LMFDB - Embedded newform 196.2.p.a.59.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(3,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 1]))

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

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

chi := DirichletCharacter("196.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.p (of order $42$, degree $12$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$26$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			59.12
Character	$\chi$	$=$	196.59
Dual form			196.2.p.a.103.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.167781 + 1.40423i) q^{2} +(-1.97899 + 1.34925i) q^{3} +(-1.94370 - 0.471205i) q^{4} +(-0.0159493 + 0.00119524i) q^{5} +(-1.56262 - 3.00533i) q^{6} +(-2.59622 - 0.509531i) q^{7} +(0.987794 - 2.65033i) q^{8} +(0.999898 - 2.54770i) q^{9} +(0.000997612 - 0.0225970i) q^{10} +(1.65591 - 0.649897i) q^{11} +(4.48234 - 1.69003i) q^{12} +(-2.07204 - 1.65240i) q^{13} +(1.15109 - 3.56019i) q^{14} +(0.0299509 - 0.0238850i) q^{15} +(3.55593 + 1.83176i) q^{16} +(-3.29762 + 3.55399i) q^{17} +(3.40978 + 1.83154i) q^{18} +(-0.682883 - 1.18279i) q^{19} +(0.0315639 + 0.00519222i) q^{20} +(5.82539 - 2.49461i) q^{21} +(0.634772 + 2.43431i) q^{22} +(-3.75388 - 4.04572i) q^{23} +(1.62114 + 6.57777i) q^{24} +(-4.94390 + 0.745173i) q^{25} +(2.66799 - 2.63237i) q^{26} +(-0.140232 - 0.614395i) q^{27} +(4.80618 + 2.21373i) q^{28} +(0.487147 - 2.13433i) q^{29} +(0.0285148 + 0.0460653i) q^{30} +(-4.96153 + 8.59362i) q^{31} +(-3.16882 + 4.68600i) q^{32} +(-2.40016 + 3.52038i) q^{33} +(-4.43732 - 5.22689i) q^{34} +(0.0420170 + 0.00502358i) q^{35} +(-3.14399 + 4.48080i) q^{36} +(1.78032 - 0.549155i) q^{37} +(1.77548 - 0.760473i) q^{38} +(6.33006 + 0.474372i) q^{39} +(-0.0125869 + 0.0434517i) q^{40} +(-1.78963 + 3.71620i) q^{41} +(2.52560 + 8.59871i) q^{42} +(4.01716 + 8.34173i) q^{43} +(-3.52483 + 0.482931i) q^{44} +(-0.0129026 + 0.0418292i) q^{45} +(6.31094 - 4.59250i) q^{46} +(-9.62933 - 1.45139i) q^{47} +(-9.50867 + 1.17282i) q^{48} +(6.48076 + 2.64571i) q^{49} +(-0.216899 - 7.06738i) q^{50} +(1.73073 - 11.4826i) q^{51} +(3.24881 + 4.18812i) q^{52} +(-8.11554 - 2.50331i) q^{53} +(0.886278 - 0.0938331i) q^{54} +(-0.0256339 + 0.0123446i) q^{55} +(-3.91496 + 6.37755i) q^{56} +(2.94730 + 1.41935i) q^{57} +(2.91535 + 1.04216i) q^{58} +(0.462993 - 6.17821i) q^{59} +(-0.0694703 + 0.0323123i) q^{60} +(2.72001 + 8.81806i) q^{61} +(-11.2349 - 8.40895i) q^{62} +(-3.89409 + 6.10492i) q^{63} +(-6.04853 - 5.23596i) q^{64} +(0.0350227 + 0.0238781i) q^{65} +(-4.54071 - 3.96102i) q^{66} +(4.78628 + 2.76336i) q^{67} +(8.08423 - 5.35403i) q^{68} +(12.8876 + 2.94151i) q^{69} +(-0.0141039 + 0.0581585i) q^{70} +(13.9367 - 3.18096i) q^{71} +(-5.76456 - 5.16666i) q^{72} +(-1.28303 - 8.51233i) q^{73} +(0.472434 + 2.59210i) q^{74} +(8.77851 - 8.14527i) q^{75} +(0.769984 + 2.62076i) q^{76} +(-4.63026 + 0.843540i) q^{77} +(-1.72819 + 8.80924i) q^{78} +(-0.651250 + 0.376000i) q^{79} +(-0.0589041 - 0.0249652i) q^{80} +(7.12534 + 6.61135i) q^{81} +(-4.91812 - 3.13655i) q^{82} +(2.16800 + 2.71859i) q^{83} +(-12.4983 + 2.10381i) q^{84} +(0.0483469 - 0.0606251i) q^{85} +(-12.3877 + 4.24142i) q^{86} +(1.91569 + 4.88111i) q^{87} +(-0.0867456 - 5.03068i) q^{88} +(1.89685 + 0.744461i) q^{89} +(-0.0565728 - 0.0251363i) q^{90} +(4.53754 + 5.34577i) q^{91} +(5.39005 + 9.63251i) q^{92} +(-1.77615 - 23.7010i) q^{93} +(3.65369 - 13.2782i) q^{94} +(0.0123052 + 0.0180485i) q^{95} +(-0.0515237 - 13.5491i) q^{96} +12.1281i q^{97} +(-4.80253 + 8.65654i) q^{98} -4.86859i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25}+ \cdots + 183 q^{98}+O(q^{100}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{13}{42}\right)$

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 $

$2$	−0.167781	+	1.40423i	−0.118639	+	0.992937i
$2$	−0.167781	+	1.40423i	−0.118639	+	0.992937i
$3$	−1.97899	+	1.34925i	−1.14257	+	0.778992i	−0.978253	−	0.207416i	$-0.933495\pi$
$3$	−1.97899	+	1.34925i	−1.14257	+	0.778992i	−0.164318	+	0.986407i	$0.552542\pi$
$4$	−1.94370	−	0.471205i	−0.971850	−	0.235602i
$5$	−0.0159493	+	0.00119524i	−0.00713275	+	0.000534526i	−0.0782960	−	0.996930i	$-0.524948\pi$
$5$	−0.0159493	+	0.00119524i	−0.00713275	+	0.000534526i	0.0711632	+	0.997465i	$0.477329\pi$
$6$	−1.56262	−	3.00533i	−0.637936	−	1.22692i
$7$	−2.59622	−	0.509531i	−0.981280	−	0.192585i
$7$	−2.59622	−	0.509531i	−0.981280	−	0.192585i
$8$	0.987794	−	2.65033i	0.349238	−	0.937034i
$9$	0.999898	−	2.54770i	0.333299	−	0.849233i
$10$	0.000997612	−	0.0225970i	0.000315473	−	0.00714580i
$11$	1.65591	−	0.649897i	0.499276	−	0.195951i	−0.102321	−	0.994751i	$-0.532627\pi$
$11$	1.65591	−	0.649897i	0.499276	−	0.195951i	0.601597	+	0.798800i	$0.294532\pi$
$12$	4.48234	−	1.69003i	1.29394	−	0.487870i
$13$	−2.07204	−	1.65240i	−0.574681	−	0.458293i	0.292514	−	0.956261i	$-0.405508\pi$
$13$	−2.07204	−	1.65240i	−0.574681	−	0.458293i	−0.867195	+	0.497968i	$0.834080\pi$
$14$	1.15109	−	3.56019i	0.307643	−	0.951502i
$15$	0.0299509	−	0.0238850i	0.00773329	−	0.00616709i
$16$	3.55593	+	1.83176i	0.888983	+	0.457940i
$17$	−3.29762	+	3.55399i	−0.799790	+	0.861968i	−0.992868	−	0.119215i	$-0.961962\pi$
$17$	−3.29762	+	3.55399i	−0.799790	+	0.861968i	0.193079	+	0.981183i	$0.438153\pi$
$18$	3.40978	+	1.83154i	0.803693	+	0.431698i
$19$	−0.682883	−	1.18279i	−0.156664	−	0.271350i	0.777000	−	0.629501i	$-0.216741\pi$
$19$	−0.682883	−	1.18279i	−0.156664	−	0.271350i	−0.933664	+	0.358151i	$0.883407\pi$
$20$	0.0315639	+	0.00519222i	0.00705790	+	0.00116102i
$21$	5.82539	−	2.49461i	1.27120	−	0.544368i
$22$	0.634772	+	2.43431i	0.135334	+	0.518997i
$23$	−3.75388	−	4.04572i	−0.782738	−	0.843591i	0.208175	−	0.978092i	$-0.433248\pi$
$23$	−3.75388	−	4.04572i	−0.782738	−	0.843591i	−0.990914	+	0.134500i	$0.957057\pi$
$24$	1.62114	+	6.57777i	0.330913	+	1.34268i
$25$	−4.94390	+	0.745173i	−0.988780	+	0.149035i
$26$	2.66799	−	2.63237i	0.523236	−	0.516251i
$27$	−0.140232	−	0.614395i	−0.0269876	−	0.118240i
$28$	4.80618	+	2.21373i	0.908283	+	0.418355i
$29$	0.487147	−	2.13433i	0.0904609	−	0.396335i	−0.909345	−	0.416043i	$-0.863417\pi$
$29$	0.487147	−	2.13433i	0.0904609	−	0.396335i	0.999806	+	0.0197080i	$0.00627365\pi$
$30$	0.0285148	+	0.0460653i	0.00520607	+	0.00841033i
$31$	−4.96153	+	8.59362i	−0.891116	+	1.54346i	−0.0525777	+	0.998617i	$0.516744\pi$
$31$	−4.96153	+	8.59362i	−0.891116	+	1.54346i	−0.838539	+	0.544842i	$0.816590\pi$
$32$	−3.16882	+	4.68600i	−0.560174	+	0.828375i
$33$	−2.40016	+	3.52038i	−0.417814	+	0.612820i
$34$	−4.43732	−	5.22689i	−0.760994	−	0.896404i
$35$	0.0420170	+	0.00502358i	0.00710217	+	0.000849140i
$36$	−3.14399	+	4.48080i	−0.523998	+	0.746801i
$37$	1.78032	−	0.549155i	0.292682	−	0.0902805i	−0.144937	−	0.989441i	$-0.546298\pi$
$37$	1.78032	−	0.549155i	0.292682	−	0.0902805i	0.437619	+	0.899160i	$0.355822\pi$
$38$	1.77548	−	0.760473i	0.288020	−	0.123365i
$39$	6.33006	+	0.474372i	1.01362	+	0.0759603i
$40$	−0.0125869	+	0.0434517i	−0.00199016	+	0.00687031i
$41$	−1.78963	+	3.71620i	−0.279493	+	0.580373i	−0.992704	−	0.120576i	$-0.961526\pi$
$41$	−1.78963	+	3.71620i	−0.279493	+	0.580373i	0.713211	+	0.700949i	$0.247240\pi$
$42$	2.52560	+	8.59871i	0.389708	+	1.32681i
$43$	4.01716	+	8.34173i	0.612612	+	1.27210i	0.944416	+	0.328753i	$0.106628\pi$
$43$	4.01716	+	8.34173i	0.612612	+	1.27210i	−0.331804	+	0.943348i	$0.607657\pi$
$44$	−3.52483	+	0.482931i	−0.531388	+	0.0728047i
$45$	−0.0129026	+	0.0418292i	−0.00192341	+	0.00623553i
$46$	6.31094	−	4.59250i	0.930497	−	0.677127i
$47$	−9.62933	−	1.45139i	−1.40458	−	0.211707i	−0.597369	−	0.801967i	$-0.703787\pi$
$47$	−9.62933	−	1.45139i	−1.40458	−	0.211707i	−0.807213	+	0.590260i	$0.799025\pi$
$48$	−9.50867	+	1.17282i	−1.37246	+	0.169281i
$49$	6.48076	+	2.64571i	0.925822	+	0.377959i
$50$	−0.216899	−	7.06738i	−0.0306741	−	0.999478i
$51$	1.73073	−	11.4826i	0.242350	−	1.60789i
$52$	3.24881	+	4.18812i	0.450529	+	0.580788i
$53$	−8.11554	−	2.50331i	−1.11475	−	0.343856i	−0.317959	−	0.948105i	$-0.602997\pi$
$53$	−8.11554	−	2.50331i	−1.11475	−	0.343856i	−0.796796	+	0.604248i	$0.793474\pi$
$54$	0.886278	−	0.0938331i	0.120607	−	0.0127691i
$55$	−0.0256339	+	0.0123446i	−0.00345647	+	0.00166455i
$56$	−3.91496	+	6.37755i	−0.523159	+	0.852235i
$57$	2.94730	+	1.41935i	0.390379	+	0.187997i
$58$	2.91535	+	1.04216i	0.382804	+	0.136843i
$59$	0.462993	−	6.17821i	0.0602765	−	0.804334i	−0.882373	−	0.470550i	$-0.844055\pi$
$59$	0.462993	−	6.17821i	0.0602765	−	0.804334i	0.942650	−	0.333784i	$-0.108326\pi$
$60$	−0.0694703	+	0.0323123i	−0.00896857	+	0.00417150i
$61$	2.72001	+	8.81806i	0.348262	+	1.12904i	0.945129	+	0.326697i	$0.105936\pi$
$61$	2.72001	+	8.81806i	0.348262	+	1.12904i	−0.596867	+	0.802340i	$0.703588\pi$
$62$	−11.2349	−	8.40895i	−1.42684	−	1.06794i
$63$	−3.89409	+	6.10492i	−0.490609	+	0.769147i
$64$	−6.04853	−	5.23596i	−0.756066	−	0.654495i
$65$	0.0350227	+	0.0238781i	0.00434403	+	0.00296171i
$66$	−4.54071	−	3.96102i	−0.558923	−	0.487567i
$67$	4.78628	+	2.76336i	0.584737	+	0.337598i	0.763014	−	0.646382i	$-0.223719\pi$
$67$	4.78628	+	2.76336i	0.584737	+	0.337598i	−0.178277	+	0.983980i	$0.557052\pi$
$68$	8.08423	−	5.35403i	0.980357	−	0.649271i
$69$	12.8876	+	2.94151i	1.55148	+	0.354116i
$70$	−0.0141039	+	0.0581585i	−0.00168574	+	0.00695127i
$71$	13.9367	−	3.18096i	1.65398	−	0.377510i	0.709147	−	0.705061i	$-0.249080\pi$
$71$	13.9367	−	3.18096i	1.65398	−	0.377510i	0.944834	+	0.327551i	$0.106223\pi$
$72$	−5.76456	−	5.16666i	−0.679360	−	0.608897i
$73$	−1.28303	−	8.51233i	−0.150167	−	0.996293i	−0.929271	−	0.369399i	$-0.879564\pi$
$73$	−1.28303	−	8.51233i	−0.150167	−	0.996293i	0.779104	−	0.626895i	$-0.215674\pi$
$74$	0.472434	+	2.59210i	0.0549193	+	0.301326i
$75$	8.77851	−	8.14527i	1.01365	−	0.940534i
$76$	0.769984	+	2.62076i	0.0883232	+	0.300622i
$77$	−4.63026	+	0.843540i	−0.527667	+	0.0961303i
$78$	−1.72819	+	8.80924i	−0.195679	+	0.997450i
$79$	−0.651250	+	0.376000i	−0.0732714	+	0.0423033i	−0.536188	−	0.844099i	$-0.680136\pi$
$79$	−0.651250	+	0.376000i	−0.0732714	+	0.0423033i	0.462917	+	0.886402i	$0.346803\pi$
$80$	−0.0589041	−	0.0249652i	−0.00658568	−	0.00279119i
$81$	7.12534	+	6.61135i	0.791704	+	0.734594i
$82$	−4.91812	−	3.13655i	−0.543115	−	0.346374i
$83$	2.16800	+	2.71859i	0.237969	+	0.298404i	0.886447	−	0.462829i	$-0.153166\pi$
$83$	2.16800	+	2.71859i	0.237969	+	0.298404i	−0.648478	+	0.761233i	$0.724594\pi$
$84$	−12.4983	+	2.10381i	−1.36367	+	0.229545i
$85$	0.0483469	−	0.0606251i	0.00524396	−	0.00657572i
$86$	−12.3877	+	4.24142i	−1.33580	+	0.457364i
$87$	1.91569	+	4.88111i	0.205384	+	0.523309i
$88$	−0.0867456	−	5.03068i	−0.00924711	−	0.536272i
$89$	1.89685	+	0.744461i	0.201066	+	0.0789127i	0.463737	−	0.885973i	$-0.346508\pi$
$89$	1.89685	+	0.744461i	0.201066	+	0.0789127i	−0.262671	+	0.964885i	$0.584603\pi$
$90$	−0.0565728	−	0.0251363i	−0.00596330	−	0.00264960i
$91$	4.53754	+	5.34577i	0.475663	+	0.560389i
$92$	5.39005	+	9.63251i	0.561952	+	1.00426i
$93$	−1.77615	−	23.7010i	−0.184178	−	2.45768i
$94$	3.65369	−	13.2782i	0.376850	−	1.36955i
$95$	0.0123052	+	0.0180485i	0.00126249	+	0.00185173i
$96$	−0.0515237	−	13.5491i	−0.00525861	−	1.38285i
$97$			12.1281i			1.23142i	0.787973	+	0.615710i	$0.211131\pi$
$97$			12.1281i			1.23142i	−0.787973	+	0.615710i	$0.788869\pi$
$98$	−4.80253	+	8.65654i	−0.485129	+	0.874443i
$99$		−	4.86859i		−	0.489312i
$100$	9.96059	+	0.881197i	0.996059	+	0.0881197i
$101$	−6.66276	−	9.77248i	−0.662970	−	0.972398i	−0.999528	−	0.0307352i	$-0.990215\pi$
$101$	−6.66276	−	9.77248i	−0.662970	−	0.972398i	0.336558	−	0.941663i	$-0.390737\pi$
$102$	15.8338	+	4.35690i	1.56778	+	0.431397i
$103$	0.411098	+	5.48572i	0.0405067	+	0.540524i	0.980136	+	0.198329i	$0.0635513\pi$
$103$	0.411098	+	5.48572i	0.0405067	+	0.540524i	−0.939629	+	0.342195i	$0.888830\pi$
$104$	−6.42616	+	3.85937i	−0.630136	+	0.378443i
$105$	−0.0899294	+	0.0467500i	−0.00877621	+	0.00456233i
$106$	4.87685	−	10.9760i	0.473681	−	1.06609i
$107$	9.13170	+	3.58393i	0.882794	+	0.346471i	0.763055	−	0.646334i	$-0.223699\pi$
$107$	9.13170	+	3.58393i	0.882794	+	0.346471i	0.119740	+	0.992805i	$0.461794\pi$
$108$	−0.0169377	+	1.26028i	−0.00162983	+	0.121270i
$109$	−3.93663	−	10.0304i	−0.377061	−	0.960736i	−0.985884	−	0.167430i	$-0.946453\pi$
$109$	−3.93663	−	10.0304i	−0.377061	−	0.960736i	0.608823	−	0.793306i	$-0.291642\pi$
$110$	−0.0130338	−	0.0380670i	−0.00124272	−	0.00362954i
$111$	−2.78228	+	3.48887i	−0.264082	+	0.331149i
$112$	−8.29866	−	6.56752i	−0.784149	−	0.620572i
$113$	−8.16471	−	10.2382i	−0.768072	−	0.963131i	0.231882	−	0.972744i	$-0.425512\pi$
$113$	−8.16471	−	10.2382i	−0.768072	−	0.963131i	−0.999954	+	0.00961243i	$0.996940\pi$
$114$	−2.48758	+	3.90054i	−0.232983	+	0.365319i
$115$	0.0647075	+	0.0600397i	0.00603400	+	0.00559874i
$116$	−1.95257	+	3.91895i	−0.181292	+	0.363865i
$117$	−6.28165	+	3.62671i	−0.580738	+	0.335289i
$118$	8.59791	+	1.68673i	0.791502	+	0.155276i
$119$	10.3722	−	7.54670i	0.950820	−	0.691805i
$120$	−0.0337180	−	0.102973i	−0.00307802	−	0.00940014i
$121$	−5.74390	+	5.32956i	−0.522172	+	0.484505i
$122$	−12.8389	+	2.34001i	−1.16238	+	0.211854i
$123$	−1.47244	−	9.76899i	−0.132765	−	0.880840i
$124$	13.6931	−	14.3655i	1.22967	−	1.29006i
$125$	0.155926	−	0.0355892i	0.0139465	−	0.00318319i
$126$	−7.91933	−	6.49247i	−0.705510	−	0.578395i
$127$	−6.66561	−	1.52138i	−0.591477	−	0.135001i	−0.0837027	−	0.996491i	$-0.526675\pi$
$127$	−6.66561	−	1.52138i	−0.591477	−	0.135001i	−0.507775	+	0.861490i	$0.669532\pi$
$128$	8.36730	−	7.61500i	0.739572	−	0.673077i
$129$	−19.2050	−	11.0880i	−1.69091	−	0.976247i
$130$	−0.0394063	+	0.0451735i	−0.00345616	+	0.00396197i
$131$	1.06471	+	0.725905i	0.0930239	+	0.0634226i	0.608939	−	0.793217i	$-0.291596\pi$
$131$	1.06471	+	0.725905i	0.0930239	+	0.0634226i	−0.515915	+	0.856640i	$0.672548\pi$
$132$	6.32401	−	5.71160i	0.550434	−	0.497131i
$133$	1.17025	+	3.41873i	0.101474	+	0.296442i
$134$	−4.68343	+	6.25738i	−0.404586	+	0.540555i
$135$	0.00297095	+	0.00963158i	0.000255699	+	0.000828954i
$136$	6.16188	+	12.2504i	0.528377	+	1.05046i
$137$	−1.17209	+	15.6405i	−0.100138	+	1.33626i	0.690215	+	0.723604i	$0.257516\pi$
$137$	−1.17209	+	15.6405i	−0.100138	+	1.33626i	−0.790354	+	0.612651i	$0.790103\pi$
$138$	−6.29284	+	17.6036i	−0.535682	+	1.49852i
$139$	−14.2955	−	6.88434i	−1.21253	−	0.583922i	−0.285306	−	0.958437i	$-0.592095\pi$
$139$	−14.2955	−	6.88434i	−1.21253	−	0.583922i	−0.927221	+	0.374515i	$0.877809\pi$
$140$	−0.0793013	−	0.0295629i	−0.00670218	−	0.00249853i
$141$	21.0146	−	10.1201i	1.76975	−	0.852268i
$142$	2.12847	+	20.1040i	0.178617	+	1.68709i
$143$	−4.50501	−	1.38961i	−0.376728	−	0.116205i
$144$	8.22235	−	7.22787i	0.685195	−	0.602323i
$145$	−0.00521864	+	0.0346234i	−0.000433384	+	0.00287532i
$146$	12.1685	−	0.373453i	1.00707	−	0.0309072i
$147$	−16.3951	+	3.50834i	−1.35224	+	0.289363i
$148$	−3.71916	+	0.228498i	−0.305713	+	0.0187824i
$149$	−14.0126	−	2.11206i	−1.14796	−	0.173027i	−0.452616	−	0.891705i	$-0.649509\pi$
$149$	−14.0126	−	2.11206i	−1.14796	−	0.173027i	−0.695343	+	0.718678i	$0.744747\pi$
$150$	9.96492	+	13.6936i	0.813633	+	1.11808i
$151$	−1.77169	+	5.74368i	−0.144178	+	0.467414i	−0.998642	−	0.0520968i	$-0.983410\pi$
$151$	−1.77169	+	5.74368i	−0.144178	+	0.467414i	0.854464	+	0.519511i	$0.173886\pi$
$152$	−3.80933	+	0.641517i	−0.308977	+	0.0520339i
$153$	5.75721	+	11.9550i	0.465443	+	0.966501i
$154$	−0.407651	−	6.64346i	−0.0328495	−	0.535345i
$155$	0.0688616	−	0.142993i	0.00553110	−	0.0114854i
$156$	−12.0802	−	3.90479i	−0.967190	−	0.312633i
$157$	23.1508	+	1.73491i	1.84763	+	0.138461i	0.951955	−	0.306238i	$-0.0990705\pi$
$157$	23.1508	+	1.73491i	1.84763	+	0.138461i	0.895680	+	0.444700i	$0.146690\pi$
$158$	−0.418721	−	0.977588i	−0.0333116	−	0.0777727i
$159$	19.4382	−	5.99588i	1.54155	−	0.475505i
$160$	0.0449397	−	0.0785260i	0.00355280	−	0.00620802i
$161$	7.68449	+	12.4163i	0.605623	+	0.978543i
$162$	−10.4793	+	8.89633i	−0.823333	+	0.698961i
$163$	−9.13348	+	13.3964i	−0.715390	+	1.04928i	0.280601	+	0.959825i	$0.409466\pi$
$163$	−9.13348	+	13.3964i	−0.715390	+	1.04928i	−0.995990	+	0.0894592i	$0.971486\pi$
$164$	5.22959	−	6.37989i	0.408362	−	0.498186i
$165$	0.0340732	−	0.0590165i	0.00265260	−	0.00459443i
$166$	−4.18126	+	2.58824i	−0.324529	+	0.200886i
$167$	0.311301	−	1.36390i	0.0240892	−	0.105542i	−0.961454	−	0.274965i	$-0.911334\pi$
$167$	0.311301	−	1.36390i	0.0240892	−	0.105542i	0.985543	+	0.169424i	$0.0541907\pi$
$168$	−0.857252	−	17.9034i	−0.0661384	−	1.38128i
$169$	−1.32983	−	5.82638i	−0.102295	−	0.448183i
$170$	0.0770196	+	0.0780617i	0.00590714	+	0.00598706i
$171$	−3.69620	+	0.557113i	−0.282656	+	0.0426035i
$172$	−3.87750	−	18.1067i	−0.295656	−	1.38062i
$173$	−1.13526	−	1.22352i	−0.0863122	−	0.0930225i	0.688419	−	0.725313i	$-0.258305\pi$
$173$	−1.13526	−	1.22352i	−0.0863122	−	0.0930225i	−0.774731	+	0.632291i	$0.782115\pi$
$174$	−7.17559	+	1.87111i	−0.543980	+	0.141848i
$175$	13.2152	+	0.584436i	0.998972	+	0.0441792i
$176$	7.07876	+	0.722242i	0.533582	+	0.0544411i
$177$	7.41971	+	12.8513i	0.557699	+	0.965964i
$178$	−1.36365	+	2.53871i	−0.102210	+	0.190284i
$179$	−13.2242	+	14.2523i	−0.988424	+	1.06527i	0.00944103	+	0.999955i	$0.496995\pi$
$179$	−13.2242	+	14.2523i	−0.988424	+	1.06527i	−0.997865	+	0.0653121i	$0.979196\pi$
$180$	0.0447889	−	0.0752236i	0.00333837	−	0.00560684i
$181$	6.08611	−	4.85351i	0.452377	−	0.360759i	−0.370639	−	0.928777i	$-0.620861\pi$
$181$	6.08611	−	4.85351i	0.452377	−	0.360759i	0.823016	+	0.568018i	$0.192290\pi$
$182$	−8.26797	+	5.47481i	−0.612863	+	0.405820i
$183$	−17.2807	−	13.7809i	−1.27742	−	1.01871i
$184$	−14.4306	+	5.95270i	−1.06384	+	0.438839i
$185$	−0.0277385	+	0.0108865i	−0.00203937	+	0.000800395i
$186$	33.5796	+	1.48247i	2.46218	+	0.108700i
$187$	−3.15084	+	8.02820i	−0.230412	+	0.587080i
$188$	18.0326	+	7.35845i	1.31516	+	0.536670i
$189$	0.0510193	+	1.66656i	0.00371111	+	0.121224i
$190$	−0.0274087	+	0.0142511i	−0.00198844	+	0.00103389i
$191$	−18.0930	+	1.35588i	−1.30916	+	0.0981081i	−0.710957	−	0.703236i	$-0.751738\pi$
$191$	−18.0930	+	1.35588i	−1.30916	+	0.0981081i	−0.598204	+	0.801344i	$0.704119\pi$
$192$	19.0346	+	2.20093i	1.37371	+	0.158838i
$193$	−19.9473	+	13.5998i	−1.43583	+	0.978936i	−0.439079	+	0.898448i	$0.644695\pi$
$193$	−19.9473	+	13.5998i	−1.43583	+	0.978936i	−0.996756	+	0.0804872i	$0.974352\pi$
$194$	−17.0306	−	2.03486i	−1.22272	−	0.146095i
$195$	−0.101527			−0.00727051
$196$	−11.3500	−	8.19624i	−0.810712	−	0.585445i
$197$	26.2360			1.86924			0.934620	−	0.355648i	$-0.115740\pi$
$197$	26.2360			1.86924			0.934620	+	0.355648i	$0.115740\pi$
$198$	6.83661	+	0.816858i	0.485856	+	0.0580516i
$199$	17.6162	−	12.0105i	1.24878	−	0.851402i	0.255460	−	0.966820i	$-0.417773\pi$
$199$	17.6162	−	12.0105i	1.24878	−	0.851402i	0.993317	+	0.115418i	$0.0368206\pi$
$200$	−2.90860	+	13.8391i	−0.205669	+	0.978569i
$201$	−13.2005	+	0.989239i	−0.931090	+	0.0697755i
$202$	14.8406	−	7.71639i	1.04418	−	0.542923i
$203$	−2.35225	+	5.29298i	−0.165096	+	0.371495i
$204$	−8.77468	+	21.5032i	−0.614351	+	1.50553i
$205$	0.0241016	−	0.0614099i	0.00168333	−	0.00428905i
$206$	−7.77216	−	0.343125i	−0.541512	−	0.0239067i
$207$	−14.0608	+	5.51845i	−0.977292	+	0.383559i
$208$	−4.34124	−	9.67130i	−0.301011	−	0.670584i
$209$	−1.89948	−	1.51479i	−0.131390	−	0.104780i
$210$	−0.0505591	−	0.134125i	−0.00348891	−	0.00925550i
$211$	−10.2851	+	8.20209i	−0.708056	+	0.564655i	−0.909933	−	0.414755i	$-0.863867\pi$
$211$	−10.2851	+	8.20209i	−0.708056	+	0.564655i	0.201877	+	0.979411i	$0.435296\pi$
$212$	14.5946	+	8.68976i	1.00236	+	0.596815i
$213$	−23.2887	+	25.0992i	−1.59571	+	1.71977i
$214$	−6.56477	+	12.2216i	−0.448758	+	0.835455i
$215$	−0.0740414	−	0.128243i	−0.00504958	−	0.00874613i
$216$	−1.76687	−	0.235235i	−0.120220	−	0.0160057i
$217$	17.2599	−	19.7829i	1.17168	−	1.34295i
$218$	14.7454	−	3.84501i	0.998685	−	0.260417i
$219$	14.0244	+	15.1147i	0.947681	+	1.02136i
$220$	0.0556414	−	0.0119154i	0.00375134	−	0.000803338i
$221$	12.7054	−	1.91503i	0.854658	−	0.128819i
$222$	−4.43235	−	4.49232i	−0.297480	−	0.301504i
$223$	−3.04308	−	13.3326i	−0.203779	−	0.892816i	−0.968610	−	0.248585i	$-0.920035\pi$
$223$	−3.04308	−	13.3326i	−0.203779	−	0.892816i	0.764831	−	0.644231i	$-0.222823\pi$
$224$	10.6146	−	10.5513i	0.709220	−	0.704987i
$225$	−3.04492	+	13.3407i	−0.202995	+	0.889378i
$226$	15.7467	−	9.74732i	1.04745	−	0.648382i
$227$	10.8866	−	18.8562i	0.722571	−	1.25153i	−0.237396	−	0.971413i	$-0.576294\pi$
$227$	10.8866	−	18.8562i	0.722571	−	1.25153i	0.959966	−	0.280116i	$-0.0903729\pi$
$228$	−5.05986	−	4.14756i	−0.335098	−	0.274679i
$229$	−5.05667	+	7.41677i	−0.334154	+	0.490114i	−0.956138	−	0.292916i	$-0.905374\pi$
$229$	−5.05667	+	7.41677i	−0.334154	+	0.490114i	0.621984	+	0.783030i	$0.286327\pi$
$230$	−0.0951660	+	0.0807903i	−0.00627506	+	0.00532716i
$231$	8.02509	−	7.91675i	0.528012	−	0.520884i
$232$	−5.17549	−	3.39938i	−0.339787	−	0.223180i
$233$	23.3834	−	7.21284i	1.53190	−	0.472529i	0.589712	−	0.807614i	$-0.299241\pi$
$233$	23.3834	−	7.21284i	1.53190	−	0.472529i	0.942188	+	0.335085i	$0.108765\pi$
$234$	−4.03878	−	9.42934i	−0.264023	−	0.616415i
$235$	0.155316	+	0.0116393i	0.0101317	+	0.000759266i
$236$	−3.81112	+	11.7904i	−0.248083	+	0.767490i
$237$	0.781500	−	1.62280i	0.0507639	−	0.105412i
$238$	8.85701	+	15.8311i	0.574115	+	1.02618i
$239$	−2.20801	−	4.58497i	−0.142824	−	0.296577i	0.817270	−	0.576255i	$-0.195487\pi$
$239$	−2.20801	−	4.58497i	−0.142824	−	0.296577i	−0.960094	+	0.279678i	$0.909772\pi$
$240$	0.150255	−	0.0300707i	0.00969892	−	0.00194106i
$241$	1.50596	−	4.88220i	0.0970073	−	0.314490i	−0.894043	−	0.447982i	$-0.852143\pi$
$241$	1.50596	−	4.88220i	0.0970073	−	0.314490i	0.991050	+	0.133492i	$0.0426191\pi$
$242$	−6.52018	−	8.95992i	−0.419133	−	0.575966i
$243$	−21.1519	−	3.18814i	−1.35689	−	0.204519i
$244$	−1.13177	−	18.4213i	−0.0724543	−	1.17931i
$245$	−0.106526	−	0.0344513i	−0.00680569	−	0.00220101i
$246$	13.9649	−	0.428585i	0.890370	−	0.0273256i
$247$	−0.539475	+	3.57918i	−0.0343260	+	0.227738i
$248$	17.8750	+	21.6384i	1.13506	+	1.37404i
$249$	−7.95852	−	2.45488i	−0.504351	−	0.155572i
$250$	0.0238138	+	0.224927i	0.00150611	+	0.0142256i
$251$	7.64898	−	3.68355i	0.482799	−	0.232504i	−0.176620	−	0.984279i	$-0.556516\pi$
$251$	7.64898	−	3.68355i	0.482799	−	0.232504i	0.659419	+	0.751775i	$0.270802\pi$
$252$	10.4456	−	10.0312i	0.658012	−	0.631907i
$253$	−8.84540	−	4.25972i	−0.556105	−	0.267806i
$254$	3.25473	−	9.10476i	0.204220	−	0.571284i
$255$	−0.0138795	+	0.185209i	−0.000869167	+	0.0115982i
$256$	9.28931	+	13.0272i	0.580582	+	0.814202i
$257$	−1.56299	−	5.06709i	−0.0974967	−	0.316077i	0.893665	−	0.448734i	$-0.148125\pi$
$257$	−1.56299	−	5.06709i	−0.0974967	−	0.316077i	−0.991162	+	0.132658i	$0.957649\pi$
$258$	18.7923	−	25.1078i	1.16996	−	1.56315i
$259$	−4.90191	+	0.518602i	−0.304590	+	0.0322244i
$260$	−0.0568221	−	0.0629146i	−0.00352396	−	0.00390180i
$261$	−4.95053	−	3.37522i	−0.306430	−	0.208921i
$262$	−1.19797	+	1.37330i	−0.0740110	+	0.0848425i
$263$	0.775770	+	0.447891i	0.0478360	+	0.0276182i	0.523727	−	0.851886i	$-0.324541\pi$
$263$	0.775770	+	0.447891i	0.0478360	+	0.0276182i	−0.475891	+	0.879504i	$0.657874\pi$
$264$	6.95933	+	9.83863i	0.428317	+	0.605526i
$265$	0.132429	+	0.0302261i	0.00813507	+	0.00185678i
$266$	−4.99702	+	1.06970i	−0.306387	+	0.0655873i
$267$	−4.75832	+	1.08606i	−0.291205	+	0.0664656i
$268$	−8.00098	−	7.62646i	−0.488738	−	0.465860i
$269$	−1.46427	−	9.71481i	−0.0892783	−	0.592323i	−0.988077	−	0.153961i	$-0.950797\pi$
$269$	−1.46427	−	9.71481i	−0.0892783	−	0.592323i	0.898799	−	0.438362i	$-0.144441\pi$
$270$	−0.0140234	+	0.00255589i	−0.000853436	+	0.000155546i
$271$	−0.444104	+	0.412069i	−0.0269774	+	0.0250314i	−0.693546	−	0.720412i	$-0.743953\pi$
$271$	−0.444104	+	0.412069i	−0.0269774	+	0.0250314i	0.666569	+	0.745443i	$0.267762\pi$
$272$	−18.2362	+	6.59729i	−1.10573	+	0.400019i
$273$	−16.1925	−	4.45694i	−0.980017	−	0.269746i
$274$	−21.7661	−	4.27005i	−1.31494	−	0.257963i
$275$	−7.70238	+	4.44697i	−0.464471	+	0.268162i
$276$	−23.6636	−	11.7901i	−1.42438	−	0.709681i
$277$	−11.8402	−	10.9861i	−0.711411	−	0.660093i	0.239025	−	0.971013i	$-0.423172\pi$
$277$	−11.8402	−	10.9861i	−0.711411	−	0.660093i	−0.950436	+	0.310921i	$0.899363\pi$
$278$	12.0657	−	18.9190i	0.723651	−	1.13469i
$279$	16.9329	+	21.2332i	1.01375	+	1.27120i
$280$	0.0548183	−	0.106397i	0.00327602	−	0.00635843i
$281$	−2.78044	+	3.48656i	−0.165867	+	0.207991i	−0.857818	−	0.513954i	$-0.828180\pi$
$281$	−2.78044	+	3.48656i	−0.165867	+	0.207991i	0.691951	+	0.721945i	$0.256752\pi$
$282$	10.6851	+	31.2073i	0.636287	+	1.85837i
$283$	1.35965	+	3.46433i	0.0808227	+	0.205933i	0.965573	−	0.260133i	$-0.0837663\pi$
$283$	1.35965	+	3.46433i	0.0808227	+	0.205933i	−0.884750	+	0.466066i	$0.845671\pi$
$284$	−28.5876	−	0.384208i	−1.69636	−	0.0227986i
$285$	−0.0487039	−	0.0191149i	−0.00288497	−	0.00113227i
$286$	2.70718	−	6.09290i	0.160079	−	0.360281i
$287$	6.53979	−	8.73622i	0.386032	−	0.515683i
$288$	8.77001	+	12.7587i	0.516778	+	0.751815i
$289$	−0.486127	−	6.48691i	−0.0285957	−	0.381583i
$290$	−0.0477435	−	0.0131373i	−0.00280359	−	0.000771448i
$291$	−16.3639	−	24.0014i	−0.959266	−	1.40698i
$292$	−1.51723	+	17.1500i	−0.0887893	+	1.00363i
$293$		−	24.3816i		−	1.42439i	−0.701982	−	0.712195i	$-0.747701\pi$
$293$		−	24.3816i		−	1.42439i	0.701982	−	0.712195i	$-0.252299\pi$
$294$	−2.17571	−	23.6110i	−0.126890	−	1.37702i
$295$			0.0990916i			0.00576934i
$296$	0.303142	−	5.26088i	0.0176198	−	0.305783i
$297$	−0.631505	−	0.926248i	−0.0366436	−	0.0537463i
$298$	5.31687	−	19.3225i	0.307998	−	1.11932i
$299$	1.09306	+	14.5858i	0.0632130	+	0.843519i
$300$	−20.9009	+	11.6955i	−1.20671	+	0.675238i
$301$	−6.17909	−	23.7039i	−0.356157	−	1.36627i
$302$	−7.76816	−	3.45153i	−0.447008	−	0.198613i
$303$	26.3711	+	10.3499i	1.51498	+	0.594586i
$304$	−0.261701	−	5.45679i	−0.0150096	−	0.312969i
$305$	−0.0539220	−	0.137391i	−0.00308757	−	0.00786699i
$306$	−17.7534	+	6.07860i	−1.01490	+	0.347490i
$307$	−13.1605	+	16.5027i	−0.751109	+	0.941860i	−0.999642	−	0.0267631i	$-0.991480\pi$
$307$	−13.1605	+	16.5027i	−0.751109	+	0.941860i	0.248533	+	0.968623i	$0.420051\pi$
$308$	9.39731	+	0.542212i	0.535461	+	0.0308954i
$309$	−8.21518	−	10.3015i	−0.467345	−	0.586033i
$310$	0.189240	+	0.120689i	0.0107481	+	0.00685465i
$311$	−16.4397	−	15.2538i	−0.932211	−	0.864965i	0.0588647	−	0.998266i	$-0.481252\pi$
$311$	−16.4397	−	15.2538i	−0.932211	−	0.864965i	−0.991076	+	0.133301i	$0.957442\pi$
$312$	7.51003	−	16.3082i	0.425172	−	0.923269i
$313$	15.4240	−	8.90503i	0.871814	−	0.503342i	0.00386363	−	0.999993i	$-0.498770\pi$
$313$	15.4240	−	8.90503i	0.871814	−	0.503342i	0.867951	+	0.496650i	$0.165437\pi$
$314$	−6.32047	+	32.2179i	−0.356685	+	1.81816i
$315$	0.0548113	−	0.102024i	0.00308827	−	0.00574838i
$316$	1.44301	−	0.423958i	0.0811755	−	0.0238495i
$317$	−7.86770	+	7.30016i	−0.441894	+	0.410018i	−0.869489	−	0.493953i	$-0.835552\pi$
$317$	−7.86770	+	7.30016i	−0.441894	+	0.410018i	0.427595	+	0.903971i	$0.359361\pi$
$318$	5.15822	+	28.3016i	0.289258	+	1.58707i
$319$	−0.580423	−	3.85086i	−0.0324975	−	0.215607i
$320$	0.102728	+	0.0762807i	0.00574268	+	0.00426422i
$321$	−22.9072	+	5.22841i	−1.27855	+	0.291822i
$322$	−18.7246	+	8.70754i	−1.04348	+	0.485252i
$323$	6.45550	+	1.47343i	0.359194	+	0.0819836i
$324$	−10.7342	−	16.2080i	−0.596345	−	0.900443i
$325$	11.4753	+	6.62526i	0.636535	+	0.367504i
$326$	−17.2791	−	15.0731i	−0.957000	−	0.834823i
$327$	21.3241	+	14.5385i	1.17922	+	0.803981i
$328$	8.08138	+	8.41395i	0.446220	+	0.464583i
$329$	24.2604	+	8.67457i	1.33752	+	0.478245i
$330$	0.0771557	+	0.0577483i	0.00424728	+	0.00317894i
$331$	−1.29386	−	4.19458i	−0.0711168	−	0.230555i	0.913036	−	0.407880i	$-0.133732\pi$
$331$	−1.29386	−	4.19458i	−0.0711168	−	0.230555i	−0.984152	+	0.177325i	$0.943256\pi$
$332$	−2.93293	−	6.30569i	−0.160966	−	0.346070i
$333$	0.381054	−	5.08481i	0.0208816	−	0.278646i
$334$	1.86299	+	0.665972i	0.101938	+	0.0364404i
$335$	−0.0796408	−	0.0383530i	−0.00435124	−	0.00209545i
$336$	25.2842	+	1.80007i	1.37937	+	0.0982020i
$337$	−19.0708	+	9.18402i	−1.03885	+	0.500286i	−0.873946	−	0.486023i	$-0.838447\pi$
$337$	−19.0708	+	9.18402i	−1.03885	+	0.500286i	−0.164908	+	0.986309i	$0.552733\pi$
$338$	8.40468	−	0.889831i	0.457154	−	0.0484004i
$339$	29.9719	+	9.24509i	1.62785	+	0.502125i
$340$	−0.122539	+	0.0950557i	−0.00664559	+	0.00515512i
$341$	−2.63088	+	17.4547i	−0.142470	+	0.945228i
$342$	−0.162160	−	5.28377i	−0.00876859	−	0.285714i
$343$	−15.4774	−	10.1710i	−0.835702	−	0.549183i
$344$	26.0765	−	2.40692i	1.40595	−	0.129772i
$345$	−0.209064	−	0.0315114i	−0.0112556	−	0.00169652i
$346$	1.90857	−	1.38888i	0.102605	−	0.0746665i
$347$	4.10622	−	13.3120i	0.220433	−	0.714627i	−0.776037	−	0.630687i	$-0.782773\pi$
$347$	4.10622	−	13.3120i	0.220433	−	0.714627i	0.996471	−	0.0839405i	$-0.0267506\pi$
$348$	−1.42353	−	10.3901i	−0.0763092	−	0.556967i
$349$	3.28486	+	6.82108i	0.175835	+	0.365124i	0.970196	−	0.242321i	$-0.0779087\pi$
$349$	3.28486	+	6.82108i	0.175835	+	0.365124i	−0.794362	+	0.607445i	$0.792194\pi$
$350$	−3.03793	+	18.4590i	−0.162384	+	0.986676i
$351$	−0.724660	+	1.50477i	−0.0386795	+	0.0803188i
$352$	−2.20187	+	9.81900i	−0.117360	+	0.523355i
$353$	24.1002	+	1.80606i	1.28272	+	0.0961267i	0.698584	−	0.715528i	$-0.253814\pi$
$353$	24.1002	+	1.80606i	1.28272	+	0.0961267i	0.584138	+	0.811655i	$0.301433\pi$
$354$	−19.2910	+	8.26274i	−1.02531	+	0.439160i
$355$	−0.218479	+	0.0673918i	−0.0115956	+	0.00357678i
$356$	−3.33612	−	2.34081i	−0.176814	−	0.124063i
$357$	−10.3441	+	28.9296i	−0.547469	+	1.53112i
$358$	−17.7947	−	20.9610i	−0.940478	−	1.10783i
$359$	8.07426	−	11.8428i	0.426143	−	0.625037i	−0.551783	−	0.833988i	$-0.686052\pi$
$359$	8.07426	−	11.8428i	0.426143	−	0.625037i	0.977926	+	0.208951i	$0.0670048\pi$
$360$	0.0981162	+	0.0755148i	0.00517118	+	0.00397998i
$361$	8.56734	−	14.8391i	0.450913	−	0.781004i
$362$	5.79429	+	9.36060i	0.304541	+	0.491982i
$363$	4.17620	−	18.2971i	0.219193	−	0.960349i
$364$	−6.30065	−	12.5287i	−0.330244	−	0.656681i
$365$	0.0306377	+	0.134232i	0.00160365	+	0.00702605i
$366$	22.2508	−	21.9538i	1.16307	−	1.14754i
$367$	−6.78258	+	1.02231i	−0.354048	+	0.0533641i	−0.323658	−	0.946174i	$-0.604913\pi$
$367$	−6.78258	+	1.02231i	−0.354048	+	0.0533641i	−0.0303895	+	0.999538i	$0.509675\pi$
$368$	−5.93775	−	21.2625i	−0.309527	−	1.10839i
$369$	7.67832	+	8.27526i	0.399717	+	0.430793i
$370$	−0.0106332	−	0.0407776i	−0.000552793	−	0.00211993i
$371$	19.7942	+	10.6343i	1.02767	+	0.552104i
$372$	−7.71575	+	46.9046i	−0.400043	+	2.43189i
$373$	3.50987	+	6.07927i	0.181734	+	0.314773i	0.942471	−	0.334288i	$-0.108496\pi$
$373$	3.50987	+	6.07927i	0.181734	+	0.314773i	−0.760737	+	0.649060i	$0.775162\pi$
$374$	−10.7448	−	5.77146i	−0.555598	−	0.298435i
$375$	−0.260558	+	0.280815i	−0.0134552	+	0.0145012i
$376$	−13.3584	+	24.0873i	−0.688909	+	1.24221i
$377$	−4.53615	+	3.61746i	−0.233624	+	0.186309i
$378$	−2.34879	−	0.207974i	−0.120809	−	0.0106971i
$379$	17.7291	+	14.1385i	0.910683	+	0.726246i	0.962176	−	0.272428i	$-0.0878265\pi$
$379$	17.7291	+	14.1385i	0.910683	+	0.726246i	−0.0514928	+	0.998673i	$0.516398\pi$
$380$	−0.0154132	−	0.0408791i	−0.000790678	−	0.00209705i
$381$	15.2439	−	5.98280i	0.780970	−	0.306508i
$382$	1.13169	−	25.6341i	0.0579025	−	1.31155i
$383$	−6.38262	+	16.2627i	−0.326137	+	0.830983i	0.669934	+	0.742421i	$0.266322\pi$
$383$	−6.38262	+	16.2627i	−0.326137	+	0.830983i	−0.996071	+	0.0885623i	$0.971773\pi$
$384$	−6.28425	+	26.3596i	−0.320692	+	1.34516i
$385$	0.0728413	−	0.0189882i	0.00371234	−	0.000967726i
$386$	−15.7504	−	30.2922i	−0.801676	−	1.54183i
$387$	25.2690	−	1.89365i	1.28449	−	0.0962595i
$388$	5.71481	−	23.5733i	0.290125	−	1.19675i
$389$	6.71120	−	4.57562i	0.340271	−	0.231993i	−0.381112	−	0.924529i	$-0.624459\pi$
$389$	6.71120	−	4.57562i	0.340271	−	0.231993i	0.721384	+	0.692536i	$0.243506\pi$
$390$	0.0170343	−	0.142567i	0.000862566	−	0.00721916i
$391$	26.7573			1.35317
$392$	13.4137	−	14.5627i	0.677493	−	0.735529i
$393$	−3.08648			−0.155692
$394$	−4.40191	+	36.8413i	−0.221765	+	1.85604i
$395$	0.00993760	−	0.00677534i	0.000500015	−	0.000340904i
$396$	−2.29411	+	9.46308i	−0.115283	+	0.475538i
$397$	20.7211	−	1.55283i	1.03996	−	0.0779342i	0.456214	−	0.889870i	$-0.349205\pi$
$397$	20.7211	−	1.55283i	1.03996	−	0.0779342i	0.583746	+	0.811936i	$0.301586\pi$
$398$	13.9098	+	26.7522i	0.697235	+	1.34097i
$399$	−6.92865	−	5.18668i	−0.346866	−	0.259659i
$400$	−18.9452	−	6.40626i	−0.947258	−	0.320313i
$401$	−3.07366	+	7.83157i	−0.153491	+	0.391090i	−0.986849	−	0.161644i	$-0.948320\pi$
$401$	−3.07366	+	7.83157i	−0.153491	+	0.391090i	0.833358	+	0.552734i	$0.186415\pi$
$402$	0.825675	−	18.7024i	0.0411809	−	0.932792i
$403$	24.4806	−	9.60792i	1.21946	−	0.478604i
$404$	8.34557	+	22.1343i	0.415208	+	1.10122i
$405$	−0.121546	−	0.0969301i	−0.00603969	−	0.00481649i
$406$	−7.03788	−	4.19115i	−0.349284	−	0.208003i
$407$	2.59115	−	2.06637i	0.128439	−	0.102426i
$408$	−28.7232	−	15.9295i	−1.42201	−	0.788626i
$409$	−21.3546	+	23.0148i	−1.05592	+	1.13801i	−0.0657930	+	0.997833i	$0.520958\pi$
$409$	−21.3546	+	23.0148i	−1.05592	+	1.13801i	−0.990126	+	0.140177i	$0.955233\pi$
$410$	0.0821896	+	0.0441475i	0.00405905	+	0.00218029i
$411$	−18.7834	−	32.5338i	−0.926516	−	1.60477i
$412$	1.78585	−	10.8563i	0.0879823	−	0.534851i
$413$	−4.35002	+	15.8041i	−0.214051	+	0.777669i
$414$	−5.39002	−	20.6704i	−0.264905	−	1.01589i
$415$	−0.0378275	−	0.0407684i	−0.00185688	−	0.00200124i
$416$	14.3091	−	4.47342i	0.701560	−	0.219328i
$417$	37.5793	−	5.66417i	1.84027	−	0.277376i
$418$	2.44580	−	2.41315i	0.119628	−	0.118031i
$419$	3.56358	+	15.6130i	0.174092	+	0.762747i	0.984285	+	0.176585i	$0.0565049\pi$
$419$	3.56358	+	15.6130i	0.174092	+	0.762747i	−0.810193	+	0.586163i	$0.800638\pi$
$420$	0.196825	−	0.0484928i	0.00960405	−	0.00236620i
$421$	−7.33975	+	32.1576i	−0.357718	+	1.56726i	0.401146	+	0.916014i	$0.368612\pi$
$421$	−7.33975	+	32.1576i	−0.357718	+	1.56726i	−0.758864	+	0.651249i	$0.774245\pi$
$422$	−9.79195	−	15.8188i	−0.476664	−	0.770045i
$423$	−13.3260	+	23.0814i	−0.647935	+	1.12226i
$424$	−14.6511	+	19.0361i	−0.711520	+	0.924476i
$425$	13.6548	−	20.0279i	0.662353	−	0.971494i
$426$	−31.3376	−	36.9137i	−1.51831	−	1.78847i
$427$	−2.56868	−	24.2796i	−0.124307	−	1.17497i
$428$	−16.0605	−	11.2690i	−0.776314	−	0.544706i
$429$	10.7903	−	3.32837i	0.520961	−	0.160695i
$430$	0.192506	−	0.0824540i	0.00928344	−	0.00397629i
$431$	6.81769	+	0.510915i	0.328396	+	0.0246099i	0.237908	−	0.971288i	$-0.423538\pi$
$431$	6.81769	+	0.510915i	0.328396	+	0.0246099i	0.0904881	+	0.995898i	$0.471157\pi$
$432$	0.626770	−	2.44162i	0.0301555	−	0.117472i
$433$	−7.81590	+	16.2299i	−0.375608	+	0.779959i	−0.999999	−	0.00115329i	$-0.999633\pi$
$433$	−7.81590	+	16.2299i	−0.375608	+	0.779959i	0.624391	+	0.781112i	$0.285347\pi$
$434$	24.8838	+	27.5561i	1.19446	+	1.32273i
$435$	−0.0363881	−	0.0755606i	−0.00174468	−	0.00362286i
$436$	2.92527	+	21.3510i	0.140095	+	1.02253i
$437$	−2.22177	+	7.20280i	−0.106282	+	0.344557i
$438$	−23.5775	+	17.1575i	−1.12658	+	0.819815i
$439$	−6.08892	−	0.917757i	−0.290608	−	0.0438021i	0.00212023	−	0.999998i	$-0.499325\pi$
$439$	−6.08892	−	0.917757i	−0.290608	−	0.0438021i	−0.292728	+	0.956196i	$0.594563\pi$
$440$	0.00739639	+	0.0801323i	0.000352609	+	0.00382016i
$441$	13.2206	−	13.8656i	0.629551	−	0.660265i
$442$	0.557411	+	18.1626i	0.0265133	+	0.863905i
$443$	4.50741	−	29.9047i	0.214154	−	1.42082i	−0.580751	−	0.814082i	$-0.697241\pi$
$443$	4.50741	−	29.9047i	0.214154	−	1.42082i	0.794904	−	0.606735i	$-0.207521\pi$
$444$	7.05189	−	5.47029i	0.334668	−	0.259608i
$445$	−0.0311434	−	0.00960645i	−0.00147634	−	0.000455390i
$446$	19.2325	−	2.03621i	0.910687	−	0.0964174i
$447$	30.5806	−	14.7268i	1.44641	−	0.696555i
$448$	13.0354	+	16.6756i	0.615867	+	0.787850i
$449$	−9.58460	−	4.61570i	−0.452325	−	0.217828i	0.193829	−	0.981035i	$-0.437909\pi$
$449$	−9.58460	−	4.61570i	−0.452325	−	0.217828i	−0.646154	+	0.763207i	$0.723624\pi$
$450$	−18.2224	−	6.51407i	−0.859014	−	0.307076i
$451$	−0.548316	+	7.31677i	−0.0258192	+	0.344533i
$452$	11.0454	+	23.7473i	0.519534	+	1.11698i
$453$	−4.24352	−	13.7571i	−0.199378	−	0.646367i
$454$	24.6518	+	18.4510i	1.15696	+	0.865948i
$455$	−0.0787601	−	0.0798379i	−0.00369233	−	0.00374286i
$456$	6.67306	−	6.40931i	0.312495	−	0.300143i
$457$	−10.9773	−	7.48419i	−0.513496	−	0.350096i	0.278684	−	0.960383i	$-0.410102\pi$
$457$	−10.9773	−	7.48419i	−0.513496	−	0.350096i	−0.792180	+	0.610287i	$0.791054\pi$
$458$	−9.56640	−	8.34510i	−0.447009	−	0.389941i
$459$	2.64598	+	1.52766i	0.123504	+	0.0713050i
$460$	−0.0974808	−	0.147190i	−0.00454507	−	0.00686275i
$461$	0.584631	+	0.133438i	0.0272290	+	0.00621484i	0.236114	−	0.971725i	$-0.424126\pi$
$461$	0.584631	+	0.133438i	0.0272290	+	0.00621484i	−0.208885	+	0.977940i	$0.566983\pi$
$462$	9.77045	+	12.5973i	0.454562	+	0.586080i
$463$	−29.5541	+	6.74552i	−1.37349	+	0.313491i	−0.844691	−	0.535254i	$-0.820216\pi$
$463$	−29.5541	+	6.74552i	−1.37349	+	0.313491i	−0.528803	+	0.848745i	$0.677359\pi$
$464$	5.64184	−	6.69720i	0.261916	−	0.310910i
$465$	0.0566567	+	0.375893i	0.00262739	+	0.0174316i
$466$	6.20515	+	34.0458i	0.287448	+	1.57714i
$467$	−25.2631	+	23.4408i	−1.16904	+	1.08471i	−0.174048	+	0.984737i	$0.555685\pi$
$467$	−25.2631	+	23.4408i	−1.16904	+	1.08471i	−0.994990	+	0.0999718i	$0.968125\pi$
$468$	13.9186	−	4.08929i	0.643385	−	0.189028i
$469$	−11.0182	−	9.61306i	−0.508775	−	0.443890i
$470$	−0.0424033	+	0.216146i	−0.00195592	+	0.00997007i
$471$	−48.1561	+	27.8029i	−2.21891	+	1.28109i
$472$	−15.9170	−	7.32988i	−0.732638	−	0.337385i
$473$	12.0733	+	11.2024i	0.555133	+	0.515088i
$474$	2.14766	+	1.36968i	0.0986452	+	0.0629114i
$475$	4.25749	+	5.33872i	0.195347	+	0.244957i
$476$	−23.7165	+	9.78108i	−1.08704	+	0.448315i
$477$	−14.4924	+	18.1729i	−0.663561	+	0.832080i
$478$	6.80880	−	2.33127i	0.311427	−	0.106630i
$479$	−2.26375	−	5.76795i	−0.103434	−	0.263544i	0.869783	−	0.493434i	$-0.164259\pi$
$479$	−2.26375	−	5.76795i	−0.103434	−	0.263544i	−0.973217	+	0.229890i	$0.926163\pi$
$480$	0.0170161	+	0.216037i	0.000776677	+	0.00986071i
$481$	−4.59631	−	1.80392i	−0.209574	−	0.0822517i
$482$	6.60304	+	2.93385i	0.300760	+	0.133633i
$483$	−31.9603	−	14.2035i	−1.45424	−	0.646280i
$484$	13.6757	−	7.65250i	0.621623	−	0.347841i
$485$	−0.0144959	−	0.193435i	−0.000658226	−	0.00878342i
$486$	8.02575	−	29.1671i	0.364055	−	1.32305i
$487$	14.0665	+	20.6317i	0.637412	+	0.934911i	0.999996	+	0.00296028i	$0.000942286\pi$
$487$	14.0665	+	20.6317i	0.637412	+	0.934911i	−0.362584	+	0.931951i	$0.618105\pi$
$488$	26.0576	+	1.50149i	1.17957	+	0.0679692i
$489$		−	38.8347i		−	1.75616i
$490$	0.0662505	−	0.143806i	0.00299289	−	0.00649650i
$491$			18.3343i			0.827414i	0.910410	+	0.413707i	$0.135766\pi$
$491$			18.3343i			0.827414i	−0.910410	+	0.413707i	$0.864234\pi$
$492$	−1.74122	+	19.6818i	−0.0785001	+	0.887324i
$493$	5.97896	+	8.76952i	0.269279	+	0.394959i
$494$	−4.93547	−	1.35806i	−0.222057	−	0.0611022i
$495$	0.00581912	+	0.0776508i	0.000261550	+	0.00349014i
$496$	−33.3843	+	21.4700i	−1.49900	+	0.964031i
$497$	−37.8036	+	1.15730i	−1.69572	+	0.0519120i
$498$	4.78249	−	10.7637i	0.214309	−	0.482332i
$499$	−1.37167	−	0.538342i	−0.0614045	−	0.0240995i	0.334440	−	0.942417i	$-0.391453\pi$
$499$	−1.37167	−	0.538342i	−0.0614045	−	0.0240995i	−0.395845	+	0.918318i	$0.629548\pi$
$500$	−0.319844	−	0.00429860i	−0.0143039	−	0.000192239i
$501$	1.22418	+	3.11916i	0.0546924	+	0.139354i
$502$	3.88919	+	11.3589i	0.173583	+	0.506973i
$503$	−9.18796	+	11.5213i	−0.409671	+	0.513711i	−0.943270	−	0.332027i	$-0.892268\pi$
$503$	−9.18796	+	11.5213i	−0.409671	+	0.513711i	0.533599	+	0.845737i	$0.320839\pi$
$504$	12.3335	+	16.3510i	0.549378	+	0.728333i
$505$	0.117947	+	0.147901i	0.00524857	+	0.00658150i
$506$	7.46570	−	11.7062i	0.331891	−	0.520406i
$507$	10.4930	+	9.73608i	0.466010	+	0.432394i
$508$	12.2391	+	6.09798i	0.543021	+	0.270554i
$509$	−11.0515	+	6.38058i	−0.489849	+	0.282814i	−0.724512	−	0.689262i	$-0.757935\pi$
$509$	−11.0515	+	6.38058i	−0.489849	+	0.282814i	0.234663	+	0.972077i	$0.424601\pi$
$510$	−0.257746	−	0.0505644i	−0.0114132	−	0.00223903i
$511$	−1.00627	+	22.7537i	−0.0445149	+	1.00656i
$512$	−19.8517	+	10.8586i	−0.877331	+	0.479885i
$513$	−0.630938	+	0.585424i	−0.0278566	+	0.0258471i
$514$	7.37758	−	1.34463i	0.325411	−	0.0593091i
$515$	−0.0131135	−	0.0870021i	−0.000577848	−	0.00383377i
$516$	32.1041	+	30.6013i	1.41330	+	1.34715i
$517$	−16.8886	+	3.85470i	−0.742758	+	0.169530i
$518$	0.0942133	−	6.97040i	0.00413950	−	0.306262i
$519$	3.89751	+	0.889581i	0.171082	+	0.0390483i
$520$	0.0978800	−	0.0692352i	0.00429232	−	0.00303616i
$521$	−23.8562	−	13.7734i	−1.04516	−	0.603422i	−0.123868	−	0.992299i	$-0.539530\pi$
$521$	−23.8562	−	13.7734i	−1.04516	−	0.603422i	−0.921290	+	0.388877i	$0.872863\pi$
$522$	5.57017	−	6.38537i	0.243800	−	0.279480i
$523$	3.47822	+	2.37141i	0.152092	+	0.103695i	0.636975	−	0.770884i	$-0.280185\pi$
$523$	3.47822	+	2.37141i	0.152092	+	0.103695i	−0.484883	+	0.874579i	$0.661138\pi$
$524$	−1.72742	−	1.91264i	−0.0754627	−	0.0835539i
$525$	−26.9412	+	16.6740i	−1.17581	+	0.727713i
$526$	−0.759100	+	1.01421i	−0.0330983	+	0.0442216i
$527$	−14.1804	−	45.9716i	−0.617707	−	2.00256i
$528$	−14.9833	+	8.12173i	−0.652064	+	0.353453i
$529$	−0.557448	+	7.43862i	−0.0242369	+	0.323418i
$530$	−0.0646635	+	0.180889i	−0.00280880	+	0.00785733i
$531$	−15.2773	−	7.35714i	−0.662977	−	0.319273i
$532$	−0.663690	−	7.19642i	−0.0287746	−	0.312004i
$533$	9.84883	−	4.74295i	0.426600	−	0.205440i
$534$	−0.726712	−	6.86398i	−0.0314479	−	0.297034i
$535$	−0.149928	−	0.0462467i	−0.00648195	−	0.00199942i
$536$	12.0517	−	9.95560i	0.520553	−	0.430017i
$537$	6.94062	−	46.0480i	0.299510	−	1.98712i
$538$	13.8875	−	0.426208i	0.598731	−	0.0183751i
$539$	12.4510	+	0.169243i	0.536302	+	0.00728981i
$540$	−0.00123618	−	0.0201208i	−5.31969e−5	−	0.000865862i
$541$	−19.0789	−	2.87568i	−0.820266	−	0.123635i	−0.274515	−	0.961583i	$-0.588517\pi$
$541$	−19.0789	−	2.87568i	−0.820266	−	0.123635i	−0.545751	+	0.837947i	$0.683756\pi$
$542$	−0.504125	−	0.692760i	−0.0216540	−	0.0297566i
$543$	−5.49574	+	17.8168i	−0.235845	+	0.764591i
$544$	−6.20440	−	26.7146i	−0.266012	−	1.14538i
$545$	0.0747753	+	0.155273i	0.00320302	+	0.00665114i
$546$	8.97535	−	21.9902i	0.384109	−	0.941093i
$547$	2.89015	−	6.00145i	0.123574	−	0.256604i	−0.830000	−	0.557764i	$-0.811660\pi$
$547$	2.89015	−	6.00145i	0.123574	−	0.256604i	0.953574	+	0.301160i	$0.0973738\pi$
$548$	9.64805	−	29.8481i	0.412144	−	1.27505i
$549$	25.1855	+	1.88739i	1.07489	+	0.0805520i
$550$	−4.95223	−	11.5620i	−0.211164	−	0.493005i
$551$	−2.85713	+	0.881306i	−0.121718	+	0.0375449i
$552$	20.5263	−	31.2508i	0.873656	−	1.33012i
$553$	1.88238	−	0.644347i	0.0800467	−	0.0274004i
$554$	17.4136	−	14.7831i	0.739832	−	0.628074i
$555$	0.0402055	−	0.0589706i	0.00170663	−	0.00250316i
$556$	24.5422	+	20.1172i	1.04082	+	0.853159i
$557$	11.6149	−	20.1176i	0.492139	−	0.852410i	−0.507820	−	0.861463i	$-0.669548\pi$
$557$	11.6149	−	20.1176i	0.492139	−	0.852410i	0.999959	+	0.00905307i	$0.00288172\pi$
$558$	−32.6573	+	20.2151i	−1.38249	+	0.855774i
$559$	5.46013	−	23.9224i	0.230939	−	1.01181i
$560$	0.140208	+	0.0948286i	0.00592486	+	0.00400724i
$561$	−4.59660	−	20.1390i	−0.194068	−	0.850270i
$562$	−4.42941	−	4.48934i	−0.186843	−	0.189371i
$563$	−5.68010	+	0.856137i	−0.239388	+	0.0360819i	−0.267640	−	0.963519i	$-0.586244\pi$
$563$	−5.68010	+	0.856137i	−0.239388	+	0.0360819i	0.0282526	+	0.999601i	$0.491006\pi$
$564$	−45.6148	+	9.76827i	−1.92073	+	0.411318i
$565$	0.142459	+	0.153534i	0.00599329	+	0.00645923i
$566$	−5.09282	+	1.32800i	−0.214067	+	0.0558202i
$567$	−15.1303	−	20.7951i	−0.635412	−	0.873313i
$568$	5.33597	−	40.0790i	0.223892	−	1.68168i
$569$	13.3255	+	23.0804i	0.558633	+	0.967581i	0.997611	+	0.0690828i	$0.0220073\pi$
$569$	13.3255	+	23.0804i	0.558633	+	0.967581i	−0.438978	+	0.898498i	$0.644659\pi$
$570$	0.0350132	−	0.0651842i	0.00146654	−	0.00273026i
$571$	19.0145	−	20.4927i	0.795731	−	0.857594i	−0.196691	−	0.980465i	$-0.563020\pi$
$571$	19.0145	−	20.4927i	0.795731	−	0.857594i	0.992423	+	0.122871i	$0.0392102\pi$
$572$	8.10159	+	4.82377i	0.338744	+	0.201692i
$573$	33.9764	−	27.0953i	1.41938	−	1.13192i
$574$	11.1704	+	10.6491i	0.466242	+	0.444486i
$575$	21.5736	+	17.2044i	0.899680	+	0.717471i
$576$	−19.3876	+	10.1744i	−0.807816	+	0.423933i
$577$	33.7461	−	13.2444i	1.40487	−	0.551370i	0.462702	−	0.886514i	$-0.346880\pi$
$577$	33.7461	−	13.2444i	1.40487	−	0.551370i	0.942167	+	0.335144i	$0.108785\pi$
$578$	9.19065	+	0.405749i	0.382280	+	0.0168769i
$579$	21.1259	−	53.8278i	0.877961	−	2.23701i
$580$	0.0264582	−	0.0648384i	0.00109862	−	0.00269227i
$581$	−4.24341	−	8.16273i	−0.176046	−	0.338647i
$582$	36.4489	−	18.9516i	1.51085	−	0.785568i
$583$	−15.0655	+	1.12900i	−0.623949	+	0.0467585i
$584$	−23.8279	−	5.00798i	−0.986005	−	0.207232i
$585$	0.0958532	−	0.0653516i	0.00396304	−	0.00270196i
$586$	34.2373	+	4.09077i	1.41433	+	0.168988i
$587$	−28.8478			−1.19068			−0.595339	−	0.803475i	$-0.702982\pi$
$587$	−28.8478			−1.19068			−0.595339	+	0.803475i	$0.702982\pi$
$588$	33.5203	+	0.906299i	1.38235	+	0.0373752i
$589$	13.5526			0.558424
$590$	−0.139147	−	0.0166257i	−0.00572859	−	0.000684469i
$591$	−51.9209	+	35.3990i	−2.13574	+	1.45612i
$592$	7.33660	+	1.30836i	0.301533	+	0.0537731i
$593$	7.48994	−	0.561293i	0.307575	−	0.0230496i	0.0799514	−	0.996799i	$-0.474523\pi$
$593$	7.48994	−	0.561293i	0.307575	−	0.0230496i	0.227624	+	0.973749i	$0.426904\pi$
$594$	1.40662	−	0.731369i	0.0577141	−	0.0300084i
$595$	−0.156410	+	0.132762i	−0.00641218	+	0.00544272i
$596$	26.2411	+	10.7080i	1.07488	+	0.438618i
$597$	−18.6570	+	47.5374i	−0.763582	+	1.94557i
$598$	−20.6652	−	0.912326i	−0.845061	−	0.0373078i
$599$	−18.2262	+	7.15325i	−0.744701	+	0.292274i	−0.707191	−	0.707022i	$-0.750038\pi$
$599$	−18.2262	+	7.15325i	−0.744701	+	0.292274i	−0.0375104	+	0.999296i	$0.511943\pi$
$600$	−12.9163	−	31.3118i	−0.527306	−	1.27830i
$601$	−15.7473	−	12.5581i	−0.642346	−	0.512254i	0.247279	−	0.968944i	$-0.420463\pi$
$601$	−15.7473	−	12.5581i	−0.642346	−	0.512254i	−0.889626	+	0.456690i	$0.849035\pi$
$602$	34.3223	−	4.69977i	1.39887	−	0.191548i
$603$	11.8260	−	9.43092i	0.481592	−	0.384057i
$604$	6.15008	−	10.3292i	0.250243	−	0.420287i
$605$	0.0852412	−	0.0918681i	0.00346555	−	0.00373497i
$606$	−18.9582	+	35.2945i	−0.770122	+	1.43374i
$607$	4.51123	+	7.81368i	0.183105	+	0.317147i	0.942936	−	0.332973i	$-0.108052\pi$
$607$	4.51123	+	7.81368i	0.183105	+	0.317147i	−0.759831	+	0.650120i	$0.774718\pi$
$608$	7.70648	+	0.548059i	0.312539	+	0.0222267i
$609$	−2.48649	−	13.6485i	−0.100758	−	0.553067i
$610$	0.201975	−	0.0526671i	0.00817774	−	0.00213243i
$611$	17.5541	+	18.9188i	0.710163	+	0.765374i
$612$	−5.55704	−	25.9497i	−0.224630	−	1.04895i
$613$	−20.0368	+	3.02006i	−0.809277	+	0.121979i	−0.540631	−	0.841260i	$-0.681814\pi$
$613$	−20.0368	+	3.02006i	−0.809277	+	0.121979i	−0.268646	+	0.963239i	$0.586576\pi$
$614$	−20.9655	−	21.2491i	−0.846098	−	0.857545i
$615$	0.0351606	+	0.154049i	0.00141781	+	0.00621185i
$616$	−2.33808	+	13.1050i	−0.0942039	+	0.528014i
$617$	−2.25673	+	9.88738i	−0.0908525	+	0.398051i	−0.999823	−	0.0188095i	$-0.994012\pi$
$617$	−2.25673	+	9.88738i	−0.0908525	+	0.398051i	0.908971	+	0.416860i	$0.136870\pi$
$618$	15.8440	−	9.80757i	0.637339	−	0.394518i
$619$	6.71696	−	11.6341i	0.269977	−	0.467614i	−0.698878	−	0.715241i	$-0.746317\pi$
$619$	6.71696	−	11.6341i	0.269977	−	0.467614i	0.968856	+	0.247626i	$0.0796504\pi$
$620$	−0.201225	+	0.245487i	−0.00808139	+	0.00985898i
$621$	−1.95926	+	2.87370i	−0.0786223	+	0.115318i
$622$	24.1781	−	20.5258i	0.969453	−	0.823008i
$623$	−4.54533	−	2.89929i	−0.182105	−	0.116158i
$624$	21.6403	+	13.2820i	0.866306	+	0.531705i
$625$	23.8857	−	7.36775i	0.955426	−	0.294710i
$626$	9.91683	+	23.1528i	0.396356	+	0.925373i
$627$	5.80290	+	0.434867i	0.231745	+	0.0173669i
$628$	−44.1807	−	14.2809i	−1.76300	−	0.569870i
$629$	−3.91911	+	8.13812i	−0.156265	+	0.324488i
$630$	0.134068	+	0.0940851i	0.00534140	+	0.00374844i
$631$	−2.19768	−	4.56353i	−0.0874883	−	0.181671i	0.852634	−	0.522509i	$-0.175004\pi$
$631$	−2.19768	−	4.56353i	−0.0874883	−	0.181671i	−0.940122	+	0.340837i	$0.889289\pi$
$632$	0.353223	+	2.09744i	0.0140505	+	0.0834317i
$633$	9.28742	−	30.1091i	0.369142	−	1.19673i
$634$	−8.93102	−	12.2729i	−0.354696	−	0.487417i
$635$	0.108130	+	0.0162980i	0.00429102	+	0.000646768i
$636$	−40.6073	+	2.49483i	−1.61018	+	0.0989265i
$637$	−9.05662	−	16.1908i	−0.358837	−	0.641504i
$638$	5.50486	−	0.168945i	0.217939	−	0.00668858i
$639$	5.83114	−	38.6871i	0.230677	−	1.53044i
$640$	−0.124351	+	0.131455i	−0.00491541	+	0.00519622i
$641$	16.1599	+	4.98467i	0.638278	+	0.196883i	0.596970	−	0.802264i	$-0.296371\pi$
$641$	16.1599	+	4.98467i	0.638278	+	0.196883i	0.0413080	+	0.999146i	$0.486847\pi$
$642$	−3.49848	−	33.0441i	−0.138074	−	1.30415i
$643$	0.547630	−	0.263725i	0.0215964	−	0.0104003i	−0.423054	−	0.906104i	$-0.639042\pi$
$643$	0.547630	−	0.263725i	0.0215964	−	0.0104003i	0.444651	+	0.895704i	$0.353328\pi$
$644$	−9.08571	−	27.7546i	−0.358027	−	1.09368i
$645$	0.319560	+	0.153892i	0.0125827	+	0.00605950i
$646$	−3.15213	+	8.81777i	−0.124019	+	0.346930i
$647$	−0.686199	+	9.15669i	−0.0269773	+	0.359987i	0.967336	+	0.253496i	$0.0815805\pi$
$647$	−0.686199	+	9.15669i	−0.0269773	+	0.359987i	−0.994314	+	0.106491i	$0.966039\pi$
$648$	24.5606	−	12.3539i	0.964833	−	0.485306i
$649$	−3.24852	−	10.5315i	−0.127516	−	0.413396i
$650$	−11.2287	+	15.0023i	−0.440426	+	0.588439i
$651$	−7.46515	+	62.4382i	−0.292582	+	2.44715i
$652$	24.0652	−	21.7347i	0.942465	−	0.851198i
$653$	18.1920	+	12.4031i	0.711908	+	0.485371i	0.864317	−	0.502947i	$-0.167751\pi$
$653$	18.1920	+	12.4031i	0.711908	+	0.485371i	−0.152409	+	0.988317i	$0.548703\pi$
$654$	−23.9931	+	27.5045i	−0.938205	+	1.07551i
$655$	−0.0178490	−	0.0103051i	−0.000697418	−	0.000402654i
$656$	−13.1710	+	9.93639i	−0.514241	+	0.387951i
$657$	−22.9698	−	5.24270i	−0.896136	−	0.204537i
$658$	−16.2515	+	32.6116i	−0.633549	+	1.27133i
$659$	−1.32496	+	0.302413i	−0.0516131	+	0.0117804i	−0.248250	−	0.968696i	$-0.579855\pi$
$659$	−1.32496	+	0.302413i	−0.0516131	+	0.0117804i	0.196636	+	0.980476i	$0.436998\pi$
$660$	−0.0940369	+	0.0986549i	−0.00366038	+	0.00384014i
$661$	4.85335	+	32.1998i	0.188773	+	1.25243i	0.859659	+	0.510868i	$0.170676\pi$
$661$	4.85335	+	32.1998i	0.188773	+	1.25243i	−0.670886	+	0.741561i	$0.734086\pi$
$662$	6.10722	−	1.11310i	0.237364	−	0.0432617i
$663$	−22.5600	+	20.9326i	−0.876159	+	0.812956i
$664$	9.34670	−	3.06052i	0.362722	−	0.118771i
$665$	−0.0227509	−	0.0531278i	−0.000882242	−	0.00206021i
$666$	7.07628	+	1.38822i	0.274200	+	0.0537924i
$667$	−10.4636	+	6.04116i	−0.405152	+	0.233915i
$668$	−1.24775	+	2.50432i	−0.0482769	+	0.0968950i
$669$	24.0113	+	22.2792i	0.928329	+	0.861363i
$670$	0.0672185	−	0.105399i	0.00259688	−	0.00407191i
$671$	10.2349	+	12.8342i	0.395115	+	0.495459i
$672$	−6.76992	+	35.2027i	−0.261155	+	1.35797i
$673$	−16.2378	+	20.3616i	−0.625923	+	0.784883i	−0.989164	−	0.146812i	$-0.953099\pi$
$673$	−16.2378	+	20.3616i	−0.625923	+	0.784883i	0.363241	+	0.931695i	$0.381670\pi$
$674$	−9.69672	−	28.3206i	−0.373504	−	1.09087i
$675$	1.15112	+	2.93301i	0.0443067	+	0.112892i
$676$	−0.160623	+	11.9514i	−0.00617779	+	0.459668i
$677$	−25.4226	−	9.97763i	−0.977070	−	0.383472i	−0.177550	−	0.984112i	$-0.556817\pi$
$677$	−25.4226	−	9.97763i	−0.977070	−	0.383472i	−0.799519	+	0.600640i	$0.794912\pi$
$678$	−18.0109	+	40.5361i	−0.691705	+	1.55678i
$679$	6.17964	−	31.4872i	0.237153	−	1.20837i
$680$	−0.112920	−	0.188021i	−0.00433028	−	0.00721026i
$681$	3.89724	+	52.0050i	0.149343	+	1.99284i
$682$	−24.0690	−	6.62292i	−0.921649	−	0.253605i
$683$	1.00702	+	1.47703i	0.0385326	+	0.0565170i	0.845022	−	0.534732i	$-0.179587\pi$
$683$	1.00702	+	1.47703i	0.0385326	+	0.0565170i	−0.806489	+	0.591249i	$0.798635\pi$
$684$	7.44682	+	0.658808i	0.284736	+	0.0251902i
$685$		−	0.250856i		−	0.00958471i
$686$	16.8792	−	20.0273i	0.644451	−	0.764645i
$687$		−	21.5004i		−	0.820293i
$688$	−0.995284	+	37.0211i	−0.0379448	+	1.41142i
$689$	12.6793	+	18.5971i	0.483042	+	0.708492i
$690$	0.0793261	−	0.288286i	0.00301989	−	0.0109749i
$691$	−2.29888	−	30.6764i	−0.0874536	−	1.16699i	−0.852399	−	0.522892i	$-0.824853\pi$
$691$	−2.29888	−	30.6764i	−0.0874536	−	1.16699i	0.764945	−	0.644095i	$-0.222766\pi$
$692$	1.63008	+	2.91309i	0.0619662	+	0.110739i
$693$	−2.48070	+	12.6400i	−0.0942341	+	0.480152i
$694$	18.0042	+	7.99956i	0.683428	+	0.303659i
$695$	0.236232	+	0.0927141i	0.00896078	+	0.00351685i
$696$	14.8289	−	0.255699i	0.562087	−	0.00969223i
$697$	−7.30582	−	18.6149i	−0.276728	−	0.705090i
$698$	−10.1295	+	3.46824i	−0.383406	+	0.131275i
$699$	−36.5437	+	45.8243i	−1.38221	+	1.73323i
$700$	−25.4109	−	7.36302i	−0.960442	−	0.278296i
$701$	−13.4474	−	16.8625i	−0.507900	−	0.636886i	0.460091	−	0.887872i	$-0.347817\pi$
$701$	−13.4474	−	16.8625i	−0.507900	−	0.636886i	−0.967991	+	0.250986i	$0.919245\pi$
$702$	−1.99145	−	1.27006i	−0.0751626	−	0.0479352i
$703$	−1.86528	−	1.73073i	−0.0703504	−	0.0652756i
$704$	−13.4187	−	4.73937i	−0.505735	−	0.178622i
$705$	−0.323073	+	0.186527i	−0.0121676	+	0.00702500i
$706$	−6.57966	+	33.5390i	−0.247629	+	1.26226i
$707$	12.3186	+	28.7664i	0.463290	+	1.08187i
$708$	−8.36608	−	28.4753i	−0.314417	−	1.07017i
$709$	−1.77131	+	1.64354i	−0.0665231	+	0.0617244i	−0.712734	−	0.701435i	$-0.752543\pi$
$709$	−1.77131	+	1.64354i	−0.0665231	+	0.0617244i	0.646211	+	0.763159i	$0.276353\pi$
$710$	−0.0579767	−	0.318100i	−0.00217583	−	0.0119381i
$711$	0.306750	+	2.03515i	0.0115040	+	0.0763241i
$712$	3.84677	−	4.29192i	0.144164	−	0.160847i
$713$	53.3924	−	12.1865i	1.99956	−	0.456386i
$714$	−38.8882	−	19.3793i	−1.45535	−	0.725252i
$715$	0.0735127	+	0.0167788i	0.00274922	+	0.000627492i
$716$	32.4196	−	21.4709i	1.21158	−	0.802405i
$717$	10.5559	+	6.09446i	0.394218	+	0.227602i
$718$	15.2752	+	13.3251i	0.570065	+	0.497287i
$719$	34.2294	+	23.3372i	1.27654	+	0.870331i	0.995986	−	0.0895071i	$-0.0285292\pi$
$719$	34.2294	+	23.3372i	1.27654	+	0.870331i	0.280555	+	0.959838i	$0.409482\pi$
$720$	−0.122502	+	0.125107i	−0.00456537	+	0.00466247i
$721$	1.72784	−	14.4516i	0.0643482	−	0.538206i
$722$	19.4000	+	14.5202i	0.721992	+	0.540386i
$723$	3.60704	+	11.6937i	0.134147	+	0.434895i
$724$	−14.1166	+	6.56596i	−0.524638	+	0.244022i
$725$	−0.817961	+	10.9149i	−0.0303783	+	0.405370i
$726$	24.9926	+	8.93423i	0.927562	+	0.331580i
$727$	−37.1888	−	17.9092i	−1.37926	−	0.664215i	−0.410416	−	0.911898i	$-0.634616\pi$
$727$	−37.1888	−	17.9092i	−1.37926	−	0.664215i	−0.968841	+	0.247683i	$0.920331\pi$
$728$	18.6502	−	6.74547i	0.691223	−	0.250004i
$729$	19.8885	−	9.57779i	0.736611	−	0.354733i
$730$	−0.193633	+	0.0205006i	−0.00716668	+	0.000758760i
$731$	−42.8935	−	13.2309i	−1.58647	−	0.489362i
$732$	27.0948	+	34.9286i	1.00145	+	1.29100i
$733$	−1.11455	+	7.39457i	−0.0411669	+	0.273125i	−0.999939	−	0.0110518i	$-0.996482\pi$
$733$	−1.11455	+	7.39457i	−0.0411669	+	0.273125i	0.958772	+	0.284176i	$0.0917201\pi$
$734$	−0.297565	−	9.69580i	−0.0109833	−	0.357878i
$735$	0.257297	−	0.0755516i	0.00949056	−	0.00278676i
$736$	30.8536	−	4.77050i	1.13728	−	0.175843i
$737$	9.72155	+	1.46529i	0.358098	+	0.0539746i
$738$	−12.9086	+	9.39366i	−0.475172	+	0.345785i
$739$	2.35749	−	7.64279i	0.0867217	−	0.281145i	−0.901816	−	0.432121i	$-0.857765\pi$
$739$	2.35749	−	7.64279i	0.0867217	−	0.281145i	0.988537	+	0.150976i	$0.0482416\pi$
$740$	0.0590450	−	0.00808967i	0.00217054	−	0.000297382i
$741$	−3.76161	−	7.81106i	−0.138186	−	0.286946i
$742$	−18.2540	+	26.0113i	−0.670126	+	0.954906i
$743$	9.02492	−	18.7404i	0.331092	−	0.687520i	−0.667265	−	0.744820i	$-0.732535\pi$
$743$	9.02492	−	18.7404i	0.331092	−	0.687520i	0.998357	+	0.0573007i	$0.0182494\pi$
$744$	−64.5701	−	18.7044i	−2.36726	−	0.685735i
$745$	0.226016	+	0.0169376i	0.00828060	+	0.000620545i
$746$	−9.12556	+	3.90866i	−0.334110	+	0.143106i
$747$	9.09393	−	2.80511i	0.332729	−	0.102633i
$748$	9.90720	−	14.1197i	0.362243	−	0.516268i
$749$	−21.8818	−	13.9576i	−0.799544	−	0.509998i
$750$	−0.350611	−	0.412998i	−0.0128025	−	0.0150806i
$751$	−5.48368	+	8.04308i	−0.200102	+	0.293496i	−0.913154	−	0.407616i	$-0.866360\pi$
$751$	−5.48368	+	8.04308i	−0.200102	+	0.293496i	0.713051	+	0.701112i	$0.247313\pi$
$752$	−31.5826	−	22.7997i	−1.15170	−	0.831418i
$753$	−10.1672	+	17.6101i	−0.370514	+	0.641749i
$754$	−4.31865	−	6.97672i	−0.157276	−	0.254077i
$755$	0.0213922	−	0.0937254i	0.000778542	−	0.00341102i
$756$	0.686125	−	3.26333i	0.0249541	−	0.118686i
$757$	9.91684	+	43.4485i	0.360434	+	1.57916i	0.752096	+	0.659054i	$0.229043\pi$
$757$	9.91684	+	43.4485i	0.360434	+	1.57916i	−0.391662	+	0.920109i	$0.628100\pi$
$758$	−22.8282	+	22.5235i	−0.829159	+	0.818091i
$759$	23.2524	−	3.50474i	0.844009	−	0.127214i
$760$	0.0599895	−	0.0147848i	0.00217605	−	0.000536301i
$761$	−21.9654	−	23.6731i	−0.796245	−	0.858148i	0.196235	−	0.980557i	$-0.437128\pi$
$761$	−21.9654	−	23.6731i	−0.796245	−	0.858148i	−0.992480	+	0.122409i	$0.960938\pi$
$762$	5.84356	+	22.4097i	0.211690	+	0.811818i
$763$	5.10959	+	28.0469i	0.184980	+	1.01537i
$764$	35.8062	+	5.89007i	1.29542	+	0.213095i
$765$	−0.106113	−	0.183792i	−0.00383651	−	0.00664503i
$766$	−21.7656	−	11.6912i	−0.786422	−	0.422421i
$767$	−11.1682	+	12.0365i	−0.403260	+	0.434611i
$768$	−35.9605	−	13.2471i	−1.29761	−	0.478015i
$769$	−18.8484	+	15.0311i	−0.679689	+	0.542034i	−0.901351	−	0.433090i	$-0.857423\pi$
$769$	−18.8484	+	15.0311i	−0.679689	+	0.542034i	0.221662	+	0.975124i	$0.428852\pi$
$770$	0.0144423	+	0.105471i	0.000520463	+	0.00380093i
$771$	9.92994	+	7.91886i	0.357618	+	0.285191i
$772$	45.1798	−	17.0347i	1.62605	−	0.613092i
$773$	−34.8770	+	13.6882i	−1.25444	+	0.492331i	−0.897176	−	0.441672i	$-0.854385\pi$
$773$	−34.8770	+	13.6882i	−1.25444	+	0.492331i	−0.357263	+	0.934004i	$0.616290\pi$
$774$	−1.58055	+	35.8011i	−0.0568115	+	1.28684i
$775$	18.1256	−	46.1832i	0.651089	−	1.65895i
$776$	32.1434	+	11.9800i	1.15388	+	0.430058i
$777$	9.00111	−	7.64023i	0.322913	−	0.274092i
$778$	5.29919	+	10.1917i	0.189985	+	0.365392i
$779$	5.61758	−	0.420980i	0.201271	−	0.0150832i
$780$	0.197338	+	0.0478401i	0.00706584	+	0.00171295i
$781$	21.0106	−	14.3248i	0.751819	−	0.512582i
$782$	−4.48937	+	37.5733i	−0.160539	+	1.34362i
$783$	−1.37964			−0.0493042
$784$	18.1988	+	21.2792i	0.649958	+	0.759970i
$785$	−0.371313			−0.0132527
$786$	0.517852	−	4.33411i	0.0184712	−	0.154593i
$787$	43.8957	−	29.9276i	1.56471	−	1.06680i	0.601214	−	0.799088i	$-0.294684\pi$
$787$	43.8957	−	29.9276i	1.56471	−	1.06680i	0.963498	−	0.267715i	$-0.0862685\pi$
$788$	−50.9949	−	12.3625i	−1.81662	−	0.440397i
$789$	−2.13956	+	0.160338i	−0.0761704	+	0.00570818i
$790$	0.00784676	+	0.0150914i	0.000279175	+	0.000536928i
$791$	15.9807	+	30.7409i	0.568209	+	1.09302i
$792$	−12.9034	−	4.80917i	−0.458502	−	0.170886i
$793$	8.93497	−	22.7659i	0.317290	−	0.808442i
$794$	−1.29608	+	29.3576i	−0.0459961	+	1.04186i
$795$	−0.302859	+	0.118864i	−0.0107413	+	0.00421565i
$796$	−39.8999	+	15.0440i	−1.41422	+	0.533220i
$797$	−25.2648	−	20.1480i	−0.894926	−	0.713679i	0.0638150	−	0.997962i	$-0.479673\pi$
$797$	−25.2648	−	20.1480i	−0.894926	−	0.713679i	−0.958741	+	0.284282i	$0.908245\pi$
$798$	8.44576	−	8.85916i	0.298977	−	0.313611i
$799$	36.9120	−	29.4364i	1.30585	−	1.04138i
$800$	12.1745	−	25.5284i	0.430432	−	0.902566i
$801$	3.79332	−	4.08823i	0.134030	−	0.144451i
$802$	−10.4816	−	5.63010i	−0.370118	−	0.198806i
$803$	−7.65672	−	13.2618i	−0.270200	−	0.468000i
$804$	26.1239	+	4.29734i	0.921319	+	0.151556i
$805$	−0.137403	−	0.188847i	−0.00484282	−	0.00665599i
$806$	9.38431	+	35.9883i	0.330548	+	1.26763i
$807$	16.0055	+	17.2499i	0.563421	+	0.607224i
$808$	−32.4818	+	8.00535i	−1.14270	+	0.281627i
$809$	−21.0742	+	3.17642i	−0.740929	+	0.111677i	−0.508651	−	0.860973i	$-0.669856\pi$
$809$	−21.0742	+	3.17642i	−0.740929	+	0.111677i	−0.232277	+	0.972650i	$0.574618\pi$
$810$	0.156505	−	0.154416i	0.00549902	−	0.00542561i
$811$	−10.6791	−	46.7881i	−0.374993	−	1.64295i	−0.712531	−	0.701640i	$-0.752451\pi$
$811$	−10.6791	−	46.7881i	−0.374993	−	1.64295i	0.337538	−	0.941312i	$-0.390406\pi$
$812$	7.06615	−	9.17957i	0.247973	−	0.322140i
$813$	0.322894	−	1.41469i	0.0113244	−	0.0496153i
$814$	2.46691	+	3.98526i	0.0864651	+	0.139683i
$815$	0.129661	−	0.224580i	0.00454183	−	0.00786668i
$816$	27.1878	−	37.6612i	0.951762	−	1.31840i
$817$	7.12324	−	10.4479i	0.249211	−	0.365525i
$818$	−28.7351	−	33.8482i	−1.00470	−	1.18347i
$819$	18.1565	−	6.21506i	0.634439	−	0.217172i
$820$	−0.0757829	+	0.108006i	−0.00264645	+	0.00377172i
$821$	−41.2874	+	12.7355i	−1.44094	+	0.444471i	−0.914099	−	0.405492i	$-0.867100\pi$
$821$	−41.2874	+	12.7355i	−1.44094	+	0.444471i	−0.526842	+	0.849963i	$0.676624\pi$
$822$	48.8363	−	20.9176i	1.70336	−	0.729584i
$823$	−14.2018	−	1.06428i	−0.495044	−	0.0370984i	−0.175131	−	0.984545i	$-0.556035\pi$
$823$	−14.2018	−	1.06428i	−0.495044	−	0.0370984i	−0.319914	+	0.947447i	$0.603654\pi$
$824$	14.9451	+	4.32921i	0.520636	+	0.150815i
$825$	9.24285	−	19.1930i	0.321795	−	0.668213i
$826$	−21.4627	−	8.76004i	−0.746782	−	0.304801i
$827$	−7.33131	−	15.2236i	−0.254935	−	0.529377i	0.733744	−	0.679426i	$-0.237771\pi$
$827$	−7.33131	−	15.2236i	−0.254935	−	0.529377i	−0.988679	+	0.150049i	$0.952057\pi$
$828$	29.9302	−	4.10070i	1.04015	−	0.142509i
$829$	−0.443712	+	1.43848i	−0.0154108	+	0.0499604i	−0.962952	−	0.269674i	$-0.913084\pi$
$829$	−0.443712	+	1.43848i	−0.0154108	+	0.0499604i	0.947541	+	0.319635i	$0.103560\pi$
$830$	0.0635947	−	0.0462782i	0.00220741	−	0.00160634i
$831$	38.2548	+	5.76598i	1.32704	+	0.200020i
$832$	3.88091	+	20.8437i	0.134546	+	0.722626i
$833$	−30.7739	+	14.3080i	−1.06625	+	0.495742i
$834$	1.64868	+	53.7202i	0.0570891	+	1.86018i
$835$	−0.00333486	+	0.0221253i	−0.000115407	+	0.000765678i
$836$	2.97825	+	3.83934i	0.103005	+	0.132786i
$837$	5.97564	+	1.84324i	0.206548	+	0.0637117i
$838$	−22.5221	+	2.38449i	−0.778014	+	0.0823709i
$839$	9.13161	−	4.39755i	0.315258	−	0.151820i	−0.269563	−	0.962983i	$-0.586879\pi$
$839$	9.13161	−	4.39755i	0.315258	−	0.151820i	0.584821	+	0.811163i	$0.301165\pi$
$840$	0.0350714	+	0.284522i	0.00121008	+	0.00981695i
$841$	21.8100	+	10.5032i	0.752070	+	0.362178i
$842$	−43.9250	−	15.7021i	−1.51376	−	0.541130i
$843$	0.798210	−	10.6514i	0.0274918	−	0.366853i
$844$	23.8560	−	11.0960i	0.821158	−	0.381941i
$845$	0.0281739	+	0.0913374i	0.000969210	+	0.00314210i
$846$	−30.1756	−	22.5854i	−1.03746	−	0.776502i
$847$	17.6280	−	10.9100i	0.605706	−	0.374873i
$848$	−24.2728	−	23.7673i	−0.833532	−	0.816173i
$849$	−7.36499	−	5.02136i	−0.252766	−	0.172333i
$850$	25.8326	+	22.5347i	0.886051	+	0.772932i
$851$	−8.90482	−	5.14120i	−0.305253	−	0.176238i
$852$	57.0930	−	37.8116i	1.95597	−	1.29540i
$853$	11.5293	+	2.63148i	0.394754	+	0.0901000i	0.415290	−	0.909689i	$-0.363680\pi$
$853$	11.5293	+	2.63148i	0.394754	+	0.0901000i	−0.0205359	+	0.999789i	$0.506537\pi$
$854$	34.5250	+	0.466647i	1.18142	+	0.0159683i
$855$	0.0582860	−	0.0133034i	0.00199334	−	0.000454967i
$856$	18.5188	−	20.6619i	0.632961	−	0.706208i
$857$	0.443523	+	2.94258i	0.0151504	+	0.100517i	0.995128	−	0.0985913i	$-0.0314337\pi$
$857$	0.443523	+	2.94258i	0.0151504	+	0.100517i	−0.979978	+	0.199108i	$0.936196\pi$
$858$	2.86337	+	15.7105i	0.0977539	+	0.536346i
$859$	−12.8656	+	11.9375i	−0.438968	+	0.407302i	−0.868453	−	0.495771i	$-0.834885\pi$
$859$	−12.8656	+	11.9375i	−0.438968	+	0.407302i	0.429485	+	0.903074i	$0.358695\pi$
$860$	0.0834853	+	0.284155i	0.00284682	+	0.00968962i
$861$	−1.15483	+	26.1127i	−0.0393564	+	0.889920i
$862$	−1.86132	+	9.48785i	−0.0633967	+	0.323157i
$863$	−6.26823	+	3.61896i	−0.213373	+	0.123191i	−0.602878	−	0.797833i	$-0.705979\pi$
$863$	−6.26823	+	3.61896i	−0.213373	+	0.123191i	0.389505	+	0.921024i	$0.372646\pi$
$864$	3.32342	+	1.28978i	0.113065	+	0.0438794i
$865$	0.0195690	+	0.0181574i	0.000665367	+	0.000617370i
$866$	−21.4791	−	13.6984i	−0.729888	−	0.465489i
$867$	9.71452	+	12.1816i	0.329922	+	0.413710i
$868$	−42.8699	+	30.3190i	−1.45510	+	1.02909i
$869$	−0.834052	+	1.04587i	−0.0282933	+	0.0354786i
$870$	0.112209	−	0.0384194i	0.00380426	−	0.00130254i
$871$	−5.35120	−	13.6346i	−0.181319	−	0.461992i
$872$	−30.4724	+	0.525445i	−1.03193	+	0.0177938i
$873$	30.8987	+	12.1268i	1.04576	+	0.410432i
$874$	−9.74159	−	4.32836i	−0.329514	−	0.146409i
$875$	−0.422954	+	0.0129481i	−0.0142984	+	0.000437726i
$876$	−20.1371	−	35.9868i	−0.680369	−	1.21588i
$877$	−0.985992	−	13.1571i	−0.0332946	−	0.444285i	−0.988793	−	0.149290i	$-0.952301\pi$
$877$	−0.985992	−	13.1571i	−0.0332946	−	0.444285i	0.955499	−	0.294995i	$-0.0953180\pi$
$878$	2.31034	−	8.39623i	0.0779703	−	0.283359i
$879$	32.8970	+	48.2510i	1.10959	+	1.62747i
$880$	−0.113765	−	0.00305848i	−0.00383501	−	0.000103101i
$881$			22.5672i			0.760308i	0.924923	+	0.380154i	$0.124129\pi$
$881$			22.5672i			0.760308i	−0.924923	+	0.380154i	$0.875871\pi$
$882$	17.2522	+	20.8911i	0.580913	+	0.703439i
$883$			19.3774i			0.652102i	0.945352	+	0.326051i	$0.105718\pi$
$883$			19.3774i			0.652102i	−0.945352	+	0.326051i	$0.894282\pi$
$884$	−25.5979	−	2.26460i	−0.860949	−	0.0761668i
$885$	−0.133700	−	0.196101i	−0.00449427	−	0.00659188i
$886$	41.2367	+	11.3469i	1.38537	+	0.381206i
$887$	1.79030	+	23.8899i	0.0601124	+	0.802145i	0.943049	+	0.332653i	$0.107944\pi$
$887$	1.79030	+	23.8899i	0.0601124	+	0.802145i	−0.882937	+	0.469492i	$0.844437\pi$
$888$	6.49835	+	10.8203i	0.218070	+	0.363104i
$889$	16.5302	+	7.34619i	0.554406	+	0.246383i
$890$	0.0187149	−	0.0421205i	0.000627325	−	0.00141188i
$891$	16.0956	+	6.31707i	0.539224	+	0.211630i
$892$	−0.367555	+	27.3484i	−0.0123066	+	0.915694i
$893$	4.85902	+	12.3806i	0.162601	+	0.414300i
$894$	15.5489	+	45.4129i	0.520035	+	1.51883i
$895$	0.193882	−	0.243121i	0.00648077	−	0.00812663i
$896$	−25.6035	+	15.5068i	−0.855352	+	0.518047i
$897$	−21.8431	−	27.3904i	−0.729320	−	0.914538i
$898$	8.08960	−	12.6845i	0.269953	−	0.423288i
$899$	15.9246	+	14.7759i	0.531116	+	0.492804i
$900$	12.2046	−	24.4955i	0.406820	−	0.816516i
$901$	35.6587	−	20.5875i	1.18796	−	0.685871i
$902$	−10.1824	−	1.99758i	−0.339037	−	0.0665120i
$903$	44.2109	+	38.5726i	1.47125	+	1.28362i
$904$	−35.1998	+	11.5260i	−1.17073	+	0.383348i
$905$	−0.0912683	+	0.0846846i	−0.00303386	+	0.00281501i
$906$	20.0301	−	3.65067i	0.665456	−	0.121285i
$907$	6.47292	+	42.9450i	0.214930	+	1.42597i	0.792623	+	0.609712i	$0.208715\pi$
$907$	6.47292	+	42.9450i	0.214930	+	1.42597i	−0.577694	+	0.816254i	$0.696047\pi$
$908$	−30.0454	+	31.5209i	−0.997093	+	1.04606i
$909$	−31.5594	+	7.20323i	−1.04676	+	0.238916i
$910$	0.125325	−	0.0972017i	0.00415448	−	0.00322220i
$911$	−3.37807	−	0.771024i	−0.111921	−	0.0255451i	0.166194	−	0.986093i	$-0.446852\pi$
$911$	−3.37807	−	0.771024i	−0.111921	−	0.0255451i	−0.278114	+	0.960548i	$0.589709\pi$
$912$	7.88050	+	10.4458i	0.260949	+	0.345896i
$913$	5.35682	+	3.09276i	0.177285	+	0.102356i
$914$	12.3513	−	14.1589i	0.408544	−	0.468334i
$915$	0.292087	+	0.199141i	0.00965609	+	0.00658341i
$916$	13.3235	−	12.0332i	0.440219	−	0.397589i
$917$	−2.39435	−	2.42711i	−0.0790683	−	0.0801504i
$918$	−2.58912	+	3.45924i	−0.0854538	+	0.114172i
$919$	−13.7486	−	44.5719i	−0.453524	−	1.47029i	−0.837239	−	0.546838i	$-0.815831\pi$
$919$	−13.7486	−	44.5719i	−0.453524	−	1.47029i	0.383714	−	0.923452i	$-0.374645\pi$
$920$	0.223043	−	0.112189i	0.00735351	−	0.00369878i
$921$	3.77812	−	50.4156i	0.124493	−	1.66125i
$922$	−0.285467	+	0.798565i	−0.00940136	+	0.0262993i
$923$	−34.1336	−	16.4379i	−1.12352	−	0.541059i
$924$	−19.3288	+	11.6063i	−0.635870	+	0.381820i
$925$	−8.39249	+	4.04161i	−0.275943	+	0.132887i
$926$	−4.51362	−	42.6323i	−0.148327	−	1.40099i
$927$	14.3870	+	4.43781i	0.472532	+	0.145757i
$928$	8.45778	+	9.04608i	0.277640	+	0.296952i
$929$	−5.45352	+	36.1818i	−0.178924	+	1.18709i	0.701419	+	0.712749i	$0.252550\pi$
$929$	−5.45352	+	36.1818i	−0.178924	+	1.18709i	−0.880344	+	0.474337i	$0.842688\pi$
$930$	−0.537344	+	0.0164911i	−0.0176202	+	0.000540766i
$931$	−1.29628	−	9.47208i	−0.0424838	−	0.310435i
$932$	−48.8491	+	3.00119i	−1.60011	+	0.0983074i
$933$	53.1153	+	8.00585i	1.73892	+	0.262100i
$934$	−28.6774	−	39.4080i	−0.938355	−	1.28947i
$935$	0.0406581	−	0.131810i	0.00132966	−	0.00431066i
$936$	3.40702	+	20.2309i	0.111362	+	0.661267i
$937$	−11.9140	−	24.7397i	−0.389213	−	0.808210i	−0.999867	−	0.0163121i	$-0.994807\pi$
$937$	−11.9140	−	24.7397i	−0.389213	−	0.808210i	0.610654	−	0.791898i	$-0.290907\pi$
$938$	15.3476	−	13.8592i	0.501115	−	0.452519i
$939$	−18.5088	+	38.4338i	−0.604010	+	1.25424i
$940$	−0.296403	−	0.0958090i	−0.00966760	−	0.00312495i
$941$	−8.77309	−	0.657452i	−0.285995	−	0.0214323i	−0.0690395	−	0.997614i	$-0.521993\pi$
$941$	−8.77309	−	0.657452i	−0.285995	−	0.0214323i	−0.216955	+	0.976182i	$0.569613\pi$
$942$	−30.9619	−	72.2868i	−1.00879	−	2.35523i
$943$	21.7528	−	6.70984i	0.708367	−	0.218502i
$944$	12.9634	−	21.1212i	0.421922	−	0.687436i
$945$	−0.00280566	−	0.0265195i	−9.12680e−5	−	0.000862680i
$946$	−17.7564	+	15.0741i	−0.577310	+	0.490102i
$947$	0.783324	−	1.14892i	0.0254546	−	0.0373350i	−0.813301	−	0.581844i	$-0.802332\pi$
$947$	0.783324	−	1.14892i	0.0254546	−	0.0373350i	0.838755	+	0.544509i	$0.183284\pi$
$948$	−2.28367	+	2.78599i	−0.0741702	+	0.0904848i
$949$	−11.4073	+	19.7580i	−0.370296	+	0.641371i
$950$	−8.21110	+	5.08274i	−0.266403	+	0.164906i
$951$	5.72035	−	25.0625i	0.185495	−	0.812706i
$952$	−9.75567	−	34.9444i	−0.316183	−	1.13256i
$953$	0.875727	+	3.83681i	0.0283676	+	0.124287i	0.987129	−	0.159925i	$-0.0511253\pi$
$953$	0.875727	+	3.83681i	0.0283676	+	0.124287i	−0.958762	+	0.284212i	$0.908268\pi$
$954$	−23.0873	−	23.3997i	−0.747479	−	0.757592i
$955$	0.286950	−	0.0432507i	0.00928548	−	0.00139956i
$956$	2.13124	+	9.95223i	0.0689292	+	0.321878i
$957$	6.34443	+	6.83767i	0.205086	+	0.221031i
$958$	8.47932	−	2.21107i	0.273954	−	0.0714364i
$959$	11.0123	−	40.0089i	0.355606	−	1.29196i
$960$	−0.306220	−	0.0123525i	−0.00988321	−	0.000398674i
$961$	−33.7335	−	58.4281i	−1.08818	−	1.88478i
$962$	3.30428	−	6.15160i	0.106534	−	0.198335i
$963$	18.2615	−	19.6813i	0.588470	−	0.634220i
$964$	−5.22764	+	8.77991i	−0.168371	+	0.282782i
$965$	0.301890	−	0.240749i	0.00971819	−	0.00775000i
$966$	25.3072	−	42.4964i	0.814245	−	1.36730i
$967$	−35.1758	−	28.0517i	−1.13118	−	0.902083i	−0.135122	−	0.990829i	$-0.543143\pi$
$967$	−35.1758	−	28.0517i	−1.13118	−	0.902083i	−0.996054	+	0.0887462i	$0.971714\pi$
$968$	8.45131	+	20.4877i	0.271636	+	0.658501i
$969$	−14.7634	+	5.79421i	−0.474269	+	0.186137i
$970$	0.274058	+	0.0120991i	0.00879947	+	0.000388479i
$971$	9.48708	−	24.1727i	0.304455	−	0.775738i	−0.693990	−	0.719985i	$-0.744149\pi$
$971$	9.48708	−	24.1727i	0.304455	−	0.775738i	0.998445	−	0.0557534i	$-0.0177561\pi$
$972$	39.6107	+	16.1637i	1.27051	+	0.518449i
$973$	33.6065	+	25.1573i	1.07737	+	0.806505i
$974$	−31.3316	+	16.2909i	−1.00393	+	0.521993i
$975$	−31.6487	+	2.37174i	−1.01357	+	0.0759565i
$976$	−6.48040	+	36.3388i	−0.207433	+	1.16318i
$977$	46.3862	−	31.6256i	1.48403	−	1.01179i	0.494225	−	0.869334i	$-0.335452\pi$
$977$	46.3862	−	31.6256i	1.48403	−	1.01179i	0.989801	−	0.142458i	$-0.0455005\pi$
$978$	54.5326	+	6.51572i	1.74376	+	0.208350i
$979$	3.62485			0.115851
$980$	0.190821	+	0.117159i	0.00609554	+	0.00374249i
$981$	−29.4906			−0.941563
$982$	−25.7455	−	3.07614i	−0.821571	−	0.0981637i
$983$	−14.4865	+	9.87674i	−0.462048	+	0.315019i	−0.771876	−	0.635774i	$-0.780681\pi$
$983$	−14.4865	+	9.87674i	−0.462048	+	0.315019i	0.309827	+	0.950793i	$0.399729\pi$
$984$	−27.3455	−	5.74729i	−0.871744	−	0.183217i
$985$	−0.418447	+	0.0313583i	−0.0133328	+	0.000999157i
$986$	−13.3175	+	6.92445i	−0.424117	+	0.220519i
$987$	−59.7152	+	15.5665i	−1.90076	+	0.495486i
$988$	2.73510	−	6.70265i	0.0870153	−	0.213240i
$989$	18.6684	−	47.5662i	0.593619	−	1.51252i
$990$	−0.110016	−	0.00485697i	−0.00349652	−	0.000154365i
$991$	1.08722	−	0.426702i	0.0345366	−	0.0135546i	−0.348010	−	0.937491i	$-0.613142\pi$
$991$	1.08722	−	0.426702i	0.0345366	−	0.0135546i	0.382546	+	0.923936i	$0.375047\pi$
$992$	−24.5475	−	50.4813i	−0.779382	−	1.60278i
$993$	8.22008	+	6.55530i	0.260856	+	0.208026i
$994$	4.71761	−	53.2789i	0.149633	−	1.68990i
$995$	−0.266611	+	0.212615i	−0.00845213	+	0.00674035i
$996$	14.3122	+	8.52164i	0.453500	+	0.270018i
$997$	21.0632	−	22.7007i	0.667078	−	0.718939i	−0.305325	−	0.952248i	$-0.598765\pi$
$997$	21.0632	−	22.7007i	0.667078	−	0.718939i	0.972403	+	0.233310i	$0.0749555\pi$
$998$	0.986095	−	1.83582i	0.0312143	−	0.0581117i
$999$	−0.587055	−	1.01681i	−0.0185736	−	0.0321704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.p.a.59.12	✓	312
4.3	odd	2	inner	196.2.p.a.59.15	yes	312
49.5	odd	42	inner	196.2.p.a.103.15	yes	312
196.103	even	42	inner	196.2.p.a.103.12	yes	312

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.p.a.59.12	✓	312	1.1	even	1	trivial
196.2.p.a.59.15	yes	312	4.3	odd	2	inner
196.2.p.a.103.12	yes	312	196.103	even	42	inner
196.2.p.a.103.15	yes	312	49.5	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.167781 + 1.40423i) q^{2} +(-1.97899 + 1.34925i) q^{3} +(-1.94370 - 0.471205i) q^{4} +(-0.0159493 + 0.00119524i) q^{5} +(-1.56262 - 3.00533i) q^{6} +(-2.59622 - 0.509531i) q^{7} +(0.987794 - 2.65033i) q^{8} +(0.999898 - 2.54770i) q^{9} +(0.000997612 - 0.0225970i) q^{10} +(1.65591 - 0.649897i) q^{11} +(4.48234 - 1.69003i) q^{12} +(-2.07204 - 1.65240i) q^{13} +(1.15109 - 3.56019i) q^{14} +(0.0299509 - 0.0238850i) q^{15} +(3.55593 + 1.83176i) q^{16} +(-3.29762 + 3.55399i) q^{17} +(3.40978 + 1.83154i) q^{18} +(-0.682883 - 1.18279i) q^{19} +(0.0315639 + 0.00519222i) q^{20} +(5.82539 - 2.49461i) q^{21} +(0.634772 + 2.43431i) q^{22} +(-3.75388 - 4.04572i) q^{23} +(1.62114 + 6.57777i) q^{24} +(-4.94390 + 0.745173i) q^{25} +(2.66799 - 2.63237i) q^{26} +(-0.140232 - 0.614395i) q^{27} +(4.80618 + 2.21373i) q^{28} +(0.487147 - 2.13433i) q^{29} +(0.0285148 + 0.0460653i) q^{30} +(-4.96153 + 8.59362i) q^{31} +(-3.16882 + 4.68600i) q^{32} +(-2.40016 + 3.52038i) q^{33} +(-4.43732 - 5.22689i) q^{34} +(0.0420170 + 0.00502358i) q^{35} +(-3.14399 + 4.48080i) q^{36} +(1.78032 - 0.549155i) q^{37} +(1.77548 - 0.760473i) q^{38} +(6.33006 + 0.474372i) q^{39} +(-0.0125869 + 0.0434517i) q^{40} +(-1.78963 + 3.71620i) q^{41} +(2.52560 + 8.59871i) q^{42} +(4.01716 + 8.34173i) q^{43} +(-3.52483 + 0.482931i) q^{44} +(-0.0129026 + 0.0418292i) q^{45} +(6.31094 - 4.59250i) q^{46} +(-9.62933 - 1.45139i) q^{47} +(-9.50867 + 1.17282i) q^{48} +(6.48076 + 2.64571i) q^{49} +(-0.216899 - 7.06738i) q^{50} +(1.73073 - 11.4826i) q^{51} +(3.24881 + 4.18812i) q^{52} +(-8.11554 - 2.50331i) q^{53} +(0.886278 - 0.0938331i) q^{54} +(-0.0256339 + 0.0123446i) q^{55} +(-3.91496 + 6.37755i) q^{56} +(2.94730 + 1.41935i) q^{57} +(2.91535 + 1.04216i) q^{58} +(0.462993 - 6.17821i) q^{59} +(-0.0694703 + 0.0323123i) q^{60} +(2.72001 + 8.81806i) q^{61} +(-11.2349 - 8.40895i) q^{62} +(-3.89409 + 6.10492i) q^{63} +(-6.04853 - 5.23596i) q^{64} +(0.0350227 + 0.0238781i) q^{65} +(-4.54071 - 3.96102i) q^{66} +(4.78628 + 2.76336i) q^{67} +(8.08423 - 5.35403i) q^{68} +(12.8876 + 2.94151i) q^{69} +(-0.0141039 + 0.0581585i) q^{70} +(13.9367 - 3.18096i) q^{71} +(-5.76456 - 5.16666i) q^{72} +(-1.28303 - 8.51233i) q^{73} +(0.472434 + 2.59210i) q^{74} +(8.77851 - 8.14527i) q^{75} +(0.769984 + 2.62076i) q^{76} +(-4.63026 + 0.843540i) q^{77} +(-1.72819 + 8.80924i) q^{78} +(-0.651250 + 0.376000i) q^{79} +(-0.0589041 - 0.0249652i) q^{80} +(7.12534 + 6.61135i) q^{81} +(-4.91812 - 3.13655i) q^{82} +(2.16800 + 2.71859i) q^{83} +(-12.4983 + 2.10381i) q^{84} +(0.0483469 - 0.0606251i) q^{85} +(-12.3877 + 4.24142i) q^{86} +(1.91569 + 4.88111i) q^{87} +(-0.0867456 - 5.03068i) q^{88} +(1.89685 + 0.744461i) q^{89} +(-0.0565728 - 0.0251363i) q^{90} +(4.53754 + 5.34577i) q^{91} +(5.39005 + 9.63251i) q^{92} +(-1.77615 - 23.7010i) q^{93} +(3.65369 - 13.2782i) q^{94} +(0.0123052 + 0.0180485i) q^{95} +(-0.0515237 - 13.5491i) q^{96} +12.1281i q^{97} +(-4.80253 + 8.65654i) q^{98} -4.86859i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25}+ \cdots + 183 q^{98}+O(q^{100}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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