LMFDB - Embedded newform 180.7.c.b.91.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,7,Mod(91,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("180.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, 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:	$41.4097350516$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.15
Character	$\chi$	$=$	180.91
Dual form			180.7.c.b.91.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36400 - 7.88286i) q^{2} +(-60.2790 - 21.5045i) q^{4} +55.9017 q^{5} -86.8984i q^{7} +(-251.737 + 445.839i) q^{8} +O(q^{10})$	\(q+(1.36400 - 7.88286i) q^{2} +(-60.2790 - 21.5045i) q^{4} +55.9017 q^{5} -86.8984i q^{7} +(-251.737 + 445.839i) q^{8} +(76.2500 - 440.665i) q^{10} -1545.70i q^{11} +3187.34 q^{13} +(-685.008 - 118.530i) q^{14} +(3171.12 + 2592.54i) q^{16} -4062.12 q^{17} -536.854i q^{19} +(-3369.70 - 1202.14i) q^{20} +(-12184.5 - 2108.34i) q^{22} -18107.3i q^{23} +3125.00 q^{25} +(4347.53 - 25125.3i) q^{26} +(-1868.70 + 5238.15i) q^{28} -14939.5 q^{29} +11771.9i q^{31} +(24762.0 - 21461.2i) q^{32} +(-5540.73 + 32021.1i) q^{34} -4857.77i q^{35} -34906.3 q^{37} +(-4231.95 - 732.270i) q^{38} +(-14072.5 + 24923.2i) q^{40} -108362. q^{41} -91972.0i q^{43} +(-33239.4 + 93173.2i) q^{44} +(-142737. - 24698.4i) q^{46} -17272.4i q^{47} +110098. q^{49} +(4262.50 - 24633.9i) q^{50} +(-192130. - 68542.0i) q^{52} -238792. q^{53} -86407.2i q^{55} +(38742.7 + 21875.6i) q^{56} +(-20377.5 + 117766. i) q^{58} +95677.8i q^{59} -144057. q^{61} +(92796.3 + 16056.9i) q^{62} +(-135401. - 224469. i) q^{64} +178178. q^{65} +494031. i q^{67} +(244860. + 87353.7i) q^{68} +(-38293.1 - 6626.01i) q^{70} +263745. i q^{71} -225002. q^{73} +(-47612.3 + 275162. i) q^{74} +(-11544.8 + 32361.0i) q^{76} -134319. q^{77} -318736. i q^{79} +(177271. + 144927. i) q^{80} +(-147806. + 854203. i) q^{82} -880209. i q^{83} -227079. q^{85} +(-725003. - 125450. i) q^{86} +(689133. + 389110. i) q^{88} +198618. q^{89} -276975. i q^{91} +(-389388. + 1.09149e6i) q^{92} +(-136156. - 23559.5i) q^{94} -30011.1i q^{95} -141679. q^{97} +(150173. - 867885. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	$ 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) $ 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.36400	−	7.88286i	0.170500	−	0.985358i
$2$	1.36400	−	7.88286i	0.170500	−	0.985358i
$3$		0			0
$3$		0			0
$4$	−60.2790	−	21.5045i	−0.941859	−	0.336007i
$5$	55.9017			0.447214
$5$	55.9017			0.447214
$6$		0			0
$7$		−	86.8984i		−	0.253348i	−0.991944	−	0.126674i	$-0.959570\pi$
$7$		−	86.8984i		−	0.253348i	0.991944	−	0.126674i	$-0.0404302\pi$
$8$	−251.737	+	445.839i	−0.491675	+	0.870779i
$9$		0			0
$10$	76.2500	−	440.665i	0.0762500	−	0.440665i
$11$		−	1545.70i		−	1.16131i	−0.814151	−	0.580653i	$-0.802797\pi$
$11$		−	1545.70i		−	1.16131i	0.814151	−	0.580653i	$-0.197203\pi$
$12$		0			0
$13$	3187.34			1.45077			0.725384	−	0.688344i	$-0.241662\pi$
$13$	3187.34			1.45077			0.725384	+	0.688344i	$0.241662\pi$
$14$	−685.008	−	118.530i	−0.249639	−	0.0431959i
$15$		0			0
$16$	3171.12	+	2592.54i	0.774198	+	0.632943i
$17$	−4062.12			−0.826810			−0.413405	−	0.910547i	$-0.635661\pi$
$17$	−4062.12			−0.826810			−0.413405	+	0.910547i	$0.635661\pi$
$18$		0			0
$19$		−	536.854i		−	0.0782701i	−0.999234	−	0.0391350i	$-0.987540\pi$
$19$		−	536.854i		−	0.0782701i	0.999234	−	0.0391350i	$-0.0124602\pi$
$20$	−3369.70	−	1202.14i	−0.421212	−	0.150267i
$21$		0			0
$22$	−12184.5	−	2108.34i	−1.14430	−	0.198003i
$23$		−	18107.3i		−	1.48823i	−0.668052	−	0.744115i	$-0.732871\pi$
$23$		−	18107.3i		−	1.48823i	0.668052	−	0.744115i	$-0.267129\pi$
$24$		0			0
$25$	3125.00			0.200000
$26$	4347.53	−	25125.3i	0.247356	−	1.42953i
$27$		0			0
$28$	−1868.70	+	5238.15i	−0.0851269	+	0.238618i
$29$	−14939.5			−0.612549			−0.306275	−	0.951943i	$-0.599083\pi$
$29$	−14939.5			−0.612549			−0.306275	+	0.951943i	$0.599083\pi$
$30$		0			0
$31$			11771.9i			0.395150i	0.980288	+	0.197575i	$0.0633066\pi$
$31$			11771.9i			0.395150i	−0.980288	+	0.197575i	$0.936693\pi$
$32$	24762.0	−	21461.2i	0.755676	−	0.654945i
$33$		0			0
$34$	−5540.73	+	32021.1i	−0.140971	+	0.814704i
$35$		−	4857.77i		−	0.113301i
$36$		0			0
$37$	−34906.3			−0.689127			−0.344563	−	0.938763i	$-0.611973\pi$
$37$	−34906.3			−0.689127			−0.344563	+	0.938763i	$0.611973\pi$
$38$	−4231.95	−	732.270i	−0.0771240	−	0.0133451i
$39$		0			0
$40$	−14072.5	+	24923.2i	−0.219884	+	0.389424i
$41$	−108362.			−1.57226			−0.786132	−	0.618058i	$-0.787919\pi$
$41$	−108362.			−1.57226			−0.786132	+	0.618058i	$0.787919\pi$
$42$		0			0
$43$		−	91972.0i		−	1.15678i	−0.815761	−	0.578389i	$-0.803681\pi$
$43$		−	91972.0i		−	1.15678i	0.815761	−	0.578389i	$-0.196319\pi$
$44$	−33239.4	+	93173.2i	−0.390207	+	1.09379i
$45$		0			0
$46$	−142737.	−	24698.4i	−1.46644	−	0.253743i
$47$		−	17272.4i		−	0.166363i	−0.996534	−	0.0831817i	$-0.973492\pi$
$47$		−	17272.4i		−	0.166363i	0.996534	−	0.0831817i	$-0.0265082\pi$
$48$		0			0
$49$	110098.			0.935815
$50$	4262.50	−	24633.9i	0.0341000	−	0.197072i
$51$		0			0
$52$	−192130.	−	68542.0i	−1.36642	−	0.487469i
$53$	−238792.			−1.60395			−0.801977	−	0.597355i	$-0.796219\pi$
$53$	−238792.			−1.60395			−0.801977	+	0.597355i	$0.796219\pi$
$54$		0			0
$55$		−	86407.2i		−	0.519352i
$56$	38742.7	+	21875.6i	0.220610	+	0.124565i
$57$		0			0
$58$	−20377.5	+	117766.i	−0.104440	+	0.603580i
$59$			95677.8i			0.465860i	0.972494	+	0.232930i	$0.0748312\pi$
$59$			95677.8i			0.465860i	−0.972494	+	0.232930i	$0.925169\pi$
$60$		0			0
$61$	−144057.			−0.634666			−0.317333	−	0.948314i	$-0.602787\pi$
$61$	−144057.			−0.634666			−0.317333	+	0.948314i	$0.602787\pi$
$62$	92796.3	+	16056.9i	0.389364	+	0.0673731i
$63$		0			0
$64$	−135401.	−	224469.i	−0.516512	−	0.856280i
$65$	178178.			0.648803
$66$		0			0
$67$			494031.i			1.64259i	0.570501	+	0.821297i	$0.306749\pi$
$67$			494031.i			1.64259i	−0.570501	+	0.821297i	$0.693251\pi$
$68$	244860.	+	87353.7i	0.778739	+	0.277814i
$69$		0			0
$70$	−38293.1	−	6626.01i	−0.111642	−	0.0193178i
$71$			263745.i			0.736902i	0.929647	+	0.368451i	$0.120112\pi$
$71$			263745.i			0.736902i	−0.929647	+	0.368451i	$0.879888\pi$
$72$		0			0
$73$	−225002.			−0.578386			−0.289193	−	0.957271i	$-0.593387\pi$
$73$	−225002.			−0.578386			−0.289193	+	0.957271i	$0.593387\pi$
$74$	−47612.3	+	275162.i	−0.117496	+	0.679036i
$75$		0			0
$76$	−11544.8	+	32361.0i	−0.0262993	+	0.0737194i
$77$	−134319.			−0.294215
$78$		0			0
$79$		−	318736.i		−	0.646471i	−0.946318	−	0.323236i	$-0.895229\pi$
$79$		−	318736.i		−	0.646471i	0.946318	−	0.323236i	$-0.104771\pi$
$80$	177271.	+	144927.i	0.346232	+	0.283061i
$81$		0			0
$82$	−147806.	+	854203.i	−0.268071	+	1.54924i
$83$		−	880209.i		−	1.53940i	−0.638406	−	0.769700i	$-0.720406\pi$
$83$		−	880209.i		−	1.53940i	0.638406	−	0.769700i	$-0.279594\pi$
$84$		0			0
$85$	−227079.			−0.369761
$86$	−725003.	−	125450.i	−1.13984	−	0.197231i
$87$		0			0
$88$	689133.	+	389110.i	1.01124	+	0.570985i
$89$	198618.			0.281740			0.140870	−	0.990028i	$-0.455010\pi$
$89$	198618.			0.281740			0.140870	+	0.990028i	$0.455010\pi$
$90$		0			0
$91$		−	276975.i		−	0.367550i
$92$	−389388.	+	1.09149e6i	−0.500056	+	1.40170i
$93$		0			0
$94$	−136156.	−	23559.5i	−0.163928	−	0.0283650i
$95$		−	30011.1i		−	0.0350034i
$96$		0			0
$97$	−141679.			−0.155235			−0.0776175	−	0.996983i	$-0.524731\pi$
$97$	−141679.			−0.155235			−0.0776175	+	0.996983i	$0.524731\pi$
$98$	150173.	−	867885.i	0.159557	−	0.922112i
$99$		0			0
$100$	−188372.	−	67201.5i	−0.188372	−	0.0672015i
$101$	−1.23128e6			−1.19506			−0.597532	−	0.801845i	$-0.703852\pi$
$101$	−1.23128e6			−1.19506			−0.597532	+	0.801845i	$0.703852\pi$
$102$		0			0
$103$			1.34540e6i			1.23123i	0.788047	+	0.615615i	$0.211092\pi$
$103$			1.34540e6i			1.23123i	−0.788047	+	0.615615i	$0.788908\pi$
$104$	−802372.	+	1.42104e6i	−0.713306	+	1.26330i
$105$		0			0
$106$	−325713.	+	1.88236e6i	−0.273475	+	1.58047i
$107$		−	1.09887e6i		−	0.897006i	−0.893781	−	0.448503i	$-0.851957\pi$
$107$		−	1.09887e6i		−	0.897006i	0.893781	−	0.448503i	$-0.148043\pi$
$108$		0			0
$109$	−1.90361e6			−1.46994			−0.734968	−	0.678101i	$-0.762803\pi$
$109$	−1.90361e6			−1.46994			−0.734968	+	0.678101i	$0.762803\pi$
$110$	−681136.	−	117860.i	−0.511747	−	0.0885496i
$111$		0			0
$112$	225287.	−	275565.i	0.160355	−	0.196142i
$113$	2.70511e6			1.87478			0.937389	−	0.348284i	$-0.113236\pi$
$113$	2.70511e6			1.87478			0.937389	+	0.348284i	$0.113236\pi$
$114$		0			0
$115$		−	1.01223e6i		−	0.665557i
$116$	900536.	+	321265.i	0.576935	+	0.205821i
$117$		0			0
$118$	754215.	+	130505.i	0.459038	+	0.0794291i
$119$			352992.i			0.209471i
$120$		0			0
$121$	−617624.			−0.348632
$122$	−196494.	+	1.13558e6i	−0.108211	+	0.625373i
$123$		0			0
$124$	253149.	−	709599.i	0.132773	−	0.372176i
$125$	174693.			0.0894427
$126$		0			0
$127$		−	1.50271e6i		−	0.733606i	−0.930299	−	0.366803i	$-0.880452\pi$
$127$		−	1.50271e6i		−	0.733606i	0.930299	−	0.366803i	$-0.119548\pi$
$128$	−1.95414e6	+	761169.i	−0.931807	+	0.362953i
$129$		0			0
$130$	243035.	−	1.40455e6i	0.110621	−	0.639303i
$131$		−	4.39609e6i		−	1.95547i	−0.209832	−	0.977737i	$-0.567292\pi$
$131$		−	4.39609e6i		−	1.95547i	0.209832	−	0.977737i	$-0.432708\pi$
$132$		0			0
$133$	−46651.8			−0.0198296
$134$	3.89438e6	+	673860.i	1.61854	+	0.280063i
$135$		0			0
$136$	1.02259e6	−	1.81105e6i	0.406522	−	0.719969i
$137$	−2.14601e6			−0.834584			−0.417292	−	0.908772i	$-0.637021\pi$
$137$	−2.14601e6			−0.834584			−0.417292	+	0.908772i	$0.637021\pi$
$138$		0			0
$139$		−	3.06053e6i		−	1.13960i	−0.821784	−	0.569800i	$-0.807021\pi$
$139$		−	3.06053e6i		−	1.13960i	0.821784	−	0.569800i	$-0.192979\pi$
$140$	−104464.	+	292822.i	−0.0380699	+	0.106713i
$141$		0			0
$142$	2.07907e6	+	359749.i	0.726112	+	0.125642i
$143$		−	4.92666e6i		−	1.68479i
$144$		0			0
$145$	−835141.			−0.273940
$146$	−306903.	+	1.77366e6i	−0.0986150	+	0.569917i
$147$		0			0
$148$	2.10412e6	+	750642.i	0.649060	+	0.231552i
$149$	1.56754e6			0.473871			0.236936	−	0.971525i	$-0.423857\pi$
$149$	1.56754e6			0.473871			0.236936	+	0.971525i	$0.423857\pi$
$150$		0			0
$151$		−	5.43173e6i		−	1.57764i	−0.614626	−	0.788819i	$-0.710693\pi$
$151$		−	5.43173e6i		−	1.57764i	0.614626	−	0.788819i	$-0.289307\pi$
$152$	239351.	+	135146.i	0.0681559	+	0.0384834i
$153$		0			0
$154$	−183211.	+	1.05882e6i	−0.0501637	+	0.289907i
$155$			658070.i			0.176716i
$156$		0			0
$157$	6.05232e6			1.56395			0.781976	−	0.623309i	$-0.214212\pi$
$157$	6.05232e6			1.56395			0.781976	+	0.623309i	$0.214212\pi$
$158$	−2.51255e6	−	434756.i	−0.637006	−	0.110223i
$159$		0			0
$160$	1.38424e6	−	1.19972e6i	0.337949	−	0.292900i
$161$	−1.57350e6			−0.377040
$162$		0			0
$163$			1.11984e6i			0.258578i	0.991607	+	0.129289i	$0.0412695\pi$
$163$			1.11984e6i			0.258578i	−0.991607	+	0.129289i	$0.958731\pi$
$164$	6.53195e6	+	2.33027e6i	1.48085	+	0.528292i
$165$		0			0
$166$	−6.93856e6	−	1.20061e6i	−1.51686	−	0.262468i
$167$			2.51799e6i			0.540636i	0.962771	+	0.270318i	$0.0871288\pi$
$167$			2.51799e6i			0.540636i	−0.962771	+	0.270318i	$0.912871\pi$
$168$		0			0
$169$	5.33232e6			1.10473
$170$	−309736.	+	1.79003e6i	−0.0630443	+	0.364347i
$171$		0			0
$172$	−1.97781e6	+	5.54398e6i	−0.388686	+	1.08952i
$173$	−4153.24			−0.000802137			−0.000401069	−	1.00000i	$-0.500128\pi$
$173$	−4153.24			−0.000802137			−0.000401069		1.00000i	$0.500128\pi$
$174$		0			0
$175$		−	271558.i		−	0.0506696i
$176$	4.00728e6	−	4.90159e6i	0.735041	−	0.899081i
$177$		0			0
$178$	270916.	−	1.56568e6i	0.0480368	−	0.277615i
$179$		−	3.95787e6i		−	0.690084i	−0.938587	−	0.345042i	$-0.887865\pi$
$179$		−	3.95787e6i		−	0.690084i	0.938587	−	0.345042i	$-0.112135\pi$
$180$		0			0
$181$	9.51906e6			1.60531			0.802654	−	0.596446i	$-0.203421\pi$
$181$	9.51906e6			1.60531			0.802654	+	0.596446i	$0.203421\pi$
$182$	−2.18335e6	−	377794.i	−0.362168	−	0.0626673i
$183$		0			0
$184$	8.07293e6	+	4.55828e6i	1.29592	+	0.731725i
$185$	−1.95132e6			−0.308187
$186$		0			0
$187$			6.27881e6i			0.960180i
$188$	−371433.	+	1.04116e6i	−0.0558993	+	0.156691i
$189$		0			0
$190$	−236573.	−	40935.1i	−0.0344909	−	0.00596809i
$191$		−	6.63547e6i		−	0.952295i	−0.879365	−	0.476148i	$-0.842033\pi$
$191$		−	6.63547e6i		−	0.952295i	0.879365	−	0.476148i	$-0.157967\pi$
$192$		0			0
$193$	−4.88164e6			−0.679037			−0.339519	−	0.940599i	$-0.610264\pi$
$193$	−4.88164e6			−0.679037			−0.339519	+	0.940599i	$0.610264\pi$
$194$	−193250.	+	1.11683e6i	−0.0264676	+	0.152962i
$195$		0			0
$196$	−6.63658e6	−	2.36759e6i	−0.881406	−	0.314441i
$197$	−3.69499e6			−0.483297			−0.241649	−	0.970364i	$-0.577688\pi$
$197$	−3.69499e6			−0.483297			−0.241649	+	0.970364i	$0.577688\pi$
$198$		0			0
$199$			137140.i			0.0174023i	0.999962	+	0.00870113i	$0.00276969\pi$
$199$			137140.i			0.0174023i	−0.999962	+	0.00870113i	$0.997230\pi$
$200$	−786679.	+	1.39325e6i	−0.0983349	+	0.174156i
$201$		0			0
$202$	−1.67946e6	+	9.70598e6i	−0.203759	+	1.17757i
$203$			1.29822e6i			0.155188i
$204$		0			0
$205$	−6.05762e6			−0.703138
$206$	1.06056e7	+	1.83513e6i	1.21320	+	0.209925i
$207$		0			0
$208$	1.01074e7	+	8.26329e6i	1.12318	+	0.918254i
$209$	−829815.			−0.0908955
$210$		0			0
$211$		−	372967.i		−	0.0397029i	−0.999803	−	0.0198515i	$-0.993681\pi$
$211$		−	372967.i		−	0.0397029i	0.999803	−	0.0198515i	$-0.00631933\pi$
$212$	1.43941e7	+	5.13509e6i	1.51070	+	0.538940i
$213$		0			0
$214$	−8.66225e6	−	1.49886e6i	−0.883872	−	0.152940i
$215$		−	5.14139e6i		−	0.517327i
$216$		0			0
$217$	1.02296e6			0.100111
$218$	−2.59653e6	+	1.50059e7i	−0.250625	+	1.44841i
$219$		0			0
$220$	−1.85814e6	+	5.20854e6i	−0.174506	+	0.489157i
$221$	−1.29473e7			−1.19951
$222$		0			0
$223$		−	1.01313e7i		−	0.913591i	−0.889572	−	0.456795i	$-0.848997\pi$
$223$		−	1.01313e7i		−	0.913591i	0.889572	−	0.456795i	$-0.151003\pi$
$224$	−1.86495e6	−	2.15178e6i	−0.165929	−	0.191449i
$225$		0			0
$226$	3.68978e6	−	2.13240e7i	0.319650	−	1.84733i
$227$			4.30252e6i			0.367829i	0.982942	+	0.183914i	$0.0588769\pi$
$227$			4.30252e6i			0.367829i	−0.982942	+	0.183914i	$0.941123\pi$
$228$		0			0
$229$	1.34915e7			1.12345			0.561724	−	0.827325i	$-0.310138\pi$
$229$	1.34915e7			1.12345			0.561724	+	0.827325i	$0.310138\pi$
$230$	−7.97926e6	−	1.38068e6i	−0.655811	−	0.113478i
$231$		0			0
$232$	3.76082e6	−	6.66059e6i	0.301175	−	0.533395i
$233$	2.26239e7			1.78855			0.894273	−	0.447521i	$-0.147693\pi$
$233$	2.26239e7			1.78855			0.894273	+	0.447521i	$0.147693\pi$
$234$		0			0
$235$		−	965554.i		−	0.0744000i
$236$	2.05750e6	−	5.76736e6i	0.156532	−	0.438774i
$237$		0			0
$238$	2.78258e6	+	481481.i	0.206404	+	0.0357148i
$239$			4.98771e6i			0.365348i	0.983173	+	0.182674i	$0.0584754\pi$
$239$			4.98771e6i			0.365348i	−0.983173	+	0.182674i	$0.941525\pi$
$240$		0			0
$241$	3.64828e6			0.260637			0.130319	−	0.991472i	$-0.458400\pi$
$241$	3.64828e6			0.260637			0.130319	+	0.991472i	$0.458400\pi$
$242$	−842439.	+	4.86864e6i	−0.0594419	+	0.343528i
$243$		0			0
$244$	8.68361e6	+	3.09787e6i	0.597766	+	0.213252i
$245$	6.15465e6			0.418509
$246$		0			0
$247$		−	1.71114e6i		−	0.113552i
$248$	−5.24838e6	−	2.96343e6i	−0.344088	−	0.194285i
$249$		0			0
$250$	238281.	−	1.37708e6i	0.0152500	−	0.0881331i
$251$			9.91942e6i			0.627285i	0.949541	+	0.313643i	$0.101549\pi$
$251$			9.91942e6i			0.627285i	−0.949541	+	0.313643i	$0.898451\pi$
$252$		0			0
$253$	−2.79884e7			−1.72829
$254$	−1.18456e7	−	2.04969e6i	−0.722865	−	0.125080i
$255$		0			0
$256$	3.33473e6	+	1.64425e7i	0.198766	+	0.980047i
$257$	−1.34441e7			−0.792015			−0.396008	−	0.918247i	$-0.629605\pi$
$257$	−1.34441e7			−0.792015			−0.396008	+	0.918247i	$0.629605\pi$
$258$		0			0
$259$			3.03331e6i			0.174589i
$260$	−1.07404e7	−	3.83161e6i	−0.611082	−	0.218003i
$261$		0			0
$262$	−3.46537e7	−	5.99627e6i	−1.92684	−	0.333409i
$263$			2.04971e7i			1.12674i	0.826204	+	0.563371i	$0.190496\pi$
$263$			2.04971e7i			1.12674i	−0.826204	+	0.563371i	$0.809504\pi$
$264$		0			0
$265$	−1.33489e7			−0.717310
$266$	−63633.1	+	367750.i	−0.00338095	+	0.0195392i
$267$		0			0
$268$	1.06239e7	−	2.97797e7i	0.551924	−	1.54709i
$269$	2.45721e7			1.26237			0.631183	−	0.775634i	$-0.282570\pi$
$269$	2.45721e7			1.26237			0.631183	+	0.775634i	$0.282570\pi$
$270$		0			0
$271$		−	1.41101e7i		−	0.708962i	−0.935063	−	0.354481i	$-0.884658\pi$
$271$		−	1.41101e7i		−	0.708962i	0.935063	−	0.354481i	$-0.115342\pi$
$272$	−1.28814e7	−	1.05312e7i	−0.640115	−	0.523324i
$273$		0			0
$274$	−2.92716e6	+	1.69167e7i	−0.142297	+	0.822364i
$275$		−	4.83031e6i		−	0.232261i
$276$		0			0
$277$	−3.78003e7			−1.77851			−0.889255	−	0.457412i	$-0.848777\pi$
$277$	−3.78003e7			−1.77851			−0.889255	+	0.457412i	$0.848777\pi$
$278$	−2.41257e7	−	4.17457e6i	−1.12291	−	0.194302i
$279$		0			0
$280$	2.16578e6	+	1.22288e6i	0.0986599	+	0.0557071i
$281$	−1.02523e7			−0.462066			−0.231033	−	0.972946i	$-0.574210\pi$
$281$	−1.02523e7			−0.462066			−0.231033	+	0.972946i	$0.574210\pi$
$282$		0			0
$283$			3.79250e7i			1.67327i	0.547762	+	0.836635i	$0.315480\pi$
$283$			3.79250e7i			1.67327i	−0.547762	+	0.836635i	$0.684520\pi$
$284$	5.67170e6	−	1.58983e7i	0.247604	−	0.694058i
$285$		0			0
$286$	−3.88362e7	−	6.71998e6i	−1.66012	−	0.287256i
$287$			9.41649e6i			0.398330i
$288$		0			0
$289$	−7.63676e6			−0.316385
$290$	−1.13913e6	+	6.58330e6i	−0.0467069	+	0.269929i
$291$		0			0
$292$	1.35629e7	+	4.83855e6i	0.544759	+	0.194342i
$293$	1.51174e7			0.601000			0.300500	−	0.953782i	$-0.402847\pi$
$293$	1.51174e7			0.601000			0.300500	+	0.953782i	$0.402847\pi$
$294$		0			0
$295$			5.34855e6i			0.208339i
$296$	8.78723e6	−	1.55626e7i	0.338826	−	0.600077i
$297$		0			0
$298$	2.13813e6	−	1.23567e7i	0.0807951	−	0.466932i
$299$		−	5.77141e7i		−	2.15908i
$300$		0			0
$301$	−7.99222e6			−0.293068
$302$	−4.28176e7	−	7.40889e6i	−1.55454	−	0.268988i
$303$		0			0
$304$	1.39181e6	−	1.70243e6i	0.0495405	−	0.0605965i
$305$	−8.05303e6			−0.283831
$306$		0			0
$307$			3.85776e7i			1.33328i	0.745382	+	0.666638i	$0.232267\pi$
$307$			3.85776e7i			1.33328i	−0.745382	+	0.666638i	$0.767733\pi$
$308$	8.09660e6	+	2.88845e6i	0.277109	+	0.0988584i
$309$		0			0
$310$	5.18747e6	+	897608.i	0.174129	+	0.0301302i
$311$			4.61860e7i			1.53543i	0.640794	+	0.767713i	$0.278605\pi$
$311$			4.61860e7i			1.53543i	−0.640794	+	0.767713i	$0.721395\pi$
$312$		0			0
$313$	−1.41773e7			−0.462339			−0.231170	−	0.972913i	$-0.574255\pi$
$313$	−1.41773e7			−0.462339			−0.231170	+	0.972913i	$0.574255\pi$
$314$	8.25538e6	−	4.77096e7i	0.266654	−	1.54105i
$315$		0			0
$316$	−6.85424e6	+	1.92131e7i	−0.217219	+	0.608885i
$317$	−6.05126e7			−1.89963			−0.949813	−	0.312817i	$-0.898727\pi$
$317$	−6.05126e7			−1.89963			−0.949813	+	0.312817i	$0.898727\pi$
$318$		0			0
$319$			2.30919e7i			0.711357i
$320$	−7.56912e6	−	1.25482e7i	−0.230991	−	0.382940i
$321$		0			0
$322$	−2.14625e6	+	1.24036e7i	−0.0642854	+	0.371520i
$323$			2.18077e6i			0.0647145i
$324$		0			0
$325$	9.96043e6			0.290154
$326$	8.82750e6	+	1.52746e6i	0.254792	+	0.0440876i
$327$		0			0
$328$	2.72788e7	−	4.83120e7i	0.773042	−	1.36909i
$329$	−1.50094e6			−0.0421479
$330$		0			0
$331$			1.01477e7i			0.279824i	0.990164	+	0.139912i	$0.0446820\pi$
$331$			1.01477e7i			0.279824i	−0.990164	+	0.139912i	$0.955318\pi$
$332$	−1.89284e7	+	5.30581e7i	−0.517250	+	1.44990i
$333$		0			0
$334$	1.98490e7	+	3.43454e6i	0.532720	+	0.0921785i
$335$			2.76172e7i			0.734590i
$336$		0			0
$337$	5.39701e7			1.41014			0.705072	−	0.709136i	$-0.250915\pi$
$337$	5.39701e7			1.41014			0.705072	+	0.709136i	$0.250915\pi$
$338$	7.27329e6	−	4.20339e7i	0.188356	−	1.08855i
$339$		0			0
$340$	1.36881e7	+	4.88322e6i	0.348263	+	0.124242i
$341$	1.81958e7			0.458890
$342$		0			0
$343$		−	1.97908e7i		−	0.490435i
$344$	4.10047e7	+	2.31528e7i	1.00730	+	0.568759i
$345$		0			0
$346$	−5665.02	+	32739.4i	−0.000136765	+	0.000790392i
$347$			4.90499e7i			1.17395i	0.809605	+	0.586975i	$0.199681\pi$
$347$			4.90499e7i			1.17395i	−0.809605	+	0.586975i	$0.800319\pi$
$348$		0			0
$349$	2.30969e7			0.543346			0.271673	−	0.962390i	$-0.412423\pi$
$349$	2.30969e7			0.543346			0.271673	+	0.962390i	$0.412423\pi$
$350$	−2.14065e6	−	370405.i	−0.0499277	−	0.00863918i
$351$		0			0
$352$	−3.31726e7	−	3.82746e7i	−0.760592	−	0.877572i
$353$	8.59041e7			1.95294			0.976472	−	0.215642i	$-0.0691844\pi$
$353$	8.59041e7			1.95294			0.976472	+	0.215642i	$0.0691844\pi$
$354$		0			0
$355$			1.47438e7i			0.329553i
$356$	−1.19725e7	−	4.27118e6i	−0.265360	−	0.0946668i
$357$		0			0
$358$	−3.11993e7	−	5.39854e6i	−0.679980	−	0.117660i
$359$			4.12084e7i			0.890640i	0.895371	+	0.445320i	$0.146910\pi$
$359$			4.12084e7i			0.890640i	−0.895371	+	0.445320i	$0.853090\pi$
$360$		0			0
$361$	4.67577e7			0.993874
$362$	1.29840e7	−	7.50374e7i	0.273705	−	1.58180i
$363$		0			0
$364$	−5.95619e6	+	1.66958e7i	−0.123499	+	0.346180i
$365$	−1.25780e7			−0.258662
$366$		0			0
$367$		−	5.40236e7i		−	1.09291i	−0.837488	−	0.546456i	$-0.815977\pi$
$367$		−	5.40236e7i		−	1.09291i	0.837488	−	0.546456i	$-0.184023\pi$
$368$	4.69438e7	−	5.74203e7i	0.941965	−	1.15218i
$369$		0			0
$370$	−2.66161e6	+	1.53820e7i	−0.0525459	+	0.303674i
$371$			2.07506e7i			0.406359i
$372$		0			0
$373$	5.45778e7			1.05169			0.525847	−	0.850579i	$-0.323748\pi$
$373$	5.45778e7			1.05169			0.525847	+	0.850579i	$0.323748\pi$
$374$	4.94950e7	+	8.56431e6i	0.946121	+	0.163711i
$375$		0			0
$376$	7.70069e6	+	4.34810e6i	0.144866	+	0.0817967i
$377$	−4.76171e7			−0.888667
$378$		0			0
$379$		−	7.14006e7i		−	1.31155i	−0.754957	−	0.655774i	$-0.772342\pi$
$379$		−	7.14006e7i		−	1.31155i	0.754957	−	0.655774i	$-0.227658\pi$
$380$	−645372.	+	1.80904e6i	−0.0117614	+	0.0329683i
$381$		0			0
$382$	−5.23065e7	−	9.05079e6i	−0.938352	−	0.162367i
$383$			2.38242e7i			0.424055i	0.977264	+	0.212028i	$0.0680067\pi$
$383$			2.38242e7i			0.424055i	−0.977264	+	0.212028i	$0.931993\pi$
$384$		0			0
$385$	−7.50865e6			−0.131577
$386$	−6.65856e6	+	3.84813e7i	−0.115776	+	0.669095i
$387$		0			0
$388$	8.54026e6	+	3.04673e6i	0.146210	+	0.0521601i
$389$	3.32214e7			0.564377			0.282188	−	0.959359i	$-0.408940\pi$
$389$	3.32214e7			0.564377			0.282188	+	0.959359i	$0.408940\pi$
$390$		0			0
$391$			7.35540e7i			1.23048i
$392$	−2.77157e7	+	4.90858e7i	−0.460116	+	0.814888i
$393$		0			0
$394$	−5.03997e6	+	2.91271e7i	−0.0824023	+	0.476221i
$395$		−	1.78179e7i		−	0.289111i
$396$		0			0
$397$	−4.02591e7			−0.643417			−0.321709	−	0.946839i	$-0.604257\pi$
$397$	−4.02591e7			−0.643417			−0.321709	+	0.946839i	$0.604257\pi$
$398$	1.08106e6	+	187059.i	0.0171474	+	0.00296709i
$399$		0			0
$400$	9.90974e6	+	8.10167e6i	0.154840	+	0.126589i
$401$	−3.97745e7			−0.616839			−0.308420	−	0.951250i	$-0.599800\pi$
$401$	−3.97745e7			−0.616839			−0.308420	+	0.951250i	$0.599800\pi$
$402$		0			0
$403$			3.75211e7i			0.573271i
$404$	7.42201e7	+	2.64779e7i	1.12558	+	0.401550i
$405$		0			0
$406$	1.02337e7	+	1.77077e6i	0.152916	+	0.0264596i
$407$			5.39547e7i			0.800287i
$408$		0			0
$409$	−1.31428e7			−0.192097			−0.0960483	−	0.995377i	$-0.530620\pi$
$409$	−1.31428e7			−0.192097			−0.0960483	+	0.995377i	$0.530620\pi$
$410$	−8.26260e6	+	4.77514e7i	−0.119885	+	0.692842i
$411$		0			0
$412$	2.89321e7	−	8.10993e7i	0.413702	−	1.15965i
$413$	8.31425e6			0.118025
$414$		0			0
$415$		−	4.92052e7i		−	0.688440i
$416$	7.89249e7	−	6.84042e7i	1.09631	−	0.950174i
$417$		0			0
$418$	−1.13187e6	+	6.54132e6i	−0.0154977	+	0.0895646i
$419$			7.92855e6i			0.107783i	0.998547	+	0.0538917i	$0.0171626\pi$
$419$			7.92855e6i			0.107783i	−0.998547	+	0.0538917i	$0.982837\pi$
$420$		0			0
$421$	9.38186e7			1.25731			0.628655	−	0.777684i	$-0.283606\pi$
$421$	9.38186e7			1.25731			0.628655	+	0.777684i	$0.283606\pi$
$422$	−2.94004e6	−	508727.i	−0.0391216	−	0.00676936i
$423$		0			0
$424$	6.01129e7	−	1.06463e8i	0.788624	−	1.39669i
$425$	−1.26941e7			−0.165362
$426$		0			0
$427$			1.25183e7i			0.160791i
$428$	−2.36306e7	+	6.62388e7i	−0.301401	+	0.844854i
$429$		0			0
$430$	−4.05289e7	−	7.01287e6i	−0.509752	−	0.0882044i
$431$			2.86716e7i			0.358114i	0.983839	+	0.179057i	$0.0573046\pi$
$431$			2.86716e7i			0.358114i	−0.983839	+	0.179057i	$0.942695\pi$
$432$		0			0
$433$	8.16883e7			1.00623			0.503114	−	0.864220i	$-0.332188\pi$
$433$	8.16883e7			1.00623			0.503114	+	0.864220i	$0.332188\pi$
$434$	1.39532e6	−	8.06386e6i	0.0170689	−	0.0986447i
$435$		0			0
$436$	1.14748e8	+	4.09361e7i	1.38447	+	0.493910i
$437$	−9.72098e6			−0.116484
$438$		0			0
$439$		−	1.61778e8i		−	1.91217i	−0.293085	−	0.956086i	$-0.594682\pi$
$439$		−	1.61778e8i		−	1.91217i	0.293085	−	0.956086i	$-0.405318\pi$
$440$	3.85237e7	+	2.17519e7i	0.452241	+	0.255352i
$441$		0			0
$442$	−1.76602e7	+	1.02062e8i	−0.204517	+	1.18195i
$443$		−	1.00373e8i		−	1.15453i	−0.816556	−	0.577266i	$-0.804120\pi$
$443$		−	1.00373e8i		−	1.15453i	0.816556	−	0.577266i	$-0.195880\pi$
$444$		0			0
$445$	1.11031e7			0.125998
$446$	−7.98638e7	−	1.38191e7i	−0.900214	−	0.155767i
$447$		0			0
$448$	−1.95060e7	+	1.17661e7i	−0.216937	+	0.130857i
$449$	4.56145e7			0.503922			0.251961	−	0.967737i	$-0.418925\pi$
$449$	4.56145e7			0.503922			0.251961	+	0.967737i	$0.418925\pi$
$450$		0			0
$451$			1.67495e8i			1.82588i
$452$	−1.63061e8	−	5.81720e7i	−1.76578	−	0.629939i
$453$		0			0
$454$	3.39162e7	+	5.86865e6i	0.362443	+	0.0627149i
$455$		−	1.54834e7i		−	0.164373i
$456$		0			0
$457$	−1.29981e8			−1.36186			−0.680928	−	0.732350i	$-0.738423\pi$
$457$	−1.29981e8			−1.36186			−0.680928	+	0.732350i	$0.738423\pi$
$458$	1.84024e7	−	1.06351e8i	0.191548	−	1.10700i
$459$		0			0
$460$	−2.17674e7	+	6.10161e7i	−0.223632	+	0.626861i
$461$	1.24776e8			1.27358			0.636791	−	0.771036i	$-0.280261\pi$
$461$	1.24776e8			1.27358			0.636791	+	0.771036i	$0.280261\pi$
$462$		0			0
$463$			1.12030e8i			1.12874i	0.825523	+	0.564369i	$0.190880\pi$
$463$			1.12030e8i			1.12874i	−0.825523	+	0.564369i	$0.809120\pi$
$464$	−4.73748e7	−	3.87311e7i	−0.474235	−	0.387709i
$465$		0			0
$466$	3.08591e7	−	1.78341e8i	0.304947	−	1.76236i
$467$		−	1.67693e8i		−	1.64651i	−0.567670	−	0.823256i	$-0.692155\pi$
$467$		−	1.67693e8i		−	1.64651i	0.567670	−	0.823256i	$-0.307845\pi$
$468$		0			0
$469$	4.29306e7			0.416148
$470$	−7.61133e6	−	1.31702e6i	−0.0733106	−	0.0126852i
$471$		0			0
$472$	−4.26569e7	−	2.40857e7i	−0.405661	−	0.229051i
$473$	−1.42161e8			−1.34337
$474$		0			0
$475$		−	1.67767e6i		−	0.0156540i
$476$	7.59090e6	−	2.12780e7i	0.0703837	−	0.197292i
$477$		0			0
$478$	3.93174e7	+	6.80324e6i	0.359999	+	0.0622920i
$479$		−	7.64619e7i		−	0.695726i	−0.937545	−	0.347863i	$-0.886907\pi$
$479$		−	7.64619e7i		−	0.695726i	0.937545	−	0.347863i	$-0.113093\pi$
$480$		0			0
$481$	−1.11258e8			−0.999763
$482$	4.97625e6	−	2.87588e7i	0.0444387	−	0.256821i
$483$		0			0
$484$	3.72297e7	+	1.32817e7i	0.328363	+	0.117143i
$485$	−7.92009e6			−0.0694232
$486$		0			0
$487$		−	4.97455e7i		−	0.430692i	−0.976538	−	0.215346i	$-0.930912\pi$
$487$		−	4.97455e7i		−	0.430692i	0.976538	−	0.215346i	$-0.0690880\pi$
$488$	3.62645e7	−	6.42262e7i	0.312049	−	0.552653i
$489$		0			0
$490$	8.39495e6	−	4.85162e7i	0.0713559	−	0.412381i
$491$		−	1.85343e8i		−	1.56578i	−0.622158	−	0.782891i	$-0.713744\pi$
$491$		−	1.85343e8i		−	1.56578i	0.622158	−	0.782891i	$-0.286256\pi$
$492$		0			0
$493$	6.06859e7			0.506462
$494$	−1.34886e7	−	2.33399e6i	−0.111889	−	0.0193606i
$495$		0			0
$496$	−3.05191e7	+	3.73301e7i	−0.250107	+	0.305924i
$497$	2.29191e7			0.186693
$498$		0			0
$499$		−	1.92003e8i		−	1.54527i	−0.634848	−	0.772637i	$-0.718937\pi$
$499$		−	1.92003e8i		−	1.54527i	0.634848	−	0.772637i	$-0.281063\pi$
$500$	−1.05303e7	−	3.75668e6i	−0.0842425	−	0.0300534i
$501$		0			0
$502$	7.81934e7	+	1.35301e7i	0.618100	+	0.106952i
$503$			8.45476e7i			0.664351i	0.943218	+	0.332175i	$0.107783\pi$
$503$			8.45476e7i			0.664351i	−0.943218	+	0.332175i	$0.892217\pi$
$504$		0			0
$505$	−6.88304e7			−0.534449
$506$	−3.81762e7	+	2.20629e8i	−0.294674	+	1.70298i
$507$		0			0
$508$	−3.23149e7	+	9.05817e7i	−0.246497	+	0.690954i
$509$	1.50345e8			1.14008			0.570040	−	0.821617i	$-0.306928\pi$
$509$	1.50345e8			1.14008			0.570040	+	0.821617i	$0.306928\pi$
$510$		0			0
$511$			1.95523e7i			0.146533i
$512$	1.34162e8	−	3.85971e6i	0.999586	−	0.0287571i
$513$		0			0
$514$	−1.83378e7	+	1.05978e8i	−0.135039	+	0.780418i
$515$			7.52101e7i			0.550623i
$516$		0			0
$517$	−2.66979e7			−0.193199
$518$	2.39111e7	+	4.13743e6i	0.172033	+	0.0297675i
$519$		0			0
$520$	−4.48540e7	+	7.94385e7i	−0.319000	+	0.564964i
$521$	2.12869e8			1.50521			0.752607	−	0.658470i	$-0.228796\pi$
$521$	2.12869e8			1.50521			0.752607	+	0.658470i	$0.228796\pi$
$522$		0			0
$523$		−	1.22260e7i		−	0.0854635i	−0.999087	−	0.0427317i	$-0.986394\pi$
$523$		−	1.22260e7i		−	0.0854635i	0.999087	−	0.0427317i	$-0.0136061\pi$
$524$	−9.45355e7	+	2.64992e8i	−0.657054	+	1.84178i
$525$		0			0
$526$	1.61575e8	+	2.79580e7i	1.11024	+	0.192110i
$527$		−	4.78189e7i		−	0.326714i
$528$		0			0
$529$	−1.79838e8			−1.21483
$530$	−1.82079e7	+	1.05227e8i	−0.122302	+	0.706807i
$531$		0			0
$532$	2.81212e6	+	1.00322e6i	0.0186767	+	0.00666288i
$533$	−3.45386e8			−2.28099
$534$		0			0
$535$		−	6.14288e7i		−	0.401153i
$536$	−2.20258e8	−	1.24366e8i	−1.43034	−	0.807622i
$537$		0			0
$538$	3.35164e7	−	1.93699e8i	0.215234	−	1.24388i
$539$		−	1.70178e8i		−	1.08677i
$540$		0			0
$541$	−2.07093e8			−1.30790			−0.653949	−	0.756539i	$-0.726889\pi$
$541$	−2.07093e8			−1.30790			−0.653949	+	0.756539i	$0.726889\pi$
$542$	−1.11228e8	−	1.92462e7i	−0.698581	−	0.120878i
$543$		0			0
$544$	−1.00586e8	+	8.71781e7i	−0.624801	+	0.541515i
$545$	−1.06415e8			−0.657376
$546$		0			0
$547$			1.70930e8i			1.04438i	0.852831	+	0.522188i	$0.174884\pi$
$547$			1.70930e8i			1.04438i	−0.852831	+	0.522188i	$0.825116\pi$
$548$	1.29359e8	+	4.61488e7i	0.786061	+	0.280426i
$549$		0			0
$550$	−3.80767e7	−	6.58855e6i	−0.228860	−	0.0396006i
$551$			8.02032e6i			0.0479443i
$552$		0			0
$553$	−2.76976e7			−0.163782
$554$	−5.15597e7	+	2.97975e8i	−0.303236	+	1.75247i
$555$		0			0
$556$	−6.58151e7	+	1.84486e8i	−0.382914	+	1.07334i
$557$	1.13400e8			0.656215			0.328107	−	0.944640i	$-0.393589\pi$
$557$	1.13400e8			0.656215			0.328107	+	0.944640i	$0.393589\pi$
$558$		0			0
$559$		−	2.93146e8i		−	1.67822i
$560$	1.25939e7	−	1.54046e7i	0.0717130	−	0.0877172i
$561$		0			0
$562$	−1.39842e7	+	8.08177e7i	−0.0787823	+	0.455300i
$563$			1.29905e8i			0.727947i	0.931409	+	0.363973i	$0.118580\pi$
$563$			1.29905e8i			0.727947i	−0.931409	+	0.363973i	$0.881420\pi$
$564$		0			0
$565$	1.51220e8			0.838426
$566$	2.98957e8	+	5.17297e7i	1.64877	+	0.285293i
$567$		0			0
$568$	−1.17588e8	−	6.63946e7i	−0.641679	−	0.362316i
$569$	−1.43283e8			−0.777783			−0.388892	−	0.921284i	$-0.627142\pi$
$569$	−1.43283e8			−0.777783			−0.388892	+	0.921284i	$0.627142\pi$
$570$		0			0
$571$		−	1.43037e8i		−	0.768318i	−0.923267	−	0.384159i	$-0.874491\pi$
$571$		−	1.43037e8i		−	0.768318i	0.923267	−	0.384159i	$-0.125509\pi$
$572$	−1.05945e8	+	2.96974e8i	−0.566101	+	1.58683i
$573$		0			0
$574$	7.42289e7	+	1.28441e7i	0.392498	+	0.0679154i
$575$		−	5.65853e7i		−	0.297646i
$576$		0			0
$577$	−2.37146e8			−1.23449			−0.617245	−	0.786771i	$-0.711751\pi$
$577$	−2.37146e8			−1.23449			−0.617245	+	0.786771i	$0.711751\pi$
$578$	−1.04166e7	+	6.01996e7i	−0.0539437	+	0.311752i
$579$		0			0
$580$	5.03415e7	+	1.79593e7i	0.258013	+	0.0920460i
$581$	−7.64888e7			−0.390004
$582$		0			0
$583$			3.69100e8i			1.86268i
$584$	5.66414e7	−	1.00315e8i	0.284378	−	0.503647i
$585$		0			0
$586$	2.06201e7	−	1.19168e8i	0.102471	−	0.592199i
$587$			2.64831e8i			1.30935i	0.755912	+	0.654674i	$0.227194\pi$
$587$			2.64831e8i			1.30935i	−0.755912	+	0.654674i	$0.772806\pi$
$588$		0			0
$589$	6.31980e6			0.0309284
$590$	4.21619e7	+	7.29543e6i	0.205288	+	0.0355218i
$591$		0			0
$592$	−1.10692e8	−	9.04959e7i	−0.533521	−	0.436178i
$593$	1.78125e8			0.854200			0.427100	−	0.904204i	$-0.359535\pi$
$593$	1.78125e8			0.854200			0.427100	+	0.904204i	$0.359535\pi$
$594$		0			0
$595$			1.97328e7i			0.0936782i
$596$	−9.44898e7	−	3.37091e7i	−0.446320	−	0.159224i
$597$		0			0
$598$	−4.54952e8	−	7.87221e7i	−2.12746	−	0.368123i
$599$		−	1.67621e8i		−	0.779915i	−0.920833	−	0.389958i	$-0.872490\pi$
$599$		−	1.67621e8i		−	0.779915i	0.920833	−	0.389958i	$-0.127510\pi$
$600$		0			0
$601$	2.23815e7			0.103102			0.0515508	−	0.998670i	$-0.483584\pi$
$601$	2.23815e7			0.103102			0.0515508	+	0.998670i	$0.483584\pi$
$602$	−1.09014e7	+	6.30016e7i	−0.0499681	+	0.288777i
$603$		0			0
$604$	−1.16806e8	+	3.27419e8i	−0.530098	+	1.48591i
$605$	−3.45262e7			−0.155913
$606$		0			0
$607$		−	2.34167e8i		−	1.04703i	−0.852017	−	0.523515i	$-0.824620\pi$
$607$		−	2.34167e8i		−	1.04703i	0.852017	−	0.523515i	$-0.175380\pi$
$608$	−1.15216e7	−	1.32936e7i	−0.0512626	−	0.0591468i
$609$		0			0
$610$	−1.09843e7	+	6.34809e7i	−0.0483932	+	0.279675i
$611$		−	5.50528e7i		−	0.241355i
$612$		0			0
$613$	3.31792e8			1.44040			0.720202	−	0.693765i	$-0.244049\pi$
$613$	3.31792e8			1.44040			0.720202	+	0.693765i	$0.244049\pi$
$614$	3.04102e8	+	5.26199e7i	1.31375	+	0.227324i
$615$		0			0
$616$	3.38131e7	−	5.98845e7i	0.144658	−	0.256196i
$617$	−2.84884e8			−1.21287			−0.606433	−	0.795135i	$-0.707400\pi$
$617$	−2.84884e8			−1.21287			−0.606433	+	0.795135i	$0.707400\pi$
$618$		0			0
$619$			2.80053e8i			1.18078i	0.807119	+	0.590389i	$0.201026\pi$
$619$			2.80053e8i			1.18078i	−0.807119	+	0.590389i	$0.798974\pi$
$620$	1.41514e7	−	3.96678e7i	0.0593780	−	0.166442i
$621$		0			0
$622$	3.64078e8	+	6.29977e7i	1.51294	+	0.261790i
$623$		−	1.72596e7i		−	0.0713784i
$624$		0			0
$625$	9.76562e6			0.0400000
$626$	−1.93379e7	+	1.11758e8i	−0.0788289	+	0.455570i
$627$		0			0
$628$	−3.64828e8	−	1.30152e8i	−1.47302	−	0.525499i
$629$	1.41794e8			0.569777
$630$		0			0
$631$		−	1.42135e8i		−	0.565733i	−0.959159	−	0.282867i	$-0.908715\pi$
$631$		−	1.42135e8i		−	0.565733i	0.959159	−	0.282867i	$-0.0912854\pi$
$632$	1.42105e8	+	8.02377e7i	0.562934	+	0.317854i
$633$		0			0
$634$	−8.25393e7	+	4.77013e8i	−0.323887	+	1.87181i
$635$		−	8.40039e7i		−	0.328079i
$636$		0			0
$637$	3.50918e8			1.35765
$638$	1.82030e8	+	3.14974e7i	0.700941	+	0.121287i
$639$		0			0
$640$	−1.09240e8	+	4.25506e7i	−0.416717	+	0.162318i
$641$	−2.05020e8			−0.778435			−0.389217	−	0.921146i	$-0.627255\pi$
$641$	−2.05020e8			−0.778435			−0.389217	+	0.921146i	$0.627255\pi$
$642$		0			0
$643$		−	8.84803e7i		−	0.332823i	−0.986056	−	0.166412i	$-0.946782\pi$
$643$		−	8.84803e7i		−	0.332823i	0.986056	−	0.166412i	$-0.0532180\pi$
$644$	9.48487e7	+	3.38372e7i	0.355119	+	0.126688i
$645$		0			0
$646$	1.71907e7	+	2.97457e6i	0.0637669	+	0.0110338i
$647$		−	3.76256e8i		−	1.38922i	−0.719387	−	0.694609i	$-0.755577\pi$
$647$		−	3.76256e8i		−	1.38922i	0.719387	−	0.694609i	$-0.244423\pi$
$648$		0			0
$649$	1.47889e8			0.541006
$650$	1.35860e7	−	7.85167e7i	0.0494713	−	0.285905i
$651$		0			0
$652$	2.40815e7	−	6.75025e7i	0.0868840	−	0.243544i
$653$	−1.08922e8			−0.391180			−0.195590	−	0.980686i	$-0.562662\pi$
$653$	−1.08922e8			−0.391180			−0.195590	+	0.980686i	$0.562662\pi$
$654$		0			0
$655$		−	2.45749e8i		−	0.874515i
$656$	−3.43629e8	−	2.80932e8i	−1.21724	−	0.995154i
$657$		0			0
$658$	−2.04729e6	+	1.18317e7i	−0.00718622	+	0.0415308i
$659$		−	2.73716e8i		−	0.956410i	−0.878248	−	0.478205i	$-0.841288\pi$
$659$		−	2.73716e8i		−	0.956410i	0.878248	−	0.478205i	$-0.158712\pi$
$660$		0			0
$661$	−3.25447e8			−1.12687			−0.563437	−	0.826159i	$-0.690521\pi$
$661$	−3.25447e8			−1.12687			−0.563437	+	0.826159i	$0.690521\pi$
$662$	7.99932e7	+	1.38415e7i	0.275727	+	0.0477101i
$663$		0			0
$664$	3.92431e8	+	2.21581e8i	1.34048	+	0.756884i
$665$	−2.60792e6			−0.00886806
$666$		0			0
$667$			2.70513e8i			0.911614i
$668$	5.41481e7	−	1.51782e8i	0.181658	−	0.509203i
$669$		0			0
$670$	2.17703e8	+	3.76699e7i	0.723834	+	0.125248i
$671$			2.22669e8i			0.737041i
$672$		0			0
$673$	−1.53428e7			−0.0503339			−0.0251669	−	0.999683i	$-0.508012\pi$
$673$	−1.53428e7			−0.0503339			−0.0251669	+	0.999683i	$0.508012\pi$
$674$	7.36153e7	−	4.25439e8i	0.240430	−	1.38950i
$675$		0			0
$676$	−3.21427e8	−	1.14669e8i	−1.04050	−	0.371197i
$677$	1.41403e8			0.455715			0.227857	−	0.973694i	$-0.426828\pi$
$677$	1.41403e8			0.455715			0.227857	+	0.973694i	$0.426828\pi$
$678$		0			0
$679$			1.23117e7i			0.0393285i
$680$	5.71643e7	−	1.01241e8i	0.181802	−	0.321980i
$681$		0			0
$682$	2.48191e7	−	1.43435e8i	0.0782408	−	0.452171i
$683$			2.86757e8i			0.900020i	0.893024	+	0.450010i	$0.148580\pi$
$683$			2.86757e8i			0.900020i	−0.893024	+	0.450010i	$0.851420\pi$
$684$		0			0
$685$	−1.19966e8			−0.373237
$686$	−1.56008e8	−	2.69947e7i	−0.483254	−	0.0836193i
$687$		0			0
$688$	2.38441e8	−	2.91654e8i	0.732175	−	0.895576i
$689$	−7.61111e8			−2.32697
$690$		0			0
$691$			7.86675e7i			0.238430i	0.992868	+	0.119215i	$0.0380378\pi$
$691$			7.86675e7i			0.238430i	−0.992868	+	0.119215i	$0.961962\pi$
$692$	250353.	+	89313.2i	0.000755500	+	0.000269524i
$693$		0			0
$694$	3.86653e8	+	6.69041e7i	1.15676	+	0.200159i
$695$		−	1.71089e8i		−	0.509644i
$696$		0			0
$697$	4.40179e8			1.29996
$698$	3.15041e7	−	1.82069e8i	0.0926406	−	0.535390i
$699$		0			0
$700$	−5.83970e6	+	1.63692e7i	−0.0170254	+	0.0477237i
$701$	3.28382e8			0.953290			0.476645	−	0.879096i	$-0.341853\pi$
$701$	3.28382e8			0.953290			0.476645	+	0.879096i	$0.341853\pi$
$702$		0			0
$703$			1.87396e7i			0.0539380i
$704$	−3.46961e8	+	2.09289e8i	−0.994403	+	0.599829i
$705$		0			0
$706$	1.17173e8	−	6.77170e8i	0.332977	−	1.92435i
$707$			1.06996e8i			0.302768i
$708$		0			0
$709$	−2.06210e8			−0.578591			−0.289296	−	0.957240i	$-0.593421\pi$
$709$	−2.06210e8			−0.578591			−0.289296	+	0.957240i	$0.593421\pi$
$710$	1.16223e8	+	2.01106e7i	0.324727	+	0.0561888i
$711$		0			0
$712$	−4.99996e7	+	8.85517e7i	−0.138525	+	0.245334i
$713$	2.13157e8			0.588074
$714$		0			0
$715$		−	2.75409e8i		−	0.753459i
$716$	−8.51118e7	+	2.38576e8i	−0.231873	+	0.649962i
$717$		0			0
$718$	3.24840e8	+	5.62083e7i	0.877599	+	0.151854i
$719$		−	1.06671e8i		−	0.286986i	−0.989651	−	0.143493i	$-0.954167\pi$
$719$		−	1.06671e8i		−	0.286986i	0.989651	−	0.143493i	$-0.0458334\pi$
$720$		0			0
$721$	1.16913e8			0.311930
$722$	6.37775e7	−	3.68584e8i	0.169456	−	0.979321i
$723$		0			0
$724$	−5.73799e8	−	2.04702e8i	−1.51197	−	0.539395i
$725$	−4.66858e7			−0.122510
$726$		0			0
$727$			4.85082e8i			1.26244i	0.775602	+	0.631222i	$0.217446\pi$
$727$			4.85082e8i			1.26244i	−0.775602	+	0.631222i	$0.782554\pi$
$728$	1.23486e8	+	6.97249e7i	0.320054	+	0.180715i
$729$		0			0
$730$	−1.71564e7	+	9.91506e7i	−0.0441020	+	0.254875i
$731$			3.73601e8i			0.956436i
$732$		0			0
$733$	2.57203e8			0.653077			0.326538	−	0.945184i	$-0.394118\pi$
$733$	2.57203e8			0.653077			0.326538	+	0.945184i	$0.394118\pi$
$734$	−4.25860e8	−	7.36883e7i	−1.07691	−	0.186342i
$735$		0			0
$736$	−3.88605e8	−	4.48373e8i	−0.974709	−	1.12462i
$737$	7.63624e8			1.90755
$738$		0			0
$739$		−	7.60588e8i		−	1.88459i	−0.334787	−	0.942294i	$-0.608664\pi$
$739$		−	7.60588e8i		−	1.88459i	0.334787	−	0.942294i	$-0.391336\pi$
$740$	1.17624e8	+	4.19622e7i	0.290269	+	0.103553i
$741$		0			0
$742$	1.63574e8	+	2.83039e7i	0.400409	+	0.0692843i
$743$			2.14669e8i			0.523363i	0.965154	+	0.261682i	$0.0842770\pi$
$743$			2.14669e8i			0.523363i	−0.965154	+	0.261682i	$0.915723\pi$
$744$		0			0
$745$	8.76282e7			0.211922
$746$	7.44442e7	−	4.30229e8i	0.179314	−	1.03630i
$747$		0			0
$748$	1.35022e8	−	3.78480e8i	0.322627	−	0.904354i
$749$	−9.54902e7			−0.227255
$750$		0			0
$751$			3.72415e8i			0.879239i	0.898184	+	0.439620i	$0.144887\pi$
$751$			3.72415e8i			0.879239i	−0.898184	+	0.439620i	$0.855113\pi$
$752$	4.47792e7	−	5.47726e7i	0.105299	−	0.128798i
$753$		0			0
$754$	−6.49498e7	+	3.75359e8i	−0.151518	+	0.875655i
$755$		−	3.03643e8i		−	0.705541i
$756$		0			0
$757$	−2.17431e8			−0.501227			−0.250613	−	0.968087i	$-0.580632\pi$
$757$	−2.17431e8			−0.501227			−0.250613	+	0.968087i	$0.580632\pi$
$758$	−5.62841e8	−	9.73906e7i	−1.29234	−	0.223619i
$759$		0			0
$760$	1.33801e7	+	7.55491e6i	0.0304803	+	0.0172103i
$761$	3.79154e7			0.0860322			0.0430161	−	0.999074i	$-0.486303\pi$
$761$	3.79154e7			0.0860322			0.0430161	+	0.999074i	$0.486303\pi$
$762$		0			0
$763$			1.65421e8i			0.372406i
$764$	−1.42692e8	+	3.99980e8i	−0.319978	+	0.896928i
$765$		0			0
$766$	1.87803e8	+	3.24963e7i	0.417846	+	0.0723015i
$767$			3.04957e8i			0.675854i
$768$		0			0
$769$	−4.55616e8			−1.00189			−0.500945	−	0.865479i	$-0.667014\pi$
$769$	−4.55616e8			−1.00189			−0.500945	+	0.865479i	$0.667014\pi$
$770$	−1.02418e7	+	5.91896e7i	−0.0224339	+	0.129650i
$771$		0			0
$772$	2.94260e8	+	1.04977e8i	0.639558	+	0.228162i
$773$	5.34167e8			1.15648			0.578241	−	0.815866i	$-0.303739\pi$
$773$	5.34167e8			1.15648			0.578241	+	0.815866i	$0.303739\pi$
$774$		0			0
$775$			3.67872e7i			0.0790300i
$776$	3.56659e7	−	6.31659e7i	0.0763251	−	0.135175i
$777$		0			0
$778$	4.53140e7	−	2.61880e8i	0.0962263	−	0.556113i
$779$			5.81746e7i			0.123061i
$780$		0			0
$781$	4.07671e8			0.855769
$782$	5.79816e8	+	1.00328e8i	1.21247	+	0.209798i
$783$		0			0
$784$	3.49132e8	+	2.85432e8i	0.724506	+	0.592318i
$785$	3.38335e8			0.699420
$786$		0			0
$787$		−	2.05724e8i		−	0.422048i	−0.977481	−	0.211024i	$-0.932320\pi$
$787$		−	2.05724e8i		−	0.422048i	0.977481	−	0.211024i	$-0.0676798\pi$
$788$	2.22730e8	+	7.94588e7i	0.455198	+	0.162391i
$789$		0			0
$790$	−1.40456e8	−	2.43036e7i	−0.284878	−	0.0492934i
$791$		−	2.35070e8i		−	0.474972i
$792$		0			0
$793$	−4.59158e8			−0.920753
$794$	−5.49135e7	+	3.17357e8i	−0.109703	+	0.633996i
$795$		0			0
$796$	2.94913e6	−	8.26667e6i	0.00584728	−	0.0163905i
$797$	7.54211e8			1.48977			0.744883	−	0.667195i	$-0.232505\pi$
$797$	7.54211e8			1.48977			0.744883	+	0.667195i	$0.232505\pi$
$798$		0			0
$799$			7.01624e7i			0.137551i
$800$	7.73813e7	−	6.70664e7i	0.151135	−	0.130989i
$801$		0			0
$802$	−5.42525e7	+	3.13537e8i	−0.105171	+	0.607807i
$803$			3.47785e8i			0.671684i
$804$		0			0
$805$	−8.79611e7			−0.168618
$806$	2.95773e8	+	5.11788e7i	0.564877	+	0.0977428i
$807$		0			0
$808$	3.09958e8	−	5.48951e8i	0.587583	−	1.04064i
$809$	1.88932e8			0.356828			0.178414	−	0.983955i	$-0.442903\pi$
$809$	1.88932e8			0.356828			0.178414	+	0.983955i	$0.442903\pi$
$810$		0			0
$811$		−	4.32976e8i		−	0.811711i	−0.913937	−	0.405855i	$-0.866974\pi$
$811$		−	4.32976e8i		−	0.811711i	0.913937	−	0.405855i	$-0.133026\pi$
$812$	2.79174e7	−	7.82552e7i	0.0521444	−	0.146166i
$813$		0			0
$814$	4.25317e8	+	7.35942e7i	0.788569	+	0.136449i
$815$			6.26007e7i			0.115640i
$816$		0			0
$817$	−4.93756e7			−0.0905411
$818$	−1.79269e7	+	1.03603e8i	−0.0327525	+	0.189284i
$819$		0			0
$820$	3.65147e8	+	1.30266e8i	0.662257	+	0.236259i
$821$	−3.31612e8			−0.599239			−0.299620	−	0.954059i	$-0.596860\pi$
$821$	−3.31612e8			−0.599239			−0.299620	+	0.954059i	$0.596860\pi$
$822$		0			0
$823$			6.15322e8i			1.10383i	0.833900	+	0.551916i	$0.186103\pi$
$823$			6.15322e8i			1.10383i	−0.833900	+	0.551916i	$0.813897\pi$
$824$	−5.99831e8	−	3.38687e8i	−1.07213	−	0.605365i
$825$		0			0
$826$	1.13406e7	−	6.55401e7i	0.0201232	−	0.116297i
$827$			6.51923e8i			1.15260i	0.817237	+	0.576301i	$0.195505\pi$
$827$			6.51923e8i			1.15260i	−0.817237	+	0.576301i	$0.804495\pi$
$828$		0			0
$829$	5.30210e8			0.930645			0.465323	−	0.885141i	$-0.345938\pi$
$829$	5.30210e8			0.930645			0.465323	+	0.885141i	$0.345938\pi$
$830$	−3.87877e8	−	6.71159e7i	−0.678360	−	0.117379i
$831$		0			0
$832$	−4.31567e8	−	7.15457e8i	−0.749340	−	1.24226i
$833$	−4.47230e8			−0.773741
$834$		0			0
$835$			1.40760e8i			0.241780i
$836$	5.00204e7	+	1.78447e7i	0.0856108	+	0.0305416i
$837$		0			0
$838$	6.24997e7	+	1.08146e7i	0.106205	+	0.0183771i
$839$			6.26328e8i			1.06051i	0.847837	+	0.530256i	$0.177904\pi$
$839$			6.26328e8i			1.06051i	−0.847837	+	0.530256i	$0.822096\pi$
$840$		0			0
$841$	−3.71636e8			−0.624783
$842$	1.27969e8	−	7.39559e8i	0.214372	−	1.23890i
$843$		0			0
$844$	−8.02045e6	+	2.24821e7i	−0.0133405	+	0.0373946i
$845$	2.98086e8			0.494050
$846$		0			0
$847$			5.36705e7i			0.0883254i
$848$	−7.57237e8	−	6.19077e8i	−1.24178	−	1.01521i
$849$		0			0
$850$	−1.73148e7	+	1.00066e8i	−0.0281943	+	0.162941i
$851$			6.32059e8i			1.02558i
$852$		0			0
$853$	−1.11124e8			−0.179045			−0.0895226	−	0.995985i	$-0.528534\pi$
$853$	−1.11124e8			−0.179045			−0.0895226	+	0.995985i	$0.528534\pi$
$854$	9.86803e7	+	1.70750e7i	0.158437	+	0.0274150i
$855$		0			0
$856$	4.89919e8	+	2.76627e8i	0.781094	+	0.441035i
$857$	−3.71125e7			−0.0589627			−0.0294814	−	0.999565i	$-0.509386\pi$
$857$	−3.71125e7			−0.0589627			−0.0294814	+	0.999565i	$0.509386\pi$
$858$		0			0
$859$		−	6.43708e8i		−	1.01557i	−0.861484	−	0.507784i	$-0.830465\pi$
$859$		−	6.43708e8i		−	1.01557i	0.861484	−	0.507784i	$-0.169535\pi$
$860$	−1.10563e8	+	3.09918e8i	−0.173826	+	0.487249i
$861$		0			0
$862$	2.26015e8	+	3.91082e7i	0.352870	+	0.0610584i
$863$			4.60361e8i			0.716253i	0.933673	+	0.358126i	$0.116584\pi$
$863$			4.60361e8i			0.716253i	−0.933673	+	0.358126i	$0.883416\pi$
$864$		0			0
$865$	−232173.			−0.000358727
$866$	1.11423e8	−	6.43938e8i	0.171562	−	0.991494i
$867$		0			0
$868$	−6.16631e7	−	2.19982e7i	−0.0942900	−	0.0336379i
$869$	−4.92669e8			−0.750751
$870$		0			0
$871$			1.57465e9i			2.38302i
$872$	4.79210e8	−	8.48704e8i	0.722731	−	1.27999i
$873$		0			0
$874$	−1.32594e7	+	7.66291e7i	−0.0198605	+	0.114778i
$875$		−	1.51805e7i		−	0.0226602i
$876$		0			0
$877$	1.15420e9			1.71113			0.855563	−	0.517699i	$-0.173211\pi$
$877$	1.15420e9			1.71113			0.855563	+	0.517699i	$0.173211\pi$
$878$	−1.27528e9	−	2.20666e8i	−1.88417	−	0.326026i
$879$		0			0
$880$	2.24014e8	−	2.74007e8i	0.328720	−	0.402081i
$881$	−1.14212e9			−1.67026			−0.835132	−	0.550049i	$-0.814609\pi$
$881$	−1.14212e9			−1.67026			−0.835132	+	0.550049i	$0.814609\pi$
$882$		0			0
$883$			1.26032e9i			1.83062i	0.402753	+	0.915309i	$0.368053\pi$
$883$			1.26032e9i			1.83062i	−0.402753	+	0.915309i	$0.631947\pi$
$884$	7.80453e8	+	2.78426e8i	1.12977	+	0.403044i
$885$		0			0
$886$	−7.91227e8	−	1.36909e8i	−1.13763	−	0.196848i
$887$		−	4.41568e8i		−	0.632742i	−0.948636	−	0.316371i	$-0.897536\pi$
$887$		−	4.41568e8i		−	0.632742i	0.948636	−	0.316371i	$-0.102464\pi$
$888$		0			0
$889$	−1.30583e8			−0.185858
$890$	1.51446e7	−	8.75242e7i	0.0214827	−	0.124153i
$891$		0			0
$892$	−2.17869e8	+	6.10706e8i	−0.306973	+	0.860474i
$893$	−9.27274e6			−0.0130213
$894$		0			0
$895$		−	2.21252e8i		−	0.308615i
$896$	6.61444e7	+	1.69812e8i	0.0919536	+	0.236072i
$897$		0			0
$898$	6.22182e7	−	3.59572e8i	0.0859188	−	0.496544i
$899$		−	1.75866e8i		−	0.242049i
$900$		0			0
$901$	9.70001e8			1.32617
$902$	1.32034e9	+	2.28463e8i	1.79915	+	0.311313i
$903$		0			0
$904$	−6.80978e8	+	1.20604e9i	−0.921781	+	1.63252i
$905$	5.32131e8			0.717915
$906$		0			0
$907$		−	3.16399e8i		−	0.424046i	−0.977265	−	0.212023i	$-0.931995\pi$
$907$		−	3.16399e8i		−	0.424046i	0.977265	−	0.212023i	$-0.0680052\pi$
$908$	9.25235e7	−	2.59352e8i	0.123593	−	0.346443i
$909$		0			0
$910$	−1.22053e8	−	2.11193e7i	−0.161966	−	0.0280257i
$911$		−	6.09185e8i		−	0.805738i	−0.915258	−	0.402869i	$-0.868013\pi$
$911$		−	6.09185e8i		−	0.805738i	0.915258	−	0.402869i	$-0.131987\pi$
$912$		0			0
$913$	−1.36054e9			−1.78771
$914$	−1.77294e8	+	1.02462e9i	−0.232197	+	1.34192i
$915$		0			0
$916$	−8.13252e8	−	2.90127e8i	−1.05813	−	0.377487i
$917$	−3.82013e8			−0.495416
$918$		0			0
$919$		−	7.84705e8i		−	1.01102i	−0.862821	−	0.505510i	$-0.831304\pi$
$919$		−	7.84705e8i		−	1.01102i	0.862821	−	0.505510i	$-0.168696\pi$
$920$	4.51291e8	+	2.54816e8i	0.579553	+	0.327237i
$921$		0			0
$922$	1.70194e8	−	9.83589e8i	0.217146	−	1.25493i
$923$			8.40646e8i			1.06907i
$924$		0			0
$925$	−1.09082e8			−0.137825
$926$	8.83120e8	+	1.52810e8i	1.11221	+	0.192450i
$927$		0			0
$928$	−3.69931e8	+	3.20619e8i	−0.462889	+	0.401186i
$929$	5.54301e8			0.691350			0.345675	−	0.938354i	$-0.387650\pi$
$929$	5.54301e8			0.691350			0.345675	+	0.938354i	$0.387650\pi$
$930$		0			0
$931$		−	5.91064e7i		−	0.0732463i
$932$	−1.36375e9	−	4.86516e8i	−1.68456	−	0.600965i
$933$		0			0
$934$	−1.32190e9	−	2.28734e8i	−1.62240	−	0.280731i
$935$			3.50996e8i			0.429405i
$936$		0			0
$937$	−2.98563e8			−0.362925			−0.181462	−	0.983398i	$-0.558083\pi$
$937$	−2.98563e8			−0.362925			−0.181462	+	0.983398i	$0.558083\pi$
$938$	5.85573e7	−	3.38416e8i	0.0709533	−	0.410055i
$939$		0			0
$940$	−2.07637e7	+	5.82026e7i	−0.0249989	+	0.0700744i
$941$	1.17672e8			0.141222			0.0706111	−	0.997504i	$-0.477505\pi$
$941$	1.17672e8			0.141222			0.0706111	+	0.997504i	$0.477505\pi$
$942$		0			0
$943$			1.96214e9i			2.33989i
$944$	−2.48048e8	+	3.03405e8i	−0.294863	+	0.360668i
$945$		0			0
$946$	−1.93908e8	+	1.12064e9i	−0.229046	+	1.32370i
$947$		−	9.83597e8i		−	1.15816i	−0.815272	−	0.579078i	$-0.803413\pi$
$947$		−	9.83597e8i		−	1.15816i	0.815272	−	0.579078i	$-0.196587\pi$
$948$		0			0
$949$	−7.17158e8			−0.839105
$950$	−1.32248e7	−	2.28834e6i	−0.0154248	−	0.00266901i
$951$		0			0
$952$	−1.57377e8	−	8.88612e7i	−0.182403	−	0.102992i
$953$	−3.21501e8			−0.371453			−0.185726	−	0.982601i	$-0.559464\pi$
$953$	−3.21501e8			−0.371453			−0.185726	+	0.982601i	$0.559464\pi$
$954$		0			0
$955$		−	3.70934e8i		−	0.425879i
$956$	1.07258e8	−	3.00654e8i	0.122760	−	0.344107i
$957$		0			0
$958$	−6.02738e8	−	1.04294e8i	−0.685539	−	0.118621i
$959$			1.86485e8i			0.211440i
$960$		0			0
$961$	7.48926e8			0.843857
$962$	−1.51756e8	+	8.77034e8i	−0.170460	+	0.985124i
$963$		0			0
$964$	−2.19914e8	−	7.84542e7i	−0.245484	−	0.0875760i
$965$	−2.72892e8			−0.303675
$966$		0			0
$967$		−	5.12381e8i		−	0.566648i	−0.959024	−	0.283324i	$-0.908563\pi$
$967$		−	5.12381e8i		−	0.566648i	0.959024	−	0.283324i	$-0.0914372\pi$
$968$	1.55479e8	−	2.75361e8i	0.171414	−	0.303582i
$969$		0			0
$970$	−1.08030e7	+	6.24330e7i	−0.0118367	+	0.0684067i
$971$			7.48118e8i			0.817170i	0.912720	+	0.408585i	$0.133978\pi$
$971$			7.48118e8i			0.817170i	−0.912720	+	0.408585i	$0.866022\pi$
$972$		0			0
$973$	−2.65955e8			−0.288715
$974$	−3.92137e8	−	6.78530e7i	−0.424386	−	0.0734331i
$975$		0			0
$976$	−4.56821e8	−	3.73473e8i	−0.491357	−	0.401707i
$977$	−1.19213e9			−1.27832			−0.639160	−	0.769074i	$-0.720718\pi$
$977$	−1.19213e9			−1.27832			−0.639160	+	0.769074i	$0.720718\pi$
$978$		0			0
$979$		−	3.07004e8i		−	0.327187i
$980$	−3.70996e8	−	1.32352e8i	−0.394177	−	0.140622i
$981$		0			0
$982$	−1.46103e9	−	2.52808e8i	−1.54286	−	0.266966i
$983$		−	1.48663e9i		−	1.56510i	−0.622590	−	0.782548i	$-0.713920\pi$
$983$		−	1.48663e9i		−	1.56510i	0.622590	−	0.782548i	$-0.286080\pi$
$984$		0			0
$985$	−2.06556e8			−0.216137
$986$	8.27756e7	−	4.78378e8i	0.0863519	−	0.499046i
$987$		0			0
$988$	−3.67971e7	+	1.03146e8i	−0.0381542	+	0.106950i
$989$	−1.66536e9			−1.72155
$990$		0			0
$991$		−	1.07762e9i		−	1.10725i	−0.832768	−	0.553623i	$-0.813245\pi$
$991$		−	1.07762e9i		−	1.10725i	0.832768	−	0.553623i	$-0.186755\pi$
$992$	2.52640e8	+	2.91496e8i	0.258802	+	0.298605i
$993$		0			0
$994$	3.12616e7	−	1.80668e8i	0.0318312	−	0.183959i
$995$			7.66637e6i			0.00778252i
$996$		0			0
$997$	8.35952e8			0.843521			0.421760	−	0.906707i	$-0.361412\pi$
$997$	8.35952e8			0.843521			0.421760	+	0.906707i	$0.361412\pi$
$998$	−1.51353e9	−	2.61892e8i	−1.52265	−	0.263470i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.7.c.b.91.15		24
3.2	odd	2		60.7.c.a.31.10	yes	24
4.3	odd	2	inner	180.7.c.b.91.16		24
12.11	even	2		60.7.c.a.31.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.9	✓	24	12.11	even	2
60.7.c.a.31.10	yes	24	3.2	odd	2
180.7.c.b.91.15		24	1.1	even	1	trivial
180.7.c.b.91.16		24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36400 - 7.88286i) q^{2} +(-60.2790 - 21.5045i) q^{4} +55.9017 q^{5} -86.8984i q^{7} +(-251.737 + 445.839i) q^{8} +O(q^{10})\)	\(q+(1.36400 - 7.88286i) q^{2} +(-60.2790 - 21.5045i) q^{4} +55.9017 q^{5} -86.8984i q^{7} +(-251.737 + 445.839i) q^{8} +(76.2500 - 440.665i) q^{10} -1545.70i q^{11} +3187.34 q^{13} +(-685.008 - 118.530i) q^{14} +(3171.12 + 2592.54i) q^{16} -4062.12 q^{17} -536.854i q^{19} +(-3369.70 - 1202.14i) q^{20} +(-12184.5 - 2108.34i) q^{22} -18107.3i q^{23} +3125.00 q^{25} +(4347.53 - 25125.3i) q^{26} +(-1868.70 + 5238.15i) q^{28} -14939.5 q^{29} +11771.9i q^{31} +(24762.0 - 21461.2i) q^{32} +(-5540.73 + 32021.1i) q^{34} -4857.77i q^{35} -34906.3 q^{37} +(-4231.95 - 732.270i) q^{38} +(-14072.5 + 24923.2i) q^{40} -108362. q^{41} -91972.0i q^{43} +(-33239.4 + 93173.2i) q^{44} +(-142737. - 24698.4i) q^{46} -17272.4i q^{47} +110098. q^{49} +(4262.50 - 24633.9i) q^{50} +(-192130. - 68542.0i) q^{52} -238792. q^{53} -86407.2i q^{55} +(38742.7 + 21875.6i) q^{56} +(-20377.5 + 117766. i) q^{58} +95677.8i q^{59} -144057. q^{61} +(92796.3 + 16056.9i) q^{62} +(-135401. - 224469. i) q^{64} +178178. q^{65} +494031. i q^{67} +(244860. + 87353.7i) q^{68} +(-38293.1 - 6626.01i) q^{70} +263745. i q^{71} -225002. q^{73} +(-47612.3 + 275162. i) q^{74} +(-11544.8 + 32361.0i) q^{76} -134319. q^{77} -318736. i q^{79} +(177271. + 144927. i) q^{80} +(-147806. + 854203. i) q^{82} -880209. i q^{83} -227079. q^{85} +(-725003. - 125450. i) q^{86} +(689133. + 389110. i) q^{88} +198618. q^{89} -276975. i q^{91} +(-389388. + 1.09149e6i) q^{92} +(-136156. - 23559.5i) q^{94} -30011.1i q^{95} -141679. q^{97} +(150173. - 867885. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8}+O(q^{10}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8	\( 24 q - 20 q^{2} - 246 q^{4} + 340 q^{8} - 750 q^{10} + 5040 q^{13} + 2596 q^{14} + 4194 q^{16} - 7000 q^{20} + 45780 q^{22} + 75000 q^{25} - 75852 q^{26} + 54300 q^{28} - 132800 q^{29} + 10700 q^{32} - 173484 q^{34} - 69840 q^{37} - 215800 q^{38} - 14250 q^{40} + 70448 q^{41} + 395668 q^{44} - 158760 q^{46} - 642984 q^{49} - 62500 q^{50} - 210240 q^{52} + 644320 q^{53} + 917708 q^{56} - 1345020 q^{58} - 222864 q^{61} - 1948520 q^{62} + 935922 q^{64} - 266000 q^{65} - 572680 q^{68} + 220500 q^{70} + 771120 q^{73} + 589164 q^{74} - 191544 q^{76} - 1383840 q^{77} + 946000 q^{80} + 2672520 q^{82} - 372000 q^{85} - 1781528 q^{86} + 956940 q^{88} + 1566224 q^{89} + 3040560 q^{92} - 3788352 q^{94} - 1666800 q^{97} + 2709660 q^{98}+O(q^{100}) \) 24 * q - 20 * q^2 - 246 * q^4 + 340 * q^8 - 750 * q^10 + 5040 * q^13 + 2596 * q^14 + 4194 * q^16 - 7000 * q^20 + 45780 * q^22 + 75000 * q^25 - 75852 * q^26 + 54300 * q^28 - 132800 * q^29 + 10700 * q^32 - 173484 * q^34 - 69840 * q^37 - 215800 * q^38 - 14250 * q^40 + 70448 * q^41 + 395668 * q^44 - 158760 * q^46 - 642984 * q^49 - 62500 * q^50 - 210240 * q^52 + 644320 * q^53 + 917708 * q^56 - 1345020 * q^58 - 222864 * q^61 - 1948520 * q^62 + 935922 * q^64 - 266000 * q^65 - 572680 * q^68 + 220500 * q^70 + 771120 * q^73 + 589164 * q^74 - 191544 * q^76 - 1383840 * q^77 + 946000 * q^80 + 2672520 * q^82 - 372000 * q^85 - 1781528 * q^86 + 956940 * q^88 + 1566224 * q^89 + 3040560 * q^92 - 3788352 * q^94 - 1666800 * q^97 + 2709660 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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