LMFDB - Embedded newform 840.2.bt.a.97.11

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			97.11
Character	$\chi$	$=$	840.97
Dual form			840.2.bt.a.433.11

$q$-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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

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

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	0.202511	−	0.979280i	$-0.435090\pi$
$13$	−2.80068	−	2.80068i	−0.776769	−	0.776769i	−0.979280	+	0.202511i	$0.935090\pi$
$14$		0			0
$15$	2.23534	−	0.0572249i	0.577161	−	0.0147754i
$16$		0			0
$17$	−0.927660	+	0.927660i	−0.224991	+	0.224991i	−0.810596	−	0.585606i	$-0.800857\pi$
$17$	−0.927660	+	0.927660i	−0.224991	+	0.224991i	0.585606	+	0.810596i	$0.300857\pi$
$18$		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	0.0526316	−	0.998614i	$-0.483239\pi$
$23$	5.04160	−	5.04160i	1.05125	−	1.05125i	0.998614	−	0.0526316i	$-0.0167609\pi$
$24$		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	$-0.866410\pi$
$29$		−	4.38863i		−	0.814947i	0.913217	−	0.407474i	$-0.133590\pi$
$30$		0			0
$31$			5.01010i			0.899840i	0.893069	+	0.449920i	$0.148547\pi$
$31$			5.01010i			0.899840i	−0.893069	+	0.449920i	$0.851453\pi$
$32$		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	0.197042	−	0.980395i	$-0.436866\pi$
$37$	−4.76495	−	4.76495i	−0.783353	−	0.783353i	−0.980395	+	0.197042i	$0.936866\pi$
$38$		0			0
$39$		−	3.96076i		−	0.634229i
$40$		0			0
$41$			0.992301i			0.154971i	0.996993	+	0.0774857i	$0.0246892\pi$
$41$			0.992301i			0.154971i	−0.996993	+	0.0774857i	$0.975311\pi$
$42$		0			0
$43$	7.33404	−	7.33404i	1.11843	−	1.11843i	0.126459	−	0.991972i	$-0.459639\pi$
$43$	7.33404	−	7.33404i	1.11843	−	1.11843i	0.991972	−	0.126459i	$-0.0403612\pi$
$44$		0			0
$45$	1.62109	+	1.54016i	0.241657	+	0.229593i
$46$		0			0
$47$	−8.09377	+	8.09377i	−1.18060	+	1.18060i	−0.201008	+	0.979590i	$0.564422\pi$
$47$	−8.09377	+	8.09377i	−1.18060	+	1.18060i	−0.979590	+	0.201008i	$0.935578\pi$
$48$		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	−0.460882	−	0.887461i	$-0.652467\pi$
$53$	3.10555	−	3.10555i	0.426580	−	0.426580i	0.887461	+	0.460882i	$0.152467\pi$
$54$		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	$-0.991604\pi$
$61$		−	0.411959i		−	0.0527460i	0.999652	−	0.0263730i	$-0.00839576\pi$
$62$		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	0.983940	+	0.178497i	$0.0571235\pi$
$67$	9.51496	+	9.51496i	1.16244	+	1.16244i	0.178497	+	0.983940i	$0.442876\pi$
$68$		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	0.706225	−	0.707988i	$-0.250397\pi$
$73$	−0.0150660	−	0.0150660i	−0.00176334	−	0.00176334i	−0.707988	+	0.706225i	$0.750397\pi$
$74$		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	$0.0591562\pi$
$79$			3.28466i			0.369554i	−0.982781	+	0.184777i	$0.940844\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−1.33325	−	1.33325i	−0.146343	−	0.146343i	0.630139	−	0.776482i	$-0.282998\pi$
$83$	−1.33325	−	1.33325i	−0.146343	−	0.146343i	−0.776482	+	0.630139i	$0.782998\pi$
$84$		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	−0.444858	−	0.895601i	$-0.646746\pi$
$97$	4.43930	−	4.43930i	0.450743	−	0.450743i	0.895601	+	0.444858i	$0.146746\pi$
$98$		0			0
$99$			3.30657i			0.332323i
$100$		0			0
$101$			12.2398i			1.21790i	0.793207	+	0.608952i	$0.208410\pi$
$101$			12.2398i			1.21790i	−0.793207	+	0.608952i	$0.791590\pi$
$102$		0			0
$103$	13.8964	+	13.8964i	1.36925	+	1.36925i	0.861511	+	0.507738i	$0.169518\pi$
$103$	13.8964	+	13.8964i	1.36925	+	1.36925i	0.507738	+	0.861511i	$0.330482\pi$
$104$		0			0
$105$	−5.39478	−	2.42824i	−0.526477	−	0.236972i
$106$		0			0
$107$	1.10288	+	1.10288i	0.106620	+	0.106620i	0.758404	−	0.651784i	$-0.225979\pi$
$107$	1.10288	+	1.10288i	0.106620	+	0.106620i	−0.651784	+	0.758404i	$0.725979\pi$
$108$		0			0
$109$			9.72802i			0.931775i	0.884844	+	0.465887i	$0.154265\pi$
$109$			9.72802i			0.931775i	−0.884844	+	0.465887i	$0.845735\pi$
$110$		0			0
$111$		−	6.73866i		−	0.639605i
$112$		0			0
$113$	−1.92001	+	1.92001i	−0.180620	+	0.180620i	−0.791626	−	0.611006i	$-0.790765\pi$
$113$	−1.92001	+	1.92001i	−0.180620	+	0.180620i	0.611006	+	0.791626i	$0.290765\pi$
$114$		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	0.108816	−	0.994062i	$-0.465294\pi$
$127$	−9.97622	−	9.97622i	−0.885246	−	0.885246i	−0.994062	+	0.108816i	$0.965294\pi$
$128$		0			0
$129$	10.3719			0.913195
$130$		0			0
$131$		−	6.98425i		−	0.610216i	−0.952318	−	0.305108i	$-0.901307\pi$
$131$		−	6.98425i		−	0.610216i	0.952318	−	0.305108i	$-0.0986926\pi$
$132$		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	0.597738	−	0.801692i	$-0.296066\pi$
$137$	−2.38722	−	2.38722i	−0.203954	−	0.203954i	−0.801692	+	0.597738i	$0.796066\pi$
$138$		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	$0.137648\pi$
$149$			10.2311i			0.838165i	−0.907948	+	0.419083i	$0.862352\pi$
$150$		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	−0.914661	−	0.404223i	$-0.867542\pi$
$157$	−6.39577	+	6.39577i	−0.510438	+	0.510438i	0.404223	+	0.914661i	$0.367542\pi$
$158$		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	−0.500436	+	0.865774i	$0.666827\pi$
$163$	−17.4426	+	17.4426i	−1.36621	+	1.36621i	−0.865774	+	0.500436i	$0.833173\pi$
$164$		0			0
$165$	7.39129	−	0.189218i	0.575412	−	0.0147306i
$166$		0			0
$167$	−10.8547	+	10.8547i	−0.839965	+	0.839965i	−0.988854	−	0.148889i	$-0.952430\pi$
$167$	−10.8547	+	10.8547i	−0.839965	+	0.839965i	0.148889	+	0.988854i	$0.452430\pi$
$168$		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	−0.844732	−	0.535189i	$-0.820240\pi$
$173$	−18.1500	−	18.1500i	−1.37992	−	1.37992i	−0.535189	−	0.844732i	$-0.679760\pi$
$174$		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	$0.0699669\pi$
$179$			5.83440i			0.436083i	−0.975939	+	0.218042i	$0.930033\pi$
$180$		0			0
$181$			8.93968i			0.664481i	0.943195	+	0.332241i	$0.107805\pi$
$181$			8.93968i			0.664481i	−0.943195	+	0.332241i	$0.892195\pi$
$182$		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	−0.293040	−	0.956100i	$-0.594667\pi$
$193$	9.21153	−	9.21153i	0.663061	−	0.663061i	0.956100	+	0.293040i	$0.0946668\pi$
$194$		0			0
$195$	−6.42073	−	6.10019i	−0.459798	−	0.436844i
$196$		0			0
$197$	17.9454	+	17.9454i	1.27856	+	1.27856i	0.941477	+	0.337079i	$0.109439\pi$
$197$	17.9454	+	17.9454i	1.27856	+	1.27856i	0.337079	+	0.941477i	$0.390561\pi$
$198$		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	0.868303	−	0.496034i	$-0.165211\pi$
$223$	5.55915	+	5.55915i	0.372269	+	0.372269i	−0.496034	+	0.868303i	$0.665211\pi$
$224$		0			0
$225$	4.99345	−	0.255834i	0.332897	−	0.0170556i
$226$		0			0
$227$	−9.17610	+	9.17610i	−0.609039	+	0.609039i	−0.942695	−	0.333656i	$-0.891718\pi$
$227$	−9.17610	+	9.17610i	−0.609039	+	0.609039i	0.333656	+	0.942695i	$0.391718\pi$
$228$		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	−0.0613399	+	0.998117i	$0.519537\pi$
$233$	−16.1719	+	16.1719i	−1.05946	+	1.05946i	−0.998117	+	0.0613399i	$0.980463\pi$
$234$		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	$-0.898243\pi$
$239$		−	9.71673i		−	0.628523i	0.949336	−	0.314262i	$-0.101757\pi$
$240$		0			0
$241$		−	6.15398i		−	0.396413i	−0.980160	−	0.198206i	$-0.936488\pi$
$241$		−	6.15398i		−	0.396413i	0.980160	−	0.198206i	$-0.0635116\pi$
$242$		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	$0.0679307\pi$
$251$			6.71090i			0.423588i	−0.977314	+	0.211794i	$0.932069\pi$
$252$		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	−0.971222	−	0.238178i	$-0.923450\pi$
$257$	−11.7516	+	11.7516i	−0.733044	+	0.733044i	0.238178	+	0.971222i	$0.423450\pi$
$258$		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	−0.483202	−	0.875509i	$-0.660526\pi$
$263$	6.36216	−	6.36216i	0.392308	−	0.392308i	0.875509	+	0.483202i	$0.160526\pi$
$264$		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	$-0.904604\pi$
$271$		−	9.72015i		−	0.590457i	0.955427	−	0.295229i	$-0.0953958\pi$
$272$		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	0.143001	−	0.989722i	$-0.454325\pi$
$277$	−14.0922	−	14.0922i	−0.846721	−	0.846721i	−0.989722	+	0.143001i	$0.954325\pi$
$278$		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	0.977273	−	0.211985i	$-0.0679928\pi$
$283$	12.8741	+	12.8741i	0.765288	+	0.765288i	−0.211985	+	0.977273i	$0.567993\pi$
$284$		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	0.999103	+	0.0423367i	$0.0134802\pi$
$293$	17.8266	+	17.8266i	1.04144	+	1.04144i	0.0423367	+	0.999103i	$0.486520\pi$
$294$		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	−0.813343	−	0.581785i	$-0.802355\pi$
$307$	−4.05722	+	4.05722i	−0.231558	+	0.231558i	0.581785	+	0.813343i	$0.302355\pi$
$308$		0			0
$309$			19.6524i			1.11799i
$310$		0			0
$311$		−	13.8490i		−	0.785305i	−0.919687	−	0.392652i	$-0.871558\pi$
$311$		−	13.8490i		−	0.785305i	0.919687	−	0.392652i	$-0.128442\pi$
$312$		0			0
$313$	−17.1203	−	17.1203i	−0.967695	−	0.967695i	0.0317993	−	0.999494i	$-0.489876\pi$
$313$	−17.1203	−	17.1203i	−0.967695	−	0.967695i	−0.999494	+	0.0317993i	$0.989876\pi$
$314$		0			0
$315$	−2.09766	−	5.53171i	−0.118190	−	0.311677i
$316$		0			0
$317$	2.01391	+	2.01391i	0.113112	+	0.113112i	0.761398	−	0.648285i	$-0.224514\pi$
$317$	2.01391	+	2.01391i	0.113112	+	0.113112i	−0.648285	+	0.761398i	$0.724514\pi$
$318$		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	0.618969	−	0.785416i	$-0.287551\pi$
$337$	−3.05556	−	3.05556i	−0.166447	−	0.166447i	−0.785416	+	0.618969i	$0.787551\pi$
$338$		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	0.846360	−	0.532611i	$-0.178789\pi$
$347$	5.84450	+	5.84450i	0.313749	+	0.313749i	−0.532611	+	0.846360i	$0.678789\pi$
$348$		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	−0.988387	−	0.151961i	$-0.951441\pi$
$353$	−21.4252	−	21.4252i	−1.14035	−	1.14035i	−0.151961	−	0.988387i	$-0.548559\pi$
$354$		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	$-0.959431\pi$
$359$		−	4.81661i		−	0.254211i	0.991889	−	0.127106i	$-0.0405687\pi$
$360$		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	−0.527256	−	0.849707i	$-0.676779\pi$
$367$	6.17728	−	6.17728i	0.322451	−	0.322451i	0.849707	+	0.527256i	$0.176779\pi$
$368$		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	0.277413	−	0.960751i	$-0.410523\pi$
$373$	23.9129	−	23.9129i	1.23816	−	1.23816i	0.960751	−	0.277413i	$-0.0894770\pi$
$374$		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	$-0.902746\pi$
$379$		−	11.7119i		−	0.601599i	0.953687	−	0.300800i	$-0.0972536\pi$
$380$		0			0
$381$		−	14.1085i		−	0.722800i
$382$		0			0
$383$	−0.575801	−	0.575801i	−0.0294221	−	0.0294221i	0.692243	−	0.721665i	$-0.256623\pi$
$383$	−0.575801	−	0.575801i	−0.0294221	−	0.0294221i	−0.721665	+	0.692243i	$0.756623\pi$
$384$		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	$0.00136589\pi$
$389$			0.169265i			0.00858209i	−0.999991	+	0.00429104i	$0.998634\pi$
$390$		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	−0.564452	−	0.825466i	$-0.690912\pi$
$397$	5.20067	−	5.20067i	0.261014	−	0.261014i	0.825466	+	0.564452i	$0.190912\pi$
$398$		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	0.804281	−	0.594249i	$-0.202551\pi$
$433$	4.37049	+	4.37049i	0.210032	+	0.210032i	−0.594249	+	0.804281i	$0.702551\pi$
$434$		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	−0.988485	−	0.151317i	$-0.951649\pi$
$443$	−17.6204	+	17.6204i	−0.837168	+	0.837168i	0.151317	+	0.988485i	$0.451649\pi$
$444$		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	$-0.842525\pi$
$449$		−	20.1212i		−	0.949576i	0.880100	−	0.474788i	$-0.157475\pi$
$450$		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	0.671861	−	0.740677i	$-0.265495\pi$
$457$	−1.47111	−	1.47111i	−0.0688157	−	0.0688157i	−0.740677	+	0.671861i	$0.765495\pi$
$458$		0			0
$459$		−	1.31191i		−	0.0612347i
$460$		0			0
$461$		−	18.2023i		−	0.847768i	−0.905717	−	0.423884i	$-0.860666\pi$
$461$		−	18.2023i		−	0.847768i	0.905717	−	0.423884i	$-0.139334\pi$
$462$		0			0
$463$	−5.77953	+	5.77953i	−0.268598	+	0.268598i	−0.828535	−	0.559937i	$-0.810825\pi$
$463$	−5.77953	+	5.77953i	−0.268598	+	0.268598i	0.559937	+	0.828535i	$0.310825\pi$
$464$		0			0
$465$	0.286702	+	11.1992i	0.0132955	+	0.519353i
$466$		0			0
$467$	20.6171	−	20.6171i	0.954046	−	0.954046i	−0.0449436	−	0.998990i	$-0.514311\pi$
$467$	20.6171	−	20.6171i	0.954046	−	0.954046i	0.998990	+	0.0449436i	$0.0143108\pi$
$468$		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	0.649843	−	0.760069i	$-0.274835\pi$
$487$	−2.43248	−	2.43248i	−0.110226	−	0.110226i	−0.760069	+	0.649843i	$0.774835\pi$
$488$		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	$0.159242\pi$
$499$			21.4299i			0.959334i	−0.877451	+	0.479667i	$0.840758\pi$
$500$		0			0
$501$	−15.3509			−0.685829
$502$		0			0
$503$	29.5361	+	29.5361i	1.31695	+	1.31695i	0.916179	+	0.400770i	$0.131257\pi$
$503$	29.5361	+	29.5361i	1.31695	+	1.31695i	0.400770	+	0.916179i	$0.368743\pi$
$504$		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	$0.103992\pi$
$521$			14.6502i			0.641837i	−0.947107	+	0.320918i	$0.896008\pi$
$522$		0			0
$523$	20.0200	+	20.0200i	0.875413	+	0.875413i	0.993056	−	0.117643i	$-0.0375337\pi$
$523$	20.0200	+	20.0200i	0.875413	+	0.875413i	−0.117643	+	0.993056i	$0.537534\pi$
$524$		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	0.628748	−	0.777609i	$-0.283568\pi$
$547$	−3.48155	−	3.48155i	−0.148861	−	0.148861i	−0.777609	+	0.628748i	$0.783568\pi$
$548$		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	0.852192	−	0.523229i	$-0.175273\pi$
$557$	7.76382	+	7.76382i	0.328964	+	0.328964i	−0.523229	+	0.852192i	$0.675273\pi$
$558$		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	0.838681	−	0.544624i	$-0.183328\pi$
$563$	6.97727	+	6.97727i	0.294057	+	0.294057i	−0.544624	+	0.838681i	$0.683328\pi$
$564$		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	$-0.916594\pi$
$569$		−	12.3582i		−	0.518082i	0.965866	−	0.259041i	$-0.0834064\pi$
$570$		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	−0.542448	−	0.840090i	$-0.682502\pi$
$577$	7.14961	−	7.14961i	0.297642	−	0.297642i	0.840090	+	0.542448i	$0.182502\pi$
$578$		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	−0.420135	−	0.907461i	$-0.638017\pi$
$587$	11.8070	−	11.8070i	0.487326	−	0.487326i	0.907461	+	0.420135i	$0.138017\pi$
$588$		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	0.546867	−	0.837220i	$-0.315820\pi$
$593$	−7.07055	−	7.07055i	−0.290353	−	0.290353i	−0.837220	+	0.546867i	$0.815820\pi$
$594$		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	$0.355623\pi$
$599$			43.9995i			1.79777i	−0.438182	+	0.898886i	$0.644377\pi$
$600$		0			0
$601$		−	36.1285i		−	1.47371i	−0.676051	−	0.736855i	$-0.736310\pi$
$601$		−	36.1285i		−	1.47371i	0.676051	−	0.736855i	$-0.263690\pi$
$602$		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	−0.956894	−	0.290437i	$-0.906199\pi$
$607$	−16.4198	+	16.4198i	−0.666457	+	0.666457i	0.290437	+	0.956894i	$0.406199\pi$
$608$		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	−0.839329	−	0.543624i	$-0.817052\pi$
$613$	−7.32133	+	7.32133i	−0.295706	+	0.295706i	0.543624	+	0.839329i	$0.317052\pi$
$614$		0			0
$615$	0.0567843	+	2.21812i	0.00228976	+	0.0894434i
$616$		0			0
$617$	19.2296	+	19.2296i	0.774156	+	0.774156i	0.978830	−	0.204675i	$-0.0656136\pi$
$617$	19.2296	+	19.2296i	0.774156	+	0.774156i	−0.204675	+	0.978830i	$0.565614\pi$
$618$		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	0.994804	−	0.101804i	$-0.0324614\pi$
$643$	22.6442	+	22.6442i	0.893001	+	0.893001i	−0.101804	+	0.994804i	$0.532461\pi$
$644$		0			0
$645$	15.9744	−	16.8137i	0.628990	−	0.662040i
$646$		0			0
$647$	−13.4030	+	13.4030i	−0.526925	+	0.526925i	−0.919654	−	0.392729i	$-0.871531\pi$
$647$	−13.4030	+	13.4030i	−0.526925	+	0.526925i	0.392729	+	0.919654i	$0.371531\pi$
$648$		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	−0.980602	−	0.196010i	$-0.937201\pi$
$653$	−20.0493	+	20.0493i	−0.784591	+	0.784591i	0.196010	+	0.980602i	$0.437201\pi$
$654$		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	$0.0556213\pi$
$659$			8.92589i			0.347703i	−0.984772	+	0.173852i	$0.944379\pi$
$660$		0			0
$661$			35.9123i			1.39683i	0.715695	+	0.698413i	$0.246110\pi$
$661$			35.9123i			1.39683i	−0.715695	+	0.698413i	$0.753890\pi$
$662$		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	−0.813651	−	0.581353i	$-0.802523\pi$
$673$	−6.02633	+	6.02633i	−0.232298	+	0.232298i	0.581353	+	0.813651i	$0.302523\pi$
$674$		0			0
$675$	3.71180	+	3.35000i	0.142867	+	0.128942i
$676$		0			0
$677$	13.6480	−	13.6480i	0.524536	−	0.524536i	−0.394402	−	0.918938i	$-0.629048\pi$
$677$	13.6480	−	13.6480i	0.524536	−	0.524536i	0.918938	+	0.394402i	$0.129048\pi$
$678$		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	−0.827967	−	0.560777i	$-0.810503\pi$
$683$	−6.98283	+	6.98283i	−0.267190	+	0.267190i	0.560777	+	0.827967i	$0.310503\pi$
$684$		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	$0.119468\pi$
$691$			19.2720i			0.733140i	−0.930390	+	0.366570i	$0.880532\pi$
$692$		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	$0.259136\pi$
$709$			38.7214i			1.45421i	−0.686524	+	0.727107i	$0.740864\pi$
$710$		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	−0.928500	−	0.371333i	$-0.878901\pi$
$727$	−15.0229	+	15.0229i	−0.557167	+	0.557167i	0.371333	+	0.928500i	$0.378901\pi$
$728$		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	0.997491	−	0.0707944i	$-0.0225534\pi$
$733$	25.0894	+	25.0894i	0.926697	+	0.926697i	−0.0707944	+	0.997491i	$0.522553\pi$
$734$		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	$-0.914127\pi$
$739$		−	14.4902i		−	0.533032i	0.963830	−	0.266516i	$-0.0858726\pi$
$740$		0			0
$741$		−	31.8139i		−	1.16871i
$742$		0			0
$743$	4.39593	−	4.39593i	0.161271	−	0.161271i	−0.621859	−	0.783130i	$-0.713622\pi$
$743$	4.39593	−	4.39593i	0.161271	−	0.161271i	0.783130	+	0.621859i	$0.213622\pi$
$744$		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	0.679402	−	0.733766i	$-0.262239\pi$
$757$	−1.49575	−	1.49575i	−0.0543639	−	0.0543639i	−0.733766	+	0.679402i	$0.762239\pi$
$758$		0			0
$759$	23.5755			0.855736
$760$		0			0
$761$		−	39.8014i		−	1.44280i	−0.692519	−	0.721400i	$-0.743499\pi$
$761$		−	39.8014i		−	1.44280i	0.692519	−	0.721400i	$-0.256501\pi$
$762$		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	−0.998024	−	0.0628341i	$-0.979986\pi$
$773$	−29.4949	−	29.4949i	−1.06086	−	1.06086i	−0.0628341	−	0.998024i	$-0.520014\pi$
$774$		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	0.0665308	−	0.997784i	$-0.478807\pi$
$787$	29.8578	−	29.8578i	1.06432	−	1.06432i	0.997784	−	0.0665308i	$-0.0211931\pi$
$788$		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	−0.825177	−	0.564875i	$-0.808924\pi$
$797$	−7.34863	+	7.34863i	−0.260302	+	0.260302i	0.564875	+	0.825177i	$0.308924\pi$
$798$		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	$-0.847185\pi$
$809$		−	26.2729i		−	0.923705i	0.886957	−	0.461852i	$-0.152815\pi$
$810$		0			0
$811$		−	37.7025i		−	1.32391i	−0.749541	−	0.661957i	$-0.769726\pi$
$811$		−	37.7025i		−	1.32391i	0.749541	−	0.661957i	$-0.230274\pi$
$812$		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	−0.994568	−	0.104093i	$-0.966806\pi$
$823$	−25.5459	+	25.5459i	−0.890474	+	0.890474i	0.104093	+	0.994568i	$0.466806\pi$
$824$		0			0
$825$	11.0770	−	12.2733i	0.385652	−	0.427303i
$826$		0			0
$827$	24.9245	+	24.9245i	0.866711	+	0.866711i	0.992107	−	0.125396i	$-0.0400201\pi$
$827$	24.9245	+	24.9245i	0.866711	+	0.866711i	−0.125396	+	0.992107i	$0.540020\pi$
$828$		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	0.858889	−	0.512161i	$-0.171155\pi$
$853$	10.1266	+	10.1266i	0.346728	+	0.346728i	−0.512161	+	0.858889i	$0.671155\pi$
$854$		0			0
$855$	13.0210	+	12.3710i	0.445309	+	0.423078i
$856$		0			0
$857$	−5.64323	+	5.64323i	−0.192769	+	0.192769i	−0.796892	−	0.604122i	$-0.793524\pi$
$857$	−5.64323	+	5.64323i	−0.192769	+	0.192769i	0.604122	+	0.796892i	$0.293524\pi$
$858$		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	−0.0710211	−	0.997475i	$-0.522626\pi$
$863$	27.2163	−	27.2163i	0.926454	−	0.926454i	0.997475	+	0.0710211i	$0.0226258\pi$
$864$		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	0.313000	−	0.949753i	$-0.398666\pi$
$877$	−18.8569	−	18.8569i	−0.636753	−	0.636753i	−0.949753	+	0.313000i	$0.898666\pi$
$878$		0			0
$879$			25.2106i			0.850332i
$880$		0			0
$881$		−	9.31247i		−	0.313745i	−0.987619	−	0.156872i	$-0.949859\pi$
$881$		−	9.31247i		−	0.313745i	0.987619	−	0.156872i	$-0.0501412\pi$
$882$		0			0
$883$	−3.39683	+	3.39683i	−0.114313	+	0.114313i	−0.761949	−	0.647637i	$-0.775757\pi$
$883$	−3.39683	+	3.39683i	−0.114313	+	0.114313i	0.647637	+	0.761949i	$0.275757\pi$
$884$		0			0
$885$	−6.19060	+	0.158480i	−0.208095	+	0.00532725i
$886$		0			0
$887$	−35.4671	+	35.4671i	−1.19087	+	1.19087i	−0.214046	+	0.976824i	$0.568664\pi$
$887$	−35.4671	+	35.4671i	−1.19087	+	1.19087i	−0.976824	+	0.214046i	$0.931336\pi$
$888$		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	0.990338	−	0.138675i	$-0.0442842\pi$
$907$	25.6491	+	25.6491i	0.851663	+	0.851663i	−0.138675	+	0.990338i	$0.544284\pi$
$908$		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	$-0.981704\pi$
$919$		−	3.48300i		−	0.114894i	0.998349	−	0.0574468i	$-0.0182959\pi$
$920$		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	−0.387852	−	0.921722i	$-0.626783\pi$
$937$	16.3420	−	16.3420i	0.533869	−	0.533869i	0.921722	+	0.387852i	$0.126783\pi$
$938$		0			0
$939$		−	24.2117i		−	0.790120i
$940$		0			0
$941$		−	50.4764i		−	1.64548i	−0.568416	−	0.822741i	$-0.692444\pi$
$941$		−	50.4764i		−	1.64548i	0.568416	−	0.822741i	$-0.307556\pi$
$942$		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	−0.999811	−	0.0194338i	$-0.993814\pi$
$947$	−31.3656	−	31.3656i	−1.01924	−	1.01924i	−0.0194338	−	0.999811i	$-0.506186\pi$
$948$		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	−0.516032	−	0.856569i	$-0.672592\pi$
$953$	10.5126	−	10.5126i	0.340537	−	0.340537i	0.856569	+	0.516032i	$0.172592\pi$
$954$		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	0.805685	−	0.592344i	$-0.201797\pi$
$967$	6.63418	+	6.63418i	0.213341	+	0.213341i	−0.592344	+	0.805685i	$0.701797\pi$
$968$		0			0
$969$	−10.5376			−0.338517
$970$		0			0
$971$		−	47.0663i		−	1.51043i	−0.655477	−	0.755215i	$-0.727532\pi$
$971$		−	47.0663i		−	1.51043i	0.655477	−	0.755215i	$-0.272468\pi$
$972$		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	0.569485	−	0.822002i	$-0.307143\pi$
$977$	−7.89292	−	7.89292i	−0.252517	−	0.252517i	−0.822002	+	0.569485i	$0.807143\pi$
$978$		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	0.741687	−	0.670746i	$-0.234026\pi$
$983$	2.22421	+	2.22421i	0.0709413	+	0.0709413i	−0.670746	+	0.741687i	$0.734026\pi$
$984$		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	−0.653712	−	0.756744i	$-0.726789\pi$
$997$	3.25326	−	3.25326i	0.103032	−	0.103032i	0.756744	+	0.653712i	$0.226789\pi$
$998$		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.97.11	✓	24
4.3	odd	2		1680.2.cz.f.97.2		24
5.3	odd	4		840.2.bt.b.433.2	yes	24
7.6	odd	2		840.2.bt.b.97.2	yes	24
20.3	even	4		1680.2.cz.e.433.11		24
28.27	even	2		1680.2.cz.e.97.11		24
35.13	even	4	inner	840.2.bt.a.433.11	yes	24
140.83	odd	4		1680.2.cz.f.433.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bt.a.97.11	✓	24	1.1	even	1	trivial
840.2.bt.a.433.11	yes	24	35.13	even	4	inner
840.2.bt.b.97.2	yes	24	7.6	odd	2
840.2.bt.b.433.2	yes	24	5.3	odd	4
1680.2.cz.e.97.11		24	28.27	even	2
1680.2.cz.e.433.11		24	20.3	even	4
1680.2.cz.f.97.2		24	4.3	odd	2
1680.2.cz.f.433.2		24	140.83	odd	4

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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