LMFDB - Embedded newform 325.2.f.d.307.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(18,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("325.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 111x^{12} + 329x^{8} + 168x^{4} + 16 $ x^16 + 111x^12 + 329x^8 + 168*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.5
Root			$2.27933 + 2.27933i$ of defining polynomial
Character	$\chi$	$=$	325.307
Dual form			325.2.f.d.18.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.438725i q^{2} +(-0.242722 + 0.242722i) q^{3} +1.80752 q^{4} +(-0.106488 - 0.106488i) q^{6} +0.438725 q^{7} +1.67045i q^{8} +2.88217i q^{9} +O(q^{10})$	\(q+0.438725i q^{2} +(-0.242722 + 0.242722i) q^{3} +1.80752 q^{4} +(-0.106488 - 0.106488i) q^{6} +0.438725 q^{7} +1.67045i q^{8} +2.88217i q^{9} +(3.04588 - 3.04588i) q^{11} +(-0.438725 + 0.438725i) q^{12} +(-2.89520 + 2.14891i) q^{13} +0.192479i q^{14} +2.88217 q^{16} +(3.09120 - 3.09120i) q^{17} -1.26448 q^{18} +(-1.59454 + 1.59454i) q^{19} +(-0.106488 + 0.106488i) q^{21} +(1.33630 + 1.33630i) q^{22} +(2.95305 + 2.95305i) q^{23} +(-0.405455 - 0.405455i) q^{24} +(-0.942781 - 1.27019i) q^{26} +(-1.42773 - 1.42773i) q^{27} +0.793004 q^{28} +0.138324i q^{29} +(-1.27019 - 1.27019i) q^{31} +4.60539i q^{32} +1.47860i q^{33} +(1.35619 + 1.35619i) q^{34} +5.20959i q^{36} -7.13783 q^{37} +(-0.699566 - 0.699566i) q^{38} +(0.181140 - 1.22432i) q^{39} +(0.0318365 + 0.0318365i) q^{41} +(-0.0467189 - 0.0467189i) q^{42} +(-2.20677 - 2.20677i) q^{43} +(5.50549 - 5.50549i) q^{44} +(-1.29558 + 1.29558i) q^{46} +7.44688 q^{47} +(-0.699566 + 0.699566i) q^{48} -6.80752 q^{49} +1.50060i q^{51} +(-5.23313 + 3.88420i) q^{52} +(7.84090 - 7.84090i) q^{53} +(0.626381 - 0.626381i) q^{54} +0.732869i q^{56} -0.774061i q^{57} -0.0606864 q^{58} +(-6.01404 - 6.01404i) q^{59} -9.35550 q^{61} +(0.557266 - 0.557266i) q^{62} +1.26448i q^{63} +3.74385 q^{64} -0.648699 q^{66} -11.1798i q^{67} +(5.58741 - 5.58741i) q^{68} -1.43354 q^{69} +(-1.51194 - 1.51194i) q^{71} -4.81453 q^{72} -15.1546i q^{73} -3.13154i q^{74} +(-2.88217 + 2.88217i) q^{76} +(1.33630 - 1.33630i) q^{77} +(0.537138 + 0.0794704i) q^{78} +10.0951i q^{79} -7.95343 q^{81} +(-0.0139674 + 0.0139674i) q^{82} -15.7648 q^{83} +(-0.192479 + 0.192479i) q^{84} +(0.968164 - 0.968164i) q^{86} +(-0.0335744 - 0.0335744i) q^{87} +(5.08800 + 5.08800i) q^{88} +(-9.98527 - 9.98527i) q^{89} +(-1.27019 + 0.942781i) q^{91} +(5.33770 + 5.33770i) q^{92} +0.616608 q^{93} +3.26713i q^{94} +(-1.11783 - 1.11783i) q^{96} -1.50802i q^{97} -2.98663i q^{98} +(8.77875 + 8.77875i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 16 * q - 8 * q^4 + 12 * q^6	$ 16 q - 8 q^{4} + 12 q^{6} - 20 q^{11} - 8 q^{16} - 16 q^{19} + 12 q^{21} - 16 q^{24} - 16 q^{26} + 8 q^{31} + 44 q^{34} - 28 q^{39} + 4 q^{41} + 76 q^{44} + 12 q^{46} - 72 q^{49} + 4 q^{54} - 24 q^{59} + 24 q^{61} + 16 q^{64} - 48 q^{66} + 112 q^{69} - 20 q^{71} + 8 q^{76} - 40 q^{84} + 12 q^{86} - 36 q^{89} + 8 q^{91} - 72 q^{96} + 52 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 + 12 * q^6 - 20 * q^11 - 8 * q^16 - 16 * q^19 + 12 * q^21 - 16 * q^24 - 16 * q^26 + 8 * q^31 + 44 * q^34 - 28 * q^39 + 4 * q^41 + 76 * q^44 + 12 * q^46 - 72 * q^49 + 4 * q^54 - 24 * q^59 + 24 * q^61 + 16 * q^64 - 48 * q^66 + 112 * q^69 - 20 * q^71 + 8 * q^76 - 40 * q^84 + 12 * q^86 - 36 * q^89 + 8 * q^91 - 72 * q^96 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			0.438725i			0.310225i	0.987897	+	0.155113i	$0.0495740\pi$
$2$			0.438725i			0.310225i	−0.987897	+	0.155113i	$0.950426\pi$
$3$	−0.242722	+	0.242722i	−0.140135	+	0.140135i	−0.773694	−	0.633559i	$-0.781593\pi$
$3$	−0.242722	+	0.242722i	−0.140135	+	0.140135i	0.633559	+	0.773694i	$0.281593\pi$
$4$	1.80752			0.903760
$5$		0			0
$5$		0			0
$6$	−0.106488	−	0.106488i	−0.0434736	−	0.0434736i
$7$	0.438725			0.165822			0.0829112	−	0.996557i	$-0.473578\pi$
$7$	0.438725			0.165822			0.0829112	+	0.996557i	$0.473578\pi$
$8$			1.67045i			0.590594i
$9$			2.88217i			0.960724i
$10$		0			0
$11$	3.04588	−	3.04588i	0.918367	−	0.918367i	−0.0785436	−	0.996911i	$-0.525027\pi$
$11$	3.04588	−	3.04588i	0.918367	−	0.918367i	0.996911	+	0.0785436i	$0.0250270\pi$
$12$	−0.438725	+	0.438725i	−0.126649	+	0.126649i
$13$	−2.89520	+	2.14891i	−0.802983	+	0.596001i
$13$	−2.89520	+	2.14891i	−0.802983	+	0.596001i
$14$			0.192479i			0.0514423i
$15$		0			0
$16$	2.88217			0.720543
$17$	3.09120	−	3.09120i	0.749726	−	0.749726i	−0.224701	−	0.974428i	$-0.572141\pi$
$17$	3.09120	−	3.09120i	0.749726	−	0.749726i	0.974428	+	0.224701i	$0.0721406\pi$
$18$	−1.26448			−0.298041
$19$	−1.59454	+	1.59454i	−0.365814	+	0.365814i	−0.865948	−	0.500134i	$-0.833284\pi$
$19$	−1.59454	+	1.59454i	−0.365814	+	0.365814i	0.500134	+	0.865948i	$0.333284\pi$
$20$		0			0
$21$	−0.106488	+	0.106488i	−0.0232376	+	0.0232376i
$22$	1.33630	+	1.33630i	0.284901	+	0.284901i
$23$	2.95305	+	2.95305i	0.615754	+	0.615754i	0.944439	−	0.328685i	$-0.106606\pi$
$23$	2.95305	+	2.95305i	0.615754	+	0.615754i	−0.328685	+	0.944439i	$0.606606\pi$
$24$	−0.405455	−	0.405455i	−0.0827632	−	0.0827632i
$25$		0			0
$26$	−0.942781	−	1.27019i	−0.184895	−	0.249106i
$27$	−1.42773	−	1.42773i	−0.274767	−	0.274767i
$28$	0.793004			0.149864
$29$			0.138324i			0.0256862i	0.999918	+	0.0128431i	$0.00408820\pi$
$29$			0.138324i			0.0256862i	−0.999918	+	0.0128431i	$0.995912\pi$
$30$		0			0
$31$	−1.27019	−	1.27019i	−0.228134	−	0.228134i	0.583779	−	0.811913i	$-0.301573\pi$
$31$	−1.27019	−	1.27019i	−0.228134	−	0.228134i	−0.811913	+	0.583779i	$0.801573\pi$
$32$			4.60539i			0.814125i
$33$			1.47860i			0.257392i
$34$	1.35619	+	1.35619i	0.232584	+	0.232584i
$35$		0			0
$36$			5.20959i			0.868264i
$37$	−7.13783			−1.17345			−0.586726	−	0.809785i	$-0.699584\pi$
$37$	−7.13783			−1.17345			−0.586726	+	0.809785i	$0.699584\pi$
$38$	−0.699566	−	0.699566i	−0.113485	−	0.113485i
$39$	0.181140	−	1.22432i	0.0290056	−	0.196047i
$40$		0			0
$41$	0.0318365	+	0.0318365i	0.00497202	+	0.00497202i	0.709588	−	0.704616i	$-0.248881\pi$
$41$	0.0318365	+	0.0318365i	0.00497202	+	0.00497202i	−0.704616	+	0.709588i	$0.748881\pi$
$42$	−0.0467189	−	0.0467189i	−0.00720889	−	0.00720889i
$43$	−2.20677	−	2.20677i	−0.336529	−	0.336529i	0.518530	−	0.855059i	$-0.326479\pi$
$43$	−2.20677	−	2.20677i	−0.336529	−	0.336529i	−0.855059	+	0.518530i	$0.826479\pi$
$44$	5.50549	−	5.50549i	0.829984	−	0.829984i
$45$		0			0
$46$	−1.29558	+	1.29558i	−0.191022	+	0.191022i
$47$	7.44688			1.08624			0.543120	−	0.839655i	$-0.317243\pi$
$47$	7.44688			1.08624			0.543120	+	0.839655i	$0.317243\pi$
$48$	−0.699566	+	0.699566i	−0.100974	+	0.100974i
$49$	−6.80752			−0.972503
$50$		0			0
$51$			1.50060i			0.210127i
$52$	−5.23313	+	3.88420i	−0.725705	+	0.538642i
$53$	7.84090	−	7.84090i	1.07703	−	1.07703i	0.0802557	−	0.996774i	$-0.474426\pi$
$53$	7.84090	−	7.84090i	1.07703	−	1.07703i	0.996774	−	0.0802557i	$-0.0255737\pi$
$54$	0.626381	−	0.626381i	0.0852397	−	0.0852397i
$55$		0			0
$56$			0.732869i			0.0979337i
$57$		−	0.774061i		−	0.102527i
$58$	−0.0606864			−0.00796851
$59$	−6.01404	−	6.01404i	−0.782962	−	0.782962i	0.197368	−	0.980330i	$-0.436761\pi$
$59$	−6.01404	−	6.01404i	−0.782962	−	0.782962i	−0.980330	+	0.197368i	$0.936761\pi$
$60$		0			0
$61$	−9.35550			−1.19785			−0.598924	−	0.800806i	$-0.704405\pi$
$61$	−9.35550			−1.19785			−0.598924	+	0.800806i	$0.704405\pi$
$62$	0.557266	−	0.557266i	0.0707728	−	0.0707728i
$63$			1.26448i			0.159310i
$64$	3.74385			0.467981
$65$		0			0
$66$	−0.648699			−0.0798494
$67$		−	11.1798i		−	1.36583i	−0.730498	−	0.682915i	$-0.760712\pi$
$67$		−	11.1798i		−	1.36583i	0.730498	−	0.682915i	$-0.239288\pi$
$68$	5.58741	−	5.58741i	0.677573	−	0.677573i
$69$	−1.43354			−0.172578
$70$		0			0
$71$	−1.51194	−	1.51194i	−0.179435	−	0.179435i	0.611675	−	0.791109i	$-0.290496\pi$
$71$	−1.51194	−	1.51194i	−0.179435	−	0.179435i	−0.791109	+	0.611675i	$0.790496\pi$
$72$	−4.81453			−0.567398
$73$		−	15.1546i		−	1.77371i	−0.462046	−	0.886856i	$-0.652884\pi$
$73$		−	15.1546i		−	1.77371i	0.462046	−	0.886856i	$-0.347116\pi$
$74$		−	3.13154i		−	0.364035i
$75$		0			0
$76$	−2.88217	+	2.88217i	−0.330608	+	0.330608i
$77$	1.33630	−	1.33630i	0.152286	−	0.152286i
$78$	0.537138	+	0.0794704i	0.0608189	+	0.00899825i
$79$			10.0951i			1.13579i	0.823100	+	0.567896i	$0.192243\pi$
$79$			10.0951i			1.13579i	−0.823100	+	0.567896i	$0.807757\pi$
$80$		0			0
$81$	−7.95343			−0.883715
$82$	−0.0139674	+	0.0139674i	−0.00154245	+	0.00154245i
$83$	−15.7648			−1.73041			−0.865203	−	0.501422i	$-0.832811\pi$
$83$	−15.7648			−1.73041			−0.865203	+	0.501422i	$0.832811\pi$
$84$	−0.192479	+	0.192479i	−0.0210012	+	0.0210012i
$85$		0			0
$86$	0.968164	−	0.968164i	0.104400	−	0.104400i
$87$	−0.0335744	−	0.0335744i	−0.00359955	−	0.00359955i
$88$	5.08800	+	5.08800i	0.542382	+	0.542382i
$89$	−9.98527	−	9.98527i	−1.05844	−	1.05844i	−0.998183	−	0.0602534i	$-0.980809\pi$
$89$	−9.98527	−	9.98527i	−1.05844	−	1.05844i	−0.0602534	−	0.998183i	$-0.519191\pi$
$90$		0			0
$91$	−1.27019	+	0.942781i	−0.133153	+	0.0988303i
$92$	5.33770	+	5.33770i	0.556494	+	0.556494i
$93$	0.616608			0.0639393
$94$			3.26713i			0.336979i
$95$		0			0
$96$	−1.11783	−	1.11783i	−0.114088	−	0.114088i
$97$		−	1.50802i		−	0.153117i	−0.997065	−	0.0765584i	$-0.975607\pi$
$97$		−	1.50802i		−	0.153117i	0.997065	−	0.0765584i	$-0.0243932\pi$
$98$		−	2.98663i		−	0.301695i
$99$	8.77875	+	8.77875i	0.882297	+	0.882297i
$100$		0			0
$101$			4.55137i			0.452878i	0.974025	+	0.226439i	$0.0727084\pi$
$101$			4.55137i			0.452878i	−0.974025	+	0.226439i	$0.927292\pi$
$102$	−0.658352			−0.0651866
$103$	5.64609	+	5.64609i	0.556326	+	0.556326i	0.928259	−	0.371934i	$-0.121305\pi$
$103$	5.64609	+	5.64609i	0.556326	+	0.556326i	−0.371934	+	0.928259i	$0.621305\pi$
$104$	−3.58966	−	4.83629i	−0.351995	−	0.474238i
$105$		0			0
$106$	3.43999	+	3.43999i	0.334122	+	0.334122i
$107$	7.73632	+	7.73632i	0.747899	+	0.747899i	0.974084	−	0.226186i	$-0.0726256\pi$
$107$	7.73632	+	7.73632i	0.747899	+	0.747899i	−0.226186	+	0.974084i	$0.572626\pi$
$108$	−2.58065	−	2.58065i	−0.248324	−	0.248324i
$109$	10.2876	−	10.2876i	0.985376	−	0.985376i	−0.0145186	−	0.999895i	$-0.504622\pi$
$109$	10.2876	−	10.2876i	0.985376	−	0.985376i	0.999895	+	0.0145186i	$0.00462157\pi$
$110$		0			0
$111$	1.73251	−	1.73251i	0.164442	−	0.164442i
$112$	1.26448			0.119482
$113$	2.25349	−	2.25349i	0.211990	−	0.211990i	−0.593122	−	0.805112i	$-0.702105\pi$
$113$	2.25349	−	2.25349i	0.211990	−	0.211990i	0.805112	+	0.593122i	$0.202105\pi$
$114$	0.339600			0.0318064
$115$		0			0
$116$			0.250024i			0.0232142i
$117$	−6.19354	−	8.34446i	−0.572593	−	0.771446i
$118$	2.63851	−	2.63851i	0.242894	−	0.242894i
$119$	1.35619	−	1.35619i	0.124321	−	0.124321i
$120$		0			0
$121$		−	7.55476i		−	0.686796i
$122$		−	4.10449i		−	0.371603i
$123$	−0.0154548			−0.00139351
$124$	−2.29590	−	2.29590i	−0.206178	−	0.206178i
$125$		0			0
$126$	−0.554759			−0.0494218
$127$	−12.7337	+	12.7337i	−1.12993	+	1.12993i	−0.139747	+	0.990187i	$0.544629\pi$
$127$	−12.7337	+	12.7337i	−1.12993	+	1.12993i	−0.990187	+	0.139747i	$0.955371\pi$
$128$			10.8533i			0.959305i
$129$	1.07126			0.0943193
$130$		0			0
$131$	11.9329			1.04259			0.521293	−	0.853378i	$-0.325450\pi$
$131$	11.9329			1.04259			0.521293	+	0.853378i	$0.325450\pi$
$132$			2.67260i			0.232620i
$133$	−0.699566	+	0.699566i	−0.0606601	+	0.0606601i
$134$	4.90485			0.423715
$135$		0			0
$136$	5.16371	+	5.16371i	0.442784	+	0.442784i
$137$	3.37863			0.288656			0.144328	−	0.989530i	$-0.453898\pi$
$137$	3.37863			0.288656			0.144328	+	0.989530i	$0.453898\pi$
$138$		−	0.628930i		−	0.0535380i
$139$			15.3123i			1.29877i	0.760458	+	0.649387i	$0.224975\pi$
$139$			15.3123i			1.29877i	−0.760458	+	0.649387i	$0.775025\pi$
$140$		0			0
$141$	−1.80752	+	1.80752i	−0.152221	+	0.152221i
$142$	0.663327	−	0.663327i	0.0556652	−	0.0556652i
$143$	−2.27309	+	15.3638i	−0.190086	+	1.28478i
$144$			8.30692i			0.692243i
$145$		0			0
$146$	6.64870			0.550250
$147$	1.65233	−	1.65233i	0.136282	−	0.136282i
$148$	−12.9018			−1.06052
$149$	−6.72153	+	6.72153i	−0.550649	+	0.550649i	−0.926628	−	0.375979i	$-0.877306\pi$
$149$	−6.72153	+	6.72153i	−0.550649	+	0.550649i	0.375979	+	0.926628i	$0.377306\pi$
$150$		0			0
$151$	5.88524	−	5.88524i	0.478934	−	0.478934i	−0.425857	−	0.904791i	$-0.640027\pi$
$151$	5.88524	−	5.88524i	0.478934	−	0.478934i	0.904791	+	0.425857i	$0.140027\pi$
$152$	−2.66361	−	2.66361i	−0.216047	−	0.216047i
$153$	8.90937	+	8.90937i	0.720280	+	0.720280i
$154$	0.586269	+	0.586269i	0.0472429	+	0.0472429i
$155$		0			0
$156$	0.327414	−	2.21298i	0.0262141	−	0.177180i
$157$	8.26499	+	8.26499i	0.659618	+	0.659618i	0.955290	−	0.295672i	$-0.0955434\pi$
$157$	8.26499	+	8.26499i	0.659618	+	0.659618i	−0.295672	+	0.955290i	$0.595543\pi$
$158$	−4.42899			−0.352352
$159$			3.80631i			0.301860i
$160$		0			0
$161$	1.29558	+	1.29558i	0.102106	+	0.102106i
$162$		−	3.48937i		−	0.274151i
$163$			20.6325i			1.61606i	0.589142	+	0.808030i	$0.299466\pi$
$163$			20.6325i			1.61606i	−0.589142	+	0.808030i	$0.700534\pi$
$164$	0.0575450	+	0.0575450i	0.00449351	+	0.00449351i
$165$		0			0
$166$		−	6.91639i		−	0.536816i
$167$	6.02897			0.466535			0.233268	−	0.972413i	$-0.425058\pi$
$167$	6.02897			0.466535			0.233268	+	0.972413i	$0.425058\pi$
$168$	−0.177883	−	0.177883i	−0.0137240	−	0.0137240i
$169$	3.76434	−	12.4431i	0.289565	−	0.957158i
$170$		0			0
$171$	−4.59575	−	4.59575i	−0.351446	−	0.351446i
$172$	−3.98878	−	3.98878i	−0.304142	−	0.304142i
$173$	−14.1676	−	14.1676i	−1.07714	−	1.07714i	−0.996764	−	0.0803789i	$-0.974387\pi$
$173$	−14.1676	−	14.1676i	−1.07714	−	1.07714i	−0.0803789	−	0.996764i	$-0.525613\pi$
$174$	0.0147299	−	0.0147299i	0.00111667	−	0.00111667i
$175$		0			0
$176$	8.77875	−	8.77875i	0.661723	−	0.661723i
$177$	2.91948			0.219441
$178$	4.38078	−	4.38078i	0.328354	−	0.328354i
$179$	−16.0951			−1.20301			−0.601504	−	0.798870i	$-0.705432\pi$
$179$	−16.0951			−1.20301			−0.601504	+	0.798870i	$0.705432\pi$
$180$		0			0
$181$		−	6.55476i		−	0.487211i	−0.969874	−	0.243606i	$-0.921670\pi$
$181$		−	6.55476i		−	0.487211i	0.969874	−	0.243606i	$-0.0783303\pi$
$182$	−0.413621	−	0.557266i	−0.0306597	−	0.0413073i
$183$	2.27078	−	2.27078i	0.167861	−	0.167861i
$184$	−4.93294	+	4.93294i	−0.363661	+	0.363661i
$185$		0			0
$186$			0.270521i			0.0198356i
$187$		−	18.8308i		−	1.37705i
$188$	13.4604			0.981700
$189$	−0.626381	−	0.626381i	−0.0455625	−	0.0455625i
$190$		0			0
$191$	22.0657			1.59662			0.798309	−	0.602249i	$-0.205728\pi$
$191$	22.0657			1.59662			0.798309	+	0.602249i	$0.205728\pi$
$192$	−0.908713	+	0.908713i	−0.0655807	+	0.0655807i
$193$			10.5065i			0.756276i	0.925749	+	0.378138i	$0.123435\pi$
$193$			10.5065i			0.756276i	−0.925749	+	0.378138i	$0.876565\pi$
$194$	0.661608			0.0475007
$195$		0			0
$196$	−12.3047			−0.878910
$197$			10.3630i			0.738335i	0.929363	+	0.369168i	$0.120357\pi$
$197$			10.3630i			0.738335i	−0.929363	+	0.369168i	$0.879643\pi$
$198$	−3.85145	+	3.85145i	−0.273711	+	0.273711i
$199$	19.2548			1.36493			0.682467	−	0.730916i	$-0.260907\pi$
$199$	19.2548			1.36493			0.682467	+	0.730916i	$0.260907\pi$
$200$		0			0
$201$	2.71358	+	2.71358i	0.191401	+	0.191401i
$202$	−1.99680			−0.140494
$203$			0.0606864i			0.00425935i
$204$			2.71237i			0.189904i
$205$		0			0
$206$	−2.47708	+	2.47708i	−0.172586	+	0.172586i
$207$	−8.51121	+	8.51121i	−0.591570	+	0.591570i
$208$	−8.34446	+	6.19354i	−0.578584	+	0.429445i
$209$			9.71358i			0.671902i
$210$		0			0
$211$	9.04519			0.622697			0.311348	−	0.950296i	$-0.399219\pi$
$211$	9.04519			0.622697			0.311348	+	0.950296i	$0.399219\pi$
$212$	14.1726	−	14.1726i	0.973377	−	0.973377i
$213$	0.733963			0.0502903
$214$	−3.39412	+	3.39412i	−0.232017	+	0.232017i
$215$		0			0
$216$	2.38496	−	2.38496i	0.162276	−	0.162276i
$217$	−0.557266	−	0.557266i	−0.0378297	−	0.0378297i
$218$	4.51344	+	4.51344i	0.305688	+	0.305688i
$219$	3.67835	+	3.67835i	0.248560	+	0.248560i
$220$		0			0
$221$	−2.30692	+	15.5924i	−0.155180	+	1.04886i
$222$	0.760094	+	0.760094i	0.0510142	+	0.0510142i
$223$	−8.93448			−0.598297			−0.299148	−	0.954207i	$-0.596703\pi$
$223$	−8.93448			−0.598297			−0.299148	+	0.954207i	$0.596703\pi$
$224$			2.02050i			0.135000i
$225$		0			0
$226$	0.988660	+	0.988660i	0.0657647	+	0.0657647i
$227$			22.4564i			1.49048i	0.666796	+	0.745240i	$0.267665\pi$
$227$			22.4564i			1.49048i	−0.666796	+	0.745240i	$0.732335\pi$
$228$		−	1.39913i		−	0.0926598i
$229$	7.22432	+	7.22432i	0.477396	+	0.477396i	0.904298	−	0.426902i	$-0.140395\pi$
$229$	7.22432	+	7.22432i	0.477396	+	0.477396i	−0.426902	+	0.904298i	$0.640395\pi$
$230$		0			0
$231$			0.648699i			0.0426813i
$232$	−0.231065			−0.0151701
$233$	−13.1537	−	13.1537i	−0.861725	−	0.861725i	0.129814	−	0.991538i	$-0.458562\pi$
$233$	−13.1537	−	13.1537i	−0.861725	−	0.861725i	−0.991538	+	0.129814i	$0.958562\pi$
$234$	3.66092	−	2.71726i	0.239322	−	0.177633i
$235$		0			0
$236$	−10.8705	−	10.8705i	−0.707610	−	0.707610i
$237$	−2.45031	−	2.45031i	−0.159165	−	0.159165i
$238$	0.594992	+	0.594992i	0.0385676	+	0.0385676i
$239$	21.7527	−	21.7527i	1.40706	−	1.40706i	0.632519	−	0.774545i	$-0.282021\pi$
$239$	21.7527	−	21.7527i	1.40706	−	1.40706i	0.774545	−	0.632519i	$-0.217979\pi$
$240$		0			0
$241$	−18.3999	+	18.3999i	−1.18524	+	1.18524i	−0.206873	+	0.978368i	$0.566329\pi$
$241$	−18.3999	+	18.3999i	−1.18524	+	1.18524i	−0.978368	+	0.206873i	$0.933671\pi$
$242$	3.31446			0.213061
$243$	6.21367	−	6.21367i	0.398607	−	0.398607i
$244$	−16.9103			−1.08257
$245$		0			0
$246$		−	0.00678040i		−	0.000432303i
$247$	1.18998	−	8.04306i	0.0757169	−	0.511768i
$248$	2.12180	−	2.12180i	0.134735	−	0.134735i
$249$	3.82645	−	3.82645i	0.242491	−	0.242491i
$250$		0			0
$251$		−	9.08078i		−	0.573174i	−0.958054	−	0.286587i	$-0.907479\pi$
$251$		−	9.08078i		−	0.573174i	0.958054	−	0.286587i	$-0.0925207\pi$
$252$			2.28557i			0.143978i
$253$	17.9893			1.13098
$254$	−5.58660	−	5.58660i	−0.350534	−	0.350534i
$255$		0			0
$256$	2.72609			0.170381
$257$	−11.8624	+	11.8624i	−0.739958	+	0.739958i	−0.972570	−	0.232612i	$-0.925273\pi$
$257$	−11.8624	+	11.8624i	−0.739958	+	0.739958i	0.232612	+	0.972570i	$0.425273\pi$
$258$			0.469989i			0.0292602i
$259$	−3.13154			−0.194585
$260$		0			0
$261$	−0.398675			−0.0246774
$262$			5.23527i			0.323436i
$263$	13.4047	−	13.4047i	0.826568	−	0.826568i	−0.160472	−	0.987040i	$-0.551302\pi$
$263$	13.4047	−	13.4047i	0.826568	−	0.826568i	0.987040	+	0.160472i	$0.0513017\pi$
$264$	−2.46994			−0.152014
$265$		0			0
$266$	−0.306917	−	0.306917i	−0.0188183	−	0.0188183i
$267$	4.84729			0.296649
$268$		−	20.2077i		−	1.23438i
$269$		−	13.8800i		−	0.846278i	−0.906065	−	0.423139i	$-0.860928\pi$
$269$		−	13.8800i		−	0.846278i	0.906065	−	0.423139i	$-0.139072\pi$
$270$		0			0
$271$	−6.00270	+	6.00270i	−0.364638	+	0.364638i	−0.865517	−	0.500879i	$-0.833010\pi$
$271$	−6.00270	+	6.00270i	−0.364638	+	0.364638i	0.500879	+	0.865517i	$0.333010\pi$
$272$	8.90937	−	8.90937i	0.540210	−	0.540210i
$273$	0.0794704	−	0.537138i	0.00480977	−	0.0325090i
$274$			1.48229i			0.0895484i
$275$		0			0
$276$	−2.59115			−0.155969
$277$	−7.05072	+	7.05072i	−0.423637	+	0.423637i	−0.886454	−	0.462817i	$-0.846839\pi$
$277$	−7.05072	+	7.05072i	−0.423637	+	0.423637i	0.462817	+	0.886454i	$0.346839\pi$
$278$	−6.71789			−0.402912
$279$	3.66092	−	3.66092i	0.219174	−	0.219174i
$280$		0			0
$281$	−10.2285	+	10.2285i	−0.610182	+	0.610182i	−0.942993	−	0.332811i	$-0.892003\pi$
$281$	−10.2285	+	10.2285i	−0.610182	+	0.610182i	0.332811	+	0.942993i	$0.392003\pi$
$282$	−0.793004	−	0.793004i	−0.0472227	−	0.0472227i
$283$	1.69674	+	1.69674i	0.100861	+	0.100861i	0.755737	−	0.654876i	$-0.227279\pi$
$283$	1.69674	+	1.69674i	0.100861	+	0.100861i	−0.654876	+	0.755737i	$0.727279\pi$
$284$	−2.73287	−	2.73287i	−0.162166	−	0.162166i
$285$		0			0
$286$	−6.74046	−	0.997262i	−0.398572	−	0.0589694i
$287$	0.0139674	+	0.0139674i	0.000824472	+	0.000824472i
$288$	−13.2735			−0.782150
$289$		−	2.11105i		−	0.124179i
$290$		0			0
$291$	0.366030	+	0.366030i	0.0214571	+	0.0214571i
$292$		−	27.3923i		−	1.60301i
$293$			0.654334i			0.0382266i	0.999817	+	0.0191133i	$0.00608433\pi$
$293$			0.654334i			0.0382266i	−0.999817	+	0.0191133i	$0.993916\pi$
$294$	0.724920	+	0.724920i	0.0422782	+	0.0422782i
$295$		0			0
$296$		−	11.9234i		−	0.693035i
$297$	−8.69739			−0.504674
$298$	−2.94890	−	2.94890i	−0.170825	−	0.170825i
$299$	−14.8955	−	2.20382i	−0.861431	−	0.127450i
$300$		0			0
$301$	−0.968164	−	0.968164i	−0.0558040	−	0.0558040i
$302$	2.58200	+	2.58200i	0.148577	+	0.148577i
$303$	−1.10472	−	1.10472i	−0.0634643	−	0.0634643i
$304$	−4.59575	+	4.59575i	−0.263584	+	0.263584i
$305$		0			0
$306$	−3.90876	+	3.90876i	−0.223449	+	0.223449i
$307$	5.69696			0.325143			0.162571	−	0.986697i	$-0.448021\pi$
$307$	5.69696			0.325143			0.162571	+	0.986697i	$0.448021\pi$
$308$	2.41539	−	2.41539i	0.137630	−	0.137630i
$309$	−2.74086			−0.155922
$310$		0			0
$311$			9.12203i			0.517263i	0.965976	+	0.258631i	$0.0832715\pi$
$311$			9.12203i			0.517263i	−0.965976	+	0.258631i	$0.916729\pi$
$312$	2.04516	+	0.302585i	0.115785	+	0.0171305i
$313$	16.2726	−	16.2726i	0.919784	−	0.919784i	−0.0772297	−	0.997013i	$-0.524607\pi$
$313$	16.2726	−	16.2726i	0.919784	−	0.919784i	0.997013	+	0.0772297i	$0.0246075\pi$
$314$	−3.62605	+	3.62605i	−0.204630	+	0.204630i
$315$		0			0
$316$			18.2472i			1.02648i
$317$		−	23.5257i		−	1.32133i	−0.750680	−	0.660666i	$-0.770274\pi$
$317$		−	23.5257i		−	1.32133i	0.750680	−	0.660666i	$-0.229726\pi$
$318$	−1.66992			−0.0936447
$319$	0.421320	+	0.421320i	0.0235894	+	0.0235894i
$320$		0			0
$321$	−3.75555			−0.209614
$322$	−0.568402	+	0.568402i	−0.0316758	+	0.0316758i
$323$			9.85812i			0.548520i
$324$	−14.3760			−0.798666
$325$		0			0
$326$	−9.05197			−0.501342
$327$			4.99406i			0.276172i
$328$	−0.0531813	+	0.0531813i	−0.00293645	+	0.00293645i
$329$	3.26713			0.180123
$330$		0			0
$331$	−11.6859	−	11.6859i	−0.642317	−	0.642317i	0.308807	−	0.951125i	$-0.400070\pi$
$331$	−11.6859	−	11.6859i	−0.642317	−	0.642317i	−0.951125	+	0.308807i	$0.900070\pi$
$332$	−28.4951			−1.56387
$333$		−	20.5725i		−	1.12736i
$334$			2.64506i			0.144731i
$335$		0			0
$336$	−0.306917	+	0.306917i	−0.0167437	+	0.0167437i
$337$	−10.1125	+	10.1125i	−0.550863	+	0.550863i	−0.926690	−	0.375827i	$-0.877359\pi$
$337$	−10.1125	+	10.1125i	−0.550863	+	0.550863i	0.375827	+	0.926690i	$0.377359\pi$
$338$	5.45908	+	1.65151i	0.296935	+	0.0898303i
$339$			1.09394i			0.0594147i
$340$		0			0
$341$	−7.73772			−0.419021
$342$	2.01627	−	2.01627i	0.109027	−	0.109027i
$343$	−6.05770			−0.327085
$344$	3.68630	−	3.68630i	0.198752	−	0.198752i
$345$		0			0
$346$	6.21568	−	6.21568i	0.334157	−	0.334157i
$347$	−6.58258	−	6.58258i	−0.353371	−	0.353371i	0.507991	−	0.861362i	$-0.330388\pi$
$347$	−6.58258	−	6.58258i	−0.353371	−	0.353371i	−0.861362	+	0.507991i	$0.830388\pi$
$348$	−0.0606864	−	0.0606864i	−0.00325313	−	0.00325313i
$349$	−17.5571	−	17.5571i	−0.939812	−	0.939812i	0.0584769	−	0.998289i	$-0.481376\pi$
$349$	−17.5571	−	17.5571i	−0.939812	−	0.939812i	−0.998289	+	0.0584769i	$0.981376\pi$
$350$		0			0
$351$	7.20164	+	1.06549i	0.384395	+	0.0568719i
$352$	14.0275	+	14.0275i	0.747666	+	0.747666i
$353$	25.0043			1.33084			0.665421	−	0.746468i	$-0.268252\pi$
$353$	25.0043			1.33084			0.665421	+	0.746468i	$0.268252\pi$
$354$			1.28085i			0.0680763i
$355$		0			0
$356$	−18.0486	−	18.0486i	−0.956573	−	0.956573i
$357$			0.658352i			0.0348437i
$358$		−	7.06134i		−	0.373203i
$359$	−1.66770	−	1.66770i	−0.0880179	−	0.0880179i	0.661727	−	0.749745i	$-0.269824\pi$
$359$	−1.66770	−	1.66770i	−0.0880179	−	0.0880179i	−0.749745	+	0.661727i	$0.769824\pi$
$360$		0			0
$361$			13.9149i			0.732361i
$362$	2.87573			0.151145
$363$	1.83370	+	1.83370i	0.0962445	+	0.0962445i
$364$	−2.29590	+	1.70410i	−0.120338	+	0.0893189i
$365$		0			0
$366$	0.996249	+	0.996249i	0.0520748	+	0.0520748i
$367$	8.72948	+	8.72948i	0.455675	+	0.455675i	0.897233	−	0.441558i	$-0.145574\pi$
$367$	8.72948	+	8.72948i	0.455675	+	0.455675i	−0.441558	+	0.897233i	$0.645574\pi$
$368$	8.51121	+	8.51121i	0.443677	+	0.443677i
$369$	−0.0917581	+	0.0917581i	−0.00477674	+	0.00477674i
$370$		0			0
$371$	3.43999	−	3.43999i	0.178596	−	0.178596i
$372$	1.11453			0.0577858
$373$	−9.69421	+	9.69421i	−0.501947	+	0.501947i	−0.912043	−	0.410096i	$-0.865495\pi$
$373$	−9.69421	+	9.69421i	−0.501947	+	0.501947i	0.410096	+	0.912043i	$0.365495\pi$
$374$	8.26156			0.427195
$375$		0			0
$376$			12.4397i			0.641527i
$377$	−0.297247	−	0.400477i	−0.0153090	−	0.0206256i
$378$	0.274809	−	0.274809i	0.0141346	−	0.0141346i
$379$	16.8307	−	16.8307i	0.864536	−	0.864536i	−0.127325	−	0.991861i	$-0.540639\pi$
$379$	16.8307	−	16.8307i	0.864536	−	0.864536i	0.991861	+	0.127325i	$0.0406391\pi$
$380$		0			0
$381$		−	6.18150i		−	0.316688i
$382$			9.68076i			0.495311i
$383$	−23.8645			−1.21942			−0.609709	−	0.792625i	$-0.708714\pi$
$383$	−23.8645			−1.21942			−0.609709	+	0.792625i	$0.708714\pi$
$384$	−2.63433	−	2.63433i	−0.134433	−	0.134433i
$385$		0			0
$386$	−4.60947			−0.234616
$387$	6.36029	−	6.36029i	0.323311	−	0.323311i
$388$		−	2.72579i		−	0.138381i
$389$	12.7910			0.648528			0.324264	−	0.945967i	$-0.394883\pi$
$389$	12.7910			0.648528			0.324264	+	0.945967i	$0.394883\pi$
$390$		0			0
$391$	18.2570			0.923294
$392$		−	11.3716i		−	0.574355i
$393$	−2.89638	+	2.89638i	−0.146103	+	0.146103i
$394$	−4.54652			−0.229050
$395$		0			0
$396$	15.8678	+	15.8678i	0.797385	+	0.797385i
$397$	15.7318			0.789558			0.394779	−	0.918776i	$-0.370821\pi$
$397$	15.7318			0.789558			0.394779	+	0.918776i	$0.370821\pi$
$398$			8.44755i			0.423437i
$399$		−	0.339600i		−	0.0170013i
$400$		0			0
$401$	−4.12698	+	4.12698i	−0.206092	+	0.206092i	−0.802604	−	0.596512i	$-0.796553\pi$
$401$	−4.12698	+	4.12698i	−0.206092	+	0.206092i	0.596512	+	0.802604i	$0.296553\pi$
$402$	−1.19051	+	1.19051i	−0.0593775	+	0.0593775i
$403$	6.40700	+	0.947927i	0.319156	+	0.0472196i
$404$			8.22669i			0.409293i
$405$		0			0
$406$	−0.0266246			−0.00132136
$407$	−21.7410	+	21.7410i	−1.07766	+	1.07766i
$408$	−2.50669			−0.124100
$409$	3.54342	−	3.54342i	0.175211	−	0.175211i	−0.614054	−	0.789264i	$-0.710462\pi$
$409$	3.54342	−	3.54342i	0.175211	−	0.175211i	0.789264	+	0.614054i	$0.210462\pi$
$410$		0			0
$411$	−0.820068	+	0.820068i	−0.0404510	+	0.0404510i
$412$	10.2054	+	10.2054i	0.502785	+	0.502785i
$413$	−2.63851	−	2.63851i	−0.129833	−	0.129833i
$414$	−3.73408	−	3.73408i	−0.183520	−	0.183520i
$415$		0			0
$416$	−9.89658	−	13.3335i	−0.485220	−	0.653729i
$417$	−3.71663	−	3.71663i	−0.182004	−	0.182004i
$418$	−4.26159			−0.208441
$419$			29.6710i			1.44952i	0.689001	+	0.724761i	$0.258050\pi$
$419$			29.6710i			1.44952i	−0.689001	+	0.724761i	$0.741950\pi$
$420$		0			0
$421$	7.57981	+	7.57981i	0.369418	+	0.369418i	0.867265	−	0.497847i	$-0.165876\pi$
$421$	7.57981	+	7.57981i	0.369418	+	0.369418i	−0.497847	+	0.867265i	$0.665876\pi$
$422$			3.96835i			0.193176i
$423$			21.4632i			1.04358i
$424$	13.0979	+	13.0979i	0.636088	+	0.636088i
$425$		0			0
$426$			0.322008i			0.0156013i
$427$	−4.10449			−0.198630
$428$	13.9836	+	13.9836i	0.675921	+	0.675921i
$429$	−3.17739	−	4.28085i	−0.153406	−	0.206681i
$430$		0			0
$431$	28.4803	+	28.4803i	1.37185	+	1.37185i	0.857704	+	0.514144i	$0.171890\pi$
$431$	28.4803	+	28.4803i	1.37185	+	1.37185i	0.514144	+	0.857704i	$0.328110\pi$
$432$	−4.11497	−	4.11497i	−0.197981	−	0.197981i
$433$	−6.79819	−	6.79819i	−0.326700	−	0.326700i	0.524630	−	0.851330i	$-0.324204\pi$
$433$	−6.79819	−	6.79819i	−0.326700	−	0.326700i	−0.851330	+	0.524630i	$0.824204\pi$
$434$	0.244486	−	0.244486i	0.0117357	−	0.0117357i
$435$		0			0
$436$	18.5951	−	18.5951i	0.890544	−	0.890544i
$437$	−9.41755			−0.450502
$438$	−1.61378	+	1.61378i	−0.0771096	+	0.0771096i
$439$	5.31643			0.253740			0.126870	−	0.991919i	$-0.459507\pi$
$439$	5.31643			0.253740			0.126870	+	0.991919i	$0.459507\pi$
$440$		0			0
$441$		−	19.6204i		−	0.934307i
$442$	−6.84075	−	1.01210i	−0.325381	−	0.0481408i
$443$	−2.05415	+	2.05415i	−0.0975958	+	0.0975958i	−0.754219	−	0.656623i	$-0.771984\pi$
$443$	−2.05415	+	2.05415i	−0.0975958	+	0.0975958i	0.656623	+	0.754219i	$0.271984\pi$
$444$	3.13154	−	3.13154i	0.148617	−	0.148617i
$445$		0			0
$446$		−	3.91978i		−	0.185607i
$447$		−	3.26292i		−	0.154331i
$448$	1.64252			0.0776017
$449$	22.4041	+	22.4041i	1.05731	+	1.05731i	0.998254	+	0.0590595i	$0.0188102\pi$
$449$	22.4041	+	22.4041i	1.05731	+	1.05731i	0.0590595	+	0.998254i	$0.481190\pi$
$450$		0			0
$451$	0.193940			0.00913228
$452$	4.07322	−	4.07322i	0.191588	−	0.191588i
$453$			2.85695i			0.134231i
$454$	−9.85216			−0.462385
$455$		0			0
$456$	1.29303			0.0605518
$457$		−	8.38353i		−	0.392165i	−0.980587	−	0.196083i	$-0.937178\pi$
$457$		−	8.38353i		−	0.392165i	0.980587	−	0.196083i	$-0.0628220\pi$
$458$	−3.16949	+	3.16949i	−0.148100	+	0.148100i
$459$	−8.82681			−0.412000
$460$		0			0
$461$	−16.6582	−	16.6582i	−0.775851	−	0.775851i	0.203272	−	0.979122i	$-0.434842\pi$
$461$	−16.6582	−	16.6582i	−0.775851	−	0.775851i	−0.979122	+	0.203272i	$0.934842\pi$
$462$	−0.284600			−0.0132408
$463$			20.8398i			0.968506i	0.874928	+	0.484253i	$0.160909\pi$
$463$			20.8398i			0.968506i	−0.874928	+	0.484253i	$0.839091\pi$
$464$			0.398675i			0.0185080i
$465$		0			0
$466$	5.77083	−	5.77083i	0.267329	−	0.267329i
$467$	26.1022	−	26.1022i	1.20786	−	1.20786i	0.236146	−	0.971718i	$-0.424116\pi$
$467$	26.1022	−	26.1022i	1.20786	−	1.20786i	0.971718	−	0.236146i	$-0.0758845\pi$
$468$	−11.1949	−	15.0828i	−0.517487	−	0.697202i
$469$		−	4.90485i		−	0.226485i
$470$		0			0
$471$	−4.01219			−0.184872
$472$	10.0462	−	10.0462i	0.462413	−	0.462413i
$473$	−13.4431			−0.618114
$474$	1.07501	−	1.07501i	0.0493770	−	0.0493770i
$475$		0			0
$476$	2.45133	−	2.45133i	0.112357	−	0.112357i
$477$	22.5988	+	22.5988i	1.03473	+	1.03473i
$478$	9.54344	+	9.54344i	0.436507	+	0.436507i
$479$	19.7704	+	19.7704i	0.903334	+	0.903334i	0.995723	−	0.0923887i	$-0.0294502\pi$
$479$	19.7704	+	19.7704i	0.903334	+	0.903334i	−0.0923887	+	0.995723i	$0.529450\pi$
$480$		0			0
$481$	20.6654	−	15.3386i	0.942263	−	0.699379i
$482$	−8.07248	−	8.07248i	−0.367692	−	0.367692i
$483$	−0.628930			−0.0286173
$484$		−	13.6554i		−	0.620699i
$485$		0			0
$486$	2.72609	+	2.72609i	0.123658	+	0.123658i
$487$			15.6213i			0.707867i	0.935271	+	0.353934i	$0.115156\pi$
$487$			15.6213i			0.707867i	−0.935271	+	0.353934i	$0.884844\pi$
$488$		−	15.6279i		−	0.707443i
$489$	−5.00795	−	5.00795i	−0.226467	−	0.226467i
$490$		0			0
$491$		−	12.6196i		−	0.569516i	−0.958599	−	0.284758i	$-0.908087\pi$
$491$		−	12.6196i		−	0.569516i	0.958599	−	0.284758i	$-0.0919133\pi$
$492$	−0.0279349			−0.00125940
$493$	0.427589	+	0.427589i	0.0192576	+	0.0192576i
$494$	3.52869	+	0.522076i	0.158763	+	0.0234893i
$495$		0			0
$496$	−3.66092	−	3.66092i	−0.164380	−	0.164380i
$497$	−0.663327	−	0.663327i	−0.0297543	−	0.0297543i
$498$	1.67876	+	1.67876i	0.0752269	+	0.0752269i
$499$	−22.5427	+	22.5427i	−1.00915	+	1.00915i	−0.00919352	+	0.999958i	$0.502926\pi$
$499$	−22.5427	+	22.5427i	−1.00915	+	1.00915i	−0.999958	+	0.00919352i	$0.997074\pi$
$500$		0			0
$501$	−1.46336	+	1.46336i	−0.0653782	+	0.0653782i
$502$	3.98396			0.177813
$503$	−5.50096	+	5.50096i	−0.245275	+	0.245275i	−0.819028	−	0.573753i	$-0.805487\pi$
$503$	−5.50096	+	5.50096i	−0.245275	+	0.245275i	0.573753	+	0.819028i	$0.305487\pi$
$504$	−2.11225			−0.0940873
$505$		0			0
$506$			7.89234i			0.350857i
$507$	2.10651	+	3.93389i	0.0935535	+	0.174710i
$508$	−23.0165	+	23.0165i	−1.02119	+	1.02119i
$509$	−18.5018	+	18.5018i	−0.820077	+	0.820077i	−0.986119	−	0.166042i	$-0.946901\pi$
$509$	−18.5018	+	18.5018i	−0.820077	+	0.820077i	0.166042	+	0.986119i	$0.446901\pi$
$510$		0			0
$511$		−	6.64870i		−	0.294121i
$512$			22.9026i			1.01216i
$513$	4.55316			0.201027
$514$	−5.20434	−	5.20434i	−0.229554	−	0.229554i
$515$		0			0
$516$	1.93633			0.0852420
$517$	22.6823	−	22.6823i	0.997567	−	0.997567i
$518$		−	1.37389i		−	0.0603651i
$519$	6.87757			0.301892
$520$		0			0
$521$	14.5848			0.638971			0.319485	−	0.947591i	$-0.396490\pi$
$521$	14.5848			0.638971			0.319485	+	0.947591i	$0.396490\pi$
$522$		−	0.174909i		−	0.00765554i
$523$	−9.37818	+	9.37818i	−0.410079	+	0.410079i	−0.881766	−	0.471687i	$-0.843645\pi$
$523$	−9.37818	+	9.37818i	−0.410079	+	0.410079i	0.471687	+	0.881766i	$0.343645\pi$
$524$	21.5690			0.942247
$525$		0			0
$526$	5.88096	+	5.88096i	0.256422	+	0.256422i
$527$	−7.85286			−0.342076
$528$			4.26159i			0.185462i
$529$		−	5.55896i		−	0.241694i
$530$		0			0
$531$	17.3335	−	17.3335i	0.752210	−	0.752210i
$532$	−1.26448	+	1.26448i	−0.0548222	+	0.0548222i
$533$	−0.160587	−	0.0237591i	−0.00695578	−	0.00102912i
$534$			2.12662i			0.0920280i
$535$		0			0
$536$	18.6753			0.806651
$537$	3.90664	−	3.90664i	0.168584	−	0.168584i
$538$	6.08949			0.262537
$539$	−20.7349	+	20.7349i	−0.893115	+	0.893115i
$540$		0			0
$541$	0.153054	−	0.153054i	0.00658032	−	0.00658032i	−0.703809	−	0.710389i	$-0.748519\pi$
$541$	0.153054	−	0.153054i	0.00658032	−	0.00658032i	0.710389	+	0.703809i	$0.248519\pi$
$542$	−2.63353	−	2.63353i	−0.113120	−	0.113120i
$543$	1.59098	+	1.59098i	0.0682756	+	0.0682756i
$544$	14.2362	+	14.2362i	0.610371	+	0.610371i
$545$		0			0
$546$	0.235655	+	0.0348656i	0.0100851	+	0.00149211i
$547$	−20.1505	−	20.1505i	−0.861574	−	0.861574i	0.129947	−	0.991521i	$-0.458519\pi$
$547$	−20.1505	−	20.1505i	−0.861574	−	0.861574i	−0.991521	+	0.129947i	$0.958519\pi$
$548$	6.10695			0.260876
$549$		−	26.9642i		−	1.15080i
$550$		0			0
$551$	−0.220565	−	0.220565i	−0.00939637	−	0.00939637i
$552$		−	2.39466i		−	0.101924i
$553$			4.42899i			0.188340i
$554$	−3.09333	−	3.09333i	−0.131423	−	0.131423i
$555$		0			0
$556$			27.6773i			1.17378i
$557$	−14.6986			−0.622799			−0.311400	−	0.950279i	$-0.600798\pi$
$557$	−14.6986			−0.622799			−0.311400	+	0.950279i	$0.600798\pi$
$558$	1.60614	+	1.60614i	0.0679932	+	0.0679932i
$559$	11.1312	+	1.64688i	0.470799	+	0.0696555i
$560$		0			0
$561$	4.57066	+	4.57066i	0.192973	+	0.192973i
$562$	−4.48750	−	4.48750i	−0.189294	−	0.189294i
$563$	−2.85777	−	2.85777i	−0.120441	−	0.120441i	0.644317	−	0.764758i	$-0.277142\pi$
$563$	−2.85777	−	2.85777i	−0.120441	−	0.120441i	−0.764758	+	0.644317i	$0.777142\pi$
$564$	−3.26713	+	3.26713i	−0.137571	+	0.137571i
$565$		0			0
$566$	−0.744403	+	0.744403i	−0.0312896	+	0.0312896i
$567$	−3.48937			−0.146540
$568$	2.52563	−	2.52563i	0.105973	−	0.105973i
$569$	4.12855			0.173078			0.0865390	−	0.996248i	$-0.472419\pi$
$569$	4.12855			0.173078			0.0865390	+	0.996248i	$0.472419\pi$
$570$		0			0
$571$		−	30.4821i		−	1.27564i	−0.770187	−	0.637819i	$-0.779837\pi$
$571$		−	30.4821i		−	1.27564i	0.770187	−	0.637819i	$-0.220163\pi$
$572$	−4.10866	+	27.7703i	−0.171792	+	1.16113i
$573$	−5.35582	+	5.35582i	−0.223743	+	0.223743i
$574$	−0.00612786	+	0.00612786i	−0.000255772	+	0.000255772i
$575$		0			0
$576$			10.7904i			0.449601i
$577$			10.4982i			0.437046i	0.975832	+	0.218523i	$0.0701239\pi$
$577$			10.4982i			0.437046i	−0.975832	+	0.218523i	$0.929876\pi$
$578$	0.926169			0.0385235
$579$	−2.55016	−	2.55016i	−0.105981	−	0.105981i
$580$		0			0
$581$	−6.91639			−0.286940
$582$	−0.160587	+	0.160587i	−0.00665653	+	0.00665653i
$583$		−	47.7648i		−	1.97822i
$584$	25.3151			1.04754
$585$		0			0
$586$	−0.287073			−0.0118589
$587$		−	30.4911i		−	1.25850i	−0.777202	−	0.629251i	$-0.783362\pi$
$587$		−	30.4911i		−	1.25850i	0.777202	−	0.629251i	$-0.216638\pi$
$588$	2.98663	−	2.98663i	0.123166	−	0.123166i
$589$	4.05076			0.166909
$590$		0			0
$591$	−2.51533	−	2.51533i	−0.103467	−	0.103467i
$592$	−20.5725			−0.845523
$593$			34.5161i			1.41741i	0.705506	+	0.708704i	$0.250720\pi$
$593$			34.5161i			1.41741i	−0.705506	+	0.708704i	$0.749280\pi$
$594$		−	3.81576i		−	0.156563i
$595$		0			0
$596$	−12.1493	+	12.1493i	−0.497655	+	0.497655i
$597$	−4.67355	+	4.67355i	−0.191276	+	0.191276i
$598$	0.966870	−	6.53504i	0.0395382	−	0.267237i
$599$		−	27.5663i		−	1.12633i	−0.826345	−	0.563164i	$-0.809584\pi$
$599$		−	27.5663i		−	1.12633i	0.826345	−	0.563164i	$-0.190416\pi$
$600$		0			0
$601$	−31.0403			−1.26616			−0.633081	−	0.774086i	$-0.718210\pi$
$601$	−31.0403			−1.26616			−0.633081	+	0.774086i	$0.718210\pi$
$602$	0.424757	−	0.424757i	0.0173118	−	0.0173118i
$603$	32.2221			1.31219
$604$	10.6377	−	10.6377i	0.432841	−	0.432841i
$605$		0			0
$606$	0.484666	−	0.484666i	0.0196882	−	0.0196882i
$607$	12.6624	+	12.6624i	0.513952	+	0.513952i	0.915735	−	0.401783i	$-0.131609\pi$
$607$	12.6624	+	12.6624i	0.513952	+	0.513952i	−0.401783	+	0.915735i	$0.631609\pi$
$608$	−7.34349	−	7.34349i	−0.297818	−	0.297818i
$609$	−0.0147299	−	0.0147299i	−0.000596886	−	0.000596886i
$610$		0			0
$611$	−21.5602	+	16.0027i	−0.872232	+	0.647400i
$612$	16.1039	+	16.1039i	0.650961	+	0.650961i
$613$	9.95690			0.402155			0.201078	−	0.979575i	$-0.435556\pi$
$613$	9.95690			0.402155			0.201078	+	0.979575i	$0.435556\pi$
$614$			2.49940i			0.100867i
$615$		0			0
$616$	2.23223	+	2.23223i	0.0899391	+	0.0899391i
$617$			23.8211i			0.959001i	0.877542	+	0.479501i	$0.159182\pi$
$617$			23.8211i			0.959001i	−0.877542	+	0.479501i	$0.840818\pi$
$618$		−	1.20248i		−	0.0483709i
$619$	−20.8503	−	20.8503i	−0.838046	−	0.838046i	0.150556	−	0.988602i	$-0.451894\pi$
$619$	−20.8503	−	20.8503i	−0.838046	−	0.838046i	−0.988602	+	0.150556i	$0.951894\pi$
$620$		0			0
$621$		−	8.43233i		−	0.338378i
$622$	−4.00206			−0.160468
$623$	−4.38078	−	4.38078i	−0.175512	−	0.175512i
$624$	0.522076	−	3.52869i	0.0208998	−	0.141261i
$625$		0			0
$626$	7.13921	+	7.13921i	0.285340	+	0.285340i
$627$	−2.35770	−	2.35770i	−0.0941574	−	0.0941574i
$628$	14.9391	+	14.9391i	0.596137	+	0.596137i
$629$	−22.0645	+	22.0645i	−0.879768	+	0.879768i
$630$		0			0
$631$	−15.0474	+	15.0474i	−0.599027	+	0.599027i	−0.940054	−	0.341027i	$-0.889225\pi$
$631$	−15.0474	+	15.0474i	−0.599027	+	0.599027i	0.341027	+	0.940054i	$0.389225\pi$
$632$	−16.8635			−0.670793
$633$	−2.19547	+	2.19547i	−0.0872619	+	0.0872619i
$634$	10.3213			0.409911
$635$		0			0
$636$			6.87999i			0.272809i
$637$	19.7091	−	14.6288i	0.780904	−	0.579613i
$638$	−0.184843	+	0.184843i	−0.00731802	+	0.00731802i
$639$	4.35768	−	4.35768i	0.172387	−	0.172387i
$640$		0			0
$641$			22.0567i			0.871188i	0.900143	+	0.435594i	$0.143462\pi$
$641$			22.0567i			0.871188i	−0.900143	+	0.435594i	$0.856538\pi$
$642$		−	1.64765i		−	0.0650276i
$643$	−5.50564			−0.217121			−0.108561	−	0.994090i	$-0.534624\pi$
$643$	−5.50564			−0.217121			−0.108561	+	0.994090i	$0.534624\pi$
$644$	2.34178	+	2.34178i	0.0922792	+	0.0922792i
$645$		0			0
$646$	−4.32500			−0.170165
$647$	−7.18604	+	7.18604i	−0.282512	+	0.282512i	−0.834110	−	0.551598i	$-0.814018\pi$
$647$	−7.18604	+	7.18604i	−0.282512	+	0.282512i	0.551598	+	0.834110i	$0.314018\pi$
$648$		−	13.2858i		−	0.521917i
$649$	−36.6361			−1.43809
$650$		0			0
$651$	0.270521			0.0106026
$652$			37.2936i			1.46053i
$653$	−3.66293	+	3.66293i	−0.143342	+	0.143342i	−0.775136	−	0.631794i	$-0.782319\pi$
$653$	−3.66293	+	3.66293i	−0.143342	+	0.143342i	0.631794	+	0.775136i	$0.282319\pi$
$654$	−2.19102			−0.0856756
$655$		0			0
$656$	0.0917581	+	0.0917581i	0.00358255	+	0.00358255i
$657$	43.6782			1.70405
$658$			1.43337i			0.0558786i
$659$		−	5.69188i		−	0.221724i	−0.993836	−	0.110862i	$-0.964639\pi$
$659$		−	5.69188i		−	0.221724i	0.993836	−	0.110862i	$-0.0353612\pi$
$660$		0			0
$661$	24.8493	−	24.8493i	0.966527	−	0.966527i	−0.0329310	−	0.999458i	$-0.510484\pi$
$661$	24.8493	−	24.8493i	0.966527	−	0.966527i	0.999458	+	0.0329310i	$0.0104842\pi$
$662$	5.12691	−	5.12691i	0.199263	−	0.199263i
$663$	−3.22467	−	4.34455i	−0.125236	−	0.168728i
$664$		−	26.3343i		−	1.02197i
$665$		0			0
$666$	9.02565			0.349737
$667$	−0.408480	+	0.408480i	−0.0158164	+	0.0158164i
$668$	10.8975			0.421636
$669$	2.16859	−	2.16859i	0.0838426	−	0.0838426i
$670$		0			0
$671$	−28.4957	+	28.4957i	−1.10006	+	1.10006i
$672$	−0.490419	−	0.490419i	−0.0189183	−	0.0189183i
$673$	−21.9648	−	21.9648i	−0.846679	−	0.846679i	0.143038	−	0.989717i	$-0.454313\pi$
$673$	−21.9648	−	21.9648i	−0.846679	−	0.846679i	−0.989717	+	0.143038i	$0.954313\pi$
$674$	−4.43660	−	4.43660i	−0.170892	−	0.170892i
$675$		0			0
$676$	6.80413	−	22.4911i	0.261697	−	0.865042i
$677$	−33.7205	−	33.7205i	−1.29598	−	1.29598i	−0.931024	−	0.364959i	$-0.881083\pi$
$677$	−33.7205	−	33.7205i	−1.29598	−	1.29598i	−0.364959	−	0.931024i	$-0.618917\pi$
$678$	−0.479939			−0.0184319
$679$		−	0.661608i		−	0.0253902i
$680$		0			0
$681$	−5.45065	−	5.45065i	−0.208869	−	0.208869i
$682$		−	3.39473i		−	0.129991i
$683$		−	19.8074i		−	0.757909i	−0.925415	−	0.378955i	$-0.876284\pi$
$683$		−	19.8074i		−	0.757909i	0.925415	−	0.378955i	$-0.123716\pi$
$684$	−8.30692	−	8.30692i	−0.317623	−	0.317623i
$685$		0			0
$686$		−	2.65766i		−	0.101470i
$687$	−3.50700			−0.133800
$688$	−6.36029	−	6.36029i	−0.242484	−	0.242484i
$689$	−5.85154	+	39.5504i	−0.222926	+	1.50675i
$690$		0			0
$691$	−31.2449	−	31.2449i	−1.18861	−	1.18861i	−0.977451	−	0.211162i	$-0.932275\pi$
$691$	−31.2449	−	31.2449i	−1.18861	−	1.18861i	−0.211162	−	0.977451i	$-0.567725\pi$
$692$	−25.6082	−	25.6082i	−0.973479	−	0.973479i
$693$	3.85145	+	3.85145i	0.146305	+	0.146305i
$694$	2.88794	−	2.88794i	0.109625	−	0.109625i
$695$		0			0
$696$	0.0560844	−	0.0560844i	0.00212587	−	0.00212587i
$697$	0.196826			0.00745531
$698$	7.70275	−	7.70275i	0.291553	−	0.291553i
$699$	6.38536			0.241516
$700$		0			0
$701$			34.2135i			1.29223i	0.763241	+	0.646114i	$0.223607\pi$
$701$			34.2135i			1.29223i	−0.763241	+	0.646114i	$0.776393\pi$
$702$	−0.467459	+	3.15954i	−0.0176431	+	0.119249i
$703$	11.3816	−	11.3816i	0.429265	−	0.429265i
$704$	11.4033	−	11.4033i	0.429778	−	0.429778i
$705$		0			0
$706$			10.9700i			0.412861i
$707$			1.99680i			0.0750973i
$708$	5.27702			0.198322
$709$	4.07045	+	4.07045i	0.152869	+	0.152869i	0.779398	−	0.626529i	$-0.215525\pi$
$709$	4.07045	+	4.07045i	0.152869	+	0.152869i	−0.626529	+	0.779398i	$0.715525\pi$
$710$		0			0
$711$	−29.0960			−1.09118
$712$	16.6799	−	16.6799i	0.625107	−	0.625107i
$713$		−	7.50191i		−	0.280949i
$714$	−0.288835			−0.0108094
$715$		0			0
$716$	−29.0923			−1.08723
$717$			10.5597i			0.394359i
$718$	0.731661	−	0.731661i	0.0273054	−	0.0273054i
$719$	−40.4409			−1.50819			−0.754095	−	0.656765i	$-0.771924\pi$
$719$	−40.4409			−1.50819			−0.754095	+	0.656765i	$0.771924\pi$
$720$		0			0
$721$	2.47708	+	2.47708i	0.0922512	+	0.0922512i
$722$	−6.10479			−0.227197
$723$		−	8.93211i		−	0.332189i
$724$		−	11.8479i		−	0.440322i
$725$		0			0
$726$	−0.804491	+	0.804491i	−0.0298575	+	0.0298575i
$727$	−14.6406	+	14.6406i	−0.542988	+	0.542988i	−0.924404	−	0.381415i	$-0.875437\pi$
$727$	−14.6406	+	14.6406i	−0.542988	+	0.542988i	0.381415	+	0.924404i	$0.375437\pi$
$728$	−1.57487	−	2.12180i	−0.0583686	−	0.0786392i
$729$		−	20.8439i		−	0.771997i
$730$		0			0
$731$	−13.6431			−0.504609
$732$	4.10449	−	4.10449i	0.151706	−	0.151706i
$733$	31.6272			1.16818			0.584089	−	0.811690i	$-0.301452\pi$
$733$	31.6272			1.16818			0.584089	+	0.811690i	$0.301452\pi$
$734$	−3.82984	+	3.82984i	−0.141362	+	0.141362i
$735$		0			0
$736$	−13.6000	+	13.6000i	−0.501301	+	0.501301i
$737$	−34.0523	−	34.0523i	−1.25433	−	1.25433i
$738$	−0.0402566	−	0.0402566i	−0.00148186	−	0.00148186i
$739$	−10.0736	−	10.0736i	−0.370563	−	0.370563i	0.497119	−	0.867682i	$-0.334391\pi$
$739$	−10.0736	−	10.0736i	−0.370563	−	0.370563i	−0.867682	+	0.497119i	$0.834391\pi$
$740$		0			0
$741$	1.66339	+	2.24106i	0.0611062	+	0.0823274i
$742$	1.50921	+	1.50921i	0.0554049	+	0.0554049i
$743$	5.70595			0.209331			0.104666	−	0.994507i	$-0.466623\pi$
$743$	5.70595			0.209331			0.104666	+	0.994507i	$0.466623\pi$
$744$			1.03001i			0.0377622i
$745$		0			0
$746$	−4.25309	−	4.25309i	−0.155717	−	0.155717i
$747$		−	45.4367i		−	1.66244i
$748$		−	34.0371i		−	1.24452i
$749$	3.39412	+	3.39412i	0.124018	+	0.124018i
$750$		0			0
$751$			11.6268i			0.424269i	0.977240	+	0.212134i	$0.0680415\pi$
$751$			11.6268i			0.424269i	−0.977240	+	0.212134i	$0.931959\pi$
$752$	21.4632			0.782682
$753$	2.20410	+	2.20410i	0.0803220	+	0.0803220i
$754$	0.175699	−	0.130410i	0.00639858	−	0.00474924i
$755$		0			0
$756$	−1.13220	−	1.13220i	−0.0411776	−	0.0411776i
$757$	12.4158	+	12.4158i	0.451261	+	0.451261i	0.895773	−	0.444512i	$-0.146623\pi$
$757$	12.4158	+	12.4158i	0.451261	+	0.451261i	−0.444512	+	0.895773i	$0.646623\pi$
$758$	7.38405	+	7.38405i	0.268201	+	0.268201i
$759$	−4.36639	+	4.36639i	−0.158490	+	0.158490i
$760$		0			0
$761$	−1.74841	+	1.74841i	−0.0633797	+	0.0633797i	−0.738086	−	0.674706i	$-0.764270\pi$
$761$	−1.74841	+	1.74841i	−0.0633797	+	0.0633797i	0.674706	+	0.738086i	$0.264270\pi$
$762$	2.71198			0.0982446
$763$	4.51344	−	4.51344i	0.163397	−	0.163397i
$764$	39.8842			1.44296
$765$		0			0
$766$		−	10.4699i		−	0.378294i
$767$	30.3355	+	4.48819i	1.09535	+	0.162059i
$768$	−0.661681	+	0.661681i	−0.0238764	+	0.0238764i
$769$	−8.83323	+	8.83323i	−0.318534	+	0.318534i	−0.848204	−	0.529670i	$-0.822316\pi$
$769$	−8.83323	+	8.83323i	−0.318534	+	0.318534i	0.529670	+	0.848204i	$0.322316\pi$
$770$		0			0
$771$		−	5.75854i		−	0.207389i
$772$			18.9907i			0.683492i
$773$	−49.9877			−1.79793			−0.898967	−	0.438017i	$-0.855681\pi$
$773$	−49.9877			−1.79793			−0.898967	+	0.438017i	$0.855681\pi$
$774$	2.79041	+	2.79041i	0.100299	+	0.100299i
$775$		0			0
$776$	2.51908			0.0904299
$777$	0.760094	−	0.760094i	0.0272682	−	0.0272682i
$778$			5.61171i			0.201190i
$779$	−0.101529			−0.00363766
$780$		0			0
$781$	−9.21039			−0.329574
$782$			8.00978i			0.286429i
$783$	0.197490	−	0.197490i	0.00705773	−	0.00705773i
$784$	−19.6204			−0.700730
$785$		0			0
$786$	−1.27072	−	1.27072i	−0.0453249	−	0.0453249i
$787$	11.2437			0.400793			0.200396	−	0.979715i	$-0.435777\pi$
$787$	11.2437			0.400793			0.200396	+	0.979715i	$0.435777\pi$
$788$			18.7314i			0.667278i
$789$			6.50722i			0.231663i
$790$		0			0
$791$	0.988660	−	0.988660i	0.0351527	−	0.0351527i
$792$	−14.6645	+	14.6645i	−0.521080	+	0.521080i
$793$	27.0860	−	20.1042i	0.961853	−	0.713919i
$794$			6.90195i			0.244941i
$795$		0			0
$796$	34.8034			1.23357
$797$	−16.9617	+	16.9617i	−0.600815	+	0.600815i	−0.940529	−	0.339714i	$-0.889670\pi$
$797$	−16.9617	+	16.9617i	−0.600815	+	0.600815i	0.339714	+	0.940529i	$0.389670\pi$
$798$	0.148991			0.00527422
$799$	23.0198	−	23.0198i	0.814382	−	0.814382i
$800$		0			0
$801$	28.7793	−	28.7793i	1.01687	−	1.01687i
$802$	−1.81061	−	1.81061i	−0.0639349	−	0.0639349i
$803$	−46.1591	−	46.1591i	−1.62892	−	1.62892i
$804$	4.90485	+	4.90485i	0.172981	+	0.172981i
$805$		0			0
$806$	−0.415879	+	2.81091i	−0.0146487	+	0.0990101i
$807$	3.36898	+	3.36898i	0.118594	+	0.118594i
$808$	−7.60285			−0.267467
$809$		−	12.9602i		−	0.455657i	−0.973701	−	0.227828i	$-0.926837\pi$
$809$		−	12.9602i		−	0.455657i	0.973701	−	0.227828i	$-0.0731625\pi$
$810$		0			0
$811$	10.8170	+	10.8170i	0.379836	+	0.379836i	0.871043	−	0.491207i	$-0.163444\pi$
$811$	10.8170	+	10.8170i	0.379836	+	0.379836i	−0.491207	+	0.871043i	$0.663444\pi$
$812$			0.109692i			0.00384943i
$813$		−	2.91397i		−	0.102198i
$814$	−9.53830	−	9.53830i	−0.334317	−	0.334317i
$815$		0			0
$816$			4.32500i			0.151405i
$817$	7.03758			0.246214
$818$	1.55459	+	1.55459i	0.0543548	+	0.0543548i
$819$	−2.71726	−	3.66092i	−0.0949487	−	0.127923i
$820$		0			0
$821$	5.30454	+	5.30454i	0.185130	+	0.185130i	0.793587	−	0.608457i	$-0.208211\pi$
$821$	5.30454	+	5.30454i	0.185130	+	0.185130i	−0.608457	+	0.793587i	$0.708211\pi$
$822$	−0.359784	−	0.359784i	−0.0125489	−	0.0125489i
$823$	34.1224	+	34.1224i	1.18943	+	1.18943i	0.977224	+	0.212208i	$0.0680655\pi$
$823$	34.1224	+	34.1224i	1.18943	+	1.18943i	0.212208	+	0.977224i	$0.431935\pi$
$824$	−9.43153	+	9.43153i	−0.328563	+	0.328563i
$825$		0			0
$826$	1.15758	−	1.15758i	0.0402773	−	0.0402773i
$827$	−5.27056			−0.183275			−0.0916376	−	0.995792i	$-0.529210\pi$
$827$	−5.27056			−0.183275			−0.0916376	+	0.995792i	$0.529210\pi$
$828$	−15.3842	+	15.3842i	−0.534637	+	0.534637i
$829$	20.9932			0.729125			0.364562	−	0.931179i	$-0.381219\pi$
$829$	20.9932			0.729125			0.364562	+	0.931179i	$0.381219\pi$
$830$		0			0
$831$		−	3.42273i		−	0.118733i
$832$	−10.8392	+	8.04520i	−0.375781	+	0.278917i
$833$	−21.0434	+	21.0434i	−0.729111	+	0.729111i
$834$	1.63058	−	1.63058i	0.0564623	−	0.0564623i
$835$		0			0
$836$			17.5575i			0.607239i
$837$			3.62699i			0.125367i
$838$	−13.0174			−0.449678
$839$	7.12698	+	7.12698i	0.246051	+	0.246051i	0.819348	−	0.573297i	$-0.194336\pi$
$839$	7.12698	+	7.12698i	0.246051	+	0.246051i	−0.573297	+	0.819348i	$0.694336\pi$
$840$		0			0
$841$	28.9809			0.999340
$842$	−3.32545	+	3.32545i	−0.114603	+	0.114603i
$843$		−	4.96537i		−	0.171016i
$844$	16.3494			0.562769
$845$		0			0
$846$	−9.41643			−0.323744
$847$		−	3.31446i		−	0.113886i
$848$	22.5988	−	22.5988i	0.776046	−	0.776046i
$849$	−0.823673			−0.0282684
$850$		0			0
$851$	−21.0784	−	21.0784i	−0.722558	−	0.722558i
$852$	1.32665			0.0454504
$853$			5.81669i			0.199160i	0.995030	+	0.0995798i	$0.0317498\pi$
$853$			5.81669i			0.199160i	−0.995030	+	0.0995798i	$0.968250\pi$
$854$		−	1.80074i		−	0.0616201i
$855$		0			0
$856$	−12.9232	+	12.9232i	−0.441705	+	0.441705i
$857$	1.83206	−	1.83206i	0.0625819	−	0.0625819i	−0.675123	−	0.737705i	$-0.735910\pi$
$857$	1.83206	−	1.83206i	0.0625819	−	0.0625819i	0.737705	+	0.675123i	$0.235910\pi$
$858$	1.87811	−	1.39400i	0.0641177	−	0.0475903i
$859$		−	5.10411i		−	0.174150i	−0.996202	−	0.0870750i	$-0.972248\pi$
$859$		−	5.10411i		−	0.174150i	0.996202	−	0.0870750i	$-0.0277520\pi$
$860$		0			0
$861$	−0.00678040			−0.000231076
$862$	−12.4950	+	12.4950i	−0.425582	+	0.425582i
$863$	51.8953			1.76654			0.883268	−	0.468869i	$-0.155338\pi$
$863$	51.8953			1.76654			0.883268	+	0.468869i	$0.155338\pi$
$864$	6.57526	−	6.57526i	0.223695	−	0.223695i
$865$		0			0
$866$	2.98253	−	2.98253i	0.101351	−	0.101351i
$867$	0.512397	+	0.512397i	0.0174019	+	0.0174019i
$868$	−1.00727	−	1.00727i	−0.0341890	−	0.0341890i
$869$	30.7486	+	30.7486i	1.04307	+	1.04307i
$870$		0			0
$871$	24.0244	+	32.3677i	0.814036	+	1.09674i
$872$	17.1850	+	17.1850i	0.581958	+	0.581958i
$873$	4.34639			0.147103
$874$		−	4.13171i		−	0.139757i
$875$		0			0
$876$	6.64870	+	6.64870i	0.224639	+	0.224639i
$877$		−	15.4765i		−	0.522604i	−0.965257	−	0.261302i	$-0.915848\pi$
$877$		−	15.4765i		−	0.522604i	0.965257	−	0.261302i	$-0.0841518\pi$
$878$			2.33245i			0.0787164i
$879$	−0.158821	−	0.158821i	−0.00535691	−	0.00535691i
$880$		0			0
$881$		−	46.8033i		−	1.57684i	−0.615135	−	0.788422i	$-0.710898\pi$
$881$		−	46.8033i		−	1.57684i	0.615135	−	0.788422i	$-0.289102\pi$
$882$	8.60797			0.289846
$883$	−3.15723	−	3.15723i	−0.106249	−	0.106249i	0.651984	−	0.758233i	$-0.273937\pi$
$883$	−3.15723	−	3.15723i	−0.106249	−	0.106249i	−0.758233	+	0.651984i	$0.773937\pi$
$884$	−4.16980	+	28.1835i	−0.140246	+	0.947914i
$885$		0			0
$886$	−0.901208	−	0.901208i	−0.0302767	−	0.0302767i
$887$	4.34803	+	4.34803i	0.145993	+	0.145993i	0.776325	−	0.630333i	$-0.217081\pi$
$887$	4.34803	+	4.34803i	0.145993	+	0.145993i	−0.630333	+	0.776325i	$0.717081\pi$
$888$	2.89407	+	2.89407i	0.0971188	+	0.0971188i
$889$	−5.58660	+	5.58660i	−0.187368	+	0.187368i
$890$		0			0
$891$	−24.2252	+	24.2252i	−0.811575	+	0.811575i
$892$	−16.1493			−0.540717
$893$	−11.8744	+	11.8744i	−0.397361	+	0.397361i
$894$	1.43153			0.0478774
$895$		0			0
$896$			4.76161i			0.159074i
$897$	4.15038	−	3.08055i	0.138577	−	0.102857i
$898$	−9.82922	+	9.82922i	−0.328005	+	0.328005i
$899$	0.175699	−	0.175699i	0.00585989	−	0.00585989i
$900$		0			0
$901$		−	48.4756i		−	1.61496i
$902$			0.0850862i			0.00283306i
$903$	0.469989			0.0156402
$904$	3.76434	+	3.76434i	0.125200	+	0.125200i
$905$		0			0
$906$	−1.25341			−0.0416419
$907$	17.2267	−	17.2267i	0.572004	−	0.572004i	−0.360684	−	0.932688i	$-0.617457\pi$
$907$	17.2267	−	17.2267i	0.572004	−	0.572004i	0.932688	+	0.360684i	$0.117457\pi$
$908$			40.5903i			1.34704i
$909$	−13.1178			−0.435091
$910$		0			0
$911$	21.4109			0.709373			0.354687	−	0.934985i	$-0.384588\pi$
$911$	21.4109			0.709373			0.354687	+	0.934985i	$0.384588\pi$
$912$		−	2.23098i		−	0.0738751i
$913$	−48.0175	+	48.0175i	−1.58915	+	1.58915i
$914$	3.67806			0.121659
$915$		0			0
$916$	13.0581	+	13.0581i	0.431452	+	0.431452i
$917$	5.23527			0.172884
$918$		−	3.87254i		−	0.127813i
$919$		−	12.1389i		−	0.400425i	−0.979753	−	0.200212i	$-0.935837\pi$
$919$		−	12.1389i		−	0.400425i	0.979753	−	0.200212i	$-0.0641632\pi$
$920$		0			0
$921$	−1.38278	+	1.38278i	−0.0455640	+	0.0455640i
$922$	7.30837	−	7.30837i	0.240688	−	0.240688i
$923$	7.62641	+	1.12834i	0.251026	+	0.0371398i
$924$			1.17254i			0.0385737i
$925$		0			0
$926$	−9.14292			−0.300455
$927$	−16.2730	+	16.2730i	−0.534475	+	0.534475i
$928$	−0.637038			−0.0209118
$929$	13.8895	−	13.8895i	0.455700	−	0.455700i	−0.441541	−	0.897241i	$-0.645568\pi$
$929$	13.8895	−	13.8895i	0.455700	−	0.455700i	0.897241	+	0.441541i	$0.145568\pi$
$930$		0			0
$931$	10.8549	−	10.8549i	0.355755	−	0.355755i
$932$	−23.7755	−	23.7755i	−0.778793	−	0.778793i
$933$	−2.21411	−	2.21411i	−0.0724869	−	0.0724869i
$934$	11.4517	+	11.4517i	0.374710	+	0.374710i
$935$		0			0
$936$	13.9390	−	10.3460i	0.455611	−	0.338170i
$937$	−21.6718	−	21.6718i	−0.707988	−	0.707988i	0.258124	−	0.966112i	$-0.416896\pi$
$937$	−21.6718	−	21.6718i	−0.707988	−	0.707988i	−0.966112	+	0.258124i	$0.916896\pi$
$938$	2.15188			0.0702614
$939$			7.89945i			0.257789i
$940$		0			0
$941$	24.4870	+	24.4870i	0.798255	+	0.798255i	0.982820	−	0.184565i	$-0.0590878\pi$
$941$	24.4870	+	24.4870i	0.798255	+	0.798255i	−0.184565	+	0.982820i	$0.559088\pi$
$942$		−	1.76025i		−	0.0573519i
$943$			0.188029i			0.00612308i
$944$	−17.3335	−	17.3335i	−0.564158	−	0.564158i
$945$		0			0
$946$		−	5.89782i		−	0.191755i
$947$	40.4688			1.31506			0.657530	−	0.753429i	$-0.271601\pi$
$947$	40.4688			1.31506			0.657530	+	0.753429i	$0.271601\pi$
$948$	−4.42899	−	4.42899i	−0.143847	−	0.143847i
$949$	32.5659	+	43.8756i	1.05713	+	1.42426i
$950$		0			0
$951$	5.71019	+	5.71019i	0.185166	+	0.185166i
$952$	2.26545	+	2.26545i	0.0734235	+	0.0734235i
$953$	−1.33281	−	1.33281i	−0.0431741	−	0.0431741i	0.685190	−	0.728364i	$-0.259719\pi$
$953$	−1.33281	−	1.33281i	−0.0431741	−	0.0431741i	−0.728364	+	0.685190i	$0.759719\pi$
$954$	−9.91466	+	9.91466i	−0.320999	+	0.320999i
$955$		0			0
$956$	39.3184	−	39.3184i	1.27165	−	1.27165i
$957$	−0.204527			−0.00661142
$958$	−8.67378	+	8.67378i	−0.280237	+	0.280237i
$959$	1.48229			0.0478656
$960$		0			0
$961$		−	27.7732i		−	0.895910i
$962$	6.72942	+	9.06644i	0.216965	+	0.292314i
$963$	−22.2974	+	22.2974i	−0.718524	+	0.718524i
$964$	−33.2582	+	33.2582i	−1.07117	+	1.07117i
$965$		0			0
$966$		−	0.275927i		−	0.00887780i
$967$			40.2629i			1.29477i	0.762164	+	0.647384i	$0.224137\pi$
$967$			40.2629i			1.29477i	−0.762164	+	0.647384i	$0.775863\pi$
$968$	12.6199			0.405618
$969$	−2.39278	−	2.39278i	−0.0768672	−	0.0768672i
$970$		0			0
$971$	22.8739			0.734059			0.367030	−	0.930209i	$-0.380375\pi$
$971$	22.8739			0.734059			0.367030	+	0.930209i	$0.380375\pi$
$972$	11.2313	−	11.2313i	0.360245	−	0.360245i
$973$			6.71789i			0.215366i
$974$	−6.85343			−0.219598
$975$		0			0
$976$	−26.9642			−0.863102
$977$		−	14.0612i		−	0.449857i	−0.974375	−	0.224929i	$-0.927785\pi$
$977$		−	14.0612i		−	0.449857i	0.974375	−	0.224929i	$-0.0722149\pi$
$978$	2.19711	−	2.19711i	0.0702559	−	0.0702559i
$979$	−60.8279			−1.94407
$980$		0			0
$981$	29.6507	+	29.6507i	0.946674	+	0.946674i
$982$	5.53655			0.176678
$983$			35.4794i			1.13162i	0.824537	+	0.565808i	$0.191436\pi$
$983$			35.4794i			1.13162i	−0.824537	+	0.565808i	$0.808564\pi$
$984$		−	0.0258165i		−	0.000823001i
$985$		0			0
$986$	−0.187594	+	0.187594i	−0.00597420	+	0.00597420i
$987$	−0.793004	+	0.793004i	−0.0252416	+	0.0252416i
$988$	2.15092	−	14.5380i	0.0684299	−	0.462515i
$989$		−	13.0334i		−	0.414438i
$990$		0			0
$991$	−11.0591			−0.351303			−0.175652	−	0.984452i	$-0.556203\pi$
$991$	−11.0591			−0.351303			−0.175652	+	0.984452i	$0.556203\pi$
$992$	5.84974	−	5.84974i	0.185729	−	0.185729i
$993$	5.67287			0.180023
$994$	0.291018	−	0.291018i	0.00923053	−	0.00923053i
$995$		0			0
$996$	6.91639	−	6.91639i	0.219154	−	0.219154i
$997$	2.10621	+	2.10621i	0.0667044	+	0.0667044i	0.739672	−	0.672968i	$-0.234981\pi$
$997$	2.10621	+	2.10621i	0.0667044	+	0.0667044i	−0.672968	+	0.739672i	$0.734981\pi$
$998$	−9.89005	−	9.89005i	−0.313064	−	0.313064i
$999$	10.1909	+	10.1909i	0.322426	+	0.322426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.f.d.307.5	yes	16
5.2	odd	4		325.2.k.d.268.4	yes	16
5.3	odd	4		325.2.k.d.268.5	yes	16
5.4	even	2	inner	325.2.f.d.307.4	yes	16
13.5	odd	4		325.2.k.d.57.5	yes	16
65.18	even	4	inner	325.2.f.d.18.4	✓	16
65.44	odd	4		325.2.k.d.57.4	yes	16
65.57	even	4	inner	325.2.f.d.18.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.f.d.18.4	✓	16	65.18	even	4	inner
325.2.f.d.18.5	yes	16	65.57	even	4	inner
325.2.f.d.307.4	yes	16	5.4	even	2	inner
325.2.f.d.307.5	yes	16	1.1	even	1	trivial
325.2.k.d.57.4	yes	16	65.44	odd	4
325.2.k.d.57.5	yes	16	13.5	odd	4
325.2.k.d.268.4	yes	16	5.2	odd	4
325.2.k.d.268.5	yes	16	5.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.438725i q^{2} +(-0.242722 + 0.242722i) q^{3} +1.80752 q^{4} +(-0.106488 - 0.106488i) q^{6} +0.438725 q^{7} +1.67045i q^{8} +2.88217i q^{9} +O(q^{10})\)	\(q+0.438725i q^{2} +(-0.242722 + 0.242722i) q^{3} +1.80752 q^{4} +(-0.106488 - 0.106488i) q^{6} +0.438725 q^{7} +1.67045i q^{8} +2.88217i q^{9} +(3.04588 - 3.04588i) q^{11} +(-0.438725 + 0.438725i) q^{12} +(-2.89520 + 2.14891i) q^{13} +0.192479i q^{14} +2.88217 q^{16} +(3.09120 - 3.09120i) q^{17} -1.26448 q^{18} +(-1.59454 + 1.59454i) q^{19} +(-0.106488 + 0.106488i) q^{21} +(1.33630 + 1.33630i) q^{22} +(2.95305 + 2.95305i) q^{23} +(-0.405455 - 0.405455i) q^{24} +(-0.942781 - 1.27019i) q^{26} +(-1.42773 - 1.42773i) q^{27} +0.793004 q^{28} +0.138324i q^{29} +(-1.27019 - 1.27019i) q^{31} +4.60539i q^{32} +1.47860i q^{33} +(1.35619 + 1.35619i) q^{34} +5.20959i q^{36} -7.13783 q^{37} +(-0.699566 - 0.699566i) q^{38} +(0.181140 - 1.22432i) q^{39} +(0.0318365 + 0.0318365i) q^{41} +(-0.0467189 - 0.0467189i) q^{42} +(-2.20677 - 2.20677i) q^{43} +(5.50549 - 5.50549i) q^{44} +(-1.29558 + 1.29558i) q^{46} +7.44688 q^{47} +(-0.699566 + 0.699566i) q^{48} -6.80752 q^{49} +1.50060i q^{51} +(-5.23313 + 3.88420i) q^{52} +(7.84090 - 7.84090i) q^{53} +(0.626381 - 0.626381i) q^{54} +0.732869i q^{56} -0.774061i q^{57} -0.0606864 q^{58} +(-6.01404 - 6.01404i) q^{59} -9.35550 q^{61} +(0.557266 - 0.557266i) q^{62} +1.26448i q^{63} +3.74385 q^{64} -0.648699 q^{66} -11.1798i q^{67} +(5.58741 - 5.58741i) q^{68} -1.43354 q^{69} +(-1.51194 - 1.51194i) q^{71} -4.81453 q^{72} -15.1546i q^{73} -3.13154i q^{74} +(-2.88217 + 2.88217i) q^{76} +(1.33630 - 1.33630i) q^{77} +(0.537138 + 0.0794704i) q^{78} +10.0951i q^{79} -7.95343 q^{81} +(-0.0139674 + 0.0139674i) q^{82} -15.7648 q^{83} +(-0.192479 + 0.192479i) q^{84} +(0.968164 - 0.968164i) q^{86} +(-0.0335744 - 0.0335744i) q^{87} +(5.08800 + 5.08800i) q^{88} +(-9.98527 - 9.98527i) q^{89} +(-1.27019 + 0.942781i) q^{91} +(5.33770 + 5.33770i) q^{92} +0.616608 q^{93} +3.26713i q^{94} +(-1.11783 - 1.11783i) q^{96} -1.50802i q^{97} -2.98663i q^{98} +(8.77875 + 8.77875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 16 * q - 8 * q^4 + 12 * q^6	\( 16 q - 8 q^{4} + 12 q^{6} - 20 q^{11} - 8 q^{16} - 16 q^{19} + 12 q^{21} - 16 q^{24} - 16 q^{26} + 8 q^{31} + 44 q^{34} - 28 q^{39} + 4 q^{41} + 76 q^{44} + 12 q^{46} - 72 q^{49} + 4 q^{54} - 24 q^{59} + 24 q^{61} + 16 q^{64} - 48 q^{66} + 112 q^{69} - 20 q^{71} + 8 q^{76} - 40 q^{84} + 12 q^{86} - 36 q^{89} + 8 q^{91} - 72 q^{96} + 52 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 + 12 * q^6 - 20 * q^11 - 8 * q^16 - 16 * q^19 + 12 * q^21 - 16 * q^24 - 16 * q^26 + 8 * q^31 + 44 * q^34 - 28 * q^39 + 4 * q^41 + 76 * q^44 + 12 * q^46 - 72 * q^49 + 4 * q^54 - 24 * q^59 + 24 * q^61 + 16 * q^64 - 48 * q^66 + 112 * q^69 - 20 * q^71 + 8 * q^76 - 40 * q^84 + 12 * q^86 - 36 * q^89 + 8 * q^91 - 72 * q^96 + 52 * q^99

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