LMFDB - Embedded newform 225.7.g.a.118.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,7,Mod(82,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("225.82");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	225.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$51.7621688145$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	225.118
Dual form			225.7.g.a.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.00000 + 3.00000i) q^{2} +46.0000i q^{4} +(-207.000 + 207.000i) q^{7} +(-330.000 - 330.000i) q^{8} +O(q^{10})$	\(q+(-3.00000 + 3.00000i) q^{2} +46.0000i q^{4} +(-207.000 + 207.000i) q^{7} +(-330.000 - 330.000i) q^{8} +1188.00 q^{11} +(-1548.00 - 1548.00i) q^{13} -1242.00i q^{14} -964.000 q^{16} +(3252.00 - 3252.00i) q^{17} -5060.00i q^{19} +(-3564.00 + 3564.00i) q^{22} +(5313.00 + 5313.00i) q^{23} +9288.00 q^{26} +(-9522.00 - 9522.00i) q^{28} -8910.00i q^{29} +25432.0 q^{31} +(24012.0 - 24012.0i) q^{32} +19512.0i q^{34} +(-20592.0 + 20592.0i) q^{37} +(15180.0 + 15180.0i) q^{38} +19008.0 q^{41} +(-80343.0 - 80343.0i) q^{43} +54648.0i q^{44} -31878.0 q^{46} +(16137.0 - 16137.0i) q^{47} +31951.0i q^{49} +(71208.0 - 71208.0i) q^{52} +(-155892. - 155892. i) q^{53} +136620. q^{56} +(26730.0 + 26730.0i) q^{58} +360180. i q^{59} +178112. q^{61} +(-76296.0 + 76296.0i) q^{62} +82376.0i q^{64} +(240273. - 240273. i) q^{67} +(149592. + 149592. i) q^{68} +617328. q^{71} +(306612. + 306612. i) q^{73} -123552. i q^{74} +232760. q^{76} +(-245916. + 245916. i) q^{77} +232760. i q^{79} +(-57024.0 + 57024.0i) q^{82} +(-134097. - 134097. i) q^{83} +482058. q^{86} +(-392040. - 392040. i) q^{88} +270270. i q^{89} +640872. q^{91} +(-244398. + 244398. i) q^{92} +96822.0i q^{94} +(-810612. + 810612. i) q^{97} +(-95853.0 - 95853.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{2} - 414 q^{7} - 660 q^{8}+O(q^{10}) $ 2 * q - 6 * q^2 - 414 * q^7 - 660 * q^8	$ 2 q - 6 q^{2} - 414 q^{7} - 660 q^{8} + 2376 q^{11} - 3096 q^{13} - 1928 q^{16} + 6504 q^{17} - 7128 q^{22} + 10626 q^{23} + 18576 q^{26} - 19044 q^{28} + 50864 q^{31} + 48024 q^{32} - 41184 q^{37} + 30360 q^{38} + 38016 q^{41} - 160686 q^{43} - 63756 q^{46} + 32274 q^{47} + 142416 q^{52} - 311784 q^{53} + 273240 q^{56} + 53460 q^{58} + 356224 q^{61} - 152592 q^{62} + 480546 q^{67} + 299184 q^{68} + 1234656 q^{71} + 613224 q^{73} + 465520 q^{76} - 491832 q^{77} - 114048 q^{82} - 268194 q^{83} + 964116 q^{86} - 784080 q^{88} + 1281744 q^{91} - 488796 q^{92} - 1621224 q^{97} - 191706 q^{98}+O(q^{100}) $ 2 * q - 6 * q^2 - 414 * q^7 - 660 * q^8 + 2376 * q^11 - 3096 * q^13 - 1928 * q^16 + 6504 * q^17 - 7128 * q^22 + 10626 * q^23 + 18576 * q^26 - 19044 * q^28 + 50864 * q^31 + 48024 * q^32 - 41184 * q^37 + 30360 * q^38 + 38016 * q^41 - 160686 * q^43 - 63756 * q^46 + 32274 * q^47 + 142416 * q^52 - 311784 * q^53 + 273240 * q^56 + 53460 * q^58 + 356224 * q^61 - 152592 * q^62 + 480546 * q^67 + 299184 * q^68 + 1234656 * q^71 + 613224 * q^73 + 465520 * q^76 - 491832 * q^77 - 114048 * q^82 - 268194 * q^83 + 964116 * q^86 - 784080 * q^88 + 1281744 * q^91 - 488796 * q^92 - 1621224 * q^97 - 191706 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−3.00000	+	3.00000i	−0.375000	+	0.375000i	−0.869295	−	0.494295i	$-0.835426\pi$
$2$	−3.00000	+	3.00000i	−0.375000	+	0.375000i	0.494295	+	0.869295i	$0.335426\pi$
$3$		0			0
$3$		0			0
$4$			46.0000i			0.718750i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−207.000	+	207.000i	−0.603499	+	0.603499i	−0.941239	−	0.337741i	$-0.890337\pi$
$7$	−207.000	+	207.000i	−0.603499	+	0.603499i	0.337741	+	0.941239i	$0.390337\pi$
$8$	−330.000	−	330.000i	−0.644531	−	0.644531i
$9$		0			0
$10$		0			0
$11$	1188.00			0.892562			0.446281	−	0.894893i	$-0.352748\pi$
$11$	1188.00			0.892562			0.446281	+	0.894893i	$0.352748\pi$
$12$		0			0
$13$	−1548.00	−	1548.00i	−0.704597	−	0.704597i	0.260797	−	0.965394i	$-0.416015\pi$
$13$	−1548.00	−	1548.00i	−0.704597	−	0.704597i	−0.965394	+	0.260797i	$0.916015\pi$
$14$		−	1242.00i		−	0.452624i
$15$		0			0
$16$	−964.000			−0.235352
$17$	3252.00	−	3252.00i	0.661917	−	0.661917i	−0.293914	−	0.955832i	$-0.594958\pi$
$17$	3252.00	−	3252.00i	0.661917	−	0.661917i	0.955832	+	0.293914i	$0.0949581\pi$
$18$		0			0
$19$		−	5060.00i		−	0.737717i	−0.929486	−	0.368858i	$-0.879749\pi$
$19$		−	5060.00i		−	0.737717i	0.929486	−	0.368858i	$-0.120251\pi$
$20$		0			0
$21$		0			0
$22$	−3564.00	+	3564.00i	−0.334711	+	0.334711i
$23$	5313.00	+	5313.00i	0.436673	+	0.436673i	0.890891	−	0.454218i	$-0.150081\pi$
$23$	5313.00	+	5313.00i	0.436673	+	0.436673i	−0.454218	+	0.890891i	$0.650081\pi$
$24$		0			0
$25$		0			0
$26$	9288.00			0.528448
$27$		0			0
$28$	−9522.00	−	9522.00i	−0.433765	−	0.433765i
$29$		−	8910.00i		−	0.365329i	−0.983175	−	0.182664i	$-0.941528\pi$
$29$		−	8910.00i		−	0.365329i	0.983175	−	0.182664i	$-0.0584722\pi$
$30$		0			0
$31$	25432.0			0.853681			0.426840	−	0.904327i	$-0.359627\pi$
$31$	25432.0			0.853681			0.426840	+	0.904327i	$0.359627\pi$
$32$	24012.0	−	24012.0i	0.732788	−	0.732788i
$33$		0			0
$34$			19512.0i			0.496438i
$35$		0			0
$36$		0			0
$37$	−20592.0	+	20592.0i	−0.406531	+	0.406531i	−0.880527	−	0.473996i	$-0.842811\pi$
$37$	−20592.0	+	20592.0i	−0.406531	+	0.406531i	0.473996	+	0.880527i	$0.342811\pi$
$38$	15180.0	+	15180.0i	0.276644	+	0.276644i
$39$		0			0
$40$		0			0
$41$	19008.0			0.275794			0.137897	−	0.990447i	$-0.455966\pi$
$41$	19008.0			0.275794			0.137897	+	0.990447i	$0.455966\pi$
$42$		0			0
$43$	−80343.0	−	80343.0i	−1.01051	−	1.01051i	−0.999944	−	0.0105707i	$-0.996635\pi$
$43$	−80343.0	−	80343.0i	−1.01051	−	1.01051i	−0.0105707	−	0.999944i	$-0.503365\pi$
$44$			54648.0i			0.641529i
$45$		0			0
$46$	−31878.0			−0.327505
$47$	16137.0	−	16137.0i	0.155428	−	0.155428i	−0.625109	−	0.780537i	$-0.714946\pi$
$47$	16137.0	−	16137.0i	0.155428	−	0.155428i	0.780537	+	0.625109i	$0.214946\pi$
$48$		0			0
$49$			31951.0i			0.271579i
$50$		0			0
$51$		0			0
$52$	71208.0	−	71208.0i	0.506429	−	0.506429i
$53$	−155892.	−	155892.i	−1.04712	−	1.04712i	−0.998834	−	0.0482859i	$-0.984624\pi$
$53$	−155892.	−	155892.i	−1.04712	−	1.04712i	−0.0482859	−	0.998834i	$-0.515376\pi$
$54$		0			0
$55$		0			0
$56$	136620.			0.777947
$57$		0			0
$58$	26730.0	+	26730.0i	0.136998	+	0.136998i
$59$			360180.i			1.75373i	0.480734	+	0.876867i	$0.340370\pi$
$59$			360180.i			1.75373i	−0.480734	+	0.876867i	$0.659630\pi$
$60$		0			0
$61$	178112.			0.784700			0.392350	−	0.919816i	$-0.371662\pi$
$61$	178112.			0.784700			0.392350	+	0.919816i	$0.371662\pi$
$62$	−76296.0	+	76296.0i	−0.320130	+	0.320130i
$63$		0			0
$64$			82376.0i			0.314240i
$65$		0			0
$66$		0			0
$67$	240273.	−	240273.i	0.798878	−	0.798878i	−0.184040	−	0.982919i	$-0.558918\pi$
$67$	240273.	−	240273.i	0.798878	−	0.798878i	0.982919	+	0.184040i	$0.0589178\pi$
$68$	149592.	+	149592.i	0.475753	+	0.475753i
$69$		0			0
$70$		0			0
$71$	617328.			1.72481			0.862404	−	0.506220i	$-0.168958\pi$
$71$	617328.			1.72481			0.862404	+	0.506220i	$0.168958\pi$
$72$		0			0
$73$	306612.	+	306612.i	0.788171	+	0.788171i	0.981194	−	0.193023i	$-0.0618292\pi$
$73$	306612.	+	306612.i	0.788171	+	0.788171i	−0.193023	+	0.981194i	$0.561829\pi$
$74$		−	123552.i		−	0.304898i
$75$		0			0
$76$	232760.			0.530234
$77$	−245916.	+	245916.i	−0.538660	+	0.538660i
$78$		0			0
$79$			232760.i			0.472092i	0.971742	+	0.236046i	$0.0758517\pi$
$79$			232760.i			0.472092i	−0.971742	+	0.236046i	$0.924148\pi$
$80$		0			0
$81$		0			0
$82$	−57024.0	+	57024.0i	−0.103423	+	0.103423i
$83$	−134097.	−	134097.i	−0.234523	−	0.234523i	0.580055	−	0.814577i	$-0.303031\pi$
$83$	−134097.	−	134097.i	−0.234523	−	0.234523i	−0.814577	+	0.580055i	$0.803031\pi$
$84$		0			0
$85$		0			0
$86$	482058.			0.757886
$87$		0			0
$88$	−392040.	−	392040.i	−0.575284	−	0.575284i
$89$			270270.i			0.383379i	0.981456	+	0.191689i	$0.0613966\pi$
$89$			270270.i			0.383379i	−0.981456	+	0.191689i	$0.938603\pi$
$90$		0			0
$91$	640872.			0.850447
$92$	−244398.	+	244398.i	−0.313859	+	0.313859i
$93$		0			0
$94$			96822.0i			0.116571i
$95$		0			0
$96$		0			0
$97$	−810612.	+	810612.i	−0.888174	+	0.888174i	−0.994348	−	0.106174i	$-0.966140\pi$
$97$	−810612.	+	810612.i	−0.888174	+	0.888174i	0.106174	+	0.994348i	$0.466140\pi$
$98$	−95853.0	−	95853.0i	−0.101842	−	0.101842i
$99$		0			0
$100$		0			0
$101$	1.76240e6			1.71057			0.855283	−	0.518161i	$-0.173383\pi$
$101$	1.76240e6			1.71057			0.855283	+	0.518161i	$0.173383\pi$
$102$		0			0
$103$	938817.	+	938817.i	0.859151	+	0.859151i	0.991238	−	0.132088i	$-0.0421680\pi$
$103$	938817.	+	938817.i	0.859151	+	0.859151i	−0.132088	+	0.991238i	$0.542168\pi$
$104$			1.02168e6i			0.908270i
$105$		0			0
$106$	935352.			0.785340
$107$	1.52166e6	−	1.52166e6i	1.24213	−	1.24213i	0.283008	−	0.959118i	$-0.408668\pi$
$107$	1.52166e6	−	1.52166e6i	1.24213	−	1.24213i	0.959118	−	0.283008i	$-0.0913322\pi$
$108$		0			0
$109$			117920.i			0.0910559i	0.998963	+	0.0455279i	$0.0144970\pi$
$109$			117920.i			0.0910559i	−0.998963	+	0.0455279i	$0.985503\pi$
$110$		0			0
$111$		0			0
$112$	199548.	−	199548.i	0.142034	−	0.142034i
$113$	965448.	+	965448.i	0.669104	+	0.669104i	0.957509	−	0.288405i	$-0.0931248\pi$
$113$	965448.	+	965448.i	0.669104	+	0.669104i	−0.288405	+	0.957509i	$0.593125\pi$
$114$		0			0
$115$		0			0
$116$	409860.			0.262580
$117$		0			0
$118$	−1.08054e6	−	1.08054e6i	−0.657650	−	0.657650i
$119$			1.34633e6i			0.798932i
$120$		0			0
$121$	−360217.			−0.203333
$122$	−534336.	+	534336.i	−0.294263	+	0.294263i
$123$		0			0
$124$			1.16987e6i			0.613583i
$125$		0			0
$126$		0			0
$127$	−716247.	+	716247.i	−0.349665	+	0.349665i	−0.859985	−	0.510320i	$-0.829527\pi$
$127$	−716247.	+	716247.i	−0.349665	+	0.349665i	0.510320	+	0.859985i	$0.329527\pi$
$128$	1.28964e6	+	1.28964e6i	0.614948	+	0.614948i
$129$		0			0
$130$		0			0
$131$	963468.			0.428572			0.214286	−	0.976771i	$-0.431258\pi$
$131$	963468.			0.428572			0.214286	+	0.976771i	$0.431258\pi$
$132$		0			0
$133$	1.04742e6	+	1.04742e6i	0.445211	+	0.445211i
$134$			1.44164e6i			0.599159i
$135$		0			0
$136$	−2.14632e6			−0.853253
$137$	66792.0	−	66792.0i	0.0259754	−	0.0259754i	−0.694000	−	0.719975i	$-0.744153\pi$
$137$	66792.0	−	66792.0i	0.0259754	−	0.0259754i	0.719975	+	0.694000i	$0.244153\pi$
$138$		0			0
$139$			426580.i			0.158839i	0.996841	+	0.0794193i	$0.0253066\pi$
$139$			426580.i			0.158839i	−0.996841	+	0.0794193i	$0.974693\pi$
$140$		0			0
$141$		0			0
$142$	−1.85198e6	+	1.85198e6i	−0.646803	+	0.646803i
$143$	−1.83902e6	−	1.83902e6i	−0.628897	−	0.628897i
$144$		0			0
$145$		0			0
$146$	−1.83967e6			−0.591128
$147$		0			0
$148$	−947232.	−	947232.i	−0.292194	−	0.292194i
$149$		−	3.08880e6i		−	0.933751i	−0.884323	−	0.466875i	$-0.845380\pi$
$149$		−	3.08880e6i		−	0.933751i	0.884323	−	0.466875i	$-0.154620\pi$
$150$		0			0
$151$	3.91415e6			1.13686			0.568430	−	0.822732i	$-0.307551\pi$
$151$	3.91415e6			1.13686			0.568430	+	0.822732i	$0.307551\pi$
$152$	−1.66980e6	+	1.66980e6i	−0.475482	+	0.475482i
$153$		0			0
$154$		−	1.47550e6i		−	0.403995i
$155$		0			0
$156$		0			0
$157$	3.94337e6	−	3.94337e6i	1.01899	−	1.01899i	0.0191701	−	0.999816i	$-0.493898\pi$
$157$	3.94337e6	−	3.94337e6i	1.01899	−	1.01899i	0.999816	−	0.0191701i	$-0.00610240\pi$
$158$	−698280.	−	698280.i	−0.177035	−	0.177035i
$159$		0			0
$160$		0			0
$161$	−2.19958e6			−0.527063
$162$		0			0
$163$	−661023.	−	661023.i	−0.152635	−	0.152635i	0.626659	−	0.779294i	$-0.284422\pi$
$163$	−661023.	−	661023.i	−0.152635	−	0.152635i	−0.779294	+	0.626659i	$0.784422\pi$
$164$			874368.i			0.198227i
$165$		0			0
$166$	804582.			0.175892
$167$	1.71693e6	−	1.71693e6i	0.368640	−	0.368640i	−0.498341	−	0.866981i	$-0.666057\pi$
$167$	1.71693e6	−	1.71693e6i	0.368640	−	0.368640i	0.866981	+	0.498341i	$0.166057\pi$
$168$		0			0
$169$		−	34201.0i		−	0.00708563i
$170$		0			0
$171$		0			0
$172$	3.69578e6	−	3.69578e6i	0.726308	−	0.726308i
$173$	−3.90871e6	−	3.90871e6i	−0.754910	−	0.754910i	0.220481	−	0.975391i	$-0.429237\pi$
$173$	−3.90871e6	−	3.90871e6i	−0.754910	−	0.754910i	−0.975391	+	0.220481i	$0.929237\pi$
$174$		0			0
$175$		0			0
$176$	−1.14523e6			−0.210066
$177$		0			0
$178$	−810810.	−	810810.i	−0.143767	−	0.143767i
$179$		−	7.47846e6i		−	1.30393i	−0.758251	−	0.651963i	$-0.773946\pi$
$179$		−	7.47846e6i		−	1.30393i	0.758251	−	0.651963i	$-0.226054\pi$
$180$		0			0
$181$	−8.80042e6			−1.48412			−0.742058	−	0.670336i	$-0.766150\pi$
$181$	−8.80042e6			−1.48412			−0.742058	+	0.670336i	$0.766150\pi$
$182$	−1.92262e6	+	1.92262e6i	−0.318918	+	0.318918i
$183$		0			0
$184$		−	3.50658e6i		−	0.562899i
$185$		0			0
$186$		0			0
$187$	3.86338e6	−	3.86338e6i	0.590802	−	0.590802i
$188$	742302.	+	742302.i	0.111714	+	0.111714i
$189$		0			0
$190$		0			0
$191$	−5.68339e6			−0.815657			−0.407828	−	0.913059i	$-0.633714\pi$
$191$	−5.68339e6			−0.815657			−0.407828	+	0.913059i	$0.633714\pi$
$192$		0			0
$193$	1.25593e6	+	1.25593e6i	0.174701	+	0.174701i	0.789041	−	0.614341i	$-0.210578\pi$
$193$	1.25593e6	+	1.25593e6i	0.174701	+	0.174701i	−0.614341	+	0.789041i	$0.710578\pi$
$194$		−	4.86367e6i		−	0.666130i
$195$		0			0
$196$	−1.46975e6			−0.195197
$197$	−3.97319e6	+	3.97319e6i	−0.519685	+	0.519685i	−0.917476	−	0.397791i	$-0.869777\pi$
$197$	−3.97319e6	+	3.97319e6i	−0.519685	+	0.519685i	0.397791	+	0.917476i	$0.369777\pi$
$198$		0			0
$199$		−	7.74160e6i		−	0.982362i	−0.871058	−	0.491181i	$-0.836565\pi$
$199$		−	7.74160e6i		−	0.982362i	0.871058	−	0.491181i	$-0.163435\pi$
$200$		0			0
$201$		0			0
$202$	−5.28719e6	+	5.28719e6i	−0.641462	+	0.641462i
$203$	1.84437e6	+	1.84437e6i	0.220475	+	0.220475i
$204$		0			0
$205$		0			0
$206$	−5.63290e6			−0.644363
$207$		0			0
$208$	1.49227e6	+	1.49227e6i	0.165828	+	0.165828i
$209$		−	6.01128e6i		−	0.658458i
$210$		0			0
$211$	−5.05899e6			−0.538538			−0.269269	−	0.963065i	$-0.586782\pi$
$211$	−5.05899e6			−0.538538			−0.269269	+	0.963065i	$0.586782\pi$
$212$	7.17103e6	−	7.17103e6i	0.752617	−	0.752617i
$213$		0			0
$214$			9.12994e6i			0.931594i
$215$		0			0
$216$		0			0
$217$	−5.26442e6	+	5.26442e6i	−0.515195	+	0.515195i
$218$	−353760.	−	353760.i	−0.0341460	−	0.0341460i
$219$		0			0
$220$		0			0
$221$	−1.00682e7			−0.932770
$222$		0			0
$223$	−4.71111e6	−	4.71111e6i	−0.424824	−	0.424824i	0.462037	−	0.886861i	$-0.347119\pi$
$223$	−4.71111e6	−	4.71111e6i	−0.424824	−	0.424824i	−0.886861	+	0.462037i	$0.847119\pi$
$224$			9.94097e6i			0.884473i
$225$		0			0
$226$	−5.79269e6			−0.501828
$227$	497697.	−	497697.i	0.0425488	−	0.0425488i	−0.685512	−	0.728061i	$-0.740422\pi$
$227$	497697.	−	497697.i	0.0425488	−	0.0425488i	0.728061	+	0.685512i	$0.240422\pi$
$228$		0			0
$229$		−	8.23619e6i		−	0.685835i	−0.939365	−	0.342918i	$-0.888585\pi$
$229$		−	8.23619e6i		−	0.685835i	0.939365	−	0.342918i	$-0.111415\pi$
$230$		0			0
$231$		0			0
$232$	−2.94030e6	+	2.94030e6i	−0.235466	+	0.235466i
$233$	1.29896e7	+	1.29896e7i	1.02690	+	1.02690i	0.999628	+	0.0272739i	$0.00868262\pi$
$233$	1.29896e7	+	1.29896e7i	1.02690	+	1.02690i	0.0272739	+	0.999628i	$0.491317\pi$
$234$		0			0
$235$		0			0
$236$	−1.65683e7			−1.26050
$237$		0			0
$238$	−4.03898e6	−	4.03898e6i	−0.299600	−	0.299600i
$239$		−	3.93228e6i		−	0.288039i	−0.989575	−	0.144019i	$-0.953997\pi$
$239$		−	3.93228e6i		−	0.288039i	0.989575	−	0.144019i	$-0.0460027\pi$
$240$		0			0
$241$	1.16542e7			0.832590			0.416295	−	0.909230i	$-0.363328\pi$
$241$	1.16542e7			0.832590			0.416295	+	0.909230i	$0.363328\pi$
$242$	1.08065e6	−	1.08065e6i	0.0762499	−	0.0762499i
$243$		0			0
$244$			8.19315e6i			0.564003i
$245$		0			0
$246$		0			0
$247$	−7.83288e6	+	7.83288e6i	−0.519793	+	0.519793i
$248$	−8.39256e6	−	8.39256e6i	−0.550224	−	0.550224i
$249$		0			0
$250$		0			0
$251$	−3.69025e6			−0.233365			−0.116682	−	0.993169i	$-0.537226\pi$
$251$	−3.69025e6			−0.233365			−0.116682	+	0.993169i	$0.537226\pi$
$252$		0			0
$253$	6.31184e6	+	6.31184e6i	0.389758	+	0.389758i
$254$		−	4.29748e6i		−	0.262248i
$255$		0			0
$256$	−1.30099e7			−0.775451
$257$	7.78483e6	−	7.78483e6i	0.458617	−	0.458617i	−0.439585	−	0.898201i	$-0.644874\pi$
$257$	7.78483e6	−	7.78483e6i	0.458617	−	0.458617i	0.898201	+	0.439585i	$0.144874\pi$
$258$		0			0
$259$		−	8.52509e6i		−	0.490681i
$260$		0			0
$261$		0			0
$262$	−2.89040e6	+	2.89040e6i	−0.160714	+	0.160714i
$263$	1.46742e6	+	1.46742e6i	0.0806655	+	0.0806655i	0.746288	−	0.665623i	$-0.231834\pi$
$263$	1.46742e6	+	1.46742e6i	0.0806655	+	0.0806655i	−0.665623	+	0.746288i	$0.731834\pi$
$264$		0			0
$265$		0			0
$266$	−6.28452e6			−0.333908
$267$		0			0
$268$	1.10526e7	+	1.10526e7i	0.574194	+	0.574194i
$269$		−	1.96214e7i		−	1.00803i	−0.863695	−	0.504016i	$-0.831855\pi$
$269$		−	1.96214e7i		−	1.00803i	0.863695	−	0.504016i	$-0.168145\pi$
$270$		0			0
$271$	−9.20313e6			−0.462410			−0.231205	−	0.972905i	$-0.574267\pi$
$271$	−9.20313e6			−0.462410			−0.231205	+	0.972905i	$0.574267\pi$
$272$	−3.13493e6	+	3.13493e6i	−0.155783	+	0.155783i
$273$		0			0
$274$			400752.i			0.0194816i
$275$		0			0
$276$		0			0
$277$	2.06153e7	−	2.06153e7i	0.969954	−	0.969954i	−0.0296080	−	0.999562i	$-0.509426\pi$
$277$	2.06153e7	−	2.06153e7i	0.969954	−	0.969954i	0.999562	+	0.0296080i	$0.00942590\pi$
$278$	−1.27974e6	−	1.27974e6i	−0.0595645	−	0.0595645i
$279$		0			0
$280$		0			0
$281$	3.63956e7			1.64032			0.820162	−	0.572132i	$-0.193883\pi$
$281$	3.63956e7			1.64032			0.820162	+	0.572132i	$0.193883\pi$
$282$		0			0
$283$	−1.63095e6	−	1.63095e6i	−0.0719585	−	0.0719585i	0.670212	−	0.742170i	$-0.266203\pi$
$283$	−1.63095e6	−	1.63095e6i	−0.0719585	−	0.0719585i	−0.742170	+	0.670212i	$0.766203\pi$
$284$			2.83971e7i			1.23971i
$285$		0			0
$286$	1.10341e7			0.471672
$287$	−3.93466e6	+	3.93466e6i	−0.166441	+	0.166441i
$288$		0			0
$289$			2.98656e6i			0.123731i
$290$		0			0
$291$		0			0
$292$	−1.41042e7	+	1.41042e7i	−0.566498	+	0.566498i
$293$	1.31150e7	+	1.31150e7i	0.521392	+	0.521392i	0.917992	−	0.396600i	$-0.129810\pi$
$293$	1.31150e7	+	1.31150e7i	0.521392	+	0.521392i	−0.396600	+	0.917992i	$0.629810\pi$
$294$		0			0
$295$		0			0
$296$	1.35907e7			0.524043
$297$		0			0
$298$	9.26640e6	+	9.26640e6i	0.350157	+	0.350157i
$299$		−	1.64490e7i		−	0.615357i
$300$		0			0
$301$	3.32620e7			1.21969
$302$	−1.17425e7	+	1.17425e7i	−0.426322	+	0.426322i
$303$		0			0
$304$			4.87784e6i			0.173623i
$305$		0			0
$306$		0			0
$307$	6.04419e6	−	6.04419e6i	0.208893	−	0.208893i	−0.594904	−	0.803797i	$-0.702810\pi$
$307$	6.04419e6	−	6.04419e6i	0.208893	−	0.208893i	0.803797	+	0.594904i	$0.202810\pi$
$308$	−1.13121e7	−	1.13121e7i	−0.387162	−	0.387162i
$309$		0			0
$310$		0			0
$311$	2.97849e7			0.990181			0.495091	−	0.868841i	$-0.335135\pi$
$311$	2.97849e7			0.990181			0.495091	+	0.868841i	$0.335135\pi$
$312$		0			0
$313$	400752.	+	400752.i	0.0130690	+	0.0130690i	0.713611	−	0.700542i	$-0.247058\pi$
$313$	400752.	+	400752.i	0.0130690	+	0.0130690i	−0.700542	+	0.713611i	$0.747058\pi$
$314$			2.36602e7i			0.764240i
$315$		0			0
$316$	−1.07070e7			−0.339316
$317$	−4.06611e7	+	4.06611e7i	−1.27644	+	1.27644i	−0.333801	+	0.942644i	$0.608331\pi$
$317$	−4.06611e7	+	4.06611e7i	−1.27644	+	1.27644i	−0.942644	+	0.333801i	$0.891669\pi$
$318$		0			0
$319$		−	1.05851e7i		−	0.326078i
$320$		0			0
$321$		0			0
$322$	6.59875e6	−	6.59875e6i	0.197649	−	0.197649i
$323$	−1.64551e7	−	1.64551e7i	−0.488308	−	0.488308i
$324$		0			0
$325$		0			0
$326$	3.96614e6			0.114476
$327$		0			0
$328$	−6.27264e6	−	6.27264e6i	−0.177758	−	0.177758i
$329$			6.68072e6i			0.187601i
$330$		0			0
$331$	9.62073e6			0.265292			0.132646	−	0.991163i	$-0.457653\pi$
$331$	9.62073e6			0.265292			0.132646	+	0.991163i	$0.457653\pi$
$332$	6.16846e6	−	6.16846e6i	0.168563	−	0.168563i
$333$		0			0
$334$			1.03016e7i			0.276480i
$335$		0			0
$336$		0			0
$337$	2.14318e7	−	2.14318e7i	0.559976	−	0.559976i	−0.369325	−	0.929300i	$-0.620411\pi$
$337$	2.14318e7	−	2.14318e7i	0.559976	−	0.559976i	0.929300	+	0.369325i	$0.120411\pi$
$338$	102603.	+	102603.i	0.00265711	+	0.00265711i
$339$		0			0
$340$		0			0
$341$	3.02132e7			0.761963
$342$		0			0
$343$	−3.09672e7	−	3.09672e7i	−0.767396	−	0.767396i
$344$			5.30264e7i			1.30262i
$345$		0			0
$346$	2.34523e7			0.566183
$347$	5.13445e7	−	5.13445e7i	1.22887	−	1.22887i	0.264476	−	0.964392i	$-0.414801\pi$
$347$	5.13445e7	−	5.13445e7i	1.22887	−	1.22887i	0.964392	−	0.264476i	$-0.0851991\pi$
$348$		0			0
$349$			2.11304e7i			0.497087i	0.968621	+	0.248544i	$0.0799519\pi$
$349$			2.11304e7i			0.497087i	−0.968621	+	0.248544i	$0.920048\pi$
$350$		0			0
$351$		0			0
$352$	2.85263e7	−	2.85263e7i	0.654059	−	0.654059i
$353$	−2.69882e7	−	2.69882e7i	−0.613550	−	0.613550i	0.330320	−	0.943869i	$-0.392843\pi$
$353$	−2.69882e7	−	2.69882e7i	−0.613550	−	0.613550i	−0.943869	+	0.330320i	$0.892843\pi$
$354$		0			0
$355$		0			0
$356$	−1.24324e7			−0.275553
$357$		0			0
$358$	2.24354e7	+	2.24354e7i	0.488972	+	0.488972i
$359$		−	9.01692e6i		−	0.194883i	−0.995241	−	0.0974417i	$-0.968934\pi$
$359$		−	9.01692e6i		−	0.194883i	0.995241	−	0.0974417i	$-0.0310660\pi$
$360$		0			0
$361$	2.14423e7			0.455774
$362$	2.64013e7	−	2.64013e7i	0.556543	−	0.556543i
$363$		0			0
$364$			2.94801e7i			0.611259i
$365$		0			0
$366$		0			0
$367$	−4.10576e7	+	4.10576e7i	−0.830606	+	0.830606i	−0.987600	−	0.156994i	$-0.949820\pi$
$367$	−4.10576e7	+	4.10576e7i	−0.830606	+	0.830606i	0.156994	+	0.987600i	$0.449820\pi$
$368$	−5.12173e6	−	5.12173e6i	−0.102772	−	0.102772i
$369$		0			0
$370$		0			0
$371$	6.45393e7			1.26387
$372$		0			0
$373$	−9.56009e6	−	9.56009e6i	−0.184219	−	0.184219i	0.608972	−	0.793192i	$-0.291582\pi$
$373$	−9.56009e6	−	9.56009e6i	−0.184219	−	0.184219i	−0.793192	+	0.608972i	$0.791582\pi$
$374$			2.31803e7i			0.443102i
$375$		0			0
$376$	−1.06504e7			−0.200356
$377$	−1.37927e7	+	1.37927e7i	−0.257410	+	0.257410i
$378$		0			0
$379$			6.67649e7i			1.22639i	0.789930	+	0.613197i	$0.210117\pi$
$379$			6.67649e7i			1.22639i	−0.789930	+	0.613197i	$0.789883\pi$
$380$		0			0
$381$		0			0
$382$	1.70502e7	−	1.70502e7i	0.305871	−	0.305871i
$383$	6.61994e7	+	6.61994e7i	1.17830	+	1.17830i	0.980176	+	0.198128i	$0.0634862\pi$
$383$	6.61994e7	+	6.61994e7i	1.17830	+	1.17830i	0.198128	+	0.980176i	$0.436514\pi$
$384$		0			0
$385$		0			0
$386$	−7.53559e6			−0.131025
$387$		0			0
$388$	−3.72882e7	−	3.72882e7i	−0.638375	−	0.638375i
$389$			3.44779e7i			0.585723i	0.956155	+	0.292861i	$0.0946075\pi$
$389$			3.44779e7i			0.585723i	−0.956155	+	0.292861i	$0.905393\pi$
$390$		0			0
$391$	3.45558e7			0.578083
$392$	1.05438e7	−	1.05438e7i	0.175041	−	0.175041i
$393$		0			0
$394$		−	2.38391e7i		−	0.389764i
$395$		0			0
$396$		0			0
$397$	−4.03512e7	+	4.03512e7i	−0.644889	+	0.644889i	−0.951753	−	0.306864i	$-0.900720\pi$
$397$	−4.03512e7	+	4.03512e7i	−0.644889	+	0.644889i	0.306864	+	0.951753i	$0.400720\pi$
$398$	2.32248e7	+	2.32248e7i	0.368386	+	0.368386i
$399$		0			0
$400$		0			0
$401$	7.48541e7			1.16087			0.580433	−	0.814308i	$-0.302883\pi$
$401$	7.48541e7			1.16087			0.580433	+	0.814308i	$0.302883\pi$
$402$		0			0
$403$	−3.93687e7	−	3.93687e7i	−0.601501	−	0.601501i
$404$			8.10703e7i			1.22947i
$405$		0			0
$406$	−1.10662e7			−0.165356
$407$	−2.44633e7	+	2.44633e7i	−0.362854	+	0.362854i
$408$		0			0
$409$		−	1.30148e8i		−	1.90226i	−0.308795	−	0.951128i	$-0.599926\pi$
$409$		−	1.30148e8i		−	1.90226i	0.308795	−	0.951128i	$-0.400074\pi$
$410$		0			0
$411$		0			0
$412$	−4.31856e7	+	4.31856e7i	−0.617514	+	0.617514i
$413$	−7.45573e7	−	7.45573e7i	−1.05838	−	1.05838i
$414$		0			0
$415$		0			0
$416$	−7.43412e7			−1.03264
$417$		0			0
$418$	1.80338e7	+	1.80338e7i	0.246922	+	0.246922i
$419$		−	1.04966e8i		−	1.42694i	−0.700686	−	0.713470i	$-0.747123\pi$
$419$		−	1.04966e8i		−	1.42694i	0.700686	−	0.713470i	$-0.252877\pi$
$420$		0			0
$421$	−3.25297e7			−0.435947			−0.217974	−	0.975955i	$-0.569945\pi$
$421$	−3.25297e7			−0.435947			−0.217974	+	0.975955i	$0.569945\pi$
$422$	1.51770e7	−	1.51770e7i	0.201952	−	0.201952i
$423$		0			0
$424$			1.02889e8i			1.34980i
$425$		0			0
$426$		0			0
$427$	−3.68692e7	+	3.68692e7i	−0.473565	+	0.473565i
$428$	6.99962e7	+	6.99962e7i	0.892778	+	0.892778i
$429$		0			0
$430$		0			0
$431$	1.97042e7			0.246108			0.123054	−	0.992400i	$-0.460731\pi$
$431$	1.97042e7			0.246108			0.123054	+	0.992400i	$0.460731\pi$
$432$		0			0
$433$	7.02136e7	+	7.02136e7i	0.864883	+	0.864883i	0.991900	−	0.127017i	$-0.0405404\pi$
$433$	7.02136e7	+	7.02136e7i	0.864883	+	0.864883i	−0.127017	+	0.991900i	$0.540540\pi$
$434$		−	3.15865e7i		−	0.386396i
$435$		0			0
$436$	−5.42432e6			−0.0654464
$437$	2.68838e7	−	2.68838e7i	0.322141	−	0.322141i
$438$		0			0
$439$		−	1.09253e8i		−	1.29134i	−0.763616	−	0.645671i	$-0.776578\pi$
$439$		−	1.09253e8i		−	1.29134i	0.763616	−	0.645671i	$-0.223422\pi$
$440$		0			0
$441$		0			0
$442$	3.02046e7	−	3.02046e7i	0.349789	−	0.349789i
$443$	−2.07006e6	−	2.07006e6i	−0.0238106	−	0.0238106i	0.695101	−	0.718912i	$-0.255360\pi$
$443$	−2.07006e6	−	2.07006e6i	−0.0238106	−	0.0238106i	−0.718912	+	0.695101i	$0.755360\pi$
$444$		0			0
$445$		0			0
$446$	2.82667e7			0.318618
$447$		0			0
$448$	−1.70518e7	−	1.70518e7i	−0.189643	−	0.189643i
$449$		−	8.47044e7i		−	0.935765i	−0.883791	−	0.467883i	$-0.845017\pi$
$449$		−	8.47044e7i		−	0.935765i	0.883791	−	0.467883i	$-0.154983\pi$
$450$		0			0
$451$	2.25815e7			0.246163
$452$	−4.44106e7	+	4.44106e7i	−0.480918	+	0.480918i
$453$		0			0
$454$			2.98618e6i			0.0319116i
$455$		0			0
$456$		0			0
$457$	4.53668e7	−	4.53668e7i	0.475323	−	0.475323i	−0.428309	−	0.903632i	$-0.640890\pi$
$457$	4.53668e7	−	4.53668e7i	0.475323	−	0.475323i	0.903632	+	0.428309i	$0.140890\pi$
$458$	2.47086e7	+	2.47086e7i	0.257188	+	0.257188i
$459$		0			0
$460$		0			0
$461$	−8.63813e7			−0.881692			−0.440846	−	0.897583i	$-0.645321\pi$
$461$	−8.63813e7			−0.881692			−0.440846	+	0.897583i	$0.645321\pi$
$462$		0			0
$463$	9.36068e7	+	9.36068e7i	0.943114	+	0.943114i	0.998467	−	0.0553526i	$-0.0176283\pi$
$463$	9.36068e7	+	9.36068e7i	0.943114	+	0.943114i	−0.0553526	+	0.998467i	$0.517628\pi$
$464$			8.58924e6i			0.0859807i
$465$		0			0
$466$	−7.79378e7			−0.770176
$467$	2.65425e7	−	2.65425e7i	0.260610	−	0.260610i	−0.564692	−	0.825302i	$-0.691005\pi$
$467$	2.65425e7	−	2.65425e7i	0.260610	−	0.260610i	0.825302	+	0.564692i	$0.191005\pi$
$468$		0			0
$469$			9.94730e7i			0.964244i
$470$		0			0
$471$		0			0
$472$	1.18859e8	−	1.18859e8i	1.13034	−	1.13034i
$473$	−9.54475e7	−	9.54475e7i	−0.901947	−	0.901947i
$474$		0			0
$475$		0			0
$476$	−6.19311e7			−0.574233
$477$		0			0
$478$	1.17968e7	+	1.17968e7i	0.108014	+	0.108014i
$479$		−	6.72646e7i		−	0.612040i	−0.952025	−	0.306020i	$-0.901003\pi$
$479$		−	6.72646e7i		−	0.612040i	0.952025	−	0.306020i	$-0.0989974\pi$
$480$		0			0
$481$	6.37528e7			0.572881
$482$	−3.49626e7	+	3.49626e7i	−0.312221	+	0.312221i
$483$		0			0
$484$		−	1.65700e7i		−	0.146146i
$485$		0			0
$486$		0			0
$487$	−8.32276e7	+	8.32276e7i	−0.720577	+	0.720577i	−0.968723	−	0.248145i	$-0.920179\pi$
$487$	−8.32276e7	+	8.32276e7i	−0.720577	+	0.720577i	0.248145	+	0.968723i	$0.420179\pi$
$488$	−5.87770e7	−	5.87770e7i	−0.505764	−	0.505764i
$489$		0			0
$490$		0			0
$491$	−1.69895e8			−1.43528			−0.717638	−	0.696416i	$-0.754777\pi$
$491$	−1.69895e8			−1.43528			−0.717638	+	0.696416i	$0.754777\pi$
$492$		0			0
$493$	−2.89753e7	−	2.89753e7i	−0.241817	−	0.241817i
$494$		−	4.69973e7i		−	0.389845i
$495$		0			0
$496$	−2.45164e7			−0.200915
$497$	−1.27787e8	+	1.27787e8i	−1.04092	+	1.04092i
$498$		0			0
$499$		−	1.12386e8i		−	0.904500i	−0.891891	−	0.452250i	$-0.850621\pi$
$499$		−	1.12386e8i		−	0.904500i	0.891891	−	0.452250i	$-0.149379\pi$
$500$		0			0
$501$		0			0
$502$	1.10708e7	−	1.10708e7i	0.0875117	−	0.0875117i
$503$	8.49728e7	+	8.49728e7i	0.667692	+	0.667692i	0.957181	−	0.289490i	$-0.0934856\pi$
$503$	8.49728e7	+	8.49728e7i	0.667692	+	0.667692i	−0.289490	+	0.957181i	$0.593486\pi$
$504$		0			0
$505$		0			0
$506$	−3.78711e7			−0.292318
$507$		0			0
$508$	−3.29474e7	−	3.29474e7i	−0.251321	−	0.251321i
$509$		−	4.35675e7i		−	0.330376i	−0.986262	−	0.165188i	$-0.947177\pi$
$509$		−	4.35675e7i		−	0.330376i	0.986262	−	0.165188i	$-0.0528232\pi$
$510$		0			0
$511$	−1.26937e8			−0.951320
$512$	−4.35072e7	+	4.35072e7i	−0.324154	+	0.324154i
$513$		0			0
$514$			4.67090e7i			0.343963i
$515$		0			0
$516$		0			0
$517$	1.91708e7	−	1.91708e7i	0.138729	−	0.138729i
$518$	2.55753e7	+	2.55753e7i	0.184006	+	0.184006i
$519$		0			0
$520$		0			0
$521$	−1.06987e8			−0.756516			−0.378258	−	0.925700i	$-0.623477\pi$
$521$	−1.06987e8			−0.756516			−0.378258	+	0.925700i	$0.623477\pi$
$522$		0			0
$523$	9.22477e7	+	9.22477e7i	0.644838	+	0.644838i	0.951741	−	0.306903i	$-0.0992927\pi$
$523$	9.22477e7	+	9.22477e7i	0.644838	+	0.644838i	−0.306903	+	0.951741i	$0.599293\pi$
$524$			4.43195e7i			0.308036i
$525$		0			0
$526$	−8.80454e6			−0.0604992
$527$	8.27049e7	−	8.27049e7i	0.565066	−	0.565066i
$528$		0			0
$529$		−	9.15800e7i		−	0.618633i
$530$		0			0
$531$		0			0
$532$	−4.81813e7	+	4.81813e7i	−0.319995	+	0.319995i
$533$	−2.94244e7	−	2.94244e7i	−0.194324	−	0.194324i
$534$		0			0
$535$		0			0
$536$	−1.58580e8			−1.02980
$537$		0			0
$538$	5.88643e7	+	5.88643e7i	0.378012	+	0.378012i
$539$			3.79578e7i			0.242401i
$540$		0			0
$541$	−2.44414e8			−1.54360			−0.771800	−	0.635865i	$-0.780643\pi$
$541$	−2.44414e8			−1.54360			−0.771800	+	0.635865i	$0.780643\pi$
$542$	2.76094e7	−	2.76094e7i	0.173404	−	0.173404i
$543$		0			0
$544$		−	1.56174e8i		−	0.970090i
$545$		0			0
$546$		0			0
$547$	−3.23171e7	+	3.23171e7i	−0.197456	+	0.197456i	−0.798909	−	0.601452i	$-0.794589\pi$
$547$	−3.23171e7	+	3.23171e7i	−0.197456	+	0.197456i	0.601452	+	0.798909i	$0.294589\pi$
$548$	3.07243e6	+	3.07243e6i	0.0186698	+	0.0186698i
$549$		0			0
$550$		0			0
$551$	−4.50846e7			−0.269509
$552$		0			0
$553$	−4.81813e7	−	4.81813e7i	−0.284907	−	0.284907i
$554$			1.23692e8i			0.727465i
$555$		0			0
$556$	−1.96227e7			−0.114165
$557$	−5.41757e6	+	5.41757e6i	−0.0313501	+	0.0313501i	−0.722608	−	0.691258i	$-0.757057\pi$
$557$	−5.41757e6	+	5.41757e6i	−0.0313501	+	0.0313501i	0.691258	+	0.722608i	$0.257057\pi$
$558$		0			0
$559$			2.48742e8i			1.42401i
$560$		0			0
$561$		0			0
$562$	−1.09187e8	+	1.09187e8i	−0.615121	+	0.615121i
$563$	3.71439e7	+	3.71439e7i	0.208143	+	0.208143i	0.803478	−	0.595335i	$-0.202981\pi$
$563$	3.71439e7	+	3.71439e7i	0.208143	+	0.208143i	−0.595335	+	0.803478i	$0.702981\pi$
$564$		0			0
$565$		0			0
$566$	9.78572e6			0.0539689
$567$		0			0
$568$	−2.03718e8	−	2.03718e8i	−1.11169	−	1.11169i
$569$		−	2.17499e8i		−	1.18065i	−0.807166	−	0.590324i	$-0.799000\pi$
$569$		−	2.17499e8i		−	1.18065i	0.807166	−	0.590324i	$-0.201000\pi$
$570$		0			0
$571$	1.55107e8			0.833151			0.416575	−	0.909101i	$-0.363230\pi$
$571$	1.55107e8			0.833151			0.416575	+	0.909101i	$0.363230\pi$
$572$	8.45951e7	−	8.45951e7i	0.452019	−	0.452019i
$573$		0			0
$574$		−	2.36079e7i		−	0.124831i
$575$		0			0
$576$		0			0
$577$	2.22401e8	−	2.22401e8i	1.15773	−	1.15773i	0.172772	−	0.984962i	$-0.444728\pi$
$577$	2.22401e8	−	2.22401e8i	1.15773	−	1.15773i	0.984962	−	0.172772i	$-0.0552724\pi$
$578$	−8.95968e6	−	8.95968e6i	−0.0463991	−	0.0463991i
$579$		0			0
$580$		0			0
$581$	5.55162e7			0.283068
$582$		0			0
$583$	−1.85200e8	−	1.85200e8i	−0.934619	−	0.934619i
$584$		−	2.02364e8i		−	1.01600i
$585$		0			0
$586$	−7.86898e7			−0.391044
$587$	1.72770e8	−	1.72770e8i	0.854188	−	0.854188i	−0.136458	−	0.990646i	$-0.543572\pi$
$587$	1.72770e8	−	1.72770e8i	0.854188	−	0.854188i	0.990646	+	0.136458i	$0.0435718\pi$
$588$		0			0
$589$		−	1.28686e8i		−	0.629775i
$590$		0			0
$591$		0			0
$592$	1.98507e7	−	1.98507e7i	0.0956776	−	0.0956776i
$593$	6.50582e7	+	6.50582e7i	0.311988	+	0.311988i	0.845679	−	0.533691i	$-0.179196\pi$
$593$	6.50582e7	+	6.50582e7i	0.311988	+	0.311988i	−0.533691	+	0.845679i	$0.679196\pi$
$594$		0			0
$595$		0			0
$596$	1.42085e8			0.671133
$597$		0			0
$598$	4.93471e7	+	4.93471e7i	0.230759	+	0.230759i
$599$		−	8.19720e6i		−	0.0381404i	−0.999818	−	0.0190702i	$-0.993929\pi$
$599$		−	8.19720e6i		−	0.0381404i	0.999818	−	0.0190702i	$-0.00607060\pi$
$600$		0			0
$601$	1.71402e8			0.789575			0.394787	−	0.918772i	$-0.370818\pi$
$601$	1.71402e8			0.789575			0.394787	+	0.918772i	$0.370818\pi$
$602$	−9.97860e7	+	9.97860e7i	−0.457383	+	0.457383i
$603$		0			0
$604$			1.80051e8i			0.817118i
$605$		0			0
$606$		0			0
$607$	−1.24642e8	+	1.24642e8i	−0.557310	+	0.557310i	−0.928541	−	0.371230i	$-0.878936\pi$
$607$	−1.24642e8	+	1.24642e8i	−0.557310	+	0.557310i	0.371230	+	0.928541i	$0.378936\pi$
$608$	−1.21501e8	−	1.21501e8i	−0.540590	−	0.540590i
$609$		0			0
$610$		0			0
$611$	−4.99602e7			−0.219028
$612$		0			0
$613$	3.56605e6	+	3.56605e6i	0.0154813	+	0.0154813i	0.714805	−	0.699324i	$-0.246515\pi$
$613$	3.56605e6	+	3.56605e6i	0.0154813	+	0.0154813i	−0.699324	+	0.714805i	$0.746515\pi$
$614$			3.62652e7i			0.156670i
$615$		0			0
$616$	1.62305e8			0.694366
$617$	1.92655e8	−	1.92655e8i	0.820211	−	0.820211i	−0.165927	−	0.986138i	$-0.553062\pi$
$617$	1.92655e8	−	1.92655e8i	0.820211	−	0.820211i	0.986138	+	0.165927i	$0.0530615\pi$
$618$		0			0
$619$		−	1.66125e8i		−	0.700427i	−0.936670	−	0.350213i	$-0.886109\pi$
$619$		−	1.66125e8i		−	0.700427i	0.936670	−	0.350213i	$-0.113891\pi$
$620$		0			0
$621$		0			0
$622$	−8.93547e7	+	8.93547e7i	−0.371318	+	0.371318i
$623$	−5.59459e7	−	5.59459e7i	−0.231368	−	0.231368i
$624$		0			0
$625$		0			0
$626$	−2.40451e6			−0.00980176
$627$		0			0
$628$	1.81395e8	+	1.81395e8i	0.732396	+	0.732396i
$629$			1.33930e8i			0.538179i
$630$		0			0
$631$	−2.32977e8			−0.927310			−0.463655	−	0.886016i	$-0.653462\pi$
$631$	−2.32977e8			−0.927310			−0.463655	+	0.886016i	$0.653462\pi$
$632$	7.68108e7	−	7.68108e7i	0.304278	−	0.304278i
$633$		0			0
$634$		−	2.43967e8i		−	0.957333i
$635$		0			0
$636$		0			0
$637$	4.94601e7	−	4.94601e7i	0.191354	−	0.191354i
$638$	3.17552e7	+	3.17552e7i	0.122279	+	0.122279i
$639$		0			0
$640$		0			0
$641$	1.98771e8			0.754710			0.377355	−	0.926069i	$-0.376834\pi$
$641$	1.98771e8			0.754710			0.377355	+	0.926069i	$0.376834\pi$
$642$		0			0
$643$	−3.10831e8	−	3.10831e8i	−1.16921	−	1.16921i	−0.982396	−	0.186811i	$-0.940185\pi$
$643$	−3.10831e8	−	3.10831e8i	−1.16921	−	1.16921i	−0.186811	−	0.982396i	$-0.559815\pi$
$644$		−	1.01181e8i		−	0.378827i
$645$		0			0
$646$	9.87307e7			0.366231
$647$	−1.85002e8	+	1.85002e8i	−0.683066	+	0.683066i	−0.960690	−	0.277624i	$-0.910453\pi$
$647$	−1.85002e8	+	1.85002e8i	−0.683066	+	0.683066i	0.277624	+	0.960690i	$0.410453\pi$
$648$		0			0
$649$			4.27894e8i			1.56532i
$650$		0			0
$651$		0			0
$652$	3.04071e7	−	3.04071e7i	0.109706	−	0.109706i
$653$	5.38585e7	+	5.38585e7i	0.193426	+	0.193426i	0.797175	−	0.603749i	$-0.206327\pi$
$653$	5.38585e7	+	5.38585e7i	0.193426	+	0.193426i	−0.603749	+	0.797175i	$0.706327\pi$
$654$		0			0
$655$		0			0
$656$	−1.83237e7			−0.0649086
$657$		0			0
$658$	−2.00422e7	−	2.00422e7i	−0.0703504	−	0.0703504i
$659$			1.24841e8i			0.436215i	0.975925	+	0.218108i	$0.0699884\pi$
$659$			1.24841e8i			0.436215i	−0.975925	+	0.218108i	$0.930012\pi$
$660$		0			0
$661$	2.46400e8			0.853170			0.426585	−	0.904447i	$-0.359716\pi$
$661$	2.46400e8			0.853170			0.426585	+	0.904447i	$0.359716\pi$
$662$	−2.88622e7	+	2.88622e7i	−0.0994845	+	0.0994845i
$663$		0			0
$664$			8.85040e7i			0.302314i
$665$		0			0
$666$		0			0
$667$	4.73388e7	−	4.73388e7i	0.159529	−	0.159529i
$668$	7.89786e7	+	7.89786e7i	0.264960	+	0.264960i
$669$		0			0
$670$		0			0
$671$	2.11597e8			0.700393
$672$		0			0
$673$	3.32338e8	+	3.32338e8i	1.09027	+	1.09027i	0.995499	+	0.0947737i	$0.0302128\pi$
$673$	3.32338e8	+	3.32338e8i	1.09027	+	1.09027i	0.0947737	+	0.995499i	$0.469787\pi$
$674$			1.28591e8i			0.419982i
$675$		0			0
$676$	1.57325e6			0.00509280
$677$	−3.92435e8	+	3.92435e8i	−1.26474	+	1.26474i	−0.315973	+	0.948768i	$0.602331\pi$
$677$	−3.92435e8	+	3.92435e8i	−1.26474	+	1.26474i	−0.948768	+	0.315973i	$0.897669\pi$
$678$		0			0
$679$		−	3.35593e8i		−	1.07202i
$680$		0			0
$681$		0			0
$682$	−9.06396e7	+	9.06396e7i	−0.285736	+	0.285736i
$683$	−8.00187e7	−	8.00187e7i	−0.251148	−	0.251148i	0.570293	−	0.821441i	$-0.306830\pi$
$683$	−8.00187e7	−	8.00187e7i	−0.251148	−	0.251148i	−0.821441	+	0.570293i	$0.806830\pi$
$684$		0			0
$685$		0			0
$686$	1.85803e8			0.575547
$687$		0			0
$688$	7.74507e7	+	7.74507e7i	0.237826	+	0.237826i
$689$			4.82642e8i			1.47559i
$690$		0			0
$691$	1.24099e8			0.376126			0.188063	−	0.982157i	$-0.439779\pi$
$691$	1.24099e8			0.376126			0.188063	+	0.982157i	$0.439779\pi$
$692$	1.79801e8	−	1.79801e8i	0.542592	−	0.542592i
$693$		0			0
$694$			3.08067e8i			0.921651i
$695$		0			0
$696$		0			0
$697$	6.18140e7	−	6.18140e7i	0.182553	−	0.182553i
$698$	−6.33914e7	−	6.33914e7i	−0.186408	−	0.186408i
$699$		0			0
$700$		0			0
$701$	6.65394e8			1.93163			0.965817	−	0.259225i	$-0.0834670\pi$
$701$	6.65394e8			1.93163			0.965817	+	0.259225i	$0.0834670\pi$
$702$		0			0
$703$	1.04196e8	+	1.04196e8i	0.299905	+	0.299905i
$704$			9.78627e7i			0.280478i
$705$		0			0
$706$	1.61929e8			0.460162
$707$	−3.64816e8	+	3.64816e8i	−1.03232	+	1.03232i
$708$		0			0
$709$			4.10060e8i			1.15056i	0.817957	+	0.575279i	$0.195107\pi$
$709$			4.10060e8i			1.15056i	−0.817957	+	0.575279i	$0.804893\pi$
$710$		0			0
$711$		0			0
$712$	8.91891e7	−	8.91891e7i	0.247099	−	0.247099i
$713$	1.35120e8	+	1.35120e8i	0.372779	+	0.372779i
$714$		0			0
$715$		0			0
$716$	3.44009e8			0.937197
$717$		0			0
$718$	2.70508e7	+	2.70508e7i	0.0730813	+	0.0730813i
$719$			3.16685e8i			0.852003i	0.904722	+	0.426001i	$0.140078\pi$
$719$			3.16685e8i			0.852003i	−0.904722	+	0.426001i	$0.859922\pi$
$720$		0			0
$721$	−3.88670e8			−1.03699
$722$	−6.43268e7	+	6.43268e7i	−0.170915	+	0.170915i
$723$		0			0
$724$		−	4.04819e8i		−	1.06671i
$725$		0			0
$726$		0			0
$727$	4.32150e8	−	4.32150e8i	1.12468	−	1.12468i	0.133657	−	0.991028i	$-0.457328\pi$
$727$	4.32150e8	−	4.32150e8i	1.12468	−	1.12468i	0.991028	−	0.133657i	$-0.0426721\pi$
$728$	−2.11488e8	−	2.11488e8i	−0.548140	−	0.548140i
$729$		0			0
$730$		0			0
$731$	−5.22551e8			−1.33775
$732$		0			0
$733$	1.76123e8	+	1.76123e8i	0.447202	+	0.447202i	0.894423	−	0.447221i	$-0.147586\pi$
$733$	1.76123e8	+	1.76123e8i	0.447202	+	0.447202i	−0.447221	+	0.894423i	$0.647586\pi$
$734$		−	2.46345e8i		−	0.622955i
$735$		0			0
$736$	2.55152e8			0.639977
$737$	2.85444e8	−	2.85444e8i	0.713048	−	0.713048i
$738$		0			0
$739$			6.86279e8i			1.70046i	0.526409	+	0.850232i	$0.323538\pi$
$739$			6.86279e8i			1.70046i	−0.526409	+	0.850232i	$0.676462\pi$
$740$		0			0
$741$		0			0
$742$	−1.93618e8	+	1.93618e8i	−0.473951	+	0.473951i
$743$	1.85043e8	+	1.85043e8i	0.451136	+	0.451136i	0.895731	−	0.444596i	$-0.146653\pi$
$743$	1.85043e8	+	1.85043e8i	0.451136	+	0.451136i	−0.444596	+	0.895731i	$0.646653\pi$
$744$		0			0
$745$		0			0
$746$	5.73605e7			0.138165
$747$		0			0
$748$	1.77715e8	+	1.77715e8i	0.424639	+	0.424639i
$749$			6.29966e8i			1.49924i
$750$		0			0
$751$	1.85169e8			0.437168			0.218584	−	0.975818i	$-0.429856\pi$
$751$	1.85169e8			0.437168			0.218584	+	0.975818i	$0.429856\pi$
$752$	−1.55561e7	+	1.55561e7i	−0.0365802	+	0.0365802i
$753$		0			0
$754$		−	8.27561e7i		−	0.193057i
$755$		0			0
$756$		0			0
$757$	−1.39488e8	+	1.39488e8i	−0.321550	+	0.321550i	−0.849362	−	0.527811i	$-0.823013\pi$
$757$	−1.39488e8	+	1.39488e8i	−0.321550	+	0.321550i	0.527811	+	0.849362i	$0.323013\pi$
$758$	−2.00295e8	−	2.00295e8i	−0.459898	−	0.459898i
$759$		0			0
$760$		0			0
$761$	3.92794e7			0.0891274			0.0445637	−	0.999007i	$-0.485810\pi$
$761$	3.92794e7			0.0891274			0.0445637	+	0.999007i	$0.485810\pi$
$762$		0			0
$763$	−2.44094e7	−	2.44094e7i	−0.0549521	−	0.0549521i
$764$		−	2.61436e8i		−	0.586253i
$765$		0			0
$766$	−3.97196e8			−0.883728
$767$	5.57559e8	−	5.57559e8i	1.23568	−	1.23568i
$768$		0			0
$769$		−	4.31054e8i		−	0.947878i	−0.880558	−	0.473939i	$-0.842832\pi$
$769$		−	4.31054e8i		−	0.947878i	0.880558	−	0.473939i	$-0.157168\pi$
$770$		0			0
$771$		0			0
$772$	−5.77729e7	+	5.77729e7i	−0.125566	+	0.125566i
$773$	5.53092e7	+	5.53092e7i	0.119745	+	0.119745i	0.764440	−	0.644695i	$-0.223016\pi$
$773$	5.53092e7	+	5.53092e7i	0.119745	+	0.119745i	−0.644695	+	0.764440i	$0.723016\pi$
$774$		0			0
$775$		0			0
$776$	5.35004e8			1.14491
$777$		0			0
$778$	−1.03434e8	−	1.03434e8i	−0.219646	−	0.219646i
$779$		−	9.61805e7i		−	0.203458i
$780$		0			0
$781$	7.33386e8			1.53950
$782$	−1.03667e8	+	1.03667e8i	−0.216781	+	0.216781i
$783$		0			0
$784$		−	3.08008e7i		−	0.0639165i
$785$		0			0
$786$		0			0
$787$	−2.33171e8	+	2.33171e8i	−0.478355	+	0.478355i	−0.904605	−	0.426250i	$-0.859834\pi$
$787$	−2.33171e8	+	2.33171e8i	−0.478355	+	0.478355i	0.426250	+	0.904605i	$0.359834\pi$
$788$	−1.82767e8	−	1.82767e8i	−0.373524	−	0.373524i
$789$		0			0
$790$		0			0
$791$	−3.99695e8			−0.807606
$792$		0			0
$793$	−2.75717e8	−	2.75717e8i	−0.552897	−	0.552897i
$794$		−	2.42107e8i		−	0.483667i
$795$		0			0
$796$	3.56114e8			0.706073
$797$	−5.73297e8	+	5.73297e8i	−1.13241	+	1.13241i	−0.142638	+	0.989775i	$0.545558\pi$
$797$	−5.73297e8	+	5.73297e8i	−1.13241	+	1.13241i	−0.989775	+	0.142638i	$0.954442\pi$
$798$		0			0
$799$		−	1.04955e8i		−	0.205761i
$800$		0			0
$801$		0			0
$802$	−2.24562e8	+	2.24562e8i	−0.435325	+	0.435325i
$803$	3.64255e8	+	3.64255e8i	0.703492	+	0.703492i
$804$		0			0
$805$		0			0
$806$	2.36212e8			0.451126
$807$		0			0
$808$	−5.81591e8	−	5.81591e8i	−1.10251	−	1.10251i
$809$			3.03739e8i			0.573660i	0.957981	+	0.286830i	$0.0926016\pi$
$809$			3.03739e8i			0.573660i	−0.957981	+	0.286830i	$0.907398\pi$
$810$		0			0
$811$	−7.53778e8			−1.41313			−0.706563	−	0.707650i	$-0.749755\pi$
$811$	−7.53778e8			−1.41313			−0.706563	+	0.707650i	$0.749755\pi$
$812$	−8.48410e7	+	8.48410e7i	−0.158467	+	0.158467i
$813$		0			0
$814$		−	1.46780e8i		−	0.272140i
$815$		0			0
$816$		0			0
$817$	−4.06536e8	+	4.06536e8i	−0.745474	+	0.745474i
$818$	3.90445e8	+	3.90445e8i	0.713346	+	0.713346i
$819$		0			0
$820$		0			0
$821$	−1.61977e8			−0.292700			−0.146350	−	0.989233i	$-0.546753\pi$
$821$	−1.61977e8			−0.292700			−0.146350	+	0.989233i	$0.546753\pi$
$822$		0			0
$823$	3.26681e8	+	3.26681e8i	0.586037	+	0.586037i	0.936556	−	0.350519i	$-0.113995\pi$
$823$	3.26681e8	+	3.26681e8i	0.586037	+	0.586037i	−0.350519	+	0.936556i	$0.613995\pi$
$824$		−	6.19619e8i		−	1.10750i
$825$		0			0
$826$	4.47344e8			0.793782
$827$	4.04807e8	−	4.04807e8i	0.715700	−	0.715700i	−0.252021	−	0.967722i	$-0.581095\pi$
$827$	4.04807e8	−	4.04807e8i	0.715700	−	0.715700i	0.967722	+	0.252021i	$0.0810954\pi$
$828$		0			0
$829$			8.57650e8i			1.50538i	0.658375	+	0.752690i	$0.271244\pi$
$829$			8.57650e8i			1.50538i	−0.658375	+	0.752690i	$0.728756\pi$
$830$		0			0
$831$		0			0
$832$	1.27518e8	−	1.27518e8i	0.221412	−	0.221412i
$833$	1.03905e8	+	1.03905e8i	0.179763	+	0.179763i
$834$		0			0
$835$		0			0
$836$	2.76519e8			0.473267
$837$		0			0
$838$	3.14897e8	+	3.14897e8i	0.535102	+	0.535102i
$839$		−	3.20361e8i		−	0.542443i	−0.962517	−	0.271222i	$-0.912572\pi$
$839$		−	3.20361e8i		−	0.542443i	0.962517	−	0.271222i	$-0.0874277\pi$
$840$		0			0
$841$	5.15435e8			0.866535
$842$	9.75892e7	−	9.75892e7i	0.163480	−	0.163480i
$843$		0			0
$844$		−	2.32713e8i		−	0.387074i
$845$		0			0
$846$		0			0
$847$	7.45649e7	−	7.45649e7i	0.122711	−	0.122711i
$848$	1.50280e8	+	1.50280e8i	0.246441	+	0.246441i
$849$		0			0
$850$		0			0
$851$	−2.18811e8			−0.355042
$852$		0			0
$853$	−3.88384e8	−	3.88384e8i	−0.625770	−	0.625770i	0.321231	−	0.947001i	$-0.395903\pi$
$853$	−3.88384e8	−	3.88384e8i	−0.625770	−	0.625770i	−0.947001	+	0.321231i	$0.895903\pi$
$854$		−	2.21215e8i		−	0.355174i
$855$		0			0
$856$	−1.00429e9			−1.60118
$857$	5.62507e8	−	5.62507e8i	0.893687	−	0.893687i	−0.101181	−	0.994868i	$-0.532262\pi$
$857$	5.62507e8	−	5.62507e8i	0.893687	−	0.893687i	0.994868	+	0.101181i	$0.0322621\pi$
$858$		0			0
$859$		−	8.47273e8i		−	1.33673i	−0.743834	−	0.668365i	$-0.766994\pi$
$859$		−	8.47273e8i		−	1.33673i	0.743834	−	0.668365i	$-0.233006\pi$
$860$		0			0
$861$		0			0
$862$	−5.91125e7	+	5.91125e7i	−0.0922906	+	0.0922906i
$863$	−7.79332e8	−	7.79332e8i	−1.21252	−	1.21252i	−0.970194	−	0.242329i	$-0.922089\pi$
$863$	−7.79332e8	−	7.79332e8i	−1.21252	−	1.21252i	−0.242329	−	0.970194i	$-0.577911\pi$
$864$		0			0
$865$		0			0
$866$	−4.21281e8			−0.648662
$867$		0			0
$868$	−2.42164e8	−	2.42164e8i	−0.370296	−	0.370296i
$869$			2.76519e8i			0.421372i
$870$		0			0
$871$	−7.43885e8			−1.12577
$872$	3.89136e7	−	3.89136e7i	0.0586884	−	0.0586884i
$873$		0			0
$874$			1.61303e8i			0.241606i
$875$		0			0
$876$		0			0
$877$	7.41247e8	−	7.41247e8i	1.09892	−	1.09892i	0.104378	−	0.994538i	$-0.466715\pi$
$877$	7.41247e8	−	7.41247e8i	1.09892	−	1.09892i	0.994538	−	0.104378i	$-0.0332851\pi$
$878$	3.27760e8	+	3.27760e8i	0.484253	+	0.484253i
$879$		0			0
$880$		0			0
$881$	−3.83908e8			−0.561435			−0.280717	−	0.959790i	$-0.590572\pi$
$881$	−3.83908e8			−0.561435			−0.280717	+	0.959790i	$0.590572\pi$
$882$		0			0
$883$	−5.05244e7	−	5.05244e7i	−0.0733869	−	0.0733869i	0.669461	−	0.742848i	$-0.266525\pi$
$883$	−5.05244e7	−	5.05244e7i	−0.0733869	−	0.0733869i	−0.742848	+	0.669461i	$0.766525\pi$
$884$		−	4.63137e8i		−	0.670429i
$885$		0			0
$886$	1.24203e7			0.0178580
$887$	1.31857e8	−	1.31857e8i	0.188944	−	0.188944i	−0.606296	−	0.795239i	$-0.707345\pi$
$887$	1.31857e8	−	1.31857e8i	0.188944	−	0.188944i	0.795239	+	0.606296i	$0.207345\pi$
$888$		0			0
$889$		−	2.96526e8i		−	0.422044i
$890$		0			0
$891$		0			0
$892$	2.16711e8	−	2.16711e8i	0.305342	−	0.305342i
$893$	−8.16532e7	−	8.16532e7i	−0.114662	−	0.114662i
$894$		0			0
$895$		0			0
$896$	−5.33911e8			−0.742241
$897$		0			0
$898$	2.54113e8	+	2.54113e8i	0.350912	+	0.350912i
$899$		−	2.26599e8i		−	0.311874i
$900$		0			0
$901$	−1.01392e9			−1.38621
$902$	−6.77445e7	+	6.77445e7i	−0.0923112	+	0.0923112i
$903$		0			0
$904$		−	6.37196e8i		−	0.862517i
$905$		0			0
$906$		0			0
$907$	−7.39820e7	+	7.39820e7i	−0.0991526	+	0.0991526i	−0.754943	−	0.655790i	$-0.772336\pi$
$907$	−7.39820e7	+	7.39820e7i	−0.0991526	+	0.0991526i	0.655790	+	0.754943i	$0.272336\pi$
$908$	2.28941e7	+	2.28941e7i	0.0305820	+	0.0305820i
$909$		0			0
$910$		0			0
$911$	−5.22927e8			−0.691649			−0.345824	−	0.938299i	$-0.612401\pi$
$911$	−5.22927e8			−0.691649			−0.345824	+	0.938299i	$0.612401\pi$
$912$		0			0
$913$	−1.59307e8	−	1.59307e8i	−0.209326	−	0.209326i
$914$			2.72201e8i			0.356493i
$915$		0			0
$916$	3.78865e8			0.492944
$917$	−1.99438e8	+	1.99438e8i	−0.258642	+	0.258642i
$918$		0			0
$919$			8.71858e8i			1.12331i	0.827372	+	0.561655i	$0.189835\pi$
$919$			8.71858e8i			1.12331i	−0.827372	+	0.561655i	$0.810165\pi$
$920$		0			0
$921$		0			0
$922$	2.59144e8	−	2.59144e8i	0.330634	−	0.330634i
$923$	−9.55624e8	−	9.55624e8i	−1.21530	−	1.21530i
$924$		0			0
$925$		0			0
$926$	−5.61641e8			−0.707336
$927$		0			0
$928$	−2.13947e8	−	2.13947e8i	−0.267708	−	0.267708i
$929$			3.45641e8i			0.431100i	0.976493	+	0.215550i	$0.0691544\pi$
$929$			3.45641e8i			0.431100i	−0.976493	+	0.215550i	$0.930846\pi$
$930$		0			0
$931$	1.61672e8			0.200348
$932$	−5.97523e8	+	5.97523e8i	−0.738086	+	0.738086i
$933$		0			0
$934$			1.59255e8i			0.195458i
$935$		0			0
$936$		0			0
$937$	−4.65552e8	+	4.65552e8i	−0.565913	+	0.565913i	−0.930981	−	0.365068i	$-0.881046\pi$
$937$	−4.65552e8	+	4.65552e8i	−0.565913	+	0.565913i	0.365068	+	0.930981i	$0.381046\pi$
$938$	−2.98419e8	−	2.98419e8i	−0.361591	−	0.361591i
$939$		0			0
$940$		0			0
$941$	−1.13629e9			−1.36370			−0.681851	−	0.731491i	$-0.738825\pi$
$941$	−1.13629e9			−1.36370			−0.681851	+	0.731491i	$0.738825\pi$
$942$		0			0
$943$	1.00990e8	+	1.00990e8i	0.120432	+	0.120432i
$944$		−	3.47214e8i		−	0.412744i
$945$		0			0
$946$	5.72685e8			0.676460
$947$	−5.38433e8	+	5.38433e8i	−0.633989	+	0.633989i	−0.949066	−	0.315077i	$-0.897970\pi$
$947$	−5.38433e8	+	5.38433e8i	−0.633989	+	0.633989i	0.315077	+	0.949066i	$0.397970\pi$
$948$		0			0
$949$		−	9.49271e8i		−	1.11069i
$950$		0			0
$951$		0			0
$952$	4.44288e8	−	4.44288e8i	0.514937	−	0.514937i
$953$	1.36529e8	+	1.36529e8i	0.157742	+	0.157742i	0.781565	−	0.623823i	$-0.214422\pi$
$953$	1.36529e8	+	1.36529e8i	0.157742	+	0.157742i	−0.623823	+	0.781565i	$0.714422\pi$
$954$		0			0
$955$		0			0
$956$	1.80885e8			0.207028
$957$		0			0
$958$	2.01794e8	+	2.01794e8i	0.229515	+	0.229515i
$959$			2.76519e7i			0.0313523i
$960$		0			0
$961$	−2.40717e8			−0.271229
$962$	−1.91258e8	+	1.91258e8i	−0.214830	+	0.214830i
$963$		0			0
$964$			5.36093e8i			0.598424i
$965$		0			0
$966$		0			0
$967$	3.28178e8	−	3.28178e8i	0.362936	−	0.362936i	−0.501957	−	0.864893i	$-0.667386\pi$
$967$	3.28178e8	−	3.28178e8i	0.362936	−	0.362936i	0.864893	+	0.501957i	$0.167386\pi$
$968$	1.18872e8	+	1.18872e8i	0.131055	+	0.131055i
$969$		0			0
$970$		0			0
$971$	−1.35791e9			−1.48324			−0.741621	−	0.670819i	$-0.765943\pi$
$971$	−1.35791e9			−1.48324			−0.741621	+	0.670819i	$0.765943\pi$
$972$		0			0
$973$	−8.83021e7	−	8.83021e7i	−0.0958589	−	0.0958589i
$974$		−	4.99366e8i		−	0.540433i
$975$		0			0
$976$	−1.71700e8			−0.184680
$977$	−2.90834e7	+	2.90834e7i	−0.0311862	+	0.0311862i	−0.722528	−	0.691342i	$-0.757020\pi$
$977$	−2.90834e7	+	2.90834e7i	−0.0311862	+	0.0311862i	0.691342	+	0.722528i	$0.257020\pi$
$978$		0			0
$979$			3.21081e8i			0.342189i
$980$		0			0
$981$		0			0
$982$	5.09684e8	−	5.09684e8i	0.538228	−	0.538228i
$983$	5.98046e8	+	5.98046e8i	0.629613	+	0.629613i	0.947971	−	0.318358i	$-0.103131\pi$
$983$	5.98046e8	+	5.98046e8i	0.629613	+	0.629613i	−0.318358	+	0.947971i	$0.603131\pi$
$984$		0			0
$985$		0			0
$986$	1.73852e8			0.181363
$987$		0			0
$988$	−3.60312e8	−	3.60312e8i	−0.373601	−	0.373601i
$989$		−	8.53725e8i		−	0.882529i
$990$		0			0
$991$	−1.00844e9			−1.03617			−0.518084	−	0.855330i	$-0.673354\pi$
$991$	−1.00844e9			−1.03617			−0.518084	+	0.855330i	$0.673354\pi$
$992$	6.10673e8	−	6.10673e8i	0.625567	−	0.625567i
$993$		0			0
$994$		−	7.66721e8i		−	0.780690i
$995$		0			0
$996$		0			0
$997$	−1.06301e9	+	1.06301e9i	−1.07264	+	1.07264i	−0.0754885	+	0.997147i	$0.524052\pi$
$997$	−1.06301e9	+	1.06301e9i	−1.07264	+	1.07264i	−0.997147	+	0.0754885i	$0.975948\pi$
$998$	3.37156e8	+	3.37156e8i	0.339188	+	0.339188i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.7.g.a.118.1		2
3.2	odd	2		25.7.c.b.18.1	yes	2
5.2	odd	4	inner	225.7.g.a.82.1		2
5.3	odd	4		225.7.g.b.82.1		2
5.4	even	2		225.7.g.b.118.1		2
15.2	even	4		25.7.c.b.7.1	yes	2
15.8	even	4		25.7.c.a.7.1	✓	2
15.14	odd	2		25.7.c.a.18.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.7.c.a.7.1	✓	2	15.8	even	4
25.7.c.a.18.1	yes	2	15.14	odd	2
25.7.c.b.7.1	yes	2	15.2	even	4
25.7.c.b.18.1	yes	2	3.2	odd	2
225.7.g.a.82.1		2	5.2	odd	4	inner
225.7.g.a.118.1		2	1.1	even	1	trivial
225.7.g.b.82.1		2	5.3	odd	4
225.7.g.b.118.1		2	5.4	even	2

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	225.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.00000 + 3.00000i) q^{2} +46.0000i q^{4} +(-207.000 + 207.000i) q^{7} +(-330.000 - 330.000i) q^{8} +O(q^{10})\)	\(q+(-3.00000 + 3.00000i) q^{2} +46.0000i q^{4} +(-207.000 + 207.000i) q^{7} +(-330.000 - 330.000i) q^{8} +1188.00 q^{11} +(-1548.00 - 1548.00i) q^{13} -1242.00i q^{14} -964.000 q^{16} +(3252.00 - 3252.00i) q^{17} -5060.00i q^{19} +(-3564.00 + 3564.00i) q^{22} +(5313.00 + 5313.00i) q^{23} +9288.00 q^{26} +(-9522.00 - 9522.00i) q^{28} -8910.00i q^{29} +25432.0 q^{31} +(24012.0 - 24012.0i) q^{32} +19512.0i q^{34} +(-20592.0 + 20592.0i) q^{37} +(15180.0 + 15180.0i) q^{38} +19008.0 q^{41} +(-80343.0 - 80343.0i) q^{43} +54648.0i q^{44} -31878.0 q^{46} +(16137.0 - 16137.0i) q^{47} +31951.0i q^{49} +(71208.0 - 71208.0i) q^{52} +(-155892. - 155892. i) q^{53} +136620. q^{56} +(26730.0 + 26730.0i) q^{58} +360180. i q^{59} +178112. q^{61} +(-76296.0 + 76296.0i) q^{62} +82376.0i q^{64} +(240273. - 240273. i) q^{67} +(149592. + 149592. i) q^{68} +617328. q^{71} +(306612. + 306612. i) q^{73} -123552. i q^{74} +232760. q^{76} +(-245916. + 245916. i) q^{77} +232760. i q^{79} +(-57024.0 + 57024.0i) q^{82} +(-134097. - 134097. i) q^{83} +482058. q^{86} +(-392040. - 392040. i) q^{88} +270270. i q^{89} +640872. q^{91} +(-244398. + 244398. i) q^{92} +96822.0i q^{94} +(-810612. + 810612. i) q^{97} +(-95853.0 - 95853.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{2} - 414 q^{7} - 660 q^{8}+O(q^{10}) \) 2 * q - 6 * q^2 - 414 * q^7 - 660 * q^8	\( 2 q - 6 q^{2} - 414 q^{7} - 660 q^{8} + 2376 q^{11} - 3096 q^{13} - 1928 q^{16} + 6504 q^{17} - 7128 q^{22} + 10626 q^{23} + 18576 q^{26} - 19044 q^{28} + 50864 q^{31} + 48024 q^{32} - 41184 q^{37} + 30360 q^{38} + 38016 q^{41} - 160686 q^{43} - 63756 q^{46} + 32274 q^{47} + 142416 q^{52} - 311784 q^{53} + 273240 q^{56} + 53460 q^{58} + 356224 q^{61} - 152592 q^{62} + 480546 q^{67} + 299184 q^{68} + 1234656 q^{71} + 613224 q^{73} + 465520 q^{76} - 491832 q^{77} - 114048 q^{82} - 268194 q^{83} + 964116 q^{86} - 784080 q^{88} + 1281744 q^{91} - 488796 q^{92} - 1621224 q^{97} - 191706 q^{98}+O(q^{100}) \) 2 * q - 6 * q^2 - 414 * q^7 - 660 * q^8 + 2376 * q^11 - 3096 * q^13 - 1928 * q^16 + 6504 * q^17 - 7128 * q^22 + 10626 * q^23 + 18576 * q^26 - 19044 * q^28 + 50864 * q^31 + 48024 * q^32 - 41184 * q^37 + 30360 * q^38 + 38016 * q^41 - 160686 * q^43 - 63756 * q^46 + 32274 * q^47 + 142416 * q^52 - 311784 * q^53 + 273240 * q^56 + 53460 * q^58 + 356224 * q^61 - 152592 * q^62 + 480546 * q^67 + 299184 * q^68 + 1234656 * q^71 + 613224 * q^73 + 465520 * q^76 - 491832 * q^77 - 114048 * q^82 - 268194 * q^83 + 964116 * q^86 - 784080 * q^88 + 1281744 * q^91 - 488796 * q^92 - 1621224 * q^97 - 191706 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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