LMFDB - Embedded newform 840.2.bt.a.433.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(97,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.97"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bt (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.11
Character	$\chi$	$=$	840.433
Dual form			840.2.bt.a.97.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{3} +(1.54016 + 1.62109i) q^{5} +(-2.38404 + 1.14733i) q^{7} -1.00000i q^{9} +3.30657 q^{11} +(-2.80068 + 2.80068i) q^{13} +(2.23534 + 0.0572249i) q^{15} +(-0.927660 - 0.927660i) q^{17} +8.03228 q^{19} +(-0.874484 + 2.49705i) q^{21} +(5.04160 + 5.04160i) q^{23} +(-0.255834 + 4.99345i) q^{25} +(-0.707107 - 0.707107i) q^{27} +4.38863i q^{29} -5.01010i q^{31} +(2.33810 - 2.33810i) q^{33} +(-5.53171 - 2.09766i) q^{35} +(-4.76495 + 4.76495i) q^{37} +3.96076i q^{39} -0.992301i q^{41} +(7.33404 + 7.33404i) q^{43} +(1.62109 - 1.54016i) q^{45} +(-8.09377 - 8.09377i) q^{47} +(4.36727 - 5.47056i) q^{49} -1.31191 q^{51} +(3.10555 + 3.10555i) q^{53} +(5.09264 + 5.36023i) q^{55} +(5.67968 - 5.67968i) q^{57} -2.76943 q^{59} +0.411959i q^{61} +(1.14733 + 2.38404i) q^{63} +(-8.85363 - 0.226654i) q^{65} +(9.51496 - 9.51496i) q^{67} +7.12989 q^{69} -8.33595 q^{71} +(-0.0150660 + 0.0150660i) q^{73} +(3.35000 + 3.71180i) q^{75} +(-7.88299 + 3.79373i) q^{77} -3.28466i q^{79} -1.00000 q^{81} +(-1.33325 + 1.33325i) q^{83} +(0.0750738 - 2.93256i) q^{85} +(3.10323 + 3.10323i) q^{87} -6.49108 q^{89} +(3.46362 - 9.89023i) q^{91} +(-3.54267 - 3.54267i) q^{93} +(12.3710 + 13.0210i) q^{95} +(4.43930 + 4.43930i) q^{97} -3.30657i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 + 20 * q^17 + 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 - 4 * q^45 - 24 * q^47 + 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 + 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	1.54016	+	1.62109i	0.688779	+	0.724971i
$5$	1.54016	+	1.62109i	0.688779	+	0.724971i
$6$		0			0
$7$	−2.38404	+	1.14733i	−0.901081	+	0.433650i
$7$	−2.38404	+	1.14733i	−0.901081	+	0.433650i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	3.30657			0.996968			0.498484	−	0.866899i	$-0.333890\pi$
$11$	3.30657			0.996968			0.498484	+	0.866899i	$0.333890\pi$
$12$		0			0
$13$	−2.80068	+	2.80068i	−0.776769	+	0.776769i	−0.979280	−	0.202511i	$-0.935090\pi$
$13$	−2.80068	+	2.80068i	−0.776769	+	0.776769i	0.202511	+	0.979280i	$0.435090\pi$
$14$		0			0
$15$	2.23534	+	0.0572249i	0.577161	+	0.0147754i
$16$		0			0
$17$	−0.927660	−	0.927660i	−0.224991	−	0.224991i	0.585606	−	0.810596i	$-0.300857\pi$
$17$	−0.927660	−	0.927660i	−0.224991	−	0.224991i	−0.810596	+	0.585606i	$0.800857\pi$
$18$		0			0
$19$	8.03228			1.84273			0.921365	−	0.388698i	$-0.127075\pi$
$19$	8.03228			1.84273			0.921365	+	0.388698i	$0.127075\pi$
$20$		0			0
$21$	−0.874484	+	2.49705i	−0.190828	+	0.544902i
$22$		0			0
$23$	5.04160	+	5.04160i	1.05125	+	1.05125i	0.998614	+	0.0526316i	$0.0167609\pi$
$23$	5.04160	+	5.04160i	1.05125	+	1.05125i	0.0526316	+	0.998614i	$0.483239\pi$
$24$		0			0
$25$	−0.255834	+	4.99345i	−0.0511667	+	0.998690i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			4.38863i			0.814947i	0.913217	+	0.407474i	$0.133590\pi$
$29$			4.38863i			0.814947i	−0.913217	+	0.407474i	$0.866410\pi$
$30$		0			0
$31$		−	5.01010i		−	0.899840i	−0.893069	−	0.449920i	$-0.851453\pi$
$31$		−	5.01010i		−	0.899840i	0.893069	−	0.449920i	$-0.148547\pi$
$32$		0			0
$33$	2.33810	−	2.33810i	0.407011	−	0.407011i
$34$		0			0
$35$	−5.53171	−	2.09766i	−0.935030	−	0.354569i
$36$		0			0
$37$	−4.76495	+	4.76495i	−0.783353	+	0.783353i	−0.980395	−	0.197042i	$-0.936866\pi$
$37$	−4.76495	+	4.76495i	−0.783353	+	0.783353i	0.197042	+	0.980395i	$0.436866\pi$
$38$		0			0
$39$			3.96076i			0.634229i
$40$		0			0
$41$		−	0.992301i		−	0.154971i	−0.996993	−	0.0774857i	$-0.975311\pi$
$41$		−	0.992301i		−	0.154971i	0.996993	−	0.0774857i	$-0.0246892\pi$
$42$		0			0
$43$	7.33404	+	7.33404i	1.11843	+	1.11843i	0.991972	+	0.126459i	$0.0403612\pi$
$43$	7.33404	+	7.33404i	1.11843	+	1.11843i	0.126459	+	0.991972i	$0.459639\pi$
$44$		0			0
$45$	1.62109	−	1.54016i	0.241657	−	0.229593i
$46$		0			0
$47$	−8.09377	−	8.09377i	−1.18060	−	1.18060i	−0.979590	−	0.201008i	$-0.935578\pi$
$47$	−8.09377	−	8.09377i	−1.18060	−	1.18060i	−0.201008	−	0.979590i	$-0.564422\pi$
$48$		0			0
$49$	4.36727	−	5.47056i	0.623895	−	0.781508i
$50$		0			0
$51$	−1.31191			−0.183704
$52$		0			0
$53$	3.10555	+	3.10555i	0.426580	+	0.426580i	0.887461	−	0.460882i	$-0.152467\pi$
$53$	3.10555	+	3.10555i	0.426580	+	0.426580i	−0.460882	+	0.887461i	$0.652467\pi$
$54$		0			0
$55$	5.09264	+	5.36023i	0.686691	+	0.722774i
$56$		0			0
$57$	5.67968	−	5.67968i	0.752292	−	0.752292i
$58$		0			0
$59$	−2.76943			−0.360549			−0.180274	−	0.983616i	$-0.557699\pi$
$59$	−2.76943			−0.360549			−0.180274	+	0.983616i	$0.557699\pi$
$60$		0			0
$61$			0.411959i			0.0527460i	0.999652	+	0.0263730i	$0.00839576\pi$
$61$			0.411959i			0.0527460i	−0.999652	+	0.0263730i	$0.991604\pi$
$62$		0			0
$63$	1.14733	+	2.38404i	0.144550	+	0.300360i
$64$		0			0
$65$	−8.85363	−	0.226654i	−1.09816	−	0.0281130i
$66$		0			0
$67$	9.51496	−	9.51496i	1.16244	−	1.16244i	0.178497	−	0.983940i	$-0.442876\pi$
$67$	9.51496	−	9.51496i	1.16244	−	1.16244i	0.983940	−	0.178497i	$-0.0571235\pi$
$68$		0			0
$69$	7.12989			0.858338
$70$		0			0
$71$	−8.33595			−0.989296			−0.494648	−	0.869093i	$-0.664703\pi$
$71$	−8.33595			−0.989296			−0.494648	+	0.869093i	$0.664703\pi$
$72$		0			0
$73$	−0.0150660	+	0.0150660i	−0.00176334	+	0.00176334i	−0.707988	−	0.706225i	$-0.750397\pi$
$73$	−0.0150660	+	0.0150660i	−0.00176334	+	0.00176334i	0.706225	+	0.707988i	$0.250397\pi$
$74$		0			0
$75$	3.35000	+	3.71180i	0.386825	+	0.428602i
$76$		0			0
$77$	−7.88299	+	3.79373i	−0.898350	+	0.432335i
$78$		0			0
$79$		−	3.28466i		−	0.369554i	−0.982781	−	0.184777i	$-0.940844\pi$
$79$		−	3.28466i		−	0.369554i	0.982781	−	0.184777i	$-0.0591562\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−1.33325	+	1.33325i	−0.146343	+	0.146343i	−0.776482	−	0.630139i	$-0.782998\pi$
$83$	−1.33325	+	1.33325i	−0.146343	+	0.146343i	0.630139	+	0.776482i	$0.282998\pi$
$84$		0			0
$85$	0.0750738	−	2.93256i	0.00814290	−	0.318080i
$86$		0			0
$87$	3.10323	+	3.10323i	0.332701	+	0.332701i
$88$		0			0
$89$	−6.49108			−0.688053			−0.344026	−	0.938960i	$-0.611791\pi$
$89$	−6.49108			−0.688053			−0.344026	+	0.938960i	$0.611791\pi$
$90$		0			0
$91$	3.46362	−	9.89023i	0.363086	−	1.03678i
$92$		0			0
$93$	−3.54267	−	3.54267i	−0.367358	−	0.367358i
$94$		0			0
$95$	12.3710	+	13.0210i	1.26923	+	1.33593i
$96$		0			0
$97$	4.43930	+	4.43930i	0.450743	+	0.450743i	0.895601	−	0.444858i	$-0.146746\pi$
$97$	4.43930	+	4.43930i	0.450743	+	0.450743i	−0.444858	+	0.895601i	$0.646746\pi$
$98$		0			0
$99$		−	3.30657i		−	0.332323i
$100$		0			0
$101$		−	12.2398i		−	1.21790i	−0.793207	−	0.608952i	$-0.791590\pi$
$101$		−	12.2398i		−	1.21790i	0.793207	−	0.608952i	$-0.208410\pi$
$102$		0			0
$103$	13.8964	−	13.8964i	1.36925	−	1.36925i	0.507738	−	0.861511i	$-0.330482\pi$
$103$	13.8964	−	13.8964i	1.36925	−	1.36925i	0.861511	−	0.507738i	$-0.169518\pi$
$104$		0			0
$105$	−5.39478	+	2.42824i	−0.526477	+	0.236972i
$106$		0			0
$107$	1.10288	−	1.10288i	0.106620	−	0.106620i	−0.651784	−	0.758404i	$-0.725979\pi$
$107$	1.10288	−	1.10288i	0.106620	−	0.106620i	0.758404	+	0.651784i	$0.225979\pi$
$108$		0			0
$109$		−	9.72802i		−	0.931775i	−0.884844	−	0.465887i	$-0.845735\pi$
$109$		−	9.72802i		−	0.931775i	0.884844	−	0.465887i	$-0.154265\pi$
$110$		0			0
$111$			6.73866i			0.639605i
$112$		0			0
$113$	−1.92001	−	1.92001i	−0.180620	−	0.180620i	0.611006	−	0.791626i	$-0.290765\pi$
$113$	−1.92001	−	1.92001i	−0.180620	−	0.180620i	−0.791626	+	0.611006i	$0.790765\pi$
$114$		0			0
$115$	−0.408007	+	15.9377i	−0.0380469	+	1.48620i
$116$		0			0
$117$	2.80068	+	2.80068i	0.258923	+	0.258923i
$118$		0			0
$119$	3.27591	+	1.14724i	0.300302	+	0.105168i
$120$		0			0
$121$	−0.0665922			−0.00605383
$122$		0			0
$123$	−0.701663	−	0.701663i	−0.0632668	−	0.0632668i
$124$		0			0
$125$	−8.48883	+	7.27597i	−0.759264	+	0.650782i
$126$		0			0
$127$	−9.97622	+	9.97622i	−0.885246	+	0.885246i	−0.994062	−	0.108816i	$-0.965294\pi$
$127$	−9.97622	+	9.97622i	−0.885246	+	0.885246i	0.108816	+	0.994062i	$0.465294\pi$
$128$		0			0
$129$	10.3719			0.913195
$130$		0			0
$131$			6.98425i			0.610216i	0.952318	+	0.305108i	$0.0986926\pi$
$131$			6.98425i			0.610216i	−0.952318	+	0.305108i	$0.901307\pi$
$132$		0			0
$133$	−19.1492	+	9.21567i	−1.66045	+	0.799100i
$134$		0			0
$135$	0.0572249	−	2.23534i	0.00492513	−	0.192387i
$136$		0			0
$137$	−2.38722	+	2.38722i	−0.203954	+	0.203954i	−0.801692	−	0.597738i	$-0.796066\pi$
$137$	−2.38722	+	2.38722i	−0.203954	+	0.203954i	0.597738	+	0.801692i	$0.296066\pi$
$138$		0			0
$139$	−4.89319			−0.415035			−0.207517	−	0.978231i	$-0.566538\pi$
$139$	−4.89319			−0.415035			−0.207517	+	0.978231i	$0.566538\pi$
$140$		0			0
$141$	−11.4463			−0.963954
$142$		0			0
$143$	−9.26065	+	9.26065i	−0.774414	+	0.774414i
$144$		0			0
$145$	−7.11434	+	6.75917i	−0.590813	+	0.561319i
$146$		0			0
$147$	−0.780143	−	6.95639i	−0.0643451	−	0.573753i
$148$		0			0
$149$		−	10.2311i		−	0.838165i	−0.907948	−	0.419083i	$-0.862352\pi$
$149$		−	10.2311i		−	0.838165i	0.907948	−	0.419083i	$-0.137648\pi$
$150$		0			0
$151$	20.5091			1.66901			0.834504	−	0.551002i	$-0.185755\pi$
$151$	20.5091			1.66901			0.834504	+	0.551002i	$0.185755\pi$
$152$		0			0
$153$	−0.927660	+	0.927660i	−0.0749969	+	0.0749969i
$154$		0			0
$155$	8.12179	−	7.71633i	0.652358	−	0.619791i
$156$		0			0
$157$	−6.39577	−	6.39577i	−0.510438	−	0.510438i	0.404223	−	0.914661i	$-0.367542\pi$
$157$	−6.39577	−	6.39577i	−0.510438	−	0.510438i	−0.914661	+	0.404223i	$0.867542\pi$
$158$		0			0
$159$	4.39191			0.348301
$160$		0			0
$161$	−17.8037	−	6.23498i	−1.40313	−	0.491385i
$162$		0			0
$163$	−17.4426	−	17.4426i	−1.36621	−	1.36621i	−0.865774	−	0.500436i	$-0.833173\pi$
$163$	−17.4426	−	17.4426i	−1.36621	−	1.36621i	−0.500436	−	0.865774i	$-0.666827\pi$
$164$		0			0
$165$	7.39129	+	0.189218i	0.575412	+	0.0147306i
$166$		0			0
$167$	−10.8547	−	10.8547i	−0.839965	−	0.839965i	0.148889	−	0.988854i	$-0.452430\pi$
$167$	−10.8547	−	10.8547i	−0.839965	−	0.839965i	−0.988854	+	0.148889i	$0.952430\pi$
$168$		0			0
$169$		−	2.68763i		−	0.206740i
$170$		0			0
$171$		−	8.03228i		−	0.614244i
$172$		0			0
$173$	−18.1500	+	18.1500i	−1.37992	+	1.37992i	−0.535189	+	0.844732i	$0.679760\pi$
$173$	−18.1500	+	18.1500i	−1.37992	+	1.37992i	−0.844732	+	0.535189i	$0.820240\pi$
$174$		0			0
$175$	−5.11922	−	12.1981i	−0.386977	−	0.922090i
$176$		0			0
$177$	−1.95828	+	1.95828i	−0.147193	+	0.147193i
$178$		0			0
$179$		−	5.83440i		−	0.436083i	−0.975939	−	0.218042i	$-0.930033\pi$
$179$		−	5.83440i		−	0.436083i	0.975939	−	0.218042i	$-0.0699669\pi$
$180$		0			0
$181$		−	8.93968i		−	0.664481i	−0.943195	−	0.332241i	$-0.892195\pi$
$181$		−	8.93968i		−	0.664481i	0.943195	−	0.332241i	$-0.107805\pi$
$182$		0			0
$183$	0.291299	+	0.291299i	0.0215335	+	0.0215335i
$184$		0			0
$185$	−15.0632	−	0.385619i	−1.10747	−	0.0283513i
$186$		0			0
$187$	−3.06737	−	3.06737i	−0.224308	−	0.224308i
$188$		0			0
$189$	2.49705	+	0.874484i	0.181634	+	0.0636093i
$190$		0			0
$191$	−20.8302			−1.50722			−0.753611	−	0.657321i	$-0.771690\pi$
$191$	−20.8302			−1.50722			−0.753611	+	0.657321i	$0.771690\pi$
$192$		0			0
$193$	9.21153	+	9.21153i	0.663061	+	0.663061i	0.956100	−	0.293040i	$-0.0946668\pi$
$193$	9.21153	+	9.21153i	0.663061	+	0.663061i	−0.293040	+	0.956100i	$0.594667\pi$
$194$		0			0
$195$	−6.42073	+	6.10019i	−0.459798	+	0.436844i
$196$		0			0
$197$	17.9454	−	17.9454i	1.27856	−	1.27856i	0.337079	−	0.941477i	$-0.390561\pi$
$197$	17.9454	−	17.9454i	1.27856	−	1.27856i	0.941477	−	0.337079i	$-0.109439\pi$
$198$		0			0
$199$	11.2957			0.800729			0.400364	−	0.916356i	$-0.368884\pi$
$199$	11.2957			0.800729			0.400364	+	0.916356i	$0.368884\pi$
$200$		0			0
$201$		−	13.4562i		−	0.949126i
$202$		0			0
$203$	−5.03520	−	10.4626i	−0.353402	−	0.734334i
$204$		0			0
$205$	1.60860	−	1.52830i	0.112350	−	0.106741i
$206$		0			0
$207$	5.04160	−	5.04160i	0.350415	−	0.350415i
$208$		0			0
$209$	26.5593			1.83714
$210$		0			0
$211$	−11.9867			−0.825196			−0.412598	−	0.910913i	$-0.635379\pi$
$211$	−11.9867			−0.825196			−0.412598	+	0.910913i	$0.635379\pi$
$212$		0			0
$213$	−5.89441	+	5.89441i	−0.403878	+	0.403878i
$214$		0			0
$215$	−0.593531	+	23.1847i	−0.0404785	+	1.58118i
$216$		0			0
$217$	5.74824	+	11.9443i	0.390216	+	0.810829i
$218$		0			0
$219$			0.0213066i			0.00143977i
$220$		0			0
$221$	5.19616			0.349531
$222$		0			0
$223$	5.55915	−	5.55915i	0.372269	−	0.372269i	−0.496034	−	0.868303i	$-0.665211\pi$
$223$	5.55915	−	5.55915i	0.372269	−	0.372269i	0.868303	+	0.496034i	$0.165211\pi$
$224$		0			0
$225$	4.99345	+	0.255834i	0.332897	+	0.0170556i
$226$		0			0
$227$	−9.17610	−	9.17610i	−0.609039	−	0.609039i	0.333656	−	0.942695i	$-0.391718\pi$
$227$	−9.17610	−	9.17610i	−0.609039	−	0.609039i	−0.942695	+	0.333656i	$0.891718\pi$
$228$		0			0
$229$	9.02967			0.596697			0.298349	−	0.954457i	$-0.403564\pi$
$229$	9.02967			0.596697			0.298349	+	0.954457i	$0.403564\pi$
$230$		0			0
$231$	−2.89154	+	8.25668i	−0.190250	+	0.543250i
$232$		0			0
$233$	−16.1719	−	16.1719i	−1.05946	−	1.05946i	−0.998117	−	0.0613399i	$-0.980463\pi$
$233$	−16.1719	−	16.1719i	−1.05946	−	1.05946i	−0.0613399	−	0.998117i	$-0.519537\pi$
$234$		0			0
$235$	0.655014	−	25.5864i	0.0427284	−	1.66907i
$236$		0			0
$237$	−2.32261	−	2.32261i	−0.150870	−	0.150870i
$238$		0			0
$239$			9.71673i			0.628523i	0.949336	+	0.314262i	$0.101757\pi$
$239$			9.71673i			0.628523i	−0.949336	+	0.314262i	$0.898243\pi$
$240$		0			0
$241$			6.15398i			0.396413i	0.980160	+	0.198206i	$0.0635116\pi$
$241$			6.15398i			0.396413i	−0.980160	+	0.198206i	$0.936488\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	15.5945	−	1.34580i	0.996297	−	0.0859802i
$246$		0			0
$247$	−22.4958	+	22.4958i	−1.43138	+	1.43138i
$248$		0			0
$249$			1.88549i			0.119488i
$250$		0			0
$251$		−	6.71090i		−	0.423588i	−0.977314	−	0.211794i	$-0.932069\pi$
$251$		−	6.71090i		−	0.423588i	0.977314	−	0.211794i	$-0.0679307\pi$
$252$		0			0
$253$	16.6704	+	16.6704i	1.04806	+	1.04806i
$254$		0			0
$255$	−2.02055	−	2.12672i	−0.126531	−	0.133180i
$256$		0			0
$257$	−11.7516	−	11.7516i	−0.733044	−	0.733044i	0.238178	−	0.971222i	$-0.423450\pi$
$257$	−11.7516	−	11.7516i	−0.733044	−	0.733044i	−0.971222	+	0.238178i	$0.923450\pi$
$258$		0			0
$259$	5.89285	−	16.8268i	0.366164	−	1.04557i
$260$		0			0
$261$	4.38863			0.271649
$262$		0			0
$263$	6.36216	+	6.36216i	0.392308	+	0.392308i	0.875509	−	0.483202i	$-0.160526\pi$
$263$	6.36216	+	6.36216i	0.392308	+	0.392308i	−0.483202	+	0.875509i	$0.660526\pi$
$264$		0			0
$265$	−0.251326	+	9.81738i	−0.0154389	+	0.603077i
$266$		0			0
$267$	−4.58989	+	4.58989i	−0.280896	+	0.280896i
$268$		0			0
$269$	14.2170			0.866829			0.433414	−	0.901195i	$-0.357309\pi$
$269$	14.2170			0.866829			0.433414	+	0.901195i	$0.357309\pi$
$270$		0			0
$271$			9.72015i			0.590457i	0.955427	+	0.295229i	$0.0953958\pi$
$271$			9.72015i			0.590457i	−0.955427	+	0.295229i	$0.904604\pi$
$272$		0			0
$273$	−4.54430	−	9.44260i	−0.275034	−	0.571492i
$274$		0			0
$275$	−0.845932	+	16.5112i	−0.0510116	+	0.995663i
$276$		0			0
$277$	−14.0922	+	14.0922i	−0.846721	+	0.846721i	−0.989722	−	0.143001i	$-0.954325\pi$
$277$	−14.0922	+	14.0922i	−0.846721	+	0.846721i	0.143001	+	0.989722i	$0.454325\pi$
$278$		0			0
$279$	−5.01010			−0.299947
$280$		0			0
$281$	30.8301			1.83917			0.919584	−	0.392894i	$-0.128526\pi$
$281$	30.8301			1.83917			0.919584	+	0.392894i	$0.128526\pi$
$282$		0			0
$283$	12.8741	−	12.8741i	0.765288	−	0.765288i	−0.211985	−	0.977273i	$-0.567993\pi$
$283$	12.8741	−	12.8741i	0.765288	−	0.765288i	0.977273	+	0.211985i	$0.0679928\pi$
$284$		0			0
$285$	17.9548	+	0.459646i	1.06355	+	0.0272271i
$286$		0			0
$287$	1.13850	+	2.36568i	0.0672033	+	0.139642i
$288$		0			0
$289$		−	15.2789i		−	0.898758i
$290$		0			0
$291$	6.27812			0.368030
$292$		0			0
$293$	17.8266	−	17.8266i	1.04144	−	1.04144i	0.0423367	−	0.999103i	$-0.486520\pi$
$293$	17.8266	−	17.8266i	1.04144	−	1.04144i	0.999103	−	0.0423367i	$-0.0134802\pi$
$294$		0			0
$295$	−4.26535	−	4.48948i	−0.248338	−	0.261387i
$296$		0			0
$297$	−2.33810	−	2.33810i	−0.135670	−	0.135670i
$298$		0			0
$299$	−28.2398			−1.63315
$300$		0			0
$301$	−25.8992	−	9.07006i	−1.49280	−	0.522790i
$302$		0			0
$303$	−8.65484	−	8.65484i	−0.497207	−	0.497207i
$304$		0			0
$305$	−0.667821	+	0.634482i	−0.0382393	+	0.0363303i
$306$		0			0
$307$	−4.05722	−	4.05722i	−0.231558	−	0.231558i	0.581785	−	0.813343i	$-0.302355\pi$
$307$	−4.05722	−	4.05722i	−0.231558	−	0.231558i	−0.813343	+	0.581785i	$0.802355\pi$
$308$		0			0
$309$		−	19.6524i		−	1.11799i
$310$		0			0
$311$			13.8490i			0.785305i	0.919687	+	0.392652i	$0.128442\pi$
$311$			13.8490i			0.785305i	−0.919687	+	0.392652i	$0.871558\pi$
$312$		0			0
$313$	−17.1203	+	17.1203i	−0.967695	+	0.967695i	−0.999494	−	0.0317993i	$-0.989876\pi$
$313$	−17.1203	+	17.1203i	−0.967695	+	0.967695i	0.0317993	+	0.999494i	$0.489876\pi$
$314$		0			0
$315$	−2.09766	+	5.53171i	−0.118190	+	0.311677i
$316$		0			0
$317$	2.01391	−	2.01391i	0.113112	−	0.113112i	−0.648285	−	0.761398i	$-0.724514\pi$
$317$	2.01391	−	2.01391i	0.113112	−	0.113112i	0.761398	+	0.648285i	$0.224514\pi$
$318$		0			0
$319$			14.5113i			0.812477i
$320$		0			0
$321$		−	1.55971i		−	0.0870547i
$322$		0			0
$323$	−7.45122	−	7.45122i	−0.414597	−	0.414597i
$324$		0			0
$325$	−13.2686	−	14.7016i	−0.736007	−	0.815496i
$326$		0			0
$327$	−6.87875	−	6.87875i	−0.380396	−	0.380396i
$328$		0			0
$329$	28.5821	+	10.0096i	1.57578	+	0.551848i
$330$		0			0
$331$	2.92509			0.160777			0.0803886	−	0.996764i	$-0.474384\pi$
$331$	2.92509			0.160777			0.0803886	+	0.996764i	$0.474384\pi$
$332$		0			0
$333$	4.76495	+	4.76495i	0.261118	+	0.261118i
$334$		0			0
$335$	30.0791	+	0.770029i	1.64340	+	0.0420712i
$336$		0			0
$337$	−3.05556	+	3.05556i	−0.166447	+	0.166447i	−0.785416	−	0.618969i	$-0.787551\pi$
$337$	−3.05556	+	3.05556i	−0.166447	+	0.166447i	0.618969	+	0.785416i	$0.287551\pi$
$338$		0			0
$339$	−2.71531			−0.147475
$340$		0			0
$341$		−	16.5662i		−	0.897112i
$342$		0			0
$343$	−4.13519	+	18.0527i	−0.223279	+	0.974754i
$344$		0			0
$345$	10.9812	+	11.5582i	0.591206	+	0.622271i
$346$		0			0
$347$	5.84450	−	5.84450i	0.313749	−	0.313749i	−0.532611	−	0.846360i	$-0.678789\pi$
$347$	5.84450	−	5.84450i	0.313749	−	0.313749i	0.846360	+	0.532611i	$0.178789\pi$
$348$		0			0
$349$	−18.0309			−0.965172			−0.482586	−	0.875849i	$-0.660302\pi$
$349$	−18.0309			−0.965172			−0.482586	+	0.875849i	$0.660302\pi$
$350$		0			0
$351$	3.96076			0.211410
$352$		0			0
$353$	−21.4252	+	21.4252i	−1.14035	+	1.14035i	−0.151961	+	0.988387i	$0.548559\pi$
$353$	−21.4252	+	21.4252i	−1.14035	+	1.14035i	−0.988387	+	0.151961i	$0.951441\pi$
$354$		0			0
$355$	−12.8387	−	13.5133i	−0.681406	−	0.717211i
$356$		0			0
$357$	3.12764	−	1.50519i	0.165532	−	0.0796633i
$358$		0			0
$359$			4.81661i			0.254211i	0.991889	+	0.127106i	$0.0405687\pi$
$359$			4.81661i			0.254211i	−0.991889	+	0.127106i	$0.959431\pi$
$360$		0			0
$361$	45.5175			2.39566
$362$		0			0
$363$	−0.0470878	+	0.0470878i	−0.00247147	+	0.00247147i
$364$		0			0
$365$	−0.0476273	−	0.00121927i	−0.00249293	−	6.38193e-5i
$366$		0			0
$367$	6.17728	+	6.17728i	0.322451	+	0.322451i	0.849707	−	0.527256i	$-0.176779\pi$
$367$	6.17728	+	6.17728i	0.322451	+	0.322451i	−0.527256	+	0.849707i	$0.676779\pi$
$368$		0			0
$369$	−0.992301			−0.0516571
$370$		0			0
$371$	−10.9668	−	3.84065i	−0.569369	−	0.199397i
$372$		0			0
$373$	23.9129	+	23.9129i	1.23816	+	1.23816i	0.960751	+	0.277413i	$0.0894770\pi$
$373$	23.9129	+	23.9129i	1.23816	+	1.23816i	0.277413	+	0.960751i	$0.410523\pi$
$374$		0			0
$375$	−0.857624	+	11.1474i	−0.0442875	+	0.575649i
$376$		0			0
$377$	−12.2911	−	12.2911i	−0.633026	−	0.633026i
$378$		0			0
$379$			11.7119i			0.601599i	0.953687	+	0.300800i	$0.0972536\pi$
$379$			11.7119i			0.601599i	−0.953687	+	0.300800i	$0.902746\pi$
$380$		0			0
$381$			14.1085i			0.722800i
$382$		0			0
$383$	−0.575801	+	0.575801i	−0.0294221	+	0.0294221i	−0.721665	−	0.692243i	$-0.756623\pi$
$383$	−0.575801	+	0.575801i	−0.0294221	+	0.0294221i	0.692243	+	0.721665i	$0.256623\pi$
$384$		0			0
$385$	−18.2910	−	6.93606i	−0.932195	−	0.353494i
$386$		0			0
$387$	7.33404	−	7.33404i	0.372810	−	0.372810i
$388$		0			0
$389$		−	0.169265i		−	0.00858209i	−0.999991	−	0.00429104i	$-0.998634\pi$
$389$		−	0.169265i		−	0.00858209i	0.999991	−	0.00429104i	$-0.00136589\pi$
$390$		0			0
$391$		−	9.35377i		−	0.473041i
$392$		0			0
$393$	4.93861	+	4.93861i	0.249120	+	0.249120i
$394$		0			0
$395$	5.32472	−	5.05890i	0.267916	−	0.254541i
$396$		0			0
$397$	5.20067	+	5.20067i	0.261014	+	0.261014i	0.825466	−	0.564452i	$-0.190912\pi$
$397$	5.20067	+	5.20067i	0.261014	+	0.261014i	−0.564452	+	0.825466i	$0.690912\pi$
$398$		0			0
$399$	−7.02410	+	20.0570i	−0.351645	+	1.00411i
$400$		0			0
$401$	−2.69380			−0.134522			−0.0672610	−	0.997735i	$-0.521426\pi$
$401$	−2.69380			−0.134522			−0.0672610	+	0.997735i	$0.521426\pi$
$402$		0			0
$403$	14.0317	+	14.0317i	0.698968	+	0.698968i
$404$		0			0
$405$	−1.54016	−	1.62109i	−0.0765310	−	0.0805524i
$406$		0			0
$407$	−15.7556	+	15.7556i	−0.780978	+	0.780978i
$408$		0			0
$409$	20.1291			0.995319			0.497659	−	0.867373i	$-0.334193\pi$
$409$	20.1291			0.995319			0.497659	+	0.867373i	$0.334193\pi$
$410$		0			0
$411$			3.37604i			0.166528i
$412$		0			0
$413$	6.60241	−	3.17745i	0.324884	−	0.156352i
$414$		0			0
$415$	−4.21471	−	0.107897i	−0.206892	−	0.00529646i
$416$		0			0
$417$	−3.46001	+	3.46001i	−0.169437	+	0.169437i
$418$		0			0
$419$	−14.3204			−0.699599			−0.349800	−	0.936825i	$-0.613750\pi$
$419$	−14.3204			−0.699599			−0.349800	+	0.936825i	$0.613750\pi$
$420$		0			0
$421$	24.1470			1.17685			0.588426	−	0.808551i	$-0.299748\pi$
$421$	24.1470			1.17685			0.588426	+	0.808551i	$0.299748\pi$
$422$		0			0
$423$	−8.09377	+	8.09377i	−0.393533	+	0.393533i
$424$		0			0
$425$	4.86955	−	4.39490i	0.236208	−	0.213184i
$426$		0			0
$427$	−0.472653	−	0.982127i	−0.0228733	−	0.0475284i
$428$		0			0
$429$			13.0965i			0.632307i
$430$		0			0
$431$	10.9386			0.526894			0.263447	−	0.964674i	$-0.415141\pi$
$431$	10.9386			0.526894			0.263447	+	0.964674i	$0.415141\pi$
$432$		0			0
$433$	4.37049	−	4.37049i	0.210032	−	0.210032i	−0.594249	−	0.804281i	$-0.702551\pi$
$433$	4.37049	−	4.37049i	0.210032	−	0.210032i	0.804281	+	0.594249i	$0.202551\pi$
$434$		0			0
$435$	−0.251139	+	9.81005i	−0.0120412	+	0.470356i
$436$		0			0
$437$	40.4955	+	40.4955i	1.93716	+	1.93716i
$438$		0			0
$439$	29.6474			1.41499			0.707497	−	0.706717i	$-0.249824\pi$
$439$	29.6474			1.41499			0.707497	+	0.706717i	$0.249824\pi$
$440$		0			0
$441$	−5.47056	−	4.36727i	−0.260503	−	0.207965i
$442$		0			0
$443$	−17.6204	−	17.6204i	−0.837168	−	0.837168i	0.151317	−	0.988485i	$-0.451649\pi$
$443$	−17.6204	−	17.6204i	−0.837168	−	0.837168i	−0.988485	+	0.151317i	$0.951649\pi$
$444$		0			0
$445$	−9.99728	−	10.5226i	−0.473916	−	0.498819i
$446$		0			0
$447$	−7.23449	−	7.23449i	−0.342179	−	0.342179i
$448$		0			0
$449$			20.1212i			0.949576i	0.880100	+	0.474788i	$0.157475\pi$
$449$			20.1212i			0.949576i	−0.880100	+	0.474788i	$0.842525\pi$
$450$		0			0
$451$		−	3.28111i		−	0.154502i
$452$		0			0
$453$	14.5021	−	14.5021i	0.681369	−	0.681369i
$454$		0			0
$455$	21.3674	−	9.61769i	1.00172	−	0.450884i
$456$		0			0
$457$	−1.47111	+	1.47111i	−0.0688157	+	0.0688157i	−0.740677	−	0.671861i	$-0.765495\pi$
$457$	−1.47111	+	1.47111i	−0.0688157	+	0.0688157i	0.671861	+	0.740677i	$0.265495\pi$
$458$		0			0
$459$			1.31191i			0.0612347i
$460$		0			0
$461$			18.2023i			0.847768i	0.905717	+	0.423884i	$0.139334\pi$
$461$			18.2023i			0.847768i	−0.905717	+	0.423884i	$0.860666\pi$
$462$		0			0
$463$	−5.77953	−	5.77953i	−0.268598	−	0.268598i	0.559937	−	0.828535i	$-0.310825\pi$
$463$	−5.77953	−	5.77953i	−0.268598	−	0.268598i	−0.828535	+	0.559937i	$0.810825\pi$
$464$		0			0
$465$	0.286702	−	11.1992i	0.0132955	−	0.519353i
$466$		0			0
$467$	20.6171	+	20.6171i	0.954046	+	0.954046i	0.998990	−	0.0449436i	$-0.0143108\pi$
$467$	20.6171	+	20.6171i	0.954046	+	0.954046i	−0.0449436	+	0.998990i	$0.514311\pi$
$468$		0			0
$469$	−11.7672	+	33.6008i	−0.543360	+	1.55154i
$470$		0			0
$471$	−9.04498			−0.416771
$472$		0			0
$473$	24.2505	+	24.2505i	1.11504	+	1.11504i
$474$		0			0
$475$	−2.05493	+	40.1088i	−0.0942865	+	1.84032i
$476$		0			0
$477$	3.10555	−	3.10555i	0.142193	−	0.142193i
$478$		0			0
$479$	22.7500			1.03947			0.519737	−	0.854327i	$-0.326030\pi$
$479$	22.7500			1.03947			0.519737	+	0.854327i	$0.326030\pi$
$480$		0			0
$481$		−	26.6902i		−	1.21697i
$482$		0			0
$483$	−16.9979	+	8.18034i	−0.773433	+	0.372219i
$484$		0			0
$485$	−0.359265	+	14.0337i	−0.0163134	+	0.637238i
$486$		0			0
$487$	−2.43248	+	2.43248i	−0.110226	+	0.110226i	−0.760069	−	0.649843i	$-0.774835\pi$
$487$	−2.43248	+	2.43248i	−0.110226	+	0.110226i	0.649843	+	0.760069i	$0.274835\pi$
$488$		0			0
$489$	−24.6676			−1.11551
$490$		0			0
$491$	−18.2591			−0.824022			−0.412011	−	0.911179i	$-0.635173\pi$
$491$	−18.2591			−0.824022			−0.412011	+	0.911179i	$0.635173\pi$
$492$		0			0
$493$	4.07115	−	4.07115i	0.183355	−	0.183355i
$494$		0			0
$495$	5.36023	−	5.09264i	0.240925	−	0.228897i
$496$		0			0
$497$	19.8732	−	9.56409i	0.891436	−	0.429008i
$498$		0			0
$499$		−	21.4299i		−	0.959334i	−0.877451	−	0.479667i	$-0.840758\pi$
$499$		−	21.4299i		−	0.959334i	0.877451	−	0.479667i	$-0.159242\pi$
$500$		0			0
$501$	−15.3509			−0.685829
$502$		0			0
$503$	29.5361	−	29.5361i	1.31695	−	1.31695i	0.400770	−	0.916179i	$-0.368743\pi$
$503$	29.5361	−	29.5361i	1.31695	−	1.31695i	0.916179	−	0.400770i	$-0.131257\pi$
$504$		0			0
$505$	19.8417	−	18.8512i	0.882946	−	0.838867i
$506$		0			0
$507$	−1.90044	−	1.90044i	−0.0844014	−	0.0844014i
$508$		0			0
$509$	9.47432			0.419942			0.209971	−	0.977708i	$-0.432663\pi$
$509$	9.47432			0.419942			0.209971	+	0.977708i	$0.432663\pi$
$510$		0			0
$511$	0.0186323	−	0.0532037i	0.000824243	−	0.00235359i
$512$		0			0
$513$	−5.67968	−	5.67968i	−0.250764	−	0.250764i
$514$		0			0
$515$	43.9298	+	1.12461i	1.93578	+	0.0495561i
$516$		0			0
$517$	−26.7626	−	26.7626i	−1.17702	−	1.17702i
$518$		0			0
$519$			25.6680i			1.12670i
$520$		0			0
$521$		−	14.6502i		−	0.641837i	−0.947107	−	0.320918i	$-0.896008\pi$
$521$		−	14.6502i		−	0.641837i	0.947107	−	0.320918i	$-0.103992\pi$
$522$		0			0
$523$	20.0200	−	20.0200i	0.875413	−	0.875413i	−0.117643	−	0.993056i	$-0.537534\pi$
$523$	20.0200	−	20.0200i	0.875413	−	0.875413i	0.993056	+	0.117643i	$0.0375337\pi$
$524$		0			0
$525$	−12.2452	−	5.00552i	−0.534424	−	0.218459i
$526$		0			0
$527$	−4.64767	+	4.64767i	−0.202455	+	0.202455i
$528$		0			0
$529$			27.8354i			1.21023i
$530$		0			0
$531$			2.76943i			0.120183i
$532$		0			0
$533$	2.77912	+	2.77912i	0.120377	+	0.120377i
$534$		0			0
$535$	3.48648	+	0.0892544i	0.150734	+	0.00385880i
$536$		0			0
$537$	−4.12554	−	4.12554i	−0.178030	−	0.178030i
$538$		0			0
$539$	14.4407	−	18.0888i	0.622004	−	0.779139i
$540$		0			0
$541$	−11.4133			−0.490696			−0.245348	−	0.969435i	$-0.578902\pi$
$541$	−11.4133			−0.490696			−0.245348	+	0.969435i	$0.578902\pi$
$542$		0			0
$543$	−6.32131	−	6.32131i	−0.271273	−	0.271273i
$544$		0			0
$545$	15.7699	−	14.9827i	0.675510	−	0.641787i
$546$		0			0
$547$	−3.48155	+	3.48155i	−0.148861	+	0.148861i	−0.777609	−	0.628748i	$-0.783568\pi$
$547$	−3.48155	+	3.48155i	−0.148861	+	0.148861i	0.628748	+	0.777609i	$0.283568\pi$
$548$		0			0
$549$	0.411959			0.0175820
$550$		0			0
$551$			35.2507i			1.50173i
$552$		0			0
$553$	3.76860	+	7.83076i	0.160257	+	0.332998i
$554$		0			0
$555$	−10.9239	+	10.3786i	−0.463695	+	0.440547i
$556$		0			0
$557$	7.76382	−	7.76382i	0.328964	−	0.328964i	−0.523229	−	0.852192i	$-0.675273\pi$
$557$	7.76382	−	7.76382i	0.328964	−	0.328964i	0.852192	+	0.523229i	$0.175273\pi$
$558$		0			0
$559$	−41.0806			−1.73753
$560$		0			0
$561$	−4.33792			−0.183147
$562$		0			0
$563$	6.97727	−	6.97727i	0.294057	−	0.294057i	−0.544624	−	0.838681i	$-0.683328\pi$
$563$	6.97727	−	6.97727i	0.294057	−	0.294057i	0.838681	+	0.544624i	$0.183328\pi$
$564$		0			0
$565$	0.155383	−	6.06963i	0.00653702	−	0.255351i
$566$		0			0
$567$	2.38404	−	1.14733i	0.100120	−	0.0481833i
$568$		0			0
$569$			12.3582i			0.518082i	0.965866	+	0.259041i	$0.0834064\pi$
$569$			12.3582i			0.518082i	−0.965866	+	0.259041i	$0.916594\pi$
$570$		0			0
$571$	−1.05801			−0.0442764			−0.0221382	−	0.999755i	$-0.507047\pi$
$571$	−1.05801			−0.0442764			−0.0221382	+	0.999755i	$0.507047\pi$
$572$		0			0
$573$	−14.7292	+	14.7292i	−0.615321	+	0.615321i
$574$		0			0
$575$	−26.4648	+	23.8852i	−1.10366	+	0.996080i
$576$		0			0
$577$	7.14961	+	7.14961i	0.297642	+	0.297642i	0.840090	−	0.542448i	$-0.182502\pi$
$577$	7.14961	+	7.14961i	0.297642	+	0.297642i	−0.542448	+	0.840090i	$0.682502\pi$
$578$		0			0
$579$	13.0271			0.541387
$580$		0			0
$581$	1.64883	−	4.70818i	0.0684052	−	0.195328i
$582$		0			0
$583$	10.2687	+	10.2687i	0.425286	+	0.425286i
$584$		0			0
$585$	−0.226654	+	8.85363i	−0.00937099	+	0.366053i
$586$		0			0
$587$	11.8070	+	11.8070i	0.487326	+	0.487326i	0.907461	−	0.420135i	$-0.138017\pi$
$587$	11.8070	+	11.8070i	0.487326	+	0.487326i	−0.420135	+	0.907461i	$0.638017\pi$
$588$		0			0
$589$		−	40.2425i		−	1.65816i
$590$		0			0
$591$		−	25.3786i		−	1.04394i
$592$		0			0
$593$	−7.07055	+	7.07055i	−0.290353	+	0.290353i	−0.837220	−	0.546867i	$-0.815820\pi$
$593$	−7.07055	+	7.07055i	−0.290353	+	0.290353i	0.546867	+	0.837220i	$0.315820\pi$
$594$		0			0
$595$	3.18563	+	7.07746i	0.130598	+	0.290148i
$596$		0			0
$597$	7.98724	−	7.98724i	0.326896	−	0.326896i
$598$		0			0
$599$		−	43.9995i		−	1.79777i	−0.438182	−	0.898886i	$-0.644377\pi$
$599$		−	43.9995i		−	1.79777i	0.438182	−	0.898886i	$-0.355623\pi$
$600$		0			0
$601$			36.1285i			1.47371i	0.676051	+	0.736855i	$0.263690\pi$
$601$			36.1285i			1.47371i	−0.676051	+	0.736855i	$0.736310\pi$
$602$		0			0
$603$	−9.51496	−	9.51496i	−0.387479	−	0.387479i
$604$		0			0
$605$	−0.102562	−	0.107952i	−0.00416975	−	0.00438886i
$606$		0			0
$607$	−16.4198	−	16.4198i	−0.666457	−	0.666457i	0.290437	−	0.956894i	$-0.406199\pi$
$607$	−16.4198	−	16.4198i	−0.666457	−	0.666457i	−0.956894	+	0.290437i	$0.906199\pi$
$608$		0			0
$609$	−10.9586	−	3.83778i	−0.444066	−	0.155515i
$610$		0			0
$611$	45.3361			1.83410
$612$		0			0
$613$	−7.32133	−	7.32133i	−0.295706	−	0.295706i	0.543624	−	0.839329i	$-0.317052\pi$
$613$	−7.32133	−	7.32133i	−0.295706	−	0.295706i	−0.839329	+	0.543624i	$0.817052\pi$
$614$		0			0
$615$	0.0567843	−	2.21812i	0.00228976	−	0.0894434i
$616$		0			0
$617$	19.2296	−	19.2296i	0.774156	−	0.774156i	−0.204675	−	0.978830i	$-0.565614\pi$
$617$	19.2296	−	19.2296i	0.774156	−	0.774156i	0.978830	+	0.204675i	$0.0656136\pi$
$618$		0			0
$619$	−42.1535			−1.69429			−0.847146	−	0.531360i	$-0.821681\pi$
$619$	−42.1535			−1.69429			−0.847146	+	0.531360i	$0.821681\pi$
$620$		0			0
$621$		−	7.12989i		−	0.286113i
$622$		0			0
$623$	15.4750	−	7.44741i	0.619992	−	0.298374i
$624$		0			0
$625$	−24.8691	−	2.55499i	−0.994764	−	0.102199i
$626$		0			0
$627$	18.7803	−	18.7803i	0.750011	−	0.750011i
$628$		0			0
$629$	8.84050			0.352494
$630$		0			0
$631$	12.6561			0.503831			0.251916	−	0.967749i	$-0.418939\pi$
$631$	12.6561			0.503831			0.251916	+	0.967749i	$0.418939\pi$
$632$		0			0
$633$	−8.47585	+	8.47585i	−0.336885	+	0.336885i
$634$		0			0
$635$	−31.5372	−	0.807357i	−1.25152	−	0.0320390i
$636$		0			0
$637$	3.08996	+	27.5526i	0.122429	+	1.09167i
$638$		0			0
$639$			8.33595i			0.329765i
$640$		0			0
$641$	−38.5669			−1.52330			−0.761650	−	0.647989i	$-0.775610\pi$
$641$	−38.5669			−1.52330			−0.761650	+	0.647989i	$0.775610\pi$
$642$		0			0
$643$	22.6442	−	22.6442i	0.893001	−	0.893001i	−0.101804	−	0.994804i	$-0.532461\pi$
$643$	22.6442	−	22.6442i	0.893001	−	0.893001i	0.994804	+	0.101804i	$0.0324614\pi$
$644$		0			0
$645$	15.9744	+	16.8137i	0.628990	+	0.662040i
$646$		0			0
$647$	−13.4030	−	13.4030i	−0.526925	−	0.526925i	0.392729	−	0.919654i	$-0.371531\pi$
$647$	−13.4030	−	13.4030i	−0.526925	−	0.526925i	−0.919654	+	0.392729i	$0.871531\pi$
$648$		0			0
$649$	−9.15730			−0.359456
$650$		0			0
$651$	12.5105	+	4.38125i	0.490324	+	0.171715i
$652$		0			0
$653$	−20.0493	−	20.0493i	−0.784591	−	0.784591i	0.196010	−	0.980602i	$-0.437201\pi$
$653$	−20.0493	−	20.0493i	−0.784591	−	0.784591i	−0.980602	+	0.196010i	$0.937201\pi$
$654$		0			0
$655$	−11.3221	+	10.7568i	−0.442389	+	0.420304i
$656$		0			0
$657$	0.0150660	+	0.0150660i	0.000587782	+	0.000587782i
$658$		0			0
$659$		−	8.92589i		−	0.347703i	−0.984772	−	0.173852i	$-0.944379\pi$
$659$		−	8.92589i		−	0.347703i	0.984772	−	0.173852i	$-0.0556213\pi$
$660$		0			0
$661$		−	35.9123i		−	1.39683i	−0.715695	−	0.698413i	$-0.753890\pi$
$661$		−	35.9123i		−	1.39683i	0.715695	−	0.698413i	$-0.246110\pi$
$662$		0			0
$663$	3.67424	−	3.67424i	0.142696	−	0.142696i
$664$		0			0
$665$	−44.4322	−	16.8490i	−1.72301	−	0.653375i
$666$		0			0
$667$	−22.1257	+	22.1257i	−0.856710	+	0.856710i
$668$		0			0
$669$		−	7.86183i		−	0.303956i
$670$		0			0
$671$			1.36217i			0.0525861i
$672$		0			0
$673$	−6.02633	−	6.02633i	−0.232298	−	0.232298i	0.581353	−	0.813651i	$-0.302523\pi$
$673$	−6.02633	−	6.02633i	−0.232298	−	0.232298i	−0.813651	+	0.581353i	$0.802523\pi$
$674$		0			0
$675$	3.71180	−	3.35000i	0.142867	−	0.128942i
$676$		0			0
$677$	13.6480	+	13.6480i	0.524536	+	0.524536i	0.918938	−	0.394402i	$-0.129048\pi$
$677$	13.6480	+	13.6480i	0.524536	+	0.524536i	−0.394402	+	0.918938i	$0.629048\pi$
$678$		0			0
$679$	−15.6768	−	5.49011i	−0.601621	−	0.210691i
$680$		0			0
$681$	−12.9770			−0.497278
$682$		0			0
$683$	−6.98283	−	6.98283i	−0.267190	−	0.267190i	0.560777	−	0.827967i	$-0.310503\pi$
$683$	−6.98283	−	6.98283i	−0.267190	−	0.267190i	−0.827967	+	0.560777i	$0.810503\pi$
$684$		0			0
$685$	−7.54659	−	0.193194i	−0.288340	−	0.00738155i
$686$		0			0
$687$	6.38494	−	6.38494i	0.243601	−	0.243601i
$688$		0			0
$689$	−17.3953			−0.662708
$690$		0			0
$691$		−	19.2720i		−	0.733140i	−0.930390	−	0.366570i	$-0.880532\pi$
$691$		−	19.2720i		−	0.733140i	0.930390	−	0.366570i	$-0.119468\pi$
$692$		0			0
$693$	3.79373	+	7.88299i	0.144112	+	0.299450i
$694$		0			0
$695$	−7.53628	−	7.93228i	−0.285867	−	0.300888i
$696$		0			0
$697$	−0.920517	+	0.920517i	−0.0348671	+	0.0348671i
$698$		0			0
$699$	−22.8705			−0.865043
$700$		0			0
$701$	−22.4067			−0.846288			−0.423144	−	0.906062i	$-0.639074\pi$
$701$	−22.4067			−0.846288			−0.423144	+	0.906062i	$0.639074\pi$
$702$		0			0
$703$	−38.2734	+	38.2734i	−1.44351	+	1.44351i
$704$		0			0
$705$	−17.6291	−	18.5555i	−0.663951	−	0.698839i
$706$		0			0
$707$	14.0431	+	29.1801i	0.528144	+	1.09743i
$708$		0			0
$709$		−	38.7214i		−	1.45421i	−0.686524	−	0.727107i	$-0.740864\pi$
$709$		−	38.7214i		−	1.45421i	0.686524	−	0.727107i	$-0.259136\pi$
$710$		0			0
$711$	−3.28466			−0.123185
$712$		0			0
$713$	25.2589	−	25.2589i	0.945953	−	0.945953i
$714$		0			0
$715$	−29.2751	−	0.749448i	−1.09483	−	0.0280278i
$716$		0			0
$717$	6.87077	+	6.87077i	0.256593	+	0.256593i
$718$		0			0
$719$	−22.0846			−0.823616			−0.411808	−	0.911271i	$-0.635103\pi$
$719$	−22.0846			−0.823616			−0.411808	+	0.911271i	$0.635103\pi$
$720$		0			0
$721$	−17.1857	+	49.0732i	−0.640030	+	1.82758i
$722$		0			0
$723$	4.35152	+	4.35152i	0.161835	+	0.161835i
$724$		0			0
$725$	−21.9144	−	1.12276i	−0.813880	−	0.0416982i
$726$		0			0
$727$	−15.0229	−	15.0229i	−0.557167	−	0.557167i	0.371333	−	0.928500i	$-0.378901\pi$
$727$	−15.0229	−	15.0229i	−0.557167	−	0.557167i	−0.928500	+	0.371333i	$0.878901\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	13.6070i		−	0.503273i
$732$		0			0
$733$	25.0894	−	25.0894i	0.926697	−	0.926697i	−0.0707944	−	0.997491i	$-0.522553\pi$
$733$	25.0894	−	25.0894i	0.926697	−	0.926697i	0.997491	+	0.0707944i	$0.0225534\pi$
$734$		0			0
$735$	10.0754	−	11.9786i	0.371635	−	0.441838i
$736$		0			0
$737$	31.4619	−	31.4619i	1.15891	−	1.15891i
$738$		0			0
$739$			14.4902i			0.533032i	0.963830	+	0.266516i	$0.0858726\pi$
$739$			14.4902i			0.533032i	−0.963830	+	0.266516i	$0.914127\pi$
$740$		0			0
$741$			31.8139i			1.16871i
$742$		0			0
$743$	4.39593	+	4.39593i	0.161271	+	0.161271i	0.783130	−	0.621859i	$-0.213622\pi$
$743$	4.39593	+	4.39593i	0.161271	+	0.161271i	−0.621859	+	0.783130i	$0.713622\pi$
$744$		0			0
$745$	16.5855	−	15.7575i	0.607646	−	0.577311i
$746$		0			0
$747$	1.33325	+	1.33325i	0.0487809	+	0.0487809i
$748$		0			0
$749$	−1.36394	+	3.89469i	−0.0498374	+	0.142309i
$750$		0			0
$751$	42.5913			1.55418			0.777089	−	0.629390i	$-0.216695\pi$
$751$	42.5913			1.55418			0.777089	+	0.629390i	$0.216695\pi$
$752$		0			0
$753$	−4.74533	−	4.74533i	−0.172929	−	0.172929i
$754$		0			0
$755$	31.5872	+	33.2470i	1.14958	+	1.20998i
$756$		0			0
$757$	−1.49575	+	1.49575i	−0.0543639	+	0.0543639i	−0.733766	−	0.679402i	$-0.762239\pi$
$757$	−1.49575	+	1.49575i	−0.0543639	+	0.0543639i	0.679402	+	0.733766i	$0.262239\pi$
$758$		0			0
$759$	23.5755			0.855736
$760$		0			0
$761$			39.8014i			1.44280i	0.692519	+	0.721400i	$0.256501\pi$
$761$			39.8014i			1.44280i	−0.692519	+	0.721400i	$0.743499\pi$
$762$		0			0
$763$	11.1612	+	23.1920i	0.404064	+	0.839605i
$764$		0			0
$765$	−2.93256	−	0.0750738i	−0.106027	−	0.00271430i
$766$		0			0
$767$	7.75628	−	7.75628i	0.280063	−	0.280063i
$768$		0			0
$769$	−16.3914			−0.591087			−0.295544	−	0.955329i	$-0.595501\pi$
$769$	−16.3914			−0.591087			−0.295544	+	0.955329i	$0.595501\pi$
$770$		0			0
$771$	−16.6192			−0.598528
$772$		0			0
$773$	−29.4949	+	29.4949i	−1.06086	+	1.06086i	−0.0628341	+	0.998024i	$0.520014\pi$
$773$	−29.4949	+	29.4949i	−1.06086	+	1.06086i	−0.998024	+	0.0628341i	$0.979986\pi$
$774$		0			0
$775$	25.0177	+	1.28175i	0.898661	+	0.0460419i
$776$		0			0
$777$	−7.73146	−	16.0652i	−0.277365	−	0.576336i
$778$		0			0
$779$		−	7.97043i		−	0.285570i
$780$		0			0
$781$	−27.5634			−0.986297
$782$		0			0
$783$	3.10323	−	3.10323i	0.110900	−	0.110900i
$784$		0			0
$785$	0.517598	−	20.2186i	0.0184739	−	0.721632i
$786$		0			0
$787$	29.8578	+	29.8578i	1.06432	+	1.06432i	0.997784	+	0.0665308i	$0.0211931\pi$
$787$	29.8578	+	29.8578i	1.06432	+	1.06432i	0.0665308	+	0.997784i	$0.478807\pi$
$788$		0			0
$789$	8.99745			0.320318
$790$		0			0
$791$	6.78027	+	2.37449i	0.241079	+	0.0844273i
$792$		0			0
$793$	−1.15377	−	1.15377i	−0.0409715	−	0.0409715i
$794$		0			0
$795$	6.76422	+	7.11965i	0.239902	+	0.252508i
$796$		0			0
$797$	−7.34863	−	7.34863i	−0.260302	−	0.260302i	0.564875	−	0.825177i	$-0.308924\pi$
$797$	−7.34863	−	7.34863i	−0.260302	−	0.260302i	−0.825177	+	0.564875i	$0.808924\pi$
$798$		0			0
$799$			15.0165i			0.531247i
$800$		0			0
$801$			6.49108i			0.229351i
$802$		0			0
$803$	−0.0498169	+	0.0498169i	−0.00175800	+	0.00175800i
$804$		0			0
$805$	−17.3131	−	38.4642i	−0.610207	−	1.35569i
$806$		0			0
$807$	10.0530	−	10.0530i	0.353881	−	0.353881i
$808$		0			0
$809$			26.2729i			0.923705i	0.886957	+	0.461852i	$0.152815\pi$
$809$			26.2729i			0.923705i	−0.886957	+	0.461852i	$0.847185\pi$
$810$		0			0
$811$			37.7025i			1.32391i	0.749541	+	0.661957i	$0.230274\pi$
$811$			37.7025i			1.32391i	−0.749541	+	0.661957i	$0.769726\pi$
$812$		0			0
$813$	6.87319	+	6.87319i	0.241053	+	0.241053i
$814$		0			0
$815$	1.41160	−	55.1403i	0.0494461	−	1.93148i
$816$		0			0
$817$	58.9091	+	58.9091i	2.06097	+	2.06097i
$818$		0			0
$819$	−9.89023	−	3.46362i	−0.345593	−	0.121029i
$820$		0			0
$821$	34.9203			1.21873			0.609364	−	0.792891i	$-0.291425\pi$
$821$	34.9203			1.21873			0.609364	+	0.792891i	$0.291425\pi$
$822$		0			0
$823$	−25.5459	−	25.5459i	−0.890474	−	0.890474i	0.104093	−	0.994568i	$-0.466806\pi$
$823$	−25.5459	−	25.5459i	−0.890474	−	0.890474i	−0.994568	+	0.104093i	$0.966806\pi$
$824$		0			0
$825$	11.0770	+	12.2733i	0.385652	+	0.427303i
$826$		0			0
$827$	24.9245	−	24.9245i	0.866711	−	0.866711i	−0.125396	−	0.992107i	$-0.540020\pi$
$827$	24.9245	−	24.9245i	0.866711	−	0.866711i	0.992107	+	0.125396i	$0.0400201\pi$
$828$		0			0
$829$	−12.4782			−0.433384			−0.216692	−	0.976240i	$-0.569527\pi$
$829$	−12.4782			−0.433384			−0.216692	+	0.976240i	$0.569527\pi$
$830$		0			0
$831$			19.9294i			0.691345i
$832$		0			0
$833$	−9.12615	+	1.02348i	−0.316202	+	0.0354614i
$834$		0			0
$835$	0.878455	−	34.3145i	0.0304002	−	1.18750i
$836$		0			0
$837$	−3.54267	+	3.54267i	−0.122453	+	0.122453i
$838$		0			0
$839$	−27.5888			−0.952470			−0.476235	−	0.879318i	$-0.657999\pi$
$839$	−27.5888			−0.952470			−0.476235	+	0.879318i	$0.657999\pi$
$840$		0			0
$841$	9.73996			0.335861
$842$		0			0
$843$	21.8002	−	21.8002i	0.750837	−	0.750837i
$844$		0			0
$845$	4.35687	−	4.13936i	0.149881	−	0.142398i
$846$		0			0
$847$	0.158758	−	0.0764032i	0.00545500	−	0.00262525i
$848$		0			0
$849$		−	18.2068i		−	0.624855i
$850$		0			0
$851$	−48.0459			−1.64699
$852$		0			0
$853$	10.1266	−	10.1266i	0.346728	−	0.346728i	−0.512161	−	0.858889i	$-0.671155\pi$
$853$	10.1266	−	10.1266i	0.346728	−	0.346728i	0.858889	+	0.512161i	$0.171155\pi$
$854$		0			0
$855$	13.0210	−	12.3710i	0.445309	−	0.423078i
$856$		0			0
$857$	−5.64323	−	5.64323i	−0.192769	−	0.192769i	0.604122	−	0.796892i	$-0.293524\pi$
$857$	−5.64323	−	5.64323i	−0.192769	−	0.192769i	−0.796892	+	0.604122i	$0.793524\pi$
$858$		0			0
$859$	−47.0785			−1.60630			−0.803149	−	0.595778i	$-0.796844\pi$
$859$	−47.0785			−1.60630			−0.803149	+	0.595778i	$0.796844\pi$
$860$		0			0
$861$	2.47783	+	0.867751i	0.0844442	+	0.0295729i
$862$		0			0
$863$	27.2163	+	27.2163i	0.926454	+	0.926454i	0.997475	−	0.0710211i	$-0.0226258\pi$
$863$	27.2163	+	27.2163i	0.926454	+	0.926454i	−0.0710211	+	0.997475i	$0.522626\pi$
$864$		0			0
$865$	−57.3766	−	1.46885i	−1.95086	−	0.0499424i
$866$		0			0
$867$	−10.8038	−	10.8038i	−0.366917	−	0.366917i
$868$		0			0
$869$		−	10.8610i		−	0.368433i
$870$		0			0
$871$			53.2967i			1.80589i
$872$		0			0
$873$	4.43930	−	4.43930i	0.150248	−	0.150248i
$874$		0			0
$875$	11.8898	−	27.0857i	0.401947	−	0.915663i
$876$		0			0
$877$	−18.8569	+	18.8569i	−0.636753	+	0.636753i	−0.949753	−	0.313000i	$-0.898666\pi$
$877$	−18.8569	+	18.8569i	−0.636753	+	0.636753i	0.313000	+	0.949753i	$0.398666\pi$
$878$		0			0
$879$		−	25.2106i		−	0.850332i
$880$		0			0
$881$			9.31247i			0.313745i	0.987619	+	0.156872i	$0.0501412\pi$
$881$			9.31247i			0.313745i	−0.987619	+	0.156872i	$0.949859\pi$
$882$		0			0
$883$	−3.39683	−	3.39683i	−0.114313	−	0.114313i	0.647637	−	0.761949i	$-0.275757\pi$
$883$	−3.39683	−	3.39683i	−0.114313	−	0.114313i	−0.761949	+	0.647637i	$0.775757\pi$
$884$		0			0
$885$	−6.19060	−	0.158480i	−0.208095	−	0.00532725i
$886$		0			0
$887$	−35.4671	−	35.4671i	−1.19087	−	1.19087i	−0.976824	−	0.214046i	$-0.931336\pi$
$887$	−35.4671	−	35.4671i	−1.19087	−	1.19087i	−0.214046	−	0.976824i	$-0.568664\pi$
$888$		0			0
$889$	12.3377	−	35.2297i	0.413792	−	1.18157i
$890$		0			0
$891$	−3.30657			−0.110774
$892$		0			0
$893$	−65.0114	−	65.0114i	−2.17552	−	2.17552i
$894$		0			0
$895$	9.45805	−	8.98589i	0.316148	−	0.300365i
$896$		0			0
$897$	−19.9686	+	19.9686i	−0.666731	+	0.666731i
$898$		0			0
$899$	21.9874			0.733322
$900$		0			0
$901$		−	5.76178i		−	0.191953i
$902$		0			0
$903$	−24.7270	+	11.9000i	−0.822863	+	0.396007i
$904$		0			0
$905$	14.4920	−	13.7685i	0.481730	−	0.457681i
$906$		0			0
$907$	25.6491	−	25.6491i	0.851663	−	0.851663i	−0.138675	−	0.990338i	$-0.544284\pi$
$907$	25.6491	−	25.6491i	0.851663	−	0.851663i	0.990338	+	0.138675i	$0.0442842\pi$
$908$		0			0
$909$	−12.2398			−0.405968
$910$		0			0
$911$	−16.6517			−0.551696			−0.275848	−	0.961201i	$-0.588959\pi$
$911$	−16.6517			−0.551696			−0.275848	+	0.961201i	$0.588959\pi$
$912$		0			0
$913$	−4.40847	+	4.40847i	−0.145899	+	0.145899i
$914$		0			0
$915$	−0.0235743	+	0.920868i	−0.000779343	+	0.0304429i
$916$		0			0
$917$	−8.01324	−	16.6507i	−0.264620	−	0.549855i
$918$		0			0
$919$			3.48300i			0.114894i	0.998349	+	0.0574468i	$0.0182959\pi$
$919$			3.48300i			0.114894i	−0.998349	+	0.0574468i	$0.981704\pi$
$920$		0			0
$921$	−5.73778			−0.189066
$922$		0			0
$923$	23.3463	−	23.3463i	0.768454	−	0.768454i
$924$		0			0
$925$	−22.5745	−	25.0126i	−0.742245	−	0.822408i
$926$		0			0
$927$	−13.8964	−	13.8964i	−0.456417	−	0.456417i
$928$		0			0
$929$	−43.7356			−1.43492			−0.717460	−	0.696600i	$-0.754695\pi$
$929$	−43.7356			−1.43492			−0.717460	+	0.696600i	$0.754695\pi$
$930$		0			0
$931$	35.0791	−	43.9410i	1.14967	−	1.44011i
$932$		0			0
$933$	9.79272	+	9.79272i	0.320599	+	0.320599i
$934$		0			0
$935$	0.248237	−	9.69671i	0.00811822	−	0.317116i
$936$		0			0
$937$	16.3420	+	16.3420i	0.533869	+	0.533869i	0.921722	−	0.387852i	$-0.126783\pi$
$937$	16.3420	+	16.3420i	0.533869	+	0.533869i	−0.387852	+	0.921722i	$0.626783\pi$
$938$		0			0
$939$			24.2117i			0.790120i
$940$		0			0
$941$			50.4764i			1.64548i	0.568416	+	0.822741i	$0.307556\pi$
$941$			50.4764i			1.64548i	−0.568416	+	0.822741i	$0.692444\pi$
$942$		0			0
$943$	5.00278	−	5.00278i	0.162913	−	0.162913i
$944$		0			0
$945$	2.42824	+	5.39478i	0.0789907	+	0.175492i
$946$		0			0
$947$	−31.3656	+	31.3656i	−1.01924	+	1.01924i	−0.0194338	+	0.999811i	$0.506186\pi$
$947$	−31.3656	+	31.3656i	−1.01924	+	1.01924i	−0.999811	+	0.0194338i	$0.993814\pi$
$948$		0			0
$949$		−	0.0843902i		−	0.00273942i
$950$		0			0
$951$		−	2.84809i		−	0.0923558i
$952$		0			0
$953$	10.5126	+	10.5126i	0.340537	+	0.340537i	0.856569	−	0.516032i	$-0.172592\pi$
$953$	10.5126	+	10.5126i	0.340537	+	0.340537i	−0.516032	+	0.856569i	$0.672592\pi$
$954$		0			0
$955$	−32.0818	−	33.7675i	−1.03814	−	1.09269i
$956$		0			0
$957$	10.2610	+	10.2610i	0.331692	+	0.331692i
$958$		0			0
$959$	2.95229	−	8.43016i	0.0953345	−	0.272224i
$960$		0			0
$961$	5.89893			0.190288
$962$		0			0
$963$	−1.10288	−	1.10288i	−0.0355399	−	0.0355399i
$964$		0			0
$965$	−0.745473	+	29.1199i	−0.0239976	+	0.937402i
$966$		0			0
$967$	6.63418	−	6.63418i	0.213341	−	0.213341i	−0.592344	−	0.805685i	$-0.701797\pi$
$967$	6.63418	−	6.63418i	0.213341	−	0.213341i	0.805685	+	0.592344i	$0.201797\pi$
$968$		0			0
$969$	−10.5376			−0.338517
$970$		0			0
$971$			47.0663i			1.51043i	0.655477	+	0.755215i	$0.272468\pi$
$971$			47.0663i			1.51043i	−0.655477	+	0.755215i	$0.727532\pi$
$972$		0			0
$973$	11.6655	−	5.61410i	0.373980	−	0.179980i
$974$		0			0
$975$	−19.7779	−	1.01330i	−0.633399	−	0.0324514i
$976$		0			0
$977$	−7.89292	+	7.89292i	−0.252517	+	0.252517i	−0.822002	−	0.569485i	$-0.807143\pi$
$977$	−7.89292	+	7.89292i	−0.252517	+	0.252517i	0.569485	+	0.822002i	$0.307143\pi$
$978$		0			0
$979$	−21.4632			−0.685967
$980$		0			0
$981$	−9.72802			−0.310592
$982$		0			0
$983$	2.22421	−	2.22421i	0.0709413	−	0.0709413i	−0.670746	−	0.741687i	$-0.734026\pi$
$983$	2.22421	−	2.22421i	0.0709413	−	0.0709413i	0.741687	+	0.670746i	$0.234026\pi$
$984$		0			0
$985$	56.7297	+	1.45229i	1.80756	+	0.0462737i
$986$		0			0
$987$	27.2885	−	13.1327i	0.868601	−	0.418019i
$988$		0			0
$989$			73.9506i			2.35149i
$990$		0			0
$991$	36.0131			1.14399			0.571997	−	0.820256i	$-0.306169\pi$
$991$	36.0131			1.14399			0.571997	+	0.820256i	$0.306169\pi$
$992$		0			0
$993$	2.06835	−	2.06835i	0.0656370	−	0.0656370i
$994$		0			0
$995$	17.3971	+	18.3112i	0.551525	+	0.580505i
$996$		0			0
$997$	3.25326	+	3.25326i	0.103032	+	0.103032i	0.756744	−	0.653712i	$-0.226789\pi$
$997$	3.25326	+	3.25326i	0.103032	+	0.103032i	−0.653712	+	0.756744i	$0.726789\pi$
$998$		0			0
$999$	6.73866			0.213202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bt.a.433.11	yes	24
4.3	odd	2		1680.2.cz.f.433.2		24
5.2	odd	4		840.2.bt.b.97.2	yes	24
7.6	odd	2		840.2.bt.b.433.2	yes	24
20.7	even	4		1680.2.cz.e.97.11		24
28.27	even	2		1680.2.cz.e.433.11		24
35.27	even	4	inner	840.2.bt.a.97.11	✓	24
140.27	odd	4		1680.2.cz.f.97.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.11	✓	24	35.27	even	4	inner
840.2.bt.a.433.11	yes	24	1.1	even	1	trivial
840.2.bt.b.97.2	yes	24	5.2	odd	4
840.2.bt.b.433.2	yes	24	7.6	odd	2
1680.2.cz.e.97.11		24	20.7	even	4
1680.2.cz.e.433.11		24	28.27	even	2
1680.2.cz.f.97.2		24	140.27	odd	4
1680.2.cz.f.433.2		24	4.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bt (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.54016 + 1.62109i) q^{5} +(-2.38404 + 1.14733i) q^{7} -1.00000i q^{9} +3.30657 q^{11} +(-2.80068 + 2.80068i) q^{13} +(2.23534 + 0.0572249i) q^{15} +(-0.927660 - 0.927660i) q^{17} +8.03228 q^{19} +(-0.874484 + 2.49705i) q^{21} +(5.04160 + 5.04160i) q^{23} +(-0.255834 + 4.99345i) q^{25} +(-0.707107 - 0.707107i) q^{27} +4.38863i q^{29} -5.01010i q^{31} +(2.33810 - 2.33810i) q^{33} +(-5.53171 - 2.09766i) q^{35} +(-4.76495 + 4.76495i) q^{37} +3.96076i q^{39} -0.992301i q^{41} +(7.33404 + 7.33404i) q^{43} +(1.62109 - 1.54016i) q^{45} +(-8.09377 - 8.09377i) q^{47} +(4.36727 - 5.47056i) q^{49} -1.31191 q^{51} +(3.10555 + 3.10555i) q^{53} +(5.09264 + 5.36023i) q^{55} +(5.67968 - 5.67968i) q^{57} -2.76943 q^{59} +0.411959i q^{61} +(1.14733 + 2.38404i) q^{63} +(-8.85363 - 0.226654i) q^{65} +(9.51496 - 9.51496i) q^{67} +7.12989 q^{69} -8.33595 q^{71} +(-0.0150660 + 0.0150660i) q^{73} +(3.35000 + 3.71180i) q^{75} +(-7.88299 + 3.79373i) q^{77} -3.28466i q^{79} -1.00000 q^{81} +(-1.33325 + 1.33325i) q^{83} +(0.0750738 - 2.93256i) q^{85} +(3.10323 + 3.10323i) q^{87} -6.49108 q^{89} +(3.46362 - 9.89023i) q^{91} +(-3.54267 - 3.54267i) q^{93} +(12.3710 + 13.0210i) q^{95} +(4.43930 + 4.43930i) q^{97} -3.30657i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} + 20 q^{17} + 8 q^{19} + 24 q^{23} - 4 q^{25} + 4 q^{37} - 16 q^{43} - 4 q^{45} - 24 q^{47} + 36 q^{49} + 16 q^{53} + 28 q^{55} + 4 q^{57} + 8 q^{59} + 24 q^{65}+ \cdots - 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 + 20 * q^17 + 8 * q^19 + 24 * q^23 - 4 * q^25 + 4 * q^37 - 16 * q^43 - 4 * q^45 - 24 * q^47 + 36 * q^49 + 16 * q^53 + 28 * q^55 + 4 * q^57 + 8 * q^59 + 24 * q^65 + 16 * q^67 - 8 * q^69 + 8 * q^71 - 28 * q^73 + 20 * q^77 - 24 * q^81 + 64 * q^83 - 20 * q^85 + 20 * q^87 + 16 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 28 * q^97

Introduction

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