321.453 + 556.773i) q^{87} +(485.794 - 841.419i) q^{89} +(224.588 - 340.704i) q^{91} +(49.6018 - 85.9129i) q^{93} +(885.892 + 1534.41i) q^{95} -355.197 q^{97} +1088.69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 72 q^{9}+O(q^{10}) \) 12 * q + 6 * q^5 - 72 * q^9	\( 12 q + 6 q^{5} - 72 q^{9} + 144 q^{13} + 138 q^{17} - 66 q^{21} + 72 q^{25} + 144 q^{29} + 714 q^{33} - 6 q^{37} - 576 q^{41} - 120 q^{45} + 948 q^{49} - 30 q^{53} - 3420 q^{57} - 54 q^{61} - 120 q^{65} - 924 q^{69} + 2694 q^{73} - 4062 q^{77} - 3666 q^{81} + 5268 q^{85} + 3558 q^{89} + 2190 q^{93} - 768 q^{97}+O(q^{100}) \) 12 * q + 6 * q^5 - 72 * q^9 + 144 * q^13 + 138 * q^17 - 66 * q^21 + 72 * q^25 + 144 * q^29 + 714 * q^33 - 6 * q^37 - 576 * q^41 - 120 * q^45 + 948 * q^49 - 30 * q^53 - 3420 * q^57 - 54 * q^61 - 120 * q^65 - 924 * q^69 + 2694 * q^73 - 4062 * q^77 - 3666 * q^81 + 5268 * q^85 + 3558 * q^89 + 2190 * q^93 - 768 * q^97

Introduction

L-functions

Modular forms

Varieties

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